空间变系数地理加权自回归模型的局部GMM估计

Local GMM Estimation in Spatial Varying Coefficient Geographically Weighted Autoregressive Model

近年来,空间数据的分析与建模得到了广泛关注和重视。空间自相关性和空间异质性是空间数据最重要的两类性质。现有研究大都是单独分析这两类特性。在空间自回归模型和地理加权回归模型的基础上,研究了一类空间变系数地理加权回归模型,该模型将普通的空间自回归模型的空间滞后参数和回归系数都设置成空间变系数,既考虑了空间自相关性,又反映了空间异质性。因为,空间变系数地理加权自回归模型是一类具有内生变量的变系数模型,为了解决内生变量问题,基于局部线性平滑法和广义矩法,构造了未知系数函数的局部GMM估计。对于表达式中的正定加权矩阵,进行了三种选择,并进行了数值模拟。为了比较空间变系数地理加权自回归模型局部GMM方法下的参数估计效果与地理加权回归模型和空间自回归模型下的估计效果,在模拟中根据不同的模型形式生成数据,结果表明提出的模型和方法表现良好。最后,利用所研究的模型和估计方法对中国省域城镇居民消费与收入的关系进行了研究,所提出的方法在实例分析中也取得了较好的结果。研究表明,所研究的模型和估计方法效果良好,适应性广,可以避免模型设置错误的风险,具有广泛的应用前景。

Spatial econometrics is a subfield of econometrics that deals with the treatment of spatial effects in econometric methods.In recent years,spatial econometrics models have received a lot of attentions among both theoretical and empirical economists.Spatial dependence and spatial heterogeneity are the most important spatial effects.To deal with spatial dependence,many models including spatial autoregressive model,spatial error model,spatial Durbin model are proposed and applied in real data analysis.spatial autoregressive(SAR)model as a popular method to capture spatial dependence among cross-sectional units,has received much attention in the literature.To deal with spatial heterogeneity,some useful models have been proposed in the literature.A popular alternative to these methods is geographically weighted regression(GWR),which is a nonparametric technique to explore spatial heterogeneity by allowing regression coefficients of the explanatory variables are spatially varying,and can be estimated by local weighted least-squares approach.However,studies for dealing at the same time with both spatial dependence and spatial heterogeneity are still rare in the literature.To deal simultaneously with spatial autocorrelation and spatial heterogeneity,this paper considers a spatial varying coefficient geographically weighted autoregressive model by allowing both spatial lag parameter and regression coefficients of the explanatory variables are spatially varying.This semiparametric spatial model includes classical linear model,geographically weighted regression model,spatial autoregressive model and geographically weighted autoregression model as special cases.The spatial varying coefficient geographically weighted autoregressive model is a varying coefficient model with endogenous variables in the statistical and econometric literature.How to estimate it is interesting and important.To solve the problem of endogenous variables,based on local linear smoothing method and Generalized Method of Moments,the local GMM estimate for the unknown coefficient functions are constructed.For the positive definite weighting matrix in the expression,three choices are made,and Monte Carlo numerical simulation is carried out.The results of root mean square error and the drawn simulation diagram show that the proposed method performs well in limited samples.Generally speaking,the estimation result corresponding to the third positive definite weighting matrix is the best.The data are generated according to different model forms for simulation.The parameter estimation effect under the local GMM method of spatial varying coefficient geographic weighted autoregressive model is compared with the estimation effect under geographic weighted regression model and spatial autoregressive model.The results show that the model and method proposed in this paper have good results,have wide adaptability,and can avoid the risk of wrong model setting.An example analysis of the relationship between consumption and income of urban residents is carried out,and the proposed estimation also obtains good results in the example analysis.