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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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    Cited by:

    1. Shaw Philip & Cohen Michael Andrew & Chen Tao, 2016. "Nonparametric Instrumental Variable Estimation in Practice," Journal of Econometric Methods, De Gruyter, vol. 5(1), pages 153-177, January.
    2. Breunig, Christoph, 2015. "Goodness-of-fit tests based on series estimators in nonparametric instrumental regression," Journal of Econometrics, Elsevier, vol. 184(2), pages 328-346.
    3. Breunig, Christoph, 2012. "Goodness-of-fit tests based on series estimators in nonparametric instrumental regression," Working Papers 12-13, University of Mannheim, Department of Economics.
    4. Christoph Breunig, 2016. "Specification Testing in Nonparametric Instrumental Quantile Regression," SFB 649 Discussion Papers SFB649DP2016-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    5. Christoph Breunig, 2019. "Goodness-of-Fit Tests based on Series Estimators in Nonparametric Instrumental Regression," Papers 1909.10133,

    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.;
    All these keywords.

    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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