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Robustness of Bootstrap in Instrumental Variable Regression

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Abstract

This paper studies robustness of bootstrap inference methods for instrumental variable regression models. In particular, we compare the uniform weight and implied probability bootstrap approximations for parameter hypothesis test statistics by applying the breakdown point theory, which focuses on behaviors of the bootstrap quantiles when outliers take arbitrarily large values. The implied probabilities are derived from an information theoretic projection from the empirical distribution to a set of distributions satisfying orthogonality conditions for instruments. Our breakdown point analysis considers separately the effects of outliers in dependent variables, endogenous regressors, and instruments, and clarifies the situations where the implied probability bootstrap can be more robust than the uniform weight bootstrap against outliers. Effects of tail trimming introduced by Hill and Renault (2010) are also analyzed. Several simulation studies illustrate our theoretical findings.

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File URL: http://cowles.econ.yale.edu/P/cd/d17b/d1796.pdf
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Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1796.

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Length: 24 pages
Date of creation: Apr 2011
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Handle: RePEc:cwl:cwldpp:1796

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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Bootstrap; Breakdown point; Instrumental variable regression;

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  1. Hill, Jonathan B. & Aguilar, Mike, 2013. "Moment condition tests for heavy tailed time series," Journal of Econometrics, Elsevier, vol. 172(2), pages 255-274.
  2. Imbens, G.W. & Johnson, P. & Spady, R.H., 1995. "Information Theoretic Approaches to Inference in Movement Condition Models," Economics Papers 99, Economics Group, Nuffield College, University of Oxford.
  3. Hélène Bonnal & Éric Renault, 2004. "On the Efficient Use of the Informational Content of Estimating Equations: Implied Probabilities and Euclidean Empirical Likelihood," CIRANO Working Papers 2004s-18, CIRANO.
  4. Romer, David, 1993. "Openness and Inflation: Theory and Evidence," The Quarterly Journal of Economics, MIT Press, vol. 108(4), pages 869-903, November.
  5. Russell Davidson & James G. MacKinnon, 2007. "Wild Bootstrap Tests For Iv Regression," Departmental Working Papers 2007-14, McGill University, Department of Economics.
  6. Hall, Peter & Horowitz, Joel L, 1996. "Bootstrap Critical Values for Tests Based on Generalized-Method-of-Moments Estimators," Econometrica, Econometric Society, vol. 64(4), pages 891-916, July.
  7. Hadi, Ali S. & Luceno, Alberto, 1997. "Maximum trimmed likelihood estimators: a unified approach, examples, and algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 25(3), pages 251-272, August.
  8. Rodolphe Desbordes & Vincenzo Verardi, 2012. "A robust instrumental-variables estimator," Stata Journal, StataCorp LP, vol. 12(2), pages 169–181, June.
  9. Whitney Newey & Richard Smith, 2003. "Higher order properties of GMM and generalised empirical likelihood estimators," CeMMAP working papers CWP04/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. Guido W Imbens, Phillip Johnson & Richard H Spady, . "Information theoretic approaches to inference in moment condition model," Economics Papers W12., Economics Group, Nuffield College, University of Oxford.
  11. Allen, Jason & Gregory, Allan W. & Shimotsu, Katsumi, 2011. "Empirical likelihood block bootstrapping," Journal of Econometrics, Elsevier, vol. 161(2), pages 110-121, April.
  12. Gagliardini, Patrick & Trojani, Fabio & Urga, Giovanni, 2005. "Robust GMM tests for structural breaks," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 139-182.
  13. Lorenzo Camponovo & Taisuke Otsu, 2011. "Breakdown Point Theory for Implied Probability Bootstrap," Cowles Foundation Discussion Papers 1793, Cowles Foundation for Research in Economics, Yale University.
  14. Yuichi Kitamura & Taisuke Otsu & Kirill Evdokimov, 2013. "Robustness, Infinitesimal Neighborhoods, and Moment Restrictions," Econometrica, Econometric Society, vol. 81(3), pages 1185-1201, 05.
  15. Jonathan B. Hill, 2013. "Least tail-trimmed squares for infinite variance autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(2), pages 168-186, 03.
  16. Krasker, William S & Welsch, Roy E, 1985. "Resistant Estimation for Simultaneous-Equations Models Using Weighted Instrumental Variables," Econometrica, Econometric Society, vol. 53(6), pages 1475-88, November.
  17. Ronchetti, Elvezio & Trojani, Fabio, 2001. "Robust inference with GMM estimators," Journal of Econometrics, Elsevier, vol. 101(1), pages 37-69, March.
  18. Brown, Bryan W & Newey, Whitney K, 2002. "Generalized Method of Moments, Efficient Bootstrapping, and Improved Inference," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 507-17, October.
  19. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
  20. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
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