An algorithm to solve heterogenous agent models with aggregate uncertainty

General equilibrium models with heterogeneous agents are very difficult to solve because the wealth distribution, a multidimensional and infinite object, must be part of the state space. Krussell and Smith propose a numerical solution where the wealth distribution is summarized by its first moment. However, the volatility of equity in their model is unrealistically low. I show that markets do not clear in a model with more realistic volatility if the wealth distribution is summarized by its first moment only. I propose an alternate algorithm where the wealth distribution is summarized by a finite set of probability density functions which come from simulating the model. This algorithm can solve both the Krussell and Smith model, as well the more volatile version.