The role of human capital in economic growth

Applied Economics Letters, 25, 2, 583 587 The role of human capital in economic growth Vladimir K. Teles Getulio Vargas Foundation, Sao Paulo School of Economics, Rua Itapeva, 474, 3 andar, Bela Vista, EP 332-, Sao Paulo, SP, Brazil E-mail: vkteles@fgvsp.br This study presents stylized facts for economic growth for the second half of the 2th century, and evaluates the explanatory capacity of these facts by two of the main theoretical approaches that deal with the relation between human capital and growth: the Lucas (988) model, and the Nelson and Phelps (966) model. The results obtained indicate that the Lucas (988) model satisfactorily explains the growth of rich countries, but does not explain the poverty traps in which poor countries found themselves during the period under study. onversely, the simulations conducted according to the Nelson Phelps approach (966) adequately replicate the poverty traps, but the approach is unable to do so for rich country dynamics. I. Introduction Human capital and growth are intimately related; however, the relation between them is not a trivial one. The main objective of this article is to develop a quantitative analysis of this relation, based on the principal theoretical models put forth in the endogenous growth literature. For this analysis, two theoretical models are tested, and are then evaluated with regard to their capacity to predict the movement of countries during the second half of the 2th century. The modelling of the relation between human capital and growth is a controversial issue in the economic literature. In this context, Aghion and Howitt (998) have pointed out two main approaches from among the endogenous growth models: the Lucas approach (988), and the Nelson and Phelps approach (966). The Lucas model establishes that the driving force behind economic growth is the rate of accumulation of human capital, in which the rate of economic growth is proportional to the rate of accumulation of human capital, and since human capital imposes externalities upon production, the rate of economic growth will respond more than proportionally to increases in human capital accumulation rates, thus configuring increasing returns to scale. On the other hand, the Nelson Phelps approach considers that high levels of human capital increase the capacity of individuals to innovate (by discovering new technology) or to adopt new technology. Therefore, this approach indicates that the level of human capital affects economic growth, and not its rate of accumulation. This approach has received much academic attention after the appearance of endogenous technological progress models a` la Romer (99), Grossman and Helpman (99) and Aghion and Howitt (992), for considering that an increase in the number of researchers in an economy, by increasing the number of innovations, would lead to an increase in the rate of economic growth. As is well pointed out by Aghion and Howitt (998), an economy with a high human capital stock has a alculated as the average years of study. Applied Economics Letters ISSN 35 485 print/issn 466 429 online # 25 Taylor & Francis Group Ltd 583 http://www.tandf.co.uk/journals DOI:.8/354855773

584 V. K. Teles greater potential number of researchers than in other economies, meaning that the Nelson Phelps approach is similar to the other models mentioned above. Given the theoretical controversy regarding the influence human capital has upon economic growth, this article shall attempt to confront these two approaches with simulations based on the hypotheses of both models, and then compare the probability transition matrices obtained from these simulations with those obtained by real values. II. Stylized Facts of Economic Growth In this section, an attempt is made to construct stylized facts observed in economic growth for the second half of the 2th century. Initially, a probability transition matrix was estimated based on a temporal partition in 95. Thus, the probability of an economy with a low rate of growth before 95 having an accelerated rate of growth after 95 may be observed, for example. In order to evaluate country growth before 95, the countries per capita GNP was considered as a measurement of accumulated growth rates, while the evaluation of growth after 95 was determined by simply calculating the growth rates of countries between 95 and 2. However, in order to determine the states in the state-space model, it is necessary to define the criterion used to determine whether a country has a low rate of growth or a high rate of growth. Two definitions will be used in this study, and will be presented below. Definition. A uniform state is determined from the uniform probability distribution of countries among states, so that all states have approximately the same number of countries. Definition 2. A weighted state is determined from a growth rate probability distribution of countries, so that all states have different numbers of countries, but for which states are determined by the constant growth intervals. Table describes the variations in long-term growth rates of the countries. In other words, a matrix with three uniformly defined shows that a country that had a high rate of growth up to 95, had a 29% probability of maintaining a high rate of growth, and a 24% chance of presenting a low rate of growth, up to the year 2. The analysis was repeated with 96 as the limit year, since this increased the sample to 98 countries, generating the probabilities transition matrices shown in Table 2. By analysing the estimated probabilities transition matrices, it may be observed that a country that Table. Transition probability matrices (5 countries) :29 :47 :24 T ¼ @ :53 :2 :35 A :9 :44 :38 : :43 :57 T ¼ @ :3 :47 :4 A :4 :8 :68 Table 2. Transition probability matrices (98 countries) :44 :44 :3 T ¼ @ :27 :33 :39 A :27 :24 :48 : :3 :88 T ¼ @ : :43 :57 A :7 :6 :78 :5 :46 :3 :8 :5 :8 :7 :25 @ :25 :7 :25 :33 A :5 :23 :23 :38 : :3 :63 :25 : :3 :3 :4 @ : :56 : :33 A :3 :9 :26 :52 :36 :4 :2 :4 :25 :29 :33 :3 @ :7 :2 :7 :46 A :24 :8 :28 :4 : : :5 :5 : : :42 :58 @ : :5 :38 :46 A :3 :2 :4 :7 had reached a higher stage of development would probably not maintain it; in other words, if a country had a high rate of growth up to 95, this would probably not be maintained up to the year 2. Thus, it seems that some countries tend to converge towards a good equilibrium. On the other hand it may also be noted that there is a strong probability of other poorer countries maintaining low rates of growth in the long run, thus tending to remain at a bad equilibrium. Therefore, the observed stylized facts seem to point towards a situation of multiple equilibria, with regard to countries stages of development. These results corroborate the notion of multiple equilibria in increasing returns models, as in Matsuyama (99), in which poorer, or non-industrialized economies, tend to remain at this level of equilibrium, while other economies, that tend towards industrialization, converge towards a good equilibrium. III. Theoretical Models versus Stylized Facts The database and the determining of parameters In order to observe the models degree of explanation when confronted with reality, simulations were

The role of human capital in economic growth 585 conducted in order to verify whether the human capital models are able to replicate the stylized facts for the periods analysed in Section II. Toward this end, the Nehru and Dhareshwar (993) database was used, which contains annual human capital stock data (average years of study) from 95 to 99. Thus, in order to complete the series up to the year 2, a polynomial interpolation was conducted so that an annual series for human capital could be constructed. The per capita GNP data used in the simulations were obtained from the Penn World Table, version 6.. The growth rates predicted by Lucas (988) framework was obtained by the following equation: _y y ¼ þ _h h ðþ where y represents production, h the human capital stock, the marginal product of capital, and the effect of externalities on the production of an economy. At the same time, the ideas production function that follows Nelson Phelps framework may be written as follows: A tþ ¼ t ða t þ Þþð t ÞA t ð2þ where A t represents the economy s level of technology at t, t represents the probability of the occurrence of a technological innovation at t, and is the constant representing the technological gain of each innovation. In this way, the probability of the arrival of an innovation is given by: t ¼ þ e ð3þ ð þ A t þ 2 H t Þ In order to quantify the level of technology A, the 95 per capita GNP was considered as the proxy for the level of productivity in 95 (A ). Thus, the technology increments are defined as being sudden increases in per capita GNP. This proxy, besides simplifying the simulations, is supported by the literature, as in De astro and Gonc alves (22). Therefore, in order to perform the Lucas model simulations, it was assumed that ¼.3, according to the standard found in the literature, as in Mankiw et al. (992), and ¼.5. At the same time, in order to perform the Phelps model simulations, an innovation was considered to represent a US$ 4 increase in per capita GNP and, from this, a binary variable P defined, where P ¼ if there was an increase in per capita GNP greater than or equal to US$ 4, and P ¼ if the opposite took place. A Logit model was estimated in order to estimate the logistic function, reaching the approximate values for the parameters considered, which appear in Table 3. Table 4. Lucas model: transition probability matrices (5 countries) :7 :27 :67 T ¼ @ :2 :4 :4 A :69 :3 : : : : T ¼ @ : :4 :86 A :5 :62 :23 Results Table 3. Estimated parameters from (Equation 3) Parameter Value 5.5 2.5 : : :33 :67 :8 :8 :36 :27 @ :36 :36 :8 :9 A :5 :42 :8 : : : :4 :86 : : :4 :5 @ : :3 :38 :5 A : : :7 : Table 5. Nelson Phelps model: transition probability matrices (5 countries) :33 :6 :7 T ¼ @ :4 :33 :27 A :25 :6 :69 : : : T ¼ @ :7 :79 :4 A :8 :38 :54 :7 :5 :33 :33 :45 :8 :8 :8 @ :27 :9 :8 :45 A :7 :7 :25 :42 : :29 :7 : : :4 :6 : @ :3 :25 :5 :3 A :5 :24 :38 :33 With the parameters and the database described in the previous section, simulations were made from the theoretical models outlined above so that annual series for per capita GNP for all countries could be constructed from each model specified. Therefore, with these artificial series, it was possible to estimate the probability transitions matrices. These results appear in Tables 4 7. When comparing these results with the stylized facts described in Section II, it is possible to observe the points that were correctly projected by the theoretical models, as well as those that were not

586 V. K. Teles Table 6. Lucas model: transition probability matrices (98 countries) :8 :3 :79 T ¼ @ :25 :63 :3 A :63 :25 :3 : : : T ¼ @ : :4 :86 A :8 :5 :3 : :6 :28 :67 : :39 :28 :22 @ :39 :33 :22 :6 A :5 :22 :22 :6 : : :33 :67 : : :7 :83 @ : :9 :27 :64 A :3 :22 :54 : Table 7. Nelson Phelps model: transition probability matrices (98 countries) :92 :8 : T ¼ @ : :29 :7 A :8 :63 :29 :86 :4 : T ¼ @ :57 :2 :2 A : : : : : : : : :5 :44 :6 @ : : :6 :94 A : :6 :94 : : : : : :33 :67 : : @ :9 :8 :27 :45 A : : :2 :98 so well predicted. In this regard, it may be ascertained that the Lucas model (988) is able to explain the growth dynamics of the rich countries with a certain degree of accuracy, which are classified in state S. This capacity becomes clear when the results obtained for the 98-country sample are analysed, for which the weighted state definition was used. In this case, the results obtained in the simulation corroborate the stylized facts presented, making it clear that there is a tendency for those countries in S to have lower rates of growth when compared with the other countries. On the other hand, however, the poverty traps made evident by the stylized facts are not obtained in the Lucas model (988) simulations. These results seem to support the supposition put forth by Azariadis and Drazen (99), that states that the linearity proposed by Lucas (988) for the human capital movement equation, which indicates that the returns to education remain constant, is not supported by the observed evidence. This becomes clear in this study s simulations, for poor countries would have a higher level of growth according to the results obtained, since these countries had a higher rate of human capital growth than did rich countries. With regard to this aspect of the analysis, poor countries had a higher human capital growth rate because their initial human capital stock was very small. As an illustration, let the case of Kenya be taken. This country s human capital stock was a mere. year of study per capita at the initial period (95), reaching an average of one year of study in the final year of the sample (2). Its economy would have had to increase -fold, given its high human capital growth rate, in spite of its extremely low level, which evidently did not take place. This result illustrates how difficult it is for the Lucas model to interpret the poverty traps, in spite of its capacity of explaining the growth of rich countries relatively well. Regarding the simulations made with the idea production function models, the poverty traps are well explained by these models, since the results obtained by these models simulations corroborate the stylized facts according to which poor countries have a high probability of maintaining a low rate of economic growth. On the other hand, these models fail to explain the growth dynamics of rich countries, since there is no downturn in the growth rate of these countries. In spite of the fact that these models do indicate that human capital is the driving force behind growth, they reach very opposite consequences regarding their capacity of explanation. Although the Lucas model was able to explain the growth of rich countries relatively well, although failing to explain the growth of poor countries, the Nelson Phelps approach explained the growth of poor countries relatively well, but was not able to satisfactorily explain the growth of rich countries. IV. onclusions The recent economic growth theories, as well as empirical studies, have made clear that investment in human capital has attributes that are fundamentally different than those of investment in physical capital, when their effect upon economic growth is considered (see Dowrick, 23). Knowing this, the manner in which human capital affects economic growth has been the subject of ongoing debate in the economic literature, given its non-triviality. This study presents stylized facts for economic growth for the second half of the 2th century, and evaluates the explanatory capacity of these facts by two of the main theoretical approaches that deal with the relation between human capital and growth: the Lucas (988) model, and the Nelson Phelps (966) model.

The role of human capital in economic growth 587 The results obtained indicate that the Lucas (988) model satisfactorily explains the growth of rich countries, but does not explain the poverty traps in which poor countries found themselves during the period under study. onversely, the simulations conducted according to the Nelson Phelps approach (966) adequately replicate the poverty traps, but the approach is unable to do so for rich country dynamics. The results make it evident that the way human capital is dealt with in economic growth models is still not totally free of imperfections. Theory development possibilities remain open, for it remains clear that human capital is an intrinsic part of the growth process of nations. Acknowledgments The author would like to thank Joaquim P. Andrade, Jorge Arbache, Stephen de astro, Adolfo Sachsida, Bernardo Mu ller and Samuel Pessoˆ a for valuable comments and insights. The usual disclaimer applies. References Aghion, P. and Howitt, P. (992) A model of growth through creative destruction, Econometrica, 6, 323 5. Aghion, P. and Howitt, P. (998) Endogenous Growth Theory, MIT Press, ambridge, MA. Azariadis,. and Drazen, A. (99) Threshold externalities in economic development. Quarterly Journal of Economics, 5(2), 5 26. De astro, S. and Gonçalves, F. (22) False contagion and false convergence clubs in stochastic growth theory, Textos para Discussão UnB, no. 237. Dowrick, S. (23) Ideas and education: level or growth effects?, NBER Working Papers, no. 979. Grossman, G. and Helpman, E. (99) Quality ladders in the theory of growth, Review of Economic Studies, 58, 43 6. Lucas, R. (988) On the mechanics of economic development, Journal of Monetary Economics, 22(), 3 42. Mankiw, G., Romer, D. and Weil, D. (992) A contribution to the empirics of economic growth, Quarterly Journal of Economics, 7(2), 47 37. Matsuyama, K. (99) Increasing returns, industrialization, and indeterminacy of equilibrium, Quarterly Journal of Economics, 6, 67 5. Nehru, V. and Dhareshwar, A. (993) A new database on physical capital stock: sources, methodology and results, Revista de Analisis Economico, 8(), 37 59. Nelson, R. and Phelps, E. (966) Investment in humans, technological diffusion, and economic growth, American Economic Review: Papers and Proceedings, 5(2), 69 75. Romer, P. (99) Endogenous technological change, Journal of Political Economy, 89(5), Part 2, S7 2.