Can I use group mean centered variables in an OLS regression?

Hi everyone,

I have a question about some analyses I'm working through. I originally ran the model as an HLM because of the nested structure of my data. However the ICC is very low and all significant variables in my HLM are also significant in OLS. My question is: can I can still use my group mean centered variable in OLS regression? Basically I found the mean value for a variable for each school and assigned that one value to each student in the school. I then centered the values to make a group mean centered variable. I don't see why I wouldn't be able to use this variable in these analyses, but i want to make sure. Does anyone else see a problem?

Thanks for any help I can get.