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SEMIPARAMETRIC STRUCTURAL MODELS OF BINARY RESPONSE: SHAPE RESTRICTIONS AND PARTIAL IDENTIFICATION

Published online by Cambridge University Press:  30 July 2012

Andrew Chesher
Andrew Chesher*
Affiliation:
CeMMAP and University College London
*
*Address correspondence to Andrew Chesher, University College London, Gower St., London WC1E 6BT, United Kingdom; e-mail: andrew.chesher@ucl.ac.uk.
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Abstract

I study the partial identifying power of structural single-equation threshold-crossing models for binary responses when explanatory variables may be endogenous. The sharp identified set of threshold functions is derived for the case in which explanatory variables are discrete, and I provide a constructive proof of sharpness. There is special attention to a widely employed semiparametric shape restriction, which requires the threshold-crossing function to be a monotone function of a linear index involving the observable explanatory variables. The restriction brings great computational benefits, allowing calculation of the identified set of index coefficients without calculating the nonparametrically specified threshold function. With the restriction in place, the methods of the paper can be applied to produce identified sets in a class of binary response models with mismeasured explanatory variables.

Type
Articles
Information
Econometric Theory , Volume 29 , Issue 2 , April 2013 , pp. 231 - 266
Copyright
Copyright © Cambridge University Press 2012 

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Footnotes

I thank Martin Cripps, Lars Nesheim, Adam Rosen, and Richard Spady for stimulating comments and discussions and Konrad Smolinski for excellent research assistance. Some of the results of this paper were presented at seminars at Caltech, UCLA, and USC in November 2007, at the Malinvaud Seminar in Paris in December 2007, and at the inaugural Asian Econometric Theory Lecture at the SETA Conference, Kyoto, Japan, July 30, 2009. I thank participants, two referees, and a co-editor for helpful comments. I gratefully acknowledge the financial support of the UK Economic and Social Research Council through a grant (RES-589-28-0001) to the ESRC Centre for Microdata Methods and Practice (CeMMAP).

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