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Institutions of Foreign Exchange Settlement in a Two-Country Model. The Economics of Payments March 31, 2004 Federal Reserve Bank of Atlanta Hiroshi Fujiki Bank of Japan, IMES (An usual disclaimer applies). An Illustration.

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Institutions of foreign exchange settlement in a two country model l.jpg

Institutions of Foreign Exchange Settlement in a Two-Country Model

The Economics of Payments

March 31, 2004

Federal Reserve Bank of Atlanta

Hiroshi FujikiBank of Japan, IMES

(An usual disclaimer applies)


An illustration l.jpg

An Illustration

  • Two economies, suppliers (endowed with goods) and consumers (endowed with domestic currency).

  • Consumers want to get goods from foreign suppliers, but they need foreign currencies to do so.

  • Consumers travel a “turnpike” that connects two economies.

  • Consumers meet foreign consumers at the trading post, exchange their fiat money, and continue their travel to get goods from foreign suppliers.


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An Illustration: Liquidity Problem

  • Suppose that consumers’ arrival rate at the foreign exchange market are not equal (say, some come mourning but others come evening).

  • Nominal exchange rate (m/M) fluctuates between 2 and 0.5 within a day.


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Problem and Solutions

  • Liquidity Problem: Nominal exchange rate fluctuates between 2 and 0.5 within a day because consumers’ arrival rate at the foreign exchange market are not equal.

  • Want to achieve one by one trade between m and M, and keep nominal exchange rate constant.

  • The key to a solution: The overall supplies of fiat monies in the foreign exchange market are known ex ante (3m and 3M).


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Solution 1

Early-arriving consumers from economy 1 can wait for the arrival of their counterparties from economy 2 (Payment Versus Payment).


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Solution2

Suppliers can wait for cash delivery. Consumers purchase negotiable certificate of deposit (NCD) which can be withdrawn at the end of day in terms of foreign currency. Consumers transfer their deposits to suppliers at the end of the day.


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Solution3

Consumers and suppliers can use the same currency. Shut down the foreign exchange market (Currency Union)!


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About this paper

  • Use Fujiki (2003)’s two-country general equilibrium model. Gold Standard, two central banks, and two currencies.

  • Fiat monies are essential due to special separations and country specific cash in advance constraints.

  • Study the relationship between central bank activities in the domestic credit markets and those in the foreign exchange market.

  • The transactions shown in the three illustrations are based on agents’ optimization over their life cycle consumptions.

  • Evaluate the effects of these three solutions for this liquidity problem by average agent’s ex-ante expected utility.


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Related works

  • Freeman (1996) shows that “elastic money supply made by the central bank based on real bills doctrine” stops the fluctuation of nominal interest rate, and leads to an optimal allocation of resources.

  • Fujiki (2003) adds international gold standard to Freeman, and assumes some domestic agents with fiat money want to consume foreign goods with a small probability.

  • Fujiki (2003) shows that, given domestic elastic money supply, a central bank intervention in the foreign exchange market is welfare improving if it could resolve the liquidity problem in the foreign exchange market.

  • This intervention makes the consumptions of foreign goods by agents independent of the timing of arrival to the foreign exchange market. Given the strictly concave utility function, the equilibrium with this intervention dominates the equilibrium with domestic elastic money supply alone.


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Question in this paper

  • “Are there any alternative institutions that achieve the same welfare improvement done by central bank intervention, given domestic elastic money supply?”

  • This paper answers “Yes, there are at least two private institutions do that (Payment versus Payment, a negotiable certificate of deposit like Eurodollar). An official arrangement (Currency Union) sometimes works.”

  • Three institutions keep the foreign exchange rate at the gold standard parity, make the foreign goods consumption of agents equal, and achieve the same welfare level as the combination of domestic elastic money supply and central bank intervention does.


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Why interested in this question?

  • Academic issue: Follow up Green (1996): He asks if any private arrangements could achieve the same welfare improvement achieved by Freeman’s central bank.

  • Practical issue: Different arrival rates at the foreign exchange market sometimes led to serious liquidity problems in the market. Examples are: Time zone gap (Herstatt Risk), RTGS intra-day credit.

  • Note: Freeman model excludes ex-ante insurance among agents. Maybe a restrictive model of modern foreign exchange market.

  • But foreign exchange market is quite decentralized compared with other domestic short-term credit markets, consistent with the sprit of Freeman.


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Outline of this presentation

  • Review Freeman (1996) and Fujiki (2003)

  • Move on to more practical issues applying Fujiki (2003) model to three other institutions:

  • A private arrangement based on a payment versus payment settlement standard supported by central banks’ free intraday credit,

  • A financial institution that provides a negotiable certificate of deposit,

  • A currency union.


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Freeman(1996)

  • Creditors and debtors scatter and live in small villages (spatial separation). Their populations are one. They live two periods.

  • Creditors and debtors are endowed with goods specific to their villages when young.

  • Creditors consume their own good when young, and consume debtor’s good when old.

  • Debtors consume their own good and creditor’s good when young.

  • Usual OGM: Old creditor buy young debtor’s good via money. Then, young debtor buy young creditor’s good via money, etc…


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Freeman(1996): When young

Young debtors eat a part of their endowment, then visit young creditors (Debtors do not have money).

Young debtors issue debts, buy young creditors’ good.

Young debtors go back their villages.

Young debtors sell goods to old creditors, get money, save money to pay back their debts when old.


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Freeman(1996): When old

  • Old creditors arrive at the central clearing area.

  • Old debtors arrive at the central clearing area.

  • All contracts are honored at the central clearing area. Old creditors get money in exchange for their loan certificate (money to settle debt).

  • Old creditors visit young debtors, buy goods by money.


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Liquidity Problem in Freeman

  • Fraction l of debtors arrive at the central clearing area. But fraction 1- of creditors want to depart.

  • All creditors visit the central clearing area.

  • If (1-a)>l,  creditors purchase fraction 1- of creditors' safe debt at discount price (liquidity constraint).

  • Fraction 1- of creditors scatter to debtor village.

  • 1-l of debtors come. All debts are repaid.

  • Remaining fraction  of creditors scatter to debtor village.


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Solution by Freeman

  • A central bank issues additional fiat money at the central clearing area.

  • It purchases the IOUs of fraction (1-) of creditors to clear their IOUs at par value.

  • It receives fiat money from the (1-) (late-arriving) debtors in the central clearing area.

  • Money stock remains constant, as long as this central bank takes the money received from the late-arriving debtors out of circulation.

  • Such a central bank intervention improves allocation of resources.


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Fujiki (2003): Two-country model

  • Fujiki (2003) add international gold standard to Freeman.

  • Old domestic (Swiss) creditors want to consume young foreign debtors’ goods when old with probability (1- ) (probability (1-) in abroad, Germany),immediately after domestic debt settlements.

  • The central clearing areas of two countries are connected by a tunnel. Old creditors go through the tunnel.

  • With Freeman’s central bank intervention in each domestic credit market, a reasonable exchange rate is eF = (1- )m/(1- )M (Gold standard parity).

  • The timings of arrivals to the foreign exchange market matter, since the transactions are done upon meeting.


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Fujiki (2003): When youngAlmost the same as Freeman (1996)

  • Young debtors eat a part of their endowment, then visit young creditors.

  • Young debtors issue debts, buy young creditors’ good.

  • Young debtors go back their villages.

  • Young debtors sell goods to either Swiss or Germanold creditors, get national money, and keep national money to pay back their debts when old.


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Fujiki (2003): When oldAnother liquidity problem

  • Once domestic debts are cleared, proportion (1- ) ((1- ) in Germany) of old creditors identify their taste shock, and go to the tunnel immediately.

  • In the tunnel, they exchange their fiat money.

  • They scatter to the foreign debtor village.

The timings of arrivals to the foreign exchange may differ due to the timing of domestic credit market settlement.


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Liquidity problem in Fujiki (2003)

  • If Germany is inhabited by many many late-departing creditors, A > .

  • Market for early-departing: eF1= (1-)(1- )m/(1-A)(1-)M.

  • Market for late-departing: eF2 = (1- )m/A(1- )M.

  • If A >, eF1>eF >eF2, whereeF = gold standard parity =(1- )m/(1- )M


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Fujiki (2003)’s Liquidity problem and a solution

  • The fiat money of Swiss, though its value is backed by gold, might be exchanged at a discount (premium) in early (later) stage of transaction.

  • The departure from gold standard could happen even though the central banks intervene to clear all domestic debt at per value.

  • A central bank intervention into the foreign exchange market can prevent a departure of the market exchange rate from the gold standard parity, and can improve the ex-ante expected utility of agents.

  • The central bank should be subject to a gold standard or price level target.


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This paper: Three institutions that may improve ex-ante overall utility

  • An institution which specializes in foreign exchange settlement at the gold standard parity on a PVP basis (a final transfer of one currency occurs if and only if a final transfer of the other currency takes place), with the central banks’ credit in the foreign exchange market.

  • A financial institution that provides a negotiable certificate of deposit which can be withdrawn at the end of day in terms of foreign currency (imagine Eurodollar).

  • The introduction of a currency union.


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Solution 1: Payment versus Payment

  • The overall supplies of fiat monies in the foreign exchange market are known ex ante.

  • Let early-departing creditors, whose currencies are in excess supply, wait until their counterparties are ready to make payment.

  • Consider an institution which specializes in foreign exchange settlement at the gold standard parity on a PVP basis.

  • This institution assigns a trading partner in the foreign exchange market to early-departing old creditors with a taste shock upon their initial arrival at the tunnel.


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PVP + central bank overdraft

  • The institution randomly selects (1-)(-) early-departing old Swiss creditors who are not allowed to go through the tunnel until the arrival of late-departing old German creditors at the other end of the tunnel.

  • The institution ensures PVP at the gold standard parity eF,but it alters the timing of consumption of (1-)(-) early-departing old Swiss creditors within a period.

  • The daylight overdraft from the German central bank up to the amount (1-)(-) M allow (1-)(-) early-departing old Swiss creditors to go through the tunnel.

  • The overdraft changes the timing of transaction, but does not change the timing of consumptions.


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PVP in practice: the CLS Bank

  • The CLS (Continuous Link Settlement) Bank does similar job.

  • The CLS Bank is a private, intraday, multi-currency, clearing bank that eliminates settlement risk through the world’s simultaneous and irrevocable global multi-currency settlement system.

  • NOTE: “Cross-border cash collateral pool facility” proposed by the Payment Systems Risk Committee discusses the idea of accepting foreign currency as collateral for intraday credit.


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Solution 2: Negotiable certificate of deposit (NCD)

  • Young debtors need fiat money at hand by the end of their first period of lifetimes, since they repay their debt in the next period.

  • Let young debtors wait the delivery of fiat money by the end of their first period of lifetimes.

  • Consider a financial institution that provides a negotiable certificate of deposit (NCD), like Eurodollar, for old creditors with taste shock, which can be withdrawn at the end of time period in terms of foreign fiat money.


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Does NCD work?

  • Old creditors with taste shock transfer their deposit to foreign young debtors and purchase foreign young debtor’s goods.

  • Foreign young debtors make withdrawals and obtain foreign fiat money at the end of their first lifetimes.

  • This institution has enough fiat money to distribute to the young debtors in exchange for negotiable certificate of deposit at the gold standard parity.

  • NCD changes the timing of settlement in the foreign exchange market, and achieves efficiency gains.


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Solution 3: Currency Union

  • A unified currency may lead to more efficient resource allocation if it equates the terms of trade faced by early-departing creditors and late-departing creditors with a taste shock.

  • Shut down the foreign exchange market!

  • In our model, the proportion of fiat money circulated in two countries could change over time even constant world money supply.

  • Currency union member countries might experience either deflation or inflation.

  • Difficult to make general welfare comparison.


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Does currency union work?

  • If  =  =0.5, we could we reproduce the same stationary equilibrium.

  • Unified currency equilibrium with domestic credit market interventions achieves the same welfare level as the multiple currencies equilibrium with the foreign exchange interventions by a central bank and central banks’ domestic credit market interventions.

  • Unified currency equilibrium with domestic credit market interventions dominates multiple currency equilibrium with central banks’ domestic credit market interventions only.


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Reservations and Future works

  • This model is silent about the reason why we have country-specific cash-in-advance constraints.

  • This model is not explicit about why a currency union is created.

  • This model assumes that all agents honor their contracts and that the agents in the foreign exchange market are honest.

  • What about the effects of limited enforcement?

  • Analysis on default?


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