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

  • Magnac, Thierry
  • Maurin, Eric

We investigate identification in semi-parametric binary regression models, y = 1(xβ+υ+ε > 0) when υ is either discrete or measured within intervals. The error term ε is assumed to be uncorrelated with a set of instruments z, ε is independent of υ conditionally on x and z, and the support of −(xβ + ε) is finite. We provide a sharp characterization of the set of observationally equivalent parameters β. When there are as many instruments z as variables x, the bounds of the identified intervals of the different scalar components β k of parameter β can be expressed as simple moments of the data. Also, in the case of interval data, we show that additional information on the distribution of υ within intervals shrinks the identified set. Specifically, the closer the conditional distribution of υ given z is to uniformity, the smaller is the identified set. Point identified is achieved if and only if υ is uniform within intervals. Copyright 2008, Wiley-Blackwell.

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Paper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 280.

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Date of creation: Sep 2004
Date of revision: Jan 2005
Publication status: Published in The Review of Economic Studies, vol.�75, n°3, juillet 2008, p.�835-864.
Handle: RePEc:ide:wpaper:2259
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  1. Bo E. Honore & Arthur Lewbel, 2002. "Semiparametric Binary Choice Panel Data Models Without Strictly Exogeneous Regressors," Econometrica, Econometric Society, vol. 70(5), pages 2053-2063, September.
  2. Bierens, Herman J. & Hartog, Joop, 1988. "Non-linear regression with discrete explanatory variables, with an application to the earnings function," Journal of Econometrics, Elsevier, vol. 38(3), pages 269-299, July.
  3. 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.
  4. 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.
  5. 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.
  6. Leamer, Edward E, 1987. "Errors in Variables in Linear Systems," Econometrica, Econometric Society, vol. 55(4), pages 893-909, July.
  7. Green, Donald & Jacowitz, Karen E. & Kahneman, Daniel & McFadden, Daniel, 1998. "Referendum contingent valuation, anchoring, and willingness to pay for public goods," Resource and Energy Economics, Elsevier, vol. 20(2), pages 85-116, June.
  8. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, vol. 73(5), pages 1525-1550, 09.
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