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

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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.

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  • Eva F. Janssens & Sean McCrary, 2023. "Finite-State Markov-Chain Approximations: A Hidden Markov Approach," Finance and Economics Discussion Series 2023-040, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:96642
    DOI: 10.17016/FEDS.2023.040
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    Cited by:

    1. Bence Bardóczy & Mateo Velásquez-Giraldo, 2024. "HANK Comes of Age," Finance and Economics Discussion Series 2024-052, Board of Governors of the Federal Reserve System (U.S.).

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    More about this item

    Keywords

    numerical methods; Kullback–Leibler divergence; misspecified model; earnings process;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models
    • D15 - Microeconomics - - Household Behavior - - - Intertemporal Household Choice; Life Cycle Models and Saving
    • E21 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Consumption; Saving; Wealth

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