Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models
Adrien Auclert, Bence Bardóczy, Matthew Rognlie, Ludwig Straub
Econometrica · 2021 · Volume 89 · Issue 5
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 ofsequence-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.
Keywords
Computational methods, general equilibrium, heterogeneous agents, linearization
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