论文标题

识别具有主观顺序结果的因果效应

Identifying causal effects with subjective ordinal outcomes

论文作者

Goff, Leonard

论文摘要

调查问题通常会要求受访者从有序的量表中选择这些类别的含义是主观的,而每个人都可以自由地在答案中应用自己的定义。本文研究了这些响应作为因果推断中结果变量的使用,这考虑了跨个体类别的解释的变化。我发现,当连续的治疗变量在统计上独立于这两种i)潜在结果; ii)报告样式中的异质性,该处理变量的反应类别数量的非参数回归恢复了与连续反应类别之间边缘差的个体中平均因果效应成正比的数量。给定回归系数的幅度本身并不有意义,但是相对于两个这样的处理变量,局部回归衍生物的比率标识了其效应的凸平平均值的相对幅度。这些结果可以看作是二元处理变量类似结果的限制案例,尽管涉及离散治疗的数量级的比较并不容易在极限之外解释。我获得了涉及进一步假设下离散治疗的比较的部分识别结果。经验应用说明了结果,通过重新审视收入比较对主观幸福感的影响,而不假设反应的人际关系或人际可比性。

Survey questions often ask respondents to select from ordered scales where the meanings of the categories are subjective, leaving each individual free to apply their own definitions in answering. This paper studies the use of these responses as an outcome variable in causal inference, accounting for variation in interpretation of the categories across individuals. I find that when a continuous treatment variable is statistically independent of both i) potential outcomes; and ii) heterogeneity in reporting styles, a nonparametric regression of response category number on that treatment variable recovers a quantity proportional to an average causal effect among individuals who are on the margin between successive response categories. The magnitude of a given regression coefficient is not meaningful on its own, but the ratio of local regression derivatives with respect to two such treatment variables identifies the relative magnitudes of convex averages of their effects. These results can be seen as limiting cases of analogous results for binary treatment variables, though comparisons of magnitude involving discrete treatments are not as readily interpretable outside of the limit. I obtain a partial identification result for comparisons involving discrete treatments under further assumptions. An empirical application illustrates the results by revisiting the effects of income comparisons on subjective well-being, without assuming cardinality or interpersonal comparability of responses.

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