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RIVAL NOTIONS OF MONEY
ThomasM. Humphrey

Introduction

Bullionist Controversy

The rise of Milton Friedman’s version of monetarism in the 1960s and early 1970s provoked an
antimonetarist
backlash culminating in the late
Nicholas Kaldor’s The Scourge of Monetarism (1982).
Friedman stressed the ideas of exogenous (i.e.,
central bank determined) money, money-to-price
causality, inflation as a monetary phenomenon, and
controllability of money through the high-powered
monetary base. He traced a chain of causation running from open market operations to bank reserves
to the nominal stock of money and thence to aggregate spending, nominal income, and prices.
By contrast, Kaldor postulated the opposite notions
money,
of endogenous (i.e., demand-determined)
reverse causality, and inflation as a cost-push or
supply-shock phenomenon. He denied the possibility
of base control given the central bank’s responsibility to guarantee bank liquidity and the financial
sector’s ability to engineer changes in the turnover
velocity of money via the manufacture of money
substitutes. Kaldor’s transmission mechanism runs
from wages (and other factor costs) to prices to
money and thence to bank reserves. Wages determine prices, prices influence loan demands, and loan
demands via their accommodation in the form of new
checking deposits created by commercial banks
determine the money stock, with central banks
passively supplying the necessary reserves.
Kaldor claimed his attack on monetarism was in
the tradition of Keynes’s General Theory. So much so
that he labeled it “a Keynesian perspective on
money. ” In so doing, he contributed to the standard
textbook
tendency
to treat the monetaristantimonetarist debate as a post-Keynesian development. This article shows that the debate long
predates Keynes, that it is rooted in classical
monetary tradition, and that it traces back at least
to the bullionist-antibullionist
and currency schoolbanking school disputes in England in the nineteenth
century. More precisely, the following paragraphs
demonstrate that the arguments of Friedman and
Kaldor were fully anticipated by their classical
predecessors.

Monetarism did not begin with Friedman nor did
antimonetarism originate with Kaldor or Keynes’s
General Theory. Those doctrines clashed as early as
the Bank Restriction period of the Napoleonic wars
when the Bank of England suspended the convertibility of its notes into gold at a fixed price on demand. The suspension of specie payments and the
resulting move to inconvertible paper was followed
by a rise in the paper pound price of commodities,
gold bullion, and foreign currencies. A debate between strict bullionists, moderate bullionists, and antibullionists then arose over the question: Was there
inflation in England and if so what was its cause?

FEDERAL

RESERVE

Strict Bullionists:

(1797-1821)

the classical monetarists

Led by David Ricardo, the strict bullionists argued
that inflation did exist, that overissue of banknotes
by the Bank of England was the cause, and that the
premium on gold (the difference between the market
and official mint price of gold in terms of paper
money) together with the pound’s depreciation on
the foreign exchange constituted the proof. Price
index numbers not then being in general use, the
bullionists used the gold premium and depreciated
exchange rate to measure inflation.
The bullionists arrived at their conclusions via the
following route: The Bank of England determines the
quantity of inconvertible paper money. The quantity of money via its impact on aggregate spending
determines domestic prices. Domestic prices, given
foreign prices, determine the exchange rate so as to
equalize worldwide the common-currency
price of
goods. Finally, the exchange rate between inconvertible paper and gold standard currencies determines the paper premium on specie so as to equalize
everywhere the gold price of goods. In short, causality
runs unidirectionally from money to prices to the exchange rate and the gold premium. It followed that
the depreciation of the exchange rate below gold
parity (i.e., below the ratio of the respective mint
prices of gold in each country) together with the
premium on specie constituted evidence that prices
were higher and the quantity of money greater in
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England than would have been the case had convertibility reigned. Here is a straightforward application of the monetarist ideas of exogenous money,
money-to-price
causality, inflation as a monetary
phenomenon, and purchasing power parity. On these
grounds the strict bullionists attributed depreciation
of the internal and external value of the pound
solely to the redundancy of money and reproached
the Bank for having taken advantage of the suspension of convertibility to overissue the currency.
The strict bullionists also enunciated the monetarist
notion of control of the money stock through the
high-powered monetary base. With respect to base
control, they argued that the Bank of England could,
through its own note issue, regulate the note issue
of the country (non-London) banks as well as other
privately issued means of payment (bills of exchange
and checking deposits). Two circumstances, they
said, worked to ensure base controllability. First,
country banks tended to hold in reserve Bank of
England notes (or balances with London agents
transferable into such notes) equal to a relatively fixed
fraction of their own note liabilities. This established a constant relationship between the Bank note
base and the country note component of the money
stock. Second, a fixed-exchange-rate regional balance
of payments or specie-flow mechanism kept country bank notes in line with the Bank’s own issues.
Country bank notes were fully convertible into Bank
of England notes but did not circulate in London.
Should country banks overissue, the resulting rise
in local prices over London prices would lead to a
demand to convert local currency into Bank of
England notes to make cheaper purchases in London. The ensuing drain on reserves would force
country banks to contract their note issue, thus
eliminating the excess. For these reasons, the quantity of country notes was tied by a rigid link to the
volume of Bank notes and could only expand and
contract with the latter. The implication was clear:
Bank of England notes drove the entire money stock.
Country banks were exonerated as a source of
inflation.
The strict bullionists displayed another monetarist
trait in prescribing rules rather than discretion in
the conduct of monetary policy. Their rule called
for the Bank of England to contract its note issue
upon the first sign of exchange depreciation or rise
in the price of gold. This rule derived from the
famous Ricardian definition of excessaccording to which
if the exchange was depreciated and gold was commanding a premium the currency was by definition
excessive and should be contracted.
4

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Moderate

Bullionists

Moderate bullionists, led by Henry Thornton,
Thomas Malthus, and William Blake, modified the
strict bullionists’ analysis in one respect: they argued
that it applied to the long run but not necessarily to
the short. They held that in the short run real as well
as monetary shocks could affect the exchange rate
such that temporary depreciation did not necessarily signify monetary overissue. In the long run,
however, real shocks were self-correcting and only
monetary disturbances remained. Their position is
best exemplified by Blake’s distinction between the
real and nominal exchanges. The real exchange or
barter terms of trade, he said, registers the impact
of nonmonetary disturbances-crop
failures, unilateral
transfers, trade embargoes and the like-to
the
balance of payments. By contrast, the nominal exchange reflects the relative purchasing powers of
foreign and domestic currencies as determined by
their relative supplies. Both components contribute
to exchange rate movements in the short run. In the
long run, however, the real exchange is self-correcting
(i.e., returns to its natural equilibrium level) and
only the nominal exchange can remain permanently
depressed. Therefore, persistent exchange depreciation is a sure sign of monetary overissue. On this
point the moderate bullionists agreed with their strict
bullionist colleagues.
Antibullionists:

the classical

nonmonetarists

Opposed to the bullionists were the antibullionist
defenders of the Bank of England. They denied that
the Bank had overissued or that domestic monetary
policy had anything to do with the depreciating
exchange rate and rising price of gold. Such inflationary symptoms they attributed to real rather than
monetary causes. In so doing, they contributed two
key ideas that today appear in Kaldor’s work.
First was their supply-shock or cost-push theory
of inflation. They argued that crop failures and wartime disturbances to foreign trade had raised the price
of wheat and other staple foodstuffs that constituted
the main component of workers’ budgets. These
price increases then passed through into money
wages and thus raised the price of all goods produced by labor. Ricardo, however, convincingly
replied that this explanation confused relative with
absolute prices. For without excessive money growth,
a rise in the relative price of wheat that required
workers to spend more on that commodity would
leave them with less to spend on other goods whose
prices would accordingly fall. In that case the rise
in wheat’s price would be offset by compensating falls

SEPTEMBER/OCTOBER

1988

in other relative prices leaving general prices
unchanged.
Second, the antibullionists enunciated the notion
of an endogenous, demand-determined money stock.
This came in the form of their real bills doctrine, which
they employed to assert the impossibility of an excess supply of money ever developing to spill over
into the commodity market to put upward pressure
on prices. The real bills doctrine states that money
can never be excessive if issued upon the discount
of sound, short-term commercial bills drawn to
finance real goods in the process of production and
distribution. It purports to match money creation with
real output so that no inflation occurs.
The antibullionists used this idea to defend the
Bank of England against the charge that it had
caused inflation through overissue. The Bank, they
said, was blameless since it had restricted its issues
to real bills of exchange and so had merely responded to the real needs of trade. In other words,
the Bank, by limiting its advances to commercial
paper representing
actual output, had merely
responded to a loan demand for money already in
existence and had done nothing inflationary to create
that demand.
The real bills doctrine was an early version of
Kaldor’s notion that a passive, demand-determined
money stock cannot be overissued and so cannot
cause inflation. Antibullionists also anticipated Kaldor
in arguing that since no one would borrow at interest
money not needed, the Bank could not force an excess issue on the market. Such excess, they said,
would be speedily extinguished as borrowers returned
it to the Bank to pay off costly loans. In short, the
antibullionists held that the Bank could not cause
inflation since it merely supplied money passively in
response to a loan demand for it. Thus there could
be no excess issue to spill over into the commodity
market in the form of an excess demand for goods
to bid up prices.
Critique of the Real Bills Doctrine
Monetarists today criticize Kaldor’s notion of a
transmission mechanism running unidirectionally
from wages to prices to money for ignoring the feedback effect of money on prices. Adding this feedback loop produces a two-way interaction in which
prices and money can chase each other upward ad
infinitum in a self-reinforcing inflationary spiral.
Monetarists argue that such a spiral is sure to result
if banks, in passively creating new money in response
to loan demands for it, set the loan rate of interest
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below the expected rate of profit on the use of the
borrowed funds. In this case loan demands will be
insatiable and the resulting rise in money and prices
will be without limit.
Bullionists, especially Henry Thornton, advanced
exactly this same argument against the antibullionists’
real bills doctrine. That doctrine, they said, suffers
from two basic flaws. First, it links the nominal
money stock with the nominal volume of bills, a
variable that moves in step with prices and thus the
money stock itself. In so doing it renders both
variables indeterminate.
It thus ensures that any
inadvertant jump in money and prices will, by
raising the nominal value of goods in the process of
production and hence the nominal quantity of bills
eligible for discount, lead to further increases in
money and prices ad infinitum in a self-justifying
inflationary spiral. Second, it overlooks that the
demand for loans and volume of bills offered for discount depend not so much on real output to be
financed as on the perceived profitability of borrowing as indicated by the differential between the loan
rate of interest and the expected rate of profit on the
use of the borrowed funds. In particular, it fails to
see that when the profit rate exceeds the loan rate
the demand for loans becomes insatiable and the real
bills criterion fails to limit the quantity of money in
existence.
This last flaw, bullionists argued, rendered the real
bills doctrine an especially dangerous policy guide
under inconvertibility. To be sure, even under specie
convertibility a central bank that set its loan rate too
low relative to the expected profit rate would find
itself inundated with a potentially unlimited supply
of eligible bills clamoring for discount. But the
resulting rise in money and prices would, by
making home goods dearer than foreign ones, lead
to a trade deficit and a matching gold drain that would
force the bank to protect its metallic reserves by
raising its loan rate thereby ending the inflation. No
such result was assured under paper currency
regimes, however. For without the crucial check of
convertibility, the profit rate-loan rate differential
could persist indefinitely and with it the selfreinforcing rise in money, prices, and commercial
bills. This point was particularly telling during the
suspension period when usury ceilings constrained
the Bank of England’s lending rate to 5 percent at
a time when the expected profit rate, buoyed by the
boom conditions of the Napoleonic wars, was well
in excess of that level.
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Currency School-Banking
(1821-1845)

School Debate

Monetarist and antimonetarist doctrines clashed
again in the three decades following the Bank of
England’s restoration of the gold convertibility of its
notes in 1821. This time the debate focused on how
to protect the currency from overissue so as to secure
the gold reserve and ensure the maintenance of convertibility. The protagonists in this dispute were
known collectively as the currency school and the
banking school, but they were the intellectual heirs
of the bullionists and antibullionists. Leaders of the
currency school included such names as Samuel Jones
Loyd (Lord Overstone), George Warde Norman, and
Robert Torrens. Similarly, Thomas Tooke, John
Fullarton, James Wilson, and J.B. Gilbart led the
banking school.
The currency school’s bullionist predecessors had
assumed that a convertible currency needed no protection. If the currency were convertible, they reasoned, any excess issue of notes which raised British
prices relative to foreign prices would be converted
into gold to make cheaper purchases abroad. The
resulting loss of specie reserves would force the Bank
immediately to contract its note issue thus quickly
arresting the drain and restoring the money stock and
prices to their preexisting equilibrium levels. Given
smooth and rapid adjustment
(monetary
selfcorrection) convertibility was its own safeguard.
A series of monetary crises in the 1820s and 1830s,
however, convinced the currency school that adjustment was far from smooth and that convertibility per
se was not a guaranteed safeguard to overissue. It
was an inadequate safeguard because it allowed
banks-commercial
and central-too
much discretion in the management of their note issue. Banks
could and did continue to issue notes even as gold
was flowing out, delaying contraction until the last
possible minute, and then contracting with a violence
that sent shock waves throughout the economy.
Currency

School’s Prescription

What was needed, the currency school thought,
was a law removing the note issue from the discretion of bankers and placing it under strict regulation.
To be effective, this law should require the banking
system to contract its note issue one-for-one with
outflows of gold so as to put a gradual and early stop
to specie drains. Such a law would embody the currency school’s principle of metallic fluctuation according to which a mixed currency of paper and coin
should be made to behave exactly as if it were
wholly metallic, automatically expanding and con6

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tracting to match inflows and outflows of gold.
Departure from this rule, the currency school argued,
would permit persistent overissue of paper, forcing
an efflux of specie through the balance of payments,
which in turn would endanger the gold reserve,
threaten gold convertibility, compel the need for
sharp contraction, and thereby precipitate financial
panics. Such panics would be exacerbated if internal gold drains coincided with external ones as
moneyholders, alarmed by the possibility of suspension, sought to convert paper currency into gold. No
such consequences would ensue, however, if the
currency conformed
to the metallic principle.
Forced to behave like gold (regarded by the currency school as the stablest of monetary standards)
the currency would be spared those sharp procyclical
fluctuations in quantity that constitute a prime source
of economic disturbance.
The currency school scored a triumph when its
ideas were enacted into law. The Bank Charter Act
of 1844 embodied its prescription that, except for
a small fixed fiduciary issue, Bank notes were to
be backed by an identical amount of gold while the
country bank note issue was frozen at its 1842 level.
In modern terminology, the Act effectively established a marginal gold reserve requirement of 100
percent behind note issues. With notes tied to gold
in this fashion, their volume would start to shrink
as soon as specie drains signaled the earliest appearance of overissue. Monetary overexpansion
would be corrected automatically before it could do
much damage.
Banking School
The rival banking school flatly rejected the currency school’s prescription of mandatory 100 percent
gold cover for notes. Indeed, the banking school
denied the need for statutory note control of any kind,
arguing that a convertible note issue was automatically
regulated by the needs of trade and required no further limitation. This conclusion stemmed directly
from the real bills doctrine and law of reflux, which
the banking school took from the antibullionists and
applied to convertible currency regimes.
The school’s real bills doctrine stated that money
could never be excessive if issued on loans made to
finance real transactions in goods and services. Similarly the law of reflux asserted that overissue was
impossible because any excess notes would be
returned instantaneously to the banks for conversion into coin or for repayment of loans. Both doctrines embodied the notions of a passive, demanddetermined money supply and of reverse causality
running from economic activity and prices to money

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1988

rather than vice versa as in the currency school’s view.
According to the reverse causality hypothesis,
changes in the level of prices and production induce
corresponding shifts in the demand for bank loans
which the banks accommodate via variations in the
note issue. In this way prices help determine the note
component of the money stock, the expansion of
which is the result, not the cause, of price inflation.
As for the price level itself, the banking school
attributed its determination to factor incomes or costs
(wages, interest, rents, etc.) thus establishing the
essentials of a cost-push theory of inflation. The importance of the cost-push idea to the banking school
cannot be overestimated: it even led Thomas Tooke
to argue that high-interest-rate tight-money policies
were inflationary since they raised the interest component of business costs.
Antimonetarist

Ideas

The concepts of cost inflation, reverse causality
and passive money are the hallmarks of an extreme
antimonetarist view of the monetary transmission
mechanism to which the banking school adhered. Its
list of antimonetarist ideas also included the propositions (1) that international gold movements are
absorbed by and released from idle hoards and have
no effect on the volume of money in circulation,
(2) that an efflux of specie stems from real shocks
to the balance of payments and not from domestic
price inflation, (3) that changes in the stock of money
tend to be offset by compensating changes in the
stock of money substitutes leaving the total circulation unchanged, and (4) that discretion is superior
to rules in the conduct of monetary policy.
In its critique of the monetarist doctrines of the
currency school, which contended that note overissue
is the root cause of domestic inflation and specie
drains, the banking school argued as follows:
Overissue is impossible since the stock of notes is
determined by the needs of trade and cannot exceed
demand. Therefore,
no excess supply of money
exists to spill over into the goods market to bid up
prices. In any case, causality runs from real activity
and prices to money rather than vice versa. Finally,
specie drains stem from real rather than monetary
disturbances and occur independently of domestic
price level movements.
These arguments severed all but one of the links
in the currency school’s monetary transmission
mechanism running from money to prices to the trade
balance, thence to specie flows and their impact on
the high-powered monetary base and finally back
again to money. The final link was broken when the
banking school asserted that gold flows come from
FEDERAL

RESERVE

idle hoards (i.e., buffer stocks of specie reserves) and
could not affect the volume of money in circulation.
Falling solely on the hoards, gold drains would find
their monetary effects neutralized (sterilized) by the
implied fall in reserve-note and reserve-deposit ratios.
To ensure that these hoards would be sufficient to
accommodate gold drains, the banking school recommended that the Bank of England hold larger metallic
reserves. With regard to the currency school’s
prescription that discretionary policy be replaced by
a fixed rule, the banking school rejected it on the
grounds that rigid rules would prevent the banking
system from responding to the needs of trade and
would hamper the central bank’s power to deal with
financial crises. Finally, the banking school asserted
the impossibility of controlling the entire stock of
money and money substitutes through the bank note
component alone since limitation of notes would
simply induce the public to use money substitutes
(deposits and bills of exchange) instead. In other
words, the total circulation is like a balloon; when
squeezed at one end, it expands at the other. More
generally, the banking school questioned the efficacy
of base control in a financial system that could
generate an endless supply of money substitutes.
The currency school, however, rejected this
criticism on the grounds that the volume of deposits
and bills was rigidly constrained by the volume of
notes and therefore could be controlled through notes
alone. In short, the total circulation was like an inverted pyramid resting on a bank note base, with
variations in the base inducing equiproportional variations in the superstructure of money substitutes. In
counting deposits as part of the superstructure, the
currency school excluded them from its concept of
money. It did so on the grounds that deposits, unlike
notes and coin, were not generally acceptable in final
payments during financial crises.
Subsequent Developments
In retrospect, the currency school erred in failing
to define deposits as money to be regulated like
notes. This failure enabled the Bank of England to
exercise discretionary control over a large and growing part of the money stock, contrary to the intentions of the school. The school also erred in not
recognizing the need for a lender of last resort to avert
liquidity panics and domestic specie drains. With
respect to specie drains, the currency school refused to distinguish between domestic (internal) and
foreign (external) ones. As far as policy was concerned, both drains were to be handled the same way,
namely by monetary contraction. By the time Walter
Bagehot wrote his celebrated Lombard Street in 1873,
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however, it was widely recognized that the two drains
required different treatment and that the surest way
to arrest an internal drain was through a policy of
liberal lending. Such drains were caused by panicinduced demands for high-powered money (gold and
Bank notes) and could be terminated by the central
bank’s announced readiness to satiate those demands.
The currency school nevertheless
remained opposed to such a policy, fearing it would place too
much discretionary power in the hands of the central bank. These shortcomings in no way invalidated
the currency school’s contention that convertibility
is an inadequate safeguard to overissue and therefore
must be reinforced by positive regulation. Nor did
they undermine its monetary theory of inflation,
which was superior to any explantion its critics had
to offer.
As for the banking school, it rightly stressed the
importance of checking deposits in the payments
mechanism. But it was wrong in insisting that the
real bills doctrine, which tied note issues to loans
made for productive purposes, would prevent inflationary money growth. The currency school triumphantly exposed this flaw by pointing out that rising
prices would require an ever-growing volume of loans
just to finance the same level of real transactions. In
this way inflation would justify the monetary expansion necessary to sustain it and the real bills criterion
would fail to limit the quantity of money in existence.
Also, by the 1890s Knut Wicksell had rigorously
demonstrated the same point made by Henry Thornton in 1802, namely that an insatiable demand for
loans results when the loan rate of interest is below
the expected rate of profit on capital. In such cases
the real bills criterion provides no bar to overissue.
Despite this criticism the real bills doctrine survived in banking tradition to be incorporated as a key
concept in the Federal Reserve Act of 1913. And
during the German hyperinflation of 1922-23 the doctrine formed the basis of the Reichsbank’s policy of
issuing astronomical sums of money to satisfy the
needs of trade at ever-rising prices. Oblivious to the
Thornton-Wicksell
demonstration that the real bills
test provides no check to overissue when lenders peg
loan rates below the going profit rate, the Reichsbank
insisted on pegging its discount rate at 12 percent
(later raised to 90 percent) at a time when the going
market rate of interest was well in excess of 7000
percent per annum. This huge differential of course
made it extremely profitable for commercial banks
to rediscount bills with the Reichsbank and to loan
out the proceeds,
thereby producing additional
inflationary expansion of the money supply and further upward pressure on interest rates. The authori8

ECONOMIC

REVIEW,

ties failed to perceive this inflationary sequence and
did nothing to stop it. On the contrary, they saw their
duty as passively supplying on demand the growing
sums of money required to mediate real transactions
at skyrocketing prices. They simply refused to
believe that issuing money on loan against genuine
commercial bills could have an inflationary effect.
After the hyperinflation debacle of the 1920s, banking school doctrines reappeared in renovated form
as part of the Keynesian revolution. Keynes in his
General Theory (1936) stressed the banking school’s
notion of money entering idle hoards (liquidity traps)
rather than active circulation. He also stressed the
school’s ideas (1) of variable velocity absorbing the
impact of money-stock changes leaving spending and
prices unaffected, (2) of real rather than monetary
causes of cyclical depressions, and (3) of prices determined by autonomous factor costs. And in the immediate postwar period, Keynesians developed the
notion of cost-push inflation emanating from growing union bargaining strength, business monopoly
power, supply shortages, and other institutional
forces that produce autonomous increases in labor
and other factor costs. Only the banking school ideas
of unlimited money substitutes and the futility of base
control were missing. And these were provided in
the famous report of the British Radcliffe Committee (1959). Representing the apogee of postKeynesian skepticism of the relevancy of the quantity theory, the Radcliffe Report concluded that
attempts to control inflation by limiting the stock of
a narrowly defined monetary aggregate would merely
induce spenders to turn to money substitutes instead.
Velocity would rise to offset monetary restriction,
The Debate Goes On
Today currency school doctrines survive in Friedman’s work just as banking school doctrines appear
in Kaldor’s writings. When Friedman argues that rules
are preferable to discretion, that inflation is largely
or solely the result of excessive monetary growth,
that monetary shocks are a primary cause of cyclical
swings, and that the entire stock of money and money
substitutes can be governed by control of the highpowered monetary base, he echoes currency school
opinion.
Likewise, Kaldor echoes the doctrines of the banking school. The school’s cost-push theory informs
his view of inflation. Inflation, he argues, stems
mainly from increasing militancy of trade unions and
the resulting rise in unit labor costs caused by money
wages advancing faster than labor-hour productivity. The banking school’s notion of passive money
appears in his statement that money is a demand-

SEPTEMBER/OCTOBER

1988

determined variable that comes into existence as
banks accommodate loan demands and central banks
acting as lenders of last resort permissively supply
the necessary reserves. The school’s law of reflux
surfaces in his declaration that because money is
demand-determined
its supply can never exceed
demand; any oversupply is extinguished automatically
as borrowers return it to the banks to pay off costly
loans. Finally, the banking school notion of a potentially unlimited supply of money substitutes underlies
his belief in the futility of base control. Like the bank-

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ing school, he argues that restriction of the monetary
base induces offsetting rises in the stock of money
substitutes thereby thwarting base control.
In short, Kaldor emerges as the intellectual heir
of the banking school and the antibullionists just as
Friedman is the heir of the currency school and the
bullionists. It follows that the debate between the
monetarists and antimonetarists
is not of postKeynesian origin. Rather it has its roots in policy
controversies
going back to the era of classical
monetary thought.

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THE FORECAST PERFORMANCE OF
ALTERNATIVEMODELS OFINFLATION
Yash P. Mehra*
I
INTRODUCTION
What determines inflation? Several theoretical
models of the inflation process have been advanced
in the literature, and these models typically yield different predictions about the role of certain variables
in determining prices. To illustrate, consider, for example, the expectations-augmented
Phillips curve
model. This model generally assumes prices are set
as a markup over labor costs, the latter being determined by expected inflation and the degree of demand pressure. It is assumed further that expected
inflation is a function of past price history, and demand pressure can be measured by the excess of real
growth over potential (termed the output gap). Thus,
in the reduced-form price equation associated with
the Phillips curve model, past prices and the output
gap (or another demand pressure variable) play a key
role in determining the price level. This model thus
implies that by monitoring the behavior of these two
variables one could assess the outlook for inflation.
Another example is provided by the price equation
associated with the traditional monetarist model. In
this equation, lagged money growth is the predominant force in price determination. Thus, depending
upon the nature of the price structure chosen different
determinants of inflation have been suggested in the
literature.
The most controversial question raised by these
competing inflation models is, however, the following: which one of the theoretical models (equivalently, the key variables implied by the associated
reduced form price equations) can most accurately
describe the actual behavior of prices in recent years?
Interest in this question has revived as a result of
some recent evidence that the relationship that had
existed in the past between money and prices has
been severed in recent years. For example, in an important contribution, Stockton and Glassman (1987)
select four inflation models (three structural and one
* Economist and Researchthe Federal Reserve Bank
Officer,
of Richmond. The views expressed are those of the author, and
do not necessarily reflect the views of the Federal Reserve Bank
of Richmond or the Federal Reserve System.
10

ECONOMIC

REVIEW,

nonstructural), estimate the associated reduced form
price equations, and evaluate their comparative
forecast performance over a common period 197784. In two of the structural models (termed by
them as the traditional monetarist model and the
rational expectations
model with instantaneous
market clearing), actual or expected money (M1)
plays a key role in determining the price level. The
third structural model examined is the expectationsaugmented Phillips curve, in which past prices and
the output gap are the prominent variables. They
report that over the period 1977-84 the Phillips
curve model rarely performs worse and in the period
1981-84 performs substantially better than the other
two structural models. They also show that in many
cases a simple nonstructural time series model of inflation provides quite respectable forecasts relative
to the theoretically based price equations. They conclude that, at least in the 1980s, there is no support
for the monetarist view of the inflation process.
The main objective of this article is to present
additional evidence on the forecast performance of
alternative inflation models. It is now widely known
that the recent financial deregulation and disinflation
have altered the character of M1 demand. However,
such developments have not affected as much the
character of M2 demand.1 Hence, the relative poor
forecast performance of the inflation models in which
money growth as gauged by the behavior of M1 plays
a key role might be due to shifts in M1 demand. This
paper, therefore, reexamines the evidence using the
broader monetary aggregate M2. This article also
considers Fama’s (1982, 1983) alternative structural
model of the inflation process, in which inflation is
explained by money growth in excess of growth in
real money demand. The Fama model implies that
in assessing implications of higher money growth for
future inflation it is necessary to control for changes
in the demand for money.2
1 Simpson and Porter (1984), Mehra (1986), Judd and Trehan
(1987), Rasche (1987), Hetzel and Mehra (1988), and Moore,
Porter and Small (1988).
2 Hetzel (1984) implements this approach in the context of the
M1 demand function. Fama’s model is monetarist in the sense
that excessive monetary growth leads to higher prices in the long
run.

SEPTEMBER/OCTOBER

1988

This article compares over the period 1977 to 1987
the relative forecast performance of the four inflation models including the one due to Fama. The
evidence reported here is very favorable to Fama’s
model. Consistent with Stockton and Glassman’s
results, the Phillips curve model outperforms the
monetary models in predicting the rate of inflation
when money is defined as M1, but that is not always
the case when money is defined as M2. The evidence
shows that over the period 1977 to 1987 the Fama
model based on M2 demand outperforms the Phillips
curve model in predicting the rate of inflation. In the
subperiod 1981 to 1987, however, its performance
is second to that of the Phillips curve model. Both
the Fama money demand and the Phillips curve
models outperform the simple time series model.
This evidence thus implies that it is inappropriate
to ignore the role of money in explaining the generation and perpetuation of inflation.3 In particular, the
results imply that a sustained increase in M2 growth
in excess of growth in real money demand will be
associated with a higher inflation rate.
Section II describes briefly the specification and
estimation of the inflation models used. Section III
reports the empirical results. Concluding remarks are
in the final section.
II
SPECIFICATION AND ESTIMATION ISSUES
2.1

Specification

of Inflation Models

This section describes briefly the price equations
that underlie this study. I have chosen three structural models of the inflation process: the traditional
monetarist
model, the expectations-augmented
Phillips curve, and the Fama money demand model.4
The specification of price equations used for the first
two inflation models is similar to those described in
Glassman and Stockton (1983) and Stockton and
Glassman (1987). The price equation that underlies
the money demand model is similar to those given
in Fama (1982) and Hetzel and Mehra (1988).
3 In Stockton and Glassman (1987) the forecast performance
of alternative models is evaluated conditional on actual as well
as projected values of the right-hand side exogenous variables
in the price equations. In this paper the forecast performance
is conditional only on actual values of the right-hand side
exogenous variables. This means that the evidence reported in
this paper does not necessarily imply that the inflation model
based on M2 demand can be used as a forecasting tool.
4 I have not considered the rational expectations model in this
paper. It is quite difficult in practice to measure rational expectations accurately and thus test this mode!. See Stockton and
Glassman (1987) and Stockton and Struckmeyer (1988) for an
attempt in this direction.
FEDERAL

RESERVE

The Traditional Monetarist Model The traditional
monetarist price equation considered here expresses
inflation as a-function of current and past values of
the monetary variable (measured commonly by M1)
and the fiscal policy variable (measured commonly
by high employment government expenditures). As
pointed out in Glassman and Stockton (1983), this
equation can be shown to be the reduced form equation associated with a structural model that is similar
in spirit to the St. Louis structural model discussed
in Andersen and Carlson (1970).
To illustrate this, consider the following aggregate
supply, aggregate demand, and expected inflation
equations.

Equation (1.1) shows the aggregate supply curve
which includes expected inflation (Pe), excess demand as measured by the rate of change of real output (ÿ) over potential output (yp), and the supply
shocks (SH). Equation (1.2) shows the aggregate demand curve which includes current and past values
of money growth (M) and government expenditures
(G). Equation (1.3) describes the formation of ex
pected inflation, which is modeled as a function of
current and past values of money growth. Solving
equation (1.2) for the growth of real output and then
substituting it and equation (1.3) into equation (1.1)
enables one to express inflation in general form as

Thus, in equation (1.4) inflation is determined by
current and past values of the growth rates in money
and government expenditure variables. In the empirical work reported below, supply shocks (SHt) are
captured by relative food and energy prices, and the
government expenditure variable by high employBANK

OF RICHMOND

11

behavior. Prices are marked up over productivityadjusted labor costs (W-qn) and are influenced by
cyclical demand (measured by the GAP variable) and
the exogenous relative price shocks (SHp). Wage
inflation (2.2) is assumed to be a function of cyclical
demand and expected price inflation
the latter
modeled as a lag on past inflation as in equation (2.3).
Combining (2.1), (2.2), and (2.3) yields the Phillips
curve equation (2.4) below

ment government expenditures.5 Hence, the inflation equation (hereafter called Monetarist) estimated
here is of the following form

where E is the growth rate of high employment
government expenditures; RËP, change in the relative price of energy; RFP, change in the relative
price of food; and other variables are defined as
before. Each ni is the number of lagged values of the
relevant variable included in the equation.

where fi's are the parameters and where other
variables are as defined before.
The empirical work below estimates an alternative
version of equation (2.4). Noting that the GAP
variable can be expressed as

The Phillips Curve
Model The expectationsaugmented Phillips curve model expresses inflation
as a function of its own lagged values (capturing expectations), the output gap (a demand pressure
variable), and changes in the relative prices of food
and energy. As shown in Glassman and Stockton
(1983), this inflation equation can be derived from
separate wage and price equations. To see this, consider the following price and wage equations

where Yt is the log of nominal GNP; yt, the log of
real GNP; and yp, the log of potential GNP. Taking
first difference of (2.5) results in expressing GAP as

If we substitute (2.6) into (2.4), the Phillips curve
inflation equation can be expressed as

This specification of the Phillips curve equation
allows explicitly the influence of nominal aggregate
demand (via the term Yt - ypt) on inflation. SHp
and SHw terms in (2.7) are captured in the empirical
work by changes in relative food and energy prices.
Hence, the Phillips curve equation estimated is of
the form (2.8).

where W is wage growth; qn, trend growth rate of
labor productivity; SHpt, supply shocks affecting the
price equation; SHwt, supply shocks affecting the
wage equation; GAP, the GNP gap variable defined
as the difference between actual real output and
potential real output; and
the expected rate of
inflation. Equation (2.1) describes price markup
5 An alternative specification used in Stockton and Glassman
(1987) has inflation determined primarily by current and past
values of money growth. This specification reflects the empirical
assumption, consistent with the monetarist view, that fiscal policy
actions have no long-run effect on nominal aggregate demand.
However, I have kept the specification used here somewhat more
general by letting government expenditures stay in the inflation
equation. The main conclusions of this paper are unaffected if
one excludes government expenditures when estimating the inflation equation.
12

ECONOMIC

REVIEW,

SEPTEMBER/OCTOBER

1988

Money Demand Model The price equation based
on money demand views inflation as being caused
by money growth in excess of growth in real money
demand. In order to derive the inflation equation used
here, consider the following relationship

where mdt is the public’s demand for real money;
Mt, actual level of money balances; Pt, the price level;
and ln is the natural logarithm. Equation (3.1) says
that the price level is determined by the actual level
of money balances in excess of real money demand.
It is assumed that actual level of money balances are
exogenously given by the monetary authority. The
price level then adjusts so as to equate the public’s
demand for real money balances to the nominal
money balances. Thus in (3.1) an increase in nominal
money stock given real money demand causes the
price level to rise, and a rise in the public’s real money
demand given the fixed money stock causes the price
level to fall.
The empirical work reported below assumes that
the public’s demand for real money balances depends
positively on real income y (which measures the
real value of transactions financed by money) and
inversely on the opportunity cost variable defined as
the difference between the market rate of interest
(R) and the own rate on money (RM).6 This is
expressed as

In equation (3.3) the price level depends upon levels
of the actual money stock (M), real income (y), and
the nominal interest rate (R - RM). An increase in
real income raises the public’s demand for real money
balances. Given the exogenous money stock, the
price level would have to fall to equate the rise in
real money demand to the real money supply. Thus,
an increase in real income depresses the price level.
Similarly, a rise in the opportunity cost of holding
money would reduce the public’s demand for real
money balances, and the price level would have to
rise to equate the reduced demand for real money
6 Hetzel and Mehra (1987) and Moore, Porter and Small (1988).
See Reichenstein and Elliott (1987) for a different specification
of the money demand function.
FEDERAL

RESERVE

balances to the predetermined stock of money. Thus,
a rise in the opportunity cost of holding money raises
the price level.
Since, in the short run, there are lags in the
adjustment of the price level to changes in its determinants identified in (3.3), the inflation equation consistent with this approach could be expressed as

where ki’s are the parameters and where other
variables are as defined before.
It should, however, be pointed out that the aggregate labeled M in the price equation (3.1) is presumed to possess some well-defined properties. In
particular, it should fulfill two conditions as discussed in Patinkin (1961) and Fama (1983). The first
is that the aggregate has a well-defined real demand.
The second is that the interest rate on this aggregate
is fixed at below its free-market value. If these two
conditions are fulfilled, then one could view the price
level as being causally determined by the supply of
this monetary asset in excess of its real demand.
Fama (1982) has argued that the relevant aggregate
in the U.S. inflation process is the monetary base.
Before 1981 the monetary base and perhaps M1
fulfilled the above noted two conditions. That has
not been the case during the period since then. As
noted before, there is considerable evidence consistent with the view that the character of M1 and base
demands has changed during the 1980s, and M1
since 1981 includes assets that pay explicit market
interest rates. In case of M2, only one of the above
conditions appears to hold. M2 demand has been
relatively stable during the 1980s. But some components of M2 do pay market-determined
interest
rates.
Time Series Model
As an alternative to the
theoretically based models of the inflation process,
the study included a simple autoregressive model of
inflation

If the theories are of any value they should at least
outperform this simple time series model.
BANK

OF RICHMOND

13

2.2

Estimation, Data, and Forecast
Evaluation Strategy

The inflation equations (1.5), (2.8), (3.4), and (4)
were estimated using quarterly data that span the
period 1959-87. The price index used as the dependent variable in these equations is the fixed-weight
GNP deflator. In equation (1) the monetary variable
used is either M1 or M2 and the fiscal policy variable
used is high employment government expenditures.
Relative food and energy prices were calculated as
the prices of food and energy in the fixed-weight
personal consumption expenditure deflator relative
to the fixed weight consumption expenditure deflator
excluding food and energy. In the Phillips curve equation (2.8) potential output was an extended Council
of Economic Advisers series. Since 1984 potential
output is assumed to grow at a 2.5 percent annual
rate.7 In the money demand equation (3.4) the scale
variable used is real GNP and the opportunity cost
variable is the 4-6 month commercial paper rate
minus the own rate of return on the monetary aggregate used. Thus, in case of M2 the own rate is
the weighted average of the explicit deposit rates paid
on the various components of M2, with weights given
by relative component shares. In case of M1, the own
rate is the weighted average of the rates paid on
NOW and Super NOW accounts.
The price equations associated with inflation
models were estimated either by ordinary least
squares (equations (2.8) and (4)) or by generalized
least squares to correct for the presence of first order
serial correlation (equations (1.5) and (3.4)).8 Another issue in the estimation of these equations was
the choice of lag lengths on various monetary and
fiscal policy variables. Since economic theory provides no guidance on this issue, one approach commonly used has been to select either 8- or 16-quarter
lags on the key variables and estimate lag shapes
using polynomial lag structures. This study follows
a similar procedure with two differences. The first
7 Estimates of growth in potential output range from 2 to 3 percent. I have used the midpoint of this suggested range in this
paper.
8 It should, however, be pointed out that some of the right-hand
side explanatory variables included in these price equations could
be correlated with the error term and hence not strictly exogenous in a statistical sense. Therefore, estimation by ordinary (or
generalized) least squares could have produced biased coefficient
estimates. In order to examine the effect of this potential bias,
the price equations were reestimated using only lagged values
of the key right-hand side explanatory variables and the
forecasting exercise was repeated. This had no effect on major
conclusions of the paper (see footnote 10 for the resulting ranking of inflation models).

14

ECONOMIC

that the lag shape is not restricted a priori. All lags
are estimated freely. The second is that F-tests were
performed to choose between 8- and 16-quarter lags.
This procedure indicated 8-quarter lags for most of
the key variables used, except those on M2 in Fama’s
model and past prices in the Phillips curve model.
On these two variables 16-quarter lags were used.9
is

REVIEW.

The focus of this study is on the relative forecast
performance of the above four inflation models over
a relatively longer-term forecast horizon. With this
goal in mind, the 8-quarter ahead inflation forecasts
from these models were generated and evaluated over
a ten-year period in the following manner. Each
model’s coefficients were estimated using quarterly
data from 1963Q2 to 1976Q4. Out-of-sample
dynamic forecasts conditional on actual values of the
exogenous
variables were constructed
for the
8-quarter period from 1977Q1 to 1978Q4. These
quarterly forecasts were then assembled to calculate
the expected 8-quarter inflation rate

where

is the 8-quarter

inflation rate expected

at time t and where
are the model’s quarterly
forecasts for eight quarters. The error was calculated
as the subsequent actual g-quarter inflation rate minus
the rate predicted. In order to generate another observation on the prediction error, each model’s coefficients were reestimated using data from 1963Q2 to
1977Q1, and out-of-sample forecast constructed from
1977Q2 to 1979Q1. That procedure was repeated
until the model was reestimated
and forecasts
prepared based on data ending in each quarter
through 1985Q4. Thus, the last estimation period
was 1963Q2 to 1985Q4, and the last out-of-sample
forecast interval, 1986Q1 to 1987Q4. This procedure generated for each model 37 observations on
the error in predicting the subsequent 8-quarter
inflation rate spanning the period 1977-87. These
forecast errors were then compared across models
for their relative performance.10

9 The sample period over which the lag lengths were searched
is 1963Q2-1987Q4. This amounts to assuming that lag lengths
had been invariant over the period. Alternatively, the choice
between 8- and 16-quarter lags within each model group could
be made on the basis of the out-of-sample forecast performance. This procedure was also employed and yielded lag lengths
similar to those based on F-tests.
10 Reichenstein
SEPTEMBER/OCTOBER

and Elliott (1987) adopt a similar approach.
1988

III
EMPIRICAL RESULTS

forecast intervals spanning 1977Q1 to 1987Q4. The
mean error (ME) and the mean absolute error (MAE)
are also presented. Charts 1 through 3 display for
some models period-by-period expected and subsequent actual 8-quarter inflation rates.
If one ranks inflation models by the RMSE
criterion, then the M2 demand model outperforms
the Phillips curve in predicting inflation over the 1977
to 1987 period. The Phillips curve model, in turn,
performs much better than M1 demand, the time
series, and Monetarist models by a substantial margin
(see Table I).11

Table I reports the estimated coefficients in the
four inflation models for the whole sample period,
1963Q2 to 1987Q4. As can be seen, these estimated
coefficients have the theoretically predicted signs and
in most cases are significant at the conventional
5 percent level. The parameter estimates for the
Phillips curve and M2 demand equations are
statistically significant and pass the Chow test of
structural stability over the sample period (see Fs in
the last column of Table I). However,
the
parameters that appear on the monetary aggregate
used in the Monetarist and M1 demand equations
are generally not significant. Furthermore,
the
parameter estimates of the Monetarist equations are
not stable over time (see Fs in the last column of
Table I).

11 As
explained in footnote 7, the forecasting exercise was
repeated using price equations that were estimated omitting contemporaneous values of the right-hand side key explanatory
variables. Thus, in the reestimated Monetarist and money
demand equations, only past values of money, government expenditures, real income, and opportunity cost appear. In the
Phillips curve equation, the past value of output gap appears.
Other remaining variables appear in the form shown in equations reported in Table I. For the estimating periods ending in
1976Q4 to 1985Q4, the six inflation models ranked by the
RMSE criterion are: Money Demand (M2), 1.94; Phillips Curve,
2.86; Monetarist (M2) 3.69; Monetarist (M1), 3.89; Tie Series,
3.93; and Money Demand (M1), 3.99. Money demand (M2)
and Phillips curve models continue to be the best two performing models, doing much better than the time series model.
The worst performing model is the M1 demand model.

Table II reports the results of the forecast experiment described in the previous section. Column 1
ranks the inflation equations (which are summarized in Table I) by the root mean squared error
(RMSE) calculated using errors over 37 overlapping

Table

I

Estimates of Inflation Equations, 1963Q2-1987Q4

Notes:
All variables are in first differences
employment government expenditures;
GNP; Y, the log of nominal GNP; R, 4-6
are sums of lagged coefficients,
with t
included. SER is the standard error of
constant over time.
* Significant
** Significant

at .05
at .10

of logs except the interest rate variables which are in first differences of the levels. M is M1 or M2; E, high
REP, the relative price of energy; RFP, the relative price of food; y, the log of real GNP; YP, the log of the potential
month commercial paper rate; RM, the own rate on money, and p, the log of the price level. Coefficients reported
values and lag lengths reported in parentheses. A zero lag length implies that only the contemporaneous
value is
the regression, and DW is the Durbin-Watson
statistic. F tests the hypothesis that the estimated coefficients are

level
level
FEDERAL

RESERVE

BANK

OF RICHMOND

15

Table

II

Summary Statistics for Errorsin Predicting the Eight-Quarter Inflation Rate
from Alternative Inflation Models
Estimation

Periods

End 1976Q4

Subperiod

to 1985Q4a

Results

Notes:
The inflation equations that underlie these models are reported in Table I. See the text for the procedure
the root mean squared error; ME, the mean error; and MAE, the mean absolute error.
a. The forecast
b. The forecast
c. The forecast

period is 1977Q1
period is 1977Q1
period is 1981Q1

forecast

errors. RMSE

is

to 1987Q4
to 1982Q3
to 1987Q4

The inflation model that performs poorly, in some
cases even worse than the time series model, is the
Monetarist
model in which money growth is
measured by M1. This can be seen in Chart 1 which
graphs predictions from the Monetarist model; the
inflation rate is consistently overpredicted during the
1980s. With the acceleration of M1 growth first in
1982-83 and then in 1985-86, this inflation model
predicts an acceleration of inflation that did not
occur. This breakdown reflects the random shifts that
have occurred in M1 demand during this period due
to factors such as financial deregulation and disinflation. This point is further illustrated by predictions
of the M1 demand model, also graphed in Chart 1,
which does control for the systematic shifts in money
demand due to changes in real income and the
nominal interest rate. Early in the period it performs
better than the Monetarist model; its performance,
however, also deteriorates over time as M1 demand
has changed during the 1980s.
Another point suggested by the results in
Table I is that the M2 demand model performs much
16

used to generate

ECONOMIC

REVIEW,

Chart 1

Expected and the Subsequent Actual
Eight-Quarter Inflation Rate
Percent
24
20
16
12
8
4

77Ql
Note:

79Ql

X axis measures

81Q1
the end

83Q1

of the sample

period

85Ql
over

which

the model is estimated. Y axis measures the inflation rate over the
out-of-sample

SEPTEMBER/OCTOBER

eight-quarter
1988

prediction

interval.

better than the Monetarist model based on M1!
measure of money. This result suggests that it is not
M2 growth per se but M2 growth in excess of growth
in real M2 demand that determines inflation. This
point is illustrated further in Chart 2 which graphs
predictions from these two inflation models.
The Phillips curve model is the second best performing model. The predictions from this model are
displayed in Chart 3. In contrast with the Monetarist
equations,
the Phillips curve model predicts
reasonably well the sharp deceleration in the rate of
inflation which occurred in the early 1980s. The
recession in 1982 generated a great deal of slack in
labor and product markets and widened the gap between actual and potential GNP. The Phillips curve
model views the widening gap as a source of decelerating prices. But, as can be seen, it does not
predict the sharp acceleration in inflation that
occurred in the 1977-79 period.
The predictions from the time series model are
also graphed in Chart 3. As is clear, this model lags
in predicting turning points in the rate of inflation.
Turning to the subperiods, no clearcut ranking of
models emerges (see Table II). During the estimating periods ending in 1976Q4 to 1980Q3, a
period of rapidly accelerating prices, money demand
models based on M1 or M2 substantially outperform
the Phillips curve model. The root mean squared

error value from the M2 demand model is 1.35,12
which is substantially lower than the value 3.77 from
the Phillips curve model. However, during the
estimating periods ending in 1980Q4 to 1985Q4, a
period of decelerating prices, the Phillips curve model
turns in a somewhat better performance than the M2
demand model, as measured by their relative root
mean squared error values ( 1.28 vs 1.79). This point
is also clear if we compare Charts 2 and 3 over these
two subperiods.
As noted before, Fama (1982) has argued that the
relevant monetary variable in the U.S. inflation process is the monetary base (MB). In order to evaluate
the role of the monetary base, the forecast performance of the inflation equation (3.4) using MB was
also evaluated.13 For the estimation periods ending
in 1976Q4 to 1985Q4 the root mean squared error
12 should he noted that over the early subperiod there is no
It
difference in the RMSE values of the M1 and M2 demand
models, suggesting that the non-M1 components of M2 did not
matter. However, that is not the case for the latter subperiod.
13 Fama’s MB demand model was estimated using the measure
of base collected by the Federal Reserve Bank of St. Louis. Four
lagged values of the monetary base, real income, and the nominal
interest rate were used in the inflation equation. The monetary
base equation did not pass the Chow test for structural stability. Estimation was by generalized least squares to correct for
the presence of first order serial correlation. The base equation
was also estimated using only past values of the right-hand side
explanatory variables. It did not have any major effect on the
relative rankings of the inflation models.

Chart 3

Chart 2

Expected and the Subsequent Actual
Eight-Quarter Inflation Rate

Expected and the Subsequent Actual
Eight-Quarter Inflation Rate

Percent
24

Percent
24

20

20

16

16

12

12

8

8

4

4

77Q1

79Q1

81Q1

83Q1

77Q1

85Q1

Note: X axis measures the end of the sample period over which
the model is estimated. Y axis measures the inflation rate over the
out-of-sample eight-quarter prediction interval.
FEDERAL

RESERVE

79Q1

81Q1

83Q1

85Q1

Note: X axis measures the end of the sample period over which
the model is estimated. Y axis measures the inflation rate over the
out-of-sample eight-quarter prediction interval.
BANK

OF RICHMOND

17

in predicting the 8-quarter inflation rate is 3.07, which
makes it the third best performing model after M2
demand and the Phillips curve models (compare with
the RMSE values reported in Table II). For the
estimating subperiods ending in 1976Q4 to 1980Q3
and 1980Q4 to 1985Q4, the RMSE values for the
MB demand model are 2.59 and 3.39, respectively. Thus, even over the subperiods the inflation
model based on M2 demand outperforms its counterpart using MB.

The empirical results presented here lead to two
observations.
First, the relatively poor forecast
performance of inflation models in which M1 growth
appears suggests that the character of M1 demand
has changed. In contrast, the M2 demand model,
in which inflation is related to M2 growth in excess
of growth in real money demand, performs reasonably
well, suggesting that M2 demand has been relatively stable over time. This result implies that a
sustained increase in M2 growth in excess of growth
in its real demand has been associated with higher
inflation. Second, two structural models of the inflation process, the Phillips curve and the M2 demand
model, outperform a simple time series model by a
substantial margin.
A 1987 study by Reichenstein and Elliott reaches
a similar conclusion about M2. These authors compare forecasts of the long-term inflation rate from
several nonstructural inflation models (drawn from
time series and interest rate relationships) to forecasts
generated by Fama’s M2 demand model. They find
that over the period 1975 to 1982 Fama’s structural
model is best in predicting the long-term inflation
rate.14
The relative superior forecast performance of M2
in Fama-type inflation equations raises an interesting
question about the nature of the monetary aggregate
that is causal in determining the price level. Fama
(1982, 1983) has suggested that in theory the price
level can be determined by the supply of a nominal
asset that has a well-defined real demand and pays
a fixed below-market rate of interest. He has argued
that the relevant monetary asset is the monetary base.
The empirical evidence reported in this paper,
14The results presented in Stockton and Struckmeyer (1988)
also suggest that the monetarist models contain information about
aggregate inflation that is not incorporated in an expectationsaugmented version of the Phillips curve.
ECONOMIC

References
Andersen, Leonall C., and Keith M. Carbon. “A Monetarist
Model for Economic Stabilization.” Federal Reserve Bank
of St. Louis Review 52 (April 1970): 7-25.

IV
CONCLUDING OBSERVATIONS

18

however, favors M2 as the relevant aggregate, even
though it violates one of the conditions laid down
by Fama. While this might suggest some caution, the
results overall do imply that it might be inappropriate
to ignore the role of money in explaining the generation and evolution of inflation over time.

REVIEW,

Fama, Eugene F. “Financial Intermediation and Price Level
Control.” Journal of Monetary Econonmics 12 (July 1983):
7-28.
“Inflation, Output, and Money.”
Business 55 (April 1982): 201-31.

Journal of

Classman, James E., and David J. Stockton. “An Evaluation
of Alternative Price Forecasting Models: Theoretical Considerations.” Board of Governors of the Federal Reserve
System, December 1983. Photocopy.
Hetzel, Robert L. “Estimating Money Demand Functions.”
Journal of Money, Credit and Banking 16 (May 1984): 185-93.
Hetzel, Robert L., and Yash P. Mehra. “The Behavior of
Money Demand in the 1980s.” Federal Reserve Bank of
Richmond, June 1988. Photocopy.
Mehra, Yash P. “Recent Financial Deregulation
and the
Interest-Elasticity of M1 Demand.” Federal Reserve Bank
of Richmond Economic Review 72 (July/August 1986):
13-24.
Moore, George R., Richard D. Porter, and David H. Small.
“Modeling the Disaggregated Demands for M2 and M1
in the 1980s: The U.S. Experience.” Board of Governors
of the Federal Reserve System, May 1988. Photocopy.
Patinkin, Don. “Financial Intermediaries
and the Logical
Structure of Monetary Theory.” American Economic Review
51 (March 1961): 95-116.
Rasche, Robert H. “M1-Velocity and Money-Demand
Functions: Do Stable Relationships Exist?” In Empirical Studies
of Velocity, Red Exchange Rates, Unemployment and Productivity Carnegie-Rochester
Conference Series on Public
Policy, Vol. 27, ed. by Karl Brunner and Allan H. Meltzer.
Amsterdam: North Holland, Autumn 1987, pp. 9-88.
Reichenstein, William, and J. Walter Elliott. “A Comparison
of Models of Long-Term Inflationary Expectations.” Journal of Monetary Economics 19 (May 1987): 405-25.
Stockton, David J., and James E. Glassman. “An Evaluation
of the Forecast Performance of Alternative Models of Inflation.” The Review of Economics and Statistics 69 (February
1987): 108-17.
Stockton, David J., and Charles S. Struckmeyer. “Tests of the
Specification and Predictive Accuracy of Nonnested Models
of Inflation.” Review of Economics and Statistics. Forthcoming.

SEPTEMBER/OCTOBER

1988

THE MONETARY RESPONSIBILITIES
OF A CENTRAL BANK
Robert L. Hetzel*
I.
INTRODUCTION
In today’s world of paper money, money consists
of currency created by the printing press and bank
deposits created by the bookkeeping operations of
bankers. What limits the ability of the printing presses
and the pens of bankers to create money? The currency component of money is central bank money
(dollar bills). The bank deposits component of money
is backed by central bank money (bookkeeping
entries at the central bank). It is the central bank’s
monopoly of its own money that allows it to limit
creation of the public’s money. In turn, limitation of
central bank money and the public’s money limits
the price level. The essence of central banking lies
in the responsibility to limit the money stock in order
to tie down the price level.
In practice, central banks typically do not decide
explicitly how much of their money to create. Instead,
they create and extinguish their money in response
to the current behavior of financial markets. The particular nature of this process of central bank money
creation determines how the money stock and the
price level are actually limited. The nature of this
process depends in turn upon the macroeconomic
goals of the central bank. How then does the way
the central bank selects macroeconomic goals and
weights their relative importance determine the
behavior of the price level?
In order to answer these questions, it is necessary
to have a model that captures the connection between the goals of the central bank and nominal
(dollar) variables: the monetary base (central bank
money), the money stock and the price level. The
purpose of this article is to lay out such a model. The
model is general in that it applies to any central bank
that operates in a regime of paper money, although
occasional specific references are made to the Federal
Reserve System.

* The author is indebted to Marvin Goodfriend for patient encouragement and to Alfred Broaddus, Timothy Cook, William
Cullison, Michael Dotsey, and Carl Walsh for critical comments.
FEDERAL

RESERVE

Section II presents an intuitive discussion of
the model. The actual model is presented in the
Appendix.1 Section III elucidates the working of the
model by showing how the central bank smooths interest rate fluctuations. Section IV uses the model
to discuss money stock and price level determination. This section states the two major responsibilities
of the modern central bank. First, the central bank
gives the price level an equilibrium value. Specifically,
the central bank gives the price level a well-defined
or particular value such that market forces operate
to eliminate departures of the actual price level from
this value. Second, the central bank determines how
the equilibrium value of the price level changes over
time. The article concludes with suggestions for clarifying the responsibility of the central bank for the
behavior of the price level.

Il.
THE MODEL
The Structure of the Economy
the Interest Rate

and

The model gives substance to the natural rate
hypothesis. This hypothesis summarizes the inherent
limitations on the central bank’s ability to influence
real variables. These limitations derive from the fact
that paper money creation, or monetary base creation, does not alter the real resources available to the
economy. The public cares only about real variables,
while the central bank only determines the behavior
of a nominal variable, the monetary base.
In the literature that follows the work of Lucas
(1972), the natural rate hypothesis is given content
by allowing only changes in money and the price level
not expected by the public to affect real variables.
Furthermore, the public is assumed to form its expectations “rationally,” that is, in a way that is consistent with assumptions made about the structure
1 This model has been worked on especially by economists
associated with the Federal Reserve Bank of Richmond. [See
Dotsey and King (1983), McCallum (1981 and 1986), and Goodfriend (1987)].
BANK OF RICHMOND

19

The Demand and Supply of Money

of the economy and the behavior of the central bank.
The natural rate hypothesis then implies that the central bank cannot systematically affect the level of real
variables. For example, the central bank cannot
systematically lower the level of the real (inflationadjusted) rate of interest [Sargent (1973)]. Through
the policy process it chooses for determining the
monetary base, however, it can influence the way
random macroeconomic disturbances affect fluctuations in real variables.
Equation (1) summarizes the determinants of the
market rate (rt).2

Equation (2) is a money demand function.

Nominal money demand
equals the product of
the price level (Pt), real money demand (given by
the function Fmd), and a random disturbance term
(Vt). Real money demand varies inversely with the
market rate of interest (rt) and positively with real
output. The function Fmd, instead of showing real
output as a variable, shows the variable (Pt - Et - 1Pt)
because real output varies positively with this variable,
the contemporaneous
price level error.
The money supply function has the form of a
money-multiplier
formula.

This equation is derived from two more fundamental relationships. One, the IS function, summarizes the conditions under which the goods market
clears. For different values of real output, it shows
the values of the expected real rate of interest that
cause investment and saving to be equal. The other
function makes the supply of real output depend upon
the contemporaneous price level error (Pt - Et - 1Pt).
The IS function and the aggregate supply function
are equated, and output is eliminated from the
resulting expression. (The goods market must clear
at a level compatible with the aggregate supply of
output.) The resulting partially reduced form, when
solved for the market rate, is equation (1).
The first right-hand term of (1) equals the rate of
inflation the public expects. In the second right-hand
term, the function Frr is the expected real rate of interest. The real rate depends upon a constant (c) and
the contemporaneous price level error (Pt - Et - 1Pt).
This functional form derives from the particular form
of the natural rate hypothesis, which makes fluctuations in output respond to discrepancies between the
contemporaneous
price level and the public’s prior
expectation of the contemporaneous
price level.
When the price level is higher than the public had
expected in the prior period, that is, when Pt exceeds
Et - 1Pt, real output and saving rise, and the real rate
of interest falls, and conversely. (These real effects
of inaccurate forecasts of the price level can be
thought of as deriving from the existence of oneperiod contracts fixed in dollar terms.) Finally, the
expected real rate is affected by real sector disturbances (Qt).
2 E indicates an expectation formed by the public and the
subscript t indicates the time period when the public formed
that expectation. The subscript t is the contemporaneous
time
period, while t - 1 and t + 1 are the prior period and the following period, respectively.
20

ECONOMIC

REVIEW,

The money supply
equals the product of the
monetary base (Bt) and the multiplier, which is given
by the function Fmm. This function depends upon
the market rate (rt). There is a positive relationship
between the market rate and the multiplier because
of the effect of the market rate on the reservesdeposit
ratio desired by banks and the currency-deposit ratio
desired by the nonbank public. The multiplier is also
affected by a random term (Xt).
The Monetary

Policy Process

The monetary policy process is summarized by the
procedure the central bank puts into place for creating
and extinguishing the monetary base (Bt). This
procedure is shown in equation (4).

The three ø parameters of (4) determine the
series behavior of the monetary base.3 They
marize the information the public needs
monetary policy to form an expectation of the
price level.

timesumabout
future

3 Equation (4) summarizes the policy process through the timeseries behavior of the monetary base, as determined by the ø
parameters. Equation (4) could, alternatively, be solved in a way
that makes the market rate (rt) the left-hand variable. With this
formulation, the policy process would be summarized by the
time-series behavior of the market rate. The model is unaffected
by the choice of whether to summarize the policy process in
terms of the behavior of the base or the market rate. Although
monetary policy can be summarized by the behavior of the
interest rate, the effect of monetary policy on the economy is
transmitted
solely through the process that generates the
monetary base [Goodfriend and King (1988)].

SEPTEMBER/OCTOBER

1988

The first parameter, øtrend,
specifies the trend rate
of growth of the monetary base. With the simplifying assumption that real output does not grow over
time, this rate of growth is also the trend rate of inflation. The second parameter, øsmooth, is the rate
smoothing parameter. øsmooth specifies the change
in the monetary base the central bank makes in
response to deviations in the market rate from a
reference rate Et - 1rt. It follows from the natural rate
hypothesis that the central bank must set this
reference rate equal to the model’s expected real rate
plus the trend rate of inflation (c + øtrend).
Each period, random disturbances impact the
economy and move the market rate away from the
reference rate. When the market rate exceeds the
reference
rate, the central bank increases the
monetary base by an amount that depends upon the
value of øsmooth, and conversely. The result is that
each period there is a change in the monetary base
that could not have been predicted in the previous
period. The base drift parameter, ødrift, specifies how
much of the prior period’s unpredictable change in
the monetary base the central bank offsets in the
subsequent period. There are two general cases. In
the case of either no offset or only a partial offset
(ødrift not equal to one), the level of the monetary
base will be affected permanently each period by
some random amount. Because there is then no path
to which the base tends to return, the monetary base
follows a random walk (superimposed on the persistent movement given by the value of the growth rate
parameter øtrend). In the case of a complete offset,
the base fluctuates over time around a well-defined
path. These two cases are also said to produce,
respectively, nonstationary and stationary behavior
of the monetary base.
Central

Bank Objectives

Assume now that the central bank possesses two
macroeconomic objectives: an economic stabilization
objective and a monetary stabilization objective.
These objectives can be expressed by the loss function (5).

The first right-hand term in (5) measures the variability of contemporaneous
price level errors. The
central bank considers the fluctuations in output
caused by these errors to be undesirable. It therefore
attempts to limit the variability of these errors. The
FEDERAL

RESERVE

second right-hand term measures the variability in
the rate of inflation the public expects. The central
bank also attempts to minimize this variability. The
coefficients on the two right-hand terms reflect the
relative importance of the economic stabilization and
inflation stability objectives. The central bank
chooses the values of the ø parameters in (4) in order
to minimize the value of C in (5).4
The Complete
The equations

Model
of the model are listed below.

With the constraints imposed by rational expectations and the assumption that money demand equals
money supply, equations (1)-(4) can be solved for
rt, Pt, Mt, Bt, Et - 1Pt and EtPt +1. The resulting
values for [Pt - Et- 1Pt] and (EtPt+1/Pt - 1] are
substituted into the central bank’s loss function (5).
The loss function is now expressed in terms of the
structural parameters of the model, the disturbances,
and the ø parameters. Finally, the central bank sets
the ø values in order to minimize this expression for
the loss function.
4 The model is intended for policy analysis. Policy analysis
involves the conceptual exercise of assuming different objective
functions for the central bank as a way of discussing how the
central bank affects the behavior of the economy. In contrast
to this kind of analysis, the model could be used to forecast,
say, inflation. In this case, it would be necessary to use the
actual objective function of the central bank and to be explicit
about the way this function changes over time. This kind of
exercise is more difficult because of the need to understand how
in the real world the policy process affects the way the public
forms its expectations. In a world in which monetary policy
evolves in unexpected ways, it will be inherently difficult to model
realistically the way in which the expectations formation of the
public is shaped by the policy process. In order to form
expectations, the public must evaluate how the central bank’s
objective function will change and how such changes will alter
the time series behavior of the monetary base.
BANK

OF RICHMOND

21

Policy Analysis
The nature of the model imposes a discipline on
policy analysis. The model is dynamic, that is, it is
concerned with how the monetary aggregates and the
price level change over time. Furthermore,
the
public’s expectations of the future values of these
variables are shaped by the process the central bank
uses to generate changes in the monetary base. (That
is, the public’s expectations depend upon the ø
parameters the central bank chooses to govern
monetary base creation.) It follows that one can use
the model to ask what happens when the central bank
takes a particular policy action
only if the policy
process that generated the particular action is also
specified. That is, one must know the ø values of
(4). For example, the model cannot be used to
predict the effect on the money stock and the price
level of a change in the monetary base of a given
amount, if that change is all that is specified. The
reason is that the effect of a particular policy action
depends upon the public’s expectation of subsequent
policy actions, and this expectation depends upon
the nature of the policy process.5

of the rational expectations assumption, both the
error in predicting the price level and the associated
rise in output will be transitory. Because the rise in
output is transitory, the public saves a relatively high
proportion of it. This increased saving offsets to some
extent the initial rise in the real rate of interest and
in the market rate.
The market rate is also smoothed as a consequence
of the interaction between the rate smoothing and
base drift parameters. As noted above, with a positive
øsmoothparameter, the positive real sector disturbance
increases the money stock and raises the price level.
Because the central bank is assumed not to allow
complete base drift, the public will expect that the
central bank will offset next period at least some of
the current period’s increase in money. The public
will then expect that, after adjusting for trend growth,
the money stock and the price level will be higher
in the present period than in the next period. The
expected future one-period inflation rate will fall
below trend. A fall in the premium in the market rate
for expected inflation will mitigate the rise in the
market rate caused by the real disturbance.

IV.
MONEY STOCK AND PRICE LEVEL
DETERMINATION

III.
RATE SMOOTHING
Insight into the way the model works can be
gainedit to understand how the central bank
by using
smooths interest rates. The central bank can smooth
fluctuations in the market rate in two ways. Assume
that the policy process that governs the behavior of
the monetary base makes øsmooth positive. Assume
also that ødrift is greater than zero. (There is at least
some subsequent offset of random variations in the
monetary base.) Consider an unanticipated, positive
real sector disturbance
(Qt), for example,
a
technological innovation that increases investment.
This disturbance increases the market rate and the
central bank responds by increasing the monetary
base. The money stock and the price level rise. The
price level will now exceed the value the public had
predicted last period, so real output rises. Because
5 In the model, for example, the effect of a change in the
monetary base can only be predicted with an understanding of
how the market rate is affected. The public, however, in order
to set the market rate, must form an expectation of the future
price level. (It needs this expectation to estimate the inflation
premium to put into the market rate.) In order to form an
expectation of the future price level, it must know the value of
the base drift parameter. The reason is that the base drift
parameter determines the extent to which the change in the
monetary base will be incorporated permanently into the future
level of prices.
22

ECONOMIC

REVIEW,

Graphical Analysis
of the Price Level

and Determinacy

The determination of the money stock and the
price level is shown graphically in Figure 1. The
inverse of the price level (the goods price of
money) is shown on the vertical axis. The nominal
amounts of money demanded and supplied are shown
on the horizontal axis. The nominal money demand
and supply schedules are derived by substituting
(1) into (2) and (3), respectively. The money demand
(supply) schedule then expresses the relationship
between the price level and nominal money demand
(supply) given a partially-reduced form that assumes
fixed values for price level expectations (Et - 1Pt and
EtPt+1) and the monetary base, but allows the
interest rate and output to vary.
Before discussing these schedules, it is useful to
note that, given the public’s prior expectation of the
contemporaneous
price level (Et - 1Pt), a rise in the
contemporaneous price level (Pt) produces a positive
price level forecast error, that is, [Pt - Et- 1Pt]
becomes positive. As a result, there is a transitory
increase in output. Also, under the assumption that
both Et - 1Pt and EtPt+1 are fixed, a rise in the price
level lowers the market rate of interest in two ways.

SEPTEMBER/OCTOBER

1988

First, the transitory increase in output just described increases saving, which lowers the real rate
of interest. Second, an increase in the price level
reduces the expected one-period rate of inflation, that
is, (EtPt+1 - Pt) declines. The market rate then
declines from a reduction in the inflation premium.
With this discussion in mind, now consider the
ways in which money demand is increased by a rise
in the price level (a fall in the inverse of the price
level). First, a rise in the price level produces a direct
proportional increase in the demand for money.
Second, money demand is increased by the increase
in output produced by a positive price level prediction error. Third, the fall in the market rate of interest produced by the price rise increases money
demand.
Consider next the effect of a price rise on nominal
money supply. A rise in the price level causes the
market rate to decline for the reasons mentioned
above. This decline in the market rate decreases the
money supply by lowering the value of the money
multiplier function, Fmm, for a given value of the
monetary base.
The money stock and the price level are endogenously determined through the intersection of the
money demand and supply schedules. These variables possess well-defined equilibrium values because

of the existence of these schedules. If the price level
falls below its equilibrium level, the nominal amount
of money supplied exceeds the nominal amount of
money demanded, and the price level returns to its
equilibrium value, and conversely. The nominal
money demand and supply schedules exist because
the central banks policy process (4) permits the
public to form an expectation of the future price level
(EtPt+1).
This policy process specifies the ø parameters upon
which EtPt+1 depends.6 These parameters derive
from the objectives of the central bank as summarized
in (5). One can, therefore, ask the question, “How
are nominal variables made well defined?” by asking
“What characteristics must the central bank’s objective (loss) function possess in order to permit the
public to form an expectation of the future price
level?” With the loss function (5) the central bank
cares about the contemporaneous price level (through
the first right-hand term) and the change in the price
level (through the second right-hand term). This loss
function, therefore,
constrains the behavior of
nominal variables sufficiently for the public to be able
to form an expectation of the future price level. In
short, it is the central bank that gives nominal
variables (the price level and money stock)
equilibrium values.
The Effect of Macroeconomic
on the Money Stock

Figure 1

Disturbances

Consider first the way in which an unexpected,
positive real sector disturbance (Qt) influences the
money stock and the price level with rate smoothing
(øsmooth greater than zero) and base drift (ødrift less
than one). As the market rate begins to rise, the central bank supplies reserves and the money supply
schedule shifts rightward. In Figure 1, MS shifts to
(MS)'. Two opposing forces shift the position of the
nominal money demand schedule. On the one hand,
an increase in the market rate shifts it leftward. On
the other, the unexpected increase in the monetary
base and the money stock requires a higher price level
than the public had expected, so real output rises.
The increase in output shifts the money demand
schedule rightward. In Figure 1, the net result is
assumed to yield a rightward shift from Md to (Md)'.

NOMINAL MONEY DEMAND
AND SUPPLY SCHEDULES

6 The solution for EtPt+1 yielded by (1) - (4) includes values
of the ø parameters in all its terms. These terms are a) a constant; b) the value of the monetary base in the prior period
multiplied by the two-period growth rate (1 + øtrend)2; c) a
negative term, ødrift, multiplied by the prior period’s unexpected
change in the monetary base; d) a term, øsmooth(1 -ødrift
multiplied by a linear combination of the monetary and real
disturbances:
FEDERAL

RESERVE

BANK

OF RICHMOND

23

The rightward shift in the money supply schedule
dominates the rightward shift in the money demand
schedule, and the price level rises.7,8
Consider next the effect of a positive money demand disturbance (Vt) with significant rate smoothing
(øsmooth large) and significant base drift (ødrift near
zero). Because the model is dynamic and accounts
for the way the policy process affects the expectations of the public, it yields strikingly different results
than the standard static models of money stock determination. The following example illustrates that,
when there is base drift, rate smoothing does not insulate the price level and the real sector from money
demand shocks. The positive disturbance to money
demand causes an incipient increase in the market
rate. For a large value of øsmooth, the central bank
increases the monetary base by enough to make the
money supply schedule shift rightward in line with
the money demand schedule. In Figure 2, (Md) and
(Ms) shift rightward by the same amount to (Md)'
and (MS)', with no effect on the price level. In the
absence of base drift, there are no further effects.
The price level and real variables are unaffected.
If the central bank allows base drift, however, the
money demand disturbance will increase permanently
the level of the monetary base and the money stock.
Because the model assumes that the increase in
money demand due to the monetary disturbance is
transitory, the public will expect a higher price level
next period. The expected one-period inflation rate
will rise, and the market rate will start to rise further

7 These shifts in the money demand and supply schedules are
the primary shifts due to a øsmooth greater than zero. There are
secondary shifts (not shown in Figure 1) due to the interaction
between øsmooth and ødrift. The real sector disturbance produces
a higher money stock in the contemporaneous
period. The
increase in the price level required by the higher money stock,
however, is mitigated by the rise in the demand for real money
produced by the higher level of output. The rise in real output
is transitory. The existence of base drift in the monetary aggregates implies that, in contrast, at least some of the increase in
the money stock is permanent. Consequently,
the public will
expect (adjusting for trend growth) a price level in the future
that is higher than the contemporaneous
price level. The inflation premium in the market rate will rise. The consequent
rise in the market rate will cause the central bank to increase
further the monetary base. The shifts in the money demand
and supply schedules shown in Figure 1 are then amplified.
The initial change in the money stock is proportional to øsmooth.
The additional
change is proportional
to the product
øsmooth - ødrift). With no base drift ødrift equal to one), there
(1
are no secondary effects.
8 As noted above, the rise in the price level, relative to both
the prior’ period’s expectation of the price level and the contemporaneous expectation of next period’s price level, affects
the public’s savings behavior and inflationary expectations in a
way that mitigates the rise in the market rate.
24

ECONOMIC

REVIEW.

Figure 2

NOMINAL MONEY DEMAND
AND SUPPLY SCHEDULES

Note:

The dashed lines show the effect of a positive disturbance
to money demand. The dashed lines marked by a double
prime show that part of the effect due to base drift.

due to an increase in the inflation premium. In
response, the central bank will then increase the
monetary base again, and the money supply schedule
will shift rightward again. In Figure 2, (MS)' shifts
rightward to (MS)“. As in the case of the real sector
disturbance, the price level rises and real output is
stimulated. It then follows that (Md)’ shifts to (Md)“.9
Rate smoothing does not insulate the real sector from
monetary disturbances.10

9 The increase in output increases saving. Increased saving
lowers the real rate and offsets the increase in the market rate
caused by the increase in the inflation premium. The rise in
the market rate caused by the money demand disturbance is,
therefore, mitigated. These secondary effects from the money
demand disturbance are analogous to those described in footnote 7.
10 The model is constructed with nominal money demand and
supply schedules that derive from different behavioral relations.
The money demand schedule comes from (2), the real money
demand function. The money supply schedule comes from (3).
the money-multiplier function. The determinants of real money
demand and nominal money supply are different. The model,
therefore,
makes the quantity-theory
assumption
that
macroeconomic disturbances will produce divergent shifts in the
nominal money demand and supply schedules. In the jargon of
econometrics, the model assumes that the money demand and
supply schedules are identified. Independent
shifts in these
schedules occur that permit the econometrician to use actual
observations on the money stock and the price level to identify
separate demand and supply schedules.

SEPTEMBER/OCTOBER

1988

The Central Bank and the Behavior
of the Price Level
Although with rate smoothing the monetary base
is determined endogenously, the procedure the central bank puts into place for altering the monetary
base determines how the monetary base, the money
stock, and the price level are affected by macroeconomic disturbances. Furthermore, while particular
random realizations of the monetary base are produced by macroeconomic
disturbances,
the
timeseries behavior of the monetary base is largely
determined by the central bank. The ø parameters,
which are set by the central bank, determine the
general behavior over time of the monetary base and
also the time series behavior of the money stock and
the price level.
The rate smoothing parameter (øsmooth)determines
the variability of the monetary aggregates and price
level. A higher value of øsmooth requires increased
variability in the monetary aggregates and, after some
point, increased variability in the price level. The
trend growth rate parameter (øtrend) determines the
trend growth rate of the monetary aggregates and the
price level. With a positive value of øtrend, the money
supply schedule (MS) shifts rightward over time down
the money demand schedule (Md) at the rate given
by øtrend. The price level rises at the rate given by
øtrend.
Sustained inflation is always and everywhere
a monetary phenomenon [Friedman (1968)].
The base drift parameter ødrift determines how a
change in the money stock shifts the initial position
of the money supply schedule in the subsequent
period. With a value of ødrift different from one, transitory macroeconomic disturbances shift permanently
the position of the money supply schedule. In this
way, transitory disturbances are incorporated permanently into the price level. An implication of the
model is that a random walk in prices is always and
everywhere a monetary phenomenon. The model is
special in that it does not allow for a permanent component to real sector and money demand disturbances. If these disturbances possessed a significant
permanent component, base drift in the price level
could still occur even in the absence of base drift in
the monetary aggregates. There would, however, still
be truth to the statement that a random walk in prices
is a monetary phenomenon. The central bank can
have any time series behavior of the price level it
desires. For example, nonstationary behavior in the
price level could never arise if the central bank had
price stability as one of its objectives. Such an
objective would introduce into the central bank’s
objective function a term like k(Pt - P), where k is
a constant and P is the central bank’s stable price
level objective.
FEDERAL

RESERVE

V.
POLICY CHOICES FACED BY
THE CENTRAL BANK
The model makes possible a comparison of alternative policies by elucidating the trade-offs made in
selecting one policy rather than another. First, the
model identifies those policies that do not require
the policymaker to make trade&s among objectives.
When it is necessary to make trade-offs, the model
clarifies their nature. The policymaker can ask, “In
order to gain the benefits from adoption of a particular
policy, what benefits must be foregone by rejection
of alternative policies?
When Must the Policymaker

Trade Off?

The standard discussion of trade-offs in policymaking is by Tinbergen (1967). Tinbergen points
out that the policymaker with multiple objectives
need not make compromises when seeking to attain
these objectives if he possesses as many policy instruments as he has objectives. Attainment of the
objectives of policy is then constrained only by the
structure of the economy. If the number of objectives exceeds the number of policy instruments, the
policymaker must make a choice about the relative
importance of each objective. An increase in the
significance attached to one objective necessarily
decreases the significance that can be attached to the
other
objectives.
This
section
reformulates
Tinbergen’s discussion in terms of the dynamic model
used here.
In order to discuss policy choices, it is necessary
to posit an objective function. An objective function
makes explicit the central bank’s objectives and the
relative importance it assigns to achievement of its
different objectives. In (5), the objective function is
expressed as a loss function that the central bank attempts to minimize through the choice of the ø
parameters in (4). The parameters ß and y express
the relative importance the central bank assigns to
achievement
of the two objectives of economic
stabilization and inflation stabilization.
The central bank has available two degrees of
freedom (øsmooth and ødrift) to use in pursuit of its
objectives. It can vary these parameters in order to
influence the way macroeconomic
disturbances
affect the relationship between the contemporaneous
price level and the prior period’s expectation of this
variable. Also, it can vary these parameters in order
to influence the way macroeconomic
disturbances
affect the relationship between the contemporaneous
price level and the contemporaneous
expectations
of next period’s price level. These variations in the
BANK

OF RICHMOND

25

price level and the contemporaneous
expectation of
next period’s price level. These variations in the
policy process can only be effected through changes
in øsmooth and ødrift. Under the assumption that the
public’s expectations are formed rationally, the central bank’s choice of the trend growth-rate parameter
(øtrend) cannot affect the first relationship and affects
the second relationship only by the addition of a constant. The choice of a value for øtrend greater than
zero does not help the central bank attain any of its
macroeconomic
objectives.11
With the loss function (5), the central bank
possesses two objectives and possesses two degrees
of freedom for manipulating the behavior of the
monetary base. The central bank is not forced to
trade off between achievement of its objectives. It
can minimize the variability of inaccurate forecasts
of the price level without reducing its ability to
minimize the variability of expected inflation, and vice
versa. Its pursuit of each objective is constrained only
by the inherent uncertainty
caused by random
macroeconomic disturbances. Formally, this result
shows up in the central bank’s choices of øsmoothand
ødrift that minimize (5). The optimal values of the
øs do not depend upon the relative magnitudes of
ß and y. Even if the central bank were to weight
heavily one objective, it would not have to sacrifice
achievement of its other objective.
The Optimal Choice of øsmooth
The optimal value of the rate smoothing parameter
increases as the variability of money demand disturbances (the variability of the Vt) rises relative to the
variability of the real sector disturbances (the variability of the Qt). Increases in the value of the ratesmoothing parameter up to its optimal value reduce
variability in the price level and reduce undesirable
fluctuations in output. Further increases raise the
variability of the price level and increase fluctuations
in output. This result can be understood by considering the allocative role played by the interest rate in
the price system.
The real rate of interest is a price (the price of current output in terms of future output) whose varia11 A function like (5) that contains only macroeconomic
loss
objectives cannot rationalize a positive rate of inflation. Barro
and Gordon (1983) attempt to explain the existence of positive
inflation in a model like the one here in that the central bank
understands the structure of the economy. Their explanation
turns on the discretionary character of policy (the inability of
the central bank to precommit itself to a particular objective
function) and a desire by the central bank to lower persistently
the value of a real variable like unemployment.
Hetzel (1988)
explains inflation as a way of generating revenue through an
inflation tax.
26

ECONOMIC

REVIEW,

tions distribute aggregate demand across time. The
interest rate varies in order to cause the goods market
to clear at a level of output compatible with aggregate
supply. A change in the interest rate due to a disturbance in money demand, however, offers a misleading signal for intertemporal resource allocation.
The greater the importance of disturbances from the
monetary sector relative to disturbances from the real
sector, the more frequently changes in interest rates
will be misleading guides to resource allocation and
the higher the optimal value of the rate-smoothing
parameter. If monetary disturbances are large relative
to real disturbances, it is desirable for the central bank
to supply the monetary base in a way that smooths
fluctuations in the market rate.
The Optimal Choice of ødrift
One striking result derived from minimizing (5)
is that it is optimal for the central bank to eliminate
completely base drift. This result can be understood
intuitively. The optimal value of the rate smoothing
parameter puts an amount of interest rate sensitivity into the monetary base that reflects the
likelihood that an interest rate fluctuation is due to
a money demand disturbance. Because such disturbances are assumed to be transitory, there is no reason
to allow fluctuations in the monetary aggregates due
to fluctuations in the market rate to affect permanently the money stock.12 Base drift would increase
the variability of expected inflation, the second righthand term in (5), without reducing the variability of
inaccurate forecasts of the price level, the first righthand term in (5).
Trade-offs

in the Choice

of Policies

The loss function (5) cannot explain the actual time
series behavior of the monetary aggregates and the
price level. An obvious problem with (5), given the
result noted in the preceding paragraph, is that it cannot explain the significant amount of base drift
12 If there is a permanent component to either money demand
disturbances or real output disturbances and if the central bank
desires to render the price level stationary, it needs to allow some
amount of base drift in the monetary base and the money stock
[Walsh (1986)). Whether shocks to the money demand function exercise a transitory or a permanent effect upon the demand
for money is an empirical issue. (In fact, it appears to depend
upon the monetary aggregate considered. M1 velocity appears
to be a random walk. but M2 velocity is stationary. There may
be a permanent element to disturbandes in real output, although
the time series behavior of output is disputed by economists.)
In any event, the nonstationarity in the price level that appeared
after countries abandoned the gold standard for a paper money
standard can only be explained by the nonstationarity introduced into the monetary base at this time.

SEPTEMBER/OCTOBER

1988

in these variables [Broaddus and Goodfriend (1984)].
A loss function [from Goodfriend (1987)] that can
explain base drift is shown in (6).

With (6), the central bank attempts to minimize the
variability of three variables: the market rate of
interest, inaccurate price level forcasts, and expected
inflation. Minimization of this loss function can
generate the kind of base drift that has characterized nominal variables in the post-World War II era.
Now, while the central bank possesses three objectives, it still has only two degrees of freedom for
varying its policy process; consequently, it must trade
off among achievement of its objectives. Minimization of (6) implies that in general the central bank
will allow base drift. It will also set a higher value
for the rate smoothing parameter than is optimal for
minimizing fluctuations in real output. The central
bank trades off achievement of reduced variability
in price level forecast errors and expected inflation
in order to obtain a reduction in variability in the
market rate. With (6), in contrast to (5), the optimal
values of the ø parameters depend upon the ratios
of the trade-off parameters:

VI.
CLARIFYING THE MONETARY RESPONSIBILITIES
OF THE CENTRAL BANK
The Role of Money in the Formulation
of Monetary Policy
There is an ongoing debate over the importance
to assign to the behavior of money in the formulation of monetary policy. With the financial deregulation of the early 1980s and the resulting uncertainty
over the behavior of the public’s M1 demand function, this debate has centered on the contention that
the role of money should be reduced when money
demand is highly variable.13 For example, Stephen
13 The nationwide introduction of NOW accounts in 1981 and
their incorporation into M1 altered the character of the public’s
demand for M1. Because NOWs pay explicit interest, they have
caused M1 to become more highly substitutible with deposits
used for saving, rather than for transactions. Because that part
of M2 that is not included in M1 contains primarily savingsrelated deposits, M1 including NOWs has become more highly
substitutible with the non-M1 component of M2. The result has
been to alter the character of the public’s M1 demand function.
[The character of the M2 demand function has remained unFEDERAL

RESERVE

Axilrod (Staff Director of the Office for Monetary
and Financial Policy at the Board of Governors until
July 1986) uses the increased uncertainty over the
behavior of money demand to explain the deemphasis of money in the policy process after 1982:
. . . money became less useful as a policy instrument
because of a combination of market developments
and
attitudinal shifts that made it more unstable in relation
to the economy and its own history. So money was deemphasized after 1982 for pragmatic economic reasons.
[Axilrod (1988) p. 59]
[See also Axilrod (1985), p. 17.)
The most important aspect of monetary policy is
the central bank’s objective function. The objective
function determines the policy process (4) through
the values set for the ø parameters. This policy
process can be formulated with the monetary base
as the left-hand variable or the interest rate as the
left-hand variable. In the former formulation (the one
employed here), it is natural to discuss monetary
policy in terms of the behavior of the monetary
aggregates. In the latter formulation, it is natural to
discuss monetary policy in terms of the behavior of
the interest rate. In actual practice, central banks have
not usually formulated policy discussions in terms of
the behavior of the monetary aggregates. Instead,
they have discussed monetary policy in terms of the
behavior of the discount rate and its effect on money
market rates.14
There is, however, a reason to discuss monetary
policy in terms of the behavior of the monetary aggregates. The time series behavior of the aggregates
translates into the time series behavior of the price
level more directly than is the case with the interest
rate. A given increase in the trend rate of growth of
the monetary aggregates (øtrend) implies the same increase for the trend rate of inflation. An increase in
rate smoothing (øsmooth)beyond an optimal value implies an increase in the variability of the price level.
Base drift in the monetary aggregates (ødrift different
from one) implies base drift in the price level (apart
changed (Hetzel and Mehra, 1988).] As a result, a debate has
occurred over the usefulness of M1 in the policy process. Also,
M1 has often been accepted as the definition of money. Consequently, the debate has often taken the form of whether money
can play a role in the formulation of monetary policy when money
demand is highly variable. [Angell (1987) and Johnson (1988),
for example, have sought replacements, at least temporarily, for
money in policy discussions. Their work concentrates on the
role of money as an indicator variable.]
14 In the United States, the Federal Reserve System has
modified the traditional discount rate procedure by choosing a
combination of the discount rate and borrowed reserves. The
market rate is then determined as the sum of the discount rate
and some positive amount that is proportional to the level of
borrowed reserves.
BANK OF RICHMOND

27

from whatever drift is allowed to compensate for any
permanent component in disturbances to money demand and output). This connection between the time
series behavior of the monetary aggregates and the
price level holds regardless of the degree of variability
in money demand.
The importance of clarifying the implications of
monetary policy for the behavior of the price level
is increased due to the indirect way the behavior of
the price level is produced in actual practice. Typically, the central bank possesses multiple macroeconomic objectives.15 It has, however, only the
two degrees of freedom for pursuing these objectives
given by the two parameters (øsmoothand ødrift) that
alter the time series behavior of the monetary base.
The behavior of the price level (and the monetary
aggregates) emerges as a by-product of the trade-offs
the central bank must make in order to pursue multiple objectives with a more limited number of degrees
of freedom to manipulate in setting the policy process. Furthermore, the central bank’s objective function is not made explicit in policy discussions. The
trade-offs that must be made in pursuit of multiple
objectives are not discussed explicitly. The link
between these trade-offs and the price level is
obscured when the central bank’s objective function
is not made explicit in policy discussions and when
policy is discussed in terms of interest rates (or a
money market proxy). In contrast, the implications
for the price level of these trade-offs are clearer
when policy is discussed in terms of the monetary
aggregates.
Explicit Targets

for the Money Stock

Determination of the monetary base in part on the
basis of current conditions in the money market
obscures the responsibility of the central bank for
the behavior of the monetary base, the money stock,
and the price level. The consequent endogeneity of
15The Federal Reserve Act stipulates
that the Federal Open
Market Committee should set its ranges for the monetary
aggregates “taking account of past and prospective developments
in employment, unemployment,
production, investment, real
income, productivity, international trade and payments, and
prices” [Board of Governors (1984)].

28

ECONOMIC

REVIEW,

the monetary base facilitates special factors explanations of inflation, that is, explanations that confine
the causes of inflation to the macroeconomic disturbances that impinge upon the economy.16 Endogenous determination
of the monetary base also
obscures the way the central bank gives the money
stock and the price level well-defined equilibrium
values. In the absence of explicit limitation of the
monetary base, the money stock and the price level
are made well-defined economic variables by the way
the central bank determines the public’s expectation
of the future price level. This indirectness obscures
central bank responsibility.
In order to clarify the way it determines the
behavior of prices, the central bank could formulate
the policy process in terms of the monetary aggregates. The central bank could select a single definition of the money stock as a substantive intermediate
target and explain to the public the relationship that
it believes will hold over time between the money
stock and an explicitly formulated path for the price
level.17 The central bank could also use the monetary
base as the policy variable it sets in order to achieve
its intermediate money target. [See Black (1986).]
Conclusion
Clarification of the monetary responsibilities of the
central bank requires an explicit statement of the
objectives of the central bank and the relative importance attached to these objectives. It also requires
an explicit statement of how the central bank believes
its monetary policy will achieve its objectives. It is
necessary to make explicit the consequences
of
monetary policy for the behavior of the price level.
Hopefully, the model presented in this article will
aid in discussion of the monetary responsibilities of
the central bank.

16 See Cullison (1988) for a discussion of the possible influence
on monetary policy of special factors explanations of inflation
in the 1970s.
17 In order to make the money stock a substantive intermediate
target, it would be necessary to make the decision whether co
allow base drift in its targeted value an explicit part of the
decision-making process.

SEPTEMBER/OCTOBER

1988

References
Angell, Wayne
Aggregate
Institute,
Governors

D. “A Commodity Price Guide to Monetary
Targeting.” Speech given at the Lehrman
New York, December
10, 1987. Board of
of the Federal Reserve System. Processed.

Axilrod, Stephen H. “U.S. Monetary Policy in Recent Years:
An Overview.” Federal Resume Bulletin 71 (January 1985):
14-24.
“What Really Went on in the Temple.”
the Board (March 1988), pp. 58-61.

Across

Barro, Robert J., and David B. Gordon. “A Positive Theory
of Monetary Policy in a Natural Rate Model.” Journal of
Political Economy 91 (August 1983): 589-610.
Black, Robert P. “A Proposal to Clarify the Fed’s Policy
Mandate.” Cato Journals (Winter 1986): 787-95.
Board of Governors of the Federal Reserve System. Federal
Reserve Act and Other Statutory Provisions Affecting the
Federal Reserve System, As Amended Through April 20, 1983.
Washington, D.C.: Board of Governors, 1984.
Broaddus, Alfred, and Marvin Goodfriend. “Base Drift and the
Longer Run Growth of M1: Experience from a Decade of
Monetary Targeting.” Federal Reserve Bank of Richmond
Economic Review 70 (November/December
1984): 3-14.
Cullison, William. “On Recognizing Inflation.” Federal Reserve
Bank of Richmond Economic Review 74 (July/August 1988):
4-12.
Dotsey, Michael, and Robert G. King. “Monetary Instruments
and Policy Rules in a Rational Expectations Environment.”
Journal of Monetary Economics12 (September 1983): 357-82.
Friedman, Milton. “Inflation: Causes and Consequences.”
In
Dollars and Deficits. Englewood Cliffs, New Jersey: Prentice
Hall, 1968.
Goodfriend, Marvin. “Discount Window Borrowing, Monetary
Policy, and the Post-October
6, 1979, Federal Reserve
Operating Procedure.” Journal of Monetary Economics 12
(September 1983): 343-56.

Hetzel, Robert L. “The Political Economy of Inflation.” Federal
Reserve Bank of Richmond, April 1988. Processed.
Hetzel, Robert L., and Yash Mehra. “The Behavior of Money
Demand in the 1980s.” Federal Reserve Bank of Richmond,
June 1988. Processed.
Johnson, Manuel H. “Recent Economic Developments
and
Indicators of Monetary Policy.” Speech given to the Money
Marketeers of New York University, New York, March 15,
1988. Board of Governors of the Federal Reserve System.
Processed.
Keynes, John Maynard. A Tract on Monetary Reform (1923). In
The Collected Writings of John Maynard Keynes, vol. 4.
London: The Macmillan Press, 1971.
Lucas, Robert E., Jr. “Econometric
Policy Evaluation, A
Critique” (1976). Reprinted in Studies in Business-Cycle
Theory. Cambridge, Mass.: MIT Press, 1983a, pp. 104-30.
. “Econometric
Testing of the Natural Rate
Hypothesis” (1972). Reprinted in Studies in Business-Cycle
Theory. Cambridge, Mass.: MIT Press, 1983b, pp. 90-103.
McCallum, Bennett T. “Price Level Determinacy with an
Interest Rate Policy Rule and Rational Expectations.”
Journal of Monetary Economics 8 (November 1981): 319-29.
. “Some Issues Concerning Interest Rate Pegging,
Price Level Determinacy, and the Real Bills Doctrine.”
Journal of Monetary Economics 17 (January 1986): 135-60.
Poole, William. “Optimal Choice of Monetary Policy Instruments in a Simple Stochastic Macro Model.” Quarterly
Journal of Economics 84 (May 1970): 197-216.
Sargent, Thomas J. “The Demand for Money during Hyperinflations under Rational Expectations” (1977). In Rational
Expectations and Econometric Practice, edited by Robert E.
Lucas, Jr. and Thomas J. Sargent, vol. 2. Minneapolis,
Minn.: The University of Minnesota Press, 1981a, pp.
429-52.
. “Rational Expectations, the Real Rate of Interest,
and the Natural Rate of Unemployment” (1973). In Rational
Expectations and Econometric Practice, edited by Robert E.
Lucas, Jr. and Thomas J. Sargent, vol. 1. Minneapolis,
Minn.: The University of Minnesota Press, 1981b, pp.
159-98.

. “Interest Rate Smoothing and Price Level
Trend-Stationarity.” Journal of Monetary Economics 19 (May
1987): 335-48.
Goodfriend, Marvin, and Robert G. King. “Financial Deregulation, Monetary Policy, and Central Banking.” Federal
Reserve Bank of Richmond Economic Review 74 (May/June
1988): 3-22.

FEDERAL

RESERVE

Tinbergen, Jan. Economic Policy: Principles and Design. Chicago:
Rand McNally, 1967.
Walsh, Carl E. “In Defense of Base Drift.” American Economic
Review 76 (September 1986): 692-700.

BANK

OF RICHMOND

29

APPENDIX
b2rt captures the effect on the multiplier of the interest sensitivity of excess-reserves
and currencydeposit ratios. The variable xt is a seriallyuncorrelated, zero-mean shock to the value of these
ratios.
Equation (6) describes the behavior of the central
bank.

Equation (1) is an IS function. It shows the combinations of real output and the real rate of interest
that equate the public’s desired
saving and
investment.

Real output is yt; the interest rate rt; and the price
level pt. (All the variables are logarithms, except for
rt.) The subscript t indicates the time period. E is
the expectations
operator with the subscript indicating the time period at which the expectation was
formed. The variable wt is a serially-uncorrelated,
zero-mean random shock. Equation (2) is an aggregate supply function.

The public’s supply of goods varies positively with
its error in predicting the contemporaneous
price
level. It is assumed that this monetary nonneutrality arises from one-period contracts specified in
nominal terms.
Next, equate the IS function (1) and the aggregate
supply function (2) in order to eliminate output yt;
solve the resulting expression for rt; and simplify the
notation for the coefficients and error term (qt is a
transformation
of wt and remains a seriallyuncorrelated, zero-mean random error).

The market for the quantity of money is described by a money demand function and a money
supply function. The money demand function is

Nominal money demand
depends positively
upon the price level (pt) and real output (yt) and
negatively upon the market rate of interest (rt). The
variable vt is a serially-uncorrelated,
zero-mean
random shock.
The money supply function is

Bt is the (log of the) monetary base. The term b1
is a constant that captures the effect on the moneymultiplier of the legal required reserve ratio. The term
30

ECONOMIC

REVIEW.

The central bank specifies three parameters (the
three øs) that determine the time series behavior of
the monetary base. The parameter ø3 is the trend
rate of growth of the base. The parameter ø1 determines the interest elasticity of the monetary base.
It specifies the extent to which the central bank
smooths movements of the market interest rate
around a reference level Et-1rt. The central bank
cannot smooth the market rate around an arbitrary
level. It is constrained to smooth around the prior
period’s expectation of the market rate. This expectation is the sum of the expected real rate and of the
trend rate of inflation. (The solution of the model
is determinate only for this value.) Specifically, the
central bank must smooth the market rate around
the value (c1 + ø3), which is Et- 1rt from (3). The
variable [rt - (c1 + ø3)] measures innovations (unpredictable changes) in the market rate. Interest-rate
innovations cause the central bank to produce innovations in the monetary base, which, from (6), equal
ø1 times the interest rate innovations.
The third term on the right side of (6) measures
the extent to which the central bank offsets, in the
contemporaneous period, last period’s innovation in
the monetary base. There are two general cases. In
one case, ø2 differs from one, so that there is not an
exact offset to last period’s innovation. The monetary
base then behaves like a random walk with a persistence over time given by ø3. In the second case,
ø2 is one so that the central bank offsets exactly last
period’s innovation. In this case, Et-2Bt-1
can be
defined as ø0 + ø3(t - 1), where t is the number of
time periods that have elapsed since a base period
0. The constant ø0 is the (log of the) monetary base
at time 0. This expression defines a path for the
monetary base that grows over time at the rate ø3
and around which the monetary base fluctuates.
The model’s equations are listed below. [Equation
(7) comes from substituting
from the aggregate
supply function (2) into (4), the money demand
function, and simplifying the notation for the
coefficients.]

SEPTEMBER/OCTOBER

1988

(11) also minimize each term of (11) separately. Consequently, the ß and y parameters do not enter into
the expression for the øS. The central bank is not
forced to trade off among conflicting objectives.
Consider now the cost function (14).

The ø values that minimize this cost function involve
The model is completed with a cost function [from
Goodfriend (1987)] for the central bank. Var is
variance.

With the assumption that money demand equals
money supply and the assumption of rational expectations, equations (7)-(10) can be solved for mt, pt,
rt, and Bt. The solutions for the contemporaneous
price level prediction error Ipt - Et - 1pt] and for
expected inflation [Etpt+1 - pt] are substituted
into (11). With these substitutions, the central bank’s
cost function is expressed
in terms of the ø
parameters that characterize the behavior of the
monetary base. The central bank chooses these
parameters in order to minimize (11).
The ø parameters that minimize (11) are

Poole (1970, p. 208) for a solution for ø1 in a static
model.] The model does not determine a value for
ø3. Note that the values of ø1 and ø2 that minimize

the process for generating the monetary base in a
way that reflects the relative importance it assigns
to achieving conflicting objectives. With (14), the optimal rate smoothing parameter ø1 is larger than the
ø1 in (12). The base drift parameter ø2 is in general
different from one. Its value is greater or less than
one depending upon the parameters of the cost function (14) and the structural parameters of the model.
For example, ø2 is less than one if and y are large
and the magnitude of c2 is large.
(The structural parameters of the model, a2, a3,
b2, and c2, are functions of the ø parameters. Different objective functions imply different structural
coefficients [Lucas (1976)].) For some issues, it is
important to model how the policy process affects
the structural relationships that summarize the
economy. For example, the model incorporates a
money demand function and a money supply function. Sargent (1981a) and Goodfriend (1983) discuss,
respectively,
the way in which a change in the
monetary policy process affects the structural form
of the money demand function and the money supply
function. The major policy issue of interest here is
the way different objective functions affect the general
time series behavior of the price level. For this
issue, the main assumption that must be made is that
the signs of the structural parameters remain unchanged when the policy process that generates the
monetary base changes.

FEDERAL RESERVE BANK OF RICHMOND

31