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Simple Inference on Functionals of Set-Identified Parameters Defined by Linear Moments
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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