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Partial identification using random set theory

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  • Arie Beresteanu

    (Institute for Fiscal Studies and Duke)

  • Ilya Molchanov
  • Francesca Molinari

    ()
    (Institute for Fiscal Studies and Cornell University)

Abstract

This paper illustrates how the use of random set theory can benefit partial identification analysis. We revisit the origins of Manski's work in partial identification (e.g., Manski (1989, 1990)), focusing our discussion on identification of probability distributions and conditional expectations in the presence of selectively observed data, statistical independence and mean independence assumptions, and shape restrictions. We show that the use of the Choquet capacity functional and of the Aumann expectation of a properly defined random set can simplify and extend previous results in the literature. We pay special attention to explaining how the relevant random set needs to be constructed, depending on the econometric framework at hand. We also discuss limitations in the applicability of specific tools of random set theory to partial identification analysis.

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Bibliographic Info

Paper provided by Centre for Microdata Methods and Practice, Institute for Fiscal Studies in its series CeMMAP working papers with number CWP40/10.

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Date of creation: Dec 2010
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Handle: RePEc:ifs:cemmap:40/10

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  1. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, 09.
  2. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May.
  3. Guido Imbens & Charles F. Manski, 2003. "Confidence intervals for partially identified parameters," CeMMAP working papers CWP09/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2008. "Sharp identification regions in games," CeMMAP working papers CWP15/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Toru Kitagawa, 2009. "Identification region of the potential outcome distributions under instrument independence," CeMMAP working papers CWP30/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Manski, Charles F. & Molinari, Francesca, 2010. "Rounding Probabilistic Expectations in Surveys," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 219-231.
  7. Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, Econometric Society, vol. 78(1), pages 119-157, 01.
  8. Victor Chernozhukov & Sokbae 'Simon' Lee & Adam Rosen, 2011. "Intersection bounds: estimation and inference," CeMMAP working papers CWP34/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  9. Arie Beresteanu & Francesca Molinari, 2006. "Asymptotic properties for a class of partially identified models," CeMMAP working papers CWP10/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. Jörg Stoye, 2008. "More on confidence intervals for partially identified parameters," CeMMAP working papers CWP11/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  11. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
  12. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2010. "Sharp identification regions in models with convex moment predictions," CeMMAP working papers CWP25/10, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  13. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, 03.
  14. Maria Ponomareva & Elie Tamer, 2011. "Misspecification in moment inequality models: back to moment equalities?," Econometrics Journal, Royal Economic Society, vol. 14(2), pages 186-203, 07.
  15. Philip Haile, 2000. "Inference with an Incomplete Model of English Auctions," Econometric Society World Congress 2000 Contributed Papers 1546, Econometric Society.
  16. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
  17. Galichon, Alfred & Henry, Marc, 2009. "A test of non-identifying restrictions and confidence regions for partially identified parameters," Journal of Econometrics, Elsevier, vol. 152(2), pages 186-196, October.
  18. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  19. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
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Cited by:
  1. Liao, Yuan & Simoni, Anna, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," MPRA Paper 43262, University Library of Munich, Germany.
  2. Magnac, Thierry, 2014. "Identification partielle: méthodes et conséquences pour les applications empiriques," TSE Working Papers 14-458, Toulouse School of Economics (TSE).
  3. Sara Bleninger, 2013. "Welfare Effects of the Euro Cash Changeover: Do Assumptions Really Matter?," SOEPpapers on Multidisciplinary Panel Data Research 577, DIW Berlin, The German Socio-Economic Panel (SOEP).
  4. Hoshino, Tadao, 2013. "Partial identification in binary response models with nonignorable nonresponses," Economics Letters, Elsevier, vol. 121(1), pages 74-78.
  5. Juan Carlos Escanciano & Lin Zhu, 2013. "Set inferences and sensitivity analysis in semiparametric conditionally identified models," CeMMAP working papers CWP55/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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