Panel Data Model With Variable Coefficients Statistical Inference

Statistical inference with panel data models is one of the mature and widely applied branches in statistics and econometrics. For a long time,however, its main theory is about the parametric regressions. Over the last two decades, with the improvement of computing facilities, some useful seiniparametric panel data models have been proposed to capture the underlying relationships between response variables and their associated covariates, examples include nonparametric panel data models, partially linear panel data models, varying coefficient panel data models.Firstly, this paper is concerned with the estimation and testing of a varying-coefficient fixed-effects panel data model. We first construct estimators of the fixed effects and varying coefficients functions by profile least-squares approach. Then we propose a test statistic which is based on comparing the residual sum of squares under null and alternative hypothesis in the problem of testing fixed effects. Secondly, partially linear varying coefficient fixed effects panel data models was discussed. We construct a profile least-squares estimator of the fixed effects, the parametric component and the nonparametric components. When some additional linear restrictions on the parametric component are available, we propose a restricted profile least-squares estimator for the model. Simulation studies are conducted to illustrate the proposed methods.