Lerner Symmetry

Uncommon sense about tariffs

I wanted to refresh my memory about the Lerner Symmetry Theorem, and thus decided to ask ChatGPT this question:

Is the effect of a 10% tax on all imports equivalent to a 10% tax on all exports? And does the answer depend on whether trade starts from a balanced position?

Before getting to the response, let me reiterate that these exercises are not an attempt to criticize ChatGPT. (FWIW, I lean toward David Sachs’ view of AI.) I’m more interested in learning the conventional wisdom on these issues and simply use LLMs to get a quick take on the subject. In addition, ChatGPT reminded me of all the assumptions required for Lerner Symmetry to hold, which I would have been unable to cite without checking an international trade textbook. And finally, I use the free version of ChatGPT available on the internet, and more expensive versions are undoubtedly better.

ChatGPT provided a four-part answer summarizing how the two taxes have different effects, which is too long to reproduce here in full. Part one contained this summary sentence:

So, they affect different sides of the trade balance — consumption vs. production — and will have different distributional effects within the economy (consumers vs. producers).

Part 2 was quite different:

2. Symmetry Under Economic Theory (Lerner Symmetry Theorem)

In theory, under certain assumptions, a tax on imports is equivalent to a tax on exports. This is known as the Lerner Symmetry Theorem.

Assumptions:

Perfect competition.

Full employment.

Balanced trade (exports = imports).

No capital flows.

Prices and wages are flexible.

No retaliation.

Result: A 10% import tariff has the same effect on the real exchange rate and relative prices as a 10% export tax.

Intuition: If you tax imports, imports fall, causing the exchange rate to appreciate, which reduces exports. If you tax exports, exports fall, causing the exchange rate to depreciate, which reduces imports. The end result in real trade terms can be similar.

Lots of average people would look at that long list of assumptions and conclude they don’t apply in the real world. But a Chicago trained economist like me is not put off so easily. Studies have found that many industries that are not perfectly competitive are at least “workably competitive” and behave in a way that is close to predictions of a perfect competition model.

Don’t believe me? Then consider that the famous supply and demand model technically requires perfect competition. And yet there is hardly a single industry on the planet that is 100% perfectly competitive. For that assumption to hold, a company must have zero control over the price of the product it sells. Thus, under perfect competition, even a one penny price increase would cause a firm’s sales to plummet to zero. How many industries does that describe? And yet I bet most of my readers will occasionally use the supply and demand model when analyzing changes in the economy. It’s a good approximation for industries that are merely workably competitive.

Here’s another way of thinking about the problem. According to Lerner Symmetry, a uniform 10% import tariff reduces exports by just as much as a uniform 10% export tax reduces exports. That’s deeply counterintuitive. More importantly, that result is deeply counterintuitive even in a world where all 6 assumptions above hold true. If this is not what you expected, then you may not have been exposed to general equilibrium trade theory. “General equilibrium” refers to analysis that considers all indirect effects, not just the direct effect on a given sector of the economy. Most people think in partial equilibrium terms, which is fine for many issues, but not macro problems such as uniform tariffs on all imports.

Fortunately, there is a way of making this deeply counterintuitive concept much more intuitive. You may recall from Econ101 that a tax has an identical impact regardless of whether it is legally placed on the seller or the buyer. If Congress writes a law imposing a 23-cent tax on gasoline, it makes no difference whether Congress specifies that the tax is to be paid by the retailer, or whether they specify that the tax is to be paid by the consumer. If you are confused by this distinction, think about the difference between gasoline taxes (paid by the retailer and incorporated into the sticker price) and sales taxes (paid by the consumer and not incorporated into the sticker price.) Either way, the result is the same.

Now imagine that international trade is actually, you know . . . trade. That is, imagine a system of barter. Countries give up valuable goods and in return receive other valuable goods from other countries. In that case, both a 10% import tariff and a 10% export tax are simply two methods of taxing international trade. They represent a 10% tax on the transaction of exchanging one good for another. It makes no difference whether the tax is formally imposed on the importer or the exporter, just as it makes no difference whether a gasoline tax is formally imposed on the seller or the buyer.

Now return to the six special assumptions above, which I would group into three categories. The no retaliation assumption refers to the fact that in the real world countries may (foolishly) retaliate more to import tariffs than to export taxes. But no-retaliation is not a wildly unrealistic assumption—I don’t see many countries retaliating to the Trump tariffs.

A second category is competitive markets, full employment and flexible prices. All three of those assumptions are questionable in the short run (which is why Keynes thought tariffs might help during a depression), but reasonable approximations when considering the long run effects of permanent policy changes.

Unless I’m mistaken, the third category (balanced trade and no capital flows) is actually a single assumption, at least if ChatGPT means no net capital flows. The US has a big trade deficit, which means an import tax would raise more revenue than an export tax, and thus presumably discourage international trade to a greater extent. Importantly, however, it remains true that an American import tariff should reduce both imports and exports even if there were no formal retaliation.

Recall that the current account balance equals domestic saving minus domestic investment. Both import tariffs and export taxes might be expected to raise revenue, which would raise government saving (i.e., reduce dissaving) and thus reduce the trade deficit. In the US case, however, other parts of our fiscal policy are pushing in the opposite direction, which is one reason why the trade deficit did not fall during the first Trump administration.

Of course, if you make tariffs high enough then trade falls to zero, and by definition you’d have no deficit at all. So I’m not suggesting that tariffs cannot reduce the trade deficit, just that it is not a straightforward issue. Clearly ChatGPT fell short when it claimed the two taxes are quite different because one tax affects producers and the other affects consumers. If that were true, then Lerner Symmetry would not hold—the two taxes would have quite different effects even in a world where all six assumptions held true.

Now consider export subsidies. If Lerner Symmetry holds, then an across the board 10% export subsidy would exactly offset a 10% across the board import tariff. Again, the intuition is easy to see if you look at ordinary taxes. If the government puts a 23-cent tax of gasoline, and at the same time creates a 23-cent per gallon subsidy, the two net out to zero—leading to a completely free gasoline market with no distortions. But to the average person a combination of tariffs and export subsidies seems like a quite “mercantilist” policy regime. A friend of mine joked that someone should convince Trump to impose an across-the-board import tariff combined with an equal size export subsidy.

To summarize, this post had two main objectives:

1. To get people thinking about trade in general equilibrium terms. In the late 20th century, development experts compared countries with “import substitution models” (Latin America) with those having “export led growth models” (East Asia). I don’t like that terminology. I prefer to say that Latin America had an anti-trade model and East Asia had a pro-trade model. South Korea doesn’t just export a lot more than Argentina; it imports a lot more than Argentina. (More than eight times more, despite similar populations.) Indeed, South Korea had consistent trade deficits during its high growth years (mid-60s to mid-90s). And yet when you read advocates of industrial policy, they often leave the impression that Korea is a “mercantilist” country. It may have a mercantilist mindset, but it certainly didn’t have a mercantilist public policy during its boom period.

2. I also wish to encourage people to refrain from discarding an economic model just because some of its assumptions are unrealistic. All social science models are wrong. The question is which ones are useful approximations of reality, despite being imperfect. Like supply and demand, Lerner Symmetry does not precisely describe the real world. But as with supply and demand, we ignore its implications at our peril. Import tariffs may not reduce exports to the exact same extent as an export tax, but as our agricultural sector is now discovering, they are still a major drag on exports. Here’s Bloomberg:

   The widening deficit marks a historic reversal for the US agricultural sector, which for the past five decades had consistently run major trade surpluses — even serving as a key foreign policy tool during the Cold War. The shift in fortunes began during President Donald Trump’s trade war with China in his first term, with the initial annual deficits recorded in 2019 and 2020. More followed, with negative flows seen over the past three years.

PS. Brian Albrecht has an excellent post explaining why tariffs are an especially bad way of raising government revenue.

Photo by Fleur on Unsplash

Update: Right after posting this, I was sent a copy of GPT-5. I asked it the same question, and got a fairly similar response. The following (I won’t indent) is a bit disappointing:

2. Why they differ in the real world

Once we relax those simple assumptions:

a. Trade imbalance matters

• If you start with a trade surplus, a 10% export tax cuts into that surplus directly; an import tax might not reduce the surplus as much.

• If you start with a trade deficit, a 10% import tax directly reduces imports, but an export tax mostly reduces exports — which could worsen the deficit unless imports fall for other reasons.