{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T02:04:04Z","timestamp":1775181844954,"version":"3.50.1"},"reference-count":36,"publisher":"The Econometric Society","issue":"2","license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["QE"],"abstract":"<jats:p>We consider inference about a scalar coefficient in a linear regression model. One previously considered approach to dealing with many controls imposes sparsity, that is, it is assumed known that nearly all control coefficients are (very nearly) zero. We instead impose a bound on the quadratic mean of the controls' effect on the dependent variable, which also has an interpretation as an<jats:italic>R<\/jats:italic><jats:sup>2<\/jats:sup>\u2010type bound on the explanatory power of the controls. We develop a simple inference procedure that exploits this additional information in general heteroskedastic models. We study its asymptotic efficiency properties and compare it to a sparsity\u2010based approach in a Monte Carlo study. The method is illustrated in three empirical applications.<\/jats:p>","DOI":"10.3982\/qe1577","type":"journal-article","created":{"date-parts":[[2021,4,20]],"date-time":"2021-04-20T12:52:55Z","timestamp":1618923175000},"page":"405-442","source":"Crossref","is-referenced-by-count":12,"title":["Linear regression with many controls of limited explanatory power"],"prefix":"10.3982","volume":"12","author":[{"given":"Chenchuan (Mark)","family":"Li","sequence":"first","affiliation":[{"name":"Department of Economics, Princeton University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ulrich K.","family":"M\u00fcller","sequence":"additional","affiliation":[{"name":"Department of Economics, Princeton University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2359","published-online":{"date-parts":[[2021]]},"reference":[{"key":"quan200146-bib-0001","doi-asserted-by":"crossref","first-page":"570","DOI":"10.1214\/aoms\/1177729752","volume":"21","author":"Anderson","year":"1949","journal-title":"The Annals of Mathematical Statistics"},{"key":"quan200146-bib-0002","doi-asserted-by":"crossref","unstructured":"Armstrong, T. B. and M. Koles\u00e1r (2016), \u201cOptimal inference in a class of regression models.\u201d arXiv:1511.06028v2.","DOI":"10.2139\/ssrn.2998236"},{"key":"quan200146-bib-0003","doi-asserted-by":"crossref","DOI":"10.3982\/ECTA14434","volume":"86","author":"Armstrong","year":"2018","journal-title":"Econometrica"},{"issue":"2","key":"quan200146-bib-0004","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1093\/restud\/rdt044","volume":"81","author":"Belloni","year":"2014","journal-title":"The Review of Economic Studies"},{"issue":"2","key":"quan200146-bib-0005","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1017\/S026646661600013X","volume":"34","author":"Cattaneo","year":"2018","journal-title":"Econometric Theory"},{"issue":"523","key":"quan200146-bib-0006","doi-asserted-by":"crossref","first-page":"1350","DOI":"10.1080\/01621459.2017.1328360","volume":"113","author":"Cattaneo","year":"2018","journal-title":"Journal of the American Statistical Association"},{"issue":"1","key":"quan200146-bib-0007","doi-asserted-by":"crossref","first-page":"260","DOI":"10.1162\/REST_a_00139","volume":"94","author":"Conley","year":"2012","journal-title":"Review of Economics and Statistics"},{"key":"quan200146-bib-0008","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4899-2887-0","volume-title":"Theoretical Statistics","author":"Cox","year":"1974"},{"issue":"1","key":"quan200146-bib-0009","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1214\/aos\/1176325367","volume":"22","author":"Donoho","year":"1994","journal-title":"The Annals of Statistics"},{"key":"quan200146-bib-0010","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1162\/00335530151144050","volume":"CXVI","author":"Donohue","year":"2001","journal-title":"Quarterly Journal of Economics"},{"key":"quan200146-bib-0011","doi-asserted-by":"crossref","first-page":"771","DOI":"10.3982\/ECTA10535","volume":"83","author":"Elliott","year":"2015","journal-title":"Econometrica"},{"issue":"456","key":"quan200146-bib-0012","doi-asserted-by":"crossref","first-page":"1348","DOI":"10.1198\/016214501753382273","volume":"96","author":"Fan","year":"2001","journal-title":"Journal of the American Statistical Association"},{"key":"quan200146-bib-0013","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1162\/qjec.2008.123.1.407","volume":"123","author":"Foote","year":"2008","journal-title":"The Quarterly Journal of Economics"},{"issue":"1","key":"quan200146-bib-0014","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1080\/00401706.1970.10488634","volume":"12","author":"Hoerl","year":"1970","journal-title":"Technometrics"},{"key":"quan200146-bib-0015","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1257\/aer.91.4.778","volume":"91","author":"Imbens","year":"2001","journal-title":"American Economic Review"},{"key":"quan200146-bib-0016","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139025751","volume-title":"Causal Inference for Statistics, Social, and Biomedical Sciences","author":"Imbens","year":"2015"},{"key":"quan200146-bib-0017","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1257\/jel.47.1.5","volume":"47","author":"Imbens","year":"2009","journal-title":"Journal of Economic Literature"},{"issue":"1","key":"quan200146-bib-0018","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/3559003","volume":"39","author":"Joyce","year":"2004","journal-title":"Journal of Human Resources"},{"issue":"1","key":"quan200146-bib-0019","doi-asserted-by":"crossref","first-page":"112","DOI":"10.1162\/rest.91.1.112","volume":"91","author":"Joyce","year":"2009","journal-title":"The Review of Economics and Statistics"},{"key":"quan200146-bib-0020","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1017\/S0266466605050036","volume":"21","author":"Leeb","year":"2005","journal-title":"Econometric Theory"},{"issue":"2","key":"quan200146-bib-0021","first-page":"338","volume":"24","author":"Leeb","year":"2008","journal-title":"Econometric Theory"},{"issue":"2","key":"quan200146-bib-0022","first-page":"319","volume":"24","author":"Leeb","year":"2008","journal-title":"Econometric Theory"},{"key":"quan200146-bib-0023","doi-asserted-by":"crossref","unstructured":"Li, C. (M.) and U. K. M\u00fcller (2021), \u201cSupplement to \u2018Linear regression with many controls of limited explanatory power\u2019.\u201d Quantitative Economics Supplemental Material, 12, https:\/\/doi.org\/10.3982\/QE1577.","DOI":"10.3982\/QE1577"},{"key":"quan200146-bib-0024","doi-asserted-by":"crossref","first-page":"2911","DOI":"10.1257\/aer.20120141","volume":"105","author":"Macchiavello","year":"2015","journal-title":"American Economic Review"},{"key":"quan200146-bib-0025","series-title":"Wiley Series in Probability and Statistics","volume-title":"Directional Statistics","author":"Mardia","year":"2000"},{"key":"quan200146-bib-0026","doi-asserted-by":"crossref","first-page":"2183","DOI":"10.3982\/ECTA14023","volume":"84","author":"M\u00fcller","year":"2016","journal-title":"Econometrica"},{"key":"quan200146-bib-0027","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.jeconom.2018.11.016","volume":"209","author":"M\u00fcller","year":"2019","journal-title":"Journal of Econometrics"},{"key":"quan200146-bib-0028","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1080\/00401706.1977.10489582","volume":"19","author":"Obenchain","year":"1977","journal-title":"Technometrics"},{"key":"quan200146-bib-0029","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1080\/01621459.1961.10480644","volume":"56","author":"Pratt","year":"1961","journal-title":"Journal of the American Statistical Association"},{"key":"quan200146-bib-0030","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1111\/j.2517-6161.1996.tb02080.x","volume":"58","author":"Tibshirani","year":"1996","journal-title":"Journal of the Royal Statistical Society. Series B (Methodological)"},{"key":"quan200146-bib-0031","first-page":"1166","volume":"42","author":"Geer","year":"2014","journal-title":"Annals of Statistics"},{"key":"quan200146-bib-0032","doi-asserted-by":"crossref","first-page":"97","DOI":"10.2307\/1403577","volume":"259","author":"Vaart","year":"1991","journal-title":"International Statistical Review"},{"key":"quan200146-bib-0033","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511802256","volume-title":"Asymptotic Statistics","author":"Vaart","year":"1998"},{"key":"quan200146-bib-0034","doi-asserted-by":"crossref","first-page":"817","DOI":"10.2307\/1912934","volume":"48","author":"White","year":"1980","journal-title":"Econometrica"},{"key":"quan200146-bib-0035","unstructured":"W\u00fcthrich, K. and Y. Zhu (2020), \u201cOmitted variable bias of lasso-based inference methods: A finite sample analysis.\u201d arXiv:1903.08704."},{"key":"quan200146-bib-0036","first-page":"217","volume":"76","author":"Zhang","year":"2014","journal-title":"Journal of the Royal StatisticalSociety: Series B (Statistical Methodology)"}],"container-title":["Quantitative Economics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.3982\/QE1577","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,12,24]],"date-time":"2022-12-24T20:49:20Z","timestamp":1671914960000},"score":1,"resource":{"primary":{"URL":"http:\/\/qeconomics.org\/ojs\/index.php\/qe\/article\/view\/QE1577"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"references-count":36,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021]]}},"alternative-id":["10.3982\/QE1577"],"URL":"https:\/\/doi.org\/10.3982\/qe1577","relation":{},"ISSN":["1759-7323"],"issn-type":[{"value":"1759-7323","type":"print"}],"subject":[],"published":{"date-parts":[[2021]]}}}