{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,5]],"date-time":"2026-09-05T21:16:08Z","timestamp":1788642968185,"version":"build-2803163510"},"reference-count":32,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2017,11,2]],"date-time":"2017-11-02T00:00:00Z","timestamp":1509580800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["www.cambridge.org"],"crossmark-restriction":true},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2018,12]]},"abstract":"The intercept of the binary response model is not regularly identified (i.e., $\\sqrt n$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> consistently estimable) when the support of both the special regressor V<\/jats:italic> and the error term \u03b5<\/jats:italic> are the whole real line. The estimator of the intercept potentially has a slower than $\\sqrt n$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> convergence rate, which can result in a large estimation error in practice. This paper imposes additional tail restrictions which guarantee the regular identification of the intercept and thus the $\\sqrt n$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-consistency of its estimator. We then propose an estimator that achieves the $\\sqrt n$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> rate. Last, we extend our tail restrictions to a full-blown model with endogenous regressors.<\/jats:p>","DOI":"10.1017\/s026646661700041x","type":"journal-article","created":{"date-parts":[[2017,11,2]],"date-time":"2017-11-02T10:53:47Z","timestamp":1509620027000},"page":"1180-1206","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":2,"title":["ROOT-N CONSISTENCY OF INTERCEPT ESTIMATORS IN A BINARY RESPONSE MODEL UNDER TAIL RESTRICTIONS"],"prefix":"10.1017","volume":"34","author":[{"given":"Lili","family":"Tan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yichong","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2017,11,2]]},"reference":[{"key":"S026646661700041X_ref22","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/0304-4076(75)90032-9","article-title":"Maximum score estimation of the stochastic utility model of choice","volume":"3","author":"Manski","year":"1975","journal-title":"Journal of Econometrics"},{"key":"S026646661700041X_ref11","unstructured":"Hill, J.B. & Renault, E. (2010) Generalized method of moments with tail trimming. Working paper, University of North Carolina, Chapel Hill."},{"key":"S026646661700041X_ref26","doi-asserted-by":"crossref","first-page":"1403","DOI":"10.2307\/1913713","article-title":"Semiparametric estimation of index coefficients","volume":"57","author":"Powell","year":"1989","journal-title":"Econometrica"},{"key":"S026646661700041X_ref10","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1016\/0304-4076(87)90030-3","article-title":"Non-parametric analysis of a generalized regression model: The maximum rank correlation estimator","volume":"35","author":"Han","year":"1987","journal-title":"Journal of Econometrics"},{"key":"S026646661700041X_ref5","doi-asserted-by":"crossref","unstructured":"De Haan, L. & Ferreira, A. (2007) Extreme Value Theory: An Introduction, Springer Science & Business Media.","DOI":"10.1007\/0-387-34471-3"},{"key":"S026646661700041X_ref20","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1016\/j.jeconom.2010.11.006","article-title":"Estimating features of a distribution from binomial data","volume":"162","author":"Lewbel","year":"2011","journal-title":"Journal of Econometrics"},{"key":"S026646661700041X_ref12","doi-asserted-by":"crossref","first-page":"505","DOI":"10.2307\/2951582","article-title":"A smoothed maximum score estimator for the binary response model","volume":"60","author":"Horowitz","year":"1992","journal-title":"Econometrica"},{"key":"S026646661700041X_ref13","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0304-4076(93)90114-K","article-title":"Semiparametric least squares (SLS) and weighted SLS estimation of single-index models","volume":"58","author":"Ichimura","year":"1993","journal-title":"Journal of Econometrics"},{"key":"S026646661700041X_ref30","first-page":"99","volume-title":"Nonparametric and Semiparametric Methods in Econometrics and Statistics","author":"Stoker","year":"1991"},{"key":"S026646661700041X_ref28","volume-title":"Heavy-tail Phenomena: Probabilistic and Statistical Modeling","author":"Resnick","year":"2007"},{"key":"S026646661700041X_ref6","doi-asserted-by":"crossref","first-page":"1795","DOI":"10.1214\/aos\/1176347396","article-title":"On the estimation of the extreme-value index and large quantile estimation","volume":"17","author":"Dekkers","year":"1989","journal-title":"Annals of Statistics"},{"key":"S026646661700041X_ref17","doi-asserted-by":"crossref","first-page":"32","DOI":"10.1017\/S0266466600005636","article-title":"Semiparametric estimation of location and other discrete choice moments","volume":"13","author":"Lewbel","year":"1997","journal-title":"Econometric Theory"},{"key":"S026646661700041X_ref21","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/j.jeconom.2006.06.005","article-title":"Identification and information in monotone binary models","volume":"139","author":"Magnac","year":"2007","journal-title":"Journal of Econometrics"},{"key":"S026646661700041X_ref7","unstructured":"D\u2019Haultfoeuille, X. , Maurel, A. , & Zhang, Y. (2016) Extremal quantile regressions for selection models and the black-white wage gap. Working paper, Duke University."},{"key":"S026646661700041X_ref15","doi-asserted-by":"crossref","first-page":"2021","DOI":"10.3982\/ECTA7372","article-title":"Irregular identification, support conditions, and inverse weight estimation","volume":"78","author":"Khan","year":"2010","journal-title":"Econometrica"},{"key":"S026646661700041X_ref1","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1111\/1467-937X.00055","article-title":"Semiparametric estimation of the intercept of a sample selection model","volume":"65","author":"Andrews","year":"1998","journal-title":"The Review of Economic Studies"},{"key":"S026646661700041X_ref24","doi-asserted-by":"crossref","first-page":"729","DOI":"10.1080\/01621459.1988.10478655","article-title":"Identification of binary response models","volume":"83","author":"Manski","year":"1988","journal-title":"Journal of the American Statistical Association"},{"key":"S026646661700041X_ref23","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0304-4076(85)90009-0","article-title":"Semiparametric analysis of discrete response: Asymptotic properties of the maximum score estimator","volume":"27","author":"Manski","year":"1985","journal-title":"Journal of Econometrics"},{"key":"S026646661700041X_ref16","doi-asserted-by":"crossref","first-page":"387","DOI":"10.2307\/2951556","article-title":"An efficient semiparametric estimator for binary response models","volume":"61","author":"Klein","year":"1993","journal-title":"Econometrica"},{"key":"S026646661700041X_ref27","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-387-75953-1","volume-title":"Extreme Values, Regular Variation, and Point Processes","author":"Resnick","year":"1987"},{"key":"S026646661700041X_ref19","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/j.jeconom.2005.08.005","article-title":"A simple ordered data estimator for inverse density weighted expectations","volume":"136","author":"Lewbel","year":"2007","journal-title":"Journal of Econometrics"},{"key":"S026646661700041X_ref4","doi-asserted-by":"crossref","first-page":"162","DOI":"10.1016\/j.jeconom.2015.12.018","article-title":"Informational content of special regressors in heteroskedastic binary response models","volume":"193","author":"Chen","year":"2016","journal-title":"Journal of Econometrics"},{"key":"S026646661700041X_ref2","doi-asserted-by":"crossref","first-page":"655","DOI":"10.1111\/j.1467-937X.2004.00299.x","article-title":"Endogeneity in semiparametric binary response models","volume":"71","author":"Blundell","year":"2004","journal-title":"The Review of Economic Studies"},{"key":"S026646661700041X_ref31","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511802256","volume-title":"Asymptotic Statistics","volume":"vol. 3","author":"Van der Vaart","year":"1998"},{"key":"S026646661700041X_ref18","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/S0304-4076(00)00015-4","article-title":"Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables","volume":"97","author":"Lewbel","year":"2000","journal-title":"Journal of Econometrics"},{"key":"S026646661700041X_ref32","unstructured":"Yang, T . (2015) Asymptotic trimming and rate adaptive inference for endogenous selection estimates. Working paper."},{"key":"S026646661700041X_ref9","doi-asserted-by":"crossref","first-page":"359","DOI":"10.1016\/0304-4149(91)90100-Q","article-title":"A note on the inverse bootstrap process for large quantiles","volume":"38","author":"Falk","year":"1991","journal-title":"Stochastic Processes and Their Applications"},{"key":"S026646661700041X_ref25","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/0304-4076(95)01761-5","article-title":"Optimal bandwidth choice for density-weighted averages","volume":"75","author":"Powell","year":"1996","journal-title":"Journal of Econometrics"},{"key":"S026646661700041X_ref14","doi-asserted-by":"crossref","first-page":"847","DOI":"10.1017\/S0266466609090732","article-title":"Efficiency bounds for semiparametric estimation of inverse conditional-density-weighted functions","volume":"25","author":"Jacho-Ch\u00e1vez","year":"2009","journal-title":"Econometric Theory"},{"key":"S026646661700041X_ref3","unstructured":"Chaudhuri, S. & Hill, J.B. (2015) Robust estimation for average treatment effects. Working paper, University of North Carolina, Chapel Hill."},{"key":"S026646661700041X_ref29","doi-asserted-by":"crossref","first-page":"931","DOI":"10.2307\/1912705","article-title":"Root-N-consistent semiparametric regression","volume":"56","author":"Robinson","year":"1988","journal-title":"Econometrica"},{"key":"S026646661700041X_ref8","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1080\/07474938.2014.944470","article-title":"A simple estimator for binary choice models with endogenous regressors","volume":"34","author":"Dong","year":"2015","journal-title":"Econometric Reviews"}],"container-title":["Econometric Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S026646661700041X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,12]],"date-time":"2020-12-12T00:59:35Z","timestamp":1607734775000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S026646661700041X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,11,2]]},"references-count":32,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2018,12]]}},"alternative-id":["S026646661700041X"],"URL":"https:\/\/doi.org\/10.1017\/s026646661700041x","relation":{},"ISSN":["0266-4666","1469-4360"],"issn-type":[{"value":"0266-4666","type":"print"},{"value":"1469-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,11,2]]},"assertion":[{"value":"Copyright \u00a9 Cambridge University Press 2017\u00a0","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}