Regression-based causal inference with factorial experiments: estimands, model specifications and design-based properties

Are Emily and Greg more employable than Lakisha and Jamal? A field experiment on labor market discrimination

Anqi Zhao and Peng Ding

Biometrika, 2022, vol. 109, issue 3, 799-815

Abstract: SummaryFactorial designs are widely used because of their ability to accommodate multiple factors simultaneously. Factor-based regression with main effects and some interactions is the dominant strategy for downstream analysis, delivering point estimators and standard errors simultaneously via one least-squares fit. Justification of these convenient estimators from the design-based perspective requires quantifying their sampling properties under the assignment mechanism while conditioning on the potential outcomes. To this end, we derive the sampling properties of the regression estimators under a wide range of specifications, and establish the appropriateness of the corresponding robust standard errors for Wald-type inference. The results help to clarify the causal interpretation of the coefficients in these factor-based regressions, and motivate the definition of general factorial effects to unify the definitions of factorial effects in various fields. We also quantify the bias-variance trade-off between the saturated and unsaturated regressions from the design-based perspective.

Keywords: Factorial effect; Potential outcome; Randomization inference; Robust standard error (search for similar items in EconPapers)
Date: 2022
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Citations: View citations in EconPapers (2)

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