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Vol. 25, No. 2
ECONOMIC REVIEW
1989 Quarter 2
Removing the Hazard
ot Fedwire Daylight
2
Overdrafts
b y E.J. S te ve n s
Capital Subsidies and
the Infrastructure Crisis:
Evidence from the Local
Mass-Transit Industry
11
b y Brian A . C rom w e ll
Employment Distortions
Under Sticky Wages
and Monetary Policies
to Minimize Them
by J a m e s G. H oehn
FEDERAL RESERVE BANK
OF CLEVELAND
22
r a
r r r
M I C
R E V I E W
1989 Quarter 2
Vol. 2 5 . No. 2
Removing the Hazard
2
of Fedwire Daylight
Overdrafts
Economic Review
is published
quarterly b y the Research
b y E.J. S te ve n s
D e p a rtm e n t o f the Federal
R eserve B an k of C leve lan d.
Review
Free Federal Reserve daylight overdrafts misallocate resources. One reason is
Cop ie s o f the
the moral hazard of fully insuring a paying bank’s access to whatever volume
available through our Public
of daylight overdraft credit it needs. This paper contrasts the effects of three
A ffa irs and B an k Relations
recent proposals for pricing daylight overdrafts and demonstrates that reduc
D e p a rtm e n t, 2 1 6 / 5 7 9 -2 1 5 7 .
are
ing moral hazard depends on how, rather than on how much, pricing affects
daylight overdrafts. If payment practices and modes of bank financing were
unresponsive to pricing, it would suggest that the moral hazard of Federal
Reserve daylight overdrafts has been an insidious force behind the rapid
C oordin ating Ec o n o m is t:
Randall W . Eb erts
growth of interbank lending and securities-market trading in recent decades.
Ed ito rs : W illia m G . M u rm a n n
Robin Ratliff
Capital Subsidies and
11
the Infrastructure Crisis:
Evidence from the Local
Mass-Transit Industry
D e s ig n : M ich ae l G a lk a
T y p e s e ttin g : L iz H a n n a
Op in ion s s ta te d in
Review
by Brian A. C ro m w e ll
Economic
are th o s e of the
a u th ors an d not necessarily
those o f the Federal R e s e rve
Public investment and maintenance decisions are potentially distorted by
B a n k of C le ve la n d or o f the
budget procedures, political pressures, and capital subsidies. Empirical evi
B oard of G o ve rn o rs o f th e F e d
dence from two recent studies of the mass-transit industry is summarized
eral R e s e rve S y s te m .
and suggests that federal capital subsidies have important effects on infra
structure decisions of local governments.
M aterial m a y be reprinted pro
vid e d th a t th e source is credited.
Employment Distortions
Under Sticky Wages
2 2
and Monetary Policies
to Minimize Them
b y J a m e s G. H oehn
Sticky nominal wages can result in distortion of employment levels as
demand for goods and labor productivity change. This article shows that
employment distortions can be minimized by a monetary policy that allows
some price deflation when productivity improves. Policies that target nominal
income or the price level result in smaller distortions than do policies that
target output or money.
Ple as e send copies of reprinted
m aterial to the editor.
I S S N 0 0 13 -0 2 8 1
Rem oving the H a za rd
of Fedw ire Daylight
Overdrafts
by E.J. Stevens
E .J . Stevens is an assistant vice
president and economist at the Fed
eral Reserve Bank of Cleveland. The
author thanks John Carlson, Charles
Carlstrom, Randall Eberts, and Wil
liam Gavin for their useful comments
on earlier drafts of this paper.
Introduction
The 12 Federal Reserve District Banks extend
about $115 billion of credit within a few hours
on an average business day, only to take it back
again before the close of business. This huge sum
reflects banks’ daylight overdrafts of their deposit
accounts at Federal Reserve Banks when making
large-dollar-value payments to other banks using
Federal Reserve wire transfer systems. 1 If all
goes well, subsequent receipts from other banks
extinguish the daylight overdrafts before the end
of the day.
Daylight overdrafts via Fedwire are not allo
cated by any market process and are free, a result
of the order in which a bank’s payments and
receipts occur. The same might seem to be true
of checks presented and deposits made to any
checking account during a day, but there is a
■
crucial distinction: a Fedwire payment is irrevo
cable upon receipt, while a check is only a pro
visional payment. Therefore, the Federal Reserve
is the party at risk if a daylight overdraft is not
repaid by the end of a day.
Free daylight overdrafts are costly. O f course,
the Federal Reserve faces no financing or resource
costs in issuing daylight credit because it has the
power to create money; failure of a bank to elimi
nate its daylight overdraft by the end of a day
would simply add to Federal Reserve assets
(claims on a bank) and liabilities (bank reserve
deposits) . 2 The costs arise from resource
misallocations.
One source of these inefficiencies, and the
focus of this paper, is the “moral hazard” involved
in providing free daylight overdrafts. 3 Fedwire
fully insures a payor bank’s access to whatever
volume of daylight overdraft credit it needs to
make payments that are immediately available
1 These systems include Fedwire, for transfer of resen/e balances from
one bank to another, and the securities wire, for transfer of book-entry U .S .
government securities from one bank to another in return for reserve balances.
■ 2
The term Fedwire will be used here to refer to both systems. A third system,
ing the value of the asset, causing a charge against Federal Reserve income
C H IP S (Clearing House Interbank Payment System ), is operated by the private
that would reduce Treasury receipts.
Failure to repay might result from a bank’s insolvency, perhaps impair
New York Clearing House Association; credit extended among participants in
this system adds another $45 billion of interbank daylight credit on an
■ 3
average day.
resource misallocations resulting from this moral hazard.
Stevens (1988) provides a discussion of the probable nature of some
and irrevocable. The result is a form of insurance
that removes any incentive for payee banks to
monitor or manage credit risk in receiving pay
ments that payor banks fund with daylight credit.
Suggestions have been made to price Fedwire
daylight overdrafts in an effort to control them.
Market sources of funding would replace some or
all Fedwire daylight overdrafts in making pay
ments and would require compensation based
on credit risk. Market discipline would then pro
vide the now-missing incentive for payor banks
to attend to risk, thereby avoiding moral hazard.
This paper suggests that economizing need not
bring about the market discipline that would elimi
nate moral hazard. The first section provides a
brief review of Fedwire daylight overdraft history,
Federal Reserve payment system risk policy, and
the problem of moral hazard. The second part
shows how differences among three recently pro
posed daylight overdraft pricing mechanisms can
influence the extent of daylight overdraft reduc
tion and, more important, the way in which banks
reduce daylight overdrafts. The final part argues
that reducing Fedwire moral hazard does not
but on
banks reduce
depend on
daylight overdrafts, and that this should be a cri
terion for choosing among pricing proposals.
how much,
how
I. Fedwire Daylight
Overdrafts and
Moral Hazard
A bank goes into daylight overdraft when it has
made more payments from its account at a Fed
eral Reserve Bank by some point during a day
than can be covered by its opening reservedeposit balance plus payments received by that
point in the day. A common example is that of a
bank dependent on continuous overnight
federal funds borrowing. Operational conve
nience leads it to return the borrowed funds each
morning, before borrowing replacement funds
in the afternoon. The midday period is spent in
overdraft, funded by the Federal Reserve.
As recently as 30 years ago, the U.S. largedollar-value payments system was for the most
part a cash-in-advance system. Irrevocable Fed
wire payments were riskless both to payees and
to the Federal Reserve because they were drawn
against positive balances. Since then, Federal
Reserve daylight risk exposure has mushroomed,
associated with the telecommunications revolu
tion in the payments mechanism, the prolifera
tion of new financial instruments, and the explo
sion of trading volumes in worldwide money
and capital markets.
A simple comparison illustrates the extent of
the change. In 1947, reserve-deposit balances
represented 700 percent of (seven times) the
value of daily debits (Fedwire, checks, etc.) to
member-bank reserve accounts. That is, the aver
age bank could make all of its own and its cus
tomers’ payments for seven successive business
days without ever receiving a single offsetting
payment, and without exhausting its initial
reserve-deposit balance. By 1983, balances were
a minuscule 4 percent of daily debits. The aver
age bank could meet demands for payment for
only 2 0 minutes of a single eight-hour business
day before it would have to receive some offset
ting payments, or go into overdraft. 4
Initially, the evolution from a cash-in-advance
system toward automatic daylight credit seems to
have gone undetected, but confronting the grow
ing daylight credit risk problem became unavoid
able in the late 1970s under the pressures of
technological change and a demand for sameday net settlement service by potentially compet
ing private large-dollar-value payment networks.
Originally, starting in 1918, telegraph, telephone,
or mail messages to the Federal Reserve were
the only mechanisms for transferring ownership
of reserve-deposit balances between banks with
same-day finality. Related devices were official
checks, offering only next-day finality, and inter
bank messages that simply instructed a bank to
use Fedwire to transfer funds.
Introducing computer-to-computer telecom
munications technology for payments by Fed
wire and by the Clearing House Interbank Pay
ment System (CHIPS), and for interbank
message systems, suggested a new possibility in
the 1970s. Private payment networks like CHIPS
and the then-proposed CashWire network each
would be capable of clearing payment messages
among its own participants continuously during
the day before presenting a single balanced set
of net debit and credit positions to the Fed in
time to achieve same-day final settlement.
Compared to the next-day systems prevalent
then, this would offer the advantage of reducing
costly overnight float financing of banks in net
debit position by those in net credit position. In
addition, it would shorten the length of time
during which overnight float exposed banks to
credit risk. Operating details of telecommunica
tion devices, accounting-system modifications,
backup facilities, and daily time schedules were
laid out quickly, but the enterprise foundered on
■ 4
Reduced reserve requirements represent only a small portion of this
change. To have maintained the 1947 reserve deposits/debits ratio with the
1983 volume of debits would have involved reserve deposits equal to an
impossible two-and-a-third times the total assets of all commercial banks.
the “unpostable debit”—what to do if one of the
participants had insufficient funds in its reserve
account to cover its private network net debit at
settlement hour.
Some found the unpostable debit an opera
tional inconvenience to be ignored: from an
operations perspective, it was no problem as long
as the accounting system accepted negative
numbers. After all, a Federal Reserve Bank did
not check to see whether a bank had sufficient
funds to cover a Fedwire transfer. Why should a
net settlement message be treated any differently?
Others found it troubling to design a system in
which the central bank automatically would guar
antee a private network settlement by accepting
an unpostable debit as an offset to irrevocable
credits. That issue is not fully resolved even
today, but two developments did force some
action with respect to daylight overdrafts. 5
One development was the increasing inci
dence of
overdrafts of reserve
accounts and adoption of the current Federal
Reserve overnight overdraft policy.6 High inter
est rates, escalating wire-transfer traffic, and de
clining reserve requirements were making
reserve-deposit accounts a less and less effective
buffer stock in banks’ daily reserve-balance man
agement. With no formal overnight overdraft pol
icy other than Regulation D (that banks maintain
an average required balance over a one- or twoweek reserve maintenance period), concern was
mounting that banks might abuse the Federal
Reserve by running overnight overdrafts when
especially profitable opportunities arose.
Developing an overnight overdraft policy led
to more widespread realization within the Fed
eral Reserve that daylight overdrafts were a fact
of life. Not only was there no mechanism in
place to prevent daylight overdrafts, but neither
was there a way to know how widespread the
practice was. The second development was a
carefully constructed survey of the incidence of
daylight overdrafts. This provided the factual
foundation for debating and developing the
overnight
initial Federal Reserve payment system risk (PSR)
policy: guidelines for determining limits on day
light overdraft positions; continued recording of
daylight overdraft positions (in addition to a real
time mechanism to control daylight overdrafts at
problem banks and special institutions); and a
stated intention to ratchet-down limits over time.
Pricing daylight overdrafts now is being sug
gested as a next step for this policy.
The problem with free Fedwire daylight over
drafts is moral hazard. The term refers to the
hazard an insurer faces as a result of the elimina
tion of incentives for an insured party to avoid a
risk precisely because any losses arising from
that risk are covered by insurance. Fire, life, and
casualty insurers protect against moral hazard in
a variety of ways. For example, coinsurance in
the form of deductibles or copayments gives the
insured a stake in preventing loss; inspection
and requirements to remove risks give the
insurer the ability to manage risk.
Fedwire does have some similar protections.
The payor bank’s net worth is at stake if it is
unable to repay its credit, constituting a form of
coinsurance. Regulation, supervision, and exam
ination of banks guard against imprudent bank
ing practices, now extended to include payment
practices. However, initial limits on daylight
overdraft exposure deliberately have been set
high, and do not yet apply to overdrafts from
book-entry securities transfers. As a result, Fed
wire moral hazard is real, particularly in the short
run between bank examinations.
Payee banks have no reason to limit payments
received during a day, regardless of the volume
of daylight overdrafts per dollar of net worth of
the payor bank, because the Federal Reserve is at
risk. Payor banks face no external disincentives
that would raise the cost of daylight overdraft
credit as the volume they use increases and as
their credit quality falls. Federal Reserve protec
tions against moral hazard are not yet very strong.
II. Avoiding Daylight
Overdrafts
■5
Adjustments
The most recent effort to resolve the unpostable debit issue is that of
the New York Clearing House Association, which has adopted a requirement
that C H IP S members participate in a loss-sharing arrangement. It also has
proposed federal legislation apparently intended to give legal priority to net
work payment claims over all others if a network member becomes insolvent.
See
American Banker,
■
6
April 7 ,1 9 8 9 , pp. 1 and 16.
Overnight overdrafts are subject to a penalty of the larger of $50, or the
larger of 10 percent or a rate 2 percentage points above the federal funds rate
prevailing on the day the overdraft is incurred. The penalty charge is in addi
tion to the cost of making up the reserve-deposit deficiency for reserverequirement purposes,
Any bank could eliminate daylight overdrafts by
holding more overnight reserve deposit balances,
by borrowing balances for a few moments or
hours during the day, or by modifying its own or
its customers’ payment practices to prevent a
negative balance. Such adjustments might be
costly, of course, but would be worthwhile if
they cost less per dollar than a daylight overdraft.
A cost-minimizing bank might acquire excess
reserves in the federal funds market. After meet
ing its temporary daylight need to cover pay
ments, the bank would then have these extra
funds available to hold, or to loan out overnight,
if it could. The marginal cost of preventing a day
light overdraft would be the difference between
the cost of borrowing and the return on lending.
A private daylight loan market does not now
operate, but such a market would provide a
second possibility for avoiding Federal Reserve
daylight overdrafts. 7 Daylight loans could redis
tribute existing reserve balances from banks hav
ing them and not needing them during the day
for payment purposes, but only overnight for
reserve-requirement purposes, to banks not hav
ing them and needing them during the day, but
not overnight. Free Federal Reserve daylight
credit preempts such a market now, but if day
light overdrafts were to become costly, and
timely delivery were assured, borrowing in a
daylight loan market might become an inexpen
sive way for a bank to prevent overdrawing its
reserve account during a day, with repayment
before close of business.
Finally, a bank could alter the amounts of debits
and credits to its account, or their sequence dur
ing the day. It might do this by lengthening the
maturity of its liabilities, or by adopting a con
tinuing contract for federal funds borrowing,
with daily renegotiation of the rate but no daily
repayment and re-receipt of funds. Or, pairs of
institutional customers operating in securities
markets might be induced to net their transac
tions obligations during a day, producing a single
net obligation for daily payment, again reducing
debits that might now precede credits. Or,
groups of banks might join in private payment
networks, substituting daylight credit on the pri
vate networks for Federal Reserve daylight over
drafts. Only net settlement of end-of-day posi
tions would need to be accomplished through
Federal Reserve accounts.8
Modifying payment practices in these ways would
involve some costs, too, such as paying higher
rates on longer-term liabilities, or receiving
lower prices or revenues for payment services
when institutional customers engage in obliga
tion netting, or sharing the cost of a private pay
ment network. Some tactics would be more
expensive than others, so the marginal cost of
preventing daylight overdrafts in reserve
accounts by modifying payment practices would
increase with the volume of overdrafts avoided.
In equilibrium, cost-minimizing banks would
adopt the unique combination of adjustment
mechanisms having marginal costs equal to or
less than the marginal cost of a daylight over
draft. Pricing daylight overdrafts would lead
banks to adjust from today’s zero marginal cost
to something higher.
Throe Proposals to Price
Daylight Overdrafts
Three specific pricing proposals that have been
receiving attention are evaluated in this section.9
One would treat each daylight overdraft as an
automatic overnight discount-window loan,
booked at a penalty rate. A second would
require a bank to hold additional balances at a
Federal Reserve Bank in proportion to its day
light overdrafts. A third would simply impose a
slight fee per dollar of daylight overdraft.
The penalty rate proposal
comes from Wayne Angell, member of the Board
of Governors of the Federal Reserve System. A
bank would be required to borrow the amount
of any daylight overdraft as a collateralized loan
from its Federal Reserve Bank discount window
at an above-market penalty rate, but the Federal
Reserve Bank would pay an explicit (belowmarket) rate of return on excess reserves. 10 The
combination of the two features means that,
under normal circumstances, no bank would run
a daylight overdraft intentionally and pay the
penalty discount rate, because the maximum
alternative cost would be only the interest-rate
spread between the cost of financing extra
excess reserves, perhaps the federal funds rate,
and the earnings rate on excess reserves.
The same spread would become the cost of
borrowing daylight funds in the likely event that
a private daylight loan market developed. Banks
Penalty Rate
■
9 These proposals are described in VanHoose (1988), the Angell proposal
of a penalty rate; Hamdani and Wenninger (1988), supplemental balances; and
■
7
Simmons (1987) contains an extensive discussion of daylight funds
market possibilities.
■
8
Humphrey (1987) and Board of Governors of the Federal Reserve Sys
tem, Large-Dollar Payments System Advisory Group (1988) contain detailed
Board of Governors of the Federal Reserve System , Large-Dollar Payments
System Advisory Group (1988), fees.
■
10
Penalty-rate borrowing would differ from an overnight overdraft in that
a bank would be required to post eligible collateral for the loan associated with
explanations of a number of these potential modifications of payment
a daylight overdraft, but would not involve the cost of making up a reserve-
practices.
deposit deficiency for reserve-requirement purposes.
would never pay more than this spread for a day
light loan because they could always borrow re
serves in the federal funds market and lend at the
overnight rate; lenders would never charge less
than this spread because they could always sell
their reserves at the federal funds rate, of course
forgoing the rate earned on excess reserves.
Note, however, that excess reserves and a day
light loan market would be relevant only to the
extent that daylight overdrafts were not elimi
nated by modifications in payment practices that
were less costly than the rate spread. 11
The supplemental
balance proposal has been described by the staff
of the Federal Reserve Bank of New York. A bank
would be required to hold a special interestbearing deposit (the supplemental balance) in a
current period equal to some fraction (the sup
plemental balance ratio) of prior-period daylight
overdrafts of its combined reserve and supple
mental deposit accounts. The maximum cost of a
dollar’s daylight overdraft today would be the
supplemental balance ratio multiplied by the
expected next-period spread between the cost of
financing a dollar’s supplemental balance and
the rate earned on the supplemental balance.
With both this rate spread and the ratio adminis
tratively fixed, the maximum cost of a daylight
overdraft would be a simple constant amount
per dollar of daylight overdraft.
The cost would set an upper limit on the mar
ket rate for daylight loans. And, as in the penalty
rate case, supplemental balances and daylight
lending would emerge only to the extent that
less-expensive modifications in payment practices
failed to eliminate daylight overdrafts.
Banks would not use ordinary non-interestbearing excess reserves to avoid daylight over
drafts, because the cost of financing them at the
federal funds rate normally would be greater
than the supplemental balance ratio times the
rate spread. Unlike the penalty rate proposal, the
supplemental balance approach would not
Supplemental Balances
■
11
necessarily eliminate all daylight overdrafts. Only
at a very low earnings rate on supplemental bal
ances (perhaps even a negative rate) would it be
certain that banks would find payment-system
modifications (or excess reserves) a cheaper way
to avoid daylight overdrafts.
The fee proposal has been suggested by
the Federal Reserve System’s Large-Dollar Pay
ments System Advisory Group. It would simply
have the Federal Reserve impose a fee for Fed
wire overdrafts in excess of a base amount estab
lished for each bank. The maximum cost to a
bank of a dollar’s daylight overdraft would be
that fee.
Extra excess reserves would not be used in
this case unless the fee were set
than the
federal funds rate. A limited daylight loan market
could develop, redistributing the required re
serves of banks whose need for daylight balances
was less than their need for required reserve
balances. And, of course, neither daylight over
drafts nor daylight loans might be necessary if
sufficient modifications in payment practices were
forthcoming at a marginal cost less than the fee.
In brief summary, then, each of the three pric
ing proposals might be capable of eliminating Fed
eral Reserve daylight overdrafts entirely through
inexpensive modifications in payment practices.
However, if modifying payment practices and
redistributing required reserves through a day
light loan market were not sufficiently respon
sive to price, the outcome of pricing would
differ substantially among the three proposals:
. The penalty rate regime would eliminate
remaining daylight overdrafts by expand
ed holdings of excess reserves and their
redistribution in a daylight loan market.
. The supplemental balance regime would
eliminate
of the remaining daylight
overdrafts by expanded holdings of
reserves in the form of supplemental bal
ances and their redistribution in a daylight
loan market.
• The fee regime would eliminate
of
the remaining daylight overdrafts, unless
the fee became a penalty rate.
Fees
higher
all
some
none
Note also that the penalty rate proposal contains the seeds of a prob
lem for monetary policy. Extra demand for excess reserves would be matched,
III. Pricing and
on average, by extra supply through open market operations, maintaining a
Moral Hazard
policy-desired level of the federal funds rate, on average. However, the varia
bility of the federal funds rate around the average rate might increase, reflect
ing variations in payment needs for balances within a day, or pertiaps day-today, unrelated to reserve requirements and monetary growth. A bulge in
payment needs that drove up the daylight loan rate during a day would drive
up the federal funds rate by the same amount, because the overnight earnings
rate on excess reserves is administratively fixed. No creditor would lend fed
eral funds during the day for less than the sum of the daylight loan rate and
the overnight rate. A s long as policymakers value the federal funds rate as a
tool or information variable, adopting the penalty rate proposal might involve
some risk of less-precise policy implementation.
Each of the three pricing proposals could reduce
daylight overdrafts, but to what extent would they
reduce moral hazard? None of the proposals
would directly relate price to a bank’s credit
quality or to the volume of its daylight overdrafts.
Nor would any of them introduce the kind of
actuarial relation between price and risk expo
sure needed to establish an insurance fund.
Reduced moral hazard would have to come as
a by-product of pricing, in some form of en
hanced market discipline. This could not be
administered by payee banks on Fedwire, for they
remain free of any risk in receiving payments.
Results, therefore, could come only from the
behavior of other creditors, or from eliminating
payments requiring daylight funding. Investigat
ing the adjustment mechanisms banks could use
in response to pricing, however, reveals an
uncertain basis for expecting market discipline
to flourish.
Excsss Reserves
Both the penalty rate and the supplemental
balance proposals could create a need to finance
extra holdings of interest-bearing reserve bal
ances. In both proposals, the earnings rate on
those balances would be uniform across all banks,
but the rate paid in the market to finance the
extra balances might vary with the credit quality
of a payor bank. If so, then the marginal cost of
avoiding or funding a daylight overdraft would
vary with the credit quality of the borrowing
bank, injecting market discipline into payments.
O f course, moral hazard in the current depositinsurance systems tends to dampen the role of
credit quality in pricing both deposits and de
posit insurance, and in pricing any kind of financ
ing for a bank considered “too big to let fail.”
However, to the extent that a bank’s marginal
cost of funds can vary with credit quality, moral
hazard would be diminished relative to the cur
rent arrangement of free daylight overdrafts.
Daylight Loans
Similar assertions are made about the market
discipline of a daylight loan market: if pricing
induced banks needing daylight funds to borrow
them from banks having surplus daylight funds,
risk premiums would emerge in daylight loan
rates, as market scrutiny sorted borrowers by
credit quality.
■ 12
Another strand of thinking about daylight overdrafts would add a third
qualification, also relevant to excess reserves: the “event risk” problem. Credi
tors might not have a w ay to assure themselves that the debtor would not
borrow additional sums, an event raising the riskiness of their loans after-thefact. If this were the case, early credit would be underpriced and risk premi
ums too low. This is a problem for any creditor, and gives rise to restrictive
covenants in lending agreements. To be a serious qualification in the daylight
loan case, however, would require a demonstration both that the second quali
fication does not hold, so that private lenders actually are at risk, and that
covenants in standard daylight loan agreements combined with innovations in
electronics network monitoring, such as already exist in C H IP S , could not deal
with the problem. A n elaborate treatment of the underpricing/overlending case
can be found in Gelfand and Lindsey (1989).
This argument needs two qualifications. 12 One
is that neither the supplemental balance nor,
more especially, the fee proposal provides much
basis for an extensive daylight loan market. Bal
ances available for daylight lending would be
limited to those of banks whose need for pay
ment balances was less than their required, or
required plus supplemental, reserve balances.
This suggests only a limited stock of reserve
deposits available for market allocation of day
light loans to replace free daylight overdrafts, at
least relative to the penalty rate proposal.
The second qualification recognizes the tooeasy presumption that daylight lenders actually
would be at risk. The presumption rests on an
apparent analogy between unsecured overnight
interbank loans in the federal funds market and
the envisioned unsecured intraday interbank
loans in a daylight loan market. Whatever the
similarity between overnight and intraday lend
ing, it does not extend readily to risk of loss.
Federal funds loans are risky even though their
dominant maturity is only one day. While deposit
insurance and the “too big to let fail” maxim
may minimize risk, it is still possible for a bank
to be closed, resulting in at least a delay in repay
ment, if not partial or complete loss of interest
and principal to its federal funds market creditors.
Even with assurance that a loan is for only one
day, banks routinely impose limits on their lend
ing to individual banks as a matter of credit pol
icy, and risk premiums sometimes are required.
Daylight loans would seem to be much closer
to a riskless opportunity. Under what circum
stances could a borrower fail to repay? One is if
regulatory authorities closed the bank
a
day, rather than following the precedent of clos
ing banks only after close of business.
Closing a bank in the midst of a day’s business
would seem exceedingly awkward in a financial
and legal environment where the timing of
competing claims arriving by different means
(over the counter, mail, messenger, telephone,
day-ahead magnetic tape, off-line telecommuni
cation, on-line telecommunication) is not readily
distinguished. In fact, one by-product of pricing
daylight overdrafts could be a standard timetable
for posting each off-line activity to the daylight
balance monitor, and use of that standard for
defining priorities among claimants. Such a m on
itor could make intraday closings easier to
arrange, but unless all of this were to become
well established, authorities are not likely to
close a bank during daylight hours.
Ruling out unexpected daylight closings means
that all lending and borrowing banks would have
access to Fedwire, and could make irrevocable
repayment of daylight loans if they wished to do
during
so. Daylight loans could be riskless because, in
the normal case, a bank
in trouble
would in no way be prevented from sending
Fedwires to repay daylight loans, even though
that were to result in a daylight overdraft.
It may seem ludicrous to imagine a bank bor
rowing in the daylight loan market in order to
avoid a daylight overdraft, but then repaying the
loan later the same day by going into daylight
overdraft— except as part of a tactic calculated to
trigger a discount-window loan or an overnight
overdraft. Nonetheless, the point is made— that
any bank on the ex post monitor could make
irrevocable repayment of a daylight loan during
banking hours
Daylight
loans would carry the risk of nonpayment only if
the borrowing bank preferred to default on the
loan rather than overdraw its account at a
Reserve Bank. Daylight loans are riskless unless
there are good reasons to think that any unex
pectedly insolvent bank would prefer default in
the market to overdraft at the Federal Reserve
and potential closing.
The inexpensive technology of ex post m oni
toring of daylight overdrafts is perfectly adequate
for ex post booking of a penalty rate loan, or ex
post calculating of a supplemental balance to be
held in the future, or ex post billing of a simple
fee. The difficulty with the technology is that it
leaves unclear who is at risk, or perhaps makes
only too clear who is
at risk, in interbank
daylight lending. As long as interbank daylight
lending is riskless, no market discipline emerges
from it. The moral hazard of free Federal Reserve
daylight overdrafts would remain the moral
hazard of private daylight loans.
unexpectedly
if it wanted to do so.
not
Payment Practices
Modifying payment practices would be expected
to reduce moral hazard. For example, as banks
replace overnight federal funds with longermaturity financing, their creditors would accept
and demand compensation for additional risk.
This risk formerly was accepted by the Federal
Reserve, when daylight overdrafts provided an
automatic means for an unexpectedly insolvent
bank to close without having renewed its over
night credit.
A different example of risk shifting is that of
netting the many payments of two customers
into a single obligation. This would eliminate
moral hazard because self-interest of the parties
in the netting process would demand risk eval
uation and compensation and would impose
limits on any credit-risk exposure they might
assume with respect to one another.
As a third example, pricing would encourage
the migration of payments from Fedwire to pri
vate networks. Moral hazard would diminish as
payments shifted to private systems because,
with prerequisite credit limits and loss-sharing
agreements in place among participants, banks
would be expected to ration and/or price net
work credit on the basis of credit quality.
How Much Good Would
Pricing Do?
One thing certain is that none of the proposals
would enlist the self-interest of payee banks
directly in monitoring the credit quality of payor
banks. As long as Fedwire provides irrevocable
ownership of good funds upon receipt, payee
banks do not extend credit in the Fedwire pay
ment process, are not at risk, and have no incen
tive to monitor the credit quality of payor banks.
Market discipline would have to originate
from other pressures on payor banks to manage
payment risks. That said, the most crucial
unknown factor is the rate at which the marginal
cost of modifying payment practices rises as the
volume of eliminated daylight overdrafts
increases. If this marginal cost rises relatively
slowly, so that inexpensive modifications effec
tively will eliminate all Fedwire daylight over
drafts, then moral hazard should disappear, sup
planted by the market discipline of risk-sharing
agreements in private payment networks, by net
ting agreements among banks’ customers, and
by the risk aversion of banks’ creditors (and,
perhaps in the future, of banks’ insurers).
On the other hand, if this marginal cost rises
relatively rapidly, the major burden of rationing
daylight overdrafts would have to be borne
through the direct mechanism of a pricing
scheme. In this event, conjecture becomes
somewhat more dependable — at least concern
ing the relative strengths of the three proposals.
The penalty rate proposal, while eliminating
daylight overdrafts altogether, is not likely to be
effective in removing moral hazard. Ex post day
light overdraft monitoring would leave the Fed
eral Reserve bearing the credit risk of an active
interbank daylight loan market, redistributing a
much enlarged volume of excess reserves. Highquality banks could borrow excess reserves
needed to avoid the penalty rate, not only for
their own accounts, but also for riskless lending
to lower-quality banks, with repayment assured
by irrevocable Fedwire transfers.
The supplemental balance approach would
more successfully tie the cost of daylight funding
to perceptions of a bank’s credit quality in the
interday markets (via a risk spread paid for sup
plemental balances). This seems to be the most
effective of the three pricing devices for injecting
market discipline into the cost of funding
payments.
The simple fee proposal offers little protection
against moral hazard to the extent that changes
in payment practices fail to eliminate daylight
overdrafts. Flat-rate pricing of assured access to
daylight credit may discourage its use, but pro
vides no basis for scrutiny of the credit quality of
payor banks, and no risk-based market disincen
tive for payor banks to limit daylight funding of
payments. 13
The higher the proposed price, the more scope
there will be for modifications in payment prac
tices to eliminate Fedwire daylight overdrafts.
But, in the limit, if sufficient modifications were
not forthcoming, a price above the federal funds
rate would guarantee elimination of daylight
overdrafts, no matter which proposal was
adopted, because excess reserves would be the
economical way to avoid the price. Charging this
high price would transform each proposal into a
variant of the penalty rate proposal. However,
unless a substantial earnings rate was offered on
overnight holdings of excess reserves, daylight
overdraft elimination would be quite costly to the
banking system. In any case, imposing this net
cost on banks and their customers to eliminate
daylight overdrafts would not avoid moral hazard
to the extent that excess reserves would feed an
extensive market in riskless daylight loans.
IV. Conclusion
Fedwire daylight overdrafts of Federal Reserve
deposit accounts create a moral hazard that pric
ing might reduce. Pricing could have the desired
result to the extent that banks would respond by
modifying payment practices, or by bringing
payments-related credit needs under more effec
tive market discipline based on risk evaluation.
Much of Fedwire payment and daylight over
draft volume can be traced to unsecured inter
bank lending and to settlement of securitiesmarket trading. Rapid growth of these activities
has taken place within the nationwide frame-
■ 13
This m ay overstate the case in one w ay. Pricing would operate only
on daylight overdrafts in excess of a "free" allowance, determined as a per
cent of capital. Price then depends on credit quality, in that capital influences
price. Beyond that first step, however, no discipline from the market or from
regulatory credit evaluation would discourage additional borrowing.
work of free Fedwire daylight overdrafts. There is
little basis in actual experience, therefore, for
predicting the responsiveness to pricing of either
Fedwire daylight overdrafts or the financialmarket activities they reflect.
The hope is that modifications in payment
practices would be sufficiently responsive to
price that there would be no need to test the
strength of credit-market discipline; that moral
hazard could be eliminated at relatively low cost.
The danger is that payment practices would be
unresponsive to price and that market discipline
would not be engaged because of a large residual
element of moral hazard in the form of priced day
light overdrafts or riskless daylight loans. If this
were to be the actual outcome, it would suggest
that, in addition to efficient allocation of finan
cial resources, an insidious driving force in the
rapid growth of interbank lending and securitiesmarket trading in recent decades has been the
moral hazard of Fedwire daylight overdrafts.
References
Board o f Governors o f the Federal Reserve Sys
tem, “A Strategic Plan for Managing Risk in the
Payments System,” Report of the Large-Dollar
Payments System Advisory Group to the Pay
ments System Policy Committee of the Federal
Reserve System, Washington, D.C., August 1988.
Gelfand, Matthew D. and Lindsey, David E.,
“The Simple Microanalytics of Payments Sys
tem Risk,” Finance and Economics Discussion
Series No. 61, Board of Governors of the Fed
eral Reserve System, March 1989Hamdani, Kausar and Wenninger, John A., “The
Macroeconomics of Supplemental Balances,
Appendix C,”
Report of the Task Force on Control
ling Payments System Risk to the Payments
System Policy Committee of the Federal
Reserve System, Board of Governors of the
Federal Reserve System, August 1988.
System,
Controlling Risk in the Payments
Humphrey, David B., “Payments System Risk,
Market Failure, and Public Policy,” in Elinor
Harris Solomon, ed.,
Electronic Funds Trans
fers and Payments: The Public Policy Issues,
Boston: Kluwer-Nijhoff Publishing, 1987.
Simmons, Richard D., “Would Banks Buy Day
time Fed Funds?”
Fed
eral Reserve Bank of Chicago, May/June 1987,
36-43.
Economic Perspectives,
Stevens, E.J., “Pricing Daylight Overdrafts,”
8816, Federal Reserve Bank
of Cleveland, December 1988.
Working Paper
VanHoose, David, “The Angell Proposal: An
Overview,” mimeo, Board of Governors of the
Federal Reserve System, June 1988.
Capital Subsidies and the
Infrastru ctu re C risis:
Evidence from the Local
M a s s -T ra n s it Industry
by Brian A. Cromwell
Brian a . Cromwell is an economist
at the Federal Reserve Bank of
Cleveland. The author would like to
thank Paul Bauer, Michael Bell, John
Davis, Randall Eberts, Erica Groshen,
Jam es Poterba, and William Wheaton
for useful suggestions and discus
sion. William Lyons and Dottie
Nicholas of the Transportation Sys
tem Center provided invaluable
assistance with the data. Financial
support from the National Graduate
Fellowship Program and the M IT
Center for Transportation Studies is
gratefully acknowledged.
tions and
concluded that “...the quality of Ameri
ca’s infrastructure is barely adequate to fulfill
current requirements, and insufficient to meet
the demand of future economic growth and
development. ” 2
Debates and studies of the infrastructure “cri
sis” involve a wide range of policy issues related
to measuring the costs and benefits of public
capital. The issue of what level of infrastructure
is optimal involves addressing questions of how
to measure the current state of and future needs
for public capital, how to measure the impact of
infrastructure on productivity and regional
growth, and how expenditures on public capital
should be weighed against other uses of public
monies. Questions of financing involve tradi
tional issues of fiscal federalism and public
finance, including what level of government
should provide infrastructure services, who
should pay, and what financing mechanisms
raise revenue with the least economic cost.
While most studies argue that increased public
investment is needed, a more provocative set of
Introduction
The condition of the public capital stock—
perceived by many to be dilapidated and
inadequate— has received considerable attention
in political, media, and academic circles in
recent years.
Pat Choate and Susan Walter’s
gave striking examples of crumbling infra
structure and suggested that enormous increases
in infrastructure investment were needed just to
maintain the existing levels of services. The media
and political attention given this work was high
lighted by tragedies such as the 1983 collapse of
the Interstate 95 bridge in Connecticut. More sys
tematic studies by the Urban Institute and the
Congressional Budget Office (1983) catalogued
the existing state of public infrastructure and pro
jected the need for new public investment. 1
More recently, the National Council of Public
Works Improvement (1988) completed a series
of studies examining the state of the nation’s
public infrastructure, entitled
Ruins
America in
Fragile Founda
■
1 The Urban Institute project included a series of case studies on munici
pal infrastructure. For example, see Humphrey et al. (1979). For a review of
infrastructure needs studies, see Peterson et al. (1986).
■
2
National Council of Public Works Improvement (1988), p. 1.
questions focuses on how public infrastructure
arrived at its present condition and critiques the
decision-making process itself In particular, it is
alleged that the structure of infrastructure financ
ing mechanisms, combined with political and
budgetary pressures, induce public officials to
systematically underfund the maintenance of the
existing capital stock, leading to excessive dete
rioration of public infrastructure. The study of
infrastructure maintenance, however, has received
little empirical attention due to the lack of data
on local maintenance policies and a lack of natu
ral experiments with which to evaluate publicsector maintenance.
This article reviews questions regarding infra
structure policy with a focus on how the costs and
benefits of public capital and maintenance deci
sions are potentially distorted by budget proce
dures, political pressures, and the structure of
federal grant policies. I then describe how the
local mass-transit industry provides an opportu
nity to investigate public-sector investment and
maintenance decisions. Empirical evidence from
two recent studies of the local mass-transit indus
try, Cromwell (1988a, 1988b), is then summar
ized. The results suggest the structure of federal
grant policies has important effects on infrastruc
ture decisions of state and local governments.
I. Infrastructure
Policy Incentives
Budget Processes
Leonard (1986) argues that ignoring deprecia
tion and deferring maintenance are both power
ful forms of hidden spending that are not
accounted for by local governments. Failure to
reinvest or maintain existing infrastructure is, in
effect, to live off an inherited bank account. Cur
rent taxpayers spend assets provided to them by
previous generations. This spending is obscured,
however, by the lack of records and comprehen
sive accounting for fixed-asset investments from
year to year.
Current accounting procedures for capital and
maintenance by local governments appear to be
inadequate for effective management of public
infrastructure.3 The Government Accounting
Standards Board, which sets standards for publicsector accounting, requires governments to
■ 3
These arguments were first advanced by Leonard (1986) and are also
presented in Blumenfeld (1986) and the National Council of Public Works
Improvement (1988).
maintain records of fixed assets recorded at his
torical cost in a separate account group held
apart from operating funds. Recording the value
of immovable infrastructure assets— bridges,
roads, sewers— is explicitly optional, as is the
recording of depreciation. Even if a governmen
tal unit does recognize depreciation, it is shown
as an offset to the value of assets, not as an oper
ating cost as in the private sector. When tight
funds result in deferred maintenance, there is no
notation in capital records of the decline in asset
values from the failure to maintain them, making
preventive and routine maintenance an attractive
target for budget cuts.
In a 1983 survey of city and county officials by
the American Planning Association, 29 percent
reported having poor information on the current
conditions of the city’s or county’s capital stock
and 48 percent felt they had weak methods of
evaluating the cost-effectiveness of proposed
projects. Hatry et al. (1984, 1986) surveyed over
40 public works agencies and found capital
investment decisions to be highly decentralized.
In general, agency management determined
what analysis should be undertaken and deter
mined priorities. While most agencies had for
mal procedures for rating and ranking potential
projects, these rankings were often based prima
rily on subjective information. They found few
explicit estimates of expected improvement in
service levels or expected reductions in future
costs from individual proposed projects.
Budgeting procedures for maintenance were
found to be even more deficient. The agencies
surveyed undertook only a small amount of reg
ular, systematic examination of capital mainte
nance and repair options and did not regularly
and systematically examine trade-offs between
preventive maintenance activity (such as painting
bridges or cleaning sewers) and other major
options, such as rehabilitation or reconstruction.
The Hatry study found no examples in which a
local government considered the costs of
deferred maintenance.
Several proposals for maintenance evaluation
procedures have surfaced in recent years for sev
eral common forms of public infrastructure. For
example, Archuleta (1986) proposed a program
for effective preventive maintenance for water
and wastewater facilities. Pavement maintenance
management systems promoted by the American
Public Works Association (1987) enable managers
to monitor road pavement conditions and sched
ule needed repairs. Carlson (1986) of the Fed
eral Highway Administration proposed a similar
systematic maintenance review process for
bridges. Implementation of such proposals,
however, often requires a crisis atmosphere. The
state of Connecticut, for example, instituted a
comprehensive bridge inspection and repair
program that identified and ranked needed
bridge reconstruction following the 1-95 tragedy.
There is no obvious general groundswell of pub
lic opinion, however, for the reform of infrastruc
ture accounting procedures.
Maintenance and
Visibility
Many aspects of the infrastructure problem, par
ticularly issues of maintenance and rehabilitation,
have low levels of visibility and are not readily
apparent to voters and elected officials. The costs
of neglected infrastructure accrue over time and
are not immediately apparent or measurable. As
discussed in Eberts (1988), often they occur in
the form of lost productivity and slower regional
growth. Even when observed, the long-run
benefits of maintenance practices are potentially
discounted by elected officials with short time
horizons. Cohen and Noll (1984), for example,
demonstrate that legislators maximizing the
probability of reelection seek to defer such costs.
Elected officials may also derive greater utility
from new investment than from maintenance.
Possible sources of utility from capital projects
for public officials include political support and
contributions from direct project beneficiaries.
Weingast et al. (1981) present a model of legisla
tive behavior in which the geographic incidence
of benefits and costs systematically biases public
decisions toward larger-than-efficient projects.
Capital projects give benefits directly to a small
group, while their costs are widely distributed.
Further political benefits come from being
associated with large and visible investment proj
ects that do not accrue from the more mundane
activities of maintenance. An assistant secretary
for Housing and Urban Development asked,
“Have you ever seen a politician presiding over a
ribbon-cutting for an old sewer line that was
repaired?” 4 Such effects further encourage the
substitution of investment for maintenance.
financing of new capital and the traditional
emphasis of federal grant policies on capital
subsidies.
Local governments often finance new pur
chases of capital, as well as major reconstruction
and rehabilitation, through borrowing. Ordinary
maintenance expenditures, however, are counted
as operating expenses and are financed through
current funds. This treatment of maintenance
stems in part from the wide variance of mainte
nance activities. Certain maintenance activities,
such as sweeping sidewalks or patching potholes,
have immediate short-term benefits and, accord
ing to the benefit principle of public finance
(those who benefit from public services should
pay), should be paid for by the immediate bene
ficiaries through current revenues. The benefits
of other maintenance activities, such as painting
bridges or flushing sewers, accrue over many
years. Maintenance of this sort constitutes a form
of public investment that according to the
benefit principle should be paid over many years
through debt-financing. 5
Treating all maintenance activities as current
expenses ineligible for debt-financing ignores
their investment component and results in under
financing when operating budgets are tight. Dur
ing periods of budget constraints, officials choose
between funding preventive maintenance at the
expense of cutting back on other programs, or
allowing infrastructure to deteriorate until major
reconstruction is needed, which can be funded
through debt. As the mayor of Lincoln, Nebraska
observed, “In the choice between laying off
police and maintaining sewers, the sewers
always lose. ” 6
Federal grant policies for public infrastructure
further exacerbate the bias against infrastructure
maintenance. Under the rationale that local tax
payers should pay to operate the facilities pre
sented to them, federal grants often heavily sub
sidize new construction, but provide no assistance
for maintenance or other operating expense.
A wide range of federal grant programs pro
vide major assistance for infrastructure at the
■
Capital Financing Policies
5
Maintenance is often considered in the operations research and
investment literature to be a fixed operating expense. For a standard example,
see the optimal equipment replacement model in Jorgenson et al. (1967) and
the discussion in Nickell (1978). For good reviews of models of preventive
The political and budgetary bias against infra
structure maintenance is reinforced by two
common features of capital financing: debt-
maintenance, see Pierskall and Voelker (1976) and Sherif and Smith (1981).
The treatment of maintenance as a form of investment is shown in Bitros
(1976). This approach is used in models of housing stock maintenance, in
which maintenance expenditures have important effects on rental income and
sale price. See Vorst (1987), Arnott et al. (1983), and Sweeney (1974) for
examples of such models.
■
4
Newsweek,
August 2 ,1 9 8 2 . Also cited in Leonard (1986).
■
6 Newsweek,
op. cit.
state and local level. In 1988, $25 billion in fed
eral grants accounted for 2 6 percent of state and
local capital spending. This included $13-7 bil
lion granted by the Federal Highway Administra
tion (FHWA) for the construction and rehabilita
tion of highways; $2 . 6 billion from the
Environmental Protection Agency for pollution
control and abatement; $2.4 billion in capital
financing for mass transit administered by the
Urban Mass Transit Administration (UMTA); and
$3.1 billion granted through the Community
Development Block Grant program .7
While the structure of grants varies from pro
gram to program, most provide capital assistance
at a high matching rate, with the state and local
government required to meet the matching
share. The FWHA provides financing for comple
tion, rehabilitation, and reconstruction of the
interstate highway system at a 90 percent match
ing rate. Discretionary grants from UMTA for
major rail and subway systems provide funds up
to a 75 percent matching rate. Formula grants
from UMTA pay 80 percent of the cost of regular
transit vehicle replacement. No corresponding
subsidies, however, are provided for mainte
nance. These subsidies distort the relative prices
facing local governments for new investment
versus maintenance of existing infrastructure.
Even if the federal matching rate is not specified
in formula, the expectation of federal aid poten
tially induces local officials to substitute away
from maintenance. The empirical work we now
turn to attempts to identify such substitution.
ever, I examine the impact of capital subsidies
on investment and maintenance decisions of
local governments, using data on the maintenance
policies of both publicly and privately owned
local mass-transit providers. While not address
ing all issues of infrastructure maintenance, these
studies suggest that the structure of federal
grants has significant effects on the infrastructure
decisions of state and local governments.
The data used were collected under the Sec
tion 15 Reporting System administered by the
Urban Mass Transportation Administration
(UMTA). Section 15 data for fiscal year (FY) 1979
through FY1985 are available for 435 transit sys
tems. The data set contains extensive informa
tion on vehicle fleets as well as expenditures
and labor hours for vehicle maintenance, provid
ing a consistent measure of public capital and
maintenance efforts not previously seen. These
data provide an unusually detailed panel of local
governments’ physical assets. Vehicle inventories
for each system are broken down by model, year
of manufacture, and mileage.
Data are also available for certain privately
owned and operated systems. Their inclusion in
the Section 15 data results from contracting with
a public recipient of Section 9 funds to provide
transit services. As these contracts often provide
for the leasing of public vehicles, care was taken
to examine maintenance and scrappage decisions
only on vehicles owned outright by private
operators.
Federal Transit Policies
II. Local Mass Transit:
A Natural Experiment
on Subsidies
and Infrastructure
As discussed in the previous section, several
elements of public accounting, political and bud
get processes, and capital financing potentially
lead to underfunding of infrastructure mainte
nance and result in excessive deterioration of
public capital. Empirical research on the relative
importance of these issues, however, has been
limited by a dearth of data on capital assets and
maintenance, and by a lack of obvious natural
experiments with which to evaluate public-sector
maintenance practices. In two recent studies,
Cromwell (1988a) and Cromwell (1988b), how-
■ 7
See U .S . Office of Management and Budget (1989). For further discus
sion of federal grants-in-aid, see Delmar and Menendez (1986).
The federal government finances a major part of
local public mass transportation. The principal
federal grant program for entities that only oper
ate bus lines (the focus of these studies) is the
Section 9 formula grant program that distributes
funds to urbanized areas for use in transit operat
ing and capital expenditures. The Section 9 capi
tal funds are principally used for vehicle replace
ment and pay up to 80 percent of the cost of a
new vehicle. As funds are adequate for normal
vehicle replacement, this matching rate represents
an enormous marginal subsidy for new capital.
Vehicle maintenance, however, is counted as
an operating expense and is ineligible for the
capital subsidy. Due to a desire by UMTA to
wean local entities away from operating assis
tance, the Surface Transportation Act of 1982
capped the level of funds available for operating
assistance for FY1983 and beyond to some 90
percent of the FY1982 level, or to 50 percent of a
property’s operating deficit, whichever was
T A B L E
III. Empirical Evidence
on Subsidies and
Transit Capital
1
Used Transit Vehicle Prices
in 1 9 8 7 and 1988
Evidence from
Used-Bus Prices
Year of
Manufacture
Average
Price
Public
1961-65
1966-70
1971-75
1976-80
Private
1961-65
1966-70
1971-75
1976-80
$ 301
841
1,648
Max.
Price
Min.
Price
$
$
8,863
1 ,0 0 0
3,500
6 ,0 0 0
17,000
$3,500
6,590
7,500
18,000
10 0
400
250
3,300
Number <
Observatic
255
163
239
8
—
—
11
—
—
11
—
—
—
9
1
SOURCE: Telephone survey by author.
lower. The overwhelming majority of publictransit properties are constrained by the cap and
receive no operating assistance on the margin.
Federal control over maintenance principally
consists of setting an upper limit for deteriora
tion of federally purchased equipment. UMTA
requires local transit properties to operate buses
purchased with federal funds for at least 1 2 years
or 500,000 miles.8 Failure to do so results in a
penalty in federal assistance for new capital pur
chases. This 12-year limit, however, is below the
potential operating life of 15 to 20 years for
standard bus models when properly maintained.
The structure of the UMTA grants results in a
large distortion in the relative price of mainte
nance versus new investment for buses over 1 2
years old. If the capital and maintenance deci
sions of local government are sensitive to the
structure of subsidies, we would expect the fol
lowing results. First, publicly owned buses
should depreciate quickly, with little physical or
financial value left after 12 years. Second, we
would expect higher average levels of mainte
nance in the private sector compared to the pub
lic sector. Finally, in the public sector we would
expect low levels of scrappage before the 1 3 year point, a marked shift in scrappage at year
13, then high levels of scrappage thereafter. A
similar pattern for privately owned vehicles is
unlikely, as they are not subject to such a discon
tinuity in the price of new equipment.9
Evidence from used-bus prices supports the thesis
that public equipment depreciates rapidly. The
used-bus market is highly fragmented and ad hoc
in nature. The disposition of equipment is not re
ported in the Section 15 data, and no central data
source of used-bus prices or sales exists. UMTA
officials report, however, that the used transit bus
market is depressed. The supply of public vehi
cles over 1 2 years old far exceeds demand— and
vehicles are most commonly sold for scrap.
Depressed prices, however, are also consistent
with systematic undermaintenance of equipment.
To confirm this, I collected transaction prices
for some 645 transit vehicles sold in 1987 and
1988 by contacting all properties that solicited
bids for used vehicles during this period . 10 The
results of this survey are shown in table 1. Prices
for publicly owned vehicles manufactured
before 1971 ranged from $100 to $3,500, with an
■9
Previous studies on transit subsidies have used detailed engineering
data from specific transit systems to simulate the effects of capital bias in the
subsidy structure on scrappage dates. Tye (1969) used data from the Cleve
land and Chicago transit systems to simulate the effect of subsidies in the late
1960s that paid for new capital at a 66.6 percent rate, but which provided no
assistance for operating expenses. He calculated that the subsidy would lead
a cost-minimizing transit firm to replace buses at half the efficient age. For
average levels of utilization, this implied scrappage at 8 to 10 years versus an
efficient 1 7 to 20 years, with the resulting waste of resources equaling 2 7 per
cent of the subsidy. Similarly, Armour (1980) used data from Seattle Metro
and calculated that the 80 percent federal capital subsidy reduced the optimal
scrappage point from 20.5 to 26 years to 8.5 to 10 years.
Frankena (1987) is the paper closest in spirit to the empirical work pre
sented here. Using probit estimation with 1961 to 1983 data on scrappage of
Canadian buses, this study shows that scrappage increases with age, and that
significantly higher average scrappage rates followed the imposition of a
capital-biased subsidy program in 1972. He finds no significant change, how
ever, in the scrappage rate when the capital subsidies take effect at age 15
(the critical point in the Canadian subsidy program). In general, the hazardmodel estimators used here dominate the probit approach. They allow for vari
ation in the underlying hazard rate over time, and control for bias introduced by
vehicles dropping out of the sample when scrapped. The results, as will be
seen, show a significant impact on scrappage when subsidies take effect.
■ 10
bids in
Used-bus prices were obtained by contacting all agencies soliciting
Passenger Transport
between January 1987 and June 1988. Typically,
less than 10 bids were received per auction with a mean of five bids reported
by properties that would provide this information. Those bidding included
Caribbean nations, church groups, charter-bus operators, people planning to
make recreational vehicles, and farmers in need of storage space. If the vehi
cles were purchased with federal funds, U M T A collected 80 percent of the
proceeds with an allowance made for administrative expenses. The costs of
soliciting bids or holding an auction, however, often were reported to exceed
■8
See U M T A (June 1985).
the remaining local share.
T A B L E
2
Vehicle Maintenance Expenses
and Labor Hours1
Private
Public
Expenses per
mile ($ 1 .0 0 )
0.77
( 0 .1 2 )
0.53
( 0 .0 2 )
Labor hours
per 1 , 0 0 0 miles
37.8
(3.6)
29.3
(1.4)
Percent of fleet
> 1 2 years old
38.4
2 2 .0
Percent mileage on
vehicles > 1 2 years old
26.7
1 1 .2
Number of observations
22
10 0
a. 1984 cross-section sample means (standard errors).
SOURCE: Author’s calculations.
average price of $511. Even vehicles reported to
be well-maintained typically did not sell for over
$3,000. Prices for vehicles manufactured between
1971 and 1975 ranged from $250 for scrapped
vehicles to $6 , 0 0 0 for well-maintained vehicles.
Prices for newer vehicles manufactured between
1976 and 1980 averaged $8,863.
I was also able to obtain used-vehicle prices
for a much smaller sample of privately owned
vehicles. These prices, also shown in table 1,
suggest that the private vehicles are in better
condition and command a higher price, with
prices averaging from $3,500 to $7,500 for vehi
cles manufactured before 1976. Other private
companies, however, reported selling their vehi
cles for scrap at the depressed prices similar to
those received by public agencies.
The extremely low prices on used buses sug
gest that maintenance practices can lead to rapid
deterioration of equipment in the public sector. It
is important, however, to distinguish between
variations in maintenance and depreciation attrib
utable to unavoidable operating conditions, and
variations due to capital grant policies or bureau
cratic behavior that are potential sources of gov
ernment inefficiency. The empirical work that fol
lows attempts to identity these separate effects.
Evidence on Maintenance
The impact of the capital grant structure on aver
age levels of maintenance is examined in
Cromwell (1988a). My initial empirical work
examines a cross-section of Section 15 data for
FY1984 from 122 transit properties. The sample
consists of single-mode bus operators—
properties that provide only fixed-route bus ser
vice as opposed to rail or demand-response
service— that operated at least five revenue vehi
cles. Table 2 reports sample means for mainte
nance expenses and maintenance employees,
scaled by annual vehicle miles. In general, the
average levels of both expenses and labor hours
follow the predicted patterns. The private sys
tems, on average, spend 45 percent more on
maintenance per mile and devote 29 percent
more labor hours to maintenance than do the
public systems.
The average age of vehicles in private systems
is substantially higher than that for public fleets,
with 38.4 percent of the private fleets being
more than 1 2 years old compared to 2 2 . 0 percent
of the public fleets. The distribution of vehicles
weighted by miles is similar, with 26.7 and 11.2
percent of the mileage being run on vehicles
older than 1 2 years for the private and public
systems, respectively. The older fleet in the pri
vate systems is consistent with privately owned
capital deteriorating slower than publicly owned
capital as a result of greater maintenance efforts.
The means shown in table 2, while consistent
with the predicted results regarding the private
versus public operators, do not control for sys
tematic differences due to wages, operating condi
tions, and fleet composition. For example, many
of the private systems operate in the New York
metropolitan area, which is noted for its harsh
operating conditions. To examine the public/
private differential more systematically, I use
pooled time-series cross-section regression anal
ysis on a sample of systems between 1 9 8 2 and
1985. Independent variables include maintenance
wage rates, operating conditions, fleet composi
tion, fleet age, and a dummy variable for opera
tion in the New York area. The results show that,
controlling for wages, operating conditions, and
fleet composition, privately owned transit com
panies devote some 14 to 17 percent more labor
hours to maintenance than do publicly owned
and managed transit companies. The analysis then
uses this public/private differential, along with
cross-state variation in grant policies, to measure
the elasticity of maintenance with respect to cap
ital subsidies. The point estimates suggest an
elasticity of -0 .1 6 , meaning that a 1 0 percent
increase in the subsidy rate for transit capital
reduces vehicle maintenance by 1 . 6 percent.
The estimates are statistically significant and
suggest that average maintenance levels are
higher in the private sector. They do not neces
sarily demonstrate, however, that public capital
deteriorates at a faster rate than privately owned
F
I
G
U
R
E
capital. The higher levels of maintenance labor
hours could be attributed to less capital-intensive
maintenance practices. Furthermore, an implicit
assumption that maintenance is qualitatively sim
ilar between the two sectors could be false. If
one sector fixes equipment upon failure, as
opposed to conducting preventive maintenance,
differences in overall maintenance levels could
result. The companion analysis in Cromwell
( 1 9 8 8 b), however, directly examines the scrap
page and retirement rates of private versus pub
lic equipment to determine whether the higher
maintenance in the private sector is reflected in
longer equipment life.
Scrappage Rate
Public Vehicles
Percent
Evidence on Scrappage
Vehicle Age (years)
SOURCE: Author’s calculations.
F
I
G
U
R
E
Scrappage Rate
Private Vehicles
Percent
2
Cromwell (1988b) examines the impact of sub
sidies on equipment life by tracking vehicles in
the UMTA data set from 1982 through 1985.
Scrappage decisions were observed for 15,829
vehicles, including 1,005 privately owned vehi
cles from 11 privately owned companies. Vehi
cles that changed from active to inactive status or
that were dropped from the fleets between report
years were counted as scrapped. The results pro
vide strong evidence that federal grant policies
have a direct impact on local scrappage decisions.
The probability of scrappage for public and
private vehicles of different ages (or empirical
hazard) can be estimated directly from the
observed scrappage rates and is plotted, with 95
percent confidence intervals, in figures 1 and 2 . 11
The estimates in general suggest the importance
of federal grant policies for public-sector scrap
page. The hazard for public vehicles averages
under 4 percent for years prior to age 13, then
jumps to over 1 1 percent at age 1 3 , decreases
slightly at age 14, then rises steadily to 37 per
cent by age 19. Standard errors calculated for
these estimates suggest that the hazards for pub
lic vehicles are measured with much precision
and that the shift at the 1 3 -year point is statisti
cally significant.
■
11
The empirical scrappage rate presented here is also known as the
Kaplan-Meier (1958) hazard estimator, which directly estimates the hazard
function from the sample of vehicles. For each time /, the number of failures
D(t)
(that is, the number of vehicles scrapped) is divided by the total number
of vehicles at risk at the start of time
t, R(t).
Censored spells (that is, vehicles
that are not observed to be scrapped) are included in the risk set previous to
their censor time and are dropped thereafter. This treatment of censoring
Vehicle Age (years)
SOURCE: Author’s calculations.
yields a consistent estimate of the true hazard at each time
t
as long as the
censoring mechanism and vehicle age are independent of each other. The
standard errors were estimated following a suggestion in Kalbfleisch and
Prentice (1980).
F
I
G
U
R
E
Scrappage Rate
Private vs. Public Vehicles
Percent
Vehicle Age (years)
SOURCE: Author’s calculations.
Percent
3
The private-vehicle hazards are estimated with
less precision and exhibit more volatility, but in
general show a rise in scrappage from near 0 for
the 1 -to 6 -year period to an average 5 percent
for the 7- to 10-year period to 9 percent at the
13-year point. Due to only one scrappage out of
143 in the age- 1 2 risk set, however, the esti
mated hazard at year 1 2 is quite low, and a shift
appears to occur at the 1 3 -year point— contrary
to the predicted pattern. This shift can be attrib
uted, however, to the smallness of the sample
size and, given the estimated hazards in the sur
rounding years, the pattern of estimated hazards
for private vehicles appears to be markedly dif
ferent from the public sector.
These empirical hazard rates do not account
for heterogeneity across transit systems in prices
of maintenance and operating conditions. Given
the large number of private vehicles operating in
the New York metropolitan area, for example,
adverse operating conditions might have a major
impact on observed private-sector scrappage. To
account for this heterogeneity, I employed a haz
ard estimator that allows for nonparametric esti
mation of the baseline scrappage rate, while per
mitting estimation of the impact of operating
conditions, wage rates, and other explanatory var
iables. 12 The resulting baseline hazards are shown
in figure 3. The impact of the grant structure on
public-sector scrappage is readily apparent.
While the private-sector baseline remains under
5 percent until year 16, and then rises steadily
through year 2 0 , the public-sector baseline takes
a distinct and significant jump at the 1 3 -year
point from 1 percent to over 8 percent, twice
that of the private sector. Scrappage then rises to
over 14 percent for 15- and 16 -year-old vehicles
and remains above the private sector until year
19. The distinct difference in scrappage rates can
be attributed to the availability of federal grants.
An alternative approach to examining public
and private scrappage is to look at the survivor
functions for the two sectors. The survivor func
tion is defined as the percentage of vehicles of a
given vintage that survive to a given age, as
shown in figure 4. The functions further empha
size the difference between public and private
■ 12
The baseline hazard estimates shown here are estimated using the
semiparametric hazard estimator shown in M eyer (1988) and first developed in
Vehicle Age (years)
Prentice and Gloeckler (1978). This estimator allows for control of explanatory
variables without imposing a specific structural form on the underlying baseline
SOURCE: Author’s calculations.
hazard. Cromwell (1988b) also presents estimates using the fully parametric
estimator which imposes the commonly used Weibull baseline as shown in
Lancaster (1979) and Katz (1986).
scrappage policies. They track closely through
year 1 2 , then diverge as public scrappage sharply
increases. Again, this shift in the survivor func
tion at the 1 3 -year point can be attributed to the
sudden availability of federal subsidies. By age
1 6 , only 47 percent of the public vehicles sur
vive, compared to 73 percent for private vehicles.
At age 20, 45 percent of private vehicles are still
estimated to be in operation, versus 2 0 percent
for the public sector.
The consistently lower survival rate of publicly
owned vehicles after the availability of federal
funds is direct evidence that federal capital
grants reduce equipment life in the local public
sector. It suggests that federal grant policies that
subsidize the purchase of new capital, but that
ignore the maintenance of existing capital, result
in the increased deterioration of public infra
structure. The magnitude of savings for the tran
sit industry from a shift in policies, however, may
be small if increased maintenance expenses
offset reduced vehicle expenditures. In a simula
tion of vehicle replacement reported in Crom
well (1988b), this is the case. In spite of
increased deterioration of public capital, the net
efficiency losses of the federal subsidies appear
to be low. There may be unobserved costs, how
ever, in terms of quality of service that result
from lower maintenance levels and increased
deterioration of equipment.
IV. Conclusion
Several aspects of public accounting, political
and budgetary procedures, and capital financing
potentially lead local governments to systemati
cally underfund the maintenance of public infra
structure. The resulting excessive deterioration
of public capital has been advanced as a possible
source of the “infrastructure crisis” of recent
years.
This article summarizes the results of two stud
ies of one aspect of infrastructure maintenance:
the impact of large federal capital subsidies for
new investment with no corresponding subsi
dies for maintenance. Using data from the local
mass-transit industries, the empirical results sug
gest federal subsidies for new transit vehicles
lower maintenance levels and increase scrap
page rates in public transit systems. The
extremely low resale value of used vehicles
further suggests excessive deterioration. In the
case of local mass transit, however, the net cost
of the distortion appears to be small. The results
suggest that increased purchases of vehicles are
offset by lower maintenance costs.
While the efficiency losses of the transit subsi
dies for new vehicles appear to be small, they
still show that local governments respond signifi
cantly to incentives in the price of maintenance
versus new investment introduced by federal
subsidies. Given the several other biases against
infrastructure maintenance discussed in section
I, this suggests that federal policies should focus
more on the maintenance and upkeep of facili
ties purchased with federal funds. Possible pro
posals to support maintenance include reducing
the distortion in the relative price of mainte
nance versus new investment facing local author
ities through direct federal subsidies of impor
tant maintenance activities or through a
reduction in the federal subsidy rate for capital
projects. Adoption of preventive maintenance
programs developed by public works experts
could also be a requirement of receiving federal
aid. Leonard suggests the development of a
maintenance schedule at the time of acquisition
of a new capital facility. The financial require
ments for maintenance would be a formal liabil
ity recorded on a jurisdiction’s financial state
ment. Reforms in this direction would help
ensure that existing capital is better preserved
and that large projected investments in new
infrastructure are not wasted.
Finally, future research in this area could
include analysis on how the incentive effects
described here for the local mass-transit industry
apply to other forms of infrastructure. Using the
standard optimal equipment replacement model
in Cromwell (1988b), one would expect that the
elasticity of optimal equipment life with respect
to capital subsidies is larger for capital goods
with shorter useful equipment lives, and larger
for capital goods whose acquisition costs are
large relative to maintenance costs. It would be
interesting to examine the difference in magni
tude of the distorting effects of federal subsidies
for infrastructure with these characteristics.
Furthermore, the distorting effects of capital
subsidies are likely to be more severe when the
deterioration of infrastructure is less visible— as
in the case of sewers, water mains, or the under
sides of bridges. Less visibility reduces the ability
of voters or federal bureaucrats to monitor the
condition of local infrastructure. Such monitor
ing potentially acts as a check on the incentives
to undermaintain that are introduced by capital
subsidies.
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89,
Em ploym en t Distortions
Under S tic ky W ages
and M on e tary Policies
to M in im ize Them
by James G. Hoehn
Jam es G. Hoehn is an economist at
the Federal Reserve Bank of Cleve
land. The author would like to thank
Charles Carlstrom, Brian Cromwell,
Randall Eberts, William Gavin, Anil
Kashyap, and John Roberts for help
ful discussions and comments on
drafts of this paper.
Introduction
A major problem that monetary authorities must
address is that contracts are made in nominal
terms. During the contract interval, the terms
may become inappropriate and cause misalloca
tions if one of the parties has discretion over
activity levels.
The prototype case emphasized by macroecon
omists is that of the labor contract, which may
run for three years, during which the nominal
wage is stuck, despite changes in the marginal
productivity and disutility of labor caused by var
ious events. Employers have some discretion over
employment levels and can improve profits by
adjusting employment in response to changes in
the state of the economy. The profit-maximizing
employment level will not, generally, be the
same as the socially optimal level because the
wage is stuck and does not perfectly reflect
changes in the disutility of labor. An optimal
monetary policy has the effect of tending to
make the real wage match the marginal disutility
of work in various states of the economy.
This article explores how the money supply can
be manipulated by the Federal Reserve to keep
the real wage close to the marginal disutility of
work in various states of the economy, and there
by minimize social welfare losses associated with
the employment distortions arising from sticky
wages. The primary contribution of the analysis
is to provide a social welfare metric defined in
terms of the outcomes of an IS-LM Phillips Curve
model. Simulations are run to compare the social
loss under various monetary policies, including
the one that is optimal in the model, as well as
policies that target money, output, nominal
income, and the price level. The simulations are
not intended to encompass all possible struc
tures of the economy, but instead are meant to
suggest how various policies might compare
under the assumptions of the model in meeting
the social goal of labor-market efficiency.
I. Employment Distortion
Under Nominal
Wage Contracts
According to the basic neoclassical theory of
wage determination, wages tend to be set at a
level that reflects both productivity and disutility
of work. If the nominal wage is set in advance, it
will tend to be set at a level equal to the
expected marginal revenue product of labor and
the marginal disutility of work. Then, the real
wage will be expected, on average, to clear the
labor market, and employment will be at optimal
levels (leaving aside issues related to monopoly
power or other such sources of externalities,
which are not essentially monetary problems
because there is little the monetary authorities
can do to ameliorate them).
Once the nominal wage is set, unanticipated
events can render that wage incorrect and cause
misallocation. For example, if the demand for
commodities rises beyond what was expected at
the time contracts were signed, and if monetary
policy keeps the money supply constant, the
price level will rise, lowering the real wage
under contracts. This reduction in the real wage
will tend to cause an expansion of employment
by profit-maximizing firms. In an extreme case
of period-by-period profit-maximization, the
expansion of employment would carry to the
point at which the marginal product of labor falls
to the lower real wage. This expansion of
employment is socially inappropriate because
the additional employment produces less value
of output than the disutility of work it incurs.
To take another example of how predeter
mined wages can result in inefficiency, consider
an autonomous cyclical labor productivity
improvement. Further assume, for illustration,
that as output supply increases, the price level is
kept from falling by monetary expansion. The
profit-maximizing firms expand employment in
order to take advantage of the higher productivity,
but will not face increasing unit labor costs if the
contract calls for employees to supply all the labor
the firm wants at a predetermined wage. Employ
ment will overexpand because firms are not
required to consider the rising disutility of work.
Ideally, real wages should be regulated by pol
icy so that they match the marginal disutility of
work. In the case of an autonomous cyclical labor
productivity shock, real wages should rise to
keep pace with the rise in the disutility’ of work
associated with higher employment. A monetary
policy that tended to allow the price level to fall
when autonomous increases in labor productivity
occur could help real wages match the marginal
disutility of work. Then, the employment level
would still rise with productivity improvements,
but not excessively so. One policy that tends to
set up a negative relation between labor produc
tivity shocks and the price level is a nominal
income, or GNP, target. In simulations with a
model, GNP targets are close to optimal in that
people’s time tends to be allocated between
labor and leisure in an appropriate way.
II. A Simulation Model
The simulation model combines the notion of
sticky wages and the IS-LM demand apparatus
with autonomous labor productivity shocks.
Elsewhere, I have shown that a simpler
(constant-velocity) version of the model can
account for stylized facts, such as the natural-rate
hypothesis and the mild procyclicity of real
wages and productivity (see Hoehn [1988]), so
long as forward-looking expectations guide
nominal wage contractors. The IS-LM apparatus
for representing intuitions about demand is pre
ferred here over simple velocity equations,
because the effects of monetary policy can be
offset or enhanced by changes in velocity, and
because IS-LM allows assessment of the informa
tion policymakers can obtain from observations
on the nominal interest rate. The model has
three shocks: to money demand, to commodity
demand, and to the marginal labor productivity
schedule. These features provide a model con
sistent with the stylized facts and containing util
itarian welfare criteria for policy
Relative to the standard macroeconomic m od
els involving wage stickiness, four changes are
offered to make a useful policy model.
(i) Expectations of inflation and productivity
are forward-looking (Muthian rational).
(ii) Labor productivity is subject to autono
mous cyclical variations (as well as to variations
induced by shifts in commodity and labor
demand).
(iii) Employment is determined not strictly by
demand, but is also influenced by supply.
(iv) The information content of the interest
rate is used by goods demanders and the central
bank.
To incorporate these features, the following
model is offered.
Supply Sector
Following Fischer (1977), represent multiyear
nominal wage bargaining with two-period stag
gered, or overlapping, contracts. The model
economy is composed of two groups of firms,
identical in all respects, except for the date at
which currently effective labor contracts were
signed. Firms having signed wage contracts at the
end of last period
1 ) are referred to as group
one firms, while those that signed wage con
tracts at the end of the period before last
are referred to as group two firms. The groups
are competitive in that they take the commodity
price as given, and contract with workers to pay
them their expected marginal revenue product.
(t -
(t-2 )
Economywide aggregates are simulated by tak
ing the average of the two groups’ firms.
The main difference between the determina
tion of wages in the model here and that of
other sticky-wage models is that contract wages
here adjust completely and efficiently to informa
tion available at the time of wage bargains. In
some other models, such as that of Taylor
(1979), wages can take longer than a contract
interval to respond completely to events, and are
subject to random variations conceived of as
wage-setting errors. Taylor’s model can be justi
fied as more realistic. However, the model used
here is more consistent with microeconomic
theory about the determination of wages and is
consistent with the natural-rate hypothesis: the
average level of employment is invariant with
respect to the money supply rule.
As in most sticky-wage models, variations in
employment are those for a representative worker.
Implicitly, employment variations are variations
in hours worked among workers who each have
jobs in all states of the economy. The model falls
short of accounting for unemployment.
The determination of employment and wages
reflects both Keynesian and neoclassical ele
ments. Hall (1980) and Barro (1977) have
sought to reconcile the fact of sticky wages with
the neoclassical theory of employment determi
nation by arguing that sticky wages need not
have any misallocational effects. Efficient con
tracts, which could be implemented in the
absence of transactions or enforcement costs,
would involve optimal employment determina
tion as productivity varied, so that sticky wages
would have no allocational effects. Here, it is
supposed that there are constraints on optimal
contracts that prevent workers and firms from
effecting optimal contracts. However, the tradi
tional Keynesian assumption that employment is
strictly demand-determined is softened. Instead,
the employment reflects both the optimal level
(the employment level associated with the inter
section of demand and notional supply curves)
and the demand for labor at prevailing prices
and wages. This is simulated by an equation for
employment that makes it a weighted average of
both the optimal level and the notional demand.
The weight attached to the demand can be con
ceived of as the degree to which sticky wages
have misallocational effects or, alternatively, the
degree to which the problems of ideal contract
enforcement are effective constraints.
In order to derive this employment equation,
first the notional labor demand is developed,
then the notional labor supply is formulated, and
then they are put together. Finally, the employ
ment equation, in conjunction with the produc
tion function and stochastic assumptions about
productivity disturbances, implies a supply func
tion, or Phillips Curve: a semireduced form
equation for output supply as a function of the
state of technology and unexpected inflation.
Notional Labor Demand
A firm’s production function is
(1)
Yit = UtN yit , 0 <
< 1,
7
i=
1,2,
Yit
t, Nit
U
i
where
is the output of a firm in group in
period
is the labor input of a firm in group
and
is a global productivity shock. The
marginal product of labor is
i,
Vty ( N „ y ^ ^ \
(2)
«=
1,2.
In logarithmic form, output is
(3 )
y it = ut + y n it, i=
1
,2 ,
u,
n
where the lowercase letters
and
are natu
ral logarithms of their uppercase counterparts.
The (log of the) marginal product of labor is
(4)
dY'.
In i —aNjt
— ) = ut + ln ( y ) - ( l- y ) n it,
i=
1
,2.
i
The notional demand for labor by firm in
period
d
i t, is given by the condition that the
real wage equals the marginal product of labor:
t, n
(5)
( wit- p t ) = ut + In ( y ) - ( \ - y ) n d
it,
i=
1
,2,
or
(5 0
nf
p, ) + ut+ In (
=— -—
1- 7
7
)],
where wjt is the (log of the) wage received by
group firms’ workers in period
and
is the
(log of the) price level.
i
t,
p
Notional Labor Supply
The notional supply of labor to a firm is condi
tioned on the real wage rate: 1
(6 )
n% =
0
O+
jS j>
/31(w it- p t ),
, i = , .
0
1
2
Determination of
Contract Wage
Aggregate Commodity
Supply
If the labor market cleared each period, fully
reflecting the taste and technology conditions
underlying notional labor supply and demand,
These elements are sufficient to specify the
supply sector of the economy, under the
assumption that labor input partly reflects the
demand, and partly reflects the optimal level:
n 1t= n it ’ t^ien employment level at firm
i in period t would be
(11) n it = <f>nft + (l-</>)«* .
n*it = [p0+ (3xln (y)\M 0+ (3XM0 ut
(7)
where
M0 = [1+0 ^1-y)]
- 1
,
n
with * denoting the market-clearing employ
ment level. If wages were not sticky, but varied
to clear the market, they would be
w*t = p,+ [In (
(8 )
7
) - (1
-y)f30\ M0 + M0ur
The contractual wage rate is the expectation of
the rate that would clear the labor market. The con
tract wage for group is found by taking the expec
tation of ( 8 ) conditioned on information available
in period
when the contract was signed.
i
The parameter </> represents the degree to which
sticky wages cause misallocations, or employ
ment distortions.
Using (3), (5'), (7), (9), (10), and (11), it can
be shown that the (log of the) output of group
one is
( 12)
y \ t= y A+ M 2et + M\P\t t~\
+ A/]P j W /, _ 2 +
G-^pf- Et _\pt },
where
A = [J30+ J31In ( )]M0
1M0
M,:
=
+
7
t-i,
7
wit = Et i p t + [In (
+ M0E,_i ut ,
(9)
7
) - (1 -7 ) ^ 0 ]
Mq
Et i
ut= p xu, _j + t t ,
0 < p < l , e ~ N ( 0, cje2)
M0 )
A/0( l- 4 > )
7
1
1
-
7
-
7
and the output of group two is
03
) y2,= 7 ^ + M2et + M2plet_ 1
+
1
M^p]ut_2 + Gx (pt - Et_2 p t ).
Total output for the economy is taken as the
average of
and 2t:
y Xt
(14)
1
/8 1
t-i
ut
■
7
7
1 -
where
is the operator that conditions ran
dom variables on realizations at
and earlier.
Note that, in this formulation, the nominal wage
will generally be different in each of the two
periods subject to the contract.
Finally, let
be a first-order autoregressive
process,
(1 0 )
( 1
1
y
y t= y A + M 2et+
+ Mxp]ut_2 + Gq ^ (pt E^jpt^),
i =1
The notional labor supply schedule could be derived from the primitive
where
utility function:
c 0+ c ,
Yt - c 2Nct\
c, >
0, c 2 >
0, c 3 >
1,
2 (1
M.
-
+
0 7 M0
2 (l-7)
3
and the budget constraint:
7 M0)
Yr (W ,IP ,)N r
The first-order condition on
N
=
is:
Taking the natural logarithm and rearranging it, one obtains the labor supply
function:
n t = In
wt -Pi7
[ c , / c 2 c 3 ] + ------------ ^—
which is the same as equation (6) of the text for
= 1/(c
3-
7
0
2(1 - 7 )
c 1 ( ^ / P , ) = c 2c 3 A /f3 ‘ 1).
-
■
/ } Q= In
[c ,
Ic 2c 3]
1). (Thanks to Charles Carlstrom for this argument.)
and
Equation (14) provides a characterization of
the supply sector of the economy. It shows that
output depends on productivity variations and
on unanticipated inflation, both with coefficients
that depend uniquely on the elasticity of output
with respect to labor input, y, the elasticity of
notional labor supply, ,, and the degree of
misallocation, <£. Higher
values increase the
responsiveness of output to productivity varia
tions; the responsiveness of output to unantici
pated inflation is proportional to </>.
fi
(31
Demand Sector
The demand sector of the model is a variant of
the familiar IS-LM apparatus, introduced in
Hoehn (1987). The main innovation is that
goods demanders are allowed to update their
inflation expectations in light of the current
nominal interest rate and to revise their assess
ments of the real interest rate accordingly. Much
complexity in solutions results from this innova
tion. The innovation is necessary if the authori
ty’s use of the information in the interest rate is
to be studied without making the implausible
assumption that the authorities know more
(specifically, the current interest rate) than do
other people. The innovation ensures that any
influence monetary policy has over real variables
does not arise from superior information.2
The commodity demand function, or IS curve,
yf= b0 - bl[Rt- ( E \_ xp t+!-/>,)] + x t ,
bx> ,
(15)
0
xt= p2x t_ j + A,,
< p 2< , k ~ N (0 ,o 2
K)
(16)
0
1
where
E t - \ Pt+ i = E [pt + | n j ,
1
Clt =
S
observable state of economy at time
t
and = state vector (given a specific identity in
the next section). The nominal interest rate, t ,
is measured as the natural logarithm of unity
plus the coupon rate of return. The future price
■ 2
R
The effect of allowing goods demanders to extract information about
inflation from the nominal interest rate was analyzed extensively in Hoehn
(1987). It can reverse the usual effects of money supply or demand shocks on
the price level and output during the temporary period before shocks become
fully known to all. For example, output and prices m ay temporarily rise in
response to an increase in money demand. But such cases arise only in cases
of extreme policies, such as crude attempts to smooth interest rates by
expanding money greatly in response to a rise in the interest rate, or where
structural parameters or relative variances of shocks take on extreme values.
E)_ xp t+x
expectation,
, is conditioned on the
observed state of the economy, t , an informa
tion set that includes the current economywide
interest rate,
, and the lagged state vector,
j .
j can differ from
+ x be
cause people use the current nominal interest
rate to update their inflation expectations.
is a
stochastic demand shock.
The money-demand function is conventional:
St_ E +t_
Cl
Rt
Et_ xp t
xt
(17)
m dt -p '= a0 - a xRt+ a 2y t + vt ,
(18)
vt= p$)t_ x+ t\t i
0
< p 3<
1
,
r)~ N (0 ,o 2),
vt
where
is the log of the quantity of money and
is a first-order autoregressive random
disturbance.
vt
Policy Sector
Given the model, a policy rule that is adequate
for the policy targets and criteria to be consi
dered, is
(19)
mf=
qRt + n0 + iixut_ x
+ ^2^1- 1 + ^ 3 Xt - 1 + ^ 4 E [ -
2 Ut _ j
•
Harberger Welfare Metric
The loss function measures a representative indi
vidual’s frustration in obtaining an optimal alloca
tion of time between labor and leisure, as pro
ductivity and demand conditions change. The
method, due to Harberger (1971), of measuring
individual frustrations uses the labor supply and
demand curves, assuming that they accurately
reflect preferences and thereby show how
workers and firms would want to adjust output
and employment in response to changing pro
ductive opportunities. Equilibrium between
notional supply and demand is then supposed to
be optimal. Equilibrium values of output and
employment in this log-linear model are a strict
log-linear function of
, as shown in equation
(7). The welfare loss is taken as proportional to
the square of the deviation of the actual from the
optimal employment level. This welfare-loss
metric is proportional to the area of the familiar
Harberger welfare-loss triangles, as shown in the
figure of the next section.
In the model with two staggered contracting
firm groups, an approximate measure of the
expected Harberger welfare loss over the span of
a contract is
ut
F I G U R E
Optional Employment Equates
the Marginal Product of Labor With
the Marginal Disutility of Work
treatment of the simpler case in which the
authorities know the full state and can change
the money supply continuously to keep employ
ment for both groups of firms at the ideal level.
Readers interested in the final-form solution and
the optimal policy rule in the full model may
find them available in Hoehn (1989).
The optimal employment level for each group,
, is determined by the intersection of the
marginal product of labor schedule,
, and
the labor supply or marginal disutility of work
schedule, s, as shown in the figure. This
employment level will be chosen by firms only if
the real wage is equal to (
(This state
ment holds true for any degree of misallocation,
, except zero, in which case nominal wage
stickiness cannot create employment distortion.
The case illustrated here is the simple case of
pure demand-determination of employment,
</> = 1. O f course, the size of employment distor
tions will be smaller if <^> is a fraction.)
The optimal employment level and the real
wage that will induce firms to choose the
optimal employment level vary with autono
mous labor productivity shocks. For example, a
cyclical improvement in labor productivity raises
the optimal employment level and the asso
ciated real wage. The figure illustrates this with a
shift in the marginal product of labor schedule
from
to
, which raises the optimal
employment level to
This optimal level will
be chosen by firms if the real wage rises to
(
The productivity shock case reveals the suboptimality of a price-stabilization policy. Because
nominal wages are fixed during the contract
interval, stable prices imply that the real wage
would remain at the initial level of (
Firms would choose the employment level
j, at which the marginal product equals the
unchanged real wage. The expansion of
employment from * to
is an excessive
response to the improvement in productivity,
because the marginal disutility of work exceeds
the marginal product of labor for employment
levels above
The Harberger welfare loss tri
angle is BAD.
To prevent firms from overexpansion, the
monetary authorities should allow the price level
to fall by enough to raise the real wage to
(
. Somewhat ironically, this policy will
involve an expansion in the money supply. If the
money stock were unchanged, the price level
would fall too much as output rose. For exam
ple, if the velocity of money were constant and
the quantity of money were constant, then a
productivity improvement would raise the mar
ginal product of labor and— via deflation— raise
n*0
Marginal
3roduct
3f labor
MPL0
n
w/p)*0 .
Marginal
disutility
3f work
<p
*eal wage
Employment
SOURCE: Author’s calculations.
(20)
E (n Xt- n*Xt)2
+ E (n 2t- n*2t)2,
Expected Welfare Loss =
njt
where the
are actual employment levels and
the
are the market-clearing employment
levels of equation (7). This measure is the sum
of the variances of employment from optimal for
each of the two periods of any contracting firm,
during which it will first be a group-one firm,
and then a group-two firm.
n*it
MPL0 MPL x
u /p )\ .
w/p)*0 .
n
n
III. How Policy Can
Minimize Employment
Distortions
To understand how a well-chosen policy rule
can improve welfare, it is useful to examine the
nature of the money-supply responses to various
shocks that would fully prevent employment dis
tortions. Such a degree of success is not possible
in reality because of policymaker uncertainty
about shocks. In the model simulations, it is
assumed that the authorities know the structure
of the economy, the current interest rate, and the
lagged state of the economy; the authorities do
not have full information about current shocks.
This complicates analysis, motivating a heuristic
n\.
n\
u /p )\
nx
□
(u /p )
the real wage by the same amount, to
j,
leaving the profit-maximizing level of employ
ment at
. The labor market is then at point
in the figure, with welfare loss triangle EFA.
The optimal policy response to the productivity
shock is to expand the money supply enough to
moderate the deflation, so that real wages rise to
(
, but no further.
The shift from point
to point
in response
to the productivity improvement will always be
obtained under a nominal income target,
because that shift lowers the price level and
raises the output level by the same proportion,
leaving their product unchanged. In the simula
tions with the IS-LM demand apparatus, the
velocity of money falls with favorable productiv
ity shocks. Consequently, the nominal income
target will necessarily require increases in money
to obtain point . If the increase in money is
not forthcoming, as under a constant-money pol
icy, the price level will fall more than one-forone with the productivity improvement, and the
profit-maximizing employment level falls below
. The welfare loss resulting from sticky wages
under a productivity shift is greater under a con
stant money policy than under the nominal
income target, once velocity changes are
accounted for.
The optimal policy response to a commoditydemand or money-demand shock is easier to
understand than the optimal response to a pro
ductivity shock. In the model as specified, such
shocks do not alter either the marginal product
of labor schedule or the marginal disutility of
work. Consequently, the optimal level of
employment is unchanged. The optimal policy
will attempt to prevent the employment level
from changing with demand and money shocks.
Employment can be insulated from distortions
arising from such shocks by a policy that stabi
lizes the price level. A stable price level prevents
the real wage from changing, preventing firms
from desiring a change in employment. Money
supply should be decreased with increased
commodity demand by an amount adequate to
prevent inflation. Money supply should be
increased one-for-one with increases in the
money-demand function.
A policy of output stabilization is unambigu
ously worse than a policy of price stabilization.
Both of these policies give an appropriate
response to commodity-demand and moneydemand shocks, but the distortion concurrent
with a productivity shock is unambiguously
larger under the output stabilization policy. As
soon as a single-minded output-stabilizing
authority observes a productivity improvement, it
will deflate the price level by reducing the
F
n*Q
iv/p)\
E
F
n*0
F
money supply The result is deflation sufficient
to drive the real wage above (
, and
employment declines below
, say to
The ability of the authority to stabilize output
in this example is limited because recontracting
firms can offset the real-wage effects of excessive
deflation by lowering nominal wages. As soon as
one of the groups recontracts, it will reduce
wages to aim at an increased employment level,
driving the authorities to further reduce
employment in the second group via yet more
deflation. The second group cannot protect itself
against the negative employment distortions by
recontracting for lower nominal wages until one
more period passes and the old contract expires.
The second group’s employment must be
reduced, if output is to be stabilized, by enough
to offset not only the economywide increase in
productivity, but must also offset the increase in
employment at the recontracting firms, who will
rationally anticipate deflation and reduce wages
to allow employment to increase to the optimal
employment level. Because the loss function is
the sum of squared group employment distor
tions, the concentration of the employment dis
tortion in the second group of firms leads to a
sizeable welfare loss.
u /p )x
n*Q
n- .
IV. A Numerical
Simulation
In order to illustrate how various policy rules
influence employment distortions arising from
sticky wages, a simulation can be conducted
with particular numerical values for structural
parameters. The values chosen for this simula
tion were the following:
(2 1 )
/?1=
1/ 2
=
7
ax = a2 =
2
cj“ =
1
ct“
1 / 2
2 /3
= 2
0
=
bx =
1
1
a^= 5
p,= 4/5,
i-
, , .
1 2 3
The elasticity of labor supply with respect to
the cyclical variations in the real wage was set at
one-half, an arbitrary but plausible value. The
elasticity of output with respect to labor input,
7
, was set at the midpoint of its permissible
range, also arbitrary but plausible. The value
assigned to the money demand elasticity with
respect to the nominal interest rate,
, implies,
for example, that an increase in the rate from 5
to 6 percent would, for given levels of income
and prices, lower real money demand by
approximately 1.9 percent. The money-demand
elasticity with respect to output,
, was set at
somewhat less than unity, as suggested by
ax
a2
T
A
B
L
E
1
Alternative Policy Rules ( 0 = 1 )
Policy Criterion
Parameter2
q
Mi
Money
Output
Price Level
Nominal Income
Optimal
0.0
0.0
0.0
0.0
0.0
+1.06
-1.97
-2.44
+0.80
-0.05
+3.35
-1.56
+0.80
-0.84
+0.62
+0.48
+2.06
-1.98
+0.80
b
a. The m oney supply rule is m( - qR{ + /Uj u( _ j + n2 x t - l +
g oods supply, and m oney demand.
b
^3 vt - 1 + ^4 ^ t - 2 ut - V where u, x, and v are disturbances to g ood s demand,
b. The policy parameter ^4 is irrelevant to the criterion. In simulations,
SOURCE: Author’s calculations.
T A B L E
+1.73
-2.10
+0.80
-0.04
^4 is set to zero.
2
Response of Money
to Innovations ( 0 = 1 )
Policy Criterion_________________________________
Innovation
Money
Output
Price Level
-0 . 1 1
-2.17
-1.81
+3.41
+2.05
+1.25
+0.98
+1.33
+1.06
+0.25
-1 . 6 0
-1.28
-0.01
- 1.60
-1.28
+0.15
- 1.60
-1.28
+0.12
- 1.60
-1.28
+0.31
+0.80
+0.64
-0 . 0 2
+0.80
+0.64
+0.19
+0.80
+0.64
+0.15
+0.80
+0.64
Productivity
t
t- 1
t-2
0 .0
0.0
0 .0
+
0.01
Nominal Income
-
0.06
Optimal
-
0.06
Goods Demand
t
tt-2
0.0
1
0 .0
0 .0
Money Demand
t
tt-2
0 .0
1
0 .0
0 .0
SOURCE: Author’s calculations.
abstract analysis of the transactions demand for
money. The commodity-demand elasticity with
respect to the real interest rate,
, was set to
unity because, of all (equally arbitrary) values,
unity is the most straightforward choice. (Econo
metric evidence currently available does not
provide direct knowledge of this elasticity.) The
relative sizes of the disturbances give consider
able scope to demand-side influences on output
and employment, and allow for a relatively
unstable money-demand function.
In the basic simulation, firms were assumed to
choose employment to equate the marginal prod
uct of labor with the real wages, so </> = 1. In a
second simulation, </> was set equal to one-third,
in order to see whether the results of the basic
bx
simulation were robust with respect to this
parameter.
Five different policy rules were simulated,
with their response coefficients chosen so as to
target ( 1 ) money, ( 2 ) output, ( 3 ) the price level,
(4) nominal income, or (5) optimal employ
ment. The last of these is, of course, the only
optimal policy by the criterion employed, but it
is instructive to compare results of other poten
tial targets.
The policy rules’ response coefficients, and
the '■, are displayed in table 1. The final-form
solution for the money supply is determined by
both these coefficients and the solution for the
nominal interest rate (because of the
term in
the money supply rule), and is shown in table 2
q
n
qRt
T
A
B
L
E
3
Welfare Losses Under
Alternative Policies ( 0 = 1 )
Loss due to
shocks to:
______________________________________ Policy Criterion
Money
Productivity7
Goods demand
Money demand
Output
Price Level
6.91
4.52
14.99
3.04
0.24
1.80
1.96
1.28
14.29
18.27
5.04
2 .8 6
TOTAL LOSS
Nominal Income
Optimal
0 .6 6
0.19
2.35
0.76
3.51
3.30
0 .3 8
2.47
SOURCE: Author’s calculations.
for each of the five alternative policies. In the
immediate period of impact, the monetary
authority’s response to a shock is equal to , its
interest rate response coefficient, times the
response of the interest rate to the shock. For
example, under a policy of stabilizing output, the
money supply is increased 1 . 0 6 for each onepoint change in the interest rate. A productivity
shock in period reduces the interest rate by
-0 . 1 0 (not shown in tables) under this policy rule,
so the response of money at time M o a produc
tivity shock in period is 1 . 0 6 times -0 .1 0 , or
about -0 .1 1 .
Only after one period has passed can the
monetary authority observe all three shocks
independently and tailor its response to each
one separately. For example, the output-stabilizing policy contracts the money supply by 2.17 at
time for a one-unit innovation to productivity
in the previous period,
This response
reflects two channels: first, an indirect channel
involving the change in the interest rate, -0.19,
times the response coefficient = 1.06, or about
-0.20. To this is added the direct response coef
ficient on
1 productivity,
= -1.97. Together,
these add to -2.17, the total contraction of the
money supply required to prevent period
out
put from responding to period - 1 productivity
innovations. A similar calculation involving direct
and indirect effects finds that the outputstabilizing policy contracts the money supply at
time by 1.81 in response to a unit productivity
innovation in period
Aside from the constant-money policy, the pol
icies considered are identical in their moneysupply responses to goods demand or money
demand shocks, once these shocks are observed.
In this model, all the activist targets are essentially
equivalent in terms of the implied response of
the money supply to these demand-side shocks.
The main difference among the active moneysupply policies lies in the response of money to
q
t
t
t
et_ x .
q
t-
n]
t
t
t-2 .
-t
productivity shocks. The output-stabilizing poli
cy’s response is too restrictive; it contracts
money at time by 2.17 after a unit productivity
innovation in period
1 , contrasting with an
optimal increase of 1.33. The price-stabilization
rule responds too expansively; it expands the
money supply by 3-41. The nominal income
target’s response is to expand the money supply
by 1.25, very close to optimal. These differences
among alternative active policies in their
response to productivity shocks account for the
relative rankings of their efficiency.
Expected welfare losses under alternative pol
icies, shown in table 3 , are the sum of the mean
squared deviations of group one and group two
employment levels from optimal employment
levels. Given the information constraint the
authority faces, it can reduce this loss measure to
3.30 using the optimal policy. Most of this loss,
2.35, is attributable to goods-demand shocks
occurring in the current period; a small fraction
is attributable to productivity shocks occurring in
the current period. Distortions due to shocks in
period
can be completely eliminated by
policy responses, while distortions due to
or earlier shocks are eliminated by wage recon
tracting by both groups of firms.
The nominal income targeting policy is close
to optimal; its welfare loss is 3-51, only slightly
higher than for the optimal policy. The outputstabilizing policy is far worse, with a total
expected loss of 18.27, most of which is due to
productivity shocks. The constant-money policy
is not much better than the output-stabilizing
policy; it generates substantial employment dis
tortions in the face of goods-demand and
money-demand shocks, which the activist poli
cies make active efforts to prevent. Finally, the
price-stabilization policy results in somewhat
greater losses than the nominal income policy,
but results in much smaller losses than the out
put or money targeting policies.
t
t-l
t-
t-2
Response of (nzt - n*2 t)
to Innovations ( 0 = 1)
Policy Criterion
Innovation
Money
Output
Price Level
Nominal Income
Optimal
-0.28
-1.64
-0.34
-3-84
-0.28
+1.28
0.0
-0.32
-0.42
0.0
-0.30
+0.70
0.0
+0.78
+0.76
0.0
0.0
0.36
0.0
-0.26
-0.28
Productivity
t
tt-2
1
0.0
0.0
0.0
0.0
Goods Demand
t
tt
-
+0.70
+1.58
1
+0.88
0.0
0.0
2
0.0
0.0
0.0
0.0
Money Demand
t
tt-
-
0.38
-
-0.80
0.0
1
2
0.16
0.0
0.0
-
0.0
0.0
0.0
0.0
0.0
SOURCE: Author’s calculations.
T
A
B
L
E
5
Welfare Losses Under
Alternative Policies With 0 = 1 / 3
Loss due to
shocks to:
______________________________________ Policy Criterion
Output
Money
Price Level
Productivity
Goods demand
Money demand
0.51
1.37
0.83
0 .6 0
TOTAL LOSS
2.72
Nominal Income
Optimal
0.05
0.54
0.04
0.54
0.14
0.44
0.32
0 .2 2
0 .2 2
1.78
0.98
0.80
0.79
1.03
0 .2 1
SOURCE: Author’s calculations.
The deviations of employment from optimal
for the two groups can be read from table 4. The
table lists the deviations for the second group; the
deviations for the first group, (
\,), are the
same as for the second group for period ?
shocks, but recontracting by this group makes
the period - t employment distortion equal to
zero for t 1 or earlier shocks. A one-unit inno
vation in productivity at time t raises the optimal
employment level for both groups by 0.40 in
time
Given that the effect of an innovation on
the marginal productivity schedule decays at the
rate
= .8 , optimal employment increases by
0 . 3 2 and by about 0.26 in response to unit pro
ductivity innovations in periods t - 1 and t - 2 .
The gross suboptimality of the output-
nxt - n
-
t.
px
stabilizing policy reflects the employment distor
tion in the second, nonrecontracting, group, in
response to a productivity innovation in period
Because policy responds by contracting the
money supply, generating deflation and an
excessive rise in the real wage for the nonrecon
tracting group, employment for that group falls
by 3 52, in sharp contrast with the increase of
0.32 in optimal employment. The distortion is
then -3.84. In order to keep output fixed, the
authorities must reduce employment in the
second group, and this reduction must be
enough to offset both the economywide produc
tivity improvement and the rise in employment
by 0 . 3 2 in the first, recontracting, group.
The GNP targeting policy is very close to
t-1 .
T A B
L
E
6
Relation Between Money
and Output Under Alternative Policies
(0=1)
Policy Criterion
Covariation due
to shocks to-.
Productivity
Goods demand
Money demand
CORRELATION
Money
0 .0
0 .0
0 .0
Output
Price Level
Nominal Income
Optimal
-1.51
+0 . 2 2
-1.95
+8.76
-0 . 0 1
+0 . 0 2
+3 . 1 0
+0 . 1 2
-0 . 1 2
+3.48
+0.09
-0 . 1 1
-0.30
+0.59
+0.30
+0.34
SOURCE: Author’s calculations.
optimal. It handles money-demand and
commodity-demand variations appropriately, and
generates a mild and nearly optimal deflation in
response to productivity improvements. The
degree of closeness to optimality depends on
various parameters, but is not, it appears, sensi
tive to the degree to which sticky wages cause
misallocations, 0 , at least at the chosen values
of the other structural parameters. Table 5 shows
the welfare losses in the model for </> = 1 / 3 .
The output targeting policy is generally the
worse in terms of employment distortion
(except when 0 = 1 / 3 , when the constantmoney policy is worse). The output targeting
policy generates the greatest losses when pro
ductivity shocks occur. Output targets handle
commodity- and money-demand shocks, how
ever, in an appropriate manner.
The price-stabilization policy results in over
employment when a productivity improvement
occurs. The policy is too stimulative; it does not
provide for the deflation required to raise the
real wage in line with marginal productivity at
the new optimal employment level. In the case
of commodity- and money-demand shocks,
however, a policy of price stabilization provides
essentially the same optimal response as does
the nominal and real GNP targets.
The constant-money policy accrues losses in
the case of all kinds of shocks. The loss attend
ing productivity shocks is less than in the case of
the output target, but the money-targeting policy
fails to respond appropriately to commodity- or
money-demand shocks. In the simulation, the
constant-money policy results in less employ
ment distortion than the output-stabilizing pol
icy, unless the degree of misallocation is small,
such as 0 = 1 / 3 .
V. Conclusion
A monetary policy that seeks to aid wage con
tractors in avoiding employment distortions due
to sticky wages will attempt to keep the real
wage equal to the marginal disutility of labor in
all states of the economy. Such a policy will
require money supply expansion when cyclical
improvements in labor productivity occur. To
the extent that productivity variations are an
important factor in the business cycle, the
optimal money supply rule will involve a posi
tive correlation between money and output. (See
table 6 .) Hence, the belief, common among
economists, that sticky-wage models argue for a
countercyclical or output-stabilizing policy is not
necessarily correct, once productivity shocks are
taken account of.
In simulations, it was found that a nominal
income target might be reasonably close to the
optimal policy. This result is useful because the
Federal Reserve may not be able to predict and
target optimal employment levels because of
uncertainty about the structural parameters and
shock variances needed in a welfare analysis, yet
can probably predict and target nominal income
using its models and judgmental forecasters.
After all, the main objective of macroeconomet
ric models has been the prediction and potential
control of national income. The analysis of this
paper tends to give additional justification to
proposals for nominal income targeting, includ
ing those by Meade (1978), Tobin (1980), Hall
(1983), Gordon (1985), and McCallum (1987).
The relative near-optimality of a nominal
income target might not be robust to all con
ceivable values of the labor market parameters,
7
and
however. For example, if the marginal
product of labor curve declines steeply ( 7 close
to zero), and/or if the notional labor supply
curve is nearly horizontal ( / very large), then a
price target will do as well or better than a nom
inal income target. More precisely, if
[l + /3j(l - 7 )] _ 1 is close to unity, then a
nominal income target will be close to optimal,
but if
is close to zero, then a price level
target will be close to optimal.3 In the simula
tion, 7 = 1/2 and
= 1/2, so
.8 , which is
rather close to unity. In order to adequately con
firm the relative efficiency of a nominal income
target relative to a price target, econometric evi
dence and a sensitivity analysis are needed to
rule out small values of
In general, the
optimal policy response to a productivity
improvement will be one that is less stimulative
than that implied by a price target and more stim
ulative than that implied by a nominal income
target.
If the specification of the model were modi
fied to allow for costs of changing commodity
prices ( “menu costs”), or to allow for some
degree of commodity price stickiness, then a
price-targeting policy might yet be better than a
nominal income target. Many other elements of
more detailed macroeconometric models have
unknown implications for the welfare analysis.
Much more research along these lines is needed
for an adequate welfare analysis of monetary pol
icy toward the business cycle.
M0=
Exogenous Variables
e
\
u
innovation to the productivity disturbance,
innovation to the commodity-demand dis
turbance, x
innovation to the money-demand distur
bance,
77
v
M0
/3{
M0 =
State Vector
=
r?,,
M0 .
Glossary of Variables
and Parameters
Endogenous Variables
y
y\
y2
p
R
m
w
w*
n
n\
n2*
n
■3
output
output of group 1 firms
output of group 2 firms
price level
nominal interest rate
money stock
wage rate
market-clearing wage rate
employment
employment of group 1 firms
employment of group 2 firms
optimal employment level
Bean (1983) apparently was the first to note this.
u t -1 ’ E t - 2 u t -1 ’
’ X t -1 >E t - 2 X t -1 >
v,_x , Et_2vt_l }
Information Set,
or Observed State
^
’ ^t
-1 ’
E t - 2 v t-\
E t -2
-1 ’ X t -1 ’ E l - 2
X t -1
’ ^7-1 ’
)
Parameters
All nonpolicy parameters are nonnegative.
<2 , = elasticity of money demand with respect to
interest rate =
(
(1 + )
= elasticity of money demand with respect
to output
= elasticity of aggregate demand with respect
to real interest rate
j3j = elasticity of notional labor supply with
respect to real wage
7 =
elasticity of output with respect to
labor input
coefficient of money-supply response to
interest rate
= coefficients of money-supply response to
lagged state variables (see equation 19 of
the text)
cb
din M/P ) /din
R
bx
q-
Hi
at =
2
ax =
av =
variance of productivity innovation
variance of commodity-demand innovation
variance of money-demand innovation
References
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July 1977,
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the Conduct of Monetary Policy,”
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