Interpreting ATT in PPM I am attempting PSM for my observational study. I have created a propensity score, checked balance for treated and controls (using pstest), and used psmatch2 command in STATA. My outcome is mortality (binary variable), could someone please guide me on how to interpret the output?
psmatch2 weekend, pscore(pscore) outcome(death) common caliper(0.01)
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        Variable     Sample |    Treated     Controls   Difference         S.E.   T-stat
----------------------------+-----------------------------------------------------------
           death  Unmatched | .044464845   .030251547   .014213298   .000886249    16.04
                        ATT | .044464845   .035683637   .008781208   .013085787     0.67
----------------------------+-----------------------------------------------------------
Note: S.E. does not take into account that the propensity score is estimated.


The two rows of the output correspond to the treatment effects prior to matching and after matching.
The first row indicates that the risk of dying for the treated units was .044 and for the control units was .030, for a risk difference of .014 with a standard error of .00089 and a t-statistic of 16.04, which is significant at the .05 level regardless of the degrees of freedom.
The second row indicates that the risk of dying for the treated units was .044 and for the matched control units was .036, for a risk difference of .009 with a standard error of .013 and a t-statistic of .67, which is nonsignificant at the .05 level.
The estimated effect corresponds to the ATT (average treatment effect in the treated) because no treated units were dropped and the control units were selected to resemble the treated units. The interpretation of the ATT is the effect of treatment for those who received treatment, or, perhaps more intuitively, the effect of withholding treatment from those who received it. That is, had the treated units not been treated, their estimated risk of dying would be .009 lower than observed. Importantly, this says nothing about how the control units would have responded to the treatment. See Greifer & Stuart (2021) for information on interpreting the ATT vs. other estimands (and deciding if the ATT is even the right estimand for you).
I'm not exactly sure how psmatch2 estimates the standard error, so I can't go into the assumptions required to interpret it validly. You might consider using teffects psmatch instead, which is better documented.
