Structure Identification in Panel Data Analysis

Panel data analysis is an important topic in statistics and econometrics. In such analysis, it is very common to assume the impact of a covariate on the response variable remains constant across all individuals. While the modelling based on this assumption is reasonable when only the global effect is of interest, in general, it may overlook some individual/subgroup attributes of the true covariate impact. In this paper, we propose a data driven approach to identify the groups in panel data with interactive effects induced by latent variables. It is assumed that the impact of a covariate is the same within each group, but different between the groups. An EM based algorithm is proposed to estimate the unknown parameters, and a binary segmentation based algorithm is proposed to detect the grouping. We then establish asymptotic theories to justify the proposed estimation, grouping method, and the modelling idea. Simulation studies are also conducted to compare the proposed method with the existing approaches, and the results obtained favour our method. Finally, the proposed method is applied to analyse a data set about income dynamics, which leads to some interesting findings.