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Specification Testing in Models with Many Instruments

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Author Info
Stanislav Anatolyev () (New Economic School)
Nikolay Gospodinov () (Concordia University and CIREQ)

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Abstract

This paper studies the asymptotic validity of the Anderson-Rubin (AR) test and the J test of 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, that 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.

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Publisher Info
Paper provided by Center for Economic and Financial Research (CEFIR) in its series Working Papers with number w0124.

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Length: 17 pages
Date of creation: Sep 2008
Date of revision:
Handle: RePEc:cfr:cefirw:w0124

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Related research
Keywords: Instrumental variables; many instruments; Bekker?s asymptotics; Anderson? Rubin test; test for overidentifying restrictions.;

Find related papers by JEL classification:
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing
C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 979-1014, November. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
  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 328-52, July.
    Other versions:
  4. 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. [Downloadable!] (restricted)
  5. 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, 09. [Downloadable!] (restricted)
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  6. 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.
  7. Bekker, Paul A, 1994. "Alternative Approximations to the Distributions of Instrumental Variable Estimators," Econometrica, Econometric Society, vol. 62(3), pages 657-81, May. [Downloadable!] (restricted)
  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. [Downloadable!] (restricted)
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