Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/331711 
Year of Publication: 
2025
Series/Report no.: 
IZA Discussion Papers No. 18147
Publisher: 
Institute of Labor Economics (IZA), Bonn
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.
Subjects: 
covariate balancing
difference-in-differences
double robustness
instrumental variables
inverse probability tilting
treatment effects
weighting
JEL: 
C20
C21
C23
C26
Document Type: 
Working Paper

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