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ON THE COMPLETENESS CONDITION IN NONPARAMETRIC INSTRUMENTAL PROBLEMS

Published online by Cambridge University Press:  24 September 2010

Xavier D’Haultfoeuille
Xavier D’Haultfoeuille*
Affiliation:
CREST-INSEE
*
*Address correspondence to Xavier D’Haultfoeuille, CREST-INSEE, 15 Boulevard Gabriel Péri, 92245 Malakoff Cedex, France; e-mail: xavier.dhaultfoeuille@ensae.fr.
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Abstract

The notion of completeness between two random elements has been considered recently to provide identification in nonparametric instrumental problems. This condition is quite abstract, however, and characterizations have been obtained only in special cases. This paper considers a nonparametric model between the two variables with an additive separability and a large support condition. In this framework, different versions of completeness are obtained, depending on which regularity conditions are imposed. This result allows one to establish identification in an instrumental nonparametric regression with limited endogenous regressor, a case where the control variate approach breaks down.

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Type
ARTICLES
Information
Econometric Theory , Volume 27 , Issue 3: SPECIAL ISSUE ON INVERSE PROBLEMS IN ECONOMETRICS , June 2011 , pp. 460 - 471
Copyright
Copyright © Cambridge University Press 2011

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