Near-Rational Equilibria in Heterogeneous-Agent Models: A Verification Method

Leonid Kogan and Indrajit Mitra
Working Paper 2021-16
June 2021

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Abstract: We propose a general simulation-based procedure for estimating the quality of approximate policies in heterogeneous-agent equilibrium models, which allows verification that such approximate solutions describe a near-rational equilibrium. Our procedure endows agents with superior knowledge of the future path of the economy, while imposing a suitable penalty for such foresight. The relaxed problem is more tractable than the original, and it results in an upper bound on agents’ welfare. Our method is general and straightforward to implement, and it can be used in conjunction with various solution algorithms. We illustrate our approach in two applications: the incomplete-markets model of Krusell and Smith (1998) and the heterogeneous firm model of Khan and Thomas (2008).

JEL classification: E24, E62, J22

Key words: numerical solutions, accuracy, approximations, simulations

The authors thank Santiago Bazdresch (discussant), Jack Favilukis (discussant), Ken Judd, Aubhik Khan, Jonathan Parker, Tony Smith (discussant), Julia Thomas, and seminar participants at City University of Hong Kong, Hong Kong University, INSEAD, MIT, Nanyang Technological University, Ohio State University, UC Berkeley, UCLA, University of Michigan, and the Duke AP conference, Minnesota Macro-Asset Pricing conference, MIT Capital Markets Workshop, Society for Economic Dynamics Annual Meeting, SITE Stanford, and the Western Finance Association Meeting for comments. They thank Anton Petukhov for excellent research assistance. The views expressed here are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Indrajit Mitra, Federal Reserve Bank of Atlanta, 1000 Peachtree St. NE, Atlanta, GA 30309, and Leonid Kogan, MIT Sloan and the National Bureau of Economic Research.

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