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Instrument exogeneity remains a questionable assumption in many empirical application... (2010)
BibTeX
@MISC{Guggenberger10instrumentexogeneity,
author = {Patrik Guggenberger and Gitanjali Kumar},
title = {Instrument exogeneity remains a questionable assumption in many empirical application...},
year = {2010}
}
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Abstract
Abstract: In the linear instrumental variables model, we provide theoretical and Monte Carlo evidence for the size distortion of a two-stage hypothesis test that uses a test of overidentifying restrictions in the …rst stage. We derive a lower bound for the asymptotic size of the two-stage test. The lower bound is given by the asymptotic size of a test that rejects the null hypothesis when two conditions are met: the test of overidentifying restrictions used in the …rst stage does not reject and the test in the second stage rejects. This lower bound can be as large as 1 "P; where "P is the pretest nominal size, for a parameter space that allows for local non-exogeneity of the instruments Zi but rules out weak instruments. The overrejection problem is worst asymptotically in cases where EuiZi is a nonzero multiple of EZiZ 0 i; where ui is the structural error and the reduced form vector. We also provide pointwise asymptotic rejection probabilities for various degrees of colinearity between EuiZi and EZiZ 0 i: Finite sample simulations document that severe overrejection of the two-stage test not only occurs in this knife-edge case but for a large array of parameter combinations. Despite these …ndings we recommend the use of a J test as a pretest. It can guard an applied researcher from using non-exogenous instruments. The empirical application reexamines the …ndings in
Keyphrases
instrument exogeneity many empirical application questionable assumption rst stage asymptotic size two-stage test monte carlo evidence local non-exogeneity second stage reject large array asymptotic rejection probability nonzero multiple applied researcher size distortion weak instrument non-exogenous instrument reduced form vector structural error finite sample simulation empirical application linear instrumental variable nominal size knife-edge case null hypothesis parameter space overrejection problem severe overrejection various degree two-stage hypothesis test parameter combination instrument zi
