Test for equality of coefficients of 2 different regressions

[hangbh]

Hi Sergio,
I'm using ivreghdfe to run 2 different regressions for 2 different samples. E.g.
ivreghdfe y d (x=z) if sample==1, absorb(a) cluster(clustervar)
ivreghdfe y d (x=z) if sample==2, absorb(a) cluster(clustervar)
After having the result, I want to test if the coefficients on the endogenous variable (e.g. x) of the two regressions are similar or not. I process according to what is written here https://www.stata.com/statalist/archive/2009-11/msg01485.html . i.e.
g d1=d*(sample==1)
g d2=d*(sample==2)
g x1=x*(sample==1)
g x2=x*(sample==2)
g z1=z*(sample==1)
g z2=z*(sample==2)
ivreghdfe y d? (x?=z?), absorb(a) cluster(clustervar)

But three problems occur:
i) Cluster: The cluster variable in the "stacked" regression should be sample. But in my original regression, the standard error is clustered at the clustervar level. How should I deal with the cluster in the "stacked" regression in this case? Can I do like the following:
egen clid=group(sample clustervar)
ivreghdfe y d? (x?=z?), absorb(a) cluster(clid)
ii) Fixed effect in the absorb option: do I need to generate a1=a*(sample==1) and a2=a*(sample==2), and use absorb(a?) instead of absorb(a) in the "stacked" regression?
iii) If I run the above "stacked" regression (i.e. ivreghdfe y d? (x?=z?), absorb(a) cluster(clustervar)), the coefficients on the endogenous variable for 2 different samples in the "stacked" regression are the same as the ones in the two original regressions, but the coefficients on the exogenous variable for 2 different samples in the "stacked" regression is different to the ones in the two original regressions. Did I make any mistake here?

I highly appreciate if you could reply to my questions.
Thank you!