Simulations in Models with Heterogeneous Agents, Incomplete Markets and Aggregate Uncertainty

This paper present conditions to guarantee the convergence of simulations to a stochastic steady state, characterized by an invariant probability distribution, in an endowment economy with a finite number of heterogeneous agents, aggregate uncertainty and uncountable shocks. The results are robust to the presence of multiple discontinuous equilibria and do not require ad-hoc convexification techniques, like "sunspots". Thus, our results are numerically implementable. We work on a Markov environment with an enlarged state space, applied to an incomplete markets model, to characterize ergodic equilibria and differentiate them with respect to time-independent, and stationary ones. We show that, by imposing a mild restriction on the discontinuity set, every measurable time-independent selection can be used to approximate the stochastic steady state of the model. Considering the common practice of clustering agents according to, for instance, deciles of the wealth and assuming uncountable income shocks, the results in this paper can help to design calibration and estimation methods for heterogeneous agent models based on unconditional moments.