Many inference procedures in the literature on partial identification are designed for when the inferential object of interest is the entire (partially identified) vector of parameters. However, when the researcher's inferential object of interest is a subvector or functional of the parameter vector, these inference procedures can be highly conservative, especially when the dimension of the parameter vector is large. This paper considers uniformly valid inference for continuous functionals of partially identified parameters in cases where the identified set is defined by convex (in the parameter) moment inequalities. We use a functional delta method and propose a method for constructing uniformly valid confidence sets for a (possibly stochastic) convex functional of a partially identified parameter. The proposed method amounts to bootstrapping the Lagrangian of a convex optimization problem, and subsumes subvector inference as a special case. Unlike other proposed subvector inference procedures, our procedure does not require the researcher to repeatedly invert a hypothesis test  . Finally, we discuss sufficient conditions on the moment functions to ensure uniform validity  .
 This paper considers uniformly valid (over a class of data generating processes) inference for convex functionals of partially identified parameters in cases where the identified set is defined by convex (in the parameter) moment inequalities. We propose a bootstrap procedure for constructing uniformly valid confidence sets for a convex functional of a partially identified parameter. The proposed method amounts to bootstrapping the value functions of a convex optimization problem, and subsumes subvector inference as a special case. Unlike other proposed subvector inference procedures, our procedure does not require the researcher to repeatedly invert a hypothesis test , and is extremely computationally efficient . Finally, we discuss sufficient conditions on the moment functions to ensure uniform validity , and show that our assumptions are in fact satisfied by a large class of data generating processes .
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Many inference procedures in the literature on partial identification are designed for when the inferential object of interest is the entire (partially identified) vector of parameters. However, when the researcher's inferential object of interest is a subvector or functional of the parameter vector, these inference procedures can be highly conservative, especially when the dimension of the parameter vector is large.
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inference for continuous
(over a class of data generating processes) inference for convex
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use a functional delta method and propose a method
propose a bootstrap procedure
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(possibly stochastic)
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Lagrangian
value functions
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, and is extremely computationally efficient
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, and show that our assumptions are in fact satisfied by a large class of data generating processes