Problem of collinearity onces added district fixed effects

[Kerstin Schmidt]

Dear Statalist,

I am running a logit regression in Stata 14.2. This is to test how x1 (continuous and centered), x2 (continuous and centered) and the interaction term x1*x2 affect the probability of y. Using the following commands gives no evidence on collinearity between the independent variables with VIF values around 1.0 (see picture 1_ and 2_):

logit y c.centered_x1##c.centered_x2
vif, uncentered

However, if I add district fixed effects (39 districts) to the model with i.ubigeo (see picture 3_), x1 and x2 become highly collinear (VIF values of 22.74 and 28.64 when excluding the interaction term; see picture 4_) and the interaction term is eventually omitted in the regression due to collinearity. This poses a problem as it is one of my variables of interest.

I wonder if this is only because I add 38 dummy variables or if there is another reason for this to happen?

Any help is very much appreciated!!

PS: I added pictures of the Stata outputs for better clarity. Further, I am very much aware that the Pseudo R2 is quite low - this is only a version without control variables, which would not make any difference in the problem of collinearity.

[Carlo Lazzaro]

Kerstin:
I would test whether -i.ubigeo- is worth keeping via -parmtest-.

[Kerstin Schmidt]

Dear Carlo, thanks for your reply!
Running testparm i.ubigeo after the logit regression gives me a Prob>F of 0.0000. Therefore, we reject the null that the coefficients for all districts are jointly equal to zero and district fixed effects are needed in this case. What do you think?

[Carlo Lazzaro]

Kerstin:
thanks for providing further clarifications.
My guess is that your regression model can't support that specification.
With so many observations (by the way, from your posts I assume that they are all independent, i.e., that you're not dealing with a panel dataset), the evidence that -i.ubigeo- is significant might be due to sample size.