AI 中文总结
本文批判了将自我报告生活满意度离散度作为社会不平等衡量指标的做法，指出聚焦值舍入（FVR）会导致偏差，校正后标准差排名基本不变，序数指标受影响更严重，FVR校正可改善分布的成对优势可比性。
AI 中文摘要
已有研究提出并将自我报告的生活满意度离散度用作社会不平等的综合衡量指标，跨国层面的平均生活满意度与其标准差呈负相关，这被视为该不平等本身具有福利相关性的证据，但批评者指出了响应量表的非线性和有界性。本文阐述了进一步的问题：相当大且可预测比例的受访者会将0-10分的量表简化为{0,5,10}三个值，即“聚焦值舍入（FVR）”，这种行为不仅破坏了量表的线性，甚至破坏了其顺序性。本文推导了FVR对标准差可能产生的偏差的严格界限；在经验上典型的FVR比例下，可能的偏差约为跨国离散度范围的一半。本文通过将FVR行为模型拟合到盖洛普世界民意调查的坎梯尔 ladder 及其他三项跨国生活评估，估计并校正了该偏差。结果显示，在135个国家中有133个国家的测量标准差因FVR而膨胀，中位数膨胀了0.090个点。不过，由于校正值在各国几乎符号一致，标准差的排名基本保持不变。理论上合适的序数不平等指标受FVR的影响甚至更严重。平均与标准差之间的相关性经FVR校正后仅略有减弱，但仍有一些需要注意的地方。因此，FVR本身并未推翻之前报告的相关性；不过，它为解释主观幸福感不平等的标量指标增添了进一步的谨慎理由：候选统计量受到的污染程度不同，序数修正与基数原指标受到的污染程度相当，且彼此之间存在差异。最后，本文表明，FVR校正可改善完整分布的成对优势可比性。
英文摘要
The dispersion of self-reported life satisfaction has been proposed and used as a comprehensive measure of societal inequality. A negative cross-country association between mean life satisfaction and its standard deviation has been read as evidence that this inequality is itself welfare-relevant, but critics have pointed to the nonlinearity and boundedness of response scales. I describe a further problem: a substantial and predictable share of respondents simplify the 0--10 scale to the subset {0, 5, 10} --- "focal-value rounding" (FVR) --- a behaviour that breaks not only linearity of the scale but even its order. I derive a sharp bound on the bias that FVR can induce in the standard-deviation; at empirically-typical FVR fractions the possible bias is roughly half the cross-country range of dispersion. I estimate and correct for the bias by fitting a model of FVR behavior to the Gallup World Poll Cantril ladder and three other multi-country life evaluations. FVR inflates measured standard deviation in 133 of 135 countries, by a median of 0.090 points. However, because the corrections are nearly uniform in sign across countries, rankings of the standard deviation survive essentially intact. The ordinal inequality indices advocated as the theoretically appropriate alternative suffer even worse from FVR. The correlation between mean and standard deviation survives FVR correction with modest attenuation and some caveats. Thus FVR does not, by itself, overturn previously reported correlations; it does, however, add a further reason for caution in interpreting scalar measures of subjective wellbeing inequality: candidate statistics are differently contaminated, the ordinal repairs no less than the cardinal originals, and they disagree with one another. Lastly, I show that FVR-correction can improve the pairwise dominance-comparability of full distributions.
Comments25 pages plus 12 pages appendices
