Inequality and Aggregate Uncertainty In Heterogeneous Agent Models

We develop a numerical method for performing second, and in principle higher, order approximations of equilibrium policy rules in models with heterogeneous agents and occasionally binding constraints. In a version of the Krusell and Smith (1998), we show that the higher order approximation robustly produces errors which are an order of magnitude smaller than a first order approximation. The higher order approximation generates policy rules that depend on the level of aggregate risk, which allows us to study the response of economic variables to changes in the level of aggregate uncertainty. The impulse response to an increase in uncertainty over the growth rate of TFP in a model with heterogeneous households generates nearly twice the welfare losses in asset poor compared to asset rich households.