arXiv 25 Jan 2026 · Econometrics
arXiv:2601.17648 · PDF · DOI · OpenAlex · Extracted main text
We are delighted to respond to the excellent surveys by Cattaneo et al. (2026) and Hirano (2026). Our discussion will attempt two things: first, we show how statistical decision theory can be applied to situations with partial identification; second, we connect the surveys' themes by applying these insights to an imagined policy experiment in one of Cattaneo et al.'s (2025) applications. To do so, we lay out a stylized scenario of statistical decision making under partial identification and, drawing on our own and others' earlier work, provide a complete solution for that scenario. We then apply these results to a hypothetical reduction (modelled on actual policies) in eligibility for educational subsidies. We will see that something of interest can be said, but also that bringing the theory to the application involves some leaps of faith and leaves some questions open. This leads to the final section, where we discuss what we see as the main open challenges in statistical decision theory under partial identification.
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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 | Cattaneo, Matias D. and Titiunik, Roc/'io and Yu, Ruiqi (2025) Causal Treatment Effect Aggregation in Boundary Discontinuity Designs | 0.874 | 13 | 2 | 100% |
| 2 | Kohei Yata (2021) Optimal Decision Rules Under Partial Identification | 0.874 | 6 | 2 | 100% |
| 3 | Montiel Olea, José Luis and Qiu, Chen and Stoye, Jörg (2026) Decision Theory for Treatment Choice Problems with Partial Identification self | 0.874 | 5 | 2 | 100% |
| 4 | Aradillas Fernández, Andrés and Blanchet, José and Montiel Olea, Jos… (2025) $ $-Minimax Solutions of Statistical Decision Problems self | 0.811 | 4 | 2 | 100% |
| 5 | Hirano, Keisuke (2026) Wald's Statistical Decision Theory for Policy Analysis and Adaptive Experiments | 0.737 | 3 | 2 | 100% |
| 6 | Stoye, Jörg (2012) Minimax regret treatment choice with covariates or with limited validity of experiments self | 0.737 | 3 | 2 | 100% |
| 7 | Londoño-Vélez, Juliana and Rodríguez, Catherine and Sánchez, Fabio (2020) Upstream and Downstream Impacts of College Merit-Based Financial Aid for Low-Income Students: Ser Pilo Paga in Colombia | 0.693 | 9 | 1 | 100% |
| 8 | Guggenberger, Patrik and Huang, Jiaqi (2025) On the numerical approximation of minimax regret rules via fictitious play | 0.644 | 4 | 1 | 100% |
| 9 | Charles F. Manski (2004) Statistical treatment rules for heterogeneous populations | 0.644 | 2 | 2 | 100% |
| 10 | Hirano, Keisuke and Porter, Jack R (2009) Asymptotics for statistical treatment rules | 0.511 | 2 | 1 | 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 | Boundary Discontinuity Designs: Theory and Practice | 0.405 | 1 | 1 |