President Trump has announced “reciprocal” tariffs on other countries. This usually means the US matched the foreign countries’ tariff rates. But this administration needs to warp definitions to suit their story. Here’s yet another example.
A Comparison
CNBC put together a comparison of Trump’s tariffs with the actual rates charged by other countries.
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As you can see, the Trump estimates are always larger than the actual tariffs charged by those countries.
Some Math
Instead of looking at other countries’ tariff rates, his economic team (Peter Navarro, here and here and here) decided to use this equation:
As noted, ε is the price elasticity of demand for imports and φ is the “passthrough rate,” the percentage of a tariff that will be passed through to the prices of products (the price elasticity of import supply). This calculates the tariff that will make the balance of trade equal to zero. At least, that’s what happens if the elasticities don’t change.
Say What?
Because “economists” like Peter Navarro are incapable of dealing with complexity, they (laughably) assumed demand elasticity was 4 and supply elasticity was 0.25. Conveniently, multiplying those two equals 1.0, giving the equation they actually used:
Assume m = 100 and x = 90. Then
The result is Δτ = -0.10. As long as nothing else changes, a 10% tariff will reduce imports by 10% so m = 90 and no further tariffs are required. Imports fall by 10% because of the assumptions we made about demand and supply elasticity. As we’ll see, those assumptions are not borne out by reality.
Where to Begin?
There are so many things wrong with this, it’s difficult to know where to begin. I’ll start with the price elasticity of demand for imports. Navarro assumed 4. I did some research. The best, most recent, paper I could find was by Shon M. Ferguson and Aaron Smith, “Import demand elasticities based on quantity data: Theory and evidence.”[1] Their estimates of import demand elasticity range from 1.08 to 3.37. Only three estimates are greater than 3.37 and all three are the upper bound of the value-based elasticities. An elasticity of 4 is too high. I’ll use values of 1.08, 3.37, and 2.225 (the average of the two estimates).
Alberto Cavallo, Gita Gopinath, Brent Neiman, and Jenny Tang estimated passthrough rates (among many other things) for the U.S.[2] Their best estimate is about -0.8 after one year. Here’s how the authors interpret this result:
The estimated coefficient of -0.079 means, for example, that a 10 percent tariff would be associated with a 0.8 percent lower ex-tariff price and a 9.2 percent higher overall price faced by the importer.
Thus, the passthrough rate is 92%. Here’s the summary:
| Elasticity | 1.08 | 2.225 | 3.37 |
| Elasticity x Passthrough | 0.994 | 2.047 | 3.100 |
Essentially, the product varies from 1 to 3. The low estimate is 1 (the value used by Navarro).
Implications
Using the version of the equation that includes ε and φ, we have the following possible equations:
In other words, if ε*φ is 0.994, the required tariff will be greater than implied by equation (2). If ε*φ is 2.047 or 3.100, the required tariff will be less than implied.
Conclusion
As is so often the case, making assumptions is far easier than doing actual research. And the results are usually wrong. Bad policy is often the result of bad research. Don’t do that.
- Ferguson, Shon M., and Aaron Smith (2022). “Import demand elasticities based on quantity data: Theory and evidence.” Canadian Journal of Economics, 2022:55(2) May, 2022, pp. 1027-1056. ↑
- Cavallo, Alberto, Gita Gopinath, Brent Neiman, and Jenny Tang (2019). “Tariff Passthrough at the Border and at the Store: Evidence from US Trade Policy.” National Bureau of Economic Research Working Paper 26396, October, 2019. National Bureau of Economic Research, Cambridge, MA. ↑
