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Local identification of nonparametric and semiparametric models

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  • Xiaohong Chen

    (Institute for Fiscal Studies and Yale)

  • Victor Chernozhukov

    ()
    (Institute for Fiscal Studies and Massachusetts Institute of Technology)

  • Sokbae 'Simon' Lee

    ()
    (Institute for Fiscal Studies and Seoul National University)

  • Whitney Newey

    ()
    (Institute for Fiscal Studies and Massachusetts Institute of Technology)

Abstract

In parametric models a sufficient condition for local identification is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We show that there are corresponding sufficient conditions for nonparametric models. A nonparametric rank condition and differentiability of the moment conditions with respect to a certain norm imply local identification. It turns out these conditions are slightly stronger than needed and are hard to check, so we provide weaker and more primitive conditions. We extend the results to semiparametric models. We illustrate the sufficient conditions with endogenous quantile and single index examples. We also consider a semiparametric habit-based, consumption capital asset pricing model. There we find the rank condition is implied by an integral equation of the second kind having a one-dimensional null space.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP17/11.

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Date of creation: May 2011
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Handle: RePEc:ifs:cemmap:17/11

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  1. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
  2. Arthur Lewbel & Oliver Linton & Sorawoot Srisuma, 2010. "Nonparametric Euler Equation Identification and Estimation," Boston College Working Papers in Economics 757, Boston College Department of Economics, revised 23 Feb 2011.
  3. Xiaohong Chen & Markus Reiss, 2007. "On Rate Optimality for Ill-posed Inverse Problems in Econometrics," Cowles Foundation Discussion Papers 1626, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. Erwann Sbai, 2000. "Identification in Empirical Games," Econometric Society World Congress 2000 Contributed Papers 1896, Econometric Society.
  6. Xiaohong Chen & Sydney C. Ludvigson, 2009. "Land of addicts? an empirical investigation of habit-based asset pricing models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(7), pages 1057-1093.
  7. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2009. "Instrumental Regression in Partially Linear Models," IDEI Working Papers 613, Institut d'Économie Industrielle (IDEI), Toulouse.
  8. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  9. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, 09.
  10. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sébastien, 2011. "Identification And Estimation By Penalization In Nonparametric Instrumental Regression," Econometric Theory, Cambridge University Press, vol. 27(03), pages 472-496, June.
  11. 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.
  12. Gallant, Ronald & Tauchen, George, 1989. "Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications," Econometrica, Econometric Society, vol. 57(5), pages 1091-1120, September.
  13. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, 01.
  14. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, vol. 75(4), pages 1191-1208, 07.
  15. Hansen, Lars Peter & Heaton, John & Lee, Junghoon & Roussanov, Nikolai, 2007. "Intertemporal Substitution and Risk Aversion," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 61 Elsevier.
  16. Hall, Robert E, 1978. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Political Economy, University of Chicago Press, vol. 86(6), pages 971-87, December.
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Cited by:
  1. Dunker, Fabian & Florens, Jean-Pierre & Hohage, Thorsten & Johannes, Jan & Mammen, Enno, 2014. "Iterative estimation of solutions to noisy nonlinear operator equations in nonparametric instrumental regression," Journal of Econometrics, Elsevier, vol. 178(P3), pages 444-455.

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