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Partial Identification in Monotone Binary Models : Discrete Regressors and Interval Data

  • Thierry Magnac


  • Eric Maurin


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. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, 09.
  2. 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.
  3. 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.
  4. Bierens, H.J. & Hartog, J.A., 1988. "Nonlineair regression with discrete explanatory variables : with an application to the earnings function," Serie Research Memoranda 0003, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
  5. 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.
  6. 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.
  7. Edward Leamer, 1906. "Errors in Variables in Linear Systems," UCLA Economics Working Papers 406, UCLA Department of Economics.
  8. Bo E. Honore & Arthur Lewbel, 1998. "Semiparametric Binary Choice Panel Data Models without Strictly Exogeneous Regressors," Boston College Working Papers in Economics 455, Boston College Department of Economics, revised 22 Sep 2001.
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