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CONSTRAINT QUALIFICATIONS IN PARTIAL IDENTIFICATION

Published online by Cambridge University Press:  04 June 2021

Hiroaki Kaido ,
Francesca Molinari  and
Jörg Stoye
Hiroaki Kaido
Affiliation:
Boston University
Francesca Molinari
Affiliation:
Cornell University
Jörg Stoye*
Affiliation:
Cornell University
*
Address correspondence to Jörg Stoye, Department of Economics, Cornell University, Ithaca, NY, USA; e-mail: [email protected].
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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.

Type
ARTICLES
Information
Econometric Theory , Volume 38 , Issue 3 , June 2022 , pp. 596 - 619
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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Footnotes

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).

References

REFERENCES

Andrews, D. W. K. & Soares, G. (2010) Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection. Econometrica 78, 119–157.Google Scholar
Andrews, I., Roth, J., & Pakes, A. (2019) Inference for Linear Conditional Moment Inequalities. Working Paper 26374, National Bureau of Economic Research.CrossRefGoogle Scholar
Bazaraa, M.S., Sherali, H.D., & Shetty, C. (2006) Nonlinear Programming: Theory and Algorithms. 3rd ed. Wiley-Interscience.CrossRefGoogle Scholar
Beresteanu, A., Molchanov, I. & Molinari, F. (2011) Sharp identification regions in models with convex moment predictions. Econometrica 79, 1785–1821.Google Scholar
Bonnans, J. & Shapiro, A. (2000) Perturbation Analysis of Optimization Problems. Springer.CrossRefGoogle Scholar
Bugni, F. A. (2009) Bootstrap inference in partially identified models defined by moment inequalities: Coverage of the identified set. Econometrica 78, 735–753.Google Scholar
Bugni, F. A., Canay, I. A. & Shi, X. (2017) Inference for subvectors and other functions of partially identified parameters in moment inequality models. Quantitative Economics 8, 1–38.CrossRefGoogle Scholar
Canay, I. (2010) EL inference for partially identified models: Large deviations optimality and bootstrap validity. Journal of Econometrics 156, 408–425.CrossRefGoogle Scholar
Canay, I.A. & Shaikh, A.M. (2017) Practical and Theoretical Advances in Inference for Partially Identified Models, vol. 2 of Econometric Society Monographs, pp. 271–306. Cambridge University Press.Google Scholar
Chernozhukov, V., Hong, H. & Tamer, E. (2007) Estimation and confidence regions for parameter sets in econometric models. Econometrica 75, 1243–1284.CrossRefGoogle Scholar
Cho, J. & Russell, T.M. (2019) Simple inference on functionals of set-identified parameters defined by convex moments, arXiv:1810.03180.Google Scholar
Eizenberg, A. (2014) Upstream innovation and product variety in the U.S. Home PC Market. The Review of Economic Studies 81, 1003–1045.CrossRefGoogle Scholar
Gafarov, B. (2019) Inference in high-dimensional set-identified affine models, arXiv:1904.00111.Google Scholar
Ho, K. & Pakes, A. (2014) Hospital choices, hospital prices, and financial incentives to physicians. American Economic Review 104, 3841–3884.CrossRefGoogle Scholar
Holmes, T. J. (2011) The diffusion of Wal-Mart and economies of density. Econometrica 79, 253–302.Google Scholar
Kaido, H., Molinari, F. & Stoye, J. (2019) Confidence inference for projections of partially identified parameters. Econometrica 87, 1397–1432.CrossRefGoogle Scholar
Kaido, H., Molinari, F., Stoye, J., & Thirkettle, M. (2017) Calibrated projection in MATLAB, arxiv:1710.09707.Google Scholar
Kaido, H. & Santos, A. (2014) Asymptotically efficient estimation of models defined by convex moment inequalities. Econometrica 82, 387–413.Google Scholar
Molchanov, I. S. (1998) A Limit Theorem for Solutions of Inequalities. Scandinavian Journal of Statistics 25, 235–242.CrossRefGoogle Scholar
Molinari, F. (2020) Microeconometrics with partial identification. In Durlauf, S.N., Hansen, L.P., Heckman, J.J., & Matzkin, R.L. (eds.), Handbook of Econometrics, vol. 7A, pp. 355–486. Elsevier.CrossRefGoogle Scholar
Newey, W.K. & McFadden, D. (1994) Large sample estimation and hypothesis testing. In Engle, R.F. & McFadden, D.L. (eds.), Handbook of Econometrics, vol. 4, chap. 36. Elsevier.Google Scholar
Pakes, A., Porter, J., Ho, K., & Ishii, J. (2011) Moment Inequalities and Their Application. Discussion Paper, Harvard University.Google Scholar
Pakes, A., Porter, J., Ho, K. & Ishii, J. (2015) Moment inequalities and their application. Econometrica 83, 315–334.CrossRefGoogle Scholar
Shapiro, A. (1990) On differential stability in stochastic programming. Mathematical Programming 47, 107–116.CrossRefGoogle Scholar
Shapiro, A. (1991) Asymptotic analysis of stochastic programs. Annals of Operations Research 30, 169–186.CrossRefGoogle Scholar
Shapiro, A. (1993) Asymptotic behavior of optimal solutions in stochastic programming. Mathematics of Operations Research 18, 829–845.CrossRefGoogle Scholar
Tamer, E. (2003) Incomplete simultaneous discrete response model with multiple equilibria. Review of Economic Studies 70, 147–165.CrossRefGoogle Scholar
Wachsmuth, G. (2013) On LICQ and the uniqueness of Lagrange multipliers. Operations Research Letters 41, 78–80.CrossRefGoogle Scholar
Yildiz, N. (2012) Consistency of plug-in estimators of upper contour and level sets. Econometric Theory 28, 309–327.CrossRefGoogle Scholar