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VALIDITY OF SUBSAMPLING AND “PLUG-INASYMPTOTIC” INFERENCE FOR PARAMETERS DEFINED BYMOMENT INEQUALITIES

Published online by Cambridge University Press:  01 June 2009

Donald W.K. Andrews  and
Patrik Guggenberger
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Abstract

This paper considers inference for parameters definedby moment inequalities and equalities. Theparameters need not be identified. For a specifiedclass of test statistics, this paper establishes theuniform asymptotic validity of subsampling,m out of nbootstrap, and “plug-in asymptotic” tests andconfidence intervals for such parameters.Establishing uniform asymptotic validity is crucialin moment inequality problems because the pointwiseasymptotic distributions of the test statistics ofinterest have discontinuities as functions of thetrue distribution that generates theobservations.

The size results are quite general because they holdwithout specifying the particular form of the momentconditions—only 2 + δ momentsfinite are required. The results allow forindependent and identically distributed (i.i.d.) anddependent observations and for preliminaryconsistent estimation of identified parameters.

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Type
Research Article
Information
Econometric Theory , Volume 25 , Issue 3 , June 2009 , pp. 669 - 709
Copyright
Copyright © Cambridge University Press 2009

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Footnotes

Andrews gratefully acknowledges the researchsupport of the National Science Foundation viagrant SES-0417911. Guggenberger gratefullyacknowledges research support from a facultyresearch grant from UCLA in 2005 and from theNational Science Foundation via grant SES-0748922.For helpful comments, we thank two referees, theco-editor Richard Smith, Ivan Canay, VictorChernozukhov, Azeem Shaikh, and the participantsat various seminars and conferences at which thepaper was presented. Some of the results in thispaper first appeared in D.W.K. Andrews and P.Guggenberger (2005), “The Limit of Finite-SampleSize and a Problem with Subsampling,” CowlesFoundation Discussion paper 1606, YaleUniversity.

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