Recursive equilibrium in endogenous growth models with incomplete markets

This paper analyzes the existence of recursive equilibria in a class of convex growth models with incomplete markets. Households have identical CRRA-preferences, production displays constant returns to scale with respect to physical and human capital, and all markets are competitive. There are aggregate productivity shocks that affect the aggregate returns to physical and human capital investment (stock returns and wages), and there are idiosyncratic shocks to human capital (idiosyncratic depreciation shocks) that only affect individual human capital returns. For a given history of aggregate shocks, these idiosyncratic human capital shocks are independently distributed over time and identically distributed across agents. Finally, households have the opportunity to trade assets in zero net supply with payoffs that depend on the aggregate shock, but markets are incomplete in the sense that there are no assets with payoffs depending on idiosyncratic shocks. It is shown that there exist recursive equilibria that are simple in the sense that equilibrium prices (returns) only depend on exogenous shocks. Moreover, the allocations associated with simple recursive equilibria are identical to the equilibrium allocations of an economy in which households live in autarky and face both aggregate and idiosyncratic risk.