基于分位数面板回归的组类识别与估计——对各国新冠疫情防控与股市动荡表现的聚类分析

假设面板个体单元具有潜在组类结构是刻画横截面异质性的一种灵活而简单的方法。现有识别潜在组类的方法大多只反映组间均值水平差异，而实践中，组间的差异也反映在分布的其它特征上。本项目旨在基于具有时间-个体固定效应的分位数回归面板模型来识别个体的潜在组类。我们应用复合分位数回归和极值理论分别刻画组类的分布和尾部异质性。主要研究内容包括：1、组类识别方法：（1）联合含有组类识别信息的回归分位数来识别反映异质分布的组类；（2）借助极值理论外推尾分位数的优势识别面板极值尾部上的个体组类。2、设计迭代算法实现聚类。3、推导误分率的渐近收敛速度来评估组类识别的优良。4、讨论被识别组类下的分位数回归系数估计的渐近正态性。5、应用（1）的方法对各国疫情防控的综合能力进行聚类，评估各国的防控能力；应用（2）的方法对疫情下各国股市的震荡幅度表现进行聚类，评估危机之下各国稳定国内金融市场的能力。

One flexible yet parsimonious approach to accommodate cross-sectional heterogeneity in panel data models is to cluster units into groups. Most existing methods to identify latent groups of units devote to characterize heterogeneous mean, while in practice the group pattern of heterogeneity can also exist in other characteristics of distribution. In addition, the existing grouped panel models assume time-invariant unobserved heterogeneity which are arguably restrictive. This project aims to identify latent groups of units based on quantile regression panel with two-way fixed effects. The suggested methods recover the distributional heterogeneity using composite quantile regression, and the extreme tail heterogeneity with tail quantiles extrapolated to the extremal levels. More specifically, 1) We propose two clustering approaches: one identifies the groups with heterogeneous distributions by combining those quantiles which contain information of group identification; the other identifies the group pattern of extreme tail region of panel using extreme value theory; 2) We suggest iterative algorithms who iterate between the classification and estimation steps. To deal with the individual fixed effects, we introduce a group structure to approximate the individual-level effects; 3) We derive the asymptotic behavior of the misclassification frequency to theoretically evaluate the identified group memberships. It is expected that the clustering-method that pools information across multiple panel quantiles demonstrates high accuracy in identifying the true groups, and the clustering-method for the data-sparse tail region behaves stable. 4) Given the asymptotic property of the group membership estimates, we establish asymptotic normality for the estimated group-specific slopes which is asymptotically equivalent to the corresponding infeasible estimate of slopes under the true group memberships; 5) We apply the proposed clustering-methods to identify the heterogeneity of infection control for Coronavirus and stock market crash across countries, respectively.