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ESTIMATION OF A SEMIPARAMETRIC TRANSFORMATION MODEL IN THE PRESENCE OF ENDOGENEITY

Published online by Cambridge University Press:  07 May 2018

Anne Vanhems  and
Ingrid Van Keilegom
Anne Vanhems*
Affiliation:
Toulouse Business School
Ingrid Van Keilegom*
Affiliation:
KU Leuven
*
*Address correspondence to Anne Vanhems, Toulouse Business School, 1 place Jourdain, 31068 Toulouse, France; e-mail: a.vanhems@tbs-education.fr
†Ingrid Van Keilegom, ORSTAT, KU Leuven, Naamsestraat 69, 3000 Leuven, Belgium; e-mail: ingrid.vankeilegom@kuleuven.be.
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Abstract

We consider a semiparametric transformation model, in which the regression function has an additive nonparametric structure and the transformation of the response is assumed to belong to some parametric family. We suppose that endogeneity is present in the explanatory variables. Using a control function approach, we show that the proposed model is identified under suitable assumptions, and propose a profile estimation method for the transformation. The proposed estimator is shown to be asymptotically normal under certain regularity conditions. A simulation study shows that the estimator behaves well in practice. Finally, we give an empirical example using the U.K. Family Expenditure Survey.

Type
ARTICLES
Information
Econometric Theory , Volume 35 , Issue 1 , February 2019 , pp. 73 - 110
Copyright
Copyright © Cambridge University Press 2018 

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Footnotes

We deeply thank Ying-Ying Lee for pointing out some incoherencies in a previous version of our article and for most stimulating discussions on the impact of a generated covariate on the asymptotic variance of our estimator. This research was supported by the European Research Council (2016–2021, Horizon 2020/ERC grant agreement No. 694409 and 295298), and by IAP Research Network P7/06 of the Belgian State.

References

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