Improved estimation of fixed effects panel data partially linear models with heteroscedastic errors

Fixed effects panel data regression models are useful tools in econometric and microarray analysis. In this paper, we consider statistical inferences under the setting of fixed effects panel data partially linear regression models with heteroscedastic errors. We find that the usual local polynomial estimator of the error variance function based on residuals is inconsistent, and develop a consistent estimator. Applying this consistent estimator of error variance and spline series approximation of the nonparametric component, we further construct a weighted semiparametric least squares dummy variables estimator for the parametric and nonparametric components. Asymptotic normality of the proposed estimator is derived and its asymptotic covariance matrix estimator is provided. The proposed estimator is shown to be asymptotically more efficient than those ignoring heteroscedasticity. Simulation studies are conducted to demonstrate the finite sample performances of the proposed procedure. As an application, a set of economic data is analyzed by the proposed method.