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.