Rehabilitating the Regression: Honest Causal Inference through Machine Learning

• In Event: Causal Inference: Mediation, Experiments, and Sensitivity

Abstract

The linear regression is the central tool in the quantitative researcher's toolkit. Despite this, the method suffers from two well-known flaws. First, inference using a regression is model-dependent, where specification choices by the researcher can affect our inference on a treatment variable of interest. Second, the regression is primarily a correlative tool, so its estimates do not in general return estimates of an average causal effect. Addressing these flaws is central to how the field accumulates knowledge, and whether a general tool can be used to derive reliable causal inferences from observational data. We introduce a method both shortcomings. First, it uses a machine learning method to control for background covariates. Unlike existing machine learning approaches, though, our is the first to adapt machine learning to the problem of inference rather than prediction. Second, we model the treatment variable as well as the outcome in order to recover an estimate of the average causal effect of the treatment, regardless of whether the treatment is binary, continuous, or count data. We include a proof that the method produces confidence intervals that are asymptotically valid and semiparametrically efficient. A simulation study shows that, unlike several cutting-edge methods, the method returns unbiased estimates and valid confidence intervals and application to a real-world dataset illustrates the method’s utility.

Author

• Marc Thomas Ratkovic, Princeton University