  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.
