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  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 %DIFDELCMD < \10 %%% \175 billion worth of relief funding is allocated to hospitals via an algorithmic rule. The estimates suggest that the relief funding has little effects on COVID-19-related hospital activity levels. Naive OLS and IV estimates exhibit substantial selection bias.
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 more than %DIFDELCMD < \10 %%% \175 billion 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.
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decision-making
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high-dimensional
multidimensional
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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
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the
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effects
effect