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Financial Services
WORK ING PAPER
0 1 9 6
Scale Economies,
Cost Efficiencies, and
Technological Change in
Federal Reserve Payments
by Paul W. Bauer and Gary D. Ferrier
FEDERAL
RESERVE
FINANCIAL
SERVICES
•
I
Financial Services Working Paper Series No. 01-96
SCALE ECONOMIES, COST EFFICIENCIES, AND TECHNOLOGICAL
CHANGE IN FEDERAL RESERVE PAYMENTS
by Paul W. Bauer and Gary D. Ferrier
Paul W. Bauer is a member of the Financial Services
Research Group and an economic advisor at the Federal
Reserve Bank of Cleveland. Gary D. Ferrier is an associate
professor of economics at the University of Arkansas. The
authors thank Sigb~rn Atle Berg, Allen Berger, Robert
DeYoung, Karl Gambs, Diana Hancock, David Humphrey,
Darrell Mak, Jeffrey Marquardt, Louise Roseman, Jeff
Stehm, and Florence Young for their useful comments on
earlier drafts of this paper. Professor Ferrier gratefully
acknowledges the financial support of the Federal Reserve
Bank of Cleveland. This paper was presented at the
December 1995 Conference on Payment Systems Research
and Public Policy, organized by the Board of Governors of
the Federal Reserve System and the Journal of Money,
Credit, and Banking.
Working papers of the Financial Services Research Group
are preliminary materials circulated to stimulate discussion
and critical comment. The views stated herein are those of
the authors and are not necessarily those of the Federal
Reserve Bank of Cleveland, the Financial Services Policy
Committee, or the Board of Governors of the Federal
Reserve System.
Working papers are now available electronically through the
Cleveland Fed's home page on the World Wide Web:
http://www.elev.frb.org.
August 1996
•
I
Abstract
This paper uses a stochastic cost frontier to examine the scale economies. cost efficiencies, and technological
change of three payment instruments--check, automated clearinghouse (ACH) transfers. and Fedwire processing-provided by the Federal Reserve over the period 1990-94. We find evidence of substantial scale economies and
cost inefficiencies in the ACH and Fedwire services. Check processing also exhibits substantial cost inefficiency,
but constant returns to scale. Technological progress is found to be sizable for ACH and Fedwire; check
processing is found to have experienced technological "regress," probably because of a decrease in processing
volume over the sample period .
I
r
Money is not, properly speaking, one of the subjects of commerce; but only the
instrument which men have agreed upon to facilitate the exchange of one commodity for
another. It is none of the wheels of trade: it is the oil which renders the motions of the
wheels more smooth and easy.
--David Hume, Essays Moral and Political, 1741
I. Introduction
The payments system, the means of conducting transactions in an economy (Hume's "oil"), has undergone
tremendous change over the centuries. Commodity money was replaced by fiat (usually paper) money, reducing
transportation and storage costs. The invention of checks to supplement fiat money further reduced those costs.
lessened the problem of theft, and provided a record of transactions. Most recently, the advent of electronic
payment instructions has greatly reduced the time and handling costs associated with checks. Between the great
evolutionary leaps forward that created new forms of payment instructions. smaller degrees of gradual evolution
occurred within all the payment mechanisms, refining and improving them and reducing the costs associated with
their use. The development of the payments system has indeed rendered the functioning of global commerce "more
smooth and easy."
An advanced economy has many payment instruments, each possessing different characteristics that make
it suitable for some transactions but not others. For example, cash (currency and coins) is very convenient for lowvalue consumer purchases; however. few large companies would consider paying their employees in cash. Thus.
while cash comprises about 80 percent of the volume of transactions in the U.S., it accounts for less than I percent
of their value. Checks, automated clearinghouse (ACH) transfers, and wire transfers combined account for about
99 percent of the value transferred by th~ payments system (see Humphrey and Berger [1990]). Credit cards,
point-of-sale, and automated teller machine bill payments are all experiencing rapid growth in volume, but have
yet to attract a large share of transaction value. It is unlikely that "e-cash"--digital cash that will permit
cybermai:kets to flourish--will account for a significant share for some time to come. 1
In this paper we examine the Federal Reserve's costs of processing three of the most important payment
1
Sec Humphrey. Pulley. and Vesala ( 1996) for infonnation on recent use panems for a variety of payment instruments for developed countries.
i
services: checks, ACH transfers, and wire transfers of funds (Fedwire). 2 We estimate three frontier cost systems
that allow us to derive estimates of marginal cost, scale economies, cost efficiency, and technological change for
each service. Each of these properties has important implications for the pricing, delivery, and market structure of
these payment services.
II. Overview of Check Processing, Automated Clearinghouses,
and Fedwire Funds Transfer Services
Before the Depository Institutions Deregulation and Monetary Control Act (MCA) of 1980 was passed. the Federal
Reserve offered its payments services (check processing, ACH transactions, and Fedwire) at no charge to member
banks. The MCA required the Federal Reserve to offer its payments services to all depository institutions. not just
member banks, and directed it to begin charging for these services. 3 The Board of Governors has established
guidelines for pricing payment services. Prices are set to recover all direct and indirect costs, including a markup
over cost (the "Private Sector Adjustment Factor" [PSAF]) that reflects other costs (for example. taxes) incurred by
private-sector providers of payments services. The prices of ACH and Fedwire funds transfer are determined
nationally; however, because input prices, transportation requirements. and the mix of banks served vary from
region to region. fees for check services vary substantially across Federal Reserve offices. While the passage of the
MCA increased the number of banks eligible to use Federal Reserve payment services. a large decline in the
volume of the Federal Reserve's check processing services occurred as the new pricing requirement made it easier
for private providers of payment services to compete for member banks' business. 4
The following is a brief description of each of the Federal Reserve's payments services. It is intended to
provide insight into the costs associated with these important services, but it does not reveal all of the complexities
faced by a typical Federal Reserve processing site. For example. within each of the three services. transactions
processed can be differentiated by the locations of the transmitting and receiving banks involved. the time available
2
1n llus paper. Fedwtre transactions refer lo fund transfers, not to book-entry Treasury security transfers.
3in the remainder of the paper, the term bank will be used lo refer to any depository institution.
4Jbough the Federal Reserve's diedc service volume declined, its ACH and Fedwire services have experienced steady rates of volume growth.
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for processing, and the amount of processing required by specific customers. Costs can vary significantly as a
result of this myriad of product characteristics. While our analysis attempts to control differences across sites,
some possibly important factors are no doubt missing. We hope that future research efforts will address any
deficiencies.
Check Processing
Conceptually, the processing of checks is a straightforward operation. A payor writes a check to a payee, who
deposits it at his/her bank. In the case of "on-us" items (when the payor and payee are customers of the same
bank), the bank debits the payor's account and credits the payee's account. This situation represents about 25
percent of all transactions involving checks. If the payor and the payee have accounts at different banks, then the
payee's bank must somehow present the check to the payor's bank. This type of settlement accounts for the
remaining 75 percent of check transactions. In this case, the payee's bank has the option of sending the check
directly to the payor's bank for payment, or it can employ the services of a local clearinghouse, a correspondent
bank, or a Federal Reserve office to process the "transit" check. In 1994, Federal Reserve Banks processed
approximately 35 to 40 percent of the transit checks-- approximately 17 billion of them. If the account on which a
check is drawn has insufficient funds to cover it, the check is returned to the bank of first deposit directly or
through one or more returning banks. This return process is more labor intensive, and thus more costly. than the
forward processing of checks.
Automated Clearinghouse Services
The ACH system is a value-dated electronic funds transfer system that can be used to make either credit transfers
or debit transfers. The five principal participants in ACH transactions are the payor, the payee. the payor's bank,
the payee's bank, and the provider of the ACH service. With credit transfers (for example, direct payroll deposits),
the payor's bank typically initiates the transfer and funds flow from the payor's bank to the payee's bank. With
debit transfers (such as mortgage or utility payments), the payee's bank initiates the transfer and receives funds
from the payor's bank. The Federal Reserve handled about 94 percent of the roughly 2.5 billion commercial and
government ACH transactions processed in 1994.
ACH transactions offer several key advantages over paper instruments. First, in most cases, payors know
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exactly when the funds will be removed from their accounts, and payees know exactly when the funds will be
deposited to their accounts. Second, ACH transactions may be more convenient, particularly for recurring
payments, because the payor need not remember to write and deliver a paper check, and the payee need not cash or
deposit it. Third. the total costs to all parties are much lower for ACH transactions than for paper checks. 5
Finally, accounting efficiencies may exist for business payors and payees that have implemented financial
electronic data interchange to facilitate communications with trading partners. 6
Fedwire Service
The Fedwire funds transfer service is a real-time. gross settlement system in which the sender of funds initiates the
transfer. Banks that maintain a reserve or clearing account with a Federal Reserve Bank may use Fedwire to send
payments to or receive payments from other account holders directly. In contrast with ACH payments, which take
two days to process, Fedwire is an immediate payment mechanism and is therefore used for time-critical payments.
Fedwire transfers are used primarily for payments related to interbank overnight loans, interbank settlement
transactions. payments between corporations. and settlement of securities transactions.
Unlike check and ACH debit transactions, which can be returned unpaid, Fedwire transactions have the
advantage that the funds transfer is final when credited to the receiving bank's Federal Reserve account, or when
the Federal Reserve Bank sends advice of the payment to the bank, whichever comes first. When funds are
transferred via Fedwire, Unifonn Commercial Code (UCC) 4A requires that they be made available to the recipient
upon acceptance by the recipient's bank. UCC 4A also applies to corporate ACH credit transactions.
While large-value transactions systems. like the Federal Reserve's Fedwire and the private Clearing House
Interbank Payments System (Cl-llPS), accounted for only about 120 million transactions in 1994, as compared with
60 billion check transactions and over 2.5 billion ACH transactions (Bank for International Settlements ( 1995]),
they accounted for most of the value of noncash transactions. In 1994, Fedwire and CI-IlPS transactions were
valued at over $500 trillion, whereas the values of checks processed by the Federal Reserve and total ACH
1nc full social cost of processing an ACH item is only about one-third to one-half as much as for a check (see Humphrey and Berger [ 1990]
and Wells [ 1994 ]).
6
Sec Knudson. Walton. and Young (1994) for a disrussion of the potential benefits of financial electronic data interchange (a combination of
electroruc rerruuance data and electroruc funds transfers) for business payments.
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transactions were only $13 trillion and $10 trillion, respectively. The Fedwire service accounts for more than half
of all large-value transactions, though it handles less than half of the dollar volume.
III. Estimation Technique
Frontier cost functions for each of the three payment services are estimated to measure their marginal costs,
economies of scale, cost efficiencies, and rates of technological change. A variety of methodologies exist for
calculating cost frontiers; each of them measures efficiency relative to a "best-practice" cost curve. In this paper
8
cost frontiers are estimated using a stochastic, parametric model.7· A stochastic form is chosen so that noise is less
likely to be commingled with inefficiency; a parametric form so that estimates of the underlying technology's
various properties, such as marginal costs and scale economies, can be derived.
The estimation of cost frontiers requires data on cost, output quantities, input prices, and any
environmental factors that might influence the level of costs. Let C, 1 be the level of observed cost incurred by the I
(I= 1,. .. .N) processor in period t (t = l, ....
n, y
11
be the vector of output quantities produced by the I th processor in
period t, w, 1 be the vector of input prices facing processor I in period t, and E, 1 be a vector of characteristics
describing the environment faced by the I th processor in period t. A stochastic, parametric frontier (log) cost
function can be written as:
lnC,,
=
lnC(y 11 ,w11 ,E 11 ,1;p) + v, 1 + u;,·
(1)
That is, the observed (log) cost, lnC,,, is the sum of frontier (log) cost, lnC 11 (y, 1 , w, 1 , £ 11 , t; P), random deviations
from minimal cost, v11 , and deviations from minimal cost due to inefficiencies, u, 1 • The random disturbance may
be positive, zero. or negative (v,, ~ 0), while the disturbance due to inefficiency is non-negative (u, 1
L
0), since
inefficiency cannot cause cost to be less than the frontier level.
Before estimating the cost frontier given by equation (l), two further modeling decisions must be made.
First, a functional form must be chosen to represent the parametric relationship between cost, output, input prices,
7
Sec Chames et al. ( 1994) and Greene ( 1993), respectively. for overviews of the programming and econometric approaches to frontier estimation.
Tur examples of frontiers applied to financial services, sec Aly et al. ( 1990), Bauer, Berger, and Humphrey (1993), Bauer and Hancoclc (1993),
Berger (1993). Berger, Hancoclc, and Humphrey ( 1993). Berger and Humphrey (1991 ). Elyasiani and Mehdian (1990), Ferrier and Lovell (1990),
Ferner et al. (1993). Fried. Lovell. and Vanden Eeckaut (1993), Mester (1993), and Rangan et al. (1988).
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and environmental variables. Because of its flexibility, we have chosen a hybrid cost function that combines the
terms of the standard translog model and the first-, second-. and third-order trigonometric terms of the Fourier
functional form. This hybrid cost function offers a close. global approximation to any underlying functional form
(Gallant [1981] and Berger, Leusner, and Mingo (1995]). Second. the inefficiency term must be modeled. The
availability of repeated observations over time (that is, panel data) alleviates the need to make an assumption about
the particular distribution followed by the inefficiency term. Instead, we use the distribution-free "within" frontier
model of Schmidt and Sickles (1984), modified for use with a cost function. This model identifies site-specific,
time-invariant measures of inefficiency (that is, u,, = u,) based on observation-specific constants. The within model
provides consistent estimates of the individual intercepts as T be consistently separated from the overall residual as N -
00 •
00 •
and allows the individual inefficiency effect to
Furthermore, it allows for correlation between the
inefficiency terms and the regressors. Unfortunately. any variables that do not change over time must be excluded
from the estimation, and the effects of these variables are included in the efficiency estimate.
Given our assumptions, the cost function to be estimated can be written as:
l
L
InC11
"' el
+
I: al lnyl,t
L
l
K
L
Pk
L
K
1n w.b,
+ -
k•l
+
I:
J•l
K
P1k
1n W111 In w.b,
M
6/k lnYt,, lnw.b,
L
+
k■ I
y m In£,,.,,
m • I
3
+
K
L kL■ I
21.1
LL
I• I
a,k lnYi,, lny.b,
/•l k•l
/•!
+
L
L L
2
+ -
N
4>1 QTR1
+
I: e, PS,
+
}..YEAR
(2)
r•2
L
+
L [tlJ cos :
1
111
+
w 1 sin: 111 ]
I• I
L
L
I• I
k• I
L
L
+LL
[t,kcos(:111
+=.ti,)+
w 1*sin(: 111 +
=.ti,>]
L
+LL L
[w,m,cos(:,11
+
z.b,
+
=m11>
+
w,m,sin(zl,r
+
z.b,
+
z,,.,,)]
/•l k•l m•l
+
v,,,
where C, y, w, and E are as defined above. QTR is a set of dummy variables to indicate the quarter in which an
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observation operates (one for each quarter except the first), PS is a set of dummy variables indicating which
processing site is being observed (one for each site except the first), YEAR, which indicates the year of observation,
is included as a proxy for technological change, and z is logged output mapped into the interval [0.1 ·21t, 0.9·21t]
using a linear transformation (see Berger, Leusner, and Mingo [1995]). Note that the inefficiency portion of the
"error" term (u) in equation (l) has been replaced by the site-specific dummy variables in equation (2). To
improve the statistical efficiency of the estimates, equation (2) was estimated together with its corresponding input
share equations (derived via Shephard's lemma). The usual linear homogeneity and symmetry restrictions were
imposed prior to estimation.
Note also that the translog functional form, a second-order local approximation, is nested within equation
(2). If all of the 'ljJ and w coefficients are restricted to zero in equation (2), then the hybrid translog-Fourier model
reduces to the standard translog model. These restrictions were tested in the empirical analysis reported below.
Given that u,
?
0, the observation-specific constants can be normalized so that the processing site with the
lowest intercept is deemed 100 percent efficient (that is, u, = 0) and serves as the benchmark against which other
sites' efficiencies are assessed. This can be accomplished as follows:
Lei 0
then
u,
min;(0,),
0; - 0,
(3)
i
=
1. ... ,N.
Since the estimated cost functions are in log form, the measures of cost efficiency, which range from 0 to I, are
given by exp!-u,) = exp!-(0, - 0)) .
IV. Data
We estimated three cost function/cost share systems of equations. one for the operations of each payment system
considered: check. ACH. and Fedwire. Each of the data sets used in our analysis consists of 20 quarterly
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observations over the years 1990-94. 9 Data on total costs, output volumes, input prices, and environmental
variables are included for the 47 Federal Reserve check processing sites, 12 ACH sites, and 12 Fedwire sites. 10 The
total number of observations is 931 for check processing, 232 for the ACH service, and 240 for Fedwire. 11 Though
we used data from the individual check processing sites, the check results are aggregated to the District level in the
discussion of our findings. The primary data source used was the annual functional cost accounting reports
collected by the Federal Reserve's Planning and Control System (PACS). Since the purpose of PACS is to monitor
costs and to improve resource allocation within the System, the reported data should be fairly accurate; however.
some data errors are likely to be present. The use of a stochastic frontier should mitigate the effects of
measurement error. The PACS data were supplemented with data from various Federal Reserve surveys, Bureau of
Economic Analysis and Bureau of Labor Statistics price indexes. and pricing data from industry sources. 12
N.a Total Cost and Input Prices
Total costs for all three payments services were proxied by their activity production costs. which include direct and
support costs. but exclude imputed costs and certain overhead expenses. such as special District projects. The
processing cost of each payment mechanism is composed of payments for four inputs--labor (L), materials (M),
communications equipment and transit (7), and buildings (B). Table I reports the average share of total cost
attributable to each input over the 20 quarters for each of the three payments services.
9
We chose this penod for several reasons. First. the data series are all complete for this period. Second. the Monetary Control Act of 1980
required !hat full-cost pncing be introduced for each of the Federal Reserve's payments services. For ACH, full-cost pricing was only gradually
introduced and was not completed until 1985. By 1990 markets should have adjusted fully to MCA's full-cost pricmg requirement. Third, processing
me consolidanon could cloud !he effects of scale econonues: relanve to !he 1980s. little consolidation of Federal Reserve processing sites occurred
dunng our sample period. Fourth. Expedited Funds Availability (Title 6 of the Competitive Banking Equality Act [CEBAJ of 1987) may have
changed !he technology of check processing. By 1990, the Federal Reserve could talce return items for which they hadn't handled !he forward
processmg. Furthermore. all return items were to be in a new format that would allow increased automation of thetr processing. Finally. such
dramanc technological changes have taken place that a smgle cost function may be unable 10 fit a longer sample period adequately. Consequently, we
concentrate on !he most recent data available.
10
0ne processing
S1le
each for ACH and Fedwire services was excluded from the sample for reasons detailed below.
11
Not all processmg s11es were in operation for !he full 20-quarter sample period. One check-processing site ceased operations at the end of 1992
(eight quarters pnor to the end of the sample penod): another site operated for just one month of the fourth quarter of 1994 and was therefore dropped
for !hat penod. Thus, nine "site-quarters" are missing from the check service data. One of !he ACH processing sites also ceased operations at the end
of 1992. reducmg the number of ACH service observations by eight site-quarters.
12
Data construcnon parallels Bauer and Hancoclc. ( 1992). who provide details.
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The price of labor (PJ was constructed as the sum of expenditures on labor (including salaries,
retirement, and other benefits) divided by the number of employee processing hours. Based on cost shares, check
processing is the most labor-intensive payments service, due largely to the paper-based nature of the service and. to
a lesser extent, return items. ACH is much less labor-intensive than check processing. though some return items
continue to be initiated manually. Because most banks initiate transfers electronically, Fedwire is the least laborintensive of the payments services.
Due to the massive amounts of clearing data to track. all three payments services make heavy use of
materials, which consist of computers and data processing, office equipment and supplies, printing and
duplicating. and. in the case of check processing, check reader-sorters. The price of materials (PM) is given by a
Tornquist approximation to a Divisia price index. It was constructed from the service prices of supplies, machines,
and check reader-sorters. The service price of supplies (office equipment and supplies, and printing and
duplicating) was represented by the implicit price deflator for gross domestic product (GDP). The service price of
machines (computers and data processing) was constructed from cost-accounting expenditure data supplemented
with the implicit price deflator for office. computing. and accounting machinery. To construct a price for data
system support services (primarily used for in-house. product-specific software development), we utilized
expenditures for labor and hours worked in that area of each Reserve Bank. Unlike prices for other computer
hardware. those of check reader-sorters did not decline over the sample period. Therefore, a separate price index
for check reader-sorters was constructed using historical data from industry sources. For computer hardware and
check reader-sorters, an estimate of the service value. or price. of machines was constructed using a perpetual
mvcntory model derived by Hall and Jorgenson (1967). 13
Communications and transit expenditures consist of the costs associated with data and other
communications. shipping. and travel. Communications costs fonn the bulk of this cost category for ACH and
Fedwire. Better than half of Fedwire's costs are associated with this input category. due to the communications
equipment that is needed because most transfers are sent and received electronically. Check processing is the least
1
-'The Tomqmst mdex was constructed usmg the rates of growth m the pnces for each mput category. These rates of growth were weighted by the
average propomonate shares of matenals expenses anribuiable 10 each category over adjomrng periods.
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communications- and transit-intensive service. Most of its expenditures in this category are due to the costs of
flying paper checks around the country. The implicit price deflator for communications equipment purchases by
nonresidential producers was used for data and other communications expenses. The fixed-weight aircraft price
index for private purchases of producers' durable equipment was employed for shipping and travel expenditures.
The Tornquist approximation of a Divisia price index was calculated for transit (P 1 ), based on the expenditure
shares of communications and shipping and their individual price indexes.
Buildings have the smallest cost share among the four inputs, because the Federal Reserve does not
finance buildings; thus, interest expenses associated with the acquisition of fixed assets are not present in the
PACS's cost-accounting framework. Instead, interest costs are included in the PSAF used to set prices for Federal
Reserve payments services. The share of buildings is greatest for check processing. owing to the bulkiness of
check-sorting machines. The price of buildings (P8 ), measured as square-foot replacement costs adjusted by sitespecific depreciation rates, was constructed using cost accounting information from the PACS data and annual
replacement-cost indexes available from Means (1995).
!Vh Outputs and Environmental Variables
Check Processing
Check processing is a multi product operation consisting of forward items and return items. 14 Forward items <YFoR)
are much more numerous than are return items (vRrr), 15 hut have a much lower per-item processing cost. A
collection of other factors that may affect the cost of processing checks were included as elements of the
environmental vector.£. The number of endpoints (EP). locations to which checks are delivered. was included in
the cost equation together with its squared value. The item-pass ratio (IPR). the average number of times a check
must pass through a reader-soner. is a proxy of the check-sort pattern. IPR is a function of the number of
"pockets" on a reader-sorter. the number of banks for which a site processes checks. and the distribution of checks
1
'1'me-son ,terns (1.e .. checks that are fully prcsoned by hanks) were not included m the check processing output. nor were thetr production costs
mclude<l in the cost m"-<lsure.
1
7ne ratio of forward Items to return Items handled by the Federal Reserve was approximately 70: I over the sample period.
-IO-
I
across endpoints, as well as other factors. A dummy variable indicating whether IBM (IBM= 1) or Unisys (IBM=
0) machines were used at a site during each quarter was included to control for potential differences in
maintenance expenses. failure rates, and down times. Some sites process forward and return items separately;
other sites process them simultaneously. The latter method is likely more costly. A dummy variable was used to
indicate whether a site intermingled the two items (NTRMNGLE
=1) or processed them separately (NTRMNGLE =
0). Checks are processed at three different types of offices--District Banks, branches of District Banks. and
regional check processing centers (RCPCs). Since costs are likely to vary across these settings, two dummy
variables were included to control for office type. District Banks served as the reference group; RCPCs were
indicated by RCPC = I (0 otherwise); branches of District Banks were indicated by BRANCH= I (0 otherwise).
RCPCs have three potential cost advantages over District Banks: They were set up specifically to process checks.
they are typically located outside of the central business district. and. because they do not handle securities or
currency. their physical security costs are relatively low. Branches of District Banks are also likely to have cost
advantages relative to the District Banks: Branches do not offer ACH or Fedwire services nor do they house
monetary policy functions. Government checks are processed at just one site per district; a dummy variable.
GO\'CK. was included to indicate those sites that process government checks.
Site-specific figures that focus on transactions processed. rather than the number of payments, served as our
measure of output for the ACH service (V,1rn), 1° The number of ACH processing sites fell over the sample period;
hy 1993. only the 12 District Banks processed ACH items. During the period under study. the largest volumes
were handled hy the 12 District Banks and the Los Angeles branch of the San Francisco Federal Reserve Bank.
Thus. with the exception of the Los Angeles ACH site. we aggregate ACH data to the District level. Los Angeles
1s treated as a separate site because of its large volume of transactions. One of the 12 Districts was omitted from
our empirical analysis because the hulk of its transactions were processed by a private provider of ACH services.
16 ACH pavment, m111a1ed and received at the same processing site are counted as only one transaction. Payments panially processed at one site.
then 1ransm1ued to a sc:cond slle, are counted as transamons at both the transmining and receiving sites. Thus. the processing volume of ACH sites
exceeds the actual number of ACH payments made hy the system as a whole. Note that with a single processing site, volume processed would equal
the actual number of pavments transacted.
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The empirical analysis included three control variables to account for differences in ACH sites' processing
environments. These sites have some discretion over processing schedules for government items, which may
therefore be less costly to process than items processed for commercial customers. However, because government
items are concentrated within certain relatively short periods each month, they may cause peak-load problems that
would make them more costly than commercial items. In view of these considerations, the proportion of
government items (PG[) processed was included. As was the case for check processing, the number of endpoints
(EP) and endpoints squared (EP 2 ) were included. In this case, the number of endpoints refers to the number of
banks or processors receiving ACH payments information. Finally, the proportion of banks receiving electronic
payment information (PEER) was included. since nonelectronic delivery of information via computer tapes,
diskettes, paper, and so on, increases transportation costs. 17 By contrast, increased use of electronic networks for
infonnation delivery might give rise to greater scale efficiencies.
Fedwire
Output (_vFw) was measured as the total number of Fedwire funds transfers processed at each site. PACS contains
infonnation on the number of transfers that originated within each district, the number of interdistrict originations.
and the sum of total originations and interdistrict receipts. The number of intradistrict receipts could be derived
from these three numhers. Total transfers processed for each site were defined as the sum of originations (interand intradistrict) and receipts (inter- and intradistricl), which reflects the number of reserve account entries
,L'isociated with Fedwire funds tranfers. This measure of output is consistent with the current pricing strategy
employed for the Fedwire service. under which hoth sending and receiving banks are charged a fee for Fedwire
transfers.
One processing site employed a slightly different technology than the others (for example. it had a
mainframe computer dedicated to Fedwire). Furthennore. the site's output was more than twice as large as any
other processing site's. Because it wa-, the only site operating in the upper range of output, disentangling the
effects of scale economies and cost efficiency was problematic. Therefore. the cost function for Fedwire was
,-'Over tune. ACH transacnons have migrated
to vanous electroruc fonns (tapes. diskettes. and on-hne connections). As of July I. 1993, all
cornmernal I non-federal government I ACH transactions were delivered electrorucally: as of July I. 1994. all federal government ACH transactions
were also delivered electromcall~.
-12-
i
estimated both with and without this site in the data set to determine its impact on our findings.
Three environmental variables for each Fedwire site were included to control for differences across sites
that might affect costs. Extension time (EX]). the number of extra minutes a site had to remain open to clear all of
its daily transactions. may affect costs. 18• 19 The number ofFedwire customers is also likely to affect costs.
Unfortunately. quarterly data on the number ofFedwire customers were not available for the full period of study.
Instead, the number of accounts at each processing site was used as a proxy for the number of customers (CUSJ).']J.)
Note that this variable is similar to the number of endpoints used in the analyses of check and ACH processing.
The number of financial-institution accounts should be a good proxy for the number of Fedwire customers. since
there was a 0.98 correlation between the two variables during periods for which data on both were available.
Finally, the percentage of Fedwire transfers processed on-line (ONUNE) was included, since these transactions
were probably less costly than those processed off-line. (Note the similarity with the control variable PEER used in
the analysis of ACH transactions.)
IV.c Other Variables
Three final sets of variables used in the cost analysis were dummy variables to control for quarterly effects (QTR,,
i
=2.3.4 ), dummy variables for all but the first processing site (PS,, r =2, ... N), and a time trend (YEAR = 1,. .. ,5).
The site-specific dummy variables were included to allow for the measurement of cost efficiency using the within
frontier cost model. The time trend was included to capture the effects of technological change that may have
occurred over time. Given the relatively short time period, a more elaborate model of technological change was
not practical.
i s1 ;n1ike the other environmental vanable. the actual value of EXT was used rather than its natural log. This was due to the fact that some sites
used no ex1ens10n time.
1
'Extension lime is hkely to be needed to clear transactions on peak activity days. However, extension time also may be an endogenous measure
of processmg-sne effie1ency: A less efficient site may need extension lune 10 settle the same number of 1ransacttons that an efficient site could settle
dunng 11s normal hours of operauon.
~ile the number of customers setved by each processmg site will probably affect costs, the composition of each site's customer base is likely to
he more 1llummatmg. For example. the number of customers by connection type (dial-up, leased-line, multi-drop, etc.). the proponion of low volume
customers. or the geographic dispersion of customers are all factors that future research might consider.
-13-
i
V. Results
The parameter estimates and their t-statistics for the hybrid translog-Fourier frontier cost functions for the check
and ACH services appear in tables 2 and 3, respectively. Though the nested translog fonns of the hybrid translogFourier cost frontiers were rejected for all three payments services,21 our Fedwire results (tables 4a and 4b) are
based on the nested translog frontier cost function. For the check and ACH services, the hybrid translog-Fourier
models fit the data well. most signs being as expected, and most parameter estimates being statistically significant.
However, the hybrid translog-Fourier results for Fedwire violated monotonicity: Predicted costs fell as output
increased in some ranges. In effect, the hybrid model was too flexible a functional form. as it allowed a violation
of a fundamental property of the cost function given by economic theory. Since we choose economic theory over
statistical considerations. the (nested) translog is our preferred model for Fedwire. Furthermore. due to the strong
influence of one particular processing site (PS2) on the Fedwire models, two sets of results are reported. The first
set (table 4a) includes all 12 processing sites; the second set (table 4b) excludes site PS2.
V.a Unit Cost, Marginal Cost, and Scale Economies
We are interested in the unit cost (based on activity production costs), mar~inal cost. and scale economies
associated with each of the three payment services offered by the Federal Reserve. The scale economies are
represented hy the cost elasticity. which is defined as the percentage increase in cost for a 1 percent increase in
(one of the) output(s):
cllnC(w.v.£.1:~)
oln Y,
(4)
and. in the case of check processing. the ray cost elasticity. which is given hy the following expression:
11
For all three payments services. the null hypothesis that all of the sine and cosine coefficients were equal to zero was firmly rejected. For check
processmg. F(3662. I 8) = 14.57 (Prob> F: 0.000 I): for ACH transactions. F(899 ,6) = 4.24 (Prob> F: 0.0003 ); for Fedwire (with PS2). F(884.6) =
8.69 (Prob> F: ().()()OJ). Full translog results are available from the authors upon request.
-14-
i
2
11
E 11;-
(5)
,• I
The unit costs, marginal costs, and cost elasticities and their 95 percent confidence intervals for check, ACH, and
Fedwire services are given in tables 5, 6, and 7. respectively; table 5 also shows the ray cost elasticity for check
processing. For comparison purposes. tables 5 and 6 contain the results for both the hybrid translog-Fourier cost
systems and the nested translog models for the check and ACH services. Table 7 contains the translog results for
Fedwire. both with and without PS2.
The weighted average cost of processing a check across the 47 sites is just under 2 cents per check. 22 The
marginal cost of forward items. about 1.4 cents on average. is substantially less than that of return items, 38.6 cents
on average. corroborating the view that return items are much more costly to process than forward items. 23 The
returns to scale for the joint provision of forward and return items (ray cost elasticity) averages .97 for the 47
processing sites. implying that a one percent increase in both outputs would increase costs by just .97 percent. The
confidence intervals for the cost elasticity suggest that 12 processing sites have insufficient volume to achieve scale
efficiency and that three operate with scale diseconomies: the remaining 32 sites are characterized by constant
returns to scale. indicating that they operated very near the scale efficient rate of output. Figure 1 plots the average
cost curves based on the unit costs at the sample means of the check processing sites for both the hybrid translogFourier and translog models. Note that the two plots are quite similar. The figure reveals that unit cost drops
dramatically a,; output initially rises. but quickly flattens out. 14
Our findings on scale economies for Federal Reserve check processing services differ from those of
~ecall that check processing 1s a multi product activny--both forward and return items are processe<i. However, the share of forward items is
more than 98 percent: therefore. umt cost is calculate<i on the basis of forward items only. This simplification should have a negligible effect on the
measure of umt cost.
¾e hybnd translog-Founer cost function results exhibit a few "local" violations of monotonicity; that is, some point estimates of marginal cost
are negauve. How,-ver, these violations only occur for very small processing sites. Overall. the hybrid translog-Fourier results are very similar to
those of the neste<i translog model. These problems are not as severe as for Fedwtre, where there were "nonlocal" (occurring over a broad range of
output) v10la11ons.
;,,,~ote the inh,-rent wav,- forms embedded in the hybrid translog-Founer functional form as a result of the sine and cosine terms. This is the source
of the local v10lauons of mono1omc11y for the smallest processing sites.
-15-
i
Humphrey (1980, 1981a, 1984, 1985). which were based on a single-output model for earlier time periods, and
from those of Bauer and Hancock (1993), who estimated a multiproduct cost function over the period 1979-90. It
appears that constant returns to scale, rather than increasing returns. characterize the operation of all but the
smallest. and perhaps the very largest, processing sites. The difference between our results and those of previous
studies may be partly due to our choice of functional form. First, because the hybrid translog-Fourier model allows
for a "flatter" function. the range of constant returns to scale may be broader than for the functional forms used in
earlier studies. Second, the standard-error terms for some of the hybrid translog-Fourier's coefficient are large. so
statistically the range of constant returns to scale is broader. The hybrid translog-Fourier and the (nested) translog
point estimates of cost elasticity were roughly similar. However, the standard errors of the Fourier estimates were
much larger than those of the translog estimates. making it less likely that a null hypothesis of constant returns to
scale would be rejected.
The weighted average of the unit cost of an ACH is 1.7 cents for the 12 Federal Reserve processing sites
in our sample: marginal cost averages less than a penny (0.9 cents) per transaction. The mean level of the cost
elasticity for ACH is .48. indicating that the Federal Reserve's ACH service is characterized by increasing returns
to scale. Plots of the hybrid translog-Fourier and translog average cost curves for ACH appear in figure 2. which
also reveals that increa<;ing returns exist for most of the observed output levels for ACH services provided by the
Federal Reserve. While the average cost curve for the hybrid translog-Fourier model appears to rise at the highest
level of output. this finding is ba<;ed on just one processing site whose output is significantly higher than that of any
other site.
Interestingly. Humphrey (1981h. 1982. 1984. 1985) found roughly the same magnitude of economies of
scale for Federal Reserve ACH services a, we did. even though the volume of output in our sample period is much
greater than in his. The ACH results are also broadly consistent with those of Bauer and Hancock ( 1995a).
The weighted average unit cost of a Fedwire transaction is 24.2 cents for the 12 processing sites in the
data set. As mentioned above. site PS2 exerts a strong influence over the estimation results. The average marginal
cost is 26.5 cents when PS2 is included. but just 20.4 cents when it is excluded. For the full sample. the cost
elasticity averages l. 14: the two smallest Fedwire sites are found to experience scale economies. the largest site
-16-
I
(PS2) experienced scale diseconomies (with a cost elasticity of 1.70); all other sites appear to operate under
constant returns to scale. With PS2 excluded from the analysis, the cost elasticity averages just 0.79. This cost
elasticity indicates that the 11 remaining sites experienced scale economies, though none of the cost elasticities are
statistically significantly different from 1 (constant returns to scale). The biggest differences in the cost elasticities
across the two sets of estimates are for the smallest and largest sites; for the medium-sized sites, all the results are
roughly similar. The average cost curves associated with the two translog models estimated for Fedwire. one with
and one without PS2. appear in figure 3. which also contains a scatter plot of_the raw data. The figure conveys the
influence of PS2. which is represented by the cluster of data points at the highest output levels. The right half of
the average cost curve is based solely on PS2. making it unlikely that scale economies and cost efficiency have been
correctly disentangled for PS2. If PS2 is cost efficient. then diseconomies of scale exist for the highest output
levels: however. if PS2 is cost inefficient. then it is likely that constant returns to scale--or possibly even scale
economies--exist throughout the observed range of output levels. Intuitively. the latter possibility is more
appealing. Like ACH. Fedwire would seem to be the type of service that would offer scale economies. since both
are highly dependent on communications and computers. resources for which unit costs are likely to decline as
volume increases.
Our Fed wire results are similar to those of Humphrey (1982. 1984 ). which seemed to suggest relatively
slight scale economies in the Fed wire services. Humphrey ( 1982. 1984) found that 98 percent of all Fedwire
transfers took place in offices with constant returns to scale. However. he employed only cross-sectional data and
included the largest processing site in his model. Given the large jump in volume between the largest and nextlargest site. his model. like ours. would have had trouble differentiating scale economies and cost efficiency.
Without PS2. we find ahout the same level of scale economies for Fedwire as did Bauer and Hancock (1995b). who
employed data from 1988 to 1992.
\'.h Em·ironmemal Variables
Each of the estimated frontier cost systems contains a number of environmental variables to control for differences
-17-
i
in the operating characteristics across processing sites. All of the environmental variables have statistically
significant effects on the cost of check processing. The number of endpoints (EP and EP 2) is found to have a
quadratic relationship with cost. Following an inverted-U shape. cost initially rises as the number of endpoints
increases. but eventually falls as the number of endpoints increases. Predictably, cost increases with the number of
times a check must pass through a reader-sorter (given by the item-pass ratio [IPR]). The processing sites that use
IBM equipment (IBM= I) had higher costs than those using Unisys equipment. However, this finding may result
from differences in geography rather than differences in machinery. Most of_ the population of the U.S. is located
in Districts that use Unisys equipment: most of the area of the U.S. is located in Districts that use IBM equipment.
Thus. IBM may be serving as an indirect proxy for transportation costs. The type of site where checks are
processed also has a statistically significant effect on cost: as a group. both RCPCs (RCPC = I) and branches of
District Banks (BRANCH= 1) have lower costs than did the District Banks. The intermingling of forward and
return items is found to be more costly than the separate processing of the two. Finally, sites that processed
government checks appear to have higher costs than those that did not. This finding warrants further study. It
may suggest that there are diseconomies of scope between the processing of government checks and private checks:
however. it could also result from an accounting anomaly.
For ACH transactions. the coefficient on the proportion of government items (PG/) processed is positive.
hut is not statistically significant. This suggests that either the benefit of having some discretion regarding when to
pnx:ess these items halances with any peak-load problems that they may create. or else that neither of these
2
considerations has any noticeable effect on cost. The nurnhcr of endpoints (EP and EP ) has a negative
relationship with cost--the larger the nurnhcr of endpoints. the lower the cost of carrying out ACH transactions.
The final environmental variable. the proportion of hanks receiving their payment information electronically
(PEER). docs not have a statistically significant effect on cost. possibly hecause all banks were required to receive
data electronically by the end of the sample period. leaving relatively little variation in this variable.
For Fedwire services. there is no statistical evidence that any of the three environmental variables (CUST.
EXT. ONUNE) affects processing costs. The lack of significance for ONUNE probably results from lack of
variability in the proportion of transfers processed on line; during the sample period. nearly all transfers were
-18-
i
processed on line.
V.c Cost Efficiency
Site-specific and summary statistics for the three payments services' cost efficiency scores are reported in table 8
for all models. The average levels of cost efficiency for the check and ACH services are 68.1 percent and 59.4
percent, respectively, for the hybrid translog-Fourier frontier. As discussed above. the largest Fedwire site has a
strong influence on the estimated scale economies and cost efficiencies associated with this service. The average
cost efficiencies of the Fedwire service are 58.9 percent when PS2 is included, and 66.0 percent when it is excluded
from the analysis. The measures of cost efficiency indicate the proportion of observed cost that would have been
expended had all the sites operated on the best-practice cost frontier defined by the site with an efficiency score of
l. At constant input prices. and given the linear homogeneity of the cost function. the efficiency measures also
may be interpreted as the proportion of observed input quantities needed to produce the observed level of output
relative to the best-practice performance. Comparing the consequences of unrealized scale economies and the
presence of cost inefficiencies, our findings for check processing and Fedwire are similar to that of Ferrier and
Lovell ( 1990) and Berger and Humphrey ( 1991) with regard to banks: The effects of cost inefficiencies dominate
those of scale economies. This is especially true for check processing where scale economies have been exhausted.
Fed wire. on the other hand. is characterized by substantial scale economies as well as substantial cost inefficiency.
For ACH. we find that the effect of scale economies is slightly greater than that of cost inefficiencies, though both
are substantial.
The relatively low levels of average efficiency indicate a great deal of dispersion in the ability of
processing sites to convert their inputs into services. The inefficiency may result from principal-agent problems.
Since there is no market for corporate control to "discipline" managers at Federal Reserve processing sites.
monitoring costs will be higher at the Federal Reserve than at publicly traded corporations. Furthermore, the
Federal Reserve lacks two important monitoring devices available to publicly traded firms (Puttennan [ 1993]).
First. for publicly traded firms. the value of tradeable shares serves as an indicator of incumbent managers'
perfonnance. Second. interest rates that private firms pay to finance expenditures indicate a project's perfonnance
-19-
I
or prospects. Since the Federal Reserve does not borrow funds to finance the purchase of buildings. this signal is
not available to assess managerial performance. Alternatively, the high degree of market concentration (less for
check processing than for the ACH and Fedwire services) and attendant market power within the markets for these
payment services may reduce the competitive pressure on processing sites to perform as efficiently as possible.
Instead of realizing higher "profits," the processing sites may indulge in the "quiet life" that market power affords
(Hicks [1935]). Berger and Hannan (1994) found evidence of the "quiet life" in commercial banking. concluding
that the efficiency cost of market concentration was several times greater than the social cost as measured by the
welfare triangle. However. mergers and changes in technology give the Reserve Banks increasing competition
from private providers of payment services. Finally. despite the inclusion of several environmental variables.
heterogeneity across processing sites may not have been adequately modeled. The measured "inefficiency" in this
case would reflect operating/environmental differences across sites. not true inefficiency. As Stigler (1976) noted.
measured inefficiency may result from not incorporating the right variables or the right constraints in the analysis,
or from failing to consider the correct economic objective of the organization under analysis.
Table 9 reports the rank correlation coefficients for the efficiency scores of the check, ACH, and Fedwire
operations. The efficiency rankings based on the two different models estimated for each of the three payments
services are all highly correlated. However. the efficiency rankings across the three payments services are all
negatively correlated. though not with statistical significance. Thus, while the operating performances of
processing sites are widely scattered. there is no evidence that the efficient operation of one payment service is
related to the efficiency with which the other services are provided.
Interestingly. the use of IBM. as opposed to Unisys. check processing equipment is associated with higher
costs based on the estimated parameters of the hybrid translog-Fourier frontier cost system. Indeed the mean level
of cost efficiency is 9.2 percent higher for IBM-based processing sites. This suggests that the cost disadvantage of
using IBM equipment is partially offset by other factors.
\'.d Techrwlogical Change
The rate of technological change (more properly. the rate of cost diminution) is modeled by including a time trend
-20-
i
in the frontier cost functions estimated for each payment service. Thus, disembodied technological change, which
manifests itself by shifting the cost function, is implicitly assumed. The technological change coefficients for all
three payments services are shown in table 10. Note that the results across the two models estimated for each
payment service are very similar. The cost of ACH transactions diminished at an average rate of about 11 percent
per year over the 1990-94 period. Fedwire also enjoyed technological gains during this time, as its cost diminished
at an annual rate of about 6 percent. Check processing, however, appears to have suffered the fate of technological
"regress." as costs rose about 1.7 percent per year over the period. A number of factors offer likely explanations.
First. and probably most important, processing volume declined at many sites over the sample period; cost
reductions will almost certainly lag volume declines, since sites require time to shed their fixed costs. Second. the
"quality" of checks processed declined over the period, because a high proportion of "high quality" check items
(such as payroll checks and Social Security items) migrated to ACH. The remaining, "lower-quality" items are
likely to involve greater processing costs. Third. the quality of service provided by Federal Reserve processing sites
increased over the sample period. For example. magnetic ink character recognition (MICR) information services
were added. Because the output measures are not adjusted for quality. the observed regress may reflect costs
associated with capital-intensive quality improvements. Fourth. Federal Reserve Districts were changing to the
new Funds 5.0 application during 1994 and 1995. ~ About half of the Districts made the conversion in 1994, the
last year of our study. Costs were probably increased by conversion efforts and experimentation with the new
technology to determine how to use the available advances most effectively (in other words. sites had not moved
very far along the learning curve). 16 The lack of a me,L'>ured change in output to accompany the cost increase
associated with the new technology would result in the appeara11ce of regress.
\ .e Decompositio11
The unit cost for each payment service varies substantially across processing sites (see the second column of tables
15
In addt110n. the \1mneapohs Federal Reserve 1mplemen1ed imaging software in 1994.
""An altemauve model thal employed dummy vanables to indicate the year of operation rather than the variable YEAR= 1.2.3.4,5, produced the
following results 1990. O; 199 I. -4.5: 1992. 0: 1993.2.9; I 994. 6.1. Thus. technolog1cal "advance" is observed in 1991. but "decline" is observed in
1993 and 1994. These results lend suppon to our explanauons for the technological "regress" found for the full sample penod.
-21-
i
11, 12, 13a, and 13b). Unit cost is a useful summary measure of operating performance and is thus interesting in
its own right. However. the sources of variation in unit cost may be of even greater interest. An advantage of the
functional forms used is that differences in unit cost can be traced back to their "source" by examining logarithmic
differences between a site's unit cost and the unit cost at the mean of the sample data (see Bauer [1993]). 27 There
are six potential sources for cost differences in our analysis. First, differences in cost efficiency occur across sites.
Some sites operate on the best-practice cost frontier, while others do not. Ceteris paribus, sites that lie above the
cost frontier will have higher unit costs. Second, scale economies may account for cost differences. Other things
being equal, a processing site that is too small to fully exploit scale economies will suffer a cost disadvantage.
Third. sites may face disparate input prices. Those with higher input prices will have higher unit costs, other
factors held constant. Fourth, a site's environment may be more or less advantageous compared to another site's.
Holding other influences constant. sites with a more hospitable processing environment will experience lower unit
costs. Fifth. there is a residual category that comprises all of the interactive terms of the hybrid translog-Fourier
cost function. Fortunately. these "interaction effects" account for less than I percent of any of the unit cost
differentials. Finally. there are random effects.
To discern the sources of unit cost variation. we form the (log) ratio of a site's mean cost over the sample
peri{xl to the cost at the mean of the sample data:
l
(C, / 5',)
In - - <t I 5' l
I
=
lI
IC(5',. "·,.
E, )·exp(E,)
In - - - - - - - - - In
5',
C(v.· "'· E)·exp(E)
l
.
(6)
_v
where the terms with the subscript i represent site-specific means and the other terms represent overall sample
means. Using the cost function defined in equation (2). the percentage difference between the mean unit cost of a
processing site and the unit cost at the mean of the data can be written as: 28
7
Loganthms have the property that, close to zero. they can be interpreted roughly as percentages. For example, a logarithmic difference of 0.1
converts to roughly a I fl percent difference. For the exact percentage. you would need to calrulate ( I - exp! 0.1 ) ).
:
1o simplify notation, the tngonometnc Founer terms do not appear in (7). They were. however, included in the empmcal decompositions
reported helm•
-22-
I
l
i
+
+
+
[aY(lny, - lny)
:E
K
[
+
½a:YY{(lny,
Pk(lnwki - lnw1 )
+
k•I
[f
[t
-
lny 2 )
-
(lny 1 -lny)}]
.!.:E
:E P1/lnwkilnwj,
2
K
K
- lnwklnw)
l
k•l J•I
t\(lny;lnwb - lnylnw1
k•I
+
2
(7)
)l
,
Ym(ln£m, - ln£m)l
m•l
+ [ E,
- E]
where the hracketed terms on the right-hand side of equation (7) are the efficiency effects. scale effects. input
price effects. interaction effects (between processing volumes and input prices), environmental effects, and random
dfects. respectively. The decomposition of cost differences into the first five sources is reported in tables 11. 12,
and 13 (a and h). for the check. ACH. and Fedwire operations. respectively.
For check processing. cos! efficiency appears to be the largest single factor in explaining unit cost
differences. hut scale economies. input prices. and the operating environment also account for some large cost
difkrcnccs (sec tahle 11 ). In general. these results are very similar to those reported by Bauer ( 1993), who used
data for 1983-90. Our higgest departure from Bauer (1993) is that environmental effects play a larger role for
more pnx:essing sites in our findings. For example. the coefficient on the IBM indicator variable rose from Bauer's
es11mate of 0.0925 to 0.205: thus. Unisys sites appear to have a significant cost advantage.
Cost efficiency and output effects drive the results for ACH services (see tahle 12). The existence of largescale economies places smaller processing sites at a significant cost disadvantage. However, it is worth noting that
the logarithmic differences for the cost efficiency and output effects usually take opposite signs. implying that the
less scale-efficient sites make up for this disadvantage hy being more cost efficient. and vice versa. Given that data
processing inputs. which are priced nationally. account for ahout 75 percent of the costs of this service, the
processing sites show relatively little difference on this score.
-23-
i
Two sets of results are reported for Fedwire, one which includes PS2 in the analysis (table 13a) and one
which excludes it (table 13b). The first set of results indicates that PS2's superior cost efficiency appears to offset
its large disadvantages of scale. Recall, however, that the relative effects of scale economies and cost efficiency on
PS2's observed costs is suspect, given that PS2 is the sole source of data for the upper third of the observed range of
output levels. In general, the results for Fedwire are similar to those for ACH services, though environmental
factors appear to account for a bit more of the observed unit cost differences with Fedwire. As with ACH services,
the penalty for failing to fully exploit scale economies can be large. The input price effect accounts for a very small
share: again, this is not surprising, given that data processing inputs account for more than 85 percent of Fedwire
costs.
VI. Conclusions
We estimate cost functions for the check. ACH, and Fedwire services provided by the Federal Reserve to derive
estimates of marginal costs. scale economies. cost efficiency. and technological change over the pericxi 1990-94.
There are wide differences in performance across processing sites. even after controlling for volume. input prices.
and various environmental variables.
Scale economies appear to have been exhausted for all but the 12 smallest check processing sites,
indicating that some additional consolidation may be in order. particularly if volume declines are projected to
continue. However. one cannot decide whether it would be wise to reallocate volume among processing sites. or
even to close some sites. hy looking at costs alone: one must also consider the demand for check processing
services. For example. hy locating closer to their customers. processing sites can offer higher quality service.
receiving checks later and delivering them earlier. Closing a processing site could lead to lower quality service
and loss of volume. Customers may be more than willing to pay the higher processing costs at these suboptimally
sized sites. Of course. the move towards electronic check presentment and imaging make the processing site's
location much less important. All of the ACH processing sites were found to have statistically significant scale
economies. which appears to justify the Reserve Banks' plan to consolidate to one processing site with one backup
-24-
•
I
site. The decision to consolidate the processing of all but the largest Fedwire site receives some support from our
findings, as there may be significant scale economies throughout the relevant range of output.
There appears to be a great deal of dispersion in the operating performances of the various processing sites
for all three payments services considered in this paper. This suggests that the costs of providing these services
could be reduced considerably if all sites were to move to the best-practice frontier. No single site's performance
dominated across services. In fact, there appears to be no tendency for a site's cost efficiency in one service to spill
over to other services.
The electronic services (ACH and Fedwire) have both experienced rapid technological change over the
last five years. while check processing costs have risen over that period. The first finding is consistent with the
rapid decline in the price of computer and communication equipment. key inputs into electronic services. Check
processing, on the other hand. is largely dependent on labor and the speed at which paper checks can be read
through check reader-sorters. neither of which has benefited much from the productivity improvements caused by
recent technological change.
Clearly. more empirical research is needed on how new technologies affect the efficiency of the payments
system. For example. scope economies among the various services. particularly between ACH and Fedwire
transfers. could also be important in determining the scale efficiency and optimal product mix for payment-service
providers. Such scope economies could enable many more suppliers to operate efficiently and to reduce the real
resource costs associated with processing payments. Finally. in order to construct a pricing mechanism that
enwurages efficiency in the payments system and still recovers costs. the demand side of the payment-service
market--including cross-elasticities between payment instruments--needs to be more fully understood.
The emergence of new payment instruments and nationwide branching will greatly increase the
competitive pressure on the Federal Reserve Banks. and they will need to compete both on quality and price in
providing payment services.
-25-
I
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Bauer. Paul W. "Efficiency and Technical Progress in Check Processing." &onomic Review, Federal Reserve
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_ _ _ _ . Allen N. Berger. and David B. Humphrey. "Efficiency and Productivity Growth in U.S. Banking, in
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C.A. Knox Lovell. and Shelton S. Schmidt. pp. 386-413. Oxford: Oxford University Press. 1993.
_ _ _ _ . and Diana Hancock. "The Efficiency of Federal Reserve Check Processing Facilities." Finance and
Economics Discussion Series (FEDS) no. 214, Board of Governors of the Federal Reserve System (1992).
_ _ _ _ .and _ _ _ _ . "The Efficiency of Federal Reserve Check Processing Facilities." Journal of
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-29-
Table 1: Cost Shares for Payment Services
Check
ACH
Fedwire
Labor
0.493
0.213
0.139
Materials
0.275
0.408
0.320
Communication
and Transit
0.170
0.354
0.523
Building
0.062
0.025
0.019
Source: Authors' calcularions.
I
Table 2: Hybrid Parameter Estimates for Check Processing
Intercept
lnJFOR
(hlYFoR)
2
myFoR lnwL
IJtyFOR lnWM
lnYFoR lnws
lnYFOR lnw,IJtJFOR lnyRET
lnyRET
(hlyRET)2
lnyRET lnWL
IJtyRET lnWM
lnyRET lnws
ln y RET ln W,COS(ZFoR)
sin(ZFoR)
cos(2zFoR)
sin(2zFoR)
cos(3zFoR)
sin(3zFoR)
cos(zRET)
sin(zRET)
cos(2zRET)
sin(2zRET)
cos(3zRET)
sin(3zRET)
COS(ZFOR+ZRET)
sin( ZFoR+zRET)
cos(2zFOR+zRET)
sin(2ZFoR+ZRET)
COS(ZFoR+ 2zRET)
sin(ZFOR+2zRET)
Year
Qi
Q1
Q4
IJtwL
lnwM
lnw8
hlWr
ht/PR
IBM
lnEP
Parameter Estimate
14.878
-1.262
-3.934
-0.042
0.004
-0.011
0.049
-0.120
0.432
1.201
0.071
-0.022
0.010
,-statistic
19.88
-2.63
-2.71
-6.63
0.65
-6.89
12.35
-2.13
LSO
-0.060
1.83
14.27
-4.18
7.56
-18.78
2.166
-0.501
0.480
-0.068
0.183
0.124
-0.935
-0.314
-0.152
-0.072
-0.118
-0.072
-0.098
-0.l 15
-0.143
-0.237
0.146
0.112
0.017
-0.017
-0.029
-0.054
0.505
0.271
0.063
0.161
0.157
0.205
0.091
-3.77
3.61
-1.34
5.14
5.00
-1.49
-3.17
-1.31
-1.82
-3.65
-2.91
-2.18
-2.53
-3.40
-4.85
3.74
2.28
6.56
-2.15
-3.51
-6.60
248.74
126.47
119.82
127.60
3.70
6.10
7.66
3.04
i
Table 2: Hybrid Parameter Estimates for Check Processing (continued)
(ln£P)2
(lnwL) 2
lnWtlnWM
lnWtlnW9
lnwtlnWr
(lnwM) 2
lnw.,lnw9
lnwMlnWr
(lnws>2
lnw9lnWr
(lnWr)2
PS2
PS3
PS4
PSs
PS6
PS1
PSs
PS9
PSw
PS11
PS12
BRANCH
RCPC
t-.'TRMNGLE
GOVCK
Parameter Estimate
-0.061
0.085
0.024
0.013
-0.122
-0.003
0.004
-0.025
0.001
-0.018
0.165
-0.086
-0.229
-0.223
-0.077
-0.457
-0.252
-0.475
-0.136
-0.246
-0.673
-0.394
-0.055
-0.088
0.122
0.034
Source: Authors' calculations.
r-statistic
-9.96
7.53
3.37
3.12
-12.46
-0.38
.1.65
-4.86
0.19
-3.42
13.66
-2.43
-4.51
-10.74
-4.25
-19.36
-9.94
-10.62
-2.85
-5.48
-12.50
-10.10
-4.11
-5.50
5.26
2.77
i
Table 3: Hybrid Parameter Estimates for ACH Processing
lnw.wlnwa
Parameter Estimate
12.670
0.450
4.677
-0.130
-0.070
0.010
0.010
0.210
0.400
0.030
0.360
-0.010
-0.030
0.000
0.030
-1.170
-0.070
-0.180
-0.010
0.000
0.000
-0.010
0.020
-0.010
-0.010
0.020
0.()00
In wMln »'r
(lnwB)"
-0.()40
0.()1()
lnwBlnwr
0.010
0.()40
Intercept
JnJACH
(lnYACH)
2
ln.EP
(ln.EP)2
PEER
PG/
lnwl
IDWM
IDWB
lnw-r
IDYACH IDWL
lnyAcH lnwM
lnyACH lnwB
ffiYACH illl-l'f
cos(:Arn)
sin(:Arn)
cos(2:Arn)
sin(2:AcH)
cos(3:Arn)
sin(3:Arn)
<mwd
lnwLlnW.w
lnwLlnwe
IDWLID»'r
(lnwM)"
(lntt'r}"
Q2
Q_,
Q4
YEAR
PS 3
PS4
PSs
PS6
PS?
PS8
PSQ
PSw
0.010
0.000
0.000
-0.l 00
-0.410
0.030
0.260
0.418
0.474
0.000
0.033
0.149
t-statistic
11.65
1.39
0.96
-2.26
-1.05
0.23
0.06
65.37
84.79
49.07
59.21
-0.78
-2.08
0.72
2.06
-0.92
-0.36
-0.79
-0.20
0.08
-0.04
-0.68
2.56
-8.51
-0.71
1.00
-1.47
-1.62
1.89
1.83
1.32
0.39
-0.06
-0.08
-4.10
-7.71
0.35
2.52
3.81
3.73
0.01
0.57
1.33
Table 3: Hybrid Parameter Estimates for ACH Processing (continued)
Parameter Estimate
PS11
PS12
PS13
Source: Authors' calculations.
t-statistic
0.223
3.27
0.418
-0.124
4.16
-2.27
i
Table 4a: Translog Parameter Estimates for Fedwire (with PS2)
Intercept
lnyFED
(lnYFED)
2
lnwL
lnwM
JnwB
inWr
lnYFED InwL
lnyFED lnwM
lnyFED lnwB
lnyFED lnw.,<mwd
JnwLJnWM
JnwLJnWB
JnwLinWr
(JnwM)2
JnwMlnWB
JnwMlnWr
(JnwB) 2
lnw8 lnw7
<mwd
YEAR
lnONUNE
lnCUST
EXT
PS2
PS 3
PS4
PSs
PS 0
PS7
PSx
PSo
1.219
0.837
0.549
0.137
0.334
0.021
0.509
-0.029
0.029
0.006
-0.006
0.095
0.127
-0.002
-0.220
0.306
-0.013
-0.421
0.007
0.008
0.633
-0.056
2.494
0.144
0.000
-0.798
-0.202
-0.571
-0.211
-0. l 05
-0.171
-0.173
-0.041
0.12
3.33
2.76
58.28
47.03
39.85
64.99
-6.25
2.45
5.85
-0.46
5.58
4.84
-0.53
-6.08
3.31
-1.81
-4.07
1.77
0.84
5.03
-4.09
1.13
0.66
1.52
-1.88
-1.66
-6.04
-1.75
-0.70
-0.68
-0.63
-0.13
-1.00
0.76
PS12
-0.226
0.136
-0.461
Q2
Q,
Q4
-0.043
-0.063
-0.072
-1.83
-2.49
-2.75
PS1t,
PS 11
Source: Authors· calculations.
-1.91
i
Table 4b: Translog Parameter Estimates for Fedwire (without PS2)
Intercept
lnyFED
2
(ITIYFED)
lnwl
lnwM
lnw8
lnw-,lnYFED lnwL
lnYFED lnwM
lnyFED lnwn
lnyFED lnw,(tnwd
lnwLlnWM
lnwllnwn
lnwLlnw,(lnwM) 2
lnwMlnwn
lnwMlnwr
(lnw8 ) 2
lnwelnw,(lnw,-)2
YEAR
lnONUNE
lnCUST
EXT
PS3
PS4
I'Ss
PS0
PS7
PSR
PS4
PS1n
PS11
PS12
Q2
Q,
Q.
Source: Authors· calculations.
1.145
0.758
0.151
0.139
0.320
0.019
0.523
-0.029
-0.025
0.001
0.052
0.094
0.107
-0.004
-0.197
0.421
-0.009
-0.518
0.003
0.011
0.704
-0.064
2.501
0.134
0.0002
-0.209
-0.574
-0.224
-0.095
-0.()45
-0.083
0.(149
-0.230
0.121
-0.262
-0.()45
-0.065
-o.mm
0.11
2.79
0.53
53.95
44.62
39.50
66.49
-4.66
-1.55
1.13
2.84
5.22
3.78
-1.08
-5.18
4.40
-1.43
-4.90
0.81
1.33
5.50
-4.46
l.10
0.59
l.68
-1.66
-5.88
-1.79
-0.61
-0.17
-0.29
0.15
-0.98
0.65
-0.99
-l.76
-2.40
-2.87
Table 5: Estimates of Unit C'osts. Marginal C'osts, :md C'ost Elasticities for Check
Translog
Hyhrid
Processing
Site
SI
S2
S3
S4
S5
S6
S7
S8
S9
SIO
S 11
Sl2
Sl3
Sl4
S15
Sl6
S17
Sl8
Sl9
S20
S21
S22
S23
S24
S25
S26
S27
S28
S29
S30
S31
S32
Unit Cost
0.015
0.020
0.013
0.026
0.021
0.020
0.019
0.030
0.019
0.019
0.022
0.014
0.022
0.021
0.021
0.016
0.019
0.024
0.022
0.018
0.017
0.013
0.028
0.022
0.014
0.016
0.028
0.ol8
0.021
0.014
0.016
0.021
Marginal Cost
Return
Forward
0.0 IO
0.013
0.009
0.014
0.()()9
0.019
0.013
0.014
0.012
0.016
0.018
0.{J09
0.012
0.013
0.019
0.0 I 5
0.011
-0.0 I 3
0.024
0.010
0.010
0.009
0.026
0.014
0.014
0.013
0.020
0.007
0.005
0.006
0.008
0.019
0.565
0.515
0.257
0.618
-0.056
-0.597
0.153
0.615
0.402
0.261
0.183
0.491
0.719
0.596
0.192
0.542
0.264
0.550
-0.239
0.352
0.224
0.486
0.207
0.290
0.149
-0.085
0.243
-0.044
-0.047
0.258
0.010
0.681
Cost Elasticity
Upper
Lower
Overall
l.lfd
1.060
0.903
0.891
0.399
0.696
0.811
0.877
0.968
0.979
0.937
1.()4)
1.065
1.178
1.054
1.237
0.777
-0.276
1.()49
1.014
0.826
1.159
1.030
0.915
1.065
0.779
0.970
0.316
0.188
0.662
0.510
1.165
1.529
1.192
1.235
1.038
0.556
0.958
1.020
1.130
1.067
1.236
1.211
1.173
1.213
1.350
1.147
1.510
0.936
0.554
1.576
1.386
1.007
1.557
1.146
1.172
1.370
0.973
1.544
0.911
0.815
0.890
0.814
1.772
II. 797
0.927
0.571
0.744
0.242
0.435
0.601
0.623
0.869
0.722
0.662
0.909
0.916
1.007
0.961
0.964
0.618
-1.107
0.522
0.641
0.646
0.760
0.914
0.658
0.760
0.586
0.396
-0.278
-0.440
0.435
0.206
0.557
Marginal Cost
Forward
Return
0.013
0.016
0.010
0.021
0.013
0.012
0.014
0.025
0.013
0.014
0.014
0.010
0.018
0.017
0.016
0.011
0.015
0.012
0.013
0.013
0.012
0.01 I
0.021
0.015
0.007
0.009
0.024
0.010
0.012
0.011
0.01 I
O.ot8
0.393
0.394
0.232
0.562
0.062
-0.152
0.369
0.672
0.216
0.347
0.164
0.139
0.477
0.418
0.363
0.182
0.396
-0.280
-0.645
0.218
0.201
0.359
0.516
0.273
-0.306
0.007
0.463
0.082
0.092
0.315
0.081
0.679
Overall
1.171
1.123
0.947
l.106
0.654
0.540
l.010
1.298
0.856
0.958
0.754
0.800
1.152
1.222
1.021
0.797
1.062
0.352
0.441
0.999
0.896
1.169
0.993
0.946
0.395
0.608
1.322
0.689
0.685
1.078
0.709
1.132
Cost Elasticity
Upper
l.251
1.167
0.990
1.155
0.714
0.610
l.050
1.376
0.891
0.996
0.830
0.831
1.208
l.282
1.051
0.823
1.108
0.501
0.509
· 1.040
0.939
1.251
1.025
0.985
0.492
0.691
1.383
0.801
0.799
1.138
0.741
1.229
Lower
1.092
1.078
0.904
1.056
0.594
0.469
0.969
1.220
0.822
0.921
0.679
0.769
1.096
1.163
0.990
0.771
1.016
0.203
0.372
0.959
0.853
1.088
0.962
0.907
0.299
0.525
1.262
0.577
0.571
1.017
0.676
1.036
Table 5: Estimates of Unit Costs. Marginal Costs, and Cost Elastil:ities for Check (continued)
Hyhrid
Marginal Cost
Return
Forward
Translog
Cost Elasticity
Lower
Upper
Overall
Marginal Cost
Return
Forward
Overall
Cost Elasticity
Upper
Lower
Processing
Site
S.B
S34
S35
S36
S37
S38
S39
S40
S41
S42
S43
S44
S45
S46
S47
Unit Cosl
0.013
0.014
0.022
0.022
0.024
0.017
0.017
0.021
0.019
0.017
0.027
0.015
0.023
0.016
0.020
0.014
0.0 IO
0.015
0.016
0.013
0.012
0.008
0.02 I
0.015
0.0IO
0.021
0.0 IO
0.014
0.013
0.020
0.434
0.234
0.203
0.(147
0.932
0.215
-0.030
0.200
0.161
0.188
0.572
0.417
0.254
0.593
0.330
1.361
().867
0.847
0.767
1.075
0.871
0.474
1.134
0.923
0.775
1.218
1.007
0.802
1.05 3
1.182
1.609
1.174
1.090
0.929
1.423
1.090
0.629
1.278
1.162
0.985
1.382
1.108
1.076
1.502
1.386
1.111
0.561
0.604
0.604
0.727
0.652
0.319
0.990
0.684
0.566
1.054
0.905
0.528
0.604
0.978
0.010
0.011
0.014
0.013
0.021
0.011
O.OIO
0.016
0.012
0.011
0.021
0.011
0.016
0.012
0.015
0.198
0.280
0.186
0.065
0.656
0.111
0.055
0.351
0.096
0.161
0.442
0.194
0.239
0.237
0.333
0.879
0.966
0.805
0.647
1.242
0.728
0.653
0.955
0.682
0.853
1.095
0.848
0.878
0.864
0.929
0.911
1.009
0.870
0.723
1.330
0.800
0.716
0.984
0.767
0.906
1.130
0.881
0.932
0.910
0.961
0.846
0.924
0.740
0.570
1.154
0.655
0.590
0.926
0.597
0.799
1.061
0.815
0.824
0.818
0.897
Weighted
Average
0.020
0.014
0.385
0.966
1.242
0.691
0.015
0.339
1.003
1.060
0.946
Source: Authors' calculations.
Table 6: Estimates of Unit Costs. Marginal Costs, and Cost Elasticities for ACH
Hyhrid
Processing Site
PSI
PS3
PS4
PSS
PS6
PS7
PS8
PS9
PSIO
PSII
PSl2
Unit Cost
0.020
0.015
o.ot5
0.016
0.017
0.019
0.023
0.019
0.016
0.022
0.020
Marginal Cost
0.0117
11.0088
0.0066
0.0109
II.Oil I
O.(KJl9
0.0184
0.0053
0.0113
0.1Kl50
0.0142
Upper
0.024
0.019
0.014
0.017
0.019
0.010
O.o35
0.012
0.019
0.018
0.024
Lower
-0.001
-0.001
-0.001
0.005
0.003
-0.006
0.002
-0.002
0.004
-0.008
0.004
Cost Elasticity
0.571
0.584
0.442
0.684
0.650
0.101
0.785
0.281
0.720
0.225
0.724
Marginal Cost
0.0094
0.0068
0.0072
0.0077
0.0084
0.0094
0.0106
0.0086
· 0.0076
0.0104
0.0095
Weighted Average
0.017
0.009
0.017
0.000
0.478
0.0082
Source: Authors' calculations.
Translog
Upper
Lower
O.Dl5
0.004
0.003
O.Oll
0.004
0.010
0,004
0.011
0.005
0.012
0.014
0.005
0.004
0.017
0.004
0.013
0.011
0.004
0.005
0.016
0.005
0.014
O.Qll
0.004
I
Cost Elasticity
0.460
0.454
0.480
0.485
0.493
0.502
0.452
0.458
0.485
0.465
0.483
0.403
Table 7: Estimates of Unit Costs, Marginal Costs, and Cost Elasticities for Fedwire
Without PS2
With PS2
Processing Site
Unit Cost
Marginal Cost
Upper
Lower
Cost Elasticity
Marginal Cost
Upper
Lower
Cost Elasticity
0.773
na
0.720
0.730
0.748
0.809
0.863
0.653
0.643
0.745
0.766
0.883
0.793
PSI
PS2
PS3
PS4
PSS
PS6
PS7
PS8
PS9
PSI0
PSI I
PS12
0.228
0.206
0.229
0.206
0.278
0.268
(1.280
0.321
0.357
0.252
0.3()4
0.220
0.189
CU51
0.143
0.135
0.201
0.251
0.320
0.116
0.119
0.176
0.240
0.272
0.283
0.488
0.249
0.229
0.321
0.358
0.438
0.303
0.333
0.288
0.367
0.370
0.096
0.214
0.037
0.(l42
0.080
0.144
0.202
-0.071
-0.095
0.065
0.112
0.174
0.830
1.703
0.626
0.657
0.723
0.939
1.141
0.361
0.334
0.699
0.788
1.240
0.176
na
0.165
0.150
0.208
0.217
0.242
0.210
0.230
0.188
0.233
0.194
0.274
na
0.276
0.250
0.339
0.337
0.366
0.382
0.465
0.361
0.372
0.290
0.078
na
0.054
0.050
0.076
0.096
0.118
0.038
-0.006
0.015
0.094
0.098
Weighted Average
0.242
0.265
0.387
0.143
1.144
0.204
0.329
0.079
Source: Authors' calculations.
Table 8: Cost Efficiency by Service
A'CH
Check
Translog
0.699
Processing Site
PSI
PS2
PS3
PS4
PSS
PS6
PS7
PS8
PS9
PSIO
PSI I
PS12
Hybrid
0.510
0.556
0.641
0.637
0.551
0.806
0.656
0.820
0.584
0.652
1.000
0.756
Translog
0.598
0.628
0.762
0.745
0.622
0.936
0.767
0.974
0.662
0.748
1.000
0.855
Hybrid
0.665
na
na
1.000
0.648
0.513
0.438
0.414
0.665
0.643
0.573
0.532
0.438
1.000
0.639
0.505
0.445
0.416
0.632
0.644
0.555
0.514
0.442
Mean
Median
Standard Dev.
0.681
0.647
0.141
0.775
0.755
0.139
0.594
0.573
0.165
0.590
0.555
0.166
Source: Authors' calculations.
Fedwire
With PS2
Without PS2
0.563
0.450
1.000
na
0.551
0.694
0.797
1.000
0.556
0.704
0.500
0.619
0.589
0.535
0.536
0.612
0.469
0.536
0.709
0.565
0.499
0.393
0.714
0.731
0.589
0.543
0.170
0.660
0.619
0.136
Table 9: Rank Correlation of the Cost Efficiency Estimates for the Three Services (significance levels in parentheses)
ACH
Check
Payment Service
Hybrid
Translog
Check, Hybrid
1.000
(0.000)
0.960
(0.000)
-0.260
(0.440)
-0.313
(0.348)
-0.202
(0.552)
-0.263
(0.435)
Check, Translog
0.960
(0.000)
1.000
(0.000)
-0.211
(0.534)
-0.266
(0.429)
-0.095
(0.782)
-0.179
(0.599)
ACH, Hybrid
-0.260
(0.440)
-0.211
(0.534)
1.000
(0.000)
0.995
(0.000)
-0.024
(0.945)
0.130
(0.703)
ACH. Translog
-0.313
(0.348)
-0.266
(0.429)
0.995
(0.000)
1.000
(0.000)
-0.036
(0.916)
0.115
(0.737)
Fedwire. with PS2
-0.202
(0.552)
-0.095
(0.782)
-0.024
(0.945)
-0.036
(0.916)
1.000
(0.000)
0.928
(0.000)
Fedwire, without PS2
-0.263
(0.435)
-0.179
(0.599)
0.130
(0.703)
0.115
(0.737)
0.928
(0.000)
1.000
(0.000)
Source: Authors· calculations.
Translog
Fedwire
WithPS2
Without PS2
Hybrid
Table 10: Technological Change in Payment Service Provision
Translog
Hybrid
Payment Service
Time
,-statistic
Time
,-statistic
Check
0.017
6.56
0.018
6.67
ACH
-0.112
-6.35
-0.110
-4.66
WithoutPS2
WithPS2
Payment Service
Time
I-statistic
Time
I-statistic
Fedwire
-0.056
-4.09
-0.064
-4.46
Source: Authors' calculations.
■
Table 11: Check Processing Unit Cost Decomposition, Hybrid Cost Function
(Processing Site Means Relative to Overall Sample Means, 1990-1994)
Processin Site
SI
S2
S3
S4
S5
S6
S7
S8
S9
S10
S 11
S12
S13
S14
S15
S16
S17
S18
S19
S20
S21
S22
S21
S24
S25
S26
S27
S28
S29
S30
S31
S32
S33
S34
S35
S36
S37
S38
S39
S40
S41
S42
S43
Unit Cost ($)
0.015
0.020
0.013
0.026
0.021
0.020
0.019
0.030
0.019
0.019
0.022
0.014
0.022
0.021
0.021
0.016
0.019
0.024
0.022
0.oI8
0.017
0.013
0.028
0.022
0.014
0.016
0.028
0.018
0.021
0.014
0.016
0J)21
0.013
0.014
0.022
0.022
0.024
0.017
0.017
0.021
0.019
0.017
0.027
Unit Cost
-0.247
0.066
-0.382
0.318
0.094
0.063
-0.023
0.441
-0.022
-0.008
0.165
-0.316
0.166
0.096
0.112
-0.204
0.009
0.227
0.142
-0.061
-0.115
-0.383
0.394
0.133
-0.333
-0.198
0.398
-0.065
0.093
-0.341
-0.147
0.114
-0.349
-0.282
0.134
0.128
0.250
-0.102
-0.136
().()90
0.oI5
-0.130
U.346
Logarithmic Differences from Sample Mean
Effect of
Effect of
Direct
Total
Cost
In ut Price Interactions Environment
Efficienc
Ou ut
0.048
-0.002
0.049
-0.124
-0.166
-0.159
0.001
0.029
0.013
0.214
-0.085
0.005
-0.038
-0.088
-0.166
-0.099
0.000
0.222
-0.048
0.291
-0.047
-0.003
0.019
-0.027
0.205
-0.164
-0.004
-0.104
0.113
0.214
-0.158
-0.043
-0.060
0.000
0.214
0.075
0.005
0.100
0.113
0.039
-0.108
-0.047
-0.068
0.000
0.068
-0.055
0.001
-0.036
-0.082
0.068
-0.182
-0.003
-0.045
0.059
0.214
-0.257
0.001
-0.087
-0.155
0.068
-0.096
-0.001
0.147
-0.004
0.205
0.380
0.000
0.023
0.111
-0.383
0.178
0.000
-0.010
-0.022
0.045
-0.100
-0.008
-0.134
-0.136
0.039
-0.001
-0.056
0.024
-0.061
0.039
0.084
-0.006
-0.103
0.619
-0.383
-0.015
0.010
-0.191
0.146
0.155
0.259
-0.001
-0.026
0.083
-0.383
-0.114
-0.001
-0.136
-0.001
0.039
-0.121
0.000
0.033
-0.148
-0.166
0.138
-0.001
0.234
-0.053
0.205
0.261
0.()45
0.001
0.059
0.006
-0.796
0.006
0.145
0.138
0.291
0.()49
0.139
-0.099
0.004
-0.184
0.151
0.269
0.003
0.080
-0.103
0.168
-0.001
-0.042
0.129
-0.184
0.105
-0.002
-0.089
0.167
-0.184
-0.092
-0.016
-0.131
0.000
-0.166
0.027
-0.002
-0.087
-0.200
0.039
0.193
-0.241
0.000
0.072
0.155
-0.074
-0.012
-0.123
0.005
-0.166
-0.071
0.014
0.000
-0.077
-0.166
0.187
-0.001
-0.073
0.049
0.045
0.179
-0.003
-0.105
0.030
0.045
0.219
-0.002
-0.027
-0.049
0.062
-0.155
-0.001
0.024
-0.030
0.068
-0.050
-0.005
0.023
-0.009
-0.103
-0.032
-0.022
-0.051
0.214
0.000
0.012
-0.002
-0.005
0.053
-0.103
0.290
-0.001
-0.072
0.026
-0.383
0.209
0.002
0.128
0.061
-0.103
i
Table 11: Check Processing Unit Cost Decomposition, Hybrid Cost Function (continued)
ProcessinJ?: Site
S44
S45
S46
S47
Unit Cost ($)
0.D15
0.023
0.016
0.020
Unit Cost
-0.213
0.199
-0.170
0.033
Standard Dev.
0.004
0.219
Source: Authors' calculations.
Logarithmic Differences from Sample Mean
Effect of
Direct
Effect of
Total
Cost
Price
Input
Environment
Output
Interactions
Efficiency
-0.003
-0.103
0.061
-0.035
-0.092
0.000
0.017
0.270
0.041
-0.184
0.009
0.057
-0.210
-0.174
0.205
0.000
0.291
0.140
-0.239
-0.075
0.191
0.140
0.091
0.003
0.199
i
Table 12: ACH Unit Cost Decomposition, Hybrid Cost Function
(Processing Site Means Relative to Overall Sample Means, 1990-1994)
Processing Site
PSI
PS3
PS4
PS5
Unit Cost ($)
0.0204
0.0150
Unit Cost
0.112
PS12
0.0160
0.0171
0.0188
0.0234
0.0188
0.0157
0.0224
0.0196
-0.195
-0.203
-0.135
-0.066
0.028
0.248
0.030
-0.149
0.203
0.072
Standard Dev.
0.0029
0.157
PS6
PS7
PSS
PS9
PSl0
PSll
0.0149
Source: Authors· calculations.
Logarithmic Differences from Sample Mean
Environmental Effect of
Direct
Total
Cost
Effect
Efficiency
Input Price
Interactions
Output
-0.001
0.058
0.191
-0.122
0.003
0.076
0.001
0.192
0.084
-0.530
0.023
-0.037 -0.079
0.000
-0.096
-0.001
-0.123
-0.087
0.000
0.137
-0.049
0.001
-0.019
-0.212
0.296
-0.059
-0.366
0.005
0.000
0.352
-0.001
-0.006
-0.007
0.295
-0.122
-0.007
0.002
0.101
-0.089
0.072
-0.054
-0.002
0.000
-0.140
0.026
-0.004
0.071
0.006
0.000
0.100
-0.027
-0.001
-0.185
0.296
0.072
0.255
0.205
0.056
0.044
0.001
SO.OS
W..()4
Tr ■ mlog
SO.OJ
11Hl2.
Hybrid
10.0]
so
l In
mill Ioli, rt1 Ll~n
So,1r~: A1,1rhl.}fS' cak11latiu115.
100
lSU
200
Forward I t~:m~ h1,no.af'd
pmpnrUon:111lh• '111'1 ti!! torun.l i!!ffl.:!I j
~!~ms inl"r~a~
1:'5(i
■
Table 13a: Fedwire Unit Cost Decomposition, with PS2
(Processing Site Mean Relative to Overall Sample Means, 1990-1994)
Office
PSI
PS2
PS3
PS4
PSS
PS6
PS7
PSS
PS9
PSIO
PSl 1
PS12
Standard Dev.
Logarithmic Differences from Sample Mean
Environmental Effect of
Direct
Total
Cost
Interactions
Effect
Unit Cost ($) Unit Cost Efficiency Output Input Price
0.001
-0.070
-0.122
0.036
0.235
-0.126
0.228
-0.009
0.040
0.042
0.311
-0.562
-0.227
0.206
0.001
-0.129
0.004
-0.020
-0.123
0.033
0.229
0.001
-0.061
-0.005
-0.039
-0.335
-0.228
0.206
0.001
-0.013
-0.006
-0.077
0.025
0.072
0.278
0.001
0.031
-0.027
-0.144
0.131
0.035
0.268
-0.001
0.080
-0.007
-0.128
0.064
0.081
0.280
0.002
-0.035
-0.048
0.223
0.062
0.217
0.321
-0.003
0.001
-0.009
0.263
0.194
0.324
0.357
0.001
0.056
-0.036
-0.065
0.009
-0.024
0.252
0.001
0.034
-0.01 l
-0.106
0.371
0.163
0.304
0.004
0.066
0.066
-0.096
-0.226
-0.163
0.220
0.048
0.179
0.259
0.165
0.033
0.063
0.003
Source: Authors· calculations.
Table 13b: Fedwirc Unit Cost Decomposition. without PS2
(Processing Site Mean Relative to Overall Sample Means. 1990-1994)
Office
PSI
PS3
PS4
PS.S
PS6
PS7
PS8
PS9
PSI0
PSI I
PSI2
Standard Dev.
Logarithmic Differences from Sample Mean
Effect of
Environmental
Direct
Total
Cost
Interactions
Effect
Unit Cost (S) Unit Cost Efficiency Output Input Price
-0.()64
0.000
0.040
-0.050
0.141
-0.147
0.228
0.002
0.(l44
-0.118
0.008
-0.068
-0.144
0.229
0.001
-0.052
-0.001
o.cno
-0.433
-0.249
0.206
0.001
-0.009
-0.002
-0.002
-0.083
0.052
0.278
0.002
0.039
-0.023
-0.090
0.046
0.014
0.268
0.000
0.078
-0.002
-0.152
0.096
0.060
0.280
-0.002
-0.032
-0.043
0.196
0.058
0.196
0.321
-0.001
0.005
-0.006
0.217
0.191
0.303
0.357
0.001
0.053
0.0<)9
-0.()45
-0.032
-0.089
0.252
0.001
0.032
0.3()4
-0.031
-0.007
0.262
0.143
-0.004
0.067
0.069
-0.171
-0.121
-0.183
0.220
0.()47
Source: Authors· calculations.
0.172
0.190
0.123
0.031
0.061
0.002
Figure 2: ACH
Average Cost
0.0200
0.0180
0.0160
0.0140
0.0120
0.0100
0.0080
0.0060
Translog
0.0040
0.0020
0.0000
0
20,000
40,000
60,000
80,000
100,000
Items Processed (millions)
Source: Authors' calculations.
120,000
140,000
160,000
Figure 3: Fedwire
Average Cost
0.9
0.8
•
•
0.7
Unit Cost
- - - - Without PS2
--
0.6
0.5
With PS2
0.4
♦.
0.3
_)~- -
0.2
0.1
0.0
5,000
Items Processed (millions)
Source: Authors' calculations.
10,000
15,000
@FedFRASER