We consider models defined by a set of moment restrictions that may be subject to weak identification. Following the recent literature, the identification of the structural parameters is characterized by the Jacobian of the moment conditions. We unify several definitions of identification that have been used in the literature, and show how they are linked to the consistency and asymptotic normality of GMM estimators. We then develop two tests to assess the identification strength of the structural parameters. Both tests are straightforward to apply. In simulations, our tests are well-behaved when compared to contenders, both in terms of size and power
