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Partial identification using random set theory

  • Arie Beresteanu

    (Institute for Fiscal Studies and Duke)

  • Ilya Molchanov
  • Francesca Molinari

    ()

    (Institute for Fiscal Studies and Cornell University)

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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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. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-23, May.
  2. Beresteanu, Arie & Molinari, Francesca, 2006. "Asymptotic Properties for a Class of Partially Identified Models," Working Papers 06-04, Duke University, Department of Economics.
  3. 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.
  4. 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.
  5. 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.
  6. Christian Bontemps & Thierry Magnac & Eric Maurin, 2011. "Set identified linear models," CeMMAP working papers CWP13/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. 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.
  8. 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.
  9. Jorg Stoye, 2009. "More on Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 77(4), pages 1299-1315, 07.
  10. Arie Beresteanu, 2009. "Sharp Identification Regions in Models with Convex Predictions: Games, Individual Choice, and Incomplete Data," Working Papers 428, University of Pittsburgh, Department of Economics, revised Sep 2010.
  11. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
  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. 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.
  14. 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.
  15. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, 09.
  16. repec:att:wimass:9604 is not listed on IDEAS
  17. 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.
  18. Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
  19. 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.
  20. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
  21. 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.
  22. 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.
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