Causal identification with subjective outcomes
Abstract
Survey questions often 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 regressionbased 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 integer category numbers on that variable uncovers a positivelyweighted linear combination of 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 effects. When results are extended to discrete treatment variables, different weighting schemes apply to different regressors, making comparisons of magnitude less informative. I obtain a partial identification result for comparing the effects of a discrete treatment variable to those of another treatment variable when there are many categories and individual reporting functions are linear. I also provide results for identification using instrumental variables.
 Publication:

arXiv eprints
 Pub Date:
 December 2022
 DOI:
 10.48550/arXiv.2212.14622
 arXiv:
 arXiv:2212.14622
 Bibcode:
 2022arXiv221214622G
 Keywords:

 Economics  Econometrics