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Primary Submission Category: Heterogeneous Treatment Effects

Causal identification with subjective outcomes

Authors: Leonard Goff,

Presenting Author: Leonard Goff*

Many survey questions elicit responses on ordered scales for which the definitions of the categories are subjective, possibly varying by individual. This paper clarifies what is learned when these subjective reports are used as an outcome in regression-based causal inference. When a continuous treatment variable is statistically independent of both i) potential outcomes; and ii) heterogeneity in reporting styles, a nonparametric regression of numerical subjective reports on that variable uncovers a positively-weighted linear combination of local causal responses, among individuals who are on the margin between adjacent response categories. Though the weights do not integrate to one, the ratio of local regression derivatives with respect to two such explanatory variables identifies the relative magnitudes of convex averages of their causal effects. When results are extended to discrete regressors (e.g. a binary treatment), different weighting schemes apply to different regressors, making a comparison of their magnitudes more difficult. I obtain a partial identification result for ratios that holds when there are many categories and individual reporting functions are linear. I also provide results for identification using instrumental variables.