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FRBSF

WEEKLY LETTER

August 7, 1987

Money and the Fisher Effect
Although nominal or market interest rates are
published daily, it is the anticipated real, or
inflation-adjusted rate that determines individual
and firm behavior. This distinction between real
and nominal interest rates dates back at least to
Irving Fisher, a distinguished early 20th-century
economist. Abstracting from taxes, Fisher
emphasized that the nominal rate is the sum of
the expected real interest rate and the expected
rate of inflation.
Changing expectations of inflation, therefore,
can affect nominal interest rates dramatically.
The sharp rise in long-term interest rates since
January this year has been attributed by many
analysts to upward revisions in the market's
expectations of future inflation rates prompted
by increases in the actual rate of inflation. Longterm interest rates (on 30-year U.5. government
bonds) rose 140 basis points from 7.4 percent in
January to 8.8 percent in May, while the rate of
consumer price increases on a year-over-year
basis rose 160 basis points to 3.8 percent.
Numerous other episodes of increases in inflation rates have not, however, been associated
with rising interest rates. Viewed from a long
historical perspective (shown in Chart 1), the
linkage between inflation and interest rates has
often been weak and seemingly unstable. In this
Letter we offer new insights l based on the
changing relationship between money supply
growth and inflation, into why the Fisher effect
has appeared to be so unstable.
l

can buy, and not about money itself. People are
concerned with the real, not nominal, rate of
interest because the real rate represents the
expected future purchasing power of the returns
from an initial outlay of funds. For example, the
expected real return on a default-free bond paying 10 percent interest would be two percent if
prices were expected to rise at an 8 percent rate.
The expected real interest rate, not the nominal
rate, therefore is a key determinant of economic
behavior because individual investors and savers
are concerned with the real returns (future purchasing power) yielded by their investments,
borrowers are concerned with the real costof
future payments, and firms are concerned with
the real cost of funds in evaluating their
investments.
Although the nominal rate is known with certainty, the future rate of inflation and, hence, the
expected real rate are not. Investment, saving,
and borrowing decisions must, consequently, be
made with a degree of uncertainty because of
the uncertainty regarding the real rate. When
nominal rates change, it is this very uncertainty
about future inflation that makes it difficult to
determine whether the real interest rate has
changed. However, if future inflation were easily
predictable and the Fisher effect held strongly,
there would be less uncertainty regarding real
returns on investments.

The Fisher effect
According to Fisher, in a world in which the real
rate were constant, variations in nominal interest
rates would be due solely to variations in anticipated inflation. That is, a one-percentage point
increase in the expected rate of inflation, holding constant the real rate, would result in a onepercentage point increase in the nominal ratea phenomenon known as the Fisher effect.

Lack of evidence
Surprisingly, there is only weak statistical evidence of the Fisher effect's existence. For example, for the period from 1860 through 1939,
there is no statistical evidence of a Fisher effect.
Similarly, even during the early post-war period
(up until 1960), many researchers have been
unable to find strong statistical evidence of a
Fisher effect in the U.S. This seeming lack of a
relationship for the 1870-1960 period is illustrated in Chart 1.

The theory underlying the Fisher effect relies on
the notion that individuals do not suffer from
money illusion, that is, that they are concerned
about the real goods and services that money

The lack of evidence may be due to two major
difficulties in testing for the Fisher effect. First,
real rates need not be constant. Changes in technology, demographics, preferences, and real

FRBSF
commodity prices can, for example, alter real
interest rates. Second, Fisher hypothesized a
relationship between expected, not realized,
inflation and interest rates. Since market expectations about inflation cannot be observed
directly, it is difficult to determine whether market participants are behaving as Fisher
hypothesized.
To illustrate the difficulties in testing for the
Fisher effect, consider the most extreme case in
which all market participants do behave as
Fisher hypothesized but changes in the inflation
rate are purely random and therefore not predictable. In this case, expected inflation would
be constant even though actual inflation might
be quite variable. Observed variations in the
actual inflation rate (consisting solely of random
forecast errors) therefore would be unrelated to
the expected inflation rate (which would be constant). As a result, there would be no observable
relationship between (the unpredictable) variations in the inflation rate and variations in interest rates. Moreover, there would be no statistical
way of testing whether interest rates varied with
expected inflation when expected inflation itself
was constant. (However, this is not to say that
the degree of volatility of inflation itself might
not be positively associated with the level of
nominal interest rates.)
This extreme case suggests that we could expect
a tighter relationship between actual and anticipated inflation during periods when movements
in inflation are highly regular and easily predictable. Realized or actual inflation under those
circumstances would serve as a reliable proxy
for expected inflation, and thus a closer relationship between actual inflation and interest rates
would be observed.
Empirical evidence seems to support this conclusion. Statistical work by economist Robert
Barsky suggests that inflation during the
1860-1930 period in the U.S. was largely unpredictable. That is, changes in inflation tended to
be random. As a consequence, Barsky found little evidence of a Fisher effect during this period.
Benjamin Klein, in earlier work, made essentially the same point. He found that during the
gold standard period in the U.s. (1880-1915),
the price level fluctuated randomly from year to
year around a constant level. Since these
changes in inflation were unpredictable (and
expected inflation was constant), there was no
relationship between actual inflation and nominal interest rates.

Money and inflation
Our study of the Fisher effect is based on the
belief of most economists that there is a strong
link between money supply growth and inflation. In particular, given money demand,
expected inflation to a large extent depends on
expected money supply growth in the future.
This linkage is based on theoretical underpinnings connecting money supply and demand
growth with price level determination, as well as
on a large body of statistical evidence covering
the u.s. and international experiences. Although
numerous other factors - such as oil-price
shocks, exchange rate shifts or crop failures may have significant short-term effects on inflation, money growth is the most widely recognized factor behind long-term inflation trends.
The process governing money creation can thus
have an important impact on the predictability
of inflation and hence, on whether a Fisher
effect can be observed. In particular, during a
period when money supply growth is highly predictable, inflation also will tend to follow a predictable pattern. And, because expected
inflation depends on expected future money
growth, we should be able to obtain a reasonably accurate forecast of inflation during periods
when money can easily be forecast.
This means that we should be able to observe a
Fisher effect during periods when money growth
is predictable. The upshot is that estimates of the
Fisher effect that include periods during which
money and inflation cannot be forecast may
show a very small Fisher effect even though the
effect might actually hold very strongly.
As an example, consider whether a Fisher effect
likely could be observed in a gold-based monetary system. Since the quantity of gold supplied
depends on demand and supply conditions for
gold production, the price level should be predictable over the long run because growth in the
supply of gold is predictable over the long run.
(In fact, there is evidence that the price level
over the long run is relatively stable under a
gold standard.) Yet unexpected gold discoveries
or temporary increases in gold demand can
cause short-run random fluctuations in the price
level. Since such fluctuations by definition are
unexpected, they may lead to unpredictable
effects on inflation as well. (predictable fluctuations would be incorporated into the current
price of gold and thus would not affect the price
level in the future.) This unpredictability of
short-run inflation may explain why researchers
have been unable to observe a Fisher effect
under a gold-based monetary system.

Chart 1
Inflation and Interest Rates
1870 - 1986

Percent

30

!Predictable

Unpredictable Inflation
No Fisher Effect

! Inflation

20

I'~

Rate

AAA

Bond Rate
;'

I"II

10

Inflation

! Strong Fisher Effect

"I
"I

I
d

I III

-10

-20 -J",rr""l""'""T"'"""'T''''"'''l='l''''"'nrmm''''l'''"''''''l'''''''''''"''''''1''''':':~
1880

Billions
of Dollars

1900

1920

1940

1960

1980

Chart 2
Level of the Monetary Base

240
200

Money Growth
Predictable

160

120

80
40 -h-"--rrT,.,-r-r-l-"--rrT,.,-,.,--c--rr-rrT-r-r..,-.--,-.-,,195219561960196419681972197619801984

Shift in the money supply process

The shift in 1960 is evident in Chart 2. The monetary base fluctuated randomly around a fairly
stable level from 1951 to 1960, at which point
the base began to grow exponentially.
This pattern suggests that we would likely
observe a weak link between past money growth
and inflation during the early, pre-1960 period,
and a much stronger link between the two during the later post-1960 period when money
growth was predictable. In fact, our statistical
tests did not show any evidence of a significant
cumulative impact of money on inflation during
the early period but did show a strong effect during the later period. During the post-1960
period, we found that a one percentage point
rise in money growth is matched by a one percentage point rise in inflation within a three-year
period.
These findings could help explain why there is
so little evidence of a Fisher effect prior to 1960.
They also could explain why researchers using
data from the entire post-war period have found
weak Fisher effects. In contrast to the argument
that financial markets only gradually learned
their "Fisher" or that they were irrational, we
attribute earlier doubt about the Fisher hypothesis to randomness and shifts in the money supply growth process.

Evidence of the Fisher effect

We recently conducted a test for the Fisher
effect using data from the post-1951 period,
when the U.S. Treasury and the Federal Reserve
agreed ("The Treasury Accord") to release the
Fed from its obligation to try to fix interest rates
on new U.S. Treasury issues. Since 1951, in
other words, the Federal Reserve has in principle
been allowed to determine the growth of the
monetary base (currency plus bank reserves)
independent of Treasury debt financing needs
and fiscal policy.

Consistent with the greater predictability of
money and the stronger relationship between
money and inflation during the post-1960
period, we found much stronger evidence of a
Fisher effect then. In fact, during the post-1960
period, we found that a 1 percentage point
increase in expected inflation resulted in a 0.9
percentage point increase in the nominal interest
rate. These estimates of the Fisher effect using
post-1960 data are larger than those of most
other studies.

As part of the test, we tried to distinguish possible shifts in the money supply process that may
have precluded observation of the Fisher effect.
We found that the statistical relationship
between current and past money supply growth
was very different between the periods
1951-1960 and 1961-1986. Money growth, to a
large extent, was unpredictable (on the basis of
past money growth) during the earlier period,
and highly predictable during the later period.

But more importantly, the evidence suggests that
instability in the observed Fisher effect can be
associated with shifts in the money supply
growth process. In particular, the extent to
which money can be forecasted, and hence
inflation can be forecasted, will partly determine
the extent to which the Fisher effect is statistically observable.

Michael C. Keeley and Michael M. Hutchison

Opinions expressed in this newsletter do not necessarily reflect the views of the management of the Federal Reserve Bank of San
.
. .
Francisco, or of the Board of Governors of the Federal Reserve System.
Editorial comments may be addressed to the editor (Gregory Tong) or to the author •... Free copies of Federal Reserve pubhca~lons
can be obtained from the Public Information Department, Federal Reserve Bank of San FranCISco, P.O. Box 7702, San FranCISco
94120. Phone (415) 974-2246.

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BANKING DATA-TWELFTH FEDERAL RESERVE DISTRICT
(Dollar amounts in millions)

Selected Assets and Liabilities
Large Commercial Banks
Loans, Leases and Investments 1 2
Loans and Leases1 6
Commercial and Industrial
Real estate
Loans to Individuals
Leases
U.S. Treasury and Agency Securities 2
Other Secu rities 2
Total Deposits
Demand Deposits
Demand Deposits Adjusted 3
Other Transaction Balances4
Total Non-Transaction Balances 6
Money Market Deposit
Accounts-Total
Time Deposits in Amounts of
$100,000 or more
Other Liabilities for Borrowed MoneyS

Two Week Averages
of Daily Figures

Amount
Outstanding

7/15/87
205,352
182,441
51,928
69,582
36,865
5,431
15,965
6,945
209,014
54,165
36,805
19,737
135,112

7/8/87
-

-

-

-

-

884
461
547
153
148
0
441
17
47
119
1,918
236
165

6,360
905
325
2,454
- 4,166
67
5,419
427
325
135
- 12,639
3,256
3,067

76

44,770
31,810
23,407

Change from 7/16/86
Dollar
Percent'

Change
from

-

-

2,390

7
437

-

-

4,046
3,000

Period ended

Period ended

7/13/87

6/29/87

Reserve Position, All Reporting Banks
Excess Reserves (+ )/Deficiency (-)
Borrowings
Net free reserves (+ )/Net borrowed( -)

24
18
42

217
18
199

1 Includes loss reserves, unearned income, excludes interbank loans
Excludes trading account securities
3 Excludes U.S. government and depository institution deposits and cash items
4 ATS, NOW, Super NOW and savings accounts with telephone transfers
S Includes borrowing via FRB, TT&L notes, Fed Funds, RPs and other sources
6 Includes items not shown separately
7 Annualized percent change
2

-

-

-

3.1
0.5
0.6
3.5
10.1
1.2
51.3
5.7
0.1
0.2
25.5
19.7
2.2
5.0

- 11.2
-

11.3