More on confidence intervals for partially identified parameters
This paper extends Imbens and Manski's (2004) analysis of confidence intervals for interval identified parameters. For their final result, Imbens and Manski implicitly assume superefficient estimation of a nuisance parameter. This appears to have gone unnoticed before, and it limits the result's applicability. I re-analyze the problem both with assumptions that merely weaken the superefficiency condition and with assumptions that remove it altogether. Imbens and Manski's confidence region is found to be valid under weaker assumptions than theirs, yet superefficiency is required. I also provide a different confidence interval that is valid under superefficiency but can be adapted to the general case, in which case it embeds a specification test for nonemptiness of the identified set. A methodological contribution is to notice that the difficulty of inference comes from a boundary problem regarding a nuisance parameter, clarifying the connection to other work on partial identification.
|Date of creation:||Apr 2008|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (+44) 020 7291 4800
Fax: (+44) 020 7323 4780
Web page: http://cemmap.ifs.org.uk
More information through EDIRC
|Order Information:|| Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE|
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Donald W. K. Andrews & Gustavo Soares, 2010.
"Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection,"
Econometric Society, vol. 78(1), pages 119-157, 01.
- 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.
- Leeb, Hannes & Potscher, Benedikt M., 2008.
"Sparse estimators and the oracle property, or the return of Hodges' estimator,"
Journal of Econometrics,
Elsevier, vol. 142(1), pages 201-211, January.
- Hannes Leeb & Benedikt M. Poetscher, 2005. "Sparse Estimators and the Oracle Property, or the Return of Hodges' Estimator," Cowles Foundation Discussion Papers 1500, Cowles Foundation for Research in Economics, Yale University, revised Apr 2007.
- 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.
- Fan, Yanqin & Park, Sang Soo, 2010. "Confidence sets for some partially identified parameters," MPRA Paper 37149, University Library of Munich, Germany.
- Andrews, Donald W.K. & Guggenberger, Patrik, 2009.
"Validity Of Subsampling And “Plug-In Asymptotic” Inference For Parameters Defined By Moment Inequalities,"
Cambridge University Press, vol. 25(03), pages 669-709, June.
- 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.
- Guido Imbens & Charles F. Manski, 2003.
"Confidence intervals for partially identified parameters,"
CeMMAP working papers
CWP09/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Guido W. Imbens & Charles F. Manski, 2004. "Confidence Intervals for Partially Identified Parameters," Econometrica, Econometric Society, vol. 72(6), pages 1845-1857, November.
- 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.
- Philip Haile, 2000.
"Inference with an Incomplete Model of English Auctions,"
Econometric Society World Congress 2000 Contributed Papers
1546, Econometric Society.
- Philip A. Haile & Elie Tamer, 2003. "Inference with an Incomplete Model of English Auctions," Journal of Political Economy, University of Chicago Press, vol. 111(1), pages 1-51, February.
- Haile,P.A. & Tamer,E.T., 2000. "Inference with an incomplete model of English auctions," Working papers 18, Wisconsin Madison - Social Systems.
- Bo E. Honoré & Elie Tamer, 2006. "Bounds on Parameters in Panel Dynamic Discrete Choice Models," Econometrica, Econometric Society, vol. 74(3), pages 611-629, 05.
When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:11/08. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Stephanie Seavers)
If references are entirely missing, you can add them using this form.