Composite Quantile Regression For Spatial Panel Model

This paper studies the spatial panel composite quantile regression model(SPCQAR)with spatial effects,which mainly involves spatial econometrics,panel data structure,and composite quantile regression.In spatial econometrics,spatial effects are used to measure the economic development relationship between regions and introduce them into the panel data model,which not only satisfies the spatial correlation of the cross-sectional dimension,but also preserves individual heterogeneity.However,samples with spatial correlation will result in larger variance estimates,lower significance levels of hypothesis testing,and reduced the fit of the estimated model.Parameter estimations of traditional methods such as conditional mean models will no longer be valid.Although the combination of quantile regression and spatial econometric models can effectively deal with spatial heterogeneity,choosing the appropriate quantile in practical problems is often a problem.Composite quantile regression considers the quantile regression model at multiple quantile points.It is not easily affected by the value of a single quantile,the information reflected is more comprehensive than the traditional mean or quantile regression,and the variance of the error term can tend to infinity.At the same time,panel data can overcome the shortcomings of cross-section data or single time series analysis,with larger sample size,more information,and control of individual heterogeneity.Therefore,this paper considers the statistical inference of the composite quantile for the spatial panel model.Based on the quantile regression for the spatial panel model,the instrumental variable quantile is used to focus on the endogeneity of the spatial lag term.Consider multiple quantile regression equations,that is,construct a new composite quantile regression model(SPCQAR)of spatial panel data.Constructing a suitable moment function based on the extended score vector,using the empirical likelihood method to embed the weight of the intrinsic dependence of the panel data into the loss function expression of the composite quantile regression,and then utilizing the three-step estimation method,using the idea of weighted composite quintile regression to estimate model parameters.This paper proves that the composite quantile estimation of the proposed spatial panel model satisfies the consistency and asymptotic normality.At the same time,the finite sample performance of the method was investigated by statistical simulation.Different types of sequence correlation and different distributions of error terms are set in the simulation.The experimental results show that the parameter estimation of SPCQAR method is more robust than the two-stage least squares method(TSLS)and the common quantile regression method(QR),and under the condition that the error term obeys the non-normal distribution,the stronger the sequence correlation,the more obvious the advantage of the SPCQAR method compared with other methods.In this paper,the SPCQAR method is used to empirically analyze the development of service industry.It is found that there are sequence correlation and spatial effects in the development level of service industry in 25 cities in the Yangtze River Delta.Under the premise that the development level of modern service industry in each city has the characteristics of high spatial value aggregation or low value accumulation,the “urbanization level” has a strong positive correlation with the development of modern service industry in the city.Unlike TSLS and QR,the SPCQAR method can improve parameter estimation accuracy more effectively.