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Economizing on liquidity with deferred settlement mechanisms.

* Real-time gross settlement (RTGS) systems such as the Federal Reserve's Fedwire Funds Service enable participating banks to settle payments immediately and in the full amount; however, the high level of liquidity inherent in the systems requires large intraday credit extensions.

* An examination of several deferred settlement mechanisms that could potentially complement RTGS systems considers a novel mechanism--a receipt-reactive gross settlement system--that bases the settlement of a bank's payments on the value of its receipts over a given time, rather than on the bank's balance.

* The receipt-reactive mechanism can potentially reduce intraday credit extensions significantly while modestly delaying the average time of payment settlement; the mechanism also provides good incentives for banks to submit payments earlier in the day.

1. Introduction

On a typical day, the total value of payments settled by the Federal Reserve's Fedwire Funds Service exceeds $1.8 trillion. On average, credit extended to banks using Fedwire is about $30 billion over the course of the day, while the peak intraday amount reaches $86 billion. Given this high level of credit extensions, it is worthwhile asking whether payment settlements could be managed with a lower level of outstanding credit, thus allowing system operators to economize on liquidity. (1)

Fedwire operates as a real-time gross settlement (RTGS) system. RTGS systems transfer the full amount of payment orders between commercial bank participants immediately upon receipt, thus avoiding short-term debt obligations between participants. This is a desirable feature that has prompted many central banks worldwide to implement these systems over the past decade. However, because payment transfers between participants are made immediately in the full amount, and because of the asynchronous timing of payments by participants, maintaining the liquidity needs of RTGS systems can be costly. Indeed, some system operators have altered their RTGS systems in recent years to economize on the funds needed to complete settlements.

One way to reduce a system's liquidity needs is by using deferred settlement mechanisms such as netting. In netting systems, payment orders are deferred until some designated time--usually late in the day--when the participants exchange only the net amounts they owe or are owed. If all participants successfully submit these net amounts, the system settles all the payments accumulated during the day with the least amount of funds possible--that is, just the net amounts. To achieve this economy in funds use, a netting system delays the settlement of payments so that all orders remain pending until the net settlement payments are completed successfully. This delay feature creates distinct liquidity and risk management characteristics.

Another type of deferred settlement mechanism queues payments as they enter the system. Some European RTGS systems use these "queue-augmented RTGS systems," or hybrid systems. (2) Such systems save on liquidity--as in a netting system--but with less delay than end-of-day netting imposes.

In this article, we propose alternative ways of settling payments submitted to the Fedwire Funds Service that would result in lower intraday credit extensions. We analyze the effects of complementing an RTGS system with various deferred settlement mechanisms by performing simulations on historical Fedwire data. Although others have studied the effects of such modifications on payments systems, this is the first examination in the context of Fedwire.

One function of a payments system design could be to minimize the combined cost of delaying payments and the risk of extending intraday credit to commercial banks--that is, the credit risk that a central bank assumes by providing intraday credit. We do not use an explicit, objective function to evaluate the various alternatives to an RTGS system because we do not know banks' preferences regarding delays or specific default risks. We can, however, evaluate those designs that reduce both delays and credit extensions as preferable to others. In short, some modifications may clearly be more effective than others but none compares easily with a pure RTGS system, which by definition eliminates delays. Our results suggest that, compared with RTGS systems, alternative settlement designs could significantly reduce credit extensions while modestly delaying the average time of settlement of payments.

This article is organized as follows. In the next section, we discuss the basics of deferred settlement systems, and in Section 3 we describe the systems used in our simulations. In Section 4, we describe the performance metrics and results of the basic simulations, and in Section 5 we conduct a sensitivity analysis of the results obtained from alternative levels of queued payments. Sections 6 and 7 present more detailed analyses of liquidity use and the level of end-of-day queues. In Section 8, we discuss our results and the likely behavioral responses by a bank participant to the availability of the simulated systems. We conclude with a discussion of our results in light of the previous literature.

2. Characteristics of Deferred Settlement

As a baseline case, a pure RTGS system is one in which no payments are deferred for settlement--all payments are released upon receipt by the system operator as long as the participant has adequate funds to settle the payments. If not, the payment is rejected. Deferred settlement can work in conjunction with RTGS systems. In practice, deferred settlement mechanisms can operate in many ways, but all require certain criteria by which payment orders are entered, ranked, and settled. In addition, criteria for the end-of-day closing or the emptying of queues are required in a queuing system.

The entry criterion in a deferred settlement mechanism determines whether payments are deferred or whether they are settled immediately by pure RTGS. This criterion can be based either on decisions made by participating banks or on an automatic feature created by prespecified criteria. In many European RTGS systems, deferment is automatic: Rather than reject payment orders outright, the systems automatically place payments in a queue if RTGS settlement of the payment would breach the credit limit of the participant.

The order criterion defines the ranking or ordering of payment messages that are queued. Most contemporary RTGS systems adhere to the first-in, first-out (FIFO) principle--that is, payments that enter the queue earlier have priority over payments that enter the queue later. The FIFO principle is easy to implement. Assuming liquidity constraints, FIFO performs reasonably well when a system's smaller payments are submitted generally earlier in the day. Because early, larger payments can obstruct FIFO-ordered queues, some RTGS systems now have "bypass-FIFO" algorithms that allow participants to reorder and prioritize queued payments. Some, such as the CHAPS Clearing Company in the United Kingdom, allow the participants to select the order of the queued payments according to other criteria, for example, by the value of the payments.

The settlement criterion defines the rules by which payment messages are released from the queue, triggering the flow of money from the payer's account to the payee's account. Payments can be released from the queue either individually or in groups. In most queuing arrangements, payments are released individually, but some systems employ "gridlock-resolution" algorithms that allow multiple payments to be settled from the queue simultaneously if the release of the payments on an individual basis is not possible (see Bech and Soramaki [2001, 2002]). In previously described queuing systems, the settlement criterion has been based on the balance of the participant--that is, payments are released as soon as the participant's balance is high enough to cover the payment's settlement. The release of payments from the queue can be based on other criteria as well. In this article, we propose a novel deferred settlement mechanism that bases the settlement of queued payments on the value of incoming payments rather than on a participant's account balance.

The last important element of the design of a queuing system is end-of-day close of queues, or how to "empty" the queue of payment orders at the close of business. One method used in some European systems is to settle all messages remaining in the queue after a certain length of time through an exchange of the net amounts of the payments. An alternative method of closing queues is to return unreleased payments to banks before the RTGS system closes so banks can redirect the unreleased messages to the RTGS system.

3. System Designs

In our simulations, we design a system in which payments go through one of two alternative channels--deferred settlement or real-time gross settlement. These two main channels recognize that some payments are more time-critical than others. Banks would likely want to settle their time-critical payments through the immediate RTGS channel while the less time-critical payments could go through the deferred settlement channel to save liquidity. The deferred settlement channel allows payments to take one of three possible paths: a one-hour netting system, a six-hour netting system, or a unique type of system that we call a receipt-reactive gross settlement (RRGS) system.

3.1 Receipt-Reactive Gross Settlement System

In the receipt-reactive gross settlement system that we simulate, a portion of banks' payments is randomly selected to be settled through RTGS, while the remaining set of payments is placed in a queue for deferred settlement. Queued payment messages are ranked on a first-in, first-out basis. For the release criterion, a payment message's release from the queue is triggered by the arrival of incoming funds received by the bank within a specified period of time. In our simulations, this time period is one calendar minute. (3) The system will release within one minute as many payments from the front of the queue as possible to offset--but not exceed--the amount of incoming funds. In the simulations, this process continues throughout the day until 5:30 p.m., when the queue closes. The exhibit below shows the effects of a receipt-reactive queue on a bank's balance during a minute in which the bank both sends and receives RTGS payments (see Appendix A for a detailed description of this queuing system).

An important design element of a queuing system is how to "empty" the queue of payment messages at the end of the day. In our simulations, we randomly reassign the unreleased payments a settlement time between 5:30 p.m. and 6:00 p.m. This is our approximation to returning, at 5:30 p.m., the unreleased (that is, unsettled) payments to the banks that submitted them, with the banks subsequently resubmitting the payments through the RTGS system over the next half-hour.

This feature of our queue design was chosen for a number of reasons. The end-of-day return of the queued messages is consistent with the basic design of queuing systems used as adjuncts to RTGS systems. The receipt-reactive queuing system is intended to encourage banks to submit to the queue those payments that can be settled with incoming funds. If particular payments cannot be settled that way, then the banks would likely submit the payments through the RTGS system, which is designed to settle payments immediately with available balances. Therefore, returning banks' payments that remain in the queue to the respective banks near the end of the day is consistent with the intended use of the receipt-reactive queue and of the RTGS system.

3.2 One-Hour and Six-Hour Netting Systems

We simulate the performance of two simple netting systems. In both systems, a portion of all payments is settled by RTGS while a complementary set of payments is put in a queue. The queued payments are cumulated for a certain period of time, netted, then settled--even if they cause an overdraft in the banks' account balances. In the first simulation, the payments are cumulated, netted, then settled after each hour of the operating day. In the second simulation, cumulated payments are netted and settled after six hours. (See Table 1 for a summary of the simulations.)

4. Simulations of the Three Systems

To gauge the usefulness of these three complements to RTGS systems--one-hour netting, six-hour netting, and receipt-reactive gross settlement--we simulate their performance using a program developed by the Bank of Finland. The simulator is described in detail in Leinonen and Soramaki (2003). (See also the Bank of Finland's website: <http://www.bof.fi/sc/bof-pss>.)

In the simulations, we initially assume that banks would submit half of all individual payments to the queue for deferred settlement and the other half of their payments to the RTGS system. In the simulations, we include all Fedwire funds transfers for a randomly selected set of ten days between October 1999 and February 2000. We perform a sensitivity analysis (see Section 5) and present robustness checks to gauge the effects resulting from different levels of participation in the three deferred settlement arrangements. Using three days of data, we reproduce the simulations with either 20 percent or 80 percent of all payments assigned to the deferred settlement mechanism. The simulations are conducted on historical payment transactions similar to the generalized example below:
Sender Receiver Value Sent Submit Time Routing
Account Number Account Number (Dollars) (Hour:Minutes) Flag

02100xxxx 02100yyyy 100.50 10:20 1 or 0


In this example, Bank A (with American Banking Association account number 02100xxxx) sends Bank B (02100yyyy) $100.50 at 10:20 a.m. through the Fedwire service. If the routing flag is one, the payment is routed to the deferred settlement mechanism. If the flag is zero, the payment is routed to the RTGS system. The routing flag randomly assigns a one or a zero according to a predetermined level of participation in the deferred settlement mechanism (for example, 20 percent, 50 percent, or 80 percent of the day's payments have routing flags equal to one). For any given day, several hundred thousand transactions are routed, one by one in the order of their time stamps, to the settlement mechanism assigned. If routed to RTGS, a payment will be settled immediately. If routed to the deferred settlement mechanism, settlement could be delayed. We report the detailed results of these simulations in Appendix B.

Our primary performance metrics focus on the system's impact on daylight overdrafts and on the delay in the time of payment--that is, the difference between the time the payment was submitted and the time it was settled.

4.1 Daylight Overdrafts and Delay Indicators

A bank incurs a daylight overdraft when its balance falls below $0. The Federal Reserve measures daylight overdrafts outstanding at the end of each minute of the Fedwire operating day and reports the aggregate peak and average overdrafts for all banks. The aggregate peak overdraft occurs in a specific minute in which the aggregate overdraft has the highest value of all the minutes in the Fedwire operating day; the average overdraft is the sum of all the banks' overdrafts for all minutes of the day divided by the number of minutes in the Fedwire operating day. We focus on the average overdraft because that is the basic measure used by the Federal Reserve to calculate the fees it charges banks for their credit use, which is inherent in daylight overdrafts (see Appendix C for a description).

The basic indicator of delay that we consider is the average time of settlement across all payments and banks. It is the average time at which payments settle--where the time of actual settlement is weighted by the value of the payment.

The delay statistic is a standardized indicator that may take values between zero and one. RTGS, with its immediate settlement, results in a zero-delay statistic. End-of-day netting results in a delay statistic equal to one. In comparison with the average time of settlement statistic, the delay statistic tends to weight more heavily payments that are entered early in the day, even if the payments are small in value.

We compare the three simulated queue-augmented RTGS systems with Fedwire's historical performance using these liquidity and delay metrics (Table 2). We find that only the receipt-reactive gross settlement system reduces the use of overdraft liquidity by a statistically significant amount. While the two netting systems affect the average overdraft, neither of these differences is statistically significant (see Appendix B).

The one-hour netting mechanism shows no statistically significant change in the average overdraft relative to RTGS. Payments are delayed the least under one-hour netting, with the average time of settlement of payments moving to 2:51 p.m. from the RTGS average time of 2:35 p.m. For six-hour netting, the decrease in overdrafts is higher (although it is not statistically different from no change), but so is the delay in payments, as the average payment time moves to 3:46 p.m.--the latest time of all the alternatives. The receipt-reactive gross settlement system reduces average overdrafts by about 14 percent--the largest amount among the alternatives considered here. The time of payment is 3:18 p.m., slightly later than for the one-hour netting alternative. The average time of settlement increases by seventy-one minutes for six-hour netting while it increases by forty-three minutes for the receipt-reactive queuing system--a 65 percent difference--while six-hour netting shows a 150 percent increase in the delay statistic when compared with the receipt-reactive system. Our results suggest that the receipt-reactive system performs markedly better in settling early-morning and early-afternoon payments, as well as smaller ones.

The receipt-reactive queuing system's increase in peak overdrafts, in conjunction with its decrease in average overdrafts, is a bit puzzling (Table 2). Why do peak overdrafts increase if payments remain in the queue until sufficient receipts arrive for the bank? The answer is related to the current timing of payments on Fedwire. As described in McAndrews and Rajan (2000), a high proportion of the value transferred over Fedwire occurs in the late afternoon. During that period, banks have a large number of payment receipts, as well as payment outflows. Under the receipt-reactive gross settlement system, the high level of receipts that occurs during the late afternoon (from the 50 percent of payments that continue to be settled through the RTGS system) begins to trigger the release of a large number of queued payments. That process cascades as the payments released from the queue are receipts for other banks, which triggers further releases from the queues. For many banks--primarily large banks--the outflow from the queue "absorbs" all of the bank's receipts. Few, if any, of its receipts at that time of day add to its balance; instead, the receipts facilitate the release of payments from queues. The combination of receipts being dedicated to the release of payments from the queue and the submission of many RTGS payments at that time of day drives many accounts deeply into overdraft. Smaller banks, not having the same heavy outflow of payments, enjoy significantly more positive balances at that time, as the cascade of payments occurs. On balance, this process further concentrates payment activity in time, and reduces the use of overdrafts on average, even though the peak overdraft is increased. Of course, we would expect that banks would alter their behavior if they expected such a cascade of payments to be triggered.

5. Sensitivity Analysis

To test the robustness of our results, we examine two simulations in which 20 percent and then 80 percent of payments are randomly selected for deferred payment. These simulations were conducted on three days of data. Because an analysis of only three days yields such a small sample, we do not consider statistical significance, but simply report averages. (4)

One potential problem with a receipt-reactive gross settlement system is that banks may make an excessive number of submissions to that system and very few to the RTGS system. If all banks find it convenient and economical to submit payments to the queue for deferred settlement, then a paucity of RTGS payments might cause widespread payment delays. (5) By varying the number of payments submitted for deferred settlement, we can evaluate how each of the alternative systems would perform, assuming different behavioral patterns (see Table 3 for the results of these simulations). The numbers for the RTGS system are calculated using only the three days pertinent to the alternate level simulations and thus differ from those in Table 2.

These simulations suggest that our results are relatively robust at different levels of participation.

The level of liquidity savings and the length of delays in settlement increase as more payments are submitted to the queues. Of interest is the result that the RRGS system maintains comparable or higher levels of liquidity savings for a given delay than does the six-hour netting system, at all levels of submission to the queue. In addition, even with 80 percent of payments submitted to the queue, the RRGS system imposes an average settlement delay that is no greater than the delay with six-hour netting. However, the important difference is that RRGS does this with much greater liquidity savings than six-hour netting does. The delay statistic provides some evidence for why this occurred. The average time it takes to settle a payment for the 80 percent receipt-reactive system is one minute more than the average time for six-hour netting, suggesting that the receipt-reactive system holds more large payments in its queue until the end of the day. The delay statistic for six-hour netting is about 2.5 times higher than the statistic for the receipt-reactive system, indicating that the RRGS queue outperforms the six-hour netting system in overdraft management.

5.1 Liquidity

To provide more insight into the performance of these deferred settlement systems, we need to understand how the mechanisms use liquidity throughout the day. While our initial analysis focused on the mechanisms' effects on overdrafts and delays, we now look at four measures of liquidity, assess their levels in each system, then compare the levels with those found in the RTGS system (see Appendix B for further details).

The average funds transfer statistic measures the average level of liquidity, or funds, that must be transferred from an individual account from one minute to the next, across the minutes of the day, to complete the payments for the day. For example, in the RTGS system, the average funds transfer for an account is $226,000 per minute. To make this transfer, the bank must have sufficient funds in its account or receive sufficient funds from other banks. For any bank in the system, the average funds transfer may take values between zero and the per-minute gross value of payments sent by the bank.

In general, netting exhibits lower average liquidity usage over the day as indicated by the average funds transfer measure compared with an RTGS or RRGS system. Once queued, payments must stay in the queue until the next net settlement time and do not cause any balance changes in the interim. This liquidity conservation increases with longer netting times and larger participation in the netting systems (Table 4).

If we look at the minute with the highest average funds transfer, we obtain the maximum funds transfer. Using this indicator, we see that the netting systems demonstrate very high liquidity requirements during their net settlement periods--up to $17 million. These one-minute maximums occur near the end of the day when the Federal Reserve's RTGS system experiences its usual peak in volume. The receipt-reactive gross settlement system, however, produces lower maximum liquidity outflows, demonstrating its ability to smooth the liquidity usage over time. This smoothing--a feature of the more dynamic receipt-reactive queuing mechanism--results in greater average liquidity usage than the netting alternatives, but also produces significantly smaller maximum requirements. The lower maximum requirements are important as it is generally less costly for banks to make small payments that are distributed throughout the day than to make large payments. The smoothing effect of the RRGS system is thus a desirable feature.

The correlation with the RTGS measure represents the degree of correlation and hence the exhibited independence between the end-of-minute balances of RTGS and the other simulated systems. The one- and six-hour netting mechanisms exhibit a greater correlation between their balances and the original balances created by the RTGS system, despite the netting systems' lower average figures of liquidity use. The lower correlation for RRGS indicates that, while it results in higher balance transfers than the netting systems throughout the day, these balances are circulated more rapidly, allowing earlier settlement of payments and a greater divergence in the pattern of balances from the original RTGS balances.

The skewness measures the positive differences in a bank's balances from an RTGS system across the minutes of the day. This measure is obtained by calculating the skewness of the balance differences between RTGS and the simulated system. When compared with the netting systems, the receipt-reactive gross settlement system's distribution of the differences in balances is more positively skewed, suggesting that more participants maintain positive balances--and hence a reduced need for overdrafts on average. The receipt-reactive queue acts to smooth the liquidity usage across the payments system participants and across the day, generating larger balances and smaller overdrafts from the system's liquidity.

6. End-of-Day Queue Analysis

When looking at the simulated receipt-reactive gross settlement system, it is important to determine how the end-of-day settling of payments influenced our results. The RRGS system closed at 5:30 p.m. and the remaining payments were evenly disbursed over the next thirty minutes. Table 5 gives the percentages of all payments submitted to the queue that settled by 5:30 p.m. In addition, the table presents the average value of payments in the queue at 5:30 p.m. to offer a sense of the role that size played in the settlement of these queued payments.

The one-hour netting arrangement quite naturally yields the best results here because the payments in the queue only start accumulating from 4:30 p.m. Because this time of day experiences the largest value payments (McAndrews and Rajan 2000), the average payment values are twice as high as those produced by six-hour netting and RRGS. The six-hour netting system shows that payments entered as early as 12:30 p.m. remain in the queue, which results in a low percentage of settled queued payments by 5:30 p.m. In terms of overall settlement by 5:30 p.m., the RRGS system performs similarly to a one-hour netting system at the 20 percent and 50 percent participation levels and more like a six-hour netting system at the 80 percent level. This result indicates that when 80 percent of payments are deferred to RRGS, many never get settled and are returned to the banks that sent them.

A feature of the simulated RRGS mechanism is that the FIFO rule was strictly adhered to when settling queued payments. The FIFO rule results in situations where large payments in front of the queue block smaller payments from being settled. The average value of queued payments at 5:30 p.m. was considerably higher for all levels of payments queued. The value of payments remaining in the queue rose as the participation in the queue increased. At the 80 percent level, the average value of payments that remained queued was 50 percent higher than the average value of payments in the original RTGS system ($3.45 million). This result suggests that the performance of RRGS systems could likely be improved by using a different order criterion, such as allowing smaller payments to go first, splitting the large transactions into several smaller ones, or using gridlock-resolution mechanisms.

7. Discussion of Simulation Results and Likely Behavioral Responses

Netting has long been acknowledged as an efficient way to reduce the liquidity needs of a payments system. Roberds (1993) shows that the netting of payments achieves the theoretical minimum of liquidity use for the settlement of a specific set of payments. Another way to reduce liquidity needs is to use various queuing arrangements in RTGS systems.

Many simulation studies of the behavior of queue-augmented RTGS systems have been conducted recently. The research examines the mechanical reordering of payments that is possible with a queuing system and then compares this feature with other alternative designs to see how each handles liquidity use and payment delays. Koponen and Soramaki (1998) and Leinonen and Soramaki (1999) use the simulation approach to measure the liquidity savings and settlement delays for a number of alternative queuing, netting, and payment-splitting techniques with an RTGS system using data from the Bank of Finland's RTGS system. Both studies conclude that queuing systems can contribute substantial improvements compared with pure netting systems. Bech and Soramaki (2001) analyze the effects of a simultaneous settlement algorithm based on FIFO to settle a subset of payments from queues.

A report on RTGS systems by the Bank for International Settlements (1997) discusses how to sequence payments so that incoming transfers from other banks can be used to fund payments. A pure RTGS system relies solely on the participants (in a decentralized way) to time their payments in a manner that best utilizes their incoming funds.

Our simulation results show that netting in conjunction with RTGS settlement is not very desirable. Netting every six hours yields relatively modest but statistically insignificant reductions in daylight overdrafts (3.2 percent) compared with a significant delay in payment timing (one hour and thirteen minutes in average settlement time). Compared with one-hour netting, the settlement delays in six-hour netting are much greater. The simulated RRGS mechanism outperforms the netting systems when both liquidity savings and payment delays are taken into account. The receipt-reactive system saves significant liquidity (13.6 percent) and results in relatively modest payment delays (forty-three minutes) when compared with six-hour netting. These results are in line with those of the studies cited above.

7.1 Bank Participation and Risk

One question to ask is whether banks would actually use deferred payment mechanisms if they were available. Our simulations cannot predict banks' behavior. However, by relying on how the mechanisms work in a simulated environment and applying theoretical reasoning from the models of payment behavior, we can gain insight into the likely endogenous responses to implementing these complements to an RTGS system.

Consider the netting systems, for example. The simulation shows that a netting system that settles payments each hour of the day, even if it were to attract 50 percent of the payments on Fedwire, would not create a statistically different level of daylight overdrafts. When we consider the participation risk in a netting system, it is unlikely that banks would use such a facility.

Participation risk is present in many netting systems. In the operation of most payments systems, if a bank enters payments into the system, the bank is expected and, in some cases, obligated to settle those payment orders. If the bank expects many offsetting payments to be entered, but in fact only a few are, the bank may face a larger-than-expected settlement obligation. Netting systems tend to be more effective in gathering offsetting payments as more banks participate. Hence, a start-up netting system exposes potential participants to risk. If many banks participate, the bank will have a small expected settlement obligation, but if only few others do, the bank may have a larger-than-expected settlement obligation.

If a payments system were to offer a netting arrangement in conjunction with an RTGS system, banks that choose to use the netting mechanism would face liquidity risks. Those banks that use the netting system may end the day needing more liquidity than if they had carefully managed their payments strictly through an RTGS system. RTGS system participants likely submit payments in ways meant to lessen their liquidity demands and risks endogenously. As a result, a netting service might fail to attract participation when offered in conjunction with the current Fedwire service.

Deferred settlement systems provide a means to allow participants in an RTGS system to make some payments contingent on the submission of offsetting payments by their counterparties. Allowing a participant's payment submission strategy to be contingent on the payment submissions of others reduces the risk of loss associated with making payments and the risk of having one's counterparties fail to make expected offsetting payments prior to defaulting. The reduction in that risk should lessen the incentive to delay submitting one's payments, at least in the contingent, deferred settlement payment option.

We expect that banks would face lower participation risk in the receipt-reactive queuing system. The basic operation of the queue is useful to a single bank in isolation, even if no other banks use their options to queue payments. Queuing enables the bank to automatically synchronize outgoing payments with its incoming payments. This is an important advantage in encouraging use of the queue: Banks face no risk of increasing their liquidity demands by using the queue. They can always do at least as well for themselves by using the queue to manage their liquidity demands as they would if they had their own in-house automatic queue management system.

How would the banks change the timing of their payments to the system in the new environment? Models of the timing of payments in an RTGS model have been presented by Angelini (1998, 2000), Buckle and Campbell (2002), Kobayakawa (1997), and Kahn, McAndrews, and Roberds (2003). Some of these studies consider the default risk of counterparties and focus on the possibility of payment delays in an RTGS system, partly because of the risk of sending the gross amount of a payment to a counterparty in advance of receiving an offsetting amount from that counterparty. Because payments made in an RTGS system are not contingent on the submission of payments by counterparties, banks could be reluctant to submit payments in a timely fashion, and as a result, the timing of all payments could be delayed (relative to the time that a central planner would choose to have the payments sent). Buckle and Campbell (2002) consider requirements, chosen jointly by the participants, that commit participants to submit certain percentages of their payments by certain times of the day. Such a requirement is in effect in the U.K. payments system, CHAPS, and, on the European level, guidelines issued by the European Banking Federation govern the timing of payments in the TARGET system.

Recent theoretical work by Bech and Garratt (2003) analyzes the incentives that banks have in an RTGS system--in the case in which there is no default risk among counterparties--to coordinate the timing of payments. In their model, banks wish to complete a set of payments while economizing on their holdings of overnight balances. Bech and Garratt find that banks are expected to synchronize the timing of their payment submissions to take best advantage of incoming transfers, which allows all the banks to economize on their holdings of overnight balances. McAndrews and Rajan (2000) present evidence consistent with that model for the Fedwire system.

The receipt-reactive queue mechanism can be a useful way for a bank to reduce its demand for costly liquidity. In fact, we would also expect banks to enter more of their day's activity earlier in the day, with much of it placed in the queue. We expect this to be the case because in most RTGS systems today, a bank's only method of liquidity management is simply to delay payments. In contrast, by using a receipt-reactive queue, banks would not face any downside risk to their liquidity position by the early entry of payment messages in the queue because the amount released from the queue would always be less than the incoming payment amount.

In the United States, some banks use the Clearing House Interbank Payments System, which has liquidity-saving features. The presence of such a system could serve to satisfy banks' demand for an alternative to RTGS. If that is so, then appending liquidity-saving features to the existing RTGS system may not lead to a great deal of use of the liquidity-saving features.

The primary reason why a receipt-reactive system would generate good incentives for the early submission of payments is that the release of payments from the queue is independent of the timing of a bank's own RTGS payments. Because an RRGS system does not rely on a bank's balance, but only a bank's receipts to trigger the release of payments, the history of a bank's submission of RTGS payments does not affect the release of its payments from the queue. As a result, there is no incentive to delay making RTGS payments to allow the release of queued payment messages. This situation results in incentives for earlier entry of RTGS payments, which would endogenously improve the circulation of liquidity, releasing the queued messages of others in a virtuous circle. (6)

Some degree of transparency of the queues might also offer banks information that they cannot gain by using internal queues. With the use of such features, we would tend to expect widespread participation of banks in queuing mechanisms. In this case, gridlock resolution--which requires a central queue--could be used to optimize further the queue's performance.

Finally, centralized queuing in general may be beneficial for smaller banks. While larger banks currently time the entry of their payments into RTGS systems with the aid of internal queues, the operation of the receipt-reactive queue would give more banks the option of automated payment settlement.

8. Conclusion

In this article, we simulate deferred settlement mechanisms to understand the liquidity implications of using the mechanisms to complement real-time gross settlement systems. Using historical data on all payments made over ten days on the Fedwire Funds Service, we simulate two different netting systems and a receipt-reactive gross settlement system.

We find that, unlike an RTGS system, both netting and RRGS queuing systems introduce delays to payments. However, both netting and queuing also have the potential to reduce--in some cases, significantly--daylight overdrafts. These results appear to be robust to alternative assumptions about the level at which banks are willing to submit payments to a queue for deferred settlement.

The receipt-reactive gross settlement system we examine is novel in that it releases payments from the queue based on a bank's receipts over a given time rather than on its balance. The simulations in this article indicate that an RRGS system reduces significantly more overdrafts than a six-hour netting system would, with considerably less delay in payments.

Our consideration of the receipt-reactive gross settlement system reveals that it may provide good incentives for banks to submit payments early to the queuing system, as the release of payments from the queue is independent of the submission of the bank's own RTGS payments. This feature is likely to encourage banks to quicken the timing of payments and to reduce the number of daylight overdrafts. As a result, such a system might prove to be a true liquidity-saving complement to an RTGS system.

While simulations provide a good starting point for studying enhancements to RTGS systems, our results suggest that these systems warrant further investigation. For example, how banks would change their behavior when offered these alternatives to payment settlement remains an open question. Going forward, a better theoretical and empirical understanding of banks' payment behavior would help inform policymakers considering enhancements to RTGS systems.

Appendix A: Detailed Dynamics of the Receipt-Reactive Gross Settlement System

In this appendix, we explain the features of our proposed receipt-reactive gross settlement design. A real-time gross settlement (RTGS) payment from bank i to bank j entered at time t is [p.sup.t.sub.ij]. Similarly, a queued payment message is [q.sup.t'.sub.ij](r), with t' denoting the time of entry in the queue and r denoting the message's rank in the order of its entry. A bank's funds balance at time t is denoted [b.sup.t.sub.i]. A settled payment is [s.sup.t.sub.ij], where a settled payment is either an RTGS payment or a queued payment message that has been released at time t.

The basic receipt-reactive gross settlement design operates as follows: By the end of minute m, the payment messages {q.sup.t'.sub.ij]:j [not equal to] i,t'<m,r = 1,2 ..., k} are released from the queue, where k is the maximum rank that satisfies inequality A1:

(A1) [summation over ((m-1)<t [less than or equal to] m) [summation over (j [not equal to] 1)] ([s.sup.t.sub.ji) [greater than or equal to] [k.summation over ((r = 1)] [summation over (j [not equal to] 1) ([q.sup.t'.sub.ij) (r)).

At the beginning of each minute, the rank of queued payments is reset so that the oldest queued payment is assigned rank one, the second-oldest, rank two, and so on. (The actual algorithm releases payments within the minute as soon as sufficient receipts arrive.)

Inequality A1 states that the first k queued payment messages of the bank are released in minute m when the value of the bank's receipts in that same minute are greater than or equal to the value of the k payment messages to be released. A bank's balance at the end of minute m will then be equal to:

(A2) [b.sup.m.sub.i] = [b.sup.m-1.sub.i]-[summation over ((m-1)<t[less than or equal to] m)] [summation over (j [not equal to] 1)] ([p.sup.t.sub.ij]) + ([summation over ((m-1)<t[less than or equal to] m)] [summation over (j [not equal to] 1)] ([s.sup.t.sub.ji)- [k.summation over (r = 1)([s.sup.t.sub.ji)] + [summation over (j [not equal to] 1)] ([q.sup.t'.sub.ij)([q.sup.t'.sub.ij)(r))).

Equation A2 states that a bank begins a minute with its balance of the previous minute, and its balance decreases in the minute by any RTGS payments it makes and increases by the net amount of its receipts, less any release of payments from its queue. By inequality A1, the net amount of its receipts must be at least as large as the amount that is released from the queue. If a bank's queued payments were numerous and finely divisible--so that the receipts are approximately equal to the amount released from the queue--then the bank's balance would be approximately equal to its previous balance minus its outgoing RTGS payments: [b.sup.m.sub.t] [approximately equal to] [b.sup.m-1.sub.t]-[summation over ((m-1)<t[less than or equal to] m) [summation over (j [not equal to] 1) ([p.sup.t.sub.ij)

In a theoretical limit to the use of this queuing system, banks could place in the queue all payments whose value they expect to be offset by incoming payments. Banks' real-time payments would equal the amount of net payment outflows that they would expect during the day--equivalent to the multilateral net debit of a net settlement system. If expectations were fully realized and banks held sufficient balances to fund their payments, the amount of balances held would equal the amount of settlement payments that the banks would need if they settled payments in a multilateral net settlement system. At the same time, banks would have the advantages of real-time release of payments and the associated release of payments from the queue throughout the day. This is the essential theoretical benefit of this design.

No practical implementation of this system is likely to achieve the theoretical maximum in liquidity savings. In fact, the practical implementation of this queuing system is an important aspect of the mechanism. One important element is that the receipt-reactive system relies on some funds flowing among participants to trigger the release of queued payment messages. If all banks were to queue all their payments, all payments would remain queued. In such a case, the system operator could consider using a "gridlock-resolution" mechanism to break the logjam and release some payments from the queue, as in Bech and Soramaki (2001, 2002).

Appendix B: Simulation Results and Analysis

To gauge the effects of some of the liquidity enhancements described in our article, we tested various features of these possible enhancements using a simulation program developed by the Bank of Finland. The simulation program is a version of the one described in Leinonen and Soramaki (1999) and Koponen and Soramaki (1998). (A more in-depth description can be found at the Bank of Finland's website: <http://www.bof.fi/sc/bof-pss>.) The simulations first generated baseline output data for both real-time gross settlement (RTGS) and net settlement systems. Further simulations examined an alternative enhancement that releases gross payments against the aggregate amount of incoming funds within each minute--receipt-reactive gross settlement (RRGS).

We randomly selected 20 percent, 50 percent, or 80 percent of all Fedwire Funds Service payments and placed those payments either into a queue for deferred settlement or into a netting system. Those payments not entered into the queue or netting system were settled by the RTGS system. With the exception of the changes in settlement time imposed by the queuing or netting arrangements, we assumed no behavioral changes in Fedwire that would affect the timing of payment entry. The bulk of our analysis was performed with ten days of data, directing 50 percent of payments to the deferred settlement mechanisms. The 20 percent and 80 percent simulations tested the network effect associated with varying degrees of participation in these queuing and netting arrangements. The 80 percent simulations were particularly time consuming, so the 20 percent and 80 percent sensitivity analyses were performed on only three days of data.

Because these simulations focus on reducing both the Federal Reserve's risk exposure in granting intraday credit and the liquidity use by banks, we selected statistics that assess these areas. The analysis involves average and peak overdrafts and settlement delays.

Data

The simulations were performed using ten typical days of funds transfer activity data from the Fedwire Funds Service (Table B1). The days were randomly selected from the period October 1999 through February 2000. We included all transaction types but eliminated payment transfers of less than $100. The transaction data only included master accounts. Subordinate account numbers were changed to their related master account numbers before simulation. A uniform random-number generator was used to select the 50 percent of payments to be queued in each treatment. The rest of the payments were automatically processed by the RTGS system according to their historical timing during the simulations. While not directly involved in the simulations, National Book-Entry System (NBES) securities transaction data were used for the overdraft analysis presented later.

Analytical Framework

In the following discussion, let [s.sup.t.sub.ij]represent a settlement of a payment order at time t from i to j. The balance at the end of any minute, m, is equal to the previous balance plus the difference between the cumulative value of outgoing and incoming payments: i = 1,2 ..., D.

(B1) [b.sup.m.sub.i] = [b.sup.m-1.sub.i]-[summation over ((m-1)<t[less than or equal to] m) [summation over (j [not equal to] 1) ([s.sup.t.sub.ij) + [b.sup.m.sub.i] = [b.sup.m-1.sub.i]-[summation over ((m-1)<t[less than or equal to] m) [summation over (j [not equal to] 1)] ([s.sup.t.sub.ji),

where m = 1,2 ..., M.

Overdrafts

Overdraft calculations are based on end-of-minute balances. For overdraft accounting purposes, a bank's balance is affected by several services. We attempt to extract the Fedwire Funds Service's contribution to the bank's balance, and hence its overdraft, from the bank's other non-Fedwire funds transactions using a method that mimics the Federal Reserve's overdraft accounting procedures. (7) This involves a comparison of the Fedwire funds and NBES balances to determine the applicable balance, [b.sup.m.sub.i], applied in the following formulas. The analysis assumes that same-day NBES and non-Fedwire funds activities remain unchanged (see Appendix C for further elaboration). Government-sponsored enterprises, the Clearing House Interbank Payments System, Federal Reserve System banks, and government agency accounts were included in the simulations, but removed prior to analysis.

The overdraft during the day for any minute, m, and bank, i, equals the absolute value of a negative balance or zero.

(B2) O[D.sup,m.sub.i] = |min(0,[b.sup.m.sub.i])|.

The average continuous overdraft is

(B3) Average OD = [summation over (m)], [summation over (m)] [summation over (i)] O[D.sup.m.sub.i]/1,081,

that is, the sum of overdrafts for each bank during the day divided by the number of minutes Fedwire is open (eighteen hours and one minute). (8)

Peak overdraft is

(B4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Delay and Time Statistics

The settlement delay for each payment is calculated as the time difference between payment origination by the sending bank and the final and irrevocable settlement of the payment. The two statistics that we use to measure the delay imposed by the queuing and netting arrangements in our proposed design are the delay statistic and the average time of settlement.

The delay statistic for the system is calculated as:

(B5) Delay = [summation over (t)] [summation over (i)] [summation over (j,j[not equal to] i)][s.sup.t,t'.sub.ij](t-t')/ [summation over (t)] [summation over (i)] [summation over (j,j[not equal to] i)][s.sup.t,t'.sub.ij](T-t').

In the notation for the delay statistic, we capture, for each settled payment, both its entry time, denoted by t', and its release time, denoted by t. The delay statistic measures in the numerator the value of the settled payments multiplied by the time they spent delayed in the queue. In the denominator, the value of settled payments is multiplied by the time that payments could have been queued, had their settlement been delayed until the queue is closed.

The delay statistic is a standardized indicator that may take values between zero and one. In an RTGS system, for example, payments spend no time in the queue, and t' = t, resulting in a delay statistic equal to zero. In an end-of-day netting system, the settlement of payments is delayed until end of day, and t = T, resulting in a delay statistic equal to one.

The delay statistic places greater emphasis than the average time of settlement on the settlement of both early-morning and early-afternoon payments, as well as on smaller payments. Early-morning or early-afternoon payments carry more weight than their nominal value because the delay statistic repeatedly counts these payments for every minute that they remain unsettled.

The average time of settlement (ATOS) is the average time weighted by the value of the payments settled at each minute, t.

(B6) ATOS = [summation over (t)]([summation over (i)] [summation over (j[not equal to] i)][s.sup.t.sub.ij] x t/ [T.summation over (i=0)] [summation over (i)] [summation over (j[not equal to] i)][s.sup.t.sub.ij].

These statistics are calculated for all applicable treatments. In addition, we ran a statistical test on the average continuous overdraft statistic to provide added confirmation of a scenario's overdraft savings or loss. Because the same payment data are used for each simulation treatment, the statistics for each treatment can be viewed as different variables of the same group. Furthermore, the small, ten-day sample size and unequal variances across treatments suggest that a standard parametric statistical analysis is inappropriate. Therefore, we use the nonparametric Wilcoxon matched-pairs signed-rank test to determine whether a statistical difference in average continuous overdraft exists between the dependent groups or treatments. All treatments are compared with the baseline performance of the RTGS system. When a treatment shows a nominal increase or decrease in average continuous overdraft when compared with each of these two treatments, we conduct a one-sided test to determine whether a statistically significant increase or decrease can be found versus the null hypothesis that there is no statistical difference. All tests were conducted at the 5 percent level.

Treatments and Results

To properly compare aggregate statistics from the sensitivity analysis with the 50 percent simulations, we added two lines for the RTGS simulation results, as well as for all 50 percent simulations. The sensitivity analysis average and sensitivity analysis standard deviation figures represent aggregate statistics calculated using the three days in our 20 percent and 80 percent sensitivity analysis simulations: January 6, 2000; January 26, 2000; and November 4, 1999. Real-Time Gross Settlement

The RTGS simulation provides a benchmark for the analysis of the alternative queuing and netting arrangements (Table B2). In this simulation, 100 percent of the payments are settled immediately by the RTGS system. The delay statistic for RTGS is zero by definition and the average time of settlement equals the time when an average dollar was submitted to the system.

One-Hour Net Settlement

Net settlement of queued payments occurred every hour, and the net amounts were settled immediately thereafter through the RTGS system (Table B3). Accounts had unlimited liquidity available. At 18:30, remaining queued transfers were netted and the net balances were transferred between banks.

One-hour net settlement actually increases the average overdraft by 0.6 percent, although the difference is not statistically different from the RTGS overdraft. One-hour net settlement, like six-hour net settlement, lowers the peak overdraft slightly while generating a 7.5 percentage point addition in the delay indicator. As expected, the average time of settlement is delayed by twenty-one minutes when compared with the RTGS average time of settlement--a logical result of delaying 50 percent of the payments for up to an hour.

Six-Hour Net Settlement

Net settlement of queued payments occurred every six hours (6:30, 12:30, and 18:30), and the net amounts were settled immediately thereafter through the RTGS system (Table B4). Accounts had unlimited liquidity available. At 18:30, remaining queued transfers were netted and the net balances were transferred between banks. The average and standard deviation figures represent those statistics for the three days involved in our 20 percent and 80 percent simulations: January 6, 2000; January 26, 2000; and November 4, 1999.

Six-hour net settlement produced a modest 3.2 percent reduction in average overdraft, although, once again, the difference is not statistically significant. However, this treatment produced the lowest overall peak overdraft. The 35 percent delay statistic is roughly five times that of one-hour net settlement and, as we will see, is nearly three times that of RRGS. The average time of settlement was one hour and thirteen minutes later than in RTGS.

Receipt-Reactive Gross Settlement

The gross amount of payments received during each minute provided the available liquidity for release from the queue (Table B5). The payments subject to deferral were held in the queue if they were not offset by incoming payments in that minute. The available liquidity from incoming payments resets to zero at the start of a new minute and does not accumulate past that minute. Payments settled on a first in, first out (FIFO) basis when a bank received sufficient incoming funds. Queued payment messages were transferred to RTGS for settlement. The nondeferred payments were settled immediately by the RTGS system and did not affect the incoming funds accounting. Starting at 17:30, the remaining queued payments were spread evenly over the next thirty minutes and settled by the RTGS system.

In sum, receipt-reactive gross settlement offers a significant overdraft reduction coupled with an increase in the peak overdraft. The RRGS produced statistically significant lower average continuous overdrafts than did the RTGS treatment.

Indicators of Liquidity Use

Overdraft calculations use only the negative balances and therefore measure only the lower end distribution of balances according to a cutoff point of zero. While this is useful from a risk management standpoint, we calculate further statistics regarding the performance of these systems by analyzing them in terms of their liquidity usage. Each simulation restructures the timing of the original RTGS payments by changing the release sequence of the payments. By doing so, the different systems generate different liquidity levels and balance distributions than the original RTGS system. When evaluating the different simulations' temporal restructuring of the original RTGS payments, the approaches presented here attempt to indicate efficiency of liquidity use both above and below zero, providing a better overall view of each simulation's effect on liquidity usage. We do this indirectly by measuring both the degree of difference in the simulation balances when compared with RTGS balances and the direction of that difference.

Our first liquidity calculation measures the average absolute change in balances that occurs per minute for each bank. In effect, this calculation gives the amount of money that an average bank would have to move, either in or out of its account, for any given minute of the day. A liquidity-usage measure calculates the extent to which the balance must fluctuate in order to settle the payments. An RTGS system requires the most liquidity.

To measure liquidity, we first calculated the absolute value of a bank's change in balance from one minute to the next and summed this amount across all banks for a given minute. We did this for all 1,080 difference periods, summed the results, and divided by 1080 x N,, with N being the number of banks. The [b.sup.m.sub.i] used in the liquidity equations is the sum of each bank's end-of-minute balance across the three days subject to the alternative levels of payment submission simulations.

Average funds transfer =

1/1,080 x N [1,081.summation over (m=2)][N.summation over (i=1)]|[b.sup.m.sub.i]-[b.sup.m-1.sub.i] [for all] ([b.sup.m.sub.i]-[b.sup.m-1.sub.i]<0.

Our second measure is the maximum funds transfer across the minutes:

Maximum funds transfer =

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Our third measure of liquidity use in the systems is an indirect one. We calculated the degree of difference in the balances by measuring the independence exhibited between the end-of-minute balances of RTGS and the simulated system. Our independence calculation produced Pearson correlation coefficients for each minute and summed them across the 1,081 minutes of the Fedwire day. We then divided by 1,081 to get the average per minute. For RTGS, the correlation of its end-of-minute balances with itself is one. For the simulated systems, this number is the correlation between end-of-minute balances in the simulated system and those in the RTGS system. Lower numbers demonstrate more independence from the original RTGS payment distribution. The [b.sup.m.sub.i,SIM] and [b.sup.m.sub.i,RTGS], respectively, represent the collection of the pertinent simulated balances and the RTGS balances in minute m. The balances included in this collection are the sum of each bank's end-ofminute balance across the three days subject to the alternative levels of payment submission simulations.

Correlation with RTGS = 1/1,080[1,081.summation over (m=1)][corr.sub.m]([b.sup.m.sub.i,SIM]-[b.sup.m.sub.i,RTGS]

Our fourth measure, the skewness of the difference in balances, gauges the degree of positive change in balances imposed by the simulated system on the original RTGS payments. The difference in balances between the simulated system and RTGS is calculated for each bank and minute. A skewness statistic is generated for each minute and the average for the day is then calculated. The [b.sup.m.sub.i,SIM]and [b.sup.m.sub.i,RTGS], respectively, represent the sum of each bank's simulated and RTGS end-of-minute balances across the three days subject to the alternative levels of payment submission simulations.

Skewness = 1/1,080[1,081.summation over (m=1)][skewness.sub.m]([b.sup.m.sub.i,SIM]-[b.sup.m.sub.i,RTGS].
Table B1
Summary Statistics for Fedwire Funds Data

 Number Sum of Payments
 Date of Payments (Billions of Dollars)

 1/6/00 369,094 1,181.34
 1/26/00 373,685 1,318.44
 2/23/00 406,644 1,421.39
 2/24/00 404,356 1,470.65
 10/1/99 541,075 1,840.46
 10/8/99 406,628 1,377.19
 11/4/99 373,811 1,329.56
11/10/99 395,304 1,354.38
 12/6/99 400,689 1,394.28
12/16/99 413,024 1,383.84

 Average Value
 Date Number of Banks (Millions of Dollars)

 1/6/00 6,289 3.20
 1/26/00 6,191 3.53
 2/23/00 6,339 3.50
 2/24/00 6,293 3.64
 10/1/99 6,767 3.40
 10/8/99 6,400 3.39
 11/4/99 6,228 3.56
11/10/99 6,159 3.43
 12/6/99 6,234 3.48
12/16/99 6,295 3.35

 Standard Deviation
 of Payment Value Sum of Opening Balances
 Date (Millions of Dollars) (Billions of Dollars)

 1/6/00 28.66 10.03
 1/26/00 31.84 15.61
 2/23/00 31.47 16.90
 2/24/00 32.55 16.42
 10/1/99 32.85 21.50
 10/8/99 31.23 12.76
 11/4/99 32.23 15.38
11/10/99 31.42 10.87
 12/6/99 30.95 10.88
12/16/99 30.53 12.71

Source: Authors' calculations, based on data from Federal Reserve
Bank of New York, Fedwire Funds Service.

Table B2
Real-Time Gross Settlement Simulations

 Average Overdraft Peak Overdraft
Date (Billions of Dollars) (Billions of Dollars)

 1/6/00 19.87 65.54
 1/26/00 20.57 70.73
 2/23/00 19.51 68.60
 2/24/00 21.01 67.58
 10/1/99 20.22 67.58
 10/8/99 19.69 59.68
 11/4/99 21.14 69.20
11/10/99 22.91 75.58
 12/6/99 19.67 59.10
12/16/99 18.28 59.20
 Average 20.29 66.28
 Standard deviation 1.23 5.47
 Average for three 20.52 68.49
 days
 Standard deviation 0.64 2.67
 for three days

 Time of Peak Average Time Delay Statistic
Date Overdraft of Settlement (Percent)

 1/6/00 15:31 14:28 0
 1/26/00 15:49 14:32 0
 2/23/00 15:54 14:31 0
 2/24/00 15:55 14:41 0
 10/1/99 14:23 14:39 0
 10/8/99 14:01 14:39 0
 11/4/99 14:38 14:37 0
11/10/99 15:54 14:35 0
 12/6/99 15:47 14:43 0
12/16/99 15:53 14:33 0
 Average 15:22 14:35 0
 Standard deviation 0:44 0:04 0
 Average for three 15:19 14:32 0
 days
 Standard deviation 0:36 0:04 0
 for three days

Source: Authors' calculations, based on data from Federal Reserve
Bank of New York, Fedwire Funds Service.

Note: The figures for the average for three days and the standard
deviation for three days are calculated for the days for which the
sensitivity analysis simulations were conducted.

Table B3
One-Hour Net Settlement Simulations with Alternate Levels
of Participation

 Percentage Change
 Average Overdraft from Real-Time
Date (Billions of Dollars) Gross Settlement

20 percent
 1/6/2000 19.86 0.0
 1/26/2000 20.24 -1.6
 11/4/1999 21.01 -0.6
 Average 20.37 -0.7
 Standard deviation 0.58 0.8

50 percent
 1/6/2000 20.02 0.8
 1/26/2000 20.36 -1.0
 2/23/2000 19.48 -0.2
 2/24/2000 21.36 1.6
 10/1/1999 20.27 0.2
 10/8/1999 19.96 1.4
 11/4/1999 21.27 0.6
 11/10/1999 23.49 2.5
 12/6/1999 19.65 -0.1
 12/16/1999 18.21 -0.4
 Average 20.41 0.6
 Standard deviation 1.41 1.1
 Average for three days 20.55 0.1
 Standard deviation 0.64 1.0
 for three days

80 percent
 1/6/2000 19.06 -4.1
 1/26/2000 19.77 -3.9
 11/4/1999 20.66 -2.3
 Average 19.83 -3.4
 Standard deviation 0.80 1.0

 Percentage Change
 Peak Overdraft from Real-Time
Date (Billions of Dollars) Gross Settlement

20 percent
 1/6/2000 63.78 -2.7
 1/26/2000 70.62 -0.2
 11/4/1999 67.09 -3.0
 Average 67.16 -1.9
 Standard deviation 3.42 1.6

50 percent
 1/6/2000 59.08 -9.9
 1/26/2000 68.94 -2.5
 2/23/2000 66.53 -3.0
 2/24/2000 68.30 1.1
 10/1/1999 64.18 -5.0
 10/8/1999 59.80 0.2
 11/4/1999 67.80 -2.0
 11/10/1999 76.83 1.6
 12/6/1999 57.01 -3.5
 12/16/1999 58.43 -1.3
 Average 64.69 -2.4
 Standard deviation 6.19 3.3
 Average for three days 65.27 -4.7
 Standard deviation 5.39 4.4
 for three days

80 percent
 1/6/2000 56.36 -14.0
 1/26/2000 69.67 -1.5
 11/4/1999 67.93 -1.8
 Average 64.66 -5.6
 Standard deviation 7.24 7.1

 Delay
 Time of Peak Average Time Statistic
Date Overdraft of Settlement (Percent)

20 percent
 1/6/2000 15:31 14:33 2.49
 1/26/2000 14:55 14:36 2.26
 11/4/1999 14:38 14:43 2.82
 Average 15:01 14:37 2.52
 Standard deviation 00:27 0:04 0.28

50 percent
 1/6/2000 15:31 14:43 7.24
 1/26/2000 14:53 14:46 6.86
 2/23/2000 15:54 14:46 7.03
 2/24/2000 16:10 14:55 7.38
 10/1/1999 15:10 14:54 7.72
 10/8/1999 14:01 14:54 7.72
 11/4/1999 15:23 14:52 7.84
 11/10/1999 16:31 14:50 7.54
 12/6/1999 16:07 14:58 8.00
 12/16/1999 16:22 14:49 7.97
 Average 15:36 14:51 7.53
 Standard deviation 0:46 0:04 0.39
 Average for three days 15:15 14:47 7.31
 Standard deviation 0:20 0:04 0.49
 for three days

80 percent
 1/6/2000 15:31 14:49 9.94
 1/26/2000 15:49 14:51 9.31
 11/4/1999 15:31 14:59 10.55
 Average 15:37 14:53 9.93
 Standard deviation 00:10 0:05 0.62

Source: Authors' calculations, based on data from Federal Reserve
Bank of New York, Fedwire Funds Service.

Note: The figures for the average for three days and the standard
deviation for three days are calculated for the days for which the
sensitivity analysis simulations were conducted.

Table B4
Six-Hour Net Settlement Simulations with Alternate Levels
of Participation

 Percentage Change
 Average Overdraft from Real-Time
Date (Billions of Dollars) Gross Settlement

20 percent
 1/6/2000 20.53 3.4
 1/26/2000 19.63 -4.6
 11/4/1999 21.43 1.4
 Average 20.53 0.0
 Standard deviation 0.90 4.1

50 percent
 1/6/2000 20.47 3.0
 1/26/2000 19.27 -6.3
 2/23/2000 19.58 0.4
 2/24/2000 18.83 -10.4
 10/1/1999 17.83 -11.8
 10/8/1999 20.14 2.3
 11/4/1999 19.88 -5.9
 11/10/1999 22.92 0.1
 12/6/1999 19.43 -1.2
 12/16/1999 16.19 -11.5
 Average 19.45 -4.1
 Standard deviation 1.75 5.8
 Average for three days 19.87 -3.2
 Standard deviation 0.60 5.3
 for three days

80 percent
 1/6/2000 18.15 -8.7
 1/26/2000 16.20 -21.2
 11/4/1999 17.62 -16.6
 Average 17.32 -15.6
 Standard deviation 1.01 6.4

 Percentage Change
 Peak Overdraft from Real-Time
Date (Billions of Dollars) Gross Settlement

20 percent
 1/6/2000 63.55 -3.0
 1/26/2000 65.27 -7.7
 11/4/1999 64.44 -6.9
 Average 64.42 -5.9
 Standard deviation 0.86 2.5

50 percent
 1/6/2000 69.99 6.8
 1/26/2000 60.67 -14.2
 2/23/2000 65.72 -4.2
 2/24/2000 58.67 -13.2
 10/1/1999 59.59 -11.8
 10/8/1999 56.63 -5.1
 11/4/1999 56.85 -17.8
 11/10/1999 70.41 -6.9
 12/6/1999 55.01 -6.9
 12/16/1999 47.92 -19.1
 Average 60.15 -9.3
 Standard deviation 6.95 7.7
 Average for three days 62.50 -8.7
 Standard deviation 6.76 13.3
 for three days

80 percent
 1/6/2000 51.37 -21.6
 1/26/2000 50.26 -28.9
 11/4/1999 50.67 -26.8
 Average 50.77 -25.9
 Standard deviation 0.56 3.8

 Delay
 Time of Peak Average Time Statistic
Date Overdraft of Settlement (Percent)

20 percent
 1/6/2000 15:31 14:56 13.30
 1/26/2000 14:55 15:01 14.04
 11/4/1999 14:38 15:07 14.59
 Average 15:01 15:01 13.97
 Standard deviation 00:27 0:05 0.65

50 percent
 1/6/2000 15:39 15:42 34.56
 1/26/2000 14:53 15:44 34.70
 2/23/2000 15:54 15:42 33.56
 2/24/2000 16:45 15:48 33.64
 10/1/1999 14:25 15:45 32.83
 10/8/1999 16:14 15:51 35.88
 11/4/1999 16:36 15:49 35.41
 11/10/1999 16:31 15:45 34.00
 12/6/1999 16:06 15:51 34.56
 12/16/1999 15:53 15:44 34.38
 Average 15:53 15:46 34.35
 Standard deviation 0:44 0:03 0.90
 Average for three days 15:42 15:45 34.89
 Standard deviation 0:51 0:03 0.46
 for three days

80 percent
 1/6/2000 14:23 16:25 54.70
 1/26/2000 15:57 16:29 55.94
 11/4/1999 16:06 16:31 55.67
 Average 15:29 16:28 55.44
 Standard deviation 00:57 0:03 0.65

Source: Authors' calculations, based on data from Federal Reserve
Bank of New York, Fedwire Funds Service.

Note: The figures for the average for three days and the standard
deviation for three days are calculated for the days for which the
sensitivity analysis simulations were conducted.

Table B5
Receipt-Reactive Gross Settlement Simulations with Alternate Levels
of Participation

 Percentage Change
 Average Overdraft from Real-Time
Date (Billions of Dollars) Gross Settlement

20 percent
 1/6/2000 21.41 7.8
 1/26/2000 20.20 -1.8
 11/4/1999 21.04 -0.5
 Average 20.88 1.7
 Standard deviation 0.62 5.2

50 percent
 1/6/2000 19.18 -3.4
 1/26/2000 15.06 -26.8
 2/23/2000 15.90 -18.5
 2/24/2000 17.24 -18.0
 10/1/1999 14.18 -29.9
 10/8/1999 19.05 -3.2
 11/4/1999 17.89 -15.4
 11/10/1999 21.97 -4.1
 12/6/1999 20.82 5.8
 12/16/1999 13.89 -24.0
 Average 17.52 -13.6
 Standard deviation 2.77 11.9
 Average for three days 17.38 -15.3
 Standard deviation
 for three days 2.11 11.7

80 percent
 1/6/2000 12.59 -36.7
 1/26/2000 8.61 -58.1
 11/4/1999 13.28 -37.2
 Average 11.49 -44.0
 Standard deviation 2.52 12.3

 Percentage Change
 Peak Overdraft from Real-Time
Date (Billions of Dollars) Gross Settlement

20 percent
 1/6/2000 76.52 16.8
 1/26/2000 67.91 -4.0
 11/4/1999 69.98 1.1
 Average 71.47 4.4
 Standard deviation 4.49 10.8

50 percent
 1/6/2000 78.12 19.2
 1/26/2000 60.52 -14.2
 2/23/2000 68.51 -0.1
 2/24/2000 70.92 4.9
 10/1/1999 64.44 4.6
 10/8/1999 76.50 28.2
 11/4/1999 72.58 4.9
 11/10/1999 89.96 19.0
 12/6/1999 78.78 33.3
 12/16/1999 66.23 11.9
 Average 72.66 9.6
 Standard deviation 8.55 14.9
 Average for three days 70.40 2.8
 Standard deviation 9.00 16.9
 for three days

80 percent
 1/6/2000 67.76 3.4
 1/26/2000 45.93 -35.1
 11/4/1999 66.07 -4.5
 Average 59.92 -12.5
 Standard deviation 12.15 20.3

 Delay
 Time of Peak Average Time Statistic
Date Overdraft of Settlement (Percent)

20 percent
 1/6/2000 15:45 14:44 3.51
 1/26/2000 14:55 14:46 3.01
 11/4/1999 15:24 14:55 3.53
 Average 15:21 14:48 3.35
 Standard deviation 00:25 0:05 0.30

50 percent
 1/6/2000 16:52 15:19 15.61
 1/26/2000 16:48 15:13 12.32
 2/23/2000 16:38 15:15 13.38
 2/24/2000 16:53 15:18 12.81
 10/1/1999 16:48 15:22 14.06
 10/8/1999 16:46 15:22 14.78
 11/4/1999 16:51 15:24 16.42
 11/10/1999 16:23 15:17 13.56
 12/6/1999 16:50 15:18 11.03
 12/16/1999 16:55 15:14 13.42
 Average 16:46 15:18 13.74
 Standard deviation 0:09 0:03 1.58
 Average for three days 16:50 15:18 14.78
 Standard deviation 0:02 0:05 2.17
 for three days

80 percent
 1/6/2000 17:12 16:29 19.02
 1/26/2000 17:05 16:29 23.11
 11/4/1999 17:02 16:29 25.35
 Average 17:06 16:29 22.50
 Standard deviation 00:05 0:00 3.21

Source: Authors' calculations, based on data from Federal Reserve
Bank of New York, Fedwire Funds Service.

Note: The figures for the average for three days and the standard
deviation for three days are calculated for the days for which the
sensitivity analysis simulations were conducted.


APPENDIX C: FUNDS OVERDRAFT ACCOUNTING PROCEDURE

An explanation of daylight overdrafts can be found in Coleman (2002). When determining a bank's balance, the Federal Reserve's Daylight Overdraft Reporting and Pricing System (DORPS) accounts for several funds credits and debits that we could not observe. These funds are not processed on the Fedwire Funds Service and are posted to the DORPS system through other means. We call these postings "extraneous funds" and include such funds primarily from checks, the Automated Clearing House network, return checks, currency and coins, savings bonds, and account deficiency credits and debits. Extraneous funds play a major role in a bank's balance management. To circumvent this problem, we had to employ the following method:

We had access to the following information: the DORPS total end-of-minute balances, National Book-Entry System (NBES) transaction data, and Fedwire funds data. Since the DORPS balance data contain the opening balance for Fedwire funds and the NBES has an opening balance of zero, end-of-minute balances were constructed from the transaction data. The following formulas describe the end-of-minute balance situation for each bank at a particular minute m:

(C1) [Totalbal.sub.m] = [NBESbal.sub.m] + [FedwireFundsbal.sub.m] + [XFundsbal.sub.m].

The extraneous funds balance was extracted according to the following formula:

(C2) [XFundsbal.sub.m] = [Totalbal.sub.m] -[NBESbal.sub.m]-[FedwireFundsbal.sub.m].

The RTGS extraneous funds and NBES balances were then held constant. The Bank of Finland simulator used the opening balance to create new Fedwire funds balances, [FedwireFundsbal.sup.*.sub.m]. The Fedwire funds balance was then constructed using the RTGS extraneous funds balance:

(C3) [Fundsbal.sub.m] = [NBESbal.sub.m] + [Fundsbal.sup.*.sub.m].

The new funds balance, in conjunction with the RTGS book-entry securities balance, resulted in a new total balance:

(C4) [Totalbal.sup.*.sub.m] = [NBESbal.sub.m] + [Fundsbal.sub.m].

We then compared the three components in equation C4 to determine each bank's applicable funds overdraft, [FundsOD.sub.m], according to the following DORPS accounting principles:

If [Fundsbal.sub.m] [greater than or equal] to 0, then [FundsOD.sub.m] = 0.

If [FundsOD.sub.m]<0 and [NBESbal.sub.m]<0, then [FundsOD.sub.m] = [Fundsbal.sub.m].

If [Fundsbal.sub.m]<0 and [NBESbal.sub.m] [greater than or equal to] 0:

If [Totalbal.sup.*.sub.m] [less than or equal to] 0, then [FundsOD.sub.m] = [FundsOD.sub.m].

Otherwise, [FundsOD.sub.m] = 0.

[FundsOD.sub.m] = O[D.sup.m.sub.i] in Appendix B for each bank i.
Table 1
Summary of Simulated Systems

 End-of-Day
 Entry Order Release Close of
System Criterion Criterion Criterion Queue

One-hour All payment
netting orders for
 all banks
 in queues
 are netted
 and released All payment
 at one-hour orders in queue
 intervals. Are netted at
 Not 6:30 p.m., the
Six-hour Randomly applicable All payment end of the
netting selected orders for Fedwire day.
 50 percent all banks in
 of payment queues are
 orders. In netted and
 conducting released at
 our six-hour
 sensitivity intervals.
 analysis,
Receipt- we randomly First-in, A payment Any payment
reactive selected first-out order at the orders
gross either 20 front of a remaining in
settlement percent or bank's queue queues at
 50 percent is released 5:30 p.m.
 of payments. from queue are randomly
 as receipts and uniformly
 for the assigned and
 bank, within settled by
 a calendar real-time gross
 minute, settlement over
 exceed the the next thirty
 value of the minutes.
 payment
 order to be
 released.

Table 2
Averages from Simulations with 50 Percent Participation

 Average Overdraft Percentage Change
Treatment (Billions of Dollars) from RTGS

Real-time gross 20.29 --
 settlement (RTGS)
One-hour netting 20.41 0.58
Six-hour netting 19.45 -4.10
Receipt-reactive 17.52 -13.64
 gross settlement

 Peak Overdraft Percentage Change
Treatment (Billions of Dollars) from RTGS

Real-time gross 66.28 --
 settlement (RTGS)
One-hour netting 64.69 -2.40
Six-hour netting 60.15 -9.25
Receipt-reactive 72.66 9.62
 gross settlement

 Average Time Delay Statistic
Treatment of Settlement (Percent)

Real-time gross 14:35 0
 settlement (RTGS)
One-hour netting 14:51 7.53
Six-hour netting 15:46 34.35
Receipt-reactive 15:18 13.74
 gross settlement

Source: Authors' calculations, based on data from Federal Reserve
Bank of New York, Fedwire Funds Service.

Table 3
System Averages Comparing Alternate Levels of Participation

 Average Overdraft Percentage Change
Treatment (Billions of Dollars) from RTGS

Real-time gross 20.52 --
settlement (RTGS)

One-hour netting
 20 percent 20.37 -0.74
 50 percent 20.55 0.12
 80 percent 19.83 -3.38

Six-hour netting
 20 percent 20.53 0.04
 50 percent 19.87 -3.16
 80 percent 17.32 -15.59

Receipt-reactive
 gross settlement
 20 percent 20.88 1.75
 50 percent 17.38 -15.33
 80 percent 11.49 -44.05

 Peak Overdraft Percentage Change
Treatment (Billions of Dollars) from RTGS

Real-time gross 68.49 --
settlement (RTGS)

One-hour netting
 20 percent 67.16 -1.93
 50 percent 65.27 -4.69
 80 percent 64.66 -5.59

Six-hour netting
 20 percent 64.42 -5.94
 50 percent 62.50 -8.74
 80 percent 50.77 -25.87

Receipt-reactive
 gross settlement
 20 percent 71.47 4.36
 50 percent 70.40 2.80
 80 percent 55.92 -12.52

 Average Time Delay Statistic
Treatment of Settlement (Percent)

Real-time gross 14:32 0
settlement (RTGS)

One-hour netting
 20 percent 14:37 2.52
 50 percent 14:47 7.31
 80 percent 14:53 9.93

Six-hour netting
 20 percent 15:01 13.97
 50 percent 15:45 34.89
 80 percent 16:28 55.44

Receipt-reactive
 gross settlement
 20 percent 14:48 3.35
 50 percent 15:18 14.78
 80 percent 16:29 22.50

Source: Authors' calculations, based on data from Federal Reserve
Bank of New York, Fedwire Funds Service.

Table 4
Liquidity, Correlation, and Skewness Results

 Average Funds Transfer Maximum Funds Transfer
Treatment (Thousands of Dollars) (Thousands of Dollars)

Real-time gross 226 2,206
settlement (RTGS)

One-hour netting
 20 percent 209 5,521
 50 percent 170 10,808
 80 percent 130 13,901

Six-hour netting
 20 percent 201 10,944
 50 percent 145 12,122
 80 percent 86 17,356

Receipt-reactive
 gross settlement
 20 percent 209 1,827
 50 percent 165 1,975
 80 percent 140 3,315

 Correlation with RTGS Balances
Treatment (Percent) Skewness

Real-time gross 100.0 --
settlement (RTGS)

One-hour netting
 20 percent 99.5 13.9
 50 percent 98.0 18.8
 80 percent 97.2 23.4

Six-hour netting
 20 percent 96.2 20.3
 50 percent 90.5 23.2
 80 percent 84.7 19.0

Receipt-reactive
 gross settlement
 20 percent 94.8 13.0
 50 percent 86.6 26.2
 80 percent 76.0 24.2

Source: Authors' calculations, based on data from Federal Reserve
Bank of New York, Fedwire Funds Service.

Table 5
Queue Characteristics at 5:30 p.m.

 Queued Payments
 Settled
 (Percent) Average Payment
 Value in Queue
Treatment Value Volume (Thousands of Dollars)

One-hour netting
 20 percent 73 91 10,234
 50 percent 69 90 10,653
 80 percent 73 91 10,063

Six-hour netting
 20 percent 25 41 4,338
 50 percent 26 40 4,291
 80 percent 25 41 4,310

Receipt-reactive
 gross settlement
 20 percent 64 73 4,533
 50 percent 72 80 4,890
 80 percent 28 48 5,184

Source: Authors' calculations, based on data from Federal Reserve
Bank of New York, Fedwire Funds Service.


Endnotes

(1.) On average, overnight deposits made by commercial banks are worth about $15 billion.

(2.) See McAndrews and Trundle (2001) for a description of several new designs that have been put into use in various large payment systems and for a discussion of some specific policy issues that are associated with the novel designs.

(3.) We choose one calendar minute as our time period because banks' daylight overdrafts are calculated as of the end of each calendar minute. By choosing a one-minute period within which receipts can be set against the release of payments from the queue, we prevent the release of those payments from causing an overdraft at the end of the minute.

(4.) A single day's simulation for the receipt-reactive system with 80 percent of payments placed in the queue required more than two months to complete, using the single computer we employed for the simulations.

(5.) In such a case, a gridlock-resolution method of settling payments from queues might be useful. See Bech and Soramaki (2001) for a discussion.

(6.) These and other behavioral responses of queuing systems are discussed in McAndrews and Trundle (2001) and Roberds (1999).

(7.) These are activities unrelated to the daily Fedwire Funds Service and they are posted to the Daylight Overdraft Reporting and Pricing System at particular times. These include the Automated Clearing House network, checks, currency and coins, and savings bonds.

(8.) Effective May 16, 2004, the Federal Reserve Banks expanded the operating hours of the Fedwire Funds Service from eighteen hours to twenty-one-and-a-half hours. The new hours begin at 9:00 p.m. Eastern Time (ET) on the preceding calendar day (with a cycle date of the following calendar day) and end at 6:30 p.m. ET, regardless of the Bank's location or time zone.

References

Angelini, P. 1998. "An Analysis of Competitive Externalities in Gross Settlement Systems." Journal of Banking and Finance 22, no. 1 (January): 1-18.

--. 2000. "Are Banks Risk Averse? Intraday Timing of Operations in the Interbank Market." Journal of Money, Credit, and Banking 32, no. 1 (February): 54-73.

Bank for International Settlements. 1997. "Real-Time Gross Settlement Systems." Committee on Payment and Settlement Systems Publications, no. 22, March.

Bech, M., and R. Garratt. 2003. "The Intraday Liquidity Management Game." Journal of Economic Theory 109, no. 2 (April): 198-219.

Bech, M., and K. Soramaki. 2001. "Gridlock Resolution in Interbank Payment Systems." Bank of Finland Discussion Papers, no. 9.

--. 2002. "Liquidity, Gridlocks, and Bank Failures in Large Value Payment Systems." E-money and Payment Systems Review. London: Central Banking Publications.

Board of Governors of the Federal Reserve System. 2002. Guide to the Federal Reserve's Payment System Risk Policy. May. Washington, D.C.

Buckle, S., and E. Campbell. 2002. "Settlement Bank Behaviour in a Real-Time Gross Settlement Payment System with Collateralised Intraday Credit." Bank of England Working Papers, no. 209, December.

Coleman, S. P. 2002. "The Evolution of the Federal Reserve's Intraday Credit Policies." Federal Reserve Bulletin, February.

Kahn, C., J. J. McAndrews, and W. Roberds. 2003. "Settlement Risk under Gross and Net Settlement," JOURNAL OF MONEY, CREDIT, and Banking 35, no. 4 (August): 591-608.

Kobayakawa, S. 1997. "The Comparative Analysis of Settlement Systems." Centre for Economic Policy Research Discussion Papers, no. 1667, July.

Koponen, R., and K. Soramaki. 1998. "Intraday Liquidity Needs in a Modern Interbank Payment System--A Simulation Approach." Bank of Finland Studies in Economics and Finance, series E, no. 14.

Leinonen, H., and K. Soramaki. 1999. "Optimizing Liquidity Usage and Settlement Speed in Payment Systems." Bank of Finland Discussion Papers, no. 16.

--. 2003. "Simulating Interbank Payment and Securities Settlement Mechanisms with the BoF-PSS2 Simulator." Bank of Finland Discussion Papers, no. 23.

McAndrews, J. J., and S. Rajan. 2000. "The Timing and Funding of Fedwire Funds Transfers." Federal Reserve Bank of New York Economic Policy Review 6, no. 2 (July): 17-32.

McAndrews, J. J., and J. Trundle. 2001. "New Payment System Design: Causes and Consequences." Bank of England Financial Stability Review, no. 11, December: 127-36.

Roberds, W. 1993. "The Rise of Electronic Payments Networks and the Future Role of the Fed with Regard to Payment Finality." Federal Reserve Bank of Atlanta Economic Review 78, no. 2 (March/ April): 1-22.

--. 1999. "The Incentive Effects of Settlement Systems: A Comparison of Gross Settlement, Net Settlement, and Gross Settlement with Queueing." Unpublished paper, Federal Reserve Bank of Atlanta, August.

Kurt Johnson is an economist and James J. McAndrews a vice president at the Federal Reserve Bank of New York; Kimmo Soramaki is a payment systems policy expert at the European Central Bank and a research visitor at the Federal Reserve Bank of New York. <kurt.johnson@ny.frb.org> <jamie.mcandrews@ny.frb.org> <kimmo.soramaki@ecb.int>

The authors thank Robert Ashman, Lucinda Brickler, Dara Hunt, Travis Nesmith, two anonymous referees, and seminar participants at the Bank of England, the Federal Reserve Bank of New York, the 2001 Money Transfer Conference, the First Simulator Conference at the Bank of Finland, and the European Central Bank for helpful comments. They also thank Harry Leinonen and the Bank of Finland for the use of the Bank of Finland's Payment System Simulator, and the Wholesale Product Office and Credit Risk Management Function of the Federal Reserve Bank of New York for providing the data. The views expressed are those of the authors and do not necessarily reflect the position of the Federal Reserve Bank of New York, the Federal Reserve System, or the European Central Bank.
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