Optimal Decision Rules When Payoffs are Partially Identified

This paper derives asymptotically optimal statistical decision rules for discrete choice problems when the payoffs associated with some choices are only partially identified. The research question is: how should a decision maker who can bound but not point-identify a payoff-relevant parameter θ use data to make optimal policy choices?

The framework separates two parameter types. The reduced-form parameter µ is point-identified and can be estimated from data. The structural parameter θ — such as the average treatment effect (ATE) in a target population — is set-identified, meaning only that θ ∈ Θ0(µ) can be established, where the identified set is indexed by µ. The decision maker confronts both ambiguity (arising from partial identification of θ given µ) and statistical uncertainty (µ must be estimated).

Timothy Christensen | Macro Paper Warehouse

Optimal Decision Rules When Payoffs are Partially Identified