Propensity score model specification for estimation of average treatment effects

Treatment effect estimators that utilize the propensity score as a balancing score, e.g., matching and blocking estimators are robust to misspecifications of the propensity score model when the misspecification is a balancing score. Such misspecifications arise from using the balancing property of the propensity score in the specification procedure. Here, we study misspecifications of a parametric propensity score model written as a linear predictor in a strictly monotonic function, e.g. a generalized linear model representation. Under mild assumptions we show that for misspecifications, such as not adding enough higher order terms or choosing the wrong link function, the true propensity score is a function of the misspecified model. Hence, the latter does not bring bias to the treatment effect estimator. It is also shown that a misspecification of the propensity score does not necessarily lead to less efficient estimation of the treatment effect. The results of the paper are highlighted in simulations where different misspecifications are studied.