Shrinkage Estimation and Identification of Latent Group Structures in Panel Data with Interactive Fixed Effects

This paper provides a framework for joint shrinkage estimation and identification of latent group structures in panel data models with interactive fixed effects and large number of explanatory variables. The latent structure of the model allows individuals to be classified into a number of groups where the number of groups and/or each individual’s group identity are unknown. A doubly penalized principal component estimation procedure using a pairwise fusion penalty and an adaptive LASSO (least absolute shrinkage and selection operator) penalty is introduced to detect the latent group structure and select the relevant regressors. To implement the proposed approach, an alternating direction method of multipliers algorithm has been developed. The proposed method is further illustrated by simulation studies and an empirical application of economic growth across various countries which demonstrate the good performance of the method.