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:||23 Apr 2008|
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- 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 & 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.
- 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.
- 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.
- 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.
- 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 & 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.
- 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.
- 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.
- 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.
- Fan, Yanqin & Park, Sang Soo, 2010. "Confidence sets for some partially identified parameters," MPRA Paper 37149, University Library of Munich, Germany.
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