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Local identification of nonparametric and semiparametric models

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  • Xiaohong Chen
  • Victor Chernozhukov
  • Sokbae (Simon) Lee
  • Whitney K. Newey

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 37/12, Institute for Fiscal Studies.
  • Handle: RePEc:azt:cemmap:37/12
    DOI: 10.1920/wp.cem.2012.3712
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    1. Escanciano, Juan Carlos & Hoderlein, Stefan & Lewbel, Arthur & Linton, Oliver & Srisuma, Sorawoot, 2021. "Nonparametric Euler Equation Identification And Estimation," Econometric Theory, Cambridge University Press, vol. 37(5), pages 851-891, October.
    2. 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 971-987, December.
    3. Chen, Xiaohong & Pouzo, Demian, 2009. "Efficient estimation of semiparametric conditional moment models with possibly nonsmooth residuals," Journal of Econometrics, Elsevier, vol. 152(1), pages 46-60, September.
    4. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    5. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(3), pages 497-521, June.
    6. 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, January.
    7. 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.
    8. Jean‐Pierre Florens & Jan Johannes & Sébastien Van Bellegem, 2012. "Instrumental regression in partially linear models," Econometrics Journal, Royal Economic Society, vol. 15(2), pages 304-324, June.
    9. Florens, Jean-Pierre & Sbaï, Erwann, 2010. "Local Identification In Empirical Games Of Incomplete Information," Econometric Theory, Cambridge University Press, vol. 26(6), pages 1638-1662, December.
    10. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, vol. 161(2), pages 129-146, April.
    11. 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.
    12. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(3), pages 460-471, June.
    13. FLORENS, Jean-Pierre & JOHANNES, Jan & VAN BELLEGEM, Sébastien, 2012. "Instrumental regression in partially linear models," LIDAM Reprints CORE 2456, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    14. 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.
    15. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    16. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    17. Victor Chernozhukov & Christian Hansen, 2005. "An IV Model of Quantile Treatment Effects," Econometrica, Econometric Society, vol. 73(1), pages 245-261, January.
    18. Joel L. Horowitz, 2007. "Asymptotic Normality Of A Nonparametric Instrumental Variables Estimator," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 48(4), pages 1329-1349, November.
    19. 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(3), pages 472-496, June.
    20. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    21. FLORENS, Jean-Pierre & JOHANNES, Jan & VAN BELLEGEM, Sébastien, 2011. "Identification and estimation by penalization in nonparametric instrumental regression," LIDAM Reprints CORE 2320, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    22. Xiaohong Chen & Demian Pouzo, 2008. "Estimation of nonparametric conditional moment models with possibly nonsmooth moments," CeMMAP working papers CWP12/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    23. 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.
    24. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sebastien, 2011. "Identification and estimation by penalization in Nonparametric Instrumental Regression," LIDAM Reprints ISBA 2011046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    25. Florens, Jean-Pierre & Johannes, Jan & Van Bellegem, Sebastien, 2012. "Instrumental regression in partially linear models," LIDAM Reprints ISBA 2012017, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    26. 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.
    27. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    28. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    29. 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.
    30. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    31. James H. Stock & Jonathan Wright, 2000. "GMM with Weak Identification," Econometrica, Econometric Society, vol. 68(5), pages 1055-1096, September.
    32. Joel L. Horowitz & Sokbae Lee, 2007. "Nonparametric Instrumental Variables Estimation of a Quantile Regression Model," Econometrica, Econometric Society, vol. 75(4), pages 1191-1208, July.
    33. 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.
    34. Erwann Sbai, 2000. "Identification in Empirical Games," Econometric Society World Congress 2000 Contributed Papers 1896, Econometric Society.
    35. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
    36. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-1286, September.
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    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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