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THE EARLY HISTORY OF THE REAL/NOMINAL
INTEREST RATE RELATIONSHIP
Thomas M. Humphrey
The proposition that the real rate of interest equals
the nominal rate minus the expected rate of inflation
(or alternatively, the nominal rate equals the real
rate plus expected inflation) has a long history extending back more than 240 years. William Douglass
articulated the idea as early as the 1740s to explain
how the overissue of colonial currency and the resulting depreciation of paper money relative to coin
raised the yield on loans denominated in paper compared to the yield on loans denominated in silver coin.
In 1811 Henry Thornton used the same notion to explain how an inflation premium was incorporated into
and generated a rise in British interest rates during
the Napoleonic wars. Jacob de Haas, writing in 1889,
employed the real/nominal rate idea to account for the
“third (inflationary) element” in interest rates, the
other two being a reward for capital and a payment
for risk. And in 1890, Alfred Marshall cited the
interest-inflation relationship as the key component in
his theory of the transmission mechanism through
which variations in the value of money generate trade
cycles. The relationship achieved its classic exposition in Irving Fisher’s Appreciation and Interest
(1896) where it was refined, restated, elaborated, and
presented in the form in which it appears today.
Apparently, however, some modern economists are
largely unaware of this earlier tradition. As a result,
they erroneously see the real/nominal rate relationship as a recent rather than an ancient idea. Thus,
for example, Lawrence H. Summers of the National
Bureau of Economic Research contends “that it was
not until the 20th century that the distinction” between nominal and real interest rates “was even
introduced into economic analysis.” [11; p. 48]
The purpose of this article is to show that the tworate distinction long predates the 20th century. More
precisely, this article demonstrates (1) that a rudimentary version of the real/nominal rate relationship
had already been enunciated by the mid-1700s, (2)
that the relationship was thoroughly understood and
succinctly formulated by some of the leading 19th
The author acknowledges the helpful comments of
Timothy Q. Cook.
2

century classical and neoclassical monetary theorists,
(3) that it was presented in its modern form by the
end of the century, and therefore (4) that the notion
that it is a 20th century invention is totally erroneous.
In documenting these points, the article traces the
pre-20th century evolution of the real/nominal rate
analysis from its earliest origins to its culmination in
Fisher’s Appreciation and Interest. As a preliminary
step, however, it is necessary to sketch the basic
outlines of this traditional analysis in order to demonstrate how earlier writers contributed to it.
Key Propositions

As usually presented; the real/nominal interest
rate relationship expresses the nominal rate as the
sum of the real rate and a premium for expected
inflation or, what is the same thing, the real rate as
the nominal rate adjusted for expected inflation. In
symbols,

where n is the nominal or observed market interest
rate, r is the expected real interest rate associated
with the holding of real commodities or capital goods,
and p is the expected rate of price inflation or depreciation of the value of money.
Of these three variables, the real rate r is taken
to be a fixed constant equal to the given marginal
productivity of capital. To this real rate is equated
n-p, the anticipated real (inflation-corrected) yield
on money loans. The equality between these two
real rates is maintained by arbitrage, the operation
of which ensures that the expected real rates of
return on all assets are the same. Note, however,
that while anticipated real yields are continuously
equalized, the analysis recognizes that inflation forecasting errors may cause the realized real yield on
loans to deviate temporarily from its equilibrium
level corresponding to the given real rate on capital.
Such deviations will occur, for example, if people
either neglect to predict inflation or predict it extrapolatively from past inflation rates so that it (predicted
inflation) changes slowly when actual inflation

ECONOMIC REVIEW, MAY/JUNE 1983

changes. In either case, inflation will be underpredicted and therefore will not be fully incorporated
into nominal rates. As a result, the nominal rate will
not fully adjust for inflation and the realized real
rate on money loans will fall below its equilibrium
level. The fall in the realized real rate of course will
produce windfall profits for borrowers and windfall
losses to lenders. Assuming borrowers and lenders
predict future profits extrapolatively from these
realized windfall profits and losses and then act on
the basis of these predictions, the subsequent corrective adjustment of loan demand and supply will tend
to bid up the nominal rate by the rate of inflation. In
this way the nominal rate eventually rises by the full
amount of inflation, thereby restoring the realized
real yield on loans to its equilibrium level.
From the foregoing analysis, earlier writers drew
four conclusions. First, the equilibrium nominal rate
fully adjusts for inflation leaving the realized real
rate on money loans intact. Second, such equilibrium
nominal rate adjustments render market rates high
in periods of inflation and low in periods of deflation.
Third, the same equilibrium nominal rate adjustments entail no real effects. By leaving the real
yield on loans unchanged, they alter neither profits
nor losses nor incentives to borrow and lend. Nor
do they affect the distributive shares of borrowers
and lenders. Fourth, during the transitional adjustment to equilibrium, however, incomplete nominal
rate changes can have temporary real effects. These
effects are of two kinds. First are the inevitable
income distribution effects on borrowers and lenders
owing to the incomplete adjustment of the nominal
rate and the resulting change in the realized real
rate. Second are possible output and employment
effects stemming from changes in the volume of
loans and business investment spending induced by
the real rate change. As shown below, however, the
occurrence of these output and employment effects
was postulated to depend upon the questionable assumption of differential profit expectations as between borrowers and lenders. Constituting the essentials of traditional real/nominal interest rate analysis,
the foregoing propositions originated with the 18th
and 19th century writers discussed below.
William Douglass

William Douglass, an 18th century Scottish-born
physician, pamphleteer, controversialist, and student
of American colonial currencies was perhaps the first
to distinguish between real and nominal interest

rates. 1 He did so in an effort to refute the notion
(as prevalent then as now) that easy money spells
cheap money, i.e., that rapid monetary growth lowers
market interest rates. To show that paper money
expansion raises rather than reduces market rates,
he defined the nominal rate as the rate measured in
terms of paper currency and the real rate as the rate
measured in terms of silver coin. That is, he identified the nominal rate with the yield on loans denominated in paper and the real rate with the yield on
loans denominated in coin. Then, assuming the real
(coin) rate fixed by law, he argued that an expansion
of inconvertible paper currency would depreciate the
paper money relative to coin and thus lower the real
value of loans denominated in paper relative to those
denominated in coin, This would induce lenders to
demand a compensatory premium in the nominal
rate, thereby raising the latter by the full amount of
the depreciation. As summarized by him:
The quantity of paper credit sinks the value of the
principal, and the lender to save himself, is obliged
to lay the growing loss of the principal, upon the
interest. [5; p. 243]

In other words, lenders, foreseeing an inflationinduced depreciation in the value of their principal,
will demand a premium equal to the expected rate of
depreciation to protect them from the loss. This
premium, when added to the rate of interest expressed in terms of coin, raises the nominal or paper
rate by the full amount of the expected rate of depreciation. In short, the nominal rate adjusts for
inflation to maintain equality between the real rate
on paper and the given real rate on silver.
To illustrate this point, Douglass argued that if the
rate of interest expressed in terms of coin were
legally fixed at 6 percent while paper was depreciating relative to coin at a rate of 7 percent, then “the
lender to save his principal from sinking requires a
13 percent” nominal interest rate for the period of
the loan-this 13 percent nominal rate being the sum
of the 6 percent real (coin) rate and the 7 percent
rate of depreciation of paper with respect to coin.
[5; p. 339] Similarly, he pointed out that when
paper depreciates relative to coin at a rate of 22
percent per year the nominal (paper) rate corresponding to a legal real (coin) rate of 6 percent
would be 28 percent per annum-this rate being the
sum of the 6 percent real rate and the 22 percent rate
of depreciation. In effect, he argued that the nominal
rate equals the real rate plus the expected rate of
1

On Douglass, see Dorfman [3; pp. 155-162].

FEDERAL RESERVE BANK OF RICHMOND

inflation, the latter expressed as the rate of depreciation of paper relative to coin. Since he assumed
that the rate of depreciation was fully foreseen and
incorporated into yields expressed in paper, he also
recognized that the equilibrium nominal rate fully
adjusts for actual inflation, leaving the realized real
rate unchanged. In this case currency depreciation
has no effect on real economic variables since it leaves
the real rate undisturbed.
From the foregoing propositions, Douglass concluded that the nominal rate varies equiproportionally
with the rate of inflationary overissue of paper money
such that
. . . the larger the emissions, natural [i.e., nominal]
interest becomes the higher; therefore the advocates for paper money (who are generally indigent
men, and borrowers) ought not to complain, when
they hire money at a dear nominal rate. [5; p.
340]
Accordingly debtors, he argued, have no grounds for
complaining that they are injured by high nominal
rates. For, with full adjustment of those rates with
respect to inflation, realized real rates and hence the
distribution of real income between creditors and
debtors remains unchanged. Here is the proposition
that equilibrium adjustments of the nominal rate are
neutral in their impact on real economic magnitudes.
To summarize, not only did Douglass articulate
the real/nominal interest rate relationship, he also
originated (1) the notion that the equilibrium nominal rate must fully adjust for changes in the value of

money so as to leave the real rate unchanged, and
(2) the corresponding notion of the neutrality of
equilibrium changes in the nominal rate with respect
to distributive shares. This, plus his explanation of
how expected inflation premia get embodied in market rates, marks him as an important early contributor to the two-rate analysis.
Henry Thornton (1760-1815)

The next writer to employ the real/nominal rate
r e l a t i o n s h i p 2 was Henry Thornton, the British
2

Thornton expressed the relationship (albeit verbally,
not algebraically) in the form r = n - p, where r is the
realized real rate, n the nominal rate, and p the realized
rate of inflation. He noted (1) that inflation had occurred
at an average yearly rate of 2-3 percent over the period
1800-1810 and (2) that, as a result, if a man borrowed
money at a 5 percent nominal rate in 1800 and paid it
back in 1810, he would find that he had paid an actual
real rate of only 2-3 percent and not 5 percent as he
appeared to do. That is, he argued that p = 2-3 percent,
n = 5 percent, and r = 3-2 percent. He also pointed out
that when one borrows to finance the purchase of assets
the price of which rises with the rate of inflation, the real
cost of borrowing is only that part of the interest rate
that exceeds the price gain.
4

banker, evangelist, philanthropist, member of Parliament, and the outstanding monetary theorist of the
first half of the 19th century. Writing during the
Napoleonic wars when Britain was off the gold standard and the Bank of England was released from its
obligation to convert paper into gold at a fixed price
upon demand, Thornton employed the relationship to
explain how the suspension of convertibility and the
resulting inflationary overissue of paper currency had
raised market yields in Britain. That is, he sought to
specify the mechanism through which an inflation
premium becomes embodied in market rates. More
precisely, he sought to show that the inflation premium enters the nominal rate even if nobody attempts
to predict inflation. For according to him, it is
profits and profit predictions rather than inflation
predictions per se that drive up the equilibrium
nominal rate. Tracing a chain of causation running
from unpredicted inflation and sluggish nominal rates
to realized real rates to profits both actual and expected, thence to loan demands and supplies and back
again to nominal rates, he argued that unexpected
inflation initially lowers the realized real loan rate
below the given real yield on capital. The result
is windfall realized profits for borrowers and windfall losses to lenders. Assuming borrowers and
lenders predict future profits extrapolatively from
realized past profits and then adjust their loan demands and supplies accordingly, the resulting rise

in loan demand and fall in loan supply will bid up the
nominal rate by the full amount of inflation, thereby
eliminating the real rate differential existing between
money loans and real capital investment. At this
point the real loan rate is restored to its equilibrium
level corresponding to full adjustment of the nominal
rate.
Accordingly, in countries in which the currency was
in a rapid course of depreciation, supposing that
there were no usury laws, the current rate of
interest was often, as he [Thornton] believed,
proportionably augmented. Thus, for example, at
Petersburgh, at this time, the current interest was
20 or 25 percent, which he conceived to be partly
compensation for an expected increase of depreciation of the currency. [12; p. 336]

Here is the first rigorous and systematic account of
one version of the mechanism through which an infla-

tion premium becomes incorporated into interest
rates. And, although it conflicts with that part of his
analysis that ignores anticipated inflation, here also
is the first explicit acknowledgment that the premium
refers to expected future inflation.
Thornton’s contribution, consisting as it did of a
fully-articulated theory of how inflation drives up

ECONOMIC REVIEW, MAY/JUNE 1983

interest rates, was a milestone in the evolution of the
two-rate analysis. In terms of analytical insight,
clarity, rigor, and completeness, it remained unsurpassed until Irving Fisher wrote his Appreciation
and Interest in 1896. This of course is not to say that
other economists did not discuss the real/nominal
rate relationship during this time. On the contrary,
over the 86 year interval separating Thornton and
Fisher, at least four economists-namely John Stuart
Mill, Alfred Marshall, the Dutch writer Jacob de
Haas, and the American John Bates Clark-articulated the relationship. None of these writers, however, knew of Thornton’s contribution and thus never
referred to it. Even Fisher, who acknowledged the
others as forerunners and cited them in his 1896
work, was apparently unaware of Thornton, whose
‘work had largely fallen into oblivion. Thus despite
its originality and insight, Thornton’s contribution
exerted little influence on the work of his 19th century successors, of whom Mill was the first.
John Stuart Mill (1806-1873)

Despite his ignorance of Thornton’s contribution,
John Stuart Mill nevertheless echoed the former’s
contention that interest rates include a premium for
expected inflation. Thus, in the sixth (1865) edition
of his Principles of Political Economy, Mill wrote
that “the expectation of further depreciation” of the
currency raises market yields
because lenders who expect that their interest will
be paid, and the principal perhaps redeemed, in a
less valuable currency than they lent, of course
require a rate of interest sufficient to cover this
contingent loss. [9; p. 646]

Mill’s contribution consisted of recognizing, first, that
inflation reduces the real value of the interest as well
as the principal of a loan, and, second, that lenders
will therefore demand an inflation premium to cover
both types of expected loss. This was a new insight :
earlier writers had concentrated solely on the expected loss of principal and had said nothing about
the corresponding loss of interest. Mill’s insight was
later formalized by Marshall and Fisher, both of
whom added a cross-product term to the real/
nominal rate equation to account for inflation’s impact on the real value of interest receipts.
Jacob de Haas

After Mill came the Dutch economist Jacob de
Haas. Writing in 1889, he argued that the expected
rate of change of the value of money constituted the
“third element” in market interest rates, the other

two being a payment for capital and a payment for
default risk, respectively. That is, he claimed that
the first element consists of “the remuneration for
abstinence, i.e., the hire of capital,” the second “the
insurance against loss or remuneration for risk,” and
the third “the expected change in the purchasing
power of money.” [2; pp. 110-111, 107] Since the
first two elements taken together comprise the real
rate of interest while the third element is the price
expectations term, de Haas’s formulation amounts
to the expression n = r + p where n is the nominal
or market rate, r the real rate, and p the expected
rate of price change. Depending upon whether prices
were expected to rise or fall, this latter variable, he
noted, could be either positive or negative, adding to
or subtracting from the given real rate as the case’
might be. The implication, he said, was that market
rates tend to be high during periods of inflation and
low in periods of deflation.
Finally, like Thornton, he contended that inflation
expectations get incorporated into market rates via
loan demand and supply. More precisely, he argued
that expected inflation causes lenders, who anticipate
a depreciation in the real value of their principal and
interest, to contract loan supply. Conversely, borrowers, who anticipate repaying debts in depreciated
dollars, expand their loan demands. The resulting
fall in loan supply and rise in loan demand acts to
raise market rates.
All in all, de Haas contributed little new to the
analysis of real and nominal interest rates. His work,
despite its apparent originality, contains nothing that
cannot be found in Thornton, although Fisher, being
unaware of this, thought highly of him.3 Marshall
too knew of his work and cited it in the first edition
of the Principles.
Alfred Marshall (1842-1924)

Marshall’s discussion of the real/nominal rate relationship appeared in the first (1890) edition of his
Principles of Economics in a section entitled, appropriately enough, “Note on the Purchasing Power of
Money in Relation to the Real Rate of Interest.” He
was the first to use the words real and nominal to
refer to interest rates-his predecessors having used
one but not both of those expressions. He was also
the first to compute real rates taking account of
3

In the preface to his Appreciation and Interest, Fisher
says that, of all the writers who considered the real/
nominal rate relationship, “Mr. Jacob de Haas, Jr., of
Amsterdam, seems most fully to have realized its importance.”

FEDERAL RESERVE BANK OF RICHMOND

5

inflation’s erosion of the real value of interest as well
as the principal of a loan. Specifically, he correctly
computed the annually-compounded realized real rate
(r) as the difference between the nominal rate (n),
the rate of inflation (p), and the cross-product (np)
of those two latter rates-this cross-product measuring the effect of inflation on the real value of interest
receipts. That is, although he did not state the
formula

he was the first to compute the realized real rate
according to it. He did so when he stated that a 5
percent nominal rate is equivalent to a minus 5½
percent real rate after correction for a 10 percent
rate of inflation. He did so again when he said that a
5 percent nominal rate translates into a 15½ percent
real rate when prices are falling (the value of money
is rising) at a rate of 10 percent. In both cases, the
½ percent refers to the effect of changes in the value
of money on the real value of interest receipts. In
so doing, he improved upon the work of his predecessors, all of whom, with the exception of John
Stuart Mill, computed the real rate according to the
approximation r = n - p that neglects the rate of
depreciation of interest payments.
Finally, although Marshall did not explain how
inflation expectations are formulated and embodied
in market rates, he did suggest that expectational
(i.e., inflation forecast) errors and the resulting deviations of the realized real loan rate from its equilibrium level might, when borrowers and lenders hold
different expectations, generate trade cycles. Said
he, “When we come to discuss the causes of alternating periods of inflation and depression of commercial activity we shall find that they are intimately
connected with those variations in the real rate of
interest which are caused by changes in the purchasing power of money.” [8; p. 628] Marshall’s
statement implies (1) that inflation expectations are
formed extrapolatively from realized past rates of
inflation such that expectations adjust slowly to
actual changes in inflation, and (2) that expectations
differ between borrowers and lenders so that loan
demands respond disproportionally to loan supplies
when expectations change. Of these two ideas, the
first ensures that expected inflation lags behind actual
inflation causing incomplete adjustment of the nominal rate and a corresponding change in the realized
real rate. The second ensures that loan demand
curves shift disproportionally to loan supply curves
when expectations change, thereby resulting in alterations in the volume of loans. Assuming these loans
6

are used to finance business investment projects, real
investment spending and thus the level of real economic activity will be affected. Taken together, the
assumptions of extrapolative expectations and differential expectations as between borrowers and lenders
are sufficient to generate the real economic disturbances Marshall had in mind. This is what he meant
when he suggested that fluctuations in the value of
money could generate trade cycles via the interestinflation relationship. Marshall’s suggestion was
later developed into a full-scale model of the trade
cycle by Irving Fisher.
J. B. Clark (1847-1938)

As indicated above, Marshall largely treated the
nominal rate as given and examined the impact of
observed inflation on the realized real loan rate. By
contrast, his contemporary John Bates Clark treated
the real loan rate as a constant and examined the
impact of anticipated inflation on the nominal rate.
Thus, in his 1895 article on “The Gold Standard of
Currency in the Light of Recent Theory,” Clark
argued that a perfectly foreseen inflation would be
“unerringly corrected” by equiproportional variations
in the nominal rate of interest so as to maintain the
real loan rate intact. To illustrate this, he said that
upon the anticipation of a negative 1 percent rate of
inflation, the nominal rate would immediately fall
from a 5 to a 4 percent level so as to keep the realized
real loan rate equal to the given 5 percent real yield
on capital. That is, he articulated the relationship
r = n - p according to which the nominal rate n
must vary in step with the inflation rate p to keep the
real loan rate fixed. Regarding this nominal rate
adjustment, he noted that it would have no effect on
real variables including the distribution of income
since "a debtor does not suffer nor a creditor gain
by a change in the purchasing power of coin, provided
that the change is generally anticipated.” [1 ; p. 393]
Here is the notion of the neutrality of equilibrium
nominal interest rate changes, In restating these old
propositions regarding nominal interest rate adjustment and neutrality, Clark set the stage for Fisher’s
Appreciation and Interest.
F i s h e r ’ s Appreciation and Interest ( 1 8 9 6 )

The notion that real/nominal interest rate analysis
is a 20th century phenomenon originating with Irving
Fisher is disproved in his Appreciation and Interest
(1896) where he makes it clear that he was by no
means the first to present that analysis. As proof,
he cites the earlier contributions of Douglass, Mill,

ECONOMIC REVIEW, MAY/JUNE 1983

de Haas, Marshall, and Clark-all of whom helped
lay the groundwork for his own analysis. Containing
the earliest complete account of his theory of inflation
and interest, Appreciation and Interest constitutes
the high water mark in the pre-20th century development of the subject. In it Fisher made at least four
advances over the work of his predecessors. First,
he derived the formula r = n - p - np, or alternatively, n = r + p + rp relating annuallycompounded inflation and interest rates.
Second,
having derived the formula, he discussed the limit
values and behavior of its constituent variables under
conditions of perfect and imperfect foresight, respectively, Third, he confronted the perfect foresight
(complete adjustment) hypothesis with empirical
data, and, when the facts failed to confirm the theory,
he constructed an alternative theory of sluggish nominal rate adjustment under imperfect foresight.
Finally, he employed ‘this imperfect foresight theory
to explain how price changes generate trade cycles
by altering realized real loan interest rates.
Derivation of Formula

Regarding his derivation of the formula n =
r + p + rp he argued as follows: Suppose loan
contracts can be written either in terms of money or
in terms of goods. As mentioned above, let n be the
nominal or money interest rate and r be the real or
commodity interest rate. Also suppose that prices
rise at the expected rate p over the year, so that what
costs a dollar at the beginning of the year will cost
(1+p) dollars at year’s end. Assuming that at the
start of the year one dollar will buy one basket of
commodities, a person has the option of borrowing,
say, one dollar at money rate n for a year or, alternatively, one basket of commodities at real rate r
for a year. If he chooses the first, he must pay back
(1+n) dollars principal and interest when the loan
expires. If he chooses the second, he must pay back
(1+r) baskets of commodities which he can purchase at a price of (1+p) dollars per basket when
the loan comes due. This price, when multiplied by
the number of baskets required to liquidate the loan,
results in a total dollar outlay of (1+p) (1+r). I n
short, the costs of liquidating the loans expressed
in a common unit of account are (1+n) and
(1+p) (1+r) dollars, respectively. Now it is clear
that, with perfect arbitrage, equilibrium requires that
these two money sums be equal, i.e.,
(3) (1+n) = (1+p) (1+r),

such that the maturity values of both loans are the
same when expressed in terms of a common unit of
account. For if, say, commodity loans were cheaper
than money loans (i.e., the right side of the equation
was smaller than the left), then a profit could be
made by borrowing commodities, converting them
into dollars to be lent out at the money rate n, and
subsequently using the proceeds received from the
maturing money loan to purchase commodities with
which to retire the commodity debt. Given these
conditions, everyone would want to borrow commodities and ‘to lend money. The resulting increased
demand for commodity loans and the corresponding
increased supply of money loans would raise the
commodity rate of interest and lower the money rate
until the foregoing equality was restored. Expanding
equation 3 and solving for the nominal rate yields
(4)

n = r +

P

+

rp

where p, the rate of price inflation, is the rate of
depreciation of money relative to goods-which
means of course that goods are appreciating in value
relative to money. On the basis of this equation
Fisher concluded that,
The rate of interest in the (relatively) depreciating
standard is equal to the sum of three terms, viz.,
the rate of interest in the appreciating standard,
the rate of appreciation itself, and the product of
these two elements. [6; p. 9]
Limiting Values of the Variables

Having derived the formula, Fisher next commented on the plausible values of its component
variables. He noted, first, that the nominal rate could
never be negative in a world in which money can be
costlessly held. That is, he contended that because
people would hoard money rather than lending it at a
negative rate, the money rate of interest can never be
less than zero. And if the nominal rate cannot be less
than zero, it follows, he said, that prices can never
fall at a fully anticipated rate greater than the real
rate of interest-as can be seen by setting the nominal rate at zero and solving the formula for the
resulting rate of price deflation.4 In short, he argued
that the costless storage of money sets lower and
4

The fully anticipated rate of deflation cannot exceed
the real rate of interest because, if it did, the real rate of
return on hoarded money would exceed the real cost of
commodity loans. Given this opportunity for profitable

arbitrage, everyone would want to borrow commodities
for conversion into cash. The resulting excess demand
for commodity loans would immediately bid up the real
(commodity) rate into equality with the price deflation
rate, thereby restoring parity between the two.

FEDERAL RESERVE BANK OF RICHMOND

7

upper limits, respectively, to the nominal rate and
the fully anticipated rate of price deflation.
Empirical Tests

Fisher’s third contribution was to state and empirically test the perfect and imperfect foresight interpretations of the formula.5 In this connection he
noted that if perfect foresight exists, then price
changes are accurately predicted and fully incorporated into nominal rates. As a result, these rates
fully adjust for inflation leaving the realized real loan
rate unchanged. Thus if perfect foresight prevailed,
one would expect to observe virtual constancy of the
realized real rate and one-for-one variations between
nominal rates and the rate of inflation. By contrast,
in the imperfect foresight case price changes are
incompletely anticipated and therefore are not fully
incorporated into nominal rates. As a result, the
latter do not fully adjust for inflation and consequently the realized real loan rate changes. In this
case one would expect to find realized real rates
varying inversely with nominal rates and the latter
varying less than one-for-one with inflation rates.
Putting the perfect and imperfect foresight interpretations to the empirical test, Fisher found that the
data largely contradicted the former interpretation
and confirmed the latter. That is, he found that while
nominal rates tended to move with inflation and
deflation, they did not move sufficiently to offset these
price changes and consequently realized real rates
changed. In particular, he found (1) that realized
real rates moved inversely to nominal rates, (2) that
they exhibited roughly 3½ times the variability of
nominal rates, and (3) that they were often negative
during periods of rapid inflation. Evidently price
changes drove a wedge between real and nominal
rates with the former bearing most of the adjustment
-an outcome clearly at odds with the perfect foresight (constant realized real rate) hypothesis. On
the basis of this evidence, Fisher concluded that,
contrary to the perfect foresight model,. nominal rates
adjusted slowly and incompletely to inflation and
deflation because these phenomena were inadequately
foreseen.
Lagged Adjustment Mechanism

Fisher’s fourth contribution was to outline an alternative theory of interest rate adjustment consistent
with the facts. Abandoning the perfect foresight
5

What follows draws heavily from Rutledge [10].

8

framework for an imperfect foresight one, he presented a model in which transitory changes in real
variables play a key role in the adjustment process
and in which inflationary expectations are incorporated into nominal rates with long lags. He employed the model for two different purposes. He used
it, first, to show how the nominal rate reaches its
equilibrium level consistent with full adjustment to
inflation. He used it, second, to show how price
changes generate trade cycles.
Regarding the first use of his model, he explained
the process or mechanism through which an inflation
premium gets embodied in nominal rates. Employing
the assumptions (1) that firms are net borrowers,
(2) that firm owners by virtue of being entrepreneur:
possess foresight superior to that of lenders, and (3)
that entrepreneurs forecast profits extrapolatively, he
traced a chain of causation running from rising prices
and lagging nominal rates to falling real rates to
rising profits both actual and expected, then to increasing loan demands and ‘thence back again to
nominal rates. More precisely, he argued that unexpected inflation and sluggish nominal rates produce
falling real rates and hence windfall profits to borrowers. The latter then forecast future profits extrapolatively from those realized windfall profits and
adjust their loan demands accordingly. The resulting
rise in loan demand bids up the nominal rate by the
rate of inflation. He said :
Suppose an upward movement of prices begins.
Business profits (measured in money) will rise,
for profits are the difference between gross income
and expense, and if both these rise, their difference
will also rise. Borrowers can now afford to pay
higher “money interest”. If, however, only a few
persons see this, the interest will not be fully
adjusted and borrowers will realize an extra margin of profit after deducting interest charges. This
raises an expectation of a similar profit in the
future, and this expectation, acting on the demand
for loans, will raise the rate of interest. If the
rise is still inadequate, the process is repeated,
and thus by continual trial and error the rate
approaches the true adjustment. [6; pp. 75-76]

In this way, the nominal rate eventually adjusts to
inflation, albeit with some delay.
Price Movements, Real Rates, and
The Trade Cycle

With respect to the second use of his imperfect
foresight model, Fisher attempted to show how price
changes generate trade cycles by altering realized real
loan rates. His theory relied on the same assumption
as before, namely that business borrowers, by virtue
of being entrepreneurs, possess superior foresight and

ECONOMIC REVIEW, MAY/JUNE 1983

therefore anticipate and adjust to inflation faster than
do lenders. Thus, according to him, when inflation
occurs, borrowers, perceiving that they will be able
to pay off their loans in dollars of lower purchasing
power than they borrowed, step up their loan demands. Lenders, however: perceiving no such depreciation, maintain their loan supplies unchanged.
As a result, the loan demand curve shifts upward in
response to inflation whereas the loan supply curve
remains comparatively fixed. Assuming an upward
sloping loan supply curve, the result is a rise in the
nominal rate but one that is insufficient to compensate
for inflation, which means of course that the real loan
rate falls. This realized fall in the real cost of borrowing manifests itself in the form of a windfall rise
in borrower profits. Assuming borrowers predict
future profits extrapolatively from realized past profits and make their investment decisions accordingly,
the high realized profits will stimulate real investment and generate a business boom. Conversely,
when deflation occurs, loan demands fall relatively to
loan supplies. This causes nominal rates to fall but
not sufficiently to offset the deflation. The resulting
rise in the real cost of borrowing lowers profits and
generates expectations of more of the same, thereby
discouraging investment and depressing trade.
In short, inequality of expectations rather than
imperfection of expectations constitutes the key to
Fisher’s cycle model. Only the former, he says,
produce the disproportionate shifts in loan demand
and supply schedules that affect loan volume and economic, activity. By contrast, imperfect (but equal)
expectations produce insufficient but identical adjustments of loan demand and supply that affect nothing
but the real rate and distributive shares. In his
words:
We see, therefore, that while imperfection of, foresight transfers wealth from creditor to debtor or
the reverse, inequality of foresight produces overinvestment during rising prices and relative stagnation during falling prices. [6; p. 78]

In so stating, he provided an explicit analytical model
consistent with Marshall’s conjecture that the trade
cycle largely arises from “variations in the real rate
of interest which are caused by changes in the purchasing power of money.” [8; p. 628] He also
showed how changes in nominal magnitudes can have
temporary real effects.
Summary and Conclusions

This article has traced the development of the real/
nominal interest rate relationship in pre-20th century

monetary thought. The article shows that neither the
relationship itself nor the analysis underlying it are
of recent origin. On the contrary, the article documents (1) that several 18th and 19th century economists stated the relationship, (2) that at least some
of them fully understood its implications for interest
rate adjustment and neutrality, and (3) that they
attempted to specify the mechanism or process
through which an inflation premium gets embodied in
market rates. From these findings at least four conclusions emerge.
The real/nominal rate distinction is of 18th
rather than 20th century vintage.
Irving Fisher, now generally regarded as the
father of real/nominal interest rate analysis,
originated none of the concepts now bearing his
name. Neither the so-called Fisher relationship
(according to which the nominal rate equals
the real rate plus expected inflation), nor the
Fisher effect (according to which the nominal
rate fully adjusts for inflation leaving the real
rate intact), nor the Fisher neutrality proposition (according to which equilibrium nominal
rate adjustments entail no real effects) originated with him. Rather they long predate him,
having been enunciated by earlier generations
of writers. Nevertheless, Fisher gave those
concepts their classic exposition.
For that
reason his work is best regarded as the culmination rather than the origin of classical and
neoclassical analysis of the real/nominal rate
relationship.
Except for Douglass and Mill, all the writers
surveyed above recognized the distinction between complete and incomplete adjustment of
the nominal rate to inflation. The former they
identified with the perfect foresight, constant
realized real rate model and the latter with an
imperfect foresight, lagged adjustment model.
That is, they argued that while the nominal
rate would fully adjust for inflation in steady
state equilibrium, it would not do so instantaneously. During a temporary transition period
it would exhibit lagged adjustment thereby producing deviations from equilibrium of the realized real rate. This was on the grounds that,
because expectations are formed extrapolatively,
changes in inflation are inadequately foreseen
such that expected inflation lags behind actual
inflation resulting in incomplete adjustment of
the nominal rate.
Early writers stressed that these incomplete
nominal rate movements would, by altering realized real rates, affect the distribution of income
between borrowers and lenders. To these distributional effects Marshall and Fisher added
the notions of differential expectations and unequal shifts in loan demand and supply curves
to demonstrate how incomplete nominal rate
adjustment could also affect real output and
employment. Thus, although the early formulators of the real/nominal rate analysis postulated perfect foresight, complete adjustment,
and nominal rate neutrality as necessary condi-

FEDERAL RESERVE BANK OF RICHMOND

9

tions of steady state equilibrium, they did not
assume that those conditions would hold continuously. That is, they did not adhere to the
view that the nominal rate always adjusts fully
and instantaneously to inflation so as to leave
a l l r e a l m a g n i t u d e s - i n c l u d i n g distributive
shares and real output-undisturbed.
In reaching these conclusions, they established most

of the elements of modern real/nominal rate analysis.
T h e main element missing from their analysis was

the notion that people form expectations of future

profits and inflation not so much from observed past
values of those variables as from informed predictions of future events-e.g., prospective monetary
g r o w t h - i n f l u e n c i n g t h e m . Modern analysts have
also abandoned the Marshall-Fisher doctrine of
differential expectations. Except for these elements,
however, the earlier analysis was much the same as
today’s.

References
1. Clark, John B. “The Gold Standard of Currency
in the Light of Recent Theory.” Political Science
Quarterly, 10 (September 1895), 389-403.
2. de Haas, Jacob A. “A Third Element in the Rate
of Interest.”
Journal of the Royal Statistical
Society, Series A, 52 (March 1889), 99-116.
3. Dorfman, Joseph. The Economic Mind in American
Civilization 1606-1865. Vols. l-2. New York: Augustus M. Kelley, 1966.
4. Douglass, William. “An Essay Concerning Silver
and Paper Currency” (1738). In Colonial Currency Reprints 1 6 8 2 - 1 7 5 1 .
Edited by
Vol. 3.
Andrew M. Davis.
N e w Y o r k : Augustus M.
Kelley, 1964.
5.

“A Discourse Concerning the Currencies of The ‘British Plantations in America” (1740).
In Colonial Currency Reprints 1682-1751. Vol. 3.
Edited by Andrew M. Davis. N e w Y o r k : A u gustus M. Kelley, 1964.

6. Fisher, Irving.
York : 1896.

10

Appreciation and Interest.

New

7.

T h e Rate of Interest. New Y o r k :

Macmillan, 1907.

8. Marshall, Alfred. Principles of Economics. L o n don : Macmillan, 1890.
9. Mill, John Stuart. Principles of Political Economy.
6th ed. London: Longmans, Green and Co., 1865.
10. Rutledge, John. “Irving Fisher and Autogressive
Expectations.”
American Economic Review, 67
(February 1977), 200-5.
11. Summers, Lawrence H. “The Non-Adjustment of
Nominal Interest Rates: A Study of the Fisher
Effect.” National Bureau of Economic Research
(NBER) Working Paper Series, no. 836, January
1982.
12. Thornton, Henry. Two Speeches of Henry Thornton on the Bullion Report, May 1811. Reprinted as
Appendix III to his An Enquiry Into the Nature
and Effects of the Paper Credit of Great Britain
Edited with an Introduction by F. A.
(1802).
von Hayek. New York: Rinehart and Company,
Inc., 1939

ECONOMIC REVIEW, MAY/JUNE 1983

THE RELATIONSHIP BETWEEN MONEY
AND EXPENDITURE IN 1982
Robert L. Hetzel

Introduction

The behavior of the money supply and the relationship between the money supply and the public’s
expenditure have recently been the subject of considerable interest. The interest in the behavior of
the money supply is explained below by a discussion
of the relationship between money growth and inflation.
Other things equal, an increase in money
growth will cause an increase in the inflation rate.
The monetary acceleration that began in 1982 can
then in time be expected to reverse the post-1979
trend toward a lower inflation rate. The inflationary
implications of the behavior of the money supply
must, however, be assessed in relation to the behavior of the public’s demand for money. It has been
argued that the relationship between the money
supply and the public’s expenditure in 1982 indicates
that the public’s demand for, money increased in 1982
by an abnormal extent. The high rate of growth of
money that began in 1982 does not, therefore, presage
higher inflation. This argument is appraised in the
body of the paper through an examination of whether
the recent behavior of expenditure and money is
consistent with their past behavior.

The nominal quantity of money does not affect
tastes and preferences or natural resource endowments and technology. Ultimately, therefore, real
expenditure is determined independently of the nominal quantity of money. Given that the nominal
quantity of money determines nominal expenditure
and that real expenditure is determined independently
of nominal money, the nominal quantity of money
determines the price level. The ratio of current dollar
expenditure (determined by money) to constant
dollar expenditure (determined independently of
money) is a definition of the price level. The above
relationships may require many years to work out,
but ultimately the level of the nominal quantity of
money determines the price level.
Recent Behavior of Money

The behavior of money (Ml,) in 1982 and early
1983 is displayed in Chart 1. The cones show the
four quarter target ranges set by the Federal Reserve
System for 1982 and 1983. The rapid growth of Ml

Chart 1

Money Growth and Inflation

A standard quantity theory explanation of inflation
as a monetary phenomenon is offered in this section.
It is assumed that the actions of the monetary authority determine the nominal quantity of money
(the number of dollars in circulation). The public,
however, cares about the real quantity of money it
holds (the quantity of goods and services that the
nominal quantity of money will purchase). The real
quantity of money can be expressed as the ratio of
the nominal quantity of money to the nominal (current dollar) expenditure of the public. The public’s
desire to control this ratio, given the determination
of the nominal quantity of money by the monetary
authority, causes nominal money to be stably related
to nominal expenditure.

Ml GROWTH COMPARED
TO TARGET RANGES
1982-1983
Billions of dollars

FEDERAL RESERVE BANK OF RICHMOND

Billions of dollars

11

over this period has been watched by individuals
contracting to receive nominal dollars in the future.
In itself, the rapid growth of M1 suggests a future
reversal of the post-1979 trend toward lower inflation. This result, however, need not pertain if an
unusual increase in the public’s demand for real M1
balances has occurred. In the succeeding section,
evidence is examined bearing on the possibility that
the ratio of M1 to expenditure desired by the public
has increased.
Methodology

The ratio of M1 to expenditure did rise in 1982
relative to its trend. This rise suggests an unusual
increase in the demand for real M1 balances desired
by the public. The ratio of contemporaneous money
to contemporaneous expenditure is, however, a misleading indicator of the public’s demand for real
money balances. Changes in money do not affect
expenditure immediately, but rather with a long lag,
the effect of which is distributed over time. In order
to assess the stability of the relationship between
money and expenditure, it is necessary to consider
the stability of the distributed lag relationship between them. This consideration motivates the approach used below. A historical distributed-lag
relationship between expenditure and money is calculated. The ability of the historical relationship to
explain the recent behavior of expenditure is then
examined.

before a change in money affects expenditure [3, p.
22].2

Experimentation with alternative forms of regression equations indicates that the relationship between
money and expenditure appears more clearly when
an interest rate is included as a right hand variable.
The interest rate is included with six contemporaneous and lagged terms. The estimated coefficient on
the contemporaneous term is positive. The positive
sign suggests the common influence on expenditure
and the interest rate of nonmonetary forces. The
sum of the estimated coefficients on the contemporaneous and lagged terms of the interest rate variable
is negative, however. The negative sign on the sum
of the estimated coefficients suggests that the predominant role of the interest rate term is to capture
the effect of shifts in the demand for money.
The regression equation described above is not a
reduced form derived from a model. Its justification
is that it appears to offer a useful way of organizing a
review of the data pertaining to the relationship between money and expenditure. It is offered as a
superior alternative to the common practice of looking at the behavior of the ratio of contemporaneous
expenditure to contemporaneous money, the contemporaneous velocity of money.
“Shift-adjusted” M1 is used. This series, constructed by the staff of the Board of Governors, is
the current M1 series adjusted to account for the
shifts into ATS and NOW accounts from nonmone2

Regression

Analysis

The results of regressing expenditure on a distributed lag of past values of money are presented in this
section. M1 is included as a right hand variable with
six lagged terms. The contemporaneous and lag one
term for M1 are omitted in an attempt to reduce the
correlation that does not reflect causation running
from M1 to expenditure, but rather reflects, reverse
or simultaneous causation.1 Inclusion of M1 beginning with a two quarter lag corresponds to Milton
Friedman’s estimate that two to three quarters elapse
1

In a regression of quarterly percentage growth rates of
GNP on a constant and a simple distributed lag of contemporaneous and past values of quarterly percentage
growth rates of M1, the sum of the estimated coefficients
on M1 for the three quarters of lag 0 through lag 2 is
1.22. This value is implausibly large if it is considered to
reflect the causal effect of money on expenditure.
12

Including more lagged terms does not reduce appreciably the sum of the squared residuals of the regression
equations estimated here. The true distributed lag relationship between money and expenditure is summarized
only approximately by the estimated relationship for
many reasons. The true lags, for example, are longer
than the ones shown here. Consider, say, an increase in
money that causes an initial rise in real expenditure.
This rise, in time, will be reversed. At this point, the
fall in real expenditure appears to offset the concurrent
rise in the price level, so the impact of money on nominal
expenditure is negligible. Beyond this point, however,
the initial increase in money will cause the price level,
and thus nominal expenditure, to rise. The data appear
to be too noisy to allow estimation of distributed lags
long enough to describe the full working out of a change
of money on the price level. (The author estimates that
about four years are required for the price level to reflect
fully a change in money [5].)
Another reason why the causal relationship running
from money to expenditure is obscured is that the estimation does not allow for any possible consistent pattern
in the way in which the monetary authority varies money
in response to changes in nominal expenditure. The estimation procedure also obscures variation over time in the
nature of the lag relating money to expenditure.
For
example, anticipated changes in money might affect
nominal expenditure more rapidly than unanticipated
changes.

ECONOMIC REVIEW, MAY/JUNE 1983

tary assets that occurred at the time of the introduction of these accounts in 1981.3
Two left hand variables are considered, final sales
to domestic purchasers and gross national product.
As implied by the quantity theory of money discussed
above, individuals vary their rate of expenditure in
response to discrepancies between their actual and
desired holdings of cash balances. The immediate
impact of these variations in expenditure is captured
by final sales to domestic purchasers. GNP is a
measure of production rather than spending. (GNP
minus the change in business inventories equals final
sales. Final sales less net exports equals final sales to
domestic purchasers.)
The expenditure and M1
series are expressed in per capita form, although this
form does not affect the results.
Table I displays the results of regressing annualized percentage changes in final sales to domestic
purchasers on a constant and on annualized percentage changes in the commercial paper rate and M1,
employing the simple distributed lag relationships
discussed above. The regression employing GNP as
the left hand variable is very similar, apart from a
higher standard error for the estimated residuals,
which reflects the volatility of inventories and net
exports. The magnitude of the sum of the estimated
coefficients on the interest rate term is small. The
individual coefficients considered collectively are,
however, statistically significant. The coefficients on
3

The Board staff estimated that in 1980 the growth rate
of M1, defined to include NOW and ATS accounts,
should be lowered by about half a percentage point in
order to account for transfers into these new accounts
from nonmonetary sources. (This figure is the lower
bound of the range given in the notes to the table
“Growth Ranges and Actual Monetary Growth” in the
Appendix contained in [6, p. 100]. See also [6, pp. 69
and 72] and the references in [2, p. 149].) No quarterly
breakdown is given for this figure, so growth of M1 in
each quarter of 1980 is lowered by .125 percent in order
For 1980, shiftto arrive at the shift-adjusted series.
adjusted M1 is thus derived by multiplying M1 for
quarters one through four, respectively, by .99875, .99750,
.99625, and .995. For 1981, the ratio of the Board staff’s
shift-adjusted M1 (shift-adjusted M1-B) to M1 (M1-B)
is calculated (both series use the 1981 seasonal adjustment factors). These ratios for quarters one through
four are respectively, .986, .978, .976, and .973. For 1981,
shift-adjusted M1 is thus derived by multiplying M1 by
.995 times the appropriate preceding ratio. The factor
multiplying the 1981 Q4 observation is used with the M1
observations in 1982. In 1982, shift-adjusted M1 is about
three percent below M1,
(The Board staff’s shiftadjusted M1 series for 1981 is contained in [1].)
A discontinuity arises in the M1 series in 1959 due to
the exclusion at this time of demand deposits of foreign
commercial banks and official institutions.
Post-1959
M1 was spliced with pre-1959 M1 by multiplying pre-1959
M1 by the ratio of the two series in 1959 excluding and
including these, deposits (.987).

Notes: Standard errors ore in parentheses.
NOV number of variables estimated.
R
rats and M is per capita shift-adjusted
represent annualized percentage changer.

NOB is number of
is the 4-6 month
M1 (see footnote
Simple distributed

observations and
commercial paper
4). Observations
lags are used.

M1 considered collectively are also very significant
statistically. 4
The estimated residuals for the regression equation displayed in Table I, plotted in Chart 2, measure
the difference between the actual and predicted quarterly percentage growth rates of final sales to domestic purchasers. An examination of the estimated
residuals indicates that they do not, in general, fall
randomly. The relative weakness of growth rates of
nominal expenditure shown in interval 1, 1953Q2 to
1954Q2, derives from an autonomous decline in the
inflation rate following an earlier autonomous rise
at the onset of the Korean War. (When the war
began, consumers ran their cash balances down in
anticipation of shortages of consumer durables. When
the shortages did not materialize, they returned their
holdings of cash balances to normal levels. This behavior was reflected in the behavior of expenditure
and inflation,) In interval 2, the residuals appear to
fall randomly.
Beginning in the early 1960s the estimated residuals display a wave-like appearance. Long periods
during which the actual growth rate of expenditure
persistently exceeds the predicted growth rate by a
moderate amount are followed by offsetting periods
4

The null hypothesis that the coefficients on the interest
rate term are all zero is rejected by an F-test at the
.99999 confidence level. T h e n u l l h y p o t h e s i s t h a t t h e
coefficients on the money term are all zero is rejected by
an F-test at the .9999 confidence level. An examination
of the estimated residuals of the regression equations
used in calculating the statistics for these F-tests shows
them to be approximately white noise. (The calculations
referred to in this footnote are for the regression shown
in Table II. which differs from the one in Table I by the
addition of ‘three dummies to capture intercept shifts.)

FEDERAL RESERVE BANK OF RICHMOND

13

Chart 2

ERRORS IN PREDICTING EXPENDITURE
Residuals from a Regression of Final Sales to Domestic
Purchasers per Capita on M1 per Capita and the Paper Rate

Note: Tick marks indicate first quarter of year.

during which these positive prediction errors are
offset by negative errors. In interval 3, 1961Q4 to
1968Q3, the residuals are generally positive. Chart 3,
which displays quarterly growth rates of M1, shows
that this interval is characterized by a monetary
acceleration.
Examination of interval 3 thus suggests an overshooting of expenditure in response to
monetary acceleration; the rate of growth of money
rose, while the rate of growth of nominal expenditure
rose even more. (Friedman and Schwartz [4, p. 68]
discuss one possible cause of such overshooting.)
The strength in the growth of nominal expenditure
appeared to a significant extent in the growth of real
expenditure, rather than in the inflation rate in this
interval. In interval 4, 1968Q4 to 1973Q3, the estimated residuals are generally negative. The prior
overshooting of expenditure then was followed in
this interval by an offsetting period of undershooting.
In interval 5, 1973Q4 to 1981Q1, the residuals are
generally positive. This underprediction of nominal
expenditure may have been caused by the positive
impact on prices of the rise in the price of oil that
occurred near the beginning and end of this interval.
Interval 5 is also characterized by a monetary acceleration. The positive residuals beginning in 1977
may indicate an overshooting in expenditure as a
14

consequence of this monetary acceleration. In interval 6, 1981Q2 to 1982Q4, the estimated residuals are
generally negative. Again, the prior interval of overshooting in expenditure is followed by an offsetting
period of undershooting.
The regression s h o w n i n T a b l e I I e m p l o y s
intercept-shift dummies in order to capture the effect
of the overshooting and subsequent undershooting
described above. DO, the post-Korean War dummy,
is set equal to one for interval 1 and zero elsewhere.
D1, the “overshooting” dummy, is set equal to one
for intervals 3 and 5 and zero elsewhere. D2, the
“undershooting” dummy, is set equal to one for
intervals 4 and 6. Otherwise, the specification of the
regression equation in Table II is identical to that of
Table II

REGRESSION OF FINAL SALES TO DOMESTIC PURCHASERS
ON AN INTEREST RATE AND MONEY, 1952Q1 TO 1982Q4

ECONOMIC REVIEW, MAY/JUNE 1983

Chart 3

M1 GROWTH
Quarterly Annualized Percentage Growth Rates
Continuously Compounded in Per Capita M1

Note: Tick marks indicate first quarter of year.

Table I. (Again, the use of GNP as the left hand
variable results in a regression equation similar to
the one shown in Table II.)
The. presence of the intercept-shift terms, which
capture successive periods of underprediction and
overprediction of expenditure, indicates that the relationship between money and nominal expenditure
may require a period of time as long as a decade in
order to work out fully. The importance of this
phenomenon of overshooting should not be exaggerated, however. The magnitude of the estimated
coefficients on these intercept-shift terms is about one
percentage point. This number is small relative to
the magnitude of the variation in percentage growth
rates in money and in nominal expenditure. The
variation in quarterly growth rates of nominal expenditure is significantly affected by nonmonetary
forces, as indicated by the size of the standard error
of the estimated regression residuals shown in Table
II, 2.8 percent. This variation in quarterly growth
rates is perhaps also affected by shifts in the demand
for money, as suggested by the negative sign on the
estimated sum of coefficients on the interest rate
variable. The magnitude of the estimated sum of
coefficients on the money variable, about one, is,
nevertheless, consistent with the quantity theory

proposition that, over long periods of time, the major
determinant of nominal expenditure is the money
supply.
Simulation

Results of predicting final sales to domestic purchasers and GNP out of sample are presented in this
section. Regression equations, specified as shown in
Table II, are estimated over the interval 1952Q1 to
1973Q3. The end date was chosen in order to incorporate a complete cycle of overshooting and undershooting in expenditure. For purposes of simulation,
it was considered desirable that a one percentage
point change in the rate of growth of money generate
a one percentage point change in the rate of growth
of expenditure. For this reason, the estimated coefficients on M1 are constrained to sum to one. The
estimation results are shown in Tables III and IV.
The results of predicting final sales to domestic
purchasers and GNP in the out-of-sample period are
shown in Charts 4 and 5, respectively. The percentage error in the level of the actual, relative to the predicted, series is shown. Because the phenomenon of
overshooting is not accounted for by intercept-shift
dummies, the level of the actual series rises, in each

FEDERAL RESERVE RANK OF RICHMOND

15

Table III
Chart 4

REGRESSION OF FINAL SALES TO DOMESTIC PURCHASERS
ON AN INTEREST RATE AND MONEY, 1952Q1 TO 1973Q3

ERRORS IN

Notes: See Tables I and II.

case, relative to the level of the predicted series
through 1981Q1, where the underprediction of the
actual series is about eight percent. This underprediction then lessens during the subsequent period of
undershooting of expenditure until by 1982Q4 the
level of final sales to domestic purchasers and GNP
are underpredicted by 4.1 and 2.8 percent, respectively.
Money Demand in 1982

M1 has grown from its average value for the four
weeks ending August 25, 1982, to its average value
for the four weeks ending May 25, 1983, at an annualized rate of 14.4 percent. It has been asserted
that the observed relationship between M1 and ex-

penditure in 1982 indicates a rightward shift in the
public’s demand for M1. Consequently, it is concluded, the current high rate of growth of M1 will
not be inflationary. This assertion can be evaluated
with the aid of the simulations reported in the previous section,
First, a benchmark is required as to how well
money can be expected to predict expenditure over a
four-quarter period. This benchmark was derived as
follows. The regression equation in Table I, with
final sales to domestic purchasers as the left hand
variable, was estimated over the interval 1952Q1 to
1981Q4. This estimation produces predictions of
percentage growth rates of expenditure over the four
quarter intervals ending in the fourth quarter of each
year from 1952 through 1981. Errors in predicting

Chart 5

ERRORS IN PREDICTING GNP

Note: Percentage error in the level of actual, relative to predicted, GNP 1973Q4 to 1982Q4. Predictions from regression equation estimated from
1952Q1 to 1973Q3.
Notes: See Tables I and II.

16

ECONOMIC REVIEW, MAY/JUNE 1983

calendar year percentage growth rates of expenditure
are then calculated as the actual percentage growth
rates of expenditure over the four quarter intervals
ending in the fourth quarter of each year minus the
corresponding predicted growth rates. Finally, the
root-mean-squared value of these yearly errors is
calculated. This number measures how well in an
average sense money can be expected to predict
expenditure over a calendar year. Its value is 1.5
percentage points.
The regression in Table III, estimated from 1952
to 1973, was used to predict the percentage growth
rate in 1982 of final sales to domestic purchasers.
(This prediction corresponds to the simulation reported in Chart 4.) The predicted growth rate was
7.0 percent, compared to an actual growth rate of 5.0
percent, continuously compounded, an error of two
percentage points.5 The magnitude of this error, 2.0
percentage points, is only slightly larger than the
value of the benchmark error, 1.5 percentage points.
It is concluded that expenditure in 1982 is predicted
about as well as in other calendar years. The evidence necessary to support the hypothesis that a significant rightward shift in the public’s demand for
M1 occurred in 1982, that is, the existence of an
unusually large overprediction of the growth rate of
expenditure, appears to be lacking.
The percentage growth rate of GNP in 1982, measured from fourth quarter to fourth quarter, was 2.5
percentage points less than the corresponding growth
rate of final sales to domestic purchasers. The smaller
growth in output than in final sales to domestic
purchasers derives from the adverse movements in
the change in business inventories series primarily,
and in the net exports series secondarily. These last
two series are highly volatile and their own movements cancel out over time. Their behavior is little
susceptible to control by monetary policy.
It is concluded that the relationship between money
and the public’s expenditure in 1982, while not tight,
is consistent with the relationship that existed prior
to 1982. The assertion that a rightward shift occurred in the public’s M1 demand function generally
derives from the observation that the ratio of contemporaneous M1 to contemporaneous output
(GNP) was high relative to trend in 1982. This
ratio offers misleading evidence for three reasons.
First, it fails to take account of the lag with which
money acts on expenditure. The simulation results
5

The behavior of the interest rate is such that it exerts
practically no net effect on predicted expenditure in 1982.

of the previous section indicate that the major factor
in the decline in the growth rate of expenditure in
1982 was the monetary deceleration of 1981. (From
1980 to 1981 the percentage growth rate of shiftadjusted M1, continuously compounded and measured from fourth quarter to fourth quarter, fell
from 6.5 to 2.3 percent.) The sharp deceleration of
M1 in 1981 depressed expenditure, and thus output,
in 1982. The denominator of the ratio of contemporaneous M1 to contemporaneous output therefore fell
in 1982 relative to trend. The sharp acceleration in
1982 of M1 raised the numerator of this ratio relative to trend. Consequently, the high value of the
ratio of contemporaneous M1 to contemporaneous
output in 1982 represents, to a significant degree, a
statistical artifact.
Second, converting nominal M1 to a real M1 series
by use of the ratio of M1 to GNP introduces noise
into the real M1 series because of the volatility in
changes in business inventories and net exports. The
ratio of M1 to final sales to domestic purchasers does
not possess this source of noise. In particular, in
1982, sharp declines in the change in business inventories and net exports series caused growth of GNP
to be weak relative to growth of final sales to domestic purchasers.
Third, in accounting for the lagged effect of M1
on expenditure, it is necessary to account for the
introduction of ATS and NOW accounts in 1980 and
1981. Shifts of funds from nontransactions sources
like time deposits into these new accounts distorted
the meaning of M1 by causing actual growth of M1
to appear more expansionary than it was in reality.
It is for this reason that the Federal Reserve System
targeted the shift-adjusted M1 series used in this
paper.
The importance of these factors is illustrated in
Chart 6. Quarterly observations of four-quarter percentage changes in velocity are displayed in Chart 6.
Velocity is defined as the ratio of contemporaneous
final sales to domestic purchasers to M1 (shiftadjusted) four quarters in the past. The expenditure
series is divided by M1 lagged four quarters because
four quarters is the approximate mean lag associated
with the distributed lag of expenditure on M1 estimated in the regression shown in Table II. The
solid line shown in Chart 6 is the average value of
quarterly percentage changes in the velocity series
from 1952Q1 to 1982Q4. An examination of the
velocity series shown in Chart 6 does not suggest
that the behavior of velocity in 1982 was unusual.

FEDERAL RESERVE BANK OF RICHMOND

17

Chart 6

THE BEHAVIOR OF VELOCITY
1952Q1 To 1982Q4
Quarterly Observations of Four-Quarter Percentage Changes
in Velocity. Velocity is the Ratio of Contemporaneous Final Sales
to Domestic Purchasers to M1 Shift Adjusted Four Quarters in the Past.
Percent

Percent

8

8

6

6

4

4

2

2

0

0

-2
- 4

252

54

56

58

60

62

64

66

68

70

72

74

76

78

80

82

4-

Note: Tick marks indicate first quarter of year.

Conclusions

The simulation results indicate that the reduction
in the growth rate of expenditure in 1982 was caused
primarily by the reduction in the growth rate of M1
in 1981. The reduction in the growth rate of M1
from 1980 to 1981 (4.2 percentage points using the
shift-adjusted series) has been offset by the increase
in the growth rate of M1 from 1981 to 1982 (5.9
percentage points using the shift-adjusted series).
Given that this offset has already, occurred, further
stimulus of expenditure does not require high rates
of growth of M1 in 1983.
The evidence examined here does not support the
assertion that the public’s M1 demand function
shifted rightward in 1982. This evidence does not
take account of the effect of the introduction of the
new deposit accounts in late 1982 and early 1983.
The distorting effect on M1 associated with the introduction of these new accounts, however, appears to
be small.6

6

Money market deposit accounts (MMDAs) were introduced in December 1982 and Super NOWs in January
1983. MMDAs can be used to a limited extent to effect
transactions. To the extent that the growth of MMDAs
has come out of transactions accounts in M1, this growth
causes the actual growth of M1 to understate the effect
of monetary policy on expenditure. Super NOWs, on the
other hand, pay a market rate of interest.
To the

18

M1 affects expenditure with a long lag, and it
affects inflation with an even longer lag. Also, the
relationship between M1 and expenditure over one,
or even four, quarter periods is loose. For these
reasons, it is tempting to ignore its behavior. The
evidence examined in this paper, however, reveals
no reason to believe that high rates of growth of M1
will not be inflationary. A key prediction of the
regression analysis in this paper is that the public’s
expenditure will increase dramatically in the third
quarter of 1983. If this increase does not occur, it
can be concluded that the public’s M1 demand function did shift rightward in 1982. If the increase does
occur, then it can be concluded that the public’s M1
demand function has remained stable and that M1
remains a good predictor of the inflation rate.
extent that the growth of Super NOWs has come out of
nontransactions accounts, this growth causes the actual
growth of M1 to overstate the effect of monetary policy
on expenditure.
The growth of MMDAs increases the level of a shift;
adjusted M1 series relative to the actual series. G i v e n
the significant amount of MMDAs now outstanding
($360.3 billion on May 25, 1983), and the meager
amount of Super NOWs ($30.3 billion on May 25,
1983), it seems unlikely that actual M1 growth is understating the impact of monetary policy. Many observers
believe that the biases currently distorting the meaning
of M1 are washing out, so that the introduction of the
new deposit accounts has not significantly affected the
usefulness of actual M1 as an indicator of the stance of
monetary policy.

ECONOMIC REVIEW, MAY/JUNE 1983

References
1 . B e n n e t t , B a r b a r a A . “‘Shift-Adjustments’ to the
Monetary Aggregates.” Economic Review, Federal
Reserve Bank of San Francisco (Spring 1982).
2. Board of Governors of the Federal Reserve System.
67th Annual Report. “Record of Policy Actions for
Meeting Held on October 21, 1980.” Washington,
1980.

5. Hetzel, Robert L. “The Behavior of the Demand for
Money in the 1960s and 1970s.” Unpublished paper
in process, Federal Reserve Bank of Richmond,
April 1983.

3. Friedman, Milton. “The Counter-Revolution in
Monetary Theory.” Institute of, Economic Affairs
Occasional Paper 33. Great Britain, 1970.

6. Monetary Policy Report to Congress. In F e d e r a l
Reserve’s First Monetary Policy Report for 1981.
U. S. Congress. Senate. Committee on Banking,
Housing, and Urban Affairs. Hearings. 97 Cong.
1 Sess. Washington : Government Printing Office,
Feb. 25 and March 4, 1981.

4. Friedman, Milton and Anna J. Schwartz. Monetary
Trends in the United States and the United Kingdom. Chicago: University of Chicago Press, 1982.

7. Simpson, Thomas D. and John R. Williams. “Recent
Revisions in the Money Stock.” Federal R e s e r v e
Bulletin, 67 (July 1981), 539-542.

FEDERAL RESERVE BANK OF RICHMOND

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Federal Reserve Bank of St. Louis, One Federal Reserve Bank Plaza, St. Louis, MO 63102