Estimation And Application Of Composite Quantile Regression Model For Panel Data

Statistical analysis of panel data has received extensive attention for its advantages of time series data and cross section data,covering rich information of the research object.In the case of parameter estimation of a model,the traditional method,least squares estimation(LS),has a good performance for the normal distribution data.But in many practical problems,the data often do not obey normal distribution.When a model error is non-normal distribution or some abnormal points exists,the classic mean regression will be invalid.In this paper,the composite quantile regression(CQR)is introduced to estimate the parameter of the individual fixed effect panel data model.More efficient estimate can be obtained from multiple quantile regression..This method can not only preserve the robustness of the quantile regression,but also improves the efficiency of the estimation by means of the composite method.The composite quantile regression estimation of the individual fixed effect panel data model is studied in this paper.Firstly,a specific idempotent matrix is introduced to eliminate the individual effect term,which avoids the problem of curricula.And the panel model is transformed into a linear model.Then the objective function of the regression coefficient is constructed by composite quantile regression.Under some regularity conditions,the asymptotic normality of the obtained estimation is proved.Monte Carlo simulation studies are conducted to confirm the validity of the estimator on the panel data model whose error term obeys the Standard normal distribute,T distribution and Cauchy distribution.And we compared the accuracy of the estimator with the method of LS,QR and CQR.Results show that the composite quantile regression estimation is optimal,especially for a model with non-normal distribution error.Finally,the proposed method is applied to explore the influencing factors of wage difference in China's industry.The data of annual average wage of China's various industries form 2005 to 2014 are analyzed.The validity of the proposed method is further confirmed in the actual case.Results show that the level of human capital,industry monopoly and labor productivity are the main factors influencing the wage difference between different industries.