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 â(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 2004-11, Centre de Recherche en Economie et Statistique.
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