Before revision:  The identified set is of a union bounds form that previously developed partial identification inference methods do not apply to. We develop a novel bootstrap method to construct  valid confidence intervals for the identified set and parameter of interest when the identified set is of a union bounds form, and we establish the  theoretical properties.
After revision:  The identified set is of a union bounds form that involves the minimum and maximum operators, which makes the canonical bootstrap generally inconsistent and naive methods overly conservative. By utilizing the directional inconsistency of the bootstrap distribution, we develop a novel bootstrap method to construct valid confidence intervals for the identified set and parameter of interest when the identified set is of a union bounds form, and we establish the theoretical properties.