Panel Data Models with Time-Varying Latent Group Structures

TL;DR

This paper introduces a novel method for estimating structural breaks and latent group structures in panel data models with interactive fixed effects, demonstrating high accuracy and practical applicability.

Contribution

It proposes a combined estimation approach using nuclear norm regularization and sequential testing to identify break points and latent groups in complex panel data models.

Findings

Accurate estimation of break points and group memberships with high probability

Asymptotic distributions for slope coefficient estimators established

Empirical analysis reveals structural breaks and group changes in US house prices

Abstract

This paper considers a linear panel model with interactive fixed effects and unobserved individual and time heterogeneities that are captured by some latent group structures and an unknown structural break, respectively. To enhance realism the model may have different numbers of groups and/or different group memberships before and after the break. With the preliminary nuclear-norm-regularized estimation followed by row- and column-wise linear regressions, we estimate the break point based on the idea of binary segmentation and the latent group structures together with the number of groups before and after the break by sequential testing K-means algorithm simultaneously. It is shown that the break point, the number of groups and the group memberships can each be estimated correctly with probability approaching one. Asymptotic distributions of the estimators of the slope coefficients are established. Monte Carlo simulations demonstrate excellent finite sample performance for the proposed estimation algorithm. An empirical application to real house price data across 377 Metropolitan Statistical Areas in the US from 1975 to 2014 suggests the presence both of structural breaks and of changes in group membership.