Dear Stata community,

I have a panel dataset at the regional level for a set of 10 countries (i.e several regions within each of the 10 countries). I first perform an OLS regression country by country:

Y_(i,t)=β X_(i,t)+ϵ_(i,t)

I therefore obtain a \hat{β} for each country (\hat{β}^c). I then would like to use this estimated coefficient as an independent variable in another (regional-level) regression (this time, not country by country):

Z_(i,t)= γ β_(i)+ μ_(i,t)

Is there any econometric issue of using an estimated coefficient as an independent variable in a regression? Is there a Stata command to handle this? Any reference would be helpful.

What if, for some countries, the β is not statistically significant in the first stage regression?

Many thanks in advance for your help,
Théodore

PS: sorry for the equations, I hope this is readable.