2. Balance of Payments Accounting and the Farmer’s Market

Our discussion around trade deficits begins with a bit of accounting. Consider the following accounting identity where we measure total imports of goods and services as M, total exports of goods and services as X, and the country’s capital-financial-account surplus as K

(1)\begin{equation}M = X + K.\end{equation}

We refer to this equation as Identity 1 because the right-hand and the left-hand sides measure the same thing. Double-entry accounting ensures this. Every debit has an equal credit. It is not a mathematical or economic model we are looking at, it is a rule for interpreting a world with international transactions.

A more familiar story might help us think about the identity more clearly. Rather than a country, let us say this equation applies to Sam, a produce vendor at a local farmer’s market. It is spring, and Sam is selling asparagus. Later in the year, she expects to grow and sell zucchini. Let us consider some specific transactions. First, Sam sells $483 of asparagus for cash. Second, she visits a fellow vendor who propagates plants. She buys $596 worth of zucchini plants using a cheque. You may notice that Sam has spent more than she earned, but that is okay because her cheque is good by virtue of a line of credit at her bank. Furthermore, she expects to earn much more than her daily loss once the zucchini plants start producing. Sam is happy with her transaction, but her nagging accountant forces her to keep track of things.

Let us record Sam’s transactions in a ledger that mimics our identity. When Sam sells asparagus, there is a debit to her produce account and a credit to her cash account. When Sam buys zucchini plants, there is a credit to her plant account and a debit on her line of credit. On the left-hand side of the identity, debits are negative and credits positive. On the right-hand side of the identity, debits are positive and credits are negative. Table 1 arranges the various debits and credits. Notice that we have a new addition of $113 on Sam’s line of credit. This is a new asset for Sam’s bank (a liability for Sam) which is backed by Sam’s good credit rating. Everyone is still happy – agreed?

Table 1. Sam’s ledger entries arranged on the identity.

Moving our example back to international transactions: replace Sam with Uncle Sam (the US) and scale up by a factor of 10 billion. Asparagus is US exports ($4.83 trillion) and zucchini plants are US imports ($5.96 trillion).Footnote ² The US shows a large capital-financial-account (K) surplus in 2024 ($1.13 trillion). K-account surpluses have persisted for the US since the late 1990s. Foreigners are persistent purchasers of dollar denominated assets. Like Sam’s bank, in our example foreigners are eager to extend credit to the US in the form of a K-surplus. Of course, the K surplus is the opposite of the trade deficit by our identity ( $M = {\text{ }}X + K$). A trade deficit is international borrowing. International borrowing is selling a capital or financial asset to a foreigner. We note that both the buyer and seller agree to this transaction presumably in the interest of mutual benefits, like Sam and her bank. Foreigners often buy US bonds, for example, because US bonds have historically been a safe bet in terms of preserving value, even if they pay a low interest rate relative to emerging-market bonds (denominated in a foreign currency). Any time a foreigner buys a bond in the US and there is a net debit on the K account, there must be either a credit to the M account or the X account: positive changes in M and negative changes in X. This expands the trade deficit which we now know is the K-account surplus.

3. Bilateral Trade Deficits: A Couple of Simple Hypothetical Examples

In the previous section, we defined the aggregate trade deficit. This raises a number of important policy questions regarding the US position as an international borrower and other countries, like China, as international lenders. These aggregate borrowing and lending issues are not, however, the focus of the Trump administration’s metrics for fair trade. The administration has chosen to focus on a measure that has little or no meaning, the bilateral trade imbalance. The bilateral trade balance with an individual country measures the difference between US exports to that country and US imports from that country.

Let us again consider a simple example to illustrate what this measure is, so we can examine its meaning. Consider a hypothetical trade pattern represented in Figure 1. There are three countries Germany (G), Italy (I), and Saudi Arabia (S) with three associated goods VWs, Ferraris, and Oil. The arrows and associated numbers in the figure represent exports (X). So, for example, Saudi Arabia exports $4 million worth of oil to Italy and $5 million to Germany. Notice that total exports by each country equal total imports. In this example, there is no international borrowing or lending: ${K_\text{G}} = {K_\text{I}} = {K_\text{S}} = 0$. The example in Figure 1 assumes no trade barriers (tariff or non-tariff). The trade pattern is organic. It is driven by a set of underlying supply and demand conditions, which we can, but will not, discuss for the purpose of this article.

Figure 1. Three country trade example with K = 0

We do have bilateral trade imbalances in Figure 1. Notice that Germany imports oil from Saudi Arabia but does not export any VWs to Saudi Arabia. The bilateral trade balance for country i with country j is calculated as ( ${x_{ij}} - {m_{ji}}$) where ${x_{ij}}$ are exports from i to j and $m_{ji}$ are imports by i sourced from j. Thus, we would say that Germany has a $5 million bilateral trade deficit with Saudi Arabia. This is offset by a $5 million bilateral trade surplus with Italy. Are these deficits and surpluses good or bad from any country’s perspective? The answer is an emphatic NO! There is nothing unfair about Germany’s trade with Saudi Arabia. Germany sells VWs and gets the oil and Ferraris it wants.

Imagine our friend Sam, from the previous section, claiming that she is being treated unfairly by the zucchini plant vendor, because the zucchini-plant vendor is not the same person as the one who purchased her asparagus. A measured bilateral trade deficit means absolutely nothing about winners or losers. In fact, in the example given in Figure 1, we see that it does not even indicate borrowing or lending. When a billionaire purchases fuel for their private jet, do they insist that the fuel company buy an equivalent dollar amount of their meme coins? When you or I visit the grocery store and buy broccoli, do we insist that the transaction is unfair unless the store buys an equivalent dollar amount of our labor services? No. We, like countries, engage in transactions with multiple partners, so the deficit or surplus with a given partner does not indicate our overall welfare. It does not even indicate whether we are borrowing or saving.

Any trade advisor to the President, let alone a trade economist, who claims that bilateral trade imbalances are some sort of metric of relative economic performance is either unqualified or not being honest. Yet, the President still believes that bilateral deficits indicate US losses. Folks, you have failed. Try again. Do not defend the indefensible.

We made a point about bilateral trade deficits, but maybe we should add aggregate trade deficits to our example to see if anyone is being treated very unfairly, or even unfairly, in that case. Consider that the people of Saudi Arabia are forward looking and see that their oil reserves may eventually be depleted. They may look at investing in a different sector, or even in a different country. Let us say that they decide to forgo two million dollars of Ferrari purchases in order to purchase a share of VW production. Figure 2 illustrates the resulting trade pattern. We see that Germany is now borrowing from the rest of the world because $M_{\text{G}}=X_{\text{G}}+K_{\text{G}}$ becomes $6 = 4 + 2$. Of course, on the other side of the capital transaction Saudi Arabia is lending (they now hold a German asset) with their accounting identity becoming $7=9-2$. Again, just like in our previous example, it is not clear that anyone is being treated unfairly. Germany sold assets, but the Saudis must have paid a fair price, otherwise the Germans would not have sold. If they regret the transaction, they can simply buy back the asset at the market price in some future period, and this will put them in a trade surplus for that period because they will need to pay for the asset through reduced imports or increased exports. If this seems unclear, see Equation (1).

Figure 2. Three country trade example with K ≠ 0.

The purpose of this section was to illustrate that bilateral trade imbalances are a natural feature of any pattern of trade with more than two countries. This feature does not indicate the existence or level of foreign trade distortions. It does not even indicate the level of international borrowing or lending (a country’s trade deficits or surpluses). As a matter of accounting, across all countries, net borrowing must be zero, and bilateral imbalances are organic to any system of recorded transactions. The amazing focus by the Trump administration on an utterly useless metric has led them to develop TURDs. In the following section, we show how the specific TURDs are calculated from these meaningless bilateral trade imbalances.

4. The TURD formula

The formula for calculating the administrations TURDs has a basis in a set of economic responses to tariffs. This involves the concept of US import price elasticities and tariff passthrough.Footnote ³ We relegate this bit of technical economics to the following section, because in accord with the administration’s assumptions the critical elasticity and passthrough parameters exactly offset one another in the formula. We can ignore them in the calculation of the TURDs.

Conceptually, the administration first asks: What is the additional tariff rate ( $\Delta t_i$) on goods from country i that would need to be added to eliminate the bilateral trade deficit with that county?Footnote ⁴ The idea of reciprocity comes from an incorrect assumption that the bilateral trade deficit must be caused by some tariff and non-tariff barriers imposed by country i that have artificially reduced US exports to that country. In the previous section, however, we learned that these bilateral trade imbalances are a natural feature of any trade pattern with more than two countries, regardless of tariff or non-tariff barriers. This fact alone renders the TURDs completely devoid of their ‘reciprocal’ content.Footnote ⁵

Let us forge ahead, nonetheless, to see how the TURDs are calculated. The formula for the prescriptive change in tariff rates, under the administration’s assumed parameter values, is given by

(2)\begin{equation}{\Delta }{t_i} = \frac{{{x_i} - {m_i}}}{{ - {m_i}}}\end{equation}

where $x_i$ are US goods exported to country i and $m_i$ are US goods imported from country i. Mathematically, the change in the tariff rate is bound between minus infinity and 100%. The calculated $\Delta t_i$ is then plugged into the following TURD formula to get the actual change in the tariff rates applied to goods from country i

(3)\begin{equation}\text{TURD}_i=\max\left\{0.1,\frac{\Delta t_i}2\right\}.\end{equation}

All countries on the list regardless of bilateral trade imbalance, therefore, face at least a 10% tariff. Partner countries that run a significant bilateral trade surplus with the US face one-half of the ${\Delta }{t_i}$. Why one-half? According to the President, ‘We are being very kind’ (Donald J. Trump, 2 April, Rose Garden speech).

To give a simple example of how the TURDs would be applied let us consider the trade flows in Figure 1. Now by construction there are no tariffs, other trade frictions (non-tariff barriers), and there are no trade imbalances ( $K_i = 0$ for all countries). There are, however, bilateral imbalances. Let us presume that countries are not imposing their optimal tariffs against one another because they have a cooperative trade agreement (like the WTO). The cooperative trade agreement is a set of promises that allows all countries to benefit from sharing each other’s markets. Trade is a prisoner’s dilemma game where aggregate surplus is maximized under cooperation.

Now let us say that a new German leader wakes up and decides to adopt TURDs to combat (a non-existent) very unfair treatment from its trade partners:

• • German TURD against Saudi Arabia: 50% tariff rate

• • German TURD against Italy: 10% tariff rate.

From Saudi Arabia and Italy’s perspective, it would seem clear that Germany has abandoned the principals of cooperative trade. Their rational response would be to maintain cooperative trade among themselves but move to their dominant strategy of an optimal tariff against Germany. From a strategic perspective, Germany has ensured its unilateral engagement in a trade war with the rest of the world.

5. The Economics behind the TURD Formula

In this section, we discuss the economics engineered into the TURDs.Footnote ⁶ Consider a measure of the import demand elasticity, which is assumed to be the same for aggregate import bundles from any country i:

$$\epsilon=\frac{\%\Delta m_i}{\%\Delta p_i}$$

where ${p_i}$ is a measure of the gross-of-duty price of the import bundle from country i. The parameter $\epsilon$ is less than zero given that an increased price reduces imports. The target change in imports is the amount that eliminates the bilateral trade deficit ( $x_i - m_i$), conditional on assuming the tariffs have no collateral effects on exports with country i or any other targeted country. The assumption is that there are no ‘general-equilibrium’ effects, referring to the indirect effects that the tariffs certainly have on exports and other markets.Footnote ⁷ Transforming the targeted change in imports into a percentage change, and rearranging, we have

$$\frac{x_i-m_i}{m_i}=\epsilon\left(\%\Delta p_i\right)$$

Now let us consider another parameter that indicates the elasticity of the gross-of-tariff price with respect to the change in tariff rate

\begin{equation*}{{\varphi}} = \frac{{\% \Delta {p_i}}} {\Delta {t_i}}.\end{equation*}

Substituting this parameter into the previous equation we get

$$\frac{x_i-m_i}{m_i}=\epsilon\varphi\left(\Delta t_i\right).$$

Now solving for the prescriptive tariff change, we get USTR’s reciprocal tariff formula:

(4)\begin{equation}\Delta t_i=\frac{x_i-m_i}{\epsilon\varphi{\text{m}}_i}.\end{equation}

This simplifies to the formula used in Section 4 by assuming that the price elasticity is –4 and the passthrough elasticity is 25%. Thus, the product $\epsilon\varphi=-1$. We can quibble about the parameter values (e.g. Fajgelbaum et al., Reference Fajgelbaum, Goldberg, Kennedy and Khandelwal2020; Cavallo et al., Reference Cavallo, Gopinath, Neimna and Tang2021, estimate passthrough rates close to 100%),Footnote ⁸ or the rather egregious structural assumption to ignore general equilibrium effect. The fundamental problem remains, however, that the TURDs are founded in a misguided attempt to correct bilateral trade imbalances.

6. Conclusion

Economists are often asked to comment on the effects of Trump’s disruptive tariff policies. We have, are, and will continue to do this. Even in the absence of these studies, however, we know from theory that trade wars move us away from cooperative international outcomes that are mutually beneficial. The current quantitative analysis is consistent with this theory, suggesting substantial global economic costs and acute costs for the US in the range of many thousands of dollars per US household per year. In response to the 2 April tariff announcements, however, I find these studies lacking. I feel these studies are doomed to fail as accurate or effective policy tools – even my own studies. And I like my studies.

The first problem I have with economic tariff analysis is our fundamental lack of engagement with the true problem. If we cannot convince policy makers of the irrelevance of bilateral trade imbalances, how can we hope to have them take seriously our sophisticated policy analysis models? In one of my studies, for example, we show that Trump’s campaign promise of tariffs combined with symmetric retaliation could cost the average US household $7,000 per year (Balistreri et al., Reference Balistreri, Ali and McDaniel2025). This number is never taken seriously. It is rhetorical ammunition for half the country and dismissed as Trump derangement syndrome by the other half. To be effective, we need to start with a realistic foundation in transparent arguments, not a policy impact number. The quantitative analysis is only useful to the degree that we are willing to confine our debate to a reasonable perspective on the economy. One of these reasonable perspectives is that bilateral trade deficits are meaningless measures of economic performance. They also do not indicate anything about trade distortions. Any person engaged in non-barter transactions can understand this simple truth. We do not need an economic model to tell us that the ‘trade deficit’ we experience every time we visit the grocery store is neither the source nor consequence of our economic woes. This understanding alone might have helped us side-step the 2 April TURDs.

The second problem I have with our analysis of tariffs is our inability to communicate the fragility of our model results. This is similar to the concerns over econometric models raised more than 40 years ago by Leamer (Reference Leamer1983). The quantitative estimates we make using structural models of tariffs are not robust predictors of realized outcomes by design. First, to maintain tractability our estimates are conditional on a slew of macroeconomic stability assumptions making them useful in evaluating alternative policies in an ‘all else equal’ thought experiment. Estimates of the costs of tariffs are not forecasts, even if that is the way they are interpreted. To give an example, the policy costs in (Balistreri et al., Reference Balistreri, Ali and McDaniel2025) are conditional on an assumption that Trump’s tariff policies and partner-country retaliation do not change real investment or aggregate employment in the US. That assumption died about five seconds after the TURD-chart dropped in the Rose Garden. Second, the size of the distortions embodied in the TURDs are outside the range of our historic experience, bringing even the basic price response parameters under serious suspicion. How much will the tariffs cost if they disrupt financial and labor markets? The best answer I can suggest is ‘a lot’. Once we start having significant macroeconomic adjustments to the tariff shocks, any number of things are bound to go awry.

In this paper I try to avoid the pitfalls of opaque economic models in an effort to be more effective. I use a set of accounting principles to show that the administration’s focus on bilateral trade imbalances is unfounded as are the resulting TURDs. President Trump may well believe that the bilateral trade deficit with a country represents the US’s trade losses to that country, but he is wrong. At a minimum we need to state this truth transparently. Perhaps my examples will help in that effort.