Policy Learning with New Treatments

TL;DR

This paper develops a framework for policy learning with new treatments using experimental data, shape restrictions, and minimax regret, with applications to targeted subsidies in Kenya.

Contribution

It introduces a tractable linear programming approach for policy optimization with partially identified treatment effects and analyzes the convergence of the estimated policy's regret.

Findings

Nearly the entire population should receive a new treatment not tested in the experiment.

Maximum regret can be reduced by over 60% using the proposed policy.

The convergence rate of the policy's regret depends on sample size and treatment effect estimation.

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.