Model misspecification and robustness in causal inference: comparing matching with doubly robust estimation

In this paper, we compare the robustness properties of a matching estimator with a doubly robust estimator. We describe the robustness properties of matching and subclassification estimators by showing how misspecification of the propensity score model can result in the consistent estimation of an average causal effect. The propensity scores are covariate scores, which are a class of functions that removes bias due to all observed covariates. When matching on a parametric model (e.g., a propensity or a prognostic score), the matching estimator is robust to model misspecifications if the misspecified model belongs to the class of covariate scores. The implication is that there are multiple possibilities for the matching estimator in contrast to the doubly robust estimator in which the researcher has two chances to make reliable inference. In simulations, we compare the finite sample properties of the matching estimator with a simple inverse probability weighting estimator and a doubly robust estimator. For the misspecifications in our study, the mean square error of the matching estimator is smaller than the mean square error of both the simple inverse probability weighting estimator and the doubly robust estimators.