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interest rate* and inflation
Federal lax and spending reform
The discount rate— will it float?

Interest rates and inflation

Serious em pirical research on the
relation b etw een interest rates and
inflation resu m ed in the late 1960s after
a lapse o f nearly fo u r decades.

Federal tax and spending reform

CONTENTS

In an effort to deal with w id ely felt
e co n o m ic pain, the Congress has
co n sid e re d several e co n o m ic reform
proposals to limit a n d /o r re d u ce the
role o f the federal govern m en t in the
econ om y.

The discount rate— will it float?

E C O N O M IC PERSPECTIVES

Since the Federal R eserve a d o p te d
its n ew reserve s-o rien ted operating
p ro ce d u re , the instability o f the sprea d
b etw een the federal funds rate and the
d iscou nt rate has led many o b servers to
suggest floating the discou n t rate.

May/June 1981, Volum e V , Issue 3
Economic Perspectives is published bimonthly by the Research Department of the Federal
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Interest rates and inflation
John H. W o o d *
If a trader has lent w h e a t. . . at interest,
then fo r e very g ur o f wheat he shall take
100 qa as interest. If he has lent silver at
in terest, then fo r each sh e ke l o f silver he
shall take a sixth part o f a sh ekel, plus six
grains, as interest.
The Ham m urabi C od e, No. 90,
circa 2080 B.C.
The relation betw een interest rates and infla
tion has attracted much attention in recent
years. Serious em pirical research on this sub
ject has resum ed after a lapse of nearly four
decades, from the early 1930s to the late
1960s. The point of d eparture of this w ork has
been Irving Fisher's classic study, The Theory
o f In terest [5], published in 1930. Fisherfound
interest rates during the period 1890-1927 to
respond slow ly and incom pletely to varia
tions in inflatio n . The most com m on in te r
pretation of these results is that inflationary
exp ectations, w h ich in flu en ce current inter
est rates, respond slowly to observations of
past inflation.
Th e results of most recent studies have
been consistent with Fisher's. But Eugene
Fama [4] has presented results that contradict
those of earlier w riters. M ore im portant,
Fama's w o rk suggests that interest rates im
m ediately and com pletely reflect inflationary
expectations.
This article com pares the results of Fisher
and Fama and places these results in historical
p erspective. The small d ifferences between
Fisher and Fama appear to be due less to
increases in financial m arket efficien cy, im
provem ents in statistical m ethods, and better
data (as suggested by Fama) than to the spe

*Written in collaboration with Scott Ulman. We are
grateful for helpful comments by George Kaufman, Larry
Mote, and Harvey Rosenblum.

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cial, relatively tranquil period chosen by Fama
for his em pirical w o rk.
The years 1953-71 are unique in A m eri
can history for th eir record of stable prices.
Charts 1 and 2 m ake clear that there is not,
among periods of sim ilar length, a close com
petitor after 1894 with 1953-71 for the moststable-price-period prize.
Variations in prices since 1971 have been
more like those observed by Fisher than
Fama. T h e re fo re , an understanding of the
co nn ectio n s betw een interest rates and infla
tion in the w orld in w hich we live, w hile not
neglecting Fama’s contributions, requires that
we pay special attention to Fisher's.
Real and nominal interest rates
The distinction betw een interest rates in
terms of m oney (e.g ., silver) and interest rates
in terms of goods (e.g ., wheat) has long been
recognized. It is useful to think of the form er
as nom inal rates of interest, R, and of the
latter as real rates of interest, r. In the United
States n o m in al rates of in te rest m easure
returns in dollars. These are the rates of inter
est reported in newspapers and advertised by
depository institutions. Real rates of interest,
on the other hand, m easure the productivity
of investm ent goods (i.e ., the rate of trans
form ation of current goods into future goods)
and the tim e preferences of households (i.e .,
the allocation of consum ption between cu r
rent and future goods). D ifferen ces between
real and nom inal interest rates ought to be
due to expected rates of inflation, i.e ., to
expected rates of change in the value of
m oney relative to goods. If the expected rate
of inflation is denoted p, the equilibrium
relation betw een R and r may be expressed
as:
(1)

(1 + R) = (1 + r)(1 + p).

Suppose, for exam p le, that the expected
real return to an investm ent in a m achine is
r = 3 percent per annum . That is, the m achine
is expected to produce a net output each year
worth 3 percent of the value of the m achine.
Further suppose that, due to inflation, the
prices of the m achine and its output are
expected to rise 5 percent during the next
year. That is, exp ected inflation is p = 5 p er
cent. The expected nom inal (dollar) rate of
return to this real investm ent is therefore
(1.03)(1.05) - 1 = 8.15 percent. An investor’s
choice between the m achine (or shares in the
m achine) and, say, a 52-week Treasury bill
depends on the bill's yield , or rate of return,
R. If R exceeds 8.15 p ercen t, investors w ill be
attracted to the b ill, bidding its rate down
until R equals the expected return on alterna
tive investm ents of sim ilar risk, including real
investm ents.1 If R is less than 8.15 p ercen t,

1
This argument follows Fisher and Fama in abstract
ing from complications associated with risk and taxes.

investors w ill avoid the bill until its rate
becomes com petitive with other investments.
This line of argum ent suggests that, given r =
.03 and p = .05, the e q u ilib riu m value of R is
.0815. An alternative but equivalent way of
looking at the real rate of interest, the gain in
purchasing pow er from lending m oney, is
presented in box 1.
U nder the dubious assum ption that the
Babylonian b ureaucracy fixed interest on sil
ver and wheat at rates com patible with market
forces, we can determ ine the expected rate of
change of prices in that co untry in 2080 B.C .
Since 1 gur = 300 qa of w heat and 1 shekel =
180 grains of silve r, r = 100/300 = 33 1/3 p er
cent and R = 36/180 = 20 percent. Using eq u a
tion (1), we can surm ise that H am m urabi's
subjects expected an annual rate of deflation
of 10 p ercen t.2
2Unlike paper money, there is a real return to silver
in productive activities. For the sake of completeness,
therefore, r should be interpreted in our Babylonian
example as the difference between the real returns to
wheat and silver.

Chart 1. Inflation and real and nominal interest rates

Econom ic Perspectives

Equation (1) is often expressed as the fo l
lowing linear approxim ation:
(2)

R = r + p.

This approxim ation is fairly close for
small p and r. In the two exam ples given
above, the approxim ate equilibrium nom inal
rates are 8 and -23 1/3 percent, com pared
with the exact e q u ilib riu m values of 8.15 and
-20 percent.
A lthough the connections between in
terest and inflation have been understood for
thousands of years, they have never been d is
cussed m ore than during the past 250 years.
This is due to the increased use of paper
m oney and th erefo re to the increased vo latil
ity of inflation. W illiam Douglass wrote in
1740 that large em issions of paper money
“ rise the interest to m ake good the sinking
principal [2, p. 335].” For exam p le, the Rhode
Island issue of 1739, w hich caused a d ep recia
tion of paper m oney by 7 percent, required
an increase in the rate of interest from 6 to 13

Federal Reserve Bank o f Chicago

p ercent. Speaking in the House of Com m ons
in 1811, during a period of w artim e inflation,
H enry Thornton pointed out that if a man
borrow ed m oney at a nom inal interest rate of
5 percent and repaid the loan after a period of
2 percent or 3 percent inflation, “ he would
find that he had borrow ed at 2 or 3 percent,
and not at 5 p ercent as he appeared to do [11,
p. 336].”
Fisher’s results
The first extensive statistical studies of
the relations betw een real and nominal inter
est rates and inflation w ere carried out by
Irving Fisher. His results w ere stated in their
most com plete form in The Theory o f Interest
[5, pp. 399-451]. Em pirical tests of equation (1)
are difficu lt for a variety of reasons. Most
im portant, none of the three variables is
directly observable. All are expectations of
future events: p is the expected rate of infla
tion, r is the expected real return to produc
tive activities, and R is the expected nominal

return to investm ents in debt to be repaid in
dollars. Most researchers have sim plified the
problem by assuming the real return to be
constant and by choosing high-grade short
term securities w ith the same m aturity as the
period of observation to ensure that observed
nom inal yields w ere virtually the same as
expected nom inal returns. For exam p le,
Fisher’s most thorough tests used quarterly
data and four- to six-m onth prim e co m m er
cial paper. This is not a perfect solution to the
problem , but later w riters have been able to
use Treasury bills.
This leaves expected inflation. It is co n
ceivable that the m arket’s expectation of
inflation during the period beginning on date
t is a weighted average of past inflation rates.
Then using the linear approxim ation (2), our
model may be w ritten :

w h ere R t is the yield on date t on a security
m aturing in one p erio d ; the w ’s are weights
that indicate the im portance of past rates of
inflation (pt_-j, pt_2, . . .) in determ ining
exp ectatio n s of in fla tio n for the com ing
period, pt; p nt is the weighted average of
these past rates of inflatio n , with n being the
length of the lag, i.e ., the num ber of past rates
in clu d ed ; and et is an unobserved random
error term with a mean of zero. There is no
time subscript on the real rate of interest
because it is assumed to be constant.
Fisher did not estimate the w ’s. Regres
sions in those days w ere too expensive for
such a procedure. Rather, he tried different
com binations of the w ’s and n and ran co rre
lations of the resulting p nt’s and Rt. Specifi
cally, his weighting schem e was:

(3)

(4)

n Pt-1 + (n - 1)pt_2 + • • • + Pt-n
Rt = r + w-jpt_-j + w 2pt_2 + . . . + w npt_n

P n t " -------------------— - 1)------------------ 1------------------ '
n + (n -- + . . . + ~ •

+ et = r + Pnt + et
Chart 2. Inflation and real and nominal interest rates

Econom ic Perspectives

Fisher's co rrelatio n s, using quarterly ob
servations on the com m ercial paper rate and
the w h olesale p rice in d e x, are shown in chart
3. For interest rates observed between 1890
and 1914, the highest correlation was achieved
when rates of inflation lagged 30 quarters
w ere used. The co rrelation s fell as the lag was
lengthened . But betw een 1915 and 1927, the
co rrela tio n betw een interest rates and past
inflation was co ntinuously im proved as the
lag was len g thened — up to the m axim um lag
of 120 quarters tried by Fisher. He perform ed
sim ilar tests with annual data for the United
States and G reat Britain and the results w ere
the sam e: assum ing that (a) the real rate of
interest is constant, (b) expectations of future
inflation are determ ined by past inflation in
the m anner show n in equation (4), and (c) the
approxim ate eq u ilib riu m relation (2) is satis
fie d , the cu rren t interest rate is apparently
determ ined by expectations based on past
inflation ary exp erien ces as distant as 30 years
ago. Fisher w ro te: “ It seems fantastic, at first

glance, to ascribe to events w hich occurred
last century any in flu en ce affecting the rate of
interest today. And yet that is what the co rre
lations with distributed effects of p show [5,
p. 428]." 3
Recent studies of interest rates and inflation
Studies published in 1969 and 1970 by
W illiam Gibson [6], Thom as Sargent [10], and
W illiam Yohe and Denis Karnosky [12] co r
roborated Fisher's results. Based on models
sim ilar to equation (3) and data taken from
periods both before and after W orld W ar II,
these authors, like Fisher, found that interest
rates responded slow ly and incom pletely to
inflation and that long distributed lags of past
inflation rates w ere useful in explaining in
terest rates. Sargent described his results as
3Fisher’s notation has been altered to conform to
that used in this paper. For a discussion of Fisher’s specu
lations about the reasons for these results, see Rutledge
[9, pp. 19-21],

percent
30
25

20
15

lo +

10
15
20

Federal Reserve Bank of Chicago

Box 1
The real rate of interest
Suppose you invest an am ount of m oney,
V, at the rate of interest R p revailing on dateO. If
Pq is the average p rice of goods in your “ norm al
co nsum p tio n b u n d le " on that date, you have
re lin q u is h e d p u rc h a sin g p o w e r o ve r V / P q
goods. A teenager existing e xclusively on Big
M acs priced at $1.25 gives up 80 units of curren t
consum ption w hen he deposits $100 in the local
S&L. He does this, p resum ab ly, in ord er to be
able to consum e an even greater num ber of Big
M acs in the fu tu re . At a rate of interest of 5
p ercent, his investm ent w ill grow to $105 by
next year. This w ill enab le him to consum e
105/P-j units if P-j is the p rice of Big M acs next
year. The nom inal (m oney) return on his invest
ment is the num ber of dollars gained as a p ro
portion of the n um b er of dollars invested
(relin q uish ed ) and in this exam p le is 5 percent.
The real (ham burger) return is the num ber of
Big M acs gained as a p rop ortion of the num ber
of Big M acs invested (re lin q u ish ed ). If prices are
stable, i.e ., P-j = Pq = $1.25, $105 w ill purchase 84

follow s: “ The re su ltsa re sim ila rto Fisher'sin a
couple of ways. Not only do they confirm the
im portance of the distributed lag price exp ec
tations variable, but they im ply a very long lag
in the process of exp ectatio n s form ation
[

10] . "

Eugene Fama [4] follow ed a different
method and obtained d ifferent results. He
used Treasury bill yields and described his
estimates as tests of the efficien cy of the
Treasury bill m arket.4 In efficient markets
observed prices and interest rates correctly
reflect all of the inform ation available to
market participants. This means that (a) ob
served interest rates co rrectly reflect the
m arket’s inflationary or deflationary exp ecta
tions and (b) those expectations are u n b i
ased; i.e ., expectations, on average, are co r
4More generally, Fama described his estimates as
tests of the joint hypotheses of (i) market efficiency and
(ii) the constancy of the real rate. This article is concerned
only with the first hypothesis. For discussions of the latter
hypothesis, see Carlson [1], Fama [4], and Nelson and
Schwert [8],

Big M acs next year and the real rate of return is
4/80 = 5 percent. But if a 20 percent per annum
inflation has o ccurred so that P^ is $1.50, $105
w ill be w orth only 105/1.50 = 70 Big Macs and
the real return w ill be -10/80 = -12.5 percent. He
has gained m oney but lost goods.
In general, this real rate of interest, r, may
be expressed as fo llo w s:
Y(1 + R ) P-i

Y_
P„

Letting p = (P-| - Pq)/P q denote the rate of inf lation,
the above equation may be rew ritten as:

(1 + r) =

I ;
0 + P)

or (1 + R) = (1 + r)(1 + p),

w hich is identical to equation (1).

rect. If m arket exp ectatio n s w e re biased
and/or w ere not reflected in interest rates,
there would exist opportunities to make sub
stantial sums either by borrow ing (if interest
rates are "to o lo w ") in order to buy goods or
by selling goods in order to lend (if interest
rates are “ too h ig h "). To the statistician, runs
of high or low observed real rates are in d i
cated by high autocorrelations, meaning that
real rates are highly correlated with their own
past values. The concept of efficien t m arkets,
w hich is in turn closely related to rational
expectations, is discussed in box 2. A u to
correlation is discussed in box 3.
In general, observed real rates are d iffe r
ent from the expected real rates, r, discussed
above in connection with equations (1) and
(2). This is true for several reasons. Probably
the most im portant cause of d ifferences be
tween expected and realized (observed) real
rates is the inability to forecast inflation, p,
accurately. For exam p le, the nom inal interest
rate at tim e t might be R = .07 and be based on

Econom ic Perspectives

Chart 3. Fisher’s correlations between
the commercial paper rate and
distributed lags of past inflation rates

Length of lag in quarters

an expected inflation rate of p = .03. This
means an expected real rate of approxim ately
r = .07 - .03 = .04. But suppose inflation turns
out to be 13 p ercent instead of 3 percent. The
realized real rate of return to the nominal
investm ent— the actual gain or loss in p ur
chasing p ow er— is approxim ately .07 - .13 =
-.06. Runs of high or low observed real rates
w ould suggest that the m arket was systemati
cally overp red icting or underpredicting infla
tio n . U n d er these circu m stan ces nom inal
rates of interest w ould not, on average, be
accurate predictors of inflation.
Fama's tests of efficien cy w ere lim ited to
observations betw een January 1953 and July
1971. He began his sam ple period with 1953
because before 1953 the Federal Reserve
interfered with m arket efficien cy by support
ing governm ent security prices. He excluded
observations after July 1971 because queues,
side paym ents, and increases in the various
form s of non p rice rationing caused by price
controls prevented stated prices from accu r
ately m easuring the costs of acquiring goods.
Fam a’s tests took two form s. First, he ran
auto co rrelations on realized real rates of

Federal Reserve Bank o f Chicago

Box 2
Rational expectations and efficient markets
The co ncept of rational expectations e x
tends the notion of rational behavior to the
prediction of e co n o m ic events. It assumes that
people m ake use of available inform ation in a
consistent m anner. In p articu lar, predictions of
eco n o m ic events are based upon the p u b lic’s
view s of how the econ o m y w orks. O f course,
those view s must largely be based upon what
has been learned from e xp e rie n ce , including
observations of past events.
Presented this w ay, nothing could be less
o bjectio nable than rational expectations. There
h ard ly, thus far, seem s room for debate. The
debate enters w ith the frequent assum ptions by
advocates of rational expectations that (i) peo
ple have the “ c o rre ct” view of the econom ic
stru ctu re, i.e ., that they “ kno w e ve ryth in g ,”
and (ii) new inform ation is instantly and fully
reflected in econom ic decisions. Com bined, these
assum ptions im ply no transactions costs and
free info rm atio n about all kinds of processes,
sim ple and co m p lex. The result is efficient
markets, in w hich prices and interest rates
alw ays fu lly and co rre ctly reflect all publicly
available inform ation.
By “ know ing e ve ryth in g ,” i.e ., having the
“ c o rre ct” view of the econo m ic structure, advo
cates of efficient m arkets do not mean that
people predict the future with certainty. It is
assum ed, rather, that people know the econ o
m y’s statistical tend en cies. They cannot predict
exactly what the rate of inflatio n , for exam ple,
w ill be. But th eir pred ictio n s w ill be correct on
average. Predictions w ill not be biased in the
sense of being consistently high or low.

interest. Even in efficient m arkets, p red ic
tions w ill almost always be w rong. But they
will not be biased in the sense of being co n
sistently too high or too low. An extrem e
exam ple of an inefficien t market is the period
from May 1942 to July 1947, when the Federal
Reserve pegged the discount rate on threemonth bills at 0.375 percent. During this
period the consum er and w holesale price
indices rose at average annual rates of 6.2
percent and 7.9 percent, respectively. M onthly
changes in the CPI and W P I, at annual rates,

Box 3
Autocorrelation
Suppose xt is the sales of a com p any in
period t. The au to co rrelation s of this tim e series
are the co rrelations of x w ith its own past values.
For exam ple, the first-order au to co rrelatio n , p ,
of x is the co rre la tio n betw een x{ and xt
If the
co m p any’s sales increase by some constant
am ount c so that xt = x{ ^ + c , then p = 1. In this
case, xt and x{ -j are p erfectly c o rre la te d ; one
co nsequence of this relation is that x{ may be
predicted with certainty if we kno w x , . , . O n the
other hand, if x varies in a co m p letely random
fashion such that a kno w ledge of x ^ conveys
no inform ation about xt, then p =0. Tim e series
that are subject to sm ooth cyclical fluctuations
have highly positive auto co rrelations. Those
w hich rapidly change directio n have highly
negative au to co rrelatio n s. M ost A m erican eco
nom ic tim e series, inclu d in g interest rates and
inflation, belong to the form er category.

exceeded 0.375 percent 40 and 42 tim es,
respectively, during these 62 m onths. That is,
realized real rates of interest w ere predom i
nantly negative and, in ad d ition, w ere highly
autocorrelated.
Using the CPI and Treasury bill rates,
Fama fo u n d , as exp ected , very differen t re
sults for the 1953-71 period. The first-order
autocorrelation coefficients of one-, two-,
and three-m onth real returns on one-, two-,
and three-m onth bills w ere .09, .15, and .00,
respectively. Because these autocorrelations
are “ close to z e ro ,” Fama interpreted his
results as consistent with the hypothesis that
the Treasury bill m arket is efficient.
The second series of tests perform ed by
Fama involved estimates of regression equa
tions sim ilar to the fo llo w in g :5
(5)

pt = -r + Rt + et.

5Fama actually used the rate of change in the pur
chasing power of money, A t, which is approximately
equal to -pt> in his regressions. But his results are fully
consistent with regressions of the form shown in equa
tion (5), which has been used for ease of comparison with
the work of Fisher and others.

This is sim ilar to Fish er’s equation (3)
except that (i) the actual rate of inflation, pt, is
used instead of a weighted average of past
inflation rates, p nt, and (ii) the positions of
inflation and Rt in the equation have been
reversed. The nom inal rate of interest is now
the explanatory variable instead of the d e
pendent variable. As in equation (3), et is a
random error term with mean zero. Equation
(5) asserts that, given the assumed constant
real rate, r, the m arket's expectation of the
rate of inflation during the period beginning
on date t, pt, is fu lly reflected in the nom inal
rate of interest, Rt, observed on that date.
Fama reported regressions for the period
1953-71 on one- to three-m onth bill yields. In
every case the co efficien t of Rt did not differ
significantly from unity, as suggested by equa
tion (5). His correlation co efficients (between
pt and Rt) w ere statistically significant and
ranged from .54 to .70. Fama also interpreted
these results as consistent w ith the hypothesis
that the Treasury bill market is efficient.
Earlier w riters had observed that interest
rates responded slow ly to inflatio n , i.e ., that
Rt did not fu lly reflect expected pt . This sug
gests, if sim ilar relations prevailed in the
Treasury bill m arket during 1953-71, that the
results obtained by means of equation (5)
might be im proved by adding past inflation
rates as explanatory variables. Fama estimated
regressions sim ilar to (6), w hich he rep re
sented as tests of this hypothesis:
(6)

pt = -r + R t + w-j pM + et.

But the addition of pt_-j failed to im prove
the correlations significantly and the esti
mates of the co efficien t (w-j) of pt_-| w ere
statistically insignificant, leading Fama to claim
these regressions as fu rth er eviden ce of the
efficien cy of the Treasury bill m arket. He dis
missed the results of Fisher and others that
suggested market inefficien cy as probably
having been caused by poor price data.
Back to Fisher
Fama's paper elicited critical com m ents
by w riters w ho com bined his approach with

Econom ic Perspectives

Fish er’s. Douglas Joines [7] and Charles N el
son and W illiam Schw ert [8] pointed out that
regression (6) could not fairly be com pared
with Fisher’s results, w hich depended on
many— not on e— past rates of inflation. Using
Fam a’s data, they estimated regressions of the
form :

Table 1
Inflation and real and nominal rates of interest
A*
•
Four- to six-month prime commercial paper
and the wholesale price index
Standard deviations

(7)

p, = r + b R , + w 1p ,_1 + w 2pt _2 + . • .

+ w nPt-n + et
and found that past rates of inflation co n
tained significant inform ation about future
inflation in addition to that reflected in Rt>
Fu rth erm o re, their estimates of the co effi
cient (b) of Rt w ere significantly different from
unity. A p p aren tly, during 1953-71 as during
1890-1927, interest rates responded slowly
and incom pletely to inflation.
Variations in inflation and interest rates
during the Fisher and Fama periods of obser
vation are shown in chart 1. The chart shows
the rate of change in the wholesale price
index and real and nom inal returns on fourto six-m onth prim e com m ercial paper begin
ning in June 1894, w hen four- to six-m onth
prim e com m ercial paper rates w ere first re
ported on a regular basis. O bservations are at
five-m onth intervals expressed in p ercent
ages at annual rates. O ne of the most striking
characteristics of this chart is the stability of
inflation in Fam a’s p eriod, 1953-71, com pared
with the very large fluctuations before 1953
and after 1971. A p p aren tly, Fama’s sam ple is
not typical of A m erican exp erien ce. This co n
clusion is supported by chart 2, w hich shows
the rate of change in the consum er price
index and real and nom inal returns on threemonth Treasury b ills, beginning with the reg
ular reporting of bill yields in February 1930.
O bservations are at three-m onth intervals
expressed in percentages at annual rates.
Now let’s apply Fam a’s test of market
efficien cy to the data shown in the charts. The
co lum ns headed p in table 1 list the firstorder auto co rrelations of observed real rates
during our co m plete sam ple periods and
selected su bperiods. W e have separated the

Federal Reserve Bank o f Chicago

Time period

6/94 - 4/80

.317

13.79

2.65

16.31

- 6/29
- 10/52
- 2/71
- 4/80

.264
.522
.226
-.078

17.82
13.45
2.10
7.32

1.09
1.10
1.89
3.41

22.98
12.28
2.23
5.88

7/71 - 1/74
6/74 - 4/80

.038
-.555

8.83
6.78

2.42
3.69

7.30
5.10

6/94
11/29
3/53
7/71

B
Three-month Treasury bills and the consumer price index
Standard deviations
P

2/30- 5/80

.569

6.66

2.80

5.66

2/30 - 11/52
2/53 - 5/71
8/71 - 5/80

.570
.178
.270

8.78
2.04
3.80

.70
1.68
2.50

8.07
1.40
1.97

8/71 - 2/74
5/74- 5/80

.259
.279

3.88
3.59

1.95
2.54

2.47
1.73

Time period

p is the first-order autocorrelation of r.
Standard deviations are in percentages at annual rates.

post-Fama period into observations falling
w ithin the period of price controls, August
1971 to April 1974, and those occurring after
price controls w ere abandoned. The p rin ci
pal results shown in the table may besum m arized as fo llow s:
• The first-o rd er auto co rrelatio n s are
high and significant for both of the full sam
ple periods (1894-1980 in table 1A and 1930-80
in table 1B) and for the subperiods dominated
by the Great Depression (with runs of high
real rates) and W orld W ar II (with runs of
negative real rates).

• The 1974-80 subperiod yielded a posi
tive autocorrelation in part B of th etab le but a
negative auto co rrelation in part A. This may
be due to the freq u en t acceleratio ns and
decelerations of inflation during this period.
Perhaps the five-m onth observational period
used in A allow s tim e fo r reversals in p, and
therefo re a negative serial correlation of r,
not accounted for by the three-m onth period
used in B. W e should not put much stock in
these results, h o w e ver, due to the short
period of observation.
• Perhaps surp risin g ly, in view of the d if
ferent results that have been associated with
these subperiods, the first-order a uto co rrela
tion of r during 1894-1929, w hich is largely
co incid ent with the period of Fisher's analy
sis, is only slightly greater than that for 195371, the period of Fam a’s analysis.6 M arkets
did rem arkably w ell in forecasting the large
fluctuations in inflation during the earlier
period.
• N otice, ho w ever, that the standard
6Note that the first-order autocorrelation for 1953-71
(.178) reported in table 1B is higher than the 0.00 reported
by Fama. This may be due to the use in the present study
of yields that are monthly averages of daily figures. Fama
used yields on the first business day of each month. Since
price indices are compiled from data that are collected
throughout the month, and are therefore monthly aver
ages of a sort, it was felt that comparability between
interest rates and inflation required the former also to be
expressed in terms of monthly averages.

deviation of R during 1894-1929 was much less
than the standard deviation of p. This co n
trasts with the 1953-71 p erio d, in w hich the
volatility of R was only slightly less than that of
p. But this was due less to the greater respon
siveness of R during the later period than to
the sm aller volatility of p.
Conclusions
It should be stressed that much work
rem ains to be done in this area and that none
of the results presented in this paper—whether
Fisher's, Fama's, or those in table 1— have ju s
tified any firm co nclusio ns about the p ro
cesses that determ ine observed relations b e
tween inflation and real and nom inal rates of
interest. About all that can be said on the basis
of the available data is that, during most p eri
ods (excepting especially 1929-52), the T rea
sury bill and com m ercial paper markets have
not appeared to be highly in e fficien t. A u to
correlations in real rates are not usually very
high. Yet nom inal interest rates persistently
fail to respond fu lly to inflation w hen in fla
tion is vo latile. This was true before 1953 and
after 1971. A p parently, like other reasonably
effective but im perfect processes, the short
term securities markets perform w ell if not
asked to do too m uch. They can keep up with
inflation if the pace is not too fast or too
variable.

References
1. John A. Carlson, “ Short-Term Interest Rates as Predictors of
Inflation: Co m m ent,” Am erican Econom ic R eview , vol.
67 (June 1977), pp. 469-75.
2. W illiam Douglass, A D iscourse C on cern in g the C u rrencies of
the British Plantations in Am erica (S. Kneeland and T.
G reen, 1740). (Reprinted in 1897 for the Am erican Eco
nomic Association by M acm illan, New York).
3. C h ilperic Fdwards, The Hamm urabi C o de (Watts and Co m
pany, 1921).
4. Fugene F. Fama, “ Short-Term Interest Rates as Predictors of
Inflation,” Am erican Econom ic R eview , vol. 65 (June
1975), pp. 269-82.

8. Charles R. Nelson and G. W illiam Schwert, “ Short-Term
Interest Rates as Predictors of Inflation: On Testing the
Hypothesis that the Real Rate of Interest is Constant,”
Am erican Econom ic Review , vol. 67 (June 1977), pp.
478-86.
9. John Rutledge, A M onetarist M o d e l o f Inflationary Expecta
tions (D .C. Heath, 1974).
10. Thomas J. Sargent, “ Com m odity Price Expectations and the
Interest Rate,” Q uarterly Journal o f Econom ics, vol. 83
(February 1969), pp. 127-40.

6. W illiam F. G ibson, “ Price-Expectations Effects on Interest
Rates,” Journal o f Finance, vol. 25 (M arch 1970), pp. 19-34.

11. Henry Thornton, “ Speech in the House of Com m ons on the
Report of the Bullion Com m ittee,” May 7,1811. Reprinted
in Appendix III to Thornton’s An Enquiry into the Nature
and Effects o f the Paper Credit o f Great Britain. Reprinted
in 1939 by George A llen and U n w in , Fondon, with an
introduction by F.A. Hayek.

7. Douglas Joines, “ Short-Term Interest Rates as Predictors of
Inflation: Co m m ent,” Am erican Econom ic Review , vol.
67 (June 1977), pp. 476-77.

12. W illiam P. Yohe and Denis S. Karnosky, “ Interest Rates and
Price Level Changes,” Review , Federal Reserve Bank of St.
Louis (Decem ber 1969), pp. 19-36.

5. Irving Fisher, The Theory o f Interest (M acm illan, 1930).

Econom ic Perspectives

Federal tax and spending reform
W. Step h en Sm ith
The eco n o m ic legacy of the 1970s has been
the co ntinuous upward spiral of inflation, un
em p loym ent, and interest rates. The federal
governm ent's inability todeal effectively with
these problem s has placed eco nom ic reform
at the top of the nation's agenda for the 1980s.
In an effort to deal with these problem s,
the Congress has considered a w ide variety of
eco n o m ic reform proposals in recent years.
Several of these proposals have a com m on
th em e: the role of the federal governm ent in
the eco nom y should be lim ited and/or re
duced. Four of th em — three proposed co n
stitutional am endm ents and one tax reform
b ill— have received significant attention from
prom inent politicians and the press:
• The balanced budget am endm ent, which
w ould req u ire that federal expenditures
not exceed federal revenues.
• The spending cap am endm ent, w hich
would lim it federal expenditures to some
specified portion of GN P.
• Th e re ve n u e cap a m en d m en t, w h ich
w ould lim it federal revenues to some
specified portion of GN P.
• The Kem p-Roth b ill, w hich would reduce
personal incom e taxes 30 percent over
the next three years.
This article presents an overview of these
proposals and discusses their im plications for
the nation's eco nom ic future.
The real sources of economic pain
The first rum blings of the taxpayers' revolt
w ere heard in the late 1960s, as the “ go-go"
years drew to a close and, partly as a result of
the d eficit fin an cin g of the Vietnam W ar,
inflation began to heat up. The focus of atten

Federal Reserve Bank of Chicago

tion at the tim e was reform of the local prop
erty tax, but few of the organized initiatives
met with success. H o w ever, the severity of
inflation in the late 1970s undoubtedly added
strength to the psychology of the taxpayers'
revolt m ovem ent, w hich drew widespread
attention in 1978 with the passage in C alifo r
nia of Proposition 13. As a result of the
national attention that was focused on Propo
sition 13 and its p roponents, a num ber of
other states considered and im plem ented fis
cal reform s.1
In less than a decade, the taxpayers'
revolt m ovem ent has been transformed from
a sm all, ineffective lobby to a dom inant force
on the A m erican political scene. What factors
w ere prim arily responsible for this change?
Econom ist Lester Thurow has argued that
popular support for p olicies that would bring
about a dram atic shift in the distribution of
eco nom ic resources arises only from intense
econom ic p ain .2
An obvious source of such pain was the
apparently d eclining standard of living in
A m erica. Yet, in the six years (1972-78) of eco
nom ic tu rb u len ce that gave rise to the w id e
spread popularity of tax reform , real per cap
ita disposable personal incom e rose just under
16 p ercen t, almost as much as during the “ gogo” years 1966-72. (See table 1.) To be sure,
real hourly earnings in the private nonagricultural sector w ere slightly low er in 1978
than they had been in 1972, but the decline
was m ore than offset by a sharp rise in the
proportion of the total population that is
’At least 15 states have adopted fiscal limitations
since the passage of Proposition 13. The recent recession,
however, has apparently reversed this trend, as taxlimitation proposals were defeated in six states in 1980.
For an argument that Proposition 13 was not the result of
a basic shift in taxpayer attitudes, see James M. Buchanan,
“The Potential for Taxpayer Revolt in American Demo
cracy,” Social Science Q uarterly, vol. 59 (March 1979), p.
691.
2Lester Thurow, “The Real Sources of Economic
Pain,” Wall Street Journal, July 6,1978.

Table 1
Growth in real per capita disposable income
Year

Real per capita
disposable incom e

Percent
change

(1972 dollars)
1966
1968
1970
1972
1974
1976
1978
#
o

CO
5
r-

3,290
3,493
3,668
3,880
4,050
4,216
4,487
4,567

6.2
5.0
5.8
4.4
4.1
6.4
1 .8

•Estimated.
SOURCE: Econom ic Report o f the President, Jan
uary 1981.

em ployed. H ow ever, to many households the
loss of leisure may have constituted a decline
in their standard of living.
In any case, the 16 percent rise in real per
capita disposable incom e might conceal large
disparities between groups w ithin the popu
lation; it might reflect substantial real gains
made by some w h ile many others suffered
real econom ic losses. "N o t so ,” Thurow co n
cludes. " In the six years from 1972 to 1978
there have been no significant shifts in the
distribution of incom e. The gap between rich
and poor, black and w h ite, male and fem ale
has rem ained unch an g ed .” 3 Since relative
incom es have not changed significantly, all
groups have benefited from the real eco
nom ic growth. O f course, it is still possible
that there w ere large d ifferences between
individuals within each of these broad groups.
A nother freq u en tly m entioned source of
eco nom ic pain is that the governm ent has
taken an ever-increasing share of the average
citiz e n ’s earnings. Again, the eco nom ic evi
dence does not support the popular assum p
tion. W h ile the ratio of total tax revenue at all
levels of governm ent to personal incom e
increased from 17.7 percent in 1950 to 30.1
percent in 1980, most of this increase took
Jlbid.

place during the 1950s and 1960s.4 (See table
2.) G o vernm ent exp enditures exh ib it almost
the same growth pattern. Table 3 shows that
w h ile the ratio of total exp enditures at all
levels of governm ent to G N P has risen from
23 percent in 1950 to 33 p ercent in 1980,
virtu ally all of the increase took place during
the 1950s and 1960s. Th ere has been little
growth in the ratio of governm ent exp e n d i
tures to GN P during the 1970s.
Still another possibility has been sug
gested by Lester T h u ro w . He argues that the
primary source of pain is the so-called "m oney
illu sio n ” created by the enorm ous gap be
tween the growth of real and m oney incom es
that has resulted from inflatio n . W h ile real
incom e grew 16 p ercent from 1972 to 1978,
m oney incom e grew 72 percent. People think
what life w ould be like if their incom es had
risen by 72 percent w ith no inflatio n . Some
people may even co nvin ce them selves that
their real standard of living has fa lle n .5
Most people fo rget, h o w ever, that in fla
tion raises incom e as w ell as prices. Every
price increase is a reduction in the real living
standard of some purchaser of a good or ser
vice , but it is also a real incom e increase for
some p rovider of that good or service. M ore
im portantly, most people suffering from the
"m o n ey illu sio n ” do not realize that if there
had been no inflation from 1972 to 1978, real
incom es w ould have grown by 16 p ercen t,
not 72 percent.
It is not easy to identify clearcut reasons
for the widespread perception of econom ic
stress. It may have resulted in part from a
4Richard A. Musgrave has argued that this evidence
countersthe widely held belief that inflation has resulted
in an increasing tax burden. See “The Tax Revolt: Causes
and Cure,” Social Science Q uarterly, vol. 59 (March
1979), p. 699.
5
This is clearly not the type of “ money illusion” that
is so familiar in the literature of monetary economics.
There “ money illusion” refers to the temporary failure of
people to realize that their real incomes have not kept
pace with their nominal wages. In Thurow’s use of the
term it is precisely the public’s awareness, perhaps
belated, that their real incomes lag behind their nominal
incomes that is the source of pain. The illusion consists in
their belief that somehow their real incomes could be
made to rise as rapidly as their nominal incomes.

Econom ic Perspectives

Table 2
Tax revenue as a percentage
of personal income
(all levels of government)
1950
Incom e tax
C o rp oratio n tax
Payroll tax
Property tax
O ther
Total

1960

1970

1980*

6.6
3.1
1.5
2.5
4.0

10.5
3.6
2.8
4.2
3.4

12.4
3.3
4.9
4.5
3.9

13.0
3.1
7.4
3.1
3.5

17.7

24.5

29.0

30.1

* Estimated.
SOURCE: U.S. Bureau of the Census, Governm ent
Finance, various years. Econom ic Report o f the President,
January 1981.

“ m oney illu sio n " that confuses nom inal and
real m easures of eco n o m ic p erfo rm ance.
N evertheless, d esp ite evidence that the gov
ernm ent sector did not continue to grow in
the 1970s at the rapid rates of the 1950s and
1960s, many people feel that reducing the
role of governm ent in the econom y provides
a prescription for relief from the econom ic
problem s facing the nation in the 1980s.
Balanced budget amendment
O f the proposed reform s, the balanced
budget am endm ent is probably the most
popular with the general electorate. In a
spring 1979 C BS-N ew York Tim es p oll, 73 perTable 3
Public expenditures as a percent of GNP
1950
Federal
State and local
Total

1960

1970

1980*

13.4
7.9
21.3

17.1
9.8
26.9

18.2
13.4
31.6

19.5
13.5
33.0

♦Estimated.
NOTE: Federal grants-in-aid to state and local gov
ernments are included at the level of the recipient.
SOURCE: Econom ic Report o f the President, Jan
uary 1981.

Federal Reserve Bank of Chicago

cent of the respondents favored a constitu
tional am endm ent to requ ire the Congress to
balance the budget every year. Legislators in
30 of the necessary 34 states have approved
resolutions asking the Congress to call a con
stitutional convention to consider such an
am endm ent. Th ree other states have adopted
resolutions that urge the Congress to adopt a
balanced budget am endm ent, but do not call
for a co nven tio n . The convention m ovem ent,
h o w ever, has met with significant opposition
from several key political figures who fear a
“ run aw ay" co nventio n that w ould attempt to
adopt am endm ents on other issues such as
busing and abortion.
The balanced budget amendment is some
thing of a m isnom er, because the proposal
w ould bar the federal governm ent from in
curring d eficits, but not from attaining sur
pluses. O f co urse, surpluses have been few
and far betw een in recent years. A more sub
stantive shortcom ing of the am endm ent is
that, even if it achieved the goal of elim inat
ing deficits, it w ould not necessarily limit or
reduce the role of the federal governm ent.
The governm ent could co ntin u e to increase
spending, in absolute term s and in relation to
G N P, as long as it increased tax revenues to
keep the budget balanced.
Aside from its inappropriateness as a
means to ach ieve the goals of some of its
proponents, the balanced budget amendment
might severely im pair the governm ent's abil
ity to in flu en ce the econom y. Prior to the
Depression the governm ent pursued the “ fis
cally resp onsib le" policy of balancing the
federal budget. This “ old-fashioned doctrine,”
according to econom ist Robert J. G o rdon,
“ did co nsid erab le harm to the econom y and
has since been abandoned by all econom ists,
monetarists and nonmonetarists a lik e ."6Why?
D uring a recession G N P declines along with
personal and corporate taxable incom es. If
tax rates and governm ent expenditures re
main constant, and the budget was in balance
just before the recession, the budget w ill now
6Robert J. Gordon, M acroeconom ics (Little, Brown
and Company, 1978), p. 480.

show a d eficit. To rebalance the budget, the
federal governm ent must either raise tax rates
or reduce governm ent expenditures, either
of w hich w ill exacerbate both the recession
and the deficit.
Attem pting to balance the actual budget
during a recession ignores the fact that w hile
the budget affects the eco nom y, the eco n
omy has a feedback effect on the budget.
Although, in p rin cip le, the governm ent could
stim ulate the econom y by raising both e x
penditures and tax rates during a period of
slack private d em and, thereby m aintaining
the budget in balance, the adm inistrative and
political d ifficu lties of d oin g so probably p re
clude such an approach.
The balanced budget am endm ent, in
and of itself, is u n like ly to enhance the
governm ent’s ability to control inflation. A l
though governm ent deficits have some shortrun im pact on d em and, they are not in fla
tionary in the long run unless they are fi
nanced by increases in m onetary growth in an
attempt to hold down interest rates. O ther
things being eq u al, a governm ent deficit
financed by the sale of Treasury securities,
accom panied by rising interest rates and no
increases in m oney su pply, w ould not add to
inflationary pressures. In this context the bal
anced budget am endm ent appears to be n eu
tral in its expected impact on inflation.
Even with such an am endm ent in place,
the Congress and the President would have
many ways of m aintaining expenditures. Offbudget outlays could be increased. The fed
eral governm ent in fiscal 1980 allocated $12
billion to off-budget entities and $19.1 billion
to governm ent-sponsored agencies, roughly
6 percent of the total budget. Loan guaran
tees,an o ther method of avoid ing the budget
ary process, am ounted to $284 b illio n in 1980.
In sum , the available evid en ce suggests
that a balanced budget am endm ent may
create as many problem s as it solves. W h ile it
might, in a nom inal sense, elim inate future
federal deficits, it is not u neq uivocally clear
that this is a desirable goal. Even if it w ere,
there is no assurance the governm ent would
not circum vent the intent of the proposal.

M o reo ve r, the am endm ent w ould take away
an im portant recession-fighting tool of the
federal government and, in fact, might deepen
any future recessions.
Spending cap amendment
This proposed constitutional am endm ent
w ould limit spending by the federal govern
ment to a certain percentage of G N P. The
specific percentage varies with alternative
proposals, but virtually all have fallen into the
18 percent to 21 percent range. The spending
cap am endm ent has been advocated most
strongly by econom ist M ilton Friedm an and
the National Tax Lim itation Co m m ittee. Their
am endm ent includes provisions that would
limit off-budget outlays, allow the spending
limit to be exceeded in national em ergencies,
and protect grants to state and local govern
m ents. It w ould lim it the growth of the fed
eral governm ent’s share of eco nom ic activity,
but is silent on the question of deficits.
By lim iting governm ent spending, the
am endm ent w ould tend to w eaken the gov
ernm ent’s recession-fighting capabilities. This
effect w ould not be as serious as under the
balanced budget am endm ent, h ow ever, since
the governm ent w ould retain the authority to
cut taxes during recessionary periods. In the
long run the am endm ent might be helpful in
fighting inflation caused by m onetization of
deficits because it w ould hold the growth of
governm ent expenditures below that of nom
inal GNP. O ver the past decade federal exp en
ditures grew at an annual rate of 10.5 p ercent,
w ell above the 9.5 percent growth rate of
GNP.
The am endm ent has other disadvantages.
First, since certain expenditures rise autom a
tically (for exam ple, unem ploym ent insurance
benefits during a recession), other exp en d i
tures w ould presum ably have to be reduced.
This w ould create a great deal of uncertainty
with regard to the planning of certain exp en
diture program s. Second, it w ould lim it the
ability of the governm ent to target exp en d i
tures during a recession toward certain hardhit or disadvantaged areas, industries, or indi-

Econom ic Perspectives

viduais since any increased expenditures in
these areas w ould have to be offset by d e
creases elsew here.
Revenue cap amendment
A third proposal, less frequently discuss
ed , is the reven u e cap am endm ent, w hich
w ould lim it fed eral revenues to a certain p er
centage of G N P. This am endm ent w ould not
elim inate deficits as it controls only govern
m ent reven u es, not governm ent spending.
Although it w ould w eaken the governm ent’s
ability to fight recession to a lesser extent than
the balanced budget am endm ent, the re
ven u e cap am endm ent w ould som ewhat in
hibit the governm ent's range of inflatio n
fighting strategies. O n e co nsequence of our
tax structure is that federal revenues tend to
grow faster than the general econom y during
in f la t io n a r y p e r io d s . T h e a m e n d m e n t
w ould force the governm ent to cut tax rates
to hold dow n tax revenues during inflatio n
ary tim es. As a result, fiscal policy would be of
little use in attenuating inflationary trends.
Im plem entation of the proposal would
be relatively easy, unless the cap were set at a
m uch low er level than present tax co lle c
tions. As noted e a rlie r, federal taxes did not
rise dram atically during the 1970s; had the
am endm ent been adopted in 1970, with the
cap set at the then-p revailing level, it would
not have been exceeded to date. W hile the
econom y and federal spending grew at an
nual rates of roughly 9.5 percent and 10.5
p ercen t, resp ectively, over the past decade,
federal revenues grew at roughly 8.5 percent.
Th u s, unless the cap w ere low ered to a pre1970 share of the G N P , the revenue cap
am endm ent is not likely to reduce sig nifi
cantly the g overnm ent’s share of econom ic
activity. O n the o ther hand, it should prevent
that share from growing significantly in the
future.
Kemp-Roth bill
A fourth reform proposal, and the one
w hich has received the most political atten

Federal Reserve Rank of Chicago

tio n , is the Kem p-Roth b ill, w hich calls for a 30
percent reduction in federal incom e taxes
over the next three years. Proponents of the
bill have argued that reducing personal in
com e taxes w ill increase incentives to w ork
and w ill expand the tax base so that, even at
the low er rates, no tax revenues are lost. The
theory behind this argum ent is sum m arized
by the Laffer C u rv e , named for its originator,
econom ist A rth ur Laffer (see box).
Prior tax cuts. M any proponents of the
bill have argued that prior tax cuts, particu
larly the Kenn ed y tax cu t, provide em pirical
confirm ation of the Laffer C u rve hypothesis.
W a lte r H e lle r , th e ke y a rc h ite c t of the
Kennedy tax cu t, has responded that the
supply-siders’ argum ents are flaw ed. Taxes
w ere cut by about $12 b illio n ($10 billion in d i
vidual and $2 b illion corporate) in 1962-64;
H eller notes that “ the record is crystal clear
that it was its stim ulus to d em and . . . that
powered the 1964-65 expansion and restored
a good part of the initial revenue loss.’’7
U nem ploym ent was reduced from 5.6 p er
cent in January 1964 to 4.5 percent in July
1965, and utilization rates in m anufacturing
increased, draw ing on existing excess capa
city. Since inflation rose only slightly over the
same perio d, from 1.4 percent to 1.6 percent,
most of the increase in demand was co n
verted into m ore output, not higher prices.
H o w ever, the prem ise that any change in
eco nom ic activity after a tax cut is a result of
the tax cut ignores the m ultiple causal rela
tions in a co m plex eco nom y. O th er fiscal fac
tors playing a critical role in the 1963-68
exp ansion, for exam p le, w ere the huge (over)
stim ulus of Vietnam exp en d itu res, the four
increases in payroll tax rates and base in those
years, and the $6 billion of revenues from the
1966 Tax Act. M o reo ve r, m onetary policy also
played some role in the expansion. After
slow ing in 1962, m oney supply growth accel
erated in 1963 and 1964. Sim ilar difficulties in
isolating the effects of tax cuts from other
influences plague the other historical exam7
Walter W. Heller, "The Kemp-Roth-Laffer Free
Lunch,” Wall Street Journal, July 12,1978.

pies, the M ellon tax cuts in the 1920s and the
West Germ an cuts in 1948, w hich the KempRoth proponents use to support their theory.
E co n o m ic e v id e n ce . The econom ics pro
fession has been studying questions related
to the Laffer hypothesis for several years.
There is little eco n om ic evid en ce, how ever,
to support the co nclusion that current levels
of tax rates create disincen tives to w o rk and
save. Studies of w o rk er response to changes
in take-hom e pay have yielded ambiguous
results. Some people w ill w o rk harder if a tax
cut or some other change makes each hour of
w ork worth m o re; others choose to take
additional tim e off and enjoy m ore leisure
w hile earning the same incom e.
After review ing the available evid ence,
the Congressional Budget O ffice concluded
that hours w orked w ould increase if after-tax
real wages rose, largely because of the impact
of m arried wom en entering the labor m arket.
The net effect, h o w e ver, w ould be sm all—
perhaps a 1 p ercent to 3 p ercent increase in
the labor supply as a result of a 10 percent rise
in disposable in co m e.8 This estimate falls
short of the m inim um 10 percent increase in
the labor supply w h ich w ould be necessary
for the Kem p-Roth cuts to be self-financing .9
The effect of changes in the after-tax rate
of return on savings is also an em p irical q ues
tion, and available evid en ce is also am bigu
ous.10*Some people w ill save m ore if they earn
a higher rate of retu rn ; others w ill save less
and m aintain a constant level of assets. M any
econom ists have long accepted what has
becom e know n as D enison's Law, that the
saving rate is virtu ally constant and unaf
fected by changes in the tax structure or the

The Laffer Curve
Laffer argues that taxes create a “ w ed g e”
betw een salary and take-ho m e pay and be
tw een pre-tax and after-tax investm ent p ro
fits. As the tax rate rises, people begin shift
ing out of p ro d uctive activities (w hich are
taxed) into less p ro d u ctive, freq u e n tly leis
u re, activities (w hich are not taxed) and tax
revenu e drops. If the governm ent w ere to
tax 100 percent of all earnings, Laffer argues,
no one w ould w ork and there w ould be no
revenue from taxes.
D u e, in part, to its in tu itive ap p eal, the
Laffer C u rve has enjo yed a m odicum of suc
cess in po litical circle s. M ost econom ists,
h o w e ve r, have argued that the th eo ry does
not necessarily support the co nclusio n that
tax cuts w ill be self-fin an cin g . Th e true shape
of the Laffer C u rv e is an e m p irical q uestio n.
Th e re is little e vid e n ce available to show that
the curve ever bends backw ards, m uch less
that it is sym m etrical. M o re o ve r, there is v ir
tually no eviden ce w hich dem onstrates that
o u r present tax structu re is an yw h ere near
the backw ard bending portion of the cu rve.

tax revenues (dollars)
Congressional Budget Office, An Analysis o f the
Roth-Kem p Tax Cut Proposal (Government Printing
Office, 1978), pp. 14-16.
9
This conclusion is based on the liberal assumptions
that actual output is currently 4 to 5 percent below poten
tial production and that capital-output and labor-output
ratios are constant. Ibid., pp. 8-9.
10Richard A. Musgrave and Peggy B. Musgrave, Pub
lic Finance in Theory and Practice (McGraw-Hill Book
Company, 1973), p. 478.

real after-tax rate of return on cap ital.1 Pro
1
ponents of Kem p-Roth respond with the
recent findings of Stanford's M ichael Boskin
that the total elasticity of private saving with
"Edward F. Denison, “ A Note on Private Saving,”
Review o f Econom ics and Statistics, vol. 40 (August
1958), pp. 261-7.

Econom ic Perspectives

respect to incom e is 0.3 to 0 .4.1 The m eth
2
odology of the study, how ever, has been
strongly c ritic iz e d .1 M o reo ve r, even if Bos3
k in ’s findings are accepted, the resulting
increase in saving falls far short of the m in
im um 10 percent increase necessary for the
Kem p-Roth cuts to be self-financing.1
4
E co n o m etric studies. Laffer and his sup
porters criticized the m ajor m acroeconom ic
forecasting m odels for excluding the eco
nom ic responses w hich they describe. Argu
ing that no present model could accurately
capture the eco n om ic impact of the KempRoth proposal, Laffer constructed his own
model that dem onstrates the revenue feed
back effects of his cu rve. The report des
cribing the m odel has been quoted as ac
know ledging that “ the task of quantifying the
theoretical Laffer C u rve is unach ievab le.”
M o reo ve r, the only group that responds in
accord with Laffer’s theory is the working
poor. For all other groups, the model suggests
that the governm ent should increase tax rates
to increase reven u e.1
5
O th er m odels, sp ecifically reform ulated
to inclu d e the Laffer hypothesis, have co n
cluded that the revenue feedback effects
anticipated by Laffer w ould not occu r. C o n
gressional co m m ittees co m m issioned two
consulting firm s, Data Resources, Inc. and
Evans Econom ics, to build models to test the
Laffer theory. The m odels, although quite d if
ferent in co nstru ctio n , reached sim ilar co n
clu sio n s: im plem entation of a 30 percent
across-the-board cut in tax rates, w ithout sig
12Michael J. Boskin, “Taxation, Savings, and the Rate
of Interest,” Journal o f Political Econom y, vol. 86
(March/April, 1978), pp. S3-S27.
1 Boskin defines personal saving to include consu3
merdurables; thus, increased saving does not necessarily
mean that more funds are available for investment. His
omission of the inflation rate from the estimating equa
tion and the particular time period studied may have
strongly influenced his results. Finally, the presence of
substantial serial correlation may affect the statistical sig
nificance of his findings. See Congressional Budget
Office, p. 18.
1 Congressional Budget Office, p. 9.
4
1 “ The Impact of a Reagan-Style Tax Cut,” Business
5
W eek (June 9, 1980), pp. 90, 95.

Federal Reserve Bank o f Chicago

nificant exp en ditu re reductions, would add
between $85 billion and $135 billion to the
annual budget deficit by 1985 and would add
at least 2 percentage points to the inflation
rate.1
6
W h ile Kem p-Roth may have more p oliti
cal support than any of the proposed consti
tutional am endm ents, it also has the most
potential for eco n om ic harm . W hile it will
unquestionably reduce tax rates, there is little
evidence to support the conclusion that it will
pay for itself in the short run. In fa c, nost of
the eco n om etric m odels, including those that
make Laffer C u rve assum ptions, forecast that
the bill w ill sim ply produce larger deficits and
increased inflation unless accom panied by
significant spending cuts.
Summary
The Congress has considered a variety of
proposals for eco n o m ic reform over the past
few years, several of w h ich seek to limit
and /o r reduce the role of the federal govern
ment in the eco nom y. O f the four plans ana
lyzed here, the spending cap am endm ent
appears to be the one best-suited to achieve
these ends. H o w ever, econom ic evidence
suggests that reducing and/or lim iting the
federal g o vern m en t’s role may not elim inate
the true sources of eco n om ic pain. Sim ilarly,
available evid en ce casts some doubt on the
reasonableness of the incom e and revenue
effects predicted by proponents of the KempRoth bill. But a real test must await the tax
cut's actual adoption and im plem entation. Any
determ ination as to w hich of the four pro
posals is “ best” is ultim ately a value judge
ment and w ill vary w ith the social, political,
and eco nom ic predilections of each individ
ual. The purpose of this article has been
sim ply to synthesize some of the econom ic
in fo rm a tio n n e ce ssa ry to d e te rm in e the
tradeoffs.

16lbid. See also Stephen Brooks and Otto Eckstein,
"Economic Analysis of the Kemp-Roth Proposal,” Data
Resources U.S. Review (August 1978), pp. 1.12-1.15.

The discount rate—will it float?
Paul L. Kasriel
Since the Federal Reserve adopted its new
reserves-oriented operating p ro ced u re on
O cto b er 6, 1979, the role of discount policy
has com e under greater scrutiny both inside
and outside the System. O f special interest
has been the spread betw een the federal
funds rate and the d iscount rate. Th ere is a
strong positive association betw een the fed
e ra l fu n d s r a te - d is c o u n t ra te s p re a d a n d the
am ount of reserve adjustm ent borrow ing
from the Federal R eserve.1
Some analysts have criticized the Fed for
allowing this spread to w iden as m uch as it has
on certain occasions. They argue that the
w ide spread induces depository institutions
(hereafter referred to as banks) to borrow
reserves from the Fed at what might be co nsi
dered a subsidy rate. In their view banks'
increased incen tive to borrow from the dis
count w ind ow w hen the discount rate is low
relative to m oney-m arket rates dim inishes
the Fed's control over total reserves and, thus,
the m oney supply. In ord er to keep the
spread between m oney-m arket rates and the
discount rate sm aller and m ore stable, it has
been suggested that the discount rate be
allowed to float with a m oney-m arket rate
such as the federal funds rate. This article
explains the discount m echanism and dis
cusses the im plications of a floating discount
rate w ithin the cu rren t fram ew ork of reserve
a c c o u n tin g and o p en m a rk e t o p e ra tin g
p ro ced u re— nam ely, lagged reserve account
ing and nonborrow ed reserve targeting.
The discount mechanism
U n d e r th e system of lagged reserve
accounting adopted in 1968, the average level
of reserves that a bank is req uired to hold as a
deposit at the Fed a n d /o r in vault cash in a
Reserve adjustment borrowing excludes seasonal
and special borrowing.

As reserve adjustment borrowing
from the Fed rises . . .
billion dollars

. . . the spread between the federal
funds rate and the discount rate
increases
percentage points

1979

1980

1981

given reserve settlem ent w eek is determ ined
by the reserve requirem ent ratios (set by the
Fed) applied to the average level of the bank's
reservable liabilities two w eeks prior. Thus,
changes in a bank's deposits and other reser
vable lia b ilitie sd u rin g th e c u rre n t reservesettlem ent w eek cannot change its required
reserves for this w eek. Upon entering the set
tlem ent w eek, each bank knows the average
level of reserves it must hold in order to satisfy
its reserve requirem ents and the Fed knows
what average level of reserves it must supply
so that the banking system can satisfy its
reserve requirem ents.
Reserves can be supplied in two ways—
through Fed open market operations (no n
borrow ed reserves)2 and through discount
w indow lending (borrow ed reserves). Any
shortfall in n onborrow ed reserves com pared
2So-called market factors such as float also provide
nonborrowed reserves. The Fed attempts to offset unde
sired changes in nonborrowed reserves caused by market
factors through open market operations.

Econom ic Perspectives

to req u ired reserves must be made up by
borrow ed reserves.3 U nder the Fed’s new
operating p ro ced u re, open m arket op era
tions are co nd ucted so as to hit a targeted
level of n on b orrow ed reserves on a w eekly
average basis. Since required reserves are
p redeterm ined in any given w eek because of
lagged reserve accou n tin g , the choice of a
w eekly level of n onborrow ed reserves largely
determ ines the w eekly level of borrowed
reserves.4
Although the w eekly am ount of b or
rowed reserves for the banking system is
d eterm in ed o n ce the Fed chooses a n onb or
rowed reserve target, borrow ings by ind ivid
ual banks from the discount w ind ow are not.
An individual bank can obtain reserves in
several alternative ways, including purchas
ing federal fu n d s, selling C D s, or selling a
security from its portfolio. These alternatives
redistribute the existing quantity of reserves
among banks. Th ey do not increase the re
serves of the banking system as a w hole. In
contrast, borrow ing from the Fed increases
both the borrow ing bank's reserves and those
of the banking system.
If a bank could borrow from the Fed as
m uch and as often as it desired at the discount
rate, then the discount rate w ould serve as a
cap to the fed eral funds rate. The fact that the
federal funds rate is usually above the dis
count rate w hen nonb orrow ed reserves are
less than req uired reserves is prim a facie e vi
dence that the discount rate does not m ea
sure the full cost of b orrow ing from the Fed.
The full cost of borrow ing from the Fed, or
3
This abstracts from reserve carryover, the privilege
banks have of carrying over a surplus or deficiency of up
to 2 percent of required reserves into the following
reserve settlement week.
4lf banks' demand for excess reserves (i.e., reserves
in excess of those required) were zero or constant, then
the choice of a weekly level of nonborrowed reserves
completely determines the weekly level of borrowed
reserves. To the degree that banks' demand for excess
reserves varies, then a given weekly level of nonbor
rowed reserves does not completely determine a weekly
level of borrowed reserves. Because excess reserves tend
to be relatively small and stable, the analysis is not mate
rially affected by them and, therefore, it will be assumed
that they are zero.

Federal Reserve Bank of Chicago

the effective discount rate, is the sum of the
quoted discount rate plus the nonpecuniary
costs resulting from discount w indow adm in
istration. Because the Fed tries to lim it the
am ount and duration of borrow ing by indi
vidual banks, by subjecting th eir lending and
investm ent practices to “ su rveillan ce,” and
because banks wish to assure themselves
access to the w in d o w in the future w hen they
may face liq u id ity p roblem s, the n o np ecun
iary costs of borrow ing an additional dollar
rise with the quantity and frequency of bor
row ing by an ind ivid u al bank. These costs
w ould rise even w ith an unchanged level of
borrow ing if the adm inistration of the dis
count w indow w ere to get “ tou gh er.”
To m inim ize its costs, an individual bank
w ill manage its reserve position in such a way
that the effective discount rate on an addi
tional dollar borrow ed from the Fed w ill be
equal to the cost of acquiring reserves from
alternative sources. A tth e m argin, then, there
is no subsidy involved in borrow ing from the
Fed when the effective rather than the quoted
d iscount rate is com pared with the cost of
alternative sources of fu n d s.5 Because bor
*
rowing federal funds is a substitute for bor
row ing at the discount w in d o w , this cost can
be m easured by the federal funds rate. Thus,
the e ffe ctiv e d isco u n t rate tends tow ard
equality with the federal funds rate, and the
spread betw een the federal funds rate and
the quoted discount rate measures the mar
ginal non p ecu n iary cost of borrowing from
the Fed.
If the Fed provides less nonborrow ed
reserves than req u ired , then those banks for
w hich the effective discount rate is higher
than the costs of alternative sources of funds
w ill attem pt to obtain reserves from these
sources, thereb y driving up their interest
rates. Some reserve-deficien t banks w ill be
induced to increase th eir borrowings from
5However, there is a subsidy on average because the
full nonpecuniary costs of borrowing are incurred only
on the last dollar borrowed; on the intramarginal bor
rowing the bank incurs below-market costs. For mone
tary policy purposes, of course, it is only the marginal cost
that is relevant.

the Fed as the alternative cost of funds rises to
the level of th eir effective discount rates.
Interest rates w ill co ntinue to rise until banks
are induced to b orrow enough from the Fed
to meet th eir req uired reserves. This rising
cost of reserves w ill eventually cause banks to
curtail the expansion of their assets and,
hence, slow the growth of the money supply.
It can be seen, th en , that a penalty dis
count rate p olicy— i.e ., a policy w hereby the
Fed always m aintains the quoted discount
rate above the cu rren t federal funds rate— is
theoretically inconsistent with lagged reserve
accounting and nonborrow ed reserve target
ing. The way in w hich the m arket for bank
reserves com es into eq u ilib riu m w hen the
level of nonborrow ed reserves is set below
that of required reserves is for the federal
funds rate to rise to a level above the quoted
discount rate such that individual banks are
induced to b orrow enough reserves from the
Fed to elim in ate the reserve d eficien cy for
the banking system. A penalty discount rate
would prevent the reserves m arket from
reaching eq u ilib riu m because no bank would
be w illing to b orrow from the Fed as long as it
could obtain reserves in the federal funds
m arket at a rate below the discount rate. The
federal funds rate w ould co ntinue to ratchet
upward until the Fed provided additional
nonborrow ed reserves (i.e ., above the tar
geted level) to eliminate the reserve deficiency.6
W ith contem poraneous reserve account
ing where the current week's required reserves
are determ ined by the cu rren t w eek's reservable liabilities, a penalty discount rate w o uld,
in theory, be feasible and would be eq uiva
lent to the Fed closing down the discount
w indow for reserve adjustm ent borrow ing.
As the federal funds rate rose and banks sold
securities to the nonbank p ub lic in ord er to
acquire reserves, reservable liabilities of the
banking system w ould d eclin e and, thus,
reduce the cu rren t w eek's required reserves.
The federal funds rate would continue to rise

until reservable liabilities declined to the
point w here required reserves w ere reduced
to a level equal to nonborrow ed reserves.7 In
*
p ractice, sharp increases in the federal funds
rate might occur so as to induce banks to
make the portfolio adjustm ents necessary to
reduce required reserves to the targeted level
of nonborrow ed (and in this case, total)
reserves in as short a time as a w eek.

alternatively, at some level of rates, banks might bid
so aggressively for deposits as to attract currency out of
circulation, which the banks could then ship to the Fed to
meet their reserve requirements in the current week.

7Under lagged reserve accounting, the rising federal
funds rate would also cause the current week’s reserva
ble liabilities to fall, but this would have no effect on the
current week’s required reserves.

Floating the discount rate
As m entioned at the outset, some ana
lysts have suggested that the quoted discount
rate be allowed to float with a particular
m oney-m arket rate (e.g ., the federal funds
rate) or some com posite index of moneym arket rates in order to keep the spread
b etw een m arket rates and th e d isco u n t
rate more stable. For exam ple, the quoted
disco un t rate in the c u rre n t w eek might
be set at 50 basis points (0.5 percentage
points) above the previous w eek's average
federal funds rate. But it has been seen that
the spread betw een the federal funds rate
and the quoted discount rate in the current
w eek depends critica lly on the am ount of
borrow ing forced on the banking system by
the Fed's choice of a n on b orrow ed reserves
target and the attendant n onp ecuniary costs
of such borrow ing. Floating the discount rate
would have no impact on the stability of the
federal funds rate-discount rate spread.
Floating the discount rate w o uld , how
ever, have im portant im plications for the
behavior of the federal funds rate and other
related interest rates in a fram ew ork of lagged
reserve accounting and nonborrow ed reserve
ta rg e tin g . C o n s id e r th e fo llo w in g tw o
relationships:
(1) (RFFt - RDt) = cBR t + e, c > 0, BRt > 0
(2) R D t = RFFt- l + K,

Econom ic Perspectives

w h ere RFF is the federal funds rate, RD is the
discount rate, c is the co efficient reflecting
the m arginal non p ecu n iary costs of b orro w
ing from the Fed, BR is borrow ed reserves
(dollars), e is an erro r term , K is a constant
(percentage points) and t refers to the tim e
period (e.g ., w eek). The first relationship says
that the spread (in percentage points) between
the cu rren t federal funds rate and current
discount rate is an increasing function of the
am ount of reserves borrow ed by the banking
system from the Fed. The second relationship
is a form ula for floating the discount rate. The
constant K can be assigned positive, negative,
or zero values. Substituting (2) into (1) and
ignoring e yields the follow ing relationship:

the federal funds rate and the discount rate
w ould start to ratchet up again.9
A som ewhat differen t result is possible if
K is negative, i.e ., the cu rren t p erio d’s dis
count rate is less than the previous period's
federal funds rate. If borrow ed reserves are
less than (or equal to) some critical value,
then the federal funds rate need not rise co n
tinuously but could d eclin e (or rem ain co n
stant) from period to period. This critical
value can be obtained from relationship (3a).
These conditions may be stated as:
(4) RFFt -R F F t- i ^

0 as BRt f

— •
c

This can be rearranged as:

The critical valu e, th en , is - K / c (rem em ber, in
this case, K < 0 so - K > 0). If borrow ed re
serves had been above the critical value and,
for some reason, fell b elo w , then the federal
funds rate could d eclin e.

(3a) RFFt - RFFt— = cB R t + K.
1

Conclusion

If K is p ositive, i.e ., the current period's
disco unt rate is set above the previous p eri
od's federal funds rate, then relationship (3a)

Floating the discount rate, then, would
not necessarily keep the federal funds ratediscount rate spread more stable, but because
of its possible upward ratcheting effect on the
federal funds rate, it could tend to produce
q u icker bank portfolio and deposit responses
than w ould be the case under a more co n
stant discount rate policy.
There rem ains the question w hether the
benefits of the m ore rapid deposit responses
resulting from a floating discount rate policy
w ould be greater than the costs of the conse
quent increased interest rate vo latility.1
0

(3) RFFt - RFFt- l - K = cB R t.

im p lie s th a t th e c u r r e n t p e rio d 's fe d e ra l fu n d s

rate w ill always be higher than the previous
p eriod's so long as the banking system is
forced to b orro w from the Fed. This im plica
tion also applies if K is zero. Thus, even
if borrow ing from the Fed w ere d eclining , the
federal funds rate w ould ratchet upward until
banks' deposits and other reservable liab ili
ties slowed enough to cause required reserves
to fall below the Fed's nonborrow ed reserve
path, at w hich point the federal funds rate
w ould fall rapidly toward ze ro .8 The discount
rate, being tied to the federal funds rate,
w ould also p lum m et. As soon as banks w ere
on ce m ore fo rced to borro w from the Fed,

Relationship (1) above applies only when borrowed
reserves are greater than zero. For a detailed discussion
of why the federal funds rate falls rapidly toward zero as
nonborrowed reserves are increased above required
reserves, i.e., borrowed reserves are zero, see Robert D.
Laurent, “ A Critique of the Federal Reserve’s New Oper
ating Procedure,” Staff M em oranda No. 81-4 (Federal
Reserve Bank of Chicago, forthcoming).

Federal Reserve Bank o f Chicago

9
This analysis assumes that the Fed adheres to its
nonborrowed reserves path without any interest rate
constraints being self-imposed. Notice that even with a
constant as opposed to floating discount rate, a nonbor
rowed reserves targeting policy implies a very sharp drop
in the federal funds rate once nonborrowed reserves are
greater than required reserves. However, the constant
discount rate policy does not imply a continuously rising
federal funds rate when nonborrowed reserves are less
than required reserves.
1 For a discussion of the social costs of interest rate
0
volatility, see Paul L. Kasriel, "Interest Rate Volatility in
1980,” Econom ic Perspectives, Federal Reserve Bank of
Chicago, (January/February 1981), pp. 16-17.

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Full text of Economic Perspectives (Federal Reserve Bank of Chicago) : May/June 1981, Volume V, Issue 3

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