Dummy perfectly correlated fixed effects

[raphael rodrigues]

Hello. I am estimating a regression between the GDP and social spending of municipalities and I am trying to insert a dummy variable for municipalities in the metropolitan region (municipalities in the metropolitan region = 1; municipalities outside the metropolitan region = 0). But Stata is displaying the "Omitted" message when I use a panel regression for fixed effects, and when I select neither effect or random effects, the "Omitted" does not appear. However, when I analyze the correlation matrix, it is clear that there is no perfect correlation between the dummy variable and the other variables in the equation. What could be causing this error?

The equation is LogGDPmuni = LogEducation LogHealth DummyGV LogGDPcountry

[Clyde Schechter]

The colinearity you are getting is with the fixed effects themselves. The location within the metropolitan area or not is a time-invariant attribute of the municipality. Since it never changes within municipality, it is colinear with the municipality fixed effects.

The reason you do not see that with -re- specified is that the random effects estimator does not have anything in it that is equivalent to an exact value of a fixed effect: only the variance of the random effects is actually estimated. When you specify nothing, you are getting the random effects model: random effects is the default for -xtreg-.

Anticipating your next question, you are probably wondering how you can go about adjusting for the effects of being in or out of the metropolitan area in the fixed effects model. The answer is that there is no need to do so. One of the important advantages of a fixed-effects model is that it automatically adjusts for all time-invariant attributes of the fixed-effect entities--even those for which there is no variable in the model, and even those which are, in principle, impossible to observe. So this effect is already adjusted for in the fixed-effects model without your having to do anything specific. By contrast, in the random effects model, this adjustment comes only if you include it in the model predictors.

[raphael rodrigues]

Thank you very much for the answer, for the class, and for your attention.