arXiv 7 Apr 2026 · Econometrics
arXiv:2604.05327 · PDF · DOI · OpenAlex · Extracted main text
This article introduces a framework for evaluating statistical decisions under both prior ambiguity and likelihood misspecification. We begin with an ambiguity set - a frequentist model that pairs a possibly misspecified likelihood with every possible prior - and uniformly expand it by a Kullback-Leibler radius to accommodate likelihood misspecification. We show that optimal decisions under this framework are equivalent to minimax decisions with an exponentially tilted loss function. Misspecification manifests as an exponential tilting of the loss, while ambiguity corresponds to a search for the least favorable prior. This separation between ambiguity and misspecification enables local asymptotic analysis under global misspecification, achieved by localizing the priors alone. Remarkably, for both estimation and treatment assignment, we show that optimal decisions coincide with those under correct specification, regardless of the degree of misspecification. These results extend to semi-parametric models. As a practical consequence, our findings imply that practitioners should prefer maximum likelihood over the simulated method of moments, and efficient GMM estimators - such as two-step GMM - over diagonally weighted alternatives.
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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 | Cerreia-Vioglio, Simone and Hansen, Lars Peter and Maccheroni, Fabio… (2026) Making Decisions under Model Misspecification | 1.000 | 10 | 4 | 100% |
| 2 | Andrews, Isaiah and Chen, Jiafeng and Tecchio, Otavio (2025) The Purpose of an Estimator is What it Does: Misspecification, Estimands, and Over-Identification | 1.000 | 5 | 4 | 100% |
| 3 | Van der Vaart, Aad W (2000) Asymptotic Statistics | 0.920 | 9 | 4 | 78% |
| 4 | Hansen, Lars Peter and Sargent, Thomas J (2011) Robustness | 0.811 | 4 | 2 | 100% |
| 5 | Ibragimov, IA and Hasminskii, RZ (1981) Statistical Estimation: Asymptotic Theory | 0.737 | 5 | 3 | 40% |
| 6 | Andrews, Isaiah and Gentzkow, Matthew and Shapiro, Jesse M (2020) On the Informativeness of Descriptive Statistics for Structural Estimates | 0.737 | 3 | 2 | 100% |
| 7 | Bonhomme, Stéphane and Weidner, Martin (2022) Minimizing Sensitivity to Model Misspecification | 0.737 | 3 | 2 | 100% |
| 8 | Wald, Abraham (1950) Statistical Decision Functions | 0.737 | 3 | 2 | 100% |
| 9 | Le Cam, Lucien M (1986) Asymptotic Methods in Statistical Decision Theory | 0.644 | 2 | 2 | 100% |
| 10 | Maccheroni, Fabio and Marinacci, Massimo and Rustichini, Aldo (2006) Ambiguity Aversion, Robustness, and the Variational Representation of Preferences | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 33 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Misspecification-Averse Estimation | 0.843 | 3 | 3 |
| 2 | Integrating Diagnostic Checks into Estimation | 0.644 | 2 | 2 |
| 3 | Robust Inference for Weighted Estimands | 0.405 | 1 | 1 |