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2022

Optimal Decision Rules when Payoffs are Partially Identified

Christensen, Timothy, Moon, Hyungsik Roger, Schorfheide, Frank

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We derive asymptotically optimal statistical decision rules for discrete choice problems when payoffs depend on a partially-identified parameter $\theta$ and the decision maker can use a point-identified parameter $\mu$ to deduce restrictions on $\theta$.

Examples include treatment choice under partial identification and pricing with rich unobserved heterogeneity.
Our notion of optimality combines a minimax approach to handle the ambiguity from partial identification of $\theta$ given $\mu$ with an average risk minimization approach for $\mu$.
We show how to implement optimal decision rules using the bootstrap and (quasi-)Bayesian methods in both parametric and semiparametric settings.

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Kitamura, Y., and
Original
1902
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1956
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Heckman, J. J., and
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