多元响应面板单指标分位数模型的同质性识别及应用

Homogeneity Identification of Single-Index Quantile Model of Multiple Responses Panel Data and Its Application

本文以单指标分位数模型为基础,将传统的一元响应变量拓展至多元,并针对面板数据,提出了多元响应面板单指标分位数模型。该模型嵌入了个体属性,表现为回归系数与个体有关,以此刻画总体中个体的异质性和同质性。为识别潜在的同质性结构和估计模型系数,建立了一种“四步”方法,包括估计个体系数、依据该系数估计值采用聚类方法识别同质性结构、构建信息准则确定同质群体数目,以及基于同组个体得到群体系数估计值。数值模拟发现本文所提方法的估计偏差维持在相对较低的水平,且对同质性群体的成员及其数目的估计也较为准确。另外,基于提出的模型研究了48个国家1971-2020年的经济发展状况,主要测度了年资本形成总额增长率、年人口增长率和商品贸易占GDP比率这三个指标对不同国家群体的经济发展状况影响。本文所提模型及方法可以为识别其他类似模型的同质性结构提供一定的参考价值。

Based on the traditional single-index quantile model,this paper proposes a single-index quantile model of multiple responses panel data.The model embeds individual attributes,which means that regression coefficients are related to individuals,to describe the heterogeneity and homogeneity of individuals in the population.To identify its potential homogeneity structure and estimate coefficients of the model,a"four-step"method is proposed,including obtaining individual coefficients estimators,achieving the homogeneity structure by clustering the individual coefficients estimators,constructing an optimal group number selection criterion to judge the number of homogeneous groups,and getting group coeficients estimators after clustering by establishing the model for the individuals in the same group.Numerical simulations show that deviations of coefficients estimators are maintained at a relatively low level,and members of homogeneous groups and its number are also accurate.In addition,based on the model,we analyze the economic development of 48 countries from 1971 to 2020,mainly measuring impacts of three indicators,the annual total capital formation growth rate,annual population growth rate,and the proportion of commodity trade in GDP,on the economic development in different groups.The proposed model and method can provide some reference for identifying the homogeneity structure of other similar models.