Inequality and Growth in a Panel of Countries*

Robert J. Barro, Harvard University June 1999

Abstract Evidence from a broad panel of countries shows little overall relation between income inequality and rates of growth and investment. However, for growth, higher inequality tends to retard growth in poor countries and encourage growth in richer places. The Kuznets curve—whereby inequality first increases and later decreases during the process of economic development—emerges as a clear empirical regularity. However, this relation does not explain the bulk of variations in inequality across countries or over time.

*This research has been supported by a grant from the National Science Foundation. An earlier version of this paper was presented at a conference at the American Enterprise Institute. I am grateful for excellent research assistance from Silvana Tenreyro and for

comments from Paul Collier, Bill Easterly, Jong-Wha Lee, Mattias Lundberg, Francisco Rodriguez, Heng-fu Zou, and participants of a seminar at the World Bank.

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A substantial literature analyzes the effects of income inequality on macroeconomic performance, as reflected in rates of economic growth and investment. Much of this analysis is empirical, using data on the performance of a broad group of countries. This paper contributes to this literature by using a framework for the determinants of economic growth that I have developed and used in previous studies. To motivate the extension of this framework to income inequality, I begin by discussing recent theoretical analyses of the macroeconomic consequences of income inequality. Then I develop the applied framework and describe the new empirical findings.

I. Theoretical Effects of Inequality on Growth and Investment Many theories have been constructed to assess the macroeconomic relations between inequality and economic growth.1 These theories can be classed into four broad categories corresponding to the main feature stressed: credit-market imperfections, political economy, social unrest, and saving rates.

A. Credit-Market Imperfections In models with imperfect credit markets, the limited ability to borrow means that rates of return on investment opportunities are not necessarily equated at the margin.2 The credit-market imperfections typically reflect asymmetric information and limitations of

1

Recent surveys of these theories include Benabou (1996) and Aghion, Caroli and GarciaPenalosa (1998). 2 For models of the economic effects of inequality with imperfect credit markets, see Loury (1981), Galor and Zeira (1993), and Piketty (1997), among others.

legal institutions. For example, creditors may have difficulty in collecting on defaulted loans because law enforcement is imperfect. Collection may also be hampered by a bankruptcy law that protects the assets of debtors. With limited access to credit, the exploitation of investment opportunities depends, to some extent, on individuals’ levels of assets and incomes. Specifically, poor households tend to forego human-capital investments that offer relatively high rates of return. In this case, a distortion-free redistribution of assets and incomes from rich to poor tends to raise the average productivity of investment. Through this mechanism, a reduction in inequality raises the rate of economic growth, at least during a transition to the steady state. An offsetting force arises if investments require setup costs, that is, if increasing returns to investment prevail over some range. For instance, formal education may be useful only if carried out beyond some minimal level. One possible manifestation of this effect is the apparently strong role for secondary schooling, rather than primary schooling, in enhancing economic growth (see Barro [1997]). Analogously, a business may be productive only if it goes beyond some threshold size. In the presence of credit-market imperfections, these considerations favor concentration of assets. Hence, this element tends to generate positive effects of inequality on investment and growth. If capital markets and legal institutions tend to improve as an economy develops, then the effects related to capital-market imperfections are more important in poor economies than in rich ones. Therefore, the predicted effects of inequality on economic growth (which were of uncertain sign) would be larger in magnitude for poor economies than for rich ones.

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B. Political Economy If the mean income in an economy exceeds the median income, then a system of majority voting tends to favor redistribution of resources from rich to poor.3 These redistributions may involve explicit transfer payments but can also involve publicexpenditure programs (such as education and child care) and regulatory policies. A greater degree of inequality—measured, for example, by the ratio of mean to median income—motivates more redistribution through the political process. Typically, the transfer payments and the associated tax finance will distort economic decisions. For example, means-tested welfare payments and levies on labor income discourage work effort. In this case, a greater amount of redistribution creates more distortions and tends, therefore, to reduce investment. Economic growth declines accordingly, at least in the transition to the steady state. Since a greater amount of inequality (measured before transfers) induces more redistribution, it follows through this channel that inequality would reduce growth. The data typically refer to ex-post inequality, that is, to incomes measured net of the effects from various government activities. These activities include expenditure programs, notably education and health, transfers, and non-proportional taxes. Some of the data refer to income net of taxes or to consumer expenditures, rather than to income gross of taxes. However, even the net-of-tax and expenditure data are ex post to the effects of various public sector interventions, such as public education programs.

3

For these kinds of political-economy analyses, see Perotti (1993), Bertola (1993), Alesina and Rodrik (1994), Persson and Tabellini (1994), and Benabou (1996), among others.
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The relation of ex-post inequality to economic growth is complicated in the political-economy models. If countries differ only in their ex ante distributions of income, then the redistributions that occur through the political process tend to be only partly offsetting. That is, the places that are more unequal ex ante are also those that are more unequal ex post. In this case, the predicted negative relation between inequality and growth holds for ex-post, as well as ex-ante, income inequality. The predicted relation between ex-post inequality and growth can change if countries differ by their tastes for redistribution. In this case, the countries that look more equal ex post tend to be those that have redistributed the most and, hence, caused the most distortions of economic decisions. In this case, ex-post inequality tends to be positively related to growth and investment. The effects that involve transfers through the political process arise if the distribution of political power is uniform—as is most clear in a one-person/one-vote democracy—and the allocation of economic power is unequal. If more economic resources translate into correspondingly greater political influence, then the positive link between inequality and redistribution would not apply.4 More generally, the predicted effect arises if the distribution of political power is more egalitarian than the distribution of economic power. It is also possible that the predicted negative effect of inequality on growth can arise even if no transfers are observed in equilibrium. The rich may prevent redistributive policies through lobbying and buying of votes of legislators. But then, a higher level of economic inequality would require more of these activities to prevent redistribution of

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income through the political process. The lobbying activities would consume resources and promote official corruption. Since these effects would be adverse for economic performance, inequality can have a negative effect on growth through the political channel even if no redistribution of income occurs in equilibrium.

C. Socio-political Unrest Inequality of wealth and income motivates the poor to engage in crime, riots, and other disruptive activities.5 The stability of political institutions may even be threatened by revolution, so that laws and other rules have shorter expected duration and greater uncertainty. The participation of the poor in crime and other anti-social actions represents a direct waste of resources because the time and energy of the criminals are not devoted to productive efforts. Defensive efforts by potential victims represent a further loss of resources. Moreover, the threats to property rights deter investment. Through these various dimensions of socio-political unrest, more inequality tends to reduce the productivity of an economy. Economic growth declines accordingly at least in the transition to the steady state. An offsetting force is that economic resources are required for the poor effectively to cause disruption and threaten the stability of the established regime. Hence, incomeequalizing transfers promote political stability only to the extent that the first force—the incentive of the poor to steal and disrupt, rather than work—is the dominant factor.

4 5

For discussions, see Benabou (1996) and Rodriguez (1998). For analyses in this area, see Hibbs (1973), Venieris and Gupta (1986), Gupta (1990), Alesina and Perotti (1996), and Benhabib and Rustichini (1996).
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Even in a dictatorship, self-interested leaders would favor some amount of incomeequalizing transfers if the net effect were a decrease in the tendency for social unrest and political instability. Thus, these considerations predict some provision of a social safety net irrespective of the form of government. Moreover, the tendency for redistribution to reduce crimes and riots provides a mechanism whereby this redistribution—and the resulting greater income equality—would enhance economic growth.

D. Saving Rates Some economists, perhaps influenced by Keynes’s General Theory, believe that individual saving rates rise with the level of income. If true, then a redistribution of resources from rich to poor tends to lower the aggregate rate of saving in an economy. Through this channel, a rise in inequality tends to raise investment. (This effect arises if the economy is partly closed, so that domestic investment depends, to some extent, on desired national saving.) In this case, more inequality would enhance economic growth at least in a transitional sense. The previous discussion of imperfect credit markets brought out a related mechanism by which inequality would promote economic growth. In that analysis, setup costs for investment implied that concentration of asset ownership would be beneficial for the economy. The present discussion of aggregate saving rates provides a complementary reason for a positive effect of inequality on growth.

E. Overview Many nice theories exist for assessing the effects of inequality on investment and

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economic growth. The problem is that these theories tend to have offsetting effects, and the net effects of inequality on investment and growth are ambiguous. The theoretical ambiguities do, in a sense, accord with empirical findings, which tend not to be robust. Perotti (1996) reports an overall tendency for inequality to generate lower economic growth in cross-country regressions. Benabou (1996, Table 2) also summarizes these findings. However, some researchers, such as Li and Zou (1998) and Forbes (1997), have reported relationships with the opposite sign.6 My new results about the effects of inequality on growth and investment for a panel of countries are discussed in a later section. I report evidence that the negative effect of inequality on growth shows up for poor countries, but that the relationship for rich countries is positive. However, the overall effects of inequality on growth and investment are weak.

II. The Evolution of Inequality The main theoretical approach to assessing the determinants of inequality involves some version of the Kuznets (1955) curve. Kuznets’s idea, developed further by Robinson (1976), focused on the movements of persons from agriculture to industry. In this model, the agricultural/rural sector initially constitutes the bulk of the economy. This sector features low per capita income and, perhaps, relatively little inequality within the sector. The industrial/urban sector starts out small, has higher per capita income and, possibly, a relatively high degree of inequality within the sector.

6

However, these results refer to fixed-effects estimates, which have relatively few observations and are particularly sensitive to measurement-error problems.
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Economic development involves, in part, a shift of persons and resources from agriculture to industry. The persons who move experience a rise in per capita income, and this change raises the economy’s overall degree of inequality. That is, the dominant effect initially is the expansion in size of the small and relatively rich group of persons in the industrial/urban sectors. Thus, at early stages of development, the relation between the level of per capita product and the extent of inequality tends to be positive. As the size of the agricultural sector diminishes, the main effect on inequality from the continuing urbanization is that more of the poor agricultural workers are enabled to join the relatively rich industrial sector. In addition, many workers who started out at the bottom rungs of the industrial sector tend to move up in relation to the richer workers within this sector. The decreasing size of the agricultural labor force tends, in addition, to drive up relative wages in that sector. These forces combine to reduce indexes of overall inequality. Hence, at later stages of development, the relation between the level of per capita product and the extent of inequality tends to be negative. The full relationship between an indicator of inequality, such as a Gini coefficient, and the level of per capita product is described by an inverted-U, which is the curve named after Kuznets. Inequality first rises and later falls as the economy becomes more developed. More recent models that feature a Kuznets curve generalize beyond the shift of persons and resources from agriculture to industry. The counterpart of the movement from rural agriculture to urban industry may be a shift from a financially unsophisticated environment to one of inclusion with the modern financial system (see Greenwood and Jovanovic [1990].)

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In another approach, the poor sector may be the user of an old technology, whereas the rich sector is the one that employs more recent and advanced techniques (see Helpman [1997] and Aghion and Howitt [1997].) Mobility from old to new requires a process of familiarization and reeducation. In this context, many technological innovations—such as the factory system, electrical power, computers, and the internet— tend initially to raise inequality. The dominant force here is that few persons get to share initially in the relatively high incomes of the technologically advanced sector. As more people move into this favored sector, inequality tends to rise along with expanding per capita product. But, subsequently, as more people take advantage of the superior techniques, inequality tends to fall. This equalization occurs because relatively few people remain behind eventually and because the newcomers to the more advanced sector tend to catch up to those who started ahead. The relative wage rate of those staying in the backward sector may or may not rise as the supply of factors to that sector diminishes. In these theories, inequality would depend on how long ago a new technological innovation was introduced into the economy. Since the level of per capita GDP would not be closely related to this technological history, the conventional Kuznets curve would not fit very well. The curve would fit only to the extent that a high level of per capita GDP signaled that a country had introduced advanced technologies or modern production techniques relatively recently. On an empirical level, the Kuznets curve was accepted through the 1970s as a strong empirical regularity, see especially Ahluwalia (1976a, 1976b). Papanek and Kyn (1986) find that the Kuznets relation is statistically significant but explains little of the variations in inequality across countries or over time. Subsequent work suggested that the

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relation had weakened over time, see Anand and Kanbur (1992). Li, Squire, and Zou (1998) argue that the Kuznets curve works better for a cross section of countries at a point in time than for the evolution of inequality over time within countries. My new results on the Kuznets curve and other determinants of inequality are discussed in a later section. I find that the Kuznets curve shows up as a clear empirical regularity across countries and over time and that the relationship has not weakened over time. I find, however, consistent with some earlier researchers, that this curve explains relatively little of the variations in inequality across countries or over time.

III. Framework for the Empirical Analysis of Growth and Investment The empirical framework is the one based on conditional convergence, which I have used in several places, starting in Barro (1991) and updated in Barro (1997). I will include here only a brief description of the structure. The framework, derived from an extended version of the neoclassical growth model, can be summarized by a simple equation:

(1)

Dy = F(y, y*),

where Dy is the growth rate of per capita output, y is the current level of per capita output, and y* is the long-run or target level of per capita output. In the neoclassical model, the diminishing returns to the accumulation of physical and human capital imply that an economy’s growth rate, Dy, varies inversely with its level of development, as

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represented by y.7 In the present framework, this property applies in a conditional sense, for a given value of y*. For a given value of y, the growth rate, Dy, rises with y*. The value y* depends, in turn, on government policies and institutions and on the character of the national population. For example, better enforcement of property rights and fewer market distortions tend to raise y* and, hence, increase Dy for given y. Similarly, if people are willing to work and save more and have fewer children, then y* increases, and Dy rises accordingly for given y. In this model, a permanent improvement in some government policy initially raises the growth rate, Dy, and then raises the level of per capita output, y, gradually over time. As output rises, the workings of diminishing returns eventually restore the growth rate, Dy, to a value consistent with the long-run rate of technological progress (which is determined outside of the model in the standard neoclassical framework). Hence, in the very long run, the impact of improved policy is on the level of per capita output, not its growth rate. But since the transitions to the long run tend empirically to be lengthy, the growth effects from shifts in government policies persist for a long time. The findings on economic growth reported in Barro (1997) provide estimates for the effects on economic growth and investment from a number of variables that measure government policies and other factors. That study applied to roughly 100 countries

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The starting level of per capita output, y, can be viewed more generally as referring to the starting levels of physical and human capital and other durable inputs to the production process. In some theories, the growth rate, Dy, falls with a higher starting level of overall capital per person but rises with the initial ratio of human to physical capital.
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observed from 1960 to 1990. This sample has now been updated to 1995 and has been modified in other respects. The framework includes countries at vastly different levels of economic development, and places are excluded only because of missing data. The attractive feature of this broad sample is that it encompasses great variation in the government policies and other variables that are to be evaluated. My view is that it is impossible to use the experience of one or a few countries to get an accurate empirical assessment of the longterm growth implications from factors such as legal institutions, size of government, monetary and fiscal policies, degree of income inequality, and so on. One drawback of this kind of diverse sample is that it creates difficulties in measuring variables in a consistent and accurate way across countries and over time. In particular, less developed countries tend to have a lot of measurement error in nationalaccounts and other data. The hope is that the strong signal from the diversity of the experience dominates the noise. The other empirical issue, which is likely to be more important than measurement error, is the sorting out of directions of causation. The objective is to isolate the effects of government policies and other variables on long-term growth. In practice, however, much of the government and private-sector behavior—including monetary and fiscal policies, political stability, and rates of investment and fertility—are reactions to economic events. In most cases discussed in the following, the labeling of directions of causation depends on timing evidence, whereby earlier values of explanatory variables are thought to influence subsequent economic performance. However, this approach to determining causation is not always valid.

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The empirical work considers average growth rates and average ratios of investment to GDP over three decades, 1965-75, 1975-85, and 1985-95.8 In one respect, this long-term context is forced by the data, because many of the determining variables considered, such as school attainment and fertility, are measured at best over five-year intervals. Higher frequency observations would be mainly guesswork. The low-frequency context accords, in any event, with the underlying theories of growth, which do not attempt to explain short-run business fluctuations. In these theories, the short-run response—for example, of the rate of economic growth to a change in a public institution—is not as clearly specified as the medium- and long-run response. Therefore, the application of the theories to annual or other high-frequency observations would compound the measurement error in the data by emphasizing errors related to the timing of relationships. Table 1 shows baseline panel regression estimates for the determination of the growth rate of real per capita GDP. Table 2 shows corresponding estimates for the ratio of investment to GDP.9 The estimation is by three-stage least squares. Instruments are mainly lagged values of the regressors—see the notes to Table 1. The effects of the starting level of real per capita GDP show up in the estimated coefficients on the level and square of the log of per capita GDP. The other regressors include an array of policy variables—the ratio of government consumption to GDP, a
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For the investment ratio, the periods are 1965-74, 1975-84, and 1985-92. The GDP figures in 1985 prices are the purchasing-power-parity adjusted chainweighted values from the Summers-Heston data set, version 5.6. These data are available on the internet from the National Bureau of Economic Research. See Summers and Heston (1991) for a general description of their data. The figures provided through 1992

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subjective index of the maintenance of the rule of law, a subjective index for democracy (electoral rights), and the rate of inflation. Also included are a measure of school attainment at the start of each period, the total fertility rate, the ratio of investment to GDP (in the growth regressions), and the growth rate of the terms of trade (export prices relative to import prices). The data, some of which were constructed in collaboration with Jong-Wha Lee, are available from the World Bank and NBER web sites.10 The results contained in Tables 1 and 2 are intended mainly to provide a context to assess the effects of income inequality on growth and investment. Briefly, the estimated effects on the growth rate of real per capita GDP from the explanatory variables shown in the first column of Table 1 are as follows. The relations with the level and square of the log of per capita GDP imply a nonlinear, conditional convergence relation. The implied effect of log(GDP) on growth is negative for all but the poorest countries (with per capita GDP below $670 in 1985 U.S. dollars). For richer places, growth declines at an increasing rate with rises in the level of per capita GDP. For the richest countries, the implied convergence rate is 5-6% per year. For a given value of log(GDP), growth is negatively related to the ratio of government consumption to GDP, where this consumption is measured net of outlays on public education and national defense. Growth is positively related to a subjective index of the extent of maintenance of the rule of law. Growth is only weakly related to the extent of democracy, measured by a subjective indicator of electoral rights. (This variable

have been updated to 1995 using World Bank data. Real investment (private plus public) is also from the Summers-Heston data set. 10 The schooling data are available at www.worldbank.org/html/prdmg/grthweb/growtht.htm. The overall panel data are at www.nber.org/pub/barro.lee.
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appears linearly and as a square in the equations.) Growth is inversely related to the average rate of inflation, which is an indicator of macroeconomic stability. (Although not shown in Table 1, growth is insignificantly related to the ratio of public debt to GDP, measured at the start of each period.) Growth is positively related to the stock of human capital, measured by the average years of attainment at the secondary and higher levels of adult males at the start of each period. (Growth turns out to be insignificantly related to secondary and higher attainment of females and to primary attainment of males and females.) Growth is inversely related to the fertility rate, measured as the number of prospective live births per woman over her lifetime. Growth is positively related to the ratio of investment to GDP. For most variables, the use of instruments does not much affect the estimated coefficient. However, for the investment ratio, the use of lagged values as instruments reduces the estimated coefficient by about one-half relative to the value obtained if the contemporaneous ratio is included with the instruments. This result suggests that the reverse effect from growth to investment is also important. Finally, growth is positively related to the contemporaneous growth rate of the terms of trade. The main results for the determination of the investment ratio, shown in column 1 of Table 2, are as follows. The relation with the log of per capita GDP is hump-shaped. The implied relation is positive for values of per capita GDP up to $5100 (1985 U.S. dollars) and then becomes negative. Investment is negatively related to the ratio of government consumption to GDP, positively related to the rule-of-law indicator, insignificantly related to the democracy

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index, and negatively related to the inflation rate. The interesting results here are that a number of policy variables that affect economic growth directly (for a given ratio of investment to GDP) tend to affect the investment ratio in the same direction. This effect of policy variables on investment reinforces the direct effects on economic growth. Investment is insignificantly related to the level of the schooling variable, negatively related to the fertility rate, and insignificantly related to the growth rate of the terms of trade.

IV. Measures of Income Inequality Data on income inequality come from the extensive compilation for a large panel of countries in Deininger and Squire (1996). The data provided consist of Gini coefficients and quintile shares. The compilation indicates whether inequality is computed for income gross or net of taxes or for expenditures. Also indicated is whether the income concept applies to individuals or households. These features of the data are considered in the subsequent analysis. The numbers for a particular country apply to a specified survey year. To use these data in the regressions for the growth rate or the investment ratio, I classed each observation on the inequality measure as 1960, 1970, 1980, or 1990, depending on which of these ten-year values was closest to the survey date. Deininger and Squire denote a subset of their data as high quality. The grounds for exclusion from the high-quality set include the survey being of less than national coverage; the basing of information on estimates derived from national accounts, rather than from a direct survey of incomes; limitations of the sample to the income earning

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population; and derivation of results from non-representative tax records. Data are also excluded from the high-quality set if there is no clear reference to the primary source. A serious problem with the inequality data is that many fewer observations are available than for the full sample considered in Tables 1 and 2. As an attempt to expand the sample size—even at the expense of some reduction in accuracy of measurement—I added to the high-quality set a number of observations that appeared to be based on representative, national coverage. The main reason that these observations had been excluded was the failure to identify clearly a primary source.11 In the end, considering also the data availability for the variables included in Tables 1 and 2, I end up with 84 countries with at least one observation on the Gini coefficient (of which 20 are in Sub Saharan Africa). There are 68 countries with two or more observations (of which 9 are in Sub Saharan Africa). Table 3 provides descriptive statistics on the Gini values. Much of the analysis uses the Gini coefficient as the empirical measure of income inequality. One familiar interpretation of this coefficient comes from the Lorenz curve, which graphs cumulated income shares versus cumulated population shares, when the population is ordered from low to high per capita incomes. In this context, the Gini coefficient can be computed as twice the area between the 45-degree line that extends northeastward from the origin and the Lorenz curve. Theil (1967, pp. 121 ff.) shows,
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The 48 observations added were for Benin 1960, Chad 1960, Congo 1960, Gabon 1960 and 1970, Ivory Coast 1960, Kenya 1960 and 1980, Liberia 1970, Madagascar 1960, Malawi 1970 and 1980, Morocco 1960, Niger 1960, Nigeria 1960 and 1980, Senegal 1960 and 1970, Sierra Leone 1980, Tanzania 1960 (and 1970 for quintile data only), Togo 1960, Uganda 1970, Zambia 1960 and 1970, Barbados 1970, El Salvador 1970, Argentina 1960 and 1970, Bolivia 1970, Colombia 1960, Ecuador 1970, Peru 1960, Suriname 1960, Uruguay 1970, Venezuela 1960, Burma 1960, Iraq 1960, Israel 1960, Austria 1990,

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more interestingly, that the Gini coefficient equals a weighted average of all absolute differences between per capita incomes (expressed relative to economy-wide per capita income), where the weights are the products of the corresponding population shares. If the underlying data are quintile shares, and we pretend that all persons in each quintile have the same incomes, then the Gini coefficient can be expressed in two equivalent ways in relation to the quintile shares:

(2)

Gini coefficient = 0.8*(-1 + 2Q5 + 1.5Q4 + Q3 + 0.5Q2) = 0.8*(1 -2Q1 – 1.5Q2 – Q3 – 0.5Q4),

where Qi is the share of income accruing to the ith quintile, with group 1 the poorest and group 5 the richest. The first form says that the Gini coefficient gives positive weights to each of the quintile shares from 2 to 5, where the largest weight (2) applies to the fifth quintile and the smallest weight (0.5) attaches to the second quintile. The second form says that the Gini coefficient can be viewed alternatively as giving negative weights to the quintile shares from 1 to 4, where the largest negative weight (2) applies to the first quintile and the smallest weight (0.5) attaches to the fourth quintile. In my sample, the Gini coefficient turn out to be very highly correlated with the upper quintile share, Q5, and not as highly correlated with other quintile shares. The correlations of the Gini coefficients with Q5 are 0.89 for 1960, 0.92 for 1970, 0.95 for 1980, and 0.98 for 1990. In contrast, the correlations of the Gini coefficients with Q1 are

Denmark 1960, Finland 1960, Germany 1990, Greece 1960, Netherlands 1960, Sweden 1960, Switzerland 1980, and Fiji 1970.
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smaller in magnitude: –0.76 in 1960, -0.85 in 1970, -0.83 in 1980, and –0.91 in 1990. Because of these patterns, the results that use Gini coefficients turn out to be similar to those that use Q5 but not so similar to those that use Q1 or other quintile measures. One reason that the correlation between the Gini coefficients and the Q5 values are so high is that the Q5 variables have much larger standard deviations than the other quintile shares.

V. Effects of Inequality on Growth and Investment The second columns of Tables 1 and 2 show how the baseline regressions are affected by the restriction of the samples to those for which data on the Gini coefficient are available. This restriction reduces the overall sample size for the growth-rate panel from 250 to 146 (and from 251 to 146 for the investment-ratio panel). This diminution in sample size does not affect the general nature of the coefficient estimates. The main effect is that the inflation rate is less important in the truncated sample. Table 4 shows the estimated coefficients on the Gini coefficient when this variable is added to the panel systems from Tables 1 and 2. In these results, the raw data on the Gini coefficient are entered directly. A reasonable alternative is to adjust these Gini values for differences in the method of measurement. The important differences are whether the data are for individuals or households and whether the inequality applies to income gross or net of taxes or to expenditures rather than incomes. Some of these features turn out to matter significantly for the measurement of inequality, as discussed in the next section. However, the adjustment of the inequality variables for these elements turns out to have little consequence for the estimated effects of inequality on growth and investment. Therefore, the results reported here consider only the unadjusted measures of inequality.

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For the growth rate, the estimated coefficient on the Gini coefficient in Table 4 is essentially zero. Figure 1 shows the implied partial relation between the growth rate and the Gini coefficient.12 This pattern looks consistent with a roughly zero relationship and does not suggest any obvious nonlinearities or outliers. Thus, overall, with the other explanatory variables considered in Table 1 held constant, differences in Gini coefficients for income inequality have no significant relation with subsequent economic growth. One possible interpretation is that the various theoretical effects of inequality on growth, as summarized before, are nearly fully offsetting. It is possible to modify the present system to reproduce the finding from many studies that inequality is negatively related to economic growth. If the fertility-rate variable, one of the variables that are correlated with inequality, is omitted from the system, then the estimated coefficient on the Gini variable becomes significantly negative. Table 4 shows that the estimated coefficient in this case is –0.037 (0.017). In this case, a one-standard-deviation reduction in the Gini coefficient (by 0.1, see Table 3) would be estimated to raise the growth rate on impact by 0.4 percent per year. Perotti (1996) reports effects of similar magnitude. However, it seems that this effect may just represent a proxying for the correlated fertility rate. More interesting results emerge when the effect of the Gini coefficient on economic growth is allowed to depend on the level of economic development, measured by real per capita GDP. The Gini coefficient is now entered into the growth system
12

The variable plotted on the vertical axis is the growth rate (for any of the three time periods) net of the estimated effect of all explanatory variables aside from the Gini coefficient. The value plotted was also normalized to make its mean value zero. The line

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linearly and also as a product with the log of per capita GDP. In this case, the estimated coefficients are jointly significant at usual critical levels (p-value of 0.059) and also individually significant: -0.33 (0.14) on the linear term and 0.043 (0.018) on the interaction term. This estimated relation implies that the effect of inequality on growth is negative for values of per capita GDP below $2070 (1985 U.S. dollars) and then becomes positive.13 (The median value of GDP was $1258 in 1960, $1816 in 1970, and $2758 in 1980.) Quantitatively, the estimated marginal impact of the Gini coefficient on growth ranges from a low of -0.09 for the poorest country in 1960 (a value that enters into the growth equation for 1965-75) to 0.12 for the richest country in 1980 (which appears in the equation for 1985-95). Since the standard deviation of the Gini coefficients in each period is about 0.1, the estimates imply that a one-standard-deviation increase in the Gini value would affect the typical country’s growth rate on impact by a magnitude of around 0.5 percent per year (negatively for poor countries and positively for rich ones). From a theoretical standpoint, the effects may result because rising per capita income reduces the constraints of imperfect loan markets on investment. The positive

drawn through the points is a least-squares fit (and, therefore, does not correspond precisely to the estimated coefficient of the Gini coefficient in Table 4). 13 There is some indication that the coefficients on the Gini variables—and, hence, the breakpoints for the GDP values—shift over time. If the coefficients are allowed to differ by period, the results for the Gini term are -0.33 (0.15) for the first period, -0.33 (0.15) for the second, and -0.38 (0.14) for the third, and the corresponding estimates for the interaction term are 0.047 (0.020), 0.039 (0.019), and 0.043 (0.018). These values imply breakpoints for GDP of $1097, $5219, and $6568, respectively. Thus, the breakpoints are highly sensitive to small variations in the underlying two coefficients. A Wald test for stability of the two coefficients over time has a p-value of 0.088.
21

effect of the Gini coefficient in the upper-income range may arise because the growthpromoting aspects of inequality dominate when credit-market problems are less severe. The role of credit markets can be assessed more directly by using the ratio of a broad monetary aggregate, M2, to GDP as an indicator of the state of financial development. However, if the Gini coefficients are interacted with the M2 ratio, rather than per capita GDP, the estimated effects of the Gini variables on economic growth are individually and jointly insignificant.14 This result could emerge because the M2 ratio is a poor measure—worse than per capita GDP—of the imperfection of credit markets. As a check on the results, the growth system was reestimated with the Gini coefficient allowed to have two separate coefficients. One coefficient applies for values of per capita GDP below $2070 (the break point estimated above) and the other for values of per capita GDP above $2070. The results, shown in Table 4, are that the estimated coefficient of the Gini coefficient is -0.033 (0.021) in the low range of GDP and 0.054 (0.025) in the high range.15 These estimated values are jointly significantly different from zero (p-value = 0.011) and also significantly different from each other (p-value = 0.003). Thus, this piecewise-linear form tells a similar story to that found in the representation that includes the interaction between the Gini and log(GDP). Figure 2 shows the partial relations between the growth rate and the Gini coefficient for the low and high ranges of per capita GDP. In the left panel, where per

14

The effects of the Gini variables on economic growth are also individually and jointly insignificant if the Gini values are interacted with the democracy index, rather than per capita GDP. This specification was suggested by models in which the extent of democracy influences the sensitivity of income transfers to the degree of inequality. 15 This specification also includes different intercepts for the low and high ranges of GDP.
22

capita GDP is below $2070, the estimated relation is negative. In the right panel, where per capita GDP is above $2070, the estimated relation is positive. The bottom part of Table 4 shows how the Gini coefficient relates to the investment ratio. The basic finding, when the other explanatory variables shown in Table 2 are held constant, is that the investment ratio does not depend significantly on inequality, as measured by the Gini coefficient. This conclusion holds for the linear specification and also for the one that includes an interaction between the Gini value and log(GDP). (Results are also insignificant if separate coefficients on the Gini variable are estimated for low and high values of per capita GDP.) Thus, there is no evidence that the aggregate saving rate, which would tend to influence the investment ratio, depends on the degree of income inequality.16 Table 5 shows the results for economic growth when the inequality measure is based on quintile-shares data, rather than Gini coefficients. One finding is that the highestquintile share generates results that are similar to those for the Gini coefficient.17 The estimated effect on growth is insignificant in the linear form. However, the effects are significant when an interaction with log(GDP) is included or when two separate coefficients on the highest-quintile-share variable are estimated, depending on the value of GDP. With the interaction variable included, the implied effect of more inequality (a greater share for the rich) on growth is negative when per capita GDP is less than $1473 and positive otherwise. The similarity in results with those from the Gini coefficient arises
16

In this case, the Gini variables are insignificant even when the fertility-rate variable is excluded.

23

because, as noted before, the highest-quintile share is particularly highly correlated with the Gini values. Table 5 also shows results for economic growth when other quintile-share measures are used to measure inequality—the share of the middle three quintiles and the share of the lowest fifth of the population. In these cases, the significant effects on economic growth arise only when separate coefficients are estimated on the shares variables, depending on the level of GDP.18 The effects on growth are positive in the low range of GDP (with greater shares of the middle or lowest quintiles signifying less inequality) and negative in the high range.

VI. Determinants of Inequality The determinants of inequality are assessed first by considering a panel of Gini coefficients observed around 1960, 1970, 1980, and 1990. Figure 3 shows a scatter of these values against roughly contemporaneous values of the log of per capita GDP. A Kuznets curve would show up as an inverted-U relationship between the Gini value and log(GDP). This relationship is not obvious from the scatter plot, although one can discern such a curve after staring at the diagram for a long time. In any event, the relation between the Gini coefficient and a quadratic in log(GDP) does turn out to be statistically significant, as shown in the first column of Table 6. This column reports the results from a

17

The sample size is somewhat smaller here because the quintile-share data are less abundant than the Gini values. The numbers of observations when the quintiles data are used are 33 for the first period, 40 for the second, and 43 for the third. 18 The breakpoint used, $1473, is the one implied by the system with the interaction term between the highest quintile share and log(GDP).
24

panel estimation, using the seemingly-unrelated technique. In this specification, log(GDP) and its square are the only regressors, aside from a single constant term. The estimated relation implies that the Gini value rises with GDP for values of GDP less than $1636 (1985 U.S. dollars) and declines thereafter. The fit of the relationship is not very good, as is clear from Figure 3. The R-squared values for the four periods range from 0.12 to 0.22. Thus, in line with the findings of Papanek and Kyn (1986), the level of economic development would not explain most of the variations in inequality across countries and over time. The second column of Table 6 adds to the panel estimation a number of control variables, including some corrections for the manner in which the underlying inequality data are constructed. The first dummy variable equals one if the Gini coefficient is based on income net of taxes or on expenditures. The variable equals zero if the data refer to income gross of taxes. The estimated coefficient of this variable is significantly negative— the Gini value is lower by roughly 0.05 if the data refer to income net of taxes or expenditures, rather than income gross of taxes.19 This result is reasonable because taxes tend to be equalizing and because expenditures would typically be less volatile than income. (There is no significant difference between the Gini values measured for income net of taxes versus those constructed for expenditures.)

19

I have also estimated the system with the gross-of-tax observations separated from the net-of-tax ones for the coefficients of all of the explanatory variables. The hypothesis that all of these coefficients, except for the intercepts, are jointly the same for the two sets of observations is accepted with a p-value of 0.33.
25

The second dummy variable equals one if the data refer to individuals and zero if the data refer to households. The estimated coefficient of this variable is negative but not statistically significant. It was unclear, ex ante, what sign to anticipate for this variable. The panel system also includes the average years of school attainment for adults aged 15 and over at three levels: primary, secondary, and higher. The results are that primary schooling is negatively and significantly related to inequality, secondary schooling is negatively (but not significantly) related to inequality, and higher education is positively and significantly related to inequality.20 The dummy variables for Sub-Saharan Africa and Latin America are each positive, statistically significant, and large in magnitude. Since per capita GDP and schooling are already held constant, these effects are surprising. Some aspects of these areas that matter for inequality—not captured by per capita GDP and schooling—must be omitted from the system. Preliminary results indicate that the influence of the continent dummies is substantially weakened when one holds constant variables that relate to colonial heritage and religious affiliation. I also considered measures of the heterogeneity of the population with respect to ethnicity and language and religious affiliation. The first variable, referred to as ethnolinguistic fractionalization, has been used in a number of previous studies.21 This measure can be interpreted as (one minus) the probability of meeting someone of the same ethno-

20

If one adds the ratio to GDP of public outlays on schooling, then this variable is significantly positive. The estimated coefficients on the school-attainment values do not change greatly. One possibility is that the school-spending variable picks up a reverse effect from inequality to income redistribution (brought about through expenditures on education). 21 See, for example, Mauro (1995).
26

linguistic group in a random encounter. The second variable is a Herfendahl index of the fraction of the population affiliated with nine main religious groups.22 This variable can be interpreted as the probability of meeting someone of the same religion in a chance encounter. My expectation was that more heterogeneity of ethnicity, language, and religion would be associated with greater income inequality. Moreover, unlike the schooling measures, the heterogeneity measures can be viewed as largely exogenous at least in a short- or medium-run context. It turned out, surprisingly, that the two measures of population heterogeneity had roughly zero explanatory power for the Gini coefficients. These results are especially disappointing because the heterogeneity measures would otherwise have been good instruments to use for inequality in the growth regressions. In any event, the heterogeneity variables were excluded from the regression systems shown in Table 6. The addition of the control variables in column 2 of Table 6 substantially improves the fits for the Gini coefficients—the R-squared values for the four periods now range from 0.52 to 0.67. However, this improvement in fit does not have a dramatic effect on the point estimates and statistical significance for the estimated coefficients of log(GDP) and its square. That is, a similar Kuznets curve still applies. Figure 4 provides a graphical representation of this curve. The vertical axis shows the Gini coefficient after filtering out the estimated effects (from column 2 of Table 6) of the control variables other than log(GDP) and its square. These filtered values have been

22

The underlying data are from Barrett (1982). The groupings are Catholic, Protestant, Muslim, Buddhist, Hindu, Jewish, miscellaneous eastern religions, non-religious, and other religions. See Barro (1997) for further discussion.
27

normalized to make the mean equal zero. The horizontal axis plots the log of per capita GDP. The peak in the curve occurs at a value for GDP of $3320 (1985 U.S. dollars). I have tested whether the Kuznets curve is stable, that is, whether the coefficients on log(GDP) and its square shift over time. The main result is that these coefficients are reasonably stable. The system shown in column 2 of Table 6 was extended to allow for different coefficients on the two GDP variables for each period. The estimated coefficients on the linear terms are 0.40 (0.09) in 1960, 0.38 (0.09) in 1970, 0.40 (0.09) in 1980, and 0.41 (0.09) in 1990. The corresponding estimated coefficients on the squared terms are –0.025 (0.006), –0.023 (0.006), -0.024 (0.006), and –0.025 (0.005). (In this system, the coefficients of the other explanatory variables were constrained to be the same for each period.) Given the close correspondence for the separately estimated coefficients of log(GDP) and its square, it is surprising that a Wald test rejects the hypothesis of equal coefficients over time with a p-value of 0.013. The system shown in column 2 of Table 6 was also extended to allow for different coefficients over time on the schooling variables. In this revised system, three schooling coefficients were estimated for each period, but the coefficients of the other explanatory variables were constrained to be the same for all of the periods. The estimated coefficients for the different periods are as follows: primary schooling: -0.008 (0.005), -0.013 (0.005), -0.017 (0.011), and –0.010 (0.005); secondary schooling: -0.026 (0.023), -0.017 (0.011), -0.002 (0.010), and –0.010 (0.010); and higher schooling: 0.051 (0.127), 0.043 (0.072), 0.047 (0.053), and 0.055 (0.045). There is little indication of systematic variation over time, and a Wald test for all three sets of coefficients jointly is not significant (p-value of 0.17).

28

These results conflict with the idea that increases in income inequality in the 1980s and 1990s in the United States and other advanced countries reflected new kinds of technological developments that were particularly complementary with high skills. Under this view, the positive effect of higher education on the Gini coefficient should be larger in the 1980s and 1990s than in the 1960s and 1970s. The empirical results show, instead, that the estimated coefficients in the later periods are similar to those in the earlier periods. The dummy variables for Sub-Saharan Africa and Latin America show instability over time. The estimated coefficients are, for Africa, 0.073 (0.032), 0.053 (0.023), 0.097 (0.023), and 0.152 (0.017); and for Latin America, 0.097 (0.023), 0.070 (0.016), 0.068 (0.015), and 0.121 (0.016). In this case, a Wald test for both sets of coefficients jointly rejects stability over time (p-value = 0.0001). This instability is probably a sign that the continent dummies are not fundamental determinants of inequality, but are rather unstable proxies for other variables. As mentioned before, the underlying data set expands beyond the Gini values designated as high quality by Deininger and Squire (1996). If a dummy variable for the high-quality designation is included in the panel system, then its estimated coefficient is essentially zero. The squared residuals from the panel system are, however, systematically related to the quality designation. The estimated coefficient in a least-squares regression of the squared residual on a dummy variable for quality (one if high quality, zero otherwise) is –0.0025 (0.0008). However, part of the tendency of low-quality observations to have greater residual variance relates to the tendency of these observations to come from low-income countries (which likely have poorer quality data in general). If the log of per capita GDP is also included in the system for the squared residuals, then the

29

estimated coefficient on the high-quality dummy becomes –0.0018 (0.0008), whereas that on log(GDP) is –0.0012 (0.0003). Adjustments of the weighting scheme in the estimation to take account of this type of heteroscedasticity have little effect on the results. Column 3 of Table 6 adds another control variable—the indicator for maintenance of the rule of law. The estimated coefficient is negative and marginally significant, -0.040 (0.019). Thus, there is an indication that better enforcement of laws goes along with greater equality of incomes. Column 4 includes the index of democracy (electoral rights). The estimated coefficient of this variable differs insignificantly from zero. If the square of this variable is also entered, then this additional variable is statistically insignificant (as are the linear and squared terms jointly). The magnitude of the estimated coefficients on log(GDP) and its square fall only slightly from the values shown in column 2 of Table 6. Thus, the estimated Kuznets curve, expressed in terms of the log of per capita GDP, does not involve a proxying of GDP for democracy. The results described thus far are from a random-effects specification. That is, the panel estimation allows the error terms to be correlated over time for a given country. Column 5 shows the results of a fixed-effects estimation, where an individual constant is entered for each country. This estimation is still carried out as a panel for levels of the Gini coefficients, not as first differences. Countries are now included in the sample only if they have at least two observations on the Gini coefficient for 1960, 1970, 1980, or 1990. (The observations do not have to be adjacent in time.) This estimation drops the variables—the dummies for Sub-Saharan Africa and Latin America—that do not vary over time.

30

The estimated Kuznets-curve coefficients—0.132 (0.013) on log(GDP) and –0.0083 (0.0014) on the square—are still individually and jointly significantly different from zero.23 However, the sizes of these coefficients are about one-third of those for the cases that exclude country fixed effects. With the country fixed effects present, the GDP variables pick up only time-series variations within countries. Moreover, this specification allows only for contemporaneous relations between the Gini values and GDP. Therefore, the estimates would pick up a relatively short-run link between inequality and GDP. With the country effects not present, the estimates also reflect cross-sectional variations, and the coefficients on the GDP variables pick up longer run aspects of the relationships with the Gini values. Further refinement of the dynamics of the relation between inequality and its determinants may achieve more uniformity between the panel and fixed-effects results. It is also possible to estimate Kuznets-curve relationships for the quintile-based measures of inequality. If the upper-quintile share is the dependent variable and the controls considered in column 2 of Table 6 are held constant, then the estimated coefficients turn out to be 0.353 (0.086) on log(GDP) and –0.0216 (0.0054) on the square. Thus, the share of the rich tends to rise initially with per capita GDP and subsequently decline (after per capita GDP reaches $3500). For the share of the middle three quintiles, the corresponding coefficient estimates are –0.291 (0.070) on log(GDP) and 0.0181 (0.0044) on the square. Hence, the middle share falls initially with per capita GDP and subsequently rises (after per capita GDP reaches $3100). For the share of the lowest quintile, the coefficients are –0.080 (0.024)

31

on log(GDP) and 0.0047 (0.0015) on the square. Therefore, this share also falls at first with per capita GDP and subsequently increases (when per capita GDP passes $5600).

VII. Conclusions Evidence from a broad panel of countries shows little overall relation between income inequality and rates of growth and investment. For growth, there is an indication that inequality retards growth in poor countries but encourages growth in richer places. Growth tends to fall with greater inequality when per capita GDP is below around $2000 (1985 U.S. dollars) and to rise with inequality when per capita GDP is above $2000. The results mean that income-equalizing policies might be justified on growthpromotion grounds in poor countries. For richer countries, active income redistribution appears to involve a tradeoff between the benefits of greater equality and a reduction in overall economic growth. The Kuznets curve—whereby inequality first increases and later decreases in the process of economic development—emerges as a clear empirical regularity. However, this relation does not explain the bulk of variations in inequality across countries or over time. The estimated relationship may reflect not just the influence of the level of per capita GDP but also the dynamic effect whereby the adoption of each type of new technology has a Kuznets-type dynamic effect on the distribution of income.

23

These estimates are virtually the same—0.133 (0.012) on log(GDP) and –0.0090 (0.0013) on the square—if all other regressors aside from the country fixed effects are dropped from the system.
32

References Aghion, P., E. Caroli, and C. Garcia-Penalosa (1998). “Inequality and Economic Growth: The Perspective of the New Growth Theories,” unpublished, forthcoming in the Journal of Economic Literature. Aghion, P. and P. Howitt (1997). Endogenous Economic Growth, Cambridge MA, MIT Press. Ahluwalia, M. (1976a). “Income Distribution and Development,” American Economic Review, 66, 5, 128-135. Ahluwalia, M. (1976b). “Inequality, Poverty and Development,” Journal of

Development Economics, 3, 307-342. Alesina A. and R. Perotti. (1996). “Income Distribution, Political Instability and Investment,” European Economic Review, 81, 5, 1170-1189. Alesina, A. and D. Rodrik. (1994). “Distribution Politics and Economic Growth,” Quarterly Journal of Economics, 109, 465-490. Anand S. and S. M. Kanbur (1993). “The Kuznets Process and the InequalityDevelopment Relationship,” Journal of Development Economics, 40, 25-72. Barrett, D. B., ed. (1982). University Press. Barro, R.J. (1991). “Economic Growth in a Cross Section of Countries,” World Christian Encyclopedia, Oxford, Oxford

Quarterly Journal of Economics, 106, 407-444. Barro, R.J. (1997). Determinants of Economic Growth, A Cross-Country Empirical Study, Cambridge MA, MIT Press.

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Benabou, R. (1996). “Inequality and Growth,” NBER Macroeconomics Annual, 11-73. Benhabib, J. and A. Rustichini. (1996). “Social Conflict and Growth,” Journal of Economic Growth, 1, 1, 129-146. Bertola, G. (1993). “Factor Shares and Savings in Endogenous Growth,” American Economic Review, 83, 1184-1198. Deininger, K and L. Squire (1996). “New Data Set Measuring Income

Inequality,” World Bank Economic Review, 10 (September), 565-591. Forbes, K. (1997). “A Reassessment of the Relationship between Inequality and Growth,” unpublished, MIT. Greenwood J. and B. Jovanovic (1990). “Financial Development, Growth and the Distribution of Income.,” Journal of Political Economy, 98, 5, 1076-1107. Gupta, D. (1990). The Economics of Political Violence, New York, Praeger. Helpman, E. (1997). Cambridge MA, MIT Press. Hibbs, D.(1973). York, Wiley. Kuznets, S. (1955). Economic Review, 45, 1-28. Li, H. and H. Zou (1998). “Income Inequality Is not Harmful for Growth: Theory and Evidence,” Review of Development Economics, 2, 318-334. Li H., L. Squire and H. Zou. (1998). “Explaining International and Intertemporal Variations in Income Inequality,” Economic Journal , 108, 26-43. “Economic Growth and Income Inequality,” American Mass Political Violence: A Cross-Sectional Analysis, New General Purpose Technologies and Economic Growth,

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Loury, G. (1981). “Intergenerational Transfers and the Distribution of Earnings,” Econometrica, 49, 843-867. Mauro, P. (1995). “Corruption, Country Risk, and Growth,” Quarterly Journal of Economics, 110, 681-712. Papanek, G. and O. Kyn. (1986). “The Effect on Income Distribution of Development, the Growth Rate and Economic Strategy,” Journal of Development Economics, 23, 1, :55-65. Perotti, R. (1993). “Political Equilibrium, Income Distribution and Growth,”

Review of Economic Studies, 60, 755-776. Persson, T. and G. Tabellini. (1994). “Is Inequality Harmful for Growth?. Theory and Evidence,” American Economic Review, 84, 600-621. Piketty, T. (1997). “The Dynamics of the Wealth Distribution and Interest Rates with Credit Rationing,” Review of Economic Studies, 64. Robinson, S. (1976). “A Note on the U-hypothesis Relating Income Inequality and Economic Development,” American Economic Review, 66, 3, 473-440. Rodriguez, F. (1998). “Inequality, Redistribution and Rent-Seeking,” unpublished, University of Maryland. Summers, R. and A. Heston (1991). “The Penn World Table (Mark 5): An Expanded Set of International Comparisons, 1950-1988,” Quarterly Journal of Economics, 106, 327-369. Theil, H. (1967). Holland. Economics and Information Theory, Amsterdam, North-

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Venieris Y. and D. Gupta. (1986). “Income Distribution and Sociopolitical Instability as Determinants of Savings: A Cross Sectional Model,” Journal of Political Economy, 94, 873-883.

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Table 1 Panel Regressions for Growth Rate

Independent variable

Estimated coefficient in full sample

Estimated coefficient in Gini sample

log(per capita GDP) log(per capita GDP) squared govt. consumption/GDP rule-of-law index democracy index democracy index squared inflation rate years of schooling log(total fertility rate) investment/GDP growth rate of terms of trade numbers of observations R2

0.123 (0.027) -0.0095 (0.0018) -0.149 (0.023) 0.0173 (0.0053) 0.053 (0.029) -0.047 (0.026) -0.037 (0.010) 0.0072 (0.0017) -0.0250 (0.0047) 0.059 (0.022) 0.164 (0.028) 79, 87, 84 0.67, 0.49, 0.41

0.101 (0.030) -0.0081 (0.0019) -0.153 (0.027) 0.0103 (0.0064) 0.041 (0.033) -0.036 (0.028) -0.014 (0.009) 0.0066 (0.0017) -0.0303 (0.0054) 0.062 (0.022) 0.122 (0.035) 39, 56, 51 0.73, 0.62, 0.60

37

Notes to Table 1 Dependent variables: The dependent variable is the growth rate of real per capita GDP. The growth rate is the average for each of the three periods 1965-75, 197585, and 1985-95. The first column has the full sample of observations with available data. The second panel restricts to the observations for which the Gini coefficient, used in later regressions, is available. Independent variables: Individual constants (not shown) are included in each panel for each period. The log of real per capita GDP and the average years of male secondary and higher schooling are measured at the beginning of each period. The ratios of government consumption (exclusive of spending on education and defense) and investment (private plus public) to GDP, the democracy index, the inflation rate, the total fertility rate, and the growth rate of the terms of trade (export over import prices) are period averages. The rule-of-law index is the earliest value available (for 1982 or 1985) in the first two equations and the period average for the third equation. Estimation is by three-stage least squares. Instruments are the actual values of the schooling and terms-of-trade variables, lagged values of the other variables aside from inflation, and dummy variables for prior colonial status (which have substantial explanatory power for inflation). The earliest value available for the rule-of-law index (for 1982 or 1985) is included as an instrument for the first two equations, and the 1985 value is included for the third equation. Asymptotically valid standard errors are shown in parentheses. The R2values apply to each period separately.

38

Table 2 Panel Regressions for Investment Ratio

Independent variable

Estimated Coefficient in full sample

Estimated Coefficient in Gini sample

log(per capita GDP) log(per capita GDP) squared govt. consumption/GDP rule-of-law index democracy index democracy index squared inflation rate years of schooling log(total fertility rate) growth rate of terms of trade numbers of observations R2

0.199 (0.083) -0.0119 (0.0053) -0.282 (0.072) 0.063 (0.019) 0.100 (0.079) -0.108 (0.068) -0.058 (0.026) -0.0005 (0.0058) -0.0586 (0.0140) 0.073 (0.067) 79, 87, 85 0.52, 0.59, 0.66

0.155 (0.119) -0.0099 (0.0071) -0.341 (0.105) 0.063 (0.025) 0.093 (0.123) -0.096 (0.103) -0.026 (0.028) 0.0050 (0.0066) -0.0679 (0.0189) 0.162 (0.113) 39, 56, 51 0.37, 0.64, 0.68

Notes: The dependent variable is the ratio of real investment (private plus public) to real GDP. The measure is the average of the annual observations on the ratio for each of the periods 1965-75, 1975-85, and 1985-92. See the notes to Table 1 for other information.

39

Table 3 Statistics for Gini Coefficients

Gini 1960

Gini 1970

Gini 1980

Gini 1990

Number of observations Mean Maximum Minimum Standard deviation

49

61

68

76

0.432 0.640 0.253 0.100

0.416 0.619 0.228 0.094

0.394 0.632 0.210 0.092

0.409 0.623 0.227 0.101

Correlation with: Gini 1960 Gini 1970 Gini 1980 Gini 1990 1.00 0.81 0.85 0.72 0.81 1.00 0.93 0.87 0.85 0.93 1.00 0.86 0.72 0.87 0.86 1.00

Note: The table shows descriptive statistics for the Gini coefficients. The years shown are the closest ten-year value to the actual date of the survey on income distribution. Two observations have been omitted (Hungary in 1960 and Bahamas in 1970) because the corresponding data on GDP were unavailable.

40

Table 4 Effects of Gini Coefficients on Growth Rates and Investment Ratios

Gini

Gini* log(GDP)

Gini (low GDP)

Gini (high GDP)

Wald tests (pvalues)

Growth rate regressions 0.000 (0.018) -0.328 (0.140)

0.043 (0.018) -0.033 (0.021) 0.054 (0.025)

0.061 0.011, 0.003*

fertility variable omitted -0.036 (0.017) -0.364 (0.155)

0.043 (0.020) -0.059 (0.021) -0.003 (0.026)

0.014 0.017, 0.078*

Investment ratio regressions 0.050 (0.070) 0.49 (0.48) fertility variable omitted -0.049 (0.066) 0.46 (0.49)

-0.058 (0.062)

0.48

-0.066 (0.063)

0.45

41

Notes to Table 4

Gini coefficients were added to the systems shown in Tables 1 and 2. The Gini value around 1960 appears in the equations for growth from 1965 to 1975 and for investment from 1965 to 1974, the Gini value around 1970 appears in the equations for 1975 to 1985 and 1975 to 1984, and the Gini value around 1980 appears in the equations for 1985 to 1995 and 1985 to 1992. The variable Gini*log(GDP) is the product of the Gini coefficient and the log of per capita GDP. The system with Gini (low GDP) and Gini (high GDP) allows for two separate coefficients on the Gini variable. The first coefficient applies when log(GDP) is below the break point for a negative effect of the Gini coefficient on growth, as implied by the system that includes Gini and Gini*log(GDP). The second coefficient applies for higher values of log(GDP). Separate intercepts are also included for the two ranges of log(GDP). The variables that include the Gini coefficients are included in the lists of instrumental variables. The Wald tests are for the hypothesis that both coefficients equal zero. Values denoted by an asterisk are for the hypothesis that the two coefficients are equal (but not necessarily equal to zero). See the notes to Table 1 for additional information.

42

Table 5 Effects of Quintile-Based Inequality Measures on Growth Rates

Quintile measure Highest-quintile share 0.020 (0.020) -0.44 (0.15)

Quintile measure* log(GDP)

Quintile measure (low GDP)

Quintile measure (high GDP)

Wald tests (p-values)

0.060 (0.019) -0.056 (0.031) 0.058 (0.022)

0.005

0.003, 0.001*

Middle-three-quintiles share -0.020 (0.025) -0.011 (0.163)

-0.002 (0.021) 0.057 (0.040) -0.057 (0.027)

0.66

0.022, 0.010*

Lowest-quintile share -0.044 (0.061) 0.19 (0.51)

-0.028 (0.062) 0.37 (0.12) -0.156 (0.062)

0.70

0.000, 0.000*

43

Notes to Table 5

The quintiles data on income distribution were used to form the share of the highest fifth, the share of the middle three quintiles, and the share of the lowest fifth. The quintile values around 1960 appear in the equations for growth from 1965 to 1975, the values around 1970 appear in the equations for 1975 to 1985, and the values around 1980 appear in the equations for 1985 to 1995. The interaction variable is the product of the quintile measure and the log of per capita GDP. The system with quintile share (low GDP) and quintile share (high GDP) allows for two separate coefficients on the quintile-share variable. The first coefficient applies when log(GDP) is below the break point for a change in sign of the effect of the highest-quintile-share variable on growth, as implied by the system that includes the highest quintile share and the interaction of this share with log(GDP). The second coefficient applies for higher values of log(GDP). Separate intercepts are also included for the two ranges of log(GDP). The variables that include the quintile-share variables are included in the lists of instrumental variables. The Wald tests are for the hypothesis that both coefficients equal zero. Values denoted by an asterisk are for the hypothesis that the two coefficients are equal (but not necessarily equal to zero). See the notes to Table 1 for additional information.

44

Table 6 Determinants of Inequality

Variable

No fixed effects

Fixed effects 0.415 (0.084) -0.0254 (0.0053) -0.0496 (0.0094) -0.0119 (0.0087) -0.0161 (0.0037) -0.0109 (0.0070) 0.082 (0.034) 0.113 (0.015) 0.092 (0.012) --0.003 (0.015) 35, 59 61, 70 0.56, 0.59 0.67, 0.67 0.132 (0.013) -0.0083 (0.0014) -0.0542 (0.0108) -0.0026 (0.0078) -0.0025 (0.0091) -0.0173 (0.0099) 0.102 (0.030) ----36, 56 57, 59 --

log(GDP) log(GDP) squared Dummy: net income or spending Dummy: individual vs. household data Primary schooling Secondary schooling Higher schooling Dummy: Africa Dummy: Latin Amer. Rule-of-law index Democracy index Number of observations R-squared

0.407 (0.090) -0.0275 (0.0056) --

0.407 (0.081) -0.0251 (0.0051) -0.0493 (0.0094) -0.0134 (0.0086) -0.0147 (0.0037) -0.0108 (0.0070) 0.081 (0.034) 0.113 (0.015) 0.094 (0.012) --40, 59 61, 70 0.52, 0.59 0.67, 0.67

0.437 (0.078) -0.0264 (0.0049) -0.0480 (0.0087) -0.0143 (0.0080) -0.0152 (0.0036) -0.0061 (0.0070) 0.072 (0.032) 0.135 (0.016) 0.089 (0.012) -0.040 (0.019) -40, 57 56, 67 0.50, 0.58 0.78 0.72

--

-------49, 61 68, 76 0.12, 0.15 0.18, 0.22

45

Notes to Table 6

The dependent variables are the Gini coefficients observed around 1960, 1970, 1980, and 1990. See Table 3 for statistics on these variables. Estimation is by the seemingly-unrelated (SUR) technique. The first four columns include a single constant term, which does not vary over time or across countries. The last column includes a separate, time-invariant intercept for each country (and includes only countries with two or more observations on the Gini coefficient). GDP is real per capita GDP for 1960, 1970, 1980, and 1990. The first dummy variable equals one if the Gini coefficient is based on income net of taxes or on expenditures. It equals zero if the Gini is based on income gross of taxes. The second dummy equals one if the income-distribution data refer to individuals and zero if the data refer to households. The schooling variables are the average years of attainment of the adult population aged 15 and over for 1960, 1970, 1980, and 1990. The third and fourth dummy variables equal one if the country is in SubSaharan Africa or Latin America, respectively, and zero otherwise. The rule-of-law and democracy indexes are described in the notes to Table 1. The numbers of observations and the R-squared values refer to each of the four periods, 1960, 1970, 1980, and 1990.

46

Figure 1 Growth Rate versus Gini Coefficient growth rate (unexplained part)
0.10

0.05

0.00

-0.05

-0.10 0.2

0.3

0.4

0.5

0.6

0.7

Gini coefficient

47

Figure 2

Growth Rate versus Inequality
Growth Rate versus Inequality (low GDP) growth rate (unexplained part) growth rate (unexplained part)
-0.04 -0.02 0.00 0.02 0.04 -0.06

Growth Rate versus Inequality (high GDP)

-0.06 0.2 -0.04 -0.02 0.00 0.02 0.04

Gini coefficient

Gini coefficient

48

49