Model detection and estimation for varying coefficient panel data models with fixed effects

In this paper, we study the model detection and estimation for varying coefficient panel data models with fixed effects. We first propose a data transformation approach to eliminate fixed effects. Then, using the basis function approximations and the group SCAD penalty, we develop a combined penalization procedure to select the significant covariates, detect the true structure of the model, i.e., identify the nonzero constant coefficients and the varying coefficients, and estimate the unknown regression coefficients simultaneously. Under some mild conditions, we show that the proposed procedure can identify the true model structure consistently, and the penalized estimators have the oracle properties. At last, we illustrate the finite sample performance of the proposed methods with some simulation studies and a real data application.