[Felix Bittmann]

You only need to add the actual test command to get a p-value as such:

sysuse auto, clear
expand 10
reg price mpg if foreign
est sto M1a
reg price mpg if !foreign
est sto M1b
suest M1a M1b
test [M1a_mean = M1b_mean]

[Leonardo Guizzetti]

Leonardo Guizzetti was right that my original interaction model assumed equal residual variances across the two groups:

sysuse auto, clear
reg price c.mpg##i.foreign

However, that assumption can be relaxed by using heteroskedascity-consistent standard errors, like this:

sysuse auto, clear
reg price c.mpg##i.foreign,hc3

I don’t think suest lets you test such an approach but I’ve not used it much. SEM would be the better framework to test this in because you can place equality constraints on pretty much anything. I wouldn’t worry about it at all unless you had error magnitudes that were orders of magnitude different.