Estimation of a break point in group membership structure

This paper considers linear panel data models with a grouped pattern of heterogeneity when the latent group membership structure and/or the values of slope coeffcients change at a break point. We propose a least squares approach to jointly estimate the break point, group membership structure, and coeffcients. The proposed estimators are consistent, and the asymptotic distribution of the coeffcient estimators is identical to that under known break point and group structure even when the cross-sectional sample size is much larger than the length of time series. Monte Carlo simulations and an empirical example illustrate the use of the approach and associated inference.