Estimation in partially linear time-varying coefficients panel data models with fixed effects

A partially time-varying coefficient time series panel data model with fixed effects is considered to characterize the nonlinearity and trending phenomenon in panel data model. To estimate the linear regression coefficient and the time-varying coefficient function, two methods are applied with the help of profile least squares. The first one is taking cross-sectional average to eliminate the fixed effects. The second one is local linear dummy variable approach. In each method we derive consistent estimates for both the parametric component and non-parametric trend function. The asymptotic distributions of the estimates are established when T and N tend to infinity simultaneously, where N is the cross section size, T is the time series length. The asymptotic results reveal that the parametric component (non-parametric coefficient function) estimate based on cross-sectional average has a rate of convergence T−12((Th)−12) that is slower than that based on local linear dummy variable approach, which is (NT)−12((NTh)−12), where h is the bandwidth. Furthermore, block bootstrap method is used to construct confidence interval for parametric and nonparametric components, respectively. At last, some simulation studies are conducted to examine the finite sample performance for the proposed methods and a real data example is analyzed.