A Stopping Rule for the Computation of Generalized Method of Moments Estimators

To obtain consistency and asymptotic normality, a generalized method of moments (GAM) estimator typically is defined to be an approximate global minimizer of a GAM criterion function. To compute such an estimator, however, can be problematic because of the difficulty of global optimization. To alleviate this problem, the author proposes a stopping-rule (SR) procedure for computing GAM estimators. The SR procedure eliminates the need for global search with high probability. And, it provides an explicit SR for problems of stability that may arise with local optimization problems.