The Age Structure of Human Capital and Economic Growth

The Age Structure of Human Capital and Economic Growth Amparo Castelló-Climent University of Valencia October 2017 Abstract In this paper we use the distribution of education by age groups provided by Barro and Lee (2013) in order to analyze the effect of the age structure of education on economic growth. In a panel that covers a broad number of countries from 1965 to 2010, we find the average years of schooling among younger population contributes less to growth than the education in older age groups. Specifically, we find an inverted U- shape association between the age structure of education and economic growth, with years of schooling peaking in the 40-49 age bracket. The result are not driven by the age structure of the population, as we find the age structure of education and the age structure of population affect growth independently. The findings are robust across specifications and work by means of the two channels through which human capital influences growth. JEL classification: I25, J11, O11, O50 Key words: Distribution of education, age structure, economic growth, dynamic panel data model. I am grateful to Rafael Domenech for his helpful comments and suggestions and for the financial support from the Spanish Ministry of Economy and Competitiveness through the ECO2015-65263- P project. Contact: Amparo Castelló-Climent, Institute for International Economics, Facultad de Economía, University of Valencia, Campus dels Tarongers s/n, 46022- Valencia, Spain. Email: amparo.castello@uv.es. 1

1 Introduction Human capital has been considered one of the fundamental determinants that can explain the differences in the growth rates observed between different countries (e.g. Lucas, 1988). A common approach in the empirical literature has been to proxy the human capital of the working age population using the average years of schooling of the population aged 15 years and over or 25 years and over. These measurements, however, include the years of schooling of the retired section of the population, and mask whether the effect of education on growth varies across age groups. The goal of this paper is to break down total years of schooling into its different components in order to analyze whether its effect on growth depends on the age structure of human capital. The results of the paper suggest that this is in fact the case. 1 Since the younger generations are more educated than their elders, one might assume that the years of schooling of the younger generations is more important for growth than the years of schooling of the oldest ones. This paper shows that this is not the case; the evidence indicates that average years of schooling among the population aged 15-29 contributes less to growth than the education in older age groups. It is the human capital of the middle-aged population that is more relevant for economic growth. Specifically, we find an inverted U-shape relationship between the age structure of human capital and economic growth, with a peak in the 40-49 age group. We estimate a growth accounting model that incorporates human capital both as a regular factor in the production function (e.g. Lucas, 1988; Mankiw, Romer and Weil, 1992), and as a promoter of productivity through the facilitation of innovation and the adoption of new technologies (e.g. Nelson and Phelps, 1966; Romer, 1990). In the econometric specification, the first channel is captured by the increments in the years of schooling, and the 1 Throughout the paper we use the terms human capital and education interchangeably. We are aware that human capital is a much broader concept that also includes health, knowledge, skills, abilities or experience, among others attributes. Education is therefore the element of human capital that is easier to quantify. The availability of data on the average years of schooling for a broad number of countries and periods has made years of schooling a common proxy for human capital in the empirical literature. Nevertheless, it is worth mentioning that average years of schooling is a purely quantitative measure and does not take into account the quality of schooling (e.g. Hanushek and Kimko, 2000; Hanushek and Woessmann, 2012). 2

second by the initial level of education. Results indicate the inverted U-shape relationship between the age structure of education and growth is present in both mechanisms, the peak at the human capital of the population aged 40-49 years old is found with the initial level of human capital as well as with the increments. Thus, the paper offers an alternative explanation for the weak effect of human capital on growth found in the empirical literature. The major discrepancies in the literature occur when human capital is measured in increments. 2 In this line, we also find the coeffi cient of the increment is positive, yet not statistically significant at the standard levels. If education at different ages have different effects on growth, using the average years of schooling of the total population could masks these differential effects. Certainly, when we split the total years of schooling into different ages, the coeffi cient of the increment in the average years of schooling clearly differs across age groups. The estimates of the increment in the human capital of younger population is negative, becomes positive at the age of 30 and only statistically significant for the human capital of the population that is 40 years and above. Recent evidence has studied the influence of population aging on productivity and growth (e.g. Maestas et al., 2016; Börsch-Supan and Weiss, 2016; Acemoglu and Restrepo, 2017). Feyrer s (2007) findings reveal an inverted U-shape between workers age and TFP with a peak at the proportion of the workforce aged 40-49. Thus, our results could be picking up the hump-shape effect of the workers age. We check the robustness of the results by controlling for the age structure of the population and our results hold. In line with Feyrer (2007), we also find an inverted U-shape relationship between the age structure of the population and the economic growth rates, suggesting that the age structure of education and the age structure of the population affect growth independently. The larger experience of middle aged workers with regard to the younger and better 2 Early studies by Barro (1991) and Mankiw, Romer and Weil (1992) provided evidence of a significant and positive effect of human capital on income and growth. Later evidence, however, found that human capital growth has an insignifican, and in some speficications, negative effect in explaining per capita income growth rates (Benhabib and Spiegel, Pritchett (2001)). Krueger and Lindahl (2001) indicate the lack of correlation between education and growth found in previous studies is due to measurement error and the lack of signal in the education data. If the stock of human capital is measured with error, their first differences will bias the estimated coeffi cient towards zero. Improvements in data quality lead to more precise estimates and a positive association between schooling and economic growth (Cohen and Soto, 2007; De la Fuente and Domenech, 2006). 3

educated age group could also explain the findings. Cook (2004) estimates a standard Cobb-Douglas production function and shows that average experience has a positive effect on the growth rates. Moreover, when experience is accounted for, the social returns to education are close to those found in the micro literature. We control for the average experience of the workforce to check whether the larger coeffi cients of human capital at the middle age group are picking up the effect of experience. The results slightly change. We also show that the inverted U-shape relationship between the age structure of the work force and the growth rates is not due to delayed effects in human capital. Controlling for the earlier expansion in the average years of schooling does not change the results. Finally, we check whether our findings are robust to alternative specifications that control for omitted variables and the endogeneity of human capital. We estimate a dynamic panel data model with the system GMM estimator. Again, the education of the middle-aged section of the population has the largest impact on growth, with positive but decreasing effects in older age groups. The results are in line with the microeconomic literature that finds the age-earnings profile is concave, that is, earnings rise with age, then flatten out, and eventually fall. The concavity in the life-cycle-earnings profile dates back to the human capital model (Ben- Porath, 1967; Mincer, 1974). 3 This suggests that in the early stages of a worker s career, wages rise at a decreasing rate, yet the decrease in the rate of human capital investment and the depreciation of the stock of human capital produces an eventual downturn in life-cycle earnings. 4 Using data on wage rates in 1959 and 1967 for the United States, Hurd (1971) finds evidence of an inverted U-shape in the age-wage profile, with a peak in white males wages in the 45-54 age range. 5 On the other hand, Mincer (1974) finds that 3 See Willis (1986) for a survey on the human capital earnings functions. 4 The microeconomic literature, however, has focused more on worker experience than worker age. Mincer (1974) states that experience is more important than age in terms of increasing productivity and earnings. In fact, the standard Mincerian human capital-earning function includes schooling and a quadratic form in the experience terms to capture the concavity of the observed earnings profile, where a transformation of the worker s age is used as a proxy for experience. 5 Recent evidence has questioned whether the reduction in wages is a consequence of reductions in productivity. Using data from the Health and Retirement Study (HRS) for a panel of American adults aged over 50, Casanova (2013) finds that the downward-sloping wage profile for older age groups is a consequence of the transition from full-time to part-time work, and not of a reduction in wages. In fact, 4

differences in wages across educational groups are higher in the middle-aged groups. The results are also in line with extensive literature on the nexus between age and great scientific output, which also finds that great scientific output peaks in middle age (e.g. Jones et al., 2014). The pattern is an inverted U-shape with no major scientific output in initial training periods, followed by a rise in great scientific output with a peak in the late 30s or 40s, and a subsequent slow decline. The structure of the paper is as follows. Section 2 summarizes the data on the age structure of human capital across regions. Section 3 describes the econometric model and presents the main results. Section 4 examines the sensitivity of the results. Finally, Section 5 states the conclusions reached. 2 Data on the age structure of human capital This paper uses the new dataset on attainment levels and years of schooling by Barro and Lee (2013), which includes more countries and years, reduces some measurement errors, and solves some of the shortcomings presented in previous versions (e.g. Barro and Lee, 1996, Barro and Lee, 2001). 6 The improved Barro and Lee (2013) dataset reduces measurement error by using more information from census data and a new methodology that makes use of disaggregated data by age group. 7 Previous versions by the same authors provided the distribution of educational attainments of the adult population aged 15 years and over, and 25 years and over for seven levels of schooling. However, these measures have two shortcomings when we analyze their effect on economic growth. On the one hand, they capture the years of schooling of the retired section of the population. On the other, they assume the effect of education is the same across all the age groups. The goal of this paper is to break down the total years of schooling into its different components in order to analyze whether the effect of human capital differs depending on the age structure she reports that when male workers over 50 are employed full time, their real hourly wage increases slightly. 6 Recent studies have shown that the perpetual inventory method in Barro and Lee (2001) suffers from several problems. Specifically, Cohen and Soto (2007) and de la Fuente and Doménech (2006) illustrate that the dataset show implausible time series profiles for some countries. 7 In line with Cohen and Soto (2007), the methodology fills the missing observations by backward and forward extrapolation of the census data on attainment levels by age group with an appropriate lag. It also constructs new estimates of mortality rates and completion ratios by education and age group. 5

of the population. The updated dataset by Barro and Lee (2013) breaks down the total years of schooling into five-year age intervals. The five-year age groups range from 15-19 years old, 20-24 years old, and so on up to 75 years and over, with a total of 13 age groups. The new indicators are available for 146 countries from 1950 to 2010 in five-year spans and include a total of 1898 observations. The dataset covers most of the countries in the world including data for 24 Advanced economies, 19 countries in East Asia and the Pacific region, 20 countries in Eastern Europe and Central Asia, 25 countries in Latin America and the Caribbean, 18 countries in the Middle East and North Africa, 7 countries in South Asia and 33 countries in Sub-Saharan Africa. 8 Table 1 reports descriptive statistics of the average years of schooling of the total population by age group. The first two rows show the average years of schooling for the adult population aged 15 years and over, and 25 years and over. The data illustrate the fact that the average number of years of schooling of the population aged 15 and over (5.485) is greater than that of the population over 25 (5.082). When we break down the total years of schooling into 10-year age intervals, the data show fewer years of schooling for the older population, reflecting the expansion of education around the world over the last 60 years. The age group with the largest average number of years of schooling is the population aged 20-29 years old (6.567), as some of the population aged 15-19 have not yet finished their studies. From the age of 30 and up, the average years of schooling decrease with age. As a result, the number of years of schooling of the population aged 65 and older (3.369) is about half that of the population aged 20-29. This pattern, however, has not been homogenous across regions. Table 2 shows that in some regions the largest number of years of education is concentrated in the youngest age group, 15-19 years old, instead of the population aged 20-29. Examples include East Asia and the Pacific, South Asia, and Sub-Saharan African countries, where great efforts to increase education have been made in the recent years. Table 2 also shows that the Advanced economies are the group of countries with the most years of education in the adult population, with average years of schooling of the population aged 15 years and over, equal to 8.247, followed by Eastern European and Central Asian countries, with 8 We have followed the same classification of countries as in Barro and Lee (2013). 6

7.928 years of education. At the bottom, Sub-Saharan African countries, with 3.014 years of education, have the lowest levels of education for the population aged 15 years and over, and across all other age groups. In the middle of the distribution, however, the data show that in terms of the years of education of the adult population, the country ranking changes when we look at the age structure of education. Despite the fact that the adult population in Latin American countries have, on average, more years of education than the population in East Asia and the Pacific region, the youngest population in East Asia and the Pacific have more education than their Latin American counterparts. This fact has important implications as the two regions ranking in terms of the total years of schooling and that of the population 40-49 years old will reverse in a few years. The evolution of education over time is displayed in Figure 1, which plots the average years of schooling in 1950 and in 2010. The figure shows a large increment in the average years of education across all the age groups. 9 In fact, the great effort in the less developed countries to increase the education of the population is reflected in a convergence process in the average years of schooling of the youngest cohorts. In 1950, the average years of schooling of the population aged 15-19 years old was 6 years in the Advanced countries, 3.5 years in Latin America and the Caribbean, and fewer than 2 years in the Middle East and North Africa, South Asia and Sub-Saharan Africa. In 2010, with the exception of Sub- Saharan African countries, the average years of education of the population aged 15-19 years old is about 8 years in most of the regions. The convergence process in the youngest age group is also illustrated in Figure 2. Whereas in 2010 there are still large differences in the average years of schooling for the population aged 15 years and over, the education of the population aged 15-19 years is converging across regions. This convergence reflects not only the extension of primary education to almost all segments of society, but also a large expansion of secondary education in the less developed economies. A divergence emerges, however, at university level. When we look at the years of education at typical university age - the population aged 20-29 years old - there is a clear divergence between regions. 9 There is a deceleration of investment in education in some regions. In Eastern European and Central Asian countries, the largest amount of education is concentrated in the middle age groups, those aged 40-49 years old, as opposed to the youngest generations. 7

3 Empirical specifications and main results Many studies in the literature that have estimated the role of human capital on economic growth have derived the empirical specification from the estimation of a standard Cobb- Douglas production function. From a theoretical viewpoint, education may affect growth through different channels. The first treats human capital as an ordinary input in the aggregate production function, as in Lucas (1988) or in the augmented Solow (1956) model. In this framework, economic growth is determined by changes in the stock of human capital. The second channel specifies human capital as a determinant of the level of productivity. As in Nelson and Phelps (1966), a higher level of human capital increases productivity by facilitating the adoption and diffusion of new technologies. The empirical literature has estimated several specifications of these channels finding mixing results. Benhabib and Spiegel (1994) found negative point estimates for the coefficient of the human capital growth rate when human capital was treated as a factor of production in a growth accounting regression. When the level of human capital influenced the growth of the total factor productivity, the estimated coeffi cient of the level of human capital was statistically significant with a positive sign. With an improved data set that reduces measurement error, Cohen and Soto (2007) found that schooling variables in first differences was not statistically significant in specifications similar to those of Benhabib and Spiegel (1994). Nevertheless, when they run the log-change of income on the change in the level of schooling, derived from a Mincerian equation, the coeffi cient was positive, statistically significant and similar to the average returns found in the labour literature. 10 De la Fuente and Domenech (2006) also argue that poor quality data is the reason for the weak effect on growth of human capital. If the stock of human capital is measured with error, their first differences will bias the estimated coeffi cient towards zero. In an extended aggregate production function that includes technological diffusion and permanent total factor productivity differences across countries, de la Fuente and Domenech (2001) find positive and statistically significant coeffi cients for the schooling variables in first differences in a sample that includes only OECD countries. In this section we estimate a general specification and show that the age structure of 10 Based on the wage regression estimated by Mincer (1974), Krueger and Lindalh (2001) find positive but not statistically significant coeffi cients for schooling, measured with the average years of schooling. 8

human capital provides useful information that can disentangle the lack of significance of human capital in growth regressions. We estimate a specification that includes both the effect of human capital as an input in the production function and as a determinant of the level of productivity. 11 To derive the cross-country growth accounting model we start with a standard Cobb- Douglas production function, Y it = A it Kit(h α it L it ) β (1) where aggregate output, Y, is a function of the stock of physical capital, K, labor, L, the stock of human capital per worker, h, and the level of technology, A. To express equation (1) in growth terms, we rewrite the production function in per capita terms, we take logs and then calculate the first difference to get, ln y i,t = ln a it + α ln k it + β ln h it + ln l it (2) with y being the GDP per capita, k the stock of physical capital per worker, and l the share of workers in the total population. In the spirit of Nelson and Phelps (1966) and Romer (1990) we assume that the growth of technology depends on the level of human capital. We also build on Benhabib and Spiegel s (1994) model and include initial income as a proxy for initial technological advantage. The econometric specification to be estimated is written as follows, ln y i,t = δ + γ ln y it + λ ln h it + α ln k it + β ln h it + ln l it + ε it (3) This equation incorporates the two channels through which human capital may affect the growth rates. The increment in the stock of human capital captures the effect of human capital as a direct input in the production function. The initial level of human capital captures the positive influence that a higher stock of human capital may have on domestic technological innovation, and the speed of adoption of the technology produced abroad. We can assess the validity of the model specification with a directly testable prediction. 11 Sunde and Vischer (2015) also estimate a similar model and show the econometric models that include both channels provide more precise estimates. 9

We can perform a Wald test for the null hypothesis that the implied coeffi cient of the share of workers in the total population is equal to one. Results of estimating equation (3) are displayed in Table 3. The dependent variable is the annualized growth rate of real per capita GDP during the period 1970-2010. 12 The average years of schooling of each age group are divided by the total years of schooling to account for the total amount of education in the working age population. 13 The coeffi cients should be interpreted as the share of education of a specific age group in the total years of schooling of the working age population. Column (1) shows the model fits the data quite well, the coeffi cient of the share of workers is close to 1, and the model explains about 75 percent of the variation in per capita GDP. A Wald test for the null hypothesis that the implied coeffi cient of ln l is equal to 1 clearly indicates that we fail to reject the null, with a p-value equal to 0.949. As expected, the estimates indicate that increments in the stock of physical capital are associated with higher growth rates, whereas a higher initial level of income is associated with a lower increment in per capita GDP. Results also show positive coeffi cients for the increment and the initial level of the human capital of the working age population. But, only the initial level of human capital is statistically significant. As argued before, if human capital at different ages have different effects on growth, measuring human capital with the average years of schooling could mask specific effects of the increment in the years of schooling at different ages. This hypothesis is corroborated in the remaining columns. Columns (2) and (3) display negative coeffi cients for the level and the increment of the average years of schooling of the population 15-19 and 20-29 years old. It is from the age 30 and above that the average years of schooling have a positive effect on the growth rates. Specifically, results indicate an inverted U- shape association between the age structure of human capital and the growth rates of per capita GDP. The peak is found in the 40-49 age group, with coeffi cients of the increment of human capital and the initial level of education equal to 0.817 and 0.025 respectively. The results suggest two important implications. First, the age structure of human 12 The period of analysis starts in 1970, in order to include as many countries as possible in the sample. There are only 57 countries that have data for the capital stock in 1950, 100 countries in 1960, and 122 countries in 1970. 13 If we include all schooling age groups simultaneously, most educational coeffi cient are not statistically significant at the standard levels due to severe collinearity. 10

capital matters for growth. Educational coeffi cients increase with age, peak at the age of 40-49 years, and subsequently reduce. Second, a lack of significance in the measure of human capital of the working age population in a growth equation could mask the differential effect of human capital at distinct ages. This preliminary evidence, however, is not absent of criticism. There are several problems that could contaminate previous findings. Results could suffer from omitted variable bias. For example, they do not take into account the age structure of the population or the experience of the work force. Results could also be sensitive to the estimation of alternative specifications. Delayed effects in human capital could also be driving previous findings. Moreover, cross-sectional estimates do not address the potential endogeneity of human capital. In the next section we run several tests to rule out these concerns. 4 Robustness analysis 4.1 Experience The larger effect of education at ages 40-49 could be driven by the fact that workers at that age have more experience and can be more productive than, for example, a 25 year old person, even though the latter has more education. We check whether contolling for experience affects the results on the age structure of human capital. Following Mincer (1974), it has been common in the micro literature to estimate wage equations that control for experience when computing the returns to education. However, most of the empirical macro literature has focused on the returns to schooling abstracting from the human capital accumulated outside the school. Probably because of the diffi culties in computing and controlling for average experiencey or becuase the macro literature has departed from the standard Mincer equation (see Krueger and Lindalh, 2001). Some exceptions are Cook (2004), who estimates a standard Cobb-Douglas production function where human capital enters as an input in the production function, and human capital per worker is an exponential function of the worker s years of education and experience. His findings show that when experience is accounted for, the social returns to education are close to the private returns found in the micro literature. Accounting for cross-country income differences, Klenow and Rodriguez-Clare (1997) find that adding experience to the 11

measure of human capital reduces the explanatory power of human capital with regard to that of TFP. They find that average years of experience correlates negatively with per capita GDP. 14 Caselli (2005) corroborates this finding using the age structure of the labor force, instead of the age structure of the population in the computation of potential experience. 15 Using a sample of micro data for 32 countries, Lagakos et al (2013) find lower returns to experience in poorer countries than in richer countries. As a result, taking into account human capital from experience increases the contribution of human and physical capital in explaining cross-country income differences. We follow the literature and measure experience as experience = age years of school 6. We compute the experience of the working age population as a weighted average for each age group: Experience = 6 P OP j (age j H j 6) P OP 15 64 j=1 where H i,j is the average years of schooling of the age group j, with j = 1 (aged 15 19), j = 2 (aged 20 29), j = 3 (aged 30 39), j = 4 (aged 40 49), j = 5 (aged 50 59), j = 6 (aged 60 64) and P OP is the total population in the given age group. 16 In line with Cook (2004), in Table 4 we first control for the increment in the average years of experience. We obtain similar results. Column (1) shows that controlling for experience increases the coeffi cient and the explanatory power of the average years of schooling of the working age population. statistically significant at the standard levels. The effect of experience is also positive and Nevertheless, controlling for experience does not change the results on the age structure of human capital. Columns (2-8) show a concave association between the age structure of human capital and the growth rates with a peack at the 40-49 year old bracket. At the bottom part of the table, we check the robustness of the results controlling for 14 The paper uses estimates for the returns to experience by Psacharopoulos (1994) and the extension by Bils and Klenow (2000), who found no relationship between the returns to experience and GDP per capita. 15 Recent evidence by Lagakos et al (2017) use representative household surveys for rich and poor countries and find that experience-wage profiles are steeper in rich countries than in poor countries. 16 We measure age j as the average age in each age group. For example, we take 17.5 as the age in group j = 1, age 24.5 in the age group j = 2 and so on. 12

the initial level of experience and results regarding the age structure of human capital also hold. This specification seems to better fit the model as the coeffi cient of the share of workers in the total population is as predicted by the model. Thus, the Wald test p-value fails to reject the null that the coeffi cient is equal to one, which adds to the validity of the econometric specification. Controlling for the increment and the initial level of experience increases the coeffi cients of the average years of schooling. Both the increment and the initial level of experience are also positive and statistically significant, though the initial level of experience is not significant when we control for the age structure of human capital. Overall, in line with the literature, we find that controlling for the experience of the working age population increases the estimated coeffi cient of the human capital of the labor force. We do not find, however, that the larger coeffi cient of the human capital of the population at the middle ages is due to the fact that these workers have more experience than the younger ones. Even controlling for experience, we find an inverted- U shape relationship between the age structure of human capital and the growth rates. 4.2 Age Structure of the Population One concern about previous findings is that results could be driven by the age structure of the population. As the age-distribution of the work force has sifted towards older workers, several papers have studied their influence on labor productivity and the growth rates. Using predicted variation in the rate of population aged 60 and above across U.S. states, Maestas et al. (2016) find negative effects of an increase in population aging on the rate of state growth in per capita GDP over the period 1980-2010. In a sample of 28 European countries over the period 1950-2014, Aiyar et al. (2016) also find a negative effect on the growth rates of labor productivity of an increase in the aging of the work force, measured by the ratio of workers aged 55 and above to the total work force. They find the effect is mainly driven by a reduction in the TFP growth. Some recent evidence, however, has questioned the negative effect of agging. At the micro level, Börsch-Supan and Weiss (2016) use data on a large German car manufacturer and do not find evidence that older workers are less productive than younger workers. In fact, their measure of productivity increases with the age of workers up to the age of 65. In a broad sample of countries, Acemoglu and Restrepo (2017) do not find either a negative association between 13

population aging, measured as the ratio of population above 50 to population between 20 and 49, and GDP growth rates. 17 They explain the lack of a negative association with the fact that more rapid aging countries are the ones that have adopted more new automation technologies. Other papers have analyzed the entire distribution of the age structure of the population and have found a non linear relationship between the age structure of the population and economic growth. In a sample of OCDE countries during the period 1950-1990, Lindh and Malmberg (1999) find a hump shape pattern between the age structure of the population and economic growth. They find the correlation is positive with the share of population in the upper middle-age group (50-64 years old), ambiguous with the younger age groups, and negative with the old-age people (65 years and above). Our results are very close to those by Feyrer (2007), who finds an inverted U-shape between workers age and TFP. Interestingly, he also finds a peack at the proportion of the workforce aged 40-49. Since we are not taking into account the population age structure, our results could be picking up the hump-shape effect of the workers age. In Table 5 we control for the age structure of the population. The results suggest that the age structure of the population and the age structure of human capital have an independent effect on the growth rates. In line with the literature, we find the age structure of the population is important; from the age of 40 and above all the coeffi cients are statistically significant at the one percent level. It is not only the increment in the share of population of those age groups that has a positive and significant estimate, but also their initial level of the population share. Controlling for the age structure of the population, however, does not change previous findings regarding the age structure of human capital. Column (x) show an inverted U-shape relationship between the age structure of human capital and economic growth. The educational coeffi cients increase with age, peak at the age of 40-49 years, and subsequently reduce. 17 Using different methodology, Gómez and Hernández de Cos (2008) find that the growing proportion of countries with mature population (share of working age population) or prime-age population (share of population 34-54 among population aged 15-64) is associated with about half of the increase in global per capita GDP across countries since 1960, as well as with widening global inequality. 14

4.3 Delayed Effects One could argue that since human capital has long-delayed effects on economic growth, 18 the human capital age structure is reflecting the time when countries expanded their schooling. For example, if we assume the effect of education takes place with a lagg of about 20 years, other things being equal, a country that expanded education 20 years earlier (t 20) will have higher income levels in t. In this country we will also observe better educational attainments for the 40-49 age group and a higher growth rate in per capita income. Thus, the larger growth rate could be the consequence of an earlier expansion in education instead of the better attainment levels of the population 40-49 years old. To test this hypothesis, in Table 6 we estimate a similar specification as the one in equation (X), and control for the increment in the average years of schooling during the period 1950-1970, to account for the earlier expansion in education. Results show that previous findings are not driven by delayed effects in human capital, controlling for an earlier expansion in education slightly changes the coeffi cients of the age structure of human capital. The largest coeffi cient is found for the share of education accruing to the 40-49 age group. 4.4 Different specification There are other potential problems associated to cross-section estimates that might affect previous findings. Some omitted factors that influence the investment in human capital can have a direct impact on economic growth. Moreover, as faster growing economies have more resources to invest in education, previous results could also suffer from reverse causation. We overcome the typical problems of cross-sectional regression estimating a dynamic panel data model with the system GMM estimator, which in addition to controlling for omitted variables that are intrinsic to each country and constant over time, also uses instrumental variables to minimize the endogeneity of the regressors. Other factors, however, that are time variant could also affect human capital investment and growth. 18 Delayed effects of human capital mainly work through political mechanisms as for example the effects on democratization, human rights or political stability. Alternative mechanisms also include demographic channels, since the human capital of parents influences the investment in the offspring education and health. 15

Thus, we also check the robustness of the results to alternative specifications estimating a broader version of the neoclassical growth model that includes the convergence property as well as other variables, chosen by the government or private agents, which characterize the steady-state. (e.g., Barro, 1991). We estimate the following equation: ln y i,t = β ln y i,t 5 + γh i,t 5 + X i,t 5 δ + ξ t + α i + ε it (4) where y i,t is the real GDP per capita in country i measured at year t, H i,t is a measure of education, ξ t is a time-specific effect, to capture worldwide shocks to growth that affect all countries simultaneously, α i stands for specific characteristics of every country that are constant over time, such as geography, culture or institutions, ɛ it captures the error term that varies across countries and over time, and matrix X i,t includes k explanatory variables, suggested in the literature as important determinants of the growth rates (e.g., Barro 2000). These variables are the log of the physical capital investment as a share of GDP (lns k ), the government share of real GDP (G/GDP); total trade, measured as exports plus imports divided by real GDP (Trade), and the inflation rate, measured as the annual growth rate in consumer prices (Inflation). The econometric methodology to estimate equation (4) is the system GMM estimator, developed by Arellano and Bover (1995) and Blundel and Bond (1998), which is a combination of equation (4) in first differences, together with the equation in levels. Under the assumption that the error term is not second order serially correlated, we can use the explanatory variables lagged two periods and all further lags as instruments for the explanatory variables in differences. The instruments for the equations in levels are the lagged first differences of the corresponding explanatory variables. 19 We 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 19 The instruments used in this paper 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 avoids overfitting the model and guarantees the number of instruments is lower than the number of countries (see Roodman, 2009). 16

Difference-in-Hansen test. 20 Results are displayed in Table 7. The model fits the data relatively well. The additional controls, initial income per capita, investment share, government consumption, trade, and the inflation rate, all have coeficients with the expected sign. The instruments are also valid, there is no second-order serial correlation, and the Hansen tests of overidentifying restrictions do not reject the validity of the instruments. In line with the pattern shown before, columns (2-7) reveal negative coeffi cients for the ratio of education at the younger ages, 15-19 and 20-29, and positive estimates for the remaining age groups. The results report a concave association between the age structure of human capital and the growth rates of per capita GDP. The peak in average years of schooling of the population aged 40-49 years old holds. These results suggest that using instrumental variables to overcome the endogeneity of human capital, estimating a dynamic panel data model that controls for unobservable heterogeneity and estimating an alternative especification, in line with Barro s estimation, give similar findings as the ones in Section 2. The estimates for education of the youngest cohorts are negative, they then increase with age until peaking at the education of the population aged 40-49 years old, and subsequently declining. 5 Conclusion This paper shows the age structure of human capital is a relevant characteristic to take into account when analyzing the role of human capital on economic growth. In a broad number of countries, this paper finds an inverted U-shape relationship between the age structure of education and the GDP growth rates. The impact of an increase in the share of education of the population aged 40-49 years old is found to have an effect of an order of magnitude larger than an increase in the share of education attained by any other age cohort. The results are not driven by the fact that middle age workers have more experience than the younger ones, in spite that the later have more years of schooling than the 20 It should be noted that the additional moment conditions in the level equation are valid under a mean stationarity assumption. There is not a formal test for this assumption and, therefore, mean-stationarity could or could not be supported by the data. 17

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12 Advanced 12 East Asia and Pacific 10 10 8 8 6 H 1950 H 2010 6 H 1950 H 2010 4 4 2 2 0 15-19 20-29 30-39 40-49 50-59 60-64 65plus 15plus 0 15-19 20-29 30-39 40-49 50-59 60-64 65plus 15plus 12 East Europe and Central Asia 12 Latin America and the Caribbe 10 10 8 8 6 4 H 1950 H 2010 6 4 2 2 0 15-19 20-29 30-39 40-49 50-59 60-64 65plus 15plus 0 15-19 20-29 30-39 40-49 50-59 60-64 65plus 15plus H 1950 H 2010 12 Middle East and North Africa 12 South Asia 10 10 8 8 6 6 4 4 2 2 0 15-19 20-29 30-39 40-49 50-59 60-64 65plus 15plus 0 15-19 20-29 30-39 40-49 50-59 60-64 65plus 15plus H 1950 H 2010 H 1950 H 2010 Sub-Saharan Africa 12 10 8 6 4 2 0 15-19 20-29 30-39 40-49 50-59 60-64 65plus 15plus H 1950 H 2010 Figure 1: Total Average Years of Schooling Across Age-groups