Estimation and Inference for a Semiparametric Time-Varying Panel Data Model

This article introduces a new semiparametric panel data model that accounts for time-varying coefficients and aligns with recent advancements in factor models featuring nonparametric loading functions. We propose a profile marginal integration (PMI) method to jointly estimate the unknown quantities in a series of easily implementable steps. The asymptotic properties of these estimators are established. Additionally, we provide a hypothesis test to assess the validity of parametric model specifications in applied settings. Simulation studies and an empirical application on mutual fund returns are conducted to evaluate the finite sample performance of the proposed method. The empirical results suggest that traditional parametric methods, which ignore time variation, may lead to invalid inference.