HANK on speed: Robust nonlinear solutions using automatic differentiation

Abstract

Building on automatic differentiation, I propose a robust and efficient solution method for perfect-foresight transition dynamics in heterogeneous agent models with many aggregate equations. Compared with existing methods, it allows to capture strong nonlinearities, including, e.g., occasionally binding constraints, and dynamics that deviate significantly from the steady state. A powerful and user friendly open-source reference implementation is provided, which efficiently computes nonlinear solutions to the canonical HANK model within seconds, including the transition dynamics of the full distribution. I challenge this method by studying a permanent shift in redistribution policy in a medium-scale two-asset HANK model featuring many aggregate frictions. The results indicate that, as firms seek to deplete their capital stock, the transition path is characterized by a prolonged deflationary episode, the severity of which depends on the interaction between nonlinear constraints, such as the interest rate lower bound and downward nominal wage rigidity.