More on confidence intervals for partially identified parameters

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IZA Seminar

Place: Schaumburg-Lippe-Str. 9, 53113 Bonn

Date: 12.01.2010, 12:15 - 13:30


Presentation by 

Joerg Stoye (New York University)


This paper extends Imbens and Manskiís (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 resultís applicability. I re-analyze the problem both with assumptions that merely weaken the superefficiency condition and with assumptions that remove it altogether. Imbens and Manskiís 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.

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