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Title:More on confidence intervals for partially identified parameters PDF Logo
Authors:Stoye, Jörg
Issue Date:2008
Series/Report no.:cemmap working paper CWP11/08
Abstract: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.
Subjects:bounds
identification regions
confidence intervals
uniform convergence
superefficiency
JEL:C10
C14
Persistent Identifier of the first edition:doi:10.1920/wp.cem.2008.1108
Document Type:Working Paper
Appears in Collections:cemmap working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies (IFS)

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