{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,21]],"date-time":"2026-10-21T07:58:16Z","timestamp":1792569496021,"version":"4.5.0"},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"6","license":[{"start":{"date-parts":[[2025,1,9]],"date-time":"2025-01-09T00:00:00Z","timestamp":1736380800000},"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":[[2025,11,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>I introduce a generic method for inference about a scalar parameter in research designs with a finite number of heterogeneous clusters where only a single cluster received treatment. This situation is commonplace in difference-in-differences estimation, but the test developed here applies more broadly. I show that the test controls size and has power under asymptotics where the number of observations within each cluster is large but the number of clusters is fixed. The test combines weighted, approximately Gaussian parameter estimates with a rearrangement procedure to obtain its critical values. The weights needed for most empirically relevant situations are tabulated in the paper. Calculation of the critical values is computationally simple and does not require simulation or resampling. The rearrangement test is highly robust to situations where some clusters are much more variable than others. Examples and an empirical application are provided.<\/jats:p>","DOI":"10.1093\/restud\/rdaf002","type":"journal-article","created":{"date-parts":[[2025,1,7]],"date-time":"2025-01-07T07:15:30Z","timestamp":1736234130000},"page":"3968-3994","source":"Crossref","is-referenced-by-count":11,"title":["Inference with a Single Treated Cluster"],"prefix":"10.1093","volume":"92","author":[{"given":"Andreas","family":"Hagemann","sequence":"first","affiliation":[{"name":"University of Michigan Ross School of Business ,","place":["USA"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2025,1,9]]},"reference":[{"key":"2025111022013206000_rdaf002-B1","doi-asserted-by":"crossref","first-page":"1141","DOI":"10.3982\/ECTA16907","article-title":"Finite-Sample Optimal Estimation and Inference on Average Treatment Effects Under Unconfoundedness","volume":"89","author":"Armstrong","year":"2021","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2025111022013206000_rdaf002-B2","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1162\/003355304772839588","article-title":"How Much Should We Trust Differences-in-Differences Estimates?","volume":"119","author":"Bertrand","year":"2004","journal-title":"Quarterly Journal of Economics"},{"key":"2025111022013206000_rdaf002-B3","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1016\/j.jeconom.2011.01.007","article-title":"Inference with Dependent Data Using Cluster Covariance Estimators","volume":"165","author":"Bester","year":"2011","journal-title":"Journal of Econometrics"},{"key":"2025111022013206000_rdaf002-B4","doi-asserted-by":"crossref","first-page":"414","DOI":"10.1162\/rest.90.3.414","article-title":"Bootstrap-Based Improvements for Inference with Clustered Errors","volume":"90","author":"Cameron","year":"2008","journal-title":"Review of Economics and Statistics"},{"key":"2025111022013206000_rdaf002-B5","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1093\/qje\/qjaa032","article-title":"Crimes Against Morality: Unintended Consequences of Criminalizing Sex Work","volume":"136","author":"Cameron","year":"2020","journal-title":"The Quarterly Journal of Economics"},{"key":"2025111022013206000_rdaf002-B6","doi-asserted-by":"crossref","first-page":"1013","DOI":"10.3982\/ECTA13081","article-title":"Randomization Tests Under an Approximate Symmetry Assumption","volume":"85","author":"Canay","year":"2017","journal-title":"Econometrica: Journal of the Econometric Society"},{"key":"2025111022013206000_rdaf002-B7","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1162\/rest_a_00887","article-title":"The Wild Bootstrap with a \u2018Small\u2019 Number of \u2018Large\u2019 Clusters","volume":"103","author":"Canay","year":"2021","journal-title":"Review of Economics and Statistics"},{"key":"2025111022013206000_rdaf002-B8","doi-asserted-by":"crossref","first-page":"1405","DOI":"10.1093\/qje\/qjz014","article-title":"The Effect of Minimum Wages on Low-Wage Jobs","volume":"134","author":"Cengiz","year":"2019","journal-title":"The Quarterly Journal of Economics"},{"key":"2025111022013206000_rdaf002-B9","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1162\/REST_a_00049","article-title":"Inference with \u201cDifference in Differences\u201d with a Small Number of Policy Changes","volume":"93","author":"Conley","year":"2011","journal-title":"Review of Economics and Statistics"},{"key":"2025111022013206000_rdaf002-B10","doi-asserted-by":"crossref","first-page":"3626","DOI":"10.1086\/708819","article-title":"Surprise! 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