Robust Inference on Income Inequality: $t$-Statistic Based Approaches
收入不平等的稳健推断：基于 t 统计量的方法AI 解读 ↓
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收入不平等的稳健推断：基于 t 统计量的方法
- 研究问题
- 研究收入或财富数据存在异质性、厚尾及未知相关时，如何对不平等指标和不同地区之间的指标差异进行稳健推断。
- 方法与思路
- 作者将两样本各分为固定数量组，逐组估计不平等参数，再以组估计量开展两样本 t 检验，并讨论其有效性的渐近条件。
- 材料陈述的贡献
- 摘要给出组估计量渐近独立、无偏且高斯，或收敛到独立正态尺度混合等条件下的推断依据，并以俄罗斯地区收入比较展示应用。
- 阅读关注点
- 应核对分组如何保证渐近独立、所选不平等指标在厚尾下是否满足极限条件，以及组数选择和有限样本检验表现。
- 阅读边界
- 这是 arXiv 预印本，同行评审或期刊接收未经核实；稳健性依赖组估计量的极限条件，摘要不支持对任意相关和厚尾均有效。
原文摘要
Empirical analyses on income and wealth inequality and those in other fields in economics and finance often face the difficulty that the data is heterogeneous, heavy-tailed or correlated in some unknown fashion. The paper focuses on applications of the recently developed \textit{t}-statistic based robust inference approaches in the analysis of inequality measures and their comparisons under the above problems. Following the approaches, in particular, a robust large sample test on equality of two parameters of interest (e.g., a test of equality of inequality measures in two regions or countries considered) is conducted as follows: The data in the two samples dealt with is partitioned into fixed numbers $q_1, q_2\ge 2$ (e.g., $q_1=q_2=2, 4, 8$) of groups, the parameters (inequality measures dealt with) are estimated for each group, and inference is based on a standard two-sample $t-$test with the resulting $q_1, q_2$ group estimators. Robust $t-$statistic approaches result in valid inference under general conditions that group estimators of parameters (e.g., inequality measures) considered are asymptotically independent, unbiased and Gaussian of possibly different variances, or weakly converge, at an arbitrary rate, to independent scale mixtures of normal random variables. These conditions are typically satisfied in empirical applications even under pronounced heavy-tailedness and heterogeneity and possible dependence in observations. The methods dealt with in the paper complement and compare favorably with other inference approaches available in the literature. The use of robust inference approaches is illustrated by an empirical analysis of income inequality measures and their comparisons across different regions in Russia.