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I want to analyze treatment effect for employment rate using difference in difference with propensity score matching how employment rate change if people experienced hospitalization treatment is hospitalization.

I don't know how I can do this. if I do logistic regression after matching and interpret interaction coefficient as I do for Difference in difference of linear model, I think that we can not say it as treatment effect because logistric model is nonlinear.

I tried teffects nmatch because I read that teffect can analyze model with binary outcome and tells average treatment effect(ATE). c431 is treatment and c244 is outcome(employed or not after treatment) c241 is outcome(employed or not before treatment)

enter image description here I don't know what ATE means results says and how I can interpret this. I guess ATE for this results is only difference between treatment group and control group before treatment or after treatment. However, ATE for difference in difference is [E(y11)-E(y12)]-[E(y21)-E(y22)] [y st, t=1,2 s=1,2]. Not just difference between treatment between treatment group and control group before treatment or after treatment

how can I find the ATE of difference in difference for binary outcome?

thanks.

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