Inference in dynamic discrete choice problems under local misspecification

Bugni, Federico A.; Ura, Takuya

doi:10.3982/qe917

Cited by 12 publications

(12 citation statements)

References 26 publications

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“…Part (i) is weaker than the local regularity of the estimator δ that we assumed when analyzing the minimum-MSE estimator, see equation (14). In turn, related to but differently from the conditions we used for Theorem 1, part (ii) requires a form of local asymptotic normality of the estimator.…”

Section: A2 Proof Of Theoremmentioning

confidence: 99%

“…Yet, the efficient estimator fails to exist when the matrix denominator in ( 26) is singular. 14 Here the term ( n) −1 acts as a regularization of the functional differencing projection, which makes h MMSE well-defined irrespective of the nature of identification.…”

Section: And For Any Function H E[h(y )S π (Y )] Can Be Represented By the Function E[h(ymentioning

confidence: 99%

“…Our analysis of minimum-MSE estimation and sensitivity in the OLS/IV example is related to Hahn and Hausman (2005) and Angrist et al (2017). Our approach based on local misspecification has a number of precedents, such as Newey (1985), Conley et al (2012), Guggenberger (2012), Bugni et al (2012), Kitamura et al (2013), and Bugni and Ura (2018). Also related is Claeskens and Hjort's (2003) work on the focused information criterion.…”

Section: Introductionmentioning

confidence: 99%

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Minimizing Sensitivity to Model Misspecification

Bonhomme¹,

Weidner²

2020

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We propose a framework for estimation and inference when the model may be misspecified. We rely on a local asymptotic approach where the degree of misspecification is indexed by the sample size. We construct estimators whose mean squared error is minimax in a neighborhood of the reference model, based on simple one-step adjustments. In addition, we provide confidence intervals that contain the true parameter under local misspecification. To interpret the degree of misspecification, we map it to the local power of a specification test of the reference model. Our approach allows for systematic sensitivity analysis when the parameter of interest may be partially or irregularly identified. As illustrations, we study two binary choice models: a cross-sectional model where the error distribution is misspecified, and a dynamic panel data model where the number of time periods is small and the distribution of individual effects is misspecified.

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Section: A2 Proof Of Theoremmentioning

confidence: 99%

Section: And For Any Function H E[h(y )S π (Y )] Can Be Represented By the Function E[h(ymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Minimizing Sensitivity to Model Misspecification

Bonhomme¹,

Weidner²

2020

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“…Local misspecification has been used in a number of papers, which include, among others, Newey (1985), Berkowitz, Caner, and Fang (2012), Conley, Hansen, and Rossi (2012), Guggenberger (2012), and Bugni and Ura (2019), and has antecedents in the literature on robust statistics (see Huber and Ronchetti (2009), and references therein). Andrews, Gentzkow, and Shapiro (2017) considered this setting and note that asymptotic bias of a regular estimator can be calculated using influence function weights, which they call the sensitivity, and show how such calculations can be used for sensitivity analysis in applications (see also extensions of these ideas in Andrews, Gentzkow, and Shapiro 2020 and Mukhin 2018).…”

Section: Introductionmentioning

confidence: 99%

Sensitivity analysis using approximate moment condition models

Armstrong

Kolesár

2021

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We consider inference in models defined by approximate moment conditions. We show that near‐optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard error times a critical value that takes into account the potential bias from misspecification of the moment conditions. In order to optimize performance under potential misspecification, the weighting matrix for this GMM estimator takes into account this potential bias and, therefore, differs from the one that is optimal under correct specification. To formally show the near‐optimality of these CIs, we develop asymptotic efficiency bounds for inference in the locally misspecified GMM setting. These bounds may be of independent interest, due to their implications for the possibility of using moment selection procedures when conducting inference in moment condition models. We apply our methods in an empirical application to automobile demand, and show that adjusting the weighting matrix can shrink the CIs by a factor of 3 or more.

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“…Local misspecification has been used in a number of papers, which include, among others, Newey (1985), Berkowitz et al (2012), Conley et al (2012), Guggenberger (2012), Kitamura et al (2013) and Bugni and Ura (2018). Andrews et al (2017) consider this setting and note that asymptotic bias of a regular estimator can be calculated using influence function weights, which they call the sensitivity, and show how such calculations can be used for sensitivity analysis in applications (see also extensions of these ideas in Andrews et al 2018 andMukhin 2018).…”

Section: Introductionmentioning

confidence: 99%

Sensitivity Analysis using Approximate Moment Condition Models

Armstrong¹,

Kolesár

2018

SSRN Journal

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We consider inference in models defined by approximate moment conditions. We show that near-optimal confidence intervals (CIs) can be formed by taking a generalized method of moments (GMM) estimator, and adding and subtracting the standard error times a critical value that takes into account the potential bias from misspecification of the moment conditions. In order to optimize performance under potential misspecification, the weighting matrix for this GMM estimator takes into account this potential bias, and therefore differs from the one that is optimal under correct specification. To formally show the near-optimality of these CIs, we develop asymptotic efficiency bounds for inference in the locally misspecified GMM setting. These bounds may be of independent interest, due to their implications for the possibility of using moment selection procedures when conducting inference in moment condition models.We apply our methods in an empirical application to automobile demand, and show that adjusting the weighting matrix can shrink the CIs by a factor of 3 or more. * We thank Isaiah Andrews, Gary Chamberlain, Tim Christensen, Mikkel Plagborg-Møller, Jesse Shapiro, Martin Weidner and participants at several conferences and seminars for helpful comments and suggestions, and Soonwoo Kwon for research assistance. All remaining errors are our own.

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Inference in dynamic discrete choice problems under local misspecification

Cited by 12 publications

References 26 publications

Minimizing Sensitivity to Model Misspecification

Minimizing Sensitivity to Model Misspecification

Sensitivity analysis using approximate moment condition models

Sensitivity Analysis using Approximate Moment Condition Models

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