Should ATT equal ATU?

[Chen Samulsion]

Dear Stata users,

This is a question pertaining to propensity score matching, or put it more correctly, pertaining to matching estimators (i.e. using vector norm to caculate distances on the observed covariates between treated case and control case). ATT means average treatment effect of the treated, while ATU means average treatment effect for the untreated. In Guo and Fraser's book Propensity Score Analysis: Statistical Methods and Applications(Sage Publications, Inc., 2015) that I cited below, the authors wrote that:

If the variables used in matching accounted for all cases of selection bias and the evaluation data met all the assumptions of the matching estimators, SATT and SATC would appear to have values of similar magnitude. Thus, the difference between the two coefficients holds the potential to indicate both the level of hidden selection bias and the departure of data from model assumptions(Guo and Fraser, 2015:301).

I doubt that their conclusion is reasonable. It seems that in much research, the ATT is always quite different from ATU, for example, in the famous lalonde data, the ATT is about 1778.9 and the ATU is about -12385.9.

[Chen Samulsion]

In the example section of the same book, they used data to analyse treatment effect of participation in the AFDC program. They concluded that:

Note that in this study, SATT equaled −5.23 and SATC equaled −4.47, or a difference of 0.76 units. This difference is attributable either to additional selection bias that was not accounted for in the study or to study data that violated assumptions of matching estimators, which suggests the need for further scrutiny.