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.