Hi Everybody,

I will simplify my problem to make this all more clear. Suppose I have three countries (1, 2 and 3) and I have data on migration between these countries for a single year. Let Mij be my dependent variable which is the migration from country i (the origin) to country j (the destination). So I would have

M12 M13 M21 M23 M31 M32

I also have the gross domestic product of each country (call this GDP). I want to run the regression

Mij = a + B1 GDPi + B2 GDPj + e

This is fine. But I also want to include country specific intercepts (each origin country will have its own intercept). So I want to estimate

Mij = ai + B1 GDPi + B2 GDPj + e

I will dummy variables for all 3 countries d1, d2, d3 (I get rid of the constant so there is no dummy variable trap). So my regression is

Mij = d1 + d2 + d3 + B1 GDPi + B2 GDPj + e

Even after having getting rid of the constant, I am still having a problem of perfect multicollinearity. Can anybody explain why this is? If I get rid of GDPi there is no longer a problem of perfect multicollinearity. I have a very weak understanding of matrix algebra (so if it can be dumbed down at all that would be great).

Any help would be enormously appreciated