Empirical Likelihood Inference For Spatial Panel Data Models With Fixed Effects

Our economic behaviors or other human activities are affected by many factors.Due to the difference of geographical distribution and the change of time,the spatial panel data exists.There is a relationship between spatial data,and so it is not completely independent,namely the correla-tion.The traditional statistical analysis method is based on independent samples and large samples these two basic assumptions,if we use traditional statistical analysis method to tackle the problem of such data,it will obtain extremely inaccurate results.Luckily,the spatial panel data model is one of the important models to solve the problem.It takes spatial correlation and spatial heterogeneity into account on the basis of ordinary panel data model,and synthesizes the traditional time series methods,the cross section data methods and ordinary panel data models,and it can be widely used in a lot of aspects.In addition,Because of the correlation between spatial data,spatial weight matrix are introduced into spatial panel data models to depict the correlation,and get a more effec-tive estimator.Panel data has heterogeneity,scholars introduce individual effects into the model to control the items that do not change with time and then reflect space characteristics,and individual effects is divided into fixed effects and random effects.And scholars have studied spatial panel data models deeply.Empirical likelihood method,put forward by Owen under completely sam-ples,is a nonparametric statistical inference method,and its essence is maximizing the parameter likelihood ratio function under constraints.Empirical likelihood method has been widely used in various statistical models.In statistics,empirical likelihood is a popular research topic.According to the existing literatures,there are more literatures on spatial(dynamic)panel data models,such as GMM estimation,ML estimation and QML estimation,while it is little on the application of empirical likelihood method to the estimation of spatial panel data models.Thus,in this paper,we study empirical likelihood inference for spatial panel data models with fixed effects.The main content of this paper is divided into three chapters:The first chapter is the introduction,which briefly introduces the research background of the problem,the research overview of the spatial panel data models and the empirical likelihood method,and the main content of this paper.The second chapter introduces the definition of spatial panel data models,several definition methods of spatial weight matrix and spatial correlation tests.The third chapter is the main content of this paper,which discusses empirical likelihood inference for spatial panel data models with fixed effects,it constructs empirical likelihood ratio statistics of spatial panel data model parameters,and obtains that the limit distribution of statistics is chi-square distribution under some regular conditions.Innovations of this paper:1.The empirical likelihood inference of the spatial panel data models with fixed effects is studied,by using martingale difference sequence,the quadratic form in the estimation equation of the model is transformed into a linear form,and the empirical likelihood ratio statistics of the model parameters are constructed.2.It is proved that the limit distribution of empirical likelihood ratio statistics for spatial panel data models parameters with fixed effects is chi-square distribution.