Constraint Qualifications in Partial Identification

Hiroaki Kaido, Francesca Molinari, Jörg Stoye

arXiv 24 Aug 2019 · Econometrics · publishedEconometric Theory (2021) · 13 citations (OpenAlex)

arXiv:1908.09103 · PDF · DOI · OpenAlex · Extracted main text

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.

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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

	Reference	Intensity	Mentions	Sections	Main text
1	Cho and Russell (2019) Simple Inference on Functionals of Set-Identified Parameters Defined by Convex Moments	1.000	5	4	100%
2	Gafarov (2019) Inference in high-dimensional set-identified affine models	0.928	4	4	100%
3	Kaido and Santos (2014) Asymptotically Efficient Estimation of Models Defined by Convex Moment Inequalities	0.843	3	3	100%
4	Canay and Shaikh (2017) Practical and Theoretical Advances in Inference for Partially Identified Models	0.811	4	2	100%
5	Yildiz (2012) Consistency of plug-in estimators of upper contour and level sets	0.811	4	2	100%
6	Andrews and Soares (2010) Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection	0.644	2	2	100%
7	Molinari (2020) Microeconometrics with partial identification self	0.644	2	2	100%
8	Bazaraa, Sherali, and Shetty (2006) Nonlinear programming: theory and algorithms	0.644	2	2	100%
9	Kaido, Molinari, and Stoye (2019) Confidence Inference for Projections of Partially Identified Parameters self	0.585	3	1	100%
10	Pakes, Porter, Ho, and Ishii (2011) Moment Inequalities and Their Application	0.511	2	1	100%

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Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

	Citing paper	Intensity	Mentions	Sections
1	Simple Inference on Functionals of Set-Identified Parameters Defined by Linear MomentsA previous version of this paper was circulated under the title “Inference on Functionals of Set-Identified Parameters Defined by Convex Moments." We are grateful to Ivan Canay, the associate editor, and two referees for excellent feedback that greatly improved the paper. We thank Victor Aguirregabiria, Bulat Gafarov, Christian Gourieroux, Jiaying Gu, Ismael Mourifie, Jeffrey Negrea, Adam Rosen, Brennan Thompson, Stanislav Volgushev and Yuanyuan Wan for helpful comments and discussion. We are also grateful to participants at the 7th Annual Doctoral Workshop in Applied Econometrics at the University of Toronto, as well as participants at the 2019 North America Summer Meeting of the Econometric Society at the University of Washington. This research was supported by the Social Sciences and Humanities Research Council of Canada. All errors are our own	0.511	2	1
2	Microeconometrics with Partial Identification	0.511	2	1
3	Debiased Machine Learning of Set-Identified Linear Models	0.405	1	1
4	Simple subvector inference on sharp identified set in affine models	0.405	1	1
5	Generalized Lee Bounds	0.405	1	1
6	Policy Transforms and Learning Optimal Policies I thank Jiaying Gu, Ismael Mourifie, Eduardo Souza-Rodrigues, Adam Rosen, Stanislav Volgushev and Yuanyuan Wan for their feedback and encouragement, and I am especially grateful to JoonHwan Cho for many hours of discussion that helped to improve this paper. A previous version of this paper appeared in my doctoral thesis at the University of Toronto. This research was supported by the Social Sciences and Humanities Research Council of Canada. All errors are my own	0.405	1	1
7	Identification of Dynamic Panel Logit Models with Fixed Effects We thank Victor Aguirregabiria, Roger Koenker, Ismael Mourifié and Stanislav Volgushev for useful discussion. We are grateful to numerous seminar participants for their feedback, and are especially grateful to Francesca Molinari and three anonymous referees for their helpful comments. All errors are our own	0.405	1	1
8	A Generalized Argmax Theorem with Applications	0.405	1	1
9	Testing the Solvability of Systems of Linear Inequalities	0.405	1	1
10	Testing Inequalities Linear in Nuisance Parameters	0.405	1	1