GMM, Generalized Empirical Likelihood, and Time Series

In this paper we extend the results of Kitamura (1997) for BEL to the more general class of GEL estimators. The resulting BGEL estimator is proved to be consistent and asymptotically normal and attains the semiparametric lower bound. In addition, we define the BGEL version of the classical trinity of tests, Wald, Lagrange Multiplier, and Likelihood Ratio tests. The resulting tests are as expected chi square distributed. We find via Monte Carlo experiments that the overidentification tests that stem from the BGEL estimator have generally better small sample properties than the J test.