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Nonparametric Identification and Estimation of Transformation Models

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Author Info

  • Pierre-Andre Chiappori

    (Columbia University)

  • Ivana Komunjer

    (University of California San Diego)

  • Dennis Kristensen

    (Columbia University)

Abstract

This paper derives sufficient conditions for nonparametric transformation models to be identified and develops estimators of the identified components. Our nonparametric identification result is global, and is derived under conditions that are substantially weaker than full independence. In particular, we show that a completeness assumption combined with conditional independence with respect to one of the regressors suffices for the model to be identified. The identification result is also constructive in the sense that it yields explicit expressions of the functions of interest. We show how natural estimators can be developed from these expressions, and analyze their theoretical properties. Importantly, it is demonstrated that the proposed estimator of the unknown transformation function converges at the parametric rate.

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File URL: http://www.econ.ku.dk/cam/wp0910/2011-01.pdf/
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Bibliographic Info

Paper provided by University of Copenhagen. Department of Economics. Centre for Applied Microeconometrics in its series CAM Working Papers with number 2011-01.

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Length: 37 pages
Date of creation: Jan 2011
Date of revision:
Handle: RePEc:kud:kuieca:2011_01

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Related research

Keywords: nonparametric identification; transformation models; kernel estimation;

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References

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  1. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(03), pages 460-471, June.
  2. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2003. "Identification and Estimation of Hedonic Models," CESifo Working Paper Series 1031, CESifo Group Munich.
  3. David Jacho-Chavez & Arthur Lewbel & Oliver Linton, 2006. "Identification and Nonparametric Estimation of a Transformed Additively Separable Model," Boston College Working Papers in Economics 652, Boston College Department of Economics, revised 26 Nov 2008.
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Citations

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Cited by:
  1. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, 07.
  2. Arthur Lewbel & Xun Lu & Liangjun Su, 2012. "Specification Testing for Transformation Models with an Application to Generalized Accelerated Failure-time Models," Boston College Working Papers in Economics 817, Boston College Department of Economics, revised 01 May 2013.
  3. Senay Sokullu, 2012. "Nonparametric Estimation of Semiparametric Transformation Models," Bristol Economics Discussion Papers 12/625, Department of Economics, University of Bristol, UK.
  4. Van Keilegom, Ingrid & Vanhems, Anne, 2011. "Semiparametric transformation model with endogeneity: a control function approach," TSE Working Papers 11-243, Toulouse School of Economics (TSE).

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