Non-parametric time-varying coefficient panel data models with fixed effects

Abstract

This paper is concerned with developing a non-parametric time-varying coefficient model with fixed effects to characterize non-stationarity and trending phenomenon in a non-linear panel data model. We develop two methods to estimate the trend function and the coefficient function without taking the first difference to eliminate the fixed effects. The first one eliminates the fixed effects by taking cross-sectional averages, and then uses a non-parametric local linear method to estimate both the trend and coefficient functions. The asymptotic theory for this approach reveals that although the estimates of both the trend function and the coefficient function are consistent, the estimate of the coefficient function has a rate of convergence of (Th)−1/2, which is slower than (NTh)−1/2 as the rate of convergence for the estimate of the trend function. To estimate the coefficient function more efficiently, we propose a pooled local linear dummy variable approach. This is motivated by a least squares dummy variable method proposed in parametric panel data analysis. This method removes the fixed effects by deducting a smoothed version of cross-time average from each individual. It estimates both the trend and coefficient functions with a rate of convergence of (NTh)−1/2. The asymptotic distributions of both of the estimates are established when T tends to infinity and N is fixed or both T and N tend to infinity. Both the simulation results and real data analysis are provided to illustrate the finite sample behaviour of the proposed estimation methods.