Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data
AbstractWe investigate identification in semi-parametric binary regression models, y = 1(xÎ²+Ï…+Îµ > 0) when Ï… is either discrete or measured within intervals. The error term Îµ is assumed to be uncorrelated with a set of instruments z, Îµ is independent of Ï… conditionally on x and z, and the support of âˆ’(xÎ² + Îµ) is finite. We provide a sharp characterization of the set of observationally equivalent parameters Î². When there are as many instruments z as variables x, the bounds of the identified intervals of the different scalar components Î² k of parameter Î² 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 Ï… within intervals shrinks the identified set. Specifically, the closer the conditional distribution of Ï… given z is to uniformity, the smaller is the identified set. Point identified is achieved if and only if Ï… is uniform within intervals. Copyright 2008, Wiley-Blackwell.
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Bibliographic InfoPaper provided by Institut d'Économie Industrielle (IDEI), Toulouse in its series IDEI Working Papers with number 280.
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.
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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.
- Thierry Magnac & Eric Maurin, 2004. "Partial Identification in Monotone Binary Models : Discrete Regressors and Interval Data," Working Papers, Centre de Recherche en Economie et Statistique 2004-11, Centre de Recherche en Economie et Statistique.
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