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On Completeness and Consistency in Nonparametric Instrumental Variable Models

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  • Joachim Freyberger

Abstract

This paper provides positive testability results for the identification condition in a nonparametric instrumental variable model, known as completeness, and it links the outcome of the test to properties of an estimator of the structural function. In particular, I show that the data can provide empirical evidence in favor of both an arbitrarily small identified set as well as an arbitrarily small asymptotic bias of the estimator. This is the case for a large class of complete distributions as well as certain incomplete distributions. As a byproduct, the results can be used to estimate an upper bound of the diameter of the identified set and to obtain an easy to report estimator of the identified set itself.

Suggested Citation

  • Joachim Freyberger, 2017. "On Completeness and Consistency in Nonparametric Instrumental Variable Models," Econometrica, Econometric Society, vol. 85, pages 1629-1644, September.
    • Handle: RePEc:wly:emetrp:v:85:y:2017:i::p:1629-1644
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    Cited by:

    1. Otsu, Taisuke & Sunada, Keita, 2024. "On large market asymptotics for spatial price competition models," Economics Letters, Elsevier, vol. 234(C).
    2. Escanciano, Juan Carlos & Li, Wei, 2021. "Optimal Linear Instrumental Variables Approximations," Journal of Econometrics, Elsevier, vol. 221(1), pages 223-246.
    3. Hu, Yingyao & Schennach, Susanne & Shiu, Ji-Liang, 2022. "Identification of nonparametric monotonic regression models with continuous nonclassical measurement errors," Journal of Econometrics, Elsevier, vol. 226(2), pages 269-294.
    4. Takahiro Hoshino & Keisuke Takahata, 2018. "Identification of heterogeneous treatment effects as a function of potential untreated outcome under the nonignorable assignment condition," Keio-IES Discussion Paper Series 2018-005, Institute for Economics Studies, Keio University.
    5. Jad Beyhum & Elia Lapenta & Pascal Lavergne, 2023. "One-step smoothing splines instrumental regression," Papers 2307.14867, arXiv.org, revised Apr 2024.
    6. Loh, Isaac, 2023. "Genericity of the completeness condition with constrained instruments," Economics Letters, Elsevier, vol. 224(C).
    7. Beyhum, Jad & Lapenta, Elia & Lavergne, Pascal, 2023. "One-step nonparametric instrumental regression using smoothing splines," TSE Working Papers 23-1467, Toulouse School of Economics (TSE).
    8. Otsu, Taisuke & Sunada, Keita, 2024. "On large market asymptotics for spatial price competition models," LSE Research Online Documents on Economics 120588, London School of Economics and Political Science, LSE Library.
    9. Ben Deaner, 2019. "Nonparametric Instrumental Variables Estimation Under Misspecification," Papers 1901.01241, arXiv.org, revised Dec 2022.
    10. Centorrino, Samuele & Florens, Jean-Pierre, 2021. "Nonparametric Instrumental Variable Estimation of Binary Response Models with Continuous Endogenous Regressors," Econometrics and Statistics, Elsevier, vol. 17(C), pages 35-63.
    11. Emir Malikov & Shunan Zhao & Subal C. Kumbhakar, 2020. "Estimation of firm‐level productivity in the presence of exports: Evidence from China's manufacturing," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 35(4), pages 457-480, June.
    12. Wang, Ao, 2021. "A BLP Demand Model of Product-Level Market Shares with Complementarity," The Warwick Economics Research Paper Series (TWERPS) 1351, University of Warwick, Department of Economics.
    13. Hu, Yingyao, 2017. "The Econometrics of Unobservables -- Latent Variable and Measurement Error Models and Their Applications in Empirical Industrial Organization and Labor Economics [The Econometrics of Unobservables]," Economics Working Paper Archive 64578, The Johns Hopkins University,Department of Economics, revised 2021.
    14. Yingyao Hu & Jiaxiong Yao, 2019. "Illuminating Economic Growth," IMF Working Papers 2019/077, International Monetary Fund.
    15. De Monte Enrico, 2024. "Nonparametric Instrumental Regression with Two-Way Fixed Effects," Journal of Econometric Methods, De Gruyter, vol. 13(1), pages 49-66, January.
    16. Hu, Yingyao & Yao, Jiaxiong, 2022. "Illuminating economic growth," Journal of Econometrics, Elsevier, vol. 228(2), pages 359-378.

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