شکل گیری سرمایه انسانی درون زا، فاصله تا مرز و رشد

We examine human capital's contribution to economy-wide technological progress through two channels – imitation and innovation – innovation being more skill-intensive than imitation. We develop a growth model based on the endogenous ability-driven skill acquisition decision of an individual. It is shown that skilled human capital is growth enhancing in the “imitation-innovation” regime and in the “innovation-only” regime whereas unskilled human capital is growth enhancing in the “imitation-only” regime. Steady state exists and, in the long run, the economy converges to the world technology frontier. In the diversified regime, technological progress raises the return to ability and generates an increase in wage inequality between and within groups – consistent with the pattern observed across countries.

The relationship between level of education and economic growth has been much debated upon. Krueger and Lindhal (2001) find that education is statistically significant and positively associated with subsequent growth only for countries with lowest levels of education, and is insignificant and negative for countries with middle and high levels of education. That is, an inverted U-shaped relationship is found to exist between the level of education and the growth rate of an economy.1 The relationship is insignificant when the regression is run for the Organization of Economic Cooperation and Development (OECD) countries alone. This finding is apparently puzzling – basic education helps growth but the relationship between the two dies down as the country progresses in terms of education. A possible explanation for this phenomenon could be that education favors the adoption of new technologies but the aggregate level of human capital does not matter, or its impact gets weaker as the economy progresses toward the frontier, as noticed by Nelson and Phelps (1966). On the other hand, according to Romer (1990), education favors the innovation of new technologies. But Nelson and Phelps (1960) seem to have ignored the fact that a country can also improve its technology level through innovation, while Romer (1990) overlooks the fact that technology improvement can be possible through imitation from the world technology frontier, especially for a technologically backward economy. Benhabib and Spiegel (1994) and Barro (1998) find that the catch-up component of growth is the dominant factor for the technologically backward economy. To find a possible explanation to the puzzle posed by Krueger and Lindahl (2001), we need to focus on both – an economy's distance to the world technology frontier and on the composition of its human capital (as much as on its level). The cross-country analysis of Vandenbussche et al. (2006) and the cross US-state analysis of Aghion et al. (2009) bring out the role of appropriate institutions in analyzing the relationship between growth and the composition of human capital in the diversified regime (that is, where an economy performs both imitation and innovation for further technology improvement). Using a theoretical model, they show that skilled human capital has a higher growth-enhancing effect closer to the technology frontier but unskilled human capital is the main source of growth for a technologically backward economy.2 Furthermore, Vandenbussche et al. (2006) provides evidence in favor of this prediction using a panel data set covering 19 OECD countries covering the time period 1960 and 2000. Unlike earlier research, they not only take into account the stock of human capital but also its composition, which makes a significant difference to their analysis. They are able to solve the puzzle posed by Krueger and Lindahl (2001) by showing that education has a positive and significant impact on economic growth even for an economy with high level of education. Aghion et al. (2009) confirms the same prediction in respect of cross-US-state panel data. The main drawback of both of these studies is that they assume that there exists an exogenously given composition of skilled-unskilled human capital. They only seem to consider the benefit of skilled human capital and ignore the fact that there is a cost associated with skill acquisition. Also, the growth enhancing composition of skilled human capital cannot be the same for an economy, irrespective of its distance to the frontier. We attempt to fill this important gap by endogenizing skill composition, based on an individual's decision to acquire education or not. Di Maria and Stryszowski (2009) also endogenize the composition of human capital in the above discussed setup but the purpose of their analysis is entirely different. They want to examine the impact of migration on the process of growth. They do not characterize the importance of different compositions of human capital on economic growth as we do in this paper. Moreover, the modeling setup of endogenizing the education decision of our model is completely different from Di Maria and Stryszowski (2009). Unlike them, we assume that education decision is not only affected by the cognitive ability of an individual but also on the opportunity cost of education, that is, the outside scope of income of an individual. Furthermore, Aghion et al. (2009) and Vandenbussche et al. (2006) only characterize the intermediate economies, which are performing both types of research activities – imitation and nnovation. Unlike our research, they are entirely silent about the growth enhancing education policy of sufficiently advanced and backward economies, which may be completely specializing in either imitation or innovation activities alone. The distinguishing features of our research are 1. Unlike Vandenbussche et al. (2006) and Aghion et al. (2009), we consider heterogeneous agents, and by endogenizing individual's schooling decision, the composition of skilled and unskilled human capital in any time period is ascertained. Further, we characterize the specialized economies – which are performing either only-imitation or only-innovation activities. 2. Under the assumption that innovation is skilled human capital-intensive, in the diversified regime, the level of skilled human capital increases and that of unskilled human capital decreases as the economy progresses, ascribable to the rising importance of innovation. However, this increase in the share of skilled human capital in the overall human capital composition is missing in the Aghion et al. (2009) and Vandenbussche et al. (2006) works. As a consequence, the shift of both skilled and unskilled human capital from imitation to innovation activity is relatively more pronounced in our case than in their work. Later in Section 3.5.3, we elaborate on how this changes the growth enhancing policy of the diversified regime as prescribed by Aghion et al. (2009) and Vandenbussche et al. (2006). On the other hand, in our research, there exists a fixed composition of skilled and unskilled human capital in the only-imitation and only-innovation regimes, since further technology improvement has a similar impact on both types of human capital. 3. By considering both the cost and the benefit associated with choosing to be skilled, we show that skilled human capital is growth enhancing for an economy which is performing both imitation and innovation activities and only-innovation activity, while unskilled human capital is growth enhancing for an economy which is performing only-imitation activity. Our findings contradict the policy prescription of Vandenbussche et al. (2006) and Aghion et al. (2009), since according to them, unskilled human capital is growth enhancing for a relatively technologically backward economy, which is performing both imitation and innovation activities. They did not characterize the specialized economies – which are performing either only-imitation or only-innovation activities. Also, since the motivation of the study is entirely different for Di Maria and Stryszowski (2009), they also do not say anything about the growth enhancing education policy of an economy irrespective of its distance to the frontier. Furthermore, we contradict the theory of Grossman and Helpman (1991) according to whom skilled human capital is growth enhancing whereas unskilled human capital is growth depressing irrespective of the economy's distance to frontier. 4. The dynamics of the stylized economy show that by implementing an appropriate education policy, in the long run an economy will convergence to the world technology frontier irrespective of its distance to the frontier. 5. Moreover, in the cone of diversified region, as an economy progresses technologically, the average income of skilled human capital rises while that of unskilled human capital falls. Consequently, this raises the income inequality between skilled and unskilled human capital groups. Since technology improvement has a heterogeneous effect on individuals' incomes (depending on their cognitive ability), it tends to raise within group inequality among skilled human capital. On the other hand, in the imitation-only region, due to diminishing marginal return to the imitation activity, as an economy progresses, average income and, consequently, average consumption of skilled and unskilled human capital decreases. Further, aggregate consumption of the economy decreases as an economy progresses. There exists a constant income inequality between skilled and unskilled human capital and within skilled human capital groups. In the innovation-only region, as the technology level increases, the average income and consumption of skilled and unskilled human capital increase and so does aggregate consumption of the economy. In this region also there exists a constant income inequality between and within groups of skilled and unskilled human capital.

Technological progress is a dual phenomenon. A country can attain technological progress by imitating from the technology frontier or by innovating. An economy which is lagging far behind the world technology frontier can improve its technology level by allocating its labor force mainly into imitation. Similarly, an advanced economy can progress technologically by innovating new knowledge. Under the assumption that different types of human capital are efficient in different activities, Vandenbussche et al. (2006) and Aghion et al. (2009) show that unskilled human capital is the main source of growth for the technologically backward economy and skilled human capital is the key source of growth for the technologically advanced economy among the economies which are performing both imitation and innovation activities. By relaxing their assumption of exogenous composition of the labor force, and by utilizing an endogenous growth model, we show that skilled human capital is the engine of growth in the diversified economy. We also characterize the economies which are performing only-imitation or only-innovation activity and show that unskilled human capital is growth enhancing in the imitation-only regime and skilled human capital is growth enhancing in the innovation-only regime. There exists a growth enhancing composition of skilled and unskilled human capital and by implementing that composition an economy can converge to the world technology frontier. That is, a growth enhancing education policy is crucial for both – technologically developing and developed economies. But, as has been derived, this might raise the income inequality between skilled and unskilled human capital and also within the group of skilled human capital, since due to skilled biased technological change, the reward to skilled human capital is much higher in a technologically advanced economy. Our work can be extended in several directions. First, one can allow the possibility of outsourcing of the R & D activity by a developed economy to a less developed economy. Wage rate of skilled human capital is relatively lower and the average cognitive ability of skilled human capital is higher in the less developed economy. This increases the profit of the R & D producer in the developed economy and also raises the income of skilled and unskilled human capital in the underdeveloped economy. Second, in this entire work, we assume that new knowledge is freely available to all the economies. Instead, one can characterize the growth path and the convergence condition of the economy by ruling out the assumption that world technology level is freely accessible. Third, till now all the research in this area has abstracted from international trade in commodities. One can develop a dynamic Ricardian model of international trade around the core idea of our paper and study cross-sectoral allocation of skilled and unskilled human capital in the context of international specialization in goods production and trade. Fourth, one can analyze the consequences of heterogeneous cost of education depending on an individual's parental education level and study the impact of that on the growth rate, inequality and intergenerational mobility of an economy depending on its distance to the world technology frontier. This would yield deeper insights on the interface between distance to frontier, composition of human capital and economic growth.