Alternative Methods for Solving Heterogeneous Firm Models

I implement and compare five solution methods for a benchmark heterogeneous firms model with lumpy capital adjustment and aggregate uncertainty. The Krusell–Smith algorithm performs best within a group of methods using projection in the aggregate states. Another technique, Parameterization plus Perturbation, is much faster and performs best within a group of methods using perturbation in aggregates. However, projection and perturbation have nonoverlapping strengths and weaknesses. I highlight the resulting trade‐offs with several model extensions. I recommend that researchers apply projection methods to cases with large shocks or nonlinear dynamics, while cases with explicitly distributional channels at work favor perturbation.