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Abstract

We investigate inference in semi-parametric binary regression models, y = 1(x¯ +v+² > 0) when ² is assumed uncorrelated with a set of instruments z, ² is independentof v conditionally on x and z, and the conditional support of ² is su¢ciently smallrelative to the support of v. We characterize the set of observationally equivalentparameters ¯ when interval data only are available on v or when v is discrete. Whenthere exist as many instruments z as variables x, the sets within which lie the scalarcomponents ¯k of parameter ¯ can be estimated by simple linear regressions. Also, inthe case of interval data, it is shown that additional information on the distribution ofv within intervals shrinks the identi…cation set. Namely, the closer to uniformity thedistribution of v is, the smaller the identi…cation set is. Point identi…cation is achievedif and only if v is uniform within intervals.

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Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2004-11.

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Date of creation: 2004
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Handle: RePEc:crs:wpaper:2004-11

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1. Chesher, A, 2003. "Nonparametric identification under discrete variation," Open Access publications from University College London http://discovery.ucl.ac.u, University College London.
   
   • Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, 09.
   • Andrew Chesher, 2003. "Nonparametric identification under discrete variation," CeMMAP working papers CWP19/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
2. Edward Leamer, 1906. "Errors in Variables in Linear Systems," UCLA Economics Working Papers 406, UCLA Department of Economics.
   
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4. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
5. Donald Green & Karen Jacowitz & Daniel Kahneman & Daniel McFadden, 1995. "Referendum Contingent Valuation, Anchoring, and Willingness to Pay for Public Goods," Working Papers _010, University of California at Berkeley, Econometrics Laboratory Software Archive.
   
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6. Joshua Angrist & Alan Krueger, 1990. "The Effect of Age at School Entry on Educational Attainment: An Application of Instrumental Variables with Moments from Two Samples," Working Papers 654, Princeton University, Department of Economics, Industrial Relations Section..
   
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7. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics 454, Boston College Department of Economics.
   
   • Lewbel, Arthur, 2000. "Semiparametric qualitative response model estimation with unknown heteroscedasticity or instrumental variables," Journal of Econometrics, Elsevier, vol. 97(1), pages 145-177, July.
8. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, vol. 27(3), pages 313-333, March.
9. M Arellano & Costas Megir & Mary Silles, 1990. "Female Labour Supply and On-the-Job Search: An Empirical Model Estimated using Complementary Data Sets," CEP Discussion Papers dp0009, Centre for Economic Performance, LSE.
   
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Cited by:

1. Arthur Lewbel, 2012. "An Overview of the Special Regressor Method," Boston College Working Papers in Economics 810, Boston College Department of Economics.
2. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-07, Cornell University, Center for Analytic Economics.
   
   • Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, 07.
   • Arie Beresteanu & Francesca Molinari, 2006. "Asymptotic properties for a class of partially identified models," CeMMAP working papers CWP10/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
   • Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics.
3. Yingying Dong & Arthur Lewbel, 2004. "A Simple Estimator for Binary Choice Models with Endogenous Regressors," Boston College Working Papers in Economics 604, Boston College Department of Economics, revised 15 Jun 2012.
   
   • Yingying Dong & Arthur Lewbel, 2012. "A Simple Estimator for Binary Choice Models With Endogenous Regressors," Boston College Working Papers in Economics 807, Boston College Department of Economics.
4. Tatiana Komarova & Denis Nekipelov & Evgeny Yakovlev, 2011. "Identification, data combination and the risk of disclosure," CeMMAP working papers CWP38/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
5. Tatiana Komarova, 2012. "Binary Choice Models with Discrete Regressors: Identification and Misspecification," STICERD - Econometrics Paper Series em/2012/559, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
6. Banerjee, Moulinath & Mukherjee, Debasri & Mishra, Santosh, 2009. "Semiparametric binary regression models under shape constraints with an application to Indian schooling data," Journal of Econometrics, Elsevier, vol. 149(2), pages 101-117, April.

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