A dual approach to inference for partially identified econometric models

This paper considers inference for the set ΘI of parameter values that minimize a criterion function. Chernozhukov et al. (2007) (CHT) develop a general theory of estimation and inference using the level-set of a criterion function. We establish a dual relationship between the level-set estimator and its support function and show that the properly normalized support function provides alternative Wald-type inference methods. These methods can be used to obtain confidence sets for ΘI and points inside it. For models with finitely many moment inequalities, we show that our Wald-type statistic is asymptotically equivalent to CHT’s statistic under regularity conditions.