Nonparametric Time-Varying Coefficient Panel Data Models with Fixed Effects

This paper is concerned with developing a nonparametric time-varying coefficient model with fixed effects to characterize nonstationarity and trending phenomenon in nonlinear panel data analysis. 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 nonparametric local linear approach to estimate the trend function and the coefficient function. 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 an optimal rate of convergence that is slower than that of the trend function, which also has an optimal rate of convergence. 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 the trend function and the coefficient function with an optimal rate of convergence. 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. Simulation results are provided to illustrate the finite sample behavior of the proposed estimation methods