Instrument endogeneity and identification-robust tests: Some analytical results
journal contribution
posted on 2023-05-17, 05:23 authored by Doko Tchatoka, S, Dufour, JMWhen 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 identification-robust procedures, the Anderson-Rubin (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 (non-degenerate) asymptotic non-central chi-square distributions in all cases, and describe cases where the non-centrality 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 "identification-robust" tests. © 2008 Elsevier B.V. All rights reserved.
History
Publication title
Journal of Statistical Planning and InferenceVolume
138Issue
9Pagination
2649-2661ISSN
0378-3758Department/School
TSBEPublisher
Elsevier Science BvPlace of publication
Po Box 211, Amsterdam, Netherlands, 1000 AeRights statement
The definitive version is available at http://www.sciencedirect.comRepository Status
- Restricted
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