# Central Bank Policy Making in Competing Payment Systems.

DAVID D. VANHOOSE [*]This paper analyzes the interaction between two payment systems. Administrators of both systems establish intraday credit interest fees, caps, and collateral requirements. Analysis of the model indicates that if a central bank does not take into account the effects that its policies have on its share of payment system transactions, then its efforts to contain risks associated with daylight overdrafts on its wire system will require a loss in its share of total transactions volume. If it does recognize the potential loss in its share of payments, then socially optimal policy instrument settings are unlikely to emerge. (JEL E5)

Introduction

During the 1980s, officials at the Federal Reserve System became increasingly concerned about the growth in banks' daylight overdrafts on large-dollar wire transfer systems. In 1988, staff economists at the Federal Reserve System widely agreed that significantly reducing daylight overdrafts of Fedwire accounts would require an interest fee of about 25 basis points. Nevertheless, in April 1994, the Federal Reserve initially set its administered price for intraday credit on Fedwire at only 10 basis points. The following year, the Federal Reserve raised the fee to 15 basis points instead of the 25 basis points that it originally had announced publicly. [1]

Why did the Federal Reserve backtrack from its original pricing policy? One answer might be that it has determined that 15 basis points is the socially optimal interest fee, given a multipart objective involving trade-offs among competing policy goals of maximizing bank profitability while simultaneously minimizing payment system gridlock, systemic risk, and the Federal Reserve's own risk exposure. Nevertheless, as Hancock and Wilcox [1996] have documented, the real average and peak daily volumes of Fedwire overdrafts have fallen only to the levels that existed in the mid-1980s when the Federal Reserve first determined that the overdraft problem was serious enough to warrant close scrutiny.

One purpose of this paper is to offer a possible explanation for the Federal Reserve's pricing of daylight overdrafts on Fedwire. This proposed explanation is that noncooperative rivalry with the Clearing House Interbank Payment System (CHIPS) can induce the Federal Reserve to price its intraday credit at a level that is inefficiently low. Competition with CHIPS for sufficient payments volume to cover the costs of providing Fedwire services can, in principle, lead to suboptimal fees on intraday credit extensions by the Federal Reserve. At the same time, CHIPS's interest in maximizing members' profits while maintaining sufficient payment volumes to cover system costs can induce administrators of this private system to enact socially inefficient policies regarding pricing and collateral, particularly in a noncooperative equilibrium with the Federal Reserve. This argument is not based on any presumption that either Federal Reserve or CHIPS officials intentionally seek to enact socially suboptimal policies. The fundamental point stems from the standard game-theoretic result. That is, in the absence of other complicating factors such as time inconsistency problems (which add further layers of complexity in policy games), noncooperative policy interactions in settings characterized by policy interdependence typically produce Pareto-inefficient outcomes. [2]

A broader objective of the paper is to provide a starting point for consideration of the interaction of payment systems in the U.S. and elsewhere. There has, of course, been considerable work recently on central bank policy making in payment systems. Federal Reserve studies on likely market responses to pricing, collateral requirements, and caps include Lindsey et al. [1988], Meulendyke et al. [1988], Belton et al. [1987], Humphrey [1989], Evanoff [1988], Gilbert [1989], and Stevens [1989]. More recent work on payment and clearing system risks and policies by other central bank economists and academics includes Angelini [1996, 1998], Angelini et al. [1996], Dale and Rossi [1995], Rossi [1995], Schoenmaker [1995], Chakravorti [1996], Kahn and Roberds [1997, 1998], and Lacker [1997]. While many authors touch on the relationship between Fedwire and CHIPS or among alternative European wire systems, only a few provide analytical models of payment systems and the effects of alternative policies. With very few exce ptions (notably, Chakravorti [1997]), however, all existing work presumes the existence of only one payment system. This paper, therefore, aims toward opening new ground by modeling the interactions between potentially competing payment systems and the administrators of those systems.

The second section develops the basic framework, which builds on Furfine and Stehm's [1996, 1998] model of the trade-offs faced by a central bank that supervises a single payment system. The innovation of this paper is to extend their framework to a setting with two systems that provide payment services to bank customers and with separate policy makers--envisioned to be a central bank and a private-wire administrator--which can, in principle, set prices, collateral, and caps for intraday credit extensions that they make to banks. The third section examines the determination of optimal bank choices of trading volumes and intraday credit utilization on the two systems. The fourth section discusses the objectives of payment system administrators, which can be very cumbersome to analyze in full. For this reason, attention is focused in this section on two special cases of the model that, despite their simplicity relative to the general formulation, can provide considerable insight into the interplay between paym ent system policies in interrelated payment systems. The fifth section discusses key policy implications and potential extensions.

The Model

The theoretical framework builds directly upon Furfine and Stehm's [1996] model (FS). Here, however, there are two potentially competing payment systems. One, called "CB wire," is operated by the central bank. The real-world example in the U.S. is the Federal Reserve's Fedwire system. The other payment system, called "private wire," is operated by a private firm. CHIPS is a real-world analogue for the U.S. Another is the Government Securities Clearing Corporation (GSCC), a netting system that banks use to clear transactions in government securities.

In the model, both CB wire and private wire offer wire transfer services to banks. Banks wish to make two types of transfers. Although banks could, in principle, use either CB wire or private wire for both kinds of transfers, the model includes transaction-cost differences in using the two payment systems. Ceteris paribus, this gives banks an incentive to use both systems for their electronic payment needs. This currently is the situation in the U.S. where banks typically use Fedwire for federal funds and book entry security transfers (though the GSCC is now a major private alternative for securities clearings) while directing the bulk of their foreign exchange and Eurodollar transactions to CHIPS.

The administrators of both systems have mixed objectives. As in FS, they seek to maximize objectives that include bank profits but that also account for the central bank's broader, socially benevolent concerns with the social costs stemming from any payment system gridlock, collateralized credit extension, and uncollateralized credit extension. In addition, the administrators must cover the costs of operating the systems.

The Banking Environment

As noted above, banks may use either payment system. As in FS, the customer demand for payment services faced by banks is assumed to be perfectly inelastic. On a given day, each bank transmits and receives an exogenous dollar payment volume, which, for the sake of expositional simplicity, is assumed to equal a normalized value of unity. It directs a fraction of this normalized payment volume, [tau] to clearing on CB wire and the remaining fraction, 1 - [tau], to transmission via the private wire system.

A bank also has an initial reserve account balance with each payment system. Its reserve balance at the beginning of the day is denoted as R. As in FS, a key assumption that may simplify the exposition is that this also is the desired end-of-day reserve balances. If both systems use required real-time gross settlement, then as the bank transmits payments during the day, it will have to:

1) increase its reserves in advance of payments;

2) obtain intraday credit from the central bank or the administrator of the private wire system;

3) employ cash management techniques to reduce its liquidity needs; or

4) apply some combination of 1) through 3).

Traditionally, CHIPS has been a netting system, but recently it has adopted procedures that make it function more like a gross settlement system.

Let [tau][Z.sup.CB] be the total quantity of intraday credit borrowed by the bank from the central bank in the CB wire system, under terms established by the central bank's policies regarding the provision of such credit. For [tau] = 0, the bank makes no use of the central bank's system and thereby requires no credit to cover overdrafts on that system. For [tau] [greater than] 0, [Z.sup.CB] denotes the portion of CB wire dollar payments financed by bank borrowings from the central bank. In addition, let (1 - [tau])[Z.sup.PW] be total intraday credit borrowed through credit facilities offered by the private wire administrator (more on this entity later), with [Z.sup.PW] denoting the portion of private wire payments financed by such borrowings.

At present in the U.S., the Federal Reserve provides intraday credit (which might also be called "intraday outside credit," made available by the central bank) explicitly only by permitting daylight overdrafts on the Fedwire system, according to policies it has established for such overdrafts. The CHIPS system also permits overdrafts (a form of "intraday inside credit") under its separate policies. In addition, in the current regime, interbank intraday credit extensions are nearly nonexistent. Consequently, in the present real-world environment, [Z.sup.CB] and [Z.sup.PW] typically are positive for a number of banks.

Consider first the problem faced by a bank that seeks to maximize its profit:

[pi] = [r.sup.L] L + [r.sup.S] S - [r.sup.D] D - [r.sup.CB][tau][Z.sup.CB] - [r.sup.PW] (1 - [tau])[Z.sup.PW] - [w([Z.sup.CB]) + s([Z.sup.PW])] - [tau][[rho].sup.CB] - (1 - [tau])[[rho].sup.PW] - v([tau]) - [kappa](1 - [tau]), (1)

where L [equiv] loans that earn the rate [r.sup.L], S [equiv] securities that earn the rate [r.sup.S], D [equiv] deposits that entail the interest expense [r.sup.D], [r.sup.CB] [equiv] central bank rate on intraday credit that it extends, and [r.sup.PW] [equiv] rate charged by the private wire administrator on its extension of intraday credit. As in FS, w([Z.sup.CB]) + s([Z.sup.PW]) is a separable cash management cost function, with w'([Z.sup.CB]) [less than] 0 and s'([Z.sup.PW]) [less than] 0, and with w'([Z.sup.CB]) and s'([Z.sup.PW]) assumed to be convex. Hence, funding larger portions of given volumes of wire transfers with intraday credit reduces cash management costs. Specific functional forms for w([Z.sup.CB]) and s([Z.sup.PW]) are considered below.

Furthermore, [[rho].sup.CB] is the per-unit payment processing fee charged by the central bank for use of the CB wire system, while [[rho].sup.PW] is the per-unit fee charged by the administrator of the private wire system. Banks must also devote real resources to processing wire transfers, and V([tau]) and [kappa](l - [tau]) denote real-resource cost functions, where v'([tau]) [greater than] 0, v"([tau]) [greater than] 0, [kappa]'(l - [tau]) [greater than] 0, and [kappa]"(1 - [tau]) [greater than] 0.

A bank chooses its loans (L), securities (S), reserves (R), deposits (D), intraday credit borrowings from the central bank ([Z.sup.CB]), intraday credit borrowings from the private wire administrator ([Z.sup.PW]), and the portion of payments that the bank processes on the CB wire system ([tau]). These choices are conditioned on parameters and constraints established by the central bank and the private wire administrator.

Central Bank Wire and Private Wire System Credit Policy Instruments

Both the central bank and the administrator of the private wire system have four policy instruments to influence bank choices. The central bank sets its CB wire transfer fee, [[rho].sup.CB], and its borrowing rate on extensions of intraday credit, [r.sup.CB]. It also can set a quantity limit, or cap, on the intraday credit that it is willing to extend, [[bar{Z}].sup.CB]. A fourth payment system policy instrument available to the central bank is a proportion, [[eta].sup.CB], of its intraday credit extensions that banks must back by pledging collateral to the central bank.

Previous payment system studies (for instance, Lindsey et al. [1988]) have acknowledged the possibility and importance of spillover effects that central bank policies, which are on its own payment system, may have on other systems. To date, however, authors in the literature analyzing the effects of alternative payment system policies have focused nearly undivided attention on central bank policy making in a single payment system.

In this model, there are two ways in which the CB wire and private wire systems are linked. The most important is that banks can choose the fraction, [tau], of payments that they process on the CB wire system. Central bank policies intended to achieve broad social goals or else narrower central bank objectives can influence this choice. Indirect effects also follow from the banks' choice between payment systems, because how they allocate payments between the two systems influences their decisions concerning from whom they will borrow intraday credit and what quantities of credit they will borrow.

A second linkage arises because the administrator of the private wire system also has its own payment system policy instruments, which the administrator can adjust in response to changes in the settings of policy instruments by the central bank on its CB wire system. The private wire administrator also has four instruments whose values it can determine: the private wire transfer fee, [[rho].sup.PW]; the rate on intraday credit from the private wire administrator, [r.sup.PW]; a quantity cap on such credit, [[bar{Z}].sup.PW]; and a proportional collateral requirement on such credit extensions, [[eta].sup.PW].

Banks take the settings of the central banks' and private wire administrators as given when determining their own profit-maximizing portfolio and payment system choices. The central bank determines values for these instruments with a recognition of the effects of its decisions on bank behavior.

Actual policy outcomes also depend on the interactions between the central bank and the private wire administrator. One possibility would be for the two policy makers to coordinate their policy choices with a joint aim to achieve their goals. Another would be for the two policy makers to behave noncooperatively. In such an environment, the central bank would set its instrument settings with an aim to attain its policy objectives while taking the instrument settings of the private wire administrator as given. At the same time, the private wire administrator sets its instrument values to pursue its own objectives, taking the central banks' choices as given (yet a third possibility would be the Stackelberg leader-follower behavior, which is not considered here). Next, this paper will address the objectives and possible interactions of the two payment system policy makers after determining how banks respond to their policy choices.

Bank Behavior and the Effects of Payment System Policies

The end-of-day balance sheet constraint faced by a bank is shown as:

L + S + R = D+K, (2)

where K is the bank's equity capital. The bank faces two other nonpayment system-related regulatory constraints: a reserve requirement constraint, R [geq] [delta]D, with 0 [less than] [delta] [less than]1, and a capital adequacy constraint, K [geq] [delta](L + S + R), with 0 [less than] [delta] [less than] 1. [3] If both of these constraints are binding, then D = ([[sigma].sup.-1] - 1)K and R = [delta]([[sigma].sup.-1] - 1) K follow directly. Also, following FS, let A [equiv] L + S denote earning assets and let [mu] be the portion of earning assets held as securities. Then the objective relevant to the bank for its payment system problem is to maximize:

[pi] = [[r.sup.L](1 - [mu]) + [r.sup.S][mu]]A - [r.sup.CB][tau][Z.sup.CB] - [r.sup.PW](1 - [tau])[Z.sup.PW] - w([Z.sup.CB]) - s([Z.sup.PW]) - [tau][[rho].sup.CB] - (1 - [tau])[[rho].sup.PW] - v([tau]) - k(1 - [tau]), (1)

subject to the intraday credit cap constraints [Z.sup.CB] [leq] [[bar{Z}].sup.CB]and [Z.sup.PW] [leq] [[bar{Z}].sup.PW], and to the collateral constraint, S [geq][[eta].sup.CB][Z.sup.CB] + [[eta].sup.PW] [Z.sup.PW]. As in FS, to implement a simple and tractable reason for a bank to hold securities even in the absence of the collateral constraint, it is assumed that other factors, such as risk-based capital requirements or regulatory liquidity requirements, force the bank to satisfy an additional security holdings constraint, S [geq] [mu]/A.

Optimal Bank Choices Within the Full Model

The Kuhn-Tucker conditions for this problem imply the following:

[r.sup.L] - [r.sup.S] = [[lambda].sup.C] + [[lambda].sup.S], (3)

[[rho].sup.PW] + [[r.sup.PW] + [[lambda].sup.C][[eta].sup.PW] + s'([Z.sup.PW])][Z.sup.PW]- v'(1 - [tau])

= [[rho].sup.CB] + [[r.sup.CB] + [[lambda].sup.C][[eta].sup.CB] + w'([Z.sup.CB])] [Z.sup.CB]+ [kappa]'([tau]), for [tau] [greater than] 0,

and [[rho].sup.PW] + [[r.sup.PW] + [[lambda].sup.C][[eta].sup.PW] + s'([Z.sup.PW])][Z.sup.PW]- v'(1 - [tau])

[less than] [[rho].sup.CB] + [[r.sup.CB] + [[lambda].sup.C][[eta].sup.CB] + w'([Z.sup.CB])] [Z.sup.CB]+ [kappa]'([tau]), for [tau] = 0, (4)

-w'([Z.sup.CB]) = [tau]([r.sup.CB] + [[lambda].sup.C][[eta].sup.CB]) + [[lambda].sup.CB], for [Z.sup.CB] [greater than] 0,

and -w'([Z.sup.CB]) [less than] [tau]([r.sup.CB] + [[lambda].sup.C][[eta].sup.CB]) + [[lambda].sup.CB], for [Z.sup.CB] = 0, (5)

-s'([Z.sup.PW]) = (1 - [tau])([r.sup.PW] + [[lambda].sup.C][[eta].sup.PW]) + [[lambda].sup.PW], for [Z.sup.PW] [greater than] 0 ,

and -s'([Z.sup.PW]) [less than] (1 - [tau])([r.sup.PW] + [[lambda].sup.C][[eta].sup.PW]) + [[lambda].sup.PW], for [Z.sup.PW] = 0 , (6)

[[lambda].sup.C]([mu]A - [[eta].sup.CB][Z.sup.CB] - [[eta].sup.PW][Z.sup.PW]) = 0 , (7)

[[lambda].sup.CB]([Z.sup.CB] - [[bar{Z}].sup.CB]) = 0, (8)

[[lambda].sup.PW]([Z.sup.PW] - [[bar{Z}].sup.PW]) = 0 , (9)

[[lambda].sup.S]([mu] - [mu]/) = 0 , (10)

where [[lambda].sup.C], [[lambda].sup.CB], [[lambda].sup.PW], and [[lambda].sup.S] are the shadow prices associated with the collateral requirement, central bank intraday credit cap, private wire intraday credit cap, and security portfolio allocation constraints, respectively. Both the collateral and securities portfolio allocation constraints cannot simultaneously be binding. Consequently, (3) indicates that either [[lambda].sup.C] or [[lambda].sup.S] is equal to the spread between the loan and security rates.

Equation (4) implies that the bank will make transfers on the CB wire system provided that the net unit cost of such transfers, [[rho].sup.CB] + [[r.sup.CB] + [[lambda].sup.C][[eta].sup.CB] + w'([Z.sup.CB])][Z.sup.CB] + [kappa]'([tau]), are equalized with the net unit cost of transfers on the private wire system, [[rho].sup.PW] + [[r.sup.PW] + [[lambda].sup.C][[eta].sup.PW] + s'([Z.sup.PW])][Z.sup.PW] - v'(1 - [tau]). The unit cost for each system is the sum of the transfer fee ([[rho].sup.CB] or [[rho].sup.PW]), the net marginal cost of the portion of transfers financed by borrowings from the managing system authority, and the marginal real-resource cost of transfers. The net marginal borrowing cost for each system is the sum of the intraday credit rate ([r.sup.CB] or [r.sup.PW]) and the opportunity cost of meeting a collateral constraint (if it is binding so that [[lambda].sup.C] [greater than] 0), less the marginal benefit derived from borrowing funds rather than engaging in cash-management strategies to reduce the need to better match receipts and outflows of payment transfers. As (4) indicates, if the unit cost of sending payments on the CB wire system becomes too high, the bank could decide to make sole use of the private wire system so that [tau] = 0.

Equation (5) says that the bank will borrow positive amounts of intraday credit from the central bank, provided that [tau] [greater than] 0, so that it uses the central bank-administered system, and that it can equate -w'([Z.sup.CB]), the marginal benefit (the marginal reduction in cash management cost) otherwise entailed in reducing its need for daylight credit, with the total marginal cost of such credit, [tau]([r.sup.CB] + [[lambda].sup.C][[eta].sup.CB]) + [[lambda].sup.CB]. This marginal cost of central bank credit depends on the interest charged by the central bank, the opportunity cost of the central bank's collateral constraint (again, if it is binding), and the shadow price relating to the central bank's credit cap. If the marginal cost always were to exceed the marginal benefit, then the bank would not run daylight overdrafts on the CB wire system ([Z.sup.CB] would equal 0). Equation (6) is an analogous condition for the bank's use of intraday credit granted by the private wire administrator. Finall y, (7) through (10) are the standard Kuhn-Tucker conditions associated with the payment system policy constraints that the bank faces.

There are several possible cases that could emerge. For instance, it might be that the collateral constraint binds but that only one, or both, of the cap constraints do not. Alternatively, one, or both, of the cap constraints may bind, but the collateral constraints bind. Finally, one, or both, of the cap constraints may bind while the collateral constraint simultaneously is binding.

Although caps were a central component of the Federal Reserve's stated effort to control the growth of daylight overdrafts during the 1980s, the Federal Reserve had generally recognized by 1989 that its cap-based policy was not effective (see, for instance, VanHoose and Sellon [1989]). Recent work by Hancock and Wilcox [1996] indicates that the Federal Reserve's caps apparently were not binding as they did little to constrain overdrafts. Consequently, the following analysis focuses attention on the case in which collateral constraints are binding but cap constraints are not.

Bank Behavior with Overdraft Rates and Collateral Requirements

The general framework outlined above is not readily amenable to policy analysis. To obtain more concrete solutions for optimal bank decision rules, it is useful to consider the following functional forms:

w([Z.sup.CB]) = [[omega].sub.0][Z.sup.CB] + ([[omega].sub.1]/2)[([Z.sup.CB]).sup.2], with [[omega].sub.0]/[[omega].sub.1] [greater than] [Z.sup.CB], [forall] [Z.sup.CB],

s([Z.sup.PW]) = - [[sigma].sub.0][Z.sup.PW] + ([[sigma].sub.1]/2)[([Z.sup.PW]).sup.2], with [[sigma].sub.0]/[[sigma].sub.1] [greater than] [Z.sup.PW], [forall] [Z.sup.PW],

[kappa]([tau]) = [[kappa].sub.0] [tau] + ([[kappa].sub.1]/2) [[tau].sup.2],

and v(1 - [tau]) = [v.sub.0](1 - [tau]) + ([v.sub.1]/ 2)[(1 - [tau]).sup.2], (11)

where all parameters are nonnegative constants. As noted, it is assumed that intraday credit cap constraints are not binding so that [[lambda].sup.CB] = [[lambda].sup.PW] = 0. Imposing this assumption and substituting the quadratic cash-management and real-resource cost functions in (11) into (3) through (10) can ultimately yield reduced-form solutions for [tau], [Z.sup.CB], [Z.sup.PW], and [mu].

Discussion of payment system policies typically assume that the Federal Reserve and CHIPS do not take into account the possibility that relative payment volumes on Fedwire and CHIPS are affected by policy settings. In the context of the model, this amounts to an assumption that [tau] is exogenous.

Under this assumption, and provided that intraday credit collateral constraints are binding, the solutions for the portions of transfers financed via intraday credit are given by:

[Z.sup.CB] = [[[omega].sup.-1].sub.1]{[[omega].sub.0] - [[r.sup.CB] + [[eta].sup.CB] ([r.sup.L] - [r.sup.S])][tau]}, (12a)

and

[Z.sup.PW] = [[[sigma].sup.-1].sub.1]{[[sigma].sub.0] - [[r.sup.PW] + [[eta].sup.PW]([r.sup.L] - [r.sup.S])](1 - [tau])}. (12b)

Hence, for a given allocation of wire transfers between the GB and private wire systems, the extent to which banks desire to fund wire transfers via intraday credit depends negatively on four variables:

1) the wire administrators' interest charges on intraday credit;

2) collateral requirement ratios;

3) the loan-security rate spread, which determines the marginal opportunity cost of collateral requirements; and

4) the volume of transfers on the system, a rise that pushes up the net marginal cost of borrowing, thereby requiring an offsetting reduction in intraday credit to increase the associated marginal benefit.

Of course, banks may respond to policy decisions in part by shifting payment transactions from one payment system to another so that [tau] is a choice variable for banks. [4] Solving (4) for [tau], in terms of other parameters and choice variables, yields:

[tau] = [([[kappa].sub.1] + [v.sub.1]).sup.-1]{([v.sub.0] + [v.sub.1] - [[kappa].sub.1]) + ([[rho].sup.PW] - [[rho].sup.CB]) + [[r.sup.PW] + [[eta].sup.PW] ([r.sup.L] - [r.sup.S])] [Z.sup.PW] - [[r.sup.CB] + [[eta].sup.CB] ([r.sup.L] - [r.sup.S])][Z.sup.CB]}. (12c)

Therefore, if banks respond to payment system policies by altering relative volumes of transfers on the two payment systems, then the optimal portion of transfers that banks make on the CB wire system unambiguously declines in response to an increase in the CB wire transfer fee, overdraft level and interest charge, and collateral requirement. Increases in the private wire transfer fee, collateral requirement, and overdrafts induce banks to substitute CB wire transfers for private wire transfers.

The reduced-form solutions for [Z.sup.[CB.sup.*]], [Z.sup.[PW.sup.*]], and [[tau].sup.*] may be computed from (12a) through (12c). This is a system of nonlinear equations that yields very complicated polynomial solutions for these bank decision variables. To maintain tractability while continuing to capture the fundamental aspects of the policy problem faced by payment system administrators, the analysis that follows is based on the following first-order, linear (multivariate Taylor) approximations to these solutions in the neighborhood of zero values for the intraday credit rates, collateral requirement ratios, and transfer fees:

[Z.sup.[CB.sup.*]] = [[[omega].sup.-1].sub.1][[omega].sub.0] - [alpha][[r.sup.CB] + [[eta].sup.CB]([r.sup.L] - [r.sup.S])], (13a)

[Z.sup.[PW.sup.*]] = [[[sigma].sup.-1].sub.1][[sigma].sub.0] - [beta][[r.sup.PW] + [[eta].sup.PW]([r.sup.L] - [r.sup.S])], (13b)

and

[[tau].sup.*] = [tilde{[tau]}] - [gamma][[r.sup.CB] + [[eta].sup.CB] ([r.sup.L] - [r.sup.S])] + [phi][[r.sup.PW] + [[eta].sup.PW]([r.sup.L] - [r.sup.S])] - [xi]([[rho].sup.CB] - [[rho].sub.PW]), (13c)

where:

[alpha] [equiv] [[[[omega].sub.1]([v.sub.1] + [[kappa].sub.1])].sup.-1]([v.sub.0] + [v.sub.1] - [[kappa].sub.1]),

[beta] [equiv] [[[[omega].sub.1][([v.sub.1] + [[kappa].sub.1])].sup.-1][([v.sub.0] - [[upsilon].sub.0]) + [[sigma].sub.0]([v.sub.1] + [[kappa].sub.1]) - [[upsilon].sub.1]],

[gamma] [equiv] [[[[omega].sub.1]([v.sub.1] + [[kappa].sub.1])].sup.-1][[omega].sub.0],

[phi] [equiv] [[[[sigma].sub.1]([v.sub.1] + [[kappa].sub.1])].sup.-1][[sigma].sub.0],

and [xi] [equiv] [([v.sub.1] + [[kappa].sub.1])].sup.-1],

are nonnegative parameters, and where [tilde{tau}] [equiv] [([v.sub.1] + [[kappa].sub.1])].sup.-1]([v.sub.0] + [v.sub.1] - [[kappa].sub.1]) [5]

Equations (13a) through (13c) indicate that the first-order determinants of banks' desired levels of intraday borrowings from the central bank are the central bank's explicit intraday credit rate and the implicit rate resulting from imposition of a collateral requirement. Likewise, the first-order determinants of intraday borrowings on the private wire system are the private wire administrator's explicit intraday credit rate and implicit rate owing to collateral requirements. Explicit intraday credit rates, implicit credit rates, and the transaction fees established by the two-payment system administrators all have first-order effects on the portion of payment transactions performed on the CB wire system.

Alternative Policy Choices in Competing Payment Systems

Bank payment system decisions clearly depends critically on the policy choices made by the central bank and the private wire administrator. These choices, in turn, depend significantly upon whether these public and private policy makers take into account the effects that their payment system policy instruments have on transactions volumes as well as volumes of intraday credit.

Objectives of the Payment System Administrators

It is assumed that the private wire administrator is an agent for the banks that own the private wire system. Consequently, the private wire administrator desires bank profits to be as high as possible. At the same time, the administrator of this system may wish to recognize payment system externalities of the private wire system. In addition, the administrator must earn sufficient revenues to cover the costs of its operation, which are assumed to equal a fixed amount, [C.sup.PW].

In principle, therefore, the private wire administrator can set up to four policy instruments, [[rho].sup.PW], [r.sup.PW], [[bar{Z}].sup.PW], and [[eta].sup.PW], with an aim toward maximizing:

[[chi].sup.PW] [[pi].sup.*] - [[varphi].sup.PW] g([Z.sup.[PW.sup.*]]) - [[Psi].sup.PW] h([[eta].sup.PW][Z.sup.[PW.sup.*]]) - [[Theta].sup.PW] k((1 - [[eta].sup.PW])[Z.sup.[PW.sup.*]]) , (14)

where [[chi].sup.PW], [[Theta].sup.PW], [[Psi].sup.PW], and [[varphi].sup.PW] are constant, nonnegative weights that the administrator places on various nonprofit components of the administrator's objective (discussed below). In general, the administrator maximizes (14), subject to the administrative funding constraint (where the total number of banks is normalized at unity for simplicity):

(1 - [tau]) ([[rho].sup.PW] + [r.sup.PW][Z.sup.[PW.sup.*]][cdotp]) [geq] [C.sup.PW] , (15)

where the left-hand side of (15) is the total revenue earned from making transfers on behalf of banks that use the private wire payment system and from issuing intraday credit at the rate [r.sup.PW], which must at least cover the fixed cost of operating and administering the system.

The private wire administrator cares about bank profits to an extent governed by the magnitude of [[chi].sup.PW]. The nonprofit components are the same as those proposed by FS. The function g[cdotp], assumed to be decreasing and convex in [Z.sup.[PW.sup.*]], is intended to capture the cost to private wire members of private wire gridlock, which thereby approaches 0 if sufficiently large amounts of intraday credit are provided by the administrator. The relative weight of the gridlock cost in the administrator's objective is given by [[varphi].sup.PW]. The function h[cdotp], assumed to be increasing and convex, is intended to capture the broad cost of collateralized intraday private wire credit to the banks who use the private wire system. While collateralization of this credit protects the umbrella structure of the private wire system from risk of loss, it transfers that risk back to member banks. The magnitude of the weight [[Psi].sup.PW] indicates how important this cost is to the private wire administrator. Finall y, the function k[cdotp], also assumed to be increasing and convex, represents the cost to the private wire system of issuing uncollateralized intraday credit, and the parameter [[Theta].sup.PW] measures the weight of this cost in the administrator's objective.

The central bank has an analogous objective. It has the capability to set up to four policy instruments, [[rho].sup.CB], [r.sup.CB], [[bar{Z}].sup.CB], [[eta].sup.CB], with the goal of maximizing:

[[chi].sup.CB][[pi].sup.*] - [[varphi].sup.CB] g([Z.sup.[CB.sup.*]]) - [[Psi].sup.CB] h([[eta].sup.CB][Z.sup.[CB.sup.*]]) - [[Theta].sup.CB]k((1 - [[eta].sup.CB])[Z.sup.[CB.sup.*]]). (16)

For the sake of simplicity (and tractability), the central bank's perceptions of the functional forms for g([cdots]), h([cdots]), and k([cdots]) are assumed to be identical to those for the private wire administrator. What may differ for the central bank are the sizes of the weights, [[chi].sup.CB], [[varphi].sup.CB], [[psi].sup.CB], and [[Theta].sup.CB], that it places on bank profits and on the costs of systemic gridlock, risk transfers resulting from collateralization of intraday credit, and direct credit risk to the central bank that arise from any uncollateralized intraday credit it extends. [6]

The central bank maximizes (16), subject to its own administrative funding constraint required to ensure operation of the CB wire system:

[tau]([[rho].sup.CB] + [r.sup.CB][Z.sup.[CB.sup.*]]([cdots])) [geq] [C.sup.CB], (17)

where the left-hand side of (17) is the central bank's total earnings from making transfers for banks that use its CB wire system and from issuing intraday credit at the rate [r.sup.CB]. These earnings must be sufficient to cover the central bank's fixed cost of operating and administering the CB wire system, [C.sup.CB].

Solving the general model is a daunting task whether or not the policy makers coordinate their policy choices. Note, however, that in the general case of noncooperative behavior on the part of the central bank and the private wire administrator, the general procedure for solving the model is as follows. Each policy maker maximizes its objective ((14) and (16), respectively), subject to its funding constraint ((15) and (17), respectively), taking the policy choices of the other policy maker as given. Following this solution procedure would yield best responses (reaction functions) for each policy maker's four instruments in terms of the four instruments of the other policy maker. A grand solution for all eight solutions could then be computed, given specific parameter values and functional forms.

Nevertheless, for purposes of this paper, significantly less complicated special cases are considered. Such special-case solutions, it turns out, provide considerable insight into the importance of the strategic interaction among payment system policy makers that emerges in this model.

Optimal Intraday Credit Rates and Transaction Fees Without Caps and Collateral

In the special cases that follow, it is assumed that the payment system policy makers use neither intraday credit caps ([[bar{Z}].sup.CB] and [[bar{Z}].sup.PW]) nor collateral requirements ([[eta].sup.CB] and [[eta].sup.PW]). They rely instead on transfer fees ([[rho].sup.CB] and [[rho].sup.PW]) and intraday credit interest charges ([r.sup.CB] and [r.sup.PW]). [7]

In addition, the objectives of the central bank and the private wire administrator are to maximize bank profits while reducing exposure to risks resulting from daylight overdrafts on Fedwire, subject to its administrative funding constraint. Thus, for the central bank, [[chi].sup.CB] = 1, and [[Psi].sup.CB] = [[varphi].sup.CB] = 0 in (16). In addition, it is assumed that [[Theta].sup.CB] = ([[theta].sup.CB]/2), where [[theta].sup.CB], is a nonnegative weight, and that k[cdotp] = [([Z.sup.[CB.sup.*]]).sup.2]. Under these assumptions, the central bank maximizes:

[[r.sup.L](1 - [mu]) + [r.sup.S][mu]]A - [r.sup.CB][tau][Z.sup.CB] - [r.sup.PW](1 - [tau])[Z.sup.PW] - w([Z.sup.CB]) - s([Z.sup.PW]) - [tau][[rho].sup.CB] - (1 - [tau])[[rho].sup.PW] - ([[theta].sup.CB]/2)[([Z.sup.[CB.sup.*]]).sup.2] - v([tau]) - [kappa](1 - [tau]), (18a)

subject to (17), which is assumed to be a binding constraint. Likewise, [[chi].sup.PW] = 1, and [[psi].sup.PW] = [[varphi].sup.PW] = 0 in (14), and the private wire administrator places a nonnegative weight equal to [[Theta].sup.PW] = ([[theta].sup.PW]/2) on daylight overdraft risk defined by k[cdotp] = [([Z.sup.[PW.sup.*]]).sup.2]. It follows that the objective of the private wire administrator is to maximize:

[[r.sup.L](1 - [mu]) + [r.sup.S][mu]]A - [r.sup.CB][tau][Z.sup.CB] - [r.sup.PW](1 - [tau])[Z.sup.PW] - w([Z.sup.CB]) - s([Z.sup.PW]) - [tau][[rho].sup.CB] - (1 - [tau])[[rho].sup.PW] - ([[theta].sup.PW]/2)[([Z.sup.[PW.sup.*]]).sup.2], (18b)

subject to (15), also assumed to be a binding constraint. Below, the focus is placed on the central bank's choices because the private wire administrator's decision process is analogous (though not identical because of different daylight overdraft risk weightings and potentially different shares of total wire transactions volume).

Optimal Central Bank Policy Making Without Regard to Transaction Shares

Standard analyses of central bank determination of intraday credit rates presume that a central bank sets this and other policy instruments without regard to the effects that its choices may have for the volume of transactions-and, consequently, revenues-on the payment system it manages. In the context of the present model, this implies a presumption that the central bank chooses its intraday credit rate and transfer fee to maximize (18a), subject to (17), taking the portion of total transfers on CB wire, [tau], as given. This mode of behavior yields:

[r.sup.[CB.sup.*]] = [[[alpha]([[omega].sub.1] +[[theta].sup.CB]) - 4[tau]].sup.-1] {[([alpha][[omega].sub.1]).sup.-1] [[alpha]([[omega].sub.1] + [[theta].sup.CB]) - 2[tau]]-1}[[omega].sub.0], (19)

as the solution for the optimal intraday credit rate for CB wire.

The optimal central bank intraday rate depends positively on the weight, [[theta].sup.CB], that the central bank places on risks associated with daylight overdrafts on CB wire. In the limiting case in which [[theta].sup.CB] approaches infinity, [r.sup.[CB.sup.*]] = [([alpha][[omega].sub.1]).sup.-1][[omega].sub.0] which yields [Z.sup.[CB.sup.*]] = 0. The central bank sets the intraday rate sufficiently high to induce banks to curtail all intraday GB wire overdrafts. [8]

The effect of a rise in CB wire transactions volume on the optimal intraday rate is equal to [delta][r.sup.[CB.sup.*]]/[delta][tau] = 2[[omega].sub.0][[[alpha]([[omega].sub.1] + [[theta].sup.CB]) - 4[tau]].sup.-2]([[[omega].sup.-1].sub.1][[theta].sup.CB] - 1). Thus, the key determinant of how the central bank varies its intraday credit rate in response to increased CB wire volume is the weight that it places on intraday credit risk. A higher intraday rate causes a ceteris paribus increase in bank costs. Consequently, if the central bank's risk weight is sufficiently small ([[theta].sup.CB] [less than] [[omega].sub.1] in the model), then its optimal intraday rate depends negatively on CB wire volume. In this instance, a reduction in the intraday rate pushes up bank profits. Thus, the central bank can maintain sufficient revenues to cover its CB wire operating costs at a lower intraday rate in light of the higher transfer fee income that a higher CB wire volume implies. If the central bank's risk weight is sufficiently larg e ([[theta].sup.CB] [greater than] [[omega].sub.1]), however, then for a given fraction of CB wire payments that result in overdrafts, an increase in CB wire volume results in greater central bank exposure to risk. Hence, the propensity for the central bank to respond to higher CB wire volume by increasing the intraday rate is greater for larger values of the weight, [[theta].sup.CB], than what the central bank places on the risk associated with CB wire daylight overdrafts.

The solution for the optimal transfer fee, [[rho].sup.CB], is a more complicated expression and is not reported here. Nevertheless, the central bank's optimal transfer fee also depends on CB wire payments volume and the central bank's risk weight.

An important feature of these optimal settings for the central bank's policy instruments is that they are not influenced by the private wire administrator's policy choices. The reason for this is the assumption that the central bank makes its choices taking the relative transactions volumes on the two wire systems as given. As a result, the central bank does not set its policy instruments in an effort to influence [tau] and thereby affect the CB wire share of total bank wire transactions.

Nevertheless, a key implication of these results is that if the central bank places a higher weight on reducing daylight overdrafts on its CB wire system, its share of total wire transactions will change. As noted above, an increased central bank concern about CB wire risks, reflected in a higher value of [[theta].sup.CB], leads the central bank to increase both its transfer fee and its intraday credit rate. As (13c) indicates, however, holding private wire policies unchanged, these policy changes reduce the value of [[tau].sup.*], the optimal share of payments that banks process on CB wire. Thus, a unilateral

central bank effort to place greater weight on stemming risks associated with CB wire daylight overdrafts requires central bank policies that ultimately tend to reduce its share of total wire transactions.

Optimal Policy Making When the Central Bank and Private

Wire Administrator Actively Compete for Transactions Shares

The optimal intraday rate reported in (16) is a semi-reduced-form solution. It indicates the best setting, given the presumed central bank concern with bank profitability and intraday credit risks in light of its own need to generate sufficient revenues to cover the cost of operating the CB wire system. Most discussions of central bank payment system policy making effectively halt at this point. Indeed, most ignore the potential interaction between the central bank's setting of its intraday rate and the volume of payments that banks make on the CB wire system.

Realistically, however, a central bank cannot ignore this interaction. While its CB wire system may have a comparative advantage in processing transfers of reserves among accounts of its bank clients for interbank lending transactions, it is less clear that such an advantage necessarily exists for other payment transactions. In the U.S., for instance, federal fund loans entail transfers among bank reserve accounts with Federal Reserve banks, so the Federal Reserve may have a natural advantage in offering to perform such transactions on banks' behalf via the Fedwire system that it owns and operates. Book entry security transfers, however, are more likely to be open to competition from CHIPS, the U.S. analogue to the private wire system in the model. Further technological developments undoubtedly continue to open the potential for substitutability among payment systems for these and other wire payment transactions. [9]

A key assumption of the model is that banks can choose between the two payment systems, given potentially different costs and benefits (determined by the values of the parameters [[omega].sub.0], [[omega].sub.1], [[sigma].sub.0], and [[sigma].sub.1]) and different fees and rates established by the payment system administrators (the policy variables [r.sup.CB], [r.sup.PW], [[rho].sup.CB], and [[rho].sup.PW]). Hence, from the perspective of banks, the CB wire and private wire systems are imperfectly substitutable means of accomplishing payment transfers, but banks may freely alter the relative shares of payments that they place on these systems.

Determining these relative shares and their implications for the central bank's optimal policy choices in the face of competition from the private wire system entails working out reduced-form solutions to the model. Even given the linear approximations to the banks' decision rules, the simple functional forms for policy goals, and the presumption that collateral requirements either are absent or nonbinding, however, the model generally yields nonunique solutions for all the relevant variables (the reduced-form solution for [r.sup.[CB.sup.*]], for instance, turns out to be a fourth-order polynomial expression). Nevertheless, fundamental implications of the model for central bank policy making in the face of payment system competition can be examined by considering first-order linear approximations to the optimal choices of the central bank and the private wire administrator. For the central bank, the first-order linear approximation to (19) is given by:

[r.sup.[CB.sup.*]] [approx] [[tilde{r}].sup.CB] + [Lambda]([[theta].sup.CB])([tau] - [tilde{[tau]}]), (20a)

where:

[[tilde{r}].sup.CB] [equiv] [[[alpha]([[omega].sub.1] + [[theta].sup.CB]) - 4[tilde{[tau]}]].sup.-1]{[[alpha].sup.-1][[alpha]([[omega].sub.1] + [[theta].sup.CB]) - 2[tilde{[tau]}]][[[omega].sup.-1].sub.1] -1}[[omega].sub.0],

and [Lambda]([[theta].sup.CB]) [equiv] 2[[omega].sub.0][[[alpha]([[omega].sub.1] + [[theta].sup.CB]) - 4[[tilde{[tau]}]].sup.-2] ([[[omega].sup.-1].sub.1][[theta].sup.CB] -1).

The term [Lambda]([[theta].sup.CB]) is the derivative of [r.sup.[CB.sup.*]] , respect to [tau], evaluated at [tilde{[tau]}]. As discussed above, the sign of [Lambda]([[theta].sup.CB]) may be positive or negative, depending on the magnitude of [[theta].sup.CB]. Note, however, that [Lambda]([[theta].sup.CB]) [rightarrow] 0 as [[theta].sup.CB] [rightarrow][infty]. Hence, [r.sup.[CB.sup.*]] [rightarrow] [[tilde{r}].sup.CB] [rightarrow] [([[omega].sub.1] [alpha]).sup.-1] [[omega].sub.0] so that the approximate solution continues to yield [Z.sup.CB] = 0 in the limiting case in which [[theta].sup.CB] [rightarrow] [infty].

Obtaining an approximate solution for the private wire administrator's policy choices entails maximizing (18b), subject to (15), and computing the first-order linear approximation to the optimal private wire intraday credit rate, given by:

[r.sup.[PW.sup.*]] [approx] [[tilde{r}].sup.PW] - [Gamma]([[theta].sup.PW])([tau] - [tilde{[tau]}]), (20b)

where:

[[tilde{r}].sup.PW] [equiv] [[[beta]([[sigma].sub.1] + [[theta].sup.PW]) - 4(1 - [tilde{[tau]}])].sup.-1] {[[beta].sup.-1][[beta]([[sigma].sub.1] + [[theta].sup.PW]) - 2(1 - [tilde{[tau]}])][[[sigma].sup.-1].sub.1]-1}[[sigma].sub.0],

and [Gamma]([[theta].sup.PW]) [equiv] (2[[sigma].sub.0])[[[beta]([[sigma].sub.1] + [[theta].sup.PW]) - 4(1 - [tilde{[tau]}])].sup.-2]([[[sigma].sup.-1].sub.1][[theta].sup.CB]-1).

The term [Gamma]([[theta].sup.CB]) is the derivative of [r.sup.[PW.sup.*]], respect to [tau], evaluated at [tilde{[tau]}]. As for the central bank, the sign [Gamma]([[theta].sup.CB]) depends on the magnitude of the private wire administrator's intraday credit risk weight, [[theta].sup.PW].

Equations (13c) and (20) together constitute a three-equation system that, holding the payment transfer fees for both systems ([[rho].sup.CB] and [[rho].sup.PW]) constant for the sake of simplicity, yields approximate linear solutions to the policy problems that the central bank and the private wire administrator jointly face in determining optimal intraday credit fees. To understand the policy interactions implied by these three relationships, consider Figures 1 and 2.

The schedule labeled [R.sup.CB] in panel A of both figures is the implicit central bank reaction (or best response) function obtained by substituting (13c) into (20a). Its slope is equal to [[1 + [gamma][Lambda]([[theta].sup.CB])].sup.-1] [delta][Lambda]([[theta].sup.CB]). The schedule labeled [R.sup.PW] in panel A of both figures likewise is the private wire administrator's reaction function obtained from substituting (13c) into (20b). The slope of [R.sup.PW] is equal to [[[gamma][Gamma]([[theta].sup.PW])].sup.-1] [1 + [delta][Gamma]([[theta].sup.PW])]. Panel B of each figure illustrates the inverse relationship between banks' CB wire payment volume and the central bank's intraday credit rate implied by (13c). Panel C depicts a 45-degree line that relates the CB wire payment volume to the optimal private wire intraday credit rate in panel D. This is the relationship given in (20b).

In general, the central bank's and private wire administrator's reaction functions may slope upward or downward, depending on the relative magnitudes of [[theta].sup.CB] and [[theta].sup.PW] and of the other parameters of the model. Both Figures 1 and 2 are drawn under the assumption that the central bank's intraday credit risk weight is sufficiently large to satisfy [[theta].sup.CB] [greater than] [[omega].sub.1], in which case, the central bank's reaction function unambiguously slopes upward, as illustrated in panel A of both figures.

In Figure 1, the private wire administrator's weight, [[theta].sup.PW], on intraday credit risk is assumed to be sufficiently large enough that [[theta].sup.PW] [greater than] [[sigma].sub.1] so that the private wire administrator responds to a reduction in CB wire payment volume (an increase in private wire volume) by raising its intraday credit rate, hence, the inverse relationship between [r.sup.PW] and [tau], displayed in panel B of Figure 1. In this circumstance, the private wire administrator's reaction function also slopes upward, as depicted in panel A.

By way of contrast, Figure 2 shows a situation in which the private wire administrator places a relatively low ([[theta].sup.PW] [less than] [[sigma].sub.1]) weight on intraday credit risk. In this event, the private wire administrator responds to a decline in CB wire payments volume (an increase in private wire volume) by reducing its intraday credit rate because this action improves the profitability of member banks and maintains sufficient private wire revenues to cover system costs. Hence, there is a positive relationship between [r.sup.PW] and [tau] in panel B of Figure 2, and the private wire administrator's reaction function in panel A slopes downward. [10]

Each figure shows the effects of an increased central bank concern with intraday credit risk, reflected by an increase in the value of [[theta].sup.CB]. The result in each case is an upward rotation of the central bank's reaction function in panel A of both figures. That is, an increased concern with risk exposure stemming from its extension of intraday credit on CB wire induces the central bank to raise [r.sup.[CB.sup.*]] to give banks an incentive to reduce their daylight overdrafts on the CB wire system. In part, banks also respond to this policy change by transferring some of their payment transactions to the private wire system, as depicted by the reduction in [[tau].sup.*] in panels B and C of each figure.

The ultimate responses of both payment system policy makers to the central bank's heightened concern with intraday credit risks depends crucially on the private wire administrator's concern about risks stemming from daylight overdrafts. On one hand, in Figure 1, where the private wire administrator (like the central bank) gives considerable weight to the risk associated with daylight overdrafts, the private wire administrator responds to the increase in private wire payments volume by increasing the private wire intraday credit rate, as shown in panels A and D. This action by the private wire administrator tends to have a slight counteracting effect on CB wire payment volume (depicted by the leftward shift in the [[tau].sup.*] schedule in panel B) that reinforces the central bank's decision to push up its intraday rate, inducing a further rise in the central bank's intraday rate.

On the other hand, in Figure 2, where the private wire administrator places very low weight on intraday credit risks, the decline in CB wire payments volume owing to a higher CB wire intraday rate induces the private wire administrator to reduce the private wire intraday credit rate. This action reinforces the CB wire system's decline in payment volume, which pushes the central bank's payment system revenues down further, thereby inducing the central bank to undertake a net increase in its intraday credit rate that is smaller than it would have enacted otherwise in response to the rise in [[theta].sup.CB].

Therefore, Figure 2 potentially explains the partial reversal of the Federal Reserve's policy stance in 1995. In the absence of potential payment system interactions, the Federal Reserve would otherwise have enacted an intraday credit rate of 25 basis points. After taking into account the potential for bank substitution between Fedwire and CHIPS--and, if the model is a reasonable depiction of the underlying behavior of the two payment system administrators, a lower CHIPS concern about intraday credit risks--the Federal Reserve ultimately settled on an intraday rate that was 40 percent lower.

Clearly, this possible explanation for the Federal Reserve's behavior hinges on an initially sizable Federal Reserve concern about intraday Fedwire credit risks and a relatively meager concern about intraday credit risks on the part of CHIPS participants. Both assumptions seem reasonable in light of the safety-net coverages available to CHIPS participants through federal deposit insurance and the Federal Reserve's lender-of-last-resort facilities.

The model above does not explicitly consider the moral hazard effects of the federal financial safety net, which limits the potential for using the model to conduct welfare analysis. Nevertheless, for the sake of argument, suppose that the central bank's weight, [[theta].sup.CB], is equal to the societal weight on intraday credit risk. If so, then the socially optimal (or, given the distorting effects of safety-net guarantees, second best) outcome would require:

1) inducing the private wire administrator to adopt the same social risk weight, [[theta].sup.CB]; and

2) developing a mechanism for achieving cooperative policy making by the central bank and the private wire administrator.

Under these conditions, neither Figure 1 nor Figure 2 would illustrate the truly socially optimal responses to an enhanced concern about intraday credit risks. Nonetheless, assuming roughly equivalent technologies and costs for the two systems and nearly equal costs and benefits for bank customers of the systems, the result would be higher intraday credit rates in both systems with little change in relative payment volumes.

Conclusion

Traditionally, the Federal Reserve has been regarded as a key participant in the U.S. payment system. As Stevens [1996] points out, the founders of the Federal Reserve intentionally anchored the Federal Reserve within the payment system to "weave [Federal R]eserve banks' operations into the fabric of everyday financial market activity." In today's altered technological environment, however, interrelated public and private payment systems experience credit and systemic risks owing to daylight overdrafts.

This paper has sought to examine how these interrelationships can influence the payment system policy choices of a public payment system administrator such as the Federal Reserve. The key conclusion is that examining central bank policy making solely within a single payment system may ignore important effects arising from interactions with private payment networks. Optimal policies that a central bank otherwise might pursue within an isolated payment system are unlikely to correspond to the policies that it would find optimal to pursue if the central bank recognizes that banks can shift transactions among both publicly and privately administered networks.

On one hand, if a central bank ignores potential shifts in transactions volumes from its system to private systems, then efforts to reduce risks arising from daylight overdrafts on its system are likely to reduce its share of total payments. On the other hand, if a central bank takes into account relative transactions volumes on both a public system that it manages and private systems that banks alternatively may use, then noncooperative policy making is likely to yield socially desirable central bank policy settings, assuming that the Federal Reserve's objectives match those of society as a whole.

There are at least three possible ways that the Federal Reserve might address the latter problem. One, which it has pursued to some extent, is to work with CHIPS to attain a cooperative and (if the weights in the Federal Reserve's objective function reflect societal concerns with risk, gridlock, and so on) socially optimal outcome. The Federal Reserve's objectives and risk weights may differ from those of CHIPS, however. Indeed, the presence of the federal financial safety net undoubtedly assures that such differences will exist. Furthermore, weights in the Federal Reserve's objective function may not reflect societal weights, particularly if concerns about Reserve bank employment levels and other matters of self-interest influence Federal Reserve officials. These potential mismatches ultimately could doom efforts to achieve a cooperative, socially optimal outcome.

A second, related approach would be for the Federal Reserve to take a more active regulatory role. Under this approach, which the Federal Reserve currently seems on the verge of pursuing [Federal Reserve System, 1997, 1998], the Federal Reserve essentially would create regulatory mechanisms that would force private payment providers to adopt risk weights and policies mandated by the Federal Reserve itself. The scope for independent decision making by a private wire administrator such as the one modeled in this paper thereby would be curtailed significantly. Indeed, in such a regime, the only choice variable for the private wire administrator would be the transfer fee (and, perhaps, quality and convenience of service). Whether such an approach, which would further broaden the Federal Reserve's involvement in the payment system, is socially desirable is an open question.

A third approach is more radical. The Federal Reserve could exit the payment system business. It could sell or lease its payment system hardware and facilities to private payment system firms or associations and privatize the bulk of its labor force. Taking into account the distorting effects of safety-net guarantees on private incentives, the Federal Reserve could then regulate the functioning of these systems by setting performance standards (for instance, minimal risk weights) and performing auditing functions, much as it does as a bank regulator today. This may or may not lead to a preferable outcome. Certainly, this paper provides no analysis of this alternative payment system structure. Nevertheless, the results here indicate that this option might be worthy of more study than it has received to date. [11]

This paper has concentrated on wire transfer systems because of the unique policy problems that they present. Nevertheless, similar problems of interacting public and private systems arise in check clearings. A model such as the one developed here might therefore be useful in examining the massive U.S. check collection system and the Federal Reserve's role in that system. This paper has also adopted an insular, U.S. perspective. However, European nations increasingly will confront problems of interrelated public and private payment systems as the drive toward monetary union continues. [12] Undoubtedly, a framework not unlike the one in this paper could assist in evaluating these issues as well.

The analytical framework employed in this paper can justifiably be criticized for its reliance upon a static framework, its consideration of arbitrary policy objectives, its abstraction from payment netting arrangements used in private systems, and its failure to explicitly model sources of risk. However, such modeling extensions lie well outside the bounds of this paper, which has highlighted essential policy issues that arise in the operation and regulation of interacting public and private payment systems.

(*.) University of Alabama--U.S.A. The author is grateful to Paolo Angelini, Craig Furfine, Alton Gilbert, Jeffrey Lacker, Jeffrey Stehm, Ed Stevens, participants in seminars at the University of Alabama, the Federal Reserve Bank of Atlanta, and the Federal Reserve Bank of Chicago for comments on earlier drafts of this paper. The paper also was improved by comments received at the Federal Reserve Bank of Chicago's Payment Systems Research Workshop. Any remaining errors belong to the author.

Footnotes

(1.) See Walter [1998] for a discussion of this and other subsidies.

(2.) This is a basic conclusion, for instance, in the literature on international policy coordination in two-country settings (see, for example, Oudiz and Sachs [1984], Rogoff [1985], and Canzoneri and Henderson [1991]). This paper essentially shows that the same basic point extends to an environment of two interlinked payment systems administered by separate policy makers.

(3.) The parameter [delta] is the effective reserve ratio, after accounting for the required reserve-reducing impact of sweep accounts [VanHoose and Humphrey, 1998]. For the sake of simplicity, the capital constraint is assumed to be nonrisk-based [Kopecky and VanHoose, 1999].

(4.) At present, most transactions on Fedwire entail federal funds-related and book entry security-related funds transfers, and the bulk of transactions on CHIPS are Eurocurrency-related and foreign exchange-related transfers. Nevertheless, there is no technological reason that many of the transactions currently conducted on one system could not be accomplished on the other system. Indeed, anecdotal accounts indicate that some large banks proposed to begin transferring blocks of book entry security transfers from Fedwire to CHIPS if the Federal Reserve had raised its intraday credit rate from 15 to 25 basis points as originally planned in 1995.

(5.) Sufficient, but unnecessary, conditions for [beta] [greater than] 0 are [[kappa].sub.0] [geq] [[upsilon].sub.0] and [[sigma].sub.0] [greater than] 1. The necessary condition for [alpha] [greater than] 0 and [tilde{[tau]}] [greater than] 0 is [[upsilon].sub.0] + [[upsilon].sub.1] - [[kappa].sub.1] [greater than] 0.

(6.) In its role as a public policy maker, the Federal Reserve also may incorporate concerns about CHIPS risks, collateral costs, and gridlock into its objectives. Thus, in principle, its objective function could be much broader than the one displayed in (14). Below, however, only a special case of (14) is analyzed in detail. The Federal Reserve's aversion to uncollateralized overdrafts reflect concerns about both its own exposure to credit risk and the banking system's exposure to systemic risk arising from potential interbank funds settlement failures. However, simulations by Furfine [1999] indicate that past concerns about the latter may have been overstated in previous payment system research.

(7.) CHIPS recently has made collateral requirements a central feature of its intraday credit policies. Nevertheless, the essential conclusions are not altered by focusing on an explicit intraday rate instead of a collateral requirement. The latter has identical effects, at least in this one-period model in which the spread between the loan and security rates is constant.

(8.) There likely is an upper limit for the central bank's intraday credit rate, above which banks would have an incentive to extend private intraday credit at a market-determined intraday rate (see VanHoose [1991] for analysis of such a system). This model ignores this possibility.

(9.) Federal Reserve pricing of daylight overdrafts may have encouraged the growth of the GSCC. More broadly, increased substitutability in other forms of payment is increasingly common, leading some observers such as Wilke [1996] to question the Federal Reserve's long-term viability in the face of increased competition from private payment system providers and in the absence of significant efforts to reduce the costs of maintaining its own payment systems.

(10.) In this case, [Gamma]([[theta].sup.PW]) [less than] 0. The negative slope for [R.sup.PW] in Figure 2 follows, provided that 1 + [delta][Gamma]([[theta].sup.PW]) [greater than] 0, the condition for a stable equilibrium.

(11.) Of course, another option would be to permit greater competition among Reserve banks as well as among private sector networks while maintaining an overall regulatory umbrella. This would maintain the Federal Reserve's direct involvement in the payment system and save it from having to undertake a full privatization of its payment system functions. See Toma [1997] for an interesting analysis of competition among Reserve banks earlier in the Federal Reserve's history.

(12.) For a useful review of some of these issues, see Folkerts-Landau et al. [1996].

References

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Author: | VANHOOSE, DAVID D. |
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Publication: | Atlantic Economic Journal |

Article Type: | Critical Essay |

Geographic Code: | 1USA |

Date: | Jun 1, 2000 |

Words: | 11324 |

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