Which Effect of Race? Causal Inference without Holding All Else Equal
Empirical studies of racial discrimination vary race while holding nonracial traits fixed, a design the literature defends as what credible inference requires. This defense bundles two claims: which effect of race a study should target, and whether its design can recover that effect. I separate them. The same randomization that secures credible estimation and inference recovers a family of race estimands, from the all-else-equal effect to a within-race effect that lets associated traits vary with race. Every member of that family is causal rather than descriptive, and the choice among members is a claim about what a racial category is -- a claim extending to ethnicity, religion, and other identity categories that index associated traits. I derive conditions, weaker than the literature's, for credible estimation and inference. Reanalyzing a Spanish-language campaign experiment, I find coethnic preference among Hispanic voters under the within-race effect and none under the all-else-equal effect.