Spatial-temporal Models Based On Quantile Regression

With the rapid development of the world economy,we have a great challenge in the global ecological environment.Meanwhile,urban air quality has attacked intensive atten-tion.In recent years,researchers have increasingly focused on the quantitative analysis of the impact of human social activities on urban air pollution.However,the atmospheric system is a complex system,and the urban air quality is not only affected by human ac-tivities,but also closely related to meteorological conditions,past states and air qualities of the surrounding cities.Therefore,it is meaningful and necessary to explore the impact of human activities on urban air quality after removing the spatial-temporal effects.In addition,since there is an imbalance in urban development,we believe that the impact of human activities on air quality may possesses individual heterogeneity among cities.As a result,we hope to provide analytical tools and theoretical fundament for flexibly explo-rating the impact of human activities on urban air quality with the spatio-temporal effect eliminated.Based on the above discussion,this paper proposes new spatio-temporal mod-els with heterogeneous individual effects in the framework of the spatial panel model,and utilizes quantile regression to explore the impact of space-specific covariates on response after removing spatio-temporal effects.Specifically,the main work of this paper is as follows:（1）We consider the dynamic spatial autoregressive model and assume a location-scale structure for individual random effects.This model structure combines advantages of individual random-effect models and individual fixed-effect models,and it allows for in-dividually conditional heteroscedasticity.To estimate this model,we propose a two-stage hybrid estimation procedure,where we propose a Gaussian quasi-maximum likelihood estimator（QMLE）for the spatial-temporal effects at the first stage while we construct a weighted conditional quantile estimator（WCQE）to estimate conditional quantiles of individual effects at the second stage.We verify the validity of the two-stage hybrid estimation procedure,and establish the consistency and asymptotic normality for all es-timators.Moreover,the correctness of theoretical results are demonstrated by numerical simulation.In the empirical study,based on the above model and estimation procedure,we analyze the impact of economic development on different quantile levels of air quality index（AQI）in China with the spatio-temporal effects eliminated.（2）We consider the dynamic spatial error model and assume the conditional quan-tile regression model for individual random effects.Then the model allows individual effects to be heterogeneous.Relative to the location-scale model,the structure of the conditional quantile regression model is more flexible.A hybrid two-stage estimation procedure is introduced for this model.Specifically,at the first stage,the generalized method of moments（GMM）estimator of the spatial error effect parameter is proposed and the feasible optimal GMM estimator is also discussed.And the other parameters in the spatio-temporal effects are given by feasible generalized least squares（GLS）es-timators.At the second stage,an approximation of the individual effect is obtained af-ter removing the spatio-temporal effect from response,and then the conditional quantile estimate（CQE）is obtained by quantile regression.We establish the validity of the two-stage hybrid estimation procedure,as well as asymptotic properties of all estimators.To circumvent the difficulties encountered in approximating asymptotic distributions of es-timators,we propose a two-stage hybrid bootstrapping procedure corresponding to the two-stage hybrid estimation procedure,which combines the wild bootstrap and the ran-dom weights bootstrap,and we verify the validity of the two-stage hybrid bootstrapping procedure.Simulation studies indicate that both of the proposed estimation procedure and bootstrapping procedure perform well with finite samples.In the empirical study,we analyze the impact of socioeconomic factors on the concentration of PM_2.5in Chinese cities at different quantile levels after removing the spatio-temporal effects.