Estimation of fixed effects panel data partially linear additive regression models

In this paper, we investigate the estimation problem of fixed effects panel data partially linear additive regression models. Semi-parametric fixed effects panel data regression models are tools that are well suited to econometric analysis and the analysis of cDNA micro-arrays. By applying a polynomial spline series approximation and a profile least-squares procedure, we propose a semi-parametric least-squares dummy variables estimator (SLSDVE) for the parametric component and a series estimator for the non-parametric component. Under very weak conditions, we show that the SLSDVE is asymptotically normal and that the series estimator achieves the optimal convergence rate of the non-parametric regression. In addition, we propose a two-stage local polynomial estimation for the non-parametric component by applying the additive structure and the series estimator. The resultant estimator is asymptotically normal and the asymptotic distribution of each additive component is the same as it would be if the other components were known with certainty. We conduct simulation studies to demonstrate the finite sample performance of the proposed procedures and we also present an illustrative empirical application.