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Working Paper 75-2

INTEREST RATES, EXPECTATIONS, AND THE
WICKSE3LIAN PbLICX RULE

.

Thomas M. Humphrey

Federal Reserve Bank of Richmond
July 1975

The views expressed here are solely those of
the author and do not necessarily reflect the
views of the Federal Reserve Bank of Richmond.

. * INTEREST RATES, EWECTATIONS, AND THE
WICKSELLIAN POLICY RDLE

Prominent among older theories of inflation is the view that a
rising price level stems from a divergence between two rates of interest.
Qne, the market rate, is the loan rate charged by banks.

The other is the

natural rate of interest defined as the rate that would equate the demand
for real capital, as determined by the productivity of capital, and the
supply of real capital, determined,by the volume of current saving.

First

enunciated by Henry Thornton in 1802, and developed more fully by Knut
Wicksell at the end of the century, the two-rate doctrine was endorsed by
such leading 20th century monetary theorists as Keynes, Robertson, Ohlin,
Myrdal, Hayek, and von Mises.

It was a key element in many widely held

theories of the business cycle in the 1920's and early 1930's. Moreover,
it became the basis of the celebrated p&icy

rule that the central bank

could make its greatest contribution to price stability by striving to keep
the market rate in line with the natural rate.
The two-rate doctrine has been overshadowed by rival theories in
recent years, however.

Current explanations of inflation tend to stress

other causes, including excessive money stock growth, wage-cost push
pressures, monopoly pricing policies, labor-capital immobilities, and
special (random) factors peculiar to each inflationary episode.
What accounts for the relative neglect of the two-rate doctrine?'
One reason, perhaps, is that Wicksell's version of it gives inadequate

1
The two-rate doctrine has not been totally ignored, of course,
as indicated by several recent articles that employ the Wicksellian analytical framework. At least two studies [Horwich (1968) and Tanner (197511
attempt to estimate the natural rate of interest and to evaluate Federal

-2-

treatment to the role of inflationary expectations, generally considered
to be a vital ingredient in the inflationary process.

Correction of this

shortcoming would enhance the contemporary relevancy of the doctrine,
making it more applicable to current policy.problems. Accordingly, the
main purpose of this article is to incorporate inflationary expectations
:
into the two-rate analysis and to indicate how this modification alters
2
the Wicksellian policy prescription.
The article proceeds in the following manner.

The first section

contains a brief review of the historical development of the doctrine up
to Knut Wicksell.

The second summarizes Wicksell's contribution, including

his analysis of the cumulative process and his policy prescriptions;

Section

three shows what happens when inflationary expectations are injected into
Wicksell's model.

Section four uses the revised Wicksellian model to inter-

pret recent inflationary experience.

Reserve policy against the norm of Wicksell's ideal policy rule. Another
study [Harrington (19711 uses Wicksell's two-rate doctrine to account for
the post-war growth of the volume of money substitutes and to deal with a
number of controversial issues including: the exogeneity vs. endogeneity
of money, the effectiveness of a policy rule fixing the growth rate of the
money stock, the reliability of the money stock or its growth rate as policy
indicators, and the desirability of having banks pay competitive interest on
demand deposits. Still other studies [e.g., Lutz (1974) and Sargent (1969)]
attempt to incorporate inflationary expectations into Wicksell's model and
show how it modifies the condition of monetary equilibrium. Not all of this
research is policy oriented, of course. For example, one recent study
[Laidler (1972)) contends that Wicksell's theory of the cumulative process
contains most of the key elements of the Clower-Leijonhufvud reinterpretation
of the "the economics of Keynes".as a theory of disequilibrium dynamics.
% utz (1974) also attempts to incorporate expectations into Wicksell's
model, but does not analyze the policy implications in any detail.

- 3 -'

I.

HISTORICAL EVOLUTION OF THE TWO-RATE DOCTRINE
Henry Thorton
In his classic The Paper Credit of Great Britain (1802), Henry
Thorton provided the first rigorous and sys'tematicanalysis of the relation
between interest rates and inflation. His contribution consists of four
elements.
First, he distinguished between the market or loan rate of interest
and the expected yield or marginal rate of profit on new capital projects.
He stressed that the two rates were separate

and distinct phenomena, the

first being a money rate determined in the market for loanable funds and
th,esecond a real rate determined in the commodity market by the supply of
saving and the investment demand for new capital.

This distinction between

the two types of interest rates marks an advance over the views of his
predecessors and contemporaries, many of whom regarded the loan rate as
simply the shadow or monetary expression of the yield on real capital.
Second, he was the first to express the doctrine that inflation
results from a divergence between the two rates,

He described in great

detail how such a disparity,would set in motion a process of cumulative
expansion in the demand for and supply of loans, the note issue of banks,
and the level of prices.

He pointed out that this process would persist

for as long as the loan rate remained below the commercial profit rate.
Third, he used his two-rate schema to analyze the inflationary
consequences of a central bank policy of pegging the rate of interest.
He argued that if the Bank of England were constrained by usury laws to
a ceiling loan rate of 5% at a time when the mercantile rate of profit
was in excess of 5%, it would lose control over the volume of its loans
and its note issue, both of which would expand indefinitely, producing

-

4

-’

inflation. With the rate pegged, inflation could continue without limit
because there existed no automatic corrective mechanism to bring it to an
end.

This reasoning constituted the basis of his criticism both of the

usury laws and of the Bank of England's practice of adhering to a fixed
discount rate,

He maintained that the central bank should control the

note issue by keeping its discount rate in line with the rate of profit.
He was thus the first to advocate use of the discount instrument to regulate
the money.supply. And if the usury ceiling should threaten to interfere
with the operation of discount rate policy, then, he argued, the central
bank should resort to other forms of credit-rationing to limit its 1oanS.
The essential thing was that the bank keep a firm grip on the monetary
circulation and control the note issue.
Finally, Thorton was the first economist to discuss the effect
of inflatinnary expectations on market interest rates, describing how the
anticipated rate of inflation becomes incorporated'into the nominal rate
of .interest causing the latter to rise above the real or price-deflated
rate.

Thus Thorton must be credited with originating two separate theories

of the relationship between interest and prices, the first stressing the
effect of interest rates on inflation and the second emphasizing the reverse
impact of inflation on interest rates.

The Classical Economists
Although Thornton was the first economist to clearly express the
doctrine that inflation results from a divergence between the profit rate
on capital and the loan rate of interest, that doctrine is usually identified with Knut Wicksell, the great Swedish economist who independently
reformulated it almost 100 years later. Not until Wicksell's meticulous

-5-

and systematic exposition of the theory and its policy implications did
it become thoroughly established in the mainstream of monetary analysis.
It is true that earlier in the 19th century certain elements of Thorton's
analysis had been employed by some leading 'Britishclassical economists,
notably'David Ricardo and John Stuart Mill, to explain how an injection of
bank money influences spending and prices indirectly through the interest
rate channel.

Using the two-rate doctrine, these writers explained how

bank money enters the system initially via an expansion in the supply of
bank loans, the latter tending to reduce the loan rate temporarily below
the profit rate on capital, thereby stimulating .investment spending and'
exerting upward pressure on prices.

For the most part, however, classical

economists tended to minimize the significance of the two-rate mechanism.
They argued that money exerts a much stronger influence on prices through
the direct expenditure channel than through the indirect interest rate
channel.

They claimed that any divergence between profit and loan rates

of interest would be short:lived and stressed the interdependence rather
than the disparity between the two rates.

The'classical economists, more-

over, did not fully perceive the,policy (i. e., price stabilization)
implications of Thorton's analysis. Thus, after its initial formulation
by Thornton, the two-rate doctrine fell into neglect until Wicksell made
it

II.

the center of his monetary theory.

WICKSELL'S FRAMEWORK
Money Vs. Natural Rates of Interest
The central element of Wicksell's analysis, like Thornton's, is
the sharp distinction between two interest rates:
rate and (2) the natural or equilibrium rate.

(1) the money or market

The former is the rate charged

on loans in the money market.

The latter, as Wicksell pointed out, can

be interpreted in several ways.

It is the expected marginal yield or

internal rate of return on newly created units of physical capital.

It

is also the rate that would equilibrate desired saving and investment at
the economy's full capacity level of output.

Or, what amounts to the same

thing, it is the rate that equates aggregate demand for real output with
the available supply.

It follows from this latter definition that the

natural rate is also that interest rate level that is neutral with respect
to general prices, tending neither to raise nor to lower them. According
to Wicksell, as long as the market rate is equal to the natural rate,
desired saving will just equal desired investment, aggregate demand will
therefore equal aggregate supply, and price stability will prevail.

Any

discrepancy between the two interest rates, however, will cause prices to
change.

If, for example, the market rate falls below the natural rate,

investment will exceed saving , aggregate demand will be greater than aggregate supply, and, assuming the excess demand is financed by bank loans
resulting in the creation of new money, inflation will occur.

Conversely,

if the market rate rises above the natural rate, saving will exceed investment, bank loans and the stock of money will contract, there will be a
deficiency of aggregate demand, and prices will fall.

Wicksell assumed

complete wage and price flexibility so that a decline in total spending
would manifest itself in an absolute decline in the price level and not in
production.

The Role of Money in Wicksell's Analysis
Although Wicksell's analysis is couched in terms of market and
natural rates of interest, he does not neglect the role of money.

In his

-7-

model, the price level cannot change unless there is a corresponding prior
.*
change in the quantity of money.

These money stock changes accompany

changes in the volume of bank loans used to finance excess aggregate demand.
He specifically states that these changes in the money stock are necessary
to permit price level movements to occur.

But he insists that such money

itock changes are caused by the discrepancy between the two interest rates.
To illustrate, suppose banks set and maintain the market rate below the
natural rate.

Desired investment will exceed desired saving.

The demand

for bank loans will expand, putting upward pressure on the market (loan)
rate of interest. To prevent the market rate from rising, the banks must
be willing to accommodate all borrowers at the fixed rate.

Assuming the

banks are so willing, then the volume of bank lending will rise.

And since

new loans are granted in the form of increases in the checking deposits of
borrowers, the money stock also expands.

The monetary expansion is clearly

a result of the gap between the two interest rates.
what makes Wicksell's monetary analysis unique.

This latter result is

He does not accept the

crude quantity theory view of purely exogenous monetary changes causing
changes in.the price level.

Nor does he accept the "reverse causation"

argument that price level changes produce changes in the money stock.

In

his model both money stock changes and price level movements stem from a
common cause, namely, the discrepancy between the market and natural rates
of interest.

The Cumulative Process
In Wicksell's model any discrepancy between the two interest rates
will set in motion a dynamic sequence of spending and price level changes
that will continue as long as the gap persists. Wicksell referred to this

-8-

sequence as the."cumulative process.V

He argued that the cumulative process

could be either stable or unstable depending upon the type of monetary system
a nation possessed.
I

He considered two alternative types of hypothetical

monetary arrangements, namely, (1) a "pure 'cash" system embodying the key
characteristics of the gold standard and (2) an "ideal bank" or “pure credit"
:
system using no metallic money, all payments being made by means of bookkeeping entries.

In the case of the pure cash system, Wicksell defines

money to include only full-bodied gold coin and bank notes convertible into
gold.

Demand deposits are excluded, an expansion in their volume being

treated not as an increase in the money stock per se but rather as a rise
in the "virtual velocity" of specie-reserves, enabling the,latter to support
a.larger volume of money payments.

In the case of the pure credit system,

however, money is defined as consisting solely of demand deposits. And since
there is no monetary demand for gold in the pure credit system, there is no
need for banks to hold metallic reserves. Thus, the only conceivable form
of bank reserves is central bank credit.
Wicksell maintained that in the pure cash economy the cumulative
process necessarily plays an equilibrating role.

During an inflationary

period, for example, the rise in spending, prices, and the level of nominal
national income results in (1) an internal drain of .gold into hand-to-hand
circulation and into non-monetary uses and (2) an external drain of specie
to cover an adverse foreign trade balance stemming from the domestic inflation.

The drain and threatened depletion of specie reserves forces banks

to raise the money rate of interest, thereby bringing the inflationary process
to a halt.

Contrariwise, during a period of price deflation the steady

accumulation of excess reserves will eventually induce banks, for lack of
earnings, to reduce the loan rate of interest to stimulate borrowing.

-9-

Borrowing expands, spending increases, and the price level stops falling.
As before, a reserve-induced alteration in the money rate of interest serves
to restore equilibrium.

In brief, the pure cash system contains a stabilizing

adjustment mechanism that brings the cumulative process to a halt.
According to Wicksell, however, no such automatic self-correcting
mechanism exists in the pure credit system.

Since specie drains are not a

threat, banks need hold no reserves and thus are free to set and maintain
indefinitely any money rate they choose.

In short, there exists no reserve

constraint in the hypothetical pure credit economy to limit the cumulative
process.

Consequently, any spontaneous disturbance that upsets the initial

equality between the natural and market rates of interest will set in action
an inflation or deflation that can continue indefinitely.
At this point it is tempting to argue that Wicksell overlooked
one equilibrating element-namely

competition--operating in the pure-credit

model of the cumulative process. .Woulci
not competition among borrowers and
lenders tend to equalize all interest rates, thus terminating any cumulative
process?

More specifically, would not competition among bankers--especially

in their efforts to raise loan funds--force them to raise the rate of interest paid on deposits and hence the rate charged on loans until those two
rates were bid up into equality with the natural rate?

If competition does

act to eliminate spreads between interest rates, it follows that, even in a
pure-credit economy, the cumulative process can be no more than a temporary
phenomenon, Wicksell's claim to the contrary notwithstanding. Wicksell
therefore must have neglected the influence of competition.
In fact, however, Wicksell did not overlook competition. His
model explicitly assumes a competitive banking system in which banks pay
interest on demand deposits roughly equal to the rates charged on loans.

- 10 -

In essence, however, he argues that in a pure credit economy, competition
in banking is a necessary but not a sufficient condition for price stability.
Some quantitative restraint on the money supply is also required.

Once

this-restraint is established, free competition among banks for the limited
quantity of deposits will tend to equate market and natural rates. Without
the quantitative constraint to limit deposit creation, however, competition
in banking will manifest itself in persistent inflationary expansion of the
money stock.
Finally, there is the question of which of the two hypothetical
monetary arrangements--the pure cash system or the pure credit system-_
Wicksell regarded as his standard case for purposes of policy prescription.
As.previously mentioned, according to Wicksell, the policy implications of
the two cases differ greatly.

In the pure cash economy the cumulative

process itself serves as a fundamental equilibrating mechanism, minimizing
the need for policy action.

By contrast, in the pure credit system a

cumulative process is not self-limiting (or so Wicksell argued) but may be
of indefinite duration unless halted by positive policy action.

Some

economists; notably Don Patinkin (1965; p. 589) maintain that the pure
cash system constitutes Wicksell's standard case.
points in the opposite direction.

The evidence, however,

For it was the pure credit system that

Wicksell tended to emphasize in his writings.

His only formal model of the

cumulative process is constructed on the assumption of a pure credit economy.
And most of the monetary reforms he advocated during his lifetime were de3
signed to make the hypothetical pure credit system a reality.

'See Uhr (1960) pp. 231-4.

- 11 -

The Wicksellian,Stabilization Criterion
As stated above, Wicksell's policy prescriptions follow logically
from his model of the pure credit system.

Since he believed that the latter

system contained no endogenous equilibrating mechanism, he thought that
price-level stability must be imposed by an exogenous regulator, that is,
by the central bank.

The maintenance of monetary equilibrium, he said, is

the manifest responsibility of the central bank.

It was for this purpose

that he formulated his celebrated stabilization criterion, namely, that
to preserve price-level stability the central bank should keep the money
rate of interest (i) equal to the natural rate (r), or i=r.
However correct this Wicksellian criterion may be as an abstract
principle, as a guide to policy it suffers from a serious practical defect.
For its use requires knowledge of the natural rate of interest, generally
regarded as a non-observable variable incapable of precise measurement.
But Wicksell answered this criticism by noting that the authorities can,
at least, be sure that if the price level is changing, the money rate is
too high or too low relative to the natural rate and therefore should be
changed. He proposed, therefore, that the price level itself be substituted
for the natural rate as the target and indicator of monetary policy.

Move-

ments in the price level would signal the need for adjustment of the money
rate of interest and indicate the desired direction of the change.

A

rising price level would call for an upward adjustment in the money rate,
while a falling price level would indicate that a downward adjustment was
in order.

In short, the central bank should promptly adjust the market

rate--i. e., its discount, or bank rate--in the same direction as the price
level is moving, only ceasing to do so when price movement stops.
Wicksell's own words, stabilization policy

In

- 12 -

does not mean that the banks ought actually to
ascertain the natural rate before fixing their
own rates of interest. That would, of course,
be impracticable, and would also be quite unnecessary. For the current level of commodity
prices provides a reliable test of the agreement or diversion of the two'rates. The procedure
should rather be simply as follows: So long as
prices remain unaltered the banks' rate of interest
is to remain unaltered. If prices rise, the rate of
interest is to be raised; and if prices fall, the
rate of interest is to be lowered; and the rate of
interest is henceforth to be maintained at its new
level until a further movement of prices calls for
a further change in one direction or the other.
(1936; p. 189)

III.

INFLATIONARY EXPECTATIONS AND THE WICKSELLIAN MODEL
Wicksell's Inadequate Treatment of Expectations
For the most part, W'icksell'sanalysis of the cumulative process
is conducted on the assumption of the ab,senceof inflationary or deflationary
expectations. No matter how much prices have changed in the past or are
changing currently, everyone expects them to remain unchanged over the
indefinite future. Anticipations of price stability are assumed to be
unshaken by actual price experience.
Wicksell, of course, did not ignore price expectations altogether.
He noted that after the cumulative process has continued for some time,
the assumption that anticipated future prices are identical to present ones
may have to be abandoned.

Thus he states that

. The upward movement of prices will in some
measure 'create its own draught.' When
prices have been rising steadily for some
time, entrepreneurs will begin to reckon
on the basis not merely of the prices already attained, but of a further rise in
prices. . . . Once the entrepreneurs begin
to rely on this [inflationary] process continuing--as soon, that is to say, as they
start reckoning on a future rise in prices-the actual rise will become more and more

- 13 -

rapid. In the extreme case in which the
expected rise in prices is each time fully
'discounted, the annual rise in prices will
be indefinitely great. (1936; pp. 96, 148)
In the face of such a development, stabilization policy would
have. to be modified somewhat.

In his words'

To put an immediate stop to any further rise
in prices, it would not be sufficient for the
banks to restore the rate of interest to its
original [natural] level. This would have
the same effect on the business world as
would a somewhat lower rate of interest at
a time when prices are not expected to alter.
(1936; p. 97)
The contention here apparently is that the eradication of inflationary
expectations requires that the market rate be raised temporarily above the
natural rate associated with zero inflationary expectations. With the
market rate established above the natural rate, anticipated price increases
will fail to materialize and expectations will be revised downward.

Even-

tually the market rate will fall back into equality w‘ith the natural rate.
If, on the other hand, banks persist in trying to peg the market rate below
the natural rate, "two forces [i. e., inflationary expectations and the gap
between the natural and market rates] will be operating in the direction of
higher prices, and the rise will be correspondingly more rapid." (1936; p. 97)
In view of the foregoing passages, one cannot deny that Wicksell
makes explicit allowance for price expectations. Nevertheless, it must be
admitted that he gave such phenomena only passing attention, perhaps because
he thought they could not produce a cumulative rise in prices but only accelerate such a rise once it had already begun.

He made it clear that he

regarded inflationary expectations as 'special cases peripheral to his main
field of interest. Consequently, he did not develop further the insights
contained in the passages quoted above.

In fact, the passages cited are

merely incidental remarks, i. e., isolated asides or qualifications to his

- 14 L

formal analysis of the cumulative process.
part of his main conceptual framework.

They do not form a central

In short, although Wicksell recog-

nized the possibility of inflationary expectations and even suggested how
they-might influence the behavior of interest rates, he did not integrate
them systematically into his analysis of the cumulative process.
There was perhaps greater justification for minimizing the
importance of inflationary expectations in Wicksell's time than in ours,
In the 19th century prices were downwardly as well as upwardly flexible.
Periods of inflation alternated with periods of deflation, perhaps contributing to a feeling of extreme uncertainty concerning the direction of
future price changes.

People, looking at past experiensd of both rising

and falling prices, may have decided that the safest bet was to assume
that future prices would, on balance, remain unchanged.

Then, too, actual

price changes were relatively small, perhaps well below the critical perception threshold necessary for the activation of expectations.
The situation is quite different today, however.

Inflation--both

actual and expected--seems to be firmly entrenched in the structure of the
economy. Money illusion has diminished.;recognition and adjustment lags
have shortened.

Owing both to the extensive publicity given to the

problem of inflation and to the persistence of actual rates of price increase well in excess of the critical threshold level, there is greater
awareness of inflation than ever before.

Consequently, people react to

it quicker and give it greater weight in formulating their expectations.
Moreover, there is now less uncertainty about the direction of price
movements, which appears to be steadily upward.

And a monotonic upward

trend of prices, unlike the price fluctuations of the 1800's, tends to
generate anticipations of further inflation.

Such inflationary anticipations

- 15 -

find expression,in interest rate levels that reflect both lenders' fears
of losing purchasing power and borrowers' hopes that inflation will transform nominally high rates into low real rates.
In short, expectations now play a major role in the behavior
of interest rates.

Therefore, in order to render Wicksell's analysis

applicable to current policy issues, it is necessary to introduce price
expectations into his model.

Interest Rates:

This change requires two steps.

Real Vs. Nominal

The first step is to specify that the relevant decision variable
in the Wicksellian model is not the nominal rate of interest but rather
the real or price-deflated rate, i. e., the nominal market rate adjusted
for expected changes in the purchasing power of money.

Borrowers and

lenders react to this real rate, which bears a precise relationship to
the nominal rate.

The relationship is straightforward:

the real rate is

merely the nominal rate minus the expected percentage change of prices.
Alternatively, the nominal rate is obtained by.adding to the real rate
the expected rate of inflation.
The expected rate of inflation gets incorporated into the nominal
rate in the following way.

Lenders, seeking to prevent an inflation-induced

erosion of real yields, will demand that an inflation premium be added to
the basic rate that would be charged on loans in the absence of inflation.
Borrowers will be willing to pay the premium either because they expect a
capital gain stemming from the inflation-induced appreciation of the market
price of assets purchased with the proceeds of the loan, or because they
realize that they will be able to repay the loan with depreciated dollars,
i. e., money whose value has declined in terms of purchasing power.

- 16 -

Notice that the price-change variable comprising the inflation
.Q
premium'is the anticipated rather than the actual current rate of inflation.
What matters to a banker who is deciding what real interest rate target to
aim for is not the current rate of inflation but rather the rate expected
to prevail over the life of the loan.

The rate of inflation that actually

occurs may of course differ from the anticipated rate, in which case the
realized real market rate of interest will turn out to be different from
the expected one.

Such disparities between expected.and realized real

interest rates are in fact quite likely to occur, given the existence of
lags in the formation of 'expectations. For example, suppose that bankers'
price expectations are based on past price experience and are adjusted only
with a delay,

Then, in periods in which the level of inflation is higher

than it was in the past, the anticipated rate of price increase will lag
consistently behind the actual-rate of increase, i. e., inflation will be
underestimated. As a result, the premium incorporated in

systematically

nominal rates will be too small.

The nominal rate of interest will not

rise sufficiently to compensate for inflation, and the realized real rate
will fall short of the expected one.
to be permanent.

These effects, however, are unlikely

In the long run, expectations adjust to reality, inflation

is completely anticipated and fully incorporated into nouiinalrates, and
the realized real market rate of interest turns out to be the same as the
expected one.

Exogenous Monetary Growth
The second step in integrating expectations into Wicksell's model
is to reverse his assumption that banks set the market rate of interest and
then accommodate the money supply to the investment-induced demand for bank

- 17 -

loans at that rate.

Accordingly, in the analysis that follows, the money

stock and its rate of change are treated as exogenous variables determined
by the central bank, while the market rate is treated as an endogenous or
dependent variable.
:

The assumption of exogenous monetary growth permits the model

to be in stable equil.ibriumeven though prices continue to rise.

Full

.

equilibrium, of course, also requires equality between natural and real
market rates of interest.

Such an inflationary equilibrium is impossible

in Wicksell's original model, where equality between the two interest rates
implies the absence of excess demand for capital, thus precluding the induced expansion of loans and creation of new money necessary to produce the
equilibrium rate of inflation.

To summarize; in Wicksell's original model,

inflation is solely a disequilibrium phenomenon because only in disequilibrium
can there be endogenous monetary growth to support it.

By contrast, in the

revised model inflation can also be an equilibrium phenomenon, exogenous
monetary growth being invoked to explain the equilibrium rate of inflation.

Expectations and the Concept of Monetary Equilibrium
The insertion.of expectations into Wicksell's model alters the
equilibrium relationship between the market (nominal) rate of interest and
the natural rate.

The fundamental equilibrium condition in the original

model states that the market rate (i) must equal the natural rate (r), or
i=r.

By contrast, in the modified model, the equilibrium condition states

that the market rate (i) must equal the natural rate (r) plus the percentage
rate of change of prices (c/p>, or i ='r + i/p.
from two requirements of long-run competitive

The latter condition follows

equilibrium. The first is that

expected and actual rates of inflation must be the same.

The second require-

ment is that real rates of return on all assets--real capital, demand deposits,

- 18 -

and loans--mustsbe equal.

Banks, of course, must earn at least the same

rate of return on loans that they pay-on deposits.

And in order to induce

people to hold deposits, banks must offer to pay a rate of interest at
least equal to the opportunity cost of holding deposits.

But the oppor-

tunity cost of holding deposits is the foregone yield on real capital plus
the expected rate of inflation (the depreciation cost of holding deposit
balances), which in the long run equals the actual rate of inflation.
And since competition forces deposit and loan rates into equality, it
follows that, in equilibrium, i = r + i/p.

An alternative explanation of

the equation is that in equilibrium the nominal rate of interest on monetary
assets (i) must equal the nominal yi'eldon real assets, this yield being
composed of the real rate of return on capital (r) plus the capital gain,
or rate of appreciation of the market price of the asset, due to inflation
G/P).

This equation indicates that the insertion of expectations
into Wicksell's modei changes the concept of monetary equilibrium from
one of a state of absolute price stability to one of a stable or steadystate (nonkaccelerating, non-decelerating) rate of inflation. Constancy
not of the price level per se but rather of its percentage rate of change
-is the hallmark of monetary equilibrium in the modified Mcksellian

model.

And that equilibrium is not unique since it is consistent with any steadystate,rate of inflation or deflation (including a zero rate).
To illustrate, consider the'following example.

Suppose the

economy is initially in a state of monetary equilibrium. There is no
inflation or deflation and resources are fully employed.
of interest is equal to the natural rate.

The market rate

The money stock is growing at a

rate just equal to the constant rate of growth of real output (assumed for

- 19 -

simplicity to be equal to zero).

Now assume that the monetary authority

suddenly and permanently raises the growth rate of the money stock.

-

The

newly-created money enters the system initially via an expansion in the
supply of bank loans, thereby temporarily lowering the market (loan) rate
of interest below the unchanged natural rate.

The spread between the two

interest rates creates an excess demand for goods causing prices to rise,
i. e., a positive rate of inflation emerges. With goods becoming increasingly expensive, people demand more and more bank accommodation to finance
their purchases, and the increased demand for loans bids the loan rate of
interest back to its original level.

But even though the nominal rate has

been restored to its initial level, the real (price-deflated) rate of
interest received by lenders has declined.

By way of example, suppose

that the nominal rate has returned to its original level of 7% and the
newly-established rate of inflation is 3%.
interest is only 4%, 1. e., 7% - 3%.

Then the realized real rate of

Unanticipated inflation has opened

up a gap between the real and nominal market rates of interest with the
real rate lying below the nominal rate.

The cause of this gap is imperfect

foresight, i. e., a lag of inflationary'expectations behind inflationary
experience. At first, inflation is underestimated and not fully incorporated into the nominal interest rate.

Consequently, the nominal rate

does not rise sufficiently to compensate for inflation and the corresponding
real rate falls below the natural rate.
This gap does not last indefinitely, however, because anticipations
will be influenced by experience.

In time, people will begin to adapt-their

expectations to the actual rate of inflation and to incorporate these expectations into nominal interest rates.

The inflationary component of the

nominal rate will begin to reflect the current rate of inflation. When this

- 20 -

happens, the nominal rate will begin to rise above, and the corresponding
real market rate will converge upon, the natural rate.

Thus, as the di-

vergence between anticipated and actual inflation narrows, so too will the
gap between the real market and natural rates of interest.

Eventually,

when expectations catch up with experience, the gap vanishes and monetary
equilibrium is restored.

In the new equilibrium:

(1) the rate of infla-

tion will be perfectly anticipated, i. e., the expected rate of inflation
will equal the actual rate; (2) the actual rate of inflation will be
completely incorporated in the nominal market interest rate; (3) the
nominal market rate of interest will exceed the natural rate by the actual
rate of inflation; (4) the real (price-deflated) market rate of interest
will equal the natural rate; but (5) the steady-state rate of inflation
will be higher than it was originally.

Policy Implications
Several important policy implications arise from the modified
Wicksellian analysis.

The first is that attempts to hold the real (price-

deflated) market rate below the natural rate will result in explosive,
ever-accelerating inflation. The real market rate will stay below the
natural rate only as long as expected inflation lags behind actual inflation.

But since expectations are always being adjusted in an attempt to

catch up with current inflation, the latter must be continually accelerated
via faster monetary growth to stay a step ahead of expectations. Thus, to
maintain a gap between the actual and expected rates of inflation.,the
banking system must inject ever increasing amounts of money into the
economy.

What is required to hold the real market rate of interest below

the natural rate is an accelerating inflation that is always underestimated.

- 21 -

Given time, however, even an accelerationist policy will prove ineffective
as a means of holding the real market rate below the natural rate.

The

policy will cease to be effective once people become cognizant of it and
learn to incorporate the rate of acceleration itself into their price
anticipations.
A second policy implication is that since monetary equilibrium
is consistent with s

stable rate of inflation, the best the policymakers

could do would be to choose a zero rate of inflation.

But this means that

once the economy has reached a state of non-inflationary equilibrium the
authorities should never try to reduce the marke,trate below the natural
rate, since attempts to do so inevitably lead, via shifting expectations,
4
to positive steady-state rates of inflation.
The third policy implication concerns the path that leads to the
zero or other target rate of inflation. To lower the rate of inflation
the monetary authorities must raise the nominal market rate (i) above the
natural rate (r) by more than the rate of.inflation (i/p). This policy
step will force the real market rate (i - i/p) ,above the natural rate of.
interest, causing a contraction of aggregate demand and thereby provoking
a downward cumulative process.

As long as the real market rate exceeds

the natural rate, actual inflation will fall below anticipated inflation,
leading people to revise expectations downward.

This sequence will continue

until inflationary expectations vanish (i. e., b/p.+ zero), and the monetary
authorities adjust the market rate back into equality with the natural rate.

4
One might also argue that a fully-anticipated inflation is less
socially harmful than attempts to reduce it; therefore, .once inflation has
stabilized at a given level, the best the policymakers could do would be to
leave it alone.

- 22 Here the downward cumulative process terminates at a zero rate of inflation.

,*
A crucial policy issue relates to the speed of the path to

price stability. Given that the reduction of inflation may entail temporary though painful rises in unemployment, the policymakers would want
to know how long it would take to get the rate of inflation down to some
gPven target level.

Generally, the rapidity of the route to the goal rate

of inflation would depend on the speed of adjustment of expectations.
Given that people formulate anticipations of inflation partly on the
basis of current experience, the bigger the disparity between experience
and expectations, the faster are expectations likely to be revised.

Since

the difference between expected and'experienced inflation .is likely to be
systematically related to the spread between the real and natural rates
of interest, it follows that the more rapidly is the rate of inflation
to be reduced, the higher must be the real market interest rate relative
to the natural rate while inflation is subsiding.
It should be apparent that there exists not one but rather a
variety of time

paths to price stability, some faster than others.

authorities can choose from among these alternative paths.

The

For example,

they can elect to end inflation quickly by holding the real market rate
at a very high level for a relatively short period of time.

Or they can

choose to eliminate inflation more slowly by maintaining the real rate at
a somewhat lower level for a longer period of time. The choice will depend
on the policymakers' estimates of the social harm wrought by inflation
versus the side costs (e.g., unemployment) of fighting inflation. The
policymakers will choose the path that in their estimation results in the
smallest social cost in terms of a weighted average of inflation and unemployment (taking account of both duration and magnitude of these variables)

- 23 -

where the weights represent the comparative harm caused by each evil.

If'

inflation were viewed as the more serious evil, the authorities would
assign a higher priority to its quick eradication than they would if unemployment had the highest relative weight.'
A word of caution should be inserted at this point.

The preceding

analysis assumed that any contractionary (i. e., high interest rate) policy
would eventually reverse inflationary expectations and end inflation.

In

fact, however, inflationary expectations may be extremely resistant to contractionary policy.

Such would be the case if the public, looking back at

a succession of unsuccessful stop-go economic policies, were to expect the
contractionary phase to be followed shortly by an expansionary phase and
the consequent reactivation of inflation.

In this case, inflationary

expectations would be influenced not by current policy actions or recent
and current rates of inflation, but rather by the observed past history of
stop-go policy cycles.
The fourth policy implication is that the rate of inflation
itself may have to serve as an operational guide to monetary policy, just
as the price level was to serve as the 'indicatorvariable in the practical
decision rules originally formulated by Wicksell.

Since the natural rate

is an unobservable variable, the only way to discern whether real and
nominal market rates are sufficiently high is to observe what is happening
to the rate of inflation. Accelerating inflation signifies that the real
market rate of interest is below the natural rate and therefore should b'e
raised.

Decelerating inflation, by contrast, indicates that the real rate

of interest is above the natural rate and need not be raised further as
long as inflation is subsiding at a‘pace judged satisfactory by the monetary authorities.

-

24 -

A fifth policy implication is that a money growth rate target
may be less risky than a nominal interest rate target. The revised
Wicksellian analysis indicates that an inappropriate interest rate target
will lead to an explosive cumulative process.

The gap between the target

and the natural rate of interest will widen and inflation will accelerate.
By contrast, a wrongly set money growth rate target does not carry this
risk.

Instead, it will lead to a stable rate of inflation or deflation

and will in this sense be superior to an interest rate target.

IV.

A WICKSELLIAN INTERPRETATION OF THE RECENT U. S. INFLATION
If the modified Wicksellian framework is correct, then the U. S.
experience of a generally accelerating rate of inflation over the interval
1965-1974 indicates that market interest rates were altogether too low
during that period--too low, even, to attain inflationary equilibrium,
much less absolute price stability.

This interpretation may seem to run

counter to the facts since market interest rates have reached historically
high levels in recent years.

But, as Wicksell himself pointed out, what

matters is not the absolute level of the market rate itself, but rather
that level in relation to the natural or equilibrium rate.
The rate of interest is never high or low in
itself, but only in relation to the profit
which people can make . . . and this,,of
course, varies . . . In one word, the interest on money is, in reality, very often
low when it seems to be high, and high when
it seems to be low. (1907; p. 217)
It seems likely that the expected profit rate on capital has
been high relative to real market interest rates, which explains why the
demand for bank loans and the rate of economic expansion continued strong
throughout much of the period despite phenomenally high nominal market
rates.

Far from being "too high," as was often alleged, market rates were

- 25 -

actually too low to act

as a deterrent to borrowing, spending, and the

consequent acceleration of Inflation.

.

It follows that the market rate,

by itself, has been a deceptive indicator of the degree of monetary restraint.

Policymakers along with many other observers seem to have been

seriously misled by this indicator. At a time when Wicksellian analysis
indicated that market rates should have been raised sharply to fight
inflation, the authorities, sympathetic to the many complaints that in' terest rates were already too high, were trying to keep those rates from
going any higher.

These efforts only served to keep open the gap between

natural and real market rates, thus accentuating the cumulative inflationary
process that contributed to the rise in nominal rates.
This experience underscores one of the main policy conclusions
derived from the revised Wicksellian analysis, namely that price stability
may be better served if the central bank adheres to a money growth rate
target rather than a nominal interest rate target.

- 26 -

References

1.

Blaug, Mark.
Illinois:

2.

Harrington, Richard, "The Monetarist Controversy," Manchester School
of Economic and Social Studies, 39 (December 1971), 269-92.
:

3.

Horwich, George. "The Proper Role of Monetary Policy," Compendium on
Monetary Policy Guidelines and Federal Reserve Structure. U. S.
Congress, House Committee on Banking and Currency. Subcommittee on
Domestic Finance. December 1968, pp. 294-304.

4.

Laidler, David. "On Wicksell's Theory of Price Level Dynamics,"
Manchester School of Economic and Social Studies, 40 (June 1972),
125-44.

5.

Lutz, Friedrich. 'Inflation and the Rate of Interest," Banca Nazionale
de1 Lavoro Quarterly Review, (June 1974), 99-117.

6.

Patinkin, Don. Money, Interest, and Prices.
and Row, 1965, pp. 587-97.

7.

Sargent, T. J. 'Commodity Price Expectations and the Interest Rate,'
guarterly Journal of Economics, 83 (February 1969), 127-40.

8.

Tanner, J. E. "A Wicksellian'Indicator of Monetary Policy," Journal
of Monetary Economics, 1 (1975), 171-85.

9.

Thornton, Henry., An Enquiry into the Nature and Effects of the Paper
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Economic Theory in Retrospect. Revised ed. Homewood,
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Harper

10.

Uhr, Carl, Economic Doctrines of Knut Wicksell.
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11.

Wicksell, Knut. "The Influence of the Rate of Interest on Commodity
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Berkeley:

University

12.

Interest and Prices. Trans. by R. F. Kahn. With an
: Introductio: by Professor Bertil Ohlin. London: Macmillan, 1936.

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