Grouped heterogeneity in Markov-switching panel models

Grouped heterogeneity has become a popular way of characterizing heterogeneity in panel data. Similarly, regime-switching is often used to parsimoniously characterize instability of economic relationships. In this paper, we combine both features in a single panel data model. Our panel model contains per individual a separate finite-state Markov process with different coefficients per regime. We consider different ways of grouping, ranging from grouping coefficients only and leaving the regimes unrestricted, to grouping the latent regimes and coefficients at the same time. We propose a two-step estimation procedure that combines the grouped fixed effects approach with the Expectation-Maximization algorithm. We show that our estimators for the slope coefficient and the group membership structure are consistent, also when the regimes follow a latent Markov process. Our Monte Carlo simulations demonstrate good finite sample performance of the proposed procedure, even when some assumptions are relaxed. We apply our methods to examine similarities in business cycle patterns across the U.S. states.