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

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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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    Citations

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    Cited by:

    1. 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.
    2. repec:kap:jrefec:v:58:y:2019:i:3:d:10.1007_s11146-018-9657-0 is not listed on IDEAS
    3. Kiviet, Jan, 2019. "Microeconometric Dynamic Panel Data Methods: Model Specification and Selection Issues," MPRA Paper 93147, University Library of Munich, Germany.

    More about this item

    Keywords

    difference in Sargan-Hansen tests; exclusion restrictions; maintained hypothesis; instrument validity tests; overidentifying restrictions;

    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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