Education and Economic Growth

214/ED/EFA/MRT/PI/15/REV. Background paper prepared for the Education for All Global Monitoring Report 213/4 Teaching and learning: Achieving quality for all Education and Economic Growth Amparo Castelló-Climent 213 This paper was commissioned by the Education for All Global Monitoring Report as background information to assist in drafting the 213/4 report. It has not been edited by the team. The views and opinions expressed in this paper are those of the author(s) and should not be attributed to the EFA Global Monitoring Report or to UNESCO. The papers can be cited with the following reference: Paper commissioned for the EFA Global Monitoring Report 213/4, Teaching and learning: Achieving quality for all For further information, please contact efareport@unesco.org

Education and Economic Growth* Amparo Castelló-Climent University of Valencia March 213 Abstract Using the new data set by Castelló-Climent and Doménech (212), this paper reassesses the relationship between inequality in the distribution of education and economic growth. For a sample that covers 142 countries during the period 1965-21, the system-gmm estimates show that an increase in.1 points in the Gini coefficient is associated with a.53 percentage-point reduction in the per capita GDP growth rates. The results also suggest that it is the distribution of education of the "parents" what has a greater influence on growth. When the age structure of the working-age population is accounted for, the negative effect of a more unequal distribution of education in the older generations is larger than the negative effect of a more unequal distribution of education in the younger groups. JEL classification: I25, O11, O5 Key words: Distribution of education, attainment levels, age structure, * Contact: Amparo Castelló-Climent, Institute for International Economics, Facultad de Economía, University of Valencia, Campus dels Tarongers s/n, 4622- Valencia, Spain. Email: amparo.castello@uv.es.

1- Introduction Many studies that have analyzed the relationship between the distribution of education and economic growth have used data on human capital inequality measures by Castelló and Doménech (22), based on the educational attainment levels by Barro and Lee (21). However, recent studies have shown that the perpetual inventory method in Barro and Lee (21) suffers from several problems. The main drawback is that it utilizes very few census data points and depends crucially on enrollment rates, which are usually criticized for being overstated in developing countries. Cohen and Soto (27) and de la Fuente and Doménech (26) illustrate that Barro and Lee (21) data show implausible time series profiles for some countries. As Castelló and Doménech (22) utilizes the Barro and Lee s (21) data set, the inequality measures are subject to the same criticisms as the average years of schooling. To overcome these shortcomings, Barro and Lee (21) have compiled a new data set on educational attainments that uses more information from census data and a new methodology that makes use of disaggregated data by age groups. As a result, the new data set is less subject to measurement error than previous sources. The improved attainment levels are used by Castelló-Climent and Doménech (212) to update the indicators of human capital inequality. The new data set, that comprises the Gini coefficient and the distribution of education by quintiles, is available for 146 countries from 195 to 21 in a 5 year span and include a total of 1898 observations. The data set covers most of the countries in the world including data for 23 North America and Western European countries, 17 countries in Central and Eastern Europe, 5 countries in Central Asia, 21 countries in East Asia and the Pacific region, 25 countries in Latin America and the Caribbean, 8 countries in South and West Asia, 31 countries in Sub-Saharan Africa and 16 Arab States. Using the new data set on human capital inequality indicators, this paper reassesses the relationship between inequality in the distribution of education and economic growth. The results indicate the negative effect on growth of a more unequal distribution of education is quite robust. In a sample that includes 4 more countries and extends the period of analysis up to 21, as compared to the existing literature, the estimated coefficient of the Gini index is -.53, which is similar to previous findings. The system-gmm estimates suggest that a.1 point reduction in the Gini coefficient is associated with a.53 percentage-point increase per year in the growth rates of real per capita GDP. Considering that the average growth rate of the Sub-Saharan African region during this period is about.8 percentage points, the quantitative effect of a greater inequality in the distribution of education is economically meaningful. The paper also analyzes whether the effect on growth of the level and distribution of education depends on the age structure of the working-age population (25-64 years old). Interestingly, the findings reveal that the average years of schooling of the younger and older cohorts have similar effects on the growth rates. However, the influence of the distribution of education differs across age groups. The estimated coefficient of the human capital Gini coefficient of the older population (4-64 years old) is twice as high as the estimated coefficient of the Gini index in the younger age group (25-39 years old). This evidence is in line with some of the channels that suggest a negative influence of human capital inequality on economic growth. For instance, the demographic channels show that a more unequal distribution of education of the parents may influence future investment in human capital and growth by

increasing fertility rates (De la Croix and Doepke, 23) and by reducing life expectancy (Castelló-Climent and Doménech, 28). The paper is organized as follows. Next Section surveys the literature. Section 3 discusses the data and the econometric model to be estimated. Section 4 contains an illustration of the evolution of education over time for different regions. Results are displayed in Section 5. The analysis of the education by age groups is displayed in Section 6. Finally, Section 7 contains the conclusions reached. 2- Literature Review Human capital is a fundamental source of economic grow in most theoretical models (e.g. Lucas, 1988, Romer, 199). However, the effect of education on economic growth has been under debate in the empirical literature. Bils and Klenow (2) calibrate a model and find that most of the relationship between schooling and growth, found in Barro (1991), can be explained by a channel that goes from expected growth to schooling instead of from schooling to growth. Another challenging finding is that by Pritchett (21), who in a growth accounting regression shows that the impact of growth in educational capital on growth of per worker GDP is negative. According to Pritchett, explanations for the absence of positive returns in education at the macro level could be that educated individuals work in unproductive sectors, that the supply of educated labor could have been expanded whereas the demand had been stagnated or that the quality of schooling has been so low that it has not increased cognitive skills or productivity. Recent evidence, however, shows that previous findings were driven by low quality of education data. Krueger and Lindahl (21) show that the growth regressions reported by Benhabib and Spiegel (1994) and Pritchett (21) are influenced by measurement error. Cohen and Soto (27) and De la Fuente and Doménech (26) provide new data sets on educational attainments that overcome the shortcomings of previous sources, and provide evidence that the counterintuitive results on human capital and growth can be attributed to poor quality in the data. When the signal-to-noise ratio is increased in the data, the contribution of investment in education to productivity growth is relevant. The empirical evidence also shows that it is not only important that children attend school as many years as possible, but also how much do they learn while in school. Hanushek and Kimko (2) pointed out that the average years of education is an imperfect measure of human capital. When they use data on international student achievement tests, the findings reveal that cognitive skills rise substantially the explanatory power of human capital in growth regressions. Hanushek and Woessmann (212) develop a new data series on cognitive skills and confirm that differences in cognitive skills lead to economically significant differences in economic growth. Other strand of the literature indicates that inequality in the distribution of education is another relevant dimension to consider when analyzing the effect of human capital on economic growth. In a cross-section of 83 countries, Castelló and Doménech (22) show that, other things being equal, countries with greater inequality in the distribution of education in 196 had lower growth rates during the period 196-199.

Nevertheless, cross-section estimators may be biased because of variables being omitted from the model, and because they do not properly address the treatment of some explanatory variables that, according to the theory, should be considered as endogenous. Both remarks appear to be extremely important in the relationship between income inequality and economic growth. For example, while cross-section regressions report that greater income inequality has a negative impact on the growth rates of per capita income (e.g. Alesina and Rodrik, 1994; Persson and Tabellini, 1994; Perotti, 1996), panel data models that control for country-specific effects suggest that the relationship between income inequality and economic growth is positive (Forbes 2). To analyze the robustness of the effect on growth of human capital inequality, Castelló-Climent (21a) estimates a dynamic panel data model and finds that both crosssection and panel data display a negative and significant effect of human capital inequality on economic growth. 1 Most of the empirical literature on the influence of inequality on growth has documented a reduced-form relationship in which an inequality variable (e.g. income, education, land) is added to the set of explanatory variables in a standard growth equation. However, estimating the reduced form of the model sheds no light on the underlying mechanism through which inequality influences investment and growth. In fact, theoretical arguments point to several competing channels, and estimating the reduced form does not yield any information regarding which mechanism is important or how it influences this link. In the case of the distribution of human capital, there are several channels that suggest a negative influence on growth of a more unequal distribution of education. Castelló-Climent and Doménech (28) develop a model that analyzes how human capital inequality may discourage growth by reducing life expectancy and investment in education, rather than by increasing fertility, as in De la Croix and Doepke (23) and Moav (25). Other papers show that restrictions in the credit market impede poor families to undertake profitable investment projects (e.g. Galor and Zeira, 1993; Piketty, 1997; Aghion and Bolton, 1997; Mookherjee and Ray, 23). Castelló-Climent (21b) analyzes the channels through which human capital inequality may influence growth and show that the demographic channels and the credit market imperfection approach are able to explain the entire impact of human capital inequality on economic growth. 3- Methodology and Data The model estimated in this paper is a broaden version of the neoclassical growth model that includes the convergence property, other initial conditions, and additional variables that determine the steady state. A general specification that represents this model can be written as follows: 1 Castelló-Climent and Doménech (212) suggest that while human capital inequality data might have enough signal in both cross-section and panel data models, the rather stability of the income Gini coefficient over time may be a potential explanation for the mixed evidence found in the literature that analyses the effect of income inequality on economic growth.

(ln y i,t -ln y i,t-τ )/τ = α ln y i,t-τ + β H i,t-τ + γ Gini i,t-τ h + X i,t-τ δ + u it where y i,t is the real GDP per capita in country i measured at year t, τ is the number of years of the whole period, H is an indicator of the initial level of human capital, proxied by the average years of schooling of the adult population, Gini h is the Gini coefficient of the distribution of education, X is a matrix including k explanatory variables, u it is the error term, and α, β, γ, and δ represent the parameters of interest that are estimated. In order to assess the relationship between the initial level of education and its effect on the long run growth rate, we first estimate a cross-section equation by OLS. In this equation we want to compute the effect of the average years of education and the Gini coefficient of education, measured in 1965, on the average growth rate over the period 1965-21. 2 One of the main criticisms of this kind of regressions is that cross-section estimators may be biased due to omitted variables in the model. In particular these regressions fail to control for tastes, the level of technology, resource endowments, climate, institutions or any other variable specific to every country that may be an important determinant of the growth rates and may be correlated with the explanatory variables included in the estimated equation. Measuring these variables is troublesome because sometimes they are unobservable. However, if these variables are constant over time we can control for them including a country specific effect in the model. To do so we could detach the error term in (1) into three different components: u it = ξ t + ρ i + ε it where ξ t is a time specific effect, ρ i stands for specific characteristics of every country that are constant over time and ε it collects the error term that varies across countries and across time. Using (2) we could rewrite (1) as follows: ln yi,t = α ln yi,t-τ + β Hi,t-τ + γ Ginii,t-τh + Xi,t-τ δ + ξt + ρi + εit If we consider τ different from one, we have that α=τα+1, β_{i}=τβ_{i}, γ=τγ, δ=τδ, and ε_{i,t}=τε_{i,t}. In addition to omitted variables, cross-section regressions do not tackle the problem of endogeneity of some explanatory variables. We address all concerns by estimating equation (3) with the system GMM estimator, proposed by Arellano and Bover (1995) and Blundell and 2 The real GDP per capita and the measures of education are available from 195 to 21. However, so that the estimates are as close as possible as the model estimated with the system GMM, which uses lagged values as instruments, we run the cross-section regresions from 1965 to 21.

Bond (1998). The idea of this estimator is to take first differences to eliminate the source of inconsistency, that is ρ_{i}, and use the levels of the explanatory variables lagged two and further periods as instruments, as long as the errors are not second order serially correlated and that the explanatory variables are weakly exogenous. The difference equations are combined with equations in levels, which are instrumented with the lagged first differences of the corresponding explanatory variables. In order to use these additional instruments, we need the identifying assumption that the first differences of the explanatory variables are not correlated with the specific effect, that is, although the specific effect may be correlated to the explanatory variables, the correlation is supposed to be constant over time. If the moment conditions are valid, Blundell and Bond (1998) show that in Monte Carlo simulations the system GMM estimator performs better than the first difference GMM estimator proposed by Arellano and Bond (1991). We can test the validity of the moment conditions by using the conventional test of overidentifying restrictions proposed by Sargan (1958) and Hansen (1982) and by testing the null hypothesis that the error term is not second order serially correlated. Furthermore, we will test the validity of the additional moment conditions associated with the level equation with the difference Hansen test. In this paper, the inequality in the distribution of education is measured by the education Gini coefficient and the distribution of education by quintiles. The Gini coefficient is an aggregate measure of inequality and can be defined from the Lorenz Curve diagram, which plots the cumulative education share of the total years of schooling attained by the bottom X percent of the population. For instance, if 2 percent of the population gets 2 percent of the total education, 4 percent of the population gets 4 percent of the education and so on, there is total equality. The line of equality, therefore, would be represented by the 45 degree line. Specifically, the Gini coefficient is defined as the ratio of the area that lies between the line of equality and the Lorenz curve, over the total area under the line of equality. If each individual had the same education, the Lorenz curve is equal to the equality line and the Gini coefficient is equal to zero. On the other extreme, if education is highly concentrated and one individual gets all education, the Lorenz curve will be equal to zero for all education percentiles and 1 for the 1 percentile. In this case, the Lorenz curve is equal to the total area below the equality line and the Gini coefficient is equal to one. As an illustration, Table 1 contains the distribution of education of Paraguay and Peru. In 1965, Paraguay and Peru had similar years of education, 3.37 and 3.5, respectively. However, the distribution of education was more unequal in Peru than in Paraguay. The Gini coefficient in Peru was.49 and in Paraguay was.34. The distribution of education by quintiles, that is, the share of education attained by the lowest 2, 4, 6 and 8 percent of the lowest educated individuals can be used to plot the Lorenz curve. As displayed in Figure 1, the Lorenz curve for Paraguay indicates that the share of education attained by the 2 percent of the population with the lowest education was zero. The 4 percent of the lowest educated population had 18.11 percent of the education, the 6 percent of the population had 4.33 percent of the education, the 8 percent of the population had 62.56 percent of the education, and the top 2 percent of the most educated people had 37.4 percent of the education. On the other hand, in spite of having similar average years of schooling, almost 4 percent of the population in Peru was illiterate, and the top 2 percent of the most educated individuals had a greater share of education than their counterparts in Paraguay (about 47 percent of the total education). As a result, the Lorenz curve of Peru is much further from the equality line than the Lorenz curve of

Paraguay. Thus, the higher Gini coefficient in Peru is the result of a larger area between the Lorenz curve and the equality line. There are several mathematical expressions to compute the Gini coefficient. We take the data from Castelló-Climent and Doménech (212), who use a standard formula to calculate the human capital Gini coefficient. The methodology can be defined as follows: Gini h = (1/(2H)) x i - x j n i n j where H are the average years of schooling in the population 25 years and above, i and j stand for different levels of education, x refers to the cumulative average years of schooling of each level of education and n are the share of population with a given level of education. They consider 4 levels of schooling: no schooling (), primary (1), secondary (2) and tertiary (3) education. Using the attainment levels by Barro and Lee (21), Castelló-Climent and Doménech (212) compute human capital inequality indicators for 146 countries from 195 to 21 in a five-year period span and include a total of 1898 observations. The sources of the other data used in the paper are as follows. The data on the average years of education come from the latest data set by Barro and Lee (21). This new version includes more countries and years, reduces some measurement errors and solves most of the shortcomings revealed by De la Fuente and Domenech (26) and Cohen and Soto (27). The data on real GDP per capita (lny), government spending (G/GDP), measured as government share of real GDP, and total trade (Trade), measured as exports plus imports to real GDP, are taken from the latest version of the Penn World Tables, PWT 7.1, by Heston, Summers and Aten (212). The inflation rate (Inflation), measured as the annual increment in the consumer prices, is taken from the World Development Indicators. 4- Evolution of Education over time Figure 2 displays the evolution of the average years of schooling of the population 25 years and above from 195 to 21 for different regions. 3 The figure illustrates that, despite the level of development, the average years of schooling show an increasing trend in all regions. With the exception of the regions with the lowest level of education, the relative position of each group of countries has not changed over a period of 6 years. North American and Western European countries had the largest level of education, with an average years of schooling of the total 3 Barro and Lee (21) also provide the attainment levels for the population 15 and above. Although in developing countries many people start working at early ages, the average years of schooling of the population 15 and above do not account for the population aged 15-19 that complete secondary school, and the populaton aged 2-24 that complete university. Moreover, the educational attainment of the younger generation (e.g. between 15 and 24 years old) is more likely to be correlated with current income, which may exacerbate endogeneity problems in growth regressions.

population equal to 5.47 in 195 and 1.68 in 21. The relative position within this group of countries has also remained quite stable, with Portugal being the country with the lowest years of schooling at the beginning and at the end of the sample period (2.29 in 195 and 7.73 in 21) and the United States with the largest education level over the years (8.14 in 195 and 13.27 in 21). In 21, this region is followed by Central and Eastern Europe with 1.53 years of education, Central Asia with 9.71 years, East Asia and the Pacific with 8.3 years, and Latin America and the Caribbean with 7.97 years. The most spectacular increment in the level of education has taken place in the Arab States. There are several examples that can illustrate the impressive performance in this region. For instance, Algeria has increased the average years of schooling from.9 in 195 to 7.61 in 21, Jordan from.94 to 8.65, and the United Arab Emirates from.66 to 8.86. This striking numbers have changed the relative position in the group of countries at the bottom end of the distribution. Whereas the Arab States were the countries with the lowest years of schooling in 195, this group of countries overtook Sub-Saharan African region in the 197s, and South and West Asian countries in the 198s. In 21, Sub-Saharan African countries displayed the lowest years of schooling among all the regions. In spite of the high correlation between the average years of schooling and the distribution of education, the evolution of the Gini coefficient has been different to that of the years of schooling (Figure 3). For instance, North America and Western Europe is the group of countries with a more equalitarian distribution of education in 195. However, in the most recent years, this group of countries ranks number 3 in terms of equality. In 21, the countries with the greatest equality in the distribution of education are located in Central and Eastern Europe and Central Asia, with a Gini coefficient about.1. In fact, the reduction in education inequality in Central Asia is astonishing. In 195, this region ranked as the fourth region with the largest Gini coefficient (.58), whereas it is one of the regions with a more even distribution of education (.11) in 21. In the middle of the distribution we find the East Asia and the Pacific region and the Latin America and Caribbean countries, with Gini coefficients equal to.56 and.48 in 195, and.23 and.25 in 21, respectively. At the bottom of the distribution, the Arab States have reduced the Gini coefficient more than halve, changing from a value of.88 in 195 to.42 in 21. A large reduction in education inequality is also observed in Sub-Saharan Africa and South and West Asian countries. In both regions, the average Gini coefficient in 195 was about.8 and it reduced to about.45 in 21. The large reduction in human capital inequality, observed in the less developed economies, has mainly been due to a great effort to eradicate illiteracy rates over the years. As shown by Castelló-Climent and Doménech (212), the evolution of human capital inequality presents two stages. In the first stage, the variations in the human capital Gini coefficient are mostly determined by variations in the share of illiterates. In the more developed countries, however, the overall Gini coefficient is mainly driven by the Gini among the literates. 5- Education and Growth

In this Section we analyze the effect of education on economic growth. We first estimate equation 1 over a long time period in order to check whether the results in Castelló and Doménech (22) hold with a greater number of countries and an extended number of years. The cross-section regressions include a total of 121 countries over the period 1965-21. 4 This specification allows us to test the effect of the initial level and distribution of education on economic growth in the long run. Thus, in spite of the shortcomings with the estimation of a cross-section equation, the long time period minimizes endogeneity concerns in this equation. In Table 2, the dependent variable is the growth rate of per capita GDP averaged over the period 1965-21. The explanatory variables include some initial conditions, such as the level of income and the level and distribution of education, measured in 1965. The share of government consumption over GDP, the ratio of exports plus imports divided by GDP, and the inflation rate are measured as an average over the whole period. The regression of the growth rate of GDP per capita on the initial level of education, proxied by the number of years of schooling, yields a coefficient of.4, with a standard error of.1 (column (1)). The result suggests that other things being equal, the countries whose adult population had a greater number of years of schooling in 1965, have experienced, on average, higher growth rates over the period 1965-21. The economic effect of education is also significant. The estimates imply that a one standard deviation increase in the average years of schooling in 1965 (2.33 years) would increase per capita GDP growth by about.9 percentage points per year. For example, if Central African Republic had increased the initial average years of education from.497 to the mean value for the Sub-Saharan African countries (1.32), then Central African Republic could have grown about.3 (.81*.4) percentage points faster per annum. Likewise, if in 1965 Haiti had increased its average years of education from.784 to the mean value for the Latin American and the Caribbean countries (3.621), then Haiti could have grown about.11 (2.837*.4) percentage points faster per annum. In column (2), we include the education Gini coefficient, instead of the average years of schooling, as the initial measure of schooling. The estimated coefficient is negative and statistically significant at the 1 per cent level, suggesting that the initial distribution of education is also an important predictor of future growth. To know whether the average years of schooling or the distribution of education is more important for growth is difficult to prove. The reason is that both measures are highly correlated and controlling for both variables generates a multicollinearity problem. The correlation between the average years of education and the Gini coefficient of education in 1965 for the 121 countries included in the regression is -.92. In fact, column (3) shows that the coefficient of the average years of education stops being statistically significant, and the significance of the Gini coefficient also reduces, when both indicators are included in the set of controls. As an alternative specification, in column (4) we proxy the average education level through the average years of secondary education in the adult population. The correlation among this variable and the Gini coefficient is also high (.65) but much lower than that with the total years of education, which minimizes collinearity concerns. The results indicate that both the level of education and its distribution are important determinants of growth. For example, the estimated coefficient of -.26 of the Gini coefficient 4 Although the data on educational variables are available for 146 countries, for many of these countries the data on GDP in only available since 199 onwards (e.g. Central and Eastern Europe).

implies that a one standard-deviation decrease in the education Gini in 1965 (.296) would lead to higher per capita growth rates by.8 percentage points per year. The economic impact is large, as the average growth rate for Sub-Saharan African region during this period was.8 percentage points. We can use this estimate to do quantitative comparisons. Keeping in mind that there are other variables that explain the differences in growth, we can find some examples of countries with similar initial level of development, similar average years of schooling but that differ in the initial distribution of education and the subsequent economic growth rates. We focus on pair of countries within regions to minimize differences in geography, climate, political institutions or cultural values. For example, both Pakistan and India had 1.1 average years of education among their adult population in 1965. Per capita income was also similar, $82.4 in Pakistan and $786.9 in India. However, inequality in the distribution of education was lower in India (.77) than in Pakistan (.88). The estimates suggest that if in 1965 Pakistan had had the same distribution of education as that in India, the average growth rate in Pakistan could have been.3 percentage points higher per year (.11*.26). Given that the average growth rates in India and Pakistan over the period 1965-21 were.33 and.23 respectively, the differences in the initial Gini coefficient could explain about one third of the actual difference in the growth rates. Another example could be that of Albania and Bulgaria, which had similar initial per capita income and similar years of education (5.54 years in Albania and 5.98 years in Bulgaria) but the Gini coefficient was twice as much in Albania (.4) than in Bulgaria (.19). The estimates suggest that had Albania similar Gini coefficient as that in Bulgaria, its average growth rate could have been.5 percentage points higher, which accounts for about 38 percent of the actual difference in their per capita income growth rates. Rwanda and Sierra Leone also had the same per capita income in 1965 ($65) and similar average years of education (.54 years in Rwanda and.53 years in Sierra Leone). The distribution of education, however, was different; the Gini coefficient was.89 in Rwanda and.95 in Sierra Leone. The estimates suggest that the difference in the initial distribution of education can account for the whole difference in the actual average growth rates in both countries, which was.12 and.1, respectively. Although the Gini coefficient has the advantage of summarizing the whole distribution of education in a single index, it does not provide any information on whether the different parts of the education distribution have similar effects on the growth rates. To get a greater insight on this regard, we test the effect on growth of the first, third and fifth quintiles in the distribution of education, and the ratio of the bottom to the top quintile. Column (5) shows the estimate for the first education quintile. Results suggest that the initial share of the education attained by the 2 percent of the population with the lowest education did not have any statistically significant effect on the subsequent growth rates. Instead, it is the education attained by the cumulative third quintile, and the top 2 per cent of the population that matter for growth. The estimated coefficients for both indicators are equal, with opposite sign, and almost similar to that of the Gini coefficient (columns (6) and (7)). While the results with the OLS estimator can give a good approximate of the long term effect of education on growth, one of the main criticisms of this kind of regressions is that they suffer from two inconsistency sources. On the one hand, cross-section estimations fail to control for specific characteristics of countries whose omission may bias the coefficient of the explanatory variables. On the other hand, they do not address properly the treatment of some explanatory variables that should be considered to be endogenous. As discussed in Section 3, we address

these concerns with the estimation of a dynamic panel data model with the system GMM estimator. The results of estimating equation (3) with the system GMM are reported in Table 3. 5 The regressions include 142 countries for the period ranging from 1965 to 21. The analysis updates previous work by Castelló-Climent (21b) by adding 4 more countries and extending the period up to 21. The first column analyzes the effect of the average years of education on the growth rate of real per capita GDP. Controlling for other determinants of growth, the results show that a better educated adult population has a positive and statistically significant effect on the subsequent growth rates. The estimated coefficient is positive and statistically significant at the 1 percent level. The estimate is also economically meaningful and consistent with the magnitude obtained with OLS. The system-gmm estimate is.5 with a standard error equal to.2. The coefficient suggests that if Thailand average years of schooling had been at the average of the East Asia and the Pacific region (7.88) instead of the actual 5.88 in year 25, it would have grown.1 percentage points faster per year (2*.5). Similarly, if Guatemala years of schooling had been equal to that at the average of the Latin America and the Caribbean region (7.47) instead of its 3.61 years in 25, it could have growth.19 percentage points faster per year. Many Sub-Saharan African countries have made a great effort in reducing illiteracy rates over the years. However, we still find countries in which the majority of the children do not have primary education. For example, in Niger, 8 percent of the adult population did not have formal education in 25. As a result, the average years of schooling was only 1.29 years. The estimates suggest that had Niger the same number of years as the average years of education in Sub-Saharan African countries (4.62), the growth rate in Niger could had been.17 percentage points higher per year. The estimates also corroborate the negative and statistically significant effect on growth of a more uneven distribution of education. Column (2) shows the estimated coefficient of the Gini index is negative and statistically significant at the 1 percent level. However, none coefficient is statistically significant once the average years of education and the Gini coefficient are included in the set of controls (column (3)), suggesting the collinearity problem between both variables is even higher in the panel data model than in the OLS estimates. Instead, in column (4) we proxy the average level of education by the average years of secondary education in the adult population. Results show the estimated coefficient of the Gini index is -.53, which is similar to the estimates with the system-gmm in smaller samples with fewer countries (e.g. Castelló-Climent, 21b), suggesting the quantitative effect is robust across samples. The estimate indicates the economic effect of a greater uneven distribution of education is important. For instance, both Liberia and Malawi had 3.4 average years of education in 25. However, the distribution of education was quite different; whereas the Gini 5 To avoid overfitting the model, the instruments used are the second lag of each explanatory variable in the difference equation, and the lagged first difference of the corresponding explanatory variable in the level equation. This set of instruments guarantees the number of instruments is lower than the number of countries. The AR(2), Hansen, and difference Hansen tests, reported at the bottom of the tables, suggest that the set of instruments is valid.

coefficient in Liberia was.65, in Malawi was.45. The estimate suggests that if Liberia had had greater equality in the distribution of education with a Gini coefficient similar to that of Malawi, it could have grown.11 percentage points faster per year (.2*.53). This accounts for about 48 percent (.11/.23) of the actual difference in the annual income growth rate between the two countries during the period 25-21. 6 Similarly, Togo and Tanzania also had the same number of years of education (4.8) in 25 but different inequality in the distribution of education. The Gini coefficient in Togo was.53 whereas that in Tanzania was.35. According to the estimates, the difference in the distribution of education could account for about 22 percent (.1/.45) of the actual difference in the actual growth rates. More examples include Mexico and Uruguay, with similar years of schooling in 25, 7.8 and 7.9 respectively, but different distribution of education. The Gini coefficient was.27 in Mexico and.19 in Uruguay. The estimates predict that the average growth rates in Mexico could have been.4 percentage points faster per year if Mexico had had the same distribution of education as that in Uruguay. Whereas OLS estimates suggest the middle and upper part of the education distribution is what matters for growth, the system GMM estimator indicates all parts are important. The coefficients of the first, third and fifth quintiles are all statistically significant. Moreover, the ratio between the education attained by the lowest and highest 2 percent of the population has a positive and significant effect on the growth rates. Distinguishing among different parts of the distribution is important since we can find countries with similar Gini coefficient but differences in the distribution of education by quintiles. For example, in 25 Brazil and El Salvador had similar years of education, 6.6 and 6.7 respectively. The Gini coefficient was also similar,.31 in Brazil and.34 in El Salvador. The cumulative third quintile was.37 and.36, respectively. However, the first quintile was zero in El Salvador and.34 in Brazil. As a result, the ratio between the bottom to the top education quintile was.1 in Brazil and zero in El Salvador. The estimates in column (9) suggests that had El Salvador had the same ratio as that in Brazil, the average growth rate in El Salvador could have been.6 percentage points faster per year. 6- Differences in the Age Structure of the Population Barro and Lee s (21) dataset provides the attainment levels for several age groups. This information is useful since the effect of the average attainment levels and the Gini coefficient could differ across age groups, as the younger generations are more educated than the oldest ones. Figure 4 reports the average years of education of several age groups (e.g. 15-24, 25-39, 4-64 and 65-74 years old). The figure illustrates that over a period of 6 years, the average years of education have increased in all generations. The average years of education for the population 15-24 years old was 3.64 years in 195 and increased up to 8.86 years in 21. Similarly, the average years of education for the oldest age group (65-74) was 2.28 years in 195 and raised up to 5.55 years in 21. Given that the increment has been higher in the 6 The average annual growth rate for the period 25-21 was.39 in Liberia and.62 in Malawi.

younger generations than in the older ones, in 21 the attainment levels of the younger generations in some regions are twice as high as those of the older age groups. For example, in South and West Asia region, the average years of education of the population 15-24 years old was 8.26 years in 21, while that of the population 65-74 years old was only 2.97 years. Figure 5 displays the Gini coefficient across age groups. The figure illustrates a huge reduction in human capital inequality in all age groups, specially in the younger generations. The overall Gini coefficient for the population 15-24 reduced from.49 in 195 to.18 in 21. Despite the general reduction, enormous differences across regions still remain. For example, the Gini coefficient of the age group 15-24 is greater in Sub-Saharan African region in 21 than in North America and Western European countries in 195. In fact, the Gini coefficient for the age group 15-24 in Sub-Saharan African region in 21 is similar to that of the population aged 65-74 years old in North America and Western European countries in 195. The different levels of education across age groups may have important connotations for economic growth. With the process of development, countries have experienced a demographic transition from high mortality and high fertility to low mortality and low fertility. Both, fertility and mortality rates determine the age structure of the population and this has implications for growth. The reason is that while persons in the working age are productive, children and the elderly are "dependant." Therefore, a lower dependent ratio would faster economic growth since it improves the ratio of productive workers in the population (Bloom et al., 23). To analyze the effect on growth of the human capital of different age groups, we split the population aged 25-64 into two groups, the younger generations, aged 25-39, and the oldest generations, aged 4-64. Table 4 displays the results. As the younger generations have more human capital, we could expect that a greater share of youngest in the working age population should have a beneficial effect on the growth rates. In column (1) we test the effect on growth of having a relative younger working-age population, proxied by the ratio between the population 25-39 years old divided by the population aged 4-64 years old (Population WA Youth Ratio). Results indicate the coefficient of the youth ratio of the working age population is not statistically significant at the standard levels. Thus, a relative younger work force per se is not sufficient to guarantee higher growth rates, in order to be growth enhancing, the younger generations should be educated and efficiently allocated in the labor market. 7 We test this statement in column (2), in which we multiply the population youth ratio by the corresponding years of schooling of each age group. The results indicate that the weighted ratio of the average years of schooling is positive and statistically significant at the one percent level, indicating that a greater average years of schooling of the younger generation, relative to the years of schooling of the older group, is important for growth. According to the estimates, an increase in one year of schooling of the younger generation, relative to the older one, increases the subsequent growth rates by.1 percentage points. This coefficient is significant in a statistical sense but slightly small in quantitative terms. To disentangle the effect of each age group, in columns (3) and (4) we test the effect on growth of the years of schooling of each education group separately. The results show that, although the coefficient of the younger 7 If instead of the Population WA Youth Ratio, we control for the ratio between the working age population (25-64) to the total population, in line with Bloom et al. (27), the coefficient of the share of the working age population is positive and statistically significant at the one per cent level.

population is slightly higher in quantitative terms, the average years of schooling of both age groups matter for growth. We then analyze the effect on growth of the age structure of the Gini of education. The results are reported in Table 5. Unlike the average years of schooling, column (1) shows the weighted ratio of the Gini coefficient between age groups is negative and statistically significant at the 1 percent level. This results suggests that the distribution of education of the relative older generations has a greater effect on growth than the distribution of education at the younger ages. The results in columns (2) and (3) corroborate this finding. Although both coefficients are negative and statistically significant, the coefficient of the Gini index of the population aged 4-64 years old is more than twice as much as that of the population 25-39 years older. This result is important because it suggests that a more unequal distribution of education of the current generation will have a negative effect not only on the economic growth rates in the next few years but also in the long run growth rates that will face the next generations. Thus, reducing inequality today will also reduce long term cost, in terms of future prosperity. For example, in 25, the Gini coefficient of the younger generations, aged 25-39 years old, was similar in Bolivia than in Uruguay, with a value equal to.16 in both countries. However, the Gini coefficient of the older generation was.32 in Bolivia and.19 in Uruguay. The greater inequality in the distribution of education of the older age group implies that, other things being equal, if Bolivia had had a similar level of inequality in the distribution of education in the older age group as that in Uruguay, the annual growth rate in Bolivia could have been.19 (.145*.13) percentages points higher. Similarly, in spite of having a similar inequality in the distribution of education of the younger working age population, with a Gini₂₅ ₃₉^{h} equal to.24 in Cameroon and.26 in Lesotho, the inequality in the distribution of education of the population aged 4-64 years old was.43 in Cameroon and.27 in Lesotho. The results in column (3) suggests that had Cameroon the same inequality in the distribution of education of the older population as that in Lesotho, the per capita GDP growth rate in Cameroon could have been.23 percentage points higher. A plausible explanation for this finding is that the channels through which human capital inequality discourages economic growth take place in the long term. Mechanisms that point out different fertility patterns and life expectancy among individuals with different levels of education predict that the distribution of education of the parents is what matters for growth. In these models, parents with lower human capital choose to have a higher number of children and to provide them with less education, thereby limiting the number of skilled individuals in the future and leading to reduced average levels of human capital in the economy and lower growth rates (e.g., De la Croix and Doepke 23, Moav 25)). Castelló-Climent and Doménech (28) also show that when parents' education influences their children's life expectancy, as has been shown by empirical evidence (e.g., Case et al. 22, Currie and Moretti 23), the initial distribution of education, through its impact on life expectancy, has powerful effects on a country s average rate of investment in human capital. Likewise, under imperfect credit markets and indivisibilities in the accumulation of human capital, Galor and Zeira (1993) show that the greater the share of the population credit constrained, the lower the average human capital in the economy. In this model, wealth transmission from parents to children depends on the parents human capital. As a result, the initial distribution of wealth is mainly driven by the initial distribution of human capital. In all the models, the crucial distribution of human capital is that of the parents. Thus, the distribution of education that should matter for growth is that of the previous generations, in line with the empirical findings.

In fact, Castelló-Climent (21) shows that demographic channels and, to a lower extent, the credit market imperfection approach, are able to explain the entire impact of human capital inequality on economic growth. Using more countries and a longer time period, we confirm this finding in columns (4) and (6). The evidence indicates that once the life expectancy and the fertility rates are included in the set of controls, the estimated coefficient of the Gini index stops being statistically significant. 7- Conclusion This paper shows the distribution of education is an important determinant of economic growth. The paper uses new indicators of education to reassess the relationship between human capital and growth for a broader number of countries and a longer time period, as compared to previous studies. The paper uses updated data sets on average years of education by Barro and Lee (21), which reduces measurement errors and solves some of the shortcomings revealed by De la Fuente and Domenech (26) and Cohen and Soto (27), and indicators of the inequality in the distribution of education by Castelló-Climent and Doménech (212). The new datasets improve the quality of the data as well as its coverage, including 146 countries from 195 to 21. The paper reveals that inequality in the distribution of education is an important determinant of economic growth. Keeping the level of education constant, a more unequal distribution of education has detrimental effects on the subsequent growth rates. When analyzing the distribution of education by age groups, the results indicate that a more unequal distribution of education today has long run costs. Unlike the effect of the average years of education, the negative effect of a more unequal distribution of education in the working age population is higher in the older generations than in the younger ones. This result suggests that it is the distribution of education of the "parents", rather than the distribution of education of the youngest, what has a greater influence on the growth rates. Many developing countries have made a great effort in reducing illiteracy rates and improving the education of the new generations. However, in 21 there were countries in which more than 5 percent of the population were still illiterate. The results in this paper indicate that increasing the level of education of the majority of the population can improve not only the standard of living of millions of people, but also the economic performance of a country in the coming years, as well as in future generations. References Alesina, A. and Rodrik, D. (1994). ``Distributive politics and economic growth", Quarterly Journal of Economics, vol. 19, pp. 465-9. Arellano, M. and S. R. Bond (1991). "Some Test of Specification for Panel Data: Monte Carlo Evidence and and Application to Employment Equations". Review of Economic Studies, 58 (2), 277-97.