How international trade is shaped

But what does the seemingly universal applicability of the gravity equation tell us? Mr. Davidson suggests in his piece that it’s an indication that policy can’t do much to shape trade. That’s not where I would have gone, and it’s not where those who have studied the issue closely have gone.

Here’s my take: Think about two cities with the same G.D.P. per capita (we can relax that assumption in a minute). The cities will trade if residents of City A find things being sold by residents of City B that they want, and vice versa.

So what’s the probability that a City A resident will find a City B resident with something he or she wants? Applying what one of my old teachers used to call the “principle of insignificant reason,” a good first guess would be that the probability is proportional to the number of potential sellers - City B’s population.

And how many such desirous buyers will there be? Again, applying insignificant reason, a good guess is that it’s proportional to the number of potential buyers - City A’s population. So other things being equal, we would expect exports from City B to City A to be proportional to the product of their populations.

But what if G.D.P. per capita isn’t the same? You can think of this as increasing the “effective” population, both in terms of producers and in terms of consumers. So the attraction is now the product of the G.D.P.s.

Is there anything surprising about the fact that this relationship works pretty well? A bit. Before 1980, standard trade theory envisioned countries specializing in accord with their comparative advantages - for example, Britain does cloth, Portugal wine. And these models suggest that how much countries trade should have a lot to do with whether they are similar or not. Cloth exporters should trade more with wine exporters and less with themselves. In reality, however, there’s basically no sign of any such effect: Even seemingly similar countries trade about as much as a gravity equation says they should.

Calibrated models of trade have long dealt with this reality, somewhat awkwardly, with the so-called “Armington assumption,” which simply assumes that even the same good from different countries is treated by consumers as a differentiated product - a banana isn’t just a banana, for instance, it’s an Ecuadorean banana or a Saint Lucian banana, which are imperfect substitutes. A new trade theory that some of us introduced around 1980 - or as some now call it, the “old new trade theory” - did a bit more, by introducing monopolistic competition and increasing returns, to explain why even similar countries produce differentiated products.

And there’s also a puzzle about both the effect of distance and the effect of borders, both of which seem larger than concrete costs can explain. Work continues.

Does any of this suggest the irrelevance of trade policy? Not really. Changes in trade policy do have obvious effects on how much countries trade. Look at the chart to see what happened when Mexico opened up to trade starting in the late 1980s as compared to what happened in Canada, which was fairly open all along - and which, like Mexico, mainly trades with the United States.

So what does gravity tell us? That simple Ricardian comparative advantage is clearly incomplete; and that the process of international trade is subtler, with invisible as well as visible costs. This is not trivial, but it’s not particularly unsettling either. And gravity models are very useful as benchmarks for assessing other effects.