Isaiah Andrews, Jiafeng Chen, Otavio Tecchio
arXiv 18 Aug 2025 · Econometrics
arXiv:2508.13076 · PDF · Extracted main text
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | White, Halbert (1982) Maximum likelihood estimation of misspecified models | 0.928 | 4 | 3 | 100% |
| 2 | Chen, Xiaohong and Santos, Andres (2018) Overidentification in regular models | 0.843 | 3 | 3 | 100% |
| 3 | Hall, Alastair R and Inoue, Atsushi (2003) The large sample behaviour of the generalized method of moments estimator in misspecified models | 0.811 | 4 | 2 | 100% |
| 4 | Lars Peter Hansen (1982) Large Sample Properties of Generalized Method of Moments Estimators | 0.811 | 4 | 2 | 100% |
| 5 | Koopmans, Tjalling C and Reiersol, Olav (1950) The identification of structural characteristics | 0.693 | 6 | 1 | 100% |
| 6 | Armstrong, Timothy B and Kolesár, Michal (2021) Sensitivity analysis using approximate moment condition models | 0.644 | 3 | 2 | 67% |
| 7 | Abebe, Girum and Caria, A. Stefano and Ortiz-Ospina, Esteban (2021) The Selection of Talent: Experimental and Structural Evidence from Ethiopia | 0.644 | 2 | 2 | 100% |
| 8 | Imbens, Guido W (1997) One-step estimators for over-identified generalized method of moments models | 0.644 | 2 | 2 | 100% |
| 9 | Altonji, Joseph G and Segal, Lewis M (1996) Small-sample bias in GMM estimation of covariance structures | 0.585 | 3 | 1 | 100% |
| 10 | Andrews, Isaiah and Shapiro, Jesse M (2024) Communicating Scientific Uncertainty via Approximate Posteriors self | 0.511 | 2 | 1 | 100% |
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