{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T11:41:04Z","timestamp":1791891664257,"version":"4.3.4"},"reference-count":27,"publisher":"MIT Press - Journals","issue":"3","license":[{"start":{"date-parts":[[2021,3,8]],"date-time":"2021-03-08T00:00:00Z","timestamp":1615161600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2022,5,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Applied work often studies the effect of a binary variable (\u201ctreatment\u201d) using linear models with additive effects. I study the interpretation of the OLS estimands in such models when treatment effects are heterogeneous. I show that the treatment coefficient is a convex combination of two parameters, which under certain conditions can be interpreted as the average treatment effects on the treated and untreated. The weights on these parameters are inversely related to the proportion of observations in each group. Reliance on these implicit weights can have serious consequences for applied work, as I illustrate with two well-known applications. I develop simple diagnostic tools that empirical researchers can use to avoid potential biases. Software for implementing these methods is available in R and Stata. In an important special case, my diagnostics require only the knowledge of the proportion of treated units.<\/jats:p>","DOI":"10.1162\/rest_a_00953","type":"journal-article","created":{"date-parts":[[2020,8,10]],"date-time":"2020-08-10T21:14:58Z","timestamp":1597094098000},"page":"501-509","update-policy":"https:\/\/doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":57,"title":["Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights"],"prefix":"10.1162","volume":"104","author":[{"given":"Tymon","family":"S\u0142oczy\u0144ski","sequence":"first","affiliation":[{"name":"Brandeis University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"281","published-online":{"date-parts":[[2022,5,9]]},"reference":[{"key":"2022051222594898100_B1","doi-asserted-by":"publisher","first-page":"265","DOI":"10.3982\/ECTA12675","article-title":"Sampling-Based versus Design-Based Uncertainty in Regression Analysis,","volume":"88","author":"Abadie","year":"2020","journal-title":"Econometrica"},{"key":"2022051222594898100_B2","doi-asserted-by":"publisher","first-page":"465","DOI":"10.1146\/annurev-economics-080217-053402","article-title":"Econometric Methods for Program Evaluation,","volume":"10","author":"Abadie","year":"2018","journal-title":"Annual Review of Economics"},{"key":"2022051222594898100_B3","doi-asserted-by":"publisher","first-page":"935","DOI":"10.1257\/aer.20140529","article-title":"The Long-Run Impact of Cash Transfers to Poor Families,","volume":"106","author":"Aizer","year":"2016","journal-title":"American Economic Review"},{"key":"2022051222594898100_B4","doi-asserted-by":"publisher","first-page":"469","DOI":"10.1093\/qje\/qjt005","article-title":"On the Origins of Gender Roles: Women and the Plough,","volume":"128","author":"Alesina","year":"2013","journal-title":"Quarterly Journal of Economics"},{"key":"2022051222594898100_B5","doi-asserted-by":"publisher","first-page":"249","DOI":"10.2307\/2998558","article-title":"Estimating the Labor Market Impact of Voluntary Military Service Using Social Security Data on Military Applicants,","volume":"66","author":"Angrist","year":"1998","journal-title":"Econometrica"},{"key":"2022051222594898100_B6","doi-asserted-by":"crossref","DOI":"10.1515\/9781400829828","author":"Angrist","year":"2009","journal-title":"Mostly Harmless Econometrics: An Empiricist's Companion"},{"key":"2022051222594898100_B7","doi-asserted-by":"publisher","first-page":"250","DOI":"10.1111\/ajps.12185","article-title":"Does Regression Produce Representative Estimates of Causal Effects?","volume":"60","author":"Aronow","year":"2016","journal-title":"American Journal of Political Science"},{"key":"2022051222594898100_B8","doi-asserted-by":"publisher","first-page":"988","DOI":"10.1257\/aer.96.4.988","article-title":"What Mean Impacts Miss: Distributional Effects of Welfare Reform Experiments,","volume":"96","author":"Bitler","year":"2006","journal-title":"American Economic Review"},{"key":"2022051222594898100_B9","doi-asserted-by":"publisher","first-page":"894","DOI":"10.1093\/jeea\/jvx028","article-title":"What Works? 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