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INTERCEPT ESTIMATION IN NONLINEAR SELECTION MODELS

Published online by Cambridge University Press:  24 April 2023

Wiji Arulampalam Open the ORCID record for Wiji Arulampalam [Opens in a new window] ,
Valentina Corradi  and
Daniel Gutknecht
Wiji Arulampalam
Affiliation:
University of Warwick
Valentina Corradi*
Affiliation:
University of Surrey
Daniel Gutknecht
Affiliation:
Goethe University Frankfurt
*
Address correspondence to Valentina Corradi, Department of Economics, School of Economics, University of Surrey, Guildford GU2 7XH, UK; e-mail: V.Corradi@surrey.ac.uk.
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Abstract

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We propose various semiparametric estimators for nonlinear selection models, where slope and intercept can be separately identified. When the selection equation satisfies a monotonic index restriction, we suggest a local polynomial estimator, using only observations for which the marginal cumulative distribution function of the instrument index is close to one. Data-driven procedures such as cross-validation may be used to select the bandwidth for this estimator. We then consider the case in which the monotonic index restriction does not hold and/or the set of observations with a propensity score close to one is thin so that convergence occurs at a rate that is arbitrarily close to the cubic rate. We explore the finite sample behavior in a Monte Carlo study and illustrate the use of our estimator using a model for count data with multiplicative unobserved heterogeneity.

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Type
ARTICLES
Information
Econometric Theory , Volume 40 , Issue 6 , December 2024 , pp. 1311 - 1363
Creative Commons
Creative Common License - CCCreative Common License - BYCreative Common License - NCCreative Common License - ND
This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives licence (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is unaltered and is properly cited. The written permission of Cambridge University Press must be obtained for commercial re-use or in order to create a derivative work.
Copyright
© The Author(s), 2023. Published by Cambridge University Press

Footnotes

We are grateful to the Editor (Peter Phillips), the Co-Editor (Simon Lee), and three anonymous referees for their very useful and constructive comments. We also thank Christoph Breunig, Sarawata Chaudhuri, Xavier D’Haultfoeuille, Prosper Dovonon, Jean-Marie Dufour, Bernd Fitzenberger, Mathieu Marcoux, Jeff Racine, Joao Santos Silva, Victoria Zinde-Walsh, and seminar participants at the ESEM 2018, Kent, Frankfurt, ISNPS 2018, Surrey, Concordia University-Cireq, Humboldt University Berlin, the Econometrics Study Group Meeting in Bristol 2017, and ESEM 2017 for useful comments and suggestions.

References

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