Association for Public Policy Analysis & Management

We compare a variety of methods for predicting the probability of a binary treatment (the propensity score), with the goal of causal inference. 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.  We also compare estimators for standard errors, and the size of hypothesis tests using standard methods.