Instrumental Variables Estimation And Application Of Quantile Regression Modle With Panel Data

Panel data quantile regression model is widely used in econometric,biomedical and other fields.The main reason is that the model uses the advantages of panel data fully,and also retains the advantages of quantile regression.However,in practical applications,we often encounter endogenous data.If the endogeneity of data is ignored,the estimation will be biased.In this paper,focuing on the quantile regression model of panel data with endogenous variables,we propose a quantile regression estimation method based on instrumental variables.Firstly,we solve the problem of the endogeneity of independent variable by introducing instrumental variables,and then we use the quantile regression method to estimate coefficient.The large sample property of the proposed estimation is established under some regularity conditions.And the finite sample properties of the proposed method are studied by numerical simulation.The proposed method not only retains the advantages of the quantile regression model with panel data,but also effectively deals with the endogeneity of the model.Furthermore,we analyze the impact of foreign direct investment(FDI)and economic development on China's environmental pollution.When establishing panel data model to analyze China's inter provincial panel data from 2012 to 2016,considering the endogeneity of FDI,we use the geographic distance as a tool variable of FDI.The results show that FDI restrains environmental pollution and economic development aggravates environmental pollution.On the whole,the impact of economic development on environmental pollution is inverted U-shaped.In different quantiles,the impact of FDI on environmental pollution decreases with the increasing of quantile.And the impact of economic development on environmental pollution has "inverted U" distribution.In the areas with low FDI,the impact of FDI on environmental pollution is greater.With the increasing of FDI,the impact of FDI on environmental pollution is smaller and smaller.In economically backward areas,economic development has thegreatest impact on environmental pollution,followed by economically developed areas,and finally areas with general economic development.From the perspective of regional heterogeneity analysis,the inhibition of FDI on environmental pollution in the three regions gradually weakens with the increasing of quantiles.On the low quantiles,FDI has the strongest inhibition in the western regions,the weakest in the eastern regions.On the high quantiles,FDI has the strongest inhibitory effect in the central region and the weakest in the western region.Economic development has an aggravating effect on environmental pollution in three regions.In a specific quantile,the impact of economic development on environmental pollution is the strongest in the eastern region and the weakest in the western region.With the changing of quantile,the trend of the impact of economic development on environmental pollution is similar in three regions.