This paper considers uniformly valid (over a class of data generating processes) inference for linear functionals of partially identified parameters in cases where the identified set is defined by linear (in the parameter) moment inequalities. We propose a bootstrap procedure for constructing uniformly valid confidence sets for a linear functional of a partially identified parameter. The proposed method amounts to bootstrapping the value functions of a linear optimization problem, and subsumes subvector inference as a special case. In other words, this paper shows the conditions under which "naively" bootstrapping a linear program can be used to construct a confidence set with uniform correct coverage for a partially identified linear functional. Unlike other proposed subvector inference procedures, our procedure does not require the researcher to repeatedly invert a hypothesis test, and is extremely computationally efficient. In addition to the new procedure, the paper also discusses connections between the literature on optimization and the literature on subvector inference in partially identified models.

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