Solving the Incomplete Markets Model With Aggregate Uncertainty: The Method of Mixtures

In this paper I propose a new method for computing equilibrium in economies featuring heterogeneous agents, incomplete markets and aggregate uncertainty. The new method approximates the endogenous joint distribution of wealth and income by replacing stochastic simulation procedures with iteration on distribution functions. By construction, the approximate distribution satisfies an intratemporal consistency condition that imposes stationarity on both the distribution and the law of motion for aggregate state variables. I show that the Method of Mixture Distributions is capable of obtaining a solution faster than existing computational algorithms while attaining a high level of accuracy. Lastly, I provide an extension of the algorithm for computing equilibrium in an economy with non-trivial market clearing, showing that the algorithm is suitable for computing models in which prices cannot be forecasted by a finite set of moments from the distribution.