Dear all,

I have a question on how to interpret an interaction between a continuous and dummy variable in a fixed effects panel model.

The situation is: I have data for 10 years and in each year subsidies were paid at the industry-level. I want to estimate how that differentially affected initially small and large businesses in terms of their sales. To that end, I define a dummy
Code:
initially_small
for whether a firm was large or small in the first year. Then, I run something like

Code:
xtset firm year
xtreg ln_sales i.initially_small##c.subsidies i.year, fe
Based on that, I get three coefficients:

beta_1 for 1.initially_small = this main effect is omitted because it is constant within firms / there are fixed effects
beta_2 for c.subsidies
beta_3 for 1.initially_small#c.subsidies

Is the following interpretation correct:

beta_2 is the main effect, i.e. the effect for initially small firms (so I can say initially small firms increased their sales by beta_2 % )

beta_3 is the difference to the main effect noticed by large firms, i.e. I can say something like "initially large firms increased their sales by (b_2 + b_3) %"

I´m just concerned that the interpretation of interactions with a dummy constant within panels differs in a fixed effects setting because one of the main effects is omitted.

Thanks a lot for your help!

All the best
Leon