The Pleb Economist #6: Analysis of Trump's Reciprocal Tariff Calculations1
The Trump administration's own reasoning
First, it's always best to get it from the horse's mouth, so here's the link to the official press release: https://ustr.gov/issue-areas/reciprocal-tariff-calculations
The TLDR is that Trump's tariffs are not reciprocal tariffs per se.
A reciprocal tariff would say something like: "You're charging X% tariff on our goods, so we're gonna charge f(X)% tariffs on your goods!"
But that's not what's going on. Rather, Trump's tariff rates are the rates that allegedly are needed to balance bilateral trade flows between two countries.
The reasoning the Trump administrative gives for why we can't just do direct reciprocal tariffs is as follows:
To conceptualize reciprocal tariffs, the tariff rates that would drive bilateral trade deficits to zero were computed. While models of international trade generally assume that trade will balance itself over time, the United States has run persistent current account deficits for five decades, indicating that the core premise of most trade models is incorrect.The failure of trade deficits to balance has many causes, with tariff and non-tariff economic fundamentals as major contributors. Regulatory barriers to American products, environmental reviews, differences in consumption tax rates, compliance hurdles and costs, currency manipulation and undervaluation all serve to deter American goods and keep trade balances distorted. As a result, U.S. consumer demand has been siphoned out of the U.S. economy into the global economy, leading to the closure of more than 90,000 American factories since 1997, and a decline in our manufacturing workforce of more than 6.6 million jobs, more than a third from its peak.
In other words, the Trump administration's argument proceeds as follows:
- Bilateral trade flows should balance themselves out naturally over time.
- Bilateral trade flows haven't balanced themselves out.
- The reason they're not balanced is that other countries manipulate their currency, subsidize their domestic industries, or put up other barriers that unfairly bias their economy against American-made goods. These barriers can be thought of as an implicit tariff, even if the explicit tariff rate on American goods is low.
- Therefore, the US needs to raise its own tariffs in response, to balance out bilateral trade flows.
Where I would quibble with this chain of thought is actually just on point 1. Yes, maybe in some general equilibrium models with certain assumptions, you'll get long-run balanced trade.2 I'm not even so sure about that, but let's grant that to be the case. The problem is that this would still just be the result of some academic, theoretical model that almost surely omits key, uncomfortable details about the real world---details like American imperialism, the petrodollar, and money printer go brrrr. Regardless of what theoretical models say about it, I'm skeptical that America's trade imbalances are solely, or even primarily, caused by protectionist policies of other countries.
Does the math make sense?
Let's now take a look at Trump's actual equation:
\Delta \tau_i = \frac{x_i - m_i}{ \epsilon \times \varphi \times m_i}x_i: current exports from USA to countryim_i: current imports from countryi\epsilon = \frac{\partial m_i / m_i}{\partial p_i / p_i}: elasticity of imports with respect to import prices (\epsilon < 0)\varphi = \frac{\partial p_i / p_i}{\partial \tau_i}: the passthrough of tariffs to import prices (\varphi > 0)
The equation allegedly gives us
\Delta \tau_i, the amount by which current tariffs would need to change in order to balance the bilateral trade flow between the USA and country i.To understand the equation, we'll first write an equation for the change in imports as a function of the change in tariffs:
\Delta m_i = \frac{\partial m_i}{\partial p_i} \frac{\partial p_i}{\partial \tau_i} \Delta \tau_i Essentially, this tells us that the change in tariffs (
\Delta \tau_i) affects import prices p_i through \frac{\partial p_i}{\partial \tau_i}, which in turn affects imports m_i through \frac{\partial m_i}{\partial p_i}. So far so good.Next, we note that in order to balance the trade deficit, we want
x_i - (m_i + \Delta m_i) = 0, which translates to \Delta m_i = x_i - m_i. So, we want \Delta \tau_i to satisfy:x_i - m_i = \frac{\partial m_i}{\partial p_i} \frac{\partial p_i}{\partial \tau_i} \Delta \tau_ior, rearranging:
\begin{align}
\Delta \tau_i &= \frac{x_i - m_i}{\frac{\partial m_i}{\partial p_i} \frac{\partial p_i}{\partial \tau_i}} \\
&= \frac{x_i - m_i}{\epsilon \times \varphi \times m_i}
\end{align}So at least the math isn't wrong, per se. It starts from a simple rate equation and derives the change in tariffs necessary to bring trade deficits into balance. But there's a big caveat.
The caveat
The big caveat is related to the selection of the parameters
\epsilon and \varphi. Others have written about why they were selected incorrectly, but there's an even bigger problem.The bigger problem is that you can't treat these parameters as constant.
\epsilon and \varphi are driven by human behavior, and if you do something like ignite a global trade war, peoples' behaviors are going to change. For example, if global aggregate demand drops sharply, that's going to predict a decline in both x_i and m_i that isn't captured by current estimates of \epsilon and \varphi. Thus, you can't treat \epsilon and \varphi as constant, nor can you assume that these are the only two channels by which bilateral trade flows are affected.Lastly, the equations are only about bilateral trade flows and do not take into account any other factors such as GDP or overall well-being. It seems like a short sighted and narrow minded policy to me.
A misleading chart
Trump's much bandied about chart on reciprocal tariffs is therefore quite misleading.
The left hand side of the chart says "tariffs charged to the US", but that is explicitly not true.
Instead, the left column is actually just
\Delta \tau_i! And the right column is just \Delta \tau_i divided by two, with a minimum of 10%. The left column has nothing to do with the actual tariffs charged by other countries!So, this is a totally misleading chart and makes other countries tariff behavior look worse than it is.
tl;dr
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Trump's tariff policy is motivated by a desire to balance out bilateral trade flows.
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It operates on the (IMO) faulty assumption that trade flows should balance out over time in the absence of any trade restrictions. Thus, any imbalances are a sign of unfair trade policies.
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Moreover, it's not actually a reciprocal tariff policy. It uses a faulty model to try and set the tariff to the rate needed to balance out bilateral trade flows.
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In my opinion, this is a pretty bad sign of incompetence from the Trump administration.
I called out our health officials' incompetence with regard to COVID policy back during the Biden administration, and I'm not afraid to call out our trade officials' incompetence during the Trump administration. Seems like there's plenty of incompetence to go around.
Footnotes
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The Pleb Economist is a
weekly(not quite) weeklywhenever I feel like it column where I share my thoughts as a mainstream economist who is slightly jaded by mainstream economics. I also have a somewhat libertarian and rebellious bent, as well as a deep conviction in the utility of Bitcoin. ↩ -
I'm not a trade economist, so don't ask me to find the models that show this. I'm sure I could, with enough time, but for a quicker answer you're probably better off asking ChatGPT. I only admit to the possibility of it. ↩