Accuracy, Speed and Robustness of Policy Function Iteration

Abstract

Policy function iteration methods for solving and analyzing dynamic, stochastic general equilibrium models are powerful from both a theoretical and computational perspective. Despite obvious theoretical appeal, significant startup costs and a reliance on a grid-based method have limited the use of policy function iteration as a solution algorithm. We reduce these costs by providing a user-friendly suite of MATLAB functions that introduce multi-core processing and Fortran via MATLAB's executable function. We demonstrate why policy function iteration is particularly useful in solving models with regime-dependent parameters, recursive preferences, and binding constraints. We examine a canonical real business cycle model and a new Keynesian model that features regime switching in policy parameters, Epstein-Zin preferences, and monetary policy that occasionally hits the zero-lower bound to highlight the attractiveness of our methodology. We compare our advocated approach to other familiar computational methods, highlighting the tradeoffs between accuracy and speed.

Keywords: Policy Function Iteration, Zero-Lower Bound, Epstein-Zin preferences

JEL Classification: C63, C68, E52, E62