We introduce an information-based fragility measure for GMM models that are potentially misspecified and unstable. A large fragility measure signifies a GMM model's lack of internal refutability (weak power of specification tests) and external validity (poor out-of-sample fit). The fragility of a set of model-implied moment restrictions is tightly linked to the quantity of additional information the econometrician can obtain about the model parameters by imposing these restrictions. Our fragility measure can be computed at little cost even for complex dynamic structural models. We illustrate its applications via two examples: a rare-disaster risk model and a long-run risk model.