This dissertation is composed of four essays that study macroeconomic questions in models that depart from standard frameworks by including features, such as household heterogeneity and low nominal interest rates, that during the recent two decades have become more salient in developed economies. Chapter 1, “Monetary Policy and Payment-to-Income Limits in Liquidity Traps", analyzes the macroeconomic implications of tighter Payment-to-Income (PTI) borrowing limits when an economy is up against the ZLB following a deleveraging shock, conditions that characterized the Great Recession in the US. The model suggests that, relative to a scenario with no policy intervention, the tighter PTI limits introduced in 2009 increased welfare losses (17\%) and prolonged the expected duration of the liquidity trap. Chapter 2, “A Toolkit for Solving Models with a Lower Bound on Interest Rates of Stochastic Duration", provides a fast algorithm to cope with the computational challenges introduced by the ZLB in dynamic stochastic general equilibrium (DSGE) models. The paper generalizes the solution method of Eggertsson and Woodford (2003) and uses the proposed algorithm to study a set of monetary policy strategies and their performance in recessions that lead economies into a liquidity trap. The two proposed policy rules would have allowed the the Federal Reserve to reduce the output contraction in 2008 by about 80-90 percent. Chapter 3, “Should Inequality Factor into Central Banks’ Decisions?", explores the implications of permanent income inequality on the desirable monetary policy in a simple framework. The model suggests little welfare gains of deviating from the optimal policy to a rule that emerges in the representative agent model, and larger gains from being more accomodative than a standard Taylor rule. Chapter 4, “Monetary Policy, Heterogeneous Agents, and Nominal Rigidities: a TANK Approach", analyzes the effects of monetary policy in a simple framework with price or wage rigidities. The paper suggests that the result in Kaplan, Moll, Violante (2018) depends on the assumed nominal rigidity and is not robust to the introduction of wage rigidities.
