“…To avoid this difficulty, a large part of the literature has been trying to provide a confidence region for an outer set , that is, a collection of values for the parameter of interest that contains the identified set but may also contain additional values 1 . Because of its tractability, constructing a confidence region for an outer set has been entertained in various topics of studies where the parameters of interest are only partially identified; see, for instance, Blundell, Gosling, Ichimura, and Meghir (2007), Ciliberto and Tamer (2009), Aucejo, Bugni, and Hotz (2017), Sheng (2020), De Paula, Richards‐Shubik, and Tamer (2018), Dickstein and Morales (2018), Honoré and Hu (2020), Chesher and Rosen (2020), Gualdani (2021), and Berry and Compiani (2023), among many others.…”