Estimation of Varying Coefficient Fixed Effects Models in Panel Data Based on Auxiliary Regression

In this paper, the auxiliary regression is introduced for the varying coefficient fixed effect models in panel data to explain the relationship between individual effects and covariates. We transform the varying coefficient models into partial linear varying coefficient models based on the auxiliary regression. In order to obtain the estimation of the function coefficient, the orthogonal projection and the local linear estimation method are used to eliminate the fixed effect, and estimate the function coefficient. Under some regular conditions, the asymptotic properties of the function coefficient estimation are given. Then, the finite sample property of the proposed estimation method is studied by the simulation. The simulation results show that no matter whether the individual effect is random or fixed, the proposed method is superior to the existing methods. Finally, the CD4 data of AIDS patients are analyzed.