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Treatment Choice, Mean Square Regret and Partial Identification

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  • Toru Kitagawa
  • Sokbae Lee
  • Chen Qiu

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, Lee, and Qiu (2022). 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.

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  • Toru Kitagawa & Sokbae Lee & Chen Qiu, 2023. "Treatment Choice, Mean Square Regret and Partial Identification," Papers 2310.06242, arXiv.org.
    • Handle: RePEc:arx:papers:2310.06242
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    1. Eric Mbakop & Max Tabord‐Meehan, 2021. "Model Selection for Treatment Choice: Penalized Welfare Maximization," Econometrica, Econometric Society, vol. 89(2), pages 825-848, March.
    2. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
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