Nonlinear Approximate Aggregation in Heterogeneous Agent Models ∗

The paper deals with the computation of DSGE models with a large number (or continuum) of heterogenous agents and incomplete markets. Solving this model requires approximate aggregation, representing the cross-sectional distribution by a finite number of state variables. In the existing literature, people compute nonlinear solutions with a very low-dimensional state vector, or a high-dimensional approximation where the solution is linear in aggregate states. This paper shows how to compute precise higher-order approximations with a medium-dimensional state vector. This is made possible by using a backward induction algorithm that exploits the information obtained from the high-dimensional linear solution. A quadratic approximation with up to 15 state variables can be computed in a few minutes on a PC, running Matlab.