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

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.
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Submitted on : Tuesday, November 20, 2012 - 8:52:06 AM
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Thierry Magnac, Eric Maurin. Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data. Review of Economic Studies, Oxford University Press (OUP), 2008, 75 (3), pp.835-864. ⟨10.1111/j.1467-937X.2008.00490.x⟩. ⟨halshs-00754272⟩

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