Publication Date: April 2021
Algorithms produce a growing portion of decisions and recommendations both in policy and business. Such algorithmic decisions are natural experiments (conditionally quasirandomly 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 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 high-dimensional regression discontinuity design. The proofs use tools from diﬀerential geometry and geometric measure theory, which may be of independent interest.
The practical performance of our method is ﬁrst demonstrated in a high-dimensional simulation resembling decision-making by machine learning algorithms. Our estimator has smaller mean squared errors compared to alternative estimators. We ﬁnally apply our estimator to evaluate the eﬀect of Coronavirus Aid, Relief, and Economic Security (CARES) Act, where more than $10 billion worth of relief funding is allocated to hospitals via an algorithmic rule. The 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.