Three Essays on Panel Structure Models

In panel structure models, individuals can be classified into different groups with the slope parameters being homogeneous within the same group but heterogeneous across groups, both the number of groups and each individual’s group membership are unknown. This dissertation proposes some methods to identify the panel structure models under different specifications, namely, developing a Lasso-type Panel-CARDS method in the linear panel, constructing two sequential binary segmentation algorithms in the nonlinear panel, and using K-means algorithm in the spatial panel. Chapter 2 studies the estimation of a linear panel data model with latent structures. To identify the unknown group structure of vector parameters, we design an algorithm called Panel-CARDS which is a systematic extension of the CARDS procedure proposed by Ke, Fan, and Wu (2015) in a cross-sectional framework. Chapter 3 proposes a procedure to identify latent group structures in nonlinear panel data models. Chapter 4 considers the identification of latent group structures in dynamic spatial models with interactive fixed effects. The model treats three kinds of heterogeneity at the same time, namely, the spatial heterogeneity, individuals’ heterogeneous responses to the same time factors, and heterogeneous slope coefficients.