Constrained Efficiency in a Risky Human Capital Model

This paper revisits the question whether capital in a competitive equilibrium is overaccumulated from the perspective of the social planner in an incomplete market economy with risky human capital accumulation. As in Dávila, Hong, Krusell and RíosRull (2012), we consider a constrained social planner who cannot complete markets, but can improve welfare by only internalizing how individual allocations affect prices. In a standard incomplete market economy with exogenous labor income shocks, Dávila et al. (2012) show that the pecuniary externalities tend to imply that capital in a competitive equilibrium is underaccumulated in economies with realistically high wealth inequality. We analytically show that by introducing risky human capital accumulation to this standard incomplete market model, the implication of pecuniary externalities can be overturned — the capital-labor ratio in a competitive equilibrium is likely to be too high from the perspective of the constrained planner. However, a quantitative investigation shows that an economy with human capital calibrated to match the inequalities of both wealth and earnings of the US still shows a capital-labor ratio lower than the optimal ratio. Introducing human capital does not overturn the quantitative result of Dávila et al. (2012) — underaccumulation of capital, but qualitatively, the result can be reversed.