Doubly Robust Estimation (AIPW)
Augmented Inverse Probability Weighting (AIPW) / Doubly Robust Estimation · Also known as: AIPW, augmented inverse probability weighting, doubly robust estimator, Çift Gürbüz Kestirici (Augmented IPW / AIPW)
Doubly Robust Estimation, also called Augmented Inverse Probability Weighting (AIPW), is a semiparametric method for estimating causal treatment effects that combines an outcome regression model with a propensity (treatment) model. Developed in the work of Robins & Rotnitzky (1995) and Bang & Robins (2005), it stays consistent as long as at least one of the two models is correctly specified.
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When to use it
Use doubly robust estimation when you want to estimate a causal treatment effect from observational data with a continuous or binary outcome and a binary treatment, and you are unsure which of the outcome or treatment model you can specify correctly. It applies to cross-sectional or longitudinal data and needs a reasonable sample (at least about 150 observations) for the cross-fitted nuisance models to be stable. It assumes common support and conditional independence (no unmeasured confounding) and that at least one of the two models is correctly specified. It is less suitable for small samples, where the double-robustness advantage tends to vanish.
Strengths & limitations
- Consistent if at least one of the outcome model or the propensity model is correctly specified, giving protection against misspecification of either one.
- Efficient: attains the semiparametric Cramér-Rao lower bound when both models are correct.
- Combines inverse probability weighting with outcome regression and supports flexible machine-learning nuisance models with cross-fitting.
- If both models are misspecified, consistency is lost and the estimate can be badly biased.
- Cross-fitted nuisance estimates are unstable in small samples (n < 150), so the double-robustness benefit disappears.
- Relies on the untestable assumptions of common support and conditional independence (no unmeasured confounding).
Frequently asked
Why is it called doubly robust?
Because it relies on two models — an outcome regression and a propensity (treatment) model — and stays consistent as long as at least one of them is correctly specified. You get two chances to be right instead of one.
What happens if both models are wrong?
The double-robustness guarantee no longer holds and the estimate can be biased. In that situation a more conservative method such as propensity score matching is the safer choice.
Why use cross-fitting?
Cross-fitting fits the nuisance models on one part of the data and evaluates them on another, so flexible machine-learning estimators do not overfit. It keeps the AIPW estimator close to its semiparametric efficiency bound.
How does AIPW differ from plain inverse probability weighting?
Plain IPW only re-weights by the propensity score and is consistent only if that model is right. AIPW augments IPW with an outcome regression so that the estimate survives misspecification of either model and is more efficient.
Sources
- Robins, J. M. & Rotnitzky, A. (1995). Semiparametric Efficiency in Multivariate Regression Models with Missing Data. Journal of the American Statistical Association, 90(429), 122-129. DOI: 10.1080/01621459.1995.10476494 ↗
- Bang, H. & Robins, J. M. (2005). Doubly Robust Estimation in Missing Data and Causal Inference Models. Biometrics, 61(4), 962-973. DOI: 10.1111/j.1541-0420.2005.00377.x ↗
How to cite this page
ScholarGate. (2026, June 1). Augmented Inverse Probability Weighting (AIPW) / Doubly Robust Estimation. ScholarGate. https://scholargate.app/en/causal-inference/doubly-robust-estimation
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Causal Mediation AnalysisCausal inference↔ compare
- Inverse Probability WeightingCausal inference↔ compare
- Logistic RegressionResearch Statistics↔ compare
- OLS RegressionEconometrics↔ compare
- Propensity Score MatchingResearch Statistics↔ compare