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Applications of subsampling, hybrid, and size-correction methods

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  • Andrews, Donald W.K.
  • Guggenberger, Patrik

Abstract

This paper analyzes the properties of subsampling, hybrid subsampling, and size-correction methods in two non-regular models. The latter two procedures are introduced in Andrews and Guggenberger (2009a). The models are non-regular in the sense that the test statistics of interest exhibit a discontinuity in their limit distribution as a function of a parameter in the model. The first model is a linear instrumental variables (IV) model with possibly weak IVs estimated using two-stage least squares (2SLS). In this case, the discontinuity occurs when the concentration parameter is zero. The second model is a linear regression model in which the parameter of interest may be near a boundary. In this case, the discontinuity occurs when the parameter is on the boundary. The paper shows that in the IV model one-sided and equal-tailed two-sided subsampling tests and confidence intervals (CIs) based on the 2SLS t statistic do not have correct asymptotic size. This holds for both fully- and partially-studentized t statistics. But, subsampling procedures based on the partially-studentized t statistic can be size-corrected. On the other hand, symmetric two-sided subsampling tests and CIs are shown to have (essentially) correct asymptotic size when based on a partially-studentized t statistic. Furthermore, all types of hybrid subsampling tests and CIs are shown to have correct asymptotic size in this model. The above results are consistent with "impossibility" results of Dufour (1997) because subsampling and hybrid subsampling CIs are shown to have infinite length with positive probability. Subsampling CIs for a parameter that may be near a lower boundary are shown to have incorrect asymptotic size for upper one-sided and equal-tailed and symmetric two-sided CIs. Again, size-correction is possible. In this model as well, all types of hybrid subsampling CIs are found to have correct asymptotic size.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 158 (2010)
Issue (Month): 2 (October)
Pages: 285-305

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Handle: RePEc:eee:econom:v:158:y:2010:i:2:p:285-305

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Web page: http://www.elsevier.com/locate/jeconom

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Keywords: Asymptotic size Finite-sample size Hybrid test Instrumental variable Over-rejection Parameter near boundary Size correction Subsampling confidence interval Subsampling test Weak instrument;

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References

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  1. Moreira, Marcelo J. & Porter, Jack R. & Suarez, Gustavo A., 2009. "Bootstrap validity for the score test when instruments may be weak," Journal of Econometrics, Elsevier, vol. 149(1), pages 52-64, April.
  2. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, 07.
  3. Patrik Guggenberger & Richard Smith, 2005. "Generalized empirical likelihood tests in time series models with potential identification failure," CeMMAP working papers CWP01/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
  5. Frank Kleibergen, 2002. "Pivotal Statistics for Testing Structural Parameters in Instrumental Variables Regression," Econometrica, Econometric Society, vol. 70(5), pages 1781-1803, September.
  6. Frank Kleibergen, 2001. "Testing Parameters in GMM without Assuming that they are identified," Tinbergen Institute Discussion Papers 01-067/4, Tinbergen Institute.
  7. Mathias D. Cattaneo & Richard K. Crump & Michael Jansson, 2007. "Optimal Inference for Instrumental Variables Regression with non-Gaussian Errors," CREATES Research Papers 2007-11, School of Economics and Management, University of Aarhus.
  8. Guggenberger, Patrik & Smith, Richard J., 2005. "Generalized Empirical Likelihood Estimators And Tests Under Partial, Weak, And Strong Identification," Econometric Theory, Cambridge University Press, vol. 21(04), pages 667-709, August.
  9. Donald W.K. Andrews & Gustavo Soares, 2006. "Rank Tests for Instrumental Variables Regression with Weak Instruments," Cowles Foundation Discussion Papers 1564, Cowles Foundation for Research in Economics, Yale University.
  10. Donald W.K. Andrews & Patrik Guggenberger, 2007. "Validity of Subsampling and "Plug-in Asymptotic" Inference for Parameters Defined by Moment Inequalities," Cowles Foundation Discussion Papers 1620, Cowles Foundation for Research in Economics, Yale University.
  11. Donald W. K. Andrews & Marcelo J. Moreira & James H. Stock, 2006. "Optimal Two-Sided Invariant Similar Tests for Instrumental Variables Regression," Econometrica, Econometric Society, vol. 74(3), pages 715-752, 05.
  12. Douglas Staiger & James H. Stock, 1997. "Instrumental Variables Regression with Weak Instruments," Econometrica, Econometric Society, vol. 65(3), pages 557-586, May.
  13. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
  14. Andrews, Donald W.K. & Moreira, Marcelo J. & Stock, James H., 2007. "Performance of conditional Wald tests in IV regression with weak instruments," Journal of Econometrics, Elsevier, vol. 139(1), pages 116-132, July.
  15. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Incorrect asymptotic size of subsampling procedures based on post-consistent model selection estimators," Journal of Econometrics, Elsevier, vol. 152(1), pages 19-27, September.
  16. Otsu, Taisuke, 2006. "Generalized Empirical Likelihood Inference For Nonlinear And Time Series Models Under Weak Identification," Econometric Theory, Cambridge University Press, vol. 22(03), pages 513-527, June.
  17. Andrews, Donald W.K. & Moreira, Marcelo J. & Stock, James H., 2008. "Efficient two-sided nonsimilar invariant tests in IV regression with weak instruments," Journal of Econometrics, Elsevier, vol. 146(2), pages 241-254, October.
  18. Donald W. K. Andrews, 1999. "Estimation When a Parameter Is on a Boundary," Econometrica, Econometric Society, vol. 67(6), pages 1341-1384, November.
  19. Donald W. K. Andrews & Patrik Guggenberger, 2009. "Hybrid and Size-Corrected Subsampling Methods," Econometrica, Econometric Society, vol. 77(3), pages 721-762, 05.
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Cited by:
  1. Elliott, Graham & Müller, Ulrich K., 2014. "Pre and post break parameter inference," Journal of Econometrics, Elsevier, vol. 180(2), pages 141-157.
  2. Lorenzo Camponovo & Olivier Scaillet & Fabio Trojani, 2006. "Robust Subsampling," Swiss Finance Institute Research Paper Series 06-33, Swiss Finance Institute.
  3. Guggenberger, Patrik & Ramalho, Joaquim J.S. & Smith, Richard J., 2012. "GEL statistics under weak identification," Journal of Econometrics, Elsevier, vol. 170(2), pages 331-349.
  4. Adam McCloskey, 2012. "Bonferroni-Based Size-Correction for Nonstandard Testing Problems," Working Papers 2012-16, Brown University, Department of Economics.

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