arXiv 29 Jun 2026 · Econometrics
arXiv:2606.29833 · PDF · DOI · OpenAlex · Extracted main text
This paper develops misspecification-robust sensitivity and informativeness diagnostics for GMM estimators, evaluated at pseudo-true values. The sensitivity matrix nests that of Andrews, Gentzkow, and Shapiro (2017) under correct specification. The informativeness $Δ$ measures the share of an estimator's asymptotic variance explained by sampling variation in the moments, a notion of structural efficiency that equals one under correct specification and can fall below one under misspecification, even when the Hansen $J$-test does not reject. We derive influence-function representations for one-step, two-step, iterated, and continuously updating GMM. We show that in minimum-distance estimation, estimating the optimal weight matrix adds estimator variance that the moments do not explain, lowering informativeness, while simpler weight matrices largely avoid it. The choice of weight matrix therefore involves a trade-off between classical efficiency and informativeness. In applications to the automobile demand model of Berry, Levinsohn, and Pakes (1995), the consumption insurance model of Blundell, Pistaferri, and Preston (2008), and the income-and-democracy regressions of Acemoglu, Johnson, Robinson, and Yared (2008), misspecification reorders sensitivity rankings, simpler weights preserve the informativeness that the optimal weight loses, and $Δ$ detects structural-efficiency losses that the $J$-test does not.
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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 | Andrews, Isaiah and Gentzkow, Matthew and Shapiro, Jesse M (2017) Measuring the sensitivity of parameter estimates to estimation moments | 1.000 | 5 | 4 | 100% |
| 2 | Blundell, Richard and Pistaferri, Luigi and Preston, Ian (2008) Consumption inequality and partial insurance | 1.000 | 5 | 4 | 100% |
| 3 | Hall, Alastair R and Inoue, Atsushi (2003) The large sample behaviour of the generalized method of moments estimator in misspecified models | 1.000 | 5 | 3 | 100% |
| 4 | Acemoglu, Daron and Johnson, Simon and Robinson, James A and Yared,… (2008) Income and democracy | 0.928 | 4 | 3 | 100% |
| 5 | Altonji, Joseph G. and Segal, Lewis M (1996) Small-sample bias in GMM estimation of covariance structures | 0.928 | 4 | 3 | 100% |
| 6 | Hansen, Bruce E and Lee, Seojeong (2021) Inference for iterated GMM under misspecification self | 0.920 | 9 | 4 | 78% |
| 7 | Berry, Steven and Levinsohn, James and Pakes, Ariel (1995) Automobile prices in market equilibrium | 0.843 | 3 | 3 | 100% |
| 8 | Andrews, Isaiah and Gentzkow, Matthew and Shapiro, Jesse M (2020) On the informativeness of descriptive statistics for structural estimates | 0.737 | 3 | 2 | 100% |
| 9 | Hwang, Jungbin and Kang, Byunghoon and Lee, Seojeong (2022) A doubly corrected robust variance estimator for linear GMM self | 0.737 | 3 | 2 | 100% |
| 10 | Schennach, Susanne M (2007) Point estimation with exponentially tilted empirical likelihood | 0.644 | 3 | 2 | 67% |
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