Specification Tests for Strong Identification

Abstract: We consider a GMM framework where weaker patterns of identification may arise: typically, the data generating process is allowed to depend on the sample size. We are interested in providing inference about the identification of the structural parameter. First, for a given set of moment conditions, we propose a J-type test of the null that the structural parameter is not strongly identified. In other words, it is only as long as that the null cannot be rejected that it remains necessary to resort to alternative (nearly) weak identification asymptotics. Second, we propose a consistent Hausman-type test to test whether additional moment conditions enhance its identification. Failing to reject the null means that the candidate additional moment restrictions are useless to improve the strength of identification of the structural parameter. Finally, we propose a consistent test to test whether additional moment conditions are valid. The above testing strategy is illustrated with the Epstein and Zin asset pricing model