Intergenerational mobility, composition of human capital and distance to frontier

An economy can improve its technology level through two channels -- imitating from the world technology frontier and innovating on its own technology level -- innovation being more skilled-intensive than imitation. I develop a growth model based on the endogenous ability-driven skill acquisition decision of an individual in an imperfect credit market. It is shown that there exists a constant level of skilled and unskilled human capital in the imitation-only and innovation-only regimes. In the imitation-innovation regime stock of skilled human capital rises whereas that of unskilled human capital falls in the imitation-innovation regime. Also, both skilled and unskilled human capital shift from imitation to the innovation activity as an economy progresses. Moreover, growth rate falls in the imitation-only regime. But in the diversified regime growth rate rises even if it falls initially and there exists constant level of growth rate in the innovation-only regime. In the long run all the economies will converge to the world technology frontier and grow at a same rate. In the imitation-only and innovation-only regimes, there exists constant level of upward and downward mobility. However, in the diversified regime both upward and downward mobility falls as an economy progresses to the frontier. Along with that, I show that wage rate and average income of both skilled and unskilled human capital falls in the imitation-only regime and the same rises in the innovation-only regime. However, wage rate and average income of skilled human capital rises and unskilled human capital falls in the diversified regime. Also, there exists constant level of between group income inequality in the imitation-only and innovation-only regimes. However, wage and income inequality between skilled and unskilled human capital rises as an economy bridges its gap from the world technology frontier. There exists constant level of income inequality within skilled and unskilled human capital due to parental income differences and due to difference in cognitive ability, in the imitation-only and innovation-only regime. On the other hand, income inequality within skilled and unskilled human capital rises due to parental income differences and due to difference in cognitive ability, in the imitation-innovation regime.