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Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure

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Abstract

This paper is concerned with tests and confidence intervals for parameters that are not necessarily identified and are defined by moment inequalities. In the literature, different test statistics, critical value methods, and implementation methods (i.e., the asymptotic distribution versus the bootstrap) have been proposed. In this paper, we compare these methods. We provide a recommended test statistic, moment selection critical value method, and implementation method. We provide data-dependent procedures for choosing the key moment selection tuning parameter kappa and a size-correction factor eta.

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File URL: http://cowles.econ.yale.edu/P/cd/d16b/d1676-ra.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 1676R.

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Length: 109 pages
Date of creation: Sep 2008
Date of revision: Aug 2011
Publication status: Published in Econometrics (November 2012), 80(6): 2805-2826
Handle: RePEc:cwl:cwldpp:1676r

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

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Keywords: Asymptotic size; Asymptotic power; Bootstrap; Confidence set; Generalized moment selection; Moment inequalities; Partial identification; Refined moment selection; Test; Unidentified parameter;

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  1. Federico A. Bugni, 2010. "Bootstrap Inference in Partially Identified Models Defined by Moment Inequalities: Coverage of the Identified Set," Econometrica, Econometric Society, vol. 78(2), pages 735-753, 03.
  2. 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.
  3. Hyungsik Roger Moon & Frank Schorfheide, 2006. "Boosting Your Instruments: Estimation with Overidentifying Inequality Moment Conditions," IEPR Working Papers 06.56, Institute of Economic Policy Research (IEPR).
  4. Donald W.K. Andrews, 1997. "Consistent Moment Selection Procedures for Generalized Method of Moments Estimation," Cowles Foundation Discussion Papers 1146R, Cowles Foundation for Research in Economics, Yale University.
  5. Matyas,Laszlo (ed.), 1999. "Generalized Method of Moments Estimation," Cambridge Books, Cambridge University Press, number 9780521669672, Fall.
  6. Arie Beresteanu & Ilya Molchanov & Francesca Molinari, 2008. "Sharp identification regions in games," CeMMAP working papers CWP15/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Elie Tamer & Federico Ciliberto, 2004. "Market Structure and Multiple Equilibria in Airline Markets," 2004 Meeting Papers 52, Society for Economic Dynamics.
  8. Jörg Stoye, 2008. "More on confidence intervals for partially identified parameters," CeMMAP working papers CWP11/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  9. Andrews, Donald W.K. & Guggenberger, Patrik, 2009. "Validity Of Subsampling And “Plug-In Asymptotic” Inference For Parameters Defined By Moment Inequalities," Econometric Theory, Cambridge University Press, vol. 25(03), pages 669-709, June.
  10. 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.
  11. Christian Bontemps & Thierry Magnac & Eric Maurin, 2012. "Set Identified Linear Models," Econometrica, Econometric Society, vol. 80(3), pages 1129-1155, 05.
  12. 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.
  13. 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.
  14. Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
  15. Donald W.K. Andrews & Gustavo Soares, 2007. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Cowles Foundation Discussion Papers 1631, Cowles Foundation for Research in Economics, Yale University.
  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. 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.
  18. Donald W.K. Andrews & Panle Jia, 2008. "Inference for Parameters Defined by Moment Inequalities: A Recommended Moment Selection Procedure," Cowles Foundation Discussion Papers 1676, Cowles Foundation for Research in Economics, Yale University.
  19. Galichon, Alfred & Henry, Marc, 2009. "A test of non-identifying restrictions and confidence regions for partially identified parameters," Journal of Econometrics, Elsevier, vol. 152(2), pages 186-196, October.
  20. Fan, Yanqin & Park, Sang Soo, 2010. "Confidence sets for some partially identified parameters," MPRA Paper 37149, University Library of Munich, Germany.
  21. Matyas,Laszlo (ed.), 1999. "Generalized Method of Moments Estimation," Cambridge Books, Cambridge University Press, number 9780521660136, Fall.
  22. Victor Chernozhukov & Han Hong & Elie Tamer, 2007. "Estimation and Confidence Regions for Parameter Sets in Econometric Models," Econometrica, Econometric Society, vol. 75(5), pages 1243-1284, 09.
  23. Guggenberger, Patrik & Hahn, Jinyong & Kim, Kyooil, 2008. "Specification testing under moment inequalities," Economics Letters, Elsevier, vol. 99(2), pages 375-378, May.
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