We are running a fixed effects regression to investigate the effect of different variables on weekly healthcare consumption. The data is comprised of several thousand time series, where each time series contains the weekly spending of a unique patient across the same year, so we have 52 observations per patient. Some predictors in our model include (non exhaustive, for illustrative purposes only):
- the previous week's spending
- the previous year's week's spending
- the current place of living (may change during the year if the patient moves)
In addition, there's also some variables we include as fixed effects:
- week
- height of deductibles (there's only 6 possible categories)
- height of deductibles of previous year (there's only 6 possible categories)
- previous year's total healthcare consumption spending
My question relates to the last of these fixed effects. It's unlikely that two people will have the exact same value in this variable, as such it's very much continuous. When I discovered that we had included this variable I thought it surely must be a mistake because as far as I know fixed effects are always categorical or at least they have so few unique values that they can be treated as categorical. My coworker, however, argues that they can and should indeed be included as fixed effects because they are constant for each patient, i.e., they are constant in each sub-panel of the data.
I tried to learn more about fixed effects to clear up this question online, but have not arrived at a clear conclusion yet. This other post seems to argue against the use of continuous fixed effects, but it has not left me completely convinced.
For context, we are using the feols() function from the fixest R package to implement our regression.
I'd highly appreciate any help and knowledge you might be able to share!
