Abstract
ABSTRACTThis article examines structural change tests based on generalized empirical likelihood methods in the time series context, allowing for dependent data. Standard structural change tests for the Generalized method of moments (GMM) are adapted to the generalized empirical likelihood (GEL) context. We show that when moment conditions are properly smoothed, these test statistics converge to the same asymptotic distribution as in the GMM, in cases with known and unknown breakpoints. New test statistics specific to GEL methods, and that are robust to weak identification, are also introduced. A simulation study examines the small sample properties of the tests and reveals that GEL-based robust tests performed well, both in terms of the presence and location of a structural change and in terms of the nature of identification.
Highlights
As the GMM is limited in a number of ways, a number of alternative estimators have been proposed: the Continuous Updated Estimator (CUE, Hansen, Heaton and Yaron, 1996), the Empirical Likelihood estimator (EL, Qin and Lawless, 1994) and the Exponential Tilting estimator (ET, Kitamura and Stutzer, 1997)
New test statistics specific to Generalized Empirical Likelihood (GEL) methods, and that are robust to weak identification, are introduced
In this paper we have studied tests for structural change that are based on generalized empirical likelihood methods and applicable to a time series context
Summary
As the GMM is limited in a number of ways (e.g., the existence of a bias, the requirement to compute a particular weighting matrix), a number of alternative estimators have been proposed: the Continuous Updated Estimator (CUE, Hansen, Heaton and Yaron, 1996), the Empirical Likelihood estimator (EL, Qin and Lawless, 1994) and the Exponential Tilting estimator (ET, Kitamura and Stutzer, 1997). We study standard Wald (GELW ), Lagrange multiplier (GELM ) and likelihood ratio (GELR) test statistics for parameters instability in cases of pure structural change test when the entire parameter vector is subject to structural change and partial structural change where only a subset of the parameter vector is subject to structural change We show that these statistics, when computed with properly smoothed moment conditions, follow the same asymptotic distribution as in the GMM context (Andrews, 1993). Two new tests specific to the GEL framework are proposed to detect instability of the overidentifying restrictions We show that these new statistics have the same asymptotic distribution, at first order, as the distribution derived by Hall and Sen (1999) when the moment conditions are properly smoothed.
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