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

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 processes with time-varying components. 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 can lead 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