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On the relevance of weaker instruments

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Abstract

We study the asymptotic properties of the standard GMM estimator when additional moment restrictions, weaker than the original ones, are available. We provide conditions under which these additional weaker restrictions improve the efficiency of the GMM estimator. To detect ”spurious” identification that may come from invalid moments, we rely on the Hansen J-test that assesses the compatibility between existing restrictions and additional ones. Our simulations reveal that the J-test has good power properties and that its power increases with the weakness of the additional restrictions. Our theoretical characterization of the J-test provides some intuition for why that is.

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  • Bertille Antoine & Eric Renault, 2014. "On the relevance of weaker instruments," Discussion Papers dp14-04, Department of Economics, Simon Fraser University, revised 10 Oct 2016.
    • Handle: RePEc:sfu:sfudps:dp14-04
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    3. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, January.
    4. Hahn, Jinyong & Ham, John C. & Moon, Hyungsik Roger, 2011. "The Hausman test and weak instruments," Journal of Econometrics, Elsevier, vol. 160(2), pages 289-299, February.
    5. Li, Yingying & Mykland, Per A. & Renault, Eric & Zhang, Lan & Zheng, Xinghua, 2014. "Realized Volatility When Sampling Times Are Possibly Endogenous," Econometric Theory, Cambridge University Press, vol. 30(3), pages 580-605, June.
    6. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    7. Martin S. Eichenbaum & Lars Peter Hansen & Kenneth J. Singleton, 1988. "A Time Series Analysis of Representative Agent Models of Consumption and Leisure Choice Under Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 103(1), pages 51-78.
    8. Jinyong Hahn & Jerry Hausman, 2002. "A New Specification Test for the Validity of Instrumental Variables," Econometrica, Econometric Society, vol. 70(1), pages 163-189, January.
    9. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    10. Michael P. Murray, 2006. "Avoiding Invalid Instruments and Coping with Weak Instruments," Journal of Economic Perspectives, American Economic Association, vol. 20(4), pages 111-132, Fall.
    11. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
    12. Sowell, Fallaw, 1996. "Optimal Tests for Parameter Instability in the Generalized Method of Moments Framework," Econometrica, Econometric Society, vol. 64(5), pages 1085-1107, September.
    13. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
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    Cited by:

    1. Hao, Bowen & Prokhorov, Artem & Qian, Hailong, 2018. "Moment redundancy test with application to efficiency-improving copulas," Economics Letters, Elsevier, vol. 171(C), pages 29-33.
    2. Bertille Antoine & Otilia Boldea & Niccolo Zaccaria, 2024. "Efficient two-sample instrumental variable estimators with change points and near-weak identification," Papers 2406.17056, arXiv.org.
    3. Grundke, Robert & Moser, Christoph, 2019. "Hidden protectionism? Evidence from non-tariff barriers to trade in the United States," Journal of International Economics, Elsevier, vol. 117(C), pages 143-157.
    4. Bertille Antoine & Otilia, 2015. "Inference in linear models with structural changes and mixed identification strength," Discussion Papers dp15-05, Department of Economics, Simon Fraser University.

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    More about this item

    Keywords

    GMM; Weak IV; Redundancy; J-test; Local Misspecification;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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