The principal 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 when identification may be weak. The paper makes two main contributions. Firstly, 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. Secondly, 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 iden- tification. 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.
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Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number
CWP08/03.
Length: 54 pp. Date of creation: Jul 2003 Date of revision: Handle: RePEc:ifs:cemmap:08/03
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Find related papers by JEL classification: C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
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