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Specification Testing In Models With Many Instruments

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  • Anatolyev, Stanislav
  • Gospodinov, Nikolay

Abstract

This paper studies the asymptotic validity of the Anderson–Rubin ( AR ) test and the J test for overidentifying restrictions in linear models with many instruments. When the number of instruments increases at the same rate as the sample size, we establish that the conventional AR and J tests are asymptotically incorrect. Some versions of these tests, which are developed for situations with moderately many instruments, are also shown to be asymptotically invalid in this framework. We propose modifications of the AR and J tests that deliver asymptotically correct sizes. Importantly, the corrected tests are robust to the numerosity of the moment conditions in the sense that they are valid for both few and many instruments. The simulation results illustrate the excellent properties of the proposed tests.

Suggested Citation

  • Anatolyev, Stanislav & Gospodinov, Nikolay, 2011. "Specification Testing In Models With Many Instruments," Econometric Theory, Cambridge University Press, vol. 27(02), pages 427-441, April.
  • Handle: RePEc:cup:etheor:v:27:y:2011:i:02:p:427-441_00
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Koenker, Roger & Machado, Jose A. F., 1999. "GMM inference when the number of moment conditions is large," Journal of Econometrics, Elsevier, vol. 93(2), pages 327-344, December.
    3. Andersen, Torben G & Sorensen, Bent E, 1996. "GMM Estimation of a Stochastic Volatility Model: A Monte Carlo Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 328-352, July.
    4. Burnside, Craig & Eichenbaum, Martin S, 1996. "Small-Sample Properties of GMM-Based Wald Tests," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 294-308, July.
    5. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-681, May.
    6. Andrews, Donald W.K. & Stock, James H., 2007. "Testing with many weak instruments," Journal of Econometrics, Elsevier, vol. 138(1), pages 24-46, May.
    7. 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.
    8. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    9. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    10. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, Oxford University Press, vol. 106(4), pages 979-1014.
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    Citations

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    Cited by:

    1. Pierre Chaussé, 2011. "Generalized empirical likelihood for a continuum of moment conditions," Working Papers 1104, University of Waterloo, Department of Economics, revised Oct 2011.
    2. Wenjie Wang, 2012. "Bootstrapping Anderson-Rubin Statistic and J Statistic in Linear IV Models with Many Instruments," KIER Working Papers 810, Kyoto University, Institute of Economic Research.
    3. repec:eee:ecolet:v:157:y:2017:i:c:p:107-111 is not listed on IDEAS
    4. Dick, Christian D. & Schmeling, Maik & Schrimpf, Andreas, 2013. "Macro-expectations, aggregate uncertainty, and expected term premia," European Economic Review, Elsevier, vol. 58(C), pages 58-80.
    5. Chao, John C. & Hausman, Jerry A. & Newey, Whitney K. & Swanson, Norman R. & Woutersen, Tiemen, 2014. "Testing overidentifying restrictions with many instruments and heteroskedasticity," Journal of Econometrics, Elsevier, vol. 178(P1), pages 15-21.
    6. Federico Crudu & Giovanni Mellace & Zsolt Sandor, 2017. "Inference in instrumental variables models with heteroskedasticity and many instruments," Department of Economics University of Siena 761, Department of Economics, University of Siena.
    7. 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.
    8. Yoonseok Lee & Ryo Okui, 2009. "A Specification Test for Instrumental Variables Regression with Many Instruments," Cowles Foundation Discussion Papers 1741, Cowles Foundation for Research in Economics, Yale University.
    9. Abutaliev, Albert & Anatolyev, Stanislav, 2013. "Asymptotic variance under many instruments: Numerical computations," Economics Letters, Elsevier, vol. 118(2), pages 272-274.
    10. repec:eee:econom:v:204:y:2018:i:1:p:86-100 is not listed on IDEAS
    11. Marine Carrasco & Guy Tchuente, 2016. "Regularization Based Anderson Rubin Tests for Many Instruments," Studies in Economics 1608, School of Economics, University of Kent.
    12. Travaglini, Guido, 2010. "Dynamic Econometric Testing of Climate Change and of its Causes," MPRA Paper 23600, University Library of Munich, Germany.
    13. Lee, Yoonseok & Okui, Ryo, 2012. "Hahn–Hausman test as a specification test," Journal of Econometrics, Elsevier, vol. 167(1), pages 133-139.
    14. 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.
    15. Antonia Diaz & Luis A. Puch, 2016. "Investment, Technological Progress and Energy Efficiency," Working Papers 909, Barcelona Graduate School of Economics.
    16. 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.

    More about this item

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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