Estimating Heterogeneous effects following Probit estimation with DID

[Mehreen Mookerjee]

I’m estimating a difference-in-differences (DiD) model using a binary outcome (Y) and a policy treatment (treatpost), implemented via a Probit specification. The baseline model is:

probit Y treatpost post treat `Xvars' i.district, vce(cluster district)
margins, dydx(treatpost) pred(pr)

This works fine and gives us the average marginal effect of the DiD term (treatpost). Now, I would like to assess heterogeneous effects by age group — specifically comparing younger vs older women (binary variable younger, where 1 = younger).

To do this, I interacted treatpost with younger:

probit Y treatpost##i.younger post treat `Xvars' i.district, vce(cluster district)
margins, dydx(treatpost) at(younger=(0 1)) pred(pr) post

This gives me the marginal effect of treatpost for both younger = 0 and younger = 1. Both effects are positive and significant.

My main question is:

How do I formally test whether the marginal effects at younger = 0 and 1 are statistically different from each other? Also: Is there a better or more standard way to evaluate heterogeneous effects in a nonlinear DiD model like this, given the binary outcome?

Any guidance on the correct interpretation or alternative modeling strategies would be much appreciated.

[George Ford]

As Lechner advises, proceed with caution when using non-linear models for DID. Also look at Ai and Norton (2003).

Generally, a linear model is preferred.