  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 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 integer
category numbers on that variable uncovers a positively-weighted 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.
