Propensity Score Weighting (PSW / IPW)
Also known as: PSW, inverse probability weighting, IPW, propensity-based weighting
Propensity score weighting is a causal-inference method that reweights observations so that the covariate distributions of treated and untreated units look exchangeable, enabling unbiased estimation of average treatment effects from observational data. Each unit receives a weight that is the inverse of its probability of receiving the treatment it actually received — a strategy formalised by Rosenbaum and Rubin (1983) and given its efficient semiparametric form by Hirano, Imbens and Ridder (2003).
Key highlights
- Retains the full sample: unlike matching, all units contribute to the estimate, improving efficiency.
- Targets population-level causal estimands (ATE, ATT, ATC) with a straightforward choice of weights.
- Separates the design stage (propensity model and balance check) from the analysis stage, preventing outcome-driven model fishing.
- Compatible with doubly robust estimation — combined with outcome regression, the estimator remains consistent if either model is correctly specified.
- Extends naturally to time-varying treatments through marginal structural models using stabilised IPW.
Intuition
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How it works
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When to use it
Use propensity score weighting when you want to estimate an average treatment effect (ATE or ATT) from observational data, treatment is binary or categorical, and you have a sufficient set of measured confounders. It is preferable to propensity-score matching when you want to retain all units rather than discard unmatched ones, or when the target estimand is ATE rather than ATT. It is not appropriate when important confounders are unmeasured (the ignorability assumption fails), when propensity scores are extreme (near 0 or 1) for many units creating unstable weights, or when the treated and control groups overlap very little on covariates — in those cases, instrumental variables or sensitivity analyses are needed.
Strengths & limitations
- Retains the full sample: unlike matching, all units contribute to the estimate, improving efficiency.
- Targets population-level causal estimands (ATE, ATT, ATC) with a straightforward choice of weights.
- Separates the design stage (propensity model and balance check) from the analysis stage, preventing outcome-driven model fishing.
- Compatible with doubly robust estimation — combined with outcome regression, the estimator remains consistent if either model is correctly specified.
- Extends naturally to time-varying treatments through marginal structural models using stabilised IPW.
- Relies entirely on the assumption of no unmeasured confounding (strong ignorability); violations cannot be detected from data alone.
- Extreme propensity scores (near 0 or 1) produce large, unstable weights that inflate variance and can dominate the estimate.
- Requires a correctly specified propensity model; a misspecified model yields biased weights even if all confounders are measured.
- Balance on measured covariates does not guarantee balance on unmeasured ones, and sensitivity analysis is essential in practice.
Common pitfalls
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Applications
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Frequently asked
What is the difference between propensity score weighting and propensity score matching?
Matching discards units that cannot be matched and estimates the ATT on matched pairs. Weighting retains all units and can target ATE or ATT by choosing the appropriate weight formula. Weighting is generally more efficient but more sensitive to extreme scores; matching is more transparent but discards information.
How do I check whether the weighting worked?
Compute standardised mean differences (SMD) for each covariate in the weighted sample. An SMD below 0.10 for all covariates is the conventional benchmark for adequate balance. Weighted Love plots or balance tables should be reported alongside any PSW analysis.
What should I do when some propensity scores are very close to 0 or 1?
Near-extreme scores produce enormous weights that destabilise the estimator. First, use stabilised weights. If instability persists, consider trimming the sample to the region of common support (excluding units with scores outside, say, [0.01, 0.99]), or switch to a doubly robust or matching estimator.
Can PSW handle unmeasured confounders?
No. PSW assumes strong ignorability — all confounders that affect both treatment and outcome are included in X. If important confounders are unmeasured, the weighted estimate remains biased. A sensitivity analysis (e.g., Rosenbaum bounds) can quantify how much hidden bias would be needed to overturn the conclusion.
Does PSW require a logistic regression propensity model?
Not necessarily. Logistic regression is the most common choice, but any binary classifier — gradient boosting, random forests, or LASSO-penalised logistic regression — can be used. The criterion for model selection should be covariate balance in the weighted sample, not in-sample fit.
Sources
- 1.Rosenbaum, P. R., & Rubin, D. B. (1983). The central role of the propensity score in observational studies for causal effects. Biometrika, 70(1), 41-55.
- 2.Hirano, K., Imbens, G. W., & Ridder, G. (2003). Efficient estimation of average treatment effects using the estimated propensity score. Econometrica, 71(4), 1161-1189.
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Cite this page
ScholarGate. (2026, June 3). Propensity Score Weighting. ScholarGate. https://scholargate.app/causal-inference/propensity-score-weighting