Simulations for models with heterogeneous agents, incomplete markets, real assets and aggregate uncertainty

This paper presents 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, 1 period real assets offered in zero net supply, aggregate uncertainty, incomplete markets and uncountable shocks. The results are robust to the presence of multiple discontinuous equilibria and are numerically implementable. We work on a Markov environment with an enlarged state space to characterize ergodic equilibria and differentiate them with respect to time-independent and stationary ones. We show, by imposing a mild restriction on the discontinuity set, that every measurable time-independent selection approximates the stochastic steady state of the model. The results in this paper are constructive and based on assumptions imposed on the primitives of the model. Thus, they can help to design calibration and estimation methods for heterogeneous agent models based on unconditional moments.