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Nonparametric Instrumental Variable Estimation in Practice


  • Michael Cohen

    () (New York University)

  • Philip Shaw

    () (Fordham University)

  • Tao Chen

    () (University of Connecticut)


In this paper we examine the nite sample performance of two estimators one developed by Blundell, Chen, and Kristensen (2007) (BCK) and the other by Gagliardini and Scaillet (2007) (TIR). This paper focuses on the generalization and expansion of these estimators to a full nonparametric speci cation with multiple regressors. In relation to the classic weak instruments literature, we provide intuition on the examination of instruments relevance when the structural function is assumed to be unknown. Simulations indicate that both estimators perform quite well in higher dimensions. This research also provides insights on the performance of bootstrapped con dence intervals for both estimators. We document that the BCK estimator's coverage probabilities are near their nominal levels even in small samples as long as the sieve order of expansion is restricted. The coverage probability for the TIR estimator's bootstrapped con dence intervals are near their nominal levels even when the order of sieve approximation is large. These results suggest that in small samples the TIR estimator has a much smaller bias then the BCK estimator but its variance is much larger. We provide two empirical examples. One is the classic wage returns to education example and the other looks at the relationship of corruption and GDP to economic growth. Results here suggests that the impact of corruption on growth depends nonlinearly on a countries level of development.

Suggested Citation

  • Michael Cohen & Philip Shaw & Tao Chen, 2008. "Nonparametric Instrumental Variable Estimation in Practice," Food Marketing Policy Center Research Reports 111, University of Connecticut, Department of Agricultural and Resource Economics, Charles J. Zwick Center for Food and Resource Policy.
  • Handle: RePEc:zwi:fpcrep:111

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    References listed on IDEAS

    1. Steven T. Berry & Philip A. Haile, 2014. "Identification in Differentiated Products Markets Using Market Level Data," Econometrica, Econometric Society, vol. 82, pages 1749-1797, September.
    2. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    3. Patrick GAGLIARDINI & Olivier SCAILLET, 2017. "A Specification Test for Nonparametric Instrumental Variable Regression," Annals of Economics and Statistics, GENES, issue 128, pages 151-202.
    4. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
    5. Philip Shaw & Marina‐Selini Katsaiti & Marius Jurgilas, 2011. "Corruption And Growth Under Weak Identification," Economic Inquiry, Western Economic Association International, vol. 49(1), pages 264-275, January.
    6. Severini, Thomas A. & Tripathi, Gautam, 2006. "Some Identification Issues In Nonparametric Linear Models With Endogenous Regressors," Econometric Theory, Cambridge University Press, vol. 22(2), pages 258-278, April.
    7. Gagliardini, Patrick & Scaillet, Olivier, 2012. "Tikhonov regularization for nonparametric instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 167(1), pages 61-75.
    8. Berry, Steven & Levinsohn, James & Pakes, Ariel, 1995. "Automobile Prices in Market Equilibrium," Econometrica, Econometric Society, vol. 63(4), pages 841-890, July.
    9. Hoderlein, Stefan & Holzmann, Hajo, 2011. "Demand Analysis As An Ill-Posed Inverse Problem With Semiparametric Specification," Econometric Theory, Cambridge University Press, vol. 27(3), pages 609-638, June.
    10. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
    11. Paolo Mauro, 1995. "Corruption and Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 681-712.
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    More about this item


    Nonparametric; Instrumental Variables; Information Regularized Estimators;

    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


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