HUMAN CAPITAL AND ECONOMIC GROWTH: A QUANTILE REGRESSION APPROACH MILES, William* _______________________________________________________
Abstract
A number of previous studies (Barro and Sala -i-Martin, Grier) have attempted to gauge the differential impact of regressors such as human capital and investment on the performance of fast and slow growing economies. To date, most such studies impose a single marginal impact on all countries for each such determinant by estimating only one regression coefficie nt for the whole sample.
This paper seeks to determine whether there are different payoffs to fast and slow growing countries from growth determinants, and employs the technique of quantile regression, a method frequently used in many labor and other microeconomic studies. Results indicate that human capital in particular has a larger marginal benefit for countries that have experienced fast growth, but little significant impact on slow growing nations. Policy implications, however, are not clear-cut and require careful consideration.
JEL classification: C5, J24
Keywords: Growth, Human Capital, Quantile Regression
1. Introduction
Among studies of economic growth, some have attempted to find a differential effect of regressors on fast and slow-growing economies.
It is quite plausible that education affects high and low performers differently. And some papers, such as Barro and Sala -i-Martin (1995) and Grier (2003) examine how different variables affect different levels of economic performers.
*William Miles is Lecturer at the Dept. of Economics, Wichita State University, 1845 Fairmoun, Wichita, USA. E-mail:[email protected].
This paper will examine how different growth determinants, especially human capital, affect fast and slow growers differently.
We differ from previous studies, however. In most studies to date, one regression coefficient is computed for each regressor, and then growth-accounting exercises are employed to determine if a given country has benefited from this variable.
This paper differs from this previous approach by allowing for different coefficients for fast and slow growing economies through the use of quantile regression. This technique is optimal for determining the different effects of human capital and other factors on fast, versus slow-growing economies.
While there has been one previous paper to employ quantile regression (Baretto and Hughes, (2004)), the results obtained from that paper differ from those here. Our results indicate that human capital has a significant and large effect on fast-growing countries, while slow growers do not appear to benefit. We speculate that the reason for these different results may be the inability of nations with low levels of education to take advantage of the growth opportunities of new technology, as modeled in Nelson and Phelps (1966). We explicitly account for this effect in our empirical model. In contrast physical investment has larger effects on slow growing economies than on fast growers.
2. Human Capital and Heterogeneous Effects in Growth Regressions
There have been several broad mechanisms through which education is thought to affect growth. The first recalls the Becker (1964) model of education as an investment in human capital.
Greater abilities obtained from education help make workers more productive and raise output per worker. Additionally, greater education has been shown to lower fertility rates, which means lower population growth and thus higher capital and output per worker.
Guisan, Aguayo and Esposito (2001) document the effect that greater education has in lowering fertility and thus raising the rate of economic growth.
Another mechanism through which education affects growth is that predicted by the model of Nelson and Phelps (1966). In this model, greater education allows for higher growth by increasing technology diffusion. Better- educated managers are more likely to adopt more recent, and thus presumably superior technology. With more education generally in an economy, the payoff from investing in new technologies is likely to be higher, and the risks smaller.
This type of model is suggestive that the payoff to education may differ across economies, i.e. on high and low performers. Birdsall, Ross and Sabot (1997) investigate the effect of education on growth with the purpose of contrasting the experiences of the “miracle”
countries of East Asia with Latin America. The authors suggest that there are greater payoffs to education in the fast-growing East Asian nations compared to Latin American countries.
The authors believe this may be due to the different kinds of development strategies pursued in the two regions. East Asian nations have followed export-oriented strategies. This raised demand for labor in manufacturing industries, and hence the payoff to an educated workforce in such a country was likely high. In contrast, Latin American countries tended to pursue inward-looking, capital-intensive import-substitution industrialization (ISI). This strategy did not raise demand for labor by much, so the returns from having a skilled workforce in Latin America were likely much lower.
Again, there appear to be different effects, at the margin, of growth determinants on different levels of performers.
Barro and Sala -i-Martin (1995, p. 446) run a growth regression for a large cross-section of countries, and, although only one parameter is estimated for each regressor, present a decomposition of the contributions of the different independent variables to growth in fast and slow-growing countries. Results indicate that human capital contributes relatively very little to growth in low performers, but much to high growth nations. Investment in physical capital similarly has a large effect for fast growers but is little help for low performers.
Grier (2003) examines the performance of East Asian “tiger”
economies. The author compares East Asian performance to rich- country growth by estimating the augmented Solow model of Mankiw, Romer and Weil for OECD countries. Then the coefficients from this model are used to forecast growth in East Asia, employing the actual values of investment in physical and human capital and initial income for these emerging economies. The results suggest that the performance of these Asian nations has been less than miraculous, and that some have performed below what has been forecast, for given levels of factor accumulation.
Both the Barro and Sala -i-Martin and Grier papers are informative, but both impose only one coefficient on each regressor. In order to fully investigate the heterogeneous effects of different determinants on growth, the method of quantile regression is most appropriate.
As noted, there is one previous paper which has employed the technique for economic growth. Baretto and Hughes (2004) find that human capital affects middle -performers in the main, while physical capital helps fast growers only. As will be discussed, our results are different, and in many ways the opposite (we find that physical capital is more effective for slow growers than for fast, and that human capital affects fast growers the least and high performers the most). We speculate that these divergent results arise because we allow for another channel through which human capital can affect growth. The effect specified by Nelson and Phelps (1966) in which greater education help growth, not just directly but by aiding in technology diffusion, is included in our empirical model. In addition, we also include regional dummies, which are not included in Baretto and Hughes (2004). Before presenting results, it is worthwhile to discuss quantile regression as it hasn’t typically been employed in growth studies.
3. Quantile Regression
To get a brief sense of the actual estimation involved, first note that employing OLS involves minimizing, through our choice for the value of β , the following:
i n
∑
= 1(y – X’β)2
In contrast, Median or LAD regression involves minimizing, with respect to β :
i n
∑
= 1|y – X’β|
This median regression is s special case of quantile regression. In this quantile regression problem, let τ represent the τ th quantile.
That is, if a given element of Y is chosen, and its value is at the τ th quantile, then it is greater than τ *100 percent and less than (1-
τ )*100 percent of the elements of Y. The quantile regression coefficients are estimated by choosing β (τ ) to minimize the following:
i n
∑
= 1|y – X’β(τ )|[τ I(yi > X’β (τ ) + (1-τ )I(yi ≤ X’β (τ ))]
Where I is an indicator function that equals one if the value in parentheses is true and zero other wise. Note that the coefficient β is now specified as a function of the quantile of Y. Thus the parameters of the model are allowed to take different values for different values of the dependent variable, unlike in the case where only one parameter for each X is allowed. The estimator gives a weight of τ to positive residuals and (1-τ ) to negative residuals, rather than squaring all errors. Thus different β coefficients can be estimated for different quantiles, but each β(τ ) is computed using the entire sample.
4. Data and Results
The data was obtained from the Penn World Table and the Barro and Lee data set. A standard specification is employed to examine growth in a sample of 77 countries (listed in the appendix) between 1970 and 1998. The dependent variable is the average growth rate
over this twenty-eight year period. The first regressor is the average years of secondary school attained in the country in 1970 (SEC70) for those over age twenty-five. This serves as our measure of human capital. There are other measures of schooling which could be used.
Indeed, the increase in this variable, from it’s 1970 value to it’s 1995 level was experimented with, however, the effect of this regressor, both when it was added to the standard model and when it was used as the only measure of human capital, were insignificant (results available upon request). And the init ial level of secondary schooling was employed in Mankiw, Romer and Weil (1992) and subsequently in Grier (2003). Only secondary schooling was significant at the five percent level in Barro and Sala -i-Martin (1995), whereas primary and high schooling were not. Thus secondary school attainment at the beginning of the sample is the major variable in the literature for gauging the level of human capital and we accordingly use it here.
Based on Becker’s (1964) analysis, we expect that human capital will raise the productivity of workers, all else constant, and thus forecast a positive sign based on this channel.
The second variable is the logarithm of per-capital income in the beginning year of 1970 (GDP70). This is included to test for convergence effects. The expected sign of the coefficient is negative. The next regressor is the interaction of human capital in 1970 and the logarithm of initial per capita income in 1970(GDP70*SEC70). The motivation for this, as explained in Barro and Sala -i-Martin (1995) is the notion that higher human capital can raise the speed of convergence. This situation was modeled by Nelson and Phelps (1966). A higher level of education facilitates technological diffusion. Since faster convergence means that initial income should slow growth, the expected sign of the coefficient is negative. This is another important channel through which human capital can affect growth. This interaction term was missing from the Baretto and Hughes (2004) study.
The average level of investment as a fraction of GDP (I/Y) is also an independent variable. Higher investment raises the capital stock and, a la Solow, makes labor more productive, raising the growth rate. Population growth (GPOP7098) is also included, as the Solow
model predicts that higher population growth will reduce the capital available for each worker, and thus lower output per person. Finally, regional dummies are added for Latin America and Africa (these variables were also not included in the Baretto and Hughes pa per).
In order to provide a baseline with which to compare the quantile regression results, a least squares model is estimated and presented in table 1. White’s standard errors are employed to control for heteroskedasticity. The negative effect of initial income on growth is similar in magnitude to some previous studies such as Barro (1991).
Investment has a positive effect as expected. Population growth is negative, but not quite significant at the five percent level (but clearly significant at ten percent). The regional dummies are negative but not significant. Education has a positive and clearly significant effect. The interaction of education and initial income is negative and significant, indicating that there are important effects from education on technology diffusion, and hence growth.
All of the results in table 1, of course, are the effect on the conditional mean of growth. There could be much heterogeneity in the effects of the regressors. Thus the data will be observed at quintiles (fifths) and coefficients will be compared to see if there are differing effects of regressors on growth for different levels of economic performance. Results of the regressions for the τ = 0.2, 0.4, 0.6 and 0.8 quantile s are displayed in tables 2 through 5.
Looking first at the lowest, τ = 0.2 quintile, the effect of lagged initial income, conditional on the other variables, has a greater impact than for the OLS results. Population growth is not a significant factor in this quantile. Africa has a negative and significant impact, while Latin America still has no palpable effect.
Perhaps most importantly, both the education and interaction variables for human capital are much smaller in magnitude than for the least squares model, and insignificant.
This result bears some examination. At first glance it seems pessimistic, indicating that greater education cannot help lift slow growing economies. And a look at the appendix, where the nations are ordered in terms of growth, indicates that the nations clustered
near the τ = 0.2 point include some sub-Saharan African nations such as Malawi, Senegal and Ghana, which have suffered from low economic development, as well as nations such as El Salvador, which have been buffeted by political violence. Such nations may have lacked focused development strategies, and as such what growth there has been has not been accompanied by demand for skilled labor, thus lowering the payoff to human capital (Birdsall, et al. (1997)). On a positive note, however, observe that the coefficient on investment in physical capital is actually larger than that in the least squares regression. Thus physical capital is very important for the slow growers.
Table 3 contains results for the τ = 0.4 quintile. Here, initial income has less of an effect than for either the very slow growers or overall in the least squares model. Population growth is again insignificant, as are the regional dummies. The education and interaction terms are higher in magnitude than for the bottom quintile, but are still not significant. Investment in physical capital is again significant, although the coefficient is less than for the slowest growers and the least squares regression. Results suggest human capital has less of a payoff for lower quantiles than for countries in the overall sample.
Table 4 has results for the τ =0.6 quantile; the effects we could expect on a country whose growth was slightly greater than the median. Population growth is negative and significant at the ten, but not five percent level. Africa has a negative impact. Initial income is clearly significant. Human capital has a significant impact, larger than for the preceding quantiles and the least squares results.
Education, and its interaction with initial income are both significant and signed as expected. Countries that have had moderately successful growth appear to benefit more from human capital. They also benefit less from physical capital, as the coefficient, while significant, is less than that for previous quantiles.
The model for the top quantile is presented in table 5. The effect of education, both directly and its interaction with initial income, is the
highest of any model. Fast growing countries appear to reap the greatest payoff from human capital. Physical capital has the lowest impact for these nations, but the effect is still significant. Africa is significant, while Latin America has an impact at the ten, but not five percent level. Since the τ =0.8 quintile disproportionately weights
“tigers” like Singapore, Hong Kong, and Korea, the hypothesis advanced by Birdsall, et al. seems to have been given some formal confirmation; in faster growing nations the payoff to education is higher.
The results presented here stand in contrast in important respects to some prior studies, such as Barro and Sala -i-Martin (1995) and Barretto and Hughes (2004). For physical capital, we find that slow growers can benefit tremendously, at the margin, from an addition to the capital stock. The aforementioned authors found that investment contributed little to growth in slow growing nations, while fast growers benefited substantially. Again, this is because slow growers have invested little. We believe the reason for our finding of a large effect for slow growers but a slow effect for fast performers is that the slow growers include nations with little capital. Thus some additional capital at the margin is likely to have larger effects due to diminishing returns.
The differing effects of education may seem to present a puzzle, since the slow growing economies include many with already low levels. Why should the logic of diminishing returns apply to physical, but not human capital? Again, Birdsall, et al. (1997) provide an explanation. The slow growers again include nations such as Senegal and Peru, and they have not undertaken export- oriented manufacturing. Thus education in these cases will help little. On the other hand, fast growers include Taiwan, Singapore, Korea and Hong Kong, all of which have implemented such exporting strategies, and which therefore are poised to exploit the economic benefits of a well-educated workforce.
5. Conclusion
The varying size of coefficients, especially on education, confirm that there is indeed a different “payoff” to some regressors. Human capital has an impact not only in how much countries invest in education, but given countries can, all else constant, expect less or more out of a given increase in such capital depending on growth experience.
The most plausible explanation for the results is likely related to the Nelson and Phelps (1966) phenomenon in which higher levels of education facilitate the diffusion of technology. With a better- educated workforce, manufacturing industries demanding high levels of skilled labor take root. Thus slow growers suffer from an inability to capitalize on education even if they immediately were to start investing heavily in human capital.
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Table 1.
Least Squares Results (White’s Standard Errors Employed)
Variable Coefficient Std. Error T-Stat P-Value Constant 0.105477 0.0253 4.1613 0.0001 GDP70 -0.013271 0.00312 -4.254 0.0001
I/Y 0.148815 0.024343 6.113 0.0000
GPOP7098 -0.481891 0.245893 -1.95975 0.0541
SEC70 0.003884 0.001723 2.254 0.0273
GDP70*SEC70 -0.000382 0.000187 -2.044 0.0447
LA -0.004568 0.003586 -1.273 0.207
AFRICA -0.009251 0.006185 -1.495 0.1393 R2 =0.591, N = 77
Table 2.Quantile Regression Results (τ = 0.2)
Variable Coefficient Std. Error T-Stat P-Value Constant 0.10169 0.026024 3.91 0.0000 GDP70 -0.015056 0.003523 -4.27 0.0000
I/Y 0.1594195 0.0289226 5.51 0.0000
GPOP7098 -0.119102 0.2211 -0.54 0.592 SEC70 0.0017324 0.0014316 1.21 0.23 GDP70*SEC70 -0.0001313 0.0001512 -0.87 0.388
LA -0.0050456 0.0046626 -1.08 0.283
AFRICA 0.101691 0.0260247 -2.83 0.006 Pseudo R2 =0.4505, N = 77
Table 3. Quantile Regression Results (τ = 0.4)
Variable Coefficient Std. Error T-Stat P-Value Constant 0.0817817 0.048773 1.68 0.098 GDP70 -0.0103866 0.00601 -1.73 0.089
I/Y 0.1284278 0.0391302 3.28 0.002
GPOP7098 -0.4586778 0.3796075 -1.21 0.231 SEC70 0.0033026 0.0025261 1.31 0.195 GDP70*SEC70 -0.0003249 0.0002747 -1.18 0.241
LA -0.0020721 0.0069966 -0.30 0.768
AFRICA -0.0074457 0.0073758 -1.01 0.316 Pseudo R2 =0.3709, N = 77
Table 4. Quantile Regression Results (τ = 0.6)
Variable Coefficient Std. Error T-Stat P-Value
Constant 0.0889 0.027673 3.21 0.002
GDP70 -0.0103691 0.0034033 -3.05 0.003
I/Y 0.1225239 0.0202595 6.05 0.0000
GPOP7098 -0.3957109 0.2123803 -1.86 0.067 SEC70 0.0053747 0.0014215 3.78 0.0000 GDP70*SEC70 -0.0005531 0.00015507 -3.55 0.001
LA -0.0065773 0.0037807 -1.74 0.086
AFRICA -0.0137253 0.004394 -3.21 0.003 Pseudo R2 =0.3608, N = 77
Table 5. Quantile Regression Results (τ = 0.8)
Variable Coefficient Std. Error T-Stat P-Value Constant 0.1075142 0.0334082 3.22 0.002 GDP70 -0.0118371 0.0040165 -2.95 0.004
I/Y 0.1020996 0.0232561 4.39 0.0000
GPOP7098 -0.2768506 0.2554276 -1.08 0.282 SEC70 0.0055187 0.0018182 3.04 0.003 GDP70*SEC70 -0.0005627 0.0002018 -2.79 0.007
LA -0.0075764 0.0041353 -1.83 0.071
AFRICA 0.1075142 0.0061662 -2.22 0.03 R2 =0.3874, N = 77
Appendix: Sample countries in order of growth rates
Taiwan, Sin gapore, Korea, Botswana, Hong Kong, Indonesia, Mauritius, Ireland, Thailand, Malaysia, Syria, Norway, Sri Lanka, India, Dominican Republic, Iceland, Japan, Lesotho, Spain, Paraguay, Turkey, Chile, Finland, Austria, Brazil, Israel, Greece, Italy, United States, Belgium, Columbia, Jordan, Britain, Canada, Netherlands, France, Nepal, Denmark, Uruguay, Australia, Panama, Uganda, Sweden, Pakistan, Trinidad, Ecuador, Mexico, Bangladesh, Kenya, Algeria, Philippines, Iran, Guatemala, Argentina, Costa Rica, Cameroon, Switzerland, Zimbabwe, Malawi, Honduras, Guyana, El Salvador, Mali, South Africa, Bolivia, Jamaica, Peru, Senegal, Ghana, Venezuela, Papua New Guinea, Togo, Niger, Nicaragua, Mozambique, Central African Republic, Zambia.
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