Incorporating Prior Information in Latent Structures Identification for Panel Data Models

In this paper, we explore the latent structures for panel data models in presence of available prior information. The latent structure in panel models allows individuals to be classified into several distinct groups, where the individuals within the same group share the same slope parameters, while the group-specific parameters are heterogeneous. To incorporate the prior information, we design a new alternating direction method of multipliers (ADMM) algorithm based on the pairwise group fused Lasso penalty approach. The asymptotic properties and the convergence of ADMM algorithm are well established. Simulation studies demonstrate the advantages of the proposed method over existing methods in terms of both estimation efficiency and detection accuracy. We illustrate the practical utility of the proposed procedure by analyzing the relationship between electricity consumption and GDP in China.