Finite-State Markov-Chain Approximations: A Hidden Markov Approach

61 Pages Posted: 21 Jun 2022 Last revised: 18 May 2023

See all articles by Eva F. Janssens

Eva F. Janssens

Board of Governors of the Federal Reserve System

Sean McCrary

University of Pennsylvania

Date Written: May 17, 2023

Abstract

This paper proposes a novel finite-state Markov chain approximation method for Markov processes with continuous support, providing both an optimal grid and transition probability matrix. The method can be used for multivariate processes, as well as non-stationary processes such as those with a life-cycle component. The method is based on minimizing the information loss between a Hidden Markov Model and the true data-generating process. We provide sufficient conditions under which this information loss can be made arbitrarily small if enough grid points are used. We compare our method to existing methods through the lens of an asset-pricing model, and a life-cycle consumption-savings model. We find our method leads to more parsimonious discretizations and more accurate solutions, and the discretization matters for the welfare costs of risk, the marginal propensities to consume, and the amount of wealth inequality a life-cycle model can generate.

Keywords: Numerical methods, Kullback–Leibler divergence, life-cycle dynamics, earnings process

JEL Classification: C63, C68, D15, E21

Suggested Citation

Janssens, Eva and McCrary, Sean, Finite-State Markov-Chain Approximations: A Hidden Markov Approach (May 17, 2023). Available at SSRN: https://ssrn.com/abstract=4137592 or http://dx.doi.org/10.2139/ssrn.4137592

Eva Janssens

Board of Governors of the Federal Reserve System ( email )

20th and C Streets, NW
Washington, DC 20551
United States

Sean McCrary (Contact Author)

University of Pennsylvania ( email )

Philadelphia, PA 19104
United States

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