Estimation and identification of latent group structures in panel data

This paper provides a framework for joint estimation and identification of latent group structures in panel data models using a pairwise fusion penalized approach. The latent structure of the model allows individuals to be classified into different groups where the number of groups and the group membership are unknown. The individuals within a group have common slope parameters, while parameter heterogeneity is allowed across the groups. A penalized least squares (PLS) approach is introduced for models with exogenous regressors. When the model contains endogenous regressors, a penalized generalized method of moment (PGMM) is introduced. To implement the proposed approach, an alternating direction method of multipliers algorithm has been developed. The proposed method is further illustrated by simulation studies which demonstrate the finite sample performance of the method, and is applied in an empirical analysis.