TY - JOUR
AU - Valchev, Rosen
AB - Abstract We propose a model in which the emergence of a single dominant currency is driven by the need to finance international trade. The model generates multiple stable steady states, each characterized by a different dominant asset, consistent with the historical durability of real-world currency regimes. The persistence of regimes is caused by a positive interaction between the returns to saving in an asset and the use of that asset for financing trade. A calibrated version of the model shows that the welfare gains of dominance are substantial, but accrue primarily during the transition to dominance. We perform several counterfactual experiments to assess potential threats to the dollar’s continued dominance. 1. Introduction Historically, the international financial system has been characterized by long-lasting periods in which one “dominant” asset facilitates the majority of international trade and financial flows. Since the 1950s, this role has been played by the U.S. dollar and safe U.S. assets, while the British pound enjoyed dominance before that, and the Dutch Guilder was the dominant asset throughout the 18th century. This pattern suggests that the international financial system favours the emergence of extended periods of currency dominance. The potential for such dominance has been of great interest to prior literature, but the question of why currency regimes often prove so durable has received comparatively little attention. This article provides a theory of stable dominant currency regimes. The theory relies on two frictions in international trade, imperfect contract enforcement across borders, which creates a need for collateral guarantees in trade, and a financial friction in obtaining the needed collateral. Trading firms seek to borrow collateral via frictional trade finance markets, generating a positive feedback between the use of an asset to guarantee trade and households’ incentives to save in that asset. Firms also benefit from operating with the same collateral as their trade counterparties, which reinforces the household-firm complementarity. The interaction of these forces gives rise to multiple steady states, each characterized by a different dominant asset and surrounded by a region of unique, stable equilibrium dynamics. Our model economy is composed of three regions: the U.S., the Eurozone, and a continuum of small, open, rest-of-world economies. In each country, there is a continuum of trading firms seeking to engage in profitable transactions with traders from other countries. Imperfect contract enforcement across borders requires the trading firms to collateralize their transactions with safe assets that serve as performance guarantees. To obtain collateral, firms seek an intra-period loan of either U.S. or Eurozone bonds in domestic bond-specific search and matching markets. On the other side of these credit markets are the local households, who form optimal portfolios and offer intra-period loans from their asset holdings for a fee. Other things equal, search frictions encourage firms to look for trade financing in the credit market that is less tight, and thus apply for a loan of whichever asset forms a larger share of domestic household portfolios. Conversely, households know that an asset that is heavily used by traders is more likely to be loaned out in the trade finance markets and earn the associated fee. Thus, the incentives of households and trading firms reinforce each other: a large usage of an asset in trade finance encourages households to save in that asset, while large portfolio holdings of the asset encourage firms to seek it for financing trade activities. We begin our analysis by analytically characterizing the key forces driving dominance and stability within a simplified model. First, we show that the feedback between households and trading firms leads to steady-state multiplicity, including a dollar-dominant steady state in which U.S. safe assets are both the dominant saving vehicle of rest-of-world households and the dominant means of trade finance. The other steady states are a mirror-image euro-dominant steady state, and a “multi-polar” steady state in which portfolios and trade finance use are split equally across the two assets. While this firm-household interaction can generate dominant-currency steady states, these outcomes may not be stable. Intuitively, when one asset dominates trade finance activity, the market for loans of that asset is relatively congested. Hence, an off-equilibrium shift in the portfolio composition of households can drive firms to shift their financing use away from the dominant asset. To ensure stability, we introduce a currency mismatch cost that is incurred by trading firm pairs who use different types of collateral. This cost can be micro-founded as the expected cost of default by one of the transaction counterparties, since mismatched collateral means the two promises may not be equivalent in all states of the world.1 Collateral mismatch costs introduce a second strategic complementarity, now in the type of financing sought by trading firms in different countries. On its own, this complementarity would give rise to sunspot equilibria, since trade finance choices would depend only on what firms expect their foreign counterparties to choose. Frictions in funding markets limit this indeterminacy, however, because firms’ funding choices are also influenced by the relative availability of different types of trade financing. Crucially, the interaction between the two complementarity mechanisms—one between households and firms, the other among firms—can make dominant-asset steady states locally stable. Intuitively, wide holdings of an asset make it easier for firms to source it, giving it an initial advantage in firms’ currency choices. This advantage is then reinforced by firms’ cross-country coordination incentives, uniquely anchoring their currency choice on the widely held asset. Importantly, neither mechanism can achieve this on its own: without both sources of complementarity, equilibrium is either locally unstable or subject to sunspot indeterminacy. Having illustrated the key mechanism, we embed it within a rich general equilibrium model, and explore its quantitative implications in and out of steady state. We calibrate the model to match target moments on the size of government debt, trade, currency denomination of trade finance, and import markups. The model exactly matches the target moments and a number of additional, non-targeted moments are also closely aligned with the data. Using the calibrated model, we first show that dominant-currency steady states in this richer, quantitative framework are indeed dynamically stable, and lie within large regions of the state space that uniquely converge to their respective dominant-asset steady state. Within those regions, the equilibrium paths of the economy are determinate (i.e. not subject to sunspot shocks) and the currency regime is uniquely determined by initial conditions. Essentially, the dynamic model tethers the mix of assets used for trade finance to an endogenous state variable, the composition of rest-of-world bond portfolios, generating the co-existence of distinct, stable dollar- and euro-dominant steady states. By contrast, we show that the multi-polar steady state is unstable. Hence, the model implies that durable single-currency regimes should predominate, just like in the historical record. Computing the welfare implications of the model leads to several new insights that showcase the importance of a dynamic general equilibrium analysis of currency dominance. The steady-state gain of the dominant country, relative to the other large country, is small—only |$0.03\%$| of permanent consumption—even though the equilibrium interest rate of the dominant asset is roughly one percent lower than that of the other asset, consistent with the data.2 In our general equilibrium model, this “exorbitant privilege” does not generate a long-run welfare benefit because the low interest rate is a consequence of high external demand for the dominant country’s assets, which also results in a negative net foreign asset position for the country (as is also true in the data). In our calibration, the costs of servicing this external imbalance roughly offset the benefits of paying lower interest. Though dominance has a small effect on consumption in the long-run, factoring in the transition to dominance dramatically changes welfare conclusions. For example, in the case of a transition from the (unstable) symmetric steady state, the eventual dominant country gains the equivalent of |$0.75\%$| of permanent consumption. This happens because, along the transition path, increasing external demand for the assets of the dominant country helps it to fund a temporary boom in consumption. This finding emphasizes the importance of using a dynamic model to evaluate the positive consequences of currency dominance. We conclude the paper with three counterfactual experiments. First, we analyse the formation of the Eurozone, one of the most important recent developments in the international financial system. Consistent with historical experience, the model shows that starting from a point where the U.S. is the only country furnishing safe assets on a global scale (and thus the dollar-dominant steady state is unique), the introduction of an ex-ante equivalent Eurozone asset is not sufficient to precipitate a currency regime change: while the Eurozone formation does create a second stable dominant-asset steady state, the world is already dollarized at the euro’s introduction, and nothing about the change pushes the world economy away from its dollar-dominated starting point. More broadly, the model implies that we live in a dollar-dominant world today due to the combination of path dependence and the stability of dominance. Still, the dollar’s dominant position is not guaranteed, and future shocks could push the economy into the attraction region of the now-stable euro steady state. Next, we examine a different, but equally profound, change in the structure of the global economy, the falling share of world output accounted for by the U.S. Since 1960, the U.S. share of world output has shrunk by 15%, almost all of which has been absorbed by countries outside of the G6. According to the model, dollar dominance was the (globally) unique equilibrium in the past, when the U.S. was by far the largest economy. As the relative size of the U.S. shrinks to its current level, we find that the unique transition path is indeed one in which the dollar remains the dominant international asset. This explains the historical record well, but the model also cautions that while the U.S. dominance may appear unchanged, the recent emergence of an alternative stable steady state means that its dominance is more fragile than it once was. Looking forward, these two experiments predict that a new challenger, the Chinese renminbi, could threaten dollar dominance if the Chinese economy grows substantially larger than the U.S. and the Chinese capital account is sufficiently liberalized (allowing for wider global holdings of renminbi assets). In our third counterfactual experiment, we consider the consequences of the trade policy of the central country. We find that a trade war in which the U.S. raises tariffs on all imports by 15%, and its trading partners retaliate in kind, disproportionately hurts the U.S. and could be enough to threaten the dominance of the dollar, but does not eliminate it for certain. If such a switch did occur, however, it would lower U.S. welfare by 1.5% of permanent consumption. Our analysis indicates that U.S. policies favouring free trade (in both goods and assets) have been quite helpful in establishing its preeminent role in the world financial system. 1.1. Relation to existing literature The structure of our model is motivated by both historical accounts of the origins of dollar dominance, which emphasize the role of trade finance (Eichengreen and Flandreau, 2012), and empirical studies showing that the majority of international trade transactions require external financing (Auboin, 2016). Moreover, BIS (2014) documents that outside of the U.S. and the Eurozone, the majority of trade finance is locally sourced via domestic banks, and that trade finance contracts are heavily dollarized, showing that trade is not only denominated in dollars (Gopinath, 2015), but also financed via dollar debt. Lastly, there is also substantial evidence to suggest that trade financing is indeed scarce: Di Capria et al. (2016) estimate an unmet trade finance need of $1.6 trillion, while a related literature documents how disruptions to trade finance availability cause significant reductions in international trade (e.g.Amiti and Weinstein, 2011; Ahn, 2014; Antras and Foley, 2015; Niepmann and Schmidt-Eisenlohr, 2017; Bruno and Shin, 2019). The theoretical and empirical literature on currency regimes, which Gourinchas et al. (2019) surveys quite nicely, has explored many distinct properties of dominant international currencies and assets. While this work varies in style and emphasis, much of it can be tied back to one of the three traditional roles of money as a store of value, unit of account, or medium of exchange. Among these strands, the literature exploring the store-of-value or “reserve” role of dominant assets is comparatively large. Some of this work focuses on asset prices, rationalizing the low returns on safe dollar assets with the U.S.’s large role in global consumption risk (Hassan, 2013; Richmond, 2019). Other work aims to explain the high use of dollars in financial markets: Bocola and Lorenzoni (2020), for example, provide a framework where financial dollarization occurs because of the dollar’s unique risk profile, while Brunnermeier and Huang (2018) and Bianchi et al. (2018) explore the role reserve assets play in emerging market crises. Other authors link the status of the dollar with the U.S.’s superior capacity to issue safe assets (Caballero et al., 2008; He et al., 2019), differences in financial development (Mendoza et al., 2009; Maggiori, 2017), or risk-aversion (Gourinchas et al., 2017). Papers in the unit-of-account or “currency anchor” line focus on the role of dominant currencies in trade invoicing (Gopinath, 2015). This literature emphasizes the interaction of nominal price stickiness with pricing complementarities or the denomination of firms’ borrowing (e.g.Engel, 2006; Gopinath et al., 2010; Goldberg and Tille, 2016; Mukhin, 2018; Eren and Malamud, 2021), but usually does not explain global asset or return imbalances. Authors including Ilzetzki et al. (2019) have also used this mechanism to explain why emerging market central banks “anchor” their currencies to the dollar. Finally, the literature on mediums of exchange or “global currencies” centres on search-based theories of money. These works examine the micro-foundations of different trading and payment structures, focusing on the implications for co-existence of multiple currencies (e.g.Matsuyama et al., 1993; Zhou, 1997; Rey, 2001; Wright and Trejos, 2001; Kannan, 2009; Devereux and Shi, 2013; Zhang, 2014; Doepke and Schneider, 2017). Liu et al. (2019) studies instead the co-existence of money and trade finance credit, linking financial development with trade currency choices. Also related are Vayanos and Weill (2008) and Weill (2008), who use search frictions to explain liquidity premia for over-the-counter asset markets. In our article, dominance arises from the interaction of endogenous liquidity premia and the demand for store-of-value assets. This is a unique feature of our model, and links two important empirical aspects of currency dominance, the instruments of saving and trade finance (which are different from, though related to, invoicing or settlement currency). Concurrent work by Gopinath and Stein (2020), which blends the unit of account and safety roles of dominant assets instead, is perhaps the most closely related to our own. Their model can also generate asymmetric equilibria even when alternative candidate currencies are ex-ante identical in their fundamentals. Nevertheless, the two theories have important conceptual differences, and some key implications are diametrically opposed. In their model, dollar invoicing of imports leads rest-of-world households to prefer to save in dollars. Since Treasuries are scarce offshore (by assumption), local banks have incentive to create locally sourced dollar assets by offering cheap dollar financing to firms. Attractive dollar financing then encourages firms to price exports in dollars, closing the feedback loop. By contrast, complementarity in our theory comes from the interaction between an asset’s store-of-value and liquidity properties: firms prefer to fund transactions with a widely-held, and thus more easily borrowed, asset and their use of the asset generates a liquidity premium that gives rest-of-world savers a reason to concentrate their holdings in that asset. Our alternative mechanisms have different implications for what sort of asset is likely to become dominant. Gopinath and Stein (2020) rely on the relative “scarcity” of safe dollar assets to encourage local banks to create dollar-denominated deposits, implying that a high supply of U.S. treasury bills makes the dollar less likely to become dominant. By contrast, our model implies that the safe asset in higher supply is the one with a larger region of attraction, and is thus more likely to be dominant. In Section 3.4, we discuss evidence that asset availability is indeed likely to help, rather than hinder, asset dominance. More broadly, our article differs from the literature in at least two important respects. First, our model is dynamic, and we emphasize its ability to generate both multiple long-run outcomes (e.g. dollar and euro steady states) and stable equilibrium dynamics. Using our dynamic model, we can thus explain why dominant currency regimes appear so stable in the data, and demonstrate why accounting for dynamics is crucial for evaluating welfare. Second, we implement our idea in a quantitative, general equilibrium model. Most closely related papers, including Farhi and Maggiori (2017) and Gopinath and Stein (2020), use stylized, two-period models in which some key prices or quantities are fixed. General equilibrium is central to our model’s ability to simultaneously match the evidence on U.S. return differentials, net foreign asset positions, and international financial adjustment documented by Gourinchas and Rey (2007a,b), each of which have important welfare implications. 2. Simplified Model In this section, we present a simplified version of our model that focuses on the two essential ingredients of our mechanism: the savings decisions of households and the financing decisions of firms. The simplified model allows us to characterize the key forces analytically and, in Section 3, we explore quantitative implications in a rich general equilibrium setting. The world consists of two symmetric big countries, the U.S. and the Eurozone (EZ), of equal size |$\mu_{us} = \mu_{ez}$|⁠, and a continuum of small open economies making up the rest of the world (RW) with total mass |$\mu_{rw}$|⁠. There are two ex-ante identical assets—a bond issued by the U.S. government and a bond issued by the Eurozone government—each recognized as safe and available in exogenous supply, |$\bar B$|⁠. Both assets serve as saving vehicles and, potentially, as collateral guaranteeing international transactions. Countries are indexed by |$j \in \left\{ us, ez, [0, \mu_{rw}] \right\}$| and within each country |$j$|⁠, there is representative consumer and a continuum of risk-neutral international trading firms. In the simplified model, the only decision of the household is how to allocate its savings between the two available assets and the only decision of a trading firm is which type of asset to seek for financing its trade. We describe the decisions of the two agents types in turn. 2.1. Households Households solve a standard consumption-savings problem, allocating their endowment income between consumption and the two assets. In the simplified model, we assume there is a single consumption good and both assets promise one unit of that good (we generalize this later). Hence, bonds are ex-ante equivalent—however, as we will see, they may serve different trade financing roles in equilibrium and, therefore, earn different interest rates. Households in each country |$j\in \{us, ez,[0, \mu_{rw}] \}$| solve $$ \begin{align*} \max _{C_{jt}, B_{jt}^{\$}, B_{jt}^{\euroscript}} &E_0\sum_{t=0}^\infty \beta^t \frac{C_{jt}^{1-\sigma}}{1-\sigma} \hspace{.2in} \text{subject to} \\ C_{jt} + Q_{t}^{\$} B_{jt}^{\$} + Q_t^{\eurosmall} B_{jt}^{\eurosmall} & = B_{jt-1}^{\$} + B_{jt-1}^{\eurosmall} + \Delta_{jt}^\$B_{jt}^{\$} + \Delta_{jt}^\eurosmall B_{jt}^{\eurosmall} + Y_{jt}, \end{align*}$$ and a non-negativity constraint on bond-holdings. In the above, |$Q_t^c$| where |$c \in \{ \$, \euro \}$| is the price of a U.S. or Eurozone bond, |$B_{jt}^c$| is the amount of that bond held by the household, and |$Y_{jt}$| is an exogenous endowment. Besides the interest rate, each asset earns an additional return, or “liquidity premium,” from the collateral-use fees that firms pay to bond owners. We denote these premia by |$\Delta^c_j$|⁠, and describe how they are determined below. The optimal choice of asset holdings |$B_{jt}^{\$}$| and |$B_{jt}^{\eurosmall}$| implies the Euler equations $$ \begin{align} 1 & = \beta E_t\left[ \left(\frac{C_{jt+1}}{C_{jt}}\right)^{-\sigma} \frac{1}{Q_t^{\$} -\Delta_{jt}^\$ }\right] = \beta E_t\left[ \left(\frac{C_{jt+1}}{C_{jt}}\right)^{-\sigma} \frac{1}{Q_t^{\eurosmall} - \Delta_{jt}^\eurosmall}\right]. \label{us_bond} \end{align}$$(1) In steady-state, returns are equalized across assets and countries, so that $$ \begin{align} \frac{1}{\beta} =\frac{1}{Q^\$ - \Delta_{j}^\$} = \frac{1}{Q^\eurosmall - \Delta_{j}^\eurosmall}. \label{eq: dream euler} \end{align}$$(2) Since our analytical results regard steady states, we suppress |$t$| subscripts until Section 3. 2.2. Trading firms Trading firms in each country have the opportunity to make a profitable transaction with a randomly-matched foreign partner. If executed, the transaction generates a joint surplus of |$2 \pi$| that is split evenly between the two counterparties. For now, we treat |$\pi$| as exogenous; we endogenize it as the equilibrium profit from international trade in Section 3. Because of imperfect contract enforcement, each firm must post collateral to guarantee their side of the transaction before executing the deal and realizing this profit.3 Both the U.S. and the Eurozone safe assets can serve as collateral and the firm’s choice of which collateral to seek is central to our mechanism. To obtain this collateral, firms seek an intra-period loan of one of the assets in domestic bond-specific search and matching credit markets. On the other side of these credit markets are domestic households, who make their holdings of safe assets available for loan. We assume that trading firms look for a fixed amount of funding, which we normalize to one, and that they make a binary choice, seeking either dollar or euro collateral (i.e. a U.S. or an Eurozone safe asset). This framework captures the two key empirical features of trade finance outlined in the introduction, that financing is essential for trade and that it is largely supplied domestically.4 The probability that a country-|$j$| firm seeking to borrow a U.S. asset is successful is given by $p_j^\$$ ⁠, while the probability of successfully borrowing an Eurozone asset is |$p_j^\eurosmall$|⁠. If a firm successfully borrows a unit of collateral, it pays a fee, |$r^{\$}$| or |$r^{\eurosmall}$|⁠, respectively, to the household for the use of the asset and proceeds to trade in the international market. If the firm is not successful in these credit markets, it continues on to trade using a “backup” funding plan that still provides its chosen collateral, but absorbs all surplus from the transaction.5 The only equilibrium requirement for the funding fees |$r^{\$}$| and |$r^{\eurosmall}$| is that they leave firms with a positive ex-post surplus. In parallel with the labour search literature, these prices can be treated as parameters or they could be determined via some bargaining paradigm, which can then be parameterized itself. For simplicity, we follow the first of these paths and fix the funding prices to a common value, |$r^{\$} = r^{\eurosmall} = r < \pi$|⁠.6 Once successfully funded, the firm is randomly matched with a trading counterparty from another country |$j' \neq j$|⁠. Upon matching, the pair transacts using their collateral to clear any payments needed and splits the gross transaction surplus of |$2\pi$|⁠. In the event that the two counterparties’ collateral is mismatched—i.e. that one side of the match uses U.S. assets and the other side Eurozone assets as collateral—the transaction’s surplus is reduced by a collateral mismatch cost of |$2\kappa$|⁠. Throughout, we assume that |$\kappa < \pi - r$|⁠, so that the transaction is profitable even in the event of a mismatch. This “collateral mismatch” cost can be micro-founded as an expected cost in case of default, since having collateral denominated in different currencies means two promises may not be equivalent in all states of the world.7 Putting everything together, a country-|$j$| firm chooses to apply for dollar trade financing if the expected payoffs of seeking dollar financing is higher than seeking euro financing. The differential payoff of seeking a U.S. asset over a Eurozone asset is given by $$ \begin{equation} V_{j}^\$ = p_j^\$\left[\pi - r_j^{\$} - \kappa(1-\bar X)\right] - p_j^\eurosmall \left[\pi - r_j^{\eurosmall} - \kappa\bar X\right], \label{eq:payoff} \end{equation}$$(3) where |$\bar X$| is the fraction of all trading firms in the world that use dollar funding and, hence, the probability an individual firm matches with a counterparty that uses dollar financing. Naturally, firms prefer to use dollar financing so long as |$V_{j}^\$ >0$|⁠. Since our primary aim is to explain third-party use of a dominant currency, we assume that firms in the U.S. and Eurozone always seek to be funded via their respective domestic assets, and solve for the optimal currency choice of the rest-of-world trading firms.8 Under these assumptions, the average use of dollar trade financing around the world is $$ \begin{equation*} \bar X \equiv \mu_{us} X_{us} + \mu_{ez}X_{ez} + \int _0^{\mu_{rw}} X_jdj = \mu_{us} + \int _0^{\mu_{rw}} X_jdj, \end{equation*}$$ where |$X_j$| is the fraction of firms in country |$j \in [0, \mu_{rw}]$| that apply for dollar financing. We assume that the number of matches in a given country-asset credit market is governed by the constant returns to scale den Haan et al. (2000) matching function $$\begin{equation}M^F(B,X) = \frac{BX}{ B + X }, \end{equation}$$ where |$B$| represents units of the asset on offer and |$X$|⁠, the number of trading firms demanding that asset. For example, a country-|$j$| firm searching for dollar funding succeeds with probability $$\begin{equation}p_j^\$ = \frac{M^F(B_j^\$,X_j)}{X_j} = \frac{B_j^\$}{B_j^\$ + X_j}. \end{equation}$$ Substituting expressions for the funding probabilities into equation (3) yields $$ \begin{equation} V_{j}^\$ = \frac{B_j^\$}{B_j^\$ + X_j}\left[\pi - r - \kappa(1-\bar X)\right] - \frac{B_j^\eurosmall }{B_j^\eurosmall + 1-X_j}\left[\pi - r - \kappa\bar X\right].\label{eq:payoff2} \end{equation}$$(4) Equation (4) reveals the individual firm’s three strategic incentives, two with respect to other trading firms and one with respect to the domestic household. First, with respect to other domestic firms, collateral choices are strategic substitutes: when a larger share of the other country-|$j$| traders apply for dollar funding (higher |$X_j$|⁠), the local dollar funding market becomes more congested, lowering the probability a given trader’s dollar loan is approved, thus lowering the relative payoff of seeking this type of funding. Second, funding choices with respect to foreign trading firms (⁠|$\bar X$|⁠), are strategic complements due to collateral mismatch costs. This complementarity can lead to a standard type of sunspot multiplicity, in which both dollar or euro use can be sustained as equilibria, depending on the conjecture of |$\bar X$|⁠. The third strategic interaction occurs between the collateral choice of trading firms and the savings choices of households. Equation (4) captures this interaction via the presence of |$B^{\$}_j$| and |$B^{\eurosmall}_j$| in the funding probability terms. For example, a trading firm’s expected payoff of seeking dollar financing increases with the household’s holdings of U.S. bonds (⁠|$B_j^{\$}$|⁠), as larger household U.S. asset holdings increase the firm’s probability of successfully obtaining dollar funding. This final strategic interaction works against sunspot equilibria: the funding friction makes households’ bond positions a coordination device, anchoring firms’ expectations of others’ choices to credit market conditions. To analyse this formally, we define a quasi-equilibrium in trade finance use, in analogy to Mas-Colell et al. (1995, p. 551). We focus on symmetric equilibria in which |$X_j = X_{rw}$|⁠, |$B_j^{\$} = B_{rw}^{\$}$|⁠, and |$B_{j}^{\eurosmall} = B_{rw}^{\eurosmall}$| for all |$j \in [0, \mu_{rw}]$|⁠. Definition 1 (Quasi-equilibrium) Given household asset holdings in rest-of-world countries |$\{B_{rw}^\$, B_{rw}^\eurosmall \}$|⁠, a symmetric quasi-equilibrium in funding choice is a rest-of-world traders’ funding choice |$X_{rw}$| such that no trader has an incentive to change its trade finance choice. Quasi-equilibrium describes the equilibrium funding choice among trading firms as a function of the asset holdings of the households, and we denote the set of quasi-equilibria by the correspondence |$X(B_{rw}^{\$}, B_{rw}^{\eurosmall})$|⁠. Using equation (4), the set of quasi-equilibria can be characterized by the condition $$ \begin{equation} V^{\$}X_{rw}(1-X_{rw}) = 0, \label{eq:quasi} \end{equation}$$(5) with |$V^{\$} > 0$| only if |$X_{rw} = 1$| and |$V^{\$} < 0$| only if |$X_{rw} = 0$|⁠. If there is a unique value of |$X_{rw}$| satisfying (5), then |$X(B_{rw}^{\$}, B_{rw}^{\eurosmall})$| becomes a function. Lemma 1 characterizes some key properties of the quasi-equilibria in our economy: Lemma 1. Given household portfolio holdings, the currency quasi-equilibrium is unique for any feasible bond allocation if and only if $$\begin{equation}\kappa < \kappa^{\rm sunspot} \equiv \frac{\pi - r}{ \bar B + \frac{\mu_{rw}}{2} + \frac{1}{2}}.\end{equation}$$ In that case, |$X(B_{rw}^{\$}, B_{rw}^{\eurosmall}) \in \left.\left[ {\frac{\max\{B_{rw}^{\$},B_{rw}^{\euroscript}\}}{B_{rw}^{\$} + B_{rw}^{\euroscript}}}, 1\right.\right].$| Proof. Proved in Appendix A. □ Lemma 1 shows that the quasi-equilibrium funding choice can be unique even when there are strategic complementarities across countries (i.e. |$\kappa > 0$|⁠). This happens because credit market conditions affect the accessibility of funding for firms’ counterparties and the chief determinant of that accessibility is the household portfolio position. As a result, bond holdings can become a coordination device that uniquely synchronizes trade finance choices on the asset that forms a higher proportion of rest-of-world portfolios. Naturally, if we reduce the effective financial friction, for example by raising both |$B_{rw}^{\$}$| and |$B_{rw}^{\eurosmall}$| which makes both types of funding easier to obtain and reduces the congestion effects in credit markets, the scope for indeterminacy increases and the threshold |$\kappa^{\rm sunspot}$| falls. In fact, if asset holdings of both types become arbitrarily large, potential counterparties’ choices become the only payoff-relevant factor in the funding choice of firms and the quasi-equilibrium is not unique for any level of |$\kappa$|⁠: Corollary 1. In the limit of |$B_{rw}^{\$} \rightarrow \infty$| and |$B_{rw}^{\eurosmall} \rightarrow \infty$|⁠, for any |$\kappa > 0$| $$\begin{equation}X(B_{rw}^{\$}, B_{rw}^{\eurosmall}) \rightarrow \{ 0, 1/2, 1\}.\end{equation}$$ We refer to indeterminacy in the funding choice quasi-equilibrium as “sunspot” multiplicity, because in that case the funding choices are solely determined by the beliefs of what other trading firms would do, i.e. a sunspot shock in the expectations of others’ actions. Next, we characterize the effects of firm funding decisions on household savings choices. The holding premium earned by a bond is equal to the expected intra-period loan fees that the bond earns. These fees are just the probability that a country |$j$| household successfully lends this kind of bond times the funding fee |$r$| that it receives when it does so. Hence, $$ \begin{align} \Delta_j^\$ &= \frac{M^F(B_j^\$,X_j)}{B_j^\$} \times r= \frac{X_j}{B_j^\$ + X_j} r, \label{eq: usd_prem}\\ \end{align}$$(6) $$ \begin{align} \Delta_j^\eurosmall &= \frac{M^F(B_j^\eurosmall, 1-X_j)}{B_j^\eurosmall} \times r= \frac{ (1-X_j)}{B_j^\eurosmall + (1-X_j)} r. \label{eq: eur_prem} \end{align}$$(7) Since the Euler equation (2) holds for all households |$j$|⁠, the liquidity premia earned by each asset are equalized across countries: |$\Delta_j^c = \Delta^c$| for all |$j \in \{ us, ez, [0, \mu_{rw}] \}$|⁠. Using this observation, the Euler equations, and the market clearing conditions in bond markets (⁠|$\mu_{us} B_{us}^c + \mu_{ez}B_{ez}^c + \int B_j^c dj = \bar B$|⁠), we can derive Lemma 2. Lemma 2. Equilibrium household portfolios, as a function of traders’ currency choices, are: $$ \begin{align} B^\$_j &= \bar B \frac{X_j}{\int _0^{\mu_{rw}} X_j dj + \mu_{us} } \label{eq:dollar} \\ \end{align}$$(8) $$ \begin{align} B^\eurosmall_j &= \bar B \frac{1-X_j}{\int _0^{\mu_{rw}} ( 1 - X_j) dj + \mu_{ez} }. \label{eq:euro} \end{align}$$(9) Proof. Proved in Appendix A. □ Lemma 2 describes the equilibrium household portfolios as a function of the mix of assets used for trade financing by firms. This relationship is upward sloping: higher |$X_j$| implies higher |$B_j^{\$}$|⁠. Intuitively, an asset that is heavily used for funding international transactions will deliver a higher liquidity premium ceteris paribus, increasing households’ incentive to hold that bond. Since bond premia are equalized across countries, countries with a higher dollar usage (higher |$X_j$|⁠) must also have higher portfolio holdings of U.S. bonds (⁠|$B_j^{\$}$|⁠). Together, Lemmas 1 and 2 summarize the strategic firm-household interaction that is both novel and central our mechanism: Higher holdings of a given asset by rest-of-world households tilt the quasi-equilibrium in funding choices towards that asset, while use of the asset in funding markets reinforces the rest-of-world households’ decision to save in it. 2.3. Steady-state equilibria Having characterized both the financing choices of firms and the savings choices of households, we now analyse steady-state equilibria. We consider symmetric steady states in which the strategies of the ex-ante identical rest-of-world agents are the same. Definition 1 A steady-state equilibrium is a rest-of-world currency usage |$X_{rw}$|⁠, a set of asset holdings |$\{B_{rw}^\$, B_{rw}^\eurosmall, B_{us}^\$, B_{us}^\eurosmall, B_{ez}^\$, B_{ez}^\eurosmall \}$|⁠, bond prices |$\{Q^{\$}, Q^{\eurosmall} \}$| and premia |$\{\Delta^{\$}, \Delta^{\eurosmall}\}$| such that There is a quasi-equilibrium in currency choice. The optimality conditions of household bond holdings are satisfied. Bond markets clear: $$\begin{equation}\bar B = \mu_{rw}B_{rw}^c+ \mu_{us} B^c_{us} + \mu_{ez} B^c_{ez}, \mbox{ for } c\in\{ \$, \euro \}.\end{equation}$$ The bond liquidity premia equal fees paid by firms as per equations (6) and (7). Proposition 1 summarizes the characteristics of the emerging steady-state equilibria. Proposition 1. For any |$\kappa \geq 0$|⁠, the economy has three steady-state equilibria: a dollar-dominant steady state with |$X_{rw} = 1$| and |$B_{rw}^{\eurosmall} = 0$|⁠; a euro-dominant steady state with |$X_{rw} = 0$| and |$B_{rw}^\$ = 0$|⁠; and a multipolar steady state with |$X_{rw} = 1/2$| and |$B_{rw}^\$ = B_{rw}^\eurosmall$|⁠. Outside of the knife-edge case where |$\kappa = \frac{ \pi - r}{\bar B + 1}$|⁠, these are also the only steady states. Proof. Proved in Appendix A. □ Crucially, each steady state is jointly characterized by a specific rest-of-world savings composition and a corresponding trade finance choice. For example, at the dollar-dominant steady state, the rest-of-world holds large amounts of the U.S. asset, making dollar financing the most convenient for their firms, reinforcing their trade finance choices. The rest-of-world households, in turn, are happy to concentrate their savings in U.S. assets because the demand for dollar funding supports a liquidity premium on U.S. assets. This logic also explains why steady-state multiplicity is robust to generalizing many of the details in our model. For example, any strategy that traders may take to avoid paying currency mismatch costs—such as directing their search to counterparties holding a particular type of collateral or renegotiating the settlement currency ex-post—will not eliminate the interaction between households and firms. Similarly, the result is robust to allowing households to lend their assets as collateral in foreign markets, since the optimal allocation of assets across credit markets in each country |$j$| must still satisfy (8) and (9).9 2.4. Stability of steady states One of our main objectives is to understand why dominant-asset regimes appear to be so stable in the data. We have already shown that, when |$\kappa < \kappa^{\rm sunspot}$|⁠, sunspot shocks cannot change the equilibrium in trade finance markets, given household asset positions. We now derive the conditions under which the interaction between households and firms results in locally stable dominant-asset steady states, in the sense that the best response functions of both agent types jointly define a local contraction map. Intuitively, we want to ensure that deviations in saving or trade finance choices would not unravel the dominant asset equilibrium. Proposition 2 shows that the model with intermediate values of |$\kappa$| can generate dominant-asset steady states that are both locally stable and not subject to sunspot shocks. Proposition 2. For |$\kappa > \bar \kappa$| the dominant-currency steady states are locally stable, where $$\begin{equation}\bar \kappa \equiv \frac{\pi - r}{\bar B + 1} < \kappa^{sunspot}.\end{equation}$$ Proof. Proved in Appendix A. □ The result is due to the interaction among the incentives trading firms face in their financing choice, the differential availability of financing due to the feedback between households and firms, and the cross-country coordination incentive among trading firms. To see how these forces interact, consider a situation in which the economy begins at the dollar-dominant steady state, with rest-of-world household portfolios concentrated in U.S. assets and rest-of-world firms using only U.S. safe assets for financing their trade. Suppose now that households shift their savings a little towards Eurozone assets. The increased availability of euro financing gives firms an incentive to shift towards funding via Eurozone assets. However, as long as |$\kappa > \bar \kappa$|⁠, firm choices will not change much: the small shift in portfolios still leaves dollars the most widely available in world markets and, hence, firms still coordinate strongly on dollars. Thus, for a local shift in household portfolios, the cross-country coordination of firms prevents the currency quasi-equilibrium (⁠|$X$|⁠) from changing significantly, which in turn means that the conjectured shift in household portfolios is suboptimal. Proposition 2 implies there is a range of parameter values over which dominant asset steady states are both locally stable and not subject to sunspot shocks. Corollary 2. There exist a non-empty range, |$\kappa \in (\bar \kappa, \kappa^{\rm sunspot})$|⁠, over which the dominant-asset steady states are both locally stable and not subject to sunspot shocks. The existence of this region depends crucially on the interaction of our two complementarity forces: Currency sunspots require coordination incentive across firms to be so strong that a unilateral deviation in trade finance choice can be sustained, even given fixed portfolios. By contrast, local stability requires intermediate-strength coordination incentives, such that firms will only deviate from a dominant asset equilibrium if households also dramatically change their portfolio composition. Hence, necessarily, |$\bar \kappa < \kappa^{\rm sunspot}$|⁠. By the same logic, neither the asset availability mechanism nor cross-country complementarity can achieve such stability on their own: If |$\kappa = 0$|⁠, dominant-asset steady states are unstable, while if |$\kappa > 0$| and bond supplies are infinite (so credit frictions are non-existent), the firms’ funding choices are subject to sunspot shocks. We illustrate this argument graphically in Appendix B. 3. Dynamic General Equilibrium Model Having illustrated the key intuition of our mechanism, we now embed it in a rich dynamic general equilibrium model. We calibrate the model, and show it can match both targeted and untargeted moments, quantify the welfare effects of dominance, and perform counterfactuals to better understand the conditions under which dominant currencies can fall. 3.1. Setup Like our stylized model, our general environment consists of households and firms in the U.S., Eurozone, and a continuum of rest-of-world small open economies, but each of those agents now has several margins of choice. Households choose a basket of consumption, as well as their optimal savings patterns. Trading firms make optimal choices about whether to operate and how/where to trade, as well as the choice of how to finance their activities. Finally, all prices and quantities are determined in general equilibrium. 3.1.1. Households In each country |$j \in \{ us, ez, [0, \mu_{rw}] \}$|⁠, a representative household seeks to maximize the present discounted value of utility of consumption, |$E_0\sum_{t=0}^\infty \beta^t \frac{C_{jt}^{1-\sigma}}{1-\sigma}.$| In contrast to Section 2, there are country-specific differentiated goods, and the consumption basket |$C_{jt}$| is a Cobb-Douglas aggregate of all domestic and foreign goods. The consumption share of the domestic good is |$a_h\in(0,1)$|⁠, and the consumption shares for foreign goods are proportional to the size of their origin country. For example, the U.S. consumption basked is $$ \begin{equation} C_{us,t} = ({C_{us,t}^{us}})^{a_h} (C_{us,t}^{ez})^{\frac{( 1 - a_h) \mu_{ez}}{ \mu_{ez} + \mu_{rw}}} (C_{us,t}^{rw})^{\frac{( 1 - a_h) \mu_{rw}}{ \mu_{ez} + \mu_{rw}}}. \label{eq:cdef} \end{equation}$$(10) In the above, |$C_{jt}^i$| denotes consumption of good |$i$| in country |$j$| and |$C_{jt}^{rw} \equiv (\int _{0}^{\mu_{rw}} (C_{jt}^i)^{\frac{ \eta - 1}{\eta}} di)^{\frac{\eta}{\eta-1}}$| aggregates goods from the small open economies.10The consumption baskets of the Eurozone and rest-of-world economies are analogous and presented in the Supplementary Appendix. Because of the frictions in international trade, the law of one price does not hold in our economy and goods have different equilibrium prices in different locations, with a markup on imports |$P_{j,t}^i > P_{j,t}^j$|⁠. This markup relative to the origin-country price is endogenous and depends on the equilibrium patterns of trade, as we describe below. Nevertheless, since our economy is real, all prices can be expressed in terms of a numeraire good, which we take as the (identical) domestic price of the small open economy goods, i.e. |$P_{rw,t}^{rw} \equiv 1$|⁠. In addition to consumption, households choose how much to save and how to allocate savings among U.S. and Eurozone bonds, each of which yields a risk-free unit of their respective domestic good. The household in country |$j$| faces the budget constraint: $$ \begin{align} P_{jt}C_{jt} &+ (1-\Delta_{jt}^\$)P_{us,t}^{us} Q_{t}^{\$}B_{jt}^{\$} + (1-\Delta_{jt}^\eurosmall)P_{ez,t}^{ez} Q_t^{\eurosmall}B_{jt}^{\eurosmall} + \text{adj. costs}_t \nonumber \\ &= P_{us,t}^{us} B_{jt-1}^{\$} + P_{ez,t}^{ez} B_{jt-1}^{\eurosmall} + P_{jt}^j Y_{jt} + \Pi^T_{jt} + T_{jt}, \label{hh_bc} \end{align}$$(11) where $Q_t^\$$ and |$Q_t^\eurosmall$| are the prices of the U.S. and the Eurozone bonds, |$Y_{jt}$| is the household’s endowment of its domestic good, |$\Pi^T_{jt}$| is the total profit of country |$j$|’s import/export firms (described below), and |$T_{jt}$| are lump-sum taxes. As in our simple model, a household’s bond holdings earn an endogenous liquidity premium, given by the intra-period cash flows $\Delta_{jt}^\$$ and |$\Delta_{jt}^\eurosmall$|⁠. We focus on a perfect foresight, symmetric model and assume that all endowments are constant through time and equal, |$Y_{jt} = \bar Y$| for all |$j$|⁠. Households are also subject to external portfolio adjustment costs, given by $$\begin{equation}\text{adj. costs}_t \equiv P_{us,t}^{us}Q_t^{\$} \tau(B_{jt}^\$,\underline B_{j,t-1}^\$)+ P_{ez,t}^{ez}Q_t^{\eurosmall} \tau(B_{jt}^\eurosmall,\underline B_{j,t-1}^\eurosmall).\end{equation}$$ These costs are parameterized by the function |$\tau(B,\underline B) \equiv \frac{\tau}{2}\left(\frac{B-\underline B}{\underline B}\right)^2 \underline B$|⁠, which is quadratic in terms of percent deviations from the country-wide bond holdings entering the period, |$\underline B_{j,t-1}^{\$}$| and |$\underline B_{j,t-1}^{\eurosmall}$|⁠. These adjustment costs are zero at (any) steady state, and thus have no effect on steady states, but serve to limit the volatility of capital flows outside of steady state. Intertemporal optimality implies the following household Euler equation for dollar bonds $$ \begin{align} 1 & = \beta E_t\left[ \left(\frac{C_{jt+1}}{C_{jt}}\right)^{-\sigma}\frac{P_{jt}}{P_{jt+1}}\frac{P_{us,t+1}^{us}}{P_{us,t}^{us}} \frac{1}{Q_t^{\$}\left(1-\Delta_{jt}^\$ + \tau'(B_{jt}^{\$},\underline B_{j,t-1}^{\$})\right)}\right]. \label{us_bond2} \end{align}$$(12) This equation is same as (1), except that it now reflects the consequences of relative price differences among goods and across time, as well as the influence of adjustment costs on effective bond returns. An equation that is analogous to (12) holds for euro bond holdings. 3.1.2. The import–export sector International goods trade is subject to search and matching frictions as emphasized by the recent trade literature (e.g.Antras and Costinot, 2011). International trade flows through specialized import/export firms, who organize to sell country-|$j$|’s differentiated good in country |$i$|⁠, via a match between a country-|$j$| export firm with a country-|$i$| import firm. Once matched, the exporting firm buys goods at the prevailing domestic market price and sells them to the matched foreign importer, who then resells the good to the country-|$i$| household at the prevailing market price in that location. Firms optimally choose the intensity with which they search for different types of trade partners (e.g. import from U.S. versus import from the Eurozone), and the resulting matching patterns determine the size and direction of equilibrium trade flows. The import/export firms operate within the period, return profits to households, and disband.11 As before, international trade is subject to a financial friction, which implies a need for trade finance. Firms look for a fixed amount of funding, which we normalize to one unit of the numeraire, and firms again make the binary choice of either seeking U.S. or Eurozone safe assets. Both of these assumptions can be relaxed. A trading firm’s choices occur in two stages. In the first, the firm chooses whether or not to pay a fixed cost and become operational in a given period and the likelihood that, if operational, it will pursue an import or an export opportunity and with which partner country. Second, the firm chooses the type of trade financing to apply for. We consider each stage in detail before characterizing equilibrium in the model. 3.1.3. Entry and trading pattern choice Trading firms pay a fixed cost |$\phi$| in units of their domestic good to enter the international trade market. Thus, a firm enters only if the expected profits from trading net of this cost are positive, and the ones that do enter make a probabilistic choice regarding the direction in which they will trade. Specifically, an active country-|$j$| firm chooses the probabilities with which it will become an importer from country |$i$| or an exporter to country |$i$|⁠, for all |$i$|⁠, which probabilities we denote |$p_{jit}^{im}$| and |$p_{jit}^{ex}$| respectively. In equilibrium, the pattern is such that firms are indifferent between operating as an importer or exporter in any direction. We provide a detailed description of the firm’s entry decision in the Supplementary Appendix. 3.1.4. Funding choice As in the analytical model, trading firms must arrive to international trade markets with either U.S. or Eurozone safe asset collateral, which they borrow from their domestic households through bond-specific search and matching markets. Relative to the analytical model in Section 2, we enrich our model of trade finance supply in a two ways. First, we tie the potential liquidity service of an asset to the total market value of the household’s holdings of that asset. Second, because we will calibrate our model to annual data while the typical trade finance arrangement is much shorter, we introduce a parameter |$\nu$| that corresponds to the number of times a given bond could be used to intermediate trade within one model period. Thus, the total value of trade flows that the country |$j$| holdings of U.S. and Eurozone safe assets can intermediate is given by $\nu P_{us,t}^{us}B_{jt}^{\$}Q_t^\$$ and |$\nu P_{ez,t}^{ez}B_{jt}^{\eurosmall}Q_t^\eurosmall$| respectively, the market value of holdings scaled up by |$\nu$|⁠. With these assumptions, the probability of success faced by a country-|$j$| trading firm seeking U.S. financing is $$ \begin{equation} p^{\$}_{jt} = \frac{M^F\left(m_{jt}X_{jt}, \nu P_{us,t}^{us}B_{jt}^\$ Q_t^\$ \right)}{m_{jt}X_{jt}} = M^F\left( 1, \frac{ \nu P_{us,t}^{us}B_{jt}^\$ Q_t^\$ }{ m_{jt} X_{jt}} \right),\label{eq: usd_pfind}\end{equation}$$(13) where |$m_{jt}$| is the total mass of operational country-|$j$| firms, as determined by the zero-profit entry condition, and thus |$m_{jt}X_{jt}$| is the mass of country-|$j$| firms applying for dollar funding. Note that we also use the general form of the den Haan et al. (2000) matching function |$M^F(u,v) = \frac{uv}{(u^{\frac{1}{\varepsilon_F}} + v^{\frac{1}{\varepsilon_F}})^{\varepsilon_F}}$|⁠, which allows for an elasticity parameter |$\varepsilon_F$| that we calibrate to the data. The probability a country-|$j$| trading firm seeking Eurozone bonds finds a credit match, |$p^{\eurosmall}_{jt}$|⁠, is given by an analogous expression. In sum, the market tightness of each trade finance market is given by ratio of supply to demand in each: |$\frac{\nu P_{us,t}^{us}B_{jt}^\$ Q_t^\$}{m_{jt}X_{jt}}$| and |$\frac{\nu P_{ez,t}^{ez}B_{jt}^\euroscript Q_t^\euroscript}{m_{jt}(1-X_{jt})}$|⁠. We note here that tying the effective trade finance supply to the market value of assets introduces a new channel that generally reinforces the emergence of a dominant asset: Since a dominant asset carries a high equilibrium price, an asset’s ability to facilitate trade increases as it becomes dominant. As in Section 2, we fix the collateral use in the big countries exogenously, though now we calibrate |$X_{us} = 1 - X_{ez}$| to the domestic-currency trade finance usage in the U.S. and Eurozone data, which is high but not exactly 100%. We continue to assume that the U.S. and Eurozone firms face the same financing frictions as small open economies, so equation (13) and its euro analogue apply without modification for these countries as well. In making their funding choices, rest-of-world firms compare the respective expected profits of seeking dollar and euro financing. Upon a successful funding match, the expected profit of a country-|$j$| trading firm using U.S. safe assets as a collateral guarantee is given by $$\begin{equation} \tilde{\Pi}_{jt}^{\$} = \sum_{i \neq j} p_{jit}^{im}\pi_{jit}^{\$,im} + \sum_{i \neq j} p_{jit}^{ex}\pi_{jit}^{\$,ex}, \end{equation}$$ where |$\pi_{jit}^{\$,im}$| is the expected profit of a firm importing from |$i$| to |$j$| that is financed via U.S. bonds, and |$\pi_{jit}^{\$, ex}$| is the analogous values for a country-|$j$| exporter looking to match with a country-|$i$| importer. The corresponding expected profits of a country-|$j$| firm funded with Eurozone assets, |$\tilde{\Pi}_{jt}^{\eurosmall}$| is analogous. We describe the determinants of trading profits below. In return for the intra-period use of the household’s bonds, the firm pays a fee |$r$|⁠. Thus, the expected net payoff to a country-|$j$| firm of seeking dollar funding is then given by $$ \begin{equation} \Pi_{jt}^{\$} = p_{jt}^{\$}(\tilde{\Pi}_{jt}^{\$} - r), \label{eq:j_usd} \end{equation}$$(14) which is simply the probability of obtaining dollar funding, |$p_{jt}^{\$}$|⁠, times the expected profit net of the dollar funding costs. The expected payoff to seeking euro funding is |$\Pi_{jt}^{\eurosmall} = p_{jt}^{\eurosmall}(\tilde{\Pi}_{jt}^{\eurosmall} - r^{\eurosmall})$|⁠. Lastly, to match the empirical fact that, despite its dominance, the dollar is not the only currency used to finance global trade, we introduce an i.i.d. additive idiosyncratic preference shock for the type of trade financing a firm |$l$| prefers, all else equal, |$\theta_{jt}^{(l)} \sim N(0, \sigma_{\theta}^2)$|⁠. This generates some idiosyncratic heterogeneity across firms and thus results in an interior equilibrium value for the currency mix |$X_{jt}$|⁠, which we can then calibrate to the data. Combining the probabilities of obtaining each type of funding, the expressions for profits, $\Pi_{jt}^\$$ and |$\Pi_{jt}^\eurosmall$|⁠, and the disturbance |$\theta_{it}^{(l)}$|⁠, we can compute an individual firm’s net benefit of seeking financing via U.S. assets: $$\begin{equation}V^{\$,(l)}_{jt} = \frac{ 1}{ \left[ 1 + (\frac{m_{jt}X_{jt}}{\nu P_{us,t}^{us}B_{jt}^\$ Q_t^\$ })^{\frac{1}{\varepsilon_F}} \right]^{\varepsilon_F}}( \tilde \Pi_{jt}^{\$} - r) - \frac{ 1}{ \left[ 1 + (\frac{m_{jt}(1 - X_{jt})}{\nu P_{ez,t}^{ez}B_{jt}^\euroscript Q_t^\euroscript})^{\frac{1}{\varepsilon_F}} \right]^{\varepsilon_F}} ( \tilde \Pi_{jt}^{\eurosmall} - r) + \theta_{it}^{(l)}. \end{equation}$$ Firm |$l$| in country |$j$| will then choose to seek dollar funding if and only if |$V^{\$,(l)}_{jt} > 0$|⁠. Given that the expected payoff of seeking dollar funding is increasing in |$\theta_{jt}^{(l)}$|⁠, we can express the optimal choice in terms of a threshold strategy, where the firm seeks dollar funding if and only if their idiosyncratic shock exceeds a country-specific threshold |$\bar \theta_{jt}$|⁠. Thus, the fraction of country-|$j$| trading firms using U.S. safe assets is $$\begin{equation}X_{jt} = \int_{0}^{1} {\rm 1}\kern-0.24em{\rm I}(\theta_{jt}^{(l)}>=\bar \theta_{jt})dl = 1-\Phi\left(\frac{\bar \theta_{jt}}{\sigma_\theta}\right)\!,\end{equation}$$ where |$\Phi(\cdot)$| denotes the standard normal CDF. In equilibrium, the cutoff |$\bar \theta_{jt}$| is defined by |$V_{jt}^{\$, (l)} = 0$|⁠, the value of the idiosyncratic preference shock that leaves a country-|$j$| firm indifferent between choosing one asset or the other. We focus on symmetric equilibria where all ex-ante identical rest-of-world countries have the same equilibrium allocations, hence |$\bar \theta_{jt} = \bar \theta_t$| for all |$j \in [0, \mu_{rw}]$|⁠. 3.1.5. Exchange of goods Firms that are successful in obtaining financing then discover whether they will import or export, and from/to where, according to the probabilities |$p_{jit}^{im}$| and |$p_{jit}^{ex}$| that they chose optimally upon entry. Country-|$j$| exporters match with country-|$i$| importers according to the technology |$M^T(u,v) = \frac{uv}{( u^{\frac{1}{\varepsilon_T}} + v^{\frac{1}{\varepsilon_T}})^{\varepsilon_T}}$|⁠, which is of the same functional form as the matching function in credit markets, but allows for a different elasticity parameter |$\varepsilon_T$|⁠. The probability of a country-|$j$| exporter matching with a country-|$i$| importer is $$\begin{equation} p^{e i}_{jit} = \frac{M^T\left( \tilde m_{jit}^{ex}, \tilde m_{ijt}^{im} \right)}{\tilde m_{jit}^{ex}} =\left(1 + \left(\tilde m_{jit}^{ex}/\tilde m^{im}_{ijt}\right)^{1/\varepsilon_T}\right)^{-\varepsilon_T},\end{equation}$$ where |$\tilde m^{im}_{ijt} = p_{ijt}^{im} m_{it}( p_{it}^{\$}X_{it} + p_{it}^{\eurosmall}(1-X_{it}) )$| is the mass of funded importing firms in country |$i$| seeking trade with country-|$j$| firms that are looking to export to |$i$|⁠, which are themselves of mass |$\tilde m_{jit}^{ex} = p_{jit}^{ex}m_{it}( p_{it}^{\$}X_{it} + p_{it}^{\eurosmall}(1-X_{it}) )$|⁠. Using analogous derivations, the probability of a country-|$j$| importer matching with a country-|$i$| exporter is |$p^{ie}_{jit} = \left(1 + \left(\tilde m_{jit}^{im}/\tilde m^{ex}_{ijt}\right)^{1/\varepsilon_T}\right)^{-\varepsilon_T}$|⁠. In a successful match between a country-|$j$| exporter and a country-|$i$| importer, the exporter buys the |$j$| good at its domestic market price |$P_{jt}^j$| and the importer then sells it to the country-|$i$| household at the prevailing market price in that location |$P_{it}^j$|⁠. The transaction thus generates a gross surplus of |$P_{it}^j - P_{jt}^j$|⁠, which is then also subject to a collateral mismatch cost |$\kappa$|⁠. The importer and exporter in a trading match split the surplus of their transaction via Nash bargaining, with the exporter having a Nash bargaining share of |$\alpha$|⁠. The effective “wholesale” price at which a country-|$j$| exporter sells to a country-|$i$| importer is thus |$P_{jit}^{whol} = P_{jt}^j + \alpha( P_{it}^j - P_{jt}^j).$| The expected profit of a firm looking to export from country |$j$| to |$i$| is $$ \begin{equation} \pi_{jit}^{\$,ex} = p_{jit}^{ei}\frac{ \alpha}{P_{jit}^{whol}}\left[ P_{it}^{j}-P_{jt}^{j} - \kappa P_{jit}^{whol}(1 - \tilde X_{it})\right]. \label{eq: pi_surplus} \end{equation}$$(15) The term in square brackets is the net expected surplus per unit of goods traded, which is given by the gross markup on the imported good, net of the expected currency mismatch cost |$\kappa P_{jit}^{whol}(1 - \tilde X_{it})$|⁠. In this expression, $$\begin{equation}\tilde X_{it} \equiv \frac{p^\$_{it} X_{it}}{p^\$_{it} X_{it} + p^\eurosmall_{it}(1-X_{it})} \end{equation}$$ is the average use of dollar trade financing among the funded country-|$i$| firms (which are thus actively searching for trade counterparts), hence |$1 - \tilde X_{i,t}$| is the probability of matching with a EUR-funded country-|$i$| importer, and thus having to incur the expected default cost |$\kappa$|⁠.12 Lastly, the financing friction limits the overall value of the transaction to the value of the attached safe collateral. Since we assume each firm borrows one numeraire unit of safe assets, to obtain the net expected profit from the view point of a country-|$j$| exporter (who earns |$\alpha$| fraction of the total surplus), the expected per-unit profit is then scaled by |$\frac{\alpha}{P_{jit}^{whol}}$|⁠. 3.1.6. Government We assume that government purchases are zero, and thus governments play a role only in the large countries |$j\in\{us,ez\}$|⁠, where they issue bonds in fixed supply |$\bar B = B^{\$} = B^{\eurosmall}$| and set the level of lump-sum taxes so as to keep their stock of debt constant, so that |$\bar B = T_{jt} + Q_{t}^j \bar B.$| The small rest-of-world countries |$j\in[0,\mu_{rw}]$| do not issue debt and set |$T_{jt} = 0$|⁠. 3.1.7. Equilibrium In equilibrium, the liquidity premia a country-|$j$| household can earn on lending U.S. and Eurozone bonds respectively are equal to the frequency with which the household successfully lends the asset in its respective credit market multiplied by the funding fee |$r$|⁠: $$ \begin{align} \Delta_{jt}^{\$} &= \frac{ \nu m_{jt}X_{jt} }{ \left[ \left( m_{jt}X_{jt} \right)^{ 1/\varepsilon_F} + (\nu P_{us,t}^{us}B_{jt}^\$ Q_t^\$)^{ 1/\varepsilon_F} \right]^{\varepsilon_F}}r \label{eq: delta_us} \\ \end{align}$$(16) $$ \begin{align} \Delta_{jt}^{\eurosmall} &= \frac{ \nu m_{jt}(1-X_{jt}) }{ \left[ \left( m_{jt}(1-X_{jt}) \right)^{ 1/\varepsilon_F} + (\nu P_{ez,t}^{ez}B_{jt}^\eurosmall Q_t^\eurosmall)^{ 1/\varepsilon_F} \right]^{\varepsilon_F}}r \label{eq: delta_eu} \end{align}$$(17) Given those expressions, the rest of the equilibrium is determined by the household and firms’ optimal decisions, and market clearing in real goods and bond markets. We focus on the class of symmetric equilibria where the strategies of the ex-ante identical rest-of-world trading firms and households are the same, e.g. |$X_{jt} = X_{rw,t}$| for all |$j \in [0, \mu_{rw}]$|⁠. A complete definition of equilibrium is provided in the Supplementary Appendix. 3.2. Calibration We fix a set of parameters to standard values, then use the remaining parameters to target several moments, which the model replicates exactly. Table 1 lists the exogenously-fixed parameters. Specifically, we set |$\mu_{us} = \mu_{ez} = 0.2$|⁠, consistent with the sizes of the U.S. and the Eurozone in world GDP. One model period represents a year, hence we set |$\beta = 0.96$|⁠; we also assume log preferences (⁠|$\sigma = 1$|⁠). Next, we minimize the role of the search friction between exporters and importers by using a low value for the elasticity of the trade matching function, |$\varepsilon _T = 0.01$|⁠, which ensures that firms on the less crowded side of the market are virtually guaranteed a match. We fix |$\alpha = 0.5$|⁠, thus importers and exporters have equal bargaining power, and set the currency use in the big countries (⁠|$X_{us}$| and |$X_{ez}$|⁠) so |$90\%$| of their firms use their domestic asset, to match the evidence on domestic currency usage in trade finance for the U.S. and the Eurozone (BIS, 2014). TABLE 1 Exogenously fixed parameters Parameter . Concept . Value . |$\beta$| Time preference 0.960 |$\mu_{us} = \mu_{ez}$| Big country size 0.200 |$\kappa$| Mismatch cost 0.010 |$r$| Funding fee 0.005 |$\nu$| Exog. velocity 8.000 |$X_{us}$| U.S. dollar share 0.900 |$X_{ez}$| EZ dollar share 0.100 |$\alpha$| Exporters bargaining parameter 0.500 |$\sigma$| Risk aversion 1.000 |$\varepsilon_{T}$| Elasticity of trade matching function 0.010 |$\sigma^2_\theta$| Variance of idio. shock 1e-06 |$\tau$| Portfolio adj. costs 0.040 Parameter . Concept . Value . |$\beta$| Time preference 0.960 |$\mu_{us} = \mu_{ez}$| Big country size 0.200 |$\kappa$| Mismatch cost 0.010 |$r$| Funding fee 0.005 |$\nu$| Exog. velocity 8.000 |$X_{us}$| U.S. dollar share 0.900 |$X_{ez}$| EZ dollar share 0.100 |$\alpha$| Exporters bargaining parameter 0.500 |$\sigma$| Risk aversion 1.000 |$\varepsilon_{T}$| Elasticity of trade matching function 0.010 |$\sigma^2_\theta$| Variance of idio. shock 1e-06 |$\tau$| Portfolio adj. costs 0.040 Open in new tab TABLE 1 Exogenously fixed parameters Parameter . Concept . Value . |$\beta$| Time preference 0.960 |$\mu_{us} = \mu_{ez}$| Big country size 0.200 |$\kappa$| Mismatch cost 0.010 |$r$| Funding fee 0.005 |$\nu$| Exog. velocity 8.000 |$X_{us}$| U.S. dollar share 0.900 |$X_{ez}$| EZ dollar share 0.100 |$\alpha$| Exporters bargaining parameter 0.500 |$\sigma$| Risk aversion 1.000 |$\varepsilon_{T}$| Elasticity of trade matching function 0.010 |$\sigma^2_\theta$| Variance of idio. shock 1e-06 |$\tau$| Portfolio adj. costs 0.040 Parameter . Concept . Value . |$\beta$| Time preference 0.960 |$\mu_{us} = \mu_{ez}$| Big country size 0.200 |$\kappa$| Mismatch cost 0.010 |$r$| Funding fee 0.005 |$\nu$| Exog. velocity 8.000 |$X_{us}$| U.S. dollar share 0.900 |$X_{ez}$| EZ dollar share 0.100 |$\alpha$| Exporters bargaining parameter 0.500 |$\sigma$| Risk aversion 1.000 |$\varepsilon_{T}$| Elasticity of trade matching function 0.010 |$\sigma^2_\theta$| Variance of idio. shock 1e-06 |$\tau$| Portfolio adj. costs 0.040 Open in new tab To match the observed maturity of a typical letter of credit contract in the data (45 days), we set |$\nu = 8$|⁠, implying that an asset can be used up to 8 times per year for trade finance operations. To match the typical cost of letters of credit—which includes a substantial fixed component, on average |$40$| basis points of the principal, plus a spread on top of the LIBOR—we set |$r = 0.005$|⁠.13 Next, we set the collateral mismatch cost |$\kappa = 0.01$| to be just 1% of the value of the transaction, which is in fact smaller than typical exchange rate hedging costs.14 It turns out that this value of mismatch costs is also both sufficient to ensure local stability of dominant-asset steady states and to prevent sunspot multiplicity in the collateral choice quasi-equilibrium, as we confirm in our numerical solutions described below. We fix two additional parameters in order to ensure numerical stability, but minimize their substantive impact. First, we set |$\tau = 0.04$| just large enough to prevent large instantaneous jumps in the composition of bond portfolios (e.g. a shift from a portfolio concentrated in U.S. asset, to one concentrated in Eurozone assets within a period) that could lead to equilibrium multiplicity. This value implies that a 10% change in bond positions incurs a cost of just 2 basis points on the portfolio. We also make the currency preference shocks as small as possible (⁠|$\sigma_{\theta}^2 =$|1e|$-$|06), while still ensuring numerically reliable interior solutions for |$X_{rw}$|⁠. We calibrate the remaining parameters to match a set of target steady-state moments. Like our analytical model, the calibrated model has three co-existing steady states—dollar and euro dominant ones, and a symmetric one. Since the dollar has long been the dominant currency, we match the empirical moments from the past four decades to those at the dollar-dominant steady state of the model. Panel (a) of Table 2 summarizes the targeted moments: (1) government debt of 60% of GDP, consistent with the U.S. average; (2) rest-of-world trade share (⁠|$\frac{ \text{ Imports + Exports }}{ \text{ GDP}}$| ) of 55%, consistent with trade data for non-U.S. and non-Eurozone countries from the World Bank; (3) dollar share in trade financing used by rest-of-world trading firms of 80%, consistent with the evidence on the fraction of letters of credit and trade finance loans denominated in dollars BIS (2014); and (4) import markups of 10%, consistent with micro-level estimates on import markups in Coşar et al. (2018). TABLE 2 Calibration strategy Concept . Data . Model . Gross debt/GDP 0.60 0.60 ROW trade/GDP 0.55 0.55 ROW USD usage 0.80 0.80 Import markup 1.10 1.10 (a) Calibration targets Concept . Data . Model . Gross debt/GDP 0.60 0.60 ROW trade/GDP 0.55 0.55 ROW USD usage 0.80 0.80 Import markup 1.10 1.10 (a) Calibration targets Parameter . Concept . Value . |$\bar B$| U.S./EZ asset supply 1.471 |$a_h$| Home bias 0.718 |$\varepsilon_F$| Funding match. elas. 0.294 |$\phi$| Fixed cost of entry 0.038 (b) Implied parameter values Parameter . Concept . Value . |$\bar B$| U.S./EZ asset supply 1.471 |$a_h$| Home bias 0.718 |$\varepsilon_F$| Funding match. elas. 0.294 |$\phi$| Fixed cost of entry 0.038 (b) Implied parameter values Open in new tab TABLE 2 Calibration strategy Concept . Data . Model . Gross debt/GDP 0.60 0.60 ROW trade/GDP 0.55 0.55 ROW USD usage 0.80 0.80 Import markup 1.10 1.10 (a) Calibration targets Concept . Data . Model . Gross debt/GDP 0.60 0.60 ROW trade/GDP 0.55 0.55 ROW USD usage 0.80 0.80 Import markup 1.10 1.10 (a) Calibration targets Parameter . Concept . Value . |$\bar B$| U.S./EZ asset supply 1.471 |$a_h$| Home bias 0.718 |$\varepsilon_F$| Funding match. elas. 0.294 |$\phi$| Fixed cost of entry 0.038 (b) Implied parameter values Parameter . Concept . Value . |$\bar B$| U.S./EZ asset supply 1.471 |$a_h$| Home bias 0.718 |$\varepsilon_F$| Funding match. elas. 0.294 |$\phi$| Fixed cost of entry 0.038 (b) Implied parameter values Open in new tab We target these four moments with the four remaining free parameters |$\{ \bar B, a_h, \varepsilon_F, \phi \}$|⁠. These parameters are (1) the supply of government debt |$\bar B$|⁠; (2) the home bias parameter in consumption preferences |$a_h$| which determines the trade share; (3) the elasticity of the funding matching function |$\varepsilon_F$| which helps determine the equilibrium level of currency coordination; and (4) the fixed cost of entry in the trading sector |$\phi$| which helps determine import markups. We find the model can exactly match the targeted moments, with the implied parameter values given in Panel (b) of Table 2. 3.3. Quantitative Results We now consider the model’s quantitative implications for non-targeted moments in steady-state and then proceed to use global techniques to solve for the model’s (perfect-foresight) transition dynamics. We then explore the model’s implications for three counterfactual scenarios. In the first, we examine what could have happened to dollar dominance had the Eurozone continued it expansion beyond its current size. In the second, we explore the implications of the decreasing relative size of the U.S. compared to the world economy. Finally, we explore potential consequences of trade wars initiated by the U.S. 3.3.1. Steady state Table 3 summarizes several key steady state moments in the calibrated economy, and shows that the (empirically relevant) dollar-dominant steady state matches a number of untargeted phenomena. First, since the rest-of-world countries primarily use dollars for trade finance (⁠|$X_{rw} = 0.8$|⁠), the U.S. bond earns a higher equilibrium liquidity premium: |$\Delta^{\$} > \Delta^{\eurosmall}$|⁠, which in turn results in an interest parity violation: Interest rates on Eurozone bonds must exceed rates on U.S. bonds in order to offset the lower liquidity return. Specifically, we find $$\begin{equation} \frac{1}{Q^{\eurosmall}} - \frac{1}{Q^{\$}} = \frac{ \Delta^{\$} - \Delta^{\eurosmall}}{\beta} = 1.07\%, \end{equation}$$ which implies the U.S. earns a significant “exorbitant privilege.” The size of this excess return is consistent with the Gourinchas and Rey (2007a) evidence on exorbitant privilege and the U.S. Treasury convenience yield estimated by Jiang et al. (2020). TABLE 3 Steady-state values for baseline model. . USD Dominant . Multipolar . EUR Dominant . Moments . U.S. . EZ . RW . U.S. . EZ . RW . U.S. . EZ . RW . Panel A: Benchmark model USD share trade fin. (⁠|$X_j$|⁠) 0.90 0.10 0.80 0.90 0.10 0.50 0.90 0.10 0.20 100|$\times$||$(r^\euroscript - r^\$)$| 1.07 1.07 1.07 0.00 0.00 0.00 –1.07 –1.07 –1.07 100|$\times$|Seignorage/GDP 0.88 0.23 - 0.56 0.56 - 0.23 0.88 - NFA/GDP –0.42 –0.26 0.18 –0.38 –0.38 0.19 –0.26 –0.42 0.18 Gross foreign assets/GDP 0.04 0.02 0.18 0.02 0.02 0.19 0.02 0.04 0.18 100|$\times$|Trade bal./GDP 0.87 0.86 –0.45 1.01 1.01 –0.52 0.86 0.87 –0.45 Panel B: Rest-of-world asset |$( \bar B_{rw}/(P_{rw} \bar Y) = 0.40)$| 100|$\times$||$(i^\$ - i^\euroscript)$| 1.03 - - 0.00 - - - –1.03 - NFA/GDP –0.14 0.01 0.03 –0.10 –0.10 0.05 0.01 –0.14 0.03 Gross foreign assets/GDP 0.31 0.29 0.18 0.30 0.30 0.20 0.29 0.31 0.18 100|$\times$|Trade bal./GDP –0.25 –0.28 0.14 –0.12 –0.12 0.07 –0.28 –0.25 0.14 . USD Dominant . Multipolar . EUR Dominant . Moments . U.S. . EZ . RW . U.S. . EZ . RW . U.S. . EZ . RW . Panel A: Benchmark model USD share trade fin. (⁠|$X_j$|⁠) 0.90 0.10 0.80 0.90 0.10 0.50 0.90 0.10 0.20 100|$\times$||$(r^\euroscript - r^\$)$| 1.07 1.07 1.07 0.00 0.00 0.00 –1.07 –1.07 –1.07 100|$\times$|Seignorage/GDP 0.88 0.23 - 0.56 0.56 - 0.23 0.88 - NFA/GDP –0.42 –0.26 0.18 –0.38 –0.38 0.19 –0.26 –0.42 0.18 Gross foreign assets/GDP 0.04 0.02 0.18 0.02 0.02 0.19 0.02 0.04 0.18 100|$\times$|Trade bal./GDP 0.87 0.86 –0.45 1.01 1.01 –0.52 0.86 0.87 –0.45 Panel B: Rest-of-world asset |$( \bar B_{rw}/(P_{rw} \bar Y) = 0.40)$| 100|$\times$||$(i^\$ - i^\euroscript)$| 1.03 - - 0.00 - - - –1.03 - NFA/GDP –0.14 0.01 0.03 –0.10 –0.10 0.05 0.01 –0.14 0.03 Gross foreign assets/GDP 0.31 0.29 0.18 0.30 0.30 0.20 0.29 0.31 0.18 100|$\times$|Trade bal./GDP –0.25 –0.28 0.14 –0.12 –0.12 0.07 –0.28 –0.25 0.14 Open in new tab TABLE 3 Steady-state values for baseline model. . USD Dominant . Multipolar . EUR Dominant . Moments . U.S. . EZ . RW . U.S. . EZ . RW . U.S. . EZ . RW . Panel A: Benchmark model USD share trade fin. (⁠|$X_j$|⁠) 0.90 0.10 0.80 0.90 0.10 0.50 0.90 0.10 0.20 100|$\times$||$(r^\euroscript - r^\$)$| 1.07 1.07 1.07 0.00 0.00 0.00 –1.07 –1.07 –1.07 100|$\times$|Seignorage/GDP 0.88 0.23 - 0.56 0.56 - 0.23 0.88 - NFA/GDP –0.42 –0.26 0.18 –0.38 –0.38 0.19 –0.26 –0.42 0.18 Gross foreign assets/GDP 0.04 0.02 0.18 0.02 0.02 0.19 0.02 0.04 0.18 100|$\times$|Trade bal./GDP 0.87 0.86 –0.45 1.01 1.01 –0.52 0.86 0.87 –0.45 Panel B: Rest-of-world asset |$( \bar B_{rw}/(P_{rw} \bar Y) = 0.40)$| 100|$\times$||$(i^\$ - i^\euroscript)$| 1.03 - - 0.00 - - - –1.03 - NFA/GDP –0.14 0.01 0.03 –0.10 –0.10 0.05 0.01 –0.14 0.03 Gross foreign assets/GDP 0.31 0.29 0.18 0.30 0.30 0.20 0.29 0.31 0.18 100|$\times$|Trade bal./GDP –0.25 –0.28 0.14 –0.12 –0.12 0.07 –0.28 –0.25 0.14 . USD Dominant . Multipolar . EUR Dominant . Moments . U.S. . EZ . RW . U.S. . EZ . RW . U.S. . EZ . RW . Panel A: Benchmark model USD share trade fin. (⁠|$X_j$|⁠) 0.90 0.10 0.80 0.90 0.10 0.50 0.90 0.10 0.20 100|$\times$||$(r^\euroscript - r^\$)$| 1.07 1.07 1.07 0.00 0.00 0.00 –1.07 –1.07 –1.07 100|$\times$|Seignorage/GDP 0.88 0.23 - 0.56 0.56 - 0.23 0.88 - NFA/GDP –0.42 –0.26 0.18 –0.38 –0.38 0.19 –0.26 –0.42 0.18 Gross foreign assets/GDP 0.04 0.02 0.18 0.02 0.02 0.19 0.02 0.04 0.18 100|$\times$|Trade bal./GDP 0.87 0.86 –0.45 1.01 1.01 –0.52 0.86 0.87 –0.45 Panel B: Rest-of-world asset |$( \bar B_{rw}/(P_{rw} \bar Y) = 0.40)$| 100|$\times$||$(i^\$ - i^\euroscript)$| 1.03 - - 0.00 - - - –1.03 - NFA/GDP –0.14 0.01 0.03 –0.10 –0.10 0.05 0.01 –0.14 0.03 Gross foreign assets/GDP 0.31 0.29 0.18 0.30 0.30 0.20 0.29 0.31 0.18 100|$\times$|Trade bal./GDP –0.25 –0.28 0.14 –0.12 –0.12 0.07 –0.28 –0.25 0.14 Open in new tab The third line of the table (seignorage) provides a common and simple estimate of the net benefit the U.S. receives from the “privilege” of this interest differential. This number is computed as the counterfactual additional debt servicing payments the U.S. would face if it actually paid an interest rate equal to the inverse of the time discount, holding asset positions constant. Essentially, this is the seignorage the U.S. earns from the liquidity premium on its asset and, at |$0.88\%$| of GDP, our model estimates this to be substantial. Though similar calculations have often been used to estimate the benefits of exorbitant privilege, our model implies that this is an incomplete and potentially misleading measure of privilege because it takes asset positions as given. A key insight of our theory is that widespread foreign holdings of a country’s assets are necessary to support its dominant status. But such strong external demand leads to a negative steady-state net foreign asset position for the central country, and hence the seignorage benefits of being dominant are at least partially offset by the need to service the resulting negative net foreign asset position. Indeed, the fourth line in the table shows that the dominant country (i.e. U.S.) has a significant negative net foreign asset position equal to |$-$|42% of GDP, while the other big country (i.e. Eurozone) has a much better net foreign asset position of |$-$|26% of GDP. This is a manifestation of the fact that rest-of-world households concentrate their savings in U.S. assets, which is the second sense in which those assets are dominant. In particular, the model implies that two-thirds of rest-of-world portfolios are invested in U.S. bonds, amounting to a long position in U.S. assets equal to 12% of rest-of-world GDP, consistent with the evidence in Caballero et al. (2008). Overall, at our calibration the U.S. trade balance is only slightly better than that of the Eurozone, despite the excess return the U.S. earns, suggesting that the net welfare effect of dominance is small (which we quantify precisely later) since its position as an external net debtor largely offsets the benefits of exorbitant privilege. Lastly, we emphasize that while the U.S. trade balance is positive in the benchmark model, our mechanism can indeed generate a negative net foreign asset position and a trade deficit at the same time. To illustrate this, Panel B of Table 3 considers a version of the model with a richer asset structure, in which each of the small economies also issues government debt equal to 40% of their GDP. The assets from each small country are measure zero, and hence do not finance international trade, but households in all countries may hold the basket of rest-of-world bonds for investment purposes.15 This version of the model shows the U.S. holding a significantly larger gross position in foreign assets—31% of GDP versus just 4%—as now there is a foreign asset which does not have a high liquidity value to foreigners, and thus offers high returns to Americans. This modification results in a steady-state trade deficit for the U.S., even as the U.S. net foreign asset position remains significantly negative, because the U.S. is now able to leverage its exorbitant privilege by investing in a high yielding foreign asset.16 This is an important success of our framework, and something a large class of other models of the exorbitant privilege cannot generate (e.g.Caballero et al., 2008). Still, we abstract from this in our benchmark analysis, in order to minimize the number of state variables and facilitate the global solution of the model dynamics. 3.3.2. Dynamics We now consider the out-of-steady-state dynamics of the calibrated model, with a particular focus on determining the stability properties of different steady states. Figure 1 plots the respective attraction regions of the model’s three steady states. We compute these regions by defining a fine grid on the state space of the model, which is depicted in the axes of the figure.17 We treat each grid point as a possible initial condition, and compute all perfect foresight equilibrium paths originating from that point and converging to one of the three steady states. Thus, for each grid point we run three separate attempts to compute an equilibrium path—one that ends at the dollar-dominant steady state, one that ends at the multipolar steady state, and one that ends at the euro-dominant steady state. For each point in the blue region, we find that there is only a single possible equilibrium path, which converges to the dollar-dominant steady state. Conversely, for points in the orange region, the only feasible outcome is the euro-dominant steady state. Finally, the light gray region corresponds to points where we found perfect foresight paths that arrive at both coordinated steady states—this is a region of dynamic indeterminacy. Figure 1 Open in new tabDownload slide Steady-state attraction regions. A key result of Figure 1 is that only the dominant-currency steady states are dynamically stable, i.e. dynamic paths that are initialized away from the symmetric steady state never converge there.18 Moreover, each dominant-asset steady state is contained within a large region in which it is the only possible long-run outcome. For example, whenever rest-of-world households’ initial portfolios are sufficiently biased towards U.S. assets (bottom right, blue region), the unique equilibrium path converges to the dollar-dominant steady state. This is a manifestation of the interactions we explored in Section 2: when portfolios have more U.S. assets, firms tilt their actions towards financing trade with U.S. assets, reinforcing the household decision to save primarily in those assets. These large unique attraction regions show that dominant-asset regimes in the model are endogenously persistent and sustainable indefinitely, so long as no large shocks push the economy out of the respective basins of attraction. And even in that case, the model will still converge to one or the other dominant-currency steady states, confirming that a dominant-currency regime is the eventual outcome in any given simulation. We next explore the transition paths that underly Figure 1 in more detail. As an example, Figure 2 plots the transition of several endogenous variables, when the economy starts at the (unstable) symmetric steady state and converges to the dollar-dominant steady state. The top right panel shows the evolution of the equilibrium mix of collateral used (⁠|$X_{rw}$|⁠), which starts close to equally balanced and then gradually converges to dominant dollar usage over the subsequent 15 to 20 years. Along this transition path, the exorbitant privilege of the U.S. gradually builds as rest-of-world household portfolios (right column, middle plot and also the gray line in Figure 1) shift towards U.S. assets. The shift towards U.S. assets, in turn, worsens the U.S. net foreign asset position. Figure 2 Open in new tabDownload slide Transition from the symmetric steady state to dollar-dominant steady state. The top-left panel of Figure 2 plots the paths of U.S. and Eurozone consumption during this transition and shows that U.S. consumption is elevated for an extended period. This is a result of the increasing foreign demand for U.S. assets, which allows the U.S. to steadily increase its borrowing from the rest of the world at a low interest rate. Meanwhile, Eurozone consumption is significantly depressed, as the Eurozone increases savings in order to repatriate some of its assets, which were previously held abroad but are now in lower demand externally. Though U.S. consumption is relatively high throughout the transition period depicted in Figure 1, the steady-state findings in Table 3 show that the eventual consumption levels of the U.S. and the Eurozone are similar, suggesting that transition and long run welfare implications can be very different. Table 4 summarizes the welfare effects of dominance in consumption equivalent units. TABLE 4 Welfare gain/loss at dollar-dominant steady state, as percentage of symmetric steady state consumption. . U.S. . EZ . RW . Steady-state only 0.25% 0.22% |$-$|0.12% Incl. transition 0.37% |$-$|0.37% |$-$|0.00% . U.S. . EZ . RW . Steady-state only 0.25% 0.22% |$-$|0.12% Incl. transition 0.37% |$-$|0.37% |$-$|0.00% Open in new tab TABLE 4 Welfare gain/loss at dollar-dominant steady state, as percentage of symmetric steady state consumption. . U.S. . EZ . RW . Steady-state only 0.25% 0.22% |$-$|0.12% Incl. transition 0.37% |$-$|0.37% |$-$|0.00% . U.S. . EZ . RW . Steady-state only 0.25% 0.22% |$-$|0.12% Incl. transition 0.37% |$-$|0.37% |$-$|0.00% Open in new tab While the steady-state welfare calculation (top row) shows essentially no harm of dollar dominance for the Eurozone, incorporating the transition dynamics to the dollar-dominant steady state reverses this conclusion. Taking into account the transition period, in which the U.S. is able to maintain consumption significantly above its eventual steady-state level for an extended period of time, the U.S. permanent consumption equivalent is |$0.75\%$| higher than that of the Eurozone. This is an order of magnitude larger than the |$0.03\%$| welfare gain implied by steady-state consumption difference alone. Thus, accounting for both out of steady state dynamics and general equilibrium portfolio and asset positions, is crucial for properly assessing the welfare implications of issuing the dominant currency. 3.4. The emergence of dollar dominance The model rationalizes the historical experience of prolonged dominant-asset regimes—e.g. the British pound was dominant before the 1940s, and the U.S. dollar since—because only dominant-asset steady states are dynamically stable. But why is the dollar, specifically, playing the dominant role currently? Our model suggests that both an initial advantage in the U.S.’s ability to supply safe assets and path dependence play important roles. Regarding the dollar’s initial advantage, our model suggests two features were particularly important. First, after WWII the U.S. had a unique ability to credibly supply large quantities of safe assets. Second, under the Bretton Woods agreement, the U.S. was the only country with virtually no capital controls, which facilitated international access to its (abundant) supply of safe assets.19 In such an asymmetric world, our model implies that there in fact exists only one steady state, with coordination on the single abundant asset the unique outcome globally, which explains how the dollar established its initial post-war dominance. Since the dollar gained dominance in world markets, however, the U.S. has become less unique both in terms of its ability to supply large quantities of a safe asset on a global scale, and in terms of its economic size and central role in world trade. Because historical experience suggests (occasional) transitions are possible, we next explore how empirically relevant changes to the global economy might affect the dollar’s dominant position. 3.4.1. Introduction of the Euro Many academics and policy makers once speculated that the formation of the Eurozone might precipitate a shift in the equilibrium (e.g. Chinn and Frankel, 2007). In our model, the emergence of a Eurozone block similar to the U.S. creates a second stable steady state, but path dependence prevents the economy from transiting to it absent some other precipitating shock. To illustrate this point, we simulate two alternative, counterfactual scenarios of the euro introduction. In both cases, we take the starting point (i.e. the world pre-1999) as one in which the supply of the alternative asset is 60% of the size of the U.S. safe asset supply, i.e. |$\bar B^{\eurosmall} = 0.6 \bar B^{\$}$|⁠, consistent with the supply of German bonds at the time. We then model the formation of the Eurozone as an increase in the supply of the alternative safe asset over time, reflecting the increased fiscal capacity of the Eurozone.20 Before exploring dynamics, we first look at the model’s steady-state implications before the Eurozone is introduced. When the supply of the alternative asset is only 60% of that of the U.S. asset, we find the model has a unique, dollar-dominant steady state: The initial asymmetry in the supply of the two assets is strong enough to guarantee world coordination on the dollar. Initializing the economy at this steady state, we then consider the resulting transition path(s) as the supply of Eurozone assets grows with the introduction of the euro. In the first scenario, plotted in Figure 3 with a blue line, we assume that the total supply of Eurozone safe assets converges to the same level as that of the U.S. asset over a 10 year period (i.e. to our benchmark calibration). We find that there is a unique transition path out of the dollar-dominant, pre-Eurozone steady state, a path which converges to the new dollar-dominant steady state. Along the transition path, dollar use, the interest rate differential, and the U.S. net foreign asset position are essentially unchanged, consistent with the continued dominance of the dollar in the data. Thus, our model agrees that path dependence is too strong for the introduction of the euro, by itself, to change the currency regime. The euro introduction creates a new, euro-based steady state, but without further shocks, the world would not converge to it. Figure 3 Open in new tabDownload slide Introduction of Euro In the second scenario, we consider the counterfactual possibility that the Eurozone eventually grows significantly larger than the U.S., to the point that the euro-dominant steady state becomes unique. Making the euro-dominant steady state unique requires the supply of Eurozone assets to exceed the supply of U.S. assets by 30%: i.e. |$\frac{\bar B^{\eurosmall}}{\bar B^{\$}} > 1.3$|⁠. We plot this scenario with a red line in Figure 3. Along the path to the new, uniquely stable euro-dominant steady state, the U.S. net foreign asset position shrinks towards zero, and the U.S.’s exorbitant privilege benefits disappears as U.S. safe assets largely leave international markets and return to U.S. portfolios. The welfare impact is significant: the welfare swing between the U.S. and the Eurozone is equivalent to 1.4% of permanent consumption. The figure also highlights an insight that we can only derive thanks to the model’s dynamic nature. Namely, there are significant anticipation effects, as much of the shift in portfolios and international currency usage occurs before the supply of Eurozone assets has actually converged to its new, high steady state. This means that a switch away from the dollar-dominant regime could have occurred upon the creation of the Eurozone, if investors around the world were convinced that additional countries such as the UK and Sweden would eventually join, even if this consolidation never actually ends-up happening. Just the expectation of further expansion, if held long enough for rest-of-world portfolios to rebalance towards Eurozone assets, could have precipitated a change in currency regime. Overall, these counterfactuals show that merely introducing a fundamentally equivalent asset is not enough to shift the currency regime; to become dominant, the alternative asset needs to offer a substantially bigger base than the dollar, now or in the future. Yet, the 30% threshold implied by the model is not so extreme, and it could realistically be surpassed by either the Eurozone or China in the future. 3.4.2. Growth of the rest-of-world The U.S. share of world output has shrunk by roughly 15 percentage points since 1960, with a corresponding rise in the output share of developing (non-G7) countries. A natural question is whether this fall in the relative size of the U.S. imperiled the dominance of the U.S. dollar or if, by contrast, it actually increased the benefits of issuing the dominant currency since the dollar asset intermediates a now larger quantity of rest-of-world trade. To explore this question, we consider a counterfactual experiment in which the U.S. starts as the largest economy and gradually shrinks (from |$\mu_{us}=0.35$| to |$0.20$|⁠, our benchmark calibration), while the rest-of-world reciprocally grows (from |$\mu_{rw} = 0.45$| to |$0.60$|⁠). To isolate the effects of size, we hold constant the aggregate supply of U.S. and euro bonds, |$\bar B$|⁠.21 A first insight is that at the starting point where the U.S. is substantially bigger than the Eurozone again there exists only one steady state, at which the dollar is dominant. In this case, the use of dollars in the rest of the world is anchored by the relatively high probability that rest-of-world firms will trade with dollar-intensive U.S. firms. The fall in the size of the U.S. opens the possibility of a change in the dominant currency, as our benchmark calibration features two stable steady states. In this sense, our model implies that the dollar’s dominance has become more fragile over the last 60 years, both because of the introduction of alternative assets and because of the U.S.’s reduced share of the global economy. To understand whether the changing relative economic size of the U.S. had a material impact on the U.S.’s dominance in practice, Figure 4 plots the evolution of several key variables as the economy follows the (unique) transition path, which leads to the dollar-dominant steady state of our symmetric baseline model. The top-right panel of the figure shows that, as the U.S. shrinks, the intensity of the rest-of-world dollar usage (⁠|$\bar X_{rw}$|⁠) falls somewhat but the dollar clearly remains dominant. The intensity of dollar use falls because rest-of-world trading firms now face a substantially smaller chance of encountering U.S. firms, who primarily use dollars in their trading activity. This reduces their incentive to use dollars, a reduction that is reinforced by strategic incentives in general equilibrium. Figure 4 Open in new tabDownload slide Growth of rest-of-world Even though average use of dollars among rest-of-world firms falls, the mass of rest-of-world firms that use dollars actually grows due to the increase in the economic size of the rest-of-world countries. This, in turn, increases the total external demand for U.S. assets (due to the increased volume of dollar-denominated trade), as can be seen from the bottom right panel of Figure 4 (⁠|$B_{rw}^{\$}$|⁠). Overall, the U.S.’s shrinking size gives rise to offsetting effects on U.S. dominance, which on net leave the U.S. in a similar position in 2020 as it was in 1960—the clear hegemon, with a somewhat lower exorbitant privilege in terms of the interest rate spread |$r^{\eurosmall} - r^{\$}$| (bottom left panel of the Figure, mainly due to fall in |$\bar X_{rw}$|⁠), but enjoying a higher overall external demand for its assets. These implications track the historical experience. The U.S. has indeed remained dominant through the last 60 years, although that dominance is somewhat less pronounced given the small but rising share of “other” currencies used internationally as compared to sixty years ago. Still, our model implies that the U.S. is managing to extract a similarly large effective seignorage, thanks to the increased volume of international trade. 3.4.3. Comparison to Gopinath and Stein (2020) The predictions explored in the above experiments contrast with other models. For example, according to the model of Gopinath and Stein (2020), increasing the supply of an asset (our first experiment) should decrease the likelihood it becomes dominant whereas our model implies the reverse.22 Similarly, in their model, increasing the quantity of world trade while keeping asset supplies constant should have significantly boosted dollar dominance. While these alternative mechanisms need not be mutually exclusive, we think historical experience favours the sort of relationship implied by our model. First, a strong empirical pattern is that the hegemon country carries a substantial negative net foreign asset position, as exemplified by the persistent U.S. imbalance. This observation is explained endogenously by our model—an asset that is dominant must be widely held abroad—but seems in tension with their model in which the special asset is the scarce one. Second, historical accounts of the emergence of the dollar tend to emphasize the importance of dollar “availability” rather than “scarcity.” For example, Eichengreen and Flandreau (2012) documents the crucial role played by the Federal Reserve Act of 1913, which significantly increased the availability of offshore dollar trade financing, in jump-starting the U.S. dollar’s international role. More recently, Bahaj and Reis (2020) document a similar effect in terms of the growing importance of the Chinese renminbi and the increased number of swap agreements the Chinese Central Bank has signed with rest-of-world counterparts. As a final piece of suggestive evidence, our Supplementary Appendix C documents two stylized patterns in cross-sectional data that support the hypothesis that asset availability favours an asset’s dominant status. In that appendix, we relate a country’s holdings of U.S. Treasuries with the use of dollars in invoicing and the issuance of dollar-denominated bank liabilities. In the first case, we find that larger holdings of Treasuries in country |$i$| are associated with higher dollar invoicing. In the second case, we find that larger holdings of Treasuries in country |$i$| are associated with greater issuance of dollar bank liabilities in that country.23 Both results seem to contrast with the mechanism in Gopinath and Stein (2020), which relies on the offshore scarcity of the dominant asset, but are consistent with our model which relies instead on wide-spread holdings of an asset to drive dominance. Since these are correlations, not causal relationships, we view the results as only suggestive evidence. Finally, we note there is no tension between our theoretical findings and the empirical evidence of e.g.Krishnanurthy and Vissing-Jorgensen (2011) that asset supply and convenience yields are negatively correlated. In our model, the positive association between supply and liquidity premia appears only when comparing steady states. By contrast, local increases in an asset’s supply will still imply a fall in its liquidity premium, just as in the data. 3.5. Trade policy and barriers Recent trade conflicts between the U.S. and other countries have raised the possibility that trade barriers might affect the currency regime. To shed some light on this, we consider two “trade war” scenarios in which the U.S. introduces a proportional tariff |$\gamma$| on all imports and the Eurozone and rest-of-world countries respond by levying the same tariffs on U.S. imports. Tariffs are implemented as taxes paid by consumers, so while U.S. importers receive the price of |$P_{us,t}^j$| for each imported type |$j$| good, U.S. consumers pay the effective price $$\begin{equation}\tilde P_{us,t}^j = (1 + \gamma)P_{us,t}^j.\end{equation}$$ Similarly, Eurozone and rest-of-world consumers pay import taxes on U.S. imports, and hence face the prices |$\tilde P_{jt}^{us} = (1+\gamma) P_{jt}^{us}$|⁠. In all countries, tariff revenues are reimbursed lump-sum to households. Even though they are refunded, the tariffs lead to expenditure switching on the consumer side, and thus also shift the equilibrium patterns of trade flows. We consider two scenarios, a “moderate” trade war where |$\gamma = 0.15$| and an “acute” one where |$\gamma = 0.30$|⁠. 3.5.1. Moderate trade war Figure 5(a) depicts the consequences of a permanent trade war, with tariffs set to |$\gamma = 0.15$|⁠. The tariffs change the position of the steady states and also their respective attraction regions (old steady states are marked with |$\times$|⁠; the new steady states with a dot). As the figure shows, the region of unique attraction to the dollar-dominant steady state is eliminated, and both the old and new dollar-dominant steady states lie within the region of equilibrium indeterminacy. Moreover, the region of unique attraction to the euro-dominant steady state is significantly increased. Hence, even a moderate trade war could potentially endanger the position of the dollar, as it makes the dollar-dominant regime unstable. Figure 5 Open in new tabDownload slide Attraction regions under trade war scenarios. Notes: Left panel depicts regions of attraction assuming long-lived tariffs of 15%; right panel depicts attraction regions, assuming long-lived tariffs of 30%. The right panel shows that only the Euro can be dominant in the long run in the acute trade war scenario. The trade war weakens dollar dominance for two reasons. First, it diverts rest-of-world trade away from the U.S. and towards the Eurozone. Since Eurozone firms are far more likely to use Eurozone assets in their trade, rest-of-world firms become more likely to encounter euro-funded trading partners and, hence, to prefer euros. Second, the overall world trade level falls, decreasing trade quantities relative to total asset supply. As trade financing become less scarce, the equilibrium anchoring effects of the financial friction become weaker, increasing the indeterminacy region. The first row of Table 5 reports the welfare implications of the moderate trade war, assuming the dollar remains dominant. The U.S. is disproportionately hurt by the trade war for two reasons. First, there is the standard effect from the fact that the distortions created by the tariffs hit all of its exports, while the Eurozone and the rest-of-world face tariffs only on their direct trade with the U.S. Second, as world trade levels fall, the U.S.’s seignorage revenue decreases as both fewer firms require liquidity and a smaller portion choose dollars. TABLE 5 Gain/loss as percentage of dollar-dominant steady state consumption. . U.S. . EZ . RW . Dollar remains dominant |$-$|1.34% 0.07% 0.09% Euro becomes dominant |$-$|2.13% 0.79% 0.10% . U.S. . EZ . RW . Dollar remains dominant |$-$|1.34% 0.07% 0.09% Euro becomes dominant |$-$|2.13% 0.79% 0.10% Open in new tab TABLE 5 Gain/loss as percentage of dollar-dominant steady state consumption. . U.S. . EZ . RW . Dollar remains dominant |$-$|1.34% 0.07% 0.09% Euro becomes dominant |$-$|2.13% 0.79% 0.10% . U.S. . EZ . RW . Dollar remains dominant |$-$|1.34% 0.07% 0.09% Euro becomes dominant |$-$|2.13% 0.79% 0.10% Open in new tab Since the starting position of the economy (i.e. the dollar-dominant steady state before the tariffs) is now inside the indeterminate region, however, this is not the only possible outcome. In the second row of Table 5, we report the welfare implications of the same trade war scenario, but assuming the alternative long-run outcome that is now possible—that the dollar looses dominance and the economy transitions to the euro steady state. In this second case, the U.S. is significantly worse off and Eurozone welfare is substantially improved. On the one hand, at the new steady state the U.S. loses all of its seignorage, as the world currency use and the resulting exorbitant privilege shift to the Eurozone. On the other hand, the transition to this new steady state itself, depicted by the long gray line in Figure 5(a), is particularly painful because during the transition the U.S. runs significant trade surpluses as external demand for dollar assets dries up. The welfare difference between the U.S. and Eurozone when the euro becomes dominant is 2.9% of permanent consumption. Comparing to the first line of the table, where the U.S.-EZ welfare differential is 1.4%, we conclude that the loss of currency dominance is worth 1.5% of permanent consumption. Moreover, we also find that the transition dynamics generate two-thirds of this effect, hence a steady-state-only model would understate the cost of losing special status by a factor of three. 3.5.2. Acute trade war Figure 5(b) depicts the implications of a permanent 30% tariff between the U.S. and Eurozone/rest-of-world, a scenario we call an “acute” trade war. In this case, the effects of the trade barriers are strong enough to eliminate the symmetric and the dollar-dominant steady states, thereby guaranteeing a transition to the now-unique euro steady state. This is a strong implication, but a permanent 30% tariff on all imports is (we hope) implausible. Hence, we also consider the effects of a temporary trade war of the same magnitude. Figure 6 depicts the welfare cost for different possible durations, ranging from one to 40 years. The figure shows that for trade wars lasting under 10 years, the economy cannot transition to the euro steady state absent other shocks. Within this range, longer trade wars are worse but not discretely so, highlighting the general stability of the model: Even 10 years of a very acute trade war is not enough to shift the currency regime. Figure 6 Open in new tabDownload slide Welfare costs of an acute trade war as a function of duration. For trade wars lasting more than 10 years, however, the economy enters a region of indeterminacy, and a transition to the euro-dominant steady state becomes possible. If a transition occurs, the U.S. is discretely worse off, and suffers an additional loss of roughly 1% of permanent consumption. If the trade war lasts longer than 28 years, the unique outcome is a transition to the euro-dominant steady state, despite the fact that tariffs return to zero in the long-run. Thus, certain temporary shocks, could have permanent effects. 4. Conclusions This article presents a new theory describing the emergence of dominant international assets. Our model is quantitatively realistic and tractable enough to use for standard macroeconomic analysis. Throughout, we have abstracted from risk: both the potential for short run shocks that perturb the economy around a given steady state and possible longer-run stochastic transitions between currency regimes. Both of these extensions are straightforward: Business-cycle analysis can be conducted using policy functions approximated locally around a given steady state, or via global solution techniques. Such extensions could help the model address the observation of Gourinchas et al. (2017) that an “exorbitant duty” coincides with the privilege of being the dominant currency. We leave exploration of this issue to future work. The editor in charge of this paper was Thomas Chaney. Data Availability The data and code underlying the results in this article are available in Zenodo at https://doi.org/10.5281/zenodo.5544238. Acknowledgement This article originally circulated as Boston College Working Paper 934. We are grateful to our discussants, Ozge Akinci, Saleem Bahaj, Matteo Maggiori, Federica Romei, Adrien Verdelhan, and Martin Wolf, and to seminar participants at the AEA annual meetings, Banque de France, Barcelona Summer Forum, Boston Macro Juniors Workshop, Boston University, CEBRA 2021, CEF, Chicago Booth IFM, EACBN-Mannheim, the Federal Reserve Banks of Boston, Dallas, Chicago, Richmond, and Philadelphia, Fordham Conference on Macroeconomics and International Finance, Harvard University, Indiana University, the Konstanz Seminar on Monetary Theory and Monetary Policy, the Spring 2018 NBER IFM, Oxford-Zurich Macrofinance 2021, SED, SEM, SFS, UQAM, University of Notre Dame, and the University of Wisconsin-Madison. We thank Sherty Huang for excellent research assistance. Supplementary Data Supplementary data are available at Review of Economic Studies online. And the replication packages are available at https://dx.doi.org/10.5281/zenodo.5544238. APPENDIX A. Proofs Proof of Lemma 1 First, we prove that, under the condition in the Lemma, the quasi-equilibrium correspondence |$X(B_{rw}^{\$}, B_{rw}^{\euroscript})$| is a scalar for all possible asset holdings. Since the total supply of each asset is |$\bar B$|⁠, then market clearing (⁠|$\bar B = \mu_{rw}B_{rw}^c + \mu_{us} B_{us}^c + \mu_{ez} B_{ez}^c$|⁠) puts an upper bound on the feasible rest-of-world asset holdings: $$\begin{equation}B_{rw}^{\$} < \frac{ \bar B}{\mu_{rw}}, \hspace{.2in} B_{rw}^{\euroscript} < \frac{ \bar B}{\mu_{rw}}\end{equation}$$ If either |$B_{rw}^{\$} = 0$| or |$B_{rw}^{\euroscript} =0$|⁠, it is trivially true that the quasi-equilibrium is unique. For example, if |$B^{\euroscript}_{rw} = 0$| then $$\begin{equation} V^{\$}(X_{rw}) = \frac{B^{\$}_{rw}}{B^{\$}_{rw} + X_{rw}}\left( \pi - r - \kappa( 1 - X_{rw}\mu_{rw} - \mu_{us})\right) > 0 \end{equation}$$ since |$\kappa < \pi - r$|⁠. Thus, the only quasi-equilibrium in funding is |$X_{rw}=1$|⁠. Similarly, if |$B_{rw}^{\$} = 0$|⁠, the only quasi-equilibrium is |$X_{rw} = 0$|⁠. Next, we show that for any pair of bond holdings |$\{ B^{\$}_{rw}, B^{\euroscript}_{rw} \}$|⁠, such that |$B^{\$}\in (0, \frac{\bar B}{\mu_{rw}})$| and |$B^{\euroscript} \in (0, \frac{\bar B}{\mu_{rw}})$|⁠, the net payoff of using dollars crosses zero exactly once, thus the quasi-equilibrium is unique. Using |$\mu_{us} = \mu_{eu} = \frac{1-\mu_{rw}}{2}$|⁠, and evaluating equation (4) at |$X_{rw} = 1$|⁠: $$\begin{equation} V^{\$}(1) = -\frac{\pi -r}{B^{\$}_{rw} +1} + \kappa \frac{\mu_{rw}( B^{\$}_{rw} + \frac{1}{2}) + \frac{1}{2}}{B^{\$}_{rw}+1} \end{equation}$$ This is strictly negative (and thus |$X_{rw}=1$| is not a quasi-equilibrium) if and only if $$\begin{equation}\kappa < \frac{ \pi - r}{\mu_{rw}( B^{\$}_{rw} + \frac{1}{2}) + \frac{1}{2}}.\end{equation}$$ A similar argument implies that |$V^\$(0) > 0$| if and only if $$\begin{equation}\kappa < \frac{ \pi - r}{\mu_{rw}( B^{\euroscript}_{rw} + \frac{1}{2}) + \frac{1}{2}}.\end{equation}$$ But since |$B_{rw}^{\$} < \frac{ \bar B}{\mu_{rw}}$|⁠, $$\begin{equation} \frac{ \pi - r}{\mu_{rw}( B^{\$}_{rw} + \frac{1}{2}) + \frac{1}{2}} > \frac{ \pi - r}{ \bar B + \frac{\mu_{rw}}{2} + \frac{1}{2}} = \kappa^{sunspot} \end{equation}$$ Thus, when |$\kappa < \kappa^{sunspot}$|⁠, |$X_{rw} = 1$| is not a quasi-equilibrium for any feasible allocation of asset holdings when |$B^{\$} > 0$| and |$B^{\euroscript} > 0$|⁠. A similar argument shows that |$X_{rw} = 0$| is not a quasi-equilibrium either in this case. Hence, all existing quasi-equilibria must be interior and thus solve |$V^{\$}(X_{rw}) = 0$|⁠. Evaluating equation (4) gives: $$\begin{equation}V^\$(X_{rw}) = \frac{B^{\$}_{rw}}{ B^{\$}_{rw} + X_{rw}} \left[\pi - r - \kappa (1- X_{rw}\mu_{rw} - \mu_{us})\right] - \frac{ B^{\euroscript}_{rw}}{ B^{\euroscript}_{rw} + (1- X_{rw}) } \left[\pi - r - \kappa ( X_{rw}\mu_{rw} + \mu_{ez})\right]. \end{equation}$$ Setting the above expression equal to zero and multiplying by |$\frac{1}{\kappa}(B^{\$}_{rw}+X_{rw})(B^{\euroscript}_{rw} + (1-X_{rw}))$| results in a quadratic equation in |$X_{rw}$|⁠. Simplifying further, and dividing through by |$\kappa$|⁠, allows us to express the resulting quadratic polynomial as |$P(X_{rw})$|⁠: $$ \begin{align*} P(X_{rw}) &= (B^{\euroscript}_{rw}-B^{\$}_{rw})\mu_{rw}X_{rw}^2\\ &\quad + \left( B^{\$}_{rw} \left( \frac{1}{2} + \frac{3}{2} \mu_{rw} - 2 \frac{\pi - r}{\kappa}\right) + B^{\euroscript}_{rw} \left(\frac{1}{2} - \frac{\mu_{rw}}{2} + 2 B^{\$}_{rw} \mu_{rw} - \frac{\pi - r}{\kappa}\right) \right)X_{rw} \\ &\quad + B^{\$}_{rw} \left( \frac{\pi - r}{\kappa} - \left(\frac{1}{2} + \mu_{rw}(B^{\euroscript}_{rw} + 1)\right) \right) \end{align*}$$ Since the quadratic polynomial |$P(X_{rw})$| has different signs at |$P(0)$| and |$P(1)$|⁠, it can only have a single crossing in the range |$X\in(0,1)$| and thus there is a unique quasi-equilibrium. Let |$X^* \in (0,1)$| be the unique quasi-equilibrium value that satisfies |$P(X^*) = 0$| for a given level of bond holdings |$\{B_{rw}^{\$}, B_{rw}^{\euroscript} \}$|⁠. To see that |$X^* > \frac{B^{\$}_{rw}}{B^{\$}_{rw}+ B^{\euroscript}_{rw}}$| whenever |$B^\$_{rw}>B^\euroscript_{rw}$|⁠, notice that if |$B^\$_{rw}>B^\euroscript_{rw}$| $$\begin{equation} P(X_{rw} = \frac{B_{rw}^{\$}}{B_{rw}^{\$}+ B_{rw}^{\euroscript}}) = \frac{B_{rw}^{\$}B_{rw}^{\euroscript} \mu_{rw}\left( B_{rw}^{\$} (1 + B_{rw}^{\$}) - B_{rw}^{\euroscript}(1 + B_{rw}^{\euroscript})\right)}{(B_{rw}^{\euroscript} + B_{rw}^{\$})^2} > 0.\end{equation}$$ Hence since |$P(1) < 0$|⁠, the zero of the quadratic polynomial |$P(X)$| must be at a value |$X^* > \frac{B^{\$}_{rw}}{B^{\$}_{rw}+ B^{\euroscript}_{rw}}$|⁠. To prove that |$\kappa < \frac{ \pi - r}{ \bar B^{\$} + \frac{\mu_{rw}}{2} + \frac{1}{2}}$| is a necessary condition for uniqueness, let |$\kappa > \frac{ \pi - r}{ \bar B + \frac{\mu_{rw}}{2} + \frac{1}{2}}$| and note that if |$B_{rw}^{\$} = \frac{\bar B}{\mu_{rw}}$| and |$B_{rw}^{\euroscript} = \frac{ \bar B}{\mu_{rw}}$|⁠: $$\begin{equation} V^{\$}(1) = -\frac{\pi -r}{B^{\$}_{rw} +1} + \kappa \frac{\mu_{rw}( B^{\$}_{rw} + \frac{1}{2}) + \frac{1}{2}}{B^{\$}_{rw}+1} > 0 \end{equation}$$ and $$\begin{equation} V^{\$}(0) = \frac{\pi -r}{B^{\$}_{rw} +1} - \kappa \frac{\mu_{rw}( B^{\$}_{rw} + \frac{1}{2}) + \frac{1}{2}}{B^{\$}_{rw}+1} < 0 \end{equation}$$ Thus, in this case both |$1$| and |$0$| are quasi-equilibria, and hence |$X( \frac{\bar B}{\mu_{rw}}, \frac{\bar B}{\mu_{rw}})$| is set valued, Hence, |$X(B_{rw}^{\$}, B_{rw}^{\euroscript})$| is not a scalar-valued function across the whole state space, and we conclude the quasi-equilibrium is not always unique. □ Proof of Lemma 2 Throughout, let |$j \in [0, \mu_{rw}]$| be an arbitrary index for a small open economy. Accounting explicitly for the inequality constraint in bonds, the steady-state Euler equations (2) for dollars can be written $$ \begin{equation} \frac{1}{\beta} = \frac{1}{Q^\$ - \Delta_{j}^\$} + \lambda_j^\$ = \frac{1}{Q^\$ - \Delta_{us}^\$} + \lambda_{us}^\$ = \frac{1}{Q^\$ - \Delta_{eu}^\$} + \lambda_{eu}^\$, \label{eq:euler_app} \end{equation}$$(A.1) where the weakly positive |$\lambda$|’s are appropriately scaled Lagrange multipliers and the complementarity slackness conditions $$ \begin{equation} \lambda_j B^\$_j =\lambda_{us} B^\$_{us} = \lambda_{eu} B^\$_{eu} = 0 \end{equation}$$(A.2) must hold for all countries. We being by proving the following additional Lemma which would be helpful: Lemma 3. |$B_j^\$ = 0$| if and only if |$X_j = 0$|⁠. Similarly, |$B_j^{\euroscript} = 0$| if and only if |$X_j = 1$|⁠. We prove the statement for dollar bond holdings, the statement for euro holdings follows by a parallel argument. If: If |$X_j = X_{ez} = 0$| the premia |$\Delta_{j}^\$ = \Delta_{eu}^\$ = 0$| by equation (6), while |$\Delta_{us}^\$ > 0$|⁠. Hence equation (A.1) reduces to $$ \begin{equation} \frac{1}{Q^\$ } + \lambda_j^\$ = \frac{1}{Q^\$ } + \lambda_{ez}^\$ = \frac{1}{Q^\$ - \Delta_{us}^\$} + \lambda_{us}^\$. \end{equation}$$(A.3) But this equation shows that |$\lambda_j > \lambda_{us}$| and |$\lambda_{ez} > \lambda_{us}$|⁠. Since |$\lambda_{us} \geq 0$|⁠, we know that |$\lambda_j > 0$| and |$\lambda_{ez} > 0$| and, from complementary slackness, that |$B_j^\$ = B_{eu}^\$ = 0$|⁠. Only If: To find a contradiction, suppose that |$X_j > 0$| but |$B_j^\$ = 0$|⁠. Since |$B_j^\$ = 0$|⁠, in equilibrium there must be some other country |$j'$| (it could be the U.S. or it could be another small country) which holds positive amount of U.S. bonds and pays premium |$\Delta_{j'}^\$ < r$|⁠. In this case, equation (A.1) implies $$ \begin{equation} \frac{1}{Q^\$ - \Delta_{j'}^\$} = \frac{1}{Q^\$ - r } + \lambda_j^\$. \end{equation}$$(A.4) which cannot be true since |$\lambda_j^\$\geq 0$|⁠. Hence, |$B_j^\$ > 0$|⁠. And the helper Lemma 3 is proved. An implication of the proof above is that |$B_{ez}^\$ = B^\euroscript_{us} = 0$|⁠. We can now use the equality of the remaining premia along with market clearing conditions to compute the expressions in the text. For example, $\Delta^\$_{us} = \Delta_j^\$$ implies that $$\begin{equation}\frac{X_j}{B_{j}^\$ + X_j} = \frac{X_{us}}{B_{us}^\$ + X_{us}},\end{equation}$$ which simplifies to $$\begin{equation} B_{us}^\$ = B_{j}^\$\frac{X_{us}}{X_{j}}.\end{equation}$$ Using this expression and the fact that |$B_{ez} = 0$|⁠, $B_{us}^\$$ and $B_{ez}^\$$ can be eliminated in the market clearing condition for dollar bonds. $$ \begin{align} \bar B & = \int_{\mu_{rw}} \frac{B_{us}^\$}{X_{us}}X_i di + \mu_{us} B_{us}^\$ \\ \end{align}$$(A.5) $$ \begin{align} \bar B & = \frac{B_j^\$}{X_{j}}\int_{\mu_{rw}} X_i di + \mu_{us} \frac{B_{j}^\$}{X_{j}}.\label{eq:mcfinal} \end{align}$$(A.6) Where in the second line we pick a specific country |$j$| and substitute in |$X_{us} = 1$|⁠. Solving expression (A.6) for $B_j^\$$ gives equation (8) in the Lemma 2. The same steps for euro bonds imply equation (9). □ Proof of Proposition 1 To show that the dollar-dominant steady state exists, conjecture that the rest-of-world traders all use dollars and thus |$X_{rw}=1$|⁠. Using Lemma 2, the optimal bond holdings of the rest-of-world households are then $$ \begin{align*} B_{rw}^{\$} &= \frac{ \bar B}{ \bar B + \mu_{rw} + \mu_{us}} \\ B^{\euroscript}_{rw} &= 0. \end{align*}$$ Plugging those expression into the relative payoff of seeking dollar versus euro funding for a rest-of-world trader (⁠|$V^{\$}$|⁠), we have: $$\begin{equation} V^{\$} = \frac{ \bar B}{ \bar B + \mu_{rw} + \mu_{us}}\left( \pi - r - \kappa( 1 - \mu_{rw} - \mu_{us}) \right) > 0.\end{equation}$$ Thus, using dollars is strictly preferred by any rest-of-world trader, and the dollar dominant steady state where |$X_{rw}=1$| is indeed sustained. Conjecturing |$X_{rw}= 0$|⁠, instead, and following a similar argument shows that the euro-dominant steady state |$X=0$| also exists. Lastly, we look for interior steady-state equilibria where |$X_{rw} \in (0,1)$|⁠. In that, case the optimal bond holdings for the rest-of-world households are given by: $$ \begin{align*} B^{\$}_{rw} &= \bar B \frac{ X_{rw}}{ \mu_{rw}X_{rw} + \mu_{us}} \\ B^{\euroscript}_{rw} &= \bar B \frac{ 1 - X_{rw}}{ \mu_{rw}(1-X_{rw}) + \mu_{ez}}. \end{align*}$$ Substituting in those expressions for bond holdings in the value of seeking dollar collateral relative to euro collateral for a rest-of-world trader, we have $$ \begin{align} V^\$(X_{rw}) &= \frac{\bar B}{\bar B + \mu_{rw} X_{rw} + \mu_{us}} \left[\pi - r - \kappa (1- X_{rw}\mu_{rw} - \mu_{us})\right] - \nonumber \\ & \hspace{.2in} \frac{\bar B}{\bar B + \mu_{rw} (1- X_{rw}) + \mu_{ez}} \left[\pi - r - \kappa ( X_{rw}\mu_{rw} + \mu_{us})\right] \label{eq:V_int}. \end{align}$$(A.7) Any interior equilibrium must satisfy |$V(X_{rw}) = 0$| – these are the points at which the traders are indifferent between seeking dollar and euro financing. To find the zeros of |$V^{\$}(X_{rw})$|⁠, we set (A.7) equal to 0, and multiply through with |$(\bar B + \mu_{rw} X_{rw} + \mu_{us})(\bar B + \mu_{rw} (1- X_{rw}) + \mu_{ez})$|⁠. Then further dividing by |$\bar B$|⁠, gives us the condition $$\begin{equation}(\bar B + \mu_{rw} (1- X_{rw}) + \mu_{ez})\left[\pi - r - \kappa (1- X_{rw}\mu_{rw} - \mu_{us})\right] - (\bar B + \mu_{rw} X_{rw} + \mu_{us}) \left[\pi - r - \kappa ( X_{rw}\mu_{rw} + \mu_{us})\right] = 0\end{equation}$$ Using the fact that |$\mu_{us} = \mu_{ez}$| and |$\mu_{us}+\mu_{eu}+\mu_{rw} = 1$|⁠, this equation simplifies to $$\begin{equation} \mu_{rw}(\kappa (\bar B + 1) - \pi - r)(2X_{rw} - 1) = 0.\end{equation}$$ This linear equation has the unique solution |$X_{rw} = \frac{1}{2}$| when |$\kappa \neq \frac{ \pi - r}{\bar B + 1}$|⁠, and admits any |$X_{rw} \in [0,1]$| as a solution in the knife edge case |$\kappa = \frac{ \pi - r}{\bar B + 1}$|⁠. Thus, for any |$\kappa \geq 0$| that is different from |$\frac{ \pi - r}{\bar B + 1}$| there are three steady states, |$X_{rw} \in \{0, \frac{1}{2}, 1\}$|⁠, and when |$\kappa = \frac{ \pi - r}{\bar B + 1}$| there is a continuum of steady states |$X_{rw} \in [0,1]$|⁠. The associated steady-state bond holdings are then immediately implied by Lemma 2. □ Proof of Proposition 2 To prove local stability of a steady state, we need to show that the best-response functions define a contraction in the neighbourhood of that steady state. Define the vector of best response functions of trading firms and households in country |$j$|⁠, given the actions of all other firms, |$X_{rw}$|⁠, and households in the rest of the world |$B^{\$}_{rw}$| and |$B^{\euroscript}_{rw}$|⁠: $$ \begin{align*} \varphi _X ( X, B^{\$}, B^{\euroscript}) &= \frac{ B^{\$}( \pi - \kappa( B^{\euroscript}+ 1) + \kappa (\mu_{rw}X + \mu_{us}) ( 2 B^{\euroscript} + 1))}{ (B^{\$} + B^{\euroscript}) \pi + \kappa( (\mu_{rw}X + \mu_{us}) (B^{\$} - B^{\euroscript} ) - B^{\$}) } \\ \varphi _{B^{\$}} ( X, B^{\$}, B^{\euroscript}) &= \bar B \frac{ X }{ \mu_{rw} X + \mu_{us}} \\ \varphi _{B^{\euroscript}} ( X, B^{\$}, B^{\euroscript}) & = \bar B \frac{ 1 - X }{ \mu_{rw}( 1 - X) + \mu_{ez}} \end{align*}$$ Stacking these in the vector |$\Phi \equiv [ \varphi _X, \varphi_{B^{\$}}, \varphi_{B^{\euroscript}} ]$|⁠, we want to show that |$\Phi$| is a local contraction map, which is the case whenever the eigenvalues of the Jacobian |$\triangledown \Phi$| lie inside the unit circle. The Jacobian has the form $$\begin{equation} \triangledown \Phi= \left[ \begin{array}{ccc} \frac{ \partial \varphi_X}{ \partial X} & \frac{ \partial \varphi_X}{ \partial B^{\$}} & \frac{ \partial \varphi_X}{ \partial B^{\euroscript}} \\\frac{ \partial \varphi_{B^{\$}}}{ \partial X} &0 & 0 \\ \frac{ \partial \varphi_{B^{\euroscript}}}{ \partial X} &0 & 0 \\ \end{array} \right] \end{equation}$$ hence its eigenvalues are given by the roots of the characteristic polynomial $$\begin{equation} \lambda \left( \lambda^2 - \lambda \frac{ \partial \varphi_X}{ \partial X} - \frac{ \partial \varphi_X}{ \partial B^{\$}}\frac{ \partial \varphi_{B^{\$}}}{ \partial X} - \frac{ \partial \varphi_X}{ \partial B^{\euroscript}}\frac{ \partial \varphi_{B^{\euroscript}}}{ \partial X} \right) = 0. \end{equation}$$ Clearly, one solutions is |$\lambda = 0$|⁠, but we need to check that the roots of the quadratic term in the parenthesis are smaller than unity. We now check this condition for each steady state. Case I: Symmetric steady state At the symmetric steady state we have that |$\frac{ \partial \varphi_X}{ \partial B^{\$}} = - \frac{ \partial \varphi_X}{ \partial B^{\euroscript}}$| and |$\frac{ \partial \varphi_{B^{\$}}}{ \partial X} = - \frac{ \partial \varphi_{B^{\euroscript}}}{ \partial X}$|⁠. Hence, the relevant condition for the eigenvalues reduces to $$\begin{equation} \lambda^2 - \lambda \frac{ \partial \varphi_X}{ \partial X} - 2\frac{ \partial \varphi_X}{ \partial B^{\$}} \frac{ \partial \varphi_{B^{\$}}}{ \partial X} = 0 \end{equation}$$ with roots $$\begin{equation} \lambda^* = \frac{1}{2}\left( \frac{ \partial \varphi_X}{ \partial X} \pm \sqrt{ \left( \frac{ \partial \varphi_X}{ \partial X}\right)^2 + 8 \frac{ \partial \varphi_X}{ \partial B^{\$}}\frac{ \partial \varphi_{B^{\$}}}{ \partial X} } \right).\end{equation}$$ At the symmetric steady state. $$\begin{equation} \frac{ \partial \varphi_X}{ \partial X} = \frac{(1 + 2 \bar B) \kappa \mu_{rw}}{2\pi - \kappa}> 0 \end{equation}$$ since |$\kappa < \pi$|⁠. Hence, the bigger root (in absolute value) is $$\begin{equation} \lambda^* = \frac{1}{2}\left( \frac{ \partial \varphi_X}{ \partial X} + \sqrt{ \left( \frac{ \partial \varphi_X}{ \partial X}\right)^2 + 8 \frac{ \partial \varphi_X}{ \partial B^{\$}}\frac{ \partial \varphi_{B^{\$}}}{ \partial X} } \right).\end{equation}$$ Lastly, since we also have that $$\begin{equation} \frac{ \partial \frac{ \partial \varphi_{B^{\$}}}{ \partial X} }{ \partial \kappa } = \frac{ \partial \frac{ \partial \varphi_X}{ \partial B^{\$}}}{ \partial \kappa } = 0, \end{equation}$$ the root is growing in |$\kappa$|⁠. The threshold |$\bar \kappa$| that ensures the root is within the unit circle solves |$\lambda^* = 1$|⁠, which after some rearranging results in: $$\begin{equation} 1 - \frac{ \partial \varphi_X}{ \partial X} - 2 \frac{ \partial \varphi_X}{ \partial B^{\$}}\frac{ \partial \varphi_{B^{\$}}}{ \partial X} = 0. \end{equation}$$ Solving for the threshold |$\kappa$|⁠, we obtain $$\begin{equation} \bar \kappa = \frac{ \pi - r}{\bar B + 1} \end{equation}$$ Hence, in the neighbourhood of the symmetric steady state, the roots of the characteristic polynomial are inside the unit circle so long as |$\kappa < \bar \kappa$|⁠. Case II: Dollar-dominant steady state At the dollar dominant steady state |$X_{rw} = 1$| and $$\begin{equation} \frac{ \partial \varphi_X}{ \partial X} = \frac{ \partial \varphi_X}{ \partial B^{\$}} = 0.\end{equation}$$ Hence the roots |$\lambda$| are given by $$\begin{equation} \lambda^2 = \frac{ \partial \varphi_{B^{\euroscript}}}{ \partial X} \frac{ \partial \varphi_{X}}{ \partial B^{\euroscript}}\end{equation}$$ where $$\begin{equation} \frac{ \partial \varphi_{B^{\euroscript}}}{ \partial X} \frac{ \partial \varphi_{X}}{ \partial B^{\euroscript}} = \frac{ (1 + \mu_{rw}) (\pi - r) - \kappa (\frac{1}{2} + \mu_{rw} (1 + 2 \bar B + \frac{\mu_{rw}}{2})) }{ (1 - \mu_{rw}) ( \pi -r - \frac{\kappa}{2} (1 - \mu_{rw}) )}. \end{equation}$$ If |$\kappa < \frac{ (\pi - r) (1 + \mu_{rw})}{ \frac{1}{2} + \mu_{rw} (1 + 2 \bar B + \frac{\mu_{rw}}{2})}$| then the above expression is positive. In that case, if it is also true that $$\begin{equation} \kappa > \frac{ \pi - r}{ \bar B + 1 } = \bar \kappa \end{equation}$$ (i.e. |$\kappa \in ( \bar \kappa, \frac{ (\pi - r) (1 + \mu_{rw})}{ \frac{1}{2} + \mu_{rw} (1 + 2 \bar B + \frac{\mu_{rw}}{2})})$| then |$\lambda < 1$|⁠. On the other hand, if |$\kappa > \frac{ (\pi - r) (1 + \mu_{rw})}{ \frac{1}{2} + \mu_{rw} (1 + 2 \bar B + \frac{\mu_{rw}}{2})}$| the best response function |$\varphi_X$| hits its upper bound of |$1$|⁠. In particular, in that case |$\frac{ \partial \varphi_{X}}{ \partial B^{\euroscript}} > 0$| in the neighbourhood of the dollar-dominant steady state. This implies that starting at the dollar-dominant steady state, a small increase in |$B^{\euroscript}$| will increase |$\varphi_X$| even further, going over 1. However, |$X_{rw}=1$| is the upper bound on |$X$|⁠, and enforcing this, means that for |$\kappa > \frac{ (\pi - r) (1 + \mu_{rw})}{ \frac{1}{2} + \mu_{rw} (1 + 2 \bar B + \frac{\mu_{rw}}{2})}$| effectively |$\frac{ \partial \varphi_X}{ \partial B^{\euroscript}} = 0$| and thus |$\lambda^2 = 0.$| Thus, all eigenvalues of |$\triangledown \Phi$| are zero, and the system is very stable locally. Thus, the dollar-dominant steady state is stable for any |$\kappa > \bar \kappa = \frac{ \pi - r}{ \bar B + 1 }.$| Case III: Euro-dominant steady state Can be proven with identical steps to Case II. □ B. Visual Illustration of Simplified Model Figure B.1 illustrates Proposition 2. First, the black line shows the quasi-equilibrium in trade finance choice |$X_{rw}$|⁠, as a function of bond holdings (⁠|$x$|-axis). Figure B.1(a) demonstrates local stability of dominant-asset steady states, which can be seen from the fact that the black line is relatively flat in the corners, implying that firms do not respond too much to a small change in portfolios. Figure B.1(b) showcases the possibility of sunspots when |$\kappa$| is large, in which case |$X$| becomes a correspondence. Figure B.1 Open in new tabDownload slide Best response functions Footnotes 1. Amiti et al. (2018) find evidence of such coordination incentives in firm-level trade data from Belgium. 2. While our perfect foresight model does not differentiate between covered and uncovered interest parity (UIP), the spirit of our mechanism is most consistent with a violation of UIP. Trade collateral is required to guarantee future contract performance, thus the resulting convenience yield is earned by an asset’s ability to insure a promised future dollar value, meaning synthetic dollar bonds and U.S. dollar bonds are equivalent to one another, but different from euro bonds. 3. Evidence for such frictions is widely documented, e.g.Antras and Foley (2015) and Hoefele et al. (2016). 4. While stylized, this setup closely resembled the key features of the popular letter of credit form of trade finance, in which two banks guarantee each side of an international contract, and also serves as a tractable abstraction for a wider range of trade finance arrangements used in practice (e.g. Schmidt-Eisenlohr, 2013). 5. This assumption simplifies derivations; in our quantitative model, unfunded firms exit without trading, so that trade finance constitutes a real constraint on equilibrium trade flows. 6. Nash bargaining with an appropriate choice of bargaining parameter gives identical results. 7. Note that our results require that |$\kappa$| is not too big, which would explain why it is not hedged away. 8. An earlier version of the article, Chahrour and Valchev (2017), considers endogenous funding choices for the U.S. and the Eurozone and arrives at very similar conclusions, at the cost of complicating the exposition. 9. This would be akin to global banks being active in many trade finance markets through country-specific bureaus. While the model is robust to this, our benchmark assumption that trade finance is domestically sourced in rest-of-world countries is consistent with the BIS (2014) data for emerging markets. 10. The price index corresponding to (10) is |$P_{us,t} = K^{-1}(P_{us,t}^{us})^{a_h} (P_{us,t}^{ez})^{\frac{(1-a_h) \mu_{ez}}{ \mu_{ez} + \mu_{rw}} } (P_{us,t}^{rw})^{\frac{ (1-a_h)\mu_{rw}}{ \mu_{ez} + \mu_{rw}} },$| where |$K$| is a proportionality constant and |$P_{us,t}^j$| is the price of country |$j$|’s differentiated good in the U.S. 11. This assumption aligns well with evidence of high churn in firm-to-firm trade relationships (Eaton et al., 2016). 12. Note that since a potential trading partner’s funding is uncertain, it would be costly to first match with a counterparty, agree on a particular type of collateral, and only then seek that financing. If the financing falls through, the firm looses the opportunity to earn |$\pi$|⁠, which is simply not worth the risk for potentially saving the small mismatch cost |$\kappa$|⁠. 13. See guidance by the U.S. Commerce Dept.: acetool.commerce.gov/cost-risk-topic/trade-financing-costs. 14. See for example Figure 1 in Bonetti (2018) for the historical evolution of USD-EUR hedging costs. 15. We provide the details on this version of the model in the Supplementary Appendix. 16. This compositional pattern is quite realistic, see Gourinchas and Rey (2007a). 17. The model has four state variables: rest-of-world holding of U.S. and Eurozone bonds, U.S. holdings of U.S. bonds, and Eurozone holdings of Eurozone bonds (U.S. and Eurozone foreign holdings are determined by market clearing.) To display Figure 1 in two dimensions (for illustration purposes), we initialize U.S. and Eurozone portfolios shares at their symmetric steady-state level. 18. We have also confirmed via linearization that the dominant equilibria are locally stable but the symmetric steady state is not. 19. See Ghosh et al. (2020) for a detailed description of the evidence on capital controls. 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TI - Trade Finance and the Durability of the Dollar
JF - The Review of Economic Studies
DO - 10.1093/restud/rdab072
DA - 2022-07-09
UR - https://www.deepdyve.com/lp/oxford-university-press/trade-finance-and-the-durability-of-the-dollar-sZEO0xoneH
SP - 1873
EP - 1910
VL - 89
IS - 4
DP - DeepDyve
ER -