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Learning What to Learn: Experimental Design when Combinin...
[Submitted on 27 Oct 2025 (v1), last revised 17 Jul 2026 (this v · 2025-10-27 · via math.ST updates on arXiv.org

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Abstract:Experiments deliver credible treatment-effect estimates but, because they are costly, are often restricted to specific sites, small populations, or particular mechanisms. A common practice across several fields is therefore to combine experimental estimates with reduced-form or structural external (observational) evidence to answer broader policy questions, such as those involving general equilibrium effects or external validity. We develop a unified framework for the design of experiments when combined with external evidence, i.e., choosing which experiment(s) to run and how to allocate sample size under arbitrary budget constraints. Because observational evidence may suffer bias unknown ex-ante, we evaluate designs using a minimax proportional-regret criterion that compares any candidate design to an oracle with knowledge about the observational study bias that jointly chooses the design and estimator. This yields a transparent bias-variance trade-off that does not require the researcher to specify a bias bound and relies only on information already needed for conventional power calculations. We illustrate the framework for studying the general equilibrium effects of cash transfer programs.

Submission history

From: Davide Viviano Mr. [view email]
[v1] Mon, 27 Oct 2025 15:37:23 UTC (269 KB)
[v2] Mon, 10 Nov 2025 14:06:25 UTC (218 KB)
[v3] Sun, 28 Dec 2025 18:55:21 UTC (191 KB)
[v4] Fri, 17 Jul 2026 13:46:14 UTC (158 KB)