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Repairing Locally Misspecified GMM: An Empirical Bayes Approach

Patrick Kline

arXiv 25 Aug 2026 · Econometrics

arXiv:2608.23925 · PDF · Extracted main text

Abstract

Econometric models offer parsimonious but inexact approximations to data-generating processes. This paper studies the generalized method of moments (GMM) when exchangeable specification errors of order $n^{-1/2}$ contaminate the moment conditions. I develop estimators for the mean and variance of these specification errors, establishing their consistency in an asymptotic framework where the number of overidentifying restrictions grows with the sample size. These hyperparameter estimates are used to develop a feasible bias-corrected estimator of target parameters. I also propose an empirical Bayes estimator that weakly improves precision by subtracting a best linear predictor of the first-order estimation error from the bias-corrected estimator. Using a combinatorial central limit theorem, I establish asymptotic normality of both estimators and provide variance estimators that enable misspecification-aware frequentist inference. Simulation exercises indicate the procedures can meaningfully improve on standard two-stage least squares estimation when exclusion violations are present. Revisiting the influential study of Angrist and Krueger (1991), I consider an instrument set where exchangeable excludability violations are plausible. Repairing the two-stage least squares estimates of the returns to schooling moves them in the direction of ordinary least squares and reduces sensitivity to the specification of controls.

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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1Angrist, Joshua D, Krueger, Alan B (1991) Does compulsory school attendance affect schooling and earnings?1.000113100%
2Andrews, Isaiah, Gentzkow, Matthew, Shapiro, Jesse M (2017) Measuring the sensitivity of parameter estimates to estimation moments0.92843100%
3Buckles, Kasey S, Hungerman, Daniel M (2013) Season of birth and later outcomes: Old questions, new answers0.87462100%
4Kolesr, Michal, Chetty, Raj, Friedman, John, Glaeser, Edward, Imbens… (2015) Identification and inference with many invalid instruments0.7547443%
5Brown, Lawrence D (1990) An ancillarity paradox which appears in multiple linear regression0.73732100%
6Rosenzweig, Mark R, Wolpin, Kenneth I (2000) Natural "natural experiments" in economics0.73732100%
7Altonji, Joseph G, Segal, Lewis M (1996) Small-sample bias in GMM estimation of covariance structures0.64422100%
8Angrist, Joshua D, Pischke, Jrn-Steffen (2009) Mostly harmless econometrics: An empiricist's companion0.64422100%
9Armstrong, Timothy B (2025) Misspecification in Econometrics: A Selective Review0.64422100%
10Chernozhukov, Victor, Hansen, Christian B, Kong, Lingwei, Wang, Wein… (2025) Plausible GMM: a quasi-bayesian approach0.64422100%

Showing the top 10 of 36 scored citations.