{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,26]],"date-time":"2026-03-26T12:11:27Z","timestamp":1774527087012,"version":"3.50.1"},"reference-count":9,"publisher":"Oxford University Press (OUP)","issue":"1","license":[{"start":{"date-parts":[[2025,11,26]],"date-time":"2025-11-26T00:00:00Z","timestamp":1764115200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2026,2,13]]},"abstract":"<jats:title>Summary<\/jats:title>\n                  <jats:p>Factorial experiments are ubiquitous in the social and biomedical sciences, but when units fail to comply with each assigned factor, identification and estimation of the average treatment effects become impossible without strong assumptions. Leveraging an instrumental variables approach, previous studies have shown how to define and estimate the causal effect of treatment uptake among respondents who comply with treatment. A major caveat is that these results rely on strong assumptions on the effect of randomization on treatment uptake. This work shows how to bound these complier average treatment effects for bounded outcomes under milder assumptions on noncompliance.<\/jats:p>","DOI":"10.1093\/biomet\/asaf084","type":"journal-article","created":{"date-parts":[[2025,11,20]],"date-time":"2025-11-20T13:07:30Z","timestamp":1763644050000},"source":"Crossref","is-referenced-by-count":0,"title":["Bounds on causal effects in $ 2^{K} $ factorial experiments with noncompliance"],"prefix":"10.1093","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3689-9527","authenticated-orcid":false,"given":"M","family":"Blackwell","sequence":"first","affiliation":[{"name":"Department of Government, Harvard University , 1737 Cambridge Street , Cambridge, Massachusetts 02138,","place":["U.S.A"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5900-3535","authenticated-orcid":false,"given":"N E","family":"Pashley","sequence":"additional","affiliation":[{"name":"Department of Statistics, Rutgers University , 110 Frelinghuysen Road , Piscataway, New Jersey 08854, . nicole.pashley@rutgers.edu","place":["U.S.A"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2025,11,26]]},"reference":[{"key":"2026032607092022600_asaf084-B1","doi-asserted-by":"crossref","first-page":"444","DOI":"10.1080\/01621459.1996.10476902","article-title":"Identification of causal effects using instrumental variables","volume":"91","author":"Angrist","year":"1996","journal-title":"J. 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