Omitted variables in gravity model I'm trying to construct a gravity model for EU trade flows using a panel dataset, but am suffering from what appears to be a persistent omitted variable problem. My residuals display a queer log-like, almost polynomial type pattern when plotted against the log of trade volumes. 

I have searched the literature and included every variable in the model that has appeared in previous studies, including the logs of;
- gdp per capita
- real and nominal gdp
- distance - multiple different measures.
- Real and nominal exchange rates. 
- Price levels - various measures. 
- Proxies for product differentiation. 
- Exporter / importer fixed effects. 
- Dummies for things like Schengen / Euro membership, home trade, etc. 
Still, the curvilinear / log pattern remains. 

Can anyone conjecture as to what the omitted variable may be? I have exhausted my knowledge of the theory. 

Any help would be very gratefully appreciated. 

Many thanks, 

Robert.
The omitted variable bias in gravity model is an important issue given that some factors are unobserved or difficult to quantity. To solve this issue trade economists tend to rely on various fixed effect estimators. But, the question is what is your variable of interest?

Exporter-by-year and importer-by-year fixed effects 

For instance, if you are interested in evaluating the effect of trade costs on trade, you can introduce exporter-by-year and importer-by-year fixed effects to absorb GDP, GDP per capita, price indexes etc.

Exporter-by-importer fixed effects

If you are interested in evaluating the effect of one country-specific variable on trade, you can introduce exporter-by-importer fixed effects to absorb distance or contiguity effects.

Exporter-by-year, importer-by-year + exporter-by-importer fixed effects

If you are interested in evaluating the effect of a time-varying bilateral factor, like free trade agreements, on trade (see Baier and Bergstrand, 2007), you can introduce exporter-by-year, importer-by-year + exporter-by-importer fixed effects to absorb distance or contiguity effects as well as GDP, GDP per capita, ....

References


Baier, S. L., &amp; Bergstrand, J. H. (2007). Do free trade agreements actually increase members' international trade?. Journal of international Economics, 71(1), 72-95.
Baldwin, R., &amp; Taglioni, D. (2006). Gravity for dummies and dummies for gravity equations (No. w12516). National Bureau of Economic Research.
Head, K., &amp; Mayer, T. (2013). Gravity equations: Workhorse, toolkit, and cookbook. This last reference is a must to read to construct a gravity model.