Interpreting regression and variable set-up

Question

Im working on a quantile regression model where I look at how imports (imp_i,t) of intermittent electricity (int_i,t) such as wind solar from country i in period t impact day ahead prices in Norway in period t. My current model can be simplified to this:

price_t ~ imp_i,t + int_i,t + imp_i,t*int_i,t

However, i´m not entirely certain about the implications of modelling it this way. For instance, imports can have a "main effect" on price but intermittent generation should only have an effect on price if its imported. When I look at the coefficients it seems that the int_i,t is a lot more significant than the interaction which is likely due to the imported flows (in MWh) being quite small. But in theory, that variable shouldnt be that significant because it cant have an isolated main effect on price. Could I model this in a better way? Or am I interpreting the three coefficients wrong?

If for example imp_i,t = 0.1
int_i,t = -0.01
imp_i,t*int_i,t = -0.000005

Should I interpret it as -0.01-0.000005+0.1 is the effect of importing intermittent from that country? All variables are continous.

Answer 1

I suspect that your observation:

When I look at the coefficients it seems that the int_i,t is a lot more significant than the interaction which is likely due to the imported flows (in MWh) being quite small. But in theory, that variable shouldnt be that significant because it cant have an isolated main effect on price.

comes from the attempt to interpret a so-called "main effect" for a predictor involved in an interaction. That can easily lead to confusion.

With the interaction term, the coefficient for int_i,t represents its association with outcome when inp_i,t = 0. The "significance" of that "main effect" coefficient is for a difference of the estimate from 0 when inp_i,t = 0. If you centered the inp_i,t values, the coefficient for int_i,t would change, and thus its difference from a value of 0. There's a simple explanation on this page.

With an interaction there is no simple interpretation of a "main effect." Thus you can't really compare the "significance" of that coefficient against the "significance" of the interaction coefficient, as you seem to be trying to do. Evaluate the model overall, not the individual "main effect" coefficients.