Generalized empirical likelihood tests in time models with potential identification failure

We introduce test statistics based on generalized empirical likelihood methods that can be used to test simple hypotheses involving the unknown parameter vector in moment condition time series models. The test statistics generalize those in Guggenberger and Smith (2005) from the i.i.d. to the time series context and are alternatives to those in Kleibergen (2001) and Otsu (2003). The main feature of these tests is that their empirical null rejection probabilities are not affected much by the strength or weakness of identification. More precisely, we show that the statistics are asymptotically distributed as chi-square under both classical asymptotic theory and weak instrument asymptotics of Stock and Wright (2000). A Monte Carlo study reveals that the finite-sample performance of the suggested tests is very competitive.