Staggered diff in diff with continuous treatment

[Erdem Yilmaz]

My data involves treatment exposures in multiple groups and multiple time periods and I used staggered or two ways fixed effect diff in diff model with the following command

xtset country
xtreg DV postreatment i.year, fe vce(cluster country)

I also want to measure the treatment intensity But I am not sure which regression I should run

This:

xtreg DV postreatment##c.intensity i.year, fe vce(cluster country)

which only returns a coeffcient for postreatment and.intensity interaction


or this:

xtreg DV postreatment intensity i.year, fe vce(cluster country)

which returns two coeffcients.

I am a little bit confused because some papers report two coeffcients seperatly, for instance in this paper https://www.gwern.net/docs/ai/2018-brynjolfsson.pdf on Table 3

[Erdem Yilmaz]

Sorry, the first one also returns two coeffcients, but people sometimes report only one coeffcient...