Average Treatment Effects - binary outcome - interpretation of a negative coefficient

[Stefanos Demertzis]

Dear Statalists,

in a setting where the Outcome variable is binary (1 bad outcome, 0 good outcome), how can I interprete e negative coefficient (e.g. -.31) of a significant ATE?

Thank you for your precious help and understanding

Stefanos

[Fei Wang]

If the result is from a linear probability model, then it means the treatment reduces the probability of bad outcome by 0.31 (31 percentage points).

[Stefanos Demertzis]

Thank you, I appreciate your answer! In case of a positive coefficient (e.g. 0.31) could I say that the probability of good outcome is increased by 0.31?

[Jackson Monroe]

No. If the coefficient is 0.31 and 1 is the bad outcome (in a linear probability model, i.e. you're using "reg" or something similar) then the treatment increases the probability of the bad outcome by 31%. Decreasing the probability of a bad outcome is the same thing in this case as increasing the probability of a good outcome.

[Stefanos Demertzis]

Thank you so much!