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Characterizations of identified sets delivered by structural econometric models

Listed author(s):
  • Andrew Chesher

    ()

    (Institute for Fiscal Studies and University College London)

  • Adam Rosen

    ()

    (Institute for Fiscal Studies and Duke University)

This paper develops characterizations of identifi?ed sets of structures and structural features for complete and incomplete models involving continuous or discrete variables. Multiple values of unobserved variables can be associated with particular combinations of observed variables. This can arise when there are multiple sources of heterogeneity, censored or discrete endogenous variables, or inequality restrictions on functions of observed and unobserved variables. The models generalize the class of incomplete instrumental variable (IV) models in which unobserved variables are single-valued functions of observed variables. Thus the models are referred to as Generalized IV (GIV) models, but there are important cases in which instrumental variable restrictions play no signifi?cant role. Building on a de?finition of observational equivalence for incomplete models the development uses results from random set theory which guarantee that the characterizations deliver sharp bounds, thereby dispensing with the need for case-by-case proofs of sharpness. The use of random sets de?ned on the space of unobserved variables allows identi?cation analysis under mean and quantile independence restrictions on the distributions of unobserved variables conditional on exogenous variables as well as under a full independence restriction. The results are used to develop sharp bounds on the distribution of valuations in an incomplete model of English auctions, improving on the pointwise bounds available till now. Application of many of the results of the paper requires no familiarity with random set theory.

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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 CWP44/16.

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Date of creation: 26 Aug 2016
Handle: RePEc:ifs:cemmap:44/16
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  1. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
  2. Han Hong & Elie Tamer, 2003. "Inference in Censored Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 71(3), pages 905-932, 05.
  3. Armstrong, Timothy B., 2014. "Weighted KS statistics for inference on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 181(2), pages 92-116.
  4. Bowden, Roger J, 1973. "The Theory of Parametric Identification," Econometrica, Econometric Society, vol. 41(6), pages 1069-1074, November.
  5. repec:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
  6. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, 03.
  7. Marc Henry & Romuald Méango & Maurice Queyranne, 2015. "Combinatorial approach to inference in partially identified incomplete structural models," Quantitative Economics, Econometric Society, vol. 6(2), pages 499-529, July.
  8. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
  9. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, 07.
  10. Alfred Galichon & Marc Henry, 2011. "Set Identification in Models with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 78(4), pages 1264-1298.
  11. repec:spo:wpecon:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
  12. Andres Aradillas-Lopez & Adam Rosen, 2013. "Inference in ordered response games with complete information," CeMMAP working papers CWP33/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  13. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, 01.
  14. 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.
  15. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2011. "Sharp Identification Regions in Models With Convex Moment Predictions," Econometrica, Econometric Society, vol. 79(6), pages 1785-1821, November.
  16. Khan, Shakeeb & Ponomareva, Maria & Tamer, Elie, 2011. "Sharpness in randomly censored linear models," Economics Letters, Elsevier, vol. 113(1), pages 23-25, October.
  17. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, 03.
  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.
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