We consider the limiting behavior of the overidentifying restrictions
test in the presence of neglected structural instability at a single
“break point.” It is shown that the test need not be
consistent against this type of misspecification. If it is consistent
then it emerges that the limiting behavior of this test statistic
depends on the covariance matrix estimator employed. In this paper we
consider the case in which a heteroskedasticity autocorrelation
covariance (HAC) is used. It is shown that (i) if the HAC estimator is
based on uncentered autocovariances then the overidentifying
restrictions test diverges at rate
T/bT where T is the
sample size and bT is the bandwidth; (ii)
if the HAC estimator is based on centered autocovariances then the rate
of increase of the overidentifying restrictions test is either
T/bT or T depending
on the form of the instability. These results are used to provide
conditions for the consistency of the method of moment selection of
Andrews (1999, Econometrica 67,
543–564) when certain elements of the candidate set of moments
are misspecified as a result of neglected structural instability.This work was begun while Hall was a Senior
Research Fellow and Peixe was a graduate student at the Department of
Economics, University of Birmingham, UK, and this support is gratefully
acknowledged. Peixe also gratefully acknowledges financial support from FCT
under Grant PRAXIS XXI/BD/13453/97. We are very grateful for the
very useful comments of Don Andrews and two anonymous referees.