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.
EDIT: See for instance the estimation carried out here: https://drive.google.com/file/d/1DczfoFI_mkI8Tm4H0WcaVZTz9ZXLGb2K/view?usp=drivesdk
EDIT2: Specifically, here:
[Regression table] (https://i.stack.imgur.com/TQDA3.png)
I appreciate any help!
Kind regards, Pedro!