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Validity of Subsampling and "Plug-in Asymptotic" Inference for Parameters Defined by Moment Inequalities

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Abstract

This paper considers inference for parameters defined by moment inequalities and equalities. The parameters need not be identified. For a specified class of test statistics, this paper establishes the uniform asymptotic validity of subsampling, m out of n bootstrap, and "plug-in asymptotic" tests and confidence intervals for such parameters. Establishing uniform asymptotic validity is crucial in moment inequality problems because the test statistics of interest have discontinuities in their pointwise asymptotic distributions. The size results are quite general because they hold without specifying the particular form of the moment conditions -- only 2+delta moments finite are required. The results allow for i.i.d. and dependent observations and for preliminary consistent estimation of identified parameters.

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File URL: http://cowles.econ.yale.edu/P/cd/d16a/d1620.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1620.

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Length: 43 pages
Date of creation: Jul 2007
Date of revision:
Handle: RePEc:cwl:cwldpp:1620

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

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Keywords: Asymptotic size; Confidence set; Exact size; m out of n bootstrap; Subsampling; Moment inequalities;

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References

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  1. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2003. "Consistent testing for stochastic dominance under general sampling schemes," LSE Research Online Documents on Economics 2208, London School of Economics and Political Science, LSE Library.
  2. Smith, Richard J, 1997. "Alternative Semi-parametric Likelihood Approaches to Generalised Method of Moments Estimation," Economic Journal, Royal Economic Society, vol. 107(441), pages 503-19, March.
  3. Arie Beresteanu & Francesca Molinari, 2006. "Asymptotic properties for a class of partially identified models," CeMMAP working papers CWP10/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Adam Rosen, 2006. "Confidence sets for partially identified parameters that satisfy a finite number of moment inequalities," CeMMAP working papers CWP25/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  5. Bajari, Patrick & Benkard, C. Lanier & Levin, Jonathan, 2007. "Estimating Dynamic Models of Imperfect Competition," Research Papers 1852r1, Stanford University, Graduate School of Business.
  6. Leeb, Hannes & P tscher, Benedikt M., 2005. "Model Selection And Inference: Facts And Fiction," Econometric Theory, Cambridge University Press, vol. 21(01), pages 21-59, February.
  7. Patrik Buggenberger & Richard Smith, 2003. "Generalized empirical likelihood estimators and tests under partial, weak and strong identification," CeMMAP working papers CWP08/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  8. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  9. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
  10. Whitney K. Newey & Richard J. Smith, 2004. "Higher Order Properties of Gmm and Generalized Empirical Likelihood Estimators," Econometrica, Econometric Society, vol. 72(1), pages 219-255, 01.
  11. Kabaila, Paul, 1995. "The Effect of Model Selection on Confidence Regions and Prediction Regions," Econometric Theory, Cambridge University Press, vol. 11(03), pages 537-549, June.
  12. Canay, Ivan A., 2010. "EL inference for partially identified models: Large deviations optimality and bootstrap validity," Journal of Econometrics, Elsevier, vol. 156(2), pages 408-425, June.
  13. E. Tamer & V. Chernozhukov & H. Hong, 2004. "Parameter Set Inference in a Class of Econometric Models," Econometric Society 2004 North American Winter Meetings 382, Econometric Society.
  14. Joseph P. Romano & Azeem M. Shaikh, 2010. "Inference for the Identified Set in Partially Identified Econometric Models," Econometrica, Econometric Society, vol. 78(1), pages 169-211, 01.
  15. Donald W. K. Andrews, 2000. "Inconsistency of the Bootstrap when a Parameter Is on the Boundary of the Parameter Space," Econometrica, Econometric Society, vol. 68(2), pages 399-406, March.
  16. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
  17. repec:cup:etheor:v:11:y:1995:i:3:p:537-49 is not listed on IDEAS
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