JWDID Poisson - clarifications

[Alessandro Corvasce]

Good morning everyone,

I am estimating a Poisson regression using the jwdid command in a staggered DiD setup, and I have a couple of questions:

I) Which is the more correct way to present the functional form of the regression, A or B?

• A - log(Y_nt)=∑γ_k⋅D_k⋅Treatment_c++βX_nt + FE_nt + ε_nt
• B - E[Y_nt∣ X_nt,FE_nt]=exp(∑γ_k⋅D_k⋅Treatment_c+FE_nt+β X_nt)

Y_nt is the outcome variable, measured in year [t] in unit[n] and is a count variable; X_nt is a set of control variables; FE_nt are unit and time fixed effects; Treatment_c distinguish treated unit into different cohort [c] depending on the year of first treatment; D_k are relative event-time dummies.

II) I am presenting the results of this estimation as ATT via the jwdid postestimation command estat simple.
Is it correct to state that results are already computed as differences in model-predicted counts and, therefore, can be interpreted as actual increases in the outcome?
For example: ATT = +18 would indicate a statistically significant increase of 18 in the outcome on average among treated units?

Thanks in advance for your help!

[FernandoRios]

i) B is more appropriate (see Prof Wooldridge paper for reference)
ii) It is the predicted effect on treated, averaged across all post -treatment periods and for all treated cohorts

[Alessandro Corvasce]

Thank you very much! I could not had a better conselor!