Estimation and Simultaneous Confidence Bands for Fixed-Effects Panel Data Partially Linear Models

Abstract

In this paper, we study the estimation and simultaneous confidence band (SCB) problems for fixed-effects panel data partially linear models. We remove the fixed effects and then obtain estimators for the parametric and nonparametric components, which do not depend on the fixed effects. We establish the asymptotic distribution of the maximum absolute deviation between the estimated nonparametric component and the true nonparametric component under some suitable conditions; hence, this result can be used to construct the simultaneous confidence band for the nonparametric component. Based on the asymptotic distribution, it becomes difficult to construct the simultaneous confidence band. The reason for this is that the asymptotic distribution involves estimators of the asymptotic bias and conditional variance, as well as the choice of bandwidth for estimating the second derivative of the nonparametric function. Clearly, this will result in a computational burden and accumulated errors. To overcome these problems, we propose a bootstrap method to construct the simultaneous confidence band. The Monte Carlo results indicate that the proposed bootstrap method exhibits better performance with limited samples. An empirical application is presented to evaluate the performance of the proposed method.

Keywords

• partially linear model
• simultaneous confidence band
• panel data
• fixed effects
• asymptotic property