  This paper develops a new model and estimation procedure for panel data that
allows us to identify heterogeneous structural breaks. We model individual
heterogeneity using a grouped pattern. For each group, we allow common
structural breaks in the coefficients. However, the number, timing, and size of
these breaks can differ across groups. We develop a hybrid estimation procedure
of the grouped fixed effects approach and adaptive group fused Lasso. We show
that our method can consistently identify the latent group structure, detect
structural breaks, and estimate the regression parameters. Monte Carlo results
demonstrate the good performance of the proposed method in finite samples. An
empirical application to the relationship between income and democracy
illustrates the importance of considering heterogeneous structural breaks.
