Identification and estimation in panel models with overspecified number of groups

We propose a simple and fast approach to identify and estimate the unknown group structure in panel models by adapting the M-estimation method. We consider both linear and nonlinear panel models where the regression coefficients are heterogeneous across groups but homogeneous within a group and the group membership is unknown to researchers. The main result of the paper is that under certain assumptions, our approach is able to provide uniformly consistent estimation as long as the number of groups used in estimation is not smaller than the true number of groups. We also show that, asymptotically, our method may partition some true groups into further subgroups, but cannot mix units from different groups. When the true number of groups is used in estimation, all units can be categorized correctly with probability approaching one, and we establish the limiting distribution for the estimators of the group parameters. In addition, we provide an information criterion to select the number of groups, and establish the consistency of the selection criterion under some mild conditions. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed method. The findings in the simulation confirm our theoretical results in the paper. Applications to two real datasets also highlight the necessity to consider both individual heterogeneity and group heterogeneity in the model.