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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- Andrews, Donald W.K. & Guggenberger, Patrik, 2009.
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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.
- 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.
- Philip Haile, 2000. "Inference with an Incomplete Model of English Auctions," Econometric Society World Congress 2000 Contributed Papers 1546, Econometric Society.
- Haile,P.A. & Tamer,E.T., 2000. "Inference with an incomplete model of English auctions," Working papers 18, Wisconsin Madison - Social Systems.
- Fan, Yanqin & Park, Sang Soo, 2010. "Confidence sets for some partially identified parameters," MPRA Paper 37149, University Library of Munich, Germany.
- Donald W. K. Andrews & Gustavo Soares, 2010. "Inference for Parameters Defined by Moment Inequalities Using Generalized Moment Selection," Econometrica, 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.
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