Abstract

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.