Variable Selection For Spatial Regression Models With Panel Data

The rapid development of information technology has ushered in the sharp expansion of data volume.These data bring massive information,but also carry a lot of redundant information,leading to more prominent uncertainty of models.Therefore,it is one of hot topics about how to make good use of existing data,eliminate redundant information,and select significant variables from a large number of variables to build statistical models in the academic field.Spatial regression models are the main empirical models of spatial econometrics.They can describe the spatial dependence of data,explain the spatial aggregation and spillover effect,and have important value for understanding the spatial transmission mechanism between regions.Although the theory of spatial regression models has been continuously developed and improved in the past 40 years,most of the researches still stay in the discussion of traditional estimation and statistical inference methods,and the research on variable selection is relatively lagging behind,which has been unable to meet the further needs of empirical application objectively.Based on the above considerations,this paper makes a profound study on the variable selection problems of spatial regression model with fixed effects,spatial regression model with random effects,spatial quantile autoregressive model with fixed effects,and spatial quantile autoregressive model with random effects,which has important theoretical significance and practical value.The main research contents and conclusions are summarized in the following three aspects:First,the study of variable selection for the spatial regression model with fixed effects and spatial regression model with random effects.Under the setting of the spatial regression model with fixed effects,the paper eliminates the fixed effects through a transformation method in order to avoid the problem of redundant parameters with the increase of the sample size.Then the penalized quasi-likelihood function of the model is presented by combining the quasi-likelihood function and SCAD penalty function to realize variable selection.Under the setting of the spatial regression model with random effects,although the structure of quasi-likelihood function is more complicated,the problem of redundant parameters no longer occurs.The quasi-likelihood function and SCAD penalty function are used directly to construct the penalized quasi-likelihood function of the model to realize variable selection.In order to select variables and identify spatial effects effectively,the regression coefficients and spatial autoregression coefficients are penalized differently On the basis of the above work,the paper also designs a new algorithm to solve the non-convex optimization problem of the objective function for both models,and gives the BIC information criteria to deal with the selection of the adjustment parameters in the penalty function.Under certain regular assumptions,it is proved that the constructed penalized estimators are consistent,sparse and asymptotically normal The numerical simulation results show that the penalized quasi-likelihood function methods perform well in the finite samples,and the accuracy of variable selection increases with the increase of sample size.It has the characteristics of spatial effects identification,independent variables selection and unknown parameters estimation,which is consistent with the theoretical results.In addition,the simulation results are less affected by different spatial effects and spatial weight matrices,and exhibit good robustnessSecond,the study of variable selection for the spatial quantile autoregressive model with fixed effects and the spatial quantile autoregressive model with random effects.Under the setting of spatial quantile autoregressive model with fixed effects,the quantile instrumental variable method is used to solve the endogenous problem of the model,and penalized quantile regression loss function is constructed to realize variable selection by the adaptive LASSO penalty method.In order to improve the effect of model estimation under the setting of spatial quantile autoregressive model with random effects,the paper investigates the role of random effects from the view of Bayesian,and then combines quantile instrumental variable method and quantile regression loss function to construct an adaptive LASSO penalty method to achieve variable selection.Similarly,in order to effectively select variables and identify spatial effects,the regression coefficients and spatial autoregression coefficient are penalized differently.Based on the above,a new algorithm is designed to solve the optimization problem of the objective function for both models,and the BIC information criteria are given to deal with the selection of the adjustment parameters in the penalty function.Under certain regular assumptions,it is proved that the constructed penalized estimators are consistent,sparse and asymptotically normal.The numerical simulation results show that the adaptive LASSO penalty methods perform well in the finite sample environment,and the accuracy of variable selection increases with the increase of sample size.It has the characteristics of spatial effect identification,independent variables selection and unknown parameters estimation,which is consistent with the theoretical results.In addition,the simulation results are less affected by the change of quantile,spatial effect,spatial weight matrix and disturbance term,showing strong robustness.Third,based on the relevant data of domestic provinces from 2007 to 2017,this paper studies the impact of climate and production conditions on agricultural net income according to the proposed variable selection methods of the spatial regression models for panel data.The empirical results show that there is a significant spatial correlation between the agricultural net income of different provinces in China,and the impact of rural per capita electricity consumption and disaster area can be ignored.There are positive effects for water resources per capita,fertilizer application per unit area and average temperature.At low quantiles,the impact of water resources per capita is not obvious,and the impact of fertilizer application per unit area,agricultural mechanization and population density is relatively large.With the increase of quantile,the role of water resources per capita has increased significantly,while the effects of agricultural mechanization,population density and average temperature have decreased gradually.