Identification of Latent Subgroups for Time-varying Panel Data Models

This paper introduces a time-varying panel data model that incorporates latent group structures, designed to tackle both individual heterogeneity and smooth structural changes over time. We develop an innovative centre-augmented K-power means (KPM) methodology that promotes convergence of subjects toward their respective cluster centers, enabling the identification of latent group structures without requiring prior knowledge of group composition. This approach delivers both superior precision and computational efficiency. We provide rigorous theoretical foundations, demonstrating estimation consistency, accurate subgroup identification, and consistent selection of the number of groups. The efficacy of the proposed KPM method in accurately identifying the latent group structures in panel data is demonstrated through comprehensive numerical analysis, including simulation studies and two real-world applications.