Essays in Macroeconomics Ella Getz Wold A dissertation submitted in partial fulllment of the requirements for the degree of Doctor of Philosophy in the Department of Economics at Brown University Providence, Rhode Island May 2019 © Copyright by Ella Getz Wold. All rights reserved. This dissertation by Ella Getz Wold is accepted in its present form by the Department of Economics as satisfying the dissertation requirements for the degree of Doctor of Philosophy. Date Gauti B. Eggertsson, Advisor Recommended to the Graduate Council Date Neil R. Mehrotra, Reader Date John N. Friedman, Reader Approved by the Graduate Council Date Andrew G. Campbell Dean of the Graduate School iii Curriculum Vitae Ella Getz Wold was born in Oslo, Norway. She received her Bachelor's degree in economics from the Norwegian University of Science and Technology in 2010, and her Master's degree from the University of Oslo in 2012. She worked two years in the Norwegian central bank before coming to Brown University on a presidential fellowship. She obtained a Master's degree from Brown in 2015 and a Ph.D. in 2019. iv Acknowledgments My dissertation has beneted greatly from the guidance and involvement of my advisor Gauti Eggertsson, to which I am deeply grateful. He has taught me the importance of always focusing on the big, interesting questions, even when these questions are challenging to answer. Two of the chapters in this thesis are co- authored with Gauti, and would not have been what they are today without his insights, experience and enthusiasm for macroeconomics. I am also grateful to Neil Mehrotra for thoughtful and constructive comments throughout my work with this dissertation. Neil's extensive knowledge of the literature has led me to always strive harder to nd and focus on the questions which are still unanswered. For my work involving administrative data I have beneted from the generous guidance of John Friedman. The nal chapter of this dissertation has been much improved by the knowledge and support of John. In addition to my three committee members, I have also beneted greatly from discussions with other faculty members. I would like to thank Joaquin Blaum, Oded Galor, Pascal Michaillat, Jesse Shapiro, Matthew Turner and David Weil in particular. Helpful comments and suggestions from this group have improved my dissertation in important ways. I am also thankful for generous support from the James M. and Cathleen D. Stone Wealth and Income Inequality Project, as well as kind and insightful guidance from Plamen Nenov at the BI Norwegian Business School. My fellow graduate students have been an important source of support and encouragement. I am grateful to all my oce companions in 70 Waterman, and many others, for productive discussions, as well as numerous friendly and much needed breaks. I also owe thanks to my fellow student Jacob Robbins, who is a co-author on the second chapter of this dissertation. In addition, I thank my friends and family at home for always believing in me. My parents have been a great support throughout this process. Without them, I would probably never have embarked upon this journey. Finally, I thank my husband and co-author Ragnar Juelsrud. He supported my choice to pursue a PhD at Brown from the very beginning, even though it meant several years of living apart. In addition to being a loving husband, he is also the co-author on three of the chapters in this dissertation. Without his dedication, creativity and hard work, this dissertation would have looked entirely dierent  and much worse. I am forever grateful for our continuous discussions and the way in which we make each other better. v Preface I started studying economics about the same time as the nancial crisis was unraveling. As I was taking introductory econ classes, there was a house price collapse in the US, banks were going bankrupt, and unemployment rates were increasing rapidly. Central banks around the world cut interest rates to roughly zero, and in the following years some even ventured into negative territory. These events have been a strong inuence on my dissertation, which consists of four self-contained chapters on various themes connected to the nancial crisis and its aftermath. The rst chapter investigates the eect of higher capital requirements for banks, which was one of the early regulatory responses to the nancial crisis. In this joint work with Ragnar Juelsrud, we explore how banks respond to such regulation. While higher capital ratios make banks more robust to sudden declines in their asset value, the way in which these ratios are increased matters for the economic implications. We nd that banks increase their capital ratios mainly by cutting back on lending to the rm sector, while maintaining lending to the household sector. This nding has implications for the counter-cyclical capital buers implemented in several countries in response to the crisis. If higher capital requirements have only a modest or no impact on lending to the household sector, it could limit the eectiveness of time varying capital requirements in smoothing the cycle in house prices and mortgage debt. The Federal Reserve immediately reduced the policy rate in response to the nancial crisis, but the scope for policy rate cuts was limited by the zero lower bound. In the second chapter of this thesis, we take a step back and consider the long-term trend of declining interest rates. In this joint work with Gauti Eggertsson and Jacob Robbins, we show that while the interest rate  an often used proxy of the marginal return on capital  has been declining steadily since the 1980s, the average return on capital has remained high. This is in contrast to the standard neoclassical model with constant returns to scale, which predicts that the marginal and the average return on capital should be the same. In addition to this divergence, we also present and discuss four other puzzles. First, there has been a divergence also between wealth and capital, typically assumed to be the same in standard models. Second, Tobin's Q has been consistently increasing to levels permanently above one. Third, despite the increase in Tobin's Q, the investment rate has been falling. Fourth, there appears to have been a simultaneous decline in both the capital share and the labor share. We propose a unied explanation to these puzzles, which is an increase in monopoly power in the US. By vi constructing a DSGE model to address all of these features in one framework, we show that an increase in monopoly power can match all ve trends quantitatively. While the Federal Reserve reduced the policy rate to zero and no further, a handful of central banks implemented negative interest rates for the rst time in history. In the third chapter, we explore whether or not policy rate cuts below zero are expansionary through the bank lending channel. In this joint work with Gauti Eggertsson, Ragnar Juelsrud and Larry Summers, we rst establish that the deposit rate is bounded by zero and does not respond to further policy rate cuts once it has reached this lower bound. Second, using daily bank level data from Sweden, we show that the pass-through to mortgage rates also breaks down once the deposit rate is bounded. In the cross-section, banks with higher deposit shares are less willing to reduce their mortgage rates and have lower growth in lending volumes after the deposit rate has stopped responding to further policy rate cuts. This suggests that the lack of pass-through to deposit rates  which accounts for roughly half of banks nancing costs  is spilling over into a lack of pass-through to mortgage rates. We build a New Keynesian model with a bank sector and central bank reserves, and show that negative policy rates are not expansionary once the deposit rate has reached its lower bound. The nal chapter of this dissertation addresses one of the issues which was salient from the onset of the nancial crisis  an increase in job loss risk. In this joint work with Ragnar Juelsrud, we study the impact of higher job loss risk on savings, and whether a risk induced increase in savings can amplify economic downturns. We use Norwegian tax data and a novel natural experiment to isolate the impact of higher job loss risk from other eects present during economic downturns, such as falling house prices. The 2014 collapse of the oil price had a negative impact on the Norwegian labor market, but was relatively contained to certain regions and occupations. By comparing individuals who live in the same area, but who face dierent changes in job loss risk, we nd that a one percentage point increase in job loss risk increases liquid savings by 1.2 - 2.0 percent. In order to evaluate whether the risk induced increase in savings could have worsened the economic downturn, we study employment in industries not directly aected by the shock. We show that employment in these industries falls, especially in the non-tradable sector  typically assumed to be the most sensitive to local household demand. We decompose the decline in employment, accounting for lower demand from rms and households, and show that the data is consistent with the risk induced increase in savings reducing employment. This suggests that an increase in household savings resulting from higher job loss risk could be a potential amplier of economic downturns. vii Contents 1 Risk-Weighted Capital Requirements and Portfolio Rebalancing 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Reform and data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Reform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.3 Bank level analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.4 Portfolio rebalancing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.5 Firm level analysis: Lending and employment . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5.1 Lending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.5.2 Employment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 1.6 Further evidence and aggregate eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.6.1 Further evidence: Interest rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.6.2 Aggregate eects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.7 Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2 Kaldor and Piketty's Growth Facts: The Rise of Monopoly Power in the United States 25 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.1.1 Previous literature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.2 Five macroeconomic puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.3 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.3.1 Market structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.3.2 Long run risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.3.3 Household preferences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.3.4 Equilibrium and solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 2.4 Characterizing the puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 2.5 A qualitative solution to the puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.5.1 An increase in markups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 2.5.2 A decrease in interest rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 viii 2.5.3 A decrease in productivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.6 Estimating changes in markups and interest rates . . . . . . . . . . . . . . . . . . . . . . . . . 50 2.6.1 Markups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.6.2 Interest rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.7 A quantitative solution to the puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 2.7.1 Quantitative calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.7.2 Quantitative results: Overall hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.7.3 Quantitative results: Markups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.7.4 Quantitative results: Interest rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.7.5 Other markup estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.7.6 Excess returns of nal goods rms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.8 Other explanations for the puzzles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 2.8.1 Neoclassical and zero-rent economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.8.2 Unobserved intangible capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 2.8.3 Labor bargaining power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.8.4 Capital risk premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 2.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3 Negative Nominal Interest Rates and the Bank Lending Channel 82 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.2 Negative interest rates in practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 3.2.1 Bank nancing costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 3.2.2 Bank lending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.3 Negative interest rates in theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.3.1 Negative interest rates in a partial equilibrium model of banking . . . . . . . . . . . . 99 3.3.2 Negative interest rates in general equilibrium . . . . . . . . . . . . . . . . . . . . . . . 103 3.3.3 A numerical example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 3.4 Discussion and extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4 The Saving and Employment Eects of Higher Job Loss Risk 131 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 ix 4.1.1 Literature review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 4.2 Data and institutional background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134 4.2.1 Institutional background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.3 Theoretical predictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 4.4 The eect of job loss risk on savings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 4.4.1 Natural experiment: The oil price collapse of 2014 . . . . . . . . . . . . . . . . . . . . 141 4.4.2 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 4.4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146 4.4.4 Robustness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152 4.4.5 External validity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156 4.5 The eect of higher savings on employment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 4.5.1 Cross-sectional outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160 4.5.2 Firm demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 162 4.5.3 Household demand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166 x List of Tables 1.1 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.2 Restrictive dierence in dierence estimation - capital ratios, equity, assets and risk weights . 13 1.3 Restrictive dierence in dierence estimation - rm lending . . . . . . . . . . . . . . . . . . . 15 1.4 Observed and implied change in average risk weights for low-capitalized banks . . . . . . . . . 16 1.5 Restrictive dierence in dierence estimation - loan level rm lending . . . . . . . . . . . . . 17 1.6 Restrictive dierence in dierence estimation - employment . . . . . . . . . . . . . . . . . . . 19 2.1 Eect of an increase in markups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.2 Eect of an increase in D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 2.3 Markup estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 2.4 Natural rate estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.5 Parameters taken from the data and related literature . . . . . . . . . . . . . . . . . . . . . . 54 2.6 Calibrated parameter results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 2.7 1970 calibration results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.8 Quantitative results: changes in markups, productivity growth rates, interest rates . . . . . . 57 2.9 Quantitative results: changes in markups only . . . . . . . . . . . . . . . . . . . . . . . . . . . 58 2.10 Quantitative results: changes in D only . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 2.11 Quantitative results: changes in productivity growth only . . . . . . . . . . . . . . . . . . . . 79 2.12 Quantitative results: changes in D and productivity growth . . . . . . . . . . . . . . . . . . . 79 2.13 Ramey quantitative results: changes in markups, productivity growth rates, interest rates . . 80 2.14 De Loecker quantitative results: changes in markups, productivity growth rates, interest rates 80 2.15 Gutierrez quantitative results: changes in markups, productivity growth rates, interest rates 80 2.16 Hall quantitative results: changes in markups, productivity growth rates, interest rates . . . . 81 3.1 Regression results mortgage rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 3.2 Regression results lending volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.3 Summary of log linearized equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . . . 104 3.4 Interest rates at start of recession and interest rate cuts in response to recession . . . . . . . . 110 3.5 Summary of log linearized equilibrium conditions . . . . . . . . . . . . . . . . . . . . . . . . 128 3.6 Parameter values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 4.1 Summary statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.2 Bank deposits - within oil region analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 xi 4.3 Bank deposits by tenure - within oil region analysis . . . . . . . . . . . . . . . . . . . . . . . . 150 4.4 Bank deposits - across region analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 4.5 Bank deposits - within oil region analysis with high skilled government workers in the control group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 4.6 Direct sectoral linkages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 4.7 Direct and indirect sectoral linkages . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 4.8 Predicted unemployment increases from network analysis . . . . . . . . . . . . . . . . . . . . 164 4.9 Occupations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 4.10 Bank deposits and total nancial wealth - within oil region analysis . . . . . . . . . . . . . . 172 4.11 Bank deposits - within oil region analysis with oil sector engineers in treatment group . . . . 172 4.12 Bank deposits at the municipality level within the oil region . . . . . . . . . . . . . . . . . . . 173 4.13 Sectoral unemployment rates at the municipality level within the oil region . . . . . . . . . . 173 4.14 Direct sectoral linkages - baseline adjustment for oil intensive municipalities in the oil region 173 4.15 Direct sectoral linkages - baseline adjustment for non-oil intensive municipalities in the oil region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 4.16 Direct sectoral linkages - upper bound adjustment for oil intensive municipalities in the oil region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174 4.17 Predicting job loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175 xii List of Figures 1.1 Risk-weighted capital requirements for Norwegian banks . . . . . . . . . . . . . . . . . . . . . 5 1.2 Capital ratios, equity, assets and average risk weights . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Firm lending . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.4 Interest rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.1 Wealth and capital as a share of GDP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.2 Tobin's Q . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3 Return on capital . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.4 Factor shares . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.5 Net investment as a share of net operating surplus . . . . . . . . . . . . . . . . . . . . . . . . 37 2.6 Prot distribution of nal goods rms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.7 Markups 1960-2015 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 3.1 Interest rates for the US and the Euro Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 3.2 Decomposition of liabilities for large Swedish banks . . . . . . . . . . . . . . . . . . . . . . . . 87 3.3 Aggregate deposit rates in Sweden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 3.4 Aggregate deposit rate pass-through . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 3.5 Interest rates, Sweden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 3.6 Issuance of covered bonds and deposit share, Sweden . . . . . . . . . . . . . . . . . . . . . . . 91 3.7 Estimated average funding costs, Sweden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 3.8 Aggregate lending rates, Sweden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 3.9 Bank level lending rates, Sweden . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.10 Bank level lending rates other mortgage contracts . . . . . . . . . . . . . . . . . . . . . . . . . 94 3.11 Box-plot of bank level pass-through . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 3.12 Correlation between lending rate and repo rate as a function of the deposit share . . . . . . . 96 3.13 Reserves - demand and supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100 3.14 Money - demand and supply . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 3.15 Impulse responses from preference shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.16 Dierence in impulse responses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.17 Aggregate deposit rates for Switzerland, Japan, Denmark, the Euro Area and Germany . . . 111 3.18 Actual and counterfactual commission income as a share of assets . . . . . . . . . . . . . . . . 111 3.19 Aggregate lending rates for Switzerland, Japan, Denmark, the Euro Area and Germany . . . 112 xiii 3.20 ECB survey on lending volumes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 3.21 ING survey on negative interest rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.22 Gross domestic product in constant prices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 3.23 Alternative estimated average funding costs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 3.24 Comparing bank level mortgage rates to aggregate data . . . . . . . . . . . . . . . . . . . . . 114 3.25 Reserve rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 4.1 Amplication as a function of the unemployment benet replacement ratio . . . . . . . . . . 140 4.2 Changes in unemployment rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142 4.3 Google search data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144 4.4 Unemployment rate and separation rate for engineers in the oil region and other high skilled workers in the oil region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 4.5 Bank deposits for engineers in the oil region relative to other high skilled workers in the oil region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 4.6 Bank deposits for oil sector engineers in the oil region relative to other high skilled workers in the oil region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 4.7 Unemployment rate and separation rate for engineers in the oil region and high skilled gov- ernment workers in the oil region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 4.8 Event study - wage income and bank deposits . . . . . . . . . . . . . . . . . . . . . . . . . . 158 4.9 Event study - bank deposits by income level . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 4.10 Increase in oil region unemployment by sector . . . . . . . . . . . . . . . . . . . . . . . . . . 160 4.11 Bank deposits in oil intensive and non-oil intensive municipalities within the oil region . . . . 161 4.12 Increase in oil region unemployment by sector and municipality type . . . . . . . . . . . . . . 162 4.13 Estimated increase in unemployment by sector and predicted unemployment increase from network analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 165 4.14 Estimated increase in unemployment by sector, predicted unemployment increase from net- work analysis and decomposition of the household demand eects . . . . . . . . . . . . . . . 166 4.15 US personal saving rate during recessions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 4.16 OECD harmonized unemployment rates by country . . . . . . . . . . . . . . . . . . . . . . . . 168 4.17 Oil price . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 4.18 Share of workers employed in the oil sector relative to the share of total workers by county . 169 xiv 4.19 Bank deposits in oil regions for engineers, engineer who did not lose their job following the oil price collapse, and engineers who lost their job in 2016 . . . . . . . . . . . . . . . . . . . . . . 169 4.20 Unemployment rate and separation rate for low tenure engineers in the oil region and high tenure engineers in the oil region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 4.21 Unemployment rate and separation rate for engineers in the oil region and other high skilled workers in all regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 4.22 Unemployment rate and separation rate for oil sector engineers in the oil region and other high skilled workers in the oil region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 4.23 House prices single family homes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170 4.24 Stock prices, S&P 500 index and Oslo Stock Exchange index . . . . . . . . . . . . . . . . . . 171 4.25 Other nancial assets by occupation-region . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171 4.26 Average house prices for oil intensive and non-oil intensive municipalities . . . . . . . . . . . . 171 4.27 Pseudo R2 from probit regression . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 176 xv Chapter 1 1 Risk-Weighted Capital Requirements and Portfolio Rebalancing 1.1 Introduction Bank regulation has been high on the policy agenda since the nancial crisis. An important component of the post-crisis policy reforms has been higher capital requirements for banks. The EU is scheduled to fully implement the Basel III regulation on capital requirements this year, and several member countries have already started increasing required capitalization levels. Similar policies have been adopted in the US, and further amendments are being discussed on both sides of the Atlantic. In order to understand how capital requirements aect not only the bank sector, but also the broader economy, it is crucial to identify through which channels banks react to stricter regulation. Banks can respond not only by increasing equity, but also by reducing risk-weighted assets. While the former has been referred to as good deleveraging (Gropp, Mosk, Ongena, and Wix 2017), the latter is likely to adversely aect at least some sectors of the economy. In this paper we use the Norwegian implementation of the Basel III requirements to decompose the increase in capital ratios into increases in equity, reductions in total assets and reductions in average risk weights. Further, we use administrative loan level data on the universe of Norwegian rms to trace out the eects on the real economy. Our novel data set allows us to also study the impact on smaller rms - typically not included in previous analyses - and hence provide a more comprehensive overview of the real eects of higher capital requirements. The key identication challenge is to disentangle supply from demand. Although the Norwegian re- quirements implemented in 2013 were levied on all banks, they aected banks dierentially due to their pre-reform capital ratios. Informally, our main identication strategy relies on the fact that low- and high- capitalized banks look very similar prior to the reform. We exploit this in a exible dierence in dierence framework, explicitly testing for parallel trends prior to the reform. Using loan level data, we also include industry×size×year xed eects in an attempt to control for credit demand. Further, for rms borrowing from multiple banks we include rm×year xed eects, thereby relying only on within rm-time variation for identication. Finally, the detailed administrative data allows us to investigate the interest rate response of banks, giving further support to our identication strategy. Our data comes from three main sources. First, we have quarterly bank level balance sheet data from The Norwegian Banks' Guarantee Fund. Second, we have matched rm-bank data from the Norwegian Tax 1 Authorities. Here we observe debt, deposits and interest paid/received for the universe of Norwegian limited liability rms and all their (domestic) bank connections. The tax data has the benet of also including small rms, often missed in loan level analysis due to data availability. Finally, we use rm level data from a national public register to obtain employment data on the rm level. We nd that growth in equity accounts for 13 percent of the reform-induced increase in capital ratios. However, this channel is not statistically signicant. Capital ratios are mainly increased by reducing the growth in risk-weighted assets. 36 percent of the reform-induced increase in capital ratios is due to lower growth in total assets, and 51 percent is due to a reduction in average risk weights. Hence, substituting low risk assets for high risk assets is the quantitatively most important channel in explaining the increase in capital ratios following the reform. We refer to this channel as portfolio rebalancing. Using the bank balance sheet data, we can further explore how the rebalancing is achieved. The average risk weight on mortgage lending is 0.35 (Andersen 2013), compared to an average risk weight of roughly 1.0 for corporate lending (Andersen and Winje 2017). Hence, shifting credit supply from rms to households is an ecient way to reduce average risk weights. Consistent with this, we nd an economically and statistically signicant impact on lending growth to the corporate sector. A one percentage point higher growth rate in capital ratios is found to reduce corporate credit growth by 1.0 - 1.4 percentage points. Back-of-the- envelope calculations suggest that the relative reduction in corporate credit supply can account for roughly 80 percent of the reduction in average risk weights. Consistent with the reduction in corporate credit being supply driven, we also document an increase in corporate interest rates for low-capitalized banks. This distortionary eect on credit supply highlights the need for considering not only total credit supply, but also the allocation of credit. On the loan level, we conrm that rms which borrow from low-capitalized banks prior to the reform have lower credit growth. Ultimately, the reason why we care about reductions in credit supply is that it might have adverse impacts on the real economy. We therefore investigate whether rms borrowing from low-capitalized banks have lower employment growth than other rms. We show that a negative credit supply shock leads to lower employment growth at the rm level. Firms borrowing from low-capitalized banks have approximately 0.l standard deviations lower employment growth after the reform. The negative employment eect is driven exclusively by smaller rms, highlighting the importance of good data coverage when evaluating the real eects of higher capital requirements. 2 Literature Since the nancial crisis, several countries have changed their capital requirements, resulting in a handful of recent papers on the topic. Brun, Fraisse, and Thesmar (2013) use variation in internal risk models among French banks, and document signicant eects on corporate lending from increasing risk-weighted capital requirements. Jimenez, Ongena, Peydro, and Saurina (2016) evaluate the eect of the Spanish dynamic provisioning scheme and reach similar conclusions, albeit by studying a slightly dierent policy instrument. Studies based on bank specic capital requirements in the UK also document signicant credit supply eects (Bridges, Gregory, Nielsen, Pezzini, Radia, and Spaltro 2014, Aiyar, Calomiris, and Wieladek 2016). De Jonghe, Dewachter, and Ongena (2016) uses idiosyncratic variation in capital require- ments and nd signicant credit supply eects for loans with relatively high capital charges. The paper most similar to ours is perhaps Gropp, Mosk, Ongena, and Wix (2017), which compares banks experiencing an increase in capital requirements to other banks across Europe. They show that banks respond to capital requirements by reducing risk-weighted assets rather than increasing equity. We contribute to this recent literature in three important ways. First, using a exible dierence in dierence approach we can uncover novel evidence on the dynamics of banks' adjustments to increased capital requirements. For instance, we show that the portfolio rebalancing eect is relatively short-lived compared to the eect on total asset growth. Second, after having established that a reduction in average risk weights is an important margin of adjustment, we use the richness of our data to dig deeper into how banks reduce average risk weights. We show that the shift from corporate lending to household lending can explain roughly 80 percent of the observed decline in average risk weights. This rebalancing entails a substantial distortion of the allocation of credit across sectors. From a policy perspective, this is important as several components of the new capital requirements were targeted towards reducing nancial imbalances in the household sector. Our reallocation results highlight the need to consider the eects of capital requirements at the sectoral level. Third, and most importantly, we document that the increase in capital ratios has negative spillover eects to employment using data on a much wider set of rms than is typically used in the literature. Most of the existing literature, such as Gropp, Mosk, Ongena, and Wix (2017), uses data on syndicated loans, a debt market typically skewed towards bigger and less bank-dependent rms. Gropp, Mosk, Ongena, and Wix (2017) do not nd signicant employment eects, potentially due to this sample selection issue. Using data on all limited liability rms, we nd that the negative employment eect is exclusively driven by smaller rms. Hence, the real eects of increased capital requirements will be substantially understated if smaller rms are excluded from the analysis. This is problematic as existing literature has found small rms to be especially important for understanding business cycle dynamics and job creation (Neumark, Wall, and 3 Zhang, 2011). Our paper therefore contributes to a more comprehensive understanding of the employment eects of increased capital requirements. 1.2 Reform and data 1.2.1 Reform Regulators across the globe use minimum requirements on banks' capital ratios to ensure some level of loss- absorption capacity. These requirements are usually risk-weighted, in order to account for dierences in risk across banks. Capital requirements mean that banks need to have some amount of equity for every asset they own, or for every loan they grant. Risk-weighting implies that assets with higher risk weights require banks to have more equity relative to assets with lower risk weights. Policy makers determine risk weights for dierent asset classes, and banks take these as given. The exception is so called internal ratings based (IRB) banks, which have some freedom in calculating their own risk weights. The vast majority of banks in our sample are non-IRB banks however, and our results are robust to excluding IRB-banks from the sample. Hence, we think of the risk weights as being outside of the banks' control. A simplied version of a bank's risk-weighted capital ratio is given by equation (1). The bank's capital is equal to the bank's equity, denoted by E. Bank assets are denoted by A and risk weights by α. E Capital Ratio =P (1) i αi Ai Following the nancial crisis of 2007/2008, the Basel III accord was put forward by the Basel Committee on Banking Supervision (BCBS 2010). One of the prominent features of the Basel III accord was to increase the lower bound on banks' capital ratios. As a member of the European Economic Area, Norway implemented the directive into its own legislation. However, because Norway is not a member of the EU, Norwegian policy makers did not participate in designing the reform. Hence, the new requirements were not tailored to the specics of the Norwegian bank sector in any way. A challenge with isolating the eects of increased capital requirements is that the Basel III accord was accompanied by new liquidity requirements. In Norway however, the implementation of the new liquidity regulation was postponed, and Norwegian authorities accorded priority to early phase-in of the new capital requirements (Ministry of Finance, 2014). We therefore believe that an advantage of investigating Norwe- gian banks' response to Basel III is that we to a larger extent can isolate the eects of increased capital requirements. 4 Figure 1.1: Risk-weighted capital requirements for Norwegian banks. Source: Ministry of Finance. The increase in capital requirements for Norwegian banks was proposed in late March 2013, passed in late June and adopted on the 1st of July the same year. The new requirements were phased in over a two-year period. As in the EU-legislation, capital was required to account for ten percent of risk-weighted assets. This included a minimum requirement of roughly ve percent, as well as a constant buer requirement levied on all banks. In addition, a countercyclical capital buer was adopted - set to vary between 0 and 2.5 percent. As a result, Norwegian banks faced a maximum requirement of 12.5 percent. In addition, there was an additional requirement for two systemically important banks. Only one of these banks is in our sample, and all results are robust to dropping this bank from the analysis. The requirements, along with the aggregate capital ratio, are illustrated in Figure 1.1. 1 Figure 1.1 documents a steady increase in capital ratios starting shortly after the nancial crisis. Such increases are seen also in other European countries (Gropp, Mosk, Ongena, and Wix 2017). However, as documented in the next section, high-capitalized and low-capitalized banks had similar growth rates in capital ratios prior to the reform. Only after the reform do low-capitalized banks signicantly increase their capitalization levels relative to that of high-capitalized banks. 1 The reform of 2013 contained two types of requirements - minimum requirements and buer requirements. While minimum requirements have to be strictly satised at all times, buer requirements can in theory be temporarily violated. 5 1.2.2 Data In our analysis on how banks respond to increased capital requirements, we use quarterly bank balance sheet data. The data is provided by The Norwegian Banks' Guarantee Fund, and contains information on nearly all Norwegian banks and subsidiaries. Foreign banks operating in Norway are not included in the data set. These banks were also not aected by the Norwegian regulation. Foreign nancial institutions account for 15 percent of total assets of banks operating in Norway. The second largest bank in Norway is the Norwegian subsidiary of the Swedish bank Nordea, which is not in our sample. Nordea accounts for roughly 13 percent of the remaining bank assets. Hence, our data covers 74 percent of total bank assets in Norway, and includes 110-120 dierent banks depending on the data source. Our unit of observation in the bank level analysis is the change in a given variable from quarter i in year t − 1, to quarter i in year t. As an alternative, we also consider 1-quarter growth. We use 2013q2 as our reform quarter, but it is possible that banks started reacting in 2013q1. Additionally, some bank responses are likely to appear at the start of the following year. The reason is that some decisions, such as dividend policies, are generally taken once a year at the general assembly. In our main analysis we use type and quarter interactions, which allow us to be agnostic about when the reform came into eect. The average capital ratio prior to the reform was 16.2 percent. Roughly 1/4 of the banks in our sample had capital ratios below the new (maximum) requirement of 12.5 percent. As expected, banks responded to the reform by increasing their capitalization levels. A year later the average capital ratio had increased to 16.6 percent, and then to 17.1 percent after two years. At the same time, the minimum observed capital ratio in our sample increased from 9.7 percent, to 10.7 percent, and nally to the new minimum required level of 11.5 percent. The right tail of the distribution remained relatively unchanged, reecting that the high-capitalized banks did not change their capital ratios in response to the reform. Summary statistics for 2012q4 are reported in Table 1.1. The average bank has assets worth roughly USD 3,000 million, while the largest bank has more than USD 200,000 million in assets. As reported in the third row, loans make up on average 80 percent of total bank assets. There is substantial variation in bank nancing, as captured by deposits as a share of total assets. On average, deposits account for 68 percent of assets. Average risk weights range from 0.45 to 0.99, with a mean of 0.59. These dierences reect, at least in part, dierences in lending shares to households and rms. The average bank lends almost ve times as much to households as to rms, but the standard deviation is large. Several banks lend more to rms than to households. As seen from the two last rows of Table 1.1, most banks in our sample are non-IRB, savings banks. 6 However, the distinction between commercial and savings banks in Norway is not very clear. For instance, DNB ASA, the largest bank in Norway and one of the larger banks in Northern Europe, is legally dened as a savings bank, but is  in terms of operations  very similar to traditional commercial banks. Variable Mean Median Std.dev. Min. Max. Obs. Capital Ratio (%) 16.2 15.9 4.2 9.7 31.3 119 Assets (million USD) 2,913 375 18,422 57 200,345 119 Loans 0.80 0.84 0.10 0.20 0.91 119 Assets Deposits 0.68 0.67 0.12 0.005 0.89 119 Assets Avg. Risk Weight 0.59 0.58 0.082 0.45 0.99 119 Prots (%) 0.45 0.44 0.21 -0.25 1.64 119 Assets Prots Equity (%) 5.0 4.7 2.8 -3.8 22 119 HH-Lending 4.9 2.5 17.5 0.12 179 114 Firm-Lending Savings Bank (binary) 0.87 1 0.33 0 1 119 Non-IRB Bank (binary) 0.94 1 0.24 0 1 119 Table 1.1: Summary statistics for 2012q4. NOK/USD = 8.61 (5/8/2017). Most of our analysis will rely on dividing banks into two groups based on their pre-reform capital ratios. On average, high-capitalized banks are smaller, have higher loan-to-asset ratios, and rely more heavily on deposit nancing. They are also more likely to be savings banks and less likely to be IRB-banks. In some of our analysis we exclude the 25 percent most and least capitalized banks. This leaves us with a more homogeneous group of banks. Using this sample, the only statistically signicant dierence between low- and high-capitalized banks is that the latter relies more heavily on deposit nancing. We have conrmed that our results are robust to controlling for all the variables listed in Table 1.1. After documenting how banks adjust their balance sheets in response to increased capital requirements, we proceed by using a loan level data set provided by The Norwegian Tax Authorities. This data set contains annual, matched rm-bank data for the universe of Norwegian rms. The tax data has several advantages. First, it lets us observe the entire portfolio of domestic corporate credit for all Norwegian banks, enabling us to do a more granular analysis of how banks respond. Second, it strengthens identication by allowing us to include rm-year xed eects to hold demand factors xed. Using the tax data, we can also observe the interest paid on loans. This enables us to also study the price eects of the reform. Finally, the loan level data lets us trace out the eect of bank credit contractions on the real economy by linking rms and banks. For the latter exercise we also rely on a nal data set containing rm level employment. This data comes from the rms' annual reporting, compiled in a national public register (The Bronnoysund Register ). 7 1.3 Bank level analysis We start by investigating how banks respond to increased capital requirements. Taking logs and rst dier- ences of equation (1) yields ∆ log (Capital Ratiot ) = ∆ log (Et ) − ∆ log (At ) − ∆ log (αt ) (2) P αi Ai where α≡ P is the average risk weight on the bank's assets. As seen from equation (2), banks Ai can increase their capital ratio growth rate in three ways. First, they can increase the growth in equity, for example through retained earnings. Second, they can reduce the growth in assets, which is likely to imply a reduction in credit supply. Finally, they can reduce the growth in the average risk weight α ¯. This implies shifting their asset composition towards assets with lower risk weights. In this section we decompose the reform-induced change in capital ratio growth rates, and quantify the relative importance of equity, assets and average risk weights. 1.3.1 Methodology Our analysis relies on the cross-sectional dierences in capital ratios prior to the reform. Whereas high- capitalized banks were not directly aected by the reform, low-capitalized banks had to increase their cap- italization levels. The main identication challenge is to separate supply factors from demand factors. We address this critical issue in three ways. First, we use a exible dierence in dierence methodology to explicitly test whether low- and high- capitalized banks have similar outcomes prior to the reform. Later, in Section 1.5, we use loan level data and saturate our regression with industry×size×year xed eects in an attempt to control for credit demand. Further, we follow Khwaja and Mian (2008) in including rm×year xed eects. In this case, the eect of bank capitalization on credit supply is identied while holding rm×year characteristics xed. Finally, in Section 1.6, we back out bank specic interest rates using loan level tax data. This allows us to evaluate not only how lending volumes are aected by higher requirements, but also how lending prices are aected. Because a negative supply and demand shock have dierent implications for prices, an increase in interest rates supports the interpretation of the fall in credit being supply-driven. The exible dierence in dierence regression is specied in equation (3). Our main dependent variables are the growth rates in capital ratios, equity, assets and average risk weights for bank i. Hence, we estimate equation (3), with Yit = {Capital Ratioit , Equityit , Assetsit , Risk Weightit }. The time xed eects δt 8 account for common cyclical patterns in these variables. We use a type dummy Di = 1 if bank i is low- capitalized, and Di = 0 if bank i is high-capitalized, to capture exposure to the reform. As our baseline, we dene banks as low-capitalized if their 2012q4 capital ratio is below the median. We have also explored other denitions, and our results remain robust. The coecients of interest are the γt 's on the type×time interaction terms. These coecient estimates identify the dierence in ∆log(Yit ) for high and low-capitalized banks in a given year-quarter, relative to the average dierence between the two bank types. We can directly test the parallel trends assumption by testing whether γt = 0 ∀ t < 0 , using t=0 to capture the time of the reform. Given that the parallel trends assumption holds, the treatment eects will be captured by the γt 's for t ≥ 0. A comparison of the γt 's for t≥0 will allow us to map out the dynamic treatment eects. X X ∆log(Yit ) = α + δτ 1t=τ + γDi + γτ Di × 1t=τ + it (3) τ τ The exible dierence in dierence specication is attractive because it can explicitly test the parallel trends assumption, and because it allows for dynamic treatment eects. However, it is quite data demanding, and will sometimes fail to produce signicant results in cases where more restrictive dierence in dierence estimations will produce signicant results (Reggio and Mora Villarrubia 2012). Therefore, after having veried the validity of the parallel trends assumptions, we proceed by estimating a less data demanding regression, as specied in equation (4). Instead of interacting bank type with time dummies, we now interact bank type with a dummy for the full post-reform period. That is, Itpost = 1 if t ≥ 0, and Itpost = 0 otherwise. This specication imposes a parallel trends assumption explicitly, which we are comfortable doing based on the results from the exible dierence in dierence regression. X ∆log(Yit ) = α + δτ 1t=τ + γDi + βDi × Itpost + it (4) τ Standard errors are clustered at the bank level. The baseline estimates are based on regressions without control variables. Our results are largely unchanged when controlling for numerous variables such as size, average risk weights, asset composition, deposit nancing, return on equity and organizational structure. 1.3.2 Results The upper left panel of Figure 1.2 plots ∆ log (Capital ratioit ) for low-capitalized and high-capitalized banks. In the time prior to the reform, low-capitalized and high-capitalized banks have similar changes in capital 9 ratios. At the time of the reform, a new pattern emerges. While high-capitalized banks continue to have growth rates close to zero, there is a spike in growth rates for low-capitalized banks. This divergence seems to start when the reform is announced, and grows in magnitude over time. By the end of the sample the dierence decreases, suggesting that the transitory adjustment in capital ratio growth rates is coming to an end. The upper right panel depicts the coecient estimates from equation (3) and shows that low-capitalized banks have signicantly higher growth in capital ratios in all periods following the reform. A potential concern is that the divergence in capital ratio growth rates is partly driven by mean reversion. If banks target similar capital ratios, low-capitalized banks may have high growth rates in capital ratios for reasons unrelated to the reform. To test whether mean reversion can explain the observed pattern, we have performed a falsication test in which we repeat our analysis one year prior to the reform. The results indicate that mean reversion is not important for our results. 2 How much of the increase in capital ratios is due to an increase in equity? We plot the equity results in the second row of Figure 1.2. The left panel depicts growth rates in equity for low- and high-capitalized banks, while the right panel depicts the coecient estimates when Yit = Equityit . Low-capitalized banks have consistently higher growth rates in equity prior to the reform, but the dierence between the two bank types is fairly stable. There is no apparent trend break at the time of the reform. However, an interesting pattern emerges starting as of 2014q1. Both bank types increase the growth in equity, but the magnitude is larger for low-capitalized banks and borderline insignicant. We believe this delayed response to the reform is due to banks' decision making processes. Important decisions such as dividend policies are taken at the general assembly, and apply to one calendar year at the time. The data is consistent with low-capitalized banks deciding to lower their dividend payouts for the calendar year 2013, contributing to higher equity growth through retained earnings. We next move on to consider the impact on assets in the third row of Figure 1.2. The growth in assets for low- and high-capitalized banks is plotted in the left panel. The two bank types have similar growth rates in assets prior to the reform. At the time of the reform however, there is a decline in asset growth for low-capitalized banks. High-capitalized banks on the other hand, increase their growth rates. This dierence is statistically signicant and also relatively persistent. 2 Another potential concern is that the observed divergence between low- and high-capitalized banks is aected by a policy rate cut by the Norwegian central bank in 2014q4. In an unreported falsication test, we have compared the evolution of low- and high-capitalized banks during a prior policy rate cut. There are no signicant dierences between the two bank types, suggesting that monetary policy changes are not driving our results. 10 Change in log(Capital Ratio) Change in log(Capital Ratio) 10 15 10 5 5 0 0 -5 2011q4 2012q4 2013q4 2014q4 -5 Low-capitalized (0-50) High-capitalized (50-100) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 Change in log(Equity) Change in log(Equity) 12 4 10 2 8 0 6 -2 4 2011q4 2012q4 2013q4 2014q4 -4 Low-capitalized (0-50) High-capitalized (50-100) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 Change in log(Assets) 2 Change in log(Assets) 8 7 0 6 -2 5 4 -4 3 2011q4 2012q4 2013q4 2014q4 -6 Low-capitalized (0-50) High-capitalized (50-100) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 Change in log(Risk Weights) Change in log(Risk Weight) 5 4 2 0 0 -2 -5 -4 2011q4 2012q4 2013q4 2014q4 -10 Low-capitalized (0-50) High-capitalized (50-100) -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 Figure 1.2: Capital ratios, equity, assets and average risk weights. Banks are divided into groups based on their 2012 capital ratio. Left panels: Growth rates for low-capitalized (below median) and high-capitalized (above median) banks. The growth rate for year -quarter denotes the (approximate) percentage change from year -quarter to t i t−1 i year -quarter . The solid red line marks the growth rate from 2012q2 to 2013q2 (the reform date). Right panels: t i Regression results from estimating equation (3). Interaction coecients γ are plotted relative to time t = −1. t Standard errors are clustered at the bank level. Time zero marks the growth rate from 2012q2 to 2013q3 (the reform date). Finally, we study the eect on average risk weights, and plot the results in the bottom row of Figure 1.2. High-capitalized banks have slightly lower growth in average risk weights prior to reform, but higher growth 11 in average risk weights after the reform, as illustrated in the left panel. There is a slight reduction in the relative growth of average risk weights for low-capitalized banks at the onset of the reform, followed by a larger and statistically signicant reduction in 2014. The eect is quantitatively larger than for the other outcome variables, although less persistent than the reduction in asset growth. The exible dierence in dierence regressions conrm that the parallel trends assumption holds for all our outcome variables. Hence, we are comfortable estimating the more restrictive dierence in dierence regression in equation (4). In Table 1.2 we report regression results for the four outcome variables studied above. The rst column shows results using ∆ log(Capital Ratioit ) as our dependent variable. In the post- reform period, low-capitalized banks had on average 6.3 percentage points higher growth in capital ratios than high-capitalized banks. The dierence is signicant at the one percent level. Results using the growth in equity as the dependent variable are reported in the second column. In the post-reform period, low-capitalized banks had on average 0.8 percentage points higher growth in equity than high-capitalized banks. This dierence is however not statistically signicant. Column 3 reports results using the growth in assets as the dependent variable. In the post-reform period, low-capitalized banks had on average 2.3 percentage points lower growth in assets than high-capitalized banks. The dierence is signicant at the ve percent level. Finally, column 4 reports results using the growth in average risk weights as the dependent variable. We estimate that low-capitalized banks had on average 3.3 percentage points lower growth in average risk weights than high-capitalized banks in the post-reform period. This dierence is signicant at the one percent level. In order to decompose the growth rate in capital ratios we simply divide the coecients in columns 2, 3 and 4 with the coecient in column 1. A one percentage point higher reform-induced growth rate in capital ratios leads to an increase in equity growth of 0.13 percentage points, a decrease in asset growth of 0.36 percentage points, and a decrease in the growth rate of average risk weights of 0.51 percentage points. Results using 1-quarter growth rates instead of 4-quarter growth rates are reported in the lower panel of Table 1.2. The main conclusions remain unchanged. Our results are also robust to adding the control variables listed as summary statistics in Section 1.2.2. 12 (1) (2) (3) (4) ∆log(Cap.Ratioit ) ∆log(Equityit ) ∆log(Assetsit ) ∆log(RiskW eightit ) Di × Itpost 6.33*** 0.83 -2.25** -3.25*** (5.23) (1.23) (-2.34) (-2.72) Share of response 100% 13% 36% 51% Growth rate 4q 4q 4q 4q Time FE yes yes yes yes Type FE yes yes yes yes Clusters 120 120 120 120 Observations 1,788 1,788 1,788 1,788 Di × Itpost 1.42*** 0.10 -0.49* -0.84** (3.85) (0.53) (-1.87) (-2.21) Share of response 100% 7% 35% 59% Growht rate 1q 1q 1q 1q Time FE yes yes yes yes Type FE yes yes yes yes Clusters 120 120 120 120 Observations 1,793 1,793 1,793 1,793 t statistics in parentheses, Std. err. clustered at bank level * p < .10, ** p < .05, *** p < .01 Table 1.2: Restrictive dierence in dierence estimation with 4q growth rates (upper panel) and 1q growth rates (lower panel). Based on the preceding analysis, we conclude that more than 85 percent of the increase in capital ratios is achieved by adjusting risk-weighted assets. Of these 85 percent, the majority is explained by a portfolio rebalancing eect, in which banks substitute high-risk assets with low-risk assets. In the appendix, we show theoretically that portfolio rebalancing can be optimal from the bank's perspective if risk weights are not proportional to systematic risk. In the next section, we further explore how this rebalancing takes place. 1.4 Portfolio rebalancing Due to the large dierence in average risk weights between corporate lending and household lending, the reduction in average risk weights can imply a relative reduction in rm lending. Our quarterly balance sheet data for corporate lending starts in 2012. In order to obtain a longer time series for corporate lending we aggregate the annual loan level tax data into a time series for corporate bank lending. Both data sources provide similar conclusions. The results using annual tax data are depicted in Figure 1.3. First, note that low- and high-capitalized banks look very similar prior to the reform. After the reform, their lending behavior diverges however. While high-capitalized banks continue to have fairly stable growth rates in rm lending, the growth rate in rm lending for low-capitalized banks plummets. Low-capitalized banks even experience negative corporate 13 credit growth in the year following the reform. We report interaction coecients from estimating equation (3), using the annual change in rm lending as our dependent variable. These interaction coecients are depicted in the right panel of Figure 1.3. Prior to the reform, the interaction coecients are small and insignicant. Post-reform, the interaction coecients are negative and signicantly dierent from zero. Hence, there is a signicant reduction in corporate lending growth for low-capitalized banks following the reform. Change in Corporate Lending (%') Change in Corporate Lending (%') 25 20 20 10 15 10 0 5 -10 0 2007 2008 2009 2010 2011 2012 2013 2014 2015 -20 Low-capitalized (0-50) High-capitalized (50-100) 2007 2008 2009 2010 2011 2012 2013 2014 2015 Figure 1.3: Firm lending - tax data. Banks are divided into groups based on their 2012 capital ratio. Left panel: Growth rates for low-capitalized (below median) and high-capitalized (above median) banks. The growth rate for yeart denotes the symmetric percentage change from yeart−1 to yeart . The dashed red line marks the growth rate from 2012 to 2013 (the reform year). Right panel: Regression results from estimating equation (3). Interaction coecients γt are plotted relative to year 2012. Standard errors are clustered at the bank level. After having conrmed that the parallel trends assumption is appropriate, we now move on to estimating the more restrictive dierence in dierence regression specied in equation (4). The results are reported in Table 1.3. Using the quarterly balance sheet data, we nd that following the reform, low-capitalized banks had on average 6.3 percentage points lower growth in corporate lending than high-capitalized banks. Using the aggregated tax data increases this number to 8.9, as reported in the second column. 3 These eects are substantially larger than the reduction in total assets, suggesting that low-capitalized banks are especially willing to reduce rm lending. Scaling the results with the increase in capital ratios, we nd that a one percentage point higher increase in capital ratios leads to a 1.0 to 1.4 percentage points lower growth in corporate credit supply. 3 Note that the quarterly data on corporate lending from The Norwegian Banks' Guarantee Fund is not exactly the same as the annual data on corporate lending from The Norwegian Tax Authorities, as the latter only consists of Norwegian limited liability rms and not foreign rms and sole proprietorships. 14 (1) (2) ∆log( Firm-Lending ) ∆log( Firm-Lending it ) -6.26** -8.93*** it Di × Itpost (-2.30) (-2.97) Time FE yes yes Type FE yes yes Data Source balance sheet data tax data Clusters 114 110 Observations 1,251 1,094 t statistics in parentheses, Std. err. clustered at bank level * p < .10, ** p < .05, *** p < .01 Table 1.3: Restrictive dierence in dierence estimation - rm lending. Regression results from estimating equation (4). What about household lending? While corporate lending growth for low- and high-capitalized banks suddenly diverges, no such pattern is observed for household lending. In fact, lending growth to the household sector remains relatively stable for both bank types throughout our sample period. Hence, we conclude that low-capitalized banks reduce lending growth to the rm sector relative to the household sector, whereas high-capitalized banks do not. Can the shift from rm lending to household lending quantitatively explain the reduction in average risk weights? Shifting from corporate lending to household lending will generally reduce the average risk weight on a bank's portfolio. However, banks can also reduce their average risk weights through other channels. In order to evaluate the quantitative importance of shifting from rm lending to household lending, we perform a back-of-the-envelope calculation using the balance sheet of an average low-capitalized bank. We calculate the implied change in risk weights if the only moving part of the balance sheet is the share of household versus rm lending. Comparing this estimate to the observed change in risk weights gives us a rough idea of whether the relative reduction in corporate lending is quantitatively important. We observe total assets, household lending and rm lending. We thus dene other assets to be the component of assets which is neither household nor rm lending Aother = Atot − LHH − Lf irm . The average risk weight ARW is then given by equation (5). While we observe the average risk weight, we do not observe the actual risk weights for each asset class. Hence, we assume that αHH = 0.35, which is the average risk weight on mortgages for non-IRB banks (Andersen 2013). For corporate lending we assume αf irm = 1.0, in line with the average risk weight on rm loans for non-IRB banks as outlined in Andersen and Winje (2017). The risk weight on other assets is then backed out to match the observed average risk weight, resulting in αother = 0.52. 15 LHH HH Lf irm f irm Aother other ARW = α + tot α + α (5) Atot A Atot The rst column of Table 1.4 lists the observed average risk weight for low-capitalized banks from 2013 to 2015. Over the period, average risk weights fell by 2.5 percent. Simultaneously, household lending relative to rm lending increased by 17 percent. Keeping risk weights and the share of other assets xed, we calculate the implied average risk weights in the last column of Table 1.4. Shutting down the eect of changes in risk weights for the dierent asset classes and changes in the share of other assets, we calculate a fall in implied risk weights of 2.0 percent. Hence, the increase in household lending relative to rm lending can explain 80 percent of the observed reduction in average risk weights for low-capitalized banks. We thus conclude that considering average balance sheet data, the fall in relative corporate lending can potentially account for nearly all of the reduction in average risk weights. Avg. Risk Weight LHH / Lf irms Implied Avg. Risk Weight 2013 0.630 0.692 0.630 2014 0.621 0.773 0.621 2015 0.614 0.810 0.617 Change 2013 to 2015 (%) -2.5 17 -2.0 Table 1.4: Observed and implied change in average risk weights for low-capitalized banks. When calculating Aother implied average risk weights we assume αhh = 0.35, αf irm = 1.0, and αother = 0.52, as well as A = 0.495. 1.5 Firm level analysis: Lending and employment So far we have been using bank level data, or loan level data aggregated to the bank level. In this section we use our administrative loan level data. In addition to allowing for tighter identication, this also means that every rm is matched to its relationship bank(s). We can therefore evaluate whether there are adverse employment eects at the rm level. 1.5.1 Lending The baseline regression is given by equation (6) X ˜ ijt = α + ∆L δτ 1t=τ + γDi + β l Di × Itpost + ijt (6) τ In an attempt to control for credit demand, we augment equation (6) by including industry×size×year xed eects. Firm size is a dummy for whether the rm had less than 25 employees in 2012, which corresponds 16 to the sample average. We also follow Khwaja and Mian (2008) by including rm×time xed eects. Note that this can only be done on the sub-sample of rms borrowing from more than one bank. This corresponds to approximately 10 percent of all rms and 20 percent of all loans. In order to allow for entry and exit, the dependent variable is the symmetric change in lending between a rm j and a bank i in year t.4 Results The results from estimating equation (6) are reported in the rst column of Table 1.5. In line with the bank level results, we nd that rms which borrow from low-capitalized banks have lower growth in lending in the post-reform period. The eect is signicant at the one percent level, and says that rms which borrow from low-capitalized banks have on average 4.1 percentage points lower growth in lending in the post-reform period relative to the pre-reform period. In the second column we include industry×size×year xed eects. The coecient remains largely unchanged. (1) (2) (3) (4) ˜ ijt ∆L ˜ ijt ∆L ˜ ijt ∆L ˜ ijt ∆L Di × Itpost -4.06*** -4.10** -8.74*** -11.14*** (-2.64) (-2.57) (-3.16) (-3.23) Time FE yes yes yes yes Type FE yes yes yes yes Industry × Size × Year FE no yes no no Firm × Year FE no no no yes Firms all all multiple banks multiple banks Clusters 114 114 113 111 Observations 208,351 206,327 39,289 15,807 t statistics in parentheses, Std. err. clustered at bank level * p < .10, ** p < .05, *** p < .01 Table 1.5: Restrictive dierence in dierence estimation - loan level rm lending. Regression results from estimating equation (6). In the third column we restrict the sample to only include rms with more than one bank connection. The coecient increases in absolute size and is still signicant at the one percent level. Finally, we add rm×year xed eects in the last column. The identication is now coming from within rm-year variation. The coecient remains signicant at the one percent level, implying that rms which borrow from multiple banks have lower credit growth at their low-capitalized banks in the post-reform period. Note that the coecient increases further in size, implying that if anything, low-capitalized banks are matched to rms with higher credit demand. Hence, any bias from not controlling for demand factors is likely to work against us. 4 The symmetric change is dened as ˜ t= ∆X Xt −Xt−1 and is bounded by -2 and 2. 0.5 Xt +0.5 Xt−1 17 1.5.2 Employment We have documented a signicant reduction in corporate lending growth from low-capitalized banks following the reform - both at the bank and rm level. Ultimately, the reason why we care about reductions in credit supply is that it might have adverse impacts on the real economy. We now investigate whether rms borrowing from low-capitalized banks have lower employment growth than other rms in the year following the reform. Note that we expect to nd negative eects on employment growth only if there are quantitatively important frictions in rm-bank lending. We have conrmed that there are indeed substantial frictions in rm-bank lending in our sample, both in terms of relationship lending and geographical matching. We again rely on the dierence in dierence framework to compare the employment outcomes of rms borrowing from high- and low-capitalized banks. Because there is no variation in employment growth within a rm-year, we cannot include rm×year xed eects. However, the results from the previous section imply that any bias from not controlling for rm specic factors is likely to work against us. We estimate a version of the restrictive dierence in dierence equation, interacting a dummy for bor- rowing from a low-capitalized bank with a dummy for the year following the reform. We focus on the employment eects in 2014, the year in which the negative credit eect was the largest. The results are reported in Table 1.6. The rst three columns use the full set of banks, comparing the employment growth of rms borrowing from banks with above and below median pre-reform capital ratios. While rms bor- rowing from low-capitalized banks are found to have lower employment growth in the year following the reform, the dierence is not statistically signicant. As previous literature has found smaller rms to be more vulnerable to bank specic shocks, we split the sample into rms with above and below 25 employees (the sample average). As seen from the second column, there is no statistically signicant eect for the large rms. However, there is a negative impact on small rms, as seen in the third column. This eect is statistically signicant at the 1 percent level. The parallel trends assumption is more clearly satised when excluding the 1st and the 4th quartile of banks. We therefore also show results using this restricted sample of more homogeneous banks. The results are reported in the last three columns of Table 1.6. Firms borrowing from low-capitalized banks have signicantly lower employment growth in the year following the reform - also when not conditioning on rm size. Again, the coecient increases in magnitude and statistical signicance when only considering smaller rms. To get a sense of the economic magnitudes, we append Table 1.6 with summary statistics for the dependent variable in 2012 for the various sub-samples. The average symmetric growth in employment ranges from 4.3 to 18 8.9 percent - recall that this variable is bounded between -200 and 200 percent at the rm level. Considering small rms and including all banks (column 3), we nd that rms borrowing from low-capitalized banks had on average 3.1 percentage points lower growth in employment after the reform. This compares to a mean of 4.8 percent. An alternative way to interpret the magnitude is to note that the estimated employment reduction corresponds to 0.06 standard deviations. If we exclude the very low- and high-capitalized banks from the sample (column 6), we nd that small rms borrowing from low-capitalized banks had on average 4.6 percentage points lower employment growth after the reform. The average employment growth in this sample before the reform was 4.3 percent. In terms of standard deviations, the estimated employment reduction corresponds to just below 0.1 standard deviations. (1) (2) (3) (4) (5) (6) ˜ ∆Empljt ˜ ∆Empljt ˜ ∆Empljt ˜ ∆Empljt ˜ ∆Empljt ˜ ∆Empljt Di × It2014 -1.89 -0.53 -3.12*** -3.21** -0.21 -4.58*** (-1.54) (-0.20) (-3.05) (-2.11) (-0.06) (-2.99) ˜ Mean (∆Emplj2012 ) 5.24 8.88 4.78 4.72 7.88 4.32 ˜ Median (∆Emplj2012 ) 0 3.04 0 0 2.89 0 ˜ Std (∆Emplj2012 ) 48.58 31.12 50.34 48.09 34.02 49.56 Time FE yes yes yes yes yes yes Type FE yes yes yes yes yes yes Banks all all all 25th-75th 25th-75th 25th-75th Employment all 25+ <25 all 25+ <25 Clusters 118 118 117 57 54 54 Observations 137,781 44,538 93,223 39,224 11,947 27,277 t statistics in parentheses, Std. err. clustered at bank level * p < .10, ** p < .05, *** p < .01 Table 1.6: Restrictive dierence in dierence estimation - employment. Although not reported, we have split the sample further by looking at subsets of rms with less than 25 employees. The negative employment eect for small rms seems to be present both for those with a strictly positive number of employees, and also for those with zero employees. We interpret this to mean that lower credit supply reduces the likelihood of zero-employee rms hiring the rst employee (extensive margin), as well as the probability that somewhat larger rms hire an additional employee (intensive margin). 19 1.6 Further evidence and aggregate eects 1.6.1 Further evidence: Interest rates We have documented a substantial reduction in asset growth for low-capitalized banks following the reform, and an especially large reduction in corporate credit supply. While we believe the exible dierence in dier- ence results make a convincing case for the reduction in credit being supply-driven, we now provide additional support for this interpretation. While a negative shock to demand and supply has similar implications for lending volumes, it has opposite implications for the interest rate. Although we do not directly observe interest rates, we observe the amount of outstanding debt and the amount of interest paid. In theory, it is therefore straightforward to back out the implied interest rate. In practice, because the data is annual, this procedure is likely to entail non-trivial measurement error. We address this by cutting the ten percent highest and lowest interest rates from our sample. We have conrmed that our interest rate estimate follows the aggregate interest rate closely. We aggregate the loan level interest rate data to bank level averages, and plot the resulting time series in Figure 1.4. The left panel compares interest rates for low-capitalized banks to that of high-capitalized banks. High-capitalized banks have slightly higher interest rates prior to the reform, but this gap closes after the reform. Hence, low-capitalized banks see a relative increase in interest rates post-reform, consistent with the reduction in credit being supply driven. In the right panel of Figure 1.4 we exclude the 25 percent most and least capitalized banks from our sample. Hence, we compare quartile 2 banks to quartile 3 banks. Using this more homogeneous group of banks, the results are even more striking. While quartile 2 and quartile 3 banks have almost identical interest rates prior to the reform, quartile 2 banks have consistently higher interest rates than quartile 3 banks in the post-reform period. While the results in Figure 1.4 are visually quite striking, the dierence in interest rates between high- and low-capitalized banks is not statistically dierent from zero when using the exible dierence in dierence approach specied in equation (3). However, given the parallel trends observed, we are comfortable using the standard dierence in dierence equation specied in equation (4). The results from this estimation conrm that low capitalized banks signicantly increased interest rates relative to high capitalized banks following the reform. 20 Interest Rate (%) Interest Rate (%) 7.2 7.2 7 7 6.8 6.8 6.6 6.6 6.4 6.4 6.2 6.2 2009 2010 2011 2012 2013 2014 2015 2009 2010 2011 2012 2013 2014 2015 Low-capitalized (0-50) High-capitalized (50-100) Low-capitalized (25-50) High-capitalized (50-75) Figure 1.4: Interest rates. Banks are divided into groups based on their 2012 capital ratios. Left panel: Interest rates for low-capitalized banks (below median) and high-capitalized banks (above median). Right panel: Interest rates for low-capitalized banks (25th to 50th percentile) and high-capitalized banks (50th to 75th percentile). 1.6.2 Aggregate eects Our cross-sectional results can only identify a reduction in credit growth from low-capitalized banks relative to that of high-capitalized banks. In principle, it is therefore possible that high-capitalized banks were able to pick up the slack resulting from reduced credit supply from low-capitalized banks - leaving aggregate credit supply unaected. We nd this unlikely due to three features of the data. First, because all the largest banks are low-capitalized, the combined market share of low-capitalized banks vastly exceeds that of high-capitalized banks. Hence, it seems practically dicult for high-capitalized banks to absorb all the excess demand. Second, we can explicitly calculate the number of rms which switch from low-capitalized banks to high-capitalized banks each year. There is no trend break in this series at the time of the reform, suggesting that the reform does not cause rms to switch banks. Finally and perhaps most importantly, the negative eect on employment provides indirect evidence that high-capitalized banks are not (fully) picking up the slack. If rms which were denied credit simply shifted to another bank, there should be no dierential eect on rm employment growth. Hence, we nd it overwhelmingly likely that there was a reduction in aggregate credit supply. 1.7 Concluding remarks We have documented that low-capitalized banks increased their capital ratios mainly by reducing the growth in risk-weighted assets. This was done primarily by reducing average risk weights. Consistent with the reduction in average risk weights, we found that low-capitalized banks reduced corporate lending relative 21 to household lending. Back-of-the envelope calculations suggested that the shift from corporate lending to household lending could account for roughly 80 percent of the fall in average risk weights. Reassuringly, low-capitalized banks increased their interest rates, which supports the interpretation of the reduction in lending being supply driven. The reduction in corporate credit supply was found to reduce employment growth for aected rms. Firms which borrowed from low-capitalized banks prior to the reform had lower employment growth following the increase in capital requirements. We believe our results have implications for understanding not only the impact of a one-time increase in capital requirements, but also the eectiveness of the countercyclical capital buer - introduced in many countries as part of the Basel III regulation. While the main goal of this time-varying requirement is to make banks increase their capital ratios when times are good, it has also been suggested that the buer can be used to smooth the credit cycle (Ministry of Finance, 2016). Financial regulators have a handful of indicators they look at when deciding whether the countercyclical capital buer should be increased, one of which is rapid growth in household debt. If banks respond to higher capital requirements by reducing credit supply to the household sector, the countercyclical capital buer could have a dampening eect on the credit boom. However, our results suggest that lending to the household sector is mostly unaected by capital requirements. It is important to highlight however, that this result is conditional on the current risk weights. Reducing the dierence in risk weights between mortgages and corporate lending would likely lead to more of the reduction in credit supply being directed towards the household sector. More generally, the allocation of credit across sectors matters for the macro economy, and hence should be part of the discussion surrounding the design of capital requirements. Our nding that the reduction in credit supply is directed towards rms rather than households could be undesirable for several reasons. First, the Norwegian housing market was booming in 2013 and policy makers were concerned about unsustainable price growth (IMF, 2013). Hence, a reduction in household lending would probably have been preferred to the observed decline in corporate lending. Second and more generally, we found that the reduction in rm lending lead to lower employment growth. Relatedly, and as noted in Beck, Büyükkarabacak, Rioja, and Valev (2012), directing credit away from the corporate sector towards the household sector could have detrimental impacts on the long-term growth potential of the economy. Appendix: Portfolio rebalancing In this appendix we show how risk-weighted capital requirements could induce portfolio rebalancing. Consider a static model based on Freixas and Rochet (2008). A bank allocates funds to dierent compet- 22 itive lending markets. For simplicity, we assume that equity E is xed. Although this is a strict assumption, our empirical results from the previous section suggest that the impact on equity is limited. We assume that A0 is a risk-free asset, i.e. government bonds or central bank reserves, and that assets 1, ..., n are loans to dierent markets. The bank chooses a vector of asset allocations A = {A1 , ... An } in n lending markets. For instance, we can think of A1 as being single-family mortgages, A2 as being corporate loans to BB+ rated public corporations etc. The remainder of the bank's funds is used to purchase the riskless asset. The vector of expected excess returns in the respective lending markets is joint-normal with mean ρ= {ρ1 , ...ρn }, and with invertible variance-covariance matrix Σ. The bank is subject to a capital requirement k¯. By law, the bank is required to ensure that E ≥ k¯ (7) α·A where · denotes the dot-product and α = {α1 , ..., αn } denotes a vector of risk weights corresponding to the respective loan categories. Since the zeroth asset is risk-free, it is assigned a risk weight of zero percent. We assume that the bank (or bank-owner) has CARA preferences. This, in combination with the nor- mality of the asset-returns, allows us to write the certainty equivalent of the bank-owner's pay-o as 1 U (A) = ρT A − γAT ΣA (8) 2 where γ is the bank owner's coecient of risk aversion. Thus, the portfolio allocation problem is to maximize utility given by equation (8), subject to the capital requirement (7) and the balance sheet constraint P A = D + E. Letting λ denote the shadow-value of the capital requirement constraint, the set of rst-order conditions for portfolio allocations can be written compactly as ¯ =0 ρ − γAΣ − λkα (9) or in terms of portfolio allocations (in dollars invested in each asset) ¯ ρ − λkα A = Σ−1 (10) γ In the absence of a binding capital requirement (λ = 0), this is the mean-variance ecient portfolio in the sense of the traditional capital asset pricing model (CAPM). 23 Equation (10) sheds light on how risk-weighted capital requirements aect banks' lending decisions. Because the eective excess return is reduced by a binding capital requirement, the banks overall holdings of risky assets fall. How is the provision of credit to various sectors aected? This depends on the risk weights, and how they relate to systematic risk. The traditional CAPM would require that in a competitive market, the return-vector ρ is colinear to the systematic risk of the various assets. From equation (10) it is clear that the introduction of a binding risk-weighted capital requirement (λ > 0) could lead to an inecient allocation across risky assets, relative to the mean-variance ecient benchmark. This occurs when the risk weights α are not proportional to ρ, and therefore not proportional to systematic risk. We illustrate this point further with a simple example of two lending markets, i.e. n = 2. Maximizing (8) with respect to (7) and the balance sheet condition, results in the optimal allocations ¯ 1 ρ1 − λkα ¯ 2 ρ2 − λkα A∗1 = 2 + σ2 ) , A ∗ 2 = 2 + σ2 ) γ(σ11 21 γ(σ12 22 A∗ A∗ ρ1 It is easy to show that 1 A∗ |λ>0 = 1 A∗ |λ=0 if and only if α1 α2 = ρ2 . In words, the relative asset allocation is 2 2 independent of the capital requirement only if the relative risk weights are proportional to expected returns, α1 ρ1 and thereby to systematic risk. Suppose however that this was not the case, and that α2 < ρ2 . This implies that the relative risk weight of the rst asset, A1 , is too low, causing A1 to be ineciently high relative to the ecient portfolio. In other words, the introduction of capital requirements would in this case lead to a shift in lending towards the rst market. 24 Chapter 2 2 Kaldor and Piketty's Growth Facts: The Rise of Monopoly Power in the United States 2.1 Introduction The goal of this paper is to give a unied explanation of ve puzzling trends in the US macroeconomic data. We pursue the hypothesis that an increase in monopoly prots and a decline in the natural rate of interest have been key drivers of these trends. Towards that goal, we build a quantitative model of the US economy that includes imperfect competition, barriers to entry, the trading of pure prots, and realistic asset pricing. We then explore how the economy responds to changes in market power and interest rates, and nd that our model is able to quantitatively match all of these trends. First, we briey describe the ve macroeconomic trends that motivate our research, leaving a full dis- cussion to Section 2.2. We refer to these trends as puzzles, following the tradition in the macroeconomic literature which describes as puzzles basic features of the data that are inconsistent with the canonical neoclassical model. 5 (P1) An increase in the nancial wealth-to-income ratio despite low savings rates, with a stagnating capital-to-income ratio. To paraphrase Thomas Piketty, wealth is back in the United States. Household nancial wealth, measured by the market value of housing and business assets, has increased from 250 % of income in 1970 to 400 % in 2015. The new wealth was not accumulated by traditional savings. In fact, savings rates have generally decreased since the 1970s. The nancial wealth is not embodied in new productive capital goods. The replacement value of capital goods to output has remained relatively constant over the period. This is puzzling because in the perfect-competition neoclassical model, wealth is accumulated by savings, and the market value of wealth cannot diverge in the long run from the replacement value of the capital stock. (P2) An increase in Tobin's Q to a level permanently above 1. Rather than through savings, wealth was largely accumulated through capital gains in the stock and housing markets. The value of the S&P 500 index increased by on average 8 % per year from 1970 to 2015, while the replacement value of its productive capital stock did not increase nearly as fast. This has lead to an increase in Tobin's Q, the ratio of the market value 5 See, e.g., the equity premium puzzle and the international portfolio puzzle. 25 of corporations to the replacement cost of their capital stock, of public corporations from approximately 1 in 1970 to 1.75 in 2015. This is a puzzling fact because the standard neoclassical model implies that Tobin's Q should be 1 in the long run. There has also been a boom in housing prices. The market value of all housing (plus land), relative to the replacement cost of housing, increased from 103 % in 1970 to 128 % in 2015. (P3) A decrease in the real rate of interest, while the measured average return on capital is relatively constant. There has been a substantial decrease in real interest rates since the 1970s. However, this lower return is not mirrored in the average return on corporate capital, a measure of the protability of rms, which has stayed constant. This is a puzzling fact because in the neoclassical model, the interest rate and the return on capital should move in tandem. (P4) A decrease in both the labor share and the capital share. Over the same time period, there is a growing body of evidence that suggests a marked decrease in competition, an increase in concentration (see Dorn, Katz, Patterson, Van Reenen, et al. (2017) and Grullon, Larkin, and Michaely (2016), for example), a decline in business dynamism (Decker, Haltiwanger, Jarmin, and Miranda, 2016) and an increase in prots (Barkai (2016), Barkai (2018), Chen, Karabarbounis, and Neiman (2017)). A growing literature has con- nected these trends to a decline in the labor share. 6 In our analysis, following Barkai (2016), Karabarbounis and Neiman (2014) and Rognlie (2016), we also directly estimate the capital share of income, and nd this share has been declining as well. We interpret the large and growing residual share of income as the pure prot share. 7 This is a puzzling fact because in the standard neoclassical model, there is no residual income share, let alone a growing residual share. P5) A decrease in investment-to-output, even given historically low borrowing costs and a high value of ( empirical Tobin's Q. Lower interest rates (P3) have not led to a boom in investment; in fact, investment- to-output has been sluggish for two decades, despite the high levels of Tobin's Q (P2). This is a puzzling 8 fact because in the standard model, low interest rates and a high level of Tobin's Q should lead to a boom in investment. These are not your father's growth facts. The changes over the past 40 years have overturned at least two of Kaldor's famous stylized facts: constant interest rates, and constant labor share. 9 With Kaldor's constants in doubt, it is necessary to give a thorough reexamination of the usefulness of the perfect com- 6 This decline is documented in Karabarbounis and Neiman (2014) and Elsby, Hobijn, and “ahin (2013). 7 For a dierent interpretation of the residual share, see Karabarbounis and Neiman (2018), who call the residual share factorless income. 8 See Gutiérrez and Philippon (2017) and Gutiérrez and Philippon (2016). 9 Some of Kaldor's other facts also seem more tenuous: (i) a constant growth rate in output per capita (US output growth has slowed considerably) (ii) constant capital-to-output ratio (whether this holds depends on whether you take into account the relative price of investment) (iii) a wage rate that grows at a constant rate equal to the growth rate of output (median wages have been sluggish relative to output growth) (iv) constant hours worked per capita (hours per capita have declined). 26 petition neoclassical model for explaining the macroeconomic data of the modern economy; recall that the main triumph of the neoclassical model is its ability to generate Kaldor's growth facts. More broadly, the neoclassical growth model cannot address many of the changes that have occurred over the past 40 years, discrepancies which have become increasingly clear with the work of Piketty and others, and through a careful study of the Integrated National Accounts, which was rst published in 2006. As already noted, we hypothesize that two forces are driving these broad macro-trends: (i) an increase in monopoly prots, and (ii) a decrease in the natural rate of interest. We model these forces through parsimonious modications of the neoclassical model. We depart from perfect competition, and posit that market power allows rms to make pure prots. There are barriers to entry, which prevent competition from driving these prots to zero. Crucially, claims to the (nonzero) pure prots of rms are traded and priced, and the ratio of the market value of rms (which includes the rights to pure prots) to the replacement value of the productive capital stock (Tobin's Q) is permanently above one. We model a decline in the natural rate of interest through a time varying utility wedge. This is a reduced form way of modeling factors that aect the natural rate of interest in an OLG setting, such as changes in fertility and mortality (Eggertsson, Mehrotra, and Robbins, 2017). We briey sketch how our modications to the neoclassical model solve the ve puzzles. An increase in market power leads to an increase in pure prots, thus an increase in stock prices ( P1). This leads to an increase in Tobin's Q ( P2) and nancial wealth. With an increase in markups, the pure prot share increases, and the labor and capital share both decrease ( P4). Markups will also lead to an increase in the wedge between the marginal product of capital and the rental rate, decreasing investment ( P5). An increase in pure prots will tend to drive up the average return on capital. To generate a constant average return, as we see in the data, we need a decline in interest rates, which pushes down the average return on capital. In our model, the two forces roughly cancel each other out and lead to a constant average return (P3). The decline in interest rates also increases the present discounted value of prots, which further contributes to an asset price boom, and an increase in wealth-to-income and Tobin's Q ( P1 and P2). Both changes in markups and interest rates are necessary parts of our explanation of the ve puzzles. By P1). The key itself, a secular decline in real interest rates could account for a higher wealth-to-income ratio ( challenge, however, is that a fall in real interest rates should then trigger an investment boom (P5), which did not happen, and should furthermore lead to a fall in the overall return to capital, which similarly is not seen in the data ( P3). A secular increase in market power works as a counterforce in a straightforward way to rationalize these developments. An increase in market power is also necessary in order to explain the 27 divergence between wealth and capital, and to generate a level of Tobin's Q permanently above 1. The assumption of pure prots in our model is in alignment with the eld of business strategy and man- agerial economics, in which the existence of market power is emphasized, and indeed one of the main purposes of the rm is to gain and secure this market power: the celebrated sustainable competitive advantage. 10 In our model, there is non-perfect competition. There are barriers to entry, which give market power to rms which is non reproducible in the short run. This allows the market value of rms to permanently diverge from the replacement value of the capital stock. Our paper thus follows a long tradition in the business and nance literature by using empirical Tobin's Q as a measure of rm market power. 11 Our model is also in alignment with the endogenous growth and endogenous entry literature, in which the prot share of the economy is positive even in the long run. We contrast our model with non-reproducible assets to those that assume either perfect competition, or monopolistic competition in which xed costs generally drive prots to zero. All assets in these economies are fully reproducible, either the productive capital which can be accumulated through investment, or the monopoly prots, which can be gained by paying a xed entry cost. The market value of rms can diverge from the replacement cost of capital, but only due to the presence of adjustment costs. In the long run, as stated by Tobin and Brainard (1976), the increase in stock brings market value into line with replacement cost, lowering the former and/or raising the latter. The canonical view of this position is found in Hall (2001). A key contribution of this paper is to clarify the measurement and theory of a number of important concepts. With our model in hand, we can make subtle but important distinctions: between nancial wealth and productive capital, measured labor share (which includes bargaining rents) and economic labor share, productive and nonproductive intangible investment, empirical Tobin's Q and theoretical Q, the capital and the prot share, the equity premium on prots and the equity premium on capital, and the marginal and average return. An important aspect of the paper is our integration of wealth and balance sheet data from the Integrated Financial Accounts into quantitative macroeconomics. In this paper, we are interested in matching historical movements of nancial moments such as wealth-to-income and Tobin's Q, as well as the traditional quantity moments such as productive capital and investment. We further integrate advances from the nance literature into our model to match key moments such as the equity-premium, connecting to the recent growing literature on macro-nance as in Bansal and Yaron (2004), Barro (2006), Nakamura, Steinsson, Barro, and Ursúa (2013) and Croce (2014). 10 See for example, Porter (1996), Barney (1991) and Oberholzer-Gee and Yao (2013). 11 See, for example, Lindenberg and Ross (1981), Smirlock, Gilligan, and Marshall (1984) and Salinger (1984). 28 We quantitatively test the extent to which our model can match the changes seen in US data. To do so, we estimate the change in markups in the US over the past forty years from aggregate macroeconomic data, using methods from a burgeoning literature that estimates markups. Using our estimated change in markups from 1970 to the present, along with a decline in the equilibrium real rate of 2 percentage points, our model is able to quantitatively match the ve puzzling facts described above. We explore the robustness of our results to other estimates of markups from this growing literature. The primary goal of this paper is to pursue the hypothesis that changes in monopoly prots and interest rates have been the main driver of a variety of macroeconomic changes over the past forty years. We do not, however, claim that ours is the only explanation for the ve stylized facts seen in the US over the past forty years and that other forces are not at work. There are several compelling competing hypotheses that have been put forward: (i) an increase in the risk premium of capital (ii) unmeasured intangible capital (iii) an increase in the capital-to-output ratio, along with an elasticity of substitution greater than one (iv) a decrease in the bargaining power of labor. We will nd credence to some of these other explanations: indeed, we argue that several of them are complementary. Our model, for example, generates an endogenous increase in the equity premium. In addition, many forms of intangible capital, such as investments in brand equity, advertising, and marketing, are closely related to the rise in economic rents we postulate. Our work has important welfare implications. Higher pure prots will tend to increase income and wealth inequality, since equity holders (who receive the pure prots) tend to be in the upper portion of the distribution of income and wealth. Higher monopoly power may also be inecient, and could decrease GDP through a lower capital stock and labor supply. The increase in monopoly power has likely contributed to these trends in the US over the past three decades. In order to draw policy conclusions, it is necessary to study in more detail the reasons underlying the increase in monopoly power in the US. This is important so as to assess whether this increase in market power is a malignant or benign development, for example if it is due to technological change, or instead due to lax antitrust enforcement. Such exploration is beyond the scope of our paper. Instead we focus purely on the macroeconomic eects of an increase in monopoly power, and do not take a stand on the underlying cause of this increase. An important takeaway is that the rise in monopoly power is needed to explain a host of macroeconomic developments in recent decades which otherwise may appear puzzling. Accordingly, the stakes are high in understanding the underlying forces behind this macroeconomic phenomenon, which has important policy implications in terms of capital taxation, antitrust enforcement, and optimal redistributive policies. 29 2.1.1 Previous literature For each of the ve puzzles listed above, there is a growing literature documenting them, as well as proposed explanations for the patterns in the data. Piketty (2014) and Piketty and Zucman (2014) document evidence that the wealth-to-income ratio has risen in many developed economies over the past forty years, along with an increase in Tobin's Q in the United States. Piketty et al. decompose the increase in wealth into two components, a savings component s and a valuation component. The savings component can be described by the equation β= g , where β is the ratio of wealth-to-income, s is the savings rate, and g the growth rate of output. Piketty argues that this fundamental relationship governs the evolution of the wealth-to-income ratio in the long run, i.e. over the course of centuries. In the short run, i.e. several years to several decades, there can be valuation eects, in which the price of capital goods (Tobin's Q) increases. 12 Nevertheless, he does nd substantial capital gains from 1970-2010. He proposes that changes in capital policies over the time period lead to the asset price gains. Our paper will propose a dierent explanation for the growth in Tobin's Q and wealth-to-income. Gomme, Ravikumar, and Rupert (2011) and Gomme, Ravikumar, and Rupert (2015) document that the average return on productive capital has stayed relatively constant over the past 30 years, even as interest rates have decreased. Our model will provide an explanation for this divergence. Karabarbounis and Neiman (2014) and Elsby, Hobijn, and “ahin (2013) have provided evidence that there has been a global decline in the labor share, and Barkai (2016) has provided intriguing evidence that the pure capital share has decreased and the pure prot share has increased. The work of Barkai (2016) follows work by Karabarbounis and Neiman (2014) and Rognlie (2016), who provide evidence that the capital share for the US does not oset the decline in the labor share. As in Barkai (2016), our model will use markups to explain a decline in the labor and capital share, and an increase in the pure prot share: we will also use a similar method as Barkai in order to back out markups from the prot share. Gutiérrez and Philippon (2016) show that investment is weak relative to measures of protability and valuation, particularly Tobin's Q. They nd support for the hypothesis that weak investment is being driven by a decrease in competition at the industry level. Our model will incorporate this explanation: a decrease in competition will lead to a stagnation in investment, even in spite of historically low interest rates. A few recent studies have also made connections between several of the above facts. Stiglitz (2015b) and 12 In the long run, however, Piketty believes there can be no signicant divergence between the price of consumption and capital goods. Because of this long run relationship, Piketty is comfortable using the terms wealth and capital interchangeably. We take a dierent view: a major goal of this paper is to explore empirically and theoretically the dierence between wealth and capital. 30 Stiglitz (2016) are concerned with many of the same macroeconomic data as this paper, such as the divergence between nancial wealth and capital, and connect this to an increase in rents which are capitalized in nancial assets. Caballero, Farhi, and Gourinchas (2017) note several of the above facts, and try to explain them in an accounting framework through a combination of rents, increases in risk-premia, and technical change. Auclert and Rognlie (2016) explore how changes in markups aect the supply of assets and aggregate demand. In a series of important papers that are closest to ours, Gonzalez and Trivn (2016) and Brun and González (2017) explore many of the same facts, and connect them to an increase in Tobin's Q and monopoly rents, however the modeling approaches and implications are dierent: (i) Brun and González (2017) emphasize the evolution of capital taxation and its impact on Tobin's Q and prots (ii) our model has a representative agent framework with long-run risk, while Brun and González (2017) have a Bewley-Aiyagari heterogeneous agent model. Conceptually, our paper distinguishes itself from this literature in that it presents a unied explanation of ve macroeconomic trends, spanning several literatures in macroeconomics, nance, and growth. Other papers generally focus on one or two of our ve facts: Gutiérrez and Philippon (2016) focuses on ( P5) and (P2), Barkai (2016) on (P3) and (P4), Caballero, Farhi, and Gourinchas (2017) on (P3) and (P4), Piketty and Zucman (2014) on (P1), Autor, Dorn, Katz, Patterson, Van Reenen, et al. (2017) on the fall in the labor share, Gomme, Ravikumar, and Rupert (2015) on (P3), De Loecker and Eeckhout (2017) on the rise of markups. Theoretically, our model includes a novel combination of (i) a general equilibrium model with long- run productivity risk and (ii) the pricing of the rights to pure prots, which leads to a value of Tobin's Q permanently above 1. Our model produces a results that, to the best of our knowledge, has not been discussed before: a risk premium on pure prots that is greater than the risk premium on productive capital. With the pricing of pure prots, it becomes easy to match the equity premium in a full production model, even with relatively low values for the coecient of risk aversion and capital adjustment costs. The addition of entry and exit rm dynamics allows us to closely tie our model to the data on the market valuation of equities. Our model quantitatively matches a wide range of moments in the data that other models cannot match or do not attempt to match, such as the wealth-to-income ratio, the average return on capital, and a level of Tobin's Q commensurate with the data. Simultaneously, we can also match the traditional macro and nance moments, such as the investment-to-output ratio, the real interest rate, the labor share, and the equity premium. Other papers in this literature do not have long run risk or other elements that allow them 31 to match the equity premium, which is important for our quantitative results. Without the equity premium, it is dicult to simultaneously match the real interest rate, the average return, and Tobin's Q. 2.2 Five macroeconomic puzzles Puzzle 1: Increasing wealth-to-output There has been a large increase in the wealth-to-output ratio in the US, rising from around 250% of output in 1980 to almost 400% in 2015, as illustrated in the left panel of Figure 2.1. Household wealth is taken from the distributional national accounts (see Piketty, Saez, and Zucman (2017)). 13 The puzzle lies in the fact that while wealth-to-output has increased, the ratio of capital-to-output has been stagnant, as seen in Figure 2.1; in the standard neoclassical model, wealth and capital are equal. 14 Capital refers to the value of private capital as measured by the BEA in the xed asset tables. 15 In addition, this increase in wealth has taken place despite a decline in the savings rate, as illustrated in the right panel of Figure 2.1. 16 Since the wealth was not accumulated by savings, it must have been accumulated by capital gains, as we indeed see in the data. But this does not solve the puzzle, it simply shifts it: what is the source of these capital gains? Wealth and Capital Personal Saving Rate 12 4 10 3.5 8 3 6 2.5 4 2 1980 1990 2000 2010 2 1980 1990 2000 2010 Wealth/GDP Capital/GDP Figure 2.1: Wealth and capital as a share of GDP. The trends in wealth and capital are not being driven by housing. Although the value of housing-to- income has indeed increased, from 1.32 in 1980 to 1.48 in 2015, much of the increase in wealth has come from other assets. 13 Household wealth consists of housing wealth, equities, xed income assets, business assets and pensions, less liabilities. For computational details, see Piketty, Saez, and Zucman (2017). 14 Output is Gross Domestic Product, BEA Account Code: A191RC 15 Capital is the Current-Cost Net Stock of Fixed Assets: Private (K1PTOTL1ES000). 16 The saving rate is the Personal Saving Rate, BEA Account Code: A072RC. 32 Tobin's Q Tobin's Q - Compustat 2.5 2 1.5 2 1 1.5 .5 0 1980 1990 2000 2010 1 1980 1990 2000 2010 Q1 Q2 Figure 2.2: Tobin's Q. Left: nancial accounts and BEA data. Right: Compustat. Puzzle 2: Increasing Tobin's Q There has been a large increase in empirical measures of Tobin's Q since 1980. Tobin's Q measures the market value of corporations relative to the replacement cost of their capital. We follow Hall (2001) and Gutierrez and Philippon (2016) in calculating Tobin's Q according to formula (11). Ve denotes the value of equities, as measured in the nancial accounts. 17 Corporate liabilities L and nancial assets FA are also from the nancial accounts. 18 Inventories and the value of corporate capital PK K are taken from the BEA. 19 We follow Gutierrez and Philippon (2016) in also calculating an alternative Tobin's Q which excludes miscellaneous liabilities and nancial assets, as given by formula (12). V e + (L − F A) − Inventories Q1 = (11) PK K Amisc − Lmisc Q2 = Q1 + (12) PK K Figure 2.2 depicts our measures of Tobin's Q, and shows a striking upwards trend. The two alternative measures provide qualitatively similar results. Even using our most conservative estimate, Tobin's Q has increased almost threefold since 1980, implying a large increase in the market value of capital relative to the replacement cost of capital. 20 This implies that rms are valued at less than the replacement cost of their capital, which is at odds with economic theory, and may be driven by mis-measurement in macro data. See, for example, the discussion on this point in Piketty and Zucman (2014). Measures of Tobin's Q using micro data nd qualitatively similar results. The right panel of Figure 2.2 depicts the mean Tobin's Q of publicly listed corporations using Compustat data. There has been a large 17 The value of equities source series id is LM103164103.Q. 18 The source id numbers are FL104190005.Q and FL104090005.Q respectively. 19 Nonnancial corporate capital: k1pno2es000. 20 Tobin's Q as calculated using macro data is often found to be below one for extensive periods of time, as is also the case in Figure 2.2. 33 increase in this measure of Tobin's Q since 1980, and Q has been substantially above 1 for most of the period. This large increase in Tobin's Q is a puzzle from the standpoint of standard capital adjustment costs models, which predicts that the value of Tobin's Q should be 1 in the long run. Puzzle 3: Declining corporate bond rates, constant return on business capital There has been a substantial decrease in the real interest rate of corporate bonds over the past thirty years. Figure 2.3 shows the real return for two corporate bond series, an index of AAA bonds and an index of BAA bonds. 21 Both series show a substantial decrease over the time period. Other measures of corporate borrowing costs such as bank interest rates have also decreased. 22 Corporate borrowing costs are a measure of the marginal return on capital, since economic theory tells us that corporations should invest until the marginal product on capital is equal to the interest rate. The puzzle is that while there has been a signicant decline in the marginal return of capital as measured by corporate bond markets, measures of the protability of rms that correspond to the business return of capital have not declined; in the standard neoclassical model, they should be equal. We follow Gomme, Ravikumar, and Rupert (2011) and Gomme, Ravikumar, and Rupert (2015) in calculating the business return on capital, which we will term the average return (AR). The exact denition is given in equation (13). We use data from the corporate sector of the national accounts. The numerator is a measure of corporate prots: we start with gross corporate value added, and subtract payments to labor, depreciation, and taxes. 23 The denominator is a measure of the value of the corporate capital stock, using data from the BEA. GV A − wL − δP K K − T ax AR = (13) P KK The average return on capital is depicted by the blue, solid line in Figure 2.3. The trend of the average return has not followed the decrease seen in corporate bond rates: if anything, there is a slight upward trend in the average return. 21 Moody's Seasoned Aaa Corporate Bond Yield and Moody's Seasoned Baa Corporate Bond Yield are available from FRED, Federal Reserve Bank of St. Louis. The returns are deated using a 5 year moving average of the Gross National Product: Implicit Price Deator (A001RI1). 22 See Federal Reserve data series H.15, selected interest rates. https://www.federalreserve.gov/releases/h15/. 23 The numerator is measured as net value added (BEA Account Code: A457RC) less labor expenditures (BEA Account Code: A460RC). 34 Return on Capital 15 10 5 0 -5 1980 1990 2000 2010 Average Return Corporate AAA Corporate BAA 3m Treasury Figure 2.3: Return on capital. There is a separate, but related, puzzle involving the average return raised by Gomme, Ravikumar, and Rupert (2011). In a standard real business cycle, the return on the equity, i.e. the stock market, is identical to the return on business capital. In the data, however, the S&P 500 return is roughly six times more volatile than the return to business capital. Puzzle 4: Decreasing labor share and capital share It is a well known fact that the labor share has decreased over the past 30 years in the US, and our analysis of the data conrms this. Figure 2.4, using data from the national accounts, shows that the labor share was around 64 percent in the early 1980s, and has fallen to less than 60 percent by the end of our sample. 24 The decline in the labor share in the US is not due solely to housing. 25 If we restrict our attention to simply the corporate sector the decline is seen as well. Nor is the decline entirely explained by an increase in intellectual property capital. As we will discuss in Section 2.8, even with the revisions to the national accounts to include intangible capital, the income share of invested capital has not increased over the time period. The decline in the labor share is further robust to measures which take into account the rise of S-Corporations (Zidar, Zwick, Yagan, Smith, et al., 2017). Most analyses of factor shares only separate income into two factors, labor and capital. Since labor income is observed in the data while capital income is not, the capital share is usually calculated as the residual of the labor share. Computing the capital share this way mechanically shows an increase over the time period. Rather than calculating the capital share indirectly as a residual, we can try to calculate it directly. To do so we rst need to estimate total capital income, the value of the capital stock times the rental rate of 24 The labor share is measured as compensation to labor (BEA Account Code: A460RC) relative to gross value added (BEA Account Code: A455RC). 25 The story in Europe is slightly dierent. See Rognlie (2016) and Gutierrez (2017). 35 capital. In this procedure, we follow the work of Barkai (2016). Since most rms own rather than rent their capital, we cannot observe a rental rate of capital. Instead, we must estimate it. Economic theory gives an arbitrage condition for the rental rate rK , given by equation (14). The rental rate must equal the risk free rate rrf plus the risk premium rrp , less expected ination E(π) and plus the capital depreciation rate. In addition, if the price of capital is not equal to the price of output, the rental rate on capital must account for expected price gains of holding capital E(gP K ). rPKG = P K rrf + rrp − E(π) + δ + (1 − δ)E(gP K )  (14) We use the return on the three month treasury bill to proxy for the risk free rate. As our measure of the risk premium we use the spread between the rate of return on corporate BAA bonds and long term treasury bonds. Expected ination is approximated by a ve-year moving average of realized ination. Finally, the relative price of capital PK is calculated using the price deator for investment and the price deator for consumption. To proxy for expected capital price gains we calculate the ve-year moving average of realized price gains. We calculate the rental rate under four dierent assumptions: BAA risk premium and no capital price gain, BAA risk premium with capital price gains, no risk premium and no capital price gain and no risk premium with capital price gains. Our baseline estimate is an average over these four estimates. Using the rental rate on capital, we calculate the capital share as capital income over total income, the labor share as labor income over total income, and the tax share as taxes on production over income. Finally, there is a residual share of income which is not accounted for by labor, capital, or taxes. Figure 2.4 shows that, along with the labor share, the capital share is also declining over time, from 28 percent in the 1980s to 15 percent in the present. The main driver of this decline has been a decrease in the risk free interest rate, which has driven down the rental rate of capital; the capital-to-output ratio has been relatively stable (see Figure 2.1). In 1980 there was very little residual factor income  labor, capital, and taxes accounted for virtually all of national income. However, because of the decline in the labor and capital share, the residual share increased to 18 % by 2015. In other words, there is now a missing factor of income that does not go to labor or capital. As we will argue that this missing factor is pure prots, we refer to this residual share as the prot share. 26 26 For a dierent interpretation of the residual share, see Karabarbounis and Neiman (2018), who call the residual share factorless income. 36 Factor Shares 1975-1985 2005-2015 8% 0% 18% 28% 9% 59% 64% 15% Labor Capital Tax Residual Figure 2.4: Factor shares. Puzzle 5: Low investment despite low r, high Q As the work of Gutiérrez and Philippon (2016) has shown, several measures of investment have been trending down since the 1980s. In Figure 2.5 we plot net investment as a share of net operating surplus, a measure of business operating income. 27 While 50 % of net operating surplus was invested in the early 1980s, this has declined to about 25 % in the present. Net investment as a share of GDP shows a similar decline. This decrease in investment is somewhat puzzling, given historically low interest rates and high levels of Tobin's Q, both of which should lead to higher investment. 28 Net Investment as a share of Net Operating Surplus .8 .6 .4 .2 0 1980 1985 1990 1995 2000 2005 2010 2015 Figure 2.5: Net investment as a share of net operating surplus. 2.3 Model The core of our model is a DSGE economy with long-run productivity risk. To this base, we add three elements which allow us to explain the ve puzzling facts. We focus our exposition on these modications 27 We use Net Fixed Investment: Nonresidential (BEA Account Code: A593RC1). 28 See, for example, Hayashi (1982). 37 of the standard neoclassical model, leaving the full description of the model's equations and rst order conditions to the appendix. 2.3.1 Market structure We hypothesize that an increase in pure prots is a key force behind the ve puzzles. We introduce prots into our model economy in the simplest possible manner, through Dixit-Stiglitz monopolistic competition, even though the key results are more general and hold for a number of other market structures. 29 This is the rst key departure of our model from neoclassical theory. The pure prots are distributed to the holders of securities which hold the rights to the pure prots: the value of these securities form the wedge between nancial wealth and productive capital, and will help explain ( P1) and (P2). There is a unit mass of monopolistically competitive nal goods rms that dierentiate an intermediate good and resell it to consumers. The nal good composite is the CES aggregate of these dierentiated nal goods, which are indexed by i: Z 1  ΛΛt −1 t Λt −1 Yt = ytf (i) Λt di 0  −Λt pt (i) Final goods rms set prices in each period, and face a demand curve of the form ytf (i) = Yt Pt , where Pt is the nominal price index of the nal good aggregate and Λt is a time-varying measure of a rm's market power. 30 An increase in Λt decreases a rm's market power and lowers equilibrium markups. Each nal goods producer uses ytm of intermediate goods to produce output, according to a linear tech- f pt (i) nology function yt = ytm . A nal goods rm chooses real prices Pt and ytf (i) to maximize real prots, subject to the production constraint. The marginal cost of producing a unit of nal good is the price of the pint t intermediate good Pt . The optimality condition for the real price of the rm's good is a time-varying markup µt over marginal int pt (i) Λt pt pint cost (which is the price of the intermediate good): Pt = Λt −1 Pt = µt Pt t . Since the price of the intermediate good is the same, all nal goods rms make the same pricing decisions, and thus pt (i) = Pt , pint 1 yielding t Pt = µt . 29 Although our exposition uses monopolistic competition to generate pure prots, the results of our model are more general. The reason is simple: under a wide variety of micro-founded models, market structure primarily serves to determine the level of markups µt in the economy. Thus dierent market structures with the same markups µt will give at least qualitatively similar results. To see this directly, consider equation (16). The value of securities depends only on the exit rate of rms and the level of markup in the economy. Next, examining equations (43) and (44), we see that there is a wedge between the marginal product of labor and the wage, as well as the marginal product of capital and the implicit rental rate of capital, however independent of this market structure, the wedge is equal to the markup.  1 30 The R 1 pt (i)1−Λt di 1−Λt price index for the nal aggregate is given by Pt = 0 . 38 Market power in our model is determined by the CES elasticity Λt , which determines the level of markups Λt in our economy. We posit that Λt −1 , i.e. markups µt , follow an AR(1) process, given by µ) + ρµ ln(µt−1 ) + µt . ln(µt ) = (1 − ρµ )ln(¯ (15) The long run level of markups (determined by the long-run level of Λ) in the economy is given by µ ¯. An increase in the long-run level of markups will allow us to explain an increase in the prot share, and a decrease in the labor and capital share ( P4). The second key element of our model is that there are barriers to entry for nal goods rms. There are two types of barriers to entry in our model. First, nal goods rms hold the unique rights to the specic variety they produce. This ensures that entry of new rms does not drive price equal to marginal cost, and thus prots to zero. Second, we assume that the supply of nal goods rms is xed in the short run. Individuals cannot create new nal goods rms, and thus these rms are non-reproducible. The next section will show that, in the long run, the barriers to entry are not permanent, and rms will eventually go out of business. Due to these barriers to entry, there can be nonzero pure prots in the economy; nal goods rms make µt −1 aggregate prots Πt equal to Πt = µt Yt . The prot share of income in the economy is thus given by µt −1 P St = µt . Pure prots are distributed to shareholders of nal goods rms, who own the rights to the economic rents, as dividends. Aggregate dividends distributed to shareholders at time t are thus given by dft = Πt . Since all rms make identical prots, each rm receives an equal fraction of aggregate dividends. As will be seen, the securities that hold the rights to the pure prots of nal goods rms will be priced and traded, which will allow the value of wealth to diverge from that of productive capital ( P1 and P2). Firm entry and exit dynamics Although there are strong barriers to entry for nal goods rms, these barriers are not permanent: all nal goods rms in our economy will eventually go out of business and be replaced by new rms. We include exogenous rm exit as in Melitz (2003). Firm exit in our model aects the value of the securities which hold the rights to the pure prots of rms. Having rm exit will allow us to better match the level of nancial wealth in the economy, and thus quantitatively explain ( P1) and (P2). We assume that between period t−1 and t a nal good rm has a probability ∆t of exiting the market. Thus, of all the rms that are extant in time t − 1, only (1 − ∆t ) will survive to period t, a smaller fraction Qs (1−∆t )·(1−∆t+1 ) will survive to period t+1, and an ever diminishing percent n=t (1 − ∆n ) will survive to 39 period s. When a rm exits, shareholders who hold the rights to its prots are wiped out. 31 The information on whether a rm goes out of business is revealed at the end of period t − 1, before asset decisions are made for the next period. Entry in our model is also exogenous. Each period a mass ∆t of new rms enters, replacing the rms that have exited. New IPO securities are issued at the end of timet − 1 that give the rights to these rms' prots; this corresponds to, for example, when Google was oated for the rst time on the stock exchange. Asset pricing The third key element of our model is that the rights to the pure prots of nal goods rms are traded. There are security markets in which the rights to the future prots of nal goods rms are bought and sold. The trading of these securities leads to a divergence between nancial wealth and productive capital ( P1), and allows Tobin's Q to diverge permanently away from 1 (P2). At the end of period t − 1, securities Stf are traded for each rm, which give the rights to all future dividends dft of these rms for as long as they survive. Individuals do not buy shares of individual nal goods rms, which are innitesimally small. They instead buy positive fractions of the continuum of rms. Since the continuum spans from 0 to 1, every period there is a single share of securities Stf outstanding. Due to the law of large numbers, for every mass of shares an individual purchases, exactly ∆t+1 percent of the underlying rms will go out of business between period t and t + 1. The value of these securities Stf is given by the present discounted value of the dividends the shares receive: "∞ s # f X Y Xt−1 = Et−1 ms dfs (1 − ∆n ) (16) s=t n=t+1 In this equation, mt is the stochastic discount factor that is determined in equilibrium by the optimal asset choice of households. Note that future dividends are discounted by two factors: by (1 − ∆), taking into account that some rms will go out of business, and the stochastic discount factor, taking into account that future dividends must be discounted by the riskiness of these prots and the time value of money. 32 31 From the point of view of an investor in these securities, the churning of rms is somewhat analogous to the depreciation of capital. An individual buys securities, receives a return, and some of the security depreciates through the bankruptcy of the underlying rms. 32 Note that although we have motivated the discounting of the value of shares (1 − ∆) through the notion of rm entry and exit, there are several other interpretations that can be given to this discount rate. First, it can be though of as an additional, not modeled, risk premium on pure prots. Second, it can be though of as a reduced form way to model the fact that not all rms are publicly traded in the US, and thus their pure prots are not capitalized. 40 Intermediate goods rms Production is fairly standard; the only twist from a purely neoclassical model is the presence of the markup wedge µt between the marginal product of capital and the rental rate; an increase in this wedge will be our main explanation for why investment has decreased ( P5). A representative intermediate goods rm uses labor Lt and productive capital Kt to produce output Ytm according to the production function σ  σ−1 σ−1  σ−1 Ytm = αKt σ + (1 − α)(At Lt ) σ (17) where σ is the production elasticity of substitution and At the level of labor augmenting productivity. Productive capital Kt includes both tangible and intangible capital that contributes to the production of goods and services, which is broadly in line with the BEA. 33 Here forward, we will simply use the term capital when referring to productive capital. Intermediate goods rms distribute the excess of its prots over retained investment as a dividend dit Sti = 1 m µt Yt − wt Lt − It . Investment increases the rm's future stock of capital according to Kt+1 = Φ(It /Kt )Kt + (1 − δ)Kt (18) where δ is the rate of depreciation and adjustment costs Φ(·) are a positive concave function. Following  1−ξ a1 It Jermann (1998), we use an adjustment cost function given by Φ(It /Kt ) = 1−ξ Kt + a2 . The rst order conditions from the rm's problem are derived in Appendix A. Note that markups µt create a wedge between the marginal product of capital and the rental rate. As markups increase, the increased wedge will cause investment to decrease ( P5). 2.3.2 Long run risk The value of securities Stf (and thus nancial wealth, ( P1) and (P2)) depends upon the rate at which pure prots are discounted, and thus the equity premium. In order to match the equity premium in the data, we follow the macro-nance literature and include long-run productivity risk in our model, as in Bansal and Yaron (2004) and Croce (2014). 34 There are two sources of uncertainty in productivity growth: an i.i.d short-run shock that is standard in RBC models (a ), and a long-run component (x ) that leads to small 33 We do not include in this term capitalized spending by businesses on economic competencies such as advertising, marketing research, and branding. Because this spending does not serve to increase the production of goods and services, we term this spending non-productive intangible investment. We discuss this distinction further in Section 2.8. 34 The exact way we match the equity premium is not important for our theoretical or quantitative results: our analysis would be similar if we had generated the equity premium through consumption habit formation or rare disaster risks. 41 but persistent movement in long-run growth. Let At denote the level of labor augmenting productivity, and lowercase letters denote log-units. The growth rate of productivity is given by: ∆at+1 = ζ + xt + σa a,t+1 (19) xt = ρxt−1 + σx x,t (20)       a,t+1  0  1 ρxa    ˜ iid N   ,   (21) x,t+1 0 ρxa 1 Here xt is the long run risk of productivity growth, and a,t+1 is the short run risk. 2.3.3 Household preferences Preferences are fairly standard: representative households have preferences of the Epstein and Zin (1989) variety, which will allow us to more easily match the equity premium. The one nonstandard element is a time-varying wedge in the utility between time periods. Changes in the wedge will allow us to match the path of the real interest rate in a representative agent setting, and thus match ( P3). We use this wedge as a reduced form way of modeling factors that aect the real interest rate in an OLG model, such as changes in demographics (see Eggertsson, Mehrotra, and Robbins (2017)). While an OLG structure would allow us to model the forces aecting the natural rate of interest rate in greater detail (and we have done simulations with this variation of the model) we have chosen here to work with a representative agent model. The more detailed OLG structure has not added substantive insights beyond those in Eggertsson, Mehrotra, and Robbins (2017) in the experiments we have considered, but makes the exposition more complex. The economy consists of a unit mass of identical innitely lived agents. Utility is given by θ   1−γ   1  1−γ ν 1−ν 1−γ θ Vt = (1 − β) ct (At−1 (1 − Lt )) θ + βDt Et Vt+1 (22) where the time discount factor is β, ν is a weight determining the average share of total hours worked, 1−γ γ is the risk aversion parameter, and θ is a parameter dened as θ = 1 . 1− ψ In this expression, ψ is the elasticity of intertemporal substitution. The main advantage of using Epstein-Zin utility is that there is no longer a link between the intertemporal elasticity of substitution and the coecient of risk aversion, which 42 makes it easier to match the equity-risk premium (and quantitatively explain ( P1) and (P2)). If γ = 1/ψ , the utility collapses to the CRRA variety. As in Croce (2014), leisure utility is scaled by productivity. The term Dt is an additional wedge between utility in period t + 1 and period t, beyond the time discount rate of β. It represents additional unmodeled factors, such as population growth and mortality, that might eect the supply of loanable funds (and thus the real interest rate) in an OLG model, but have no eect in a representative agent model. Dt is a lever we will use in our quantitative exercises to decrease the long-run real interest rate, and thus match ( P3).35 Individuals maximize this utility subject to a series of budget constraints, ct + Xti St+1 i + Xtf St+1 f = wt Lt + dit Sti + dft Stf + ∆t+1 Xtf + (1 − ∆t )Xtf Stf + Xti Sti (23) On the left hand side of the budget constraint, individuals use their income to purchase either consump- i i f f tion, shares of intermediate good rms (Xt St+1 ), or shares of nal goods rms (Xt St+1 ). On the right hand side of the budget equation, agents receive income from a variety of sources: labor income wt Lt , dividends from intermediate goods rms dit Sti , dividends from nal goods rms dft Stf , IPO issued securities of nal goods rms ∆t+1 Xtf , remaining share value of nal goods rms (1 − ∆t )Xtf Stf , and remaining share value of intermediate goods rms, Xti Sti . 2.3.4 Equilibrium and solution An equilibrium is a set of quantities and prices such that individuals maximize utility subject to budget constraints, intermediate and nal goods rms maximize prots subject to production constraints, and markets clear. While this model is not stationary, we can make it so by applying a standard transformation: divide all quantities (except labor) by At−1 , as well as wages and the price of securities Xti and Xtf . Appendix A contains the full denition of equilibrium and lists all of the equations of the model. A steady state equilibrium is the same as the above equilibrium denition, except that all variables are constant rather than subscripted by time. Appendix A also contains the steady state equations of the model. We solve the model using a 2nd order perturbation methods, using the software Dynare (Adjemian, Bastani, Juillard, Mihoubi, Perendia, Ratto, and Villemot, 2011); a period in our model is a month. We solve the model around the nonstochastic steady state. The work of Caldara, Fernandez-Villaverde, Rubio- Ramirez, and Yao (2012) has shown that perturbation methods are well suited to solving DSGE models with recursive preferences and long run risk, with accuracy that is competitive with Chebyshev polynomias and 35 De Groot, Richter, Throckmorton, et al. (2017) show how to model a preference shock with Epstein-Zin preferences. 43 value function iteration. Once we have solved the model, we will compare the theoretical moments generated by the model to data moments. 2.4 Characterizing the puzzles In this section, we derive model statistics that correspond to the data moments of our ve puzzles: nancial wealth, average return, Tobin's Q, etc. These statistics will be the main objects of analysis for our theoretical as well as quantitative results, and will also illustrate how our theory diers in key ways from the neoclassical model. For each macro-statistic, we will also derive steady-state equations, which will be useful in the comparative statics analysis. P1: Increasing nancial wealth-to-output ratio, constant capital-to-output ratio We measure nancial wealth in our model in a way that corresponds to the measurement in the US Financial Accounts. In the nancial accounts, wealth is dened as the market value of stocks and bonds, thus we dene nancial wealth Wt as equal to the combined value of securities and capital, Wt = Xtf + qt Kt . We immediately see from this equation a key dierence between our model and the neoclassical: when there are non-zero pure prots in the economy, the value of nancial wealth may diverge from the value of the capital stock. We now derive the steady state security price Xf as a percent of output. In a balanced growth equilibrium, d the ratio of dividends to output is given by Y = P S. In addition, dividends grow at the same rate as output, thus future dividends must be adjusted for productivity growth. Thus we have ∞ Xf X P S(exp(ζ))s (1 − ∆)s PS = = (24) Y s=0 (1 + r)s 1− exp(ζ)(1−∆) 1+r using the formula for the sum of a geometric series. The r in this expression is the steady state real interest rate. Given the steady state real interest rate, it is easy to characterize the capital-to-output ratio. The FK f.o.c. of intermediate goods rms yields r = µ − δ, which allows us to calculate steady-state capital-to- labor; combining this with steady state labor-to-output (equation (66) in the appendix) yields steady state capital-to-output. P2: increasing Tobin's Q Empirical Tobin's Q is dened both in the nancial accounts and in our model as the ratio of the market value of wealth to the value of capital goods: 44 Wt X f + qt Kt Q= = t (25) Kt Kt We immediately see from this equation a second way in which our model diers from the neoclassical: with nonzero pure prots, Tobin's Q can be permanently above 1. P3: declining interest rate, constant average return The average return on capital is measured in the data as GDP minus depreciation minus payments to labor, divided by the replacement value of capital: Yt −wt Lt −δKt ARt = Kt . In a steady state, the average return is equal to Π PS AR =r+ =r+ K (26) K Y We see from this equation that with pure prots, there can be a divergence between the average and the marginal return on capital. In a neoclassical model, they are one and the same. It is simple to characterize the steady state real interest. From equation (39) in the appendix, the stationary discount rate is −1 m = βD · exp( ζ) (27) ψ 1 The risk free interest rate is r= m − 1. P4: increasing prot share, declining labor share We measure labor share as payments to labor, wt Lt rtK qt Kt LSt = Yt , capital share as the return on productive capital, KSt = Yt , and prot share as the residual, P St = 1 − LSt − KSt . In the neoclassical model, the prot share is zero. P5: declining investment In a stationary equilibrium the capital to output ratio is constant, and thus investment must be exactly enough so that capital grows with output, i.e. at the rate of productivity growth plus depreciation. Thus in a steady state investment to output equals I K = [exp(ζ) − 1 + δ] (28) Y Y Finally, we characterize the equity premium in our model, because our quantitative results will produce interesting endogenous movements in this moment. Since there are two assets in our model (intermediate and nal goods rms), we will calculate two equity premiums, as well as the equity premium on the return 45 from holding both types of assets together, in proportion to their values. The returns of our model are 1 calculated as follows. The risk free return is given by Rt = Et [mt+1 ] , the expected return on the nal goods   f dft+1 +(1−∆t+1 )Xt+1 f rm is given by Et [Rt+1 ] = Et Xtf , and the return on intermediate good rm is given by h i i i dt+1 +qt+1 Kt+2 Et [Rt+1 ] = Et qt Kt+1 . The combined return is the total return from holding the total value of intermediate and nal good rms " # c dft+1 + (1 − ∆t+1 )Xt+1 f + dit+1 + qt+1 Kt+2 Et [Rt+1 ] = Et . Xtf + qt Kt+1 The equity premium for all three of these assets is then calculated as the expected return minus the risk free rate, adjusted for leverage. In line with Croce (2014), we use a leverage ratio of 2. We are not aware of any previous work that distinguishes between the equity premium on prots and the equity premium on productive capital, although the distinction is important for our results. Our empirical results will show that the equity premium on securities is substantially higher than the equity premium on productive capital. As discussed in detail in Section 2.7.6, because there are barriers to entry, nal goods rms are non-reproducible assets, and thus their price can have large uctuations in response to changes in pure prots. In contrast, productive capital is reproducible, and thus the price of capital q has only moderate uctuations (due to the presence of adjustment costs). As a direct result, in moving from an economy in which the value of securities is high relative to the value of the capital stock the equity premium will increase. 36 2.5 A qualitative solution to the puzzles We hypothesize that a permanent increase in markups, along with a decrease in the real interest rate, can explain the ve puzzles. We now examine the impact of both changes on our ve stylized facts of interest. We will compare analytic comparative statics in the steady state of our model, which allows us to unambiguously sign the derivatives. Our results will show that the proposed mechanisms can qualitatively solve the ve puzzles that are the subject of this paper: in the succeeding sections, we will then test whether our mechanisms can quantitatively solve them. 36 This result should be tempered somewhat by the fact that we may be missing an element. As Larry Summers has pointed out (see Summers (2017)), as equity prices rise, rms become less levered. 46 2.5.1 An increase in markups We examine the change in steady state model moments to small changes in the steady state level of markups, µ ¯. Proposition 1. The following comparative static results hold: ¯ ¯ ∂K ∂K ¯ L ∂µ ¯ < 0, ∂Yµ¯¯ < 0. (P1) An increase in steady state markups will lead to a decrease in the capital-to-labor ratio and the capital-to-output ratio. ∂Q ∂µ ¯ > 0. (P2) An increase in steady state markups will lead to an increase in empirical Tobin's Q. ∂AR ∂µ ¯ > 0. ( P3) An increase in steady state markups will lead to an increase in the average return on capital. ∂P S ∂µ ¯ > 0. (P4) An increase in steady state markups will lead to an increase in the pure prot share. ∂LS ∂µ ¯ < 0, if σ ≤ 1. (P4) An increase in steady state markups will lead to a decrease in the labor share if production is Cobb-Douglas, or the production elasticity of substitution is less than one. ∂KS ∂µ ¯ < 0, if σ ≥ 1. An increase in steady state markups will lead to a decrease in the capital share if production is Cobb-Douglas, or the production elasticity of substitution is greater than one. ¯ ∂ YI¯ ∂µ ¯ < 0. (P5) An increase in steady state markups will lead to a decrease in the investment-to-output ratio. The above proposition shows that an increase in markups can potentially explain many of the ve puzzles. We focus on the intuition here, and provide proofs in Appendix B. An increase in markups will increase prots of nal goods rms, and thus dividends to the owners of nal-goods rms securities. This will increase the value of these securities, leading to an increase in wealth- to-output ( P1) and Tobin's Q (P2). Because of the increased prot share, there is also an increase in the measured average return on capital  note that this goes against (P3), the constant average return seen in the data. However, the increase in markups leads to an increase in the wedge between the average return on capital and the risk free interest rate (see equation (26)), which is supportive of ( P3). An increase in markups will directly lead to an increase in the prot share (P4). With an increase in the prot share, there will be a decrease in the combined labor and capital share. Whether there will be an unambiguous decrease in the labor share depends on the value of σ, which determines the elasticity of the ratio of the labor to capital share to a change in markups. Under Cobb-Douglas, there is no response in the relative labor-capital share to a change in markups. If σ < 1, the relative labor share will decline with 47 an increase in markups ( P4). Although the relative capital share increases, in our simulations this is never enough to lead to an overall increase in the capital share: although with an increase in markups capital gets a bigger slice over the overall labor plus capital share pie, the shrinkage of the pie due to an increased prot share outweighs this eect. The higher markups will increase the wedge between the marginal product of capital and the rental rate of capital (see equation (43) in the appendix). However, since the interest rate does not change, neither does the rental rate of capital. Thus there must be an increase in the marginal product of capital, and hence a decrease in the capital-to-output ratio. This will also lead to lower investment (( P5), see equation (28)). All of the eects of an increase in markups are summarized in Table 2.1, which shows that an increase in markups can go a long way towards explaining the ve puzzles. One remaining challenge is that an increase in markups would tend to increase the average return on capital, while in the data it is relatively stable; the next section will suggest a possible solution to this challenge. Model statistic Symbol Eect Capital-to-output ( P1) Kt /Yt ↓ Tobin's Q ( P2) Qt ↑ P3) Average return ( ARt ↑ Prot share (P4) P St ↑ Labor share (P4) LSt ↓ if σ≤1 Investment-to-output ( P5) It /Yt ↓ Table 2.1: Eect of an increase in markups. 2.5.2 A decrease in interest rates We now study the comparative static eects of a lower real interest rate. We model the decrease in interest rates in a reduced form way, through an increase in the utility wedge D. Two key examples we have in mind are a decrease in population growth and a decrease in the mortality rate. Proposition 2. The following comparative static results hold: W > 0. (P1) ∂ ∂D Y An increase in D will lead to an increase in the wealth-to-output ratio. K K > 0. (P1) ∂ ∂ ∂D Y > 0, ∂D L An increase in D will lead to an increase in the capital-to-output ratio and the capital-to-labor ratio. ∂AR ∂D < 0. (P3) An increase in D will lead to a decrease in the average return on capital. ∂LS ∂D >0 if σ < 1. (P4) An increase in D will lead to an increase in the labor share if σ < 1. If σ > 1, ∂LS ∂D < 0. 48 ∂KS ∂D < 0 if σ < 1. (P4) An increase in D will lead to a decrease in the capital share ifσ < 1. If σ > 1, ∂KS ∂D > 0. ∂ YI ∂D > 0. (P5) An increase in D will lead to an increase in the investment-to-output ratio. Once again, we leave the proofs to Appendix B, and discuss the intuition for these results. A decrease in r would tend to decrease the marginal product of capital (see equation (43) in the appendix), and thus increase the capital-to-output ratio. In addition, a lower r means that the rights to future dividends are discounted at a lower rate, which would tend to raise the value of securities, Xtf , relative to output. Since both capital-to-output and security value-to-output increase, the wealth-to-output ratio will increase as well P1). ( The total eect on Tobin's Q is ambiguous, however, since both the numerator and denominator of this ratio will increase. As seen in equation (26), a decrease in the real interest rate would tend to decrease the measured average return on capital ( P3). Note that a decrease in interest rates thus has the opposite eect of an increase in markups. If we consider both changes simultaneously, there are two opposing forces on the average return on capital: the increase in prots would tend to raise the average return, while the decrease in r would tend to decrease it. Since a lower r means a higher capital-to-output ratio, this will tend to increase the labor share and decrease the capital share (P4), assuming, as most evidence suggests, that the production elasticity of substitution σ < 1. Because a decrease in r leads to an increase in the capital-to-output ratio, there will be also be an increase in the investment-to-output ratio (( P5), see equation (28)). Thus once again, the force of a lower r tends to counteract the force of higher prots. The eects of changes in r on the capital-to-output ratio and investment-to-output ratio are strongly dependent on whether capital and labor are complements or substitutions, i.e. the elasticity of substitution σ is less than or greater than one. The lower is σ, the smaller the eects of changes in the interest rate on capital and investment. Model statistic Symbol Eect Wealth-to-income ( P1) Wt /Yt ↑ Capital-to-output (P1) Kt /Yt ↑ Tobin's Q (P2) Qt ? Average return (P3) ARt ↓ Prot share (P4) P St 0 Labor share (P4) LSt ↑ if σ<1 Capital share (P4) KSt ↓ if σ<1 Investment-to-output (P5) It /Yt ↑ Table 2.2: Eect of an increase in D. 49 2.5.3 A decrease in productivity We also examine the eect of a decrease in the permanent growth rate of productivity, ζ. From equation (27), we see that a decrease in ζ will lead to an increase in the discount factor, and thus a decrease in the steady state real interest rate r. Depending on the elasticity of intertemporal substitution, ψ, the change in interest rates will either be greater than the change in ζ (ψ < 1), less than the change in ζ (ψ > 1), or of the same magnitude (ψ = 1). In our baseline calibration we have ψ > 1, and thus the change in interest rates will be smaller in magnitude than the change in productivity growth. Then, from equation (24), we see that when productivity growth decreases, the security value-to-output ratio will decrease. The explanation for this is fairly straightforward. A slowdown in productivity means a slowdown in the growth rate of the economy, and thus of dividends, leading to a decline in the value of securities, and with ψ > 1 this outweighs the eect of a lower discount rate of the dividends (r ) on the value of securities. The propositions in this section have suggested that a decline in interest rates and an increase markups might be able to explain the ve puzzles. In the rest of the paper we explore the quantitative implications of this explanation. 2.6 Estimating changes in markups and interest rates The comparative statics results above show that an increase in markups, combined with a decrease in the equilibrium interest rate, can potentially explain the ve trends. To test whether these qualitative predictions hold up in a quantitative sense, we need a measure of how these variables have changed in the US data. To do so, we rely upon a growing literature which estimates secular changes in markups. We estimate markups using aggregate macro data, and nd there has been a moderate increase from 1970 to the present, a result roughly in the midpoint of this recent literature on markups. We use existing ndings from the literature on the decline in the natural rate of interest, and use a conservative decline of 2 percentage points over our sample period. We emphasize that this paper is primarily concerned with explaining long term secular trends, and thus for our purposes it is the change in markups and interest rates that is important rather than their cyclicality. 37 37 Our stylized model does not include the many features and complications that the RBC literature has showed is necessary to match the co-movements and cyclicality of the major business cycle moments. See, for example, Christiano, Eichenbaum, and Evans (2005). 50 2.6.1 Markups We estimate markups using aggregate macroeconomic data, exploiting the fact that under constant returns to scale (CRS) production, markups are proportional to the prot share of the economy: in this technique we follow the work of Barkai (2016). In particular, under CRS markups equal the inverse of the share of production not accounted for by pure prots: µ−1 1 PS = =⇒ µ = . (29) µ 1 − PS As discussed in Section 2.2, we estimate the prot share from the data by taking the residual share of output after subtracting labor and capital income. 38 We use the dierent versions of the capital rental rate previously discussed, and average over the dierent estimates. Under these assumptions, the markup increases over the time period, from 1.11 in 1970 to around 1.23 in 2015. Whereas prior to 2016 it was dicult to nd an extended time series for markups, there has been a recent bumper crop of papers estimating markups. Three separate strands have emerged, each estimating markups using a dierent technique: (i) a method taken from the New Keynesian literature (ii) a method using techniques from IO and rm level data (iii) a method backing out markups from the prot share. Table 2.3 displays the various estimates, and shows that our results (ERW) fall into the midpoint of this growing literature. In our quantitative analyses we will uses these alternative markup estimates as robustness checks to our baseline results. Estimate Year Range µ pre µ post ∆µ Barkai (2017) 1984-2015 1.025 1.21 0.19 Nakarda & Ramey (2013) 1970-2014 0.95 1.07 0.12 De Loecker & Eeckhout (2017) 1980-2014 1.18 1.67 0.49 Traina (2018) 1980-2014 1.10 1.15 0.05 Gutierrez (2017) 1980-2014 1.15 1.21 0.06 Hall (2018) 1988-2015 1.12 1.27 0.15 ERW (2018) 1970-2015 1.11 1.23 0.12 Table 2.3: Markup estimates. In a recent paper, Karabarbounis and Neiman (2018) has extended the calculation of factor shares back to 1960, using a similar formula to the Hall-Jorgensen formula for the rental rate of capital used in Section 38 The estimates of capital income are dependent on factors which are dicult to measure or uncertain, in particular the risk premium on capital investments and the expected change in the relative price of capital. For this reason, we calculate four dierent versions of our markup series, each under dierent assumptions about the risk premium and the relative price of capital; these series all show a similar trend and are reported in appendix Figure 2.7. The four series dier along two dimensions: whether (i) risk premium and/or (ii) the change in the relative price of capital are included in the calculation of the rental rate of capital. See appendix Figure 2.7. 51 2.2 and in Barkai (2016). Karabarbounis and Neiman (2018) nds that factorless income, income which accrues neither to labor nor to capital, is not only high in 2015, as is emphasized in this paper and in Barkai (2016), but also high in 1960. In appendix Figure 2.7, we extend our markup calculation back to 1960, and nd a similar U shape: markups are moderately high in 1960, before declining to a nadir in 1980, after which they increase to their maximum in the present. Interestingly, papers using separate methods to calculate markups have also found a U-shape from 1960 to the present; see Traina (2018), De Loecker and Eeckhout (2017) and Gutierrez (2017). This growing literature has made it clear that pure prots are not a new phenomenon, although this paper focuses on the evolution of prots over the past half-century. Karabarbounis and Neiman (2018) raise an important objection to using the Hall-Jorgensen method to estimate the rental rate of capital; since the formula includes the real interest rate, this mechanically creates a tight negative correlation between real interest rates and the prot share at short and medium frequencies. Thus in periods where there is a dramatic rise in the real interest rate, like in the early 1980s, there is a corresponding fall in the prot share. Like many returns of nancial assets, real interest rates can be volatile in the short and medium term, and measures of the factor shares using the Hall-Jorgensen formula will inherit this volatility. We argue that although there is indeed volatility in interest rates, over the long horizon there has been clear downward trend in interest rates, and thus a decline in the rental rate of capital. Thus, for explaining long-run trends at least, declining interest rates suggest a lower rental rate of capital, even if we are not able to fully account for short-term movements in real interest rates. 2.6.2 Interest rates We use a conservative estimate of the decline in the natural rate of interest; results in the literature vary somewhat widely. Holston, Laubach, and Williams (2017), using the Laubnach-Williams model, estimate a decline of ≈ 3.5 percentage points, from 3.91 in 1970 to 0.43 % in 2015. Del Negro, Giannone, Giannoni, and Tambalotti (2017), using DSGE and time series analysis, estimate a decline of 1-1.5 percentage points, from 2-2.5 % to 1-1.5 %. A simple ve year moving average of the real federal funds rate yields a decline of 3.8 percentage points, from 2.25 % to -1.55 %. For our baseline analysis, we use a decline in the natural rate of interest of 2 percentage points, from 3 % in 1970 to 1 % in 1970. 2.7 A quantitative solution to the puzzles We now test the hypothesis that changes in markups and interest rates can quantitatively explain the ve puzzles outlined in the introduction. While the analytic comparative statics of Section 2.5 suggested our 52 Estimate r∗ 1970 r∗ 2015 Holston, Laubach, and Williams (2017) 3.91 0.43 Del Negro et. al. (2017) 2.5 1.5 5-Year MA Real Federal Funds 2.25 −1.55 Table 2.4: Natural rate estimates. model can qualitatively match the puzzles, we now investigate the magnitudes. To do so, we cannot rely purely on steady state results, since in a steady state there is no equity premium. Instead, we will compare moments of the stochastic economy. Our results will show that changes in markups and interest rates can indeed quantitatively account for the ve puzzles. The ve puzzles all involve changes in macroeconomic quantities. For this reason, we will judge our quantitative success by whether changes in our model moments can match changes in the data moments. We rst calibrate our model to US data in 1970 (matching levels only). We then solve the model, and compute moments of interest by calculating theoretical moments from the second-order approximation of the model's solution. We then change the long run level of markups from their 1970 to their 2015 level, then interest rates, and then both together, calculating the model's moments for each change. 39 We will then compare changes in our model moments between the two time periods to changes in the data moments. We emphasize that our goal in this exercise is not to understand short-run quarter to quarter movements in the economic variables of interest. It is well known that in order to explain short run co-movements in output, consumption, investment, and the real interest rate, a wide variety of frictions are needed (see, for example, Smets and Wouters (2003) and Christiano, Eichenbaum, and Evans (2005)). In this paper we are interested in long-run changes in our variables of interest over the past half century, and abstract from questions about the short and medium term. 2.7.1 Quantitative calibration We calibrate the model to the US economy in 1970. The goal of the calibration is to match the level of the model's moments to the 1970 data moments: once again, we do no target changes in moments over the time period, as this will be the main outcome and test of our analyses. We focus on matching in particular the moments which correspond to the ve macroeconomic puzzles of interest. The calibration results will show 39 Our choice of 1970 as the initial steady state is largely guided by the fact that this corresponds to the period before the onset of the great ination, which was a period of great volatility for ination and the real interest rate. The real interest rate fell in the early 1970s on account of a monetary policy expansion, before increasing dramatically during the Volker disination of the early 1980s. By choosing 1970 as a comparison point we estimate a moderate decline in interest rates of 2 % over the time period, and thus avoid exaggerating the movement on the real interest rate. Our choice of 1970 vs 1980 also aects our estimated increase in markups, as markups reached their nadir in 1980. 53 our model moments closely matching the data moments in levels for 1970, with parameter estimates within the range of values reported in the existing literature. There are three categories of parameters: (i) the long run level of markups and interest rates estimated in Section 2.6 40 (ii) parameters taken from the data and literature, and (iii) parameters chosen to match 1970 data moments, through the minimization of an objective function. Parameters from category (i) are based upon our estimation in Section 2.6: long-run markups µ ¯ are 1.11 in 1970, and the real interest rate is 3 %. Parameters from category (ii) are displayed in Table 2.5. The rate of productivity growth ζ we take from Fernald (2012). We use the estimates of Croce (2014) to calibrate our long-run and short-run productivity risks. The depreciation rate comes from Jorgenson (1996). Following Croce (2014), we choose ξ to match the variability of investment to output, and nd ξ = 0.12. Panel A: Data Symbol Value Source Productivity growth (/yr) ζ 2.02% Fernald (2012) Panel B: Related literature Long run risk persistence ρ 0.98 Croce (2014) Long run risk std. dev. σx 0.0010 Croce (2014) Short run risk std. dev. σa 0.01 Croce (2014) Depreciation rate (/yr) δ 6% Jorgensen (1996) Adjustment costs ξ 0.12 Croce (2014) Table 2.5: Parameters taken from the data and related literature. We choose the remaining parameters (with the exception of the AR(1) parameters, which are estimated separately) to match six key moments of the US economy as of 1970. All data moments are calculated through a 5-year moving average around 1970, using yearly data. The rst four moments are standard in the DSGE literature: a real interest rate of 3.0 %, an investment-to-output ratio of 16.2 %, a labor share of 71.5 %, and a share of hours worked of 18 %. In light of our above theoretical and empirical analysis, we add a new moment to the calibration: a wealth-to-output ratio of 2.66. Finally, in consideration of our goal of matching nancial moments, we calibrate our model to match an equity premium of 4.71%. The parameters chosen this way are the rate of time preference β, the capital production coecient α, the production elasticity of substitution σ, the rm exit rate ∆, the labor supply coecient ν, and the risk aversion parameter γ. There is no one-to-one mapping between these remaining parameters and the targets, hence we jointly choose all parameters to match the model output to the targets. Nevertheless, each of the parameters above correspond relatively closely with one of the key moments we are trying to match. The rate of time preference β is closely related to the real interest rate; as β increases, the real interest rate falls. The capital share 40 In Appendix C we report robustness results using alternative measures of markups. 54 parameter α along with the production elasticity σ determine the labor share as well as the investment- to-output ratio. The rate of rm exit ∆ has a large eect on the wealth-to-output ratio. The parameter ν determines the number of hours worked. Finally, the risk aversion parameter γ is the most important determinant of the equity premium. Paramters chosen to match targets Symbol Value Capital production elasticity α 0.30 Production elasticity σ 0.90 Firm exit rate ∆ 0.0048 Rate of time preference β 0.9957 Risk aversion γ 8.11 Hours supplied ν 0.21 AR(1) persistence ρµ 0.97 AR(1) error variance σρ 0.005 Table 2.6: Calibrated parameter results. We minimize a weighted sum of the squared dierence of our model moments and the 1970 data moments. Table 2.6 displays the parameter values, while Table 2.7 shows the resulting model moments and compares them with the data. With the parameters selected by our minimization, the model moments come very close to matching those in the data. We separately estimate the AR(1) parameters for markups, ρµ and σµ (the standard deviation of the error µt ). To do so, we detrend our baseline markup series and estimate ρµ = 0.97 and σµ = 0.005 via OLS. The parameters in Table 2.6 fall directly within the range of parameter values in the macro-nance literature. We now compare our parameters with previous calibrations/estimations of DSGE models with recursive preferences and/or long-run productivity risk. Our β of 0.9957 is quite close to the value of 0.9957 in Croce (2014), 0.997 in Van Binsbergen, Fernández-Villaverde, Koijen, and Rubio-Ramírez (2012) and 0.9606 in Rudebusch and Swanson (2012). While previous literature has generally used Cobb-Douglas production, we use CES, and nd σ = 0.90. 41 Our capital elasticity parameter α, 0.30, is slightly smaller than the capital share parameter in the existing literature (0.34 in Croce (2014), 0.3 in Van Binsbergen, Fernández-Villaverde, Koijen, and Rubio-Ramírez (2012), 0.33 in Rudebusch and Swanson (2012)): in order to match the labor share with a higher level of markups, α must be smaller. Our estimated coecient of risk aversion, γ = 8.11, is in line with Croce (2014), as well as the estimates of Vissing-Jørgensen and Attanasio (2003). We are able to match the equity premium with such a small coecient of risk aversion because of the presence of long-run risk in our model: in models without this feature, the estimated coecients are much higher. 41 This is line with the range of estimates in Antras (2004). 55 The monthly rm exit rate of 0.48 % yields a yearly rate of 5.71 %. This is half the exit rate used in Bilbiie, Ghironi, and Melitz (2012), but comparable in magnitude to the annual production destruction rate (in terms of share of products and market share) of 8.8 % from Bragdon, Redding, and Schott (2010). We note, however, that the ∆ parameter in our model corresponds to the notion of bankruptcy (in which the shareholders are wiped out) and/or the replacement of a rm's products with that of a competitor's (in which some portion of shareholder value is wiped out), not to the replacement of a product within a rm by the rm's own product. Data from Decker, Haltiwanger, Jarmin, and Miranda (2016) shows the average annual rm exit rate is around 9 %. However, since young rms, which tend to be the smallest, go out of business at a much higher rate than old rms, the average exit rate weighted by employment is only around 2.75 %. We note that, unlike the rm entry rate, there has not been a secular decline in rm exit rates since 1980. Targets Model Data Source Real interest rate 2.99% 3.00% Federal Reserve Wealth-to-output ratio 2.66 2.66 Financial Accounts Investment-to-output ratio 15.64% 16.15% NIPA Labor share 71.17% 71.49% Elsby (2013) Equity premium 4.64% 4.71% Croce (2014) Labor supply 0.18% 0.18% Croce(2014) Table 2.7: 1970 calibration results. We once again emphasize that we are choosing parameters only to match 1970 moments. In particular, we do not choose any parameters to try and match the change in moments from 1970 to the present. The success or failure of our exercise will be comparing changes in our model moments with changes in the data moments. 2.7.2 Quantitative results: Overall hypothesis We begin with a test of our overall hypothesis: whether changes in markups and interest rates can explain the ve macroeconomic puzzles. Table 2.8 shows the combined eects of changing markups, productivity growth, and D from their steady steady values in 1970 to their 2015 values. Overall, our model does a reasonably good job of explaining the ve macroeconomic puzzles: the changes in the model moments which correspond to the puzzles are similar in magnitude to the data moments. The rst column lists the macroeconomic moment of interest (with the corresponding puzzle in parentheses). The second column displays the calculated change in model moments between 1970 and 2015 that is the result of changing markups and interest rates. The third column lists the change in the data moments. 56 Moments ∆M odel ∆Data Wealth-to-output ratio ( P1) 0.88 0.95 Capital-to-output ratio (P1) 0.21 0.31 Tobin's Q (P2) 0.17 0.40 Real interest rate (P3) -2.00 pp -2.00 pp Average return (P3) 0.96 0.64 Prot share (P4) 8.94 8.94 Labor share (P4) -6.85 pp -6.82 pp Capital share (P4) -2.09 pp -2.12 pp Investment-to-output (P5) -1.35 pp -0.19 pp Equity premium (P1) 2.22 pp pp 0-2 pp Table 2.8: Quantitative results: changes in markups, productivity growth rates, interest rates. We discuss each puzzle result in turn. ( P1) Our model produces, in line with the data, an increase in the wealth-to-output ratio, with a relatively stable capital-to-output ratio. Our model's increase in the wealth-to-output ratio of 0.88 is quite close to the increase seen in the data, 0.95, while the increase in the capital-to-output ratio is also comparable. ( P2) Our model produces an increase in Tobin's Q, however the increase is somewhat smaller in our model: 0.17 compared to 0.40 in the data. (P3) In line with the puzzle, our results show a moderate increase in the average return, with a declining real interest rate. 42 (P4) The model does a good job of matching the increase in the prot share, as well as the decline in the labor and the capital share; however, the ability of the model to exactly match the magnitude of the prot share decline should not be surprising, since the change in markups was estimated explicitly to match the movement in this moment. ( P5) Our model produces a decline in investment, despite a high Tobin's Q and low real interest rate. The decline in investment is larger than seen in the data. In summary, we have shown that the estimated increase in markups and decrease in the real interest rate can quantitatively account relatively well for the ve facts described in the introduction. In the following two sections, we examine the impact of changes in markups and interest rates separately on our ve puzzles of interest. We will see that both changes are needed in order to match the macroeconomic data. 2.7.3 Quantitative results: Markups Table 2.9 shows the results of increasing the long-run level of markups from our baseline estimated level in 1970, 1.11, to its estimated level in 2015, 1.23. The results are overall quite supportive of our hypothesis, however it is clear that an increase in markups alone cannot fully explain all ve puzzles. ( P1) In line with puzzle 1, there is an increase in the wealth-to-output ratio, 0.50, however it is smaller 42 It is not surprising that the change in interest rates exactly matches the decline: we choose the increase in D to exactly target a decrease in r of 2 % , as further outlined below. 57 than the 0.95 increase in the data. In addition, there is a moderate decrease in the capital-to-output ratio, compared with a moderate increase in the data. ( P2) There is an increase in Tobin's Q of 0.34, quite comparable to the 0.40 in the data. (P3) Due to the increase in prots there is a large increase in the average return  much larger than the increase seen in the data. There is no change in interest rates from the increase in markups: although there is an increase in the supply of assets due to the increase in security values. In a representative agent economy this is exactly counteracted by an increase in demand, and there is no change in interest rates. This result shows that although an increase in markups can explain the divergence between the average return and the interest rate, it cannot by itself generate a roughly constant average return. P4) The increase in markups leads to an increase in the prot share of 8.94, and a corresponding decrease ( in both the labor and the capital share. (P5) Due to the increase in the wedge between the marginal product of capital and the rental rate, there is a decline in investment of 1.36 pp. Moments ∆M odel ∆Data Wealth-to-output ratio ( P1) 0.50 0.95 Capital-to-output ratio (P1) -0.17 0.31 Tobin's Q (P2) 0.34 0.40 Real interest rate (P3) -0.00 pp -2.00 pp Average return (P3) 5.09 0.64 Prot share (P4) 8.94 8.94 Labor share (P4) -7.23 pp -6.82 pp Capital share (P4) -1.70 pp -2.12 pp Investment-to-output (P5) -1.36 pp -0.19 pp Equity premium (P1) 2.34 pp pp 0-2 pp Table 2.9: Quantitative results: changes in markups only. Table 2.9 is strongly supportive of our hypothesis. Quantitatively, it shows that changes in markups alone can go a long way towards explaining several of the ve puzzles that are the subject of this paper. The large increase in the average return predicted by the model is one exception to this; however, as we will see in the next section, a decline in interest rates can serve as a check to this force, driving down the average return. 2.7.4 Quantitative results: Interest rates We now further decompose the results shown in Table 2.8. We consider two channels which lead to a decline in interest rates: (i) a decline in productivity growth and (ii) a reduced form increase in the utility wedge D. We decrease the productivity growth rate (the parameter ζ ), from 2.02 % per year in 1970 to its value 58 of 0.65 % in the present. We increase D such that the combined eect of the changes in µ, ζ , and D lead to a decrease in interest rates over the time period of 2 percentage points, which is in line with the data. The results of increasing D are shown in Table 2.10. With lower interest rates, there is a decrease in the average return ( P3), and an increase in investment (P5). There are also moderate changes in the labor and capital share, wealth-to-output, and capital-to-output. The results of changing productivity growth only are shown in Table 2.11 in the appendix. A decline in productivity growth leads to a decline in the real interest rate of 0.84  not enough to match the full decrease seen in the data. With slower productivity growth, there is also a decline in the average return on capital. Moments ∆M odel ∆Data Wealth-to-output ratio ( P1) 0.24 0.95 Capital-to-output ratio (P1) 0.21 0.31 Tobin's Q (P2) -0.05 0.40 Real interest rate (P3) -1.19 pp -2.00 pp Average return (P3) -1.89 0.64 Prot share (P4) -0.00 8.94 Labor share (P4) 0.24 pp -6.82 pp Capital share (P4) -0.24 pp -2.12 pp Investment-to-output (P5) 1.69 pp -0.19 pp Equity premium (P1) 0.25 pp pp 0-2 pp Table 2.10: Quantitative results: changes in D only. 2.7.5 Other markup estimates Appendix tables 2.13 - 2.16 show our quantitative results for other estimates of markups from the literature  those of Nekarda and Ramey (2013), De Loecker and Eeckhout (2017), Gutierrez (2017) and Hall (2018). The results for the Nekarda and Ramey and Hall estimates are quite similar to our baseline results, since the increase in markups is similar in magnitude. The results for the De Loecker and Eeckhout estimates are much larger in magnitude then our baseline results. This is unsurprising, given that they estimate a massive increase in markups, from 18 % in 1980 to 67 % in the present. Table 2.14 shows the combined results of changing markups and interest rates from their 1970 to their 2015 values. The results show a massive decline of 20.38 in the labor share, an increase in the pure prot share of 24.87, an increase in the average return of 12.89, and an increase in Tobin's Q of 0.99. These numbers are well out of line with the data. A natural question is then, is there anything in our model which could square these numbers with the data? The answer is, tentatively, yes. If the increase in markups was also accompanied by other forces that caused gross prots to decrease, this would tend to decrease the magnitudes shown in Table 2.13. We discuss two potential mitigating factors in Section 2.8. 59 2.7.6 Excess returns of nal goods rms Table 2.9 displays a surprising result: an increase in markups causes an increase in the equity premium of 2.34 %. As discussed in Section 2.4, this is due to a composition eect. The risk premium on pure prots is greater than the risk premium on productive capital. Then as the value of the pure prots increases relative to that of capital, i.e., an increase in Tobin's Q, the combined equity premium on holding prots and capital will increase. There are only negligible changes in the returns on the dierent assets: risk free bonds, intermediate goods, and nal goods rms. We now further discuss the reason why the risk premium on nal goods rms, ERf , is higher than the risk premium on intermediate goods rms, ERi . Excess returns for an asset, following Cochrane (2009), can be written as Et [rt+1 − rtf ] ≈ −covt (mt+1 , rt+1 ). Because ERf > ERi , ERf must (negatively) covary more with m than ERi . Assets must oer a higher equity premium when its return move in a direction opposite to that of the discount factor. The returns of nal goods rms show larger uctuations than the returns on physical capital because the supply of nal goods rms is xed in the short run. A key assumption of our analysis is that there are signicant barriers to entry for nal-goods rms. Thus, in contrast to productive capital, the securities which hold the rights to pure prots are non-reproducible assets. When pure prots increase, there is thus a large increase in the price of these securities. When the productivity of capital increases, rms can simply produce new capital to take advantage of this increased productivity. We should thus expect the price of nal goods rms to be more volatile than intermediate goods rms, and thus yield a greater risk premium. It is well known since Jermann (1998) that capital adjustment costs are necessary in order to generate a realistic equity premium in production economies. In the absence of adjustment costs, agents optimally choose to smooth their consumption (especially with high risk aversion), which decreases the volatility of the stochastic discount factor. Relatedly, without capital adjustment costs, the price of capital q does not uctuate, and thus the only source of uctuations of returns are in the productivity of capital. The higher the adjustment costs, the higher the capital risk premium. The existing literature generally needs high levels of adjustment costs and high risk aversion to match the equity premium. With our addition of traded monopolistic nal goods rms, we can have both lower adjustment costs and lower risk aversion. 2.8 Other explanations for the puzzles While this paper pursues the hypothesis that changes in markups and interest rates are largely responsible for the macroeconomic changes seen over the past forty years, we do not argue that other forces are not at 60 work. We see our hypothesis as complementary to three other explanations: a decrease in the bargaining power of workers, an increase in risk premia, and an increase in intangible investment. 2.8.1 Neoclassical and zero-rent economy In the neoclassical Ramsey/Koopmans/Cass model, there are no monopoly prots, and securities markets measure only the value of a rm's capital stock. In the basic version of this model, the value of wealth is always equal to the value of capital, Tobin's Q always equals one, and the average return moves in line with interest rates. This model is thus at odds with the divergence between wealth and capital in the data, the divergence between the average return and interest rates, and the increase in Tobin's Q to a level permanently above 1. Robert Hall (2001) pursues the hypothesis that a rm's stock market price measures the value of its capital. As Hall notes, if there are no barriers to entry, in the longer run capital earns no rent because it is in perfectly elastic supply to the rm; he calls this the zero-rent economy. In a zero-rent economy, movements in Tobin's Q and wealth to output can only be due to two factors (i) adjustment costs and (ii) unmeasured intangible capital. However, adjustment costs cannot explain a permanently elevated Tobin's Q, as we have seen in the data, unless the speed of adjustment of capital is unrealistically slow. 2.8.2 Unobserved intangible capital Another possible explanation for the ve facts we have observed is a large amount of capital that is unmea- sured in the national accounts. If this capital was valued by investors, it would be reected in the market price of rms, and thus explain a high level of wealth-to-capital and Tobin's Q. In addition, it would increase the measured average return on capital, since the unmeasured capital would generate income but would not be counted in the denominator of the average return equation. For many years businesses spent heavily on certain intangible products, which, although from an economic point of view appear to be capital, were counted in the national income accounts as expenses: computer software, computer databases, scientic and non-scientic R&D, mineral exploration, spending to create artistic originals, and many more (see Corrado, Hulten, and Sichel (2005) and Corrado, Hulten, and Sichel (2009) for details). However, over the past 20 years the BEA has twice revised the national income series to include many types of intangible capital, such as software investment, R&D investment, and spending on artistic originals. All of our gures and statistics in this paper already include these forms of intangible capital. 61 Corrado, Hulten, and Sichel (2005) classify intangible capital into three categories: (i) computerized information, which includes software and databases (ii) innovative property, which includes investment in R&D and artistic originals, and (iii) economic competencies, which include brand equity, advertising, mar- keting, rm specic human capital, and worker training. While much of categories (i) and (ii) are already capitalized in the GDP accounts, category (iii) is largely uncapitalized, and is by far the largest category of intangible capital according to Corrado, Hulten, and Sichel (2005). The BEA is considering adding a num- ber of categories to intangible investment, including computer design services, architectural and engineering services, management consulting services, advertising, and marketing research. A key question, however, is whether all of these activities should be considered as capital investment. In Corrado and Hulten's framework, any outlay that is intended to increase future rather than current consumption is treated as a capital investment.. From a rm's point of view, spending money in period t to increase market share in period t + 1, is indeed investment, and would be classied as such by Corrado, Hulten, and Sichel (2009) . However, from a macroeconomic point of view, this intangible capital does not lead to future production or output, it is simply a shift in output from one rm to another. In fact, there is a very close correspondence between Corrado and Hulten's third category of intangible capital and market power, branding, and product dierentiation: in other words, the "unmeasured" intangible investment may have been an investment in creating the very non-zero-rent economy which is the subject of this paper. We favor a dierent interpretation of Corrado and Hulten's third category (spending on economic compe- tencies), rather than interpreting it as intangible investment. Because spending on these categories does not contribute to the production of goods, we argue it should not be counted as investment spending and accu- mulated into the capital stock. For this reason, we term this spending non-productive intangible investment. While from a rm's point of view there may be little dierence between investing in a marketing campaign and investing in a new factory, from an economic accounting point of view there is a dierence: marketing spending will not lead to an increase in the productive capacity of a rm. This suggests that there must be a distinction between a rm's nancial accounting, where it makes a lot of sense to accumulate this intangible investment in capital, and in national economic accounting, in which we argue it makes less sense. We can include this non-productive intangible (NPI) spending in our model. If we assume this NPI µt −1 spending is done by nal goods rms, aggregate prots would then be given by Πt = µt Yt − N P It . This non-productive spending is one way to make quantitative sense of the the large increases in markups estimated by De Loecker and Eeckhout (2017). If the increase in markups estimated by De Loecker and Eeckhout was also accompanied by an increase in the share of corporate income spent on non-productive 62 Figure 2.6: Prot distribution of nal goods rms. intangibles, there would be a much smaller measured eect of these markups on Tobin's Q, the average return, and the measured labor share. 2.8.3 Labor bargaining power An alternative, and complimentary, hypothesis of what is driving the changes in the ve macro trends is that there has been a decrease in labor bargaining power over the time period. In this story, the ability of rms to outsource production abroad or to contracting rms, the decline of labor unions, and the rise of dominant rms has lead to a reduction in the bargaining power of workers (see, for example, Weil (2014), Elsby, Hobijn, and “ahin (2013), Dube and Kaplan (2010), Stiglitz (2015a) and Abdih and Danninger (2017)). To explore this hypothesis, we add a reduced form version of labor bargaining power. The pure prots of the rm, instead of being all distributed to the shareholders, are now shared with the workers. Figure 2.6 displays how the pure prots of nal goods rms are distributed. Prots ow to two distinct groups, workers and shareholders of the nal good rm. We assume workers have some level of bargaining power, ξt , which is taken as exogenous. This bargaining power may come about through a variety of channels: labor unions, powerful managers and executives who are able to bargain for their pay (Bebchuk and Fried, 2004), or matching frictions in the labor market (Rogerson, Shimer, and Wright, 2005). Due to this bargaining power, workers receive a share ξt of aggregate prots. The rest of the prots go to shareholders of nal goods rms, who own the rights to the remaining 63 pure prots, as dividends. Aggregate dividends distributed to shareholders at time t are thus given by dt = (1 − ξt )Πt . If labor's bargaining power ξt decreases, dividends to shareholders will increase. There will thus be an increase in the value of shares, wealth-to-output, and empirical Tobin's Q. However, unlike in the case of an increase in pure prots, there will not be any changes in capital or investment, since there is no change in the wedge between the marginal product capital and its rental rate. 43 In addition, the share of income which is measured to go to labor would decrease, since this measured amount includes the rents from bargaining power, and the share of income measured to go to prots would increase. 2.8.4 Capital risk premium Another factor that may be driving some of the ve macro-trends is an increase in the capital risk premium. In an analysis that also includes changes in markups, the relative price of capital, and the capital share, Caballero, Farhi, and Gourinchas (2017) nd that an increase in the capital risk premium may be driving some of the trends, such as a stable average return on capital despite a decreasing risk free rate and a decrease in the labor share. This nding is not mutually exclusive with our hypothesis of increasing markups: in many specications of their accounting exercise, Caballero, Farhi, and Gourinchas (2017) nd moderate increases in markups along with an increase in the capital risk premium. We note that one of the results of our quantitative exercises is that there may be a distinction between the risk premium on productive capital and that on pure prots. In our baseline exercise, there is a large increase in the equity premium (analogous to the equity premium measured in the data), while there is not an increase in the capital risk premium. In our reading, the data on the capital risk premium and the equity premium is somewhat mixed. Measures of the return on capital based on corporate bond rates (such as AAA, BAA, and BBB bonds) have decreased over the time along with the risk-free rate. However, there has been an increase in bond-spreads since the nancial crisis. Furthermore, some measures of the equity risk premium have increased. Duarte and Rosa (2015) compile 20 dierent measures of the equity risk premium using a variety of dierent models. The rst-principle component of these measures has increased substantially since 2000. The longer-term trend of the rst principal component, however, is less apparent: since 1980 there does not appear to have been a change in this measure of the ERP, or in other combined measures such as the cross-sectional mean 43 This is a simplication. In many search and matching model, labor bargaining power has a negative eect on investment, depending on the contract structure (see, for example, Grout (1984), Arnsperger and Croix (1990) and Acemoglu and Shimer (1999). In these models, a decrease in the labor bargaining power would lead to an increase in investment  exactly the opposite of the eect of an increase in markups. 64 of the dierent models. One counterfactual implication of an increase in the capital-risk premium is the eect on the wealth-to- output ratios. With an increase in the capital risk premium stock prices should decrease (the prots are discounted at a higher rate), and thus we would predict a decrease in the wealth-to-output ratio instead of the large increase we have seen. Of course, if there are also contemporaneous increases in dividends (perhaps through higher markups), this could oset this tendency. 2.9 Conclusion The analysis of this paper relies heavily on our estimates of the level of pure prots and markups in the US economy. Unfortunately, there is a great deal of uncertainty around these estimates. To estimate pure prots, we need a good measure of both the capital and the risk premium in the economy. To estimate markups directly, we need an estimate of marginal cost, which has always been a dicult proposition. With these caveats in mind, we discuss some implications of our results. There are important welfare implications to an increase in market power. Markups create distortions in product markets, and recent research suggests the welfare costs of markups are high, on the order of 7.5 - 40 % of GDP (see Edmond, Midrigan, and Xu (2018) and Baqaee and Farhi (2017)). These theoretical results are in contrast to the classic estimates of Harberger (1995), who suggested the cost of monopolistic distortions was only 0.1 % of GDP. In addition, an increase in markups can lead to lower investment. Markups are a wedge between the marginal product of labor and the wage, and the marginal product of capital and its rental rate. With higher labor wedges, the wage is lower and thus labor supply is lower, decreasing output. With higher capital wedges there is lower investment and a lower capital to output ratio, which also lowers output. There are also important indirect costs of monopoly power. As emphasized by Tullock (1967) and Krueger (1974), if there is competition for these monopoly prots through rent seeking behavior, in general the welfare loss is larger than in the absence of competition. If the value of pure prots is indeed in the order of 20 % of output, there is an enormous incentive for rms to compete to take, maintain, or extend these prots. In this paper we have emphasized one particular aspect of rent seeking behavior, namely rms' expenditures on product dierentiation, branding, and advertising in order to maintain market share, which the literature has often called intangible investment. Of course there is also the more traditional political rent seeking. The increase in market power also has implications for income inequality. With higher pure prots, workers receive a lower share of output and capitalists a higher share. Since individuals with higher incomes 65 receive a larger percentage of their income as capital income, and the poorest individuals generally do not hold nancial assets, this mechanism will tend to increase income inequality. There is also a potential interaction of inequality with changes in labor bargaining power. Although it is unclear whether the overall level of labor bargaining power has decreased, there is some evidence that with the fall of unionization and the rise of outsourcing the bargaining power of the poorest workers has decreased. Meanwhile, the bargaining power of the highest educated superstars and CEOs may have increased. If CEOs are taking a larger portion of the prots and workers a smaller portion, this would also tend to increase income inequality. An increase in monopoly rents also has implications for wealth inequality. We have seen how an increase in pure prots leads to a boom in stock prices, since equities hold the residual rights to corporate prots. Since those with the highest level of wealth tend to hold a greater fraction in equities, and those with lower wealth tend to hold a greater portion in housing, an increase in monopoly rents would tend to increase wealth inequality. The increase in market power has important implications for corporate tax policy. Standard economic theory tells us that taxing pure prots is generally a good idea (Guo and Lansing, 1999), while taxing capital income may not be a good idea (Judd, 1985). As shown by Guo and Lansing (1999), the optimal tax on corporate prots depends on the relative size of capital income to pure prots. Even in an economy with a moderate prot share (on the order of 8 %), relatively high levels of corporate income taxes are optimal, especially with interest deductibility and accelerated depreciation. Traditionally, it has been thought that the level of pure prots in the economy was small  a common citation is Basu and Fernald (1997)'s estimate of 3%. With a prot share of 15 - 20%, as our analysis suggests, higher level of corporate taxes may be optimal. Our model is also a theory of wealth accumulation in the US, and thus can directly address some of the questions raised in Piketty's Capital in the 21st Century. A major criticism of Piketty's theory of wealth- accumulation is that the return on capital, the r in r − g , is assumed to be constant even as capital increases. With a standard, neoclassical production function, however, as capital increases, the marginal product of capital and the return on capital must decrease. Thus there would seem to be a natural force which would tend to counteract the increase in wealth. The analysis in this paper suggests a possible reconciliation between the view of Piketty and the views of the neoclassicals. With an increase in monopoly prots, there can be an increase in wealth, without a corresponding decrease in the average return on capital. 66 Appendix A: Full equations of model Final goods rms There is a unit mass of monopolistically competitive nal goods rms that dierentiate an intermediate good and resell it to consumers. The nal good composite is the CES aggregate of these dierentiated nal goods, hR Λt −1 i ΛΛ−1 t 1 ytf (i) t which are indexed by i: Yt = 0 Λt di . Final goods rms set prices in each period, and face a demand curve that takes the following form:  −Λt pt (i) ytf (i) = Yt Pt , where Λt is a time-varying measure of a rm's market power. The nominal price R 1  1−Λ 1 1−Λt t index is dened as Pt = 0 pt (i) di . Each nal goods producer uses ytm of intermediate goods to produce output, according to a linear technol- f pt (i) ogy function yt = ytm . A nal goods rm chooses real prices Pt and ytf (i) to maximize real prots, subject −Λt pint  pt (i) f f f pt (i) Pt yt (i) − Pt yt (i) subject to yt (i) = Yt t to the production and demand constraints: max , Pt pint t where Pt is the price of the intermediate good taken as given by the rm. The optimality condition for the real price of the rm's good is a time-varying markup over the price of the intermediate good: pt (i) Λt pint t pint = = µt t (30) Pt Λ t − 1 Pt Pt where µt is the optimal markup of the rm. Since the price of the intermediate good is the same, all nal goods rms make the same pricing decisions, pint 1 and thus pt (i) = Pt , yielding t Pt = µt . Λt We posit that Λt −1 , i.e. markups µt , follow an AR(1) process, given by µ) + ρµ ln(µt−1 ) + µt ln(µt ) = (1 − ρµ )ln(¯ (31) The long run level of markups in the economy is given by µ ¯. Final goods rms make aggregate prots equal to µt − 1 Πt = Yt (32) µt Aggregate dividends distributed to shareholders at time t are given by dft = Πt (33) 67 Long run risk Let At denote the level of productivity, and lowercase letter denote log-units. The growth rate or productivity is given by: ∆at+1 = ζ + xt + σa a,t+1 (34) xt = ρxt−1 + σx x,t (35)         a,t+1  0  1 ρxa    ˜ iid N   ,   x,t+1 0 ρxa 1 Consumer's problem The model mainly follows Caldara et al. (2012) and Croce (2014). An innitely lived individual has Epstein- Zin utility given by θ   1−γ   1  1−γ ν 1−ν 1−γ θ Vt = (1 − β) ct (At−1 (1 − Lt )) θ + βD Et Vt+1 (36) where the time discount factor is β, the labor supply coecient is ν, γ is the risk aversion parameter, 1−γ and θ is dened as θ= 1 , in which 1− ψ ψ is the elasticity of intertemporal substitution. Individuals maximize utility subject a series of budget constraints, ct + Xti St+1 i + Xtf St+1 f = wt Lt + dit Sti + dft Stf + ∆t+1 Xtf + (1 − ∆t )Xtf Stf + Xti Sti (37) On the left hand side of the budget constraint, individuals use their income to purchase either consump- i i f f tion, shares of intermediate good rms (Xt St+1 ), or shares of nal goods rms (Xt St+1 ). On the right hand side of the budget equation, agents receive income from a variety of sources: labor income wt Lt , dividends from intermediate goods rms dit Sti , dividends from nal goods rms dft Stf , IPO issued securities of nal goods rms ∆t+1 Xtf , remaining share value of nal goods rms (1 − ∆t )Xtf Stf , remaining share value of intermediate goods rms, Xti Sti . Due to the nature of the recursive utility, we can write the optimal solution as a recursive function 68   1−γ   θ1 Vt (Sti , Stf ) = maxct ,Lt ,S i f (1 − β) cνt (At−1 (1 − Lt ))1−ν θ + βD Et Vt+1 (St+1 i f , St+1 )1−γ t+1 ,St+1 s.t. ct + Xti St+1 i + Xtf St+1 f = wt Lt + dit Sti + dft Stf + ∆t+1 Xtf + (1 − ∆t )Xtf Stf + Xti Sti From this equation, we can derive the rst order conditions for optimization. Setting up the Lagrangian and dierentiating with respect to ct , we have ∂L 1− 1−γ  1−γ 1 : (1 − β)Vt θ cνt (At−1 (1 − Lt ))1−ν θ ν = λt ∂ct ct Taking rst order conditions with respect to Lt , we have ∂L 1− 1−γ  1−γ 1 : (1 − β)Vt θ cνt (At−1 (1 − Lt ))1−ν θ (1 − ν) = wt λt . ∂Lt (1 − Lt ) Combining the rst order conditions with respect to labor and with respect to consumption, we have (1−ν) ct f ν (1−Lt ) = wt , and taking the rst order condition with respect to St+1 , we have ∂L f : Xtf λt = βEt [λt+1 ((1 − ∆t+1 )Xt+1 f + dft+1 )] (38) ∂St+1 Now, taking the rst order condition with respect to ct+1 , we have ∂L  1 −1   1−γ 1  1− 1−γ 1− 1−γ  1−γ θ −γ : Vt θ βD Et Vt+1 × Et Vt+1 (1 − β)Vt+1 θ cνt+1 (At (1 − Lt+1 ))1−ν θ ν ∂ct+1 ct+1 ∂ where in the last step we make a substitution by forwarding ∂ct one period. Canceling redundant terms, we get  ν(1−γ)  (1−ν)(1−γ) !1− θ1  −1  1−γ ∂Vt /∂ct+1 ct+1 θ At (1 − Lt+1 ) θ Vt+1 mt+1 = = βD 1−γ (39) ∂Vt /∂ct ct At−1 (1 − Lt ) Et Vt+1 Representative intermediate goods rms use labor Lt and capital Kt to produce intermediate goods Ytm according to the production function 69 σ  σ−1 σ−1  σ−1 Ytm = αKt σ + (1 − α)(At Lt ) σ (40) where σ is the production elasticity of substitution. The rm nances part of its investment It through retained earnings REt and issues shares to cover the remaining part, It = Xti (St+1 i − Sti ) + REt . It distributes 1 the excess of its prots over retained earnings to its shareholders as a dividend, dit Sti = µt Yt m − wt Lt − REt . 1 Since Yt = Ytm , we have dit Sti = µt Yt − wt Lt − REt . Investment increases the rm's future stock of capital according to Kt+1 = Φ(It /Kt )Kt + (1 − δ)Kt (41) where δ is the rate of depreciation and adjustment costs Φ(·) are a positive concave function. The  1−ξ a1 It adjustment costs function is given by Φ(It /Kt ) = 1−ξ Kt + a2 . Following Jermann (1998), we will choose the adjustment costs parameters so that the steady state ratio of investment to capital is not aected. In a model with productivity growth, the investment to capital ratio I is given by K = (δ + eζ − 1). From equation (41), in the steady state with productivity growth we have that K(δ + eζ − 1) = Φ(I/K)K , thus we must have in the steady state Φ(I/K) = (δ + eζ − 1). Note that this also ensures that if a rm replaces depreciation and accounts for growth, adjustment costs are zero. In addition, we also need q to be 1 in the steady state, and thus Φ0 (I/K) = 1. These conditions imply the following two conditions: a1 1−ξ δ + eζ − 1 + a2 = (δ + eζ − 1)a1 (δ + eζ − 1)−ξ = 1 1−ξ 1 Thus we have that a1 = (δ + eζ − 1)ξ , and a2 = (1 − (1−ξ) )(δ + eζ − 1). Computation of the intermediate good rm's value Intermediate goods maximize the expected value of cash ow to the shareholders, discounted by the stochastic discount factor of individuals. Dening cash 1 ow, CFti = µt Yt − wt Lt − It , the value of the intermediate good rm is given by ∞ " # s−t λs X Vti = Et β s−t D CFsi (42) s=t λt Firms maximize (42) subject to (41). The rst order conditions are given by: 70 ∂ 1 : 0 = qt ∂It Φ (It /Kt ) where qt is the the Lagrange multiplier of the maximization problem, and          ∂ λt+1 1 0 0 It+1 It+1 It+1 : −qt + Et βD f (Kt+1 )+ qt+1 −Φ +Φ + (1 − δ) . ∂Kt+1 λt µt+1 Kt+1 Kt+1 Kt+1 1  σ−1 σ−1  σ−1 −1 Then, using the fact that Φ0 (It+1 /Kt+1 ) = 1 qt+1 and F 0 (Kt+1 ) = α(Kt+1 ) σ + (1 − α)(At+1 Lt+1 ) σ αKt+1 σ , we have that   1 λt+1 1  σ−1 σ−1  σ−1 −1 qt = Et βD α(Kt+1 ) σ + (1 − α)(At+1 Lt+1 ) σ αKt+1 σ λt µt+1       It+1 It+1 − + qt+1 Φ + (1 − δ) (43) Kt+1 Kt+1 Finally, we have 1 ∂ 1  σ−1 σ−1  σ−1 −1 : α(Kt ) σ + (1 − α)(At Lt ) σ (1 − α)Lt σ = wt (44) ∂Lt µt Asset pricing implications 1 As usual, the return on the risk free rate is given by Rt = Et [mt+1 ] . The return for investing in intermediate i dit+1 St+1 i i +Xt+1 i St+1 dit+1 +Xt+1 i goods rms is given by Rt+1 = Xti St+1 i = Xti . i Now, using the fact that qt Kt+1 = Xt St+1 , we have 1 m i i i µt Yt+1 − wt+1 Lt+1 − REt+1 + Xt+1 St+1 Rt+1 = qt Kt+1 1 i i i i i µt Yt+1 − wt+1 Lt+1 − It+1 + Xt+1 (St+2 − St+1 ) + Xt+1 St+1 = qt Kt+1 1 µt Yt+1 − wt+1 Lt+1 − It+1 + qt+1 Kt+2 = qt Kt+1 i As usual, we have the asset pricing equation 1 = Et [mt+1 Rt+1 ]. The return for investing in nal goods rms is given by 71 µt+1 −1 f f dft+1 St+1 f f + (1 − ∆t+1 )St+1 f Xt+1 µt+1 Yt+1 + (1 − ∆t+1 )Xt+1 Rt+1 = f = St+1 Xtf Xtf Equilibrium An equilibrium is a set of quantities: {ct , Kt , Lt , It , Yt , Ytm , dit , dft }∞ t=0 , a set of prices {wt , Xti , Xtf , qt , mt }∞ t=0 , and a set of exogenous processes {µt , At , xt , ∆t }∞ t=0 that jointly satisfy: 1. Consumption maximizes (36) subject to (37) 2. The stochastic discount factor is given by (39) 3. Intermediate rms maximize (42) subject to (41) 4. Intermediate good production is given by (40), and nal good production is given by Yt = Ytm 5. Aggregate prots of nal goods rms are given by (32), and aggregate dividends are given by (33) 6. The price of securities satises (38) 7. The wage is given by (44) 8. The stochastic processes for µt , At , and xt are given by (31), (34), and (35) 9. The paths for ∆t is exogenously specied While this model is not stationary, we can make it so by applying a standard transformation: divide all quantities (except labor) by At−1 , as well as wages and the price of securities Xti and Xtf . Full Equations of Model Now, collecting the equations of the model, we have 72   θ ν 1−ν  1−γ  1 1−γ 1−γ θ Vt = (1 − β) ct (At−1 (1 − Lt )) θ + βD Et (Vt+1 )  ν(1−γ)  (1−ν)(1−γ) !1− θ1  −1  1−γ ct+1 θ At (1 − Lt+1 ) θ Vt+1 mt+1 = βD 1−γ ct At−1 (1 − Lt ) Et Vt+1 (1 − ν) ct wt = ν (1 − Lt ) 1 qt = 0 Φ (It /Kt )   1       1  σ−1 σ−1  σ−1 −1 It+1 It+1 qt = Et mt+1 α(Kt+1 ) σ + (1 − α)(At+1 Lt+1 ) σ αKt+1 σ − + qt+1 Φ + (1 − δ) µt+1 Kt+1 Kt+1 1 1  σ−1 σ−1  σ−1 σ−1 −1 wt = α(Kt ) σ + (1 − α)(At Lt ) σ (1 − α)At σ Lt σ µt σ  σ−1 σ−1  σ−1 Ytm = αKt σ + (1 − α)(At Lt ) σ Yt = Ytm Yt = ct + It Kt+1 = Φ(It /Kt )Kt + (1 − δ)Kt ∆at+1 = ζ + xt + σa a,t+1 xt = ρxt−1 + σx x,t µ) + ρµ ln(µt−1 ) + µt ln(µt ) = (1 − ρµ )ln(¯ 1 Rt = Et [mt+1 ] 1 i µt Yt+1 − wt+1 Lt+1 − It+1 + qt+1 Kt+2 Rt+1 = qt Kt+1 µt − 1 dft = Yt µt Xtf = Et [mt+1 ((1 − ∆t+1 )Xt+1 f + dft+1 )] µt+1 −1 f f µt+1 Yt+1 + (1 − ∆t+1 )Xt+1 Rt+1 = Xtf The variables are V, Y, Y m , c, L, m, w, q, K, I, a, x, µ, R, Ri , Rf , dft , X f . Thus there are 18 equations and 18 variables. 73 Making the model stationary We now make a standard transformation by dividing the following variables by At−1 : V, Y, Y m , c, w, K, I, X f , X i , df , di . We then have the following set of equations:   θ ν 1−ν  1−γ ( 1−γ )∆at  1 1−γ 1−γ θ Vt = (1 − β) ct ((1 − Lt )) θ +e θ βD Et (Vt+1 ) (45)  ν(1−γ)  (1−ν)(1−γ) !1− θ1  −1  1−γ ct+1 θ (1 − Lt+1 ) θ Vt+1 (1−γ) mt+1 = βD 1−γ e( θ )∆at −1 (46) ct (1 − Lt ) Et Vt+1 (1 − ν) ct wt = (47) ν (1 − Lt ) 1 qt = 0 (48) Φ (It /Kt )   1 1  σ−1 σ−1 σ−1  σ−1 −1 qt = Et mt+1 α(Kt+1 ) σ + (1 − α)e σ ∆at+1 (Lt+1 ) σ αKt+1 σ (49) µt+1       It+1 It+1 − + qt+1 Φ + (1 − δ) Kt+1 Kt+1 1 1  σ−1 σ−1 σ−1  σ−1 σ−1 −1 wt = α(Kt ) σ + (1 − α)e σ ∆at (Lt ) σ (1 − α)e σ ∆at Lt σ (50) µt σ  σ−1 σ−1 σ−1  σ−1 Ytm = αKt σ + (1 − α)e σ ∆at (Lt ) σ (51) Yt = Ytm (52) Yt = ct + It (53) Kt+1 e∆at = Φ(It /Kt )Kt + (1 − δ)Kt (54) ∆at+1 = ζ + xt + σa a,t+1 (55) xt = ρxt−1 + σx x,t (56) µ) + ρµ ln(µt−1 ) + µt ln(µt ) = (1 − ρµ )ln(¯ (57) 1 Rt = (58) Et [mt+1 ] 1 ∆at+1 i µt Yt+1 − wt+1 Lt+1 − It+1 + qt+1 Kt+2 e Rt+1 = (59) qt Kt+1 µt − 1 dft = Yt (60) µt Xtf = Et [mt+1 ((1 − ∆t+1 )Xt+1 f e∆at + dft+1 e∆at )] (61) f dft+1 e∆at + (1 − ∆t+1 )Xt+1 f e∆at Rt+1 = (62) Xtf 74 Steady State In the steady state, all transformed variables are constant. We begin by nding steady state investment. From equation (54), and using the assumed properties of I the Φ(·) function, in particular that in the steady state Φ(·) = δ + eζ + 1 we have that K = δ + eζ − 1. Next, using the fact that (1−γ) ¯ = βDe( m θ −1)ζ (63) from equation (49) we have that  1   ¯  σ−1 ! σ−1  ¯  −1 1 K σ σ−1 K σ 1=m ¯ α ¯ + (1 − α)e σ ζ α ¯ + 1 − δ µ ¯ L L Rearranging, we have σ  ¯ " σ−1 # σ−1 K (1 − α)e σ ζ ¯ =  L 1 −1+δ α  µ σ−1 −α (64) m ¯ Continuing, from (51) and (53) we have that c¯ Y¯ K¯ ¯ = ¯ − (eζ + δ − 1) ¯ (65) L L L where σ  ¯  σ−1 ! σ−1 Y¯ K σ σ−1 ζ ¯ = α ¯ + (1 − α)e σ (66) L L Now, combining the denition for the wage with the rst order condition for labor, and rearranging, we   (1−ν) have 1 µ ¯ M ¯P L = ν c¯ (1−L)¯ where 1  ¯  σ−1 ! σ−1 σ−1 K σ σ−1 M ¯P L = (1 − α)e σ ζ α ¯ + (1 − α)e σ ζ L Rearranging, we have c¯ ¯ ν (1 − L)   1 ¯ = ¯ M ¯P L (67) L 1−ν L µ ¯ Now combining (65) and (67), we have 75 Y¯ K¯ ¯ 1 ν (1 − L) ζ ¯ − (e + δ − 1) L ¯ = 1−ν ¯ M ¯P L L L µ ¯ Solving for ¯, L we have   ν 1−ν 1 µ ¯ M ¯P L ¯= L   Y¯ ¯ L¯ − (eζ + δ − 1) K ¯ + L ν 1−ν 1 µ ¯ M ¯P L Turning now to the value function, we have  θ  1−γ  1−γ ¯ 1−ν (1 − β) c¯ν ((1 − L)) θ V¯ =  1−γ  1 − e( θ ) ζ β Appendix B: Proofs Comparative statics of markups ¯ Proposition 3. ∂K ¯ L ∂µ ¯ < 0. If steady-state markups µ ¯ ¯ K increase, the steady state capital-to-labor ratio ¯ will L decrease. Proof. Equation (64) gives the steady state level of the capital-to-labor ratio. Dierentiating with respect to µ ¯, we have ¯ "  µ¯ σ−1 # 2σ−1 σ−1 ∂K 1 1−σ −1+δ −α   ¯ σ 1 1 1 L = m ¯ α σ−1 (σ − 1) −1+δ ¯σ−2 µ σ−1 ∂µ ¯ (1 − α)e σ ζ 1−σ m ¯ α (1 − α)e σ ζ σ This term is negative, since either (σ − 1) or 1−σ is negative, but not both. Note that both bracketed terms are positive: the rst, because the capital-to-labor ratio is positive; the second, because the steady state real interest rate cannot be negative. ¯ Corollary 4. ∂K ¯ Y ∂µ ¯ < 0. If steady-state markups µ ¯ ¯ K increase, the capital-to-output ratio ¯ will decrease. Y K¯ ¯ K L¯ Proof. We have Y¯ = ¯ L · Y¯ . We can write the elasticity of the capital-to-output ratio with respect to ¯ K ¯ ¯ ¯ ¯ ¯ ∂¯ µ ¯ ∂K ¯ µ ¯ L ∂Y ¯ µ ¯ L ∂Y ¯ L ∂Y K ¯ ∂ L ¯ markups as  K¯ ,¯µ ≡ Y ∂µ¯ · ¯ K = L ∂µ ¯ · ¯ K + ∂µ ¯ · ¯ L . From equation (66), we see that ∂µ ¯ = ¯ ∂µ ∂K ¯ . We thus ¯ Y ¯ ¯ ¯ ¯ Y L Y L have ¯ ¯ K¯ " # ∂ K¯ µ¯ ∂ YL¯ ¯  K¯ ,¯µ = L · K¯ 1+ L ¯ L¯ (68) ¯ Y ∂µ ¯ ¯ L ∂K ¯ Y¯ L 76 From equation (66), we have that   σ−1 ¯ ¯ ¯ Kσ ∂ YL¯ K ¯ −α ¯ L L ¯ ¯ =    σ−1 ∂K L  ¯ σ σ−1 L¯ Y¯ α K ¯ L + (1 − α)e σ ζ which is negative and less than 1 in absolute value, thus the term in square brackets in equation (68) is ¯ ∂K ¯ positive. Since we have already shown L ∂µ ¯ < 0,  K¯ ,¯µ < 0. ¯ Y ¯ Corollary 5. ∂ YI¯ ∂µ ¯ < 0. If steady-state markups µ ¯ I¯ increase, the steady state investment-to-output ratio ¯ Y will decrease. Proof. This follows from equation (28). Since investment-to-output is proportional to the capital-to-output ratio, if this ratio declines, the investment ratio will as well. Proposition 6. ∂P S ∂µ ¯ > 0. ∂LS ∂µ ¯ < 0, if σ ≤ 1. ∂KS ∂µ ¯ < 0, if σ ≥ 1. An increase in steady state markups will increase the steady state prot share. If σ ≤ 1, an increase in steady state markups will decrease the steady state labor share. if σ ≥ 1, an increase in markups will decrease the capital share. ¯ −1 µ Proof. Since the prot share is given by PS = ¯ , an increase in markups will increase the prot share. µ Thus the combined labor and capital share will decrease. From the rst order conditions of the rm, the h i −1 rk α ¯ K σ ¯ K ratio of the rental rate of capital to the wage is given by w = 1−α ¯ L . Multiplying both sides by ¯, L the left hand side is the ratio of the capital share to the labor share, and thus we have  ¯  σ−1 KS α K σ = ¯ (69) LS 1−α L ¯ K Thus if σ < 1, a decrease in ¯ will lead to a decrease in the labor share relative to the capital share. L When markups increase, there is a decrease in the combined labor and capital share. In addition, since ¯ K there is a decrease in ¯ , labor takes a smaller portion of this decreased overall share. Thus the labor share L unambiguously declines. Similarly, when σ > 1, the capital share unambiguously declines with an increase in markups. If σ = 1, production is Cobb-Douglas, and the relative factor shares of capital and labor are unchanged by the capital-to-output ratio. In this case, both the capital and labor share unambiguously decline with an increase in markups. Proposition 7. ∂Q ∂µ ¯ > 0. If markups increase, Tobin's Q will increase. 77 Xf Xf Y Proof. We can write steady state Q as Q = 1+ K = 1+ Y K . From equation (24), if markups increase Xf Y there will be an increase in Y , and since there will also be an increase in K , there will be an increase in Tobin's Q. Proposition 8. ∂AR ∂µ ¯ > 0. If markups increase, the average return will increase. Proof. This follows from equation (26). When markups increase, the prot share increases and the capital- to-output ratio will decrease, thus the average return will increase. Comparative statics of D Proposition 9. ∂AR ∂D < 0. An increase in D will lead to a decrease in the average return. Proof. From equation (63), an increase in D will increase m ¯, which will lower the steady state interest rate 1 r¯, since r¯ = ¯ . From equation (64), a decrease in m r will also increase the capital-to-output ratio. Then from equation (26), this will lower the average return. Proposition 10. ∂K Y ∂D > 0, ∂K L ∂D > 0. An increase in D will lead to an increase in the capital-to-output ratio and the capital-to-labor ratio. Proof. An increase in D will decrease r. From equation (64) and the further derivations, a decrease in r will increase the capital-to-labor ratio and the capital-to-output ratio. Corollary 11. ∂ YI ∂D > 0. An increase in D will lead to an increase in the investment-to-output ratio. Proof. This follows from equation (28). Since investment-to-output is proportional to the capital-to-output ratio, if this ratio increases, the investment ratio will as well. Proposition 12. ∂LS ∂D >0 if σ < 1. An increase in D will lead to an increase in the labor share if σ < 1. ∂LS ∂KS If σ > 1, ∂D < 0. ∂D <0 if σ < 1. An increase in D will lead to a decrease in the capital share if σ < 1. ∂KS If σ > 1, ∂D > 0. ¯ K Proof. This follows directly from equation (69). If σ < 1, an increase in ¯ will lead to a increase in the L labor share relative to the capital share. When D increases, there is an increase in the capital-to-labor ratio, and the labor share relative to the capital share increases. Since there is no change in the combined labor and capital share, the labor share unambiguously increases, and the capital share declines. Similarly, when σ > 1, the capital share unambiguously increases with an increase in D, and the labor share decreases. If 78 σ = 1, production is Cobb-Douglas, and the relative factor shares of capital and labor are unchanged by the capital-to-output ratio. In this case, both the capital and labor share do not respond to a change in D. Proposition 13. ∂W Y ∂D > 0. An increase in D will lead to an increase in wealth-to-output. Proof. From equation (24), a decrease in interest rates will lead to an increase in the ratio of the security value to output. This result, combined with an increase in the capital-to-output ratio, leads to an increase in the wealth-to-output ratio. Appendix C: Additional tables Moments ∆M odel ∆Data Wealth-to-output ratio ( P1) 0.13 0.95 Capital-to-output ratio (P1) 0.17 0.31 Tobin's Q (P2) -0.04 0.40 Real interest rate (P3) -0.84 pp -2.00 pp Average return (P3) -1.17 0.64 Prot share (P4) -0.00 8.94 Labor share (P4) 0.17 pp -6.82 pp Capital share (P4) -0.17 pp -2.12 pp Investment-to-output (P5) -1.65 pp -0.19 pp Equity premium (P1) 0.39 pp pp 0-2 pp Table 2.11: Quantitative results: changes in productivity growth only. Moments ∆M odel ∆Data Wealth-to-output ratio ( P1) 0.41 0.95 Capital-to-output ratio (P1) 0.42 0.31 Tobin's Q (P2) -0.08 0.40 Real interest rate (P3) -2.00 pp -2.00 pp Average return (P3) -3.04 0.64 Prot share (P4) -0.00 8.94 Labor share (P4) 0.42 pp -6.82 pp Capital share (P4) -0.42 pp -2.12 pp Investment-to-output (P5) 0.00 pp -0.19 pp Equity premium (P1) -0.22 pp pp 0-2 pp Table 2.12: Quantitative results: changes in D and productivity growth. 79 Moments ∆M odel ∆Data Wealth-to-output ratio ( P1) 0.90 0.95 Capital-to-output ratio (P1) 0.22 0.31 Tobin's Q (P2) 0.05 0.40 Real interest rate (P3) -2.00 pp -2.00 pp Average return (P3) 1.32 0.64 Prot share (P4) 9.77 8.94 Labor share (P4) -7.06 pp -6.82 pp Capital share (P4) -2.71 pp -2.12 pp Investment-to-output (P5) -1.78 pp -0.19 pp Equity premium (P1) 3.93 pp pp 0-2 pp Table 2.13: Ramey quantitative results: changes in markups, productivity growth rates, interest rates. Moments ∆M odel ∆Data Wealth-to-output ratio ( P1) 1.62 0.95 Capital-to-output ratio (P1) -0.17 0.31 Tobin's Q (P2) 0.99 0.40 Real interest rate (P3) -2.00 pp -2.00 pp Average return (P3) 12.89 0.64 Prot share (P4) 24.87 8.94 Labor share (P4) -20.38 pp -6.82 pp Capital share (P4) -4.49 pp -2.12 pp Investment-to-output (P5) -3.41 pp -0.19 pp Equity premium (P1) 2.95 pp pp 0-2 pp Table 2.14: De Loecker quantitative results: changes in markups, productivity growth rates, interest rates. Moments ∆M odel ∆Data Wealth-to-output ratio ( P1) 0.62 0.95 Capital-to-output ratio (P1) 0.31 0.31 Tobin's Q (P2) 0.02 0.40 Real interest rate (P3) -2.00 pp -2.00 pp Average return (P3) -1.54 0.64 Prot share (P4) 4.31 8.94 Labor share (P4) -3.29 pp -6.82 pp Capital share (P4) -1.02 pp -2.12 pp Investment-to-output (P5) -0.46 pp -0.19 pp Equity premium (P1) 0.75 pp pp 0-2 pp Table 2.15: Gutierrez quantitative results: changes in markups, productivity growth rates, interest rates. 80 Moments ∆M odel ∆Data Wealth-to-output ratio ( P1) 0.96 0.95 Capital-to-output ratio (P1) 0.17 0.31 Tobin's Q (P2) 0.23 0.40 Real interest rate (P3) -2.00 pp -2.00 pp Average return (P3) 1.78 0.64 Prot share (P4) 10.55 8.94 Labor share (P4) -8.21 pp -6.82 pp Capital share (P4) -2.33 pp -2.12 pp Investment-to-output (P5) -1.55 pp -0.19 pp Equity premium (P1) 2.36 pp pp 0-2 pp Table 2.16: Hall quantitative results: changes in markups, productivity growth rates, interest rates. Appendix D: Additional gures Estimated Markups 1.4 1.2 1 .8 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015 BAA BAA w/Price Gain No RP No RP w/Price Gain Figure 2.7: Markups, 1960-2015. 81 Chapter 3 3 Negative Nominal Interest Rates and the Bank Lending Channel 3.1 Introduction Between 2012 and 2016, a handful of central banks reduced their policy rates below zero for the rst time in history. While real interest rates have been negative on several occasions, nominal rates have not. The recent experience implies that negative policy rates have become part of the central banker's toolbox, and calls into question the relevance of the zero lower bound (ZLB). However, the impact of negative policy rates on the macroeconomy remains unknown. The goal of this paper is to contribute to lling this gap, by analyzing the eectiveness of negative policy rates in stimulating the economy through the bank lending channel. Understanding how negative nominal interest rates aect the economy is important in preparing for the next economic downturn. Interest rates have been declining steadily since the early 1980s, resulting in worries about secular stagnation (see e.g. Summers 2014, Eggertsson and Mehrotra 2014 and Caballero and Farhi 2017). In a recent paper, Kiley and Roberts (2017) estimate that the ZLB will bind 30-40 percent of the time going forward. In Figure 3.1 we report interest rate cuts during previous recessions in the US and the Euro Area since 1970. On average, nominal interest rates are reduced by 5.9 and 5.5 percentage points respectively (see Table 3.4 in Appendix A for more details). With record low interest rates, policy rate cuts of this magnitude may be dicult to achieve in the future - without rates going negative. 20 20 - 9.0 15 15 - 5.1 - 8.6 - 7.0 - 6.5 - 5.1 - 5.6 10 10 - 5.5 - 3.9 - 5.1 5 5 - 1.4 0 0 1970q1 1979q1 1988q1 1997q1 2006q1 2015q1 1970q1 1979q1 1988q1 1997q1 2006q1 2015q1 US Federal Funds Rate German Interbank Rate Euro Area Discount Rate Figure 3.1: Interest rates for the US and the Euro Area. Source: St. Louis FRED. An alternative to negative interest rates is unconventional monetary policy measures, such as credit easing, quantitative easing and forward guidance. There are several reasons, however, why it is important 82 to consider policy measures beyond these tools. Some of the credit policies used by the Federal Reserve, the FDIC and the Treasury were severely constrained by Congress following the crisis, as stressed by Bernanke, Geithner, and Paulson (2018). Hence, these options are no longer available without legislative change. Moreover, there remains little, if any, consensus among economists on how eective quantitative easing and forward guidance is. Plausible estimates range from considerable eects to none (see e.g. Greenlaw, Hamilton, Harris, and West (2018) for a somewhat skeptical review, Swanson (2017) for a more upbeat assessment, and Greenwood, Hanson, Rudolph, and Summers (2014) for a discussion of debt management at the zero lower bound). Accordingly, understanding the eectiveness of negative interest rates should be high on the research agenda. Central banks which implemented negative rates argued that there is nothing special about zero. When announcing a negative policy rate, the Swedish Riksbank wrote in their monetary policy report that "Cutting the repo rate below zero, at least if the cuts are in total not very large, is expected to have similar eects to repo-rate cuts when the repo rate is positive, as all channels in the transmission mechanism can be expected to be active (The Riksbank, 2015). Similarly, the Swiss National Bank declared that the laws of economics do not change signicantly when interest rates turn negative  (Jordan, 2016). Many were skeptical however. For instance, Mark Carney of the Bank of England was  ... not a fan of negative interest rates and argued that we see the negative consequences of them through the nancial system  (Carney, 2016). One such consequence is a reduction in bank protability, which has caused concern in the Euro Area (Financial Times, 2016). Consistent with this view, Waller (2016) coined the policy a  tax in sheep's clothing , arguing that negative interest rates act as any other tax on the banking system and thus reduces credit growth. In this paper we investigate the impact of negative rates on the macroeconomy, both from an empirical and theoretical perspective. 44 The rst main contribution of the paper is to use a combination of aggregate and bank level data to examine the pass-through of negative rates via the banking system. We focus primarily on Sweden, which is an interesting starting point for multiple reasons. First and most importantly, we have unique daily bank level data for Swedish banks, which allows us to make inference about the pass-through. Second, the Swedish Riksbank reduced the policy rate multiple times in negative territory, providing more variation to work with than in the other countries. Third, there are important features of the Swedish economy which suggests that negative rates should work relatively well in Sweden. Not only do Swedish households have limited cash use, but banks also have low deposit shares relative to banks in the Euro Area 44 Note that we do not attempt to evaluate the impact of other monetary policy measures which occurred simultaneously with negative interest rates. That is, we focus exclusively on the eect of negative interest rates, and do not attempt to address the eectiveness of asset purchase programs or programs intended to provide banks with cheap nancing (such as the TLTRO program initiated by the ECB). 83 (both considerations will turn out to be important in understanding the transmission of negative policy rates). Hence, if negative policy rates were not transmitted to lower bank rates in the Swedish banking system it is unlikely that this will happen in other countries. We document that negative policy rates have had limited pass-through to deposit rates, which are bounded close to zero. This implies that policy rate cuts to negative levels are not transmitted to the main funding source of banks. What about bank lending rates? Using daily bank level data, we document that once the deposit rate becomes bounded by zero, interest rate cuts into negative territory do not lower lending rates. We document that this holds across a range of dierent loan contracts. In addition to a signicant reduction in pass-through to lending rates, there is also a substantial increase in dispersion. We show that the rise in dispersion can be linked to banks nancing structures. Banks that rely more heavily on deposit nancing are less likely to reduce their lending rates once the policy rate goes negative. Focusing on bank level lending volumes, we show that Swedish banks which rely more heavily on deposit nancing also have lower credit growth in the post-zero period. This is consistent with similar ndings for the Euro Area (Heider, Saidi, and Schepens, 2016). Motivated by these empirical results, the second main contribution of the paper is methodological. We construct a model, building on several papers from the existing literature, that allows us to address how changes in the policy rate lters through the banking system to various other interest rates, and ultimately determines aggregate output. The framework has four main elements. First, we introduce paper currency, along with money storage costs, to capture the role of money as a store of value and illustrate how this generates a bound on bank deposit rates. Second, we incorporate a banking sector and nominal frictions along the lines of Benigno, Eggertsson, and Romei (2014), which delivers well dened deposit and lending rates. Third, we incorporate demand for central bank reserves as in Curdia and Woodford (2011) in order to obtain a policy rate which can potentially dier from the commercial bank deposit rate. Fourth, we allow for the possibility that the cost of bank intermediation depends on banks' net worth as in Gertler and Kiyotaki (2010). The central bank determines the interest rate on reserves and can set a negative policy rate as banks are willing to pay for the transaction services provided by reserves. Since money is a store of value however, the deposit rate faced by commercial bank depositors is bounded at some level (possibly negative), in line with our empirical ndings. The bound arises because the bank's customers will choose to store their wealth in terms of paper currency if charged too much by the bank. 45 Away from the lower bound on the 45 There are other reasons why there might be a lower bound on the deposit rate, which we do not explore in this paper. Rather, we choose to introduce a lower bound as a consequence of the combination of money as a store of value and storage 84 deposit rate, the central bank can stimulate the economy by lowering the policy rate. This reduces both the deposit rate and the rate at which households can borrow, thereby increasing demand. Once the deposit rate reaches its eective lower bound however, reducing the policy rate further is no longer expansionary. As the central bank loses its ability to inuence the deposit rate, it cannot stimulate the demand of savers via the traditional intertemporal substitution channel. Furthermore, as banks' funding costs (via deposits) are no longer responsive to the policy rate, the bank lending channel of monetary policy breaks down. We do not analyze other parts of the monetary policy transmission mechanism, and thus cannot exclude the possibility that negative interest rates have an eect through other channels. Examples include any expansionary eects working through the exchange rate or asset prices. The main take-away of the paper is that the bank lending channel - traditionally considered one of the most important transmission mechanisms of monetary policy - collapses once the deposit rate becomes bounded, thus substantially reducing the overall eectiveness of monetary policy. 46 Literature review Jackson (2015) and Bech and Malkhozov (2016) document the limited pass-through of negative policy rates to aggregate deposit rates, but do not evaluate the eects on the macroeconomy. Heider, Saidi, and Schepens (2016) and Basten and Mariathasan (2018) document that negative policy rates have not lead to negative deposit rates in the Euro Area and Switzerland, respectively. While Basten and Mariathasan (2018) nd that Swiss banks primarily reduce reserves in response to negative rates, Heider, Saidi, and Schepens (2016) nd that banks with higher deposit shares have lower lending growth in the post-zero environment. We contribute to the empirical literature on the pass-through of negative rates by exploiting a unique data set on daily bank level lending rates to provide novel micro evidence on the decoupling of lending rates from the policy rate. Furthermore, we show how the lack of pass-through to lending rates can be explained by cross-sectional variation in the reliance on deposit nancing. Given the radical nature of the policy experiment pursued by several central banks, the theoretical literature is perhaps surprisingly silent on the expected eects of this policy. 4748 The study which is perhaps most related to our theoretical analysis is Brunnermeier and Koby (2017), who contemplate a reversal rate in which further interest rate cuts become contractionary. The mechanism in their paper is dierent from costs, motivated by both the existing literature and survey evidence suggesting that households would withdraw cash had they faced a negative interest rate, see Figure 3.21 in Appendix A. 46 See e.g. Drechsler, Savov, and Schnabl (2017) for evidence on the importance of deposit collection for bank funding in the US. 47 There is however a large literature on the eects of the zero lower bound. See for example Krugman (1998) and Eggertsson and Woodford (2006) for two early contributions. 48 Our paper is also related to an empirical literature on the connection between interest rate levels and bank prots (Borio and Gambacorta 2017, Kerbl and Sigmund 2017), as well as a theoretical literature linking credit supply to banks net worth (Holmstrom and Tirole 1997, Gertler and Kiyotaki 2010). 85 ours, however, and not motivated by the zero lower bound that is generated by the existence of cash giving rise to a bound on deposit rates. The reversal rate they analyze depends on maturity mismatch on the bank's balance sheet and net interest margin on new business, making the reversal rate time varying and dependent on market structure and balance sheet characteristics, as well as whether interest rate changes are anticipated or not. The lower bound on the deposit rate, which is the key mechanism in our analysis, does not feature into their model. 49 Moreover, the deposit bound is independent of the features considered in Brunnermeier and Koby (2017) (such as maturity mismatch, market structure etc.). The deposit bound has strong empirical support, and we derive it theoretically from the households' portfolio allocation problem. In our model, as soon as the deposit rate reaches the lower bound, further interest rate cuts are no longer expansionary  in line with the data. Rognlie (2015) also analyses the impact of negative policy rates theoretically. However, in his model households face only one interest rate, and the central bank can control this interest rate directly. Thus, the model does not allow for a separate bound on deposit rates which is critical for our analysis. There exists an older literature, dating at least back to the work of Silvio Gesell more than a hundred years ago, which contemplates more radical monetary policy regime changes than we do here (Gesell, 1916). In our model, the storage cost of money, and hence the lower bound, is treated as xed. However, policy reforms could change this cost and thus change the lower bound directly. An example of such policies is a direct tax on paper currency, as proposed rst by Gesell and discussed in detail by Goodfriend (2000) and Buiter and Panigirtzoglou (2003) or actions that increase the storage cost of money, such as eliminating high denomination bills. Another possibility is abolishing paper currency altogether. These policies are discussed in, among others, Agarwal and Kimball (2015), Rogo (2017a) and Rogo (2017b), who also suggest more elaborate policy regimes to circumvent the ZLB. The results presented here do not contradict these ideas. Rather, they suggest that given the current institutional framework, negative interest rates are not an eective way to stimulate aggregate demand via the bank lending channel. 3.2 Negative interest rates in practice In this section, we investigate the pass-through of negative interest rates to deposit and lending rates. We focus on Sweden, for which we have daily bank level data on lending rates. 49 In an updated version of the paper, they acknowledge that if there is a lower bound on the deposit rate this can be an additional factor that can inuences the reversal rate. In their calibrated model, however, they nd a reversal rate of -1 %. This reversal rate implies that the negative rates which have been implemented so far (the lowest being -0.75% in Switzerland), should be expansionary, which is at odds with our empirical ndings for Sweden. 86 3.2.1 Bank nancing costs Most accounts of expansionary monetary policy focus on how a cut in policy rates will lower lending rates, and thus stimulate aggregate demand. The usual transmission mechanism works through a reduction in deposit rates, which lowers the nancing cost of banks. We start by exploring the rst stage of this transmission process. In Sweden, the policy rate essentially refers to the interest rate banks receive for holding transaction balances at the Riksbank. 50 The policy rate does not apply to anything on the banks liability side, but rather is the return on an asset. The policy rate then gets transmitted via arbitrage to the interbank rate, and through the interbank rate to other bank funding sources. Figure 3.2 shows the decomposition of liabilities for Swedish banks as of September 2015. 51 The most important funding source is deposits, accounting for about half of bank liabilities. We start by considering deposit nancing, before moving on to other nancing sources. 6% 10% 13% 47% 24% Deposits Covered bonds Certificates Unsecured bonds Net interbank Figure 3.2: Decomposition of liabilities (as of September 2015) for large Swedish banks. Source: The Riksbank. Bank deposits Figure 3.3 depicts aggregate deposit rates in Sweden. 52 Prior to the policy rate becoming negative, the aggregate deposit rate is below the policy rate and moves closely with the policy rate. As the policy rate turns negative this relationship breaks down. Instead of following the policy rate into negative territory, the deposit rate appears bounded at some level close to zero. In the right panel of Figure 3.3, 50 The exact implementation of negative rates dier across the countries which have implemented them, see Bech and Malkho- zov (2016) for an overview. In the case of Sweden, the Riksbank operates a corridor system. The policy rate refers to the repo rate. Banks can borrow from the Riksbank at 75 basis points above the policy rate and central bank reserves earn an interest rate 75 basis points below the policy rate. Consider for example a policy rate of - 0.5 %. In order to implement this rate, the Riksbank sells certicates in repo transactions that pay - 0.5 %. As the banks are obtaining -1.25 % on their reserves, they will use the reserves to purchase these certicates. In this sense the repo rate is essentially equivalent to the Riksbank directly paying - 0.5 % on bank reserves. 51 Note that net interbank lending need not equal zero as not only traditional banks have access to the interbank market. 52 The aggregate deposit rate is a weighted average of the interest rate on dierent deposit accounts. It thus includes both highly liquid checking accounts, as well as less liquid xed deposit accounts with minimum deposit amounts. 87 we depict a counterfactual deposit rate, constructed by assuming that the markdown from the repo rate is constant and equal to the pre-zero average. As seen from the graph, this counterfactual deposit rate is roughly a percentage point lower than the actual deposit rate. 6 1 .5 4 0 2 -.5 0 -1 2008 2010 2012 2014 2016 2018 2013 2014 2016 2017 Households Corporations Households Corporations Policy Rate Policy Rate Figure 3.3: Aggregate deposit rates in Sweden. The policy rate is dened as the repo rate. Right panel: The red and blue dashed lines capture counterfactual lending rates calculated under the assumption that the markup to the repo rate was constant and equal to the average markup in the period 2008m1-2015m1. Source: The Riksbank, Statistics Sweden. In Section 3.2.2 we move to daily data and the sample then covers the nal six interest rate cuts made between 2014 and 2016. For future reference it is useful to study the aggregate deposit rates for these nal six cuts. This is done in Figure 3.4, where we calculate the change in the deposit rate relative to the change in the repo rate. The rst bar captures the average relative change in deposit rates prior to 2014. In this case, the aggregate deposit rate changed by on average 60 percent as much as the repo rate. For the post-2014 data, the relative change in the deposit rate is somewhat lower. For the policy rate cuts in positive territory, the deposit rate falls by approximately 40 percent as much as the repo rate. For the rst two cuts in negative territory, i.e. to -0.1 percent and to -0.25 percent, the pass-through remains relatively unchanged. For the nal two interest rate cuts however, the pass-through collapses to roughly zero. As the deposit rate has reached its lower bound, reducing the policy rate deeper into negative territory does not lead to further reductions in the deposit rate. This will be important when we consider the transmission to lending rates. 88 .6 .4 .2 0 Pre-Avg. -> 0.25 -> 0 -> -0.1 -> -0.25 -> -0.35 -> -0.5 Figure 3.4: Change in the aggregate deposit rate for households relative to the change in the repo rate - at times of changes to the repo rate. Source: The Riksbank, Statistics Sweden. The reluctance of deposit rates to fall below zero is not isolated to the Swedish case. The same holds for Switzerland, Japan, Denmark, Germany and the Euro Area as a whole, as shown in Figure 3.17 in Appendix A. Even though policy rates go negative, bank deposit rates remain above zero. What is causing deposit rates to be bounded? In the model in Section 3.3, the lower bound arises because people have the alternative of holding cash. One Swedish krona today will still be worth one krona tomorrow, thus yielding a zero interest rate. Hence, a negative deposit rate would be inconsistent with people holding deposits. An alternative to this hypothesis, which is also consistent with the model, is that people view negative bank deposit rates as unfair. In any case, negative interest rates would cause households to substitute away from deposits. Consistent with this, survey evidence from ING (2015) shows that 76 percent of consumers would withdraw money from their savings accounts if rates turned negative (see Figure 3.21 in Appendix A). Even with nominal deposit rates being bounded, an increase in fees could decrease the eective deposit rate. 53 Given the importance of deposit nancing however, the increase in fees would need to be substantial. A simple calculation based on the average deposit share and the pre-zero relationship between the deposit rate and the policy rate, suggests that commission income as a share of assets would have to increase by roughly 75 percent (see Figure 3.18 in Appendix A). However, the data suggests that the income generated from fees, if anything, declined after the Riksbank introduced negative rates in 2015. Also note that, if there was full pass-through to eective deposit rates via fees, this should imply that the pass-through to lending rates would be unaected by negative policy rates. Section 3.2.2 documents that the pass-through to lending rates also collapses, consistent with the empirical evidence that fees did not have a material impact 53 Conceptually however, if the bound on deposit rates arises from the existence of cash or notions of fairness, one would expect the eective deposit rate to be subject to the same bound. 89 on eective deposit rates in Sweden. Other nancing sources About half of Swedish bank liabilities come in other forms than deposits, as shown in Figure 3.2. The largest component is covered bond issuance. Figure 3.5 compares the interest rate on covered bonds to the policy rate. As with deposit rates, the correlation between the policy rate and covered bond rates is weaker once the policy rate turns negative. This is especially true for covered bonds with longer maturities. We have limited information on unsecured bonds and certicates, which make up a smaller share of bank liabilities. 3 2 1 0 -1 2012m1 2014m1 2016m1 2018m1 Covered bond, 2Y Covered bond, 5Y Governement bond, 5Y STIBOR, 3M Repo rate Figure 3.5: Interest rates. Sweden. Source: The Riksbank. Even if the pass-through to covered bond rates is weaker, we see from Figure 3.5 that the interest rate on covered bonds with shorter maturities eventually becomes negative, suggesting a stronger pass-through than for deposit rates. If banks respond to negative policy rates by shifting away from deposit nancing, they would therefore reduce their marginal nancing costs. However, Figure 3.6 shows that this is not the case. There is no noticeable increase in bonds issuance as rates goes negative, and the deposit share actually increases. There are at least three possible explanations for why banks did not shift away from deposit nancing: i) maintaining a base of depositors creates some synergies which other nancing sources do not, ii) the room for new issuances of covered bonds may be limited by the availability of bank assets to use for collateral, and iii) Basel III regulation makes deposit nancing more attractive in terms of satisfying new requirements. In any case, the empirical evidence suggests that deposit rates is the most important component of not only average, but also marginal funding costs in Sweden during this period. 90 25,000 .6 .58 20,000 Total Issuance, Mill. EUR Deposits / Total assets .56 15,000 .54 10,000 .52 2009q3 2011q3 2013q3 2015q3 2017q3 2009m1 2011m2 2013m3 2015m4 2017m5 Figure 3.6: Left panel: Issuance of covered bonds, Swedish banks. Right panel: Deposit share, Swedish banks. Vertical lines correspond to the date negative interest rates were implemented. Source: Association of Swedish Covered Bond Issuers, The Riksbank and Statistics Sweden. An estimate of nancing costs The balance sheet composition illustrated in Figure 3.2 can be used to proxy banks' funding costs. One such estimate is depicted in Figure 3.7. The estimated time series is a relatively conservative estimate in the sense that it does not incorporate the increase in deposit reliance. Moreover, the most benecial (lowest) interest rate is assigned to the funding sources for which interest rate data is lacking. As the solid line in Figure 3.7 indicates, the estimate of the banks funding cost follows the policy rate less closely as the policy rate falls below zero. 2 1.5 1 .5 0 -.5 2012m1 2014m1 2016m1 2018m1 Est. funding cost Counterfactual Repo rate Figure 3.7: Estimated average funding costs. The estimated average funding cost is computed by taking the weighted average of the assumed interest rate of the dierent funding sources of the bank. Certicates are assumed to have the same interest rate as 2Y covered bonds, while unsecured debt are assumed to have the same interest rate as 2Y covered bonds plus a 2 percent constant risk-premium. The counterfactual series correspond to the case when the spread between the repo rate and the estimated funding cost remain xed at pre-negative levels. Weights based on the liability structure of large Swedish banks, see Figure 3.2. Source: The Riksbank. How much lower would total funding costs be if the correlation with the repo rate was unchanged? The dashed line is a counterfactual funding cost estimate generated by assuming that the markup of the funding cost over the repo rate is equal to the pre-zero markup. The estimate suggests that total funding costs would 91 have been roughly 0.25 percentage points lower if there had been no reduction in pass-through. If policy rate cuts in negative territory do not lead to meaningful reductions in bank funding costs, this raises the fundamental question of whether they can be expected to lower lending rates. The next section addresses this question. 3.2.2 Bank lending This section considers the eect of negative rates on the banks asset side, i.e. how it aects lending rates. Figure 3.8 depicts aggregate lending rates in Sweden and suggests that the transmission of policy rates to lending rates is weakened as the policy rate becomes negative. 54 This insight will be conrmed by the bank level data in the next section. A simple calculation shows that if the markup over the repo rate had stayed constant and equal to the average markup in the pre-zero environment, aggregate lending rates for both households and corporations would have been approximately 0.3 percentage points lower. This is illustrated in the right panel of Figure 3.8. 6 3 2 4 1 2 0 0 -1 2008 2010 2012 2014 2016 2018 2013 2014 2016 2017 Households Corporations Households Corporations Policy Rate Policy Rate Figure 3.8: Aggregate lending rates in Sweden. The policy rate is dened as the repo rate. Right panel: The red and blue dashed lines capture counterfactual lending rates calculated under the assumption that the markup to the repo rate was constant and equal to the average markup in the period 2008m1-2015m1. Source: The Riksbank, Statistics Sweden. Aggregate lending rates for Switzerland, Japan, Denmark, Germany and the Euro Area are depicted in Figure 3.19 in Appendix A. In the absence of bank level data it is dicult to draw inference from this aggregate data, even if in the case of Switzerland and Denmark it seems particularly clear that there is little, if any, action in the aggregate time series. A key diculty in drawing inference for the Euro area is that negative reserve rates were associated with the European Central Bank directly oering credit at the negative policy rate, unlike in the case of Sweden. Furthermore, because deposit rates are higher in the Euro 54 Aggregate lending rates are weighted averages over dierent loan contracts, including loans with and without collateral, with xed and oating interest rate periods etc. 92 Area, they have more room to fall before reaching the lower bound. Hence, we would expect a larger impact on lending rates for Euro Area banks. We proceed by using two bank level data sets for Swedish banks. First, we have daily bank level data on a rich set of mortgage rates for the largest Swedish banks, provided by the price comparison site compricer.se. We exploit the high frequency of the data to evaluate the causal eect of reductions in the policy rate, and compare the monetary policy transmission to lending rates across positive and negative territory. Second, we complement our analysis by using bank level data on monthly lending volumes from Statistics Sweden. Bank level lending rates Figure 3.9 plots daily 5 year xed-rate mortgage rates for the largest Swedish banks from 2014 to 2016. 55 The vertical lines denote days when the policy rate was cut, with the repo rate level reported on the x-axis. The rst two lines capture repo rate cuts in positive territory. For both cuts there is an immediate and homogeneous decline in bank lending rates. The third line marks the day the repo rate turned negative and the three proceeding lines capture further repo rate cuts. The response in bank lending rates to these interest rate cuts is fundamentally dierent. While there is some initial reduction in lending rates, most of the rates increase again shortly thereafter. As a result, the total impact on lending rates is limited. Figure 3.9 includes the correlation between the repo rate and the aggregate deposit rate, as illustrated by the black x'es measured on the right y-axis. The x'es correspond to the bar chart in Figure 3.4. When the deposit rate is still responsive, lending rates fall in response to policy rate cuts. Once the deposit rate has reached its lower bound, i.e. the two last policy rate cuts, lending rates no longer fall. This highlights an important point: the pass-through to lending rates is smaller once the deposit rate is unresponsive. For the two last repo rate cuts there is a complete breakdown in the transmission of policy rates to both aggregate deposit rates and to bank level mortgage rates. 55 Figure 3.24 in Appendix A shows that the bank level data aggregates well to match ocial data. 93 4 40 Relative change in deposit rate 3.5 30 Lending Rate 20 3 2.5 10 2 0 Repo: 0.75 0.25 0 -0.1 -0.25 -0.35 -0.5 (1.1.2014) (26.5.2016) Bank rates (5y) Pass-Through Deposit Rate Figure 3.9: Bank level lending rates in Sweden. Interest rate on mortgages with ve-year xed interest period. The red vertical lines mark days in which the repo rate was lowered. The label on the x-axis shows the value of the repo rate. Small x'es denote the change in the deposit rate relative to the change in the policy rate (%), measured on the right y-axis. Source: Compricer.se. The reduction in pass-through holds across a wide range of loan types. Figure 3.10 plots bank-level lending rates across three dierent contracts, a oating rate mortgage (3m), a mortgage with a 1 year xed- rate period (1y) and a mortgage with a 3 year xed-rate period (3y). In all three cases, we see that the interest rate cuts in negative territory have very limited pass-through to bank lending rates. 3 3 3 2.5 2.5 2.5 2 2 2 1.5 1.5 1.5 Repo: 0.75 0.25 0 -0.1 -0.25 -0.35 -0.5 Repo: 0.75 0.25 0 -0.1 -0.25 -0.35 -0.5 Repo: 0.75 0.25 0 -0.1 -0.25 -0.35 -0.5 (1.1.2014) (26.5.2016) (1.1.2014) (26.5.2016) (1.1.2014) (26.5.2016) Bank rates (3m) Bank rates (1y) Bank rates (3y) Figure 3.10: Bank level lending rates with a oating interest rate (3m) (left panel) and a xed interest rate period of 1y (mid panel) and a xed interest rate period of 3y (right panel). The red solid line capture days with repo rate reductions. Source: Compricer.se. Figure 3.11 depicts box plots of bank level correlations between lending rates and the policy rate. The blue box depicts the empirical distribution of correlations prior to the Riksbank going negative, in which case the median correlation is roughly 0.75. The black box corresponds to the empirical distribution for the full period of negative rates, in which case the median correlation is slightly lower. Finally, the red box corresponds to the empirical distribution of correlations after the deposit rate becomes unresponsive to 94 changes in the repo rate (i.e. the last two policy rate cuts). Consistent with the previous gure, once the deposit rate is bounded there is a substantial drop in correlations, with the median correlation becoming negative. There is furthermore a large increase in dispersion, as correlations range from roughly negative 0.5 to positive 0.5. 1 Correlation with repo rate .5 0 Pre-Zero Post-Zero -.5 Post-Bound Figure 3.11: The distribution of bank level correlations between changes in lending rates and the repo-rate when the repo rate is positive (Pre-zero), the repo rate is negative (Post-zero) and the repo rate is negative and the deposit rate is non-responsive (Post-Bound). 5-year xed interest rate period. Source: compricer.se and own calculations. Figure 3.9 and 3.11 suggest that bank behavior in the post-zero period is relatively heterogeneous. That is, some banks continue to have a positive co-movement between their lending rate and the repo rate, while the sign is reversed for others. What is causing this increase in dispersion? One theory is that dierences in the reliance on deposit nancing means that banks are being dierentially aected by negative interest rates. Given that there are frictions in raising dierent forms of nancing - and some sources of nancing are more responsive to monetary policy changes than others - cross-sectional variation in balance-sheet components can induce variation in how monetary policy aects banks (Kashyap and Stein, 2000). Figure 3.12 investigates whether banks' funding structures aect their willingness to lower lending rates, by plotting the bank level correlation between lending rates and the repo rate after the deposit rate became bounded, as a function of banks' deposit shares. The gure conrms a negative relationship between the deposit share and the correlation with the repo rate. Banks with higher deposit shares are less responsive to policy rate cuts in negative territory. Weighting observations by market shares, this relationship is statistically signicant at the one percent level. The regression line reported in the gure indicates that a ten percentage points increase in the deposit share is associated with a reduction in the correlation of approximately 0.18 correlation points. 56 56 Although average correlations drop across all xed interest-rate periods, the increase in dispersion is most prevalent across 95 1 .5 Correlation with repo rate -.5 0 -1.78 (0.45) *** -1 .2 .4 .6 .8 1 Deposit share Figure 3.12: Correlation between lending rate and repo rate after the repo rate turned negative and the deposit rate reached its lower bound, as a function of the banks' deposit share. Size of circles indicate market share. Gray square indicates Ålandsbanken, for which we do not have the market share. Regression coecient (standard.error) also reported. ∗∗∗ indicates p < 0.01. Swedish banks. Interest rate on 5 year xed-rate mortgages. Source: compricer.se, Statistics Sweden and own calculations. We conclude this section with regression evidence that is useful for the model calibration in Section 3.3. The regression is outlined in equation (70), with the dependent variable being the monthly change in lending rates for bank i, ∆ibi,t . On the right hand side is the change in the repo rate, ∆irt , and the change in the repo rate interacted with a dummy variable Itpost bound = 1 if t > 2015m4, i.e. the period in which the deposit rate is bounded. ∆ibi,t = α + β∆irt + γ∆irt × Itpost bound + i,t (70) The regression results are reported in Table 3.1. In normal times, a one percentage point decrease in the repo rate reduces bank lending rates by on average 0.53 to 0.69 percentage points. Once the deposit rate becomes bounded however, this relationship ips. A one percentage point reduction in the repo rate, now increases bank lending rates by 0.03 to 0.31 percentage points. This reversal in sign holds across all loan contracts. longer xed-rate periods. Hence, for shorter xed-rate periods the relation with deposit shares is not statistically signicant. 96 (1) (2) (3) (4) 3 months 1 year 3 years 5 years ∗∗∗ ∗∗∗ ∗∗∗ ∗∗∗ ∆irt 0.579 0.533 0.640 0.686 (34.35) (28.56) (16.74) (13.72) ∆irt × Itpost bound -0.606 ∗∗∗ -0.623 ∗∗∗ -0.926 ∗∗∗ -0.994 ∗∗∗ (-10.27) (-9.54) (-6.92) (-5.68) ∗∗ ∗∗∗ ∗∗∗ ∗∗∗ Constant -0.00480 -0.00718 -0.0162 -0.0193 (-2.94) (-3.98) (-4.37) (-3.99) N 308 308 308 308 t statistics in parentheses ∗ p < 0.05, ∗∗ p < 0.01, ∗∗∗ p < 0.001 Table 3.1: Regression results from estimating equation (70). Dependent variable is ∆ibi,t at the monthly frequency. Observations are weighted according to bank size. Bank level lending volumes So far we have investigated the eect of negative policy rates on bank inter- est rates. Here we present evidence on bank lending volumes. Motivated by the cross-sectional relationship between deposit shares and lack of pass-through shown in Figure 3.12, we now investigate whether banks with high deposit shares also have lower growth in lending volumes. The dierence in dierence regression is specied in equation (71). X ∆ log(Lendingi,t ) = α + β Itpost zero × Deposit  sharei + δi + δk 1t=k + i,t (71) k For comparison, we keep our analysis the same as that in Heider, Saidi, and Schepens (2016), who investigate the impact of negative policy rates in the Euro Area. 57 The dependent variable is the percentage 3-month growth in bank level lending. Itpost zero is an indicator variable equal to one after the policy rate became negative, while Deposit sharei is the deposit share of bank i in year 2013. As an alternative specication, we replace Deposit sharei with an indicator 1High deposit,i for whether bank i has a deposit share above the median in 2013. We include bank xed eects δi to absorb time-invariant bank characteristics, and month-year xed eects δk to absorb shocks common to all banks. Standard errors are clustered at the bank level. We restrict our sample to start in 2014, thus choosing a relatively short time period around the event date. The coecient of interest is the interaction coecient β. If banks with high deposit shares have lower credit growth than banks with low deposit shares after the policy rate breaches the zero lower bound, we expect to nd βˆ < 0. The regression results are reported in Table 3.2. Focusing on column (1) rst, the interaction coecient 57 We have also tried substituting Itpost zero with Itpost bound , and the results are similar. 97 is negative and signicant at the ve percent level. An increase in the deposit share is associated with a reduction in credit growth in the post-zero environment. The eect is economically signicant - a one standard deviation increase in the deposit share decreases lending growth by approximately 0.18 standard deviations. In column (2) we consider average credit growth for banks with above and below median deposit shares. While we lose some precision by using only an indicator variable, the coecient is still negative and statis- tically signicant at the ten percent level. On average, banks with high deposit shares had four percentage points lower growth in credit compared to banks with low deposit shares. We thus conclude that, due to the lower bound on the deposit rate, banks which rely heavily on deposit nancing are less responsive to policy rate cuts in negative territory. The cross-sectional evidence presented here is consistent with the results in Heider, Saidi, and Schepens (2016) and the survey evidence in Figure 3.20 in Appendix A, where the majority of European banks report that they have not increased lending volumes in response to negative policy rates. Dependent variable: ∆ log (Lending)i,t (1) (2) post It × Deposit share −0.09 ∗∗ ) i (−2.09 Itpost ×1High deposit,i ∗ −0.04 (−1.85 ) Clusters 40 40 Bank FE Yes Yes Month-Year FE Yes Yes Observations 1, 113 1, 113 Table 3.2: Regression results from estimating equation (71). Dependent variable: ∆ log (Lending)i,t ≡ log (Lending)i,t − log (Lending)i,t−3 . Monthly bank level data from Sweden. 3.3 Negative interest rates in theory Motivated by the empirical evidence in the previous section, we now develop a formal framework to un- derstand the impact of negative policy rates on lending rates and lending volumes. Section 3.3.1 builds a partial equilibrium banking model that is then embedded in a general equilibrium framework in Section 3.3.2, nesting the standard New Keynesian model. 98 3.3.1 Negative interest rates in a partial equilibrium model of banking The goal of this section is to illustrate how changes in policy rates normally aect deposit and lending rates, and how this changes once the deposit rate becomes bounded. For now we directly impose a bound on the deposit rate, formally derived in the full model in the next section. A bank decides how much deposits to collect, dt , how many loans to extend, lt , how much reserves to hold at the central bank, Rt , as well as how much physical cash to hold mt . Denote interest on reserves ir , interest on deposits is , and interest on loans ib . In making its choices, the bank takes these interest rates as given. Cash pays no interest, but carries a proportional storage costs S(Mt ) = γMt for some γ ≥ 0. The price level is normalized so that Pt = 1, but will be endogenous in the next section. A bank is modeled as in Curdia and Woodford (2011). All prots zt are paid out to the owner at time t. The bank thus only holds enough assets on its balance sheet to pay o depositors in the next period so that (1 + ist )dt = (1 + ibt )lt + (1 + irt )Rt + mt − S(mt ) (72) The bank faces an intermediation cost function Γ(lt , Rt, mt , zt ). Reserves lower intermediation costs for the bank up to some point ¯, R i.e. ΓR < 0 for ¯ R 0. Finally, higher bank prots weakly reduce the marginal cost of lending, i.e. Γlz ≤ 0. This assumption is discussed further below. Using equation (72), bank prots can be expressed in a static way as ibt − ist is − irt is + γ zt = s lt − t s Rt − t s mt − Γ (lt , Rt , mt , zt ) (73) 1 + it 1 + it 1 + it A partial banking equilibrium is dened by exogenous (ist , ibt , irt ) taken as given by banks and values for Rt , lt , mt , zt solving equation (73) and the rst order conditions (74) - (76): ist − irt Rt : = −ΓR (lt, Rt , m, zt ) : (74) 1 + ist ist + γ mt : = −Γm (lt , Rt , mt , zt ) (75) 1 + ist 99 ibt − ist lt : = Γl (lt , Rt , mt , zt ) (76) 1 + ist Figure 3.13 depicts the demand for reserves D given by equation (74), with R on the x-axis and is on the y-axis. The interest on reserves ir is treated as xed for now, and could for example correspond to 0 as prior to 2008 in the US. The lower the deposit rate, the more reserves are demanded by banks. We have chosen a simple specication for the function Γ for the purposes of the gure. 58 is S S0 A A¯ ir D −γ A0 0 ir D0 R R∗ ¯ R Figure 3.13: Reserves - Demand and Supply. Letting the bank be a representative bank, one way of thinking about how the central bank determines the risk-free interest rate is is with open market operations in government bonds (purchased by reserves). Open market operations directly set the supply of reserves R∗ , which pins down is at point A in Figure 3.13. This closely resembles how policy was conducted prior to 2008. An increase in reserves by the central bank would then lower is until it reaches the point ¯. R At that point, banks are fully satiated in reserves and the deposit rate and the reserve rate are equal, is = ir . Alternatively, the central bank could keep banks satiated in reserves by choosing ¯, R ≥ R implying ir = is . Changes in the reserve rate would then directly change the deposit rate as well. Such an equilibrium is illustrated at point A¯. This implementation of policy better captures the current policy regime in the US and in Sweden. Following this policy arrangement, we will refer to ir as the policy rate. In addition to reserves, banks also demand money, as given by equation (75) and depicted in Figure 3.14 with is on the y-axis. With is determined by the central bank's choice of reserves and interest on reserves, 58 It is simply linear in R until the satiation point ¯ R is reached, at which point ΓR = 0. More generally we assume that limR→0 ΓR = ∞ which implies that there is no zero lower bound on interest on reserves. 100 the central bank elastically supplies paper currency to satisfy whatever money is demanded at that rate. As in the case of reserves, we assume banks (and households) hold money because it is useful to facilitate transactions - up until some point. Typically, the monetary satiation is assumed to occur at 0 and hence the interest rate on deposits cannot fall below 0. In the next section, we show how storage costs of money can imply a bound below 0. Here, we take the bound as exogenously given at −γ . is A S −γ D M ¯ M Figure 3.14: Money - Demand and Supply. The fact that is cannot fall below −γ also has implications for the relationship between reserves, the interest on reserves and the deposit rate. Consider again Figure 3.13. What happens if the central bank changes the interest rate on reserve to some ¯? ir0 < −γ , while at the same time setting reserves so that R ≥ R The reduction in the reserve rate shifts the demand curve down to D0 . Because the deposit rate is bounded at −γ , a new equilibrium arises at point A0 . Observe that an equilibrium cannot take place at ¯. R At this point the marginal benet of holding reserves is zero (due to satiation), yet the marginal cost is higher, i.e. −ir0 . Banks will then prefer holding money, and so reserves will ow into vault cash. 59 The rst order condition for lending in equation (76) governs what happens to bank lending when the reserve rate is lowered. First consider the case in which the bound on the deposit rate is non-binding. In this case, the deposit rate also falls, thereby lowering bank nancing costs and increasing loan supply. If the deposit rate is constrained by the lower bound however, there is no reduction in nancing costs and so no increase in loan supply. Moreover, when the reserve rate is lowered without a reduction in the deposit rate, bank prots fall. This is simply because banks receive a lower interest rate on one of their assets, without having to pay a lower interest rate on their liabilities. This will in turn increase the cost of bank 59 See Box 3 in https://www.ecb.europa.eu/pub/economic-bulletin/articles/2018/html/ecb.ebart201806_03.en.html#toc8 for empirical support of this model prediction. 101 intermediation through the function Γ(l, R, m, z). As a result, the supply of loans is reduced. The eect on lending can be shown formally by solving the partial equilibrium using a linear approxima- tion. Expression (77) captures the increase in lending at a given borrowing rate ib when the interest rate on reserves is reduced and ir = ∂ˆ lt is . In this case ∂ˆ ırt < 0, as Γlz < 0 and |Γz | < 1.60 Expression (78) captures the decrease in lending when is r is xed and there is only a reduction in it , which corresponds closer to what we ∂ˆ lt have seen in the data. In this case ırt ∂ˆ > 0, so that a reduction in the reserve rate leads to a reduction in lending volumes. 61 ∂ ˆlt   1 + Γl zΓlz z + l + m + Γ =− − <0 (77) ∂ˆırt lΓll lΓll z(1 + Γz ) ∂ ˆlt zΓlz ¯ R =− >0 (78) ∂ˆırt s lΓll z(1 + Γz ) i xed The reduction in lending given by (78) relies fundamentally on the negative value of the partial derivative Γlz . This assumption captures, in a reduced form manner, the established link between banks' net worth and their operational costs - assuming there is a one-to-one mapping between net worth and prots. We do not make an attempt to microfound this assumption, which is explicitly done in among others Holmstrom and Tirole (1997) and Gertler and Kiyotaki (2010), as well as documented empirically in for instance Jiménez, Ongena, Peydró, and Saurina (2012). If Γlz = 0, there is no feedback eect from bank prots to credit supply. Importantly, however, a negative policy rate does still not increase lending. This partial equilibrium analysis already hints to very dierent eects of policy rate cuts in negative territory. If the policy rate cut does not lead to a reduction in deposit rates, there is no reduction in bank funding costs. The reduction in the reserve rate then implies lower bank prots as long as banks hold reserves in positive supply at the central bank. Hence, as the critics have stated, a negative reserve rate essentially works as a tax in the partial equilibrium banking model. To the extent that banks are constrained in their lending by their net worth, this will suppress credit supply. The argument put forward by the proponents of negative interest rates however, is that there should be a reduction in the borrowing rate faced by borrowers. This in turn could stimulate spending. In order to evaluate this claim we move on to a general equilibrium framework, in which ib is no longer held xed. 60 We have checked that |Γ | < 1 holds in all our numerical results. z 61 Throughout the paper we let x ˆ denote the deviation of xt from its steady state value x. t 102 3.3.2 Negative interest rates in general equilibrium We now embed the banking model in a general equilibrium model, in which the borrowing rate is endogenously determined by loan supply and demand. In this case the choices of the bank feed into aggregate demand, which in turn aects borrowing and lending rates in general equilibrium. Our main nding will be that a (suciently) negative policy rate is not expected to lower the borrowing rate. The full model is relegated to Appendix C, with key elements outlined in the main text and the log-linear equilibrium conditions needed to close the model summarized in Table 3.3. We rst highlight how the bound on the deposit rate is derived. Household j ∈ {s, b} consumes, holds money, saves/borrows and supplies labor. Households of type b are borrowers and make up a fraction χ of the population, while households of type s are savers and make up the remaining share 1−χ . Saver households can store their wealth either by depositing their savings in banks, thereby earning an interest rate of ist , or by! holding money which is the unit of account. ! Mtj 0 0 Mtj Let Ω be the utility from holding real money balances with Ω ≥ 0 and Ω = 0 for Pt Pt Mtj   ≥m ¯ . Letting U 0 Ctj be the marginal utility of consumption and ijt the interest rate faced by a type Pt j agent, optimal money holdings satisfy ! 0Mtj Ω   Pt ijt + S 0 Mtj   = (79) U 0 Ctj 1 + ijt The lower bound on the deposit rate is s is the lowest value of it satisfying equation (79). The lower bound therefore depends crucially on the marginal storage cost, which is typically assumed to be zero, hence the zero lower bound. We instead assume proportional storage cost S (Mts ) = γMts . This implies a lower bound is = −γ , so that the bound can be negative if γ > 0. In order to generate a recession, we consider a preference shock ζ, which reduces current consumption. This type of shock is standard in the ZLB literature. We have repeated the analysis using a debt deleveraging shock, which yields qualitatively similar results. Table 3.3 reports a log-linear approximation of the equilibrium conditions. First, total output Yˆt is given by the consumption of the two agents, Cˆtb and Cˆts , as shown in equation (80). The consumption of each agent in turn, is determined by their respective Euler equations, (81) and (82), where πˆt denotes the deviation of ination from its steady state level. These equations, together with the budget constraint of the borrower in equation (83), where ˆbb denotes the real value of the borrowers nominal debt, determine both the demand t 103 for credit and the supply of savings that is generated from the saver households. The production structure, which assumes monopolistically competitive rms that face price rigidities in the form of Calvo pricing, is borrowed from Benigno, Eggertsson, and Romei (2014) and can be summarized by the standard New Keynesian Phillips curve shown in equation (84). χC b ˆ b (1 − χ)C s ˆ s Yˆt = Ct + Ct (80) Y  Y  Cˆtb = Et Cˆt+1 b ˆt+1 − ζˆt + Et ζˆt+1 − σ ˆibt − Et π (81)   Cˆ s = Et Cˆ s − σ ˆis − Et π t t+1 t ˆt+1 − ζˆt + Et ζˆt+1 (82) ˆb ˆb cb ˆ b ˆbb = bt + it−1 − π ˆt + y Ct − χ b Yˆt (83) t b b b πβ πβ b b π ˆ ˆt = κYt + βEt π ˆt+1 (84) ˆibt = ˆist + ω ˆt (85) ˆ t = ω(ν − 1)ˆbbt − ιωˆ ω zt (86) b χb (1 + ω) ˆb d ˆis + R ˆir zˆt = i − (87) ωχbb + (1 − ι)Γ t ωχbb + (1 − ι)Γ t ωχbb + (1 − ι)Γ t ˆist = ˆirt − RRˆt (88) rˆn = ζˆt − Et ζˆt+1 − χˆ t ωt (89) ˆt + φY Yˆt ˆirt = rˆtn + φπ π (90) n o ˆist = max isbound , ˆirt (91) 1+η t L Here we assume an exponential utility function 1 − exp(−qCt ) + 1+η , where q > 0 and η > 0, and assume the bank −ι 1 2 ν Rt − R if Rt < R and Γ (lt , Rt , zt ) = ltν zt−ι otherwise. We dene  intermediation cost is given by Γ (lt , Rt , zt ) = lt zt + s 2 1 > β ≡ χβ b + (1 − χ)β s > 0, σ ≡ qY1 > 0, ω ≡ β βb − 1 > 0, κ ≡ (1 − α)(1 − αβ)(η + σ −1 )/α > 0 and isbound ≡ (1 − γ)β s − 1. Table 3.3: Summary of log linearized equilibrium conditions. The partial equilibrium banking model outlined in the previous section is directly incorporated into the model. Recall that there we treated (ibt , ist , irt ) as exogenous. Now they are determined in equilibrium by the rst order conditions of banks and households, along with policy. Equations (85) and (86) are log- linear approximations of the rst order condition for lending in equation (76). This condition no longer just determines loan supply for given values of ist and ibt , rather it species a general equilibrium interest rate spread ω ˆt associated with a particular level of bank lending. Equation (87) is an expression for bank prots, where zˆt denotes prots, while equation (88) is the banking sectors demand for reserves. 62 Equation (89) denes the natural rate of interest rˆtn , which depends on the exogenous preference shock ζˆ, 62 As in the case of the households, we simplify the exposition of the model by omitting the banks demand for currency, see Appendix C for full model. 104 as well as the endogenous interest rate spread. The model is closed by monetary and scal policy. The only government liabilities in the model are that of the central bank (currency plus reserves). Any seignorage revenues or losses are rebated to the representative saver, so that no scal variables enter directly into the equilibrium determination. Equation (90) is a Taylor rule that is formulated in terms of a policy rate that corresponds to the interest on reserves. We follow the recent literature by allowing for time variation in the intercept of the rule, rˆtn , corresponding to the natural rate of interest. There is no lower bound on interest on reserves. As discussed in the previous section, we assume a policy regime in which the central bank satiates the banking sector in reserves whenever it can so that ˆist = ˆirt . Equation (91) recognizes however, that the deposit rate is bounded in line with the data. Given the policy rule (90) and absent a bound on deposit rates, variations in ζˆt have no eect on either output or ination and ˆirt = ˆist = rˆtn always. However, this result only holds as long as the natural rate of interest is not so negative that the lower bound on the deposit rate becomes binding. The key question we are interested in answering is what happens when the deposit rate is constrained at the lower bound, and the central bank reduces the policy rate further into negative territory. 3.3.3 A numerical example We now parameterize the model to assess the eect of negative rates. The parameters of the numerical example are summarized in Table 3.6 in Appendix D, and all the standard parameters are chosen from the literature. One notable exception is the parameter ι - which is specic to our model and governs the feedback eect from bank prots to credit supply. We consider several dierent values of ι, based on the empirical estimates using Swedish bank level data in Table 3.1. As a lower bound, we let ι = 0. In this case, bank prots do not aect credit supply. In our model, a negative reserve rate should then not lead to any changes in lending rates, consistent with the behavior of some Swedish banks. For intermediate values of ι we use the average coecient estimates for all loan contracts in Sweden, and the coecient estimate for the 5 year xed-interest rate period contracts. These estimates correspond to ι = 0.66 and ι = 0.88 respectively, and we pick the latter as our baseline estimate. Finally, as a higher bound we consider the behavior of the banks that increased their lending rates the most. To arrive at an estimate for these banks we use the coecient for the 5 year loan contracts, and subtract two standard errors from the estimated coecient. Given a normal distribution, this captures the behavior of banks with lending rate increases in the 95th percentile. In this case the coecient estimate is - 105 0.75, implying ι = 1.235.63 The result of our numerical experiment is reported in Figure 3.15. It shows the dynamic evolution of interest rates, output and ination following a negative preference shock. The dashed black line depicts the r case in which there is no bound on any interest rate (No bound ). In this case, it = ist is always feasible. The preference shock reduces the natural rate of interest through equation (89). Absent policy interventions, i.e. cuts in the reserve rate, this would lead to a demand recession. With our specication of policy however, the reduction in the natural rate of interest triggers a reduction in the central bank reserve rate. When the central bank lowers the reserve rate in absence of any bounds, this lowers the deposit rate one-to-one. The reduction in the deposit rate stimulates the consumption of saver households. In addition, lowering the deposit rate reduces the banks nancing costs. This increases the banks willingness to lend, which decreases the borrowing rate, thereby stimulating the consumption of borrower households. Hence, the reduction in the reserve rate passes through to the other interest rates in the economy, thereby stimulating aggregate demand and leaving output and ination unaected by the shock. Figure 3.15: Impulse responses from a preference shock with ι = 0.88. Next, consider what happens if the deposit rate is bounded and the central bank chooses not to go 63 Note that, since we calibrate ι to match the reduced-form relationship between policy rates and lending rates, the results in this section is invariant to the assumptions we make about banks funding sources. Adding a second funding source, without a zero lower bound but with imperfect substitutability with respect to deposits, would not change the results but rather yield a larger value of ι. 106 negative, a case corresponding to the behavior of several central banks during the crisis, such as the Federal Reserve. This case is depicted by the solid black line in Figure 3.15 (Standard model ). In this case, the inability of the central bank to cut rates results in an output fall of about 4.5 percent and a 1 percent drop in ination - picked to match the data. We now move on to asking our main question - what happens is the deposit rate is bounded and the central bank still chooses to set a negative reserve rate? The result of this experiment is captured by the dashed red line (Negative rates ). As seen from the red line in Figure 3.15, a negative reserve rate is not expansionary when the deposit rate is bounded. 64 As the negative policy rate is not transmitted to deposit rates, there is no reduction in bank nancing costs, and so no reduction in lending rates. Further, the reduction in bank prots leads to an increase in intermediation costs for ι > 0. This increases the interest rate spread. Accordingly, output falls by an additional percentage point when the central bank goes negative. For the shock studied, having the central bank follow a Taylor rule implies a large negative reserve rate. However, the countries which have implemented negative rates have only ventured modestly below zero. We now explore what happens if the central bank sets a reserve rate equal to - 0.5 percent. Figure 3.16: Dierence in IRFs for ˆ ibt and yˆt between negative rates model and standard model for dierent values of ι. In Figure 3.16 we plot the dierence in the borrowing rate and output between the standard model and the negative rates model. That is, we compare the outcomes when the central bank reduces the reserve rate below the bound on the deposit rate to the outcomes when the central bank does not push below this bound. 64 Here, so as not to exaggerate the negative eect, we assume that the Taylor rule is such that the central bank targets the natural rate but does not respond to output and ination gaps when the bound is binding. 107 As seen from the gure, a negative reserve rate will tend to increase the borrowing rate and reduce output. How strong this eect is depends crucially on the ι-parameter, i.e. on the feedback from bank prots to intermediation costs. In our baseline case with ι = 0.88, the borrowing rate is approximately 15 basis points higher if the central bank goes negative, and output is approximately 7 basis points lower, a modest albeit economically signicant eect. If ι = 0, a (suciently) negative policy rate has no eect on output. 3.4 Discussion and extensions We have focused on the transmission of monetary policy through the bank sector. It is possible that negative interest rates stimulate aggregate demand through other channels, for example through wealth eects or through the exchange rate. The point we want to make is that the pass-through to bank interest rates - traditionally the most important channel of monetary policy - is weakened with negative policy rates. Even if lending volumes do not respond positively to negative policy rates, there could potentially be an eect on the composition of borrowers. It has been suggested that banks may respond to negative interest rates by increasing risk taking. Heider, Saidi, and Schepens (2016) nd support for increased risk taking in the Euro Area, using volatility in the return-to-asset ratio as a proxy for risk taking. According to their results, banks in the Euro Area responded to the negative policy rate by increasing return volatility. This is certainly not the traditional transmission mechanism of monetary policy, and it is unclear whether such an outcome is desirable. Another mechanism through which negative interest rates could have an eect is through signaling about future interest rates. While it is possible that such a signaling mechanism played a role, it is unclear why it could not be achieved via direct announcements of future policy rates. It is also worth noting that government borrowing rates might have been reduced due to negative policy rates. To the extent that this stimulated scal expansions, that would be an additional way through which negative rates could aect the economy. Finally, we have assumed that the banking sector is perfectly competitive. As shown by Drechsler, Savov, and Schnabl (2017), however, there is compelling evidence that banks have considerable market power and thus are able to pay deposit rates below the risk-free interest rate. Our model could be extended to include market power in the bank sector, but as long as there is a bound on the deposit rate, our result would still apply. In that setting, the bound on the deposit rate would have a negative eect of the banks balance sheet, independently of negative policy rates, as it would prevent banks from beneting from the interest rate spread between the deposit rate and the risk-free rate. 108 3.5 Conclusion Since 2014, several countries have experimented with negative policy rates. In this paper, we have docu- mented that negative central bank rates have not been transmitted to aggregate deposit rates, which remain stuck at levels close to zero. As a result, aggregate lending rates remain elevated as well. Using bank level data from Sweden, we documented a disconnect between the policy rate and lending rates, once the deposit rate has reached its lower bound. We further showed that this disconnect is partially explained by reliance on deposit nancing. Consistent with this, we found that Swedish banks with high deposit shares cut back on lending relative to other banks - once the policy rate turned negative. Motivated by our empirical ndings, we developed a New Keynesian model with savers, borrowers, and a bank sector. By including money storage costs and central bank reserves, we captured the disconnect between the policy rate and the deposit rate at the lower bound. In this framework, we showed that a negative policy rate was at best irrelevant, but could potentially be contractionary due to a negative eect on bank prots. A key limitation of our analysis is that the long run eects of negative interest rates might dier from the short run eects. This could either weaken or strengthen our results. On one hand, banks may become more willing to pass negative rates onto their depositors over time, either via directly lowering deposit rates or by increasing fees. On the other hand, consumers and rms may adopt alternative strategies to circumvent negative rates, such as investing in money storage facilities. If the central bank charges very negative interest rates for holding the transaction balances of commercial banks, it is possible that banks will adopt alternative payment technologies to avoid having to pay the negative rates. Given the long-term decline in interest rates, the need for unconventional monetary policy is likely to remain high in the future. Our ndings suggest that negative interest rates are not a substitute for regular interest rate cuts in positive territory, at least to the extent that these cuts are expected to work via the bank lending channel. The question remains, however, what is? Alternative monetary policy measures include quantitative easing, forward guidance and credit subsidies such as the TLTRO program implemented by the ECB. While the existing literature has made progress in evaluating these measures, the question of how monetary policy should optimally be implemented in a low interest rate environment remains a question which should be high on the research agenda. 109 Appendix A: Additional gures and tables USA Euro Area Sweden Denmark Switzerland Nominal Rates Initial Easing Initial Easing Initial Easing Initial Easing Initial Easing 1970 8.9 5.1 - - - - - - - - 1975 11 5.1 12 8.6 8.0 1.5 - - 7.0 6.5 1981 18 9.0 12 7.0 12 3.5 - - 7.5 5.7 1990 8.6 5.6 - - - - - - - - 1992 - - 9.6 6.5 12 7.5 15 11 8.8 8.0 2001 6.5 5.5 - - - - - - - - 2008 5.3 5.1 4.3 3.9 4.8 4.5 4.5 4.0 2.4 2.4 2011 - - 1.0 1.4 2.1 2.5 1.1 1.6 0.07 2.0 Average 5.9 5.5 3.9 5.5 4.9 (pre-zero) (5.9) (6.5) (4.3) (7.5) (5.7) USA Euro Area Sweden Denmark Switzerland Real Rates Initial Easing Initial Easing Initial Easing Initial Easing Initial Easing 1970 3.9 5.1 - - - - - - - - 1975 4.5 9.1 5.1 7.7 -1.0 3.9 - - -2.8 3.0 1981 8.2 3.6 5.9 4.2 1.8 2.2 - - 1.0 4.9 1990 5.5 4.9 - - - - - - - - 1992 - - 5.6 3.5 7.7 7.4 14 9.7 4.7 3.5 2001 4.1 5.8 - - - - - - - - 2008 2.5 4.5 2.1 3.3 1.9 3.3 2.5 4.6 1.6 3.9 2011 - - -0.08 2.2 1.1 2.5 -0.1 0 0.72 2.2 Average 5.5 4.2 3.9 4.8 3.5 (pre-zero) (5.5) (4.7) (4.2) (7.2) (3.8) Table 3.4: Nominal and real interest rates at start of recession (%) and interest rate cuts in response to recession (pp). Recession dates for the US are NBER recession dates. Recession rates for the Euro Area are CEPR recession dates. Recession dates for Sweden, Denmark and Switzerland are dened as the overlap between the country specic OECD recession indicators and the CEPR recession dates for the Euro Area. The interest rates are the federal funds rate for the US and short term interbank rates for the remaining countries (the German interbank rate is used for the Euro Area) Source: St. Louis FRED and own calculations. 110 Switzerland Japan Denmark 3.00 .6 6 2.00 4 .4 2 1.00 .2 0 0.00 0 -2 -1.00 -.2 2008 2010 2012 2014 2016 2018 2008 2010 2012 2014 2016 2018 2008 2010 2012 2014 2016 2018 Households Corporations Households Policy Rate Households Policy Rate Policy Rate Germany Euro Area 5 5 4 4 3 3 2 2 1 1 0 0 2008 2010 2012 2014 2016 2018 2008 2010 2012 2014 2016 2018 Households Corporations Households Corporations Policy Rate Policy Rate Figure 3.17: Aggregate deposit rates for Switzerland, Japan, Denmark, the Euro Area and Germany. The policy rates are dened as SARON (Switzerland), the Uncollaterized Overnight Call Rate (Japan), the Certicates of Deposit Rate (Denmark) and the Deposit Rate (Euro Area and Germany). The red vertical lines mark the month in which policy rates became negative. Source: the Swiss National Bank (SNB), Bank of Japan, the Danish National Bank (DNB), and the European Central Bank (ECB). 1.2 Gross Commission Income (% of Asssets) .6 .8.4 1 1995 2000 2005 2010 2015 Data Counterfactual Figure 3.18: Actual and Counterfactual Commission Income as a Share of Assets (%). The counterfactual commission income is calculated as the amount of commission income that would be necessary to make up for the bound on the nominal deposit   rate, all else equal. The counterfactual commission income is given by actual commission income plus Depositst Assetst it − icf t = 0.47 (0.03 − (−0.9)) = 0.44, where it is the average aggregate deposit rate and icf t is a counterfactual deposit rate calculated under the assumption that the markdown to the repo rate is constant and equal to the pre-zero markdown. Source: Statistics Sweden and own calculations. 111 Switzerland Japan Denmark 6 2 8 6 1.5 4 4 1 2 2 .5 0 0 0 -2 2008 2010 2012 2014 2016 2018 2008 2010 2012 2014 2016 2018 2008 2010 2012 2014 2016 2018 Households Corporations Households Policy Rate Households Policy Rate Policy Rate Germany Euro Area 6 6 4 4 2 2 0 0 2008 2010 2012 2014 2016 2018 2008 2010 2012 2014 2016 2018 Households Corporations Households Corporations Policy Rate Policy Rate Figure 3.19: Aggregate lending rates for Switzerland, Japan, Denmark, the Euro Area and Germany. The policy rates are dened as SARON (Switzerland), the Uncollaterized Overnight Call Rate (Japan), the Certicates of Deposit Rate (Denmark) and the Deposit Rate (Euro Area and Germany). The red vertical lines mark the month in which policy rates became negative. Source: the Swiss National Bank (SNB), Bank of Japan, the Danish National Bank (DNB), and the European Central Bank (ECB). 100 Unchanged or decreased lending volumes (%) 20 40 0 60 80 2016Q2 2016Q4 2017Q2 2017Q4 Loans to enterprises Loans to households Figure 3.20: Share of banks answering that the negative ECB policy rate has had a negative or neutral eect on their lending volume in the past six months. Household loans only include loans to house purchases. Source: ECB bank lending survey. 112 UK FR IT AU US RO BE ES TU DE PO CZ NL LU AS 0 20 40 60 80 100 Fraction of respondents that would withdraw money from savings account (%) Figure 3.21: Fraction of households who would withdraw money from their savings account if they were levied a negative interest rate. Solid line represent unweighted average of 76.4 %. Source: ING (2015). Real GDP in Local Currency , Indexed Real GDP in Local Currency, Indexed - Detrended 110 5 100 0 90 -5 80 -10 70 -15 1995 2000 2005 2010 2015 1995 2000 2005 2010 2015 Denmark Sweden Denmark Sweden Switzerland Euro Area Switzerland Euro Area Figure 3.22: Gross domestic product in constant prices. Local currency. Indexed so that GDP2008 =100. The right panel shows the detrended series using a linear time trend based on the 1995-2007 period. Source: St. Louis FRED and own calculations. 113 2 1.5 1 .5 0 -.5 2012m1 2014m1 2016m1 2018m1 Est. funding cost Counterfactual Repo rate Figure 3.23: Estimated average funding costs. The estimated average funding cost is computed by taking the weighted average of the assumed interest rate of the dierent funding sources of the bank. Certicates are assumed to have the same interest rate as STIBOR 3M, while unsecured debt are assumed to have the same interest rate as STIBOR 3M plus a 2 percent constant risk-premium. The counterfactual series correspond to the case when the spread between the repo rate and the estimated funding cost remain xed at pre-negative levels. Weights from Figure 3.2 used. Source: The Riksbank and own calculations. 4 3 3 2 2 1 1 0 0 -1 -1 2014m2 2014m8 2015m2 2015m8 2016m2 2014m2 2014m8 2015m2 2015m8 2016m2 Bank Level Data (3y) Aggregate Data (3y-5y) Bank Level Data (5y) Aggregate Data (3y-5y) Repo Rate Repo Rate Figure 3.24: Comparing bank level mortgage rates to aggregate data. We aggregate the bank level mortgage rates using market shares, supplemented with data on lending volumes. The blue line (Aggregate Data) depicts the ocial average mortgage interest rate for loans with a xed interest rate period of 3-5 years. Source: Swedish Banker's Association (market shares), Statistics Sweden (lending volumes, aggregate rates). Appendix B: Marginal and average rate on reserves In our model, central bank reserves earn a single interest rate ir . In reality, central banks can adopt exemption thresholds and tiered remuneration schemes so that not all reserves earn the same interest rate. Hence, even though the key policy rate is negative, not all central bank reserves necessarily earn a negative interest rate. Here we provide a short overview of the dierent remuneration schedules implemented in the Euro Area, Denmark, Japan, Sweden and Switzerland. For a more detailed analysis see Bech and Malkhozov (2016). 114 In the Euro Area, required reserves earn the main nancing operations rate - currently set at 0.00 percent. Excess reserves on the other hand, earn the central bank deposit rate - currently set at -0.40 percent. Hence, only reserves in excess of the required level earn a negative interest rate. A similar remuneration scheme is in place in Denmark. Banks can deposit funds at the Danish central bank at the current account rate of 0.00 percent. However, there are (bank-specic) limits on the amount of funds that banks can deposit at the current account rate. Funds in excess of these limits earn the interest rate on one-week certicates of deposits - currently set at -0.65 percent. The Riksbank issues one-week debt certicates, which  until recently  earned an interest rate of -0.50 percent. While there is no reserve requirement, the Swedish central bank undertakes ne-tuning operations to drain the bank sector of remaining reserves each day. The Swiss central bank has the lowest key policy rate at -0.75 percent. However, due to high exemption thresholds the majority of reserves earn a zero interest rate. The Bank of Japan adopted a three-tiered remuneration schedule when the key policy rate turned negative. As a result, central bank reserves earn an interest rate of either 0.10, 0.00 or -0.10 percent. Due to the tiered remuneration system, there is a gap between the average and the marginal reserve rate. Bech and Malkhozov (2016) calculate this gap as of February 2016, as illustrated in Figure 3.25. Figure 3.25: Reserve rates - Source: Bech and Malkhozov (2016). 115 Appendix C: Details of the model Households We consider a closed economy, populated by a unit-measure continuum of households. Households are of two types, either patient (indexed by superscript s) or impatient (indexed by superscript b). Patient households have a higher discount factor than impatient agents, i.e. βs > βb. The total mass of patient households is 1 − χ, while the total mass of impatient households is χ. In equilibrium, impatient households will borrow from patient households via the banking system, which we specify below. We therefore refer to the impatient households as borrowers and the patient households as savers. Households consume, supply labor, borrow/save and hold real money balances. At any time t, the optimal choice of consumption, labor, borrowing/saving and money holdings for a household j ∈ {s, b} maximizes the present value of the sum of utilities ∞ " ! # X j T −t   MTj   Utj CTj NTj  = Et β U +Ω − V ζt (92) PT T =t where ζt is a random variable following some stochastic process and acts as a preference shock. Ctj and Ntj denote consumption and labor for type j respectively, and the utility function satises standard assumptions. Households consume a bundle of consumption goods. Specically, there is a continuum of goods indexed by i, and each household j has preferences over the consumption index θ Z 1 θ−1  θ−1 Ctj = Ct (i) θ di (93) 0 where θ>1 measures the elasticity of substitution between goods. Agents maximize lifetime utility (equation (92)) subject to the following ow budget constraint:     Mtj + Bt−1 j 1 + ijt−1 = Wtj Ntj + Btj + Mt−1 j − Pt Ctj − S Mt−1 j + Ψjt + ψtj − Ttj (94) Btj denotes one period risk-free debt of type j ( Bts < 0 and Btb > 0). For the saver, Bts consists of s bank deposits and government bonds, both remunerated at the same interest rate it by arbitrage. Borrower   j households borrow from the bank sector only, at the banks' lending rate ibt . S Mt−1 denotes the storage 116 cost of holding money. Ψjt is type j 's share of rm prots, and ψtj is type j 's share of bank prots. Let Ztf irm denote rm prots, and Zt denote bank prots. We assume that rm prots are distributed to both household types based on their population shares, i.e. Ψbt = χZtf irm and Ψst = (1 − χ)Ztf irm . Bank prots on the other hand are only distributed to savers, which own the deposits by which banks nance themselves. 65 Hence, we have that ψtb = 0 and ψts = Zt . The optimal consumption path for an individual of type j has to satisfy the standard Euler-equation         U 0 Ctj ζt = β j 1 + ijt Et Π−1 t+1 U 0 j Ct+1 ζt+1 (95) Optimal labor supply has to satisfy the intratemporal trade-o between consumption and labor 66   V 0 Ntj Wj   = t (96) U 0 Ctj Pt Finally, optimal holdings of money have to satisfy 67 ! j M t Ω0   Pt ijt + S 0 Mtj   = (97) U 0 Ctj 1 + ijt The lower bound on the deposit rate is is typically dened as the lowest value of ist satisfying equation (97). The lower bound therefore depends crucially on the marginal storage cost. With the existence of a satiation point in real money balances, zero (or constant) storage costs imply S 0 (Mts ) = 0 and is = 0. That is, the deposit rate is bounded at exactly zero. With a non-zero marginal storage cost however, this is no longer the case. If storage cost are convex, for instance, the marginal storage cost is increasing in Mts . In this case, there is no lower bound. Based on the data from Section 3.2.1, a reasonable assumption is that the deposit rate is bounded at some value close to zero. This is consistent with a proportional storage cost S (Mts ) = γMts , with a small γ > 0. We therefore assume proportional storage costs for the rest of the paper, in which the lower bound on deposit rates is given by is = −γ . 65 Distributing bank prots to both household types would make negative interest rates even more contractionary. The reduction in bank prots would reduce the transfer income of borrower households, causing them to reduce consumption. We believe this eect to be of second order signicance, and so we abstract from it here. 66 We assume that the function V is increasing in N and convex with well dened rst and second derivatives. 67 We assume a satiation point for money. That is, at some level ¯j m households become satiated in real money balances, and so Ω0 (m ¯ j) = 0. 117 We assume that households have exponential preferences over consumption, i.e. U (Ctj ) = 1 − exp{−qCtj } for some q > 0. The assumption of exponential utility is made for simplicity, as it facilitates aggregation across agents. Under these assumptions, the labor-consumption trade-o can easily be aggregated into an economy-wide labor market condition 68 V 0 (Nt ) Wt = (98) U 0 (Ct ) Pt Letting Gt denote government spending, aggregate demand is given by Yt = χCtb + (1 − χ) Cts + Gt (99) Firms Each good i is produced by a rm i. Production is linear in labor, i.e. Yt (i) = Nt (i) (100) where Nt (i) is a Cobb-Douglas composite of labor from borrowers and savers respectively, i.e. Nt (i) =  χ 1−χ Ntb (i) (Nts (i)) , as in Benigno, Eggertsson, and Romei (2014). This ensures that each type of labor receives a total compensation equal to a xed share of total labor expenses. That is, Wtb Ntb = χWt Nt (101) Wts Nts = (1 − χ) Wt Nt (102) χ 1−χ R1 where Wt = Wtb (Wts ) and Nt = 0 Nt (i) di. Given preferences, rms face a downward-sloping demand function  −θ Pt (i) Yt (i) = Yt (103) Pt 68 To see this, just take the weighted average of equation (96) using the population shares χ and 1−χ as the respective weights. 118 We introduce nominal rigidities by assuming Calvo-pricing. That is, in each period, a fraction α of rms are not able to reset their price. Thus, the likelihood that a price set in period t applies in period T >t is αT −t . Prices are assumed to be indexed to the ination target Π. A rm that is allowed to reset their price in period t sets the price to maximize the present value of discounted prots in the event that the price remains xed. That is, each rm i choose Pt (i) to maximize ∞   X T −t Pt (i) WT Et (αβ) λT ΠT −t YT (i) − YT (i) (104) PT PT T =t   where λT ≡ q χ exp −qCTb + (1 − χ) exp {−qCTs } , which is the weighted marginal utility of consump- tion and β ≡ χβ b + (1 − χ) β s . θ Denoting the markup as µ≡ , rms set the price as a markup over the average of expected marginal θ−1 costs during the periods the price is expected to remain in place. That is, the rst-order condition for the ∗ optimal price P (i)t for rm i is ( θ )  P∞ PT 1 T −tWT Et T =t (αβ) λT YT ∗ P (i)t Pt ΠT −t PT =µ ( θ−1 ) (105) Pt P∞ T −t  PT 1 WT Et T =t (αβ) λT YT Pt ΠT −t PT This implies a law of motion for the aggregate price level Pt1−θ = (1 − α) Pt∗1−θ + αPt−1 1−θ 1−θ Π (106) where Pt∗ is the optimal price from equation (105), taking into account that in equilibrium Pt∗ (i) is identical for all i. We denote this price Pt∗ . Since prices are sticky, there exists price dispersion which we denote by Z 1  −θ Pt (i) ∆t ≡ di (107) 0 Pt with the law of motion θ   θ−1  θ−1 Πt  θ 1−α Πt  Π  ∆t = α ∆t−1 + (1 − α)  (108)   Π 1−α    119 (N j )1+η We assume that the disutility of labor takes the form V (Ntj ) = 1+η . We can then combine equations (105) - (108), together with the aggregate labor-consumption trade-o (equation (98)) to get an aggregate Phillips curve of the following form: 1   θ−1  θ−1 Πt 1 − α Π  Ft = (109)   1−α Kt     where (  θ−1 ) Πt+1 Ft = λt Yt + αβEt Ft+1 (110) Π and ( θ ) λt ∆ηt Yt1+η  Πt+1 Kt = µ + αβEt Kt+1 (111) z exp {−zYt } Π and λT ≡ z χ exp −qCTb + (1 − χ) exp {−qCTs }   (112)  −θ Pt (i) Since every rm faces demand Y (i) = Yt and Yt (i) = Nt (i), we can integrate over all rms Pt to get that Nt = ∆t Yt (113) Banks Our banking sector is made up of identical, perfectly competitive banks. Bank assets consist of one-period Mt real loans lt . In addition to loans, banks hold real reserves Rt ≥ 0 and real money balances mt = ≥ 0, Pt both issued by the central bank. 69 Bank liabilities consist of real deposits dt . Reserves are remunerated at the interest rate irt , which is set by the central bank. Loans earn a return ibt . The cost of funds, i.e. the deposit rate, is denoted ist . Banks take all of these interest-rates as given. Financial intermediation takes up real resources. Therefore, in equilibrium there is a spread between the deposit rate ist and the lending rate ibt . We assume that banks' intermediation costs are given by a function 69 Because we treat the bank problem as static - as outlined below - we can express the maximization problem in real terms. 120 Zt Γ (lt , Rt , mt , zt ), in which zt = is real bank prot. Pt We assume that the intermediation costs are increasing and convex in the amount of real loans provided. That is, Γl > 0 and Γll ≥ 0. Central bank currency plays a key role in reducing intermediation costs. 70 The marginal cost reductions from holding reserves and money are captured by ΓR ≤ 0 and Γm ≤ 0 respectively. We assume that the bank becomes satiated in reserves for some level ¯. R That is, ΓR = 0 for ¯. R ≥ R Similarly, banks become satiated in money at some level m ¯, so that Γm = 0 for m≥m ¯. Banks can thus reduce their intermediation costs by holding reserves and/or cash, but the opportunity for cost reduction can be exhausted. Finally, we assume that higher prots (weakly) reduce the marginal cost of lending. That is, we assume Γlz ≤ 0. We discuss this assumption below. Following Curdia and Woodford (2011) and Benigno, Eggertsson, and Romei (2014) we assume that any real prots from the bank's asset holdings are distributed to their owners in period t and that the bank holds exactly enough assets at the end of the period to pay o the depositors in period t + 1.71 Furthermore, we assume that storage costs of money are proportional and given by S (M ) = γM . Under these assumptions, real bank prots can be implicitly expressed as: ibt − ist is − irt is + γ zt = s lt − t s Rt − t s mt − Γ (lt , Rt , mt , zt ) (114) 1 + it 1 + it 1 + it Any interior lt , Rt and mt have to satisfy the respective rst-order conditions from the bank's optimization problem 72 ibt − ist lt : = Γl (lt , Rt , mt , zt ) (115) 1 + ist is − irt Rt : −ΓR (lt , Rt , mt , zt ) = t (116) 1 + ist is + γ mt : −Γm (lt , Rt , mt , zt ) = t s (117) 1 + it The rst-order condition for real loans says that the banks trade o the marginal prots from lending with the marginal increase in intermediation costs. The next two rst-order conditions describe banks demand for 70 For example, we can think about this as capturing in a reduced form way the liquidity risk that banks face. When banks provide loans, they take on costly liquidity risk because the deposits created when the loans are made have a stochastic point of withdrawal. More reserves helps reduce this expected cost. 71 The latter is equivalent to assuming that 1 + ibt lt + (1 + irt ) Rt + mt − S (mt ) = (1 + ist ) dt .    72 Assuming lt that Γ , R t , mt , z t is such that there exists a unique z solving equation (114). lt 121 reserves and cash. We assume that reserves and money are not perfect substitutes, and so minimizing the intermediation cost implies holding both reserves and money. This is not important for our main result. 73 The rst-order condition for loans pins down the equilibrium credit spread ωt dened as 1 + ibt ib − ist ωt ≡ s −1= t (118) 1 + it 1 + ist Specically, it says that ωt = Γl bbt , Rt , mt , zt  (119) where we have used the market clearing condition in equation (120) to express the spread as a function of the borrowers real debt holdings bbt . lt = χbbt (120) That is, the dierence between the borrowing rate and the deposit rate is an increasing function of the aggregate relative debt level, and a decreasing function of banks' net worth. Why do bank prots aect intermediation costs? We have assumed that the marginal cost of ex- tending loans (weakly) decreases with bank prots. That is, Γlz ≤ 0. This assumption captures, in a reduced form manner, the established link between banks' net worth and their operational costs. We do not make an attempt to microfound this assumption here, which is explicitly done in among others Holmstrom and Tirole (1997) and Gertler and Kiyotaki (2010). 74 In Gertler and Kiyotaki (2010) bank managers may divert funds, which means that banks must satisfy an incentive compatibility constraint in order to obtain external nancing. This constraint limits the amount of outside funding the bank can obtain based on the banks net worth. Because credit supply is determined by the total amount of internal and external funding, this means that bank lending depends on bank prots. In an early contribution, Holmstrom and Tirole (1997) achieve a similar link between credit supply and bank net worth by giving banks the opportunity to engage (or not engage) in costly monitoring of its non-nancial 73 The assumption that banks always wants to hold some reserves is however important for the eect of negative interest rates on bank protability. If we instead assume that the sum of money holdings and reserves enters the banks cost function as one argument, the bank would hold only money once ir < −γ . Hence, reducing the interest rate on reserves further would not aect bank prots. However, such a collapse in central bank reserves is not consistent with data, suggesting that banks want to hold some (excess) reserves. 74 Another way to interpret the implied link between bank prots and credit supply is to include a capital requirement. In Gerali, Neri, Sessa, and Signoretti (2010) a reduction in bank prots reduces the banks' capital ratio. In order to recapitalize the bank lowers credit supply. 122 borrowers. For recent empirical evidence on the relevance of bank net worth in explaining credit supply, see for example Jiménez, Ongena, Peydró, and Saurina (2012). Importantly, our main result is that negative interest rates are not expansionary. This does not depend on prots aecting intermediation costs. However, the link between prots and the intermediation cost is the driving force behind negative interest rates being contractionary. If we turn o this mechanism, negative interest rates still reduce bank prots, but this does not feed back into aggregate demand. Government The consolidated government budget constraint is given by Btg + Mttot + Pt Rt = (1 + igt−1 )Bt−1 g tot + Mt−1 + (1 + irt−1 )Pt Rt−1 + Gt − Tt (121) where Btg is one period government debt, Mttot = Mt + Mts + Mtb is total money supply - which is the sum of money held by banks and each household type, igt is the one period risk-free rate on government debt, Gt is government spending, and Tt = χTtb + (1 − χ) Tts is the weighted sum of taxes on the two household types. The conventional way of dening monetary and scal policy, abstracting from reserves and the banking sector (see e.g. Woodford 2003), is to say that scal policy is the determination of end of period government liabilities, i.e. Btg + Mttot , via the scal policy choice of Gt and Tt . Monetary policy on the other hand, determines the split of end of period government liabilities Btg and Mttot , via open market operations. This g in turn determines the risk-free nominal interest rate it through the money demand equations of the agents in the economy. The traditional assumption then, is that the one period risk-free rate on government debt corresponds to the policy rate which the monetary authority controls via the supply of money through the money demand equation. We dene monetary and scal policy in a similar way here. Fiscal policy is the choice of scal spending Gt and taxes Tt . This choice determines total government liabilities at the end of period t  the left hand side of equation (121). Total government liabilities are now composed of public debt and the money holdings of each agent, as well as reserves held at the central bank. Again, monetary policy is dened by how total government liabilities is split between government bonds Btg , and the overall supply of central bank issuance. r In addition, we assume that the central bank sets the interest rate on reserves it . The supply of central bank currency is then given by 123 CBCt = Pt Rt + Mt + Mts + Mtb (122) Given these assumptions, the nancial sector itself determines the allocation between reserves and money. That is, the split between the money holdings of dierent agents and reserves held by banks is an endogenous market outcome determined by the rst order conditions of banks and households. In order to clarify the discussion, it is helpful to review two policy regimes observed in the US at dierent times. Consider rst the institutional arrangement in the US prior to the crisis, when the Federal Reserve paid no interest on reserves, so that irt = 0. As seen from equation (116), this implies that banks were not satiated in reserves. The policy maker then chose CBCt so as to ensure that the risk-free rate was equal to its target. In this more general model, the policy rate is simply the risk-free nominal interest rate, which is equal to the deposit rate and, assuming that depositors can also hold government bonds, the interest rate paid on one period government bonds, i.e. ist = igt . Consider now an alternative institutional arrangement, in which paying interest on reserves is a policy tool. Such a regime seems like a good description of the post-crisis monetary policy operations, both in the US and elsewhere. The central bank now sets the interest rate on reserves equal to the risk-free rate, i.e. irt = ist = igt , and chooses CBCt to implement its desired target. From the rst order condition for reserves (116), we see that ist = irt implies that ΓR = 0 . Hence, as long as banks are satiated in reserves, the central bank implicitly controls ist via irt . A key point, however, is that ΓR = 0 is not always feasible due to the lower bound on the deposit rate. If the deposit rate is bounded at is = −γ , and the central bank lowers irt below −γ , then ist > irt . The rst order condition then implies ΓR > 0. Intuitively, it is not possible to keep banks satiated in reserves when they are being charged for their reserve holdings. More explicitly, we assume that the interest rate on reserves follows a Taylor rule given by equation (123). Because of the reserve management policy outlined above, the deposit rate in equilibrium is either equal to the reserve rate or to the lower bound, as specied in equation (124). irt = rtn Πφt π YtφY (123) ist = max {is , irt } (124) 124 Equilibrium Non-linear Equilibrium Conditions Denition 14. The non-linear equilibrium is dened as a sequence of 17 endogenous quantities {Ctb , Cts , bbt , mbt , mst , τts , cbct , Yt , Πt , Ft , Kt , ∆t , λt , lt , Rt , mt , zt }∞ t=0  s b r ∞ and three prices it , it , it which satisfy equations (125)- (144), t=0 ∞ for given initial conditions ∆0 , bb0 and a sequence of shocks {ζt }t=0 . (125) n o    n o exp −qCtb ζt = β b 1 + ibt Et Π−1 b t+1 exp −qCt+1 ζt+1 exp {−qCts } ζt = β s (1 + ist ) Et Π−1 s  t+1 exp {−qCt+1 } ζt+1 (126) Ctb + mbt + 1 + ibt−1 b Πt bt−1 = χYt + 1−γ b Πt mt−1 + bbt (127) Ω0 mbt (128)  ibt + γ  = U 0 Ctb 1 + ibt Ω0 (mst ) 0 s U (Ct ) is + γ = t s 1 + it (129) Πt cbct = cbct−1 + irt−1 Rt−1 − Πt τts (130) cbct = Rt + mt + mst + mbt (131) Yt = χCtb + (1 − χ) Cts (132)  1  θ−1  θ−1 Πt 1 − α Π Ft (133)   =   1−α Kt     ( θ−1 ) (134)  Πt+1 Ft = λt Yt + αβEt Ft+1 Π ( θ ) λt ∆ηt Yt1+η (135)  Πt+1 Kt = µ + αβEt Kt+1 q exp {−qYt } Π (136)  n o  λt = q χ exp −qCtb + (1 − χ) exp {−qCts } 125  θ  θ−1  θ−1 Πt θ 1 − α (137)  Πt  Π  ∆t = α ∆t−1 + (1 − α)    Π 1−α    zt = ibt − ist 1 + it s t is − irt l − t 1 + its is + γ Rt − t s mt − Γ (lt , Rt , mt , zt ) 1 + it (138) ibt − ist 1 + ist = Γl (lt , Rt , mt , zt ) (139) is − irt −ΓR (lt , Rt , mt , zt ) = t 1 + ist (140) is + γ −Γm (lt , Rt , mt , zt ) = t s 1 + it (141) irt = rtn Πφt π YtφY (142) ist = max {−γ, irt } (143) lt = χbbt (144) Steady state We denote the steady-state value of a variable Xt as X. First, observe that in steady-state ination is at the ination target Π . As a result, there is no price dispersion (∆ = 1). Combining this with the Phillips curve, we have that steady-state output is pinned down by the following equation Yη µ =1 (145) q exp {−qY } From the Euler equation of a household of type j we have that Π 1 + ij = (146) βj Using the steady-state interest rates, we can jointly solve for all bank-variables. Notice that in steady- state banks are satiated in reserves, and so R=R by assumption. Furthermore, if the intermediation cost function is additive between money and the other arguments (which we assume, see below), the steady-state level of money holdings for banks is independent of other bank variables. Therefore, only bank prots and bank lending have to be solved jointly. 126 Given total debt and interest rates, the borrowers budget constraint and money demand can be solved for steady state consumption and money holdings: Π − 1 − ib b Π − 1 + γ b C b = χY + b − m (147) Π Π 0 ib + γ 0 b  Ω (mb ) = U C (148) 1 + ib Then, using the aggregate resource constraint we have that 1 − χ2 Π − 1 − ib b Π − 1 + γ b   s χ C = Y + b − m (149) 1−χ 1−χ Π Π The savers money demand follows from 0 is + γ 0 s Ω (ms ) = U (C ) (150) 1 + is Finally, given the steady-state holdings of reserves and real money balances we can use the total money supply equation and the consolidated government budget constraint to solve for the remaining variables. Log-linearized equilibrium conditions Xt −X We log linearize the non-linear equilibrium conditions around steady state, and dene ˆ≡ x X . For the intermediation cost function we assume the following functional form  ltν zt−ι + 1 Rt − R 2 + 1 (mt − m)2    if Rt < R and mt < m Γ (lt , Rt , mt , zt ) = 2 2 (151) lν z −ι  if Rt ≥ R and mt ≥ m t t  The system of non-linear equations can be simplied by aggregating the production side and inserting rm and bank prots into the respective budget constraints, in addition to the government budget constraint. Log-linearizing around the unique steady states leaves us with the nal approximate equilibrium dened below. Denition 15. The approximate equilibrium is dened as a sequence of 10 endogenous quantities n o n o∞ Cˆtb , Cˆts , Yˆt , ˆbbt , π ˆt , ω ˆt ˆ t , zˆt , rˆtn , R ˆt, m and three prices ˆibt , ˆist , ˆirt t=0 n o∞ which satisfy equations in Table (3.5), for a given sequence of shocks ζˆt . t=0 127 χC b ˆ b (1 − χ)C s ˆ s Yˆt = Ct + Ct (152) Y  Y  Cˆtb = Et Cˆt+1 b ˆt+1 − ζˆt + Et ζˆt+1 − σ ˆibt − Et π (153)   Cˆts = Et Cˆt+1 s ˆt+1 − ζˆt + Et ζˆt+1 − σ ˆist − Et π (154) ˆb ˆb cb ˆ b ˆbb = bt + it−1 − π ˆt + y Ct − χ b Yˆt (155) t b b b πβ πβ b b ˆt = κYˆt + βEt π π ˆt+1 (156) ˆibt = ˆist + ω ˆt (157) ω ˆt = ω(ν − 1)ˆbbt − ιωˆ zt (158) m − m 1 − is − γ m ˆt = (159) m is + γ b χb (1 + ω) ˆb d ˆist + R ˆir zˆt = it − (160) b ωχb + (1 − ι)Γ b ωχb + (1 − ι)Γ ωχb + (1 − ι)Γ t b ˆist = ˆirt − RRˆt (161) rˆtn = ζˆt − Et ζˆt+1 − χˆωt (162) ˆirt n = rˆt + φπ π ˆt + φY Yˆt (163) n o ˆist = max isbound , ˆirt (164) Table 3.5: Summary of log linearized equilibrium conditions. Appendix D: Calibration We pick the size of the preference shock to generate an approximately 4.5 percent drop in output on impact. This reduction in output is chosen to roughly mimic the average reduction in real GDP in Sweden, Denmark, Switzerland and the Euro Area in the aftermath of the nancial crisis, as illustrated in Figure 3.22. 75 The drop in output in the US was of similar order. The persistence of the preference shock is set to generate a duration of the lower bound of approximately 12 quarters. We choose parameters from the existing literature whenever possible. We target a real borrowing rate of 4 % 76 and a real deposit rate of 1.5 %, yielding a steady state credit spread of 2.5 %. The preference parameter q is set to 0.75, which generates an intertemporal elasticity of substitution of approximately 2.75, in line with Curdia and Woodford (2011). We set the 75 Detrended real GDP fell sharply from 2008 to 2009, before partially recovering in 2010 and 2011. The partial recovery was suciently strong to induce an interest rate increase. We focus on the second period of falling real GDP (which occurred after 2011), as negative interest rates were not implemented until 2014-2015. Targeting a reduction in real GDP of 4.5 percent is especially appropriate for the Euro Area and Sweden. Real GDP fell by somewhat less in Denmark, and considerably less in Switzerland. This is consistent with the central banks in the Euro Area and Sweden implementing negative rates because of weak economic activity, and the central banks in Denmark and Switzerland implementing negative rates to stabilize their exchange rates. 76 This is consistent with the average xed-rate mortgage rate from 2010-2017. Series MORTGAGE30US in the St.Louis Fed's FRED database. 128 proportional storage cost to 0.01, yielding an eective lower bound of - 0.01 %. This is consistent with the deposit rate being bounded at zero for most types of deposits, with the exception of slightly negative rates on corporate deposits in some countries. We set R = 0.07, which yields steady-state reserve holdings in line with average excess reserves relative to total assets for commercial banks from January 2010 and until April 2017. 77 We set m = 0.01, implying that currency held by banks in steady state accounts for approximately 1.5 percent of total assets. This currency amount corresponds to the dierence between total cash assets reported at US banks and total excess reserves from January 2010 until April 2017. The parameter ν measures the sensitivity of the credit spread to private debt. We set ν so that a 1 % increase in private debt increases the credit spread by 0.12 %, as in Benigno, Eggertsson, and Romei (2014). The nal parameter is ι. In our baseline scenario we set ι = 0.88 which would generate an increase in average borrowing rates in negative territory consistent with Figure 3.9 in the main text. While ι is not important for our main result that negative interest rates are not expansionary, it is important for determining the feedback eect from bank prots to aggregate demand. All parameter values are summarized in Table 3.6. Due to the occasionally binding constraint on ist , we solve the model using OccBin (Guerrieri and Iacoviello, 2015) for the preference shock. For simplicity, we consider a cashless limit for the household's problem. 78 77 We use series EXCSRESNS for excess reserves and TLAACBW027SBOG for total assets from commercial banks, both in the St.Louis Fed's FRED database. 78 There are no additional insights provided by allowing households to hold money in the numerical experiments, even if this feature of the model was essential in deriving the bound on deposits. 129 Parameter Value Source/Target Inverse of Frisch elasticity of labor supply η=1 Justiniano et.al (2015) Preference parameter q = 0.75 Yields IES of 2.75(Curdia and Woodford, 2011) Share of borrowers χ = 0.61 Justiniano et.al (2015) Steady-state gross ination rate Π = 1.005 Match annual ination target of 2% Discount factor, saver β s = 0.9901 Annual real savings rate of 1.5 % Discount factor, borrower β b = 0.9963 Annual real borrowing rate of 4% Probability of resetting price α = 2/3 Gali (2008) Taylor coecient on ination gap φΠ = 1.5 Gali (2008) Taylor coecient on output gap φY = 0.5/4 Gali (2008) Elasticity of substitution among varieties of goods θ = 7.88 Rotemberg and Woodford (1997) Proportional storage cost of cash γ = 0.01 % Eective lower bound ist = −0.01% 130 Reserve satiation point R = 0.07 Target steady-state reserves/total assets of 13 % Money satiation points m = 0.01 Target steady-state cash/total assets of 1.5 % Marginal intermediation cost parameters ν=6 Benigno, Eggertsson, and Romei (2014) Level of safe debt l = 1.3 Target debt/GDP ratio of 95 % Link between prots and intermediation costs ι = 0.88 1 % increase in prots ≈ 0.01 % reduction in credit spread Shock Value Source/Target Preference shock 2.5 % temporary decrease in ζt Generate a 4.5 % drop in output on impact Persistence of preference shock ρ = 0.9 Duration of lower bound of 12 quarters Table 3.6: Parameter values. Chapter 4 4 The Saving and Employment Eects of Higher Job Loss Risk 4.1 Introduction Saving rates tend to increase during recessions, and the increase following the recent nancial crisis was especially large and long-lived. This has sparked a new interest in both the determinants and eects of higher saving rates during periods of economic distress. Policymakers and academics have linked the increase in savings to higher economic uncertainty. As future income becomes more volatile  for instance due to higher job loss risk  people may become less willing to consume today. The reduction in consumption implies a reduction in aggregate demand, making the increase in savings a potential amplier of economic downturns. A recent theoretical literature emphasizes the importance of higher savings in response to increased job loss risk in amplifying economic downturns (Bayer, Lütticke, Pham-Do, and Tjaden 2015, Challe and Ragot 2016, Challe, Matheron, Ragot, and Rubio-Ramirez 2017, Ravn and Sterk 2016, Ravn and Sterk 2017). However, little is known about the empirical eect of job loss risk on savings during periods of economic distress. Estimating this eect is challenging, as it requires both an exogenous increase in job loss risk and a strategy to isolate the impact of risk from other recession eects. Further, evaluating whether the saving response reduces overall employment through the household demand channel requires a strategy to separate the general equilibrium eects of higher household savings from other forces aecting employment. In this paper we use administrative panel data from Norway and a novel natural experiment to study the impact of higher job loss risk on savings. The sudden collapse of the international oil price in 2014 led to an exogenous increase in risk for certain occupations and regions. Using our individual level data, we can compare workers who live in the same area, but who are subject to dierent changes in job loss risk, allowing us to separate the eect of higher job loss risk from other local recession eects. We nd that a one percentage point increase in job loss risk increases liquid savings by 1.2 - 2.0 percent. In order to evaluate the aggregate demand eects of higher savings, we focus on employment in industries not directly aected by the oil price collapse. After accounting for lower demand from directly aected industries, we document that non-tradable sector employment declines more in regions in which the increase in individual savings is larger  consistent with the household demand channel. The tax data includes information on income and wealth, and can be merged with labor market data as of 2000. We thus have detailed information on labor market status and occupation, which will be important 131 in identifying individual level job loss risk. We use the 2014 oil price collapse to obtain an exogenous increase in risk which diers across occupations. The occupational group with the largest increase in job loss risk is engineers. As engineers have at least 1 - 3 years of higher education, we compare engineers to other high skilled workers in order to obtain a suitable control group. Prior to the oil price collapse, engineers and other high skilled workers have similar levels of job loss risk, averaging roughly one percent per year. Following the oil price collapse, job loss risk for engineers increases sixfold, while job loss risk for other high skilled workers increases only moderately. As a robustness exercise, we also use an alternative control group consisting of high skilled government workers, who did not experience any increase in job loss risk. In order to control for other local recession eects which potentially aect savings, we start by comparing individuals with dierent changes in job loss risk, but who live in the same area, in a dynamic dierence in dierence regression. Specically, we dene the oil region to be the two counties in the South-West of Norway which employ an unproportionally high share of oil workers. By comparing engineers and other high skilled workers who live in the oil region, we can control for any local recession eects  such as falling house prices  which are common across these two groups. In order to evaluate the sign and the magnitude of other local recession eects, we compare the baseline results to an alternative specication in which the control group consists of high skilled individuals not residing in oil counties. The results show an annual increase in savings for engineers relative to other high skilled workers of roughly $1,200, or three and a half percent. Scaling this by the increase in job loss risk, we nd that a one percentage point increase in job loss risk increases savings by 1.2 percent. Reassuringly, the increase in savings is driven by low-tenured engineers, who experienced the largest increase in job loss risk. Looking only at low-tenured individuals, the increase in savings for every one percentage point increase in job loss risk rises to 1.5 - 2.0 percent. Not controlling for local recession eects has a moderate, but positive impact on the results. This suggests that, if anything, not accounting for other recession eects would cause us to overstate the impact of job loss risk on savings. When investigating the relevance of the household demand channel, we aggregate the outcome variables to the municipality level and categorize municipalities based on their share of oil sector engineers. We restrict the sample to the municipalities within the oil region. Not surprisingly, municipalities with a higher number of aected individuals experience an increase in average savings. In order to evaluate the overall employment impact of higher savings, we consider industries not directly aected by the shock. We nd that non-oil sector unemployment increases more in the municipalities with a higher share of oil sector engineers, especially in the non-tradable sectors  assumed to be the most sensitive to local household demand. 132 Identifying the general equilibrium eects of the risk induced increase in savings on employment is challenging, as there are several factors at work. We attempt a rough decomposition of the increase in non- oil sector unemployment, considering three channels likely to be important. First, a negative shock to the oil sector implies lower demand for the rms producing inputs to the oil sector. Second, household demand is likely to be lower due to i) more people becoming unemployed and reducing consumption as a result of lower income, and ii) people reducing consumption in order to save more as a result of higher job loss risk. We account for lower rm demand by using input output data and network analysis from Acemoglu, Akcigit, and Kerr (2016). While lower rm demand can fully explain the unemployment increase in the tradable sector, it cannot fully explain the unemployment increase in the non -tradable sectors  suggesting that some of the increase in unemployment is due to lower household demand. While we do not have an identication strategy to separate the impact of lower consumption resulting from realized unemployment from lower consumption resulting from higher job loss risk, we argue that the latter is quantitatively more important. Back of the envelope calculations suggest that the total consumption loss resulting from the risk channel is about four times as large as the total consumption loss resulting from realized unemployment. The reason being that, although unemployed individuals have larger consumption declines, there are relatively few of them compared to the many aected workers who keep their jobs but face an increase in risk. As a result, the decomposition exercise suggests that higher job loss risk is an important driver of increased unemployment in the non-tradable sectors. We thus conclude that the data is consistent with a risk induced increase in individual savings having a negative impact on employment. 4.1.1 Literature review Several papers study the connection between job loss risk and savings. Most of these papers do not focus on economic downturns specically, and use either subjective unemployment beliefs (Guiso, Jappelli, and Terlizzese (1992), Carroll and Dunn (1997), Lusardi (1998)) or future unemployment spells (Chetty and Szeidl (2007), Basten, Fagereng, and Telle (2016), Hendren (2017)) to capture job loss risk. This has the benet of not confounding the impact of risk with other recession eects, but does not necessarily capture the impact of job loss risk on savings conditional on macroeconomic distress. In order to address endogeneity concerns, this literature has often used mass layos to control for within-rm selection into unemployment (see for example Basten, Fagereng, and Telle (2016)). However, as pointed out by Hilger (2016), this does not control for potential across-rm selection. In order to obtain an exogenous increase in job loss risk, Fuchs-Schündeln and Schündeln (2005) use 133 the German reunication as a natural experiment. The German reunication implied a permanent and once-in-a-lifetime reassignment of job loss risk across occupations however, and is therefore less relevant for understanding the implications of business cycle variations in job loss risk. An alternative approach is to instrument for (changes in) job loss risk with variables such as region of residence, occupation, sector and demographic characteristics. This approach is taken in Carroll, Dynan, and Krane (2003) and Harmenberg and Oberg (2016). Due to the many variables used as instruments, it is not clear exactly what is driving the variation in risk. However, given that region and occupation are important determinants, the exercise may be conceptually similar to the one in this paper. We expand upon the analysis in these papers by separating the impact of job loss risk from other local recession eects, such as falling house prices etc. Our analysis is also related to papers which use VARs to identify the impact of dierent types of uncer- tainty shocks on consumption and output, such as Alexopoulos, Cohen, et al. (2009), Jurado, Ludvigson, and Ng (2015), Fernández-Villaverde, Guerrón-Quintana, Kuester, and Rubio-Ramírez (2015), Leduc and Liu (2016), Larsen (2017) and Basu and Bundick (2017). Basu and Bundick (2017) show that an uncertainty shock decreases both consumption and output, and develop a model in which output falls due to an increase in desired savings. We complement their analysis, by providing micro-level evidence in favor of this mecha- nism. Note that the VAR exercise cannot rule out that output falls as a direct response to the shock, and that this reduces employment and hence consumption. We contribute to this literature by directly showing that savings increase in response to higher uncertainty, and that this increase occurs prior to the employment fall. Further, we explicitly account for intersectoral linkages and show that the employment fall is found in non-tradable sectors only, supporting the household demand channel. Finally, our paper relates to a literature which uses cross-sectional variation to uncover evidence on the local household demand channel. Mian and Su (2014) show that employment in the non-tradable sector declines in response to a fall in housing net worth, while Verner and Gyongyosi (2018) show that employment in non-exporting rms declines in response to an increase in household debt resulting from a sudden currency crisis. In addition to studying an uncertainty shock rather than a net wealth shock, we contribute to this literature by considering savings directly and documenting that the saving response precedes the employment decline - thereby oering further support for the household demand channel. 4.2 Data and institutional background We use administrative data which covers the universe of Norwegian tax lers. The main outcome variable is liquid savings, measured by bank deposits. However, we also consider other nancial assets. The tax data 134 can be merged with labor market data as of 2000, providing us with detailed information on labor market status and occupation. The latter will be important in identifying which individuals experience an increase in job loss risk. The tax data is a panel data set, covering the period 1993 to 2015. The data is annual, and variables are measured at the end of the year. It contains information on income from dierent sources, including transfers and taxes. We dene individuals as unemployed if they receive unemployment insurance in a given year. In addition to income data, there is also rich information on household wealth. We observe nancial wealth in the form of bank deposits and other nancial assets. Real wealth is reported as primary housing wealth, secondary housing wealth and other real wealth. Prior to 2010 the value of real wealth which is reported for tax purposes is substantially below market value. From 2010 and onward, eorts are made to correctly report the market value of housing wealth. The data set also contains information on total debt, allowing us to back out net wealth. Our main outcome variable is liquid savings, measured by bank deposits. As bank deposits is a highly liquid and safe nancial asset, it seems like a good candidate for precautionary saving. However, we will also consider any adjustments that come through other nancial assets or real wealth. Bank deposits are reported by the bank, and include saving accounts, checking accounts, xed term deposits etc. Bank deposits do not include investments in bonds and direct and indirect holdings of stocks, which belong to other nancial assets. Close to 100 percent of the sample have some positive holdings of bank deposits in a given year, while a substantially lower share own other nancial assets or real wealth. Income is reported and taxed individually in Norway, whereas wealth is reported individually and taxed at the household level. Our unit of analysis is the individual, and so we cannot rule out that there is some misreporting of wealth within the household. However, we expect bank deposits to be relatively well measured also at the individual level, as it is reported by the bank and must be reported as belonging to the owner of the bank account. We follow much of the existing literature in focusing exclusively on men (see for example Basten, Fagereng, and Telle (2016)). The tax data can be merged with labor market data as of 2000. Our full data set therefore covers the period 2000 to 2015. From the labor market data we obtain detailed information on occupation and sector, which is important for our identication strategy. The matched rm-worker data also allows us to calculate the observed tenure for each worker, which will be useful for identifying the groups with especially large increases in job loss risk. Occupation is only observed for employed individuals, and there are some instances of employed individ- 135 uals not having a reported occupation. We therefore dene an individual as belonging to an occupation o if we observe the individual as being employed in that occupation for at least one of the three years leading up to the shock. Similarly, the unemployment rate for an occupation o is dened as the unemployment rate for individuals in that occupation. We use the same type of assignment rule for assigning workers to a sector, and for calculating sector level unemployment rates. We divide employed individuals into three occupational groups. The rst group consists of engineers and civil engineers. The former requires 1-3 years of higher education, whereas the latter requires a minimum of four years higher education. The second group consists of individuals who are employed in occupations requiring some higher education, and who are not engineers. We refer to this group as other high skilled workers. Managers, professionals, technicians and associate professionals belong to this group. In total, close to 50 percent of employed individuals are categorized as being either engineers or other high skilled workers. The remaining working individuals are employed in occupations which do not require higher education, and are referred to as low skilled. In addition to only using men, we make some further sample restrictions. First, we use a 25 percent random sample of the tax ling population. Second, we exclude individuals with business income in order to obtain a well dened concept of job loss risk. Third, we only include individuals who are employed at baseline and who can be matched to an occupation in one of the three years leading up to the shock. We also winsorize the variables at the 99 percent level, following Basten, Fagereng, and Telle (2016) who also use administrative data from Norway. Summary statistics for the three occupational groups are reported in Table 4.1. Nearly everyone owns some bank deposits, although the average and median holdings are substantially larger for high skilled workers than for low skilled workers. Engineers and other high skilled workers hold similar amounts. Among the high skilled, just above 60 percent own other nancial assets, and other high skilled workers own somewhat more of these assets than engineers. As there is a substantial share of managers in this group, this could perhaps reect that some of the labor compensation takes the form of nancial assets. Among the low skilled, less than 40 percent own other nancial assets. Also note that these other nancial assets appear relatively skewed, with average holdings far exceeding median holdings. Engineers and other high skilled workers also look similar in terms of real wealth. Exactly 76 percent in both groups are homeowners, compared to less than 50 percent for low skilled workers. Just above 70 percent in both groups have positive net wealth. The average wage income among engineers is roughly $95,000, which is somewhat higher than for other high skilled workers, and substantially higher than for low skilled workers. 136 High skilled workers are older than low skilled workers, but engineers and other high skilled workers have similar average and median ages at 44 to 45 years. We thus conclude that engineers and other high skilled workers look fairly similar along observable characteristics, and that both groups have substantially higher wealth and income levels than low skilled workers. For this reason, we restrict the analysis to a comparison of engineers and other high skilled workers. Average Median Engineers High Skilled Low Skilled Engineers High Skilled Low Skilled Bank Deposits 35,900 34,700 19,600 14,200 11,500 5,600 Other Financial Assets 23,800 43,000 11,300 1,600 1,600 0 Prim. Housing Wealth 233,100 252,000 134,100 227,500 238,500 0 Other Real Wealth 44,600 52,300 23,200 8,300 7,700 100 Debt 183,600 197,400 104,200 153,200 161,000 33,200 Wage Income 94,600 85,600 55,400 90,300 78,800 55,600 Age 44 45 38 44 45 37 Bank Deposits > 0 99 99 98 Other Fin. Assets > 0 61 64 39 Housing Wealth > 0 76 76 48 Net Wealth > 0 72 71 67 Observations 21,901 74,113 160,223 Table 4.1: Summary statistics 2013 in 2015 USD (rounded to closest 100 with USD/NOK 7.5). 4.2.1 Institutional background The impact of job loss risk on savings is likely to depend on the unemployment insurance (UI) scheme. That is, not only job loss risk matters, but also the expected income fall upon job loss  or what we might think of as eective job loss risk. OECD data on 2015 replacement rates from the Tax and Benet Systems: OECD Indicators shows that out of the 40 countries included, Norway is ranked as number 18, i.e. close to the OECD median. For comparison, the US is ranked as number 37. All else equal, we would therefore expect job loss risk to have a smaller impact on savings in Norway than in the US. Norwegian workers who become unemployed are generally entitled to unemployment insurance of 62 percent of pre-unemployment wages for a duration of two years. While there is a requirement to qualify, this is relatively low, and workers with a non-trivial position throughout the calendar year would all be expected to qualify. There is however an upper limit on pre-unemployment wages, meaning that income above a year-specic threshold does not enter into UI calculations. High income earners therefore have an eective replacement rate of less than 62 percent. This turns out to be relevant for our sample, as the treatment group will consist of relatively high-income individuals. Using the year specic thresholds, we calculate an eective replacement ratio of close to 50 percent for our sample. 137 With regards to the level of job loss risk, Norwegian unemployment rates are among the lowest in the OECD group. Figure 4.16 in Appendix A depicts harmonized OECD unemployment rates by country, with the Norwegian unemployment rate typically falling below four percent. While the unemployment rate in Norway has generally been below that in the US, this has changed in recent years. At the same time as the US labor market has nally recovered from the Great Recession, the oil price collapse in 2014 led to a deterioration of Norwegian labor market conditions. As a result, the unemployment rates in the two countries have been similar for the past three to four years. When interpreting the results of this study in a broader context, it is useful to keep in mind that the setting is one of relatively low baseline job loss risk, and relatively generous unemployment insurance. 4.3 Theoretical predictions What does higher uncertainty imply for savings and output in macroeconomic models? Under which condi- tions can an increase in uncertainty amplify an economic downturn? In this section we briey discuss the implications of dierent types of models, and which assumptions are needed in order to generate ampli- cation. In the appendix we set up and solve a search and match model with nominal frictions, and show how higher job loss risk can amplify economic downturns given assumptions about nominal frictions and monetary policy. In general, higher uncertainty increases savings if there is prudence in the utility function (Kimball, 1990) or if there are potentially binding borrowing constraints. In standard neoclassical models, the increase in savings leads to an increase in investment. In addition, higher uncertainty induces a precautionary labor supply response, making the overall impact on output positive. Higher uncertainty therefore increases both savings and output, and there is no amplication of economic downturns. In New Keynesian models with nominal rigidities, the co-movement between savings and output can break down. If prices and interest rates do not fall suciently, the increase in investment will be insucient to make up for the decline in consumption. If labor supply is inelastic, the precautionary labor supply response is also eliminated. As a result, higher uncertainty can increase savings while reducing output. See for example Kobayashi and Nutahara (2010) and Basu and Bundick (2017). Macroeconomic models often introduce uncertainty as a mean preserving spread to future income. Job loss risk on the other hand, can both increase the variance of future income and reduce the expected level of future income, i.e. it is not a mean preserving spread. Both of these channels can lead to higher savings. Recently, a handful of papers have studied uncertainty in the form of job loss risk using search and match 138 models with nominal frictions. See Bayer, Lütticke, Pham-Do, and Tjaden (2015), Challe and Ragot (2016), Challe, Matheron, Ragot, and Rubio-Ramirez (2017), Ravn and Sterk (2016) and Ravn and Sterk (2017). In these models, a shock to the separation rate increases job loss risk and induces individuals to save more. We now briey discuss under what assumptions this type of model predicts amplication of economic downturns. Search and match models with nominal frictions In the appendix, we set up and solve a model similar to Ravn and Sterk (2017). We briey discuss the model setup here, and under which conditions higher job loss risk reduces output through an increase in savings. Individuals receive a xed wage income if employed and unemployment benets if unemployed. At the time of consumption/saving decisions, individuals face idiosyncratic job loss risk. Firms post vacancies at a xed vacancy posting cost, and the vacancy is lled with some probability that depends on the number of vacancies and the number of unemployed individuals. Firms maximize prots and are subject to a Rotemberg price adjustment cost. Matches between unemployed individuals and rms posting vacancies are governed by a matching function, and the interest rate follows a Taylor rule. Consider a shock to the separation rate in this setting, which has two eects on output. First, a reduc- tion in the number of employed individuals directly reduces output. Second, higher job loss risk induces households to save more, and thereby cut back on consumption. In order to increase consumption, prices and interest rates must fall. If prices do not fall suciently due to price rigidities, and if the interest rate does not fall suciently due to the monetary policy rule 79 , rms are going to respond by reducing vacancies. As a result, there is an additional fall in output, due to the risk induced increase in savings. In order to quantify the additional output fall, i.e. the amplication, it is useful to compare the baseline model to a complete markets version of the model. In the complete markets version, every individual receives the average income, thereby shutting down the risk channel. Figure 4.1 illustrates the additional output drop resulting from the risk channel, as a function of the UI replacement ratio. For a replacement ratio of 0.4 in line with US levels (Mitman and Rabinovich, 2015), and a Taylor coecient of 1.5 (Ravn and Sterk, 2017), output falls by 22 percent more due to the risk induced increase in savings. 79 For a standard calibration of the Taylor rule, monetary policy is not able to fully oset the shock. In practice, one could think of monetary policy not being suciently accommodative due to the zero lower bound or because the shock is regional. 139 Figure 4.1: Amplication as a function of the unemployment benet replacement ratio ν, for two dierent values of the Taylor coecient η. The model exercise shows that higher job loss risk in theory can amplify economic downturns through an increase in savings. However, with perfectly exible prices or with suciently aggressive monetary policy, the amplication would break down. We now move on to study these questions in the data, with the aim of evaluating the empirical relevance of the type of models outlined here. First, we use administrative data and a natural experiment to investigate the impact of job loss risk on savings. After having conrmed that higher job loss risk increases savings, we show that there is a decline in employment in non-tradable industries not directly aected by the shock, consistent with the reduction in household demand amplifying the economic downturn. 4.4 The eect of job loss risk on savings The empirical analysis consists of two main parts. First, we investigate the eect of higher job loss risk on savings, by comparing individuals who are subject to the same local recession eects, but who face dierent changes in risk. After having established that higher job loss risk increases individual savings, we consider the overall employment eects of higher savings, i.e. the household demand channel. The rst goal of the empirical exercise is to identify the impact of job loss risk on savings. In order to obtain an exogenous increase in job loss risk, we use the 2014 oil price collapse as a novel natural experiment. By comparing liquid savings for individuals with dierent levels of job loss risk, but who are subject to the same local recession eects, we aim to isolate the impact of job loss risk from other recession eects. 140 4.4.1 Natural experiment: The oil price collapse of 2014 The sudden collapse of the oil price in the summer of 2014 led to an exogenous increase in job loss risk for certain regions and occupations. Job loss risk increased mainly in oil producing regions in the South-West of Norway, while the hardest hit occupational group was engineers. The price of Brent crude oil fell from roughly $110 to less than $50 per barrel in the second half of 2014, as seen in Figure 4.17 in Appendix A. Popular explanations include a slowdown in global demand, especially from China, as well as high supply of shale oil from the US. Tokic (2015) notes that in contrast to the oil price busts of 1991 and 2008, the 2014 bust was not preceded by an oil price spike, and as such was completely unexpected. To the best of our knowledge, there has been no suggestions that the oil price collapse of 2014 was in any way related to the Norwegian oil sector, which stands for only about two percent of world production. We thus feel comfortable assuming that the oil price shock was both unexpected and exogenous to the Norwegian economy. At the start of 2014, the petroleum sector accounted for roughly 25 percent of Norwegian GDP and 40 percent of Norwegian exports. The large and unexpected decrease in oil prices therefore had an adverse eect on the Norwegian labor market. However, as documented below, the negative impact was to a large degree contained to certain regions and occupations. Regional and occupational variation Oil production is concentrated in the South-West of Norway, as seen from Figure 4.18 in the appendix. Two out of nineteen counties employ a disproportionately high share of oil sector workers, and we dene these two counties as the oil region. 80 The combined population of these two counties in 2014 was close to one million, or 19 percent of the total population. The left panel of Figure 4.2 depicts the percentage point change in unemployment rates by county. The red squares capture the average of the two counties dened as the oil region, while the blue dots capture the remaining seventeen counties. In 2015, the unemployment rate in the oil region increased by more than two percentage points, making it the largest increase in county level unemployment over the past fteen years. At the same time, most other counties experienced moderate or no increase in unemployment. 80 The two oil counties are Hordaland and Rogaland, and the largest city in the area is Stavanger - sometimes referred to as the oil capital. 141 Change in Unemplyment by County (pp) Change in Unemployment by Occupation (pp) 3 2 2 1 1 0 0 -1 -2 -1 2000 2005 2010 2015 2000 2003 2006 2009 2012 2015 Non-oil counties Oil counties (avg.) Low skilled Other high skilled Engineers Figure 4.2: Changes in unemployment rates (pp). No other occupational group received as much media attention as engineers following the oil price col- lapse 81 , and the data suggests that this was indeed warranted. 82 The tax data contains detailed information on occupations for employed individuals. We categorize individuals as engineers if they were employed as engineers in the time leading up to the oil price collapse, i.e. if they were employed as engineers in at least one of the years 2011-2013. The individuals in this group are either civil engineers - which in Scandinavia is a protected title - or engineers. The former requires at least four years of higher education, while the latter requires 1-3 years of higher education. Individuals who do not belong to this group, but who are employed in other occupations requiring higher education, are labeled other high skilled. High skilled individuals include managers, professionals, and technicians/associate professionals, and make up 47 percent of the work force, see Table 4.9 in Appendix B. Finally, individuals who do not belong to any of these groups, but who were employed in at least one of the years 2011-2013 are labeled low skilled. The right panel of Figure 4.2 depicts the change in unemployment by occupational group. The change in unemployment rates for low skilled workers is captured by the blue dots. Note that the labor market outcomes of this group seem to be especially cyclical, with high peaks and low busts compared to other workers. The change in unemployment rates for engineers is captured by the red squares, while the change in unemployment rates for other high skilled workers is captured by the plus-signs. These two groups look fairly similar prior to the oil price collapse, but have very dierent employment outcomes in the year following 81 Some examples of newspaper headlines: Statoil is laying o more engineers Aftenposten April 2015, One out of three engineers are worried about losing their job Aftenposten May 2015, Union leader for the engineers: Worried unemployment will rise further Aftenposten May 2015, Solberg [the prime minister] wants to help unemployed engineers DN September 2015. New report on the oil engineers: Unemployment increased 342 percent in one year - but many are nding new employment E24 March 2016. 82 The Norwegian Labour and Welfare Administration (NAV) reports unemployment rates for fteen dierent occupations, one of which is Engineers & IT workers. According to their data, the increase in unemployment for this group in 2015 was the largest observed increase for any occupational group since their sample starts in 2003. 142 the shock. In 2015, the unemployment rate for engineers increased by more than 1.5 percentage points - the highest increase observed - while the unemployment rate for other high skilled workers remained roughly unchanged. As will become evident in the upcoming analysis, this does not only reect the geographical distribution of engineers and other high skilled workers. Salience Figure 4.2 documented that the oil region experienced a sharp increase in relative unemployment in 2015. Google search data allows us to conrm that not only was the shock quantitatively large, it also appears to have been salient. Search volumes are indexed relative to the maximum search volume in the sample, which is assigned a value of 100. Further, search volumes are measured relative to the total amount of searches in a given area, allowing for meaningful comparisons across geographic areas of dierent sizes. The left panel of Figure 4.3 depicts the volume of searches which google classies as belonging to the search category Brent Blend, i.e. oil price related searches. The solid red line depicts the volume of oil price related searches in the two oil counties over time. After the oil price started falling in August 2014, there is an immediate and sustained spike in oil price related searches. As seen from the dashed blue line, the rest of the country follows a very dierent pattern. Although there is some increase also in other counties, the magnitude is modest compared to that in the oil region. We thus conclude that individuals residing in oil producing areas are especially aware of, and are paying attention to, the collapse in the oil price. Even though individuals living in aected areas are paying attention to the sudden oil price bust, they need not be aware of the negative consequences for the local labor market. In order to evaluate how salient the shock is in terms of labor market risk, the right panel of Figure 4.3 depicts the volume of searches which google classies as belonging to the search category Layo. Again, we see a rather striking pattern. While there is virtually no increase in layo related searches in other counties, there is a large and persistent increase in the two oil counties. As before, the increase starts as the oil price begins falling in mid-2014, and then peaks in early 2016. Note that this means that individuals are googling layos even before unemployment rates start to rise in the data. 83 83 Unemployment rates rise in 2015 according to the tax data, whereas layo related google searches increase also prior to 2015. Prior to the oil price collapse in August 2014, the search volume index has an average value of 12. After the oil price collapse, but prior to January 2015, the search volume index has an average value of 28. From January 2015 to December 2017 the search volume index has an average value of 45. 143 Google Searches: Brent Blend Google Searches: Layoff 100 100 80 80 60 60 40 40 20 20 0 0 2013m1 2014m7 2016m1 2017m7 2013m1 2014m7 2016m1 2017m7 Oil Region Non-Oil Region Oil Region Non-Oil Region Figure 4.3: Google search data for the oil region and other counties. The index is set to 100 for the maximum search volume in the sample. Interestingly, search volumes for layos peak in January 2016 (and search volumes for the oil price reaches its second highest value), which is exactly when the oil price reaches its minimum value of $30 per barrel. Based on the google search data, we thus conclude that not only are individuals living in oil producing areas immediately aware of the dramatic fall in the oil price, they also seem to understand that this implies an increase in job loss risk. 4.4.2 Methodology In order to isolate the impact of job loss risk from other recession eects, we use a dierence in dierence approach to compare liquid savings for engineers to that of other high skilled workers in oil producing regions. This within-region comparison allows us to control for the potential impact of other local recession eects on savings. Further, by contrasting the baseline ndings to the results from an across-region comparison, we can explicitly evaluate the importance of other local recession eects. The dynamic dierence in dierence regression is outlined in equation (165). The main outcome variable Yit is bank deposits for individual i in year t. Ti is an indicator variable equal to one if individual i is in the treatment group, and equal to zero if individual i is in the control group. In the baseline analysis, Ti = 1 for engineers residing in oil producing regions, and Ti = 0 for other high skilled workers residing in oil producing regions. Treatment status is dened based on the years prior to the oil price collapse. Year xed eects δk are included to capture time-varying aggregate eects which are common to all individuals, while individual xed eects αi are included to capture individual, time-constant factors. The coecients of interest are the βk 's, which capture the impact of the interaction term between treatment status and year indicator variables. Given that βk = 0 for k < 2014, the dynamic treatment eect is captured by the βk 's for 144 k ≥ 2014. We also estimate the more restrictive dierence in dierence regression given by equation (166), to obtain the average treatment eect, in which Itpost = 1 if t ≥ 2014. Standard errors are clustered at the individual level. X X Yit = αi + δk 1t=k + βk (Ti × 1t=k ) + it (165) k k X δk 1t=k + βk Ti × Itpost + it  Yit = αi + (166) k Because we are interested in the impact of job loss risk, rather than the impact of realized unemployment, we restrict the analysis to only include individuals who are not (yet) unemployed. 84 This turns out not to matter for the 2014 results, as the unemployment rate did not start increasing until the following year. It does however matter for the 2015 results, as some individuals had lost their job by that time and started to dis-save in order to smooth consumption. In order to evaluate the importance of local recession eects in determining savings, we complement the baseline analysis with an across-region specication. That is, we compare engineers in oil producing regions to high skilled workers residing outside of oil producing regions. The results from this comparison should reect both the impact of higher job loss risk and the impact of other local recession eects, such as a relative decline in house prices. Contrasting these results with the baseline ndings allows us to also evaluate the sign and magnitude of the impact of other recession eects on savings. Selection into unemployment Before presenting the results, we briey discuss the issue of selection into unemployment. In an event study in which job loss risk is identied by future unemployment, the main concern is that there is an individual level shock which is causing the upcoming job loss and aecting saving behavior. This concern is strongly mitigated in our setting, as job loss is caused by an exogenous fall in the oil price. However, that does not mean that job loss (risk) is randomly distributed within the aected groups. For instance, as we show in the upcoming analysis, engineers with low tenure are more likely to experience job loss than engineers with high tenure. Our estimated saving response will reect the behavior of people who experience a relatively large increase in job loss risk, which is not necessarily representative of the total population. We show in Appendix C that after controlling for tenure, other observable characteristics are not infor- 84 Specically, we condition on job loss not occurring in 2014 or 2015. We have also tried conditioning on job loss not occurring for the full period, i.e. 2010-2015, and the results are very similar. 145 mative in predicting which engineers experience job loss following the oil price collapse. Further, we show that a simple model based on observable characteristics has substantially less power in explaining job loss following the oil price collapse than in normal times. Hence, to the extent that observable characteristics are relevant for evaluating selection into unemployment, there appears to be relatively less selection into unemployment following the oil price collapse. 4.4.3 Results The empirical results conrm that higher job loss risk increases liquid savings. Reassuringly, the increase in savings is driven by low-tenured workers, who experienced an especially large increase in job loss risk. Not accounting for local recession eects produces larger estimates, suggesting that other recession eects might also contribute to higher savings. Figure 4.4 depicts the unemployment rate and the separation rate in the oil region over the period 2001-2016, for engineers and other high skilled workers. We include both the unemployment rate and the separation rate, as they capture dierent aspects of unemployment risk. The separation rate is dened as the probability of going from employed to unemployed, and corresponds to the exogenous separation rate ρt in the model in Appendix D. While the separation rate captures the risk of job loss, the unemployment rate is closer to capturing the total risk of unemployment  as it also reects the job nding rate (qt in the model). As seen from the gure, engineers and other high skilled workers have very similar unemployment and separation rates prior to 2014. This is important as it alleviates the concern that individuals are selecting into our control and treatment groups based on dierences in risk aversion, a selection issue studied in detail in Fuchs-Schündeln and Schündeln (2005). The unemployment rate for engineers increases from an average of roughly one percent prior to the oil price collapse, to an average of roughly six percent after the oil price collapse. There is some increase in unemployment rates also for other high skilled workers. However, the increase is moderate compared to engineers. In the robustness section, we use an alternative control group consisting only of high skilled government workers. This group experienced virtually no increase in job loss risk following the oil price collapse. Reassuringly, the results from this exercise are similar, suggesting that spillovers to the control group is not a concern. The separation rate is depicted in the right panel of Figure 4.4. As was the case for the unemployment rate, the separation rate for engineers and other high skilled workers is similar prior to 2014. Post-2014, there is a large and sustained increase in the separation rate for engineers relative to that of other high 146 skilled workers. Note that the separation rate increases by a similar magnitude as the unemployment rate in 2015, but by a smaller amount in 2016. This suggests that the initial increase in unemployment is driven almost exclusively by the separation rate, while a decline in the job nding rate is important in explaining the subsequent increase. Unemployment Rate In Oil Region Separation Rate In Oil Region 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 2001 2006 2011 2016 2001 2006 2011 2016 Engineers Other High Skilled Engineers Other High Skilled Figure 4.4: Unemployment rate and separation rate (%) for engineers in the oil region and other high skilled workers in the oil region. The left panel of Figure 4.5 depicts bank deposits for engineers and other high skilled workers over time. Bank deposits for the two groups follow each other closely up until 2013, when there is a divergence which persists until 2015. Reassuringly, the divergence appears to be driven by an above trend increase in bank deposits for engineers rather than a below trend increase in bank deposits for other high skilled workers. Regression results from estimating equation (165) with Yit = Bank Depositsit are depicted in the right panel of Figure 4.5. The pre-2014 coecients are all very close to zero in magnitude and not statistically signicant, suggesting that the parallel trend assumption is satised. In 2014, the coecient is positive at roughly $1,200 and statistically signicant, implying that engineers in the oil region increased their bank deposits relative to that of other high skilled workers in the oil region. In the appendix, we further decompose engineers into those who lose their job and those who do not experience job loss. 85 We show that while the average saving response occurs in 2014, engineers who lose their job in 2016 increase savings mainly in 2015. 85 Note that we are excluding those who lose their job in 2014-2015 from the analysis, as we do not want the eect of realized unemployment to inuence our saving results. The decomposition is thus engineers who do not experience job loss during the period 2014-2016 and engineers who experience job loss in 2016. 147 Deposits In Oil Region Deposits in Oil Region: Engineers vs. Other High Skilled 44000 45000 3000 2000 other high skilled engineers 34000 35000 1000 0 24000 25000 2010 2011 2012 2013 2014 2015 -1000 Engineers Other High Skilled 2010 2011 2012 2013 2014 2015 Figure 4.5: Bank deposits for engineers in the oil region relative to other high skilled workers in the oil region. Right panel: coecient estimates from estimating equation (165). The results in Figure 4.5 are further summarized in Table 4.2. As seen from the rst column, engineers increased their bank deposits by roughly $1,200 or 3.4 percent in 2014. In order to scale the saving response, we estimate the increase in unemployment rates and separation rates using a simple dierence in dierence regression as the one outlined in equation (166). Following the model outlined in the appendix, we use the next period increase in uncertainty to scale the current period saving response. The relative unemployment and separation rates increased by 3.0 and 2.9 percentage points respectively in 2015, and increased further the following year. Scaling the saving response by the relative increase in the unemployment rate, we nd that a one percentage point increase in the unemployment rate increases liquid savings by 1.1 percent. Alternatively, we can scale the increase in bank deposits by the change in the separation rate. Doing so, we nd that a one percentage point increase in the job loss rate increases liquid savings by 1.2 percent. Results averaging over 2014 and 2015 are reported in the second column of Table 4.2, and show a similar increase. Focusing on the 2014 results has the advantage of capturing the initial saving response, which occurred before unemployment started to increase in the data and before any policy changes were implemented or even discussed. This makes it less likely that other forces are behind the relative increase in savings for engineers. However, the shock increased both in size and salience over time, and so we also include results which reect the saving response in 2015 - the last year for which we have data. This increases the estimated saving response slightly, both in absolute terms and when scaled by the increase in uncertainty. 148 (1) (2) Bank Deposits Bank Deposits Ti2013 × Itpost 1,187** 1,283** (2.12) (2.32) Increase in Bank Deposits (%) 3.37 3.64 per pp increase in unemployment rate (%) 1.14 0.992 per pp increase in separation rate (%) 1.18 1.21 Sample period 2010-2014 2010-2015 Clusters 19,370 19,370 N 95,332 114,370 t statistics in parentheses. Std. errors clustered at the individual level * p < 0.1, ** p < 0.05, *** p < 0.01 Table 4.2: Bank deposits. Within oil region analysis. Regression results from estimating equation (166). Tenure While engineers residing in oil regions experienced a general increase in job loss risk post-2013, the increase in risk was not uniformly distributed. In particular, individuals with low tenure faced an especially large increase in the probability of job loss. The Basic Agreement between the Norwegian Confederation of Trade Unions (LO) and the Confederation of Norwegian Business and Industry (NHO) clearly states that tenure should be an important factor in deciding who gets laid o as a result of cutbacks or restructuring (Ÿ 8-2 Seniority in the event of dismissal due to cutbacks ). The seniority or tenure principle should only be departed from when there is due reason for this. Given that low-tenured individuals faced a particularly large and salient increase in job loss risk, one would expect these individuals to have a larger saving response. We estimate tenure by calculating the number of years an individual has worked at the same rm. Because the individual tax data can only be matched to employer information as of 2000, the maximum observed tenure prior to the oil price collapse is fourteen years. In 2013, the median observed tenure of engineers residing in oil regions is six years. We thus dene individuals with less than six years tenure in 2013 as having low tenure. Figure 4.20 in Appendix A conrms that tenure is indeed an important predictor of unemployment. While the unemployment rate for high-tenured engineers increases to a maximum of almost four percent, the unemployment rate for low-tenured engineers increases to a maximum of nearly ten percent. A similar dierence is seen in separation rates. The results are reported in Table 4.3, and show that the saving increase is driven by low-tenured workers. Low-tenured engineers increase their liquid savings by roughly $2,000, while the increase for high-tenured engineers is not statistically signicant. As low-tenured engineers have lower holdings of bank deposits to begin with, the percentage increase exceeds seven percent. Relative to other high skilled workers, low- tenured engineers experience an initial relative increase in unemployment rates and job loss risk of 4.8 and 149 4.6 percentage points respectively. Scaling the saving response by the relative increase in the unemployment rate, we nd that a one percentage point increase in the unemployment rate increases liquid savings by 1.45 percent. Alternatively, a one percentage point increase in the job loss rate increases liquid savings by 1.51 percent. The relative saving response is somewhat higher when averaging over the 2014-2015 period, reaching an increase of 2.0 percent for every one percentage point increase in the separation rate. Relative to the increase in job loss risk, the saving response of low-tenured engineers is higher than the baseline results. This is consistent with the simulation results in Engen and Gruber (2001), in which the percentage eect of risk on savings declines in age  which is positively associated with tenure  and increases in the level of risk. (1) (2) Bank Deposits Bank Deposits Ti × Itpost 437 224 (0.49) (0.26) Ti × T enurelow i × Itpost 2,009* 2,637** (1.81) (2.42) Increase in Bank Deposits (%) (low tenure) 7.02 9.21 per pp increase in unemployment rate (%) 1.45 1.60 per pp increase in separation rate (%) 1.51 2.02 Sample period 2010-2014 2010-2015 Clusters 19,046 19,046 N 93,724 112,451 t statistics in parentheses. Std. errors clustered at the individual level. * p < 0.1, ** p < 0.05, *** p < 0.01 Table 4.3: Bank deposits by tenure. Within oil region analysis. Regression results from estimating equation (166) by tenure. Other recession eects Local economic downturns can aect saving behavior not only through increased job loss risk. For instance, falling house prices may induce people to cut back on consumption and increase savings. One could also imagine a local recession leading to negative sentiments or beliefs, which might make individuals save more regardless of their employment prospects. In the baseline analysis we did a within region comparison, in order to control for such local recession eects. In this section we explore dierent specications in order to gauge whether these other recession eects are quantitatively important in terms of aecting saving behavior. The rst column in Table 4.4 simply reproduces the baseline results, in which engineers in the oil region are compared to other high skilled workers in the oil region. In the second column, we compare engineers in the oil region to other high skilled workers everywhere. Finally, in the third column we compare engineers 150 in the oil region to high skilled workers in the non-oil region. Both the coecient estimates and the scaled increase in liquid savings increase as we move to the right in the table. This suggests that other recession eects are, if anything, contributing to higher saving rates, and that not accounting for these eects would lead us to overstate the impact of job loss risk on savings. Given that engineers in the oil region are aected by both higher job loss risk and local recession eects, other high skilled workers in the oil region are aected by local recession eects only, and that other high skilled workers in the non-oil region are unaected, the impact of local recession eects can be found by comparing the results from column (3) to the baseline results in column (1). Both the regression coecient and the scaled saving response is larger in the nal column, suggesting that not accounting for local recession eects could lead us to overstate the impact of higher uncertainty on savings. However, the dierence between the coecient estimates is not statistically signicant. Note that the quantitative importance of local recession eects is likely to vary, and we do not attempt to measure the size of such eects for our given shock. It is therefore possible that other local recession eects would have larger implications for saving behavior in a dierent setting, simply because the other local recession eects would themselves be larger. (1) (2) (3) Bank Deposits Bank Deposits Bank Deposits Ti × Itpost 1,187** 1,493*** 1,560*** (2.12) (3.17) (3.28) Increase in Bank Deposits (%) 3.37 4.24 4.43 per pp increase in unemployment rate (%) 1.14 1.28 1.31 per pp increase in separation rate (%) 1.18 1.32 1.35 Control group: high skilled workers... in oil region in all regions in non-oil region Sample period 2010-2014 2010-2014 2010-2014 Clusters 19,370 78,388 65,241 N 95,332 387,296 322,387 t statistics in parentheses. Std. errors clustered at the individual level. * p < 0.1, ** p < 0.05, *** p < 0.01 Table 4.4: Bank deposits. Across region analysis. Regression results from estimating equation (166). Interpreting the increase in liquid savings Bank deposits are a safe and highly liquid way to save, and therefore a good candidate for precautionary saving. Basten, Fagereng, and Telle (2016) nd that individuals respond to future unemployment by increasing both the level and the share of safe assets in their portfolio. We have rerun the baseline analysis using total nancial wealth as the dependent variable, and the results are reported in Table 4.10 in the appendix. The increase in total nancial wealth is virtually the same as the increase in bank deposits, indicating that non-deposit nancial wealth was kept roughly unchanged. There 151 was also no statistically signicant decline in housing wealth or other real wealth for engineers relative to other high skilled workers following the oil price collapse. Because there is no decrease in other forms of wealth  and no relative increase in wages  we nd it likely that the increase in liquid savings implied a reduction in consumption. While we cannot rule out that there were other adjustments which we do not observe, we nd the 2014 increase in savings especially convincing. At this point there was still no increase in actual unemployment, and the full extent of the oil price collapse was not yet known. As a result, there were no policy measures being discussed at this time. We therefore nd it highly probable that the increase in liquid savings implied a reduction in consumption. 4.4.4 Robustness In the robustness section we show that our results are robust to two alternative specications. First, we change the treatment group to only consist of engineers who work in the oil sector, as these individuals may have been particularly eected by higher job loss risk. Second, we change the control group to only consist of high skilled government workers, who did not experience any increase in job loss risk following the oil price collapse. We further show that the estimated saving response is unlikely to be driven by wealth eects or selection into occupation based on risk aversion. Engineers in the oil sector So far, our classication of individuals into treatment and control groups have relied only on occupations. However, we also know in which sector individuals work. We now change the treatment group to only contain engineers which were employed in the oil sector prior to 2014. This leads to, if anything, a slightly higher saving response than in our baseline results. Statistics Norway denes the oil sector to contain what they refer to as petroleum sectors and petroleum related sectors. The petroleum sector includes the following sectors: extraction of crude petroleum and natural gas (06), support activities for petroleum and natural gas extraction (09.1), transport via pipeline (49.5) and support activities pipeline (52.215). In addition, Statistics Norway denes petroleum related sectors to include the following industries: building of oil-platforms and modules (31.113), installation and completion work on platforms and modules (30.116) and oshore supply terminals (52.223). According to Statistics Norway, around 84,000 individuals were employed in the oil sector in 2014 (Ekeland, 2017)  which constitutes just above three percent of all employed workers. However, a high number of individuals work in industries which produce output used in the oil sector, but which are not included in this denition. Attempts by Statistics Norway to calculate the number of workers directly or indirectly employed in the oil 152 sector based on input output data produces a number of 239,000  which constitutes just above nine percent of all employed workers (Prestmo, Strøm, and Midsem, 2015). Hence, only 35 % of oil related workers are actually employed in the oil sector. We follow the standard Statistics Norway denition and create an alternative treatment group, consisting of engineers employed in the oil sector. The new treatment group is thus a subset of our baseline treatment group, while the control group is left unchanged. The time series for unemployment and separation rates for the two groups are depicted in Figure 4.22 in the appendix, while the evolution of bank deposits is depicted below in Figure 4.6. As seen from the left panel of Figure 4.6, engineers in oil sectors and other high skilled workers have almost identical holdings of bank deposits in the four years leading up to the oil price collapse. Following the oil price collapse, engineers in oil sectors increase their bank deposits relative to other high skilled workers. As reported in Table 4.11 in the appendix, the increase in bank deposits is similar to the baseline - both in absolute value and when scaling the response with the relative increase in job loss risk. A one percentage point increase in the separation rate is now found to increase liquid assets by 1.23 percent  compared to 1.18 in the baseline. Deposits In Oil Region Deposits in Oil Region: Oil Engineers vs. Other High Skilled 45000 6000 40000 4000 35000 2000 30000 0 25000 2010 2011 2012 2013 2014 2015 -2000 Oil Sector Engineers Other High Skilled 2010 2011 2012 2013 2014 2015 Figure 4.6: Bank deposits for oil sector engineers in the oil region relative to other high skilled workers in the oil region. Right panel: coecient estimates from estimating equation (165). Spillovers to the control group The baseline analysis compared engineers residing in oil regions to other high-skilled workers residing in oil regions. It is likely that also the latter group experienced some increase in job loss risk following the oil price shock. Figure 4.4 showed that although other high-skilled workers in oil regions experienced a very modest increase in unemployment relative to engineers, they too were subject to an increase in job loss risk. This could be because some workers in this group are directly employed in the oil sector and/or because there are spillover eects to other sectors. Note that the largest spillover eects occur for low skilled workers, as alluded to by Figure 4.2. Hence, this issue is less of a concern when using 153 only high-skilled workers in the control group. If the impact of job loss risk on saving behavior is homogeneous and linear, spillover eects should not be an issue. To see this note that we are not assuming that there is no increase in job loss risk for the control group. Rather, we are using the dierence in job loss risk between the two groups, to scale the impact on liquid savings. If the control and treatment group have the same underlying linear saving response to a given increase in job loss risk, spillover eects should not aect our estimates. However, if the saving response is non-linear and/or non-homogeneous, spillover eects could be an issue. To reduce the likelihood that spillover eects are inuencing our results we redo the baseline analysis with a control group consisting only of high skilled government workers. This has the benet of only including individuals whose employment security should not be aected by (short-term) economic conditions, but has the disadvantage of producing a control group with less similar employment outcomes pre-2014. Figure 4.7 depicts unemployment rates for engineers and high skilled government workers in the oil region. As before, individuals are classied into occupations based on their occupational status in the years leading up to the oil price collapse. High skilled government workers have virtually no increase in unemployment rates or job loss risk following the oil price collapse, implying limited scope for spillover eects. Unemployment In Oil Region Separation Rate In Oil Region 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 2001 2006 2011 2016 2001 2006 2011 2016 Engineers Government High Skilled Engineers Government High Skilled Figure 4.7: Unemployment rate and separation rate (%) for engineers in the oil region and high skilled government workers in the oil region. Regression results when using only high skilled government workers in the control group are reported in Table 4.5. The coecient estimate for 2014 is almost unchanged, but the increase in uncertainty is somewhat larger. As a result, a one percentage point increase in the separation rate is found to increase liquid savings by 1.00 percent - compared to 1.18 percent in the baseline. For the 2014-2015 results, the estimated saving response is virtually the same as in the baseline. Hence, we conclude that our results are robust to controlling for spillovers to the control group. 154 (1) (2) Bank Deposits Bank Deposits Ti × Itpost 1,108 1,449** (1.53) (2.01) Increase in Bank Deposits (%) 3.14 4.12 per pp increase in unemployment rate (%) 0.954 0.841 per pp increase in separation rate (%) 1.00 1.17 Sample period 2010-2014 2010-2015 Clusters 9,031 9,031 N 44,220 53,054 t statistics in parentheses. Std. errors clustered at the individual level. * p < 0.1, ** p < 0.05, *** p < 0.01 Table 4.5: Bank deposits. Within oil region analysis. Regression results from estimating equation (166) using only high skilled government workers in the control group. House prices Although the within region analysis controls for other local recession eects, the denition of local can be disputed. There might still be price dierences within the two counties dened as the oil region. For example, engineers and their high skilled peers may live in systematically dierent areas, thereby being exposed to dierent changes in house prices. To explore this, we use house price data on the municipality level from Statistics Norway. This data is not available for the smallest municipalities, but still covers 96 percent of engineers and other high skilled workers residing in the oil region. Figure 4.23 in Appendix A depicts average house prices in the oil region over time for engineers and their high skilled peers separately. The change in house prices for engineers and other high skilled workers looks very similar. Prices are roughly constant from 2013 to 2015 for both groups, while house prices in the rest of the country are increasing. House prices in the oil region fall noticeably in 2016, but the decrease is not signicantly dierent across engineers and other high skilled workers. Hence, we nd it unlikely that house price changes are driving the increase in savings of engineers relative to other high skilled workers, within the oil region. Other wealth eects If local stock prices are aected, there could also be negative wealth eects coming from nancial assets. While there was certainly a decline in stock prices for many oil rms, the overall impact on the Norwegian stock market was limited. As illustrated in Figure 4.24 in Appendix A, at an annual level  the relevant level for our tax data  the Oslo Stock Exchange overall index increased from 2014 to 2015. Moreover, the increase was similar to that of the S&P 500 index in the US. There was a modest fall in stock prices in the following year, but this was also a low growth year for US stock markets. One reason why the oil price collapse appears to have had a relatively modest impact on average stock prices might be the large 155 exchange rate movements, which increased the international competitiveness of Norwegian rms. Figure 4.25 in Appendix A shows that there is no decline in the value of other nancial assets for engineers or other high skilled workers following the oil price collapse. Note that other nancial assets contain not only Norwegian stocks, which might have fallen slightly in value in 2016, but also other assets such as bonds and international stocks - typically held through global mutual funds. If the latter is not hedged against exchange rate movements, the value of these assets would have increased after the oil price collapse. As long as any wealth eects are constant across the control and treatment group, they are unlikely to be the driving force behind the estimated saving response. As previously discussed, there was no signicant change in nancial assets for engineers relative to other high skilled workers following the oil price collapse - see Table 4.10 in the appendix. We thus nd it unlikely that the observed increase in bank deposits for engineers relative to other high skilled workers is driven by a negative wealth eect. Selection into occupations We have used pre-2014 occupations in order to identify groups with dierent changes in job loss risk. However, occupations are not randomly assigned and engineers may be systematically dierent from their high skilled peers. Fuchs-Schündeln and Schündeln (2005) argue that individuals self- select into occupations based on their level of risk aversion, thereby potentially biasing occupation based estimates of precautionary saving. We believe this concern to be of limited importance in our case for two reasons. First, we are comparing two groups who had very similar levels of job loss risk prior to the oil price collapse. As shown in Figure 4.4, engineers and other high skilled workers had almost identical unemployment rates in the thirteen years leading up to the oil price collapse. Also, there has been a general shortage of engineers in Norway over the past years, and becoming an engineers has been considered a safe career choice. Second, we are not simply comparing wealth levels across occupations. Rather, we are considering a sudden change in job loss risk, and the following change in liquid savings. Still, if engineers are less risk averse than the general population, this would mean that the estimated saving response is a lower bound for the population wide response all else equal. 4.4.5 External validity The treatment group considered so far consists of individuals with above average education, income and wealth. By doing an event study which includes all men who experience job loss, we nd that high income individuals may exhibit stronger saving responses to heightened job loss risk than low income individuals. Hence, a shock which aected low income individuals could potentially have smaller eects on liquid savings 156 than those identied in the previous subsection. For the event study, we use a sample of men who become unemployed exactly once in the period 1995- 2012. We run the regression in equation (167), where Yit is the outcome variable for individual i in year t. Individual xed eects αi capture time invariant individual characteristics, while time xed eects δt capture common time trends. Xit is a fourth order polynomial in age. The coecients of interest are the βk 's, which capture the impact of being k years away from the start of an unemployment spell. Accordingly, Uitk is a vector of dummies for nine years around job loss (k = 0). All results are reported relative to k = −4, i.e. four years prior to the beginning of the unemployment spell. Standard errors are clustered at the individual level. k=4 X Yit = αi + δt + Xit β + Uitk βk + it (167) k=−4 The results for the full sample are depicted by the blue lines in Figure 4.8. Wage income is at in the years leading up to job loss, while bank deposits increase. Basten, Fagereng, and Telle (2016) nd similar results, and interpret the pre-unemployment increase in liquid assets as suggesting that at least some households are aware of the potential job loss several years in advance. We complement their ndings by isolating the individuals who are likely to have lost their job during the second half of the calendar year, and who are therefore unlikely to have received formal notice of job loss at time t = −1.86 As illustrated by the red lines, the increase in deposits is similar, suggesting that the increase in savings is not driven by individuals who know for sure that they will loose their job in the near future. 86 We estimate the number of months an individual is likely to have received UI in year t=0 based on pre-unemployment wages, the replacement rate, and the upper bound on income. Less than 1% are estimated to have received more than 12 months of UI, and these are dropped from the sample. The individuals who are estimated to have become unemployed during the second half of the calendar year are those who i) receive at most 6 months of UI in year t=0 according to our estimates, and ii) received some UI also in year t = 1. This group makes up 55 % of the sample. Because the maximum required notice period is 6 months, these individuals are unlikely to have been notied of unemployment in year t = −1. 157 Wage Income Bank Deposits 55000 13000 50000 12500 45000 12000 40000 35000 11500 -4 -3 -2 -1 0 1 2 3 4 -4 -3 -2 -1 0 1 2 3 4 Full sample Unemployed 2.half Full sample Unemployed 2.half Figure 4.8: Event study - wage income and bank deposits. Full sample and individuals estimated to have experienced job loss in the second half of the calendar year. How does the saving response vary with income? As seen from Figure 4.9, the increase in savings is driven by individuals with above median income. While there is some increase also for low income individuals, this is not statistically signicant. This is consistent with the results in Carroll, Dynan, and Krane (2003), who nd that savings increase in response to higher job loss risk only for those with medium or high income. However, we cannot rule out that the dierent responses (also) reect dierences in perceptions about future job loss risk between the two groups. Bank Deposits 1500 1000 500 0 -500 -1000 -4 -3 -2 -1 0 1 2 3 4 High Income Low Income Figure 4.9: Event study - bank deposits by income level (above/below median income at time t = −4). The event study results suggest that care should be taken when extrapolating results based on high income individuals to the full population. However, we believe studying high income individuals is interesting for two reasons. First, their saving behavior will have larger implications in terms of absolute amounts, due to their relatively high levels of liquid wealth. Second, and perhaps surprisingly, high-skilled individuals typically experience very similar percentage increases in job loss risk during recessions as low-skilled individuals - albeit starting from a lower level. Farber (2015) uses data from the Displaced Workers Survey (DWS) to study job loss during recessions in the US. He nds that the three-year job loss rate during the Great Recession 158 increased by 85 percent for individuals with less than 12 years education, by 90 percent for those with 12 years education, by 83 percent for individuals with 13-15 years of education, and by 77 percent for those with 16 or more years of education. During the dot com bubble, individuals with 16 or more years of education actually experienced a larger percentage increase in job loss rates than other educational groups. To summarize, we have found that a one percentage point increase in job loss risk increases liquid savings by 1.2 - 2.0 percent. This saving increase is driven by the individuals with the largest increase in job loss risk, i.e. individuals with low tenure. The results are robust to using an alternative control group with no increase in job loss risk, and are not driven by wealth eects. What does this increase in savings imply for the macro economy? In the next section we use municipality level outcomes to study the household demand channel of recessions. That is, we evaluate to what extent the increase in savings is likely to have had a negative impact on employment. 4.5 The eect of higher savings on employment In this section we investigate whether the increase in savings may have led to a decrease in employment. This is the second mechanism needed to produce amplication, as discussed in the theoretical motivation. Identifying general equilibrium eects such as this is challenging, as there are several eects at play. We show that within the oil region, non-oil sector unemployment increases more in areas with higher saving responses. We do a rough decomposition exercise, attributing the unemployment increase to either lower rm demand, or to lower household demand resulting from either realized unemployment or higher job loss risk. The decomposition exercise suggests that higher job loss risk contributed to higher unemployment in the non-tradable sector, consistent with the mechanism in the model. Consider rst the increase in unemployment for the oil region as a whole. As seen from Figure 4.10, unemployment in the oil sector increased by 3.5 percentage points from 2014 to 2015. However, unemploy- ment increased also in sectors not directly aected by the shock, indicating some sort of spillover eects. Did the risk induced increase in individual savings contribute to this rise in non-oil sector unemployment? In order to account for any factors which are constant within the oil region, we consider the cross-sectional increase in unemployment. We then proceed by doing a rough decomposition of the increase in unemploy- ment, considering three channels likely to be important. First, we consider the eect of lower rm demand, as rms in the oil industry are likely to demand fewer inputs for their production. Second, we consider the eect of lower household demand, which can take at least two forms: i) individuals who lose their job reduce consumption because their income is lower, ii) individuals who face higher job loss risk reduce consumption 159 in order to save more. Increase in unemployment 2014 to 2015 (pp) 4 3 2 1 0 Oil Tradable Non-Tradable- Non-Tradable- Construction Retail Figure 4.10: Increase in oil region unemployment by sector from 2014 to 2015 (pp). 4.5.1 Cross-sectional outcomes In order to obtain cross-sectional variation, we aggregate saving and labor market outcomes to the munic- ipality level and constrict the sample to only include the 59 municipalities in the oil region. To construct our treatment and control groups, we calculate the share of oil sector engineers by municipality at the baseline. Municipalities with an above median share of oil engineers are classied as oil intensive, whereas municipalities with a below median share of oil engineers are classied as non-oil intensive. Liquid savings Average bank deposits for the two municipality types are depicted in Figure 4.11. Oil intensive and non-oil intensive municipalities look very similar in the years leading up to the oil price collapse. In 2014 however, municipalities with an above median share of oil sector engineers increase their average bank deposits relative to other municipalities. Hence, the individual level saving response from the previous section is also observable at the municipality level. Regression results are reported in Table 4.12 in the appendix. On average, bank deposits increase by just above $400 per person. Because we only have 59 observations per year, and because we are averaging over all individuals who reside in a given municipality, the saving response is only borderline statistically signicant. 160 Bank Deposits 32000 31000 non-oil intensive oil intensive 24000 23000 2010 2011 2012 2013 2014 2015 Oil Intensive Non-oil Intensive Figure 4.11: Bank deposits in oil intensive and non-oil intensive municipalities within the oil region. Unemployment We follow the sector denitions used in Mian and Su (2014), and consider the tradable sector and the non-tradable sector separately. The tradable sector is dened as industries with export shares in the top 20th percentile. Following Mian and Su (2014), non-tradable industries are split into two groups. The rst group consists of retail, food services and accommodation, and we refer to this as the non-tradable- retail sector. The second group consists of construction and real estate rms, and we refer to this as the non-tradable-construction sector. Figure 4.12 depicts unemployment rates for oil intensive and non-oil intensive municipalities by sector. While unemployment rates are similar across municipalities up until 2014, there is a divergence in 2015 as unemployment rates increase faster in oil intensive municipalities. This is especially clear in the two non- tradable sectors, assumed to be the most dependent on local household demand. The divergence is somewhat smaller in the tradable sector, and virtually non-exiting in the oil sector itself. 87 Regression results are reported in Table 4.13 in the appendix. Unemployment increases by 1.7 percentage points in the non-tradable-retail sector, 2.0 percentage points in the non-tradable-construction sector, and 1.2 percentage points in the tradable sector. The relative increase in oil sector unemployment is small and not statistically signicant. 87 Note that the oil sector has a substantially higher export share than the tradable sector, and should be relatively insensitive to local household demand. 161 Non-Tradable-Retail Non-Tradable-Construction 6 6 4 4 2 2 0 0 2010 2011 2012 2013 2014 2015 2010 2011 2012 2013 2014 2015 Oil Intensive Non-oil Intensive Oil Intensive Non-oil Intensive Tradable Oil 6 6 4 4 2 2 0 0 2010 2011 2012 2013 2014 2015 2010 2011 2012 2013 2014 2015 Oil Intensive Non-oil Intensive Oil Intensive Non-oil Intensive Figure 4.12: Increase in oil region unemployment by sector and municipality type. 4.5.2 Firm demand In order to account for lower rm demand, we use network theory based on Acemoglu, Akcigit, and Kerr (2016). Accounting for intersectoral linkages requires the use of input output data, which we obtain from Statistics Norway. 88 Let aij = pj xij j for use in sector i, relative to pj yj be the value of inputs produced by sector    a11 ··· a1j   . .. .  the value of total output in sector j . The matrix A =  . . .  based on national input output data  . .    ai1 ··· aij is reported in Table 4.6. The bottom row is of special interest, as it tells us what share of production in each sector is used as inputs in the oil sector. For instance, a51 = 0.03 implies that three percent of production in the non-tradable-retail sector is used as an input in the oil sector. This compares to zero percent in the non-tradable-construction sector (a52 = 0.00) and ve percent in the tradable sector (a53 = 0.05). Note that the tradable sector is the most reliant on demand from the oil sector, and should therefore experience the largest increase in unemployment as a result of lower rm demand. 89 88 National input output data is available at https://www.ssb.no/en/nasjonalregnskap-og-konjunkturer/tables/supply-and- use-and-input-output. 89 It is possible that although the tradable sector produces the most inputs for the oil sector, these are the inputs which oil sector rms are the least likely to cut back on in the short term. When accounting for lower demand from the rm sector, we would then overstate the eect on the tradable sector. 162 Non-tradable-retail Non-tradable-constr. Tradable Other Oil Non-tradable-retail 0.02 0.03 0.02 0.02 0.00 Non-tradable-constr. 0.04 0.17 0.03 0.07 0.01 Tradable 0.06 0.01 0.19 0.08 0.10 Other 0.17 0.13 0.17 0.21 0.04 Oil 0.03 0.00 0.05 0.04 0.02 Table 4.6: Direct sectoral linkages 2013. A matrix. The numbers reported in Table 4.6 do not capture the full extent of intersectoral linkages however. Lower demand from the oil sector will aect not only the rms which produce inputs for the oil sector, but also the rms which produce inputs for the rms producing inputs for the oil sector, and so on. Total intersectoral linkages are given by the matrix H ≡ (I − A)−1 , referred to as the Leontief inverse and reported in Table 4.7. The bottom row now tells us the share of production which is used as inputs in the oil sector  both directly and indirectly. The share of non-tradable-retail production which is used as an input in the oil sector increases from three to ve percent when also the indirect linkages are taken into account (h11 = 0.05). In the non-tradable-construction sector, the share increases from zero to one percent (h12 = 0.01), and in the tradable sector the share increases from ve to eight percent (h13 = 0.08). Non-tradable-retail Non-tradable-constr. Tradable Other Oil Non-tradable-retail 1.03 0.04 0.03 0.03 0.01 Non-tradable-constr. 0.08 1.23 0.07 0.12 0.02 Tradable 0.11 0.04 1.28 0.14 0.14 Other 0.26 0.22 0.30 1.33 0.09 Oil 0.05 0.01 0.08 0.06 1.03 Table 4.7: Direct and indirect sectoral linkages 2013. H matrix. Adjusting for the regional importance of the oil sector In order to account for corporate sector spillovers, we would ideally want municipality level input output data. Unfortunately, input output data is only available at the national level, and so we adjust the data ourselves to allow for a greater importance of the oil sector in the oil region. Note that if oil intensive and non-oil intensive municipalities in the oil region have the same input output matrices, corporate sector spillovers would not be able to explain any of the cross-sectional increase in unemployment. We therefore allow for the possibility that rms in oil intensive municipalities are more reliant on oil sector demand than rms in non-oil intensive municipalities. For our baseline adjustment, we assume that connections to the oil sector are proportional to oil sector employment. Because there are 3.5 times as many oil sector employees in oil intensive municipalities as the national average (adjusted for population size), we assume that rms in oil intensive municipalities have 163 3.5 times as large ties to the oil sector. Similarly, because there are 1.6 times as many oil sector employees in non-oil intensive municipalities, we assume that rms in non-oil intensive municipalities have 1.6 times as large ties to the oil sector. The adjusted input output tables are reported in Tables 4.14 and 4.15 in Appendix B. We also use an alternative adjustment of the national input output data, in which we assume that only rms in oil intensive municipalities have an especially large connection to the oil sector. That is, we assume that rms in non-oil intensive municipalities have ties to the oil sector equal to the national average, whereas the additional connection to the oil sector loads only on rms in oil intensive municipalities. 90 We view this as an extreme assumption, used to provide an upper bound on the importance of corporate sector spillover in explaining the increase in cross-sectional unemployment. The employment eects of lower rm demand As shown in Acemoglu, Akcigit, and Kerr (2016), under some structural assumptions, the impact on sector i of a demand shock Z to the oil sector (sector 5), is given by ∆Yi = h5i Z . Using the fact that this equation holds also for the oil sector itself, we can rewrite the expression to get rid of the shock: ∆Yi = ∆Y5 hh55 5i . For a constant labor share across sectors and a proportional adjustment of intermediate inputs relative to labor, this same statement holds in terms of unemployment rates: ∆Ui = ∆U5 hh55 5i . 91 From Figure 4.10 we know the change in oil sector unemployment, i.e. ∆U5 = 3.5. Using the matrix elements from the adjusted H-matrix, we can then calculate the predicted increase in unemployment resulting from lower rm demand. The results are reported in Table 4.8, and range from 0.1 percentage points in the non-tradable-construction sector to 0.4 percentage points in the tradable sector under our baseline assumption. Baseline Assumption Upper Bound Assumption Implied unemployment increase (pp) Implied unemployment increase (pp) oil-intensive non-oil-intensive di. oil-intensive non-oil-intensive di. 0.17 0.09 0.25 0.05 Non-tradable-retail 1.11 × 3.5 = 0.53 1.06 × 3.5 = 0.30 0.23 1.16 × 3.5 = 0.75 1.03 × 3.5 = 0.17 0.58 0.07 0.03 0.08 0.01 Non-tradable-constr. 1.11 × 3.5 = 0.22 1.06 × 3.5 = 0.10 0.11 1.16 × 3.5 = 0.24 1.03 × 3.5 = 0.03 0.21 0.26 0.12 0.37 0.08 Tradable 1.11 × 3.5 = 0.82 1.06 × 3.5 = 0.40 0.42 1.16 × 3.5 = 1.12 1.03 × 3.5 = 0.27 0.85 Table 4.8: Predicted unemployment increases from network analysis. 90 In this case rms in oil intensive municipalities are assumed to have 3.5 + 1.6 = 5.1 times as large ties to the oil sector as the national economy. 91 Following Acemoglu, Akcigit, and Kerr (2016), let ∆Yi = αL ∆Li + Π5j=1 αij ∆xij . Assuming a proportional eect on  i  L h5i h5i α5 labor relative to intermediate inputs (i.e. Π5 j=1 αij ∆xij = h 5 Πj=1 α5j ∆x5j ), we get that ∆Li = ∆L5 . For ∆Li = 55 h55 αL i L h5i α5 αL −∆Ui , we get that ∆U i = h55 αL ∆U5 . In the data, the labor share in the oil sector is relatively low, so that 5L < 1 for i αi i = {tradable, non − tradable, construction}. Hence, not accounting for sector specic labor shares creates an upward bias in our estimates of the rm demand channel. 164 Figure 4.13 illustrates the share of the unemployment increase attributed to lower rm demand. The coecient estimates are the regression equivalences of Figure 4.12, i.e. the increase in unemployment in oil intensive municipalities relative to that of non-oil intensive municipalities. The blue bars are the predicted increases from the input output data reported in Table 4.8, with the dark blue referring to our baseline estimates and the light blue referring to our upper bound estimates. Two features are worth noticing. First, in the non-tradable sectors, lower rm demand appears to not fully account for the increase in unemployment, suggesting that there is some room for the impact of lower household demand. Second, in the tradable sector, the remaining unemployment increase after accounting for lower rm demand is not statistically signicant, consistent with the tradable sector being less sensitive to local household demand. 3 Change in unemployment (pp) 1 0 2 Non-tradable-retail Non-tradable-construction Tradable Estimated Firm demand (baseline) Firm demand (upper bound) Figure 4.13: Estimated increase in unemployment by sector and predicted unemployment increase from network analysis. 4.5.3 Household demand Figure 4.13 suggested that lower rm demand might not be able to fully account for the unemployment increase in the non-tradable sectors. Hence, lower demand from the household sector is likely to play a role. Household demand may be lower due to at least two reasons. First, individuals who experience job loss will decrease consumption because their income is lower. Second, individuals who experience an increase in job loss risk will decrease consumption in order to save more. 92 While we cannot isolate the eect of higher realized unemployment from the eect of higher job loss risk, we argue that the latter is quantitatively more important. To see this, note that for every oil worker who experienced job loss in 2014-2015, twenty-four oil workers kept their job. With some back of the envelope calculations, we can compare the total consumption loss 92 If house prices fell in oil intensive municipalities, this could also contribute to lower relative consumption. However, house price growth was roughly zero in 2015, and the dierence between oil intensive and non oil intensive municipalities was not statistically signicant - see Figure 4.26 in Appendix A. 165 coming from job losers to the total consumption loss coming from job keepers. First, assume that job keepers in the oil sector reduce their consumption by $1,200 reecting the results in Table 4.2 in the previous section. Second, assume that job losers consume all of their after tax income, and that they reduce consumption by 14 percent upon job loss (Browning and Crossley, 2001). 93 This implies that the total consumption loss 1,200 from the job loss risk channel is 24 × 0.14×51,500 = 4.0 times as large as the total consumption loss from the realized unemployment channel. If we accept that the unemployment increase which is not accounted for by lower rm demand is due to lower household demand resulting either from increased unemployment or from increased job loss risk, we can back out the importance of the latter. This is done in Figure 4.14, using the back of the envelope calculations to determine the relative magnitude of the two household demand eects. The pink area captures the unemployment increase attributed to realized unemployment, while the red area captures the unemployment increase attributed to higher job loss risk. The latter is the quantitatively most important driver of higher unemployment in the non-tradable sectors according to our decomposition. We thus conclude that, although identifying the general equilibrium impact of a risk induced increase in savings is challenging, the data appears consistent with there being negative employment eects working though this channel. 3 Change in unemployment (pp) 1 0 2 Non-tradable-retail Non-tradable-construction Tradable Estimated Firm demand (baseline) Firm demand (upper bound) HH demand: Unemployment HH demand: Job Loss Risk Figure 4.14: Estimated increase in unemployment by sector, predicted unemployment increase from network analysis and decomposition of the household demand eects. 4.6 Conclusion We have used the oil price collapse of 2014 to identify an exogenous increase in job loss risk for certain segments of the population. By doing a within-region comparison of individuals across dierent occupations, 93 Several papers use food consumption from the PSID to estimate the consumption drop upon unemployment. These papers generally nd consumption falls of less than ten percent, see for instance Chetty and Szeidl (2007). We use a consumption drop of 14 percent as estimated by Browning and Crossley (2001) using Canadian data, as they consider total consumption and Canada and Norway have similar replacement ratios. 166 we estimated that a one percentage point increase in job loss risk increases liquid savings by 1.2 - 2.0 percent. This eect was driven by low-tenured individuals, who faced the largest increase in job loss risk. We found no eect on other nancial assets, suggesting that the saving response came through bank deposits only. Further, we showed that unemployment in non-oil sectors increased more in municipalities with larger saving responses. For non-tradable sectors, the increase in unemployment was not (fully) accounted for by lower demand from the rm sector, suggesting that lower demand from the household sector was an important cause. Back of the envelope calculations suggested that lower household demand was largely driven by a risk induced increase in savings rather than realized job loss. Hence, the data appears consistent with the mechanism from the motivating theory: individual savings increase as job loss risk rises, leading to a reduction in aggregate demand and potentially amplifying the economic downturn. 167 Appendix A: Figures Average Saving Rate Recessions 1960-2018 10.5 10 9.5 9 0 5 10 Quarters after start of recession 8/8 recessions ongoing 5/8 recessionsongoing 3/8 recessions ongoing Figure 4.15: US personal saving rate. Savings as a share of disposable income. Average over past eight recessions (1960-2018). Three quarter moving average. Source: St. Louis FRED database. 30 25 OECD unemployment rate (%) 5 10 15 0 20 2000 2003 2006 2009 2012 2015 2018 USA OECD Norway Figure 4.16: OECD harmonized unemployment rates by country (%). Oil Price Brent - Dollars per Barrel 120 100 80 60 40 20 2011 2012 2013 2014 2015 2016 Figure 4.17: Oil price brent. USD per barrel. 168 Figure 4.18: Share of workers employed in the oil sector relative to the share of total workers by county. Deposits In Oil Region - Engineers 45000 38000 Engineers Job Loss 2016 Engineers (No Job Loss) 35000 28000 25000 18000 2010 2011 2012 2013 2014 2015 Engineers Engineers No Job Loss Engineers Job Loss 2016 Figure 4.19: Bank deposits in oil regions for engineers, engineer who did not lose their job following the oil price collapse, and engineers who lost their job in 2016. Unemployment In Oil Region Separation Rate In Oil Region 10 10 8 8 6 6 4 4 2 2 0 0 2001 2006 2011 2016 2001 2006 2011 2016 Engineers Low Tenure Engineers High Tenure Engineers Low Tenure Engineers High Tenure Figure 4.20: Unemployment rate and separation rate (%) for low tenure engineers in the oil region and high tenure engineers in the oil region. 169 Unemployment Separation Rate 7 7 6 6 5 5 4 4 3 3 2 2 1 1 0 0 2001 2006 2011 2016 2001 2006 2011 2016 Engineers in Oil Region Other High Skilled Engineers in Oil Region Other High Skilled Figure 4.21: Unemployment rate and separation rate (%) for engineers in the oil region and other high skilled workers in all regions. Unemployment In Oil Region Separation Rate In Oil Region 8 8 6 6 4 4 2 2 0 0 2001 2006 2011 2016 2001 2006 2011 2016 Oil Sector Engineers Other High Skilled Oil Sector Engineers Other High Skilled Figure 4.22: Unemployment rate and separation rate (%) for oil sector engineers in the oil region and other high skilled workers in the oil region. House Prices in Oil Region by Occupation 30000 25000 20000 15000 2002 2004 2006 2008 2010 2012 2014 2016 Engineers Oil Region Other High-Skilled Oil Region High-Skilled Non-Oil Region Figure 4.23: House prices single family homes. Municipality level. Average for engineers and other high skilled workers in the oil region. 170 250 200 150 100 2010 2012 2014 2016 2018 S&P 500 Oslo Stock Exchange Figure 4.24: Stock prices. S&P 500 index and Oslo Stock Exchange index. Solid lines are annual data, whereas dashed lines are monthly data. Other Financial Assets 10000 20000 30000 40000 50000 60000 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 Engineers Oil Region Other High-Skilled Oil Region High-Skilled Non-Oil Region Figure 4.25: Other nancial assets by occupation-region. House Prices 400000 300000 200000 100000 2002 2006 2010 2014 Oil Intensive Non-Oil Intensive Figure 4.26: Average house prices for oil intensive and non-oil intensive municipalities. 171 Appendix B: Tables Occupations Education/Skills Share of Workers (%) 1 - Managers Not specied 11 2 - Professionals Min. 4y of higher educ. 15 3 - Technicians/Associate prof. 1y-3y of higher educ. 21 4 - Clerical support workers High school 6 5 - Service and sales workers High school 12 6 - Skilled agriculture High school 1 7 - Craft and related trade workers High school 17 8 - Plant and machine operators High school 11 9 - Elementary occupations Not specied 4 0 - Armed forces and unspecied Not specied 2 Table 4.9: Occupations. Occupations 1-3 are classied as high skilled. (1) (2) (3) (4) Deposits Deposits FW FW Ti2013 × Itpost 1,187** 1,283** 1,281 1,221 (2.12) (2.32) (1.33) (1.24) Increase in Deposits/FW (%) 3.37 3.64 1.98 1.89 per pp increase in unemployment rate(%) 1.14 0.992 0.669 0.515 per pp increase in separation rate(%) 1.18 1.21 0.692 0.630 Sample period 2010-2014 2010-2015 2010-2014 2010-2015 Clusters 19,370 19,370 19,370 19,370 N 95,332 114,370 95,332 114,370 t statistics in parentheses. Std. errors clustered at the individual level. * p < 0.1, ** p < 0.05, *** p < 0.01 Table 4.10: Bank deposits and total nancial wealth (FW). Within oil region analysis. Regression results from estimating equation (166) with Y = {Bank Deposits, Total Financial Wealth}. (1) (2) (3) (4) Bank Deposits Bank Deposits Bank Deposits Bank Deposits T ×I post 1,187 1,283 1,869 ∗∗ 2,636 ∗∗ ∗∗ ∗∗∗ (2.12) (2.32) (2.21) (3.11) i t Increase in Bank Deposits (%) 3.37 3.64 5.27 7.43 per pp increase in unempl. rate (%) 1.14 0.992 1.26 1.35 per pp increase in sepr. rate (%) 1.18 1.21 1.23 1.55 Treatment group: Engineers Engineers Oil Engineers Oil Engineers Sample period 2010-2014 2010-2015 2010-2014 2010-2015 Clusters 19,370 19,370 15,638 15,638 N 95,370 114,370 77,105 92,488 t statistics in parentheses. Std. errors clustered at the individual level ∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Table 4.11: Bank deposits. Within oil region analysis Regression results from estimating equation (166), comparing engineers in the oil sector to other high-skilled workers. 172 (1) (2) (3) (4) Bank Deposits Bank Deposits Bank Deposits Bank Deposits Tm × Itpost 431.0 404.6 431.0 ∗ 404.6 ∗∗ (1.38) (1.13) (1.84) (2.07) Sample period 2010-2014 2010-2015 2010-2014 2010-2015 Clusters 59 59 - - N 295 354 295 354 t statistics in parentheses ∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Table 4.12: Bank deposits at the municipality level within the oil region. Tm = 1 if municipality m is an oil intensive municipality in the oil region, and Tm = 0 if municipality m is a non-oil intensive municipality in the oil region. (1) (2) (3) (4) Non-tradable-retail Non-tradable-construction Tradable Oil ∗∗∗ ∗∗∗ ∗∗ Tm × Tt2015 1.658 2.018 1.240 0.423 (3.91) (4.54) (2.52) (1.17) Clusters 59 59 59 59 N 354 353 349 349 t statistics in parentheses ∗ p < 0.1, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Table 4.13: Sectoral unemployment rates at the municipality level within the oil region. Tm = 1 if munici- pality m is an oil intensive municipality in the oil region, and Tm = 0 if municipality m is a non-oil intensive municipality in the oil region. Non-tradable-retail Non-tradable-constr. Tradable Other Oil Non-tradable-retail 0.02 0.03 0.01 0.01 0.00 Non-tradable-constr. 0.03 0.17 0.02 0.05 0.00 Tradable 0.04 0.01 0.13 0.06 0.06 Other 0.12 0.13 0.11 0.16 0.02 Oil 0.12 0.02 0.18 0.13 0.08 Table 4.14: Direct sectoral linkages 2013. A matrix. Baseline adjustment for oil intensive municipalities in the oil region. Created by taking Table 4.6 and assuming that aadjsuted 5j = 3.5a5j ∀ j and adjusting all P4 adjusted P4 otheraij 's with the same factor i=1 aij =x i=1 aij ∀ j such that the total input share is unchanged P5 adjusted P5 a i=1 ij = i=1 aadjusted ij ∀ j. 173 Non-tradable-retail Non-tradable-constr. Tradable Other Oil Non-tradable-retail 0.02 0.03 0.02 0.02 0.00 Non-tradable-constr. 0.04 0.17 0.03 0.07 0.01 Tradable 0.06 0.01 0.18 0.08 0.09 Other 0.16 0.13 0.15 0.20 0.04 Oil 0.06 0.01 0.08 0.06 0.04 Table 4.15: Direct sectoral linkages 2013. A matrix. Baseline adjustment for non-oil intensive municipalities in the oil region. Created by taking Table 4.6 and assuming that aadjsuted 5j = 1.6a5j ∀ j and adjusting all P4 adjusted P4 otheraij 's with the same factor i=1 aij =x i=1 aij ∀ j such that the total input share is unchanged P5 adjusted P5 a i=1 ij = i=1 aadjusted ij ∀ j. Non-tradable-retail Non-tradable-constr. Tradable Other Oil Non-tradable-retail 0.01 0.03 0.01 0.01 0.00 Non-tradable-constr. 0.02 0.16 0.01 0.04 0.00 Tradable 0.03 0.01 0.09 0.05 0.04 Other 0.09 0.12 0.08 0.12 0.02 Oil 0.18 0.02 0.27 0.20 0.12 Table 4.16: Direct sectoral linkages 2013. A matrix. Upper bound adjustment for oil intensive municipalities in the oil region. Created by taking Table 4.6 and assuming that aadjsuted 5j = 5.1a5j ∀ j and adjusting all P4 adjusted P4 otheraij 's with the same factor i=1 aij =x i=1 aij ∀ j such that the total input share is unchanged P5 adjusted P5 a i=1 ij = i=1 aadjusted ij ∀ j. Appendix C: Selection into unemployment In this appendix, we attempt to quantify the amount of selection into unemployment based on observable characteristics among engineers in the years following the oil price collapse. We start by evaluating to what extent we can predict job loss during the oil crisis based on baseline characteristics. Specically, we dene an indicator variable Iijobloss = 1 if engineer i experienced job loss in 2015 or 2016, and zero otherwise. We then regress this indicator variable on 2013 characteristics in a probit regression, according to equation (168). Ex-ante, we expect tenure to be an important variable in explaining job loss, as rms are obliged to follow the seniority principle in determining layos. Other control variables are captured in Xi , and include age, wage income, total income, housing wealth, real wealth, nancial wealth, bank deposits, and debt. Iijobloss = α + β T enurei + γXi + i (168) The regression results are reported in Table 4.17. As expected, tenure has a negative and signicant eect on the probability of job loss. However, after controlling for tenure, information on income, wealth 174 and debt does not have a signicant impact on the probability of job loss. The only other variable that is statistically signicant  at the ten percent level  is age. When tenure is not included in the regression, both age, nancial wealth and debt has a signicant eect on the probability of job loss. The pseudo R2 is low in both cases, but especially so when tenure is excluded from the analysis. In order to compare the amount of selection during the oil crisis to selection into unemployment during normal times, we repeat the above analysis for job loss prior to the oil price collapse. Specically, we let Iijobloss indicate job loss in one of the years 2003-2013 and rerun the regression specied in equation (168). We then compare the pseudo R2 's to the pseudo R2 reported in Table 4.17. The results are depicted in Figure 4.27. The pseudo R2 's during the oil crisis is the lowest in the sample, suggesting that the simple statistical model outlined in equation (168) has less explanatory power in predicting job loss during the oil price crisis than in normal times. Note however, that because we can only calculate tenure back until year 2000, the comparison is somewhat misleading (as the tenure variable contains more information towards the end of the sample). In order to undertake a more fair comparison, we exclude tenure from the model, and redo the analysis. The resulting pseudo R2 's are depicted in the right panel of Figure 4.27. The pseudo R2 during the oil price collapse is now much lower than in normal times, suggesting less selection on observables into unemployment. (1) (2) Job Loss Job Loss Tenure -0.0737∗∗∗ (-10.54) Age 0.00402∗ -0.00490∗∗ (1.71) (-2.22) Wage Income 0.000000240 -0.000000971 (0.22) (-0.82) Total Income -0.000000957 -0.000000244 (-1.09) (-0.24) Primary Housing Wealth 5.77e-08 -6.37e-08 (0.21) (-0.24) Real Wealth -0.000000151 -0.000000202 (-0.58) (-0.80) Financial Wealth -0.000000621 -0.000000810∗∗ (-1.63) (-2.12) Bank Deposits 9.80e-08 0.000000144 (0.14) (0.21) Debt 0.000000202 0.000000236∗ (1.41) (1.68) Constant -1.082∗∗∗ -1.009∗∗∗ (-10.76) (-10.09) Pseudo R2 0.0457 0.0133 N 6,732 6,732 t statistics in parentheses ∗ p < 0.01, ∗∗ p < 0.05, ∗∗∗ p < 0.01 Table 4.17: Regression results from estimating equation (168) with dependent variable Iijobloss = 1 if engineer i experienced job loss in 2015-2016. Probit regression. 175 Pseudo R2 - model with tenure Pseudo R2 - model without tenure .08 .08 .06 .06 .04 .04 .02 .02 0 0 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Oil 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Oil Figure 4.27: Pseudo R2 from probit regression. Appendix D: Model Households Individual i chooses a consumption index ci,t and savings bi,t in order to maximize utility U (ci,t ) subject to a borrowing limit bi,t ≥ bmin and the budget constraint outlined in equation (169). Em- ployed individuals receive a wage income wt , while unemployed individuals receive unemployment benets ξt . Employed individuals lose their current job with an exogenous probability ρt ∈ [0, 1]. Unemployed indi- viduals nd a new job with probability qt , which is endogenously determined by the number of unemployed individuals and the number of vacancies. Rt−1 ci,t + bi,t = ni,t wt + (1 − ni,t )ξt + bi,t−1 (169) 1 + πt Entrepreneurs Entrepreneur j produces output yj,t using a linear production function with labor lj,t as the only input. To hire workers the entrepreneur posts vacancies vj,t , which costs a xed cost µ and are lled with a probability ψt . The entrepreneurs marginal costs are outlined in equation (170).   µ µ mcj,t = wt + − βEt (1 − ρt ) (170) ψt ψt+1 The entrepreneur maximizes prots, given by equation (171). As seen from the last term of the prot expression, we assume Rotemberg price frictions, so that entrepreneurs face a quadratic price adjustment  −γ Pj,t cost. Due to monopolistic competition, the entrepreneur also faces the demand constraint yj,t = yt . Pt The entrepreneurs are the sole claimants to the prots they produce, which they use for consumption and to cover production costs and taxes. 176 ∞    2 ! X s Pj,t+s φ Pj,t+s Et β − mcj,t+s yj,t+s − − 1 yt (171) s=0 Pt+s 2 Pj,t+s−1 Labor Market The wage is assumed to be perfectly rigid so that wt = w, in which w is consistent with the joint matching surplus being non-negative. The matching technology is given by equation (172), in which ut is the number of unemployed individuals, vt is the number of vacancies and m and α are constant parameters. 1−α mt = m uα t vt (172) Government The government runs a balanced budget, so that the amount spent on unemployment ben- ets each period equals revenues from taxing entrepreneurs. Monetary policy follows the Taylor rule given by equation (173), in which ¯ R is the long run nominal interest rate target and π is the long run ination target.  η 1 + πt Rt = R (173) 1+π Timing The timing is as follows: i) the state of the world is realized, i.e. (the aggregate) separation rate ρt becomes known to everyone, ii) matching occurs between rms with vacancies and individuals searching for a job, iii) production and consumption occur, and iv) job separation occurs. Solving the model When solving the model we follow Ravn and Sterk (2017) in imposing bmin = 0, so that there is no saving or borrowing. This implies a degenerate wealth distribution, greatly simplifying the computations. Importantly, the precautionary saving motive is still present through the households Euler equation. In order to solve the model numerically we log-linearize the equilibrium conditions around steady state values. Non-linear equilibrium Endogenous variables: {Rt , πt , qt , mt , ut , vt , lt , yt , θt , ψt , ρt } Shocks: t 177 The 11 equilibrium conditions are Rt w−σ = βEt (1 − ρt )w−σ + ρt ξ −σ  (174) 1 + πt+1  η 1 + πt Rt = R (175) 1+π    −1 α h −1 α i yt+1 1 − γ + γ w + µm 1−α qt1−α 1−α − βE µm 1−α qt+1 = φπt (1 + πt ) − φβEt πt+1 (1 + πt+1 ) (176) yt ut = (1 − qt ) (ut−1 + ρt−1 lt−1 ) (177) lt = 1 − ut (178) ρt = ρδt−1 ρ1−δ t (179) α 1 − 1−α ψt = m 1−α qt (180) 1 1 θt = m− 1−α qt1−α (181) vt = θt ut (182) 1−α mt = m uα t vt (183) yt = lt (184) Steady state π=0 (185)  1−α γ −1 (γ − 1) − w  α q = mα (186) µ(1 − β) ρ=ρ (187) ρ(1 − q) u= (188) ρ + q − ρq Log-linearized equilibrium Xt −X Dene Xt = X , where X is the steady state value of Xt . 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