固定效应面板数据部分线性模型的加权截面LSDV估计

摘要

本文考虑误差为自回归过程的固定效应面板数据部分线性回归模型的估计.对于固定效应短时间序列面板数据,通常使用的自回归误差结构拟合方法不能得到一个一致的自回归系数估计量.因此本文提出一个替代估计并证明所提出的自回归系数估计是一致的,且该方法在任何阶的自回归误差下都是可行的.进一步,通过结合B样条近似,截面最小二乘虚拟变量(LSDV)技术和自回归误差结构的一致估计,本文使用加权截面LSDV估计参数部分和加权B样条(BS)估计非参数部分,所得到的加权截面LSDV估计量被证明是渐近正态的,且比可忽略误差的自回归结构模型更渐近有效.另外,加权BS估计量被推导出具有渐近偏差和渐近正态性.模拟研究和实际例子相应地说明了所估计程序的有限样本性.%This paper concerns with the estimation of a fixed effects panel data partially linear regression model with the idiosyncratic errors being an autoregressive process.For fixed effects short time series panel data,the commonly used autoregressive error structure fitting method will not result in a consistent estimator of the autoregressive coefficients.Here we propose an alternative estimation and show that the resulting estimator of the autoregressive coefficients is consistent and this method is workable for any order autoregressive error structure.Moreover,combining the B-spline approximation,profile least squares dummy variable (PLSDV) technique and consistently estimated the autoregressive error structure,we develop a weighted PLSDV estimator for the parametric component and a weighted B-spline series (BS) estimator for the nonparametric component.The weighted PLSDV estimator is shown to be asymptotically normal and more asymptotically efficient than the one which ignores the error autoregressive structure.In addition,this paper derives the asymptotic bias of the weighted BS estimator and establish its asymptotic normality as well.Simulation studies and an example of application are conducted to illustrate the finite sample performance of the proposed procedures.