Banking, Trade, and the Making of a Dominant Currency

Gita Gopinath and Jeremy C. Stein (Harvard University and NBER). Quarterly Journal of Economics 136(2), May 2021, pp. 783–830. This digest is of the published version, which supersedes NBER Working Paper 24485 (April 2018). “Supersedes” is the operative word: the model was reformulated between the two. Importer preferences changed, the invoicing first-order condition changed from smooth to a step function, Propositions 2, 3 and 5 were restated, and the calibration is entirely new. Proofs live in an Online Appendix rather than in the article. No talk recording specific to this paper could be found — Gopinath’s 2019 Hahn Lecture covers dominant-currency pricing more broadly — so this is a PDF-only digest.

Why a safe asset has to name its goods

Sixty percent of Turkey’s imports are invoiced in dollars; six percent of them come from the United States. Across the 43 countries in Gopinath (2015), the dollar’s import-invoicing share runs about 4.7 times the share of American goods in imports, while the euro’s runs about 1.2 times the eurozone’s. Non-U.S. banks carry something on the order of ten trillion dollars of dollar liabilities, comparable to the dollar liabilities of U.S. banks; 62 percent of banks’ foreign-currency local liabilities and 60 percent of their local claims are in dollars. Central banks hold 64 percent of reserves in dollars, 20 percent in euros, 4 percent in yen. And dollar safe assets pay less than other safe assets, which is the exorbitant privilege. These are five different literatures, and the claim of the published version is that they are one fact.

The claim rests on a definition that the paper takes more seriously than anyone else does. A financial claim is only safe if it buys a known quantity of goods at a future date. So the question which currency’s deposits are safe? is not a separate question from which currency are the goods priced in? It is the same question, and the answer feeds back on itself.

The demand leg

You are an emerging-market household. You will consume a fixed bundle of imports $M$ at date 1, priced in sticky dollars, and you hold deposits today to pay for it. Your date-1 consumption of home goods is $C_1 = D_h + \mathcal{E}_1 D_\text{USD}- \mathcal{E}_1 M$, and with mean-variance preferences your risk is exactly $(D_\text{USD}- M)^2\sigma^2$. All of it comes from the gap between the dollars you hold and the dollar-invoiced goods you are going to buy. Match them and you bear no exchange-rate risk at all. So your first-order conditions, on p. 794 of the published version, read

Dollar-deposit demand tracks the quantity of dollar-invoiced imports one for one, damped only by how expensive dollar deposits have become. A quantity, note, not a share. Readers of the working paper will remember importers maximising over a Cobb-Douglas aggregator of deposits in invoice shares, with weights $\alpha_h$ and $\alpha_\text{USD}$ that the authors themselves flagged as ad hoc; those parameters do not exist in the published version, and the consumption-based formulation that used to sit in an appendix is now the model.

The supply leg, and why it is expensive

Now be the local bank. Your collateral is a portfolio of home-currency projects, and the most depreciated the home currency can get is $\bar{\mathcal{E}} > 1$. So one unit of collateral backs one unit of safe home-currency claims but only $1/\bar{\mathcal{E}}$ units of safe dollar claims — equation (2), p. 795:

You have a comparative disadvantage in manufacturing dollar safety. You will do it anyway, but only if paid, and Proposition 1 (p. 795) says exactly what the payment is: $Q_\text{USD}> Q_h > Q_R$, with

The size of the UIP violation equals the worst-case depreciation. That is the whole exorbitant privilege, derived from import invoicing and from nothing about the United States — not its fiscal capacity, not its liquidity, not its behaviour in crises. This inverts the usual informal story (p. 787). If you take the UIP violation as given, of course unhedged firms borrow in dollars, it’s cheaper. The paper’s point is that the UIP violation is the price required to recruit badly-suited firms into producing dollar collateral in the first place. It is the wage you pay the marginal, incompetent producer of dollar safety. (Footnote 9 on p. 796 concedes that hanging everything on a single worst-case realisation is unnatural, and shows that if the collateral constraint is read as capital regulation with a tail-probability limit, $\bar{\mathcal{E}}$ becomes a proxy for exchange-rate variability generally.)

Proposition 2 (pp. 796–797) puts a cutoff on it: $\bar M = X_\text{USD}+ \theta(\bar{\mathcal{E}}-1)/(\psi\delta\sigma^2)$. Below that, the exogenous supply of dollar safe assets from abroad is enough and nothing happens. Above it, home-currency projects get pulled in as marginal collateral for dollar deposits, which is to say the currency mismatch that everyone treats as an emerging-market pathology is the equilibrium outcome of the model. And the step matters: the premium has to reach the discretely positive value $\theta(\bar{\mathcal{E}}-1)$ before the first unit of conversion happens, because even the first unit costs something proportional to $\bar{\mathcal{E}}-1$. The supply curve has a jump in it before it has a slope.

The invoicing leg, which is now bang-bang

Exporters choose an invoicing currency, and dollar invoicing raises the floor on their future dollar revenues, which is better collateral for cheap dollar debt. In the published version the bank-exporter coalition is a risk-neutral profit maximiser in home currency, so the problem is linear and the answer is a corner — equation (6), p. 802:

As soon as dollar funding is cheaper by a hair, $\eta$ goes from zero to one. Interior invoicing survives only on the knife-edge where dollar and home rates are exactly equal. Anyone who remembers the working paper’s smooth rule $\eta = (\gamma_L/\beta\varphi)(Q_\text{USD}- Q_h)$, with its adjustment-cost parameter and its IC-line-crossing-DP-curve diagram, should let it go: footnote 15 on p. 802 explicitly relegates that version to the working paper. Generalising Proposition 2 with endogenous invoicing gives Proposition 3 (pp. 802–803) three cutoffs and four regions rather than the working paper’s two and three. The genuinely new middle region, $\underline M \le M < \hat M$, is the interesting one — there is dollar invoicing, but $Q_\text{USD}- Q_h = 0$ exactly, so there is no premium and no mismatch yet. Dollar invoicing arrives first; the privilege arrives later.

Closing the loop

Put a continuum of emerging markets in and country $i$’s dollar-invoiced imports become $M_{\text{USD}i} = a + b\int_{j \ne i}\eta_j\,dj$, where $a$ is the quantity of goods imported from the United States — a volume, the paper is explicit about this on p. 808, not a share — and $b$ is the invoicing-feedback coefficient. Everyone else’s invoicing choice raises your dollar-deposit demand, which raises the dollar premium, which validates their choice. Proposition 4 (pp. 809–810) says that if $b > \gamma_L N + \theta(\bar{\mathcal{E}}-1)/(\psi\delta\sigma^2)$, then as $a$ rises from zero the dollar’s global role must jump discretely, at $\underline a$ at the earliest and $\bar a \equiv X_\text{USD}$ at the latest, with both equilibria coexisting in between and history picking.

Footnote 18 on p. 810 quietly adds a fourth cutoff splitting the low-$a$ region, where a no-mismatch equilibrium with interior $\eta$ coexists with the zero-$\eta$ one. The authors downplay it “because it is less empirically relevant, given the body of evidence on mismatch among corporate borrowers in emerging markets,” which is a fairly direct statement about which equilibrium they think we are living in.

Two candidate currencies, and the stability result

Now add the euro, with identical fundamentals, and the model has to say why the world picked one. The importers’ conditions (equations (7) and (8), p. 814) are the crux:

Read (7) and (6) together and the paper is finished. More dollar invoicing elsewhere raises the price of dollar safety; a higher price of dollar safety makes you invoice in dollars.

The stability argument follows in one line, and it is sharper in the published version than in the draft. A dual-currency world with no mismatch requires $Q_\text{USD}= Q_{\text{EUR}}$ exactly, because $\eta$ is bang-bang. Let other countries tilt an epsilon toward the dollar. Then $Q_\text{USD}$ rises, $Q_{\text{EUR}}$ falls, the knife-edge is gone, and your banks go straight to $(\eta_\text{USD}, \eta_{\text{EUR}}) = (1,0)$. The tidy two-currency world is unstable. In the mismatch region, by contrast, $Q_\text{USD}$ is pinned at $\theta(\bar{\mathcal{E}}-1)$ and is therefore independent of what anyone else does, so $d\eta_{\text{USD}i}/d\eta_{\text{USD},-i} = 0$ and the equilibrium is stable. The equilibria that survive are exactly the ones with currency mismatch. Mismatch is not a defect the system tolerates; it is the thing holding the system still.

Proposition 5 (pp. 815–817) replaces the working paper’s enumeration of three equilibrium types with four cutoffs and, under a two-sided condition on $b$, five regions in $a$. The punchline is the third region: for $\bar a^n < a < \underline a^b$, the asymmetric dominant-currency equilibrium is the unique stable outcome (p. 817). The intuition is nicely economical — $a$ proxies the generalised demand for safe claims in some non-home currency, and in the middle range there is enough of it to sustain one global currency and not enough to sustain two.

The numerical example uses an entirely new calibration (Table I, p. 817): $\beta$ 0.75, $\delta$ 0.8, $\psi$ 0.8, $N$ 2.6, $N_0$ 10, $X$ 0.3, $b$ 1.6, $\gamma_L$ 0.55, $E[\gamma]$ 1.4, $\sigma$ 0.55, $\bar{\mathcal{E}}$ 3.8, $\rho$ 0.05, $W$ 10, chosen to generate the same ordering of cutoffs as Figure V. On the single-dominant-currency branch of the ten panels of Figure VI, $M_\text{USD}$ greatly exceeds $a$ while $M_{\text{EUR}}$ equals $a$ exactly (p. 819) — which is the model reproducing the 4.7-versus-1.2 fact from the introduction without being asked to.

Which currency wins, the model cannot say from fundamentals. The authors’ selection device is history: before 1999 the largest future eurozone member had a GDP about a fifth of the United States’, so the model would then have had a unique dollar-dominant equilibrium, and the euro arrived to find the coordination already settled (p. 821). The corollary is uncomfortable for both Europe and China. Catching up with the United States is not enough to dislodge an entrenched currency; you have to get substantially bigger, far enough that your own dominance becomes the unique equilibrium.

The one that stings

Which brings us to the result that is new in the published version and absent from the working paper entirely. It has often been argued that a common eurozone safe bond would help internationalize the euro, on the theory that dominance requires a deep supply of safe assets. In this model, supply is the wrong lever. Raising $X_{\text{EUR}}$ without raising demand for euro safe assets raises euro interest rates, which reduces EM banks’ incentive to manufacture euro claims and EM exporters’ incentive to invoice in euros. Every cutoff in Proposition 5 contains $X$, and every one of them shifts leftward when $X$ falls — a smaller exogenous supply makes dominance easier, not harder. In the authors’ words (p. 822): “if such an issuance does not increase the demand for euro safe bonds it does not help with internationalization.” The European policy debate has been trying to push on the string from the wrong end.

The evidence

Equation (9), p. 824, is the mapping to data, and it is not the same object as the working paper’s equation (42): it is the ratio of dollar- to euro-invoiced import volumes, each net of a price-gap term.

A country that invoices more of its imports in dollars should hold more of its deposits in dollars. The test uses Gopinath (2015) invoicing data against BIS locational banking statistics, and the sample is built by exclusion, which is worth stating because a reader would otherwise suspect it: eurozone countries and the United States are dropped so as not to pick up own-currency use, and Brazil and India are dropped because they restrict private foreign-currency deposits. Ten countries survive. Panel A gives an R-squared of 0.72. Panel B narrows the liability measure to loans and deposits with a nonbank counterparty, stripping out interbank and wholesale funding, which cuts the sample to eight and raises the R-squared to 0.82. Denmark, Norway, Sweden and Switzerland — close to the eurozone geographically and commercially — sit low on both axes. And the authors note, disarmingly, that dropping the exclusions and using everything available makes the correlation more pronounced, not less (p. 826).

Section VI.C summarizes the companion paper on reserves. Relax the assumption that deposits are riskless in every state and a crisis state appears in which the local currency depreciates and failed banks’ deposits must be bailed out. Bailing out dollar deposits with ex post taxes is ruinously expensive precisely because the crisis state is the depreciation state, so dollar reserves hedge the central bank’s exposure as lender of last resort to a dollarized banking system. In fifteen countries, the dollar’s share of import invoicing correlates strongly with its share of central bank FX reserves — invoicing, note, not deposits, which makes the chain run from a price tag on a shipping container to the composition of a sovereign’s reserve portfolio.

Section VI.A reads sterling through the same lens. Over 60 percent of world trade was invoiced, financed and settled in pounds before the First World War, though the American economy had overtaken Britain’s in the 1870s — the model’s kind of history, in which fundamentals move and the equilibrium does not. What eventually moved it was the Federal Reserve Act of 1913 and a deliberate policy of supplying dollar trade credit at concessionary rates, such that between 1917 and 1930 the Federal Reserve held over half of all trade acceptances. In the model’s language that is a modest increase in $a_\text{USD}$, and a modest increase in $a_\text{USD}$ is exactly what produces a large discrete change. China’s renminbi settlement share of its own trade went from zero in 2010 to 25 percent in 2015, the RMB passing the euro in 2013 as the second most-used currency in trade finance before falling back to third: a policy visibly aimed at the same parameter. The conclusion extends the lens to Facebook’s Libra, on the theory that a retail payments currency with a 2.4 billion user base could generate invoicing, which generates safe-asset demand, which generates more invoicing. Libra is defunct and the example has aged, but the caveat attached to it applies to every would-be challenger: a dominant currency has to be sufficiently liquid and stable in value, which the model takes as given and which “cannot be assumed away.”

Where it sits

Presented (theory) in 3.1 — the foundation of the sub-block rather than one of its geoeconomic applications, and presented for that reason. Everything the group will read about weaponized finance presumes that invoicing, bank funding, corporate borrowing and reserves form one system, and this is the paper that shows why they must. It is also the reason the geoeconomic papers fit together: Dollar Dominance and the Transmission of Monetary Policy and Mukhin’s price-system model take the invoicing leg; Farhi–Maggiori, Bianchi–Sosa-Padilla and Global Hegemony and Exorbitant Privilege take the reserve-asset leg and ask what the hegemon can charge for it; Bahaj–Reis’s swap lines and Internationalizing Like China are attempts to jump-start the loop for a second currency, which the model says requires crossing a threshold rather than nudging a share; Eichengreen–Mehl–Chiţu’s alliance effect is the history that the indeterminate region leaves room for. The group may have seen it; it is presented anyway because the loop has to be on the board before the coercion papers can be read, and because the jump and the indeterminate region are what make “de-dollarization” a threshold question rather than a share. That last point is stronger in the published version than in the draft, which is the sort of thing a referee report does: the jump is now a genuine discontinuity in $\eta$ from zero to one, not the steepening of a smooth curve.