By now you’ll surely have seen the Trump administration’s self-cancelling and probably back-engineered tariff formula, as summarised below by a Stinson Dean tweet:
But it’s not the only bit of padding in the tariff policy note posted overnight. In the “references” section is an academic paper not mentioned in the main text: Trade Wars with Trade Deficits (2024) by Pau Pujolas and Jack Rossbach.
The paper starts with an idea associated with Canadian economist Harry Johnson: trade wars in general are counter-productive nonsense, but the country with the higher elasticity of substitution between domestic and imported goods can still claim victory. A trade deficit is similar to having a more elastic demand than the trading partner, say the authors.
Here’s what the lead author, Pau Pujolas of McMaster University in Canada, told FT Alphaville by email:
The work was done using the trade war between the US and China in 2018, it is not about the tariffs just announced.
Our paper shows that bilateral trade deficits change the way we have been understanding trade wars so far. I suspect that is the reason why the Trump administration is using the paper. It became somewhat well-known when we first put the pre-print on SSRN, as it is changing the way people should look at trade wars.
In a nutshell, the way people have been thinking about a trade war is like the Prisoner’s Dilemma: if I set tariffs and you don’t, I win, and you lose. If we both set tariffs, though, we are both made worse off.
But our results show that this result starts to crumble when there is a trade deficit: if I buy products from you and you don’t buy them from me, I can tariff you but you can’t tariff me, so I will reap the benefits of a impoverishing you, and you can’t do anything about it.
Hence, when trade deficits arise, the question about a trade war is quantitative: how much does the mechanism we uncover matter?
The paper uses a big-data trade model to figure out what tariffs a country should set and the likelihood of victory. Its authors add in a Spanish-language blog post published in January that the US could theoretically win a trade war against China, but the tariffs imposed in Trump’s first term were so poorly designed that both sides lost.
Pujolas told FTAV:
For a country like the US against a country like China (with a large trade deficit and also with rather large tariffs from China to the US) the US wins from starting a trade war. Similarly, against Canada. But we find that the US should not do that against, say, the European Union. Also, we find that the tariffs should be in the range of 10 per cent to 25 per cent. Making them higher is a bad idea for the United States.
And this is where the discrepancies between our work and the table that President Trump showed arises. Our results arise from a heavily computational exercise. We use supercomputers to find the optimal tariffs. The Trump administration seems to have taken a bit of a shortcut there. Also, our results suggest that the EU should not be tariffed, and yet they set high tariffs against them. Finally, our range of optimal tariffs is substantially lower than the ones the Administration just announced.
Jack Rossbach, of Georgetown University, the paper’s co-author, added:
I think the announcement shows we’re in a situation where it’s less about the specific numbers, and more a signal of how the administration expects things to proceed. If you want continued access to the US market, the administration is telling countries to come one-by-one to the negotiating table and start making offers.
It remains to be seen how countries will react to this. We may start seeing countries announce lower tariffs, improved market access, or commitments to buy more American goods to avoid these tariffs. If you import as much from the United States as you export, then the formula in the announcement says you’ll face zero tariffs. It’s also possible that countries might start retaliating. The paragraph in the announcement where they say the elasticity is 2, but we were conservative and went with 4, signals that the United States is happy to double these tariffs if countries try to fight instead of looking to negotiate. The passthrough talk is a signal that the administration will be closely watching how firms adjust their prices in response to the tariffs.
We’ll have to wait to see what actually happens. An all out trade war is going to have a very different impact than a joint investment venture.
We also checked in with Anson Soderbery of Purdue University, whose 2018 paper Trade elasticities, heterogeneity, and optimal tariffs gets a Trump citation. He told us:
While I do not believe reducing the US trade deficit through tariffs should be a central policy goal, if policymakers insist on this path, I urge against reductionist policy. That is to say, there are more efficient ways to craft trade policies to reduce trade deficits than a universal tariff ignoring industry and partner specific effects of tariffs.
Another paper cited in the main text, The Long and Short (Run) of Trade Elasticities (2023), is co-authored by University of Michigan’s Andrei Levchenko. Here, in full, is what he told us:
The goal of the import tariffs is to reduce imports: the higher are the tari&s, the lower imports will be. But how much lower? The formula used requires a number that gives the percent change in imports that will result from a 1% change in tariffs (called the “trade elasticity, or e in the document).
Our paper [ . . . ] is cited as a source for an estimate of this number. This note argues that our elasticity estimate should not be directly applied in this tariff calculation. The key reason is that the concept of the trade elasticity holds everything else constant (in technical terms, it is a “partial equilibrium elasticity”). This characterization applies equally to every other estimate of the trade elasticity, including the other papers cited.
In practice, everything else will not be constant. In particular, US exports (labeled xi in the document) could change. That can come from a variety of channels, but one important one is tarff retaliation by trading partners. If a trading partner puts tariffs on US exports to it, they will fall, (at least partially) un-doing the impact of lower imports on the trade deficit.
Beyond this, there are many other ways in which the change in US imports and exports will differ from the formula that directly applies a partial equilibrium trade elasticity. For example, trade elasticity estimates do not account for any impact of the change in tariffs on wages, prices, exchange rates, and the stock market. Those can go in different directions depending on the country, the product, the production technology used, etc.
For small tariff changes on individual products from individual countries, these changes might be small and could reasonably be ignored. However, the change in imports and in the bilateral trade balance implied by the partial equilibrium trade elasticity is likely to be unreliable when the tariff change is large and comprehensive (covering all goods), as is the case today. There is a way of assessing the change in imports and bilateral trade balances with large tariff changes. That would require a large-scale model of world trade with many countries, goods, adjustment mechanisms, etc. Our elasticity estimate would be one of many inputs into such a model.
And we spoke to Brent Neiman, of University of Chicago, whose co-authored work may or may not be cited in the explainer. There’s a citation in the main text to “Cavallo et al, 2021”, which might refer to Tariff Pass-Through at the Border and at the Store: Evidence from US Trade Policy — by Alberto Cavallo, Gita Gopinath, Brent Neiman and Jenny Tang — but there’s nothing in the actual reference section.
Neiman told us:
It is not clear what the government note is referencing or not from our work [ . . . ] But I believe our work suggests a much higher value should be used for the elasticity of import prices to tariffs than what the government note uses.
The government note uses a value of 0.25 for ‘the elasticity of import prices with respect to tariffs’, denoted with the Greek letter phi. But our estimates found a value of 0.943 — very close to 1 — for this elasticity. 0.943 is obtained using the very first number in Table 1, which equals -0.057. To translate this to their phi, you have to add 1 to this value, i.e. 0.943 = 1 — 0.057.
In non-technical terms, we write in the introduction to our paper, “ . . . our regressions suggest that a 20 per cent tariff, for example, would be associated with a 1.1 per cent decline in the ex-tariff price, and an 18.9 per cent increase in the total price paid by the US importer.” (Bolding added.) The government note assumes, I believe, that a 20 per cent tariff would only cause a 5 per cent increase in the price paid by the US importer.
I do not agree that the government calculation is an appropriate way to think about reciprocal tariffs. That said, using a value of 0.25 in their calculation, compared to a value closer to 1, results in reciprocal tariffs that are four times larger.
All in all, it’s a bit sloppy.
A paper about how tariffs need to be cleverly designed and carefully applied — and how Trump failed on both measures during his first term — is an odd thing to reference for a policy whose core formula is “divide this by that”. But to be fair, there’s no evidence that anyone involved in preparing the document has read it.
