everyone!

I am estimating a gravity model in order to analyze the impacts of tighter environmental regulations on international trade. More specifically, I am analyzing Brazil's trade flow.

My (linearized) model is as follows:

$ \ln(EXP) = \ln(GDP_O) + \ln(GDP_D) + \ln(POP_O) + \ln(POP_D) + \dots $

In other words, the exports from Brazil (origin) to a country D (destination) depend on both countries GDPs,Populations, Total Area and another couple of variables.

My problem is: because Brazil is the origin for the exports to all other countries, GDP_O, POP_O and any other variables representing Brazilian data will be equal for all observations and as such there will be perfect multicollinearity.

How do I circumvent this? Every gravity model uses both the exporter and importer variables in order to explain the bilateral trade flow.

I appreciate any help!

Kind regards, Pedro