{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T18:31:45Z","timestamp":1778783505712,"version":"3.51.4"},"reference-count":28,"publisher":"The Econometric Society","issue":"1","license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["ECTA"],"abstract":"<jats:p>An important goal of empirical demand analysis is choice and welfare prediction on counterfactual budget sets arising from potential policy interventions. Such predictions are more credible when made without arbitrary functional\u2010form\/distributional assumptions, and instead based solely on economic rationality, that is, that choice is consistent with utility maximization by a heterogeneous population. This paper investigates nonparametric economic rationality in the empirically important context of binary choice. We show that under general unobserved heterogeneity, economic rationality is equivalent to a pair of Slutsky\u2010like shape restrictions on choice\u2010probability functions. The forms of these restrictions differ from Slutsky inequalities for continuous goods. Unlike McFadden\u2013Richter's stochastic revealed preference, our shape restrictions (a) are global, that is, their forms do not depend on which and how many budget sets are observed, (b) are closed form, hence easy to impose on parametric\/semi\/nonparametric models in practical applications, and (c) provide computationally simple, theory\u2010consistent bounds on demand and welfare predictions on counterfactual budge sets.<\/jats:p>","DOI":"10.3982\/ecta16801","type":"journal-article","created":{"date-parts":[[2021,1,12]],"date-time":"2021-01-12T08:05:05Z","timestamp":1610438705000},"page":"457-474","source":"Crossref","is-referenced-by-count":12,"title":["The Empirical Content of Binary Choice Models"],"prefix":"10.3982","volume":"89","author":[{"given":"Debopam","family":"Bhattacharya","sequence":"first","affiliation":[{"name":"Department of Economics, University of Cambridge"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"2359","published-online":{"date-parts":[[2021]]},"reference":[{"key":"ecta200242-bib-0001","doi-asserted-by":"crossref","DOI":"10.7551\/mitpress\/2450.001.0001","volume-title":"Discrete Choice Theory of Product Differentiation","author":"Anderson","year":"1992"},{"issue":"3","key":"ecta200242-bib-0002","doi-asserted-by":"crossref","first-page":"795","DOI":"10.1017\/S0266466608080328","volume":"24","author":"Bhattacharya","year":"2008","journal-title":"Econometric Theory"},{"issue":"2","key":"ecta200242-bib-0003","doi-asserted-by":"crossref","first-page":"617","DOI":"10.3982\/ECTA12574","volume":"83","author":"Bhattacharya","year":"2015","journal-title":"Econometrica"},{"issue":"2","key":"ecta200242-bib-0004","doi-asserted-by":"crossref","first-page":"571","DOI":"10.3982\/QE931","volume":"9","author":"Bhattacharya","year":"2018","journal-title":"Quantitative Economics"},{"key":"ecta200242-bib-0005","doi-asserted-by":"crossref","unstructured":"Bhattacharya, D. (2021): \u201cSupplement to \u2018The Empirical Content of Binary Choice Models\u2019,\u201d Econometrica Supplemental Material, 89, https:\/\/doi.org\/10.3982\/ECTA16801.","DOI":"10.3982\/ECTA16801"},{"key":"ecta200242-bib-0006","first-page":"312","volume":"36","author":"Blundell","year":"2003","journal-title":"Econometric Society Monographs"},{"issue":"3","key":"ecta200242-bib-0007","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1111\/j.1467-937X.2004.00299.x","volume":"71","author":"Blundell","year":"2004","journal-title":"The Review of Economic Studies"},{"issue":"2","key":"ecta200242-bib-0008","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/S0304-4076(97)00090-0","volume":"84","author":"Cavanagh","year":"1998","journal-title":"Journal of Econometrics"},{"key":"ecta200242-bib-0009","first-page":"1","author":"Chetverikov","year":"2012","journal-title":"Econometric Theory"},{"issue":"1","key":"ecta200242-bib-0010","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1016\/j.jeconom.2015.07.004","volume":"191","author":"Dette","year":"2016","journal-title":"Journal of Econometrics"},{"issue":"4","key":"ecta200242-bib-0011","doi-asserted-by":"crossref","first-page":"1054","DOI":"10.1214\/aos\/1015956707","volume":"28","author":"Ghosal","year":"2000","journal-title":"The Annals of Statistics"},{"issue":"1","key":"ecta200242-bib-0012","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1214\/aos\/1016120363","volume":"28","author":"Hall","year":"2000","journal-title":"The Annals of Statistics"},{"issue":"2-3","key":"ecta200242-bib-0013","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0304-4076(87)90030-3","volume":"35","author":"Han","year":"1987","journal-title":"Journal of Econometrics"},{"issue":"3","key":"ecta200242-bib-0014","doi-asserted-by":"crossref","first-page":"1225","DOI":"10.3982\/ECTA11899","volume":"84","author":"Hausman","year":"2016","journal-title":"Econometrica"},{"issue":"2","key":"ecta200242-bib-0015","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1016\/j.jeconom.2011.06.015","volume":"164","author":"Hoderlein","year":"2011","journal-title":"Journal of Econometrics"},{"issue":"2","key":"ecta200242-bib-0016","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1162\/REST_a_00397","volume":"96","author":"Hoderlein","year":"2014","journal-title":"Review of Economics and Statistics"},{"issue":"5","key":"ecta200242-bib-0017","doi-asserted-by":"crossref","first-page":"1481","DOI":"10.3982\/ECTA7108","volume":"77","author":"Imbens","year":"2009","journal-title":"Econometrica"},{"issue":"6","key":"ecta200242-bib-0018","doi-asserted-by":"crossref","first-page":"1883","DOI":"10.3982\/ECTA14478","volume":"86","author":"Kitamura","year":"2016","journal-title":"Econometrica"},{"key":"ecta200242-bib-0019","doi-asserted-by":"crossref","first-page":"387","DOI":"10.2307\/2951556","author":"Klein","year":"1993","journal-title":"Econometrica"},{"issue":"2","key":"ecta200242-bib-0020","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.jeconom.2019.02.007","volume":"211","author":"Lee","year":"2019","journal-title":"Journal of Econometrics"},{"key":"ecta200242-bib-0021","doi-asserted-by":"crossref","first-page":"611","DOI":"10.1257\/aer.91.3.611","author":"Lewbel","year":"2001","journal-title":"American Economic Review"},{"issue":"3","key":"ecta200242-bib-0022","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0304-4076(75)90032-9","volume":"3","author":"Manski","year":"1975","journal-title":"Journal of Econometrics"},{"key":"ecta200242-bib-0023","doi-asserted-by":"crossref","first-page":"239","DOI":"10.2307\/2951596","author":"Matzkin","year":"1992","journal-title":"Econometrica"},{"key":"ecta200242-bib-0024","unstructured":"McFadden, D. (1973): \u201cConditional Logit Analysis of Qualitative Choice Behavior.\u201d"},{"issue":"2","key":"ecta200242-bib-0025","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s00199-004-0495-3","volume":"26","author":"McFadden","year":"2005","journal-title":"Economic Theory"},{"key":"ecta200242-bib-0026","first-page":"161","volume-title":"Preferences, Uncertainty, and Optimality, Essays in Honor of Leo Hurwicz","author":"McFadden","year":"1990"},{"key":"ecta200242-bib-0027","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4615-7676-1","volume-title":"Probability for Applications","author":"Pfeiffer","year":"1990"},{"key":"ecta200242-bib-0028","volume-title":"Discrete Choice Methods With Simulation","author":"Train","year":"2009"}],"container-title":["Econometrica"],"original-title":[],"language":"en","deposited":{"date-parts":[[2021,1,12]],"date-time":"2021-01-12T08:51:03Z","timestamp":1610441463000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.econometricsociety.org\/doi\/10.3982\/ECTA16801"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"references-count":28,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021]]}},"alternative-id":["10.3982\/ECTA16801"],"URL":"https:\/\/doi.org\/10.3982\/ecta16801","relation":{},"ISSN":["0012-9682"],"issn-type":[{"value":"0012-9682","type":"print"}],"subject":[],"published":{"date-parts":[[2021]]}}}