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Published online by Cambridge University Press:  04 June 2021

Hiroaki Kaido
Boston University
Francesca Molinari
Cornell University
Jörg Stoye*
Cornell University
Address correspondence to Jörg Stoye, Department of Economics, Cornell University, Ithaca, NY, USA; e-mail:


The literature on stochastic programming typically restricts attention to problems that fulfill 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 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.

© The Author(s), 2021. Published by Cambridge University Press

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We are grateful to Ivan Canay for conversations that helped bring this paper into focus and to three anonymous referees as well as the editor and co-editor for extremely careful readings of the manuscript. We also thank Isaiah Andrews, Lixiong Li, and seminar audiences at the Bristol Econometrics Study Group, Bristol/Warwick joint seminar, Columbia, and Duke for their feedback. Any and all errors are our own. We gratefully acknowledge financial support through NSF Grants SES-1824344 and SES-2018498 (Kaido) as well as SES-1824375 (Molinari and Stoye).



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