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Econometrica Vol. 89 No. 5 2021

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

Adrien Auclert1,2,3; Bence Bardóczy4; Matthew Rognlie5,3; Ludwig Straub6,3

1 Department of Economics, Stanford University · 2 CEPR , · 3 NBER · 4 Federal Reserve Board of Governors · 5 Department of Economics, Northwestern University · 6 Department of Economics, Harvard University

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.

DOI
10.3982/ecta17434
Volume
89
Issue
5
Pages
2375-2408
Language
en
Sources
bibtex:phds-export.bib openalex crossref

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