Near exogeneity and weak identification in generalized empirical likelihood estimators: Many moment asymptotics

This paper investigates the Generalized Empirical Likelihood (GEL) estimators when there are local violations of the exogeneity condition (near exogeneity) in the case of many weak moments. We also examine the tradeoff between the degree of violation of the exogeneity and the number of nearly exogenous instruments. In this respect, this paper extends many weak moment asymptotics of Newey and Windmeijer (2009a). The overidentifying restrictions test can detect both mild and large violations of exogeneity. In the case of minor violations, the Anderson-Rubin (1949) and Wald tests are not size distorted.