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

Tymon Sloczynski (), Derya Uysal () and Jeffrey M. Wooldridge ()
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Tymon Sloczynski: Brandeis University
Derya Uysal: LMU Munich
Jeffrey M. Wooldridge: Michigan State University

No 18147, IZA Discussion Papers from Institute of Labor Economics (IZA)

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: inverse probability tilting; instrumental variables; double robustness; difference-in-differences; covariate balancing; treatment effects; 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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