Augmenting propensity score equations to avoid misspecification bias – Evidence from a Monte Carlo simulation[Erweiterung der Propensity Score Gleichung zur Vermeidung von Fehlspezifikationen? Eine Monte Carlo Simulation]

Propensity score matching is a semi-parametric method of balancing covariates that estimates the causal effect of a treatment, intervention, or action on a specific outcome. Propensity scores are typically estimated using parametric models for binary outcomes, such as logistic regression. Therefore, model specification may still play an important role, even if the causal effect is estimated nonparametrically in the matched sample. Methodological research indicates that incorrect specification of the propensity score equation can lead to biased estimates. Augmenting the propensity score equation with terms that represent potential nonlinearity and nonadditivity, as proposed by Dehejia and Wahba and more recently by Imbens and Rubin, represents a means of avoiding such bias. Here, we conduct a Monte Carlo simulation and show that the misspecification bias is rather small in many situations. However, when the propensity score equation and/or the outcome equation are characterized by strong nonlinearity and nonadditivity, the misspecification bias can be severe. Augmentation is shown to reduce this bias, often substantially. The Dehejia-Wahba (2002) algorithm performs better than the Imbens-Rubin algorithm, especially when the outcome equation is strongly nonlinear and nonadditive.