Algorithms make a growing portion of policy and business decisions. We develop a treatment-effect estimator using algorithmic decisions as instruments for a class of stochastic and deterministic algorithms. Our estimator is consistent and asymptotically normal for well-defined causal effects. A special case of our setup is multidimensional regression discontinuity designs with complex boundaries. We apply our estimator to evaluate the Coronavirus Aid, Relief, and Economic Security Act, which allocated many billions of dollars worth of relief funding to hospitals via an algorithmic rule. The funding is shown to have little effect on COVID-19-related hospital activities. Naive estimates exhibit selection bias.

翻译：算法日益主导着政策与商业决策的制定过程。我们开发了一种基于处理效应的估计方法，将算法决策作为一类随机与确定性算法的工具变量。该估计量在良好定义的因果效应下具有一致性和渐近正态性。本方法的一个特例是边界复杂的多维回归断点设计。我们将该估计量应用于评估《新冠病毒援助、救济与经济安全法案》——该法案通过算法规则向医院分配了数十亿美元的救助资金。研究表明，该资金对医院新冠肺炎相关活动的影响甚微。而朴素估计则表现出选择偏误。