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

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

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THIERRY MAGNAC
ERIC MAURIN

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Abstract

We investigate identification in semi-parametric binary regression models, "y"= 1("x""β"+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 - ("x""β"+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 The Review of Economic Studies Limited.

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Article provided by Blackwell Publishing in its journal Review of Economic Studies.

Volume (Year): 75 (2008)
Issue (Month): 3 (07)
Pages: 835-864
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Handle: RePEc:bla:restud:v:75:y:2008:i:3:p:835-864

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Paper
- 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. [Downloadable!]
- 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. [Downloadable!]

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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics. [Downloadable!]
Other versions:
- Arie Beresteanu & Francesca Molinari, 2006. "Asymptotic properties for a class of partially identified models," CeMMAP working papers CWP10/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
- Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-07, Cornell University, Center for Analytic Economics. [Downloadable!]
- Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, 07. [Downloadable!] (restricted)

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