时变系数空间自回归面板数据模型的极大似然估计

The Maximum Likelihood Estimation of Time-varying Coefficient Spatial Autoregression Panel Data Model

本文对扰动项存在跨时期的异方差、但不存在序列相关的时变系数空间自回归模型提出了极大似然的估计方法,并证明了该估计量的一致性,同时,证明了该估计量渐进服从正态分布,由此说明该估计量具有优良的大样本性质。同时,我们还对本文所提出估计量的小样本性质进行了数值模拟。本文研究表明,估计量虽然在N较小时偏差较大,但是随着N的不断增加,估计量偏差减小,体现了比较优良的渐进性质。同时,估计量的偏差会随着时期数的增加而变大,这说明本文所提出的估计方法适用于个体数较多、时期数较少的短面板数据。

This paper researches the time-varying coefficient spatial autoregression panel data model, whose error has heteroseedasticity over time but without time serial correlation. This paper proposes a maximum likelihood estimation （MLE） for this model and proves the consistency and asymptotic normality of this MLE method, which testifies the favorite large sample properties of the MLE method. Meanwhile, we use Monte Carlo method to simulate the small properties of the MLE method, which shows that the estimator has large bias when N is small while the bias becomes smaller and smaller over the growth of N. Furthermore, we also find that the bias will increase over the growth of T, which shows that the MLE method is more suitable for the short panel data with small T and large N.