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Constraint Qualifications in Partial Identification

Hiroaki Kaido (), Francesca Molinari and Jörg Stoye

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Abstract: The literature on stochastic programming typically regularizes problems using so-called Constraint Qualifications. The literature on estimation and inference under partial identification frequently restricts the geometry of identified sets with diverse high-level assumptions. These superficially appear to be different approaches to closely related problems. We extensively analyze their relation. Among other things, we show that for partial identification through pure moment inequalities, numerous regularization assumptions from the literature essentially coincide with the Mangasarian-Fromowitz Constraint Qualification. This clarifies the relation between well-known contributions, including within econometrics, and elucidates stringency, as well as ease of verification, of some high-level assumptions in seminal papers.

Date: 2019-08
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