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Hi,
I am trying to run a trade gravity regression of the form

log_imports c log_gdp_exporter log_gdp_importer log_distance

I want the coefficient on log_gdp_exporter and log_gdp_importer to be the same for simplicity. I do not know how to combine these two.

Even when I just run this regression as written I get the error message "Near singular Matrix Error"

My workfile is attached. Thanks a lot.

Your exporter variable is a constant.

Tij = A ((Yi^a)(Yj^b))/Dij^c

ln (Tij) = ln (A) + a [ln (Yi) + ln (Yj)]-cln(Dij)

Tij = Imports
Yi = GDP_Exporter
Yj = GDP_Importer
Dij = Total_Distance_Between

I want to estimate the coefficients ln(A), a=b and c.

France is the exporter in each case, so the GDP_exporter remains the same. How can I get around this problem?

Thanks a lot for your help.

You cannot. Exporter is perfectly colinear with your constant. Either drop the exporter variable, or get more data (with different exporter values).

I have combined the two variables and this seems to fix this problem.

When I run the log linear regression, I obviously get a coefficient for the constant. But I am looking for the natural log of the constant ln(A) as shown above in the second equation. So should I take the log of this constant? or is it already the log value due to the fact i have regressed using data that is already logged?