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The propensity score has a balancing property: if customers have the same propensity score, then the difference in their risk characteristics is independent of the assigned treatment.
“Interestingly, this score has a balancing property that states that if customers have the same propensity score, then the difference in their risk characteristics is independent of the assigned treatment, or 𝑇 𝑖 ⟂ 𝑿 𝑖 |𝜋(𝑡 𝑐 , 𝑿 𝑖 ) ∀𝑐 ∈ {1, … , 𝐶} (Guo & Fraser, 2009;Imbens, 2004;Rosenbaum, 2010).”
From Customer price sensitivities in competitive insurance markets (2022) · cites this paper as Rosenbaum, 2010
Quasi-experimental methods such as instrumental variables and regression discontinuity designs allow for causal conclusions from observational snapshots when investigators make strong, explicit assumptions and articulate a credible identification strategy.
“We recognize, of course, that quasi-experimental methods such as instrumental variables and regression discontinuity designs allow for causal conclusions to be drawn from observational snapshots when investigators make strong, explicit assumptions and articulate a credible identification strategy 27-30 .”
From Quantifying the prevalence and impact of overreaching causal claims in social science (2026) · cites this paper as [27]
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AI-Aided Teaching Model in Education 5.0
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Imbens, G. W. (2019) · National Bureau of Economic Research · doi:10.3386/w26104 · Cited by 101 · see citing works
Economic performance and incumbents' support in Latin America
Murillo, M. V., & Visconti, G. (2016) · Electoral Studies · doi:10.1016/j.electstud.2016.10.007 · Cited by 97 · see citing works
- Authors
- Rosenbaum, P. R.
- Affiliations
- University of Pennsylvania (US)
- Corresponding author
- Rosenbaum, Paul R.
- ORCID
- Rosenbaum, Paul R.
- Venue
- Springer Series in Statistics
- Publisher
- Springer New York
- Published
- 2010
- ISSN
- 0172-7397 (ISSN-L)
- OpenAlex
- W253646976
- Cited by
- 1,150
- References
- 12
- Citations by year
- 2026: 33 · 2025: 72 · 2024: 58 · 2023: 58 · 2022: 73 · 2021: 115 · 2020: 108 · 2019: 71 · 2018: 73 · 2017: 68 · 2016: 75 · 2015: 85 · 2014: 84 · 2013: 58 · 2012: 55
- FWCI
- 6.61
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- Locations
- Springer series in statistics (publishedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- Digital Access to Libraries (Université catholique de Louvain (UCL), l'Université de Namur (UNamur) and the Université Saint-Louis (USL-B)) (submittedVersion)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Advanced Causal Inference Techniques
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods in Epidemiology
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Keywords
- observational studies, research design, causal inference, statistical inference, confounding
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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