Statistical Inference For Spatial Panel Autoregressive Model With Dependent Innovations

This paper studies Spatial Panel Autoregressive model,mainly involving the following two fields: the Spatial Econometrics and the structure of the Panel Data.Spatial Econometrics broke through the Gauss-Markov hypothesis in classical Econometrics and argues that the development of economy depends on its own conditions and the neighboring regions.This assumption makes the model more significant in theory and practice.However,the Spatial Panel Autoregressive model mainly focuses on the assumptions that with i.i.d,independent but heteroskedasticity and SAR disturbances at present,which it has limitations in practical applications.Information era shows various kinds of panel data constantly.Due to the augmentation of both the cross-sectional and the time dimension,the trend of obtaining Long-panel data sets and even Large-panel data sets is also unavoidable in the future.Then the problems are ensuing: time serial correlation and cross-section dependence.All in all,on the basis of summarizing the existing articles of Spatial Econometrics and Panel Econometrics,the problems elaborate in this paper can be divided into the following three parts:Firstly,when comes to the Spatial Panel Autoregressive model with endogeneity.Considering the endogenous problem caused by the spatial lag factor,this paper is based on the instrumental variables to deal with it.Secondly,when comes to the Spatial Panel Autoregressive model with time serial correlation.We propose moving block empirical likelihood method to adapt the error term which is an extremely generalized time serial process.The essential idea of moving block empirical likelihood is to treat the blocks as sampling units which preserve the dependence structure of the data,while between blocks and blocks remain asymptotically independent.Monte Carlo simulations show that the new proposed method allows the time dimension T is large(T = 200),but also to the case where the dimension T is small(T = 6).Finally,the new methods are applied to China's economic growth.Thirdly,when comes to the Spatial Panel Autoregressive model with both time serial correlation and cross-section dependence.In this paper,we base on the extended score vector of quadratic inference function to construct the moment equation,and then combines the extended score vector with the moving blocks empirical likelihood function to estimates the model.Monte Carlo simulations show that the new method is suitable for the case of T dimension.But even in the case of small T dimension,the new method still has more advantages.Finally,the new method is applied to PM2.5 pollution of Yangtze River Delta.