Double Machine Learning: Improved Point and Interval Estimation of Treatment and Causal Parameters

Most supervised machine learning (ML) methods are explicitly designed to solve prediction problems very well. Achieving this goal does not imply that these methods automatically deliver good estimators of causal parameters. Examples of such parameters include individual regression coefficients, average treatment effects, average lifts, and demand or supply elasticities. In fact, estimates of such causal parameters obtained via naively plugging ML estimators into estimating equations for such parameters can behave very poorly, for example, by formally having inferior rates of convergence with respect to the sample size n caused by regularization bias. Fortunately, this regularization bias can be removed by solving auxiliary prediction problems via ML tools. Specifically, we can form an efficient score for the target low-dimensional parameter by combining auxiliary and main ML predictions. The efficient score may then be used to build an efficient estimator of the target parameter which typically will converge at the fastest possible 1/root(n) rate and be approximately unbiased and normal, and from which valid confidence intervals for these parameters of interest may be constructed. The resulting method thus could be called a “double ML” method because it relies on estimating primary and auxiliary predictive models. Such double ML estimators achieve the fastest rates of convergence and robustness of behavior with respect to a broader class of probability distributions than naive “single” ML estimators. We illustrate the use of the proposed methods with an application to estimating the effect of 401(k) eligibility on accumulated assets.