Using margins with a double DiD continuous estimator

[Ernesto Vincenti]

I'm using individual cross-sectional survey data to estimate the impact of a continuous variable ("intervention") on a binary employment outcome variable ("employed"). I'm comparing between two years ("year", 2020 and 2021) and two sets of months ("half", where Jan-Jun=1 and Jul-Dec=2).

I'd like to calculate the marginal effect and CIs of just the double DiD term for values of intervention between 1 and 100: 2021.year#2.half.#c.intervention

The below code I tried is close but not right. It generates the marginal effect at all levels of year and half for each intervention value. I want the double difference between year = 2021 and year = 2020 as well as half = 2 and half = 1.

logit employed i.year##i.half##c.intervention
margins year#half, at(intervention=(1(1)100))

[Ernesto Vincenti]

To clarify further here, what I'd essentially like is the marginal effect (and CIs) across the values 1-100of intervention for (2021.year#2.half - 2021.year#1.half) - (2020.year#2.half - 2020.year#1.half)

[Fei Wang]

You may need Puhani's formula to compute the marginal effect. Here is a recent post regarding the issue.

For your case, it would be something like

gen year_half = (year == 2021) * (half == 2)
logit employed i.(year half)##c.intervention i.year_half i.year_half#c.intervention
margins, dydx(year_half) at(year = 2021 half = 2 intervention=(1(1)100)) subpop(if year == 2021 & half == 2) vce(unconditional)

[Ernesto Vincenti]

You may need Puhani's formula to compute the marginal effect. Here is a recent post regarding the issue.

For your case, it would be something like

gen year_half = (year == 2021) * (half == 2)
logit employed i.(year half)##c.intervention i.year_half i.year_half#c.intervention
margins, dydx(year_half) at(year = 2021 half = 2 intervention=(1(1)100)) subpop(if year == 2021 & half == 2) vce(unconditional)

Thank you for the response! This makes sense and looks promising.