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I am working on my thesis and I found that when I include dummy variable(s) in the equation, I got "Near Singular Matrix" when I try to run the model.

I have checked that "Near Singular Matrix" means that the independent variables are multicollinear, but I still cannot run the model even I exclude one dummy variable.

My two dummy variables are cityA and cityB (there are more than 50 cities in the data set) and my data set is an unbalanced panel data with fixed effect on cross section and period.

I have try the below three equations but neither one can run the model
ROA c hhirev niis hhiloan cons crops lna l_a e_a dlna dlna2 cityA
ROA c hhirev niis hhiloan cons crops lna l_a e_a dlna dlna2 cityB
ROA c hhirev niis hhiloan cons crops lna l_a e_a dlna dlna2 cityA cityB

However, I can run the model without the dummy variable, i.e. ROA c hhirev niis hhiloan cons crops lna l_a e_a dlna dlna2

Is there any method to check which part is wrong? or how to solve this problem?
Thank you very much.

I suspect cityA is collinear with the cross-section fixed effect. Try turning off fixed effects to see what happens.

Hi Startz, I can run the model after turning off cross-section fixed effects. However, my supervisor required me to run with both cross-section and period fixed effect.

The cross-section ID is the name of banks, which should not be same as the cities, Is there any method to solve this problem?
Thank you very much.

I'm not sure I understand exactly how the data is set up, but if each bank is in one city then you can't have (and don't need) both bank fixed effects and city dummies.

Hi Startz, in my data set, each bank is in one city only, but one city may have more than one bank. Does it also cause the multi-collinearity?
Thank you very much.

It does. Think of it this way, if you added 5 to the coefficient for the city and subtracted 5 from the coefficient for each bank in that city, you would get an identical fit.