Variance Estimation and Selecting Good Estimands for Causal Effect Queries

Abstract

This paper investigates the statistical efficiency of algebraic expressions ("estimands") used to answer causal queries. We first examine structural rules, developing a partial dominance relationship for front-door estimands that extends recent results on back-door estimands. In many models, however, structural rules alone may be insufficient to select an estimand. For such cases, we propose empirical techniques for estimating and comparing the variance of different estimands using both the graph and observational data: 1) a bootstrap-based method, and 2) a computationally simpler yet practically effective method for discrete models which estimates the Fisher information matrices. We illustrate both methods’ effectiveness on a variety of causal diagrams and estimand forms.