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

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  • Thierry Magnac

    (GREMAQ - Groupe de recherche en économie mathématique et quantitative - UT1 - Université Toulouse 1 Capitole - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique, IDEI - Institut d'économie industrielle - UT1 - Université Toulouse 1 Capitole, TSE - Toulouse School of Economics - Toulouse School of Economics)

  • Eric Maurin

    (PJSE - Paris-Jourdan Sciences Economiques - ENS Paris - École normale supérieure - Paris - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics)

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 βk 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.

Suggested Citation

  • Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," Post-Print halshs-00754272, HAL.
  • Handle: RePEc:hal:journl:halshs-00754272
    DOI: 10.1111/j.1467-937X.2008.00490.x
    Note: View the original document on HAL open archive server: https://hal-pjse.archives-ouvertes.fr/halshs-00754272
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    References listed on IDEAS

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