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Dilation bootstrap

Author

Listed:
  • Galichon, Alfred
  • Henry, Marc

Abstract

We propose a methodology for combining several sources of model and data incompleteness and partial identification, which we call Composition Theorem. We apply this methodology to the construction of confidence regions with partially identified models of general form. The region is obtained by inverting a test of internal consistency of the econometric structure. We develop a dilation bootstrap methodology to deal with sampling uncertainty without reference to the hypothesized economic structure. It requires bootstrapping the quantile process for univariate data and a novel generalization of the latter to higher dimensions. Once the dilation is chosen to control the confidence level, the unknown true distribution of the observed data can be replaced by the known empirical distribution and confidence regions can then be obtained as in Galichon and Henry (2011) and Beresteanu et al. (2011).

Suggested Citation

  • Galichon, Alfred & Henry, Marc, 2013. "Dilation bootstrap," Journal of Econometrics, Elsevier, vol. 177(1), pages 109-115.
  • Handle: RePEc:eee:econom:v:177:y:2013:i:1:p:109-115
    DOI: 10.1016/j.jeconom.2013.07.001
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    References listed on IDEAS

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    1. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
    2. Xiaohong Chen & Han Hong & Elie Tamer, 2005. "Measurement Error Models with Auxiliary Data," Review of Economic Studies, Oxford University Press, vol. 72(2), pages 343-366.
    3. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Oxford University Press, vol. 68(2), pages 235-260.
    4. Thierry Magnac & Eric Maurin, 2008. "Partial Identification in Monotone Binary Models: Discrete Regressors and Interval Data," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 835-864.
    5. 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.
    6. 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.
    7. Henry, Marc & Onatski, Alexei, 2012. "Set coverage and robust policy," Economics Letters, Elsevier, vol. 115(2), pages 256-257.
    8. Richard Blundell & Martin Browning & Ian Crawford, 2008. "Best Nonparametric Bounds on Demand Responses," Econometrica, Econometric Society, vol. 76(6), pages 1227-1262, November.
    9. Jovanovic, Boyan, 1989. "Observable Implications of Models with Multiple Equilibria," Econometrica, Econometric Society, vol. 57(6), pages 1431-1437, November.
    10. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
    11. Manski, Charles F, 1990. "Nonparametric Bounds on Treatment Effects," American Economic Review, American Economic Association, vol. 80(2), pages 319-323, May.
    12. repec:spo:wpmain:info:hdl:2441/5rkqqmvrn4tl22s9mc4ao8ocg is not listed on IDEAS
    13. Azeem M. Shaikh & Edward J. Vytlacil, 2011. "Partial Identification in Triangular Systems of Equations With Binary Dependent Variables," Econometrica, Econometric Society, vol. 79(3), pages 949-955, May.
    14. 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, September.
    15. 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.
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    Citations

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    Cited by:

    1. Larry G. Epstein & Hiroaki Kaido & Kyoungwon Seo, 2016. "Robust Confidence Regions for Incomplete Models," Econometrica, Econometric Society, vol. 84, pages 1799-1838, September.
    2. Ivar Ekeland & Alfred Galichon & Marc Henry, 2010. "Optimal transportation and the falsifiability of incompletely specified economic models," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 42(2), pages 355-374, February.

    More about this item

    Keywords

    Partial identification; Dilation bootstrap; Quantile process; Optimal matching;

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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