On true versus estimated propensity scores for treatment effect estimation with discrete controls

05/18/2023

∙

by   Andrew Herren, et al.

∙

0

∙

share

The finite sample variance of an inverse propensity weighted estimator is derived in the case of discrete control variables with finite support. The obtained expressions generally corroborate widely-cited asymptotic theory showing that estimated propensity scores are superior to true propensity scores in the context of inverse propensity weighting. However, similar analysis of a modified estimator demonstrates that foreknowledge of the true propensity function can confer a statistical advantage when estimating average treatment effects.