Distortions of Asymptotic Confidence Size in Locally Misspecified Moment Inequality Models

Federico A. Bugni, Ivan A. Canay, Patrik Guggenberger

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

This paper studies the behavior, under local misspecification, of several confidence sets (CSs) commonly used in the literature on inference in moment (in)equality models. We propose the amount of asymptotic confidence size distortion as a criterion to choose among competing inference methods. This criterion is then applied to compare across test statistics and critical values employed in the construction of CSs. We find two important results under weak assumptions. First, we show that CSs based on subsampling and generalized moment selection (Andrews and Soares (2010)) suffer from the same degree of asymptotic confidence size distortion, despite the fact that asymptotically the latter can lead to CSs with strictly smaller expected volume under correct model specification. Second, we show that the asymptotic confidence size of CSs based on the quasi-likelihood ratio test statistic can be an arbitrary small fraction of the asymptotic confidence size of CSs based on the modified method of moments test statistic.

Original languageEnglish (US)
Pages (from-to)1741-1768
Number of pages28
JournalEconometrica
Volume80
Issue number4
DOIs
StatePublished - Jul 1 2012

Fingerprint

Confidence
Confidence set
Moment inequalities
Test statistic
Size distortion
Inference
Misspecification
Subsampling
Equality
Likelihood ratio test
Critical value
Method of moments
Model specification
Quasi-likelihood

All Science Journal Classification (ASJC) codes

  • Economics and Econometrics

Cite this

Bugni, Federico A. ; Canay, Ivan A. ; Guggenberger, Patrik. / Distortions of Asymptotic Confidence Size in Locally Misspecified Moment Inequality Models. In: Econometrica. 2012 ; Vol. 80, No. 4. pp. 1741-1768.
@article{e6bca10e37b44df7b168f168cd85bc98,
title = "Distortions of Asymptotic Confidence Size in Locally Misspecified Moment Inequality Models",
abstract = "This paper studies the behavior, under local misspecification, of several confidence sets (CSs) commonly used in the literature on inference in moment (in)equality models. We propose the amount of asymptotic confidence size distortion as a criterion to choose among competing inference methods. This criterion is then applied to compare across test statistics and critical values employed in the construction of CSs. We find two important results under weak assumptions. First, we show that CSs based on subsampling and generalized moment selection (Andrews and Soares (2010)) suffer from the same degree of asymptotic confidence size distortion, despite the fact that asymptotically the latter can lead to CSs with strictly smaller expected volume under correct model specification. Second, we show that the asymptotic confidence size of CSs based on the quasi-likelihood ratio test statistic can be an arbitrary small fraction of the asymptotic confidence size of CSs based on the modified method of moments test statistic.",
author = "Bugni, {Federico A.} and Canay, {Ivan A.} and Patrik Guggenberger",
year = "2012",
month = "7",
day = "1",
doi = "10.3982/ECTA9604",
language = "English (US)",
volume = "80",
pages = "1741--1768",
journal = "Econometrica",
issn = "0012-9682",
publisher = "Wiley-Blackwell",
number = "4",

}

Distortions of Asymptotic Confidence Size in Locally Misspecified Moment Inequality Models. / Bugni, Federico A.; Canay, Ivan A.; Guggenberger, Patrik.

In: Econometrica, Vol. 80, No. 4, 01.07.2012, p. 1741-1768.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Distortions of Asymptotic Confidence Size in Locally Misspecified Moment Inequality Models

AU - Bugni, Federico A.

AU - Canay, Ivan A.

AU - Guggenberger, Patrik

PY - 2012/7/1

Y1 - 2012/7/1

N2 - This paper studies the behavior, under local misspecification, of several confidence sets (CSs) commonly used in the literature on inference in moment (in)equality models. We propose the amount of asymptotic confidence size distortion as a criterion to choose among competing inference methods. This criterion is then applied to compare across test statistics and critical values employed in the construction of CSs. We find two important results under weak assumptions. First, we show that CSs based on subsampling and generalized moment selection (Andrews and Soares (2010)) suffer from the same degree of asymptotic confidence size distortion, despite the fact that asymptotically the latter can lead to CSs with strictly smaller expected volume under correct model specification. Second, we show that the asymptotic confidence size of CSs based on the quasi-likelihood ratio test statistic can be an arbitrary small fraction of the asymptotic confidence size of CSs based on the modified method of moments test statistic.

AB - This paper studies the behavior, under local misspecification, of several confidence sets (CSs) commonly used in the literature on inference in moment (in)equality models. We propose the amount of asymptotic confidence size distortion as a criterion to choose among competing inference methods. This criterion is then applied to compare across test statistics and critical values employed in the construction of CSs. We find two important results under weak assumptions. First, we show that CSs based on subsampling and generalized moment selection (Andrews and Soares (2010)) suffer from the same degree of asymptotic confidence size distortion, despite the fact that asymptotically the latter can lead to CSs with strictly smaller expected volume under correct model specification. Second, we show that the asymptotic confidence size of CSs based on the quasi-likelihood ratio test statistic can be an arbitrary small fraction of the asymptotic confidence size of CSs based on the modified method of moments test statistic.

UR - http://www.scopus.com/inward/record.url?scp=84862703689&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84862703689&partnerID=8YFLogxK

U2 - 10.3982/ECTA9604

DO - 10.3982/ECTA9604

M3 - Article

AN - SCOPUS:84862703689

VL - 80

SP - 1741

EP - 1768

JO - Econometrica

JF - Econometrica

SN - 0012-9682

IS - 4

ER -