The international supply of reserve currency

Benigno, Pierpaolo Working Paper The international supply of reserve currency Discussion Papers, No. 23-13 Provided in Cooperation with: Department of Economics, University of Bern Suggested Citation: Benigno, Pierpaolo (2023) : The international supply of reserve currency, Discussion Papers, No. 23-13, University of Bern, Department of Economics, Bern This Version is available at: https://hdl.handle.net/10419/283502 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ The International Supply of Reserve Currency Pierpaolo Benigno University of Bern December, 2023 Abstract This paper provides insights into the historical ine¢ ciencies and instabilities of the international monetary system. These ine¢ ciencies are primarily linked to the limited supply of international liquidity and wedges in various money-market rates. The instabilities encompass both macroeconomic and …- nancial aspects, particularly focusing on the challenges of stabilizing in‡ation and economic activity. Innovations stemming from the competition of cryptocurrencies and the associated blockchain technology hold the potential for improving these outcomes. Paper prepared for the IMF 24th Jacques Polak Annual Research Conference in honor of Ken Rogo¤ and the IMF Economic Review. I am grateful for the comments and suggestions provided by conference participants, as well as by Olivier Jeanne, Camillo Marchesini, and Maurice Obstfeld. GaOn Kim has provided excellent research assistanship. Throughout its history, the international monetary system has been plagued by ine¢ ciencies and instabilities, primarily arising from the mechanisms of supply and demand of the dominant (reserve) currency.1Evidence from the past demonstrates a recurring pattern of a dominant currency or, at most, two currencies, closely tied to the economic and political supremacy of the issuing nation (see Eichengreen, 2005). These currencies assume the traditional roles of serving as a medium of exchange, a store of value, and a unit of account within the international monetary system.2 In the present day, the United States dollar stands as the hegemonic currency, playing a crucial role in facilitating bilateral transactions of goods in global markets. It serves as the unit of account for trade contracts and is widely demanded due to its liquidity and perceived safety, making it a highly desired safe asset.3 This paper presents an international macroeconomic model aimed at shedding light on the historical ine¢ ciencies and instabilities within the international monetary system and drawing relevant conclusions. These ine¢ ciencies pertain to the constrained supply of international liquidity and the presence of wedges between certain money-market rates. The instabilities encompass both macroeconomic and …nancial aspects, speci…cally concerning the stabilization of in‡ation and economic activity. The analysis begins with the classic Gold Standard, which establishes a link between the supply of international liquidity and the gold reserves held by the central bank of the dominant currency at a …xed gold parity. While this system succeeds in maintaining price level stability, it comes at a cost. One prominent limitation of the Gold Standard is the ine¢ ciently low supply of international liquidity. This arises from the fact that the availability of liquidity is constrained by the quantity of gold reserves and the …xed gold price, leading to adverse macroeconomic consequences. When there is a heightened demand for liquidity from the rest of the world, but the supply remains limited, it can result in de‡ationary e¤ects within the hegemonic country that can spread worldwide. These de‡ationary pressures, in turn, have the potential to trigger recessions or eventually depressions. Bernanke and James (1991) discuss the relevance of the de‡ationary pressures of the Gold Standard at the incipit of the Great Depression.4The model presented in this paper delves into the reasons behind the criticisms leveled against a rigid liquidity-backing system, as advocated by Keynes (1929) for Britain during the Gold Standard and by Tri¢ n (1961) for the 1Sargent (2010) discusses the dilemma between e¢ ciency and stability in the supply of liquidity within the national borders. 2Gourinchas, Rey and Sauzed (2019) discuss extensively the roles of international curriencies in the international monetary system. 3Gopinath and Stein (2019) analyze the connection between trade invoicing in dollars, the dominant currency, and the creation of private safe assets in dollars. 4Benati and Benigno (2023) has shown that the Gibson’s paradox, i.e. the positive relationship between prices and interest rates observed during the Gold Standard, originates from ‡uctuations in the natural real rate of interest. An excess demand of liquid assets can lead to a fall in the natural real rate and, therefore, in the price level. 1 U.S. during the Bretton Woods system. The analysis then considers an inconvertible ‘paper’currency standard that completely decouples the supply of liquidity from commodities. A somehow surprising result is that this regime does not necessarily yield substantial gains in terms of ef- …ciency and stability. A self-interested hegemonic country, in particular, may have incentives to keep the supply of liquidity low to bene…t from relatively low borrowing costs, thereby sustaining high levels of consumption for its own economy. The international supply of liquidity can be even lower than under the Gold Standard. This ine¢ ciency also entails macroeconomic costs. When the central bank of the reserve currency do not set interest rate policy by paying a rate on its liabilities (reserves), decisions regarding liquidity supply become interconnected with monetary policy stance and in‡ation objectives. Increasing the supply of liquidity leads to lower achievable in‡ation rates. A more modern monetary policy framework, in which the central bank conducts policies by paying an interest rate on reserves, untangles these linkages and enables independent decision-making regarding liquidity policy in relation to standard monetary policy stances. Nevertheless, the system remains fragile in conditions of excessive external demand for liquidity, which may compel the hegemonic country to adopt zero-lower bound policies. The analysis then addresses the role of the private sector as an alternative provider of international liquidity. The insu¢ cient supply of government liquidity naturally leads to private entities creating liquidity to exploit rents and pro…table opportunities. There are conditions, albeit quite ideal, in which private liquidity can achieve an e¢ cient global supply without compromising the stability of the system, as advocated by free banking theories, related to Smith (1776) and Hayek (1976). In a scenario characterized by a frictionless private market and perfect competition, intermediaries can provide the necessary liquidity for the world economy. This allows the central bank to remain insulated from ‡uctuations in the liquidity market and focus on macroeconomic stabilization, provided policies are set by paying an interest rate on reserves. However, this ideal environment necessitates intermediaries to invest in either risk-free illiquid private securities or raise equity at market rates to absorb any potential balance sheet risks. Frictions in private intermediation activities can disrupt e¢ ciency and potentially lead to macroeconomic instability. The model encompasses aspects of the 2007-2008 …nancial crisis, during which a liquidity crisis arose due to failures in private liquidity creation. This situation required government intervention through policies such as zero interest rates, increased government liquidity and swap intervention in international markets. The demand for dollar liquidity becomes highly inelastic, particularly during crises, suggesting potential advantages in accommodating it rather than exerting monopoly power, as discussed in Obstfeld (2023).5 5This aligns with the concept discussed by Benigno and Robatto (2019) of raising the burden of taxation during challenging periods, serving in any case as a potential constraint on the supply of liquidity. Benigno and Robatto (2019) further discuss the rationale of the various types of 2 The study of the international monetary system and its characteristics has been a fundamental topic in the …eld of international macroeconomics, with numerous noteworthy contributions. Aliber (1964) examined the advantages and disadvantages of the U.S. acting as a reserve currency, emphasizing that being the reserve currency allowed the U.S. to purchase more foreign goods due to the earnings from seigniorage pro…ts. In this study, the seigniorage pro…ts serve as the rationale for a self-interested hegemon to maintain a limited supply of international liquidity. Kenen (1960) developed a model of the gold-exchange standard that discussed the instability of this framework when faced with a shortage of liquidity.6 A contribution, closely connected to this research, is the work of Fahri and Maggiori (2019), which presents a model of the international monetary system that sheds light on historical evidence. Their study explores the fragility of the system resulting from the limited commitment of the reserve currency issuer to honor debt in real terms.7In contrast, this paper’s model abstracts from strategic choices regarding the value of money and emphasizes that in a standard international macro model rooted in the "intertemporal approach to the current account" (as presented in Obstfeld and Rogo¤, 1996), a self-oriented hegemon issuer already has a strategic incentive to manipulate the liquidity supply. There exists a trade-o¤ between satisfying liquidity for domestic objectives and exploiting liquidity premia to reduce borrowing costs and enhance the current account. Furthermore, this paper’s framework establishes a comprehensive link between liquidity choices and the conventional monetary policy framework, illustrating the potential sources of macroeconomic instability resulting from an ine¢ cient supply of liquidity. This work is also closely related to the literature that has emphasized and quanti- …ed the exorbitant privilege of the country issuing the reserve currency, as discussed in the works of Gourinchas and Rey (2007), Gourinchas, Rey and Govillot (2017), He, Krishnamurthy and Milbradt (2019) and Maggiori, Neiman and Schreger (2020) and Akinci et al. (2022). The exorbitant privilege is here modelled with the liquidity services that the debt in the reserve currency provides both domestically and in the rest of the world. It is shown that …nancial market integration equalizes the marginal bene…ts of liquidity across countries. A recent literature has studied the optimal supply of liquidity in a closed economy model in which taxes are distortionary, see the recent works of Angeletos, Collard and Dellas (2022), Benigno and Benigno (2022) and Sims (2022). This literature has shown the optimality of limiting the supply of liquidity below the satiation level because the liquidity premium allows the government to economize on distortionary taxes. Obstfeld (2011) has also emphasized the limits given by the …scal capacity to the supply of international liquidity. Here, instead, taxes are not distortionary government interventions undertaken during the …nancial crisis. 6Hagemann (1969) studies the implications of Kenen’s model for the U.S. balance of payments. 7See also Obstfeld and Rogo¤ (2007) for an analysis of the real exchange rate adjustment required to put on a sustainable ground the U.S. current account position in the 2000s. 3 but it is still optimal to supply liquidity below satiation taking into account the higher consumption that the issuer country can a¤ord. This …nding underscores the importance for the issuer of the reserve currency to extract seigniorage revenues, akin to Mundell’s (1972) discussion justifying an optimum balance of payment de…cit. Another pertinent literature is that initiated by Holmström and Tirole (1998), which explores the private supply of liquidity for the e¢ cient functioning of the productive sector and its interaction with public liquidity provision. This work is structured as it follows. Section 1 presents the model economy and Section 2 the equilibrium conditions. Section 3 discusses the optimal supply of liquidity from the global perspective. Section 4 analyzes the implications of the model under a gold-standard regime while Section 5 those under …at money. Section 6 discusses the implications of an environment in which the international supply of liquidity is also created by …nancial intermediaries. Section 7 draws the conclusions. 1 Model The world economy is composed by two countries: country H; the one in which the reserve currency is issued and country F; the rest of the world. Consider preferences for households living in country Hgiven by: 1 X t=t0 tt0fCt+L(gt) + tV(qt)g;(1) in which is the rate of time preferences, with 0<  < 1; Cis consumption of a single good that is traded internationally. To simplify the analysis, utility is linear in consumption. Households also derive utility from holding gold, g, in the form of jewelry and from the real value, q; of holdings bonds denominated in units of the reserve currency: Qis the nominal value of these bonds, and Pis the price of the traded good so that q=Q=P. The non-pecuniary advantages obtained from bonds through direct utility bene…ts encompass the characteristics that speci…c securities possess within the monetary system, enabling smooth transactions of goods and offering collateral. These essential services are provided by selected securities, which we will elaborate on momentarily. The function L()has standard concave properties and is di¤erentiable, while V()is also concave but has a satiation point at qsuch that Vq()=0for qq; where Vq()is the …rst derivative of the function V()with respect to its argument. We are going to give later more details on the functional form that V()assumes. Finally, tis a preference shock. Households are subject to the following budget constraint: Bt+Qt+StAt+PtCt+Pg;tgt= (1 + it1)Bt1+ (1 + iR t1)Qt1+ (1 + i t1)StA t1+ +PtYt+Pg;tgt1Tt+Pg;t(GtGt1):(2) 4 They can invest in three securities. Bdenotes the holdings of default-free bonds denominated in the home currency that pays an interest rate i;Qdenotes holdings of bonds that are, as well, default free and denominated in the home currency, but they provide liquidity bene…ts in the utility function (1). For this reason, they might carry a di¤erent interest rate iR.Aare the holdings of default-free bonds denominated in units of foreign currency that pays the interest rate i: S is the nominal exchange rate between the home and foreign currency. Yis the exogenous endowment of the traded goods, Tare lump-sum taxes levied by the government in country H;Pgis the price of gold and Gtis the stock of gold at time t, which accumulates for the household, with GtGt1. The …rst-order conditions of the optimization problem of the household with respect to Bt,Atand Qtimply respectively: 1 + it=1  Pt+1 Pt ;(3) 1 + i t=1  Pt+1 Pt St St+1 ;(4) 1 = tVq(qt) + 1 + iR t 1 + it :(5) Equation (3) is a Fisher equation that relates the nominal interest to the real interest rate and the in‡ation rate. Due to linear preferences in consumption, the real rate is constant and equal to 1=. Equation (4) combined with (3) implies uncovered interest-rate parity saying that the cross-country di¤erential between the nominal interest rates re‡ects variations over time of the nominal exchange rate: 1 + it 1 + i t =St+1 St : It is important to underline that UIP holds in reference to interest rates on securities that do not provide liquidity services. UIP does not hold when we put in relation the interest rate on the liquid securities issued in country Hand that on illiquid securities issued in country F, which are the two policy rates. The …nal equation, (5), equates the cost of investing one unit of currency on the left-hand side to the non-pecuniary bene…ts provided by the liquid securities, represented as the …rst addendum on the right-hand side of the equation, and the discounted value of their payo¤, which is the second addendum. Equation (5) determines the demand of liquid securities, implicitly given by Vq(qt) = 1 t itiR t 1 + it : Since Vq()is non-increasing with respect to its argument, then the real demand of liquid securities, q, is non-increasing in the spread between the nominal interest rate on illiquid and liquid securities, iiR:The higher the spread, the higher is the 5 opportunity cost of holding liquidity. Note that itiR t:Only when it=iR t, the demand of liquidity is at or beyond the satiation level. The …rst-order condition with respect to gold holdings implies Pg;t Pt =Lg(gt) + Pg;t+1 Pt+1 ;(6) which says that the relative price of gold, on the left-hand side of the above equation, is equal to the marginal utility bene…ts provided by gold to the households and the discounted future relative price, the last term on the right-hand side of (6). The optimization problem of the household is completed by the exhaustion of its intertemporal budget constraint, namely 1 X t=t0 tt0Ct+itiR t 1 + itqt=Wp t0 Pt0 + 1 X t=t0 tt0YtTt Pt+Lg(gt) (Gtgt): in which private nominal wealth is given by Wp t0= (1 + i t01)St0At01+ (1 + it01)Bt01+ (1 + iR t01)Qt01: The left-hand side of the intertemporal budget constraint of the household shows that real resources are paid to hold securities that provide liquidity services, when their interest rate is below the market rate i. On the right-hand side, the last addendum shows the resources that the households obtain by selling part of its gold endowment. These resources depends on the marginal utility that gold provides.8 Finally, we characterize the government’s budget constraint as Qs t+Pg;tgc t1= (1 + iR t1)Qs t1+Pg;tgc tTt(7) in which Qsis the total supply of liquid securities, which are held both domestically and abroad. We make the assumption that liquidity is only provided by the government of country H. The government, speci…cally through the central bank, has the ability to hold gold reserves (represented as gc) and can impose lump-sum taxes (T) through the treasury. It is important to note that the illiquid securities (B) held by households in (2) are privately issued and in zero-net supply within the private sector of country H. However, it is worth mentioning that even if the government were to issue these securities, the subsequent analysis would remain una¤ected. 1.1 The rest of the world Country Fdenotes the rest of the world. Households derive utility from consumption and the liquidity services provided by the government securities of country Hthrough 8Note that in deriving the intertemporal budget constraint of the household we have used (6). 6 the following functional form: 1 X t=t0 tt0[C t+ tV(q t)] : Variables have been previously de…ned, where an asterisk denotes the variable speci…c to country F: In particular, real liquidity is given by q t=Q t=(StP t)in which Q trepresents the foreign holdings of the liquid securities issued by the government in country Hand P tis the price of the traded good in units of foreign currency; Stis the nominal exchange rate;  tis a preference shock. The abstract representation of the utility derived by foreign households from bonds issued in the reserve currency encompasses the various functions that the reserve currency serves within the international monetary system. These functions include acting as a vehicle currency for transactions, being the unit of account for trade invoicing, and serving as the preferred …nancing instrument for working capital within global value chains, as discussed in Gourinchas, Rey, and Sauzet (2019). Foreign households are subject to the following ‡ow budget constraint: A t+Q t St +P tC t= (1 + i t1)A t1+ (1 + iR t1)Q t1 St +P tY tT t; in which variables have been already de…ned. The household’s optimization problem implies a Fisher equation of the form (1 + i t) = 1  P t+1 P t :(8) The foreign demand of the liquid security is implicitly given by the …rst-order conditions of the household’s problem with respect to q t: 1 =  tVq(q t) + (1 + iR t)P t P t+1 St St+1 :(9) We assume that there are no frictions in trading goods, so that the law of one price holds, P=SP:Using it, we can write (9) as 1 =  tVq(q t) + 1 + iR t 1 + it :(10) Comparing it with equation (4), it follows that tVq(qt) =  tVq(q t): Integrated …nancial markets for the liquid securities imply that the marginal bene…ts of liquidity are equated across countries. This feature of the model depends on the 7 Figure 1: Gold Standard regime. Equilibrium liquidity (qt) in country Hand value of money (1=Pt):Initial equilibrium at E. When the stock of gold increases, G", the A schedule shifts downward to A0and the equilibrium moves to E0:When there is a higher demand of liquidity abroad, ", then the Aschedule shifts upward to A00 and the equilibrium moves to E00: value of money through equation (19). As a result, the marginal utility of liquidity, Vq(qt), remains unchanged in equation (21). The increase in the endowment of gold is entirely absorbed by an increase in the central bank’s holdings of gold, leading to in‡ationary consequences. If there is an increase in the demand for liquidity from the rest of the world, represented by a rise in , it leads to an increase in the function Fqt q; and results in a steeper schedule (25) that moves from Ato A00.9The liquidity level in country Hremains unchanged, but it increases in country F. Since the overall stock of gold remains the same, this generates de‡ationary pressures in country H, and the equilibrium moves to E00. Proposition 3 In a gold-standard regime, new discoveries of gold have in‡ationary consequences, whereas an increase in foreign demand for liquidity has de‡ationary e¤ects. There are some important conclusions to draw from this analysis in terms of the objectives of e¢ ciency and stability. First, the gold standard by linking the supply of money to that of a commodity is able to stabilize the price level. Strict price stability, however, comes at other costs. In terms of e¢ ciency, backing liquidity with a commodity in limited supply economizes on the supply of liquidity and does not allow to achieve the desirable full satiation equilibrium from the global perspective. 9When moving from = 1 to >1, the Aschedule becomes strictly concave. 14 Despite the bene…ts of achieving a stable price level, there are costs in terms of macroeconomic stability. First, ‡uctuations in the supply of gold can be source of variations in the price level. Second, and most important, higher external demand of the reserve currency can create de‡ationary pressures with tangible macroeconomic costs. In a more detailed model incorporating also a non-traded sector and rigidity in prices, the de‡ationary pressure on the price of traded goods rises the relative price of non-traded versus traded goods inducing de‡ationary pressures in the non-traded sector and a recession. These results are consistent with the concerns many economists had on the stability of the gold-standard system. Keynes (1923) argued against the gold standard to free up monetary policy for stabilization purposes. Bernanke and James (1991) emphasize the disruptive e¤ect of de‡ation on the …nancial system. They argue that the worldwide de‡ation of the early 1930s was the result of a monetary contraction transmitted via the gold standard. In this context, the unavoidable devaluation of the dollar, as predicted by Tri¢ n (1961), is merely the outcome of the unbacked liquidity provided by the U.S. during the Bretton Woods system to counteract de‡ationary pressures resulting from a commodity peg, prompted by a surge in external demand for dollars. 5 Self-oriented hegemon in a ‘paper’currency regime Let’s examine an inconvertible ‘paper’currency monetary standard where the availability of liquidity is not necessarily tied to a speci…c commodity. This arrangement aims to alleviate the constraint of having a limited supply of liquidity. However, when considering the viewpoint of a policymaker primarily concerned with their selfinterest, it becomes apparent that they prefer to restrict the supply of liquidity, possibly even to a lesser extent than what the gold standard would suggest. Additionally, we explore the consequences in relation to macroeconomic stability. To evaluate the choice of a self-oriented policymaker, we use as a criterion the utility (1) of the households of country H. In few steps, we show how to evaluate welfare in a simple way. First, consider the current account equation (14) in real terms q tat=1 + iR t1 t q t11 + i t1  t at1+CtYt; in which q t=Q t=Pt; at=At=P t, tand tare in‡ation rates in both countries for the respective traded-good prices. De…ning ~qt=1 + iR t1 t q t11 + i t1  t at1; we can write it as ~qt+1 = ~qtitiR t 1 + it q t+CtYt; 15 and using (4) as: ~qt+1 = ~qt tVq(q t)q t+CtYt: Integrating it forward, and assuming an appropriate borrowing limit on ~qt, we obtain10 1 X t=t0 tt0Ct=~qt0+ 1 X t=t0 tt0Yt+ 1 X t=t0 tt0 tVq(q t)q t: We can use the above expression into (1) to substitute for the discounted value of consumption to obtain Ut0=~qt0+ 1 X t=t0 tt0fYt+g;tL(gt) + tV(qt) +  tVq(q t)q tg:(26) We add also constraints so that the solution of the optimal commitment problem delivers stationary policy rules. To this end, we assume that the policymaker considers an additional constraint on ~qt0that is going to be self-consistent with the equilibrium functional form it will take at a future date, as in a timeless-perspective commitment of Woodford (2003). As a consequence the self-oriented government in country Hmaximizes the following objective: 1 X t=t0 tt0ftL(gt) + tV(qt) +  tVq(q t)q tg:(27) There are important di¤erences with respect to welfare viewed from the global perspective (15). A self-oriented policymaker does not care about the bene…ts that liquidity provides to the rest world, but just about its own bene…ts, the second addendum of (27), and the rents that it can derive by supplying liquidity at a premium to the rest of the world, the last addendum of (27). The only constraint to optimal policy is the equalization of the marginal utility of liquidity across countries, equation (22). The …rst-order conditions with respect to qtand q timply respectively that Vq(qt) = Vqq (qt)t; Vq(q t) + Vqq(q t)q t=Vqq (q t)t; in which tis the Lagrange multiplier attached to the constraint (22). One solution of the above equations is to have qtand q tto be equal or greater than the satiation level. Indeed, in this case, all derivatives of the function V()are 10 The limit condition on ~qtfollows from the transversality condition of the households and equation (16) with equality, which we have assumed to hold. 16 zeros and the above equations are satis…ed. We will show shortly that this solution is not the global optimum. Let us focus now on the case qt<q, we can combine the above two equations to eliminate the Lagrange multiplier tand obtain Vq(qt) Vqq (qt)+Vq(q t) + Vqq(q t)q t Vqq (q t)= 0 (28) which describes the trade-o¤ between varying liquidity across countries. Two objectives are encompassed in (28) weighted by 1=Vqq (qt)and 1=Vqq (q t), respectively. The …rst, captured by the …rst addendum on the left of the equation, refers to the satiation of liquidity in the hegemon country, which can be obtained when Vq(qt)=0:The second captures the maximization of rents by supplying liquidity abroad, which is maximized when Vq(q t)+ Vqq(q t)q t= 0:Equation (28) together with (22) determines qtand q t. We can get further insights into the solution by utilizing Assumptions 1 and 2. Additionally, let’s begin by assuming that = 1. Using (22), we can observe that qt=q tand, therefore, we can write (28) as: 2Vq(qt) + Vqq(qt)qt= 0; which simpli…es under the preference speci…cation assumed to 21 qt 1 q1 qt = 0: The solution is qt= q=2, with liquidity supplied half of the satiation level. We now show that this dominates in terms of welfare the full satiation solution. We can write (27) disregarding utility from gold as 1 X t=t0 tt0ln qt qqt q+1qt q: Note that in the solution with full satiation, the terms in the curly brackets is equal to 1, while when qt= q=2it is equal to ln(1=2) which is a higher value. In a …at money system, a self-oriented issuer of international liquidity …nds advantageous to provide liquidity below the satiation point. The rationale behind this is the existence of a trade-o¤ between reaching the satiation point of liquidity and maintaining a higher level of consumption. This balance can be achieved by retaining pro…ts from issuing liquidity, which result in lower borrowing costs.11 A central planner would, instead, recognize that the advantages of lowering borrowing costs for country H come at the expense of lower consumption for country F, with no gains when viewed from the global perspective. Therefore, the optimal supply of liquidity 17 Figure 2: Fiat-money regime. Equilibrium liquidity (qt) in country Hand (q t)in country F: Initial equilibrium at Ewhen = 1.When there is a higher demand of liquidity abroad, ", then the Cschedule shifts to the left to C0and the equilibrium moves to E0: from the global perspective would be to supply liquidity up to the satiation level, as demonstrated in Section 3. Examining the e¢ ciency aspect, it is important to note that a ‘paper’monetary standard does not necessarily guarantee a greater supply of liquidity compared to a gold standard. Indeed, for reasonable parametrization, the level q=2is even below that implied in (23). Proposition 4 In a ‘paper’monetary standard, a self-oriented supplier of international liquidity …nds advantageous to restrict liquidity supply below the satiation level. In the more general case, with di¤erent from the unitary value, the optimal supply of liquidity is determined by equation (24) together with (28), which can be written under Assumptions 1 and 2 as: qt q=qt q2 +q t q2 :(29) Figure 2 plots (24), labelled with the letter B, and (29), labelled with C, in a diagram with coordinates (qt=q; q t=q). The schedule (24) is a semi-circle, which is increasing in q tand qtfor qtq=2and decreasing q tafterward. The schedule (29) is upward sloping. When = 1, they intersect at the equilibrium Ein which qt=q t= q=2:When instead increases above the unitary value, the schedule C shifts to the left to C0, the equilibrium liquidity in both countries falls reaching the 11 In a closed-economy model, distortionary taxation is a reason for optimally limiting the supply of liquidity. 18 point E0. If were below one and then increasing, we would have still observed a fall in liquidity in country H, but an increase in F: This di¤erent behavior depends on the fact that, given the assumed preferences, the marginal bene…ts of increasing qtare positive for qt<q=2and negative for qt>q=2while it is always marginally costly to increase liquidity for the foreign economy, because of the foregone rents in the liquidity market. In general, when there is an increase in the foreign demand of liquidity, a self-oriented hegemon accommodates it by reducing liquidity domestically. In some cases, it might even reduce the overall supply of liquidity. 5.1 Implications for macroeconomic stability Let’s consider the implications for macroeconomic stability of an international monetary system based on a self-oriented hegemon. We derive …rst the implications for the interest-rate policy and the equilibrium in‡ation rate, distinguishing between a system in which liquidity does not pay an interest rate, like in the pre-…nancial crisis where the Federal Reserve was not remunerating reserves, and one in which it does, like in the recent monetary-policy framework. In the …rst case iR t= 0, in the latter case iR tis a policy choice of the central bank and can be positive. In what follows, we refer to the interest rate ion illiquid securities as the market nominal interest rate. Let’s focus on the …rst case, where liquidity is provided through non-interest bearing securities, akin to traditional money. Having computed in the previous section the optimal supply of liquidity for country H; let’s say ^qwith ^q < q, we can use it into (5) to obtain that the corresponding market nominal interest rate, denoted by ^{, should satisfy 1 + ^{=1 1Vq(^q): The nominal interest rate is directly tied to the optimal quantity of liquidity in country Hand decreasing in it. Using this result into (3), we obtain that the corresponding in‡ation rate is ^  =  1Vq(^q): The in‡ation rate is also decreasing with liquidity. In the case of satiation of liquidity, which is the …rst-best for the world economy, the nominal interest rate is zero, since Vq(q)=0;implying a de‡ation at the rate ; as advocated by Milton Friedman in Friedman (1960). However, a self-interested supplier of liquidity …nds optimal to limit the supply below the satiation level. Therefore, the implied nominal interest rate is positive and the in‡ation rate may also be positive. Speci…cally, under Assumptions 1 and 2 and = 1, the corresponding gross in‡ation rate can be calculated as ^  = q=(q1);since ^q= q=2, which can be above one for a certain range of values for q. The decisions regarding liquidity, interest rates, and in‡ation are interconnected, particularly when the central bank does not pay interest rate on reserves, and liquidity does not carry an interest rate. In‡ation and interest rates cannot be arbitrarily set; 19 they must align with the liquidity policy if it is established …rst. Alternatively, if the central bank sets an in‡ation rate target, this will in‡uence the amount of liquidity to be issued. A higher in‡ation target implies a lower level of liquidity to be supplied in international …nancial markets. This dynamic can contribute to a shortage of liquidity. Now, let’s consider the implications for the monetary policy of the reserve currency when there is an external shock in the form of increased demand for its currency, represented by . Figure 2 has shown that a self-oriented hegemon would always reduce the liquidity in country Hfollowing a higher external demand. Since qtfalls, the equilibrium interest rate and in‡ation rate will rise. In a more complex model with tradeables and non-tradeables and price rigidities, these e¤ects will produce a contraction in the non-tradeables sector and disin‡ation. Proposition 5 In a ‘paper’currency monetary standard with zero interest rate on central bank’s reserves, liquidity, market interest rate and in‡ation rate are interconnected. An increase in the foreign demand of liquidity rises the market nominal interest rate in the issuer country. A …at-money regime, as described thus far, is susceptible to the same issues that plagued the gold standard: liquidity shortages and restrictive monetary conditions when there is an increase in the global demand for liquidity. Let’s consider the alternative framework in which the central bank pays a positive interest rate on its reserves. We set a simple monetary policy in which the interest rate on reserve is constant, iR t= ^{Rwith ^{Rthat can be generically non-negative. Given the optimal supply of liquidity discussed above, ^q, the ratio between the market and the policy interest rate is given by: 1 + i 1 + ^{R=1 1Vq(^q):(30) The key di¤erence is that ^{Rand ^qare now independent policy tools;the latter controlled through the choice of qs:Therefore, if liquidity is set …rst, then the central bank can control the interest rate iby setting the interest rate on reserves appropriately. This also allows the central bank to control the in‡ation rate at a desired target independently of the supply of liquidity. Indeed, the in‡ation rate will be determined using (3) at  = (1 + ^{R) 1Vq(^q):(31) Given ^q, the central bank can set ^{Rto achieve a certain target for in‡ation. The new way of conducting policy by paying an interest rate on reserves allows the central bank to set independently the liquidity policy and the in‡ation target. This has important implications for the macroeconomic stability of the system. 20 Proposition 6 In a ‘paper’currency monetary standard with a positive interest rate on central bank’s reserves, the market interest rate and the in‡ation rate can be insulated from liquidity policy and related shocks unless the zero-lower bound on the policy rate is achieved. Let’s analyze the same scenario as before, where there is an increase in the foreign demand for liquidity, represented by a rise in . As depicted in Figure 2, this increase will lead to a reduction in q, indicating a decrease in liquidity. However, in this case, any necessary adjustments to the optimal supply of liquidity can be made by modifying the policy rate, while keeping the interest rate on illiquid securities and the in‡ation rate unchanged. It is important to note that there is a limit to this adjustment due to the zero-lower bound on the policy rate. Once the policy rate reaches that lower bound, an increase in the foreign demand for liquidity will cause the market rate to rise and tighten monetary conditions. This limitation will be further discussed in the next section when describing the 2007-2008 …nancial crisis, which originated from private money creation. The key takeaway from this section, in terms of e¢ ciency and stability criteria, is that a self-oriented hegemon may restrict the supply of liquidity, leading to in- e¢ ciencies. However, macroeconomic stability can be maintained when the central bank conducts policy by setting the interest rate on reserves, unless external demand shocks are signi…cant enough to push the policy rate to the zero lower bound. 6 Private liquidity The analysis in the preceding sections has mainly focused on a scenario in which the government acts as the sole provider of liquidity, aiming to maximize the welfare of its residents. However, these limitations are not realistic when considering both modelbased and historical perspectives. From a modeling standpoint, we have demonstrated that by restricting the supply of liquidity in both a gold-standard and a ‘paper’ currency monetary system, the government retains certain rents. These pro…table opportunities can serve as an incentive for private intermediaries to enter the liquidity market. Furthermore, an examination of historical evidence reveals that the government’s supply of liquidity has generally been limited, often in‡uenced by …scal capacity. Liquidity, also referred to as safe assets, has taken various forms of private liquidity over time. These have included banknotes and bills of exchange in the eighteenth century, deposits in the nineteenth and twentieth centuries, and money market mutual funds in the twenty-…rst century. However, the historical record also underscores instances of liquidity crises associated with these instruments, requiring government intervention as a lender of last resort to accommodate any heightened demand for liquidity that emerged in certain adverse circumstances. 21 One fundamental reason behind these failures is that private liquidity lacks the inherent safety and backing enjoyed by government money, which is supported by the central bank. In contrast, for private liquidity to be deemed safe, it must have appropriate backing. In this context, our focus lies on liquidity provided by intermediaries, where the backing can be provided through assets and/or equity. To introduce private supply of liquidity, we amend the preferences of the households in both countries by assuming that the utility from liquidity is of the form V(qt+tdt) in which now qtdenotes government liquidity, described early, and dtis private liquidity, all in real terms. For simplicity, in what follows, we set t= t= 1. The above speci…cation also allows for private and public liquidity not to be perfect substitute. We model this through the variable t;with 0t1, which can be time varying. The lower t, the lower the contribution to utility provided by private liquidity is with respect to public liquidity. Likewise, we assume that the utility from liquidity in the rest of the world is given by V(q t+td t), where for the sake of simplicity we use the same variable tto denote the degree of substitution between private and public liquidity in foreign utility. The optimization problem of households has now to account for the demand of private liquidity that takes the form Vq(qt+tdt) = 1 t itid t 1 + it ;(32) in which id tis the interest rate on private liquid securities, which might be di¤erent from the interest rate on government liquidity iR t. The other …rst-order conditions of the household’s problem are given in Section 1, with the quali…cation of the new argument of the function V()and the assumption t= 1:Combining equation (5) with (32), we can write 1 + id t 1 + iR t =1tVq(qt+tdt) 1Vq(qt+tdt) showing that private and public liquidity have the same interest rate if both are used and t= 1, otherwise the interest rate on private liquidity will be higher than that on public liquidity, re‡ecting the worse liquidity properties of private securities. Likewise in country F, the demand of private securities is implicitly given by Vq(q t+td t) = 1 t itid t 1 + it :(33) 6.1 Creation of private liquidity by domestic intermediaries When examining the supply side, we explore di¤erent ways of creating liquidity. To begin, we consider a scenario where private liquidity is generated by intermediaries 22 located in country H. These intermediaries have the ability to invest in illiquid securities issued by households, which are free from default risk.12 This scenario represents an ideal setting where the transformation of illiquid securities into liquid ones occurs domestically, without experiencing any currency mismatches. Intermediaries live for two periods in an overlapping way. Intermediaries entering at time thave the following budget constraint Bf t+tDt=Dt;(34) since they issue liquid securities D; in units of the reserve currency, to invest in private illiquid securities, denoted by Bf, in units of the same currency. We are assuming that there are frictions in the creation of liquidity for which there is a proportional cost to the securities issued, with 0t< tat all times.13 Intermediaries’next-period pro…ts are given by t+1 = (1 + it)Bf t(1 + id t)Dt and therefore, using (34), t+1 = (1 + it)(1 t)Dt(1 + id t)Dt: Assuming free entry in the market of private intermediation, pro…ts are driven to zero, which determines the spread between lending and borrowing rates in equilibrium (1 + it) (1 + id t)=1 1t :(35) This spread is given by the cost of intermediation t. Absent this cost, free entry drives to zero any spread between the two money-market rates. Introducing a market of private liquidity supplied by competing intermediaries has strong implications for market rates and the equilibrium allocation. In what follows we focus on an equilibrium in which private and public liquidity coexist. Combine (32) and (35) to obtain Vq(qt+tdt) = t t (36) showing that the marginal utility of liquidity is determined by the ratio between the respective friction in the supply and demand market of private liquidity. It also follows that Vq(q t+td t) = t t :(37) Moreover, using equation (5), we obtain that (1 + it) (1 + iR t)=t tt :(38) 12 These are securities labelled with Bin the household’s budget constraint (2). 13 See Woodford (1995) for a similar framework in a closed-economy model. 23 which units they wish to transact with, settle contracts, or handle debit and credit operations. As envisioned by Hayek in 1976, there is no reason to doubt that this could lead to an enhancement in currency quality, driven by users seeking the best currency in terms of its macroeconomic stability. The third novelty is the blockchain technology, which introduces a means of certifying and verifying information through cryptographic guarantees— a highly objective approach compared to the traditional paper-based, subjective guarantees, see Chainlink (2022). This technology has the potential to evolve to enable cryptographicguaranteed assessments of securities, o¤ering users trustworthy information about the quality of …nancial securities, that is more accurate, accessible and auditable than current alternatives. This would replace, for example, the reliance on subjective evaluations from rating agencies, potentially reducing the sources of instability outlined in this work. In the context of the model discussed in this work, this innovation has the potential to substantially reduce the barriers that hinder the smooth interaction between the supply and demand for private safe securities. Using the notation of the model, as the parameter tapproaches 1and approaches 0due to this innovation, the e¢ cient supply of liquidity could be reached. With these three innovations in mind, it is conceivable that in the near future, competition for superior currencies could lead to the emergence of automated monetary policies solely focused on maintaining currency value stability, without the interferences arising from …scal and …nancial dominance. Simultaneously, cryptographic truth could accurately price the risk associated with securities denominated in the currency’s units, allowing private entities to compete in e¢ ciently providing liquidity with a trustworthy backing. 30 References [1] Akinci9k, Ozge, Benigno, Gianluca, Pelin, Serra, and Jonathan Turek. 2022. The Dollar’s Imperial Circle. FRB of New York Sta¤ Report, 1045. [2] Aliber, Robert Z. 1964. The Costs and Bene…ts of the US Role as a Reserve Currency Country. Quarterly Journal of Economics 78: 442-456. [3] Aliber, Robert Z. 1967. Gresham’s Law, Asset Preferences, and the Demand for International Reserves. Quarterly Journal of Economics 81: 628-638. [4] Angeletos, George-Marios, Fabrice Collard and Harris Dellas. 2022. Public Debt as Private Liquidity: Optimal Policy. Journal of Political Economy, forthcoming. [5] Benati, Luca and Pierpaolo Benigno. 2023. Gibson’s Paradox and The Natural Rate of Interest. CEPR Discussion Paper No. 17959. [6] Benigno, Gianluca and Pierpaolo Benigno. 2022. Managing Monetary Policy Normalization. CEPR Discussion Paper No. 17290. [7] Benigno, Pierpaolo and Roberto Robatto. 2019. Private Money Creation, Liquidity Crises and Government Intervention. Journal of Monetary Economics 106: 42-58. [8] Benigno, Pierpaolo, Paolo Canofari, Giovanni Di Bartolomeo and Marcello Messori. 2021. Financial Dominance in the Pandemic and Post-Pandemic European Economy. Publication for the committee on Economic and Monetary A¤airs, European Parliament. [9] Bernanke, Ben and Harold James. 1991. The Gold Standard, De‡ation, and Financial Crisis in the Great Depression: An International Comparison. In Hubbard Glenn (ed.) Financial Markets and Financial Crises, p. 33-68. [10] Brunnermeier, Marcus. 2015. Financial dominance. Banca d’Italia: Paolo Ba¢ Lecture. [11] Chainlink. 2022. Cryptographic Truth: The Future of Trust-Minimized Computing and Record-Keeping. [12] Eichengreen, Barry. 2005. Sterling’s Past, Dollar’s Future: Historical Perspectives on Reserve Currency Competition. NBER Working Paper No. 11336. [13] Fahri, Emmanuel and Matteo Maggiori. 2018. A Model of the International Monetary System. The Quarterly Journal of Economics, 295-355. [14] Friedman, Milton. 1960. A Program for Monetary Stability. Fordham University Press, New York. 31 [15] Gopinath, Gita and Jeremy Stein. 2018. Banking, Trade, and the Making of a Dominant Currency. NBER Working Paper No. 24485. [16] Gourinchas, Pierre-Olivier. 2019. The Dollar Hegemon? Evidence and Implication for Policy Makers, Unpublished manuscript, UC Berkeley. [17] Gourinchas, Pierre-Olivier and Helene Rey. 2007. From World Banker to World Venture Capitalist: US external Adjustment and the Exorbitant Privilege. G7 Currency Account Imbalances: Sustainability and Adjustment. University of Chicago Press. [18] Gourinchas, Pierre-Olivier, Helene Rey and Nicolas Govillot. 2017. Exorbitant Privilege and Exorbitant Duty. Working paper. [19] Gourinchas, Pierre-Olivier, Helene Rey and Maxime Sauzet. 2019. The International Monetary and Financial System. NBER Working Paper No. 25782. [20] Hagemann, Helmut. 1969. Reserve Policies of Central Banks and Their Implications for U.S. Balance of Payments Policy. The American Economic Review 59: 62-77. [21] Hayek, F., 1976. The Denationalization of Money. Institute of Economic A¤airs, London. [22] He, Zhiguo, Arvind Krishnamurthy, and Konstantin Milbradt. 2019. A Model of Safe Asset Determination. American Economic Review 109: 1230-62. [23] Maggiori, Matteo, Brent Neiman, and Jesse Schreger. 2020. International Currencies and Capital Allocation. Journal of Political Economy 128(6): 2019-2066. [24] Mundell, Robert. 1972. The Optimum Balance of Payments De…cit. In E. M. Claasen and P. Salin (Eds.), Stabilization Policies in Interdependent Economics. North-Holland Elsevier: 69-86. [25] Obstfeld, Maurice. 2011. International Liquidity, the Fiscal Dimension. NBER Working Paper 17379. [26] Obstfeld, Maurice. 2023. Calvo, Currencies, and Commitment. Lecture in The Credibility of Government Policies: Conference in Honor of Guillermo Calvo. [27] Obstfeld, Maurice and Kenneth Rogo¤. 1996. Foundations of International Macroeconomics. MIT Press. [28] Obstfeld, Maurice, and Kenneth Rogo¤. 2007. The Unsustainable U.S. Current Account Position Revisited. G7 current account imbalances: Sustainability and adjustment. University of Chicago Press, 339-376. 32 [29] Kenen, Peter. 1960. International Liquidity and the Balance of Payments of a Reserve-Currency Country. Quarterly Journal of Economics 74: 572-586. [30] Kenen, Peter and Elinor Yudin. 1965. The Demand for International Reserves. The Review of Economics and Statistics 47: 242-250. [31] Keynes, John Maynard. 1923. A Tract on Monetary Reform. New York: Macmillan. [32] Sargent, Thomas J. 2011. Where to Draw Lines: Stability versus E¢ ciency. Economica 78.310: 197-214. [33] Smith, Adam. 1776. An Inquiry into the Nature and Causes of The Wealth of Nations. Edited by Edwin Cannan. The University of Chicago Press: Chicago. [34] Sims, Chris. 2022. Optimal Fiscal and Monetary Policy with Distorting Taxes. Unpublished manuscript. Princeton University. [35] Woodford, Michael. 1995. Price-level Determinacy Without Control of a Monetary Aggregate. Carnegie-Rochester Conference Series on Public Policy. Vol. 43. North-Holland. [36] Woodford, Michael. 2003. Interest and Prices. Princeton University Press. 33