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Testing Overidentifying Restrictions with Many Instruments and Heteroskedasticity

Author

Listed:
  • Norman R. Swanson

    (Rutgers University)

  • John C. Chao

    (University of Maryland)

  • Jerry A. Hausman

    (MIT)

  • Whitney K. Newey

    (MIT)

  • Tiemen Woutersen

    (Johns Hopkins University)

Abstract

This paper gives a test of overidentifying restrictions that is robust to many instruments and heteroskedasticity. It is based on a jackknife version of the Sargan test statistic, having a numerator that is the objective function minimized by the JIVE2 estimator of Angrist, Imbens, and Krueger (1999). Correct asymptotic critical values are derived for this test when the number of instruments grows large, at a rate up to the sample size. It is also shown that the test is valid when the number instruments is fixed and there is homoskedasticity. This test improves on recently proposed tests by allowing for heteroskedasticity and by avoiding assumptions on the instrument projection matrix. The asymptotics is based on the heteroskedasticity robust many instrument asymptotics of Chao et. al. (2010).

Suggested Citation

  • Norman R. Swanson & John C. Chao & Jerry A. Hausman & Whitney K. Newey & Tiemen Woutersen, 2011. "Testing Overidentifying Restrictions with Many Instruments and Heteroskedasticity," Departmental Working Papers 201118, Rutgers University, Department of Economics.
  • Handle: RePEc:rut:rutres:201118
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    References listed on IDEAS

    as
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    6. John C. Chao & Norman R. Swanson, 2005. "Consistent Estimation with a Large Number of Weak Instruments," Econometrica, Econometric Society, vol. 73(5), pages 1673-1692, September.
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    4. Frank Windmeijer, 2018. "Testing Over- and Underidentification in Linear Models, with Applications to Dynamic Panel Data and Asset-Pricing Models," Bristol Economics Discussion Papers 18/696, School of Economics, University of Bristol, UK.
    5. Bekker, Paul A. & Crudu, Federico, 2015. "Jackknife instrumental variable estimation with heteroskedasticity," Journal of Econometrics, Elsevier, vol. 185(2), pages 332-342.
    6. Crudu, Federico & Mellace, Giovanni & Sándor, Zsolt, 2021. "Inference In Instrumental Variable Models With Heteroskedasticity And Many Instruments," Econometric Theory, Cambridge University Press, vol. 37(2), pages 281-310, April.
    7. Wang, Wenjie, 2022. "Wild bootstrap test of overidentification with many instruments and heteroskedasticity," MPRA Paper 115168, University Library of Munich, Germany.
    8. Kohtaro Hitomi & Masamune Iwasawa & Yoshihiko Nishiyama, 2022. "Optimal minimax rates against nonsmooth alternatives [Optimal testing for additivity in multiple nonparametric regression]," The Econometrics Journal, Royal Economic Society, vol. 25(2), pages 322-339.
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    10. Kolesár, Michal, 2018. "Minimum distance approach to inference with many instruments," Journal of Econometrics, Elsevier, vol. 204(1), pages 86-100.
    11. Stanislav Anatolyev & Mikkel S{o}lvsten, 2020. "Testing Many Restrictions Under Heteroskedasticity," Papers 2003.07320, arXiv.org, revised Jan 2021.
    12. Matsushita, Yukitoshi & Otsu, Taisuke, 2022. "A jackknife Lagrange multiplier test with many weak instruments," LSE Research Online Documents on Economics 116392, London School of Economics and Political Science, LSE Library.
    13. Paul Goldsmith-Pinkham & Isaac Sorkin & Henry Swift, 2020. "Bartik Instruments: What, When, Why, and How," American Economic Review, American Economic Association, vol. 110(8), pages 2586-2624, August.
    14. Tugrul Gurgur, 2016. "Voice, exit and local capture in public provision of private goods," Economics of Governance, Springer, vol. 17(4), pages 397-424, November.
    15. Qingliang Fan & Zijian Guo & Ziwei Mei, 2022. "Testing Overidentifying Restrictions with High-Dimensional Data and Heteroskedasticity," Papers 2205.00171, arXiv.org.
    16. Wang, Wenjie & Kaffo, Maximilien, 2016. "Bootstrap inference for instrumental variable models with many weak instruments," Journal of Econometrics, Elsevier, vol. 192(1), pages 231-268.
    17. Alla Koblyakova & Larisa Fleishman & Orly Furman, 2022. "Accuracy of Households’ Dwelling Valuations, Housing Demand and Mortgage Decisions: Israeli Case," The Journal of Real Estate Finance and Economics, Springer, vol. 65(1), pages 48-74, July.
    18. Guo, Zijian & Kang, Hyunseung & Cai, T. Tony & Small, Dylan S., 2018. "Testing endogeneity with high dimensional covariates," Journal of Econometrics, Elsevier, vol. 207(1), pages 175-187.
    19. Díaz Antonia & Puch Luis A., 2019. "Investment, technological progress and energy efficiency," The B.E. Journal of Macroeconomics, De Gruyter, vol. 19(2), pages 1-28, June.
    20. Marine Carrasco & Mohamed Doukali, 2022. "Testing overidentifying restrictions with many instruments and heteroscedasticity using regularised jackknife IV [Specification testing in models with many instruments]," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 71-97.
    21. Jafari-Sadeghi, Vahid, 2020. "The motivational factors of business venturing: Opportunity versus necessity? A gendered perspective on European countries," Journal of Business Research, Elsevier, vol. 113(C), pages 279-289.
    22. Kohtaro Hitomi & Masamune Iwasawa & Yoshihiko Nishiyama, 2018. "Rate Optimal Specification Test When the Number of Instruments is Large," KIER Working Papers 986, Kyoto University, Institute of Economic Research.
    23. Atsushi Inoue & Barbara Rossi, 2015. "Tests for the validity of portfolio or group choice in financial and panel regressions," Economics Working Papers 1523, Department of Economics and Business, Universitat Pompeu Fabra.
    24. Wang, Wenjie, 2020. "On Bootstrap Validity for the Test of Overidentifying Restrictions with Many Instruments and Heteroskedasticity," MPRA Paper 104858, University Library of Munich, Germany.

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    More about this item

    Keywords

    heteroskedasticity; instrumental variables; jackknife estimation; many instruments; weak instruments;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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