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Local identification of nonparametric and semiparametric models

Author

Listed:
  • Xiaohong Chen

    () (Institute for Fiscal Studies and Yale University)

  • Victor Chernozhukov

    () (Institute for Fiscal Studies and MIT)

  • Sokbae (Simon) Lee

    () (Institute for Fiscal Studies and Columbia University and IFS)

  • Whitney K. Newey

    () (Institute for Fiscal Studies and MIT)

Abstract

In parametric models a sufficient condition for local identification is that the vector of moment is differentiable at the true parameter with full rank derivative matrix. This paper shows that additional conditions are often needed in nonlinear, nonparametric models to avoid nonlinearities overwhelming linear effects. It give restrictions on a neighbourhood of the true value that are sufficient for local identification. These results are applied to obtain new, primitive identification conditions in several important models, including nonseparable quantile instrumental variable (IV) models, single-index IV models, and semiparametric consumption-based asset pricing models.

Suggested Citation

  • Xiaohong Chen & Victor Chernozhukov & Sokbae (Simon) Lee & Whitney K. Newey, 2012. "Local identification of nonparametric and semiparametric models," CeMMAP working papers CWP37/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  • Handle: RePEc:ifs:cemmap:37/12
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Xiaohong Chen & Demian Pouzo, 2015. "Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models," Econometrica, Econometric Society, vol. 83(3), pages 1013-1079, May.
    2. Victor H. Aguiar & Nail Kashaev, 2018. "Stochastic Revealed Preferences with Measurement Error," Papers 1810.05287, arXiv.org.
    3. Xiaohong Chen & Andres Santos, 2018. "Overidentification in Regular Models," Econometrica, Econometric Society, vol. 86(5), pages 1771-1817, September.
    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. Fabian Dunker, 2015. "Convergence of the risk for nonparametric IV quantile regression and nonparametric IV regression with full independence," Papers 1511.03977, arXiv.org.
    6. 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.
    7. Arthur Lewbel, 2018. "The Identification Zoo - Meanings of Identification in Econometrics," Boston College Working Papers in Economics 957, Boston College Department of Economics.
    8. 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.
    9. Jaroslav Borovička & Lars Peter Hansen & José A. Scheinkman, 2016. "Misspecified Recovery," Journal of Finance, American Finance Association, vol. 71(6), pages 2493-2544, December.
    10. repec:pri:metric:wp051_2013_hansen_scheinkman_stochastic-compounding-and-uncertain-valuati is not listed on IDEAS
    11. Xiaohong Chen & Demian Pouzo & James L. Powell, 2019. "Penalized Sieve GEL for Weighted Average Derivatives of Nonparametric Quantile IV Regressions," Papers 1902.10100, arXiv.org.
    12. repec:wly:emjrnl:v:21:y:2018:i:1:p:55-85 is not listed on IDEAS
    13. 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.
    14. Matzkin, Rosa L., 2016. "On independence conditions in nonseparable models: Observable and unobservable instruments," Journal of Econometrics, Elsevier, vol. 191(2), pages 302-311.
    15. Ben Deaner, 2018. "Nonparametric Estimation and Identification in Non-Separable Models Using Panel Data," Papers 1810.00283, arXiv.org.
    16. 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.
    17. 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.
    18. 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.
    19. Jean-Jacques Forneron, 2019. "A Sieve-SMM Estimator for Dynamic Models," Papers 1902.01456, arXiv.org.
    20. Christoph Breunig, 2016. "Specification Testing in Nonparametric Instrumental Quantile Regression," SFB 649 Discussion Papers SFB649DP2016-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    21. 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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