Incomplete Markets, Transitory Shocks And Welfare

Equilibrium allocations in models with incomplete markets are generally not Pareto-efficient, but some argue that the welfare losses from missing assets are small when time-horizons are long, agents are patient, and shocks are transitory. We show that even in the simplest infinite horizon model without aggregate uncertainty welfare losses can be substantial and do not disappear when agents become more patient. Our argument has two parts. First, we argue that in dynamic models the persistence of income shocks should increase when the length of a period in the model decreases. This is necessary to maintain realistic properties for the serial correlation in annual income. We show computationally that in this case, the welfare losses from incomplete markets remain constant even as we reduce the model period. Second, we reexamine the analysis in Levine and Zame (1999). They claim that the incomplete market welfare converges to the complete market welfare as the discount factor converges to one. We show that this critically relies on their implicit assumptions regarding debt constraints, and that there is no convergence with more realistic debt constraint assumptions.