Constraint Qualifications in Partial Identification

TL;DR

This paper explores the relationship between constraint qualifications in stochastic programming and the geometric assumptions in partial identification, revealing their fundamental connections and implications for econometric analysis.

Contribution

It demonstrates that many assumptions in partial identification align with the Mangasarian-Fromowitz constraint qualification, clarifying their relation and verification.

Findings

Many assumptions in partial identification coincide with the Mangasarian-Fromowitz constraint qualification.

The analysis clarifies the relation between different high-level assumptions in econometrics.

It highlights the stringency and ease of verification of these assumptions.

Abstract

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.