中文摘要
我研究如下问题: 决策者基于仅包含部分可能处理取值的实验数据, 选择一项向异质性人群分配处理的策略。新处理的效应借助处理反应 (treatment response) 上的形状约束得到部分识别。策略之间依据最小最大遗憾 (minimax regret) 准则加以比较, 我证明总体决策问题的经验对应形式具有易于求解的线性规划与整数规划表述。我证明, 估计策略的最大遗憾向最低可能最大遗憾收敛的速率, 是 N^(−1/2) 与实验数据中条件平均处理效应估计速率二者中的较大者。在一项为肯尼亚农村电网接入设计定向补贴的应用中, 我发现几乎全部人口都应被给予一种实验中未实施的处理; 与仅限于实验中所实施处理的策略相比, 这使最大遗憾降低逾 60%。
Abstract
I study the problem of a decision maker choosing a policy that 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 that the rate at which the maximum regret of the estimated policy converges to the lowest possible maximum regret 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.