We study the question of how best to assign an encouragement in a randomized encouragement study. In our setting, units arrive with covariates, receive a nudge toward treatment or control, acquire one of those statuses in a way that need not align with the nudge, and finally have a response observed. The nudge can be seen as a binary instrument that affects the response only via the treatment status. Our goal is to assign the nudge as a function of covariates in a way that best estimates the local average treatment effect (LATE). We assume a partially linear model, wherein the baseline model is non-parametric and the treatment term is linear in the covariates. Under this model, we outline a two-stage procedure to consistently estimate the LATE. Though the variance of the LATE is intractable, we derive a finite sample approximation and thus a design criterion to minimize. This criterion is convex, allowing for constraints that might arise for budgetary or ethical reasons. We prove conditions under which our solution asymptotically recovers the lowest true variance among all possible nudge propensities. We apply our method to a semi-synthetic example involving triage in an emergency department and find significant gains relative to a regression discontinuity design.

翻译：本研究探讨在随机激励试验中如何最优分配激励措施的问题。在我们的设定中，个体携带协变量进入研究，接受趋向处理组或对照组的干预引导，随后以可能偏离引导方向的方式获得实际处理状态，最终观测到响应结果。该引导可视为仅通过处理状态影响响应的二元工具变量。我们的目标是根据协变量函数分配引导干预，以最优方式估计局部平均处理效应（LATE）。我们采用部分线性模型，其中基线模型为非参数形式，处理项为协变量的线性函数。在此模型框架下，我们提出两阶段估计程序以一致地估计LATE。虽然LATE的方差难以显式表达，我们推导了有限样本近似形式，进而构建可最小化的设计准则。该准则具有凸性特征，能够兼容预算或伦理约束条件。我们证明了在特定条件下，所得解能渐近恢复所有可能引导倾向中最小的真实方差。我们将该方法应用于急诊科分诊的半合成案例，发现相较于断点回归设计可获得显著增益。