Endogenous Education and Long-Run Factor Shares

We study the determinants of factor shares in a neoclassical environment with capital- skill complementarity and endogenous education. When more physical capital raises the marginal product of skills relative to that of raw labor, an increase in a broad measure of embodied human capital raises the capital share in national income for any given rental rate. When education is chosen optimally, a dynamic equilibrium is characterized by an inverse relationship between the level of human capital and both the rental rate on capital and the difference between the interest rate and the growth rate of wages. As a consequence, estimates of the elasticity of substitution that fail to account for levels of human capital will be biased upward. We develop a model with overlapping generations, ongoing increases in educational attainment, and technology-driven neoclassical growth, and show that for a class of production functions with capital-skill complementarity, a balanced growth path exists and is characterized by an inverse relationship between the rates of capital- and labor-augmenting technological progress and the capital share in national income.