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 semiparametric profile likelihood approach based on the first-stage local linear fitting is developed to estimate both the parameter vector and the time trend function. As both the time series length T and the cross-sectional size N tend to infinity simultaneously, the resulting semiparametric estimator of the parameter vector is asymptotically normal with an optimal rate of convergence. Meanwhile, an asymptotic distribution for the estimate of the nonlinear time trend function is also established with also an optimal rate of convergence. Two simulated examples are provided to illustrate the finite sample behavior of the proposed estimation method. In addition, the proposed model and estimation method is applied to the analysis of two sets of real data