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INCOME INEQUALITY AND ECONOMIC GROWTH: THE ROLE OF CAPITAL MARKET IMPERFECTIONS AND HUMAN CAPITAL ACCUMULATION

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RIJKSUNIVERSITEIT GRONINGEN

Faculty of Economics

Department of International Economics and Business

INCOME INEQUALITY AND ECONOMIC

GROWTH:

THE ROLE OF CAPITAL MARKET

IMPERFECTIONS AND HUMAN CAPITAL

ACCUMULATION

M.A. Hospers 1257226

September 2006

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ABSTRACT

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TABLE OF CONTENTS

1. Introduction 5

2. Literature Overview 7

2.1: From economic growth to income inequality: the Kuznets curve

2.1.1: Theoretical approach 2.1.2: Empirical studies

2.2: From income inequality to economic growth 2.2.1: First theoretical work: savings 2.2.2: Social conflicts 2.2.2.1: Theoretical framework 2.2.2.2: Empirical studies 2.2.3: Political economy 2.2.4: Asset inequality 2.2.4.1: Land inequality

2.2.4.2: Human capital inequality 2.3: Discussion of the literature

3. Theoretical Model 18

3.1: Outline model 3.2: Implications

3.2.1: Capital market imperfections 3.2.2: Level of income

3.2.2.1: Poor countries 3.2.2.2: Rich countries 3.3: Hypotheses

3.4: Considerations

3.4.1: Other factors explaining growth 3.4.2: Solow

3.4.3: Thresholds

4. Empirical Model and Data 25

4.1: Types of inequality

4.2: Measure of income inequality 4.3: Measure of capital market access

4.3.1: Real interest rate

4.3.2: Financial market development 4.3.3: Private credit 4.3.4: Considerations 4.4: Data 4.4.1: Income inequality 4.4.2: GDP 4.4.3: Human capital

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5. Econometric Model 37

5.1: Regression form 5.1.1: Causality 5.1.2: Fixed effects

5.1.3: Autocorrelation and heteroskedasticity 5.1.4: Multicollinearity

5.1.5: Sample split 5.2: Expected results 5.3: Basic results 5.4: Extensions

5.4.1: Other inequality measures 5.4.2: Income interaction term 5.4.3: Level of inequality

5.4.4: Different sampling of countries 5.4.4: Human capital

6. Conclusions 52

6.1: Limitations

6.2: Suggestions for future research

References 57

Appendix A: Figures and Tables 62

A.1: Figures A.2: Tables

Appendix B: List of Countries 78

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1. INTRODUCTION

The study of income inequality has always deserved much attention because the distribution of income in a country is an important political issue. Besides the political importance, inequality has deserved much attention in the academic community as well. In these academic studies, a striking fundamental difference can be observed. On the one hand, there exists a group of research that assesses the impact of factors like economic growth and welfare transfers on the development of inequality. In this sense, inequality is taken as the exogenous variable. On the other hand, there is the strand of research that focuses on the impact that income inequality has on other variables. In this sense, income inequality is considered as an endogenous variable. The main focus of this thesis is primarily on the effect that income inequality has on economic growth.

The aim of this thesis is to contribute to this type of income inequality research. The central research question of this thesis is:

“What are the effects of income inequality on economic growth?”

As with other studies of this type, I hereby implicitly assume that the causality runs from inequality to economic growth, and not the other way around. Furthermore, there are potential endogeneity problems when income inequality itself is affected by economic growth. These potential problems shall be taken into account and will be tested before turning to the empirical part of the paper.

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through the accumulation of human capital. Partly because human capital itself has a large impact on economic growth, and partly because the accumulation of human capital captures other indirect effects of inequality on economic growth. In this human capital context, the presence of capital market imperfections is crucial. Therefore, I will explicitly account for capital market imperfections in my empirical analysis, which is an approach that has not been taken before.

Throughout this paper the terms ‘wealth distribution’ and ‘income distribution’ will be used interchangeably. Theoretically, when studying the determinants of economic growth one is interested in the level and distribution of wealth. However, no precise cross-country measure of wealth is available. Since income makes up such as large part of wealth and income is easily comparable across countries, researches often use income instead of wealth. Although income is empirically useful, it does not theoretically capture all elements of wealth. A further discussion on the measurement of wealth is presented in section 4.1.

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2. LITERATURE OVERVIEW

Two main forms of income inequality research can be distinguished. The first type studies the effects of economic development on income inequality. The question that is addressed here is whether the distribution of income changes with the different phases of economic development. This type of research focuses on who receives the gains from economic progress and the overall effect of economic progress on countrywide inequality. Thus, income inequality is the dependent variable in these studies and economic growth the independent variable. The majority of the income inequality studies over the last decade were of this type. However, in recent years the attention has shifted to a different type of research. This second type of research focuses on the way income inequality influences economic growth itself. In these studies the causality runs the other way, economic growth is the dependent variable whereas income inequality is the independent variable. Research focuses on whether the income distribution has any effect on the growth prospective of countries. If so, through what channels are the effects transmitted? Moreover, is inequality good or bad for economic growth?

Section 2.1 will give an overview of the first type of research where income inequality is endogenous. Section 2.2 provides an overview of the literature where economic growth is taken endogenous.

2.1: From economic growth to inequality: the Kuznets curve

2.1.1: Theoretical approach

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follow an ‘inverted U-shaped pattern’. Kuznets empirical work provided the first stylized facts on inequality. The theoretical framework behind the Kuznets curve is as follows: economic development involves a shift of agents being employed in the low-wage agricultural sector to agents being employed in high-low-wage industrial activities. The first agents to move see an increase in income, which raises the overall degree of inequality. Next, as many agents have gone from the agricultural to the industrial sector, falling supply of agricultural labor increases wages in the agricultural sector. The high number of individuals in manufacturing and the higher wages in agriculture tend to decrease the overall level of inequality, while leaving the country with a higher level of income. Hence, during the process of economic development, the level of inequality will follow an inverted U-shaped pattern.

2.1.2. Empirical studies

The following decades of research that focused on the impact of economic growth on the development of inequality, mainly focused on the inverted U-shape hypothesis. The research was mainly empirical and searched its answers in data rather than explicitly modeling the relation. For instance, Paukert (1973) found some crude evidence of a relation between inequality and Gross Domestic Product (GDP). Further study by Ahluwalia (1976) not only found a relation but moderate support for the Kuznets hypothesis as well. Many researchers, for instance, Cromwell (1977) and Lindert and Williamson (1985) searched for evidence of the existence of the Kuznets curve, with mixed success.

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disappeared. Structural differences between countries cause the pattern, while in reality no such pattern exists. Finally, Li, Squire and Zou (1998) argued that the Kuznets curve works better for a cross-section of countries at one point in time than for the evolution of inequality over time within countries.

Overall, the existence of the U-shaped pattern is doubtful. The causal theoretical relationship between growth and inequality is not reflected in empirical research. Fields and Jakubson (1994) drew an insightful conclusion about the debate over the Kuznets hypothesis. They concluded that the existence of an inverted U-shape is doubtful and that the only logical conclusion that can be drawn is that during the twentieth century inequality generally falls as countries develop.

The Kuznets hypothesis is concerned with the way economic growth influenced the distribution of income. However, during the 1980s a new interest in inequality emerged, an interest in how inequality itself influences economic growth. The renewed focus on inequality was partly due to the lack of theoretical founding of the Kuznets curve and partly because the there was an upward trend in inequality which could not be explained by the Kuznets hypothesis.1

2.2. From income inequality to economic growth

2.2.1: First theoretical work: savings

The first theories about how inequality influences economic growth stem from the ideas of Keynes. Keynes (1936) argued that the marginal savings rate of individuals rise with their level of income. These conjectures form the theoretical basis of the Cambridge models of income inequality, especially of the early works of Kaldor. Kaldor (1956) focused on the causal relationship between inequality and economic growth, especially on the effects of the income distribution on capital accumulation and economic growth. According to Kaldor, the rich generally have a high propensity to save and if the proportion of national income that is saved is directly linked to economic growth, through for instance investments, then a high number of rich individuals is growth enhancing. Hence, these models stress the importance of high

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inequality for economic growth. A theoretical drawback of this approach is that the rate of savings is not only influenced by income inequality. For instance, the interest rate has an important effect on the propensity to save. Furthermore, the opening up of international capital markets allowed new ways to finance investments.Therefore, the relationship between income inequality and economic growth through savings did not deserve much attention in the last decades.

Rather the attention was shifted to theories focusing on other channels through which inequality affects economic development. Three different channels have been identified in literature. First, the role of social conflicts as a channel through which income inequality affects economic growth. Second, the way that political channels are influenced by inequality and in turn affect economic growth. Third, the role of asset inequality as a factor in the relationship between income inequality and economic growth. The following sections will elaborate on each of these three strands of literature.

2.2.2: Social conflicts

2.2.2.1: Theoretical framework

The social conflict strand of literature argues that income inequality increases social discontent and fuels social unrest. These feelings of discontent in turn increase the probability of coups, revolutions and mass violence. These effects of inequality affect economic growth in two different ways.

First, the participation of agents in the above-mentioned activities is a direct waste of resources since all these activities are unproductive. Their resources are more productive when deployed in productive sectors of the economy.2 For instance, all labor devoted to the organization of a coup can be employed more productively by devoting these hours of labor to the production of goods. Second, social unrest creates uncertainty. In the presence of uncertainty, there is less willingness to invest because the pay-off is uncertain. For instance, property rights may not hold for a very long time since instability in country may cause legislation to change abruptly. This creates

2 Strictly speaking, not all directly unproductive activities need to be harmful for the economy. See

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uncertainty for investment, which reduces the overall investment levels in a country. Hence, high levels of inequality create uncertainty, which reduces subsequent investment and thereby reducing economic growth.

2.2.2.2: Empirical studies

The majority of the previous arguments are not explicitly modeled; the determination of the effect of income inequality on economic growth through social conflicts remains an empirical exercise.3 For instance, Alesina and Perotti (1996) provide and test a framework in which income inequality creates socio-political instability and social discontent. This in turn creates uncertainty for investment, which reduces overall levels of investment. Since investment is one of the engines of economic growth, this reduces subsequent economic growth. Therefore, inequality and economic growth are inversely related. They test their hypothesis on a sample of 70 countries and found that social unrest had a significant negative effect on economic growth. Others, like Barro (1991) and Mauro (1993) also find an inverse relationship between political instability and growth or investment, using different techniques, approaches and data.

2.2.3: Political economy

The previous argument shows that inequality creates social unrest, which in turn creates uncertainty for investment. However, social discontent could also directly affect the overall growth process in a country because agents directly influence it through the political system. Several authors, Bertola (1991), Perotti (1992), Persson and Tabellini (1994), Alesina and Rodrik (1994) argue that inequality could possibly affect future growth through political channels. These authors argued that through the political process inequality affects taxation and thereby investments if individuals are allowed to vote in order to choose the tax rate or redistributive policy. In an unequal society, the median voter will derive gains from redistributions of income. In general, unequal societies prefer high redistribution, whereas equal societies prefer less distribution. These redistributions can have a positive or a negative impact on economic growth. First, since redistributions involve a transfer of resources, the government must impose a tax rate on income and capital to finance the

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redistribution. This reduces the returns on investment and therefore the incentives to invest. If redistribution reduces the incentives to invest, than relatively equal societies with less redistribution will grow faster.

On the other hand, Saint-Paul and Verdier (1993) showed that redistribution could also promote economic growth. If progressive redistribution creates an increase in the public budget for education, this may create increasing investment rates in human capital in an economy. This effectively increases the stock on human capital, and therefore promotes economic growth. There is also another way in which redistribution may have positive effects. Perotti (1993) showed that in the presence of capital market imperfections or liquidity constraints, individuals are prevented from investments in profitable projects or in human capital. In this case, redistribution may help beneficiaries to overcome these barriers. More agents invest in human capital, thereby increasing the aggregate stock of human capital and hence stimulate economic growth. On the empirical side, the view that redistribution has a positive affect on growth is supported by empirical work of Lindert (1996), who found redistribution to have a positive rather than a negative influence on growth.

All these models are based on some form of median voter theorem. Benabou (1996) theorized an insightful model in which the representative voter is endogenous and affected by the growth process itself. Bourguignon and Verdier (2000) elaborated on these models. They explored the consequences of allowing political institutions to be endogenous. Consequently, they created a political economy model of income redistribution, educational investments and growth. In this framework initial income inequality positively affects the likelihood for a country to be a democracy and initial inequality increases the average rate of growth of a country.

2.2.4: Asset inequality

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found that, in both developing and developed countries, the initial distribution of assets is the key variable for individuals’ ability to start up enterprises and move up the income distribution. Furthermore, in a case study Ravallion (1998) reported a negative effect of the local Chinese asset distribution on individual consumption growth. All this suggests that assets inequality matters. Two different forms of asset inequality are especially relevant, these are land inequality and human capital inequality.

2.2.4.1: Land inequality

In developing countries, where agriculture is the main source of income, the ownership of land is the key driver behind the individual level of income. Those who possess land have a steady source of income, are insured against nutritional crises and have collateral in order to obtain a loan. Therefore, the distribution of land is more relevant that the distribution of income. Land inequality reflects the opportunities that agents have to earn a high income. Those without land have fewer opportunities than those who possess land. These arguments have been confirmed in empirical studies. For instance, Deiniger and Olinto (2000) found that high land inequality is a major determinant of economic growth in a country. Moreover, Alesina and Rodrik (1994) found a strong relation between the initial distribution of land and subsequent economic growth. On the other hand, in developed countries the possession of land is likely to play a minor role. Agriculture is not the major source of income in developed countries, but rather skilled labor. Furthermore, possession of land is not necessary as an insurance against nutritional crises, nor is it important for obtaining a loan. Rather, human capital is an important asset in developed countries.

2.2.4.2: Human capital inequality

Human capital is a major determinant of the overall level of income and growth in a country, a high stock of human capital increases the growth prospective of a country. 4 Furthermore, at an individual level, agents with a higher stock of human capital have higher incomes. Thus, human capital is an important asset determinant of the level of income, both at the country and individual level. This does not imply that the distribution of income in turn determines the distribution of human capital. Several

4 For empirical evidence of the importance of investments in human capital in explaining differences in

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authors, for instance, Lopez, Thomas and Wang (1998), Thomas, Wang and Fan (2001), Castello and Domenech (2002), World Bank (2004) found the relationship between educational inequality and income inequality to be rather weak. Probably because the income distribution influences the overall stock of human capital, rather than the distribution of human capital. Income inequality affects the possibilities that individuals have to invest in human capital, which thereby affecting economic growth.

Several authors have formally addressed how income inequality affects economic growth through human capital. For instance, Stiglitz and Weiss (1981) showed how a negative relationship between inequality and growth could emerge. If investments in human capital are lump and have to be financed through credit and if information is costly and imperfect, then in equilibrium credit rationing will arise. Hence, only agents who can post collateral are able to obtain credit and invest in human capital. Chatterjee (1991) and Tsiddon (1992) have taken this argument even further and showed that an uneven distribution of assets implies that for any given level of income per capita more individuals are credit constrained. In an economy where agents make indivisible investments in schooling, which has to be financed through credit, this implies a lower aggregate growth rate. In addition, Galor and Zeira (1993) showed that investment possibilities in schooling might not only be limited by an agents stock of assets suited for collateral, but also by neighborhood effects and social capital. This happens when agents sort into communities that are differentiated by wealth or human capital, leading to segregation; eventually this could limit the ability of a society to take advantage of exogenous technological possibilities. This can lead to permanent divergence in wealth levels and communities being caught in income traps. Banerjee and Newman (1993) showed that under these conditions the initial inequality could be maintained over time through intergenerational bequests. This implies that there will be not much change in inequality compared to the initial situation. These hypotheses are in line with the general picture of inequality: high inter-temporal stability of income inequality within countries compared to great variation across countries.

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between individuals and credit institutions. The limited amount that individuals can borrow prevents them from investing in human capital, although this might offer high rates of return. If capital markets were perfect, every individual would be able to borrow money at a rate that would equalize the rate of return to education. The distribution of income would have no effect on aggregate economic growth because each individual has the possibility to invest in human capital. However, if capital markets are not perfect then inequality does have an impact on economic growth. In this case, an unequal distribution of income would cause many individuals to be credit-constraint because the interest rate on loans is higher than the return to education. Therefore, there is no investment of these groups in human capital. For individuals with initial high incomes or with the possibility to post collateral interest rates are lower. If the interest rate is lower than the return to education, these groups will invest in human capital. Hence, under the assumption of capital market imperfections, the distribution of income is relevant to the overall level of investment in human capital.

2.3: Discussion of the literature

The overview of the literature shows that theoretically there are four channels through which inequality influences economic growth. Through savings, social conflict, political economy and asset inequality. Each channel affects economic growth in a different way, inequality stimulates growth through savings, reduces growth through asset inequality and has an ambiguous effect on growth through social unrest and the political economy. Hence, the literature provides no unanimous answer about the direction of the effect of inequality on growth. Theoretically, all channels have an impact on economic growth. However, the question remains which of the channels has the largest impact on economic growth and therefore is the relevant one to study. As I will argue below, the human capital inequality approach is best suited as theoretical basis to analyze the effect of income inequality on economic growth. There are two main reasons for the superiority of the human capital channel.

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the variation of economic development can be explained by the accumulation of human capital. Therefore, any study focusing on the determinants of economic growth should take the levels of human capital into account. Since human capital has such a large impact on economic growth, the human capital inequality approach is best suited as a theoretical basis for an empirical research.

Second, the way through which the social conflicts and political economy channels affect economic growth may be through the accumulation of human capital. Since social conflict creates uncertainty for investments of all types, it also affects the decision of agents wanting to invest in human capital. Higher inequality creates uncertainty about future pay-offs of education, thereby limiting the number of individuals investing in human capital, which effectively reduces the growth prospects of a country. Acemoglu and Robinson (2000) have formulized this argument. In their framework social unrest and political economy influence economic growth through human capital. They argue that social unrest fosters democratization, which in turn makes way for redistribution of wealth and more importantly mass education. So besides voters demand for redistribution of resources, voters demand may create access to schooling for the whole population. Effectively increasing the stock of human capital in a country and enlarging its growth prospective.

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occurs at the costs of society not realizing their full economic potential, as in the case of South America. Hence, a functional political system that transfers the social unrest need not always lead to higher growth rates. Important in their analysis is the fact that social conflict and the political economy influence economic growth through the

accumulation of human capital. Therefore, the political economy and social conflicts

approach on one hand and the human capital inequality approach on the other hand, are complements rather than substitutes. Hence, in my opinion a human capital framework combines the effects of the two other channels and is therefore best suited a theoretical framework for the rest of this paper.

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3. THEORETICAL MODEL

In the previous chapter I argued that the human capital models are best suited to analyze the effects of income inequality on economic growth. An important feature in these models is the presence of capital market imperfections. Hence, a suited theoretical model used should at least include a human capital and a capital market imperfections component. In this paper, the theoretical framework of Galor and Zeira (1993) (henceforth GZ) is used to analyze the relationship between income inequality and economic growth. Their framework explicitly models income inequality, human capital and capital market imperfections. Hence, their model contains all theoretically important variables. Besides the theoretical attractions, the model seems to formulate the intuitive thought of how inequality affects individual decisions to invest in human capital.

3.1: Outline model

The two most important assumptions of their model are the presence of imperfect capital markets and the indivisibility of investment in human capital. Capital markets are imperfect as the interest rate for individual borrowers is higher than for lenders. Indivisibility in investment in human capital carries the effect of the income distribution to the long run. At the individual level, it is assumed that technology is non-convex. The following paragraph shows how the combination of inequality and capital market imperfections affects the decision of individuals to invest in human capital. Thereafter, the effects on a country level will be discussed.

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invest in human capital and work as skilled in the second period; they earn a higher wage than unskilled workers. However, not all their descendants work as skilled workers, the critical point is g . In the long run, the economy is concentrated in two groups. First, a rich group in which every individual inherits more thang, and where generation after generation invests in human capital and has a subsequent steady state wealth level of xs. Second, a poor group in which every individual inherits less than g, where all subsequent generations work as unskilled and where every individual has a steady state wealth level xn. Hence, there is a thresholdg, above which every

individual converges to the high steady state and below which every individual converges to the low steady state level of income. Figure 1 (see appendix A.1) graphically shows the equilibrium.

The effect for the aggregate level of wealth of a country is now straightforward:

Long-run levels of wealth in a country are positively related to the number of individuals who inherit more than g. These individuals invest in human capital, which is an important determinant of income and wealth. Hence, individuals who have invested in human capital have higher incomes. Income in a country is maximized when the number of individuals above the threshold g is maximized. Furthermore, if the aggregate economic growth rate in a country is the weighted average of the productivity growth in the skilled and non-skilled sector and productivity in the skilled sector is likely to grow faster than productivity in the non-skilled sector. Then

economic growth will also be positively related to the number of individuals who inherit more than g .

The overall effect of income inequality on a country is that it divides individuals into a group that can and a group that cannot invest in human capital. In the perfectly equal case, everybody would belong to the same group and the income distribution would play no role.

3.2: Implications

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direction of the effect of inequality on economic growth is dependent on the level of income of a country.

3.2.1: Capital market imperfections

In absence of capital market imperfections inequality cannot affect economic growth. The framework of GZ shows that only individuals who inherit a sufficient amount can invest in schooling. With a perfect capital market, this would not be the case because every individual could obtain a loan and invest in schooling.5 Hence, the decision of an individual to invest in human capital would be independent of the amount inherited an individuals would not find themselves trapped at a certain income level. In this case, income inequality has no effect on economic growth. Therefore, I hypothesize that income inequality will only have an affect on economic growth in the presence of capital market imperfections.

3.2.2: Level of income

The theoretical framework shows another important feature, namely that the effect of income inequality on economic growth depends on the level of income in a country. If every individual in a country is below the threshold, then the country will end up poor in the long run because nobody can escape the income trap. Hence, the distribution of income does not play a role if the country is poor. If a country is initially rich, but the wealth is not supported by many, the country may end up poor in the long run as well. It follows from the model that the way income inequality affects economic growth may be different for poor countries than for rich countries. The next section will further explore the differences between the levels of income of a country and the way this affects the relationship between income inequality and economic growth.

3.2.2.1: Poor countries

According to GZ, economic growth is positively correlated to the number of individuals that inherit more than the threshold level of income. This implies that if a country has too few individuals with an income above g , a country finds itself a in an income trap. If a country is initially poor, it will have a low subsequent rate of economic growth. So according to GZ, the income distribution has no effect on

5 Note that strictly not every individual will invest in human capital. Individuals will only invest if the

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economic growth in poor countries, because formally it is not possible to escape the low-income trap. Suppose that for some individuals it is possible to escape the income trap. In this case, rather that initial poor countries will remain poor in every subsequent period, there might be a way for poor countries to escape the income trap. If the average individual has an initial wealth that approaches g (a ‘poor’ country) then an equal income distribution will leave a country with no individuals with an income higher thang. Clearly, allowing for some inequality might push some individuals over the threshold. Once some agents have invested in human capital and have a higher income, they might be able to influence the rest of society through pecuniary and knowledge spillovers. This could push the country to the high side of the income trap. This way, the income distribution does have an effect on economic growth.

This previous argument follows the reasoning of Galor and Tsiddon (1997). They argue that a relatively poor economy that values both equity and prosperity is confronted with a trade-off. Either equality in the short run followed by equality and

low economic growth in the long run. Alternatively, inequality in the short run followed by equality and high economic growth in the long run. An unequal distribution of human capital may be essential in order to increase the aggregate level of human capital and output during the first stages of development. Inequality may enable members of highly educated segments in a society to overcome the low economic growth trap and to increase their investment in human capital, whereas equality may trap the society as a whole at a low level of investment in human capital. Combining the arguments in the previous paragraph, I hypothesize that if a country is poor, an unequal distribution of income will have a positive effect on the rate of economic growth.

3.2.2.2: Rich countries

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growth. On the other hand, rich countries with an unequal distribution will have fewer individuals above the threshold and therefore a lower level of economic growth. Hence, equality is growth promoting in rich societies. Galor and Moav (2004) come to the same conclusion by using different arguments. They argue that in mature stages of development, the growth process is fueled by human capital accumulation, whereas

physical capital drives growth in early stages of development. Since human capital is embodied in individuals and each investment of an individual is subject to diminishing marginal returns, the aggregate return to investment in human capital is maximized if the marginal returns are equalized across agents. An equal distribution of income alleviates the adverse affects of credit constraints on investment in human capital and hence promotes economic growth. Therefore, if a country is rich, an equal

distribution of income will have a positive effect on the rate of economic growth.

3.3: Hypotheses

The statements concerning the role of the income distribution in economic growth made in the previous paragraphs can be summarized in three broad hypotheses. These hypotheses are as follows:

1) In the absence of capital market imperfections, income inequality has no effect on economic growth.

2) When combined with capital market imperfections, income inequality has a beneficial effect on the rate of economic growth in a country when the average per capita income level is lower than g .

3) When combined with capital market imperfections, income inequality has a negative effect on the rate of economic growth in a country when the average per capita income level is higher than g .

3.4: Considerations

3.4.1: Other factors explaining growth

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influenced by the initial level of income, investments in human and physical capital and political stability. In this perspective, income (in)equality is a necessary condition for economic growth. Without a certain level of (in)equality a country will never experience any economic growth. However, it is not a sufficient condition for growth; other factors have to be present as well to ensure that a country will develop. Hence, income inequality alone cannot explain the whole growth process of a country. This paper focuses on the impact that income inequality has on economic growth for the part that is not explained by the initial level of income and the level of human capital.

3.4.2: Solow

Solow (1956) was the first to show that the economic growth rate may be depended on the level of income. Solow argued that countries first grow to their individual steady states, once in the steady state income per capita grows with the rate of technological progress. However, when a country is not yet in its steady state, the level of income per capita grows with the rate of technological progress plus the rate of (human) capital accumulation. If two countries have a similar level of steady state income and one country is in its steady state while the other is not. Than the former will have a lower growth rate of income per capita than the latter. Hence, the growth rate depends upon the level income.

However, the analysis of Solow is of a different kind than the hypothesis presented in this paper. In the analysis of Solow the differences in growth rates are of temporary nature. Once every country is in its steady state all economic growth must come from technological progress. Differences in growth rates are due to differences in the ability of a country to take advantage of technological progress. However, in the steady state the growth rate is independent of the level of income. This result holds even if one would consider a Solow income trap due to, for instance, non-linear investment behavior because of the presence of economies of scale. In this case, there would be a low-income and a high-income steady state. However, the steady state growth rate would still be given by the growth rate of technological progress and hence independent of the level of income.

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goes by. In the framework of Solow, countries have a higher level of income once they escape the income trap, but have essentially the same steady state growth rate.

3.4.3: Threshold

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4. EMPIRICAL MODEL AND DATA

For the empirical part of this paper, I constructed variables that capture the variables used in the theoretical model. The construction of a variable for economic growth is straightforward since GDP figures are readily available. The same goes for human capital as this is normally measured by the years of schooling. However, it is less obvious which variables to use in the case of inequality and capital market access. The following sections explore the possibilities to quantify these variables, provide an overview of the data being used and the corresponding descriptive statistics.

4.1: Types of inequality

In theory, wealth inequality is the appropriate form of inequality for this study. Since levels of wealth determine whether agents invest in human capital and end up with high or low income. Wealth consists of several factors, including income, land and rents. Ideally, one would like to capture the full inequality of all factors of which wealth consists. This would be a variable correctly reflecting the inequality of income, land, rent and other types of wealth. However, data on wealth itself is scarce, therefore one has to use the inequality of the factors of which wealth consists. Land and income are the two widely used measures for wealth.

The distribution of land is likely to correlate with the distribution of wealth for two reasons. First, - especially in developing countries - land can be seen as the most important source of wealth, since agricultural production is the most important form of production. Second, land can be used as collateral when applying for loans, especially when capital markets are imperfect as in the framework of GZ, land may serve as collateral for credit. Agents can subsequently use the credit to invest in schooling.6 However, land is not as good a proxy for wealth in developed countries, since agriculture is not a major source of income and land not the major source of wealth. Income and rents are the main source of wealth for agents in developed countries. Obviously, wealth in developed countries does not consist of income alone, but it is the largest source of wealth. Since the focus is on both developing and developed countries, land alone cannot be the optimal proxy for wealth. Rather, to be

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able to compare the different proxies for wealth across countries, income is the appropriate measure.7 Income is the most important source of wealth in developed countries, whereas in developing countries land is the most important source of wealth. However, land itself can also be a source of income if the proceeds of land are sold. Using income as a proxy for wealth thus partially captures the ownership of land as well. For these reasons, in my opinion the income distribution is the best proxy for the wealth distribution in a country.

4.2: Measure of income inequality

Income inequality can be measured in various ways; some often-used methods are the Lorenz-curve, the Gini-coefficient, the Robin Hoods index and Atkinson’s index. All measures have advantages and disadvantages. A-priori not one measure is best suited for all situations; the choice depends on the specific characteristics of the study. For this paper, the Gini-coefficient is the best measure of income inequality for several reasons.

To start with, the Gini-coefficient satisfies the four most important criteria for inequality measurement, namely the anonymity principle, the population principle, the relative income principle and the Dalton principle. The anonymity principle states that – from an ethical point of view – it does not matter whether individual i or j is earning the income. The population principle indicates that the total size of the population should not matter. The relative income principle states that only relative income matter while the absolute level of the income does not. The shares of income relative to one another are important, not the absolute level. Finally, the Dalton principle states that if there are two incomes yiyj, and one income distribution can be achieved from another by constructing a sequence of transfers from yi to yj,

then the former distribution must be deemed more unequal than the latter.

The Gini-coefficient satisfies all of these four criteria. Hence, neither the size of the economy, nor the level of GDP nor the size of the population influences the level of the Gini-coefficient. This allows comparing the income inequality of countries with very different structures. Furthermore, the Gini-coefficient is sufficiently simple to be

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easily comparable across countries. This makes the coefficient suited for cross-section studies. Finally, the Gini-coefficient is very widely used and therefore has good data availability. For these reasons, the Gini-coefficient is in this case best suited as a measure of income inequality.

Formally, the Gini-coefficient expresses the ratio between the Lorenz-curve of a distribution and a uniform distribution. Where the Lorenz-curve expresses for the bottom x percent of the households, what percentage y of total income they hold. For instance, the poorest 50 percent of households holds 20 percent of total income. The uniform distribution line represents the line of perfect equality where each household has the same income, in this case the bottom percentage of households x

holds exactly the same percentage x of total income. For instance, the poorest 20 percent of households exactly holds 20 percent of total income in a country, or the poorest 50 percent of households exactly holds 50 percent of total income. Figure 2 (see appendix A.1) graphically demonstrates the Lorenz-curve and Gini-coefficient.

The formula to compute the Gini-coefficient is as follows:

k j k m k j m j y y n n n G= − = =1 1 2 2 1

µ

Where, mis the number of distinct incomes, and in each income class j , the number of individuals earning that income is detonated by nj. Thus the total number of

individuals n, simply equals

=

m j j

n 1

. The average income is µ.

The Gini-coefficient is a number between 0 and 1, where 0 expresses the perfect equality case in which everybody has the same income. In contrast, a Gini-coefficient of 1 indicates perfect inequality were one person has all the income and all other individuals have no income.

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transfers. Hence, the measure of inequality may understate the actual inequality among individuals due to the different unit of measurement. In this research, there is no correction for this deviation.

One possible drawback of the Gini-coefficient is that economies with similar incomes and similar Gini-coefficients can have different income distributions. Since the Lorenz-curve can have very different shapes and still yield the same Gini-coefficient. In general, the Gini-coefficient is more sensitive to the level of income of middle-income classes than to the level of higher middle-income classes. I do not correct for the possible deviations resulting from this characteristic of the Gini-coefficient. Rather it is kept in mind that same levels of Gini-coefficients need not always represent same levels of income inequality. In general, I do not expect that this drawback will distort my results since each country is equally affected by it.

4.3: Measure of capital market access

In the perfect case each individual has access to the capital market. However, in reality capital market imperfections prevent certain individuals to access the capital market. In theory, capital market imperfections are all distortions that prevent a capital market of being perfect. The four characteristics of a perfect capital market are, perfectly rational agents that pursue utility maximization, perfect information, no direct transaction costs, regulation or taxes and perfect competition in product and securities markets.

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4.3.1: Real interest rate

The real interest rate could be a proxy for capital market imperfections. If the income of an agent is too low, then without credit it is impossible to invest in schooling. When deciding whether to obtain credit to invest in schooling, the real interest rate is the relevant discount rate. Higher real interest rates make individuals demand less schooling. A high real interest rate causes less of a problem for agents able to finance some of the schooling through initial wealth. Therefore, a high real interest rate is especially problematic for initially poor agents since they cannot obtain credit. Thus, a high real interest rate makes some agents credit constraint, while others are unaffected. This makes the real interest rate especially relevant in combination with income inequality in a human capital framework.

Drawbacks of using the real interest rate are that it is a monetary instrument that is influenced by central banks. Monetary policy causes fluctuations in the interest rate while the credit market imperfections have in fact not changed. Furthermore, using the real interest rate as a proxy for capital market access assumes there actually is a capital market. In this sense, agents are only credit constrained since they cannot afford the high interest rate. This proxy does not capture the cases in which agents cannot even make a decision whether or not to obtain credit because of the non-existence of the capital market.

4.3.2: Financial market development

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agents to obtain credit than in underdeveloped financial systems. Effectively reducing the amount of credit constraint individuals in a country.

4.3.3: Private credit

The level of private credit is a good proxy for capital market access. Private credit consists of private sector credit with commercial banks and measures the credit that is directed to the private sector and not to government or other institutions. The unit of analysis – households - are part of the private sector. Therefore, the size of credit to the private sector gives an indication of the level of credit constraints of households. High levels of private credit indicate that large flows of credit are being directed to the private sector. This shows that there is a market for private credit and a steady supply of credit. The case of low private credit shows that there is not steady supply of loans towards the private sector. Possibly indicating that agents demand credit but are not able to obtain it. Hence, low levels of private credit indicate that many individuals are credit constraint.

4.3.4: Considerations

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4.4: Data

For the variables discussed in the previous paragraphs, several time series where constructed to be able to empirically test the hypotheses.

• Income inequality (GINI), • Real GDP per capita (GDP),

• Two human capital variables (EDUAVER, EDUHIGHER),

• Three capital market access variables (‘Real_Int’, ‘Bank_Deposits’,

‘Private_Credit’).

The following paragraphs will further elaborate on the features and characteristics of the individual time series.

4.4.1: Income inequality

Initially, I used the UNU/WIDER World Income Inequality Database, which has 4664 Gini-coefficient for 152 countries.8 The database is an update of the well-known Deininger and Squire database from the World Bank. Francois and Romagosa (2005) pointed out some difficulties with the use of this database. The basic problem in using this secondary dataset is that there is neither an institution nor an agreed method for the collection of macroeconomic statistics. Therefore, there is generally a lack of certainty concerning data quality and consistency. For the collection of inequality measures, this specifically implies that there may be large differences between countries in concepts (expenditure, net and gross income) and reference units (individual, household size). To overcome some of these problems Francois and Romagosa (2005) have constructed a combined inequality dataset based on a consistent grouping methodology of the heterogeneous observations from existing secondary datasets. This yields a new cross-sectional time-series dataset that will be used in this research.9-10 Although this dataset in many ways is an improvement, there are some considerations. However, these largely apply to all inequality datasets and are not specifically drawbacks of this database. For instance, it is not always clear if income is consistently defined. For instance, are capital gains, imputed house rents from home ownership and gifts included in the measure of income? I expect that in

8 Available at: http://www.wider.unu.edu/wiid/wiid.htm.

9 Available at: http://www.intereconomics.com/francois/data.htm.

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most cases they are not. If these income sources are ignored the real level of income may be higher than the measured level. Furthermore, if these other sources are unevenly spread throughout society than the measured income inequality is understated. Another source of concern is that income inequality databases ignore life cycle effects. In most Western societies, an individual tends to start life with little or no income, gradually increase income till about age 50, after which incomes will decline, eventually becoming negative. This will have the effect of significantly overstating inequality. These criticisms do not make the database of income inequality useless. Rather, they put the dataset in framework where it can be interpreted better and is more useful for quantitative research. They prevent the incorrect interpretation of research results.

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4.4.2: GDP

The Total Economy Database from the Groningen Growth and Development Centre (GGDC) provides annual real GDP per capita figures of countries. 11 The database consists of series for real GDP per capita for 103 countries from 1950 onwards.12 These countries represent about 93 percent of the world population. Since smaller and poorer countries are not included, the sample represents 98 percent of world GDP. Hence, the coverage of the database is very large. The GDP per capita series are converted at Geary Khamis PPP. After excluding some countries with too few observations, the dataset contains 3591 GDP per capita observations.

4.4.3: Human capital

The Barro and Lee dataset on educational attainment provides measures for human capital. 13 The dataset consists of 33 sets of data for 138 countries. From these large

database, two different datasets were used, namely, the percentage of the total population that has completed higher school education (EDUHIGHER) and the average years of schooling (EDUAVER). The dataset provides the estimates for two different age groups ‘over age 15’, ‘over age 25’. The data is available with a breakdown by gender at five-year intervals for the years 1960-2000. Since most education continues after the age of 15, I have used the ‘over age 25’ to be able to better compare the numbers between countries. Furthermore, the aggregate dataset without distinction between genders is used.

There are two types of observations in the dataset. In some cases, observations are year averages, in others they are yearly observations. In all cases, the five-year observations were extrapolated to five-yearly observations to be able to select on the basis of human capital numbers. For instance, a threshold that would drop all observations with a human capital lower than x, implies that 80 percent of observations would be lost because data is at a five-year interval. Effectively, the extension means that the four years following an observation have the same value. For instance, 1961, 1962, 1963 and 1964 have the same value as 1960. I do not expect the extensions to cause large distortions, some figures are already five year averages and

11 Available at: http://www.ggdc.net/dseries/totecon.html.

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the schooling figures are not likely to be subject to large year to year variation, but rather to be fairly stable over five-year time periods. The extended series both have 2710 observations.

4.4.4: Capital market access

As discussed in paragraph 4.3, three proxies for capital market access or credit constraints will be used. These are the real interest rate, the level of private credit and the development of the financial system.

The International Financial Statistics (IFS) database provides annual time series for real interest rates (Real_Int) series for the period 1960 - 2005.14 The World Bank database on Financial Development and Structure provides a rich source of time-series data on the financial structure of countries, including data on the level of private credit and the size of the financial system. 15 Two series shall be used, private credit

by deposit money banks to GDP (Private_Credit) and deposit money bank assets to GDP (Bank_Deposits).

‘Private_Credit’ equals claims of the private sector on both deposit money banks and other financial institutions. The measure isolate credit issued to the private sector as opposed to credit issued to governments and public enterprises. Furthermore, concentration is on credit issued by intermediaries other than the central bank. Hence, it measures the activity of financial intermediaries in one of its main function: channeling savings to investors. To take as much possible measures of capital market imperfections into account two types of this variable will be used. The normal ratio of private credit by deposits money banks to GDP, and the absolute level of private credit by deposits money banks. The latter will be obtained by multiplying the ratio by the level of GDP.

‘Bank_Deposits’ equals the claims on domestic real non-financial sectors by deposit money banks as a share of GDP. It measures the importance of the financial services performed by the three financial sectors relative to the size of the economy. As with

14Available at: http://www.imfstatistics.org/imf/ifsbrowser.aspx?branch=ROOT. 15 Available at:

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the ‘Private_Credit’ both the ratio and the absolute level will be incorporated in to the analysis. ‘Private_Credit’ series contain 2073 observations and ‘Bank_Deposits’ has 2069 observations. Both series cover 160 countries over the time span 1960 – 1997.

4.5: Descriptive statistics

Table 1 (see appendix A.2) shows the descriptive statistics for all series. 16 The statistics show that none of the series is normally distributed as indicated by the Jarque-Bera statistic, (every p < 0.05). Furthermore, it becomes apparent that there are much fewer observations for Gini-coefficients than for human capital and GDP series, namely 529 Gini-coefficients and 3591 GDP observations. The time series cover the period 1950-2005, although not every series has observations for each year. Included countries were selected based on availability of data on GDP and income inequality. After excluding countries for which not all data was available, 77 countries were used in econometric analysis. Table 12 (see appendix B) shows the full list of all countries including their number of observations for each variable that are used in the analysis Table 2 (see Appendix A.2) shows the correlation coefficients between all the variables.17 Correlation of all the human capital measures with GDP is high respectively 0.75 and 0.65. All variables are negatively correlated with GINI. Figure 3 (see appendix A.1) shows the scatterplot of GINI against GDP, where inequality also seems negatively correlated to the level of GDP. Figure 4a, 4b and 4c (see appendix A.1) shows the line graphs of GDP, EDUAVER and EDUHIGHER. All series are increasing with time and this is an indication that the series could be non-stationarity. Non-stationarity implies that a series its mean and variance are not constant over time and that the covariance between two values from the series depend not only on the length of time separating the two values, but also on the actual times at which the variables are observed. The difficulty in using non-stationary time-series in econometric analysis is that they may deliver spurious results. This implies that unrelated data can obtain an apparently significant result merely because one or both series are non-stationary. Table 3 (see appendix A.2) reports the results of tests on

16 All statistical and econometrical analysis has been performed using EViews 5.1.

17 Initially, the percentage of the population that has completed middle education (EDUMIDDLE) was

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stationarity. GDP, EDUAVER and EDUHIGHER are all non-stationary at level.18 However, all panel unit root test indicate that the series are integrated in the order one. This means that the series can be made stationary by taking the first difference (ytyt1). Hence, in the econometric part all series that contain a unit root will enter equations under the first difference.

18 Stationarity test on GINI, Real_Int, Private_Credit and Bank_Deposits indicate no sign of

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5. ECONOMETRIC MODEL

5.1: Regression form

Economic growth is not affected by income inequality alone but rather by a combination of factors. Therefore, the standard OLS equation should account for other factors besides income inequality. Hence, the following form of the regression is used:

( 1)

logyit α βi logyi t− γ GINIit ϕ CMIit λ GINI CMIit it εit

∆ = + ⋅ + ⋅ + ⋅ + ⋅ ⋅ + (1)

Where:

it

y = real GDP per capita in country i at time t

it

GINI = the Gini-coefficient of country i at time t

it

CMI = indicators of capital market access of country i at time t

it

ε

= omitted factors explaining economic growth of country i at time t

The standard regression form corrects for the level of income, but not yet for the level of human capital. Correcting for the level of income by using lagged income (logyi(t1)) means the conditional convergence hypothesis is incorporated.19 The conditional convergence hypothesis states that countries that are identical in their structural characteristics, for instance, preferences, technologies, rates of population growth and governmental policies, converge to one another in the long run in terms of per capita income. Provided that their initial conditions are similar as well.20

5.1.1: Causality

As mentioned in the introduction, the causality between inequality and growth can run either way. It does not suffice to merely assume that inequality causes growth and not the other way around. If the causality does not run in this direction, all subsequent regression analysis would be useless. To formally test this, GINI was taken as an

19 See Barro (1991) and Sala-i-Martin (1995) for supporting cross-country evidence for the conditional

convergence hypothesis.

20 See Galor (1996) for an overview of the theoretical treatment of different conditional convergence

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independent variable and regressed on lagged GDP and lagged GINI. The error term of this regression was added as a regressor to equation (1). The coefficient of the added error term was not significantly different from 0(p=0.751). Therefore, reverse causality is not a problem, inequality affects growth and not the other way around. A same test for the causality of capital market imperfections and growth has been performed. Again, the coefficient of the added error term is not significantly different from 0 (p =0.0689) at a 5% significance level. Hence, reverse causality is not a problem in any of the cases.

5.1.2: Fixed effects

Since not every country will have the same level of income a common effects model may not be the appropriate form for the regression. Table 4 (see appendix A.2) shows the results for a specification test. The null hypothesis that a common effects model should be used is rejected at a 5% confidence level. Therefore, a fixed effects model will be used. This implies that a separate GDP per capita intercept is estimated for each country, instead of estimating a common GDP per capita intercept for all countries.

5.1.3: Autocorrelation and heteroskedasticity

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Table 5 (see appendix A.2) provides estimates for a test on heteroskedasticity. Heteroskedasticity is often encountered in cross-sectional studies and exists when the variances for all the observations are not the same. For the linear regression model this implies that, as the size of the economic unit becomes larger, there is more uncertainty associated with the outcomes of ∆logyit. The Goldfeld-Quandt test on

heteroskedasticity compares the standard errors of two parts of a sample too see whether variances are equal. The null-hypothesis of equal variances is rejected if

c

F

GQ≥ where F is a critical value from the F -distribution with c t1−k and t2 −k

degrees of freedom. The values t1 and t2 are the number of observations in each of the subsamples, k equals the number of independent variables. The computed GQ-statistic (2.14) indicates that heteroskedasticity is present, therefore I choose to correct for it. White (1980) has developed a heteroskedasticity consistent covariance matrix estimator that provides correct estimates of the coefficient covariances in the presence of heteroskedasticity of unknown form. This estimator will be used in further regression analysis.

5.1.4: Multicollinearity

In multiple regression analysis multicollinearity could be a potential problem. Multicollinearity occurs when two independent variables are highly correlated and thus convey the same information. In this case it is impossible to assess the individual impact of a variable on the dependent variable. Although, a variable may improve the fit of the model the reported coefficient will not be significant. To check whether multicollinearity is present in the regression, the dependent variables are regressed on each other. If the R2 value is high than the estimated coefficient might not be correct.

Table 6 (see appendix A.2) reports the R2 values for the different variables. The R2

values are rather high. Therefore, the estimated coefficients are might not be correct. Although theR2 is not extremely high, the possible presence of multicollinearity will

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5.1.5: Sample split

I hypothesized that the effect of income inequality on economic growth is dependent on the level of income. Therefore, - to be able to test the hypotheses - the sample of countries has to be divided into a poor and a rich sample. This provides some challenges. Since selecting on the basis of income would lead to endogeneity problems. Sorting countries into a rich and a poor part and subsequently investigating which of these groups has a higher growth rate is not very insightful. Since the initial level of income is a major determinant of subsequent economic progress. Thus, what is needed is an instrumental variable that is exogenous yet highly correlated with the level of GDP. The growth literature offers a solution. Theoretically, human capital is an important determinant of GDP and empirically human capital is highly correlated with GDP levels.21 Therefore, human capital is used to sort countries into a rich and a poor group.

In section 3.4, the assumption of equality of the threshold level g for each country was discussed. Using human capital as construct to divide countries into a rich and a poor part does not change the basic assumption. Instead of assuming that the threshold level of income that is needed to invest in human capital is equal across countries, I now assume that the threshold level of human capital is equal across countries. In other words, in each country with a human capital value below the threshold inequality will affect economic growth through different channels than for countries with a human capital level above the threshold. Obviously, the threshold levels are not necessarily equal across countries. However, it is not possible to determine each individual threshold level and therefore I assume that there is one threshold level that divides countries into a rich and a poor group.

To find the appropriate threshold levels, several methods could be used. The mean or median are obvious candidates since they would split the sample more or less in half. However, this would be an arbitrary way of selecting a threshold since there is no evidence that the threshold lies indeed around the mean or median. Since the true value of the threshold is unknown, the selection of an instrument has to be chosen on other grounds. The Akaike Information Criterion gives information about the fit of a

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model and can therefore be used to select the threshold that yields two samples that best fit the regression. I estimated two equations based on several thresholds. Based on the Akaike Information Criterion (AIC), the threshold that left the most information has been selected. The AIC is a statistical model fit measure. It quantifies the relative goodness-of-fit of various previously derived statistical models, given a sample of data. A model with many variables will provide a very good fit for the data, but will have few degrees of freedom and be of limited utility. The AIC methodology attempts to find the minimal model that correctly explains the data. Hence, this balanced approach discourages overfitting. The preferred model is the one with the lowest AIC value. Table 7A and 7B (see appendix A.2) report the AIC values for different human capital thresholds. It follows that the threshold to divide the sample of countries into a rich and a poor sample is 9.4 years for EDUAVER and 11.3 years for EDUHIGHER. Hence, observations that have a human capital value below (above) the threshold belong to the poor (rich) sample.

The determined thresholds only hold for the basic regression. In theory the threshold should be determined for each separate regression. However, a quick scan for other regression indicates that the thresholds are more or less the same. Therefore, I assume that the estimated thresholds are applicable for each of the regression to be performed.

Hence, the final forms of the regression being estimated are:

1 ( 1) 1 1 1

logyit

α β

i logyi t

γ

GINIit

ϕ

CMIit

λ

GINI CMIit it

ε

it

∆ = + ⋅ + ⋅ + ⋅ + ⋅ ⋅ + (2)

If EDUAVER < 9.4 or EDUHIGHER < 11.3, and

2 ( 1) 2 2 2

logyit

α β

i logyi t

γ

GINIit

ϕ

CMIit

λ

GINI CMIit it

ε

it

∆ = + ⋅ + ⋅ + ⋅ + ⋅ ⋅ + (3)

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