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SEMIPARAMETRIC ESTIMATION WITH GENERATED COVARIATES

Published online by Cambridge University Press:  04 June 2015

Enno Mammen ,
Christoph Rothe  and
Melanie Schienle
Enno Mammen
Affiliation:
Heidelberg University and National Research University Higher School of Economics
Christoph Rothe*
Affiliation:
Columbia University
Melanie Schienle
Affiliation:
Karlsruhe Institute of Technology
*
*Address correspondence to Christoph Rothe, Department of Economics, Columbia University, 420 W 118th Street, New York, NY 10027, USA; e-mail: cr2690@columbia.edu.
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Abstract

We study a general class of semiparametric estimators when the infinite-dimensional nuisance parameters include a conditional expectation function that has been estimated nonparametrically using generated covariates. Such estimators are used frequently to e.g., estimate nonlinear models with endogenous covariates when identification is achieved using control variable techniques. We study the asymptotic properties of estimators in this class, which is a nonstandard problem due to the presence of generated covariates. We give conditions under which estimators are root-n consistent and asymptotically normal, derive a general formula for the asymptotic variance, and show how to establish validity of the bootstrap.

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Type
ARTICLES
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Econometric Theory , Volume 32 , Issue 5 , October 2016 , pp. 1140 - 1177
Copyright
Copyright © Cambridge University Press 2015 

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