Guggenberger, Patrik and Smith, Richard J. (2005) Generalized empirical likelihood estimators and tests under partial weak and strong identification. Econometric Theory, Vol.21 (No.4). pp. 667-709. ISSN 0266-4666

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Abstract

The purpose of this paper is to describe the performance of generalized empirical likelihood (GEL) methods for time series instrumental variable models specified by nonlinear moment restrictions as in Stock and Wright (2000, Econometrica 68, 1055–1096) when identification may be weak. The paper makes two main contributions. First, we show that all GEL estimators are first-order equivalent under weak identification. The GEL estimator under weak identification is inconsistent and has a nonstandard asymptotic distribution. Second, the paper proposes new GEL test statistics, which have chi-square asymptotic null distributions independent of the strength or weakness of identification. Consequently, unlike those for Wald and likelihood ratio statistics, the size of tests formed from these statistics is not distorted by the strength or weakness of identification. Modified versions of the statistics are presented for tests of hypotheses on parameter subvectors when the parameters not under test are strongly identified. Monte Carlo results for the linear instrumental variable regression model suggest that tests based on these statistics have very good size properties even in the presence of conditional heteroskedasticity. The tests have competitive power properties, especially for thick-tailed or asymmetric error distributions.

Item Type:	Journal Item
Subjects:	H Social Sciences > HB Economic Theory Q Science > QA Mathematics
Divisions:	Faculty of Social Sciences > Economics
Library of Congress Subject Headings (LCSH):	Statistical hypothesis testing, Equivalence relations (Set theory), Instrumental variables (Statistics), Heteroscedasticity, Chi-square test
Journal or Publication Title:	Econometric Theory
Publisher:	Cambridge University Press
ISSN:	0266-4666
Official Date:	August 2005
Volume:	Vol.21
Number:	No.4
Page Range:	pp. 667-709
Identification Number:	10.1017/S0266466605050371
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Leverhulme Trust (LT), Carl Arvid Anderson Prize Fellowship (CAAPF)
URI:	http://wrap.warwick.ac.uk/id/eprint/736

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