Shrinkage Methods for Treatment Choice

This study examines the problem of determining whether to treat individuals based on observed covariates. The most common decision rule is the conditional empirical success (CES) rule proposed by Manski (2004), which assigns individuals to treatments that yield the best experimental outcomes conditional on observed covariates. By contrast, using shrinkage estimators, which shrink unbiased but noisy preliminary estimates toward the average of these estimates, is a common approach in statistical estimation problems because it is well-known that shrinkage estimators have smaller mean squared errors than unshrunk estimators. Inspired by this idea, we propose a computationally tractable shrinkage rule that selects the shrinkage factor by minimizing an upper bound of the maximum regret. Then, we compare the maximum regret of the proposed shrinkage rule with that of CES and pooling rules when the parameter space is correctly specified and misspecified. The theoretical and numerical results show that our shrinkage rule performs well in many cases when the parameter space is correctly specified. In addition, we show that the results are robust against the misspecification of the parameter space.