We investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required, like inverse probability weighting, kernel and other variants of matching, as well as different parametric models. The simulation design used is based on real data usually employed for the evaluation of labour market programmes in Germany. We vary several dimensions of the design that are of practical importance, like sample size, the type of the outcome variable, and aspects of the selection process. We find that trimming individual observations with too much weight as well as the choice of tuning parameters are important for all estimators. A conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall, in particular when robustness to misspecifications of the propensity score and different types of outcome variables is considered an important property.

SUMMARYThis paper demonstrates the identification of causal mechanisms of a binary treatment under selection on observables, (primarily) based on inverse probability weighting; i.e. we consider the average indirect effect of the treatment, which operates through an intermediate variable (or mediator) that is situated on the causal path between the treatment and the outcome, as well as the (unmediated) direct effect. Even under random treatment assignment, subsequent selection into the mediator is generally non-random such that causal mechanisms are only identified when controlling for confounders of the mediator and the outcome. To tackle this issue, units are weighted by the inverse of their conditional treatment propensity given the mediator and observed confounders. We show that the form and applicability of weighting depend on whether some confounders are themselves influenced by the treatment or not. A simulation study gives the intuition for these results and an empirical application to the direct and indirect health effects (through employment) of the US Job Corps program is also provided.

Because of their substantially increased risk, survivors should stop smoking and may consider entering trials of secondary chemoprevention.

We derive testable implications of instrument validity in just identified treatment effect models with endogeneity and consider several tests. The identifying assumptions of the local average treatment effect allow us to both point identify and bound the mean potential outcomes (i) of the always takers under treatment and (ii) of the never takers under non-treatment. The point identified means must lie within their respective bounds, which provides us with four testable inequality moment constraints. Furthermore, we use dominance/equality restrictions on potential outcomes across subpopulations to increase the power to detect violations of instrument validity. Finally, we adapt our testing framework to the identification of distributional features (as local quantile treatment effects). A brief simulation study and an application to labor market data are also provided.

Using a simulation design that is based on empirical data, a recent study by Huber et al. (J Econom 175:1-21, 2013) finds that distance-weighted radius matching with bias adjustment as proposed in Lechneret et al. (J Eur Econ Assoc 9:742-784, 2011) is competitive among a broad range of propensity score-based estimators used to correct for mean differences due to observable covariates. In this companion paper, we further investigate the finite sample behaviour of radius matching with respect to various tuning parameters. The results are intended to help the practitioner to choose suitable values of these parameters when using this method, which has been implemented in the software packages GAUSS, STATA and R.