Semiparametric trending panel data models with cross-sectional dependence

A semiparametric fixed effects model is introduced to describe the nonlinear trending phenomenon in panel data analysis and it allows for the cross-sectional dependence in both the regressors and the residuals. A pooled semiparametric profile likelihood dummy variable approach based on the first stage local linear fitting is developed to estimate both the parameter vector and the nonparametric time trend function. As both the time series length T and the cross-sectional size N tend to infinity simultaneously, the resulting estimator of the parameter vector is asymptotically normal with a rate of convergence of Op(NT)1/2 . Meanwhile, the asymptotic distribution for the estimator of the nonparametric trend function is also established with a rate of convergence of Op(NTh)1/2. Two simulated examples are provided to illustrate the finite sample performance of the proposed method. In addition, the proposed model and estimation method is applied to analyze a CPI data set as well as an input-output data set. Cross-sectional dependence, nonlinear time trend, panel data, profile likelihood, semiparametric regression.