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

Tymon Słoczyński, Derya Uysal, Jeffrey M. Wooldridge and Tymon Sloczynski

No 12152, CESifo Working Paper Series from CESifo

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; inverse probability tilting; treatment effects; weighting (search for similar items in EconPapers)
JEL-codes: C20 C21 C23 C26 (search for similar items in EconPapers)
Date: 2025
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