{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,13]],"date-time":"2026-10-13T13:14:25Z","timestamp":1791897265599,"version":"4.3.4"},"reference-count":42,"publisher":"The Econometric Society","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>Consider a researcher estimating the parameters of a regression function based on data for all 50 states in the United States or on data for all visits to a website. What is the interpretation of the estimated parameters and the standard errors? In practice, researchers typically assume that the sample is randomly drawn from a large population of interest and report standard errors that are designed to capture sampling variation. This is common even in applications where it is difficult to articulate what that population of interest is, and how it differs from the sample. In this article, we explore an alternative approach to inference, which is partly design\u2010based. In a design\u2010based setting, the values of some of the regressors can be manipulated, perhaps through a policy intervention. Design\u2010based uncertainty emanates from lack of knowledge about the values that the regression outcome would have taken under alternative interventions. We derive standard errors that account for design\u2010based uncertainty instead of, or in addition to, sampling\u2010based uncertainty. We show that our standard errors in general are smaller than the usual infinite\u2010population sampling\u2010based standard errors and provide conditions under which they coincide.<\/jats:p>","DOI":"10.3982\/ecta12675","type":"journal-article","created":{"date-parts":[[2020,2,3]],"date-time":"2020-02-03T07:37:03Z","timestamp":1580715423000},"page":"265-296","source":"Crossref","is-referenced-by-count":233,"title":["Sampling\u2010Based versus Design\u2010Based Uncertainty in Regression Analysis"],"prefix":"10.3982","volume":"88","author":[{"given":"Alberto","family":"Abadie","sequence":"first","affiliation":[{"name":"Massachusetts Institute of Technology"},{"name":"NBER"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Susan","family":"Athey","sequence":"additional","affiliation":[{"name":"Graduate School of Business, Stanford University"},{"name":"NBER"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guido W.","family":"Imbens","sequence":"additional","affiliation":[{"name":"Graduate School of Business, Department of Economics, Stanford University"},{"name":"NBER"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jeffrey M.","family":"Wooldridge","sequence":"additional","affiliation":[{"name":"Department of Economics, Michigan State University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"2359","published-online":{"date-parts":[[2020]]},"reference":[{"key":"ecta200098-bib-0001","doi-asserted-by":"crossref","unstructured":"Abadie, A., S. Athey, G. W. Imbens, and J. M. Wooldridge (2014): \u201cFinite Population Causal Standard Errors,\u201d Technical Report, National Bureau of Economic Research.","DOI":"10.3386\/w20325"},{"key":"ecta200098-bib-0002","doi-asserted-by":"crossref","unstructured":"Abadie, A., S. Athey, G. W. Imbens, and J. Wooldridge (2017): \u201cWhen Should You Adjust Standard Errors for Clustering?\u201d Technical Report, National Bureau of Economic Research.","DOI":"10.3386\/w24003"},{"key":"ecta200098-bib-0003","doi-asserted-by":"crossref","unstructured":"Abadie, A., S. Athey G. W Imbens, and J. M Wooldridge (2020): \u201cSupplement to \u2018Sampling-Based versus Design-Based Uncertainty in Regression Analysis\u2019,\u201d Econometrica Supplemental Material, 88, https:\/\/doi.org\/10.3982\/ECTA12675.","DOI":"10.3982\/ECTA12675"},{"key":"ecta200098-bib-0004","doi-asserted-by":"crossref","first-page":"175","DOI":"10.2307\/27917244","volume":"91\/92","author":"Abadie","year":"2008","journal-title":"Annales d'Economie et de Statistique"},{"issue":"508","key":"ecta200098-bib-0005","doi-asserted-by":"crossref","first-page":"1601","DOI":"10.1080\/01621459.2014.928218","volume":"109","author":"Abadie","year":"2014","journal-title":"Journal of the American Statistical Association"},{"key":"ecta200098-bib-0006","doi-asserted-by":"crossref","DOI":"10.2307\/j.ctvcm4j72","volume-title":"Mostly Harmless Econometrics: An Empiricists' Companion","author":"Angrist","year":"2008"},{"issue":"2","key":"ecta200098-bib-0007","doi-asserted-by":"crossref","first-page":"249","DOI":"10.2307\/2998558","volume":"66","author":"Angrist","year":"1998","journal-title":"Econometrica"},{"issue":"3","key":"ecta200098-bib-0008","doi-asserted-by":"crossref","first-page":"850","DOI":"10.1214\/13-AOS1200","volume":"42","author":"Aronow","year":"2014","journal-title":"The Annals of Statistics"},{"issue":"1","key":"ecta200098-bib-0009","doi-asserted-by":"crossref","first-page":"250","DOI":"10.1111\/ajps.12185","volume":"60","author":"Aronow","year":"2016","journal-title":"American Journal of Political Science"},{"key":"ecta200098-bib-0010","series-title":"Advanced Texts in Econometrics","doi-asserted-by":"crossref","DOI":"10.1093\/0198774036.001.0001","volume-title":"Stochastic Limit Theory: An Introduction for Econometricians","author":"Davidson","year":"1994"},{"issue":"2","key":"ecta200098-bib-0011","doi-asserted-by":"crossref","first-page":"424","DOI":"10.1257\/jel.48.2.424","volume":"48","author":"Deaton","year":"2010","journal-title":"Journal of Economic Literature"},{"issue":"4","key":"ecta200098-bib-0012","doi-asserted-by":"crossref","first-page":"1969","DOI":"10.1093\/qje\/qjx015","volume":"132","author":"DellaVigna","year":"2017","journal-title":"The Quarterly Journal of Economics"},{"issue":"2","key":"ecta200098-bib-0013","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1111\/jels.12219","volume":"16","author":"Donohue","year":"2019","journal-title":"Journal of Empirical Legal Studies"},{"key":"ecta200098-bib-0014","first-page":"59","volume-title":"Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability","volume":"1","author":"Eicker","year":"1967"},{"issue":"2","key":"ecta200098-bib-0015","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1093\/qje\/qjv005","volume":"130","author":"Einav","year":"2015","journal-title":"The Quarterly Journal of Economics"},{"issue":"4","key":"ecta200098-bib-0016","doi-asserted-by":"crossref","first-page":"1975","DOI":"10.1093\/qje\/qjv026","volume":"130","author":"Farber","year":"2015","journal-title":"The Quarterly Journal of Economics"},{"key":"ecta200098-bib-0017","unstructured":"Fogarty, C. B. (2016): \u201cRegression Assisted Inference for the Average Treatment Effect in Paired Experiments,\u201d Preprint. Available at arXiv:1612.05179."},{"issue":"2","key":"ecta200098-bib-0018","doi-asserted-by":"crossref","first-page":"180","DOI":"10.1016\/j.aam.2006.12.003","volume":"40","author":"Freedman","year":"2008","journal-title":"Advances in Applied Mathematics"},{"key":"ecta200098-bib-0019","volume-title":"A Course in Econometrics","author":"Goldberger","year":"1991"},{"issue":"3","key":"ecta200098-bib-0020","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1093\/qje\/qju015","volume":"129","author":"Hanna","year":"2014","journal-title":"The Quarterly Journal of Economics"},{"issue":"396","key":"ecta200098-bib-0021","doi-asserted-by":"crossref","first-page":"945","DOI":"10.1080\/01621459.1986.10478354","volume":"81","author":"Holland","year":"1986","journal-title":"Journal of the American Statistical Association"},{"key":"ecta200098-bib-0022","first-page":"221","volume-title":"Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability","volume":"1","author":"Huber","year":"1967"},{"key":"ecta200098-bib-0023","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139025751","volume-title":"Causal Inference in Statistics, Social, and Biomedical Sciences","author":"Imbens","year":"2015"},{"issue":"1","key":"ecta200098-bib-0024","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1353\/dem.2005.0005","volume":"42","author":"Keels","year":"2005","journal-title":"Demography"},{"issue":"1","key":"ecta200098-bib-0025","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1214\/12-AOAS583","volume":"7","author":"Lin","year":"2013","journal-title":"The Annals of Applied Statistics"},{"key":"ecta200098-bib-0026","doi-asserted-by":"crossref","first-page":"72","DOI":"10.1016\/j.spl.2016.01.010","volume":"112","author":"Lu","year":"2016","journal-title":"Statistics & Probability Letters"},{"issue":"3","key":"ecta200098-bib-0027","doi-asserted-by":"crossref","first-page":"305","DOI":"10.1016\/0304-4076(85)90158-7","volume":"29","author":"MacKinnon","year":"1985","journal-title":"Journal of Econometrics"},{"key":"ecta200098-bib-0028","doi-asserted-by":"crossref","DOI":"10.4159\/harvard.9780674067547","volume-title":"Public Policy in an Uncertain World: Analysis and Decisions","author":"Manski","year":"2013"},{"issue":"2","key":"ecta200098-bib-0029","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1162\/REST_a_00689","volume":"100","author":"Manski","year":"2018","journal-title":"Review of Economics and Statistics"},{"issue":"1","key":"ecta200098-bib-0030","first-page":"25","volume":"86","author":"Munnell","year":"1996","journal-title":"The American Economic Review"},{"issue":"4","key":"ecta200098-bib-0031","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1257\/jep.31.4.103","volume":"31","author":"Muralidharan","year":"2017","journal-title":"Journal of Economic Perspectives"},{"issue":"4","key":"ecta200098-bib-0032","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1214\/ss\/1177012031","volume":"5","author":"Neyman","year":"1923","journal-title":"Statistical Science"},{"key":"ecta200098-bib-0033","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-3692-2","volume-title":"Observational Studies","author":"Rosenbaum","year":"2002"},{"issue":"1","key":"ecta200098-bib-0034","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1093\/biomet\/70.1.41","volume":"70","author":"Rosenbaum","year":"1983","journal-title":"Biometrika"},{"issue":"5","key":"ecta200098-bib-0035","doi-asserted-by":"crossref","first-page":"688","DOI":"10.1037\/h0037350","volume":"66","author":"Rubin","year":"1974","journal-title":"Journal of Educational Psychology"},{"issue":"2","key":"ecta200098-bib-0036","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/j.spl.2011.10.024","volume":"82","author":"Samii","year":"2012","journal-title":"Statistics & Probability Letters"},{"key":"ecta200098-bib-0037","volume-title":"Experimental and Quasi-Experimental Designs for Generalized Causal Inference","author":"Shadish","year":"2002"},{"key":"ecta200098-bib-0038","unstructured":"Sloczynski, T. (2018): \u201cA General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands,\u201d IZA Discussion Paper 11866."},{"issue":"1","key":"ecta200098-bib-0039","doi-asserted-by":"crossref","first-page":"817","DOI":"10.2307\/1912934","volume":"48","author":"White","year":"1980","journal-title":"Econometrica"},{"issue":"1","key":"ecta200098-bib-0040","doi-asserted-by":"crossref","first-page":"149","DOI":"10.2307\/2526245","volume":"21","author":"White","year":"1980","journal-title":"International Economic Review"},{"issue":"1","key":"ecta200098-bib-0041","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1912526","volume":"50","author":"White","year":"1982","journal-title":"Econometrica"},{"issue":"2","key":"ecta200098-bib-0042","doi-asserted-by":"crossref","first-page":"451","DOI":"10.1017\/S0266466601172075","volume":"17","author":"Wooldridge","year":"2001","journal-title":"Econometric Theory"}],"container-title":["Econometrica"],"original-title":[],"language":"en","deposited":{"date-parts":[[2021,2,25]],"date-time":"2021-02-25T12:23:16Z","timestamp":1614255796000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/ECTA12675"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020]]},"references-count":42,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020]]}},"alternative-id":["10.3982\/ECTA12675"],"URL":"https:\/\/doi.org\/10.3982\/ecta12675","relation":{},"ISSN":["0012-9682"],"issn-type":[{"value":"0012-9682","type":"print"}],"subject":[],"published":{"date-parts":[[2020]]}}}