Why those tariff numbers?

Explaining a dumb thing

So Trump put tariffs on every other country in the world yesterday, except for Russia and North Korea. (Really.) The tariffs are much higher than anticipated; people were expecting an average rate of around 15%, and it looks like the total amount is almost double that. Why are the tariff rates so high?

Some Twitter sleuths figured out that it looks like the tariff rates are, for every country, set by the simple formula of min(10%,(Trade deficit/total imports)/2). An indignant White House Deputy Press Secretary, one Kush Desai, responded that, in fact, tariffs were set by the following formula (which was then divided by two out of a sense of mercy):

But do the basic work of unpacking what those variables say, then look at the supplementary material below in that post, and you’ll see that ɛ̝ is 4 and φ is .25, so the change in the tariff rate (∆τ) is just (x-m)/m, which is the trade deficit (exports - imports) divided by total imports. Divide by two to get the final tariff rate. So the Twitter sleuths were right.

What is going on here? I’ve seen a few attempts to explain the math, but none really hits the nail on the head. I’ve read the supplementary materials a couple times (it’s short), and it’s not too hard to understand (modulo one point I’ll come back to shortly). So let me explain it to you. PLEASE NOTE: This is an explanation, not a justification. All of this is dumb.

So Trump’s basic starting point is that he thinks trade deficits are bad. They’re not, but he thinks they are. He has this very dumb idea that a trade deficit is a deficit of trade, and the dollar amount of the trade deficit is the amount that other countries are cheating us out of through nefarious… I dunno, trading?

So his solution to this injustice is to try to inflict an equal and opposite amount of damage to the other country’s economy. If they’re taking X dollars from us in trade deficit, we’ll take X dollars from them in tariffs. And that’s precisely what the formula is supposed to do. The other country is stealing X dollars from us (per the trade deficit), so we’ll take X dollars right back (with a tariff).

So, a toy example: Suppose that there is another country that we import $100 of goods from and export $21 of goods to. That’s a trade deficit of $79. So the goal is to inflict $79 of damage to them by using tariffs. If we’re trying to inflict $79 worth of damage by putting tariffs on $100 of imports, that would mean a 79% tariff rate on those $100 of imports. We get that 79% number by dividing the trade deficit ($79 in our example) by the total number of imports ($100 in our example). And hey! That’s the formula that Desai shared. So that’s pretty much the whole story.

What about that ɛ̝ and φ though? Well, in one sense, they don’t matter. The White House team assigned values to those variables that directly offset so they don’t have an impact on the final calculation. But what are they doing in the equation to begin with? They’re in there because every $1 of tariffs doesn’t inflict $1 of economic harm. First there’s a question of passthrough rate (basically, how much of the tariff gets through to impact the economy). And second there’s a question of elasticity (basically, is there a multiplier of some sort which magnifies or shrinks the total effect on the economy). The White House says that only 25% of the tariffs will get through, but the effect will have a 4x multiplier effect, and so those cancel out to a 1:1 net effect for every dollar of tariff raised.

Now I’m pretty sure that they’re making a mistake with how those numbers are applied. The passthrough effect and elasticity are, I’m pretty sure, measures of the effect of tariffs on the domestic market, not on the foreign market. So the logic here seems to be something like “If Uruguay (or whoever) is stealing $1B of money from us through a $1B trade deficit, we want to put tariffs on imports from Uruguay that will hurt US consumers by precisely $1B.” So as far as I can tell, the approach here is to shoot the US economy in the foot by the EXACT AMOUNT of the trade deficit. (That’s not how they think of things, of course, but I’m pretty sure that’s what their equation will yield.)

But even if I’m getting that wrong and the White House has indeed correctly come up with a formula that will inflict pain on other countries in the exact amount of the trade deficit, this is still a very stupid thing to do.

For one thing, again: trade deficits are not bad, we are not getting ripped off in any sense, and retaliating for the exact amount of the trade deficit is approximately the stupidest thing you can do.

For another thing, this is being pitched as a way to balance out trade, to take back the exact amount that was stolen from us (again, it wasn’t stolen). But the elasticity multiplier is about net impact on the economy, not a multiplier to gains from trade. So if a $1B tariff will only pass through 25% ($250M), and that has a multiplier of 4 on top, we’d be getting $250M from the tariff but inflicting $1B in damage to the other economy. Good for vengeance, bad for balancing trade. (I’m not sure about this point, though; the reasoning around elasticities and pass-through is very under-explained.)

But finally, and most importantly, the tariff calculation is made “Assuming that offsetting exchange rate and general equilibrium effects are small enough to be ignored.” And that is absurd. These tariff rates are the highest since the 1910s, higher even than the Smoot-Hawley tariffs that caused the great depression. The exchange rate and general equilibrium effects will not be small enough to be ignored. They will be absolutely humongous. The exchange rate effects are complicated and might, on net, be slightly positive. But the general equilbrium effects are where the horror lies. “General equlibrium” is econ-speak for talking about the total state of all the important variables in the economy (employment, output, interest rates, inflation, etc etc etc). So the White House’s calculations assume that the total effect on the overall economy from these massive tariffs will be “small enough to be ignored.” Reader, they will not be.

And exchange rate and general equlibrium effects aside, this leaves out the political dimension of the analysis. When countries get tariffs levied on them, they generally respond by retaliating and raising tariffs of their own. This is precisely what we should expect, and the effects of that on both the US economy and global trade will be profoundly terrible.

So there you have it! That’s the logic behind the size of Trump’s tariffs. It is not completely logically incoherent. But it is still very dumb, and bad things will result.

Happy Liberation Day!