The Incredible Flexibility of Moment Matching

We ask how far the choice of which moments to match can push estimates in misspecified structural models. The answer is: very far. Under regularity conditions, an adversarial researcher informed about the data distribution can choose moments that render any parameter value the unique solution to the population moment-matching problem. Moreover, in many cases they can do so with little increase in model-implied standard errors relative to maximum likelihood. We illustrate both results in a menu-cost model.