基于分组数据测算不均等与贫困等收入分配指标:兼顾数据截断问题的方法论评估

Measuring Income Distribution Indicators such as Inequality and Poverty based on Grouped Data:A Methodological Assessment Considering Data Truncation

收入不均等、贫困和中等收入群体占比等指标广受决策界、社会、学术界,乃至媒体的关注,也是众多经济社会变量(如增长、消费、投资、教育、健康和犯罪等等)的重要决定因素之一,但鲜有文献将其纳入到实证模型里,原因往往在于相关指标或数据的缺失.此外,家户调查数据顶端和底端的观察值也常常缺失,给实证估算带来偏差.本文基于2018年的中国家庭追踪调查(CFPS)数据,评估了由Shorrocks and Wan (2009)提出的基于分组数据“还原”个体观察值,进而估算不均等和贫困等指标的方法,并引入条件分布对Shorrocks and Wan (2009)的方法进行拓展,以便考虑收入分布顶端和底端的数据缺失问题.结果显示,假设变量服从Dagum分布,而非Shorrocks and Wan (2009)所使用的对数正态分布,可以使“还原”偏差保持在可接受的范围内.此外,本文对Shorrocks and Wan(2009)的方法的拓展,能够明显降低数据截断所导致的“还原”偏差,而且在该方法下Dagum分布依然占优.本文的发现表明,后续研究可在Dagum分布的假设下,对各省统计年鉴中提供的收入分组数据进行“还原”,然后测算各省的收入不均等、贫困和中等收入群体占比等等指标,并据此展开经济学分析,至少应该将相关指标纳入到实证研究中,以减少相关指标和模型估算偏误.

Indicators such as income inequality, poverty and the share of middle-income groups are widely concerned by policy makers, society, academia and even the media, and are also important determinants of many economic and social factors(e.g.growth, consumption, investment, education, health, crime, etc.). However, rarely literature included them in empirical models, mainly due to data deficiency. Furthermore, observations at the top and bottom of household survey data are often missing,causing bias in the empirical estimates. Using data from 2018 China Family Panel Studies(CFPS), this paper evaluates the method proposed by Shorrocks and Wan(2009) for “ungrouping” individual observations based on grouped data to estimate indicators of inequality and poverty, then introduces conditional distributions to this method considering the missing data at the top and bottom of the income distribution. The results show that “ungrouping” bias will keep within an acceptable range if assume variables follow Dagum distribution, rather than the lognormal distribution used by Shorrocks and Wan(2009). In addition, this improvement to Shorrocks and Wan’s(2009) method significantly reduces the “ungrouping” bias caused by data truncation, and the Dagum distribution still prevails under this method. It is suggested that subsequent research can “ungrouping” the income grouped data from provincial statistical yearbooks under the assumption of the Dagum distribution, and then measure the indicators of income inequality, poverty and middle-income share, etc. before conducting economic analyses. At least relevant indicators should be considered in the empirical study in order to reduce the bias of the relevant models.