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Set inference in latent variables models

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  • Marc Henry
  • Ismael Mourifié

Abstract

We propose a methodology for constructing valid confidence regions in incomplete models with latent variables satisfying moment equality restrictions. These include moment equality and inequality models with latent variables. The confidence regions are obtained by inverting tests based on the characterization of the identified set derived in Ekeland, Galichon, and Henry (2010). A valid boot- strap approximation of the distribution of the test statistic is derived under mild conditions and the confidence regions are shown to have correct asymptotic size.
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Suggested Citation

  • Marc Henry & Ismael Mourifié, 2013. "Set inference in latent variables models," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 93-105, February.
    • Handle: RePEc:wly:emjrnl:v:16:y:2013:i:1:p:s93-s105
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    References listed on IDEAS

    as
    1. 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.
    2. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    3. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    4. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    5. Jovanovic, Boyan, 1989. "Observable Implications of Models with Multiple Equilibria," Econometrica, Econometric Society, vol. 57(6), pages 1431-1437, November.
    6. Andrew Chesher, 2010. "Instrumental Variable Models for Discrete Outcomes," Econometrica, Econometric Society, vol. 78(2), pages 575-601, March.
    7. 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.
    8. Anthony Downs, 1957. "An Economic Theory of Political Action in a Democracy," Journal of Political Economy, University of Chicago Press, vol. 65(2), pages 135-135.
    9. 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.
    10. 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.
    11. 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, January.
    12. 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, March.
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