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On The Asymptotic Size Distortion Of Tests When Instruments Locally Violate The Exogeneity Assumption

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  • Guggenberger, Patrik

Abstract

In the linear instrumental variables model with possibly weak instruments we derive the asymptotic size of testing procedures when instruments locally violate the exogeneity assumption. We study the tests by Anderson and Rubin (1949, The Annals of Mathematical Statistics 20, 46–63), Moreira (2003, Econometrica 71, 1027–1048), and Kleibergen (2005, Econometrica 73, 1103–1123) and their generalized empirical likelihood versions. These tests have asymptotic size equal to nominal size when the instruments are exogenous but are size distorted otherwise. While in just-identified models all the tests that we consider are equally size-distorted asymptotically, the Anderson-Rubin type tests are less size-distorted than the tests of Moreira (2003) and Kleibergen in over-identified situations. On the other hand, we also show that there are parameter sequences under which the former test asymptotically overrejects more frequently. Given that strict exogeneity of instruments is often a questionable assumption, our findings should be important to applied researchers who are concerned about the degree of size distortion of their inference procedure. We suggest robustness of asymptotic size under local model violations as a new alternative measure to choose among competing testing procedures. We also investigate the subsampling and hybrid tests introduced in Andrews and Guggenberger (2010a, Journal of Econometrics 158, 285–305) and show that they do not offer any improvement in terms of size-distortion reduction over the Anderson-Rubin type tests.

Suggested Citation

  • Guggenberger, Patrik, 2012. "On The Asymptotic Size Distortion Of Tests When Instruments Locally Violate The Exogeneity Assumption," Econometric Theory, Cambridge University Press, vol. 28(02), pages 387-421, April.
  • Handle: RePEc:cup:etheor:v:28:y:2012:i:02:p:387-421_00
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    Cited by:

    1. DiTraglia, Francis J., 2016. "Using invalid instruments on purpose: Focused moment selection and averaging for GMM," Journal of Econometrics, Elsevier, vol. 195(2), pages 187-208.
    2. Caner, Mehmet, 2014. "Near exogeneity and weak identification in generalized empirical likelihood estimators: Many moment asymptotics," Journal of Econometrics, Elsevier, vol. 182(2), pages 247-268.
    3. Seojeong Lee, 2015. "A Consistent Variance Estimator for 2SLS When Instruments Identify Different LATEs," Discussion Papers 2015-01, School of Economics, The University of New South Wales.
    4. Doko Tchatoka, Firmin Sabro, 2012. "Specification Tests with Weak and Invalid Instruments," MPRA Paper 40185, University Library of Munich, Germany.
    5. Cheng, Xu & Liao, Zhipeng, 2015. "Select the valid and relevant moments: An information-based LASSO for GMM with many moments," Journal of Econometrics, Elsevier, vol. 186(2), pages 443-464.
    6. Tchatoka, Firmin Doko, 2015. "Subset Hypotheses Testing And Instrument Exclusion In The Linear Iv Regression," Econometric Theory, Cambridge University Press, vol. 31(06), pages 1192-1228, December.
    7. Lavergne, Pascal, 2015. "Model Equivalence Tests for Overidentifying Restrictions," TSE Working Papers 15-562, Toulouse School of Economics (TSE), revised Nov 2015.
    8. Lee, Seojeong, 2014. "Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 178(P3), pages 398-413.
    9. repec:oup:qjecon:v:132:y:2017:i:4:p:1553-1592. is not listed on IDEAS
    10. Michal Kolesár & Raj Chetty & John Friedman & Edward Glaeser & Guido W. Imbens, 2015. "Identification and Inference With Many Invalid Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 474-484, October.
    11. repec:eme:aecozz:s0731-905320140000033013 is not listed on IDEAS
    12. Donald W.K. Andrews & Xu Cheng & Patrik Guggenberger, 2011. "Generic Results for Establishing the Asymptotic Size of Confidence Sets and Tests," Cowles Foundation Discussion Papers 1813, Cowles Foundation for Research in Economics, Yale University.
    13. Marco Jacopo Lombardi & Madhusudan Mohanty & Ilhyock Shim, 2017. "The real effects of household debt in the short and long run," BIS Working Papers 607, Bank for International Settlements.
    14. Guggenberger, Patrik, 2012. "A note on the relation between local power and robustness to misspecification," Economics Letters, Elsevier, vol. 116(2), pages 133-135.
    15. Janus, Thorsten & Riera-Crichton, Daniel, 2016. "Banking crises, external crises and gross capital flows," Globalization and Monetary Policy Institute Working Paper 273, Federal Reserve Bank of Dallas.
    16. Francis J. DiTraglia, 2011. "Using Invalid Instruments on Purpose: Focused Moment Selection and Averaging for GMM, Second Version," PIER Working Paper Archive 14-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 09 Dec 2014.
    17. Guggenberger, Patrik, 2012. "A note on the (in)consistency of the test of overidentifying restrictions and the concepts of true and pseudo-true parameters," Economics Letters, Elsevier, vol. 117(3), pages 901-904.
    18. Jui-Chung Yang & Ke-Li Xu, 2013. "Estimation and Inference under Weak Identi cation and Persistence: An Application on Forecast-Based Monetary Policy Reaction Function," 2013 Papers pya307, Job Market Papers.
    19. Ruoyao Shi & Zhipeng Liao, 2018. "An Averaging GMM Estimator Robust to Misspecification," Working Papers 201803, University of California at Riverside, Department of Economics.
    20. Jan F. Kiviet & Jerzy Niemczyk, 2014. "On the Limiting and Empirical Distributions of IV Estimators When Some of the Instruments are Actually Endogenous," Advances in Econometrics,in: Essays in Honor of Peter C. B. Phillips, volume 33, pages 425-490 Emerald Publishing Ltd.
    21. Isaiah Andrews & Matthew Gentzkow & Jesse M. Shapiro, 2017. "Measuring the Sensitivity of Parameter Estimates to Estimation Moments," The Quarterly Journal of Economics, Oxford University Press, vol. 132(4), pages 1553-1592.
    22. Xu Cheng & Zhipeng Liao, 2012. "Select the Valid and Relevant Moments: A One-Step Procedure for GMM with Many Moments," PIER Working Paper Archive 12-045, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.

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