Neoclassical Growth with Limited Commitment

This paper characterizes the stationary equilibrium of a continuous-time neoclassical production economy with capital accumulation in which agents can insure against idiosyncratic income risk by trading agent-shock contingent assets, subject to limited commitment constraints that rule out selling these assets short. For a general N-state Poisson labor productivity process we characterize the optimal consumption-asset allocation, the stationary asset distribution as well as the aggregate supply of capital by the household sector. For the special case in which production is Cobb-Douglas, agent labor productivity takes two values, one of which is zero, and agents have log-utility, we solve the equilibrium interest rate, capital stock and the consumption distribution in closed form. The paper therefore provides a tractable alternative to the standard incomplete markets general equilibrium model as in Aiyagari (1994).