Azariadis, C. and A. Drazen, 1990, “Threshold Externalities in Economic Development,” Quarterly Journal of Economics (May), pp. 501–26.
Acemoglu, D., 1998, “Why Do New Technologies Complement Skills? Directed Technical Change and Wage Inequality,” Quarterly Journal of Economics, pp: 1055–89.
Barro, R. and J.W. Lee, 1997, “International Measures of Schooling Years and Schooling Quality,” American Economic Review, Papers and Proceedings, 86(2), pp. 218–23.
Bartel, A. and F. Lichtenberg, 1987, “The Comparative Advantage of Educated Workers in Implementing New Technology.” Review of Economics and Statistics, (Feb.), 69 (1), pp. 1–11.
Benhabib, J. and M. Speigel, 1994, “The Role of Human Capital in Growth,” Journal of Monetary Economics, September, 34(2), pp. 143-73.
Bennel, Paul, 1996, “Rates of Return to Education: Does the Conventional Pattern Prevail in sub-Saharan Africa?” World Development, 24, pp. 183–99.
Carrington, W., E. Detragiache, and T. Vishwanath, 1996, “Migration with Endogenous Moving Costs,” American Economic Review, June, 86 (4), pp. 909–30.
Deolalikar, Anil and R. Evenson, 1994, “Private Incentive Activity in Indian Manufacturing: Its Extent and Determinants,” in Science and Technology: Lessons for Development Policy, ed. by R.E. Evenson and G. Ranis (Colorado: Westview Press).
Engel, R. and C. Granger, 1987, “Co-integration and Error Correction: Representation, Estimation and Testing,” Econometrica, 35, pp. 251–76.
Foster, Andrew and Mark Rosenzweig, 1996, “Technical Change and Human-Capital Returns and Investments: Evidence from the Green Revolution,” American Economic Review, June 86 (4), pp. 931–53.
Foster, Andrew and Mark Rosenzweig, , 1995, “Learning by Doing and Learning from others: Human Capital and Technical Change in Agriculture,” Journal of Political Economy, April, 103(6), pp. 1176–1208
Galor, O. and D. Tsiddon, 1997, “The Distribution of Human Capital and Economic Growth,” Journal of Economic Growth, March, 2, pp. 93–124.
Glewwe, Paul, 1997, “Schooling, Skills, and the returns to Government Investment in Education,” Living Standards Measurement Study Working Paper 76 (World Bank, Washington, D.C.).
Goldin, C. and L. Katz, 1998, “Why the United States Led in Education: Lessons From Secondary School Expansion, 1910 to 1940,” NBER Working Paper: 6144.
Krueger, A. and M. Lindhal, 1998, “Education for Growth in Sweden and the World,” Industrial Relations Section, Working Paper No. 411, December, Princeton University.
Lau, L., D. Jamison, and F. Louat, 1991, “Education and Productivity in Developing Countries: An Aggregate Production Function Approach,” Policy Research Working Paper 612, (World Bank: Washington, D.C.).
Matsuyama, Kiminori, 1991, “Increasing Returns, Industrialization, and Indeterminacy of Equilibrium,” Quarterly Journal of Economics, May, 106(2), pp. 617–50.
Mingat, A. and J. Tan, 1998, “The Mechanics of Progress in Education: Evidence from Cross-Country Data,” Mimeo, (World Bank: Washington, D.C.).
Mingat, Alain, 1984, Measuring the Economic Efficiency of Project Related Training: Some Evidence from Agricultural Projects (World Bank, Education Department, Washington, D.C.).
Miyagiwa, K., 1991, “Scale Economies in Education and the Brain Drain Problem,” International Economic Review, August, 32(3), pp. 743–59.
Nelson, R., and E. Phelps, 1966, “Investment in Humans, Technological Diffusion, and Economic Growth,” American Economic Review 56 (2), pp. 69–75.
Pscacharopoulos, George, 1987, “Earnings and Education in Brazil: Evidence from the 1980 Census,” EDT Series 90 (World Bank, Education and Training Department, Washington, DC).
Ramcharan, Rodney, 2001, “Human Capital Formation and Factor Mobility: Theory and Evidence from the U.S. High School Movement,” mimeo, Columbia University.
Romer, Paul M., 1993, “Idea Gaps and Object Gaps in Economic Development,” Journal of Monetary Economics, December, 32, pp. 543–73.
Wozniak, Gregory, 1984, “The Adoption of Interrelated Innovations: A Human Capital Approach,” Review of Economics and Statistics, February, (66), pp. 70–79.
Without implicating, I am grateful to Don Davis, Ronald Findlay, Ken Leonard, John McLaren, Edmund Phelps, Xavier Sala-i-Martin, Reza Vaez-Zadeh, and seminar participants at Columbia, the IMF Institute, NYU, University of Georgia and Yale for their many helpful comments.
The Morrill Acts of 1862 and 1890 granted federal funds to existing and future states to endow universities and colleges that specialized in agriculture. The 1890 act provided funding for many institutions created by the first act.
Similarly, in the last few decades India and many countries in Latin America have encouraged heavy tertiary investment; in contrast, several East Asian countries have focused on basic or secondary education.
The importance of tertiary or advanced education in generating and adapting ideas is underscored by a recent study of a thousand Indian inventors. The authors (Deolalikar and Evenson (1990)) found that almost 90% had a university degree, more than half had some post graduate training, and nearly 30% held doctorate degrees.
Nelson and Phelps (1966) formalized the argument that some minimum level of education speeds the adoption process. Bartel and Lichtenberg (1987) has since found evidence of this in the U.S. manufacturing sector.
The World Bank in its recent World Development Report (1998/1999) has also noted the inherent complementarity of this relationship: “Basic education increases people’s capacity to learn and interpret information. But this is just the start. Higher education and technical training are also needed, to build a labor force that can keep up with a constant stream of technological advances, which compress product cycles and speed the depreciation of human capital.” These linkages have also been well documented in the green revolution in Asia. While advances in biotechnology, pioneered in the developed countries, made the development of the high yielding variety (HYV) seeds in such staples as rice and wheat possible, local scientists and agronomists were necessary in order to adapt these HYV to the local climatic conditions. Once developed, the use of these seed strains are non-rival, but can be excluded. However, using HYV seeds requires a greater attention to fertilizer quantity, irrigation and soil conditions. Thus, as indicated by Foster and Rosenzweig (1996) in the case of India, educated farmers adopted the more technologically advance seed strains more rapidly than those without sufficient schooling. Furthermore, the authors found that the returns to education increased in those areas where adoption had the highest potential gains. In addition, the expansion of schooling and the many agricultural extension projects designed to facilitate adoption increased the rate of return to R&D in seed technology through the market size effect, as well as through the fact that the feedback from more educated farmers was more useful in developing better seed varieties (see Pray and Ruttan (1990)).
In their investigation into the causes of inequality, Mokherjee and Ray (1998) also use the idea that the existing stock of human capital limits the availability of teachers. And empirically, Mingat and Tan (1998) found that the greater supply of potential teachers account for a significant share of the difference in educational attainment between rich and poor countries.
In their point estimates, the building a school in a village can more than double the enrollment rate for children ages 5 through 14 years of age. Likewise, in Indonesia, Duflo (2001) finds that each primary school constructed per 1000 children led to 0.12 to 0.19 increase in the years of education.
Islam (1995), Hoeffler (1997), Benhabib and Spiegel (1994), Spiegel (1994), Dasgupta and Weale (1992), Pritchett (1999), Barro and Sala-I-Martin (1995) and Lau, Jamison and Louat (1991) all find an insignificant or negative correlation between various measures of educational attainment and economic growth. Recently Krueger and Lindahl (1998) have questioned the accuracy of these results. They argue that measurement error in the education data negatively biases the human capital coefficient.
To devise these measures, it is common to divide the total number of years of schooling attained by the size of the population. See Barro and Lee (1993).
This means for example that one extra of year of primary schooling has the same effect on marginal productivity as one extra year of post secondary education.
Recently, Glewwe (1991), using detailed data drawn from Ghana’s 1988-1989 Ghana Living Standards Survey (GLSS) found that the private rate of return to secondary and tertiary schooling are much higher than primary schooling. See Nielsen and Westergard- Nielsen (1998), Bennel (1996) and Bigsten et. al (1997) for similar results using African data. Lachler (1999) reports similar findings using Mexican data.
To reiterate, the terminology tertiary and secondary is used for convenience. These linkages can potentially exist across other types of human capital.
Within a different context, Acemoglu (1998) also studies the link between the potential market for a technology and the incentives to develop that technology. Crucial to his argument, in much the same way it is here, is the idea that the use of the technology is non rival but excludable
Matsuyama (1992) uses a qualitatively similar setup, albeit with a single factor of production, to generate IRS within an industrial sector.
Romer (1986) also uses a similar framework to analyze knowledge spillovers at the sector level stemming from the use of capital at the firm level. There, the absence of demising marginal returns to capital, because of knowledge spillovers produces endogenous growth.
This is only a simplifying assumption; in equilibrium, the skill premia are always positive (Lemma 2).
In the dynamic model, I endogenize the aspect of this cost imposed by policy variables.
One interpretation of the idea that individuals are infinitely lived, and wait until the optimal date to invest in education is that generations or families pass on their existing level of education to their children. Given the cost of schooling and the demand for [skilled] labor in the current period, these children then decide whether to invest in schooling and add to their family’s capital stock or delay and pass on only the existing level to future generations. In this way, if the educational infrastructure rapidly expands, then families, and by extension society quickly become educated, otherwise it takes a longer time. See Galor and Tsiddon (1997) for an overlapping generations model with some of these characteristics.
This idea bears some resemblance to Azariadis and Drazen’s (1992) concept of threshold externalities.
To conserve notation, I assume that size of the externality, a, is the same in both categories of schooling. Relaxing this assumption does not substantially alter the results.
If the rate of return to tertiary schooling increased with the stock of tertiary educated workers, then a stable steady state would not exist. Any perturbation around a steady state, say an increase in H would raise the rate of return to tertiary investment and lead to new round of investment until the population constraint was reached.
Without the latter assumption, a single steady state occurs where the two curves share the same tangent line. The dynamics associated with this case is not very interesting.
Note that -Ru (•) is the rate of return to secondary schooling.
The level curves in Figure 5 qualitatively depict the case where the cost of schooling takes the functional form: c(•) = -tanh(•). See the Appendix for the parameter values that produce curves similar to the level curves in Figure 5. Alternatively, a similar result can be obtained by assuming a discontinuous schooling externality. The size of the externality is constant, but discontinuously jumps after some threshold level of attainment. This would produce multiple stable steady states.
For example, The Inter-American Development Bank’s 1998-1999 Annual Report argues that differences in education is the most significant factor behind wage inequality in Latin America.