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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).

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File URL: http://mpra.ub.uni-muenchen.de/32634/
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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 32634.

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Date of creation: Aug 2011
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Handle: RePEc:pra:mprapa:32634

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Keywords: Monotone instrumental variables; Bootstrap; Bias correction;

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  1. Russell Davidson & James G. MacKinnon, 2006. "Improving the Reliability of Bootstrap Tests with the Fast Double Bootstrap," Working Papers, Queen's University, Department of Economics 1044, Queen's University, Department of Economics.
  2. Charles F. Manski & John V. Pepper, 1998. "Monotone Instrumental Variables: With an Application to the Returns to Schooling," Virginia Economics Online Papers 308, University of Virginia, Department of Economics.
  3. Kreider, Brent & Pepper, John V., 2003. "Disability and Employment: Reevaluating the Evidence in Light of Reporting Errors," Staff General Research Papers 10229, Iowa State University, Department of Economics.
  4. Russell Davidson & James MacKinnon, 2002. "Fast Double Bootstrap Tests Of Nonnested Linear Regression Models," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 21(4), pages 419-429.
  5. Victor Chernozhukov & Sokbae 'Simon' Lee & Adam Rosen, 2012. "Intersection bounds: estimation and inference," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP33/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Charles F. Manski & John V. Pepper, 2009. "More on monotone instrumental variables," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 12(s1), pages S200-S216, 01.
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