Coping with Inductive Risk When Theories are Underdetermined: Decision Making with Partial Identification

Referee: [Abstract and decision-criteria section] Abstract and decision-criteria section: The central claim that the combination produces coherent approaches without relocating underdetermination requires explicit discussion of how to select among decision criteria when they disagree on the same identified set; different criteria (maximin vs. minimax regret) can yield conflicting policy rankings, and absent a further grounding that itself avoids underdetermination, the inductive-risk problem is shifted rather than eliminated.

Authors: We agree that explicit discussion of criterion selection is warranted when maximin and minimax regret (or other rules) produce conflicting rankings on the same identified set. However, this does not relocate the original inductive-risk problem. The underdetermination addressed by partial identification concerns the empirical content of the model (what outcomes are consistent with data plus maintained assumptions). In contrast, the choice among decision criteria is a normative matter of how the policy maker wishes to handle ambiguity, which can be grounded in explicit preferences or robustness considerations without reintroducing empirical underdetermination. In the revised version we will add a dedicated paragraph in the decision-criteria section clarifying this distinction and outlining practical approaches (e.g., reporting rankings under multiple criteria or adopting a meta-criterion such as maximin regret over the set of admissible rules). This addition will make the coherence claim more precise without altering the manuscript's central thesis. revision: yes

Referee: [Partial-identification applications] Partial-identification applications: The manuscript should supply at least one fully worked numerical example deriving explicit bounds on an outcome distribution from data plus assumptions and then applying a specific decision criterion to produce a policy ranking, to demonstrate that the claimed coherence is operational rather than conceptual only.

Authors: We accept that a concrete numerical illustration would better demonstrate operational coherence. Although the manuscript is primarily conceptual to facilitate dialogue between philosophy of science and econometrics, we will add a short worked example in a new subsection of the applications section. The example will derive sharp bounds on a binary outcome distribution from a simple data-generating process plus a monotonicity assumption, then apply the maximin criterion to rank two policy alternatives. This will show explicitly how the identified set feeds into a decision rule and produces a determinate policy recommendation without point identification. The addition will be kept concise to maintain the paper's focus while addressing the referee's request. revision: yes