Bootstrap inference of matching estimators for average treatment effects

Abadie and Imbens (2008) showed that the standard naive bootstrap is inconsistent to estimate the distribution of the matching estimator for treatment effects with a fixed number of matches. This article proposes an asymptotically valid inference method for the matching estimators based on the wild bootstrap. The key idea is to resample not only the regression residuals of treated and untreated observations but also the ones to estimate the average treatment effects. The proposed method is valid even for the case of vector covariates by incorporating the bias correction method in Abadie and Imbens (2011), and is applicable to estimate the average treatment effect and the counterpart for the treated population. A simulation study indicates that our wild bootstrap method is favorably comparable to the asymptotic normal approximation. As an empirical illustration, we apply our bootstrap method to the National Supported Work data.