Dear Maria Wang,
Tom may be a bit too busy to reply timely, so let me try to help a bit. You ask if it is possible to keep some regressors and drop FE instead, as in PPML. That is not a good idea because if you do that the estimates for the coefficients on those regressors are simply what you would get for the fixed effects and are not interpretable. When two variables are perfectly collinear you can drop either of them, but you need to be careful with the interpretation of the estimated coefficient on the variable not dropped because its interpretation may not be straightforward. In short, I suggest you stick to ppmlhdfe and try to understand why the variables are dropped. In my experience, that is really important.
Best wishes,
Joao
Tom may be a bit too busy to reply timely, so let me try to help a bit. You ask if it is possible to keep some regressors and drop FE instead, as in PPML. That is not a good idea because if you do that the estimates for the coefficients on those regressors are simply what you would get for the fixed effects and are not interpretable. When two variables are perfectly collinear you can drop either of them, but you need to be careful with the interpretation of the estimated coefficient on the variable not dropped because its interpretation may not be straightforward. In short, I suggest you stick to ppmlhdfe and try to understand why the variables are dropped. In my experience, that is really important.
Best wishes,
Joao
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