Statistical Inference Of Variable Coefficient Spatial Autoregressive Fixed Effect Panel Data Mode

With the development of spatial econometrics,spatial panel data model has been widely used in many fields such as geography,meteorology,ecology and economics.The research on the spatial panel data model with linear relationship between explanatory variables and response variables has been relatively perfect,but the relationship between variables in real life is relatively complex,and few variables meet strict linear relationship.At this time,if the linear spatial panel data model is adopted again,the model will not be applicable.In order to adapt the model to more complex situations,more and more scholars have proposed a large number of non-parametric space panel models.The variable coefficient space autoregressive panel data model,as an extension of the ordinary linear space autoregressive panel data model,can be flexibly applied to the practical problems in which the explanatory variables and response variables are nonlinear.In recent years,it has received extensive attention and research.This paper studies the statistical inference of two types of nonparametric spatial autoregressive panel data models.The main innovations include the following three points:Firstly,we proposes a class of partial linear time-varying coefficient space autoregressive fixed effect panel data model in this paper,constructs the profile quasi-maximum likelihood estimation of this model based on the local linear smoothing method,and derives the asymptotic properties of the estimator under large samples.Finally,the effectiveness of the linear and nonlinear estimators for finite samples under different error distributions and spatial weight matrices is considered by Monte Carlo simulation.Secondly,we study two hypothesis tests for a class of time variable coefficient spatial autoregressive fixed effect panel data models.One is to test whether the spatial autocorrelation coefficient is 0,and the other is to test whether there are partial variable coefficients that are constants.Under the local linear smoothing method,profile quasi maximum likelihood estimates of parametric and non-parametric variables were obtained using the profile likelihood method.Based on the obtained estimates,two generalized likelihood ratio test statistics for hypothesis testing were constructed,and the p-value of the test was calculated using the Bootstrap method.Finally,Monte Carlo simulations were conducted on different error distributions and spatial autocorrelation coefficients under limited samples to verify the effectiveness of the testing method.Thirdly,in order to verify the wide application of the model proposed in this paper,we applies the model to the analysis of carbon emission data of 30 provinces in China(excluding Tibet,Hong Kong,Macao and Taiwan)from 2005 to 2016.It is found that the population size,per capita GDP and energy intensity are significantly positively correlated with carbon emissions,and the impact of population size and energy intensity on carbon emissions is increasing year by year,while the impact of per capita GDP on carbon emissions is decreasing year by year,It shows that the spatial autoregressive panel data model with timevarying coefficients is more practical in actual data.