Endogenous Economic Institutions, Wage Inequality, and
Economic Growth

by
Christos Pargianas
B.A., Aristotle University of Thessaloniki, Greece, 2002
M.A., University of Macedonia, Greece, 2005
M.A., Brown University, 2006

Submitted in Partial Fulfillment of the Requirements
for the Degree of Doctor of Philosophy in the
Department of Economics at Brown University

Providence, Rhode Island
May 2011

© Copyright 2011 by Christos Pargianas

This dissertation by Christos Pargianas is accepted in its present form
by the Department of Economics as satisfying the
dissertation requirement for the degree of Doctor of Philosophy.

Date_______________

______________________________
Oded Galor, Advisor

Recommended to the Graduate Council

Date_______________

______________________________
Peter Howitt, Reader

Date_______________

______________________________
Ross Levine, Reader

Approved by the Graduate Council

Date_______________

______________________________
Peter M. Weber, Dean of the Graduate School
iii

Vita

The author was born in Thessaloniki, Greece on October 9, 1978. He obtained his
Bachelor’s degree from the Aristotle University of Thessaloniki, Greece in 2002. After
obtaining a Master’s degree from the University of Macedonia, Greece in 2005, the
author moved to Providence, RI to begin his Ph.D. in economics at Brown University.
Graduate classes in Macroeconomics and Economic Growth sparked his interest in
Economic Growth Theory. He received his Master’s degree from Brown University in
2006 and his Doctorate in 2011.

iv

Acknowledgements
I wish to thank my main advisor, Oded Galor, and my thesis committee members, Peter
Howitt and Ross Levine for their advice, support, and encouragement throughout my
graduate school career. Also, I wish to thank Brian Knight, David Weil, and seminar
participants at Brown University for their insightful comments and suggestions.

v

Contents

1. Endogenous Economic Institutions and Wage inequality
1.1. Introduction
1.2. The Model
1.2.1. Production
1.2.2. Political economy model
1.2.3. The effect of the supply of skills on skill premium
1.3. Endogenous Supply of Skills
1.4. Concluding Remarks
1.5. Appendix
1.5.1. Deadweight loss from taxation that is proportional to the square
of the tax rate
1.5.2. Proof of proposition 1.2.
2. Endogenous Economic Institutions and Persistent Income differences
2.1. Introduction
2.2. The Model
2.2.1. Production
2.2.2. The political economy model
2.2.3. The relative supply of skills
2.2.4. Steady state analysis
2.3. Concluding Remarks
Bibliography

1
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5
5
7
12
15
17
18
18
19
20
20
23
23
26
31
32
35
36

vi

CHAPTER 1

Endogenous Economic Institutions and Wage Inequality

1.1.

INTRODUCTION

In the period after 1970 economic fortunes diverged, especially in the United States.
Middle and high income Americans have continued to benefit from the massive
economic growth. But material well-being for the lower income classes has stagnated.
Households with an annual income of over $100,000 (year $2000 dollars) increased from
under 3% in 1967 to over 12% in 2000. In year 2000 dollars, median income increased
from $31,400 in 1967 to $42,200 in 2000.
Although overall inequality increased steadily after 1970, this was not the case for skill
premium. In 1970 college graduates earned 55% more than high school graduates. This
premium fell to 41% in 1980, but then increased to 62% in 1995. 1
One explanation for the rapid increase in the college premium in the 1980s is skill biased
technological change. 2 According to this explanation, an increase in the supply of skills
has two effects on skill premium. First, it decreases skill premium through the
conventional substitution effect which makes the economy move along a downward
sloping relative demand curve. Second, it increases skill premium through the directed
technology effect which shifts the relative demand for skills because the increase in the
supply of skills induces faster upgrading of skill-complementary technologies. Galor and
Moav (2000) argue that an increase in the rate of technological progress raises the returns
to ability and simultaneously generates an increase in wage inequality between and
within groups of skilled and unskilled workers and an increase in education. Finally,
1
2

See Autor, Katz, and Krueger (1998).
See Acemoglu (1998).

1

there is the international trade explanation. According to this theory, an increase in the
volume of trade will increase the demand for skill intensive goods in countries that export
these goods. This will increase both the supply of skills and the skill premium.
This paper provides another explanation that works through economic institutions and
policies. Economic institutions determine the incentives of economic actors, and shape
economic outcomes. As such they are social decisions chosen for their consequences.
Different groups and individuals benefit from different economic institutions and
policies. Thus, there is generally a conflict over these social choices, ultimately resolved
in favor of groups with greater political power. An increase in the number of skilled
individuals will increase their political power and their ability to affect economic
policies.
Economists agree that economic institutions and policies are endogenously determined.
McCarthy, Poole and Rosenthal (2006) argue about the changes in economic policy that
took place during the 1980s: ‘Reagan conservatism was a product sitting on a shelf in the
political supermarket. In 1980, customers switched brands’. As the number of those who
benefit from conservative economic policies increased dramatically during the 1970s,
both parties, and not only Republicans, adopted relatively more conservative economic
policies. McCarthy, Poole, and Rosenthal (2006) argue that both Democrats and
Republicans became more conservative in economic issues after 1975. Gerring (1998)
argues that after the 1970s Democrats have moved their platforms away from general
welfare issues to issues based on ascriptive characteristics (race and gender) of
individuals.
The basic argument is the following: low-educated voters are not able to fully understand
the impact the various policies have on their income. As a result, they rely on
advertisement in order to decide which policies will benefit them more. This gives an
incentive to political parties to choose bad policies that benefit some groups, in exchange
for campaign contributions that ‘buy’ unskilled workers’ votes. Bad policies (low
property right protection, high tax on profits, high cost to start a new firm and high
minimum wage) imply smaller support from educated voters and bigger support from
uneducated voters. An increase in the proportion of skilled workers in the labor force
implies an increase in the relative importance of skilled workers in the political process.
As a result, an increase in the proportion of skilled workers reduces skill premium in the
short run, but then it induces a change in economic policies that increases the skill
premium, possibly even above its initial value.
Empirical evidence supports the conjecture that economic institutions and policies can
account for much of the rise in dispersion of the wage distribution. DiNardo, Fortin, and
Lemieux (1996) find that from 1979 to 1988 the decrease in the minimum wage explains
24% (for men) and 32% (for women) of the change in the variance in log wages. Card
2

and Krueger (1995) conclude that 20 to 30 percent of the rise in wage dispersion during
the 1980s could be attributed to the decline in the real value of the minimum wage.
Mishel, Bernstein, and Schmitt (1996) examine the 90/10 wage differential and report
even larger effects. Lee (1999) finds that during the 1980s, the estimates for men, women
as well as the combined sample, imply that almost all of the growth in the wage gap
between the tenth and fiftieth percentiles is attributable to the erosion of the real value of
the minimum wage during the decade. He also argues that the minimum wage may
account for as much as 80% of the growth in so called ‘within-group’ wage inequality
and about 15% of the change in the return to schooling during the 1980s. This last piece
of evidence shows also that skilled workers benefit from a low minimum wage.
This paper argues that political parties will choose such bad (for skilled workers) policies
not in order to gain support from unskilled workers through redistribution, but in order to
benefit some special interest groups in exchange for campaign contributions. 3 Indeed,
Neumark, Schweitzer, and Wascher (2004) argue that low-wage workers are adversely
affected by minimum wage increases. Although wages of low-wage workers increase,
their hours and employment decline, and the combined effect of these changes is a
decline in earned income. They also find that relatively low-wage union members gain at
the expense of the low-wage nonunion workers when minimum wages increase. This
explains the vigorous support of labor unions for minimum wage increases and their
significant contributions to the political campaigns. 4 Labor market regulations, high
taxes, corruption, and restrictions that increase the cost of starting a firm are some other
policies that affect negatively skilled workers (entrepreneurs) more than unskilled. Labor
unions, corrupt bureaucrats, and firms that target government subsidies and, thus, they
prefer high tax rates and large government, are those that support these policies.
The assumption that unskilled individuals are impressionable voters is at the heart of the
model. Impressionable are those voters who are not willing or are not able to make the
calculations necessary for strategic voting. These voters pay attention to campaign
advertisement. The more a party spends (holding constant the spending of its rival), the
greater is its share of the impressionable votes. Strategic voters understand the political
environment and the implications of their votes. By voting for the party whose platform
he prefers, a strategic voter slightly increases his expected welfare. There is empirical
evidence that education increases civic participation. 5 Educated individuals participate
more actively in politics, read more often newspapers, send letters to politicians and try to
3

Alesina, Glaeser, and Sacerdote (2001) show empirically that higher inequality is not associated with
more redistribution. This implies that the traditional model of the median voter who chooses the level of
redistribution is not a good representation of reality.
4
According to Hrebenar, Burbank, and Benedict (1999), both in the 1995-1996 and in the 1997-1998
campaign cycles, five out of the top ten political action committee (PAC) contributors to federal
candidates are labor unions.
5
See Dee (2003), Glaeser, Ponzetto, and Shleifer (2007), and, Milligan, Moretti, and Oreopoulos (2004).

3

persuade others. Also, education allows those who are interested in politics to understand
and evaluate the different policies and the impact that these policies have on their
welfare. In other words, education allows individuals to become strategic voters. 6
The impact of an increase in the supply of skills on the skill premium is determined by
two competing forces: the first is the conventional substitution effect which makes the
economy move along a downward sloping relative demand curve. The second is the
political economy effect, which shifts the relative demand curve for skills as shown in
figure I, because the increase in the supply of skills induces policy changes that benefit
skilled workers.
A large increase in the supply of college graduates as in the late 1960s and 1970s first
moves the economy along a short-run (constant policy) relative demand curve, reducing
the college premium. The relative supply change also increases the fraction of strategic
voters and decreases the fraction of impressionable voters. Thus, policies change and skill
premium increases. The relative demand curve in Figure I shifts to the right. If the
political economy effect is not big enough then the skill premium first falls and then
increases, but not above its initial level. In contrast, if the political economy effect is big
enough, the model predicts that in the long run the college premium should increase. This
case (shown in Figure I) explains the change in the U.S. college premium over the past 25
years.
Shift in Relative
Supply of Skills
𝜔

Long Run Relative Demand
for Skills

Initial Skill Premium

Shift in Short Run Relative
Demand for Skills due to
Institutional Improvement

Long Run Skill Premium
Short Run Response

𝑠

Figure I

6

A similar assumption has been made by Bourguignon and Verdier (2000). They argue that only those
with high enough education vote. I argue that only those with high enough education are strategic voters.

4

1.2.

THE MODEL

1.2.1. Production

There is a sequence of discrete time periods 𝑡 = 1,2, … There is a mass 𝐿 of workers in
the economy. Workers can be skilled (entrepreneurs) or unskilled. I assume that the
number of skilled and unskilled workers is exogenous. Later I will relax this assumption.
There are 𝑠 skilled and 𝑢 unskilled individuals that supply labor inelastically. Individuals
live forever and for simplicity I assume that they cannot save or borrow. In the end of
each period they consume all their income, and thus they seek to maximize it.
People consume only one good, called the final good, which is produced by perfectly
competitive firms using as inputs unskilled labor and a continuum of intermediate goods
according to the technology: 7
1

𝛼
𝑌𝑡 = 𝑢1−𝛼 ∫0 𝛢1−𝛼
𝑖𝑡 𝑥𝑖𝑡 𝑑𝑖,

(1)

where each 𝑥𝑖𝑡 denotes the quantity of intermediate input 𝑖 used in final good production
at time 𝑡, and 𝐴𝑖𝑡 is a productivity parameter that reflects the current quality of the
intermediate good 𝑖. The coefficient 𝛼 lies between zero and one. In any period the
productivity parameters will vary across intermediate products because of the
randomness of the innovation process.
Each intermediate good is produced by a monopolist each period, using the final good as
all input, one for one. That is, for each unit of intermediate good, the monopolist must use
one unit of final good as input. Final good that is not used for intermediate production is
available for consumption.
Each monopolist at 𝑡 maximizes his profit measured in units of the final good:
𝛱𝑖𝑡 = 𝑝𝑖𝑡 𝑥𝑖𝑡 − 𝑥𝑖𝑡

(2)

where 𝑝𝑖𝑡 is the price of the intermediate good 𝑖 relative to the final good.

The inverse demand curve facing each monopolist charging the price 𝑝𝑖𝑡 is the marginal
product:
𝑝𝑖𝑡 = 𝛼(𝐴𝑖𝑡 𝑢)1−𝛼 𝑥𝑖𝑡 𝛼−1
7

This model is based on Aghion and Howitt (2009).

5

(3)

Therefore, the monopolist in sector 𝑖 chooses the quantity 𝑥𝑖𝑡 to maximize profits,
𝛱𝑖𝑡 = (𝛼(𝐴𝑖𝑡 𝑢)1−𝛼 𝑥𝑖𝑡 𝛼−1 − 1)𝑥𝑖𝑡

(4)

which implies an equilibrium quantity:

2

𝑥𝑖𝑡 = 𝛼 1−𝛼 𝛢𝑖𝑡 𝑢

(5)

The equilibrium profit of the monopolist is:

1+𝛼

𝛱𝑖𝑡 = (1 − 𝛼)𝛼 1−𝛼 𝐴𝑖𝑡 𝑢

(6)

In each period, entrepreneurs (skilled individuals) will attempt an innovation, each one in
a different sector. If an entrepreneur succeeds, the innovation will create a new version of
the intermediate good, which is more productive than previous versions. Specifically, the
productivity of the intermediate good will go from last period’s value 𝐴𝑖,𝑡−1 up to
𝐴𝑖𝑡 = 𝛾𝛢𝑖,𝑡−1 , where 𝛾 > 1. If he fails, then there will be no innovation and the
intermediate good will be the same one that was used in 𝑡 − 1, so 𝐴𝑖𝑡 = 𝐴𝑖,𝑡−1 .
In order to innovate, the entrepreneur must conduct research, a costly activity that uses
entrepreneur’s labor as its only input. The probability that an innovation occurs in any
period 𝑡 is:
𝜇𝑡 = 𝜆

𝜑𝐴𝑡
𝐴∗𝑖𝑡

(7)

where 𝐴∗𝑖𝑡 = 𝛾𝐴𝑖,𝑡−1 is the productivity parameter if he succeeds. The reason why the
probability of innovation depends on 𝐴∗𝑖𝑡 is that as technology advances it becomes more
complex and thus harder to improve upon. 𝜆 is a parameter that reflects the productivity
of the research sector. Entrepreneurial skills are produced by two inputs: time and local
knowledge. I take as given the amount of time spend in education by each entrepreneur. 8
Local knowledge is a public input which we assume to be proportional to aggregate
1

productivity 𝐴𝑡 = ∫0 𝐴𝑖𝑡 𝑑𝑖. 𝜑𝛢𝑡 is the skill level of each entrepreneur. 9
Each entrepreneur’s wage is his expected reward from innovation: 10

8

It is straightforward to endogenize the time spend on education. Suppose that 𝜑 = (1 − 𝑛)𝑛𝑚
represents the effective supply of skills, where 𝑛 is the time spent in education and 𝑚 lies between zero
and one. Each entrepreneur chooses the same 𝑛 in order to maximize 𝜑.
9
The same assumption is made by Howitt and Mayer-Foulkes (2005). They assume that the skill level
depends on the average level of technology.
10
This is not the actual wage. It is the expected wage. The actual wage is either zero or 𝛱𝑖𝑡 . To simplify the
analysis I assume that entrepreneurs can buy insurance. Thus, they receive with certainty their expected
reward from innovation.

6

𝑤𝑠 = 𝜆

𝜑𝐴𝑡
𝐴∗𝑖𝑡

𝛱𝑖𝑡 = 𝜆

𝜑𝐴𝑡
𝐴∗𝑖𝑡

1+𝛼

1+𝛼

(1 − 𝛼 )𝛼 1−𝛼 𝐴𝑖𝑡 𝑢 = 𝜆𝜑𝐴𝑡 (1 − 𝛼)𝛼 1−𝛼 𝑢

(8)

because 𝐴∗𝑖𝑡 = 𝐴𝑖𝑡 when innovation takes place. Equation (8) implies that the expected
reward is the same in all sectors.
Each unskilled worker will receive his marginal product. Simple algebra gives:
2𝛼

𝑤𝑢 = (1 − 𝛼)𝛼 1−𝛼 𝛢𝑡

(9)

Skill premium, 𝜔, is defined as follows:
𝜔=

𝑤𝑠

𝑤𝑢

= 𝜆𝜑𝛼𝑢 = 𝜆𝜑𝛼(𝐿 − 𝑠)

(10)

I assume for simplicity that 𝐿 = 1 and thus, 𝑠 is the share and the number of skilled
workers. Skill premium becomes:
𝜔 = 𝜆𝜑𝛼(1 − 𝑠)

(11)

1.2.2. Political economy model

There are two political parties, 𝐴 and 𝐵. Each party announces before the election the set
of policies that will implement if elected. To simplify the analysis I restrict the available
policies to those that affect directly only the profit of a successful innovator. 11 Such
policies are for example the tax rate on profits, efforts to reduce corruption and protect
property rights, the cost to start a new firm, labor market regulations like the minimum
wage, etc. 12 The outcome of each set of policies is a tax rate, 𝑡, such that 𝑡 is the total
fraction of the profits that the owner of each firm loses because of taxation, corruption,
labor market regulations, etc.
This tax rate affects directly the wage of skilled workers (and their relative wage, or skill
premium). The wage becomes:
𝑤𝑠 = 𝜆

𝜑𝐴𝑡
𝐴∗𝑖𝑡

1+𝛼

(1 − 𝑡)𝛱𝑖𝑡 = (1 − 𝑡)𝜆𝜑𝐴𝑡 (1 − 𝛼)𝛼 1−𝛼 𝑢

11

(12)

These policies affect directly the wage of strategic voters. All other policies that this paper doesn’t
consider affect only unskilled workers. The assumption that policies that affect unskilled workers are
exogenous is based on the basic assumption of the model that unskilled workers are impressionable
voters and they don’t take into account the proposed policies when they vote.
12
Benabou (2005) uses a similar way, through a unique tax rate, to represent the set of public policies like
taxes and transfers, minimum wage laws, firing costs, etc.

7

And the skill premium:
𝜔 = (1 − 𝑡)𝜆𝜑𝛼(1 − 𝑠)

(13)

Τhere are, also, two special interest groups, 𝑆𝐼𝐺𝐴 and 𝑆𝐼𝐺𝐵 . Members of each group are
all the economic agents that benefit from the policies of party 𝐴 and 𝐵 respectively.
When an economic agent benefits from the policies of both parties then this agent is
member of both interest groups. Members can be the firms that receive part of the total
tax revenue as a subsidy, the bureaucrats who benefit from corruption, and the labor
unions that receive contributions from their members who benefit from the higher
minimum wage and other labor market regulations. I assume that both special interest
groups are small enough such that there is no coordination cost and no free riding.
The timing of events is the following: first, the two parties announce their set of policies.
Then, each 𝑆𝐼𝐺 announces its contribution to its party, and finally election takes place. 13
Also, I assume that after a party announces its policy, it cannot change it and it is
committed to implement it, if elected.
Voters maximize the following utility:
𝑈𝑗 = 𝑐 𝑏 𝑓𝑗 𝛼

(14)

Where 𝑐 is consumption (each individual consumes all her income), and 𝑓𝑗 depends on
the political ideology of the specific individual, 𝑗, and on the political ideology of each
party.
There are two types of voters: strategic and impressionable. 14 According to Grossman
and Helpman (2001), ‘strategic voters understand the political environment and the
implications of their votes’. On the other hand, ‘impressionable voters rely on campaign
ads’. Grossman and Helpman (2001) assume that the share of strategic and
impressionable voters is exogenous. I assume that the level of education affects the
ability of people to make the calculations necessary for strategic voting. 15 Individuals
with high enough education are able to make these calculations and, thus, they know
exactly how a specific policy will affect them. Political advertisement has no effect on
them. In other words, the assumption is that political advertisement will not make them
change their mind once they know the policy that each party is willing to adopt.
13

This timing implies that SIG will not contribute money in order to influence policies. In order for this to
happen, SIG should contribute before the party announces its policy. In this paper, SIG give their
contributions after the parties announce their policies. Thus, SIG have only electoral motive. See
Grossman and Helpman (2001) for a detailed discussion about influence and electoral motive.
14
The analysis and the model presented here are based on Grossman and Helpman (1996, 2001)
15
Also, education affects civic participation. See Dee (2003), Glaeser, Ponzetto, and Shleifer (2007), and,
Milligan, Moretti, and Oreopoulos (2004).

8

Individuals with relatively low education cannot make the necessary calculations and,
thus, they don’t know how a specific policy will affect them. Political advertisement
affects their decision. If the amount of advertisement is bigger for one of the parties, this
party will attract more impressionable voters. For simplicity, I assume that skilled
individuals have high enough education and they are strategic voters, while unskilled
individuals are impressionable voters.
Strategic voter’s 𝑗 utility is:

𝑈𝑖𝑗𝑠 = (𝑓𝑖𝑗 )𝑎 (𝑤𝑠 (𝑡𝑖 ))𝑏,

where 𝑖 = 𝐴, 𝐵 denotes party 𝐴 and 𝛣.

𝑎 𝑏
𝑎 𝑏
Strategic voter 𝑗 chooses party 𝐴 if: 𝑓𝐴𝑗
𝑐𝐴 ≥ 𝑓𝐵𝑗
𝑐𝐵 →

(15)

𝑓𝐵𝑗
𝑓𝐴𝑗

≤(

𝑤𝑠(𝑡𝐴 )
𝑤𝑠(𝑡𝐵)

𝑏

)𝑎 . Where 𝑓𝑗 =

𝑓𝐵𝑗
𝑓𝐴𝑗

is

the relative popularity of party 𝐵 for voter 𝑗. I assume that 𝑓𝑗 is uniformly distributed with
mean 𝑧.16 Also: 𝑐𝑖 = 𝑤𝑠 (𝑡𝑖 ), shows that consumption is equal to the wage, and that the
wage depends on the set of policies, 𝑡𝑖 .
The share of votes for party 𝐴 among strategic voters is:
𝑉𝐴𝑠

1

𝑤𝑠 (𝑡𝐴 )

= −𝑧+�

𝑏
𝑎

� ,

(16)

𝑈𝑖𝑢 = (𝑓𝑖 )𝑎 (𝐸𝑤𝑢 (𝑡𝑖 ))𝑏 ,

(17)

2

𝑤𝑠 (𝑡𝐵)

where 𝑧 shows the relative popularity of party 𝐵’s fixed position. If 𝑧 = 1, then the two
parties are equally popular and, thus, if they choose the same policies, each will get 50%
of the votes.
Impressionable voters’ utility is:

where 𝑖 = 𝐴, 𝐵 denotes party 𝐴 and 𝐵.

Impressionable voters cannot estimate the effect of the policy on their income. They form
expectations with respect to this effect:
𝐸𝑤𝑢 (𝑡𝑖 ) = (𝐷𝑖 )𝛽 ,

(18)

𝑖 = 𝐴, 𝐵. 𝐷𝑖 is the contribution of 𝑆𝐼𝐺𝑖 to party 𝑖. This is also the amount that this party
will spend on advertising. 𝛽 is a parameter measuring the effectiveness of the campaign
spending.
16

Grossman and Helpman (1996, 2001) assume uniform distribution, too.

9

𝛽

𝛽

𝑎
𝑎
Impressionable voter 𝑗 chooses party 𝐴 if: 𝑓𝐴𝑗
(𝐷𝐴 )𝑏 ≥ 𝑓𝐵𝑗
(𝐷𝐵 )𝑏 →

𝑓𝑗 =

𝑓𝐵𝑗
𝑓𝐴𝑗

𝑓𝐵𝑗
𝑓𝐴𝑗

≤(

𝐷𝐴

𝐷𝐵

𝛽𝑏

) 𝑎 , where

is the relative popularity of party 𝐵 for voter 𝑗. Again, 𝑓𝑗 is uniformly distributed

with mean 𝑧. This means that the popularity of the two parties is the same among
strategic and impressionable voters.
The share of votes of party 𝐴 among impressionable voters is:
𝑉𝐴𝑢

1

𝐷𝐴

= −𝑧+� �
𝐷𝐵

2

And the total share of votes for party 𝐴 is:

And so:

𝑉𝐴 =

𝑉𝐴𝑠 𝑠

1

+

𝑉𝐴𝑢 (1

𝑉𝐴 = − 𝑧 + �
2

𝛽𝑏
𝑎

1

𝑤𝑠 (𝑡𝐴 )

− 𝑠) = − 𝑧 + �

𝑤𝑠 (𝑡𝐵)

2

𝑏
1+𝛼
𝑎
(1−𝑡𝐴 )𝜆𝜑𝐴𝑡 (1−𝛼)𝛼 1−𝛼 𝑢
1+𝛼
(1−𝑡𝐵)𝜆𝜑𝐴𝑡 (1−𝛼)𝛼1−𝛼 𝑢

1

𝑉𝐴 = − 𝑧 + �
2

1−𝑡𝐴

1−𝑡𝐵

(19)

𝑏
𝑎

𝐷𝐴

� 𝑠+� �
𝐷𝐵

𝐷𝐴

𝛽𝑏
𝑎

� 𝑠+� �

𝑏
𝑎

𝐷𝐴

𝛽𝑏
𝑎

� 𝑠+� �
𝐷𝐵

𝛽𝑏
𝑎

𝐷𝐵

(1 − 𝑠 )

(1 − 𝑠), and

(1 − 𝑠 ),

(20)

(21)

(22)

where 𝑠 is the fraction of skilled individuals and, thus, the fraction of strategic voters, and
(1 − 𝑠) is the fraction of unskilled individuals and, thus, the fraction of impressionable
voters. Also, again, individuals consume all their income,
1+𝛼

𝑐 = 𝑤𝑠 = (1 − 𝑡)𝜆𝜑𝐴𝑡 (1 − 𝛼 )𝛼 1−𝛼 𝑢.
1

The probability that 𝑉𝐴 ≥ , that is, the probability that party 𝐴 wins the election is equal
2

to the probability that 𝑧 ≤ �

1−𝑡𝐴

1−𝑡𝐵

𝑏
𝑎

𝐷𝐴

𝛽𝑏
𝑎

� 𝑠+� �
𝐷𝐵

(1 − 𝑠). 𝑧 is a random variable and 𝐹() is

its distribution function. The probability that party 𝐴 wins the election, 𝑃𝐴 , is equal to:
1−𝑡𝐴

𝑃𝐴 = 𝐹(�

1−𝑡𝐵

𝑏
𝑎

𝐷𝐴

𝛽𝑏
𝑎

� 𝑠+� �
𝐷𝐵

(1 − 𝑠 ))

(23)

Given 𝐷𝐵 , 𝑡𝐴 and 𝑡𝐵 (remember that first parties announce their policies and then 𝑆𝐼𝐺
choose their contributions), 𝑆𝐼𝐺𝐴 will choose 𝐷𝐴 in order to maximize its expected net
benefit:
𝐵𝐴 = 𝑃𝐴 (𝐷𝐴 )𝜁𝑡𝐴 𝜋 − 𝐷𝐴
10

(24)

Where 𝑃𝐴 (𝐷𝐴 ) is the probability that party 𝐴 wins the election when contribution is 𝐷𝐴 ,
and 𝜁𝑡𝐴 𝜋 is the total net benefit from the set of policies, 𝑡𝐴 , for 𝑆𝐼𝐺𝐴 . 𝜋 is the total profit
of all the monopolists, and 𝜁 lies between zero and one and captures the deadweight
loss. 17
The FOC is the best response function for 𝑆𝐼𝐺𝐴 :
𝐹′ (�

1−𝑡𝐴

1−𝑡𝐵

Similarly for 𝑆𝐼𝐺𝐵 :

𝑏
𝑎

𝐷𝐴

𝛽𝑏
𝑎

� 𝑠+� �
𝐷𝐵

(1 − 𝑠 ))

𝛽𝑏
𝛽𝑏 𝑎 −1
𝐷
𝑎 𝐴
𝛽𝑏
𝐷𝐵𝑎

(1 − 𝑠)𝜁𝑡𝐴 𝜋 = 1

𝐵𝛣 = 𝑃𝛣 (𝐷𝛣 )𝜁𝑡𝐵 𝜋 − 𝐷𝛣 ,

where 𝑃𝐵 = 1 − 𝑃𝐴 .

(25)

(26)

The FOC is:

𝐹′ (�

𝑏
1−𝑡𝐴 𝑎

1−𝑡𝐵

𝛽𝑏
𝐷𝐴 𝑎

� 𝑠+� �
𝐷𝐵

𝛽𝑏
𝛽𝑏 𝑎
𝐷
𝑎 𝐴
𝛽𝑏
+1
𝐷𝐵𝑎

(1 − 𝑠 ))

The two FOCs imply:
∗
𝐷𝐴

∗
𝐷𝐵

=

(1 − 𝑠)𝜁𝑡𝐵 𝜋 = 1

𝑡𝐴

(28)

𝑡𝐵

Party 𝐴 will choose 𝑡𝐴 to maximize its share of votes:
1

𝑉𝐴 = − 𝑧 + �
2

1−𝑡𝐴

1−𝑡𝐵

(27)

𝑏
𝑎

𝑡𝐴

𝛽𝑏
𝑎

� 𝑠+� �
𝑡𝐵

(1 − 𝑠 )

(29)

The FOC which is also the best response function for party 𝐴 is:
𝑏

𝑏(1−𝑡𝐴 )𝑎

Party 𝛣 maximizes:

−1
𝑏

𝑎(1−𝑡𝐵)𝑎

𝑠=

𝛽𝑏

𝛽𝑏(𝑡𝐴 ) 𝑎

−1

𝛽𝑏

𝑎(𝑡𝐵) 𝑎

17

(1 − 𝑠)

(30)

I assume here that the members of each special interest group receive an amount that is proportional
to the entire amount the firms lose because of the policy. The more realistic model with deadweight loss
that is proportional to the square of the ‘tax’ is presented in the appendix. The two approaches give
different tax rates in equilibrium, but they predict a very similar effect of the supply of skills on skill
premium.

11

1

𝑉𝐵 = 1 − 𝑉𝐴 = + 𝑧 − �

The FOC is:

2

𝑏

𝑏(1−𝑡𝐴 )𝑎
𝑏

𝑎(1−𝑡𝐵)𝑎

+1

𝑠=

The two first order conditions imply:

1−𝑡𝐴

1−𝑡𝐵

𝑏
𝑎

𝑡𝐴

𝛽𝑏
𝑎

� 𝑠−� �
𝑡𝐵

𝛽𝑏

𝛽𝑏(𝑡𝐴 ) 𝑎
𝛽𝑏

𝑎(𝑡𝐵) 𝑎

+1

(1 − 𝑠 )

(31)

(1 − 𝑠)

𝑡𝐴∗ (𝑠) = 𝑡𝐵∗ (𝑠) = 𝑡 ∗ (𝑠) =

(32)

𝛽(1−𝑠)

(33)

𝑠+(1−𝑠)𝛽

PROPOSITION 1.1. In equilibrium:

•

Both political parties choose the same policy (tax rate), 𝑡 ∗ (𝑠) =

𝛽(1−𝑠)

, which

𝑠+(1−𝑠)𝛽

is a decreasing function of the supply of skills and an increasing function of the
effectiveness of the political campaign, 𝛽.

Proof. Follows from the differentiation of 𝑡 ∗ (𝑠) with respect to 𝑠 and 𝛽.

Thus, the level of economic institutions can be expressed as a function of the percentage
of skilled workers.

1.2.3. The effect of the supply of skills on skill premium

Remember that skill premium, 𝜔, and also the relative demand for skilled labor is:
𝜔 = (1 − 𝑡)𝜆𝜑𝛼(1 − 𝑠)

(34)

It can be derived easily that, if the level of economic institutions, 𝑡, is exogenous (in
which case we have the short run demand for skilled labor, i.e. the demand for skilled
labor before institutions adjust, after an exogenous change in the relative supply of skills)
then an increase in the share of skilled workers will decrease skill premium:
−(1 − 𝑡)𝜆𝜑𝛼 < 0
12

𝜕𝜔
𝜕𝑠

=

This implies that the short run demand is always downward sloping. Given the demand
for skilled labor, an increase in the supply of skilled labor will result to a lower skill
premium.
Things are very different when the amount of skilled labor affects the level of economic
institutions (long run). In this case, skill premium becomes:

where: 𝑡 ∗ (𝑠) =

𝜔 = (1 − 𝑡 ∗ (𝑠))𝜆𝜑𝛼(1 − 𝑠)

𝛽(1−𝑠)

𝑠+(1−𝑠)𝛽

(35)

The total effect of an exogenous change of the proportion of skilled workers is the
following:
𝜕𝜔

where

𝜕𝑠

𝜕𝑡 ∗ (𝑠)
𝜕𝑠

=−

=−

𝜕𝑡 ∗ (𝑠)
𝜕𝑠

𝛽

(𝜆𝜑𝛼(1 − 𝑠)) + (1 − 𝑡 ∗ (𝑠))

(𝛽(1−𝑠)+𝑠)2

𝜕(𝜆𝜑𝛼(1−𝑠))

<0

(36)

𝜕𝑠

Thus, the total effect is decomposed into two effects: the first is the one described above
and is negative. The second effect is positive, and it is coming from the fact that the
amount of skilled labor affects the level of economic institutions and policies, and
through them, the returns to skilled labor. In other words, the supply of skilled labor
affects the demand for skilled labor.
More specifically, the second term of the right hand side of equation (36), is always
negative and shows the decrease in skill premium right after an increase in the relative
supply of skills. This captures the short run response (see Figure II) and it is simply the
movement along the short run demand curve (in the short run,

𝜕𝑡 ∗ (𝑠)
𝜕𝑠

= 0). On the other

hand, the first term is always positive and shows the increase in skill premium in the long
run caused by the institutional improvement that the increase in the relative supply of
skills induces. In Figure II this is shown by the shift to the right of the short run demand
curve.

If the second term is higher than the first, then the total effect is negative:
𝜕𝜔
𝜕𝑠

= −

𝜕𝑡 ∗ (𝑠)
𝜕𝑠

(𝜆𝜑𝛼(1 − 𝑠)) + (1 − 𝑡 ∗ (𝑠))

𝜕�𝜆𝜑𝛼(1−𝑠)�
𝜕𝑠

<0

(37)

In this case, the positive effect from institutional improvement is lower than the negative
market effect.
13

Long Run Relative Demand
for Skills

𝜔

Long Run Skill Premium

Shift in Short Run Relative
Demand for Skills due to
Institutional Improvement

Initial Skill Premium
Short Run Response

Shift in Relative
Supply of Skills

1

𝑠

Figure II

If the first term is higher than the second, then the total effect is positive.
𝜕𝜔
𝜕𝑠

= −

𝜕𝑡 ∗ (𝑠)
𝜕𝑠

(𝜆𝜑𝛼(1 − 𝑠)) + (1 − 𝑡 ∗ (𝑠))

𝜕�𝜆𝜑𝛼(1−𝑠)�
𝜕𝑠

>0

(38)

This case, shown in Figure II, is consistent with what was observed in the U.S. during the
70s and the 80s.
The above analysis is summarized in the following proposition:

PROPOSITION 1.2. Short run and long run relative demand for skills:

a. The short run relative demand for skills,
𝑤𝑠
𝜔𝑆𝑅 (𝑠) =
= (1 − 𝑡)𝜆𝜑𝛼(1 − 𝑠)
𝑤𝑢
is always downward sloping. The skill premium always decreases right after an
exogenous increase in the relative supply of skills.
b. The long run relative demand for skills:
𝑤𝑠
𝑠𝜆𝜑𝛼 (1 − 𝑠)
𝜔𝐿𝑅 (𝑠) =
= (1 − 𝑡 ∗ (𝑠))𝜆𝜑𝛼(1 − 𝑠) =
𝑠 + (1 − 𝑠 )𝛽
𝑤𝑢
is upward sloping when:
0≤𝑠<
14

�𝛽

1 + �𝛽

<1

and it is downward sloping when:
0<

�𝛽

<𝑠≤1
1 + �𝛽
For sufficiently low values of 𝑠, skill premium increases in the long run after an
exogenous increase in the relative supply of skills.
Proof. See appendix

Figure II presents the case where an increase in the relative supply of skills decreases
skill premium in the short run, but increases it in the long run above its initial value.
In order to examine whether the magnitudes of the changes in the relative wage of skilled
labor that this model predicts are similar to the ones that were observed in the United
States after 1970, it would be useful to assign numbers to the parameters and see what is
this model’s predicted short run and long run effect of the observed change in the supply
of skills. According to Barro and Lee (2001), the fraction of college graduates in the
United States in 1970 was 21%. I assume that 𝑠 = 0.21, 𝛼𝜆𝜑 = 3.5 and that 𝛽 = 0.2,
and I take 𝑡1 = 0.43, and 𝜔 = 1.56, which means that college graduates earn 56% more
than those without a college degree. This is exactly the number in the beginning of 1970s.
Again according to Barro and Lee (2001), the fraction of college graduates in the United
States in 1980 was 30%. In this case, and under the assumption that policies are constant,
𝑡1 = 0.43, I find 𝜔𝑆𝑅 = 1.4 which is the short run response that the model predicts and it
is very close to the actual value which is 1.41. Finally, in order to find the long run skill
premium I find first the new equilibrium level of 𝑡 when 𝑠 = 0.3. This is: 𝑡2 = 0.32. This
value of 𝑡 implies that the long run value of skill premium is 𝜔𝐿𝑅 = 1.67, which is very
close to the actual value that is 1.62 in 1995.

1.3.

ENDOGENOUS SUPPLY OF SKILLS

In the previous section the supply of skilled and unskilled labor was exogenous. In this
section, I assume that education choices are forward looking and respond to returns. Of
course, there can still be exogenous changes in the supply of skills caused for example by
a change in the quality of education.

15

I assume that in the beginning of every period workers must become reeducated in order
to qualify as skilled workers with the new generation of technology. 18 If an individual
decides to become educated, he or she will receive the wage of the skilled worker, 𝑤𝑠 .
The cost of education is proportional to the skilled wage, 𝜎𝜓𝑖 𝑤𝑠 , where 𝜎 is a subsidy on
education or simply the quality of education. When the quality of education is higher, 𝜎
is low, then the cost of education is lower. We could think of this cost as a time cost. If
the quality of education is higher, then a worker will spend less time in order to become
skilled. 𝜓𝑖 ≥ 0 is a random variable that captures the heterogeneity among individuals
caused by different ability or credit constraints. Lower values of 𝜓𝑖 imply higher ability.
If an individual chooses to remain uneducated, he or she will receive 𝑤𝑢 .

An individual 𝑖 will become skilled if: 𝑤𝑠 − 𝜎𝜓𝑖 𝑤𝑠 ≥ 𝑤𝑢 , which implies that all
individuals with 𝜓𝜄 ≤

is 𝑠 = 𝐺(

𝜔−1
𝜎𝜔

𝜔−1
𝜎𝜔

will choose to become skilled. The fraction of skilled workers

), where 𝐺 is the distribution function of 𝜓𝑖 , and 𝜔 is the skill premium.

This function represents the supply of skills. Under the assumption that 𝜓𝑖 is uniformly

distributed in [0,1], the supply function becomes: 𝑠 =

𝜔−1
𝜎𝜔

.

The relative supply curve is shown in Figure III. As expected, it is upward sloping. A
decrease in the cost of education, or an increase in the quality of education shifts the
relative supply curve to the right. All the results presented above, in the model with
exogenous supply of skills, hold here as well.

Figure III shows that when the quality of education is high enough there are three
equilibria: the first at 𝑠 = 0 is stable, the second, 𝑠1 , is unstable and the third, 𝑠2 , is
stable. The economy will end up in the third equilibrium only if initially the relative
supply of skills is sufficiently high, 𝑠 > 𝑠1 . If initially the relative supply of skills is
lower than this critical point, then the economy will remain in a poverty trap. Low
education levels will make beneficial for the political parties to allow high levels of
corruption and impose high taxes on profits, and these policies will offer poor incentives
for investment and innovation. This explains why poor democracies with low levels of
education cannot escape stagnation. Special interests capture the government and extract
rents through policies that keep the country poor because there is no sufficient number of
voters that is willing to support growth promoting policies.

18

An alternative assumption could be that the economy is populated by dynastic families and that each
family has one member that lives only one period, so that every period a new member replaces the old.

16

𝜔

Relative Supply of
Skills
Long Run Relative Demand
for Skills

1
𝑠1

𝑠2

1

𝑠

Figure III

1.4.

CONCLUDING REMARKS

This paper argues that there are three distinct groups in every democracy: the uneducated,
the educated, and the (political) elite. I argue that voters have the power to choose their
leaders, but not all voters are able to act as strategic voters. Strategic voting implies that
voters are able to make the calculations that are necessary in order to evaluate the effect
that policies have on their welfare. To a large extent, economic institutions and policies,
for example the level of corruption, can be determined endogenously through the political
process. If all voters were strategic then we wouldn’t observe democracies with bad
policies and economic institutions (there are several examples in Latin America and
Africa). I argue that only educated individuals act as strategic voters, and that the political
conflict is mainly between the educated individuals and the political elite (and those who
have access to it). This doesn’t mean that uneducated voters do not participate in politics.
The relative political power of the elite depends on the proportion of uneducated voters.
The elite can use its influence and money in order to ‘buy’ the support of these voters.
The level of education determines the allocation of the political power, and the allocation
of the political power determines the quality of economic institutions.
This model provides an explanation for the observed pattern of the supply of skills and
skill premium in the United States after 1970. It argues that an increase in the supply of
skills decreases skill premium in the short run, but then it induces institutional
improvement through the political process. As a result, skill premium increases, possibly
above its initial value.

17

1.5.

APPENDIX

1.5.1. Deadweight loss from taxation that is proportional to the square of the tax rate.

This appendix examines the case in which the deadweight loss from the policies is proportional to
1

the square of the ‘tax’ rate. In this case special interest groups receive �𝑡 − 𝑡 2 � 𝜋 instead of 𝜁𝑡𝜋.
2

𝑆𝐼𝐺𝐴 maximizes:

1

and 𝑆𝐼𝐺𝐵 maximizes:

𝐵𝐴 = 𝑃𝐴 (𝐷𝐴 )(𝑡𝐴 − 𝑡𝐴2 )𝜋 − 𝐷𝐴 ,
2

1

𝐵𝐵 = (1 − 𝑃𝐴 (𝐷𝐵 ))(𝑡𝐵 − 𝑡𝐵2 )𝜋 − 𝐷𝐵 .
2

The two first order conditions imply:

1 2
𝐷𝐴∗ 𝑡𝐴 − 2 𝑡𝐴
=
𝐷𝐵∗ 𝑡 − 1 𝑡 2
𝐵
2 𝐵

Party 𝐴 will choose 𝑡𝐴 to maximize its share of votes:

𝛽𝑏

𝑎
1
𝑡𝐴 − 𝑡𝐴2
1
1−
2
� 𝑠 +�
� (1 − 𝑠)
𝑉𝐴 = − 𝑧 + �
1
2
1 − 𝑡𝐵
𝑡𝐵 − 𝑡𝐵2
2
𝑏
𝑡𝐴 𝑎

The FOC which is also the best response function for party 𝐴 is:
𝑏

𝑏(1 − 𝑡𝐴 )𝑎 −1

Party 𝛣 maximizes:

The FOC is:

𝑏

𝑎(1 − 𝑡𝐵 )𝑎

1 𝛽𝑏
𝛽𝑏(1 − 𝑡𝐴 )(𝑡𝐴 − 𝑡𝐴2 ) 𝑎 −1
2
𝑠=
(1 − 𝑠)
𝛽𝑏
1
𝑎(𝑡𝐵 − 𝑡𝐵2 ) 𝑎
2
𝛽𝑏

𝑎
1
𝑡𝐴 − 𝑡𝐴2
1
1
2
� 𝑠−�
� (1 − 𝑠)
𝑉𝐵 = 1 − 𝑉𝐴 = + 𝑧 − �
1
2
1 − 𝑡𝐵
𝑡𝐵 − 𝑡𝐵2
2
𝑏
− 𝑡𝐴 𝑎

18

1 𝛽𝑏
𝛽𝑏(1 − 𝑡𝐵 )(𝑡𝐴 − 𝑡𝐴2 ) 𝑎
2
𝑠=
(1 − 𝑠)
𝑏
𝛽𝑏
1
+1
+1
2
𝑎(1 − 𝑡𝐵 )𝑎
𝑎(𝑡𝐵 − 𝑡𝐵 ) 𝑎
2
𝑏

𝑏(1 − 𝑡𝐴 )𝑎

The two first order conditions give only one solution for 𝑡 that lies between zero and one. This is
the same for both political parties:
𝑡 ∗ (𝑠) =

2𝛽(1 − 𝑠) + 𝑠 − �𝑠(2𝛽 + 𝑠 − 2𝛽𝑠)
2𝛽(1 − 𝑠) + 𝑠

The long run relative demand for skill becomes:
∗
(𝑠) = �1 −
𝜔𝐿𝑅

The equation
1

( , ∞):
2

∗ (𝑠)
𝜕𝜔𝐿𝑅

𝜕𝑠

2𝛽(1 − 𝑠) + 𝑠 − �𝑠(2𝛽 + 𝑠 − 2𝛽𝑠)
� 𝛼𝜆𝜑(1 − 𝑠)
2𝛽(1 − 𝑠) + 𝑠

1

= 0 has only one solution that lies between zero and one, ∀𝛽 ∈ �0, � ∪
2

Also, L’Hospital’s rule implies:
lim−

1
𝛽→
2

𝑠∗ =

3𝛽 − �𝛽(4 + 𝛽)
4𝛽 − 2

3𝛽 − �𝛽(4 + 𝛽)
3𝛽 − �𝛽(4 + 𝛽) 1
= lim+
=
3
4𝛽 − 2
4𝛽 − 2
1
𝛽→
2

Again, when 𝑠 < 𝑠 ∗ , the long run relative demand for skills is upward sloping, while when 𝑠 >
𝑠 ∗ , the long run relative demand for skills is downward sloping.
1.5.2. Proof of Proposition 1.2.

a. Follows from the differentiation of 𝜔𝑆𝑅 (𝑠) with respect to 𝑠.

b. The derivative of 𝜔𝐿𝑅 (𝑠) with respect to 𝑠 is:
zero and solve for 𝑠: 𝑠1∗ = −

�𝛽

1−�𝛽

and 𝑠2∗ =

𝜕𝜔𝐿𝑅 (𝑠)

�𝛽

𝜕𝑠

1+�𝛽

=

𝛼𝜑𝜆(𝛽(𝑠−1)2 −𝑠2 )
(𝛽+𝑠−𝛽𝑠) 2

. Set it equal to

. For 𝛽 > 0, 𝑠1∗ ∈ (−∞, 0) ∪ (1, +∞),

and 𝑠2∗ ∈ (0,1). The derivative of 𝜔𝐿𝑅 (𝑠) with respect to 𝑠 is positive when 𝑠 = 0 < 𝑠2∗ .
Thus, the relative demand for skills is upward sloping when 0 ≤ 𝑠 < 𝑠2∗ < 1 and
downward sloping when 0 < 𝑠2∗ < 𝑠 ≤ 1.

19

CHAPTER 2

Endogenous Economic Institutions and Persistent Income
Differences

2.1.

INTRODUCTION

A number of facts suggests that a study of income levels may be more important than a
study of growth rates. Easterly et al. (1993) show that the correlation of growth rates
across decades is low. This suggests that differences in growth rates across countries may
be mostly transitory. Mankiw et al. (1992) also emphasize that differences in growth rates
are transitory: countries grow more rapidly the further they are below their steady state.
The focus of their growth regressions is to explain the transitory differences in growth
rates across countries. On the other hand, models of idea flows across countries such as
Barro and Sala-i-Martin (1992) and Klenow and Rodriguez-Clare (2005) imply that all
countries will grow at a common rate in the long run. These models argue that technology
diffusion is easier the farther from the frontier is the country. This will keep countries
from drifting indefinitely far from each other. Furthermore, these studies argue that
differences in income levels are highly persistent. This implies that it is more important
to explain these persistent income differences among countries.
This research argues that there are 3 types of countries: leader countries that grow
through innovation, follower countries that grow through imitation, and poor countries
that grow very slowly or they don’t grow at all. Several papers explain why some
countries may not be able to escape the poverty trap. Becker and Barro (1989), and Galor
and Weil (1996) show how poverty traps can be based on multiple equilibria in physical
capital accumulation. Azariadis and Drazen (1990), Galor and Zeira (1993), Benabou
(1996), and Galor and Tsiddon (1997) show how poverty traps can be based on multiple
equilibria in human capital accumulation. On the other hand, Howitt and Mayer-Foulkes
20

(2005) explain both why some countries are not able to escape stagnation and why
countries that have escaped stagnation and grow at the same rate as the leader may not be
able to catch up with the leader. They argue that there is not only an advantage of
backwardness. 19 There is a disadvantage of backwardness as well. 20 The ability of
countries to grow depends on their level of skills. Countries that are far from the frontier
have low level of skills and thus they are not able to use ‘leading-edge R&D’. Instead,
they improve their level of technology through ‘implementation’ which is less productive
than ‘leading-edge R&D’. This implies that history (initial conditions) determines
whether a country that has escaped stagnation will catch up with the leader or not.
This paper provides a new explanation for the persistent income differences among
countries that have escaped stagnation. Following the existing literature, I show that the
follower countries will catch-up with the leader if they adopt policies similar to those of
the leader. Existing literature assumes that policies are exogenous. I argue that some
types of policy are endogenous and they are determined through the political process.
This paper develops a political economy model based on Grossman and Helpman (1996,
2001). More specifically, I argue that there are two types of voters: strategic and
impressionable. Strategic voters understand the political environment and the
implications of their votes. By voting for the party whose platform he prefers, a strategic
voter slightly increases his expected welfare. On the other hand, impressionable voters
are not willing or are not able to fully understand the impact the various policies have on
their income. As a result, they rely on advertisement in order to decide which policies
will benefit them more. This gives an incentive to political parties to choose bad policies
that benefit some groups, in exchange for campaign contributions that attract
impressionable voters. Bad policies (low property right protection, high tax on profits,
high cost to start a new firm and high minimum wage) imply smaller support from
strategic voters and bigger support from impressionable voters. I assume that education
determines whether a voter is strategic or impressionable. An increase in the amount of
education increases the proportion of strategic voters and thus implies better policies.
The main argument of the paper is the following: innovation is more skill intensive than
imitation. 21 As a result, the amount of education is higher in leader countries that grow
through innovation than in follower countries that grow through imitation. This implies
that leader countries will adopt better endogenous policies. This fact generates a
disadvantage for the follower countries. If they wish to catch-up with the leaders they
will have to adopt similar policies, but the fact that some of their policies, the endogenous
ones, are worse than the leaders’ endogenous policies, implies that the follower countries
19

See Gerschenkron (1952).
Basu and Weil (1998) and Acemoglu and Zilibotti (2001) present models with a disadvantage of
backwardness. They argue that the technologies that are being developed by the leader are not
appropriate for the followers.
21
Howitt and Mayer-Foulkes (2005) make a similar assumption.
20

21

will have to adopt significantly better exogenous policies than the leader. Such policies
may not even exist.
An important assumption of the model is that some economic policies are endogenous.
Economic policies determine the incentives of economic actors, and shape economic
outcomes. As such, they are social decisions chosen for their consequences. Different
groups and individuals benefit from different economic institutions and policies. Thus,
there is generally a conflict over these social choices, ultimately resolved in favor of
groups with greater political power. Political economists agree that to some extent
economic policies are endogenous. McCarthy, Poole and Rosenthal (2006) argue that
policies like the tax rate, labor market regulations, the minimum wage and others are
endogenously determined through the political process. They show that the significant
change in economic policies that took place in the United States during the 1980s was not
exogenous. It was caused by a change in voters’ preferences.
The assumption that education determines whether an individual is strategic or
impressionable voter, is at the heart of the model. Impressionable are those voters who
are not willing or are not able to make the calculations necessary for strategic voting.
These voters pay attention to campaign advertisement. The more a party spends (holding
constant the spending of its rival), the greater is its share of the impressionable votes.
Strategic voters understand the political environment and the implications of their votes.
There is empirical evidence that education increases civic participation. Dee (2004),
Glaeser, Ponzetto, and Shleifer (2007), and, Milligan, Moretti, and Oreopoulos (2004)
show that educated individuals participate more actively in politics, read more often
newspapers, send letters to politicians and try to persuade others. Also, education allows
those who are interested in politics to understand and evaluate the different policies and
the impact that these policies have on their welfare. In other words, education allows
individuals to become strategic voters. 22
This paper argues that only a fraction of the countries that have escaped stagnation grows
through innovation. The rest of them grow through imitation. Indeed, data on R&D
expenditure and on the number of patents suggest that only a small number of countries
accounts for almost all the global R&D expenditure and the total number of patents
awarded worldwide. 23 This doesn’t mean that there is no technological progress in the
rest of the countries. These countries grow through imitation. Imitation is a costly activity
but relatively less skill intensive than innovation. Imitation process does not produce new
technologies. In other words, it does not advance the world technological frontier. It
simply adapts a technology invented in a leader country.
22

A similar assumption has been made by Bourguignon and Verdier (2000). They argue that only those
with high enough education vote. I argue that only those with high enough education are strategic voters.
23
See OECD 2010 Factbook at: http://www.oecd-ilibrary.org/economics/oecd-factbook_18147364

22

2.2.

THE MODEL

2.2.1. Production

There is a sequence of discrete time periods 𝑡 = 1,2, … There is a mass 𝐿 of workers in
the economy. Workers can choose to be skilled (entrepreneurs) or unskilled. There are 𝑠
skilled and 𝑢 unskilled individuals that supply labor inelastically. Individuals live
forever and for simplicity I assume that they cannot save or borrow. In the end of each
period they consume all their income, and thus they seek to maximize it.
People consume only one good, called the final good, which is produced by perfectly
competitive firms using as inputs unskilled labor and an intermediate good according to
the technology: 24
𝑌𝑡 = (𝐴𝑡 𝐿)1−𝛼 𝑥𝑡𝛼

(39)

where 𝑥𝑡 denotes the quantity of the intermediate input used in final good production at
time 𝑡, and 𝐴𝑡 is a productivity parameter that reflects the current quality of the
intermediate good. The coefficient 𝛼 lies between zero and one.

The intermediate good is produced by a monopolist each period, using the final good as
all input, one for one. That is, for each unit of intermediate good, the monopolist must use
one unit of final good as input. Final good that is not used for intermediate production is
available for consumption.
The monopolist at 𝑡 maximizes his profit measured in units of the final good:
𝛱𝑡 = 𝑝𝑡 𝑥𝑡 − 𝑥𝑡

(40)

where 𝑝𝑡 is the price of the intermediate good relative to the final good.

The inverse demand curve facing the monopolist charging the price 𝑝𝑡 is the marginal
product:
𝑝𝑡 = 𝛼(𝐴𝑡 𝑢)1−𝛼 𝑥𝑡 𝛼−1

Therefore, the monopolist chooses the quantity 𝑥𝑡 to maximize profits,
𝛱𝑡 = (𝛼(𝐴𝑡 𝑢)1−𝛼 𝑥𝑡 𝛼−1 − 1)𝑥𝑡

24

This model is based on Aghion and Howitt (2009).

23

(41)

(42)

which implies an equilibrium quantity:
2

𝑥𝑡 = 𝛼 1−𝛼 𝛢𝑡 𝑢

(43)

The equilibrium profit of the monopolist is:

1+𝛼

𝛱𝑡 = (1 − 𝛼)𝛼 1−𝛼 𝐴𝑡 𝑢

(44)

In each period, entrepreneurs (skilled individuals) will attempt to improve the quality of
the intermediate good. If someone succeeds, then he or she will create a new version of
the intermediate good, which is more productive than previous versions. Specifically, the
productivity of the intermediate good will go from last period’s value 𝐴𝑡−1 up to 𝐴𝑡 =
𝛾𝛢𝑡−1 , where 𝛾 > 1. If all the entrepreneurs fail, then there will be no improvement and
the intermediate good will be the same one that was used in 𝑡 − 1, so 𝐴𝑡 = 𝐴𝑡−1 . I
assume that the period is short enough such that the probability that two entrepreneurs
succeed is assumed zero.
In order to improve the quality of the intermediate good, each entrepreneur must conduct
research, a costly activity that uses entrepreneur’s labor as its only output. I assume that
there are two countries: a leader and a follower. Leader is the country that uses state of
the art technology. An entrepreneur in this country can improve technology only through
innovation. On the other hand, follower is a country that uses older technology. An
entrepreneur in this country can improve technology either through innovation or through
imitation. The probability that an improvement in technology occurs in any period 𝑡 is:
𝜇𝑙,𝑡 = 𝜆𝑖

𝜑𝑖 𝐴𝑖,𝑡−1
𝐴∗𝑖,𝑡

(45)

where 𝑙 = 𝑛, 𝑚 denotes whether the country improves its technology through innovation
or through imitation. 𝐴∗𝑡 = 𝛾𝐴𝑡−1 is the productivity parameter if the entrepreneur
succeeds. The reason why the probability of innovation depends on 𝐴∗𝑡 is that as

technology advances it becomes more complex and thus harder to improve upon. 𝑑 =

𝐴𝑚
𝐴𝑛

is the proximity of the follower to the technological frontier (𝐴𝑚 is the level of
technology in the follower country and 𝐴𝑛 is the level of technology in the leader
country). 𝜆𝑙 is a parameter that reflects the productivity of the research sector. I assume
that 𝜆𝑚 = (1 − 𝑑)𝛿𝑚 , and that 𝜆𝑛 , the productivity of the research sector in the country
that innovates is lower than the productivity of the research sector in the follower

24

country, 𝜆𝑚 , when the latter imitates and is very far below the frontier, which means that
𝑑=

𝐴𝑚
𝐴𝑛

, is close to zero. In other words, 𝛿𝑚 > 𝜆𝑛 . 25

Entrepreneurial skills are produced by two inputs: time and local knowledge. Local
knowledge is a public input which I assume to be proportional to aggregate productivity
𝐴𝑡−1 . Entrepreneurs choose the fraction of their working time they spend in education in
𝑧
order to maximize their supply of skills, 𝜑𝑙 , where 𝜑𝑙 = (1 − 𝜀𝑙 )𝜀𝑙 𝑙 , 𝜀𝑖 is working time
spent in education and 𝑧𝑙 is a parameter. Because education is more important in
innovation than in imitation, I assume that 𝑧𝑛 > 𝑧𝑚 . Maximization implies that 𝜀𝑙∗ =

𝑧𝑙

𝑧𝑙 +1

.

∗
, that is, entrepreneurs in the country
With simple algebra it can be shown that 𝜀𝑛∗ > 𝜀𝑚
that improves the technology through innovation choose more education than
entrepreneurs in the country that imitates.
𝑧

(1−𝜀𝑙 )𝜀𝑙 𝑖 𝐴𝑙,𝑡−1

𝜇𝑙,𝑡 = 𝜆𝑙

𝐴∗𝑙,𝑡

= 𝜆𝑙

𝑧

(1−𝜀𝑙 )𝜀𝑙 𝑙
𝛾

(46)

Each entrepreneur’s wage is his expected reward from innovation: 26
𝑤𝑙,𝑠 = 𝜆𝑙

𝜑𝑙∗ 𝐴𝑙,𝑡−1
𝐴∗𝑙,𝑡

𝛱𝑡 = 𝜆𝑙

𝜑𝑙∗ 𝐴𝑙,𝑡−1
𝐴∗𝑙,𝑡

(1 − 𝛼 )𝛼

1+𝛼
1−𝛼

because 𝐴∗𝑙,𝑡 = 𝐴𝑙,𝑡 when innovation takes place.

𝐴𝑙,𝑡 𝑢 =

1+𝛼

𝜆𝑙 𝜑𝑙∗ 𝐴𝑙,𝑡 (1−𝛼)𝛼 1−𝛼 𝑢
𝛾

(47)

Also: 𝜑𝑙∗ = (1 − 𝜀𝑙∗ )(𝜀𝑙∗ ) 𝑧𝑙

Each unskilled worker will receive his marginal product. Simple algebra gives:
2𝛼

𝑤𝑙,𝑢 = (1 − 𝛼)𝛼 1−𝛼 𝛢𝑙,𝑡

Skill premium, 𝜔, is defined as follows:
𝜔=

𝑤𝑠

𝑤𝑢

=

𝜆𝑙 𝜑𝑙 𝛼
𝛾

𝑢=

𝜆𝑙 𝜑𝑙 𝛼
𝛾

(𝐿 − 𝑠)

(48)

(49)

For simplicity I assume that 𝐿 = 1 and thus, 𝑠 is the share and the number of skilled
workers. Skill premium becomes:
25

This assumption implies that imitation is easier than innovation at least in countries that are far from
the frontier. In other words, this assumption captures the advantage of backwardness.
26
This is not the actual wage. It is the expected wage. The actual wage is either zero or 𝛱𝑡 . To simplify the
analysis I assume that entrepreneurs can buy insurance. Thus, they receive with certainty their expected
reward from innovation.

25

𝜔=

𝜆𝑙 𝜑𝑙 𝛼
𝛾

(1 − 𝑠)

(50)

2.2.2. The Political Economy Model

There are two political parties, 𝐴 and 𝐵. Each party announces before the election the set
of policies that will implement if elected. To simplify the analysis I restrict the available
policies to those that affect the profit of a successful innovator. Such policies are for
example the tax rate on profits, efforts to reduce corruption and protect property rights,
the cost to start a new firm, labor market regulations like the minimum wage, etc. 27 The
outcome of each set of policies is a tax rate, 𝑡, such that 𝑡𝛱 is the total share of the profits
that the owner of the firm loses because of taxation, corruption, high cost to enter the
market, etc.
This tax rate affects directly the wage of skilled workers (and their relative wage, or skill
premium). The wage becomes:
𝑤𝑙,𝑠 = 𝜆𝑙

And the skill premium:

𝜑𝑙∗ 𝐴𝑙,𝑡−1
𝐴∗𝑙,𝑡

(1 − 𝑡)𝛱𝑡 = (1 − 𝑡)
𝜔𝑙 = (1 − 𝑡)

𝜆𝑙 𝜑𝑙 𝛼
𝛾

1+𝛼

𝜆𝑙 𝜑𝑙∗ 𝐴𝑙,𝑡 (1−𝛼)𝛼1−𝛼

(1 − 𝑠)

𝛾

(1 − 𝑠)

(51)

(52)

Τhere are, also, two special interest groups, 𝑆𝐼𝐺𝐴 and 𝑆𝐼𝐺𝐵 . The members of each group
are all the economic agents that benefit from the policies of party 𝐴 and 𝐵 respectively.
When an economic agent benefits from the policies of both parties then this agent is
member of both interest groups. Members can be the firms that receive part of the total
tax revenue as a subsidy, the bureaucrats who benefit from corruption, and the labor
unions that receive contributions from their members who benefit from the higher
minimum wage and other labor market regulations. Both special interest groups are small
enough such that there is no coordination cost and no free riding.
The timing of events is the following: first, the two parties announce their set of policies.
Then, each 𝑆𝐼𝐺 announces its contribution to its party, and finally election takes place. 28
27

Benabou (2005) uses a similar way, through a unique tax rate, to represent the set of public policies like
taxes and transfers, minimum wage laws, firing costs, etc.
28
This timing implies that SIG will not contribute money in order to influence policies. In order for this to
happen, SIG should contribute before the party announces its policy. In this paper, SIG give their

26

After a party announces its policy, it cannot change it and it is committed to implement it,
if elected.
Voters maximize the following utility:
𝑈𝑗 = 𝑓𝑗 𝛼 𝑐 𝑏

(53)

where 𝑐 is consumption (I assume that each individual consumes all her income), and 𝑓𝑗
depends on the political ideology of the specific individual, 𝑗, and on the political
ideology of each party.
There are two types of voters: strategic and impressionable. 29 According to Grossman
and Helpman (2001), ‘strategic voters understand the political environment and the
implications of their votes’. On the other hand, ‘impressionable voters rely on campaign
ads’. Grossman and Helpman (2001) assume that the share of strategic and
impressionable voters is exogenous. I assume that the level of education affects the
ability of people to make the calculations necessary for strategic voting. Individuals with
high enough education are able to make these calculations and, thus, they know exactly
how a specific policy will affect them. Political advertisement has no effect on them. In
other words, the assumption is that political advertisement will not make them change
their mind once they know the policy that each party is willing to adopt. Individuals with
relatively low education cannot make the necessary calculations and, thus, they don’t
know how a specific policy will affect them. Political advertisement affects their
decision. If the amount of advertisement is bigger for one of the parties, this party will
attract more impressionable voters. I assume that fraction ℎ𝑙 > 0 of skilled individuals
are strategic voters, and that all unskilled individuals are impressionable voters. Also,
ℎ𝑛 > ℎ𝑚 , which means that greater fraction of skilled individuals in the country that
innovates are strategic voters. This assumption is based on the fact that the amount of
education of skilled individuals in the country that innovates is greater than the amount of
education of skilled individuals in the country that imitates.
Strategic voters’ 𝑗 utility is:

𝑈𝑖𝑗𝑠 = (𝑓𝑖𝑗 )𝑎 (𝑤𝑠 (𝑡𝑖 ))𝑏,

where 𝑖 = 𝐴, 𝐵 denotes party 𝐴 and 𝛣.

𝑎 𝑏
𝑎 𝑏
Strategic voter 𝑗 chooses party 𝐴 if: 𝑓𝐴𝑗
𝑐𝐴 ≥ 𝑓𝐵𝑗
𝑐𝐵 →

(54)

𝑓𝐵𝑗
𝑓𝐴𝑗

≤(

𝑤𝑠(𝑡𝐴 )
𝑤𝑠(𝑡𝐵)

𝑏

)𝑎 , where 𝑓𝑗 =

𝑓𝐵𝑗
𝑓𝐴𝑗

is

the relative popularity of party 𝐵 for voter 𝑗. I assume that 𝑓𝑗 is uniformly distributed with

contributions after the parties announce their policies. Thus, SIG have only electoral motive. See
Grossman and Helpman (2001) for a detailed discussion about influence and electoral motive.
29
The analysis and the model presented here are based on Grossman and Helpman (1996, 2001)

27

mean 𝑧.30 Also: 𝑐𝑖 = 𝑤𝑠 (𝑡𝑖 ), shows that consumption is equal to the wage, and that the
wage depends on the set of policies, 𝑡𝑖 .
The share of votes for party 𝐴 among strategic voters is:
𝑉𝐴𝑠

1

𝑤𝑠 (𝑡𝐴 )

= −𝑧+�

𝑏
𝑎

� ,

(55)

𝑈𝑖𝑢 = (𝑓𝑖 )𝑎 (𝐸𝑤𝑢 (𝑡𝑖 ))𝑏 ,

(56)

𝑤𝑠 (𝑡𝐵)

2

where 𝑧 shows the relative popularity of party 𝐵’s fixed position. If 𝑧 = 1, then the two
parties are equally popular and, thus, if they choose the same policies, each will get 50%
of the votes.
Impressionable voters’ utility is:

where 𝑖 = 𝐴, 𝐵 denotes party 𝐴 and 𝐵.

Impressionable voters cannot estimate the effect of the policy on their income. They form
expectation with respect to this effect:
𝐸𝑤𝑢 (𝜇𝑖 ) = (𝐷𝑖 )𝛽 ,

(57)

𝑖 = 𝐴, 𝐵. 𝐷𝑖 is the contribution of 𝑆𝐼𝐺𝑖 to party 𝑖. This is also the amount that this party
will spend on advertising. 𝛽 is a parameter measuring the effectiveness of the campaign
spending.
𝛽

𝛽

𝑎
𝑎
Impressionable voter 𝑗 chooses party A if: 𝑓𝐴𝑗
(𝐷𝐴 )𝑏 ≥ 𝑓𝐵𝑗
(𝐷𝐵 )𝑏 →

𝑓𝑗 =

𝑓𝐵𝑗
𝑓𝐴𝑗

𝑓𝐵𝑗
𝑓𝐴𝑗

≤(

𝐷𝐴

𝐷𝐵

𝛽𝑏

) 𝑎 , where

is the relative popularity of party 𝐵 for voter 𝑗. Again, 𝑓𝑗 is uniformly distributed

with mean 𝑧. In other words the popularity of the two parties is the same among strategic
and impressionable voters.
The share of votes of party 𝐴 among impressionable voters is:
𝑉𝐴𝑢

1

= −𝑧+� �
𝐷𝐵

2

Thus, the total share of votes for party 𝐴 is:
𝑉𝐴 =

30

𝑉𝐴𝑠 ℎ𝑙 𝑠

+

𝑉𝐴𝑢 (1

𝛽𝑏
𝑎

𝐷𝐴

1

𝑤𝑠 (𝑡𝐴 )

− ℎ𝑙 𝑠) = − 𝑧 + �

𝑤𝑠 (𝑡𝐵)

2

(58)

𝑏
𝑎

𝛽𝑏
𝑎

� ℎ𝑙 𝑠 + � �

Grossman and Helpman (1996, 2001) assume uniform distribution, too.

28

𝐷𝐴

𝐷𝐵

(1 − ℎ𝑙 𝑠),

(59)

And so:

1

𝑉𝐴 = − 𝑧 + �
2

(1−𝑡𝐴 )

(1−𝑡𝐵)

1+𝛼
𝜆𝑙 𝜑∗𝑙 𝐴𝑙,𝑡 (1−𝛼)𝛼1−𝛼
𝛾

1+𝛼
𝜆𝑙 𝜑∗𝑙 𝐴𝑙,𝑡 (1−𝛼)𝛼1−𝛼
𝛾

1

𝑉𝐴 = − 𝑧 + �
2

1−𝑡𝐴

1−𝑡𝐵

𝑏
𝑎

(1−𝑠)
(1−𝑠)

𝑏
𝑎

𝐷𝐴

𝛽𝑏
𝑎

� ℎ𝑙 𝑠 + � �
𝐷𝐵

𝐷𝐴

𝛽𝑏
𝑎

� ℎ𝑙 𝑠 + � �
𝐷𝐵

(1 − ℎ𝑙 𝑠), and

(1 − ℎ𝑙 𝑠)

(60)

where 𝑠 is the share of skilled individuals and ℎ𝑙 𝑠 the share of strategic voters, (1 − 𝑠) is
the share of unskilled individuals and (1 − ℎ𝑙 𝑠) the share of impressionable voters. Also,
I assume again that individuals consume all their income, 𝑐 = 𝑤𝑠 .
1

The probability that 𝑉𝐴 ≥ , that is, the probability that party 𝐴 wins the election is equal
2

to the probability that 𝑧 ≤ �

1−𝑡𝐴

1−𝑡𝐵

𝑏
𝑎

𝐷𝐴

𝛽𝑏
𝑎

� ℎ𝑙 𝑠 + � �
𝐷𝐵

(1 − ℎ𝑙 𝑠). I assume that 𝑧 is a random

variable and that 𝐹() is its distribution function. The probability that party 𝐴 wins the
election, 𝑃𝐴 , is equal to:
1−𝑡𝐴

𝑃𝐴 = 𝐹(�

1−𝑡𝐵

𝑏
𝑎

𝐷𝐴

𝛽𝑏
𝑎

� ℎ𝑙 𝑠 + � �
𝐷𝐵

(1 − ℎ𝑙 𝑠))

(61)

Given 𝐷𝐵 , 𝑡𝐴 and 𝑡𝐵 (remember that parties first announce their policies and then SIGs
choose their contributions) the 𝑆𝐼𝐺𝐴 will choose 𝐷𝐴 in order to maximize its expected net
benefit:
𝐵𝐴 = 𝑃𝐴 (𝐷𝐴 )𝜁𝑡𝐴 𝜋 − 𝐷𝐴 ,

(62)

where 𝑃𝐴 (𝐷𝐴 ) is the probability that party 𝐴 wins the election when contribution is 𝐷𝐴 ,
and 𝜁𝑡𝐴 𝜋 is the total net benefit from policies for 𝑆𝐼𝐺𝐴 . 𝜋 is the total profit of all the
monopolists, and 𝜁 lies between zero and one and captures the deadweight loss 31.
The FOC is the best response function for 𝑆𝐼𝐺𝐴 :
𝐹′ (�

1−𝑡𝐴

1−𝑡𝐵

Similarly for 𝑆𝐼𝐺𝐵 :

𝑏
𝑎

𝐷𝐴

𝛽𝑏
𝑎

� ℎ𝑙 𝑠 + � �
𝐷𝐵

(1 − ℎ𝑙 𝑠))

31

𝛽𝑏
𝛽𝑏 𝑎 −1
𝐷
𝑎 𝐴
𝛽𝑏
𝐷𝐵𝑎

(1 − ℎ𝑙 𝑠)𝜁𝑡𝐴 𝜋 = 1

(63)

I assume here that the members of each special interest group receive an amount that is proportional
to the entire amount the firms lose because of the policy. The qualitative results are not affected if,
instead, the deadweight loss is proportional to the square of the ‘tax’.

29

𝐵𝛣 = 𝑃𝛣 (𝐷𝛣 )𝜁𝑡𝐵 𝜋 − 𝐷𝛣 ,

where 𝑃𝐵 = 1 − 𝑃𝐴 .

(64)

The FOC is:

𝐹′ (�

1−𝑡𝐴

1−𝑡𝐵

𝑏
𝑎

𝐷𝐴

𝛽𝑏
𝑎

� ℎ𝑙 𝑠 + � �
𝐷𝐵

𝛽𝑏
𝛽𝑏 𝑎
𝐷
𝑎 𝐴
𝛽𝑏
+1
𝐷𝐵𝑎

(1 − ℎ𝑙 𝑠))

If we solve the two FOCs we get:
∗
𝐷𝐴

∗
𝐷𝐵

=

𝑡𝐴

𝑉𝐴 = − 𝑧 + �
2

1−𝑡𝐴

1−𝑡𝐵

(65)

(66)

𝑡𝐵

Party 𝐴 will choose 𝑡𝐴 to maximize its share of votes:
1

(1 − ℎ𝑙 𝑠)𝜁𝑡𝐵 𝜋 = 1

𝑏
𝑎

𝑡𝐴

𝛽𝑏
𝑎

� ℎ𝑙 𝑠 + � �
𝑡𝐵

(1 − ℎ𝑙 𝑠)

(67)

The FOC which is also the best response function for party 𝐴 is:
𝑏

𝑏(1−𝑡𝐴 )𝑎

Party 𝛣 maximizes:

The FOC is:

−1

𝑏
𝑎(1−𝑡𝐵)𝑎

ℎ𝑙 𝑠 =

1

𝑉𝐵 = 1 − 𝑉𝐴 = + 𝑧 − �
2

𝑏

𝑏(1−𝑡𝐴 )𝑎
𝑏

𝑎(1−𝑡𝐵)𝑎

+1

ℎ𝑙 𝑠 =

𝛽𝑏

𝛽𝑏(𝑡𝐴 ) 𝑎

−1

𝛽𝑏
𝑎(𝑡𝐵) 𝑎

1−𝑡𝐴

1−𝑡𝐵

(1 − ℎ𝑙 𝑠)

𝑏
𝑎

𝑡𝐴

𝛽𝑏
𝑎

� ℎ𝑙 𝑠 − � �
𝑡𝐵

𝛽𝑏

𝛽𝑏(𝑡𝐴 ) 𝑎
𝛽𝑏

𝑎(𝑡𝐵) 𝑎

+1

(68)

(1 − ℎ𝑙 𝑠)

(1 − ℎ𝑙 𝑠)

(69)

(70)

The two first order conditions imply:
𝑡𝐴∗ (𝑠) = 𝑡𝐵∗ (𝑠) = 𝑡 ∗ (𝑠) =

𝛽(1−ℎ𝑙 𝑠)

ℎ𝑙 𝑠+(1−ℎ𝑙 𝑠)𝛽

(71)

Thus, the demand for skills in the leader country that innovates is:
𝜔 𝑛 (𝑠) =

𝑤𝑠

𝑤𝑢

= (1 − 𝑡 ∗ (𝑠))

𝜆𝑛 𝜑𝑛𝛼(1−𝑠)

30

𝛾

=

ℎ𝑛 𝑠𝜆𝑛𝜑𝑛 𝛼(1−𝑠)

𝛾(ℎ𝑛𝑠+(1−ℎ𝑛𝑠)𝛽)

(72)

The demand for skills in the follower country, if it improves its technology through
imitation is:
(1 − 𝑑)𝛿𝑚 𝜑𝑚 𝛼 (1 − 𝑠)
𝑤𝑠
= �1 − 𝑡 ∗ (𝑠)�
=
𝛾
𝑤𝑢
ℎ𝑚 𝑠(1 − 𝑑)𝛿𝑚 𝜑𝑚 𝛼 (1 − 𝑠)
=
𝛾(ℎ𝑚 𝑠 + (1 − ℎ𝑚 𝑠)𝛽)

𝜔 𝑚 (𝑠 ) =

Note that the demand for skills in the leader is independent of the level of technology.
This is not the case in the follower country. Everything else equal, the demand for skills
is greater the greater the distance from the technological frontier.

2.2.3. The Relative Supply of Skills

The supply can be found as follows: assume that in the beginning of every period
workers must become reeducated in order to qualify as skilled workers with the new
generation of technology. 32 If an individual decides to become educated, he or she will
receive the wage of the skilled worker, 𝑤𝑠 . I assume that the cost of education is
proportional to the skilled wage, 𝜎𝜓𝑗 𝑤𝑠 , where 𝜎 is a subsidy on education or simply the
quality of education. When the quality of education is higher, 𝜎 is low, then the cost of
education is lower. We could think of this cost as a time cost. If the quality of education
is higher, then a worker will spend less time in order to become skilled. 𝜓𝑗 ≥ 0 is a
random variable that captures the heterogeneity among individuals caused by different
ability or credit constraints. Lower values of 𝜓𝑗 imply higher ability. If an individual
chooses to remain uneducated, he or she will receive 𝑤𝑢 .
An individual 𝑗 will become skilled if: 𝑤𝑠 − 𝜎𝜓𝑗 𝑤𝑠 ≥ 𝑤𝑢 , which implies that all

individuals with 𝜓𝑗 ≤
is 𝑠 = 𝐺(

𝜔−1
𝜎𝜔

𝜔−1
𝜎𝜔

will choose to become skilled. The fraction of skilled workers

), where 𝐺 is the distribution function of 𝜓𝑗 , and 𝜔 is the skill premium.

This function represents the supply of skills. Under the assumption that 𝜓𝑗 is uniformly

distributed in [0,1], the supply function becomes: 𝑠 =

𝜔−1
𝜎𝜔

.

The relative supply curve is shown in Figure I. As expected, it is upward sloping. A
decrease in the cost of education, or an increase in the quality of education shifts the
relative supply curve to the right.

32

I could assume that instead of individuals that live forever, there are dynastic families and that each
member of the dynastic family lives only one period so that every period a new member replaces the old.

31

2.2.4. Steady State Analysis

The focus of this paper is first to show that steady state income differences among
countries can be observed even among countries with the exact same exogenous
characteristics and policies, in which case there is club convergence. Second, this paper
examines the conditions under which the follower can catch up and overtake the leader.
In steady state, both countries, the leader and the follower, grow at the same rate, and in
both countries the equilibrium relative supply of skills equates the supply of skills with
the demand for skills.
In the leader:
𝐴𝑡+1 = 𝜆𝑛

And thus, the growth rate is:

𝜑𝐴𝑡
𝜑𝐴𝑡
𝑠𝑛,𝑡 𝛾𝐴𝑡 + (1 − 𝜆𝑛
𝑠 )𝐴
𝛾𝐴𝑡
𝛾𝐴𝑡 𝑛,𝑡 𝑡

𝑔𝑛,𝑡+1 =

Similarly in the follower country:
𝑔𝑚,𝑡+1 =

𝐴𝑡+1 − 𝐴𝑡
𝜑
= 𝜆𝑛 𝑠𝑛,𝑡 (𝛾 − 1)
𝐴𝑡
𝛾

𝐴𝑡+1 − 𝐴𝑡
𝜑
= 𝛿𝑚 (1 − 𝑑) 𝑠𝑚,𝑡 (𝛾 − 1)
𝐴𝑡
𝛾

In steady state:𝑔𝑛,𝑡+1 = 𝑔𝑚,𝑡+1 → 𝛿𝑚 (1 − 𝑑) = 𝜆𝑛

𝑠𝑛

𝑠𝑚

Initially, follower countries grow faster and converge to the leader. Convergence implies
that 𝑑 increases and the growth rate decreases, up to the point that it becomes equal to the
growth rate of the leader.
Thus, the relative reward for skilled labor becomes:

𝜔 𝑚 (𝑠𝑚) =

𝜔 𝑛 (𝑠𝑛 ) =

ℎ𝑛𝑠𝑛𝜆𝑛 𝜑𝛼(1−𝑠𝑛)

ℎ𝑛 𝑠𝑛+(1−ℎ𝑛𝑠𝑛)𝛽

ℎ𝑚 𝑠𝑚 𝛿𝑚 (1−𝑑)𝜑𝛼(1−𝑠𝑚 )
ℎ𝑚 𝑠𝑚 +(1−ℎ𝑚 𝑠𝑚 )𝛽

=

ℎ𝑚 𝑠𝑛𝜆𝑛 𝜑𝛼(1−𝑠𝑚 )

ℎ𝑚 𝑠𝑚 +(1−ℎ𝑚 𝑠𝑚 )𝛽

(74)

(75)

PROPOSITION 2.1.: if the two countries have similar exogenous policies, i.e. 𝜎 𝑛 = 𝜎 𝑚 ,

then (see figure I):

32

a. 𝜔 𝑛 (𝑠𝑛 ) is initially upward sloping and then downward sloping. 𝜔 𝑚(𝑠𝑚 ) is always
downward sloping. When 𝑠𝑛 = 0, 𝜔 𝑛 (𝑠𝑛 ) = 0. Also, when 𝑠𝑛 = 1, 𝜔 𝑛 (𝑠𝑛 ) = 0,
and when 𝑠𝑚 = 1, 𝜔 𝑚 (𝑠𝑚 ) = 0
b. When 𝑠𝑚 = 𝑠𝑛∗ ≠ 1, 𝜔 𝑚 (𝑠𝑚) < 𝜔 𝑛 (𝑠𝑛 )

∗
As a result, in steady state: 𝑠𝑛∗ > 𝑠𝑚

Proof:
a. Follows from differentiation of 𝜔 𝑚 (𝑠𝑚) with respect to 𝑠𝑚 , and from the
differentiation of 𝜔 𝑛 (𝑠𝑛 ) with respect to 𝑠𝑛 .
b. I set 𝑠𝑛 = 𝑠𝑚 = 𝑠, and find 𝜔 𝑚 (𝑠) and 𝜔 𝑛 (𝑠). It follows that 𝜔 𝑚 (𝑠) < 𝜔 𝑛 (𝑠)
Proposition 2.1. shows that even if the two countries have similar exogenous
∗
). As a
characteristics, the leader will choose endogenously better policies, 𝑡(𝑠𝑛∗ ) < 𝑡(𝑠𝑚
result, the leader will grow at the same rate as the follower but will have higher income,
higher level of technology, lower tax rate, and fewer labor market restrictions. Figure I
shows the equilibrium.

Relative Demand
for Skills in the
Follower country

Relative Supply of
Skills

𝜔

Relative Demand for Skills in
the Leader country

1
𝑠 ∗𝑚

𝑠 ∗𝑛

1

𝑠

Figure I

In the previous analysis I assumed that the two countries have similar exogenous policies
(𝜎 𝑛 = 𝜎 𝑚 ). The analysis is similar if instead, the leader has better exogenous policies.
33

Next I derive the condition under which the follower will overtake the leader. In order for
this to take place, entrepreneurs in the follower country must switch from imitation to
innovation. In other words, their expected profit from innovation should become greater
than their expected profit from imitation.
Their expected profit from innovation is:
𝜔𝑠,𝑛 = �1 − 𝑡(𝑠𝑚 )�𝜆𝑛 𝜑𝛼 (1 − 𝑠𝑚) =

Their expected profit from imitation is:

𝜔𝑠,𝑚 = �1 − 𝑡(𝑠𝑚 )�𝜆𝑛

𝑠𝑛

𝑠𝑚

ℎ𝑚 𝑠𝑚 𝜆𝑛 𝜑𝛼(1−𝑠𝑚 )

ℎ𝑚 𝑠𝑚 +(1−ℎ𝑚 𝑠𝑚 )𝛽

𝜑𝛼 (1 − 𝑠𝑚 ) =

ℎ𝑚 𝑠𝑛 𝜆𝑛𝜑𝛼(1−𝑠𝑚 )

ℎ𝑚 𝑠𝑚 +(1−ℎ𝑚 𝑠𝑚 )𝛽

(76)

(77)

∗
And 𝜔𝑠,𝑛 > 𝜔𝑠,𝑚 if 𝑠𝑚
> 𝑠𝑛∗ .

This implies that entrepreneurs in the follower country will switch from imitation to
innovation only if, at steady state, the proportion of skilled workers is bigger in the
follower country. Proposition 1 implies that in order for this to happen it is not enough
for the follower country to adopt exogenous policies that are a little better than those in
the leader. The follower will have to adopt sufficiently better policies. This is difficult to
happen and as a result we observe persistent income differences.
The relative demand for skills in the leader country is:

The relative supply is:

𝜔𝑑𝑛 (𝑠𝑛 ) =

ℎ𝑛𝑠𝑛𝜆𝑛 𝜑𝛼(1−𝑠𝑛)
ℎ𝑛 𝑠𝑛+(1−ℎ𝑛𝑠𝑛)𝛽

𝜔𝑠𝑛 (𝑠𝑛 ) =

In equilibrium, supply is equal to the demand:

1

(79)

1−𝜎𝑛𝑠𝑛

ℎ𝑛 𝑠𝑛𝜆𝑛 𝜑𝛼(1−𝑠𝑛)
ℎ𝑛𝑠𝑛 +(1−ℎ𝑛𝑠𝑛)𝛽

=

(78)

1

1−𝜎𝑛𝑠𝑛

(80)

There is one stable solution (see Figure I): 𝑠𝑛∗ = 𝑠𝑛∗ (𝜎𝑛 )

Similarly in the follower country, in equilibrium the relative demand for skills is equal to
the relative supply:
ℎ𝑚 𝑠𝑛 𝜆𝑛𝜑𝛼(1−𝑠𝑚 )
ℎ𝑚 𝑠𝑚 +(1−ℎ𝑚 𝑠𝑚 )𝛽

=
34

1

1−𝜎𝑚 𝑠𝑚

(81)

∗
∗
The unique solution is: 𝑠𝑚
= 𝑠𝑚
(𝜎𝑚 , 𝑠𝑛∗ (𝜎𝑛 ))

∗
∗
> 𝑠𝑛∗ if 𝑠𝑚
(𝜎𝑚 , 𝑠𝑛∗ (𝜎𝑛 )) > 𝑠𝑛∗ (𝜎𝑛 )
Thus, 𝑠𝑚

This inequality has two variables, 𝜎𝑛 and 𝜎𝑚 , and shows how much bigger 𝜎𝑚 must be
from 𝜎𝑛 , in order for the entrepreneurs in the follower country to decide to switch from
imitation to innovation.

2.3.

CONCLUDING REMARKS

This research argues that some of the economic institutions and policies are determined
endogenously, by the voters, through the political process. The rest of them can be
considered exogenous. The level of education affects the ability of people to choose,
through the political process, good policies. In follower countries that rely on imitation,
the demand for education is relatively low compared with countries that grow through
innovation. As a result, given the level of technology, follower countries have lower level
of education, and because of that, voters elect relatively worse, for economic growth,
policies.
This provides a theoretical support for club convergence. More specifically, the model
predicts that countries will sort themselves into three groups: those that grow through
innovation, those that grow through imitation, and poor countries. Countries in the first
two groups grow at the same rate. The follower country can overtake the leader if it
adopts the necessary exogenous policies. The model shows that this is not very probable
because the necessary exogenous policies are significantly better than those in the leader
country.
Among others, this paper explains why voters in the U.S. elect better, for economic
growth, policies compared to the policies that European voters elect. In other words, it
provides a new theoretical explanation for the existence of the European-style ‘welfare
state’ and the U.S.-style ‘laissez faire’ social contracts.

35

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