Which Effect of Race? Causal Inference without Holding All Else Equal

Technical Summary: "Which Effect of Race? Causal Inference without Holding All Else Equal"

Problem Statement
Empirical studies of racial discrimination traditionally employ an "all-else-equal" (AEE) design, where researchers vary racial signals while holding nonracial attributes (e.g., language, neighborhood, prior record) fixed. The literature defends this design as a requirement for credible causal inference, arguing that it isolates the effect of race from confounding variables. However, this approach bundles two distinct claims: (1) an estimand commitment regarding which contrast a study should target, and (2) a recovery condition regarding whether a design can validly estimate that contrast.

The paper argues that the AEE design implicitly selects a specific estimand—the effect of nominal membership alone, stripped of the social content (associated traits) that racial categories typically index. This selection is often treated as a default necessity of causal inference rather than a substantive choice. Consequently, studies may fail to capture the "effect of the category as constituted," particularly when racial categories are understood constructively as bundles of nominal membership and associated nonracial attributes. The central problem is that the field lacks a framework to separate the choice of estimand from the conditions required for its recovery, leading to a conflation of substantive questions about the nature of race with statistical requirements for unbiased estimation.

Methodology and Formal Framework
The paper develops a formal framework that separates the definition of race estimands from the conditions required to recover them. It distinguishes between two regimes for studying discrimination:

1. Exposure-Based Regime: Race is a fixed feature of the stimulus (e.g., a résumé name or stated race) encountered by a decision-maker.
2. Perception-Based Regime: Race is the interpretation formed by the decision-maker in response to a cue (e.g., a name or photo), where the cue induces both perceived race and potentially associated nonracial perceptions.

The Family of Estimands
The author defines a family of race estimands bounded by two extremes, derived from unit-level potential outcomes $y_i(z, v)$, where $z$ is the racial attribute and $v$ represents nonracial attributes:

• All-Else-Equal Effect (AEE): Forces the distribution of nonracial attributes to be identical across racial conditions ($v = v'$). This corresponds to the Average Marginal Component Effect (AMCE) in conjoint experiments. It isolates nominal membership but may strip the category of its social content.
• All-Else-Within-Race Effect (AEWR): Allows the distribution of nonracial attributes to vary according to the racial condition ($v \sim q_1$ vs. $v' \sim q_0$). This preserves the race-conditional structure of associated traits, reflecting the category "as constituted."
• Mixed Effects: Allow researchers to hold some attributes fixed while letting others vary by race, based on substantive or normative grounds (e.g., holding legal factors fixed while allowing socioeconomic factors to vary).

In the perception-based regime, the paper introduces the Natural Race Effect among Compliers (NREC). This estimand captures the effect of a cue on compliers (those whose perceived race changes with the cue), allowing nonracial perceptions to shift alongside perceived race if the cue induces such a shift.

Recovery Conditions
The paper derives conditions for recovering these estimands that are weaker than those currently assumed in the literature:

• Exposure-Based Regime: The paper demonstrates that unit-blindness (the assignment of configurations is independent of the unit's potential outcomes) is sufficient for unbiased recovery of any member of the estimand family. The literature's requirement of profile-blindness (race is independent of nonracial profiles) is shown to be unnecessary for inference; rather, profile-blindness is a mechanism that selects the AEE estimand by forcing a common weighting distribution. Researchers can recover AEWR or mixed effects using unit-blind assignments without profile-blindness.
• Perception-Based Regime: The paper shows that the standard "excludability" conditions (requiring cues to shift only perceived race and nothing else) are stronger than necessary. To recover the NREC, it is sufficient that non-compliers (those whose perceived race does not change) do not experience isolated shifts in nonracial perceptions. The movement of nonracial perceptions among compliers does not violate recovery conditions; it simply defines the specific estimand being recovered.

Key Results and Application
The framework is applied to a reanalysis of a candidate-evaluation experiment (Zárate et al., 2024) examining coethnic preference among Hispanic voters.

• Exposure-Based Reading: When language is held fixed (AEE), the study finds no significant coethnic preference. However, when language is allowed to vary with race according to real-world campaign distributions (AEWR), a significant positive coethnic preference emerges. The divergence arises because Hispanic candidates typically campaign in native-accented Spanish, while Anglo candidates do not; the AEE compares atypical profiles, whereas the AEWR compares typical ones.
• Perception-Based Reading: Using instrumental variables to estimate the NREC, the study finds a positive coethnic preference when the candidate speaks English (where the cue strongly shifts perceived race). In Spanish conditions, the effect is indistinguishable from zero, likely because the speech itself acts as a racial cue that mutes the separate effect of the name/label.
• Conclusion of Application: The choice of estimand (AEE vs. AEWR) determines whether the study finds discrimination (or preference). The "null" result in the original study was an artifact of the AEE design, not a lack of effect.

Significance and Claims
The paper claims to resolve a debate between "cue-effects" approaches (which isolate specific signals) and "constructivist" approaches (which view race as a bundle of traits).

1. Unbundling Inference and Estimation: The primary contribution is showing that the "all-else-equal" constraint is a substantive choice about the definition of a racial category, not a prerequisite for valid causal inference.
2. Substantive Choice: Researchers can choose to study the effect of nominal membership (AEE) or the effect of the category as constituted (AEWR/NREC) without sacrificing causal rigor. Both are well-defined causal effects recoverable from the same randomized designs.
3. Normative Alignment: The framework allows empirical designs to align with normative theories of discrimination. For instance, if discrimination is defined as unfair treatment based on the entire social profile of a group, the AEWR is the appropriate target. If discrimination is defined as treatment based solely on a label, the AEE is appropriate.
4. Recovery without Manipulation Purity: In perception-based studies, the paper argues that cues that shift nonracial perceptions alongside race are not "failed manipulations" but are instead the mechanism through which the racial category operates. The NREC captures this joint movement as a valid effect of race.

The paper concludes that the choice of estimand must be driven by substantive questions about what a racial category is and what constitutes discrimination, rather than by a default assumption that all-else-equal contrasts are the only valid causal effects.