I’ve been using Bayesian model averaging to find determinants of international trade – out of the set of 71 potential determinants. What is surprising, I found that my results heavily depend on the fact whether I use variables at levels or in natural logarithms. Basically, different variable turned out to be robust depending on whether trade and explanatory were in logs or not. Do you know any references to the literature dealing with that problem?
Good morning Krzysztof,
The fact that you are seeing different variables having significance when you use levels versus logs is not surprising. When you find significance using levels you are seeing a directly linear effect. For example, if you see a $1,000 rise in income you see a $300 increase in expenditures. If you see a $2,000 rise the coefficient remains the same so expenditures would increase to $600.
If the actual relationship between the variables is not directly linear but is instead the effect of a percentage change you'll find that a log log model will find significance where a standard linear model will not. For example, instead of seeing a constant effect depending on the level of income you will see a constant percentage increase in expenditure given a percentage increase in income. If your base income was $5,000 and you increase 10% you may see a 5% increase in expenditure difference. But if your income increases by 30% you will see a 15% difference in expenditures where in levels you would multiply the coefficient by $750 and find a directly linear change in expenditures.
All of this is explained in more detail at this link.
https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faqhow-do-i-interpret-a-regression-model-when-some-variables-are-log-transformed/
Best,
Aran
If I were to complement BMA with non-Bayesian econometric models of international trade, I would focus on literature on gravity models of trade. A few references are "The log of gravity" and "Gravity with gravitas." Hope it helps.
http://www.mitpressjournals.org/doi/abs/10.1162/rest.88.4.641
https://www.aeaweb.org/articles?id=10.1257/000282803321455214
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