Estimating the variance of a propensity score matching estimator for the average treatment effect

This study considers variance estimation when estimating the asymptotic variance of a propensity score matching estimator for the average treatment effect. We investigate the role of smoothing parameters in a variance estimator based on matching. We also study the properties of estimators using local linear estimation. Simulations demonstrate that large gains can be made in terms of mean squared error, bias and coverage rate by properly selecting smoothing parameters. Alternatively, a residual-based local linear estimator could be used as an estimator of the asymptotic variance. The variance estimators are implemented in analysis to evaluate the effect of right heart catheterisation.