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A Specification Test for Nonparametric Instrumental Variable Regression


  • Olivier SCAILLET


We consider testing for correct specification of a nonparametric instrumental variable regression. First we study the notion of correct specification, misspecification and overidentification in this ill-posed inverse problem setting. Second we study a test statistic based on the empirical minimum distance criterion corresponding to the conditional moment restriction evaluated with a Tikhonov Regularized estimator of the functional parameter. The test statistic admits an asymptotic normal distribution under the null hypothesis, and the test is consistent under global alternatives. A bootstrap procedure is available to get simulation based critical values. Finally, we explore the finite sample behavior with Monte Carlo experiments, and provide an empirical illustration for an estimated Engel curve.

Suggested Citation

  • Patrick GAGLIARDINI & Olivier SCAILLET, 2017. "A Specification Test for Nonparametric Instrumental Variable Regression," Annals of Economics and Statistics, GENES, issue 128, pages 151-202.
  • Handle: RePEc:adr:anecst:y:2017:i:128:p:151-202 DOI: 10.15609/annaeconstat2009.128.0151

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    References listed on IDEAS

    1. Sokullu, Senay, 2016. "Network effects in the German magazine industry," Economics Letters, Elsevier, vol. 143(C), pages 77-79.
    2. Frédérique Fève & Jean-Pierre Florens, 2010. "The practice of non-parametric estimation by solving inverse problems: the example of transformation models," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 1-27, October.
    3. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355.
    5. Qi Li & Jeffrey Scott Racine, 2006. "Density Estimation, from Nonparametric Econometrics: Theory and Practice," Introductory Chapters,in: Nonparametric Econometrics: Theory and Practice Princeton University Press.
    6. repec:cup:etheor:v:33:y:2017:i:04:p:839-873_00 is not listed on IDEAS
    7. Florens, Jean-Pierre & Sokullu, Senay, 2017. "Nonparametric Estimation Of Semiparametric Transformation Models," Econometric Theory, Cambridge University Press, vol. 33(04), pages 839-873, August.
    8. Joel L. Horowitz, 2011. "Applied Nonparametric Instrumental Variables Estimation," Econometrica, Econometric Society, vol. 79(2), pages 347-394, March.
    9. Senay Sokullu, 2012. "Nonparametric Analysis of Two-Sided Markets," Bristol Economics Discussion Papers 12/628, Department of Economics, University of Bristol, UK.
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    More about this item


    Specification Test; Nonparametric Regression; Instrumental Variables; Minimum Distance; Tikhonov Regularization; Ill-posed Inverse Problems; Generalized Method of Moments; Bootstrap; Engel Curve.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • D12 - Microeconomics - - Household Behavior - - - Consumer Economics: Empirical Analysis


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