Despite their ubiquity, observational studies to infer the causal effect of a so-called immutable characteristic, such as race or sex, have struggled for coherence, given the unavailability of a manipulation analogous to a “treatment” in a randomized experiment and the danger of posttreatment bias. We demonstrate that a shift in focus from actual traits to perceptions of them can address both of these issues while facilitating articulation of other critical concepts, particularly the timing of treatment assignment. We illustrate concepts by discussing the designs of various studies of the role of race in trial court death penalty decisions.

This paper provides empirical evidence about the effect of unearned income on earnings, consumption, and savings. Using an original survey of people playing the lottery in Massachusetts in the mid-1980's, we analyze the effects of the magnitude of lottery prizes on economic behavior. The critical assumption is that among lottery winners the magnitude of the prize is randomly assigned. We find that unearned income reduces labor earnings, with a marginal propensity to consume leisure of approximately 11 percent, with larger effects for individuals between 55 and 65 years old. After receiving about half their prize, individuals saved about 16 percent.