The Gains From Trade Are Large

But, we really don’t know how large

It may come as a surprise that economists, if asked what the gains from trade are, will often say “not very large”. Works like “New Trade Models, Same Old Gains?” or “The US Gains From Trade” or “Trade Theory with Numbers” estimate that the losses from the United States totally blocking international trade would reduce GDP by 1 to 8 percent. This isn’t small – but it’s also surprisingly not large. This is a level increase, not a rate increase, so we can say that a hypothetical US moving from no trade to our present level would essentially gain between 1 and 4 years of economic growth. By comparison, estimates of the removal of transnational labor barriers, or open borders, would approximately double world GDP.

It is my firm belief that the gains from trade are, in fact, quite large. The reason for this is that the papers cited earlier all have to make extremely strong assumptions about the unobserved parts of the economy to work. When these assumptions are deviated from, they consistently increase the gains from trade. Thus, the low estimates are the lower bound for the gains from trade. Furthermore, we are actually far less confident in our estimates of the gains from trade than may appear. This is not to say that we do not know the direction of the effects, but estimating their magnitude requires knowing the relevant elasticities for things which we have not yet observed. I will take this subject up in a later blogpost.

Returning to the subject of low estimates, take “New Trade Models, Same Old Gains?”. Fundamentally the paper is giving an equivalence result between various trade models, of which one is the so-called “Melitz Model”, after Marc Melitz who created it in 2003. In it, we break the assumption of identical firms, and allow them to have varying levels of productivity. When trade becomes possible with another country, we assume that firms face a fixed cost to enter the market at all. As a result, the firms which export are the larger and more efficient ones, and as trade becomes freer business is reallocated to the more efficient ones. What Arkolakis, Costinot, and Rodriguez-Clare do is show that, so long as there is a Pareto distribution of firms by productivity, the gains from trade can be completely found from the share spent on imports, and the elasticity of these imports with respect to trade costs. We can abstract away from the microeconomic organization of firms entirely – all that matters is very easily obtained macroeconomic aggregates.

But this small estimate doesn’t line up all that great with actually observed gains from trade. It turns out that those estimates absolutely, positively, require a Pareto distribution of firm productivities. In other words, firms draw from a distribution which gets thinner and thinner as it increases. If you break this, the results change dramatically. Melitz and Redding (2015) show this sensitivity with simple examples, and arrive at least four times as high as in ACRc. The reason for this is that you need the Pareto distribution to make the elasticity always the same. If you are estimating the elasticity using a change from a 11 to a 10 percent tariff, there is no reason to think that a 10 to 9 percent tariff would have the same elasticity if there is not a Pareto distribution.

Nor is that the only way in which adding messiness increases the gains from trade. For example, the gains from trade might come from new products and new varieties. If firms have to pay fixed costs to enter, and they anticipate tariffs, then there will be otherwise profitable products never made. This makes the losses from a tariff much larger. Or allow for mark-ups, or the difference between price and marginal cost, to vary, as in Melitz and Ottoviano (2008) (This was best explained in Melitz and Trefler (2012)). You get this when you drop the assumption of constant elasticity of substitution, which would otherwise imply a constant markup. When market size expands, both the number of people you can sell to, and the stiffness of competition, increases. Firms with a low marginal cost are benefited more by the former than they are hurt by the latter. Arkolakis, Costinot, Donaldson, and Rodriguez-Clare argue against this, but their results are once more dependent upon a Pareto distribution of firms. Varying markups is the weakest channel for gains from trade, because it can actually plausibly reduce the gains from trade relative to counterfactual if preferences are non-homothetic. (In other words, if there are two goods, the proportion you choose of the two varies as your income varies. Homothetic preferences means that the proportion always stays the same.) Rising income means that you purchase relatively more of the goods with the highest markups.

Something I find striking is that, while the structural estimates of trade are likely low estimates, the structural estimates of immigration are likely high estimates. They generally assume that labor is identical and differences in wage rates are explained by each country have a different production function. Equilibrium is prevented by barriers. (See Moses and Letnes, (2004) for a discussion). Obviously, if labor is not identical, this breaks down! And especially since we would expect the most skilled people to move first, this is especially relevant in studies of labor misallocation in the United States. For example, Hsieh and Moretti (2019), which famously estimated that US output would be 36% higher between 1964 and 2009 if New York, San Francisco, and San Jose had zoning policies in line with the rest of the nation, is fairly sensitive to assuming that people’s higher productivity in San Francisco is due to something about the city. This does not mean that immigration is bad, or that labor reallocation isn’t important – I’ve previously argued that it’s extremely important, especially in the developing world!

This will tie into a later blog post (still in the works) on the contribution of human capital to income. If capital accumulation, physical and human, can explain growth, then there isn’t all that much in the way of possible gains from immigration in a world of free trade. If it can’t, and there is still a large unexplained residual from productivity, then immigration can have very large effects. I am, to be frank, up in the air on what to believe. The whole enterprise of identifying the relative importance of human capital from cross-country regressions is frankly not very believable, and not very well-identified.

I totally understand if this article was very hard to understand on first read. This area of trade theory was something I first read with more interest than comprehension. It took me a long time to actually grasp the essence of the papers – to understand why they came to different estimates from each other. I hope to skip over the very difficult bits, and straight to comprehension, but this may be no substitute for going and reading the papers yourself. This will take time, but it is worth it! Trade is a fun and enjoyable topic. If you are ever stuck, or don’t understand why something is the way it is, LLMs are extremely good now at answering these questions. I also urge you to consult lecture slides, which are frequently available. Many of these models have made their way out of the journals and into the classroom.