My dataset is following: 1000 firms, time period of 10 years, 20 countries 20, 15 industries.
I declare in STATA:
xtset firmid year
I want to control for the unobserved heterogeneity using fixed effect:
xtreg Y b(set of independent variables) i.years i.industries, fe vce(robust)
Does this specification allow me to capture the firm-level heterogeneity?
Then, I use random effects:
xtreg Y b(set of independent variables) i.years i.industries i.countries, mle
What is the difference between the two specifications (apart that random allows me to include time-invariant variables like countries)?