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Discriminating between (in)valid external instruments and (in)valid exclusion restrictions

Author

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  • Jan F. Kiviet

    (Amsterdam School of Economics, University of Amsterdam, PO Box 15867, 1001 NJ Amsterdam, The Netherlands)

Abstract
In models estimated by (generalized) method of moments a test on coefficient restrictions can either be based on a Wald statistic or on the difference between evaluated criterion functions. From their correspondence it easily follows that the statistic used for testing instrument validity, the Sargan-Hansen overidentifying restrictions (OR) statistic, is equivalent to an exclusion restrictions test statistic for a nonunique group of regressor variables. We prove that asymptotically this is the case too for incremental OR tests. However, we also demonstrate that, despite this equivalence of test statistics, one can nevertheless distinguish between either the (in)validity of some additional instruments or the (un)tenability of particular exclusion restrictions. This, however, requires to be explicit about the adopted maintained hypothesis. It also highlights that recent warnings in the literature that overidentifying restrictions tests may mislead practitioners should not be directed towards the test, but to practitioners who do not realize that inference based on such tests is unavoidably conditional on the validity of particular just-identifying statistically untestable assumptions.

Suggested Citation

  • Jan F. Kiviet, 2016. "Discriminating between (in)valid external instruments and (in)valid exclusion restrictions," Economic Growth Centre Working Paper Series 1508, Nanyang Technological University, School of Social Sciences, Economic Growth Centre.
    • Handle: RePEc:nan:wpaper:1508
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    References listed on IDEAS

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    Cited by:

    1. Kiviet, Jan F., 2020. "Testing the impossible: Identifying exclusion restrictions," Journal of Econometrics, Elsevier, vol. 218(2), pages 294-316.
    2. J. Michael Collins & Madelaine L’Esperance, 2023. "What do students gain from banks in schools? A field study," Review of Economics of the Household, Springer, vol. 21(2), pages 567-590, June.
    3. Kiviet, Jan F., 2023. "Instrument-free inference under confined regressor endogeneity and mild regularity," Econometrics and Statistics, Elsevier, vol. 25(C), pages 1-22.
    4. Darren K. Hayunga & R. Kelley Pace, 2019. "The Impact of TOM on Prices in the US Housing Market," The Journal of Real Estate Finance and Economics, Springer, vol. 58(3), pages 335-365, April.
    5. Kiviet, Jan F., 2016. "When is it really justifiable to ignore explanatory variable endogeneity in a regression model?," Economics Letters, Elsevier, vol. 145(C), pages 192-195.
    6. Jan F. Kiviet, 2020. "Causes Of Haze And Its Health Effects In Singapore: A Replication Study," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 65(06), pages 1367-1387, December.
    7. Kiviet, Jan F., 2020. "Microeconometric dynamic panel data methods: Model specification and selection issues," Econometrics and Statistics, Elsevier, vol. 13(C), pages 16-45.
    8. Leviticus Mensah & Murad Abdurahman Bein, 2023. "Sound Corporate Governance and Financial Performance: Is There a Link? Evidence from Manufacturing Companies in South Africa, Nigeria, and Ghana," Sustainability, MDPI, vol. 15(12), pages 1-24, June.
    9. Kiviet, Jan F. & Kripfganz, Sebastian, 2021. "Instrument approval by the Sargan test and its consequences for coefficient estimation," Economics Letters, Elsevier, vol. 205(C).

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    More about this item

    Keywords

    difference in Sargan-Hansen tests; exclusion restrictions; maintained hypothesis; instrument validity tests; overidentifying restrictions;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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