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Correct Specification and Identification of Nonparametric Transformation Models

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  • Pierre-Andre Chiappori

    ()
    (Columbia University)

  • Ivana Komunjer

    ()
    (University of California, San Diego (UCSD) - Department of Economics)

Abstract

This paper derives necessary and sufficient conditions for nonparametric transformation models to be (i) correctly speci fied, and (ii) identified. Our correct speci fication conditions come in a form of partial differential equations; when satis fied by the true distribution, they ensure that the observables are indeed generated from a nonparametric transformation model. Our nonparametric identifi cation result is global; we derive it under conditions that are substantially weaker than full independence. In particular, we show that a completeness assumption combined with independence with respect to one of the regressors suffices for the model to be identified.

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File URL: http://bfi.uchicago.edu/RePEc/bfi/wpaper/BFI_2009-003.pdf
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Bibliographic Info

Paper provided by Becker Friedman Institute for Research In Economics in its series Working Papers with number 2009-003.

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Date of creation: Dec 2008
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Handle: RePEc:bfi:wpaper:2009-003

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Related research

Keywords: specifiation testing; nonparametric identification; duration models;

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  1. 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.
  2. Tue Gorgens & Joel L. Horowitz, 1996. "Semiparametric Estimation of a Censored Regression Model with an Unknown Transformation of the Dependent Variable," Econometrics 9603001, EconWPA.
  3. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, vol. 71(5), pages 1405-1441, 09.
  4. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
  5. Darolles, Serge & Fan, Yanqin & Florens, Jean-Pierre & Renault, Eric, 2003. "Non Parametric Instrumental Regression," IDEI Working Papers 228, Institut d'Économie Industrielle (IDEI), Toulouse, revised 2010.
  6. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2003. "Nonparametric IV estimation of shape-invariant Engel curves," CeMMAP working papers CWP15/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Chernozhukov, Victor & Imbens, Guido W. & Newey, Whitney K., 2007. "Instrumental variable estimation of nonseparable models," Journal of Econometrics, Elsevier, vol. 139(1), pages 4-14, July.
  8. Severini, Thomas A. & Tripathi, Gautam, 2006. "Some Identification Issues In Nonparametric Linear Models With Endogenous Regressors," Econometric Theory, Cambridge University Press, vol. 22(02), pages 258-278, April.
  9. 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.
  10. Bo Honore & Aureo de Paula, 2008. "Interdependent Durations," PIER Working Paper Archive 08-007, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  11. Han, Aaron K., 1987. "A non-parametric analysis of transformations," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 191-209, July.
  12. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-90, July.
  13. Komunjer, Ivana, 2008. "Global Identification In Nonlinear Semiparametric Models," University of California at San Diego, Economics Working Paper Series qt2r59d87f, Department of Economics, UC San Diego.
  14. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, 09.
  15. repec:bla:restud:v:77:y:2010:i:3:p:1138-1163 is not listed on IDEAS
  16. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-37, January.
  17. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, 09.
  18. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
  19. Brown, Bryan W, 1983. "The Identification Problem in Systems Nonlinear in the Variables," Econometrica, Econometric Society, vol. 51(1), pages 175-96, January.
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