Algorithms produce a growing portion of decisions and recommendations both in policy and business. Such algorithmic decisions are natural experiments (conditionally quasi-randomly assigned instruments) since the algorithms make decisions based only on observable input variables. We use this observation to develop a treatment-effect estimator for a class of stochastic and deterministic decision-making algorithms. Our estimator is shown to be consistent and asymptotically normal for well-defined causal effects. A key special case of our estimator is a multidimensional regression discontinuity design. We apply our estimator to evaluate the effect of the Coronavirus Aid, Relief, and Economic Security (CARES) Act, where hundreds of billions of dollars worth of relief funding is allocated to hospitals via an algorithmic rule. Our estimates suggest that the relief funding has little effect on COVID-19-related hospital activity levels. Naive OLS and IV estimates exhibit substantial selection bias.

翻译：这种算法决定是自然实验(有条件的准随机分配工具),因为算法只根据可观测的投入变量作出决定。我们利用这一观察为一类随机和确定性决策算法开发一个治疗效应估计器。我们的估测器对于明确界定的因果关系效果来说,是一贯的,也是正常的。我们的估测器的一个重要特例是多层面的回归不连续设计。我们运用我们的估测器来评估科罗纳病毒援助、救济和经济安全法(CARES)的效果,在该法中,价值数百亿美元的救济资金通过算法规则分配给医院。我们的估算表明,救济资金对COVID-19相关的医院活动水平没有多大影响。Naive OLS和IV的估计显示,在选择方面有很大的偏差。