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

  • Thierry Magnac
  • Eric Maurin

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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File URL: http://hdl.handle.net/10.1111/j.1467-937X.2008.00490.x
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Article provided by Oxford University Press in its journal The Review of Economic Studies.

Volume (Year): 75 (2008)
Issue (Month): 3 ()
Pages: 835-864

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Handle: RePEc:oup:restud:v:75:y:2008:i:3:p:835-864
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