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Local Identification of Nonparametric and Semiparametric Models

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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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  • Xiaohong Chen & Victor Chernozhukov & Sokbae Lee & Whitney Newey, 2011. "Local Identification of Nonparametric and Semiparametric Models," Cowles Foundation Discussion Papers 1795, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1795
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    Cited by:

    1. Chiappori, Pierre-André & Komunjer, Ivana & Kristensen, Dennis, 2015. "Nonparametric identification and estimation of transformation models," Journal of Econometrics, Elsevier, vol. 188(1), pages 22-39.
    2. Xiaohong Chen & Andres Santos, 2015. "Overidentification in Regular Models," Cowles Foundation Discussion Papers 1999, Cowles Foundation for Research in Economics, Yale University.
    3. Hidehiko Ichimura & Whitney K. Newey, 2017. "The influence function of semiparametric estimators," CeMMAP working papers CWP06/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    4. Timothy M. Christensen, 2014. "Nonparametric identification of positive eigenfunctions," CeMMAP working papers CWP37/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    5. Matzkin, Rosa L., 2016. "On independence conditions in nonseparable models: Observable and unobservable instruments," Journal of Econometrics, Elsevier, vol. 191(2), pages 302-311.
    6. Fabian Dunker, 2015. "Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence," Papers 1511.03977, arXiv.org.
    7. Victor Chernozhukov & Whitney K. Newey & Andres Santos, 2015. "Constrained conditional moment restriction models," CeMMAP working papers CWP59/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Patrick Bajari & Chenghuan Sean Chu & Denis Nekipelov & Minjung Park, 2016. "Identification and semiparametric estimation of a finite horizon dynamic discrete choice model with a terminating action," Quantitative Marketing and Economics (QME), Springer, vol. 14(4), pages 271-323, December.
    9. repec:bla:jfinan:v:71:y:2016:i:6:p:2493-2544 is not listed on IDEAS
    10. 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.
    11. Xiaohong Chen & Demian Pouzo, 2014. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," CeMMAP working papers CWP38/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    12. Christoph Breunig, 2016. "Specification Testing in Nonparametric Instrumental Quantile Regression," SFB 649 Discussion Papers SFB649DP2016-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. Patrick Bajari & Chenghuan Sean Chu & Denis Nekipelov & Minjung Park, 2013. "A Dynamic Model of Subprime Mortgage Default: Estimation and Policy Implications," NBER Working Papers 18850, National Bureau of Economic Research, Inc.
    14. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897RR, Cowles Foundation for Research in Economics, Yale University, revised Nov 2014.
    15. Xiaohong Chen & Demian Pouzo, 2014. "Sieve Wald and QLR Inferences on Semi/nonparametric Conditional Moment Models," Papers 1411.1144, arXiv.org, revised Mar 2015.
    16. Jaroslav Borovička & Lars Peter Hansen & José A. Scheinkman, 2016. "Misspecified Recovery," Journal of Finance, American Finance Association, vol. 71(6), pages 2493-2544, December.
    17. Cazals, Catherine & Fève, Frédérique & Florens, Jean-Pierre & Simar, Léopold, 2016. "Nonparametric instrumental variables estimation for efficiency frontier," Journal of Econometrics, Elsevier, vol. 190(2), pages 349-359.

    More about this item

    Keywords

    Identification; Local identification; Nonparametric models; Asset pricing;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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