Improved Two-stage Weighted Composite Quantile Regression Estimation Of Panel Model And Its Application

The traditional panel data model is based on the assumption of mean regression and requires the error term to obey the normal distribution.However,in actual data analysis,the error term usually cannot meet the classical assumptions,resulting in the estimation result no longer being unbiased and robust.The quantile regression method just makes up for the defects of the mean regression model.It not only relaxes the restriction on the error term distribution,makes the estimation result more accurate and stable,but can also characterize the relationship between related variables for different quantile levels.The explanatory power of the model.In this paper,the panel model is analyzed,and the fixed-effect panel model and the panel threshold model with fixed effects are respectively studied.The two-stage weighted composite quantile regression method is used to solve the coefficients of the model.Among them,in the first stage of the panel model with fixed effects,the weighted compound quantile regression method is used to estimate the fixed effects,and the second stage uses quantile regression to obtain the parameter estimation results at each quantile of the model;Panel threshold model of fixed effects.In the first stage,the grid search method and weighted compound quantile regression method are used to obtain the threshold value and fixed effect estimates.In the second stage,quantile regression is used to obtain the quantile level.The estimated value of the coefficient.Different from the traditional method,the methods proposed in this paper consider the quantile regression method in the first stage,and obtain the corresponding estimated value through weighted compound quantile regression,which effectively improves the accuracy and robustness of the estimation results.In order to examine the superiority of the method proposed in this article,in the numerical simulation part,the estimation effects of different estimation methods in the two panel models are discussed separately,and the method proposed in this article is compared with other methods that are currently used more widely.The simulation results show that when the error term does not obey the normal distribution,the improved two-stage weighted composite quantile regression method is significantly better than other methods,and the estimation obtained is more robust.Further,this article applies the proposed method to the empirical analysis of two cases,and observes the superiority of the proposed method and its application value in actual analysis through two actual cases.The first case analyzes the relationship between my country's technological innovation and environmental regulations,and compares the estimation effect of the method proposed in this paper with the least square method and other quantile regression methods.In the second case,based on the energy-labor-capital-GDP framework,regression analysis was performed on the national data and the data from the eastern,central and western regions,and the threshold effect was considered to further analyze the model with the consumption of electricity as a threshold variable.