Micro-level data have had a profound influence on research in international trade over the last ten years. In many regards, this research agenda has been very successful. New stylized facts have been uncovered and new trade models have been developed to explain these facts. In this paper we investigate to which extent answers to new micro-level questions have affected answers to an old and central question in the field: How large are the gains from trade? A crude summary of our results is: “So far, not much.”
What they’re saying is:
Our analysis focuses on models featuring five basic assumptions: Dixit-Stiglitz preferences, one factor of production, linear cost functions, complete specialization, and iceberg trade costs… A common estimator of the gains from trade… only depends on the value of two aggregate statistics: (i) the share of expenditure on domestic goods, which is equal to one minus the import penetration ratio, and (ii) a gravity-based estimator of the elasticity of imports with respect to variable trade costs, which we refer to as the “trade elasticity.”… within that particular, but important class of models, the mapping between trade data and welfare is independent of the micro-level details of the model we use…
A direct corollary of our analysis under perfect competition is that two very well-known gravity models, Anderson (1979) and Eaton and Kortum (2002), have identical welfare implications. In Anderson (1979), like in any other “Armington” model, there are only con- sumption gains from trade, whereas there are both consumption and production gains from trade in Eaton and Kortum (2002). Nevertheless, our results imply that the gains from trade in these two models are the same: as we go from Anderson (1979) to Eaton and Kortum (2002), the appearance of production gains must be exactly compensated by a decline in consumption gains from trade.
Trade Diversion 
The thing that might be a bit misleading… they’re looking at a change in trade costs at the margin and they find small gains from it. That doesn’t tell us anything about the gains from trade in a larger context, i.e. versus autarky.
They say:
“We then use our assumption that epsilon is constant across equilibria to integrate small changes in real income between the initial trade equilibrium and the autarky equilibrium. This allows us to establish that the total size of the gains from trade, i.e. the percentage change in real income necessary to compensate a representative consumer for going to autarky, is equal to lambda^(1/epsilon)-1.”
Sorry, my fault.
I can’t imagine, though, what it would mean to cut most countries off from world oil markets.