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

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  • Magnac, Thierry
  • Maurin, Eric

Abstract

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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Bibliographic Info

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. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, Econometric Society, vol. 73(5), pages 1525-1550, 09.
  2. 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..
  3. Edward Leamer, 1906. "Errors in Variables in Linear Systems," UCLA Economics Working Papers, UCLA Department of Economics 406, UCLA Department of Economics.
  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. Arthur Lewbel, 1999. "Semiparametric Qualitative Response Model Estimation with Unknown Heteroskedasticity or Instrumental Variables," Boston College Working Papers in Economics, Boston College Department of Economics 454, Boston College Department of Economics.
  6. Arellano, Manuel & Meghir, Costas, 1992. "Female Labour Supply and On-the-Job Search: An Empirical Model Estimated Using Complementary Data Sets," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 59(3), pages 537-59, 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, Elsevier, vol. 20(2), pages 85-116, June.
  8. Manski, Charles F., 1985. "Semiparametric analysis of discrete response : Asymptotic properties of the maximum score estimator," Journal of Econometrics, Elsevier, Elsevier, vol. 27(3), pages 313-333, March.
  9. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, Econometric Society, vol. 70(2), pages 519-546, March.
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