The Tariff Calculation and Bad Goals
The calculation isn’t as bad as you think — given the goal is to balance trade (a Bad Goal)
The calculation for the tariff rate is not actually “crazy,” given that your goal is to “balance” trade, a Bad Goal (BG).
Let m(p) be imports as a function of import price p. Let r be passthrough from a tariff increase to import prices. Let t be a tariff. We have: m(rt p) imports after applying the tariff.
Okay, now say your goal is to equalize trade. Let x be exports. That means you want: x — m = 0
A first order approximation gives that a change in tariffs will change imports by dt x (d log m/d log p) x m x r, so letting m(0) be current imports and setting equal to zero to balance trade:
Re-arranging gives:
The administration then searched the literature for reasonable elasticity and passthrough rate values. I don’t know this empirical literature well enough to know whether what they chose was good or bad, but they ended up with r = 0.25 and (dlog m/dlog p) = 4. Or:
Which is where the much-pilloried ratio comes from.
Now, many very subtle things are going on here, and I’ll point out some issues with it as a calculation. Still, I first just want to stop and reiterate: if I were handed this task at work, couldn’t push back on the goal, and just had to do it, I don’t think this particular approach is crazy. It has issues, but it’s not nearly as strange as it initially looks.
The size of the resulting tariffs is also not that surprising. I suspect we would need pretty massive tariffs to achieve “balanced trade.”
[ The problem is that it’s silly to want to balance trade. When, on net, people send you goods and services and you send them green pieces of paper, you are not “losing”. Trade is all a bunch of transactions people want to make. Importers aren’t losing. They’re parting with green pieces of paper in exchange for goods they’re willing to give up that paper for. ]
There are some issues, even given the BG, of course, but that would be true of any feasible, transparent method the admin might have used here:
The calculation assumes exports don’t respond to tariffs. By increasing our cost of production, our ability to supply exports is worse, so exports fall as well, putting aside the fact that, of course, other countries will retaliate with tariffs of their own. Both of these factors imply that tariffs will reduce exports as well.
I get why the team decided not to model that. There’s probably not a simple, transparent way to get that export effect. You’re going to have to make specific assumptions about the strategic responses of other countries, which you might not want to do publicly, even aside from how difficult it would be to say with any certainty what will happen. They might have gotten at the increased cost of producing exports by splitting imports into final and intermediate goods. But maybe the literature doesn’t have as much on the required elasticities to turn that into an export effect.
Bringing this back to what this blog is usually about, this situation shows the challenges of balancing the fact that, as a Data Scientist/Economist/etc, you ultimately have a job and need to help your employer reach their business goal while also advising on what that goal should be.
Thankfully, most of us have employers who value our input on the goal more than the folks in this situation. But to effectively push back on BGs, we need to actually know something about how the business operates and how our product works. If all we know is statistics, then that’s the only thing we’ll be asked for input on—and rightly so.
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