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Nonparametric Identification and Estimation of Transformation Models

  • Pierre-Andre Chiappori

    (Columbia University)

  • Ivana Komunjer

    (University of California San Diego)

  • Dennis Kristensen

    (Columbia University)

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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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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  1. David Jacho-Chávez & Arthur Lewbel & Oliver Linton, 2006. "Identification and nonparametric estimation of a transformed additively separable model," LSE Research Online Documents on Economics 4416, London School of Economics and Political Science, LSE Library.
  2. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2004. "Identification and Estimation of Hedonic Models," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages S60-S109, February.
  3. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(03), pages 460-471, June.
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