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Optimal Dynamic Treatment Regimes and Partial Welfare Ordering

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Document pages: 40 pages

Abstract: Dynamic treatment regimes are treatment allocations tailored to heterogeneousindividuals. The optimal dynamic treatment regime is a regime that maximizescounterfactual welfare. We introduce a framework in which we can partiallylearn the optimal dynamic regime from observational data, relaxing thesequential randomization assumption commonly employed in the literature butinstead using (binary) instrumental variables. We propose the notion of sharppartial ordering of counterfactual welfares with respect to dynamic regimes andestablish mapping from data to partial ordering via a set of linear programs.We then characterize the identified set of the optimal regime as the set ofmaximal elements associated with the partial ordering. One main contribution ofthis paper is that we develop simple analytical conditions to establish theordering, which bypass solving a large number of large-scale linear programs,and thus facilitate estimation and inference. This paper s analytical frameworkhas broader applicability beyond the current context, e.g., in establishingsigns of various treatment effects and rankings of policies across differentcounterfactual scenarios.

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