Solving an incomplete markets model with a large cross-section of agents

This paper shows that perturbation methods can be applied to a DSGE model with incomplete markets and a finite but arbitrarily large number of heterogeneous agents. We develop a simple but general solution technique that handles many state and choice variables for each agent and thus has an extremely high-dimensional state space. The method is based on perturbations around a point at which the solution is known. The novel idea is to exploit the symmetry of the problem to overcome the curse of dimensionality. We use the analysis to demonstrate the impact of heterogeneity on macroeconomic quantities and the pricing of risk. Furthermore, we set our technique apart from standard methods used in the literature.