面板数据的贝叶斯Elastic Net分位数回归方法及其应用研究

Study on the Bayesian Elastic Net Quantile Regression for Panel Data: Methods and Applications

本文首次将Elastic Net这种用于高度相关变量的惩罚方法用于面板数据的贝叶斯分位数回归,并基于非对称Laplace先验分布推导所有参数的后验分布,进而构建Gibbs抽样。为了验证模型的有效性,本文将面板数据的贝叶斯Elastic Net分位数回归方法(BQR. EN)与面板数据的贝叶斯分位数回归方法(BQR)、面板数据的贝叶斯Lasso分位数回归方法(BLQR)、面板数据的贝叶斯自适应Lasso分位数回归方法(BALQR)进行了多种情形下的全方位比较,结果表明BQR. EN方法适用于具有高度相关性、数据维度很高和尖峰厚尾分布特征的数据。进一步地,本文就BQR. EN方法在不同扰动项假设、不同样本量的情形展开模拟比较,验证了新方法的稳健性和小样本特性。最后,本文选取互联网金融类上市公司经济增加值(EVA)作为实证研究对象,检验新方法在实际问题中的参数估计与变量选择能力,实证结果符合预期。

This paper for the first time applies Elastic Net,a penalty method for highly correlated variables,to Bayesian quantile regression model for panel data. The posterior distribution of all parameters is deduced based on asymmetric Laplace prior distribution,and Gibbs sampling is constructed. To verify the validity of our model,this paper compares Bayesian Elastic Net Quantile Regression for panel data( BQR. EN) with Bayesian Adaptive Lasso Quantile Regression for panel data( BALQR),Bayes Lasso Quantile Regression for panel data( BLQR),Bayesian Quantile Regression for panel data( BQR) in all kinds of situations. The results show that the BQR. EN model is suitable for data with high correlation,high data dimension and peak and thick tail distribution characteristics. Furthermore,this paper conducts a simulation for BQR. EN model under different disturbance assumptions and different sample sizes,which verifies the robustness and small sample characteristic of the new method. Finally,this paper chooses the economic value added of Internet financial listed companies as an empirical research object to test the new method’s ability of parameter estimation and variable selection in practical problems,and the empirical results are in line with the expected objectives.