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The purpose of an estimator is what it does: Misspecification, estimands, and over-identification

Isaiah Andrews, Jiafeng Chen, Otavio Tecchio

arXiv 18 Aug 2025 · Econometrics

arXiv:2508.13076 · PDF · Extracted main text

Abstract

In over-identified models, misspecification -- the norm rather than exception -- fundamentally changes what estimators estimate. Different estimators imply different estimands rather than different efficiency for the same target. A review of recent applications of generalized method of moments in the American Economic Review suggests widespread acceptance of this fact: There is little formal specification testing and widespread use of estimators that would be inefficient were the model correct, including the use of "hand-selected" moments and weighting matrices. Motivated by these observations, we review and synthesize recent results on estimation under model misspecification, providing guidelines for transparent and robust empirical research. We also provide a new theoretical result, showing that Hansen's J-statistic measures, asymptotically, the range of estimates achievable at a given standard error. Given the widespread use of inefficient estimators and the resulting researcher degrees of freedom, we thus particularly recommend the broader reporting of J-statistics.

Citation extraction

86
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112
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distinct cited
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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
1White, Halbert (1982) Maximum likelihood estimation of misspecified models0.92843100%
2Chen, Xiaohong and Santos, Andres (2018) Overidentification in regular models0.84333100%
3Hall, Alastair R and Inoue, Atsushi (2003) The large sample behaviour of the generalized method of moments estimator in misspecified models0.81142100%
4Lars Peter Hansen (1982) Large Sample Properties of Generalized Method of Moments Estimators0.81142100%
5Koopmans, Tjalling C and Reiersol, Olav (1950) The identification of structural characteristics0.69361100%
6Armstrong, Timothy B and Kolesár, Michal (2021) Sensitivity analysis using approximate moment condition models0.6443267%
7Abebe, Girum and Caria, A. Stefano and Ortiz-Ospina, Esteban (2021) The Selection of Talent: Experimental and Structural Evidence from Ethiopia0.64422100%
8Imbens, Guido W (1997) One-step estimators for over-identified generalized method of moments models0.64422100%
9Altonji, Joseph G and Segal, Lewis M (1996) Small-sample bias in GMM estimation of covariance structures0.58531100%
10Andrews, Isaiah and Shapiro, Jesse M (2024) Communicating Scientific Uncertainty via Approximate Posteriors self0.51121100%

Showing the top 10 of 86 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Representativeness and Efficiency in Overidentified IV1.00063
2You've Got to be Efficient: Ambiguity, Misspecification and Variational Preferences1.00054
3Misspecification-Averse Estimation0.84333
4A Misuse of Specification Tests0.73732
5Integrating Diagnostic Checks into Estimation0.64422
6Potential weights and implicit causal designs in linear regression0.40511
7Semiparametric Bayesian Inference for a Conditional Moment Equality Model0.40511
8On Local Overidentification and Efficiency Gains in Modern Causal Inference and Data Combination0.40511
9How Robust are Robustness Checks?0.40511
10True and Pseudo-True Parameters0.40511