Doko Tchatoka, Firmin Sabro and Dufour, JeanMarie (2008): Instrument endogeneity and identificationrobust tests: some analytical results. Published in: Journal of Statistical Planning and Inference , Vol. 138, (12. March 2008): pp. 26492661.

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Abstract
When some explanatory variables in a regression are correlated with the disturbance term, instrumental variable methods are typically employed to make reliable inferences. Furthermore, to avoid difficulties associated with weak instruments, identification robust methods are often proposed. However, it is hard to assess whether an instrumental variable is valid in practice because instrument validity is based on the questionable assumption that some of them are exogenous. In this paper, we focus on structural models and analyze the effects of instrument endogeneity on two identificationrobust procedures, the AndersonRubin (1949, AR) and the Kleibergen (2002, K) tests, with or without weak instruments. Two main setups are considered: (1) the level of “instrument” endogeneity is fixed (does not depend on the sample size), and (2) the instruments are locally exogenous, i.e. the parameter which controls instrument endogeneity approaches zero as the sample size increases. In the first setup, we show that both test procedures are in general consistent against the presence of invalid instruments (hence asymptotically invalid for the hypothesis of interest), whether the instruments are “strong” or “weak”. We also describe cases where test consistency may not hold, but the asymptotic distribution is modified in a way that would lead to size distortions in large samples. These include, in particular, cases where the 2SLS estimator remains consistent, but the AR and K tests are asymptotically invalid. In the second setup, we find (nondegenerate) asymptotic noncentral chisquare distributions in all cases, and describe cases where the noncentrality parameter is zero and the asymptotic distribution remains the same as in the case of valid instruments (despite the presence of invalid instruments). Overall, our results underscore the importance of checking for the presence of possibly invalid instruments when applying “identificationrobust” tests.
Item Type:  MPRA Paper 

Original Title:  Instrument endogeneity and identificationrobust tests: some analytical results 
Language:  English 
Keywords:  simultaneous equations; instrumental variables; locally weak instruments; invalid instruments; locally exogenous instruments. 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C12  Hypothesis Testing: General C  Mathematical and Quantitative Methods > C3  Multiple or Simultaneous Equation Models ; Multiple Variables > C30  General 
Item ID:  29613 
Depositing User:  Firmin Doko Tchatoka 
Date Deposited:  19. Mar 2011 21:28 
Last Modified:  31. Dec 2015 02:42 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/29613 