Difference-based estimation and model identification for panel data semiparametric models with cross-section dependence

In this article, we consider a panel data partially linear regression model with fixed effect and non parametric time trend function. The data can be dependent cross individuals through linear regressor and error components. Unlike the methods using non parametric smoothing technique, a difference-based method is proposed to estimate linear regression coefficients of the model to avoid bandwidth selection. Here the difference technique is employed to eliminate the non parametric function effect, not the fixed effects, on linear regressor coefficient estimation totally. Therefore, a more efficient estimator for parametric part is anticipated, which is shown to be true by the simulation results. For the non parametric component, the polynomial spline technique is implemented. The asymptotic properties of estimators for parametric and non parametric parts are presented. We also show how to select informative ones from a number of covariates in the linear part by using smoothly clipped absolute deviation-penalized estimators on a difference-based least-squares objective function, and the resulting estimators perform asymptotically as well as the oracle procedure in terms of selecting the correct model.