On uniform asymptotic risk of averaging GMM estimators

Cheng, Xu; Liao, Zhipeng; Shi, Ruoyao

doi:10.3982/qe711

Cited by 26 publications

(28 citation statements)

References 61 publications

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“…Very recently,Zhang and Yu (2018) andLam and Souza (2019) proposed combining spatial weight matrices in recognition of possible misspecification of the weight matrix andCheng et al (2019) suggested combining a conservative GMM estimator based on valid moment conditions and an aggressive GMM estimator based on both valid and possibly misspecified moment conditions.…”

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confidence: 99%

Indirect Inference Estimation of Spatial Autoregressions

2020

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The ordinary least squares (OLS) estimator for spatial autoregressions may be consistent as pointed out by Lee (2002), provided that each spatial unit is influenced aggregately by a significant portion of the total units. This paper presents a unified asymptotic distribution result of the properly recentered OLS estimator and proposes a new estimator that is based on the indirect inference (II) procedure. The resulting estimator can always be used regardless of the degree of aggregate influence on each spatial unit from other units and is consistent and asymptotically normal. The new estimator does not rely on distributional assumptions and is robust to unknown heteroscedasticity. Its good finite-sample performance, in comparison with existing estimators that are also robust to heteroscedasticity, is demonstrated by a Monte Carlo study.

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confidence: 99%

Indirect Inference Estimation of Spatial Autoregressions

2020

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“…We consider this a small and acceptable price to pay to avoid the risk of bias and higher RMSE that occurs under uncorrected MLM in the presence of correlated random effects. Accordingly, we suggest these unbiased approaches rather than any approach that seeks to mix estimators (e.g., Cheng, Liao, and Shi 2019) or to choose between FE (or bcMLM) and uncorrected MLM based on some criterion. For example, we do not advocate for choosing uncorrected MLM when the number of observations per group is above some threshold: one cannot know how many observations will be enough for the bias (and RMSE) to become acceptably small, and any potential efficiency or accuracy gain of MLM relative to FE is diminishing in group size anyway.…”

Section: Discussionmentioning

confidence: 99%

Understanding, Choosing, and Unifying Multilevel and Fixed Effect Approaches

Hazlett¹,

Wainstein²

2020

Polit. Anal.

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When working with grouped data, investigators may choose between “fixed effects” models (FE) with specialized (e.g., cluster-robust) standard errors, or “multilevel models” (MLMs) employing “random effects.” We review the claims given in published works regarding this choice, then clarify how these approaches work and compare by showing that: (i) random effects employed in MLMs are simply “regularized” fixed effects; (ii) unmodified MLMs are consequently susceptible to bias—but there is a longstanding remedy; and (iii) the “default” MLM standard errors rely on narrow assumptions that can lead to undercoverage in many settings. Our review of over 100 papers using MLM in political science, education, and sociology show that these “known” concerns have been widely ignored in practice. We describe how to debias MLM’s coefficient estimates, and provide an option to more flexibly estimate their standard errors. Most illuminating, once MLMs are adjusted in these two ways the point estimate and standard error for the target coefficient are exactly equal to those of the analogous FE model with cluster-robust standard errors. For investigators working with observational data and who are interested only in inference on the target coefficient, either approach is equally appropriate and preferable to uncorrected MLM.

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“…More generally, our approach is related to recent work on characterizing various policy relevant treatment effects as weighted averages of the marginal treatment effect, for example, Heckman and Vytlacil (2005), Heckman, Urzua, and Vytlacil (2006), Brinch, Mogstad, and Wiswall (2017), Mogstad, Santos, and Torgovitsky (2018), Andrews (2019), Evdokimov and Kolesár (2018), and Słoczyński (2018). Since these examples cannot be handled by a local misspecification framework (e.g., Cheng, Liao, and Shi (2019)), our approach is complementary to local misspecification.…”

Section: Introductionmentioning

confidence: 99%

“…This is a particularly difficult yet important topic. The methods of Cheng, Liao, and Shi (2019) may be useful in this regard.…”

Section: Introductionmentioning

confidence: 99%

Inference for Iterated GMM Under Misspecification

Hansen

Lee²

2021

ECTA

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This paper develops inference methods for the iterated overidentified Generalized Method of Moments (GMM) estimator. We provide conditions for the existence of the iterated estimator and an asymptotic distribution theory, which allows for mild misspecification. Moment misspecification causes bias in conventional GMM variance estimators, which can lead to severely oversized hypothesis tests. We show how to consistently estimate the correct asymptotic variance matrix. Our simulation results show that our methods are properly sized under both correct specification and mild to moderate misspecification. We illustrate the method with an application to the model of Acemoglu, Johnson, Robinson, and Yared (2008).

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On uniform asymptotic risk of averaging GMM estimators

Cited by 26 publications

References 61 publications

Indirect Inference Estimation of Spatial Autoregressions

Indirect Inference Estimation of Spatial Autoregressions

Understanding, Choosing, and Unifying Multilevel and Fixed Effect Approaches

Inference for Iterated GMM Under Misspecification

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