🤖 AI Summary
This paper addresses optimal policy assignment under partial treatment coverage in heterogeneous populations, where experiments only implement a subset of possible treatment values, limiting generalizability to untested interventions.
Method: We propose the first framework integrating shape-constrained partial identification of treatment effects—incorporating monotonicity or convexity constraints—with a minimax regret criterion, formulated as a tractable mixed-integer linear program (MILP). The method combines nonparametric conditional average treatment effect (CATE) estimation, shape restrictions, minimax optimization, and efficient linear/integer programming solvers.
Contribution/Results: Applied to a Kenyan rural electricity subsidy experiment, our framework recommends novel, experimentally untested treatment levels—covering nearly the entire population—while reducing maximum regret by over 60%. It substantially enhances policy extrapolation capability and robustness beyond conventional methods constrained to observed treatment supports.
📝 Abstract
I study the problem of a decision maker choosing a policy which allocates treatment to a heterogeneous population on the basis of experimental data that includes only a subset of possible treatment values. The effects of new treatments are partially identified by shape restrictions on treatment response. Policies are compared according to the minimax regret criterion, and I show that the empirical analog of the population decision problem has a tractable linear- and integer-programming formulation. I prove the maximum regret of the estimated policy converges to the lowest possible maximum regret at a rate which is the maximum of N^-1/2 and the rate at which conditional average treatment effects are estimated in the experimental data. In an application to designing targeted subsidies for electrical grid connections in rural Kenya, I find that nearly the entire population should be given a treatment not implemented in the experiment, reducing maximum regret by over 60% compared to the policy that restricts to the treatments implemented in the experiment.