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

Jan Kiviet

No 1508, Economic Growth Centre Working Paper Series from Nanyang Technological University, School of Social Sciences, Economic Growth Centre

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.

Keywords: difference in Sargan-Hansen tests; exclusion restrictions; maintained hypothesis; instrument validity tests; overidentifying restrictions (search for similar items in EconPapers)
JEL-codes: C01 C12 C26 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2016-05
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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http://www3.ntu.edu.sg/hss2/egc/wp/2015/2015-08.pdf (application/pdf)

Related works:
Journal Article: Discriminating between (in)valid External Instruments and (in)valid Exclusion Restrictions (2017)
Working Paper: Discriminating between (in)valid external instruments and (in)valid exclusion restrictions (2015)
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Persistent link: https://EconPapers.repec.org/RePEc:nan:wpaper:1508

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