Nonparametric Time-Varying Panel Data Models with Heterogeneity

Abstract

Since Bai (2009, Econometrica 77, 1229–1279), considerable extensions have been made to panel data models with interactive fixed effects (IFEs). However, little work has been conducted to understand the associated iterative algorithm, which, to the best of our knowledge, is the most commonly adopted approach in this line of research. In this paper, we refine the algorithm of panel data models with IFEs using the nuclear-norm penalization method and duple least-squares (DLS) iterations. Meanwhile, we allow the regression coefficients to be individual-specific and evolve over time. Accordingly, asymptotic properties are established to demonstrate the theoretical validity of the proposed approach. Furthermore, we show that the proposed methodology exhibits good finite-sample performance using simulation and real data examples.