Heterogeneous human capital, inequality and growth: The role of patience and skills

• Date: 01 December 2020
• Published date: 01 December 2020
• DOI: http://doi.org/10.1111/ijet.12200

doi: 10.1111/ijet.12200

Heterogeneous human capital, inequality and growth: The

role of patience and skills

Kirill Borissov,∗Stefano Bosi,†Thai Ha-Huy‡and Leonor Modesto§

We extendthe Lucas (1988) model, introducing two classes of agents with heterogeneous skills,

discount factors and initial human capital endowments. We consider two regimes according

to the planner’s political constraints. In the meritocratic regime, the planner faces individual

constraints. In the redistributive regime, the planner faces an aggregate constraint. We find that

heterogeneity matters, particularly with redistribution. In the meritocratic regime, the optimal

solution coincides with the balanced growth path (BGP) found by Lucas (1988) for the repre-

sentative agent’s case. In contrast, in the case of redistribution, the solution for time devoted to

capital accumulation is never interior for both agents. Either the less talented agents do not ac-

cumulate human capital or the more skilled agents do not work. Moreover, social welfare under

the redistributive regime is always higher than under meritocracy, and it is optimal to exploit

existing differences. Finally, we find that inequality in human capital distribution increases in

time and that, in the long run, inequality always promotes growth.

Key wor ds human capital, heterogenous patience and skill, inequality and growth

JEL classification J24, O15, O40

Accepted 7 September 2018

1 Introduction

Human capital as an engine of growth was incorporated into growth theory by Uzawa (1965). The

emergence of a new endogenous growth literature stimulated the interest of economists in the role

of human capital. Lucas (1988) shows that the growth rate of per capita income depends on the

growth rate of human capital, which in turn depends on the time individuals use for acquiring skills.

In recent papers Manuelli and Seshadri (2014), Jones (2014) and Lucas (2015) argue that human

capital has a central role in determining the wealth of nations.

Most endogenous growth models with human capital accumulation assume a representative

agent, which is only a fair approximation if income and wealth inequality play a negligible role in

the process of economic development.1However, it is widely recognized that inequality has a strong

impact on economic growth, although it is not clear whether this impact is positive or negative.

Empirical studies are generally inconclusive. While Alesina and Rodrik (1994), Perssonand Tabellini

(1994), and Perotti (1996) show a negativerelationship between inequality and growth, more recent

works by Partridge (1997), Forbes (2000), and Frank (2009) find a positive relationship.

∗European Universityat St. Petersburg, St. Petersburg, Russia.

†EPEE, Univ Evry,University Paris-Saclay, France. Email: stefano.bosi@ac-paris.fr

‡EPEE, Univ Evry,University Paris-Saclay, France; TIMAS, Thang Long University, Hanoi, Vietnam.

§UCP Cat ´

olica Lisbon School of Business and Economics, Lisbon, Portugal and IZA, Bonn, Germany.

1Wedo not consider here the heterogeneity in human capital across generations as in Palivos and Varvarigos (2010).

International Journal of Economic Theory XX (2018) 1–21 © IAET 1

International Journal of Economic Theory 16 (2020) 399–419 © IAET 399

International Journal of Economic Theory

Human capital, inequality and growth Kirill Borissov et al.

Economists have also paid attention to the relationship between the accumulation of human

capital and inequality. Becker and Tomes (1979), Viaene and Zilcha (2003), and Galor and Moav

(2004) emphasize educational attainment as one of the causes of greater income inequality. The

latter authors find that when human capital replaces physical capital, a greater equality improves

the growth performance. Eicher and Garc´

ıa-Pe˜

nalosa (2001) predict a non-monotonic relationship

between educational attainment and inequality.More recently, Turnovsky(2011) and Turnovsky and

Mitra (2013) find that an increase in the growth rate resulting from productivity enhancement in

the human capital sector will be accompanied by an increase in inequality, whereas a productivity

boost in the final output sector results in a reduction in inequality.

In this paper we introduce a model of human capital accumulation and economic growth with

heterogeneous agents. We assume that agents are heterogeneous in terms of (1) human capital

endowments, (2) patience, and (3) cognitive skills.2Moreover, we assume that agents with higher

cognitive skills are more patient.

In almost all growth models with infinitely lived agents, patience plays a key role. In exogenous

growth models with physical capital, higher patience implies a higher propensity to save and hence a

higher steady-state stock of physicalcapital. In the context of endogenous growth models with human

capital accumulation, higher patience implies greater incentives to devote time to the acquisition

of skills and hence leads to higher rates of growth. Recent results of H¨

ubner and Vannoorenberghe

(2015) suggest that increasing patienceby one standard deviation raises per-capita income by between

34% and 78%. Dohmen et al. (2015) show that average patience explains a considerable fraction of

the variation in growth rates in both the medium and long run and about 40% of the between-country

variation in income. Patience varies not only between countries, but also within countries. Falk et al.

(2015), find that within-country variance accounts for about 86.5% of total variation in patience.

Though there is a literature on models with infinitely lived agents heterogeneousin their discount

factor (see the survey by Becker 2006), most models with human capital accumulation have assumed

either a representative agent or agents with an identical discount factor. More recently, Suen (2014)

addresses the relationship between heterogeneity in time preferences and economic inequality in a

market economy with human and physical capital accumulation. Differently from Suen (2014), we

consider the planner’s solution and leave aside physicalcapital accumulation.

A recent empirical literature emphasizes the increasing role of cognitive skills in promoting

economic well-being. For example, Hanushek and Woessmann (2012) regress growth on initial

levels of gross domestic product and international cognitive test scores over the period 1960–2000

for a set of 50 countries and obtain very good results: their simple model can explain three-quarters

of the variance in growth rates.

The notion that more intelligent people are more patient was advanced by Rae (1905), writing

in 1834, and supported by recent studies. Frederick (2005) finds that those who scored higher on

the Cognitive Reflection Test were generally more patient, but for short horizons. A study by Burks

et al. (2009) shows that individuals with better cognitive skills are more patient, in both the short

and long run (see also Falk et al. (2015)).

Our model focuses more on the basic mechanism of saving/investment in human capital in a

model with a central planner and heterogeneous agents that differ in their discount factors, their skills

in accumulating capital and initial humancapital endowments. We provide a global analysis of human

capital dynamics.3There is no roomfor (credit) market imperfection as in Galor and Zeira (1993) and

2In a recent paper,Sedgle y and Elmslie (2018) focus on a discrimination based on skills heterogeneity.

3In a different context with human and physical capital, Antoci etal . (2014) also provide a global analysis of capital

accumulation.

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International Journal of Economic Theory 16 (2020) 399–419 © IAET

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