When Does a Tariff Pay? Theory, Two Centuries of Episodes, and the American Experiment of 2025-26

Summary

One identity and six entries

Between January 2025 and April 2026 the average effective tariff rate of the United States, as the Yale Budget Lab measures it, went from 2.4 percent to 22.4 percent, back to 7.3 percent after a Supreme Court ruling, and up again to 11.8 percent under a different statute. Customs duties collected in fiscal 2025 were $194.9 billion against $77.0 billion the year before. Most of the argument about this has been conducted in slogans. Our working paper asks a narrower question. Under what conditions does a tariff raise the welfare of the country that imposes it, and how often have those conditions held?

The answer starts with an accounting identity. In a linear model of a single import market the welfare change from a tariff is a terms-of-trade gain minus a deadweight triangle, with no third term (Proposition 3). Figure 1 draws both pieces for foreign export supply elasticities of 2, 5, 20 and infinity. The gain shrinks and the optimal rate falls toward zero as foreign supply becomes more elastic. Around that identity we build a welfare ledger with six entries: terms of trade, revenue, market-failure correction, deadweight loss, the input-cost cascade and retaliation. Table 1 gives each a sign, a closed form and an observable proxy, and we prove eight propositions about the whole.

Table 2 applies the calibration to the United States in 2025. With a foreign supply elasticity of 2 the net at the realised 2025 rate of 8.0 percent is 0.37 percent of GDP. With an elasticity of 20 it is 0.01, and at 11.8 percent it is minus 0.03. Across the range the paper gives between plus 0.24 and minus 0.33 percent of GDP, with the price data pointing to the lower half. Both countries at their optimal tariff lose in every row.

Samuelson with a tariff added

Samuelson (2004) is the paper most often cited for the view that trade with a rising China can hurt the United States. His model has no tariff in it. In his epilogue, and again in his 2005 reply to critics, he declined the protectionist conclusion himself. We take his two-good example, leave China's productivity as a free parameter and add a tariff, which gives us six further propositions (Propositions 9 to 14 and Lemma 2). What do they say? In the regime that produces the loss, the tariff can do nothing, because the partner's technology pins the world price. Against a fully specialised partner it gains until the partner answers in kind. Even then the gain has a finite ceiling. Figure 2 shows the American curve peaking at 1.323 times free trade at 600 percent and falling once China makes both goods. The mirror case raises home income; there China catches up in the American import good.

The dollar and the episodes

A textbook says the exchange rate absorbs part of a tariff. Figure 3 tracks the effective dollar around 1971, 1985, 2018-19 and 2025-26. In the first three the rate moved the way the textbook predicts, each time through a deliberate or an accommodating partner. In 2025-26 the broad dollar fell 7.75 percent while the tariff rose. We list seven explanations and find no settled weight among them. Following our earlier work we treat the real exchange rate as a forward-looking asset price, so the offset depends on what the tariff does to expected productivity and to demand for the country's assets. Because the 2025-26 rate changed at least six times in eighteen months, we also treat the rate as a stochastic process with jump risk and score the uncertainty entry from that.

Figure 7 collects the American data of 2025-26. The aggregate import price indexes excluding duties say foreign sellers did not pay. Prices of imports from China say they partly did. Revenue was large and partly refunded. Employment has not moved. The dynamic accounts point to about a one percent loss of real income by 2028.

Table 6 scores twenty-four episodes against the six entries, from the Continental blockade of 1803-15 to the tariffs of 2025-26. Nine come out "lowered" and nine "mixed". Six are "cannot say". None earns "raised". The seven colonial and treaty episodes of 1820-1950 are in that count, so the absence of a "raised" is tested rather than assumed. Where the gain entries were positive, the importer was large and unanswered, or the customs house was the only tax office. Temporary protection aimed at an externality that later work could document also scored a plus. Wherever anyone measured the loss entries they were negative. The treaty states, which had almost no tariff, show the zeros that sovereign Latin America at 34 percent does not.

Export powerhouses and thirteen proposals

Singapore, Japan, Korea, Germany and China became export powerhouses with tariffs that fell during every take-off. Figure 8 shows the export shares and the applied tariff series. The surpluses came later, from saving and from currencies that the issuer of the reserve asset cannot imitate. What transfers is the discipline and the institutions. Figure 10 gives the cross-country correlation between the applied tariff and growth over the next five years: 0.99 percentage points across countries and minus 4.07 within country, both with large standard errors and neither causal.

Table 7 grades thirteen proposals for raising comparative advantage and living standards. Few of the ones with the better evidence are tariffs. They include cutting the time and cost of moving goods, secondary and technical education, infrastructure, enforceable contracts, research, direct and time-limited support for activities with a named externality, and compensation for the places that lose. Where a tariff is still the right policy, the conditions are specific enough to write into the statute. Two centuries of tariffs say they rarely are. Section 13 lists what we could not measure.

Who this is for: Policy staff, researchers, journalists and investors who want the conditions under which a tariff raises the welfare of the country that imposes it.