Zhang Yuanqing
School of Finance and Business, Shanghai Normal University, No.100 Guilin Rd. Shanghai, 200234, P. R. China; Key Laboratory of Mathematical Economics (SUFE), Ministry of Education, Shanghai 200433, P. R. China; School of Statistics and Management, Shanghai University of Finance and Economics, Shanghai, 200433, P. R. China.
Reg Sci Urban Econ. 2015 Mar;51:37-46. doi: 10.1016/j.regsciurbeco.2015.01.003. Epub 2015 Jan 23.
This paper studies estimation of a partially specified spatial panel data linear regression with fixed-effects. Under the assumption of strictly exogenous regressors and strictly exogenous spatial weighting matrix, the unknown parameter is estimated by applying the instrumental variable estimation. Under some sufficient conditions, the proposed estimator for the finite dimensional parameter is shown to be root-N consistent and asymptotically normally distributed; The proposed estimator for the unknown function is shown to be consistent and asymptotically distributed as well, though at a rate slower than root-N. Consistent estimators for the asymptotic variance-covariance matrices of both estimators are provided. The results can be generalized to several spatial weighting matrice and spatial matrix which vary with time. The simulation results suggest that the proposed approach has some practical value.
本文研究了具有固定效应的部分指定空间面板数据线性回归的估计问题。在严格外生解释变量和严格外生空间权重矩阵的假设下，通过应用工具变量估计来估计未知参数。在一些充分条件下，所提出的有限维参数估计量被证明是根N一致的且渐近正态分布；所提出的未知函数估计量也被证明是一致的且渐近分布的，尽管其速率比根N慢。给出了这两个估计量渐近方差协方差矩阵的一致估计量。结果可以推广到几个随时间变化的空间权重矩阵和空间矩阵。模拟结果表明，所提出的方法具有一定的实用价值。
