I have data about investment preferences 1 year before the Covid and during the Covid lockdown.
Some changes appear using simple T-Test. I want to be able to assess if these changes are particularly strong for some specific demographics (e.g., older individuals ($X_1$), individuals with lower income ($X_2$), etc...).
Should I use the initial level of my dependant variable in the regressions? Basically, if I want to use OLS regressions to investigate which independant variable correlate with the change in my dependant variable, which model is preferrable?
Model 1 (apparently called Change Score Method): $(Y_2-Y_1)= \beta_1 . X_1+ \beta_2 . X_2 $
Model 2 (apparently called Regressor Variable Method) Score Method): $Y_2= \beta_1 . X_1+ \beta_2 . X_2 + \beta_3 . Y_1 $
Thank you so much for your help - Any reference would also be much appreciated!