Practical and theoretical advances in inference for partially identified models

This paper surveys some of the recent literature on inference in partially identified models. After reviewing some basic concepts, including the definition of a partially identified model and the identified set, we turn our attention to the construction of confidence regions in partially identified settings. In our discussion, we emphasize the importance of requiring confidence regions to be uniformly consistent in level over relevant classes of distributions. Due to space limitations, our survey is mainly limited to the class of partially identified models in which the identified set is characterized by a finite number of moment inequalities or the closely related class of partially identified models in which the identified set is a function of a such a set. The latter class of models most commonly arise when interest focuses on a subvector of a vector valued parameter, whose values are limited by a finite number of moment inequalities. We then rapidly review some important parts of the broader literature on inference in partially identified models and conclude by providing some thoughts on fruitful directions for future research.