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Sampling Variation, Monotone Instrumental Variables and the Bootstrap Bias Correction

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  • Qian, Hang

Abstract

This paper discusses the finite sample bias of analogue bounds under the monotone instrumental variables assumption. By analyzing the bias function, we first propose a conservative estimator which is biased downwards (upwards) when the analogue estimator is biased upwards (downwards). Using the bias function, we then show the mechanism of the parametric bootstrap correction procedure, which can reduce but not eliminate the bias, and there is also a possibility of overcorrection.This motivates us to propose a simultaneous multi-level bootstrap procedure so as to further correct the remaining bias. The procedure is justified under the assumption that the bias function can be well approximated by a polynomial. Our multi-level bootstrap algorithm is feasible and does not suffer from the curse of dimensionality. Monte Carlo evidence supports the usefulness of this approach and we apply it to the disability misreporting problem studied by Kreider and Pepper(2007).

Suggested Citation

  • Qian, Hang, 2011. "Sampling Variation, Monotone Instrumental Variables and the Bootstrap Bias Correction," MPRA Paper 32634, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:32634
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    References listed on IDEAS

    as
    1. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    2. Andrew M. Ross, 2010. "Computing Bounds on the Expected Maximum of Correlated Normal Variables," Methodology and Computing in Applied Probability, Springer, vol. 12(1), pages 111-138, March.
    3. Kreider, Brent & Pepper, John V., 2007. "Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 432-441, June.
    4. Charles E. Clark, 1961. "The Greatest of a Finite Set of Random Variables," Operations Research, INFORMS, vol. 9(2), pages 145-162, April.
    5. Davidson, Russell & MacKinnon, James G., 2007. "Improving the reliability of bootstrap tests with the fast double bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3259-3281, April.
    6. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    7. Russell Davidson & James MacKinnon, 2002. "Fast Double Bootstrap Tests Of Nonnested Linear Regression Models," Econometric Reviews, Taylor & Francis Journals, vol. 21(4), pages 419-429.
    8. Charles F. Manski & John V. Pepper, 2009. "More on monotone instrumental variables," Econometrics Journal, Royal Economic Society, vol. 12(s1), pages 200-216, January.
    9. Davidson, Russell & MacKinnon, James G., 2002. "Bootstrap J tests of nonnested linear regression models," Journal of Econometrics, Elsevier, vol. 109(1), pages 167-193, July.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Monotone instrumental variables; Bootstrap; Bias correction;
    All these keywords.

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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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