More on Confidence Intervals for Partially Identified Parameters


  • Jörg Stoye

    1. Dept. of Economics, New York University, 19 W. 4th Street, New York, NY 10012, U.S.A.;
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    • I am indebted to Adam Rosen, whose insightful comments helped to much improve this paper. I also received helpful comments from an associate editor and three anonymous referees, Don Andrews, Xiaohong Chen, Aureo de Paula, Yanqin Fan, Guido Imbens, Nick Kiefer, Thierry Magnac, Chuck Manski, Francesca Molinari, Hyungsik Roger Moon, and Sang Soo Park, seminar audiences at Brown, Cologne, Cornell, Mannheim, NYU, Penn, Penn State, Vanderbilt, and Yale, and conference audiences in Bonn, Budapest, Durham (U.S.A.), London, Montréal, Munich, and Philadelphia. Financial support from a University Research Challenge Fund, New York University, is gratefully acknowledged. Of course, any and all errors are mine.


This paper extends Imbens and Manski's (2004) analysis of confidence intervals for interval identified parameters. The extension is motivated by the discovery that for their final result, Imbens and Manski implicitly assumed locally superefficient estimation of a nuisance parameter.

I reanalyze the problem both with assumptions that merely weaken this superefficiency condition and with assumptions that remove it altogether. Imbens and Manski's confidence region is valid under weaker assumptions than theirs, yet superefficiency is required. I also provide a confidence interval that is valid under superefficiency, but can be adapted to the general case. A methodological contribution is to observe that the difficulty of inference comes from a preestimation problem regarding a nuisance parameter, clarifying the connection to other work on partial identification.