DP13890 Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models

Author(s):	Adrien Auclert, Bence Bardóczy, Matthew Rognlie, Ludwig Straub
Publication Date:	July 2019
Date Revised:	November 2020
Keyword(s):	Computational Methods, General Equilibrium, Heterogeneous Agent, linearization
JEL(s):	C63, E21, E32
Programme Areas:	Monetary Economics and Fluctuations
Link to this Page:	cepr.org/active/publications/discussion_papers/dp.php?dpno=13890

Abstract We propose a general and highly efficient method for solving and estimating general equilibrium heterogeneous-agent models with aggregate shocks in discrete time. Our approach relies on the rapid computation of sequence-space Jacobians-the derivatives of perfect-foresight equilibrium mappings between aggregate sequences around the steady state. Our main contribution is a fast algorithm for calculating Jacobians for a large class of heterogeneous-agent problems. We combine this algorithm with a systematic approach to composing and inverting Jacobians to solve for general equilibrium impulse responses. We obtain a rapid procedure for likelihood-based estimation and computation of nonlinear perfect-foresight transitions. We apply our methods to three canonical heterogeneous-agent models: a neoclassical model, a New Keynesian model with one asset, and a New Keynesian model with two assets.