A method for solving and estimating heterogeneous agent macro models

I develop a computational method for solving and estimating heterogeneous agent macro models with aggregate shocks. The main challenge is that the aggregate state vector contains the distribution of agents, which is typically infinite-dimensional. I approximate the distribution with a flexible parametric family, reducing its dimensionality to a finite set of endogenous parameters, and solve for the dynamics of these endogenous parameters by perturbation. I implement the method in Dynare and show that it is fast, general, and easy to use. As an illustration, I use the method to perform a Bayesian estimation of a heterogeneous firm model with aggregate shocks to neutral and investment-specific productivity. I find that the behavior of investment at the firm level quantitatively shapes inference about the aggregate shock processes, suggesting an important role for micro data in estimating DSGE models.