HANK on Speed: Robust Nonlinear Solutions using Automatic Differentiation

Abstract

Building on automatic differentiation, I propose a solution method for heterogeneous agent models with many aggregate equations. Compared to existing methods, it allows to capture dynamics that deviate significantly from the steady state, and strong nonlinearities, including occasionally binding constraints. A powerful 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 apply this method to study a permanent shift in redistribution policy in a medium-scale two-asset HANK model featuring multiple 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.

Keywords: Heterogeneous agents, Computational methods, General equilibrium, Nonlinear systems

JEL Classification: C63, C32, E52, E47