Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators

Lee, Seojeong

doi:10.1016/j.jeconom.2013.05.008

Cited by 23 publications

(22 citation statements)

References 72 publications

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“…Thus, the conventional variance estimators are no longer consistent under misspecification. Lee (2014) proposes variance estimators for the one-step and two-step GMM under misspecification. Hansen and Lee (2019) propose a similar robust variance estimator for the iterated GMM.…”

Section: Robustness To Misspecificationmentioning

confidence: 99%

“…Moreover, it can be easily implemented to obtain more accurate t tests and confidence intervals (smaller errors in the size and the coverage) by bootstrapping the t statistic studentized by the doubly corrected variance estimator. Lee (2014) shows that this bootstrap procedure is robust to misspecification and does not require an ad hoc correction in the bootstrap sample called recentering.The finite sample correction of the proposed formula and the Windmeijer formula works for linear models. For nonlinear models, the order of the remainder term is the same as the correction terms, so that the corrections do not necessarily provide improvements under correct specification.Even for nonlinear models, however, the doubly corrected variance estimator is still consistent for the asymptotic variance of the GMM estimator under misspecification.…”

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A Doubly Corrected Robust Variance Estimator for Linear GMM

2019

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We propose a new finite sample corrected variance estimator for the linear generalized method of moments (GMM) including the one-step, two-step, and iterated estimators. Our formula additionally corrects for the over-identification bias in variance estimation on top of the commonly used finite sample correction of Windmeijer (2005) which corrects for the bias from estimating the efficient weight matrix, so is doubly corrected. Formal stochastic expansions are derived to show the proposed double correction estimates the variance of some higher-order terms in the expansion. In addition, the proposed double correction provides robustness to misspecification of the moment condition. In contrast, the conventional variance estimator and the Windmeijer correction are inconsistent under misspecification. That is, the proposed double correction formula provides a convenient way to obtain improved inference under correct specification and robustness against misspecification at the same time.1 two-step linear GMM. Specifically, his formula corrects for the bias arising from using the efficient weight matrix being evaluated at an estimate, rather than the true value. The correction formula (the Windmeijer correction, hereinafter) has been routinely used in practice. 1 However, the Windmeijer correction does not take into account for the over-identification bias, which is another important source of bias in the GMM standard error. The over-identification bias arises from the fact that the over-identified sample moment condition is nonzero while it converges in probability to zero under correct specification.We propose a new finite sample correction which takes into account for the over-identification bias for the variance of the linear one-step, two-step, and iterated GMM estimators. For one-step GMM such as the two-stage least squares (2SLS) estimators, the proposed finite sample correction is new as the Windmeijer correction does not cover the one-step GMM. For two-step and iterated GMM, the proposed correction improves upon the Windmeijer correction by additionally correcting for the over-identification bias. Thus, we doubly correct the finite sample bias of the linear GMM variance estimator. We provide an additional formal justification of the proposed double correction by deriving the stochastic expansions of the GMM estimators under local misspecification where the moment condition is modeled as a local drifting sequence around zero. The result shows that the double correction estimates the (co)variance of some higher-order terms which increase with the overidentification bias. Rothenberg (1984) provides a general treatment of the stochastic expansion and Newey and Smith (2004) derive the stochastic expansion of GMM and the generalized empirical likelihood (GEL) estimators under correct specification. The order of our double correction equals the order of the sample moment condition. Under correct specification or local misspecification, these terms are O p (n −1/2 ) so that the double correction is a finite-sample corr...

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confidence: 99%

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A Doubly Corrected Robust Variance Estimator for Linear GMM

2019

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“…The J-test is weak in that the null hypothesis of no impact of the alternative model tends to be rejected too often. Hence too often both models are accepted as playing a role (Lee, 2011). The Vuong test is problematic in that it implicitly assumes that none of the competing models are the true model, and that all equally misspecified, such that the distance criterion, has an average value of zero under the null hypothesis (Choi and Kiefer, 2006).…”

Section: Price Levels Testsmentioning

confidence: 99%

“…The Vuong test is problematic in that it implicitly assumes that none of the competing models are the true model, and that all equally misspecified, such that the distance criterion, has an average value of zero under the null hypothesis (Choi and Kiefer, 2006). If this is not the case, the test statistic is non-standard and may not be consistently estimated (Lee, 2011). We choose to present results based on the J-test rather than the Vuong test for several reasons.…”

Section: Price Levels Testsmentioning

confidence: 99%

Disclosure-Derived Financial Statement Adjustments in Equity Valuation

Batta¹,

Ganguly²,

Rosett

2014

Rev. Pac. Basin Finan. Mark. Pol.

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In this paper, we assess the equity value relevance of disclosure-derived financial statement adjustments. In price levels and returns tests, we find that reported financial numbers have relatively superior explanatory power over adjusted Rev. Pac. Basin Finan. Mark. Pol. 2014.17. Downloaded from www.worldscientific.com by UNIVERSITY OF CALIFORNIA @ SAN DIEGO on 04/13/15. For personal use only.numbers. Only when adjustments are included along with reported numbers in pricing regressions do adjustments retain significant explanatory power. Our results suggest that for summary valuation inputs like operating profitability, assets, and liabilities, analysts should not substitute adjusted numbers for reported numbers; rather, the information in a subset of adjustments should be used along with reported numbers to produce more accurate valuations.

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Bootstrap inference for misspecified moment condition models

Giurcanu

Presnell

2017

Ann Inst Stat Math

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Asymptotic refinements of a misspecification-robust bootstrap for generalized method of moments estimators

Cited by 23 publications

References 72 publications

A Doubly Corrected Robust Variance Estimator for Linear GMM

A Doubly Corrected Robust Variance Estimator for Linear GMM

Disclosure-Derived Financial Statement Adjustments in Equity Valuation

Bootstrap inference for misspecified moment condition models

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