GENERALIZED EMPIRICAL LIKELIHOOD ESTIMATORS AND TESTS UNDER PARTIAL, WEAK, AND STRONG IDENTIFICATION
研究了广义经验似然方法在弱识别下时间序列工具变量模型中的表现，证明所有GEL估计量一阶等价，并提出具有卡方渐近零分布的新检验统计量，其大小不受识别强度影响。
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.This paper is a revision of Guggenberger's job market paper “Generalized Empirical Likelihood Tests under Partial, Weak, and Strong Identification.” We are thankful to the editor, P.C.B. Phillips, and three referees for very helpful suggestions on an earlier version of this paper. Guggenberger gratefully acknowledges the continuous help and support of his adviser, Donald Andrews, who played a prominent role in the formulation of this paper. He thanks Peter Phillips and Joseph Altonji for their extremely valuable comments. We also thank Vadim Marner for help with the simulation section and John Chao, Guido Imbens, Michael Jansson, Frank Kleibergen, Marcelo Moreira, Jonathan Wright, and Motohiro Yogo for helpful comments. Aspects of this research have been presented at the 2003 Econometric Society European Meetings; York Econometrics Workshop 2004; Seminaire Malinvaud; CREST-INSEE; and seminars at Albany, Alicante, Austin (Texas), Brown, Chicago, Chicago GSB, Harvard/MIT, Irvine, ISEG/Universidade Tecnica de Lisboa, Konstanz, Laval, Madison (Wisconsin), Mannheim, Maryland, NYU, Penn, Penn State, Pittsburgh, Princeton, Rice, Riverside, Rochester, San Diego, Texas A&M, UCLA, USC, and Yale. We thank all the seminar participants. Guggenberger and Smith received financial support through a Carl Arvid Anderson Prize Fellowship and a 2002 Leverhulme Major Research Fellowship, respectively.