Hi everybody!
I am currently working on my graduation thesis and I have a few issues with my model and I was wondering if you could maybe provide me with some of your insight.

I'm applying the gravity model not on the overall trade, but the european procurement market.

I have cross-sectional data, where each row represents procurement supplied by country Y to country X (i have grouped the data by contracting authority and supplier, eliminitating the time dimension as the data seamed too imbalanced for a panel and also for the purpose of my paper - comparison of actual vs predicted - this seemed like a more suitable option). Contracting authorities (countries X) are European countries - suppliers are from the EU as well as third countries.

What I want to do in my thesis is that I want to apply the gravity model on data excluding suppliers from tax havens and then use the estimated coefficients on the entire database. The fitted values predicted will then be compared to the actual values and what I hope to see is that for the tax haven countries the actual volume of procurement supplied is significantly greater than the value predicted (> this would prove that there is a significant portion of profits shifted without any real economic activity).

So far, I have done the traditional log-linear OLS model with simple distance (in log), log-linear model with calculated multilateral resistance terms - remoteness (Bacchetta et. al, 2008), pseudo poisson with simple distance and with the remoteness terms (each for supplier and contracting auth.) without including zero "trade" flows. These seem to yield nice results with the havens and the differences between actual and fitted values predicted by the model > up to 1700% difference for the OLS and up to 350% for the PPML (seems much more legit, as expected), tax havens being at the top of the list. However, what bothers me a bit is that some of the coefficient seem to report not very intuitive effects, such as strong negative effect of common currency, common language, or on the opposite very unexpectedly positive effect of remoteness term for the contractor:
[ATTACH=CONFIG]temp_14146_1555599142238_758[/ATTACH]

On the otherside, if I include the zeroes (for the ols I used log(procurement value +1)), the model seems to be a much better fit in terms of better R-squared, intuitive estimated coefficients,.. BUT! when I when I calculate the difference between the fitted values predicted by the model and the actuals, it results in nonsense differences - e.g. for the OLS up to 9 000 000 000% difference (i.e. Marshall Islands supply 9 000 000 000% more procurement to the EU countries than it should), for the poisson it's up to 2300% difference.
[ATTACH=CONFIG]temp_14147_1555599426575_873[/ATTACH]

I have no idea where the problem is. Also, in case I use the dataset whithout the zeroes do you think it is defendable in terms of having incomplete dataset? I tried to find a reference to cases where zeroes were not included intentionally, but I wasn't very succesful. As most of these papers are neglecting the zeros because of the use of logarithm form, thus, the zeros were not defined, but these papers are quite often criticized for having biased and inconsistent results due to the use of ols under heteroskedasticity.

Please, if you had a second and could have a look at it, I would really really appreciate it.
Thank you for your help.
Kind regards,
Trang