Abstract

Unmeasured confounding is a threat to causal inference and gives rise to bi-ased estimates. In this paper, we consider the problem of individualized decision making under partial identification. Firstly, we argue that when faced with unmeasured con-founding, one should pursue individualized decision making using partial identification in a comprehensive manner. We establish a formal link between individualized decision making under partial identification and classical decision theory by considering a lower bound perspective of value/utility function. Secondly, building on this unified framework, we provide a novel minimax solution (i.e., a rule that minimizes the maximum regret for so-called opportunists) for individualized decision making/policy assignment. Lastly, we provide an interesting paradox drawing on novel connections between two challenging domains, i.e., individualized decision making and unmeasured confounding. Although motivated by instrumental variable bounds, we emphasize that the general framework proposed in this paper would in principle apply for a rich set of bounds that might be available under partial identification.

Just Accepted - Preview

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