Semi-parametric inference for semi-varying coefficient panel data model with individual effects

We study a semi-varying coefficient panel data model with unobserved individual effects, where all the covariates are high-dimensional variables. Based on multivariate local linear fitting, the transformation technique and the profile likelihood method, we establish semi-parametric fixed effects estimators, semi-parametric random effects estimators, and their asymptotic properties. We also introduce a test for discriminating between a semi-varying coefficient random effects panel data model and a semi-varying coefficient fixed effects panel data model. The critical values are estimated by a bootstrap procedure. Monte Carlo studies exhibit the finite-sample performance of the proposed estimators and test statistics. Simulation results show that the methods perform well for moderate sample sizes. Finally, we analyze the cigarette consumption panel data from 46 American states covering the period 1963-1992.