Dear All.

I am working on a gravity model to evaluate the determinants of Colombian exports. To do this, I am using a panel with data from 2005-2019, with exports from Colombia to 150 countries (Origin: Colombia; Destination: every 150 countries) and I am using the PPML estimator.

Regarding this, I need your advice to define the estimate that I will use in my study.

In the equation, I want to implement time effects because of the benefits it offers to coefficients. However, I cannot do this because the Colombian GDP variable will be excluded from the estimate. Most of the literature that attempts to address the determinants of trade between a specific country and its partners uses random effects and includes the GDP of the specific country and the GDP of its partners. But, as I said before, I want to include time effects and Colombia's GDP will be excluded, which will go against the gravity model.

In this sense, I found an article by Soeng & Cuyvers (2018), where they discuss the determinants of Cambodian exports with their partners and do not include Cambodia's GDP. However, they do not theoretically explain why they exclude this regressor.

Could anyone help me to justify theoretically or empirically the exclusion of this regressor?

Thanks.

Carlos.