Optimal Saving and Work Hours in the Heterogeneous Agent Neoclassical Growth Model

This paper introduces work - leisure choice into a constrained optimal policy problem in a neoclassical growth model with idiosyncratic risk and incomplete markets. The constrained planner cannot complete markets, but must improve welfare subject to agents’ budget constraints. As such, rather than addressing the market failure of incomplete markets, the planner addresses the pecuniary externalities of each agents’ saving and work decision on interest and wage rates. In an economy calibrated to U.S. wealth and income inequality, the paper finds the constrained planner increases aggregate capital and reduces aggregate hours worked. The resulting increase in wages and fall in interest rates shifts the distribution of consumption towards the consumption poor, since they rely more on labor income than capital income. However, in a constrained efficient allocation, only highly productive individuals increase saving, while less productive individuals reduce saving. Moreover, only the asset poor and less productive agents reduce work hours; the wealthy and highly productive increase work hours due to wealth effects. While total work hours fall, the increase in work hours by the most productive is sufficient to increase effective labor supply.