{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,24]],"date-time":"2026-09-24T23:15:38Z","timestamp":1790291738800,"version":"4.1.0"},"reference-count":63,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T00:00:00Z","timestamp":1706227200000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2025,6]]},"abstract":"<jats:p>It is common to assume in empirical research that observables and unobservables are additively separable, especially when the former are endogenous. This is because it is widely recognized that identification and estimation challenges arise when interactions between the two are allowed for. Starting from a nonseparable IV model, where the instrumental variable is independent of unobservables, we develop a novel nonparametric test of separability of unobservables. The large-sample distribution of the test statistics is nonstandard and relies on a Donsker-type central limit theorem for the empirical distribution of nonparametric IV residuals, which may be of independent interest. Using a dataset drawn from the 2015 U.S. Consumer Expenditure Survey, we find that the test rejects the separability in Engel curves for some commodities.<\/jats:p>","DOI":"10.1017\/s026646662400001x","type":"journal-article","created":{"date-parts":[[2024,1,26]],"date-time":"2024-01-26T06:52:50Z","timestamp":1706251970000},"page":"551-583","source":"Crossref","is-referenced-by-count":3,"title":["ARE UNOBSERVABLES SEPARABLE?"],"prefix":"10.1017","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3996-6051","authenticated-orcid":false,"given":"Andrii","family":"Babii","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6708-5174","authenticated-orcid":false,"given":"Jean-Pierre","family":"Florens","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2024,1,26]]},"reference":[{"key":"S026646662400001X_r25","doi-asserted-by":"crossref","first-page":"1541","DOI":"10.3982\/ECTA6539","article-title":"Nonparametric instrumental regression","volume":"79","author":"Darolles","year":"2011","journal-title":"Econometrica"},{"key":"S026646662400001X_r38","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/j.jeconom.2011.08.006","article-title":"Tikhonov regularization for nonparametric instrumental variable estimators","volume":"167","author":"Gagliardini","year":"2012","journal-title":"Journal of Econometrics"},{"key":"S026646662400001X_r60","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1080\/07474938.2014.956621","article-title":"Testing additive separability of error term in nonparametric structural models","volume":"34","author":"Su","year":"2015","journal-title":"Econometric Reviews"},{"key":"S026646662400001X_r30","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.jeconom.2007.08.008","article-title":"Specification tests in nonparametric regression","volume":"143","author":"Einmahl","year":"2008","journal-title":"Journal of Econometrics"},{"key":"S026646662400001X_r59","first-page":"1115","volume":"17","author":"Pardo-Fern\u00e1ndez","year":"2007","journal-title":"Statistica Sinica"},{"key":"S026646662400001X_r35","doi-asserted-by":"crossref","first-page":"284","DOI":"10.1017\/CBO9780511610257.010","volume-title":"Advances in economics and econometrics: Theory and applications, eighth World Congress","volume":"II","author":"Florens","year":"2003"},{"key":"S026646662400001X_r1","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1111\/1467-9469.00254","article-title":"Non-parametric estimation of the residual distribution","volume":"28","author":"Akritas","year":"2001","journal-title":"Scandinavian Journal of Statistics"},{"key":"S026646662400001X_r12","first-page":"64","volume-title":"The Oxford handbook of applied nonparametric and semiparametric econometrics and statistics","author":"Carrasco","year":"2014"},{"key":"S026646662400001X_r6","unstructured":"Babii, A. , & Florens, J.-P. 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