Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects

Tymon Słoczyński, Derya Uysal () and Jeffrey Wooldridge
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Derya Uysal: LMU Munich

No 18147, IZA Discussion Papers from IZA Network @ LISER

Abstract: How should researchers adjust for covariates? We show that if the propensity score is estimated using a specific covariate balancing approach, inverse probability weighting (IPW), augmented inverse probability weighting (AIPW), and inverse probability weighted regression adjustment (IPWRA) estimators are numerically equivalent for the average treatment effect (ATE), and likewise for the average treatment effect on the treated (ATT). The resulting weights are inherently normalized, making normalized and unnormalized IPW and AIPW identical. We discuss implications for instrumental variables and difference-in-differences estimators and illustrate with two applications how these numerical equivalences simplify analysis and interpretation.

Keywords: covariate balancing; difference-in-differences; double robustness; instrumental variables; treatment effects; inverse probability tilting; weighting (search for similar items in EconPapers)
JEL-codes: C20 C21 C23 C26 (search for similar items in EconPapers)
Date: 2025-09
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Related works:
Working Paper: Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects (2025)
Working Paper: Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects (2025)
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