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 .
This paper considers uniformly valid inference for linear functionals and scalar subvectors of partially identified parameters defined by linear moment inequalities. Our proposed procedure amounts to bootstrapping the value functions of four carefully constructed "perturbed" linear programming problems, and does not require the researcher to grid over the parameter space. Our low-level conditions for uniform validity rely on a novel application of Sard's Theorem from differential topology, and may be of substantial separate interest. Our procedure is asymptotically conservative for the true partially identified parameter, but draws its appeal from the fact that it is valid under weak assumptions, it performs well in finite samples, and is computationally simple to implement .
D
(over a class of data generating processes)
A
and scalar subvectors
D
in cases where the identified set is
D
(in the parameter)
R
We propose a bootstrap procedure for constructing uniformly valid confidence sets for a linear functional of a partially identified parameter. The proposed method
Our proposed procedure
R
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
four carefully constructed "perturbed" linear programming problems, and
R
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
grid over the parameter space. Our low-level conditions for uniform validity rely on a novel application of Sard's Theorem from differential topology, and may be of substantial separate interest. Our procedure is asymptotically conservative for the true partially identified parameter, but draws its appeal from the fact that it is valid under weak assumptions, it performs well in finite samples, and is computationally simple to implement