We compare the performance of various matching estimators using a novel approach that is feasible in the absence of experimental data. We estimate a structural model of hospital choices and catheterization for Medicare heart attack victims using hospital chart data on patient heterogeneity. With the estimated structural parameters, we simulate data for which the treatment effect is known. We find that as measures of individual heterogeneity are added to the controls, matching estimators perform well. However, the estimators do a poor job recovering the true treatment effect when measures of individual heterogeneity are unavailable.