Quantile Regression Estimation And Application Of Semiparametric Instrumental Variable Model

The semi-parametric model contains both parametric and non-parametric components,which is more explanatory and flexible than the pure parametric model.However,when analyzing actual problems,the data often contains endogenous variables.If the influence of endogenous variables is ignored,the estimation will be biased.Therefore,for the semiparametric model,how to eliminate the influence of endogenous variables is the problem discussed in this article.Aiming at the semiparametric regression model with endogenous explanatory variables,this paper proposes the quantile regression estimation of the semiparametric model based on instrumental variables.In the estimation process,firstly,the endogeneity of explanatory variables is dealt with by introducing instrumental variables,so as to eliminate the endogeneity of explanatory variables;secondly,a three-step estimation process is used to obtain parameter and non-parametric component estimates.The first step is to treat the parameter part of the model as a non-parametric form,and use the local linear quantile regression method to obtain the initial estimate of the non-parametric component;the second step,based on the initial estimate of the non-parametric component,use quantile regression to construct Estimation of interest parameters;The third step is to update the estimation of non-parametric components by using local linear quantile regression.Then,under some regular conditions,the asymptotic properties of the parameter and non-parametric component estimates are given,and the finite sample properties of the method in this paper are further simulated.Finally,using the estimation method proposed in this paper,we explored the impact of environmental pollution on the income gap between urban and rural residents in Chongqing,and selected annual precipitation as an instrumental variable.The results show that environmental pollution has a positive impact on the urban-rural income gap,that is,the more serious the environmental pollution,the more serious it is.The greater the income gap between urban and rural residents.