Learning What to Learn: Experimental Design when Combining Experimental with Observational Evidence

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 robust regret criterion that compares any candidate design to an oracle with knowledge about the observational study bias bound 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 general equilibrium effects of cash transfer programs.