Partial Identification in Monotone Binary Models : Discrete Regressors and Interval Data
AbstractWe investigate inference in semi-parametric binary regression models, y = 1(x¯ +v+² > 0) when ² is assumed uncorrelated with a set of instruments z, ² is independentof v conditionally on x and z, and the conditional support of ² is su¢ciently smallrelative to the support of v. We characterize the set of observationally equivalentparameters ¯ when interval data only are available on v or when v is discrete. Whenthere exist as many instruments z as variables x, the sets within which lie the scalarcomponents ¯k of parameter ¯ can be estimated by simple linear regressions. Also, inthe case of interval data, it is shown that additional information on the distribution ofv within intervals shrinks the identi…cation set. Namely, the closer to uniformity thedistribution of v is, the smaller the identi…cation set is. Point identi…cation is achievedif and only if v is uniform within intervals.
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Bibliographic InfoPaper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2004-11.
Date of creation: 2004
Date of revision:
Other versions of this item:
- Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 835-864.
- Magnac, Thierry & Maurin, Eric, 2004. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," IDEI Working Papers 280, Institut d'Économie Industrielle (IDEI), Toulouse, revised Jan 2005.
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