Treatment choice, mean square regret and partial identification

Toru Kitagawa (), Sokbae (Simon) Lee and Chen Qiu ()
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Toru Kitagawa: Brown University
Chen Qiu: Cornell University

The Japanese Economic Review, 2023, vol. 74, issue 4, No 7, 573-602

Abstract: Abstract We consider a decision maker who faces a binary treatment choice when their welfare is only partially identified from data. We contribute to the literature by anchoring our finite-sample analysis on mean square regret, a decision criterion advocated by Kitagawa et al. in (2022) "Treatment Choice with Nonlinear Regret" . We find that optimal rules are always fractional, irrespective of the width of the identified set and precision of its estimate. The optimal treatment fraction is a simple logistic transformation of the commonly used t-statistic multiplied by a factor calculated by a simple constrained optimization. This treatment fraction gets closer to 0.5 as the width of the identified set becomes wider, implying the decision maker becomes more cautious against the adversarial Nature.

Keywords: Statistical decision theory; Treatment assignment rules; Mean square regret; Partial identification (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s42973-023-00144-3

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