[Maxence Morlet]

Dear Bruno,

For your first question: yes, if you believe in the conditional parallel trends assumption, i.e. that parallel trends hold only conditional on the covariates. Be mindful that covariates must be pre-determined with respect to treatment; Zeldow and Hatfield (2021) discuss the perils of controlling for endogenous covariates.

Post-treatment interaction coefficients will give you year-by-year treatment effects. That is different from the parallel trends assumption. You cannot test for parallel trends after treatment because you do not observe the untreated-post outcome for the treated group. That's why we use the trend of the control group to impute this value and calculate the ATT: E(Y1 - Y0 | D=1, Post=1).

Hope this helps.
Maxence

[Bruno Paisani]

Dear Bruno,

For your first question: yes, if you believe in the conditional parallel trends assumption, i.e. that parallel trends hold only conditional on the covariates. Be mindful that covariates must be pre-determined with respect to treatment; Zeldow and Hatfield (2021) discuss the perils of controlling for endogenous covariates.

Post-treatment interaction coefficients will give you year-by-year treatment effects. That is different from the parallel trends assumption. You cannot test for parallel trends after treatment because you do not observe the untreated-post outcome for the treated group. That's why we use the trend of the control group to impute this value and calculate the ATT: E(Y1 - Y0 | D=1, Post=1).

Hope this helps.
Maxence

Thank you, Maxence. It does help me a lot, now I got it!
I may not have been clear enough, but my second point was about the treatment effect itself. Should I be concerned if the coefficients are not statistically significant, potentially meaning that the treatment has no effect at all?

[Maxence Morlet]

This means that you fail to find a significant treatment effect. The treatment have not had an effect, or you may have committed a Type 2 error. But I would also look at the magnitude of these coefficients and their confidence intervals to comment on that before deducing a zero treatment effect.

[Bruno Paisani]

This means that you fail to find a significant treatment effect. The treatment have not had an effect, or you may have committed a Type 2 error. But I would also look at the magnitude of these coefficients and their confidence intervals to comment on that before deducing a zero treatment effect.

Thanks a lot!