Identifying causal effects with subjective ordinal outcomes

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 when answering. This paper studies the use of these responses as an outcome variable in causal inference, accounting for variation in the interpretation of categories across individuals. I find that when a continuous treatment 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. I find that comparisons involving discrete treatment variables are not as readily interpretable, but obtain a partial identification result for such cases under additional assumptions. I illustrate the results by revisiting the effects of income comparisons on subjective well-being, without assuming cardinality or interpersonal comparability of responses.