Data-driven covariate selection for nonparametric estimation of causal effects

The estimation of causal effects from non-experimental data is a fundamental problem in many fields of science. One of the main obstacles concerns confounding by observed or latent covariates, an issue which is typically tackled by adjusting for some set of observed covariates. In this contribution, we analyze the problem of inferring whether a given variable has a causal effect on another and, if it does, inferring an adjustment set of covariates that yields a consistent and unbiased estimator of this effect, based on the (conditional) independence and dependence relationships among the observed variables. We provide two elementary rules that we show to be both sound and complete for this task, and compare the performance of a straightforward application of these rules with standard alternative procedures for selecting adjustment sets.