On the limiting and empirical distributions of IV estimators when some of the instruments are actually endogenous

Jan Kiviet and Jerzy Niemczyk
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Jerzy Niemczyk: European Central Bank, Frankfurt, Germany

No 1311, Economic Growth Centre Working Paper Series from Nanyang Technological University, School of Social Sciences, Economic Growth Centre

Abstract: IV estimation is examined when some instruments may be invalid. This is relevant because the initial just-identifying orthogonality conditions are untestable, whereas their validity is required when testing the orthogonality of additional instruments by so-called over-identi?cation restriction tests. Moreover, these tests have limited power when samples are small, especially when instruments are weak. Distinguishing between conditional and unconditional settings, we analyze the limiting distribution of inconsistent IV and examine normal ?rst-order asymptotic approximations to its density in ?nite samples. For simple classes of models we compare these approxi- mations with their simulated empirical counterparts over almost the full parameter space. The latter is expressed in measures for: model ?t, simultaneity, instrument invalidity and instrument weakness. Our major ?ndings are that for the accuracy of large sample asymptotic approximations instrument weakness is much more detri- mental than instrument invalidity. Also, IV estimators obtained from strong but possibly invalid instruments are usually much closer to the true parameter values than those obtained from valid but weak instruments.

Keywords: empirical density; inconsistent estimators; invalid instruments; (un)conditional asymptotic distribution; weak instruments (search for similar items in EconPapers)
JEL-codes: C13 C15 C30 (search for similar items in EconPapers)
Pages: 45 pages
Date: 2013-11
New Economics Papers: this item is included in nep-ecm and nep-sea
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Related works:
Chapter: On the Limiting and Empirical Distributions of IV Estimators When Some of the Instruments are Actually Endogenous (2014)
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Persistent link: https://EconPapers.repec.org/RePEc:nan:wpaper:1311

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