Dynamic treatment regimes are treatment allocations tailored to heterogeneous individuals. The optimal dynamic treatment regime is a regime that maximizes counterfactual welfare. This paper investigates the possibility of identification of optimal dynamic regimes when data are generated from sequential (natural) experiments. We propose a framework in which we can partially learn the optimal dynamic regime and ordering of welfares, relaxing sequential randomization assumptions commonly employed in the literature . We establish the sharp partial ordering of counterfactual welfares with respect to dynamic regimes by using a series of linear programs. A distinct feature of our approach is that, instead of solving a large number of large-scale linear programs, we provide simple analytical conditions for the ordering. The identified set of the optimal regime is then characterized as the set of maximal elements of the partial order. We also propose topological sorts of the partial order as a policy menu. We show how policymaking can be further guided by imposing assumptions such as monotonicity/uniformity of different stringency, agent's learning, Markovian structure, and stationarity .
Dynamic treatment regimes are treatment allocations tailored to heterogeneous individuals. The optimal dynamic treatment regime is a regime that maximizes counterfactual welfare. We introduce a framework in which we can partially learn the optimal dynamic regime from observational data, relaxing the sequential randomization assumption commonly employed in the literature but instead using (binary) instrumental variables. We propose the notion of sharp partial ordering of counterfactual welfares with respect to dynamic regimes and establish 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 of maximal elements associated with the partial ordering. One main contribution of this paper is that we develop simple analytical conditions to establish the ordering, which bypass solving a large number of large-scale linear programs, and thus facilitate estimation and inference. This paper's analytical framework has broader applicability beyond the current context, e.g., in establishing signs of various treatment effects and rankings of policies across different counterfactual scenarios .
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This paper investigates the possibility of identification of optimal dynamic regimes when data are generated from sequential (natural) experiments. We propose
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and ordering of welfares, relaxing sequential randomization assumptions
from observational data, relaxing the sequential randomization assumption
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but instead using (binary) instrumental variables. We propose the notion of
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A distinct feature of our approach is that, instead of solving a large number of large-scale linear programs, we provide simple analytical conditions for the ordering. The
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of the partial order. We also propose topological sorts of the partial order as a policy menu. We show how policymaking can be further guided by imposing assumptions such as monotonicity/uniformity of different stringency, agent's learning, Markovian structure, and stationarity
associated with the partial ordering. One main contribution of this paper is that we develop simple analytical conditions to establish the ordering, which bypass solving a large number of large-scale linear programs, and thus facilitate estimation and inference. This paper's analytical framework has broader applicability beyond the current context, e.g., in establishing signs of various treatment effects and rankings of policies across different counterfactual scenarios