TY  - RPRT
        AU  - Sloczynski, Tymon
AU  - Uysal, Derya
AU  - Wooldridge, Jeffrey M.
        TI  - Covariate Balancing and the Equivalence of Weighting and Doubly Robust Estimators of Average Treatment Effects
        PY  - 2025/Sep/
        PB  - Institute of Labor Economics (IZA)
        CY  - Bonn
        T2  - IZA Discussion Paper
        IS  - 18147
        UR  - https://www.iza.org/index.php/publications/dp18147
        AB  - 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.
        KW  - covariate balancing
KW  - difference-in-differences
KW  - double robustness
KW  - instrumental variables
KW  - treatment effects
KW  - inverse probability tilting
KW  - weighting
        ER  -