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Specification Testing in Models with Many Instruments

Author

Listed:
  • Stanislav Anatolyev

    (New Economic School)

  • Nikolay Gospodinov

    (Concordia University and CIREQ)

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.

Suggested Citation

  • Stanislav Anatolyev & Nikolay Gospodinov, 2008. "Specification Testing in Models with Many Instruments," Working Papers w0124, Center for Economic and Financial Research (CEFIR).
  • Handle: RePEc:cfr:cefirw:w0124
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Instrumental variables; many instruments; Bekker?s asymptotics; Anderson? Rubin test; test for overidentifying restrictions.;
    All these keywords.

    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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