In a simulation using the Matching package in R, researchers estimated key causal effects from simulated data. The Average Treatment Effect (ATE) was calculated as 6.5, which is the average of the Average Treatment Effect on the Treated (ATT) at 8.0 and the Average Treatment Effect on the Control (ATC) at 5.0. These values were analytically determined. Interestingly, the ATE could not be directly obtained as the mean difference between the potential outcomes y1 and y0. After adjusting the calculation of y1 as suggested, the true values were successfully recovered. This simulation involved 10,000 observations with a treatment probability of 0.5.
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