Propensity Scores and Causal Inference Using Machine Learning Methods

We compare a variety of methods for predicting the probability of a binary treatment (the propensity score), with the goal of comparing otherwise like cases in treatment and control conditions for causal inference about treatment effects. Better prediction methods can under some circumstances improve causal inference both by reducing the finite sample bias and variability of estimators, but sometimes better predictions of the probability of treatment can increase bias and variance, and we clarify the conditions under which different methods produce better or worse inference (in terms of mean squared error of causal impact estimates).