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D. James Greiner & Donald B. Rubin, Causal Effects of Perceived Immutable Characteristics, 93 Rev. Econ. & Stat. 775 (2011).

Abstract: 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.