Comparing effect of a policy in 2 subpopulations

[Hania ElBanhawi]

Hello,
My model is assessing the effect of a state-wide policy (binary) on my outcome, y, adjusting for other confounders.
I have run an OLS, cluster-robust OLS and GLS -RE (using xtreg) on a model to account for within-state heterogeneity.
I am now looking to see whether this effect differs depending on a characteristic which is recorded as a dummy 0/1
If I were to run a linear regression, would it make sense to run my cluster robust OLS (or the GLS) twice adding 'if characteristic==1' & 'if characteristic==0' at the end of the regression and just compare the coefficients for the 2 groups, or is that incorrect?

e.g. regress <y> <policy> <potential_controls> if characteristic==1, vce(cluster US_states)
regress <y> <policy> <potential_controls> if characteristic==0, vce(cluster US_states)
OR
xtreg <y> <policy> <potential_controls> if characteristic==1, re
xtreg <y> <policy> <potential_controls> if characteristic==0, re

Thank you!
Hania

[Øyvind Snilsberg]

use interaction to test whether the effect differs between the two groups,

regress y characteristic##(policy controls), vce(cluster states)
test 1.characteristic#1.policy