Research On Identification Of Optimal Instrumental Variables And Likelihood Ratio Test Of Partial Linear Spatial Autoregressive Models

Partial linear spatial autoregressive models combine the flexibility of semi-parametric models for the selection of variables and the effective interpretation of spatial autoregressive models for spatial geographical factors.In the era of data diversification,they have been widely used in various fields of economic policy analysis,especially in the fields where there is strong autocorrelation spatial data such as economics,regional science and geography.Therefore,the statistical inference of partial linear spatial autoregressive models has strong theoretical value and practical application value.When spatial autoregressive term is considered as model covariate,their own structure can lead to endogenous problem in the data,leading to the loss of consistency in the estimations of model parameters obtained using classical ordinary least squares method.Starting from this issue,this paper first discusses the problem of parameter estimation of partial linear spatial autoregressive models.Aiming at the endogenous problem of model spatial autoregressive term,the identification of optimal instrumental variables of model spatial autoregressive term is explored by constructing an auxiliary regression model and combining with penalty regression estimation technology.At the same time,combined with the nonparametric kernel estimation method,the kernel estimations of the parametric and nonparametric parts of the partial linear spatial autoregressive models are obtained.Through a numerical simulation study,the robustness and effectiveness of the parameter estimations of the adjusted model based on the identification of optimal instrumental variables are verified.Then we discuss the problem of parameters test of partial linear spatial autoregressive models.Combining the optimal instrumental variables identification and the B-spline estimation technology,we construct a test statistic based on the model likelihood ratio function for the significance of the model parameters on the premise of obtaining the model parameter estimations.At the same time,because the complexity of the test statistic construction leads to the unknown distribution parameters,the test value cannot be directly obtained.In view of this problem,considering that Bootstrap method is not significant for the overall distribution,this paper discusses a method for calculating the model test p-value of Bootstrap method based on the model residual,and verifies the validity and robustness of the model hypothesis research method under different residual distributions through a numerical simulation study.Finally,combined with the relevant empirical data of economic growth and foreign trade in various provinces and regions in China,the partial linear spatial autoregressive model based on the identification of optimal instrumental variables is successfully constructed,and the results of the model parameter significance test based on Bootstrap method are given.Based on the analysis of the model results,relevant policy recommendations are given,and expanding the application scope and value of partial linear spatial autoregressive models.