Multiple Heterogeneous Structural Breaks Models and Estimation Methods for Panel Data Analysis

T his paper introduces three panel data models and their estimation methods that take heterogeneous structural breaks in the slope coefficients into consideration. Despite the fact that many empirical studies in various domains suggest the effects of certain factors may be unstable and different across clusters, not many studies have considered the development of such techniques in panel data analysis. Thus, this paper seeks to fill this gap. We model the heterogeneities through a latent group structure and consider both the case of a static group pattern and the case when the group pattern changes after each break. For the static group case, we introduce the grouped adaptive group fused lasso (GAGFL) algorithm with a penalized least squares (PLS) method to estimate the exogenous model, and propose the incorporation with a penalized GMM (PGMM) method to estimate the endogenous model. To deal with the dynamic group pattern, we propose the dynamically grouped heterogeneous structural breaks (DGHB) estimation method. Through two sets of Monte Carlo simulations, we demonstrate that our methods give high accuracy in classifications, breaks detections and coefficients estimations. We further apply our GAGFL with PGMM method to investigate the effect of foreign direct investment (FDI) inflow on economic growth. The new evidence we obtained in this application confirms the usefulness of our methods in empirical studies.