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

Author(s): Adrien Auclert, Bence Bardóczy, Matthew Rognlie and Ludwig Straub

Publication Date: July 2019

Keyword(s): Computational Methods, General Equilibrium, Heterogeneous Agent and linearization

Programme Area(s): Monetary Economics and Fluctuations

Abstract: 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.

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Bibliographic Reference

Auclert, A, Bardóczy, B, Rognlie, M and Straub, L. 2019. 'Using the Sequence-Space Jacobian to Solve and Estimate Heterogeneous-Agent Models'. London, Centre for Economic Policy Research. https://cepr.org/active/publications/discussion_papers/dp.php?dpno=13890