Panel Data Standardization

[Eva Rot]

Hello,

I want to standardize my independent variable before running the regression. I have a panel data set and I am sure that I want to standardize cross-sectionally.
Now I am unsure whether to standardize across the whole data set i.e. standardize across all different entities and across time by simply doing

egen std_VAR = std(VAR)

or whether it would make more sense to only standardize across the different entities by

by date: egen VAR_mean = mean(VAR)
by date: egen VAR_sd = sd(VAR)
by date: gen VAR_std = (VAR-VAR_mean)/VAR_sd

I do not fully get how the different approaches will change my interpretation or in which case which approach would be most appropriate.

Thank you very much!