Journal Article

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

Thierry Magnac and Eric Maurin

in The Review of Economic Studies

Published on behalf of Review of Economic Studies Ltd

Volume 75, issue 3, pages 835-864
Published in print July 2008 | ISSN: 0034-6527
Published online July 2008 | e-ISSN: 1467-937X | DOI: http://dx.doi.org/10.1111/j.1467-937X.2008.00490.x
Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data

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  • Econometric and Statistical Methods and Methodology: General
  • Single Equation Models; Single Variables

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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.

Keywords: C14; C25

Journal Article.  12027 words.  Illustrated.

Subjects: Econometric and Statistical Methods and Methodology: General ; Single Equation Models; Single Variables

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