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The Formation of Inflation Expectations
DAVID H. RESLER

I HE psychology of inflation is often cited as a
major barrier in the war against inflation. One cur
rently popular view contends that anti-inflation pol
icies must not only attack the causes of inflation but
also lower inflation expectations. In 1971, the Nixon
Administration used this argument to justify the im
position of wage and price controls. More recently,
President Carter’s March 14 economic policy initiative
was intended, in part, to calm financial markets by
signaling that inflation expectations should be
lowered. Similarly, the objective of lowering inflation
expectations has also been used to justify proposed
inflation remedies such as the tax-based incomes
policy (T IP ).1
Concern over inflation expectations has been
motivated primarily by recent developments in mac
roeconomic theory that place the expectations of im
portant economic variables at the forefront of analysis.
For instance, many economists attribute the existence
of the so-called Phillips curve trade-off between in
flation and unemployment to unrealized inflation ex
pectations rather than to inflation per se.2
Although inflation expectations have become
crucial to both theoretical and policy analysis, they
remain extraordinarily difficult to measure. Generally,
1For a discussion and analysis of the TIP program see Nancy
Ammon Jianakoplos, “A Tax-Based Incomes Policy (T IP ):
What’s It All About?” this Review (February 1978), pp. 8-12.
2Milton Friedman, in his 1977 Nobel Laureate address, details
the intellectual evolution of various theories of the inflationunemployment trade-off. See Friedman, “Nobel Lecture: In
flation and Unemployment,” Journal of Political Economy
(June 1977), pp. 451-72.

economists have relied on various distributed lag
models of past inflation rates to estimate inflation
expectations. To a lesser extent, they have employed
data gathered from surveys of economists, such as
those conducted semiannually by Joseph Livingston
of the Philadelphia Inquirer, or from surveys of
households, such as those conducted by the Institute
for Social Research of the University of Michigan.3
Although most studies using these data do so to test
alternative hypotheses about economic activity, other
scholars have been concerned with the actual process
by which price expectations are generated.4
Forecasts of inflation can be modeled in various
ways. One simple approach formulates the inflation
forecast based solely on the history of inflation.
As noted above, variations of such autoregressive
schemes have dominated studies that include
measures of inflation expectations. If independently
determined forecasts of inflation are available, then
one could test whether only the history of infla3See Joseph Livingston, (biannual surveys), Philadelphia Sun
day Bulletin, June and December, 1948-1971 and Philadelphia
Inquirer, June and December, 1972 to the present; and Rich
ard T. Curtin, ed., Surveys of Consumers 1974-75, Contribu
tions to Behavioral Economics (Ann Arbor: Institute for Social
Research, The University of Michigan, 1976).
4Some studies that have focused on this process include James
Pesando, “A Note on the Rationality of the Livingston Price
Expectations,” Journal of Political Economy (August 1975),
pp. 849-58; John A. Carlson, “A Study of Price Forecasts,”
Annals of Economic and Social Measurement (June 1977),
pp. 27-56; Donald J. Mullineaux, “Inflation Expectations and
Money Growth in the United States,” American Economic
Review (March 1980), pp. 149-161; and Edward J. Kane
and Burton G. Malkiel, “Autoregressive and Nonautoregressive
Elements in Cross-Section Forecasts of Inflation,” Econometrica (January 1976), pp. 1-16.

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F E D E R A L R E S E R V E B A N K O F ST . L O U I S

tion is important in explaining those forecasts. Al
ternately, “rational expectations” hypotheses argue
that all currently available information relevant to
the actual inflation process is considered when fore
casts are made. Although such information would not
be confined solely to the history of inflation, the set
of relevant information may be dominated by it.
In this case, again, inflation expectations would be
closely approximated by some autoregressive scheme.
Related to the process that generates inflation
expectations is the mechanism by which revisions in
expectations are determined as new information be
comes available. Knowledge of whether such revisions
are systematically related to recent forecasts is useful
in assessing the impact that inflation expectations
have on economic activity. The simplest hypothesis
is that revisions in forecasts depend on past forecast
errors.5 This approach implicitly assumes that all in
formation relevant to the forecast revision is contained
in the most recent forecast error. As Mincer has noted,
such error-leaming models can be interpreted as a
reduced form of an autoregressive forecasting model.6
If the actual inflation forecasting process is not de
scribed solely by the history of inflation, however,
then exclusive reliance on past forecast errors to
describe expectations revisions would be inappro
priate.
This article investigates the process by which in
flation expectations are formed and the relevance of
error-leaming models for analyzing revisions in these
expectations, using the Livingston survey data. The
extent of error-learning in the revision of inflation
expectations, as well as the process by which these
expectations are formed, offers useful clues about the
efficacy’ of inflation-reducing strategies.

INFLATION EXPECTATIONS AND
FORECAST REVISIONS:
THE LIVINGSTON DATA
Twice each year, Joseph Livingston, a financial re
porter for the Philadelphia Inquirer, requests selected
business, government, and academic economists to
provide forecasts of various measures of economic
activity, including levels of the Consumer Price Index
5David Meiselman pioneered the use of the “error-leaming”
model in his study, The Term Structure of Interest Rates
(Englewood Cliffs: Prentice-Hall, 1962).
®See Jacob Mincer, “Models of Adaptive Forecasting,” in
Economic Forecasts and Expectations, Jacob Mincer, ed. ( New
York: National Bureau of Economic Research, distributed by
Columbia University Press, 1969).

1980

(C P I). John Carlson used Livingston’s data on these
price level forecasts to generate a series on inflation
expectations for the period from 1947 to 1975.7 For
this article, these data have been updated through
1978 using Carlson’s methodology.
Although calculations of inflation expectations
can be derived directly from price level forecasts,
calculations of revisions in these expectations re
quire information about inflation forecasts that were
made over different time horizons. Since the price ex
pectations reported by Livingston are for 6- and 12month horizons, it is easy to calculate a rate of infla
tion expected over the 6-month period beginning
six months hence.8 Specifically, for the succeeding 6month period, the inflation rate implied by the cur
rent 6- (it?) and 12-month (it*) inflation forecasts can
be described as:

The forecast revision, Rt, is then defined as:
(2)

Rt = iX —ft.t-1,
o.t

where the t subscripts identify the moment at which
the expectations (or the implied forward inflation
rate) are formed.

INFLATION EXPECTATIONS AND
FORECAST REVISIONS:
PREVIOUS STUDIES
Pesando and Mullineaux, among others, have used
either the predictions published by Livingston or
those revised by Carlson to estimate equations that
"For details of how the expected rate of inflation is calculated
from the Livingston price level forecasts, see Carlson, “A
Study of Price Forecasts.”
8Actually, Carlson calculated an implied inflation rate for an
8- and 14-month horizon. An example will clarify this point.
The Livingston survey respondents are asked, prior to, say,
the June survey, to forecast the level of the CPI for the com
ing December and the following June. Since this forecast is
made a month or more prior to the survey’s publication, Carl
son assumed that most respondents would know only the level
of the CPI data two months before (April or October) the
survey’s publication. Thus the economists were forecasting
the CPI for 8 and 14 months ahead. In this article, these fore
casts are described as 6- or 12-month forecasts but are, in fact,
identical to those of Carlson. This means that the forecast
inflation rates for 6- and 8-month and for 12- and 14-month
horizons are assumed to be the same.
9In general, the implied j-month inflation rate for the interval
from i to i + 1 is:

*'■
'

_ (l + TtT.m,,)1
*1
(1+T t?.,)1

This expression is similar to that used in the term-struclure
of interest rate literature to describe the implied forward in
terest rate.

F E D E R A L R E S E R V E BAN K O F ST. L O U IS

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1980

Table 1
Revisions in Inflation Expectations: The
Carlson Model (ordinary least squares estimation)
R — bo 4" bi E + u
Coefficients*
Period

R7RJ

SEE

D.W.

1953-62

-.049
(-.318)

.045
(.484)

.013/-.042

.568

1.013

1963-71

-.264
(-2.458)

.085
(1.227)

.086/.029

.327

1.550'

1953-71

-.141
(-1.458)

.056
(.926)

.023/-.004

.466

1.072

1953-75

-.287
(-2.818)

.208
(4.075)

.274/.258

.539

1.513'

1953-78

-.305
(-3.319)

.212
(4.550)

.293/.279

.525

1.569'

1953-78
(omitting
1972-74)

-.250
(-2.630)

.118
(1.991)

.083/.062

.514

1.509

"t-statistics are in parentheses.
"Value of Durbin-Watson statistic permits rejection of positive serial correlation.
'Value of Durbin-Watson statistic is in the indeterminate range.

“explain” the forecasts in terms of observable eco
nomic variables, such as past actual rates of inflation,
past rates of money growth, and so on. Most of these
studies sought to investigate the rationality and effi
ciency of inflation forecasts. None have investigated
explicitly the process by which forecasters revise their
expectations.
Although Carlson did not explicitly examine the
process by which inflation forecasts are formed, he
did investigate the relevance of a simple error-learning
model in explaining forecast revisions. He did not,
however, derive his error-learning model from some
underlying structural forecasting model. Consequently,
his finding of only weak evidence that past forecast
errors affected revisions in expectations warrants
reexamination.
Carlson argued that forecast revisions depend on
the most recent forecast error ( E t ) in inflation ex
pectations. This error is defined as:
(3 )

E, = n,., - n,*,-,,

where n 6,t is the most recent 6-month rate of inflation
observed at time t. Carlson then investigated the

error-learning hypothesis by estimating the equation:
(4 )

Rt = b0 + b, Ei + ut,

where ut is a random error. This equation states that
revisions of previous forecasts depend only on the
most recent forecast error.
Carlson’s estimations of equation 4 over three dif
ferent sample periods (1953-62, 1963-71, and 1953-71)
failed to uncover any consistent evidence in support
of the error-leaming hypothesis. Although he found
some evidence of error-leaming in inflation forecasts
based on the Wholesale Price Index (W P I), he found
no evidence that error-learning significantly affected
revisions of 6-month inflation forecasts based on semi
annual observations of the CPI.
To test whether this conclusion remains valid when
more recent data are included, equation 4 was reestimated over selected time periods. The results,
reported in table 1, do not support Carlson’s conclu
sion when the sample period is extended to include
the 1970s. For example, the estimated coefficient on
past errors is positive and significant when the equa
tion is estimated through 1975 or 1978.
Because the pervasive price controls in effect dur

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F E D E R A L R E S E R V E BANK O F ST. L O U IS

1980

Table 2
Revisions in Inflation Expectations: The
Carlson Model (Cochrane-Orcutt estimation)
R = b0 + bi E + u
Coefficients*
Period

1953-62

-.149
(-.651)

1953-71

R7RJ

SEE

D.W.

Rhob

.086
(1.172)

.259/.215

.493

1.967

.482
(2.396)

-.218
(-1.642)

.077
(1.450)

.191/.168

.420

1.860

.432
(2.912)

1953-78

-.333
(-3.161)

.220
(4.684)

.340/.327

.508

2.024

.194
(1.413)

1953-78
(omitting
1972-74)

-.228
(-2.238)

.114
(2.263)

.142/.122

.440

1.759

.245
(1.674)

*t-statistics are in parentheses.
'The autocorrelation coefficient as estimated by the Cochrane-Orcutt technique; t-statistics are
in parentheses.

ing the period 1972-74 may have distorted the effect
of past errors, equation 4 was estimated through 1978
omitting 1972-74 data. Again, the hypothesis that
error-learning has been an important factor in the
formation of inflation expectations cannot be rejected.
The low Durbin-Watson (D .W .) statistics for
several versions of equation 4 suggest the presence
of serially correlated residuals (u ,). As a result,
estimates of equation 4 may not be efficient. The
Cochrane-Orcutt iterative technique was used to cor
rect for the presence of autocorrelation for those sam
ple periods in which the D.W. statistic indicated that
the hypothesis of serially correlated residuals could
not be conclusively rejected. Estimates of equation 4,
using this method, are reported in table 2 and, like
those discussed above, are less conclusive than Carl
son’s about the relevance of the error-learning hy
pothesis. For example, in the 1953-71 period, the
t-statistic for the coefficient on the forecast error,
though small, is significent at the 10 percent con
fidence level using a one-tailed test.10 Nevertheless,
over the two subsamples of the period, 1953-62 and
1963-71, the error-leaming hypothesis still must be
rejected. Coefficients for this parameter over all three
periods, however, differ by less than .01, suggesting
10The one-tailed test is appropriate for testing the null hypoth
esis that bi = 0 against the alternative hypothesis that
b, > 0.

that estimates from the shorter sample periods may
be inefficient but unbiased estimates of the true
parameter.11
Since the error-leaming model implies that all
information relevant to forecast revisions is contained
in the most recent error, the significant negative co
efficient on the constant term requires further dis
cussion. The significance of these coefficients, together
with the low coefficient of determination (R 2), could
be interpreted as evidence that important variables
have been omitted from the specification. A careful
examination of the expectations formation process
underlying equation 4 provides additional support for
this interpretation.
As noted above, the relevant error-leaming model
should be derived from and consistent with the under
lying structural expectations formation model. Recall
ing the definitions for the revision and the fore
cast error, it is easy to see that the underlying foreu The estimated coefficients for the three pre-1972 sample pe
riods do not differ significantly from each other, suggesting
that they are all unbiased estimators of the true parameter.
Because the variance of these estimated coefficients tends to
decline with increases in the size of the sample, the estimates
for the shorter periods cannot be considered efficient (i.e.,
they are not the minimum variance estimators). For a dis
cussion of the efficiency of estimators, see Jan Kmenta, Ele
ments of Econometrics (New York: MacMillan Publishing
Company, 1971), pp. 157-69.

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

cast mechanism implied by equation 4 conforms to
the following relationships:
(5a)

ir?,t == a0 + ai

(5 b )

fe.t =

and

oto + a , n?,t,

where ai = a , and the t-subscripts identify the period
in which the variable is observed.12 (For example,
ir6,t is the most recently observed six-month inflation
rate.)
Equations 5a and 5b imply a highly restrictive
( “naive”) version of the expectations process. These
specifications imply that the forecasters’ expectations
of inflation for the next period depend only on the
most recently observed rate of inflation. No other in
formation is incorporated. Note also that both equa
tions specify a constant. A nonzero constant in either
equation implies that some premium (or discount) is
added to the impact of the current 6-month inflation
rate to obtain the relevant 6-month inflation forecasts.

AN ALTERNATIVE FORECAST
MECHANISM
If the true underlying expectations formation
mechanism is less restrictive or more complex than
the one described by equations 5a and 5b, then the
revision equation given in equation 4 is misspecified.
Recent studies of inflation expectations offer some evi
dence for this interpretation.
Pesando, in his study of the Livingston data, hy
pothesized an autoregressive scheme for the price fore
casts.13 In another study of inflation forecasts based
on different survey data, Kane and Malkiel empha
sized the importance of including some retum-tonormality variable.14 The retum-to-normality model
implies that forecasters adjust their forecasts to some
notion of the “normal” rate of inflation. Mullineaux
also experimented with a variety of variables that
could potentially influence inflation expectations and
reported
. . that inflation forecasts are systematic
ally influenced by past inflation rates and past rates
of money growth, but not by fiscal-policy-related
variables. . . ,”15 Both the Kane-Malkiel and Mulli
neaux studies highlight the relevance of other informa
12The revision equation (equation 4) is obtained by lagging
each term in equation 5b and subtracting from 5a.
13Pesando, in “A Note on the Rationality,” characterized the
Livingston forecast by a highly restrictive autoregressive
scheme.
14Kane and Malkiel, “Autoregressive and Nonautoregressive
Elements.”
15Mullineaux, “Inflation Expectations and Money Growth,”
p. 160.

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1980

tion in addition to the past rate of inflation in the
formation of inflation expectations. The remainder
of this article explores an alternative inflation ex
pectations formation mechanism that is hypothesized
to depend on both the time series of past inflation
rates and on elements that embody a retum-to-nor
mality notion.

A Return-to-Normality Model
The following mechanism is hypothesized for the
expectations formation process:
(6a)
(6b)

71®, = a> + ai
<

+ a: itj.t + as tt?, and,

f j., = etc + a , n*.

This process describes the current inflation forecast
for the j-month horizon in terms of last period’s fore
cast ( T j *-i), the most recently observed j-month
T
inflation rate (Ttjit), and the currently held expected
normal rate of inflation (it?). The implied forward
rate of inflation, fJ t — the inflation rate expected to
prevail for the j-month period beginning at the com
pletion of the current j-month period — is hypothesized
to equal the currently held forecast plus some pre
mium (or discount), a 0.
This specification of inflation expectations em
bodies both autoregressive and retum-to-normality
elements.16 The presence of a lagged dependent vari
able in equation 6a can also be interpreted as cap
turing the relevance of any inertia in the forecasts.
The larger the coefficient, a1; the more reluctant
forecasters are to revise their expectations. The co
efficient, a2, which applies to the most recently ob
served inflation rate, measures the extent to which
new information about inflation is deemed relevant
for the current period’s forecast. Finally, the coeffi
cient, a3, reflects the dependence of short-run inflation
forecasts on the long-run normal rate of inflation.
Equation 6a can be rewritten in a form that cap
tures the impact of past errors. Adding and sub
16For example, by repeated substitution for the lagged depend
ent variable, equation 6a can be shown to be equivalent to
Ti:*,t = ao + a2 Ttj.t + a^ n” +
n
2 ai (ao + a2
+ as Ht-i),
i= 1
where the last term embodies primarily autoregressive com
ponents as well as the history of the normal rate of inflation.
Another point merits attention. Suppose forecasts are made for
a minimum j-month horizon and for other horizons that are
some multiple of that horizon (for example, a 6-month, a
12-month, and an 18-month horizon). If each of these fore
casts are made every j-month, then all forecasts, regardless
of the horizon, can be represented as a distributed lag on
past j-month inflation rates.

F E D E R A L R E S E R V E B A N K O F ST . L O U I S

tracting a2 i6,t-i from the right-hand side of 6a
T
produces:
(7)

iTj.t = a0 + (ai + a2) n *,-, -f- aiEj.t + a3
n?.

Lagging all terms in equation 6b one period and
subtracting from equation 7 produces a forecast re
vision equation that is consistent with this forecasting
process:
(8) R j,t = (ao - oto) + (ai + a2 - a t)

+ a^Ej,, + a3
n?.

Clearly, the simple revision equation estimated by
equation 4 is not consistent with the forecast mech
anism described here. The correct equation for esti
mating revisions in such inflation expectations is:
(9 )

Rj.t = Po + M T..-. -t" PsEj.t + P T + ut;
aT ?

where |0 = a0 - a 0, | = (a, + a2 - 0O , |2 = a2,
3
3i
3
p3 r= a3, and ut is a random error. Note that the logic
of the model implies that a0 and a 0 should be zero
since all relevant information is presumed to be em
bodied in the variables
E jjt, and Ttj. Conse
quently, estimated values of p0 also should not differ
significantly from zero.
The coefficient for the lagged dependent variable
in equation 6a can be interpreted in terms of the
speed with which forecasters adjust their expecta
tions from one period to the next. Equation 6a de
scribes the adjustment of inflation forecasts partly in
terms of previously held forecasts. The size of the
coefficient, au on the lagged term measures the ex
tent to which forecasters maintain previously held
forecasts. The speed with which forecasts are adjusted
over time, therefore, corresponds to (1 - a ,). Larger
values for ax imply that a stronger persistence effect
is embedded in the forecast process or, alternatively,
that forecasts are revised more slowly when new in
formation becomes available.

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1980

For example, Kane and Malkiel found that
“. . . return-to-normalitv elements dominate forecasts
of future inflation and [show] . . . that developments
outside the past history of prices importantly alter
respondents’ conceptions of what rate of inflation is
‘normal.’ ”17 In their investigations of the retum-tonormality hypothesis, Kane and Malkiel surveyed
large firms and major bond dealers to gather infla
tion forecasts over several horizons. They were
thereby able to calculate a normal rate forecast as a
weighted average of subperiod forecasts which ex
tended as far as 10 years into the future. Unfortu
nately, the Livingston data do not permit the
derivation of any comparable and meaningful normal
rate. Because the longest horizon forecast is only 18
months, a test of the retum-to-normality hypothesis
comparable to the Kane-Malkiel study is not pos
sible.18 Consequently, tests of the retum-to-normality
hypothesis must rely on other measures of the nor
mal rate of inflation.
One way to approximate the normal rate of in
flation is to utilize some trend growth of the money
stock. Such a proxy introduces a monetarist in
terpretation of inflation forecasts into the model —
namely, that the trend growth of prices is determined
by the trend growth of money.19 In this study, a
twenty-quarter moving average of past Ml growth
is used as a proxy for the normal rate of inflation.

Finally, the degree of persistence evident in the
forecasts could vary with the forecast horizon. Be
cause information about permanent structural changes
in the economy evolves only slowly and is costly to
distinguish from transitory phenomena, long-run in
flation expectations could be expected to change less
from one period to the next than short-run expecta
tions. As a result, longer-range forecasts should show
greater persistence than shorter-range forecasts.

The use of a surrogate for the normal rate of
inflation requires some modifications of the forego
ing interpretation regarding equations 6a, 6b and 9.
Suppose that equation 6a represents the true model
that describes inflation expectations over some
given short-run time horizon. If currently available
information affects the actual rate of inflation only
with some lag, then the forecast for the period be
ginning one period hence could differ from the
forecast made for the period now beginning. To the
extent that this currently available information is
relevant to the long-run rate of inflation, it should
be imbedded somehow in the normal rate of inflation.
The proxy for the normal rate of inflation used here
does not represent exactly the notion of the normal
rate. For example, suppose the Federal Beserve an
nounced that it intended to pursue a new money

The hypothesized forecasting process described by
equations 6a and 6b contains a retum-to-normality
variable that reflects the view that forecasters in
corporate information about the long-run expected
inflation rate. This expected normal rate of inflation
embodies relevant information from a wider variety of
sources than simply the time series of past prices.

17Kane and Malkiel, “Autoregressive and Nonautoregressive
Elements,” p. 3.
18These 18-month forecasts were collected only once each
year and were discontinued after 1971.
19See Denis Kamosky, “The Link Between Money and Prices
— 1971-76,” this Review (June 1976), pp. 17-23 for a dis
cussion of the link between the trend growth of money and
inflation.

F E D E R A L R E S E R V E B A N K O F ST . L O U I S

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1980

Table 3
Inflation Expectations: 6-Month Forecasts
■rtf — ao + aiti?. t-i + ajTt»lt + ajrc?
Coefficients*
Period

a»

R7R’

SEE

Durbin-h

Rhob

1953-78

-.413
(-1.996)

.654
(8.340)

.183
(3.832)

.186
(2.341)

.952/.949

.522

1.119

77.00

1963-78

-.197
(-.557)

.577
(6.139)

.262
(4.769)

.123
(1.064)

.947/.941

.488

.070

35.13

1953-71

-.191
(-.952)

.773
(7.445)

.039
(.660)

.156
(1.864)

.888/.878

.450

.594

52.82

1963-71

-.171
(-.593)

.552
(2.895)

.081
(1.101)

.260
(1.318)

.919/.900

.321

-.701

-.330
(-1.462)

.715
(8.317)

.100
(1.659)

.190
(2.062)

.945/.941

.515

.493

1953-78
(omitting
1972-74)

-.583
(-2.961)

17.27
73.69

■t-statistics are in parentheses.
bThe autocorrelation coefficient is reported only for that equation which was estimated by the Cochrane-Orcutt technique
because of evidence of serial correlation in the OLS estimates; t-statistic is in parentheses.
'F is the F-statistic for assessing the hypothesis that the estimates reported here do not differ from those obtained by estimat
ing the more simple model described by equation 5a. The F-statistics permit rejection of this hypothesis at the .01 level for
all time periods reported.

growth target over the coming six months. If this tar
geted growth rate differed from the previous trend
growth of money, analysts might expect the trend in
money growth to be changing during the current
6-month forecast horizon. Because the proxy for the
normal rate used here is entirely “backward-looking,”
it omits such additional information. As a result, the
implied forward rate equation could be expected to
include additional terms. Since these terms are cur
rently unmeasurable, however, they are assumed to be
imbedded in the constant term; that is, the constant
term in the implied forward inflation rate equation
reflects the effect of currently available ( but not
measurable) information on the future inflation rate.
A positive constant would reflect the forecasters’
belief that the net effect of all other currently avail
able and inflation-relevant information is to accelerate
inflation. Finally, such a positive constant would imply
a negative constant term, |0, in equation 9.
3

Empirical Tests of the Alternative
Inflation Forecast Model
Tables 3 and 4 report the results of estimating
equations 6a and 6b, respectively, over various time
periods. The first and perhaps most important obser
vation is that the coefficients of determination ( R2) in
table 3, are greater than 0.90 for four of the five

periods. For longer periods, they exceed 0.94. This
statistic indicates that over 90 percent of the variance
of the inflation forecasts is explained by this relatively
simple reduced form. Interestingly, these values for Rz
are quite close to those obtained when the forecasts
are estimated in terms of more complicated Almon
lags on past inflation rates and past money growth.20
More importantly, the coefficients of determination
adjusted for degrees of freedom ( R2) are consistently
greater than those obtained from estimates (not re
ported here) of the “naive” forecast equation given
in 5a. The rejection of the naive model in favor of
equation 6a is reinforced by F-tests (for the hypoth
esis that the two equations do not differ) conducted
for the various sample periods. Results of these tests
(based on comparisons of ordinary least squares esti
mates of the two equations) are reported in the last
column of table 3.21 The alternative model is favored
20The adjusted R!s for equation 6a. are similar to those ob
tained by Mullineaux. While the R!s reported here generally
exceed those of Mullineaux, his sample period differed from
those estimated here, making direct comparison inappropri
ate. Other estimations by the author of the inflation forecasts
based on more complicated Almon lags of past money
growth _and past inflation rates did not generate consistently
higher R!s than did the equations reported here.
- 1F-tests were made on the basis of OLS estimations of the
two equations. Cochrane-Orcutt estimations would involve
transforming all observations by some coefficient of autocor
relation. Unless each equation is characterized by the same
degree of serial correlation, the two equations would not be
directly comparable.

APRI L. 1 9 8 0

F E D E R A L R E S E R V E B A N K O F ST . L O U I S

Table 4
Inflation Expectations: The Implied Forward Rate
f.,t = cxo + a,n?.,
Coefficients*
Period

<o
X

R7R1

SEE

D.W.

Rhob

.978/.978

.338

1.963

.266
(1.974)

.525
(3.295)

.967
(34.614)
QT7
(26.087)

.980/.979

.275

2.083

.328
(1.934)

1953-71

.138
(1.530)

1.058
(21.589)

.928/.926

.384

1.553

1963-71

.164
(1.486)

1.057
(24.331)

.974/.972

.186

2.369

1953-78
(omitting
1972-74)

.163
(2.071)

1.037
(39.507)

.973/.972

.375

1.624

1953-78

.338
(3.478)

1963-78

*t-statistics are in parentheses.
"The autocorrelation coefficient is reported only for those equations which were estimated by the Cochrane-Orcutt technique
because of evidence of serial correlation in the OLS estimates; t-statistics are in parentheses.

over the naive model at the 0.01 confidence level for
all time periods.22
The estimated constants reported in table 3 re
inforce the view that this forecast mechanism is
more appropriate than the naive model. In esti
mates of that model, statistically significant, posi
tive constant terms were consistently obtained, sug
gesting the importance of omitted variables. In
contrast, estimates of the present model produced a
significant (though negative) constant term in only
one sample period — 1953-78. This constant could
capture elements related to the era of the Nixon
wage-price controls. When this three-year episode is
deleted, the constant is no longer significant at stand
ard confidence levels. Finally, it should be noted that,
unlike the naive model, the present model shows no
evidence of positive serial correlation, though the
1963-71 sample period shows some evidence of nega
tive serial correlation.23 The implied forward rate
22In several OLS estimations of the naive model, the DurbinWatson statistic was unacceptably low. While this result is
usually interpreted as evidence of positive serial correlation,
it may also indicate that important explanatory variables
have been omitted. This interpretation seems appropriate
here, since by including the two additional variables in equa
tion 6a, evidence of positive serial correlation disappears.
23The Durbin-h statistic is appropriate for testing for serial
correlation when lagged values of the dependent variable are
included. The Durbin-h is normally distributed with a zero
mean and a variance of o2. See J. Johnston, Econometric
Methods (New York; McGraw-Hill, 1972), pp. 312-13.

is also accurately described by equation 6b.24 Taken
together, these results provide favorable evidence that
the underlying forecast process conforms quite closely
to the one hypothesized here.
Although the R2s remain high over the various sam
ple periods, the variation in the estimated coefficients,
especially those for the current inflation rate and the
normal rate, suggest that the contribution of these
variables in the forecasting process has changed.25
For example, in periods ending with 1971, the cur
rent rate of inflation played virtually no independent
role in the determination of next period’s forecast.
Apparently, current inflationary phenomena was
largely discounted — at least until it became embed
ded in the past trend of inflation. As the sample
period is extended toward the present, however, the
most recent inflation rate assumes a dramatically dif
ferent role. Both the magnitude and the significance
of the a2 term indicate that forecasters viewed the
information reflected in the current inflation rate as
more relevant.
24Equation 6b implies that the implied forward rate could al
ternatively be expressed in a form similar to that given in
6a. Estimating this version of the forward rate did not pro
vide as good a fit in terms of R2 as did the more simple form.
25Mullineaux, “Inflation Expectations and Money Growth,” also
observed a changing forecast structure over time. Mullineaux’s work gives a thorough and detailed analysis of the
behavior of the temporal coefficients on past inflation.

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

APRIL

1980

Table 5
Inflation Expectations: 12- and 18-Month Forecasts
•n*,t = ao + a, itj.t-! + a, Tt«,t + a3 j = 12, 18
ir?;
(12-month forecast)
Coefficients*
Period

R’/R 1

SEE

Durbin-h

1953-78

-.266
(-1.496)

.734
(11.231)

.143
(3.529)

.146
(2.108)

.964/.962

.455

.691

1963-78

-.149
(-.451)

.641
(7.087)

.212
(4.245)

.127
(1.135)

.952/.947

.455

-.109

1953-71

-.082
(-.513)

.837
(11.099)

.030
(.619)

.113
(1.712)

.931/.925

.368

.828

1963-71

-.114
(-.428)

.585
(3.315)

.080
(1.156)

.245
(1.290)

.934/.919

.296

-.376

1953-78
(omitting
1972-74)

-.178
(-.936)

.794
(11.271)

.068
(1.307)

.141
(1.808)

.961/.958

.447

.012

-.151
(-1.341)

.809
(11.963)

.005
(.100)

.282

.604

Rho"

-.574
(-2.888)

(18-month forecast)
1953-71

.223
(4.841)

.955/.946

-.563
(-2.893)

”t-statistics are in parentheses.
bThe autocorrelation coefficient is reported only for those equations which were estimated by the Cochrane-Orcutt technique
because of evidence of serial correlation in the OLS estimates; t-statistics are in parentheses.

Examination of estimates for equation 6a over
longer forecast horizons offers an additional perspec
tive. Table 5 reports estimates of equation 6a for 12and 18-month horizons.26 Estimated coefficients for
the 12-month horizon over various time periods show
a pattern similar to that estimated for the 6-month
horizon. As expected, all coefficients on the lagged
dependent variable are larger for the 12-month
horizon than for the 6-month horizon. This suggests
that there is greater period-to-period persistence and a
slower adjustment speed in the 12-month forecasts
than in the 6-month forecasts. For the 18-month fore
casts, however, the coefficient on the lagged depend26Note that estimated equations for these forecast horizons
differ slightly from those described by equation 6a in that
the most recent 6-month inflation rate, rather than the most
recent 12- or 18-month inflation rates, is included. The rea
son for this is that the 12-month forecast, made six months
ago, already incorporated all relevant information from past
inflation. Only the most recent 6-month inflation rate is
"news.” (As noted in footnote 16, all forecasts, regardless
of horizon, can be represented as a distributed lag on
past 6-month inflation rates.) If the 12- and 18-month
forecasts were made only every 12 and 18 months, then the
exact specification given by 6a would be appropriate. (Equa
tion 6a was estimated using this latter specification, despite
the informational redundancy contained in the 12- or 18month actual inflation rate. Those results did not differ
notably from those reported here.)

ent variable was slightly (but not significantly) lower
than in the 12-month forecast horizon.
For those time periods in which the most recently
observed 6-month inflation rate significantly affected
the forecasts, its impact was greater on the short-run
(6-month) forecasts than on the longer-run (12month) forecasts. This observation provides further
evidence that the most recently observed inflationary
experience is incorporated only slowly into longer-run
forecasts.
The specification given by equation 6a permits
a useful interpretation of the coefficient for the normal
rate. Essentially, the long-run tendency for the jth
horizon forecast to converge toward the normal rate
can be represented by a long-run coefficient on the
normal rate described as a3/ ( l - a i ) . 27 Table 6 reports
calculations of this parameter for the three forecast
horizons over several periods. This long-run retum27The presence of a lagged dependent variable makes equation
6a similar to a stock-adjustment type of equation. The co
efficient, ai, in 6a is interpreted as one minus the speed of
adjustment of the forecast to the long-run “equilibrium” rate
of inflation. The long-run coefficient for any other variable in
the equation can then be described as a ratio of the esti
mated short-run coefficient to the speed of adjustment, i.e.,
aj/ (l - a,).

F E D E R A L R E S E R V E B A N K O F ST . L O U I S

APRIL

Table 6
Long-Run Response of Short-Term
Expectations to Changes in the
“Normal” Rate of Inflation*
Period

6-month
forecastsb

12-month
forecastsb

1953-78

.538
(2.908)

.549
(2.614)

1963-78

.291
(1.202)

.354
(1.326)

1953-71

.687
(2.095)

.693
(1.868)

1963-71

.580
(2.275)

.590
(2.235)

1953-78
(omitting
1972-74)

.667
(2.585)

18-month
forecasts”

.684
(2.206)

1.168
(2.649)

*Due to rounding, the calculated coefficients may differ
slightly from those calculated from results reported in
tables 3 and 5.
b
t-statistics are in parentheses. For a description of the meth
odology used to calculate the variance of as/ (1 - ai) used
in calculating the t-statistics, see Kmenta Elements of
Econometrics, p. 444.

to-normality coefficient should be higher for longer
forecast horizons, since long-run expectations would
tend to converge to the normal rate of inflation. As
expected, these long-run coefficients are larger for the
12-month than for the 6-month forecasts. While the
differences between the coefficients for these horizons
are not great, the long-run coefficient for the 18-month
horizon is larger and, in fact, does not differ signifi
cantly from unity. Thus it appears that the forecasters
do tend to form long-run expectations in a manner
consistent with the return-to-normality hypothesis.28
The estimated magnitude of this long-run coeffi
cient for both the 6- and 12-month horizons falls
dramatically when the sample period includes
only the 1960s and the 1970s.29 This observation re
inforces the view that the rapid acceleration in infla
tion experienced during the 1970s has had an important
effect on the way inflation expectations are formed.
Throughout this period, rapidly rising inflation may
have simultaneously induced forecasters to revise the
28The calculated long-run coefficients for the normal rate are
comparable to those obtained by Kane and Malkiel in their
estimations based on cross-sectional data. For example, in
equations using the CPI, their estimates of the return-tonormality coefficient ranged from about .52 for the 6-month
horizon ( in 1969) to about .63 for the 12-month horizon
(in 1972).
29Note that the coefficient deteriorates only slightly in the
subsample 1963-71.

1980

normal rate of inflation more frequently. Hence, the
proxy measure for the normal rate used here may
understate the correct value of the normal rate, when
inflation is accelerating rapidly.30 This possible meas
urement error could distort the evidence reflected in
the long-run coefficient for this variable, especially
during more recent periods.
In summary, several relevant observations emerge
from the estimations of equations 6a and 6b. The in
flation forecasting process employed by respondents
to Livingston’s survey of economists can be described
in terms of both autoregressive elements and past
money growth ( interpreted here as a proxy for returnto-normality elements). Nevertheless, although the
equation performs well over all subsamples of the
period 1953-78, the relative roles played by the cur
rent and normal rates of inflation appear to have
changed. Specifically, during the 1970s when infla
tion accelerated sharply, retum-to-normality elements
played a less important role while the most recent
rate of inflation became more important. Finally, the
emergence during the 1970s of a significant, positive
constant in the implied forward rate equation pro
vides some evidence that forecasters had begun to
anticipate accelerating inflation.

Implications for Error-Learning Models
The relevant equation for examining the errorlearning hypothesis is implied by the underlying
expectations formation process. Equation 9 satisfies
this criteria. In addition to the forecast error, it in
cludes a lagged inflation forecast term and a retum-tonormality element. Table 7 reports statistics obtained
from estimating this equation.
When the error-leaming hypothesis is examined
from the perspective implied by the forecast mecha
nism underlying equation 9, evidence of error-learning
is clearly present. The coefficient on the forecast error,
|2, differs significantly from zero at the 5 percent
3
level (one-tailed test) over all sample periods except
1953-71. Recall that this coefficient reflects the rele
vance of the most recently experienced inflation. The
results reported above reveal that the current rate of
inflation only became important in samples that in
cluded the experience of the 1970s, during which in
flation was accelerating sharply. Thus, Carlson’s earlier
conclusions about the relevance of past errors in ex30This view is reinforced by some results reported by Mullineaux. Using a two-period distributed lag on past 6-month
money growth, Mullineaux found that both lagged coeffi
cients increased dramatically during the 1970s. Thus, meas
ures of “normal” inflation based on a fixed-weight average of
past money growth would understate the “true” normal rate.

F E D E R A L R E S E R V E B A N K O F ST . L O U I S

APRIL

1980

Table 7
Revisions in Inflation Expectations: The Implied Model
R*,t = P + Pi U*t-i + Pj Ee.t + Pi Tt*
o
Coefficients*
Period

P
o

P
.

P
*

P
>

R’/R*

SEE

D.W.

1953-78

-.553
(-2.830)

-.174
(-2.932)

.215
(4.775)

.169
(2.256)

.402/.365

.493

1.708

1963-78

-.145
(-.446)

-.030
(-.394)

.312
(6.178)

-.052
(-.489)

.585/.541

.448

2.393

1953-71

-.444
(-2.711)

-.349
(-4.931)

.050
(1.039)

.245
(3.595)

.431/.381

.366

1.674

1963-71

-.153
(-.731)

-.289
(-1.826)

.116
(2.137)

.130
(.906)

.564/.463

.251

2.006

-.544
(-2.860)

-.254
(-4.256)

.091
(1.790)

.238
(3.069)

.376/.331

.434

1.622

1953-78
(omitting
1972-74)

Rhob

-.729
(-4.395)

*t-statistics are in parentheses.
''The autocorrelation coefficient is reported only for that equation which was estimated by the Cochrane-Orcutt technique
because of evidence of serial correlation in the OLS estimates; t-statistic is in parentheses.

plaining forecast revisions is, in one sense, reaffirmed.
The error-leaming hypothesis, however, appears to
have greater validity when recent, unexpectedly rapid
inflation has invalidated prior forecasts.
Equation 9 requires that the estimated coefficients
conform to restrictions implied by the underlying
forecast process. These restrictions, which are listed
below equation 9, were confirmed for all sample
periods in the estimates of the revision equation. In
no case did the coefficients from equation 9 differ
significantly from the restricted values for those co
efficients derived from the independent estimates of
the underlying forecasting process.

SUMMARY AND CONCLUSIONS
The foregoing analysis and discussion has presented
evidence concerning the nature of the inflation fore
casting process implicit in the Livingston price ex
pectations data. Although earlier conclusions about
the relevance of the error-learning hypothesis may
have been valid for certain periods over the past 25
years, they do not appear to be valid for the decade
of the 1970s.
More important, however, is the information re
vealed about the nature of the inflation forecasting
mechanism. Evidence reported here indicates that

when inflation has been accelerating, recent inflation
ary experience becomes more important in the expec
tations process. This result suggests that policies which
can successfully lower current inflation could reap im
portant longer-run dividends by simultaneously induc
ing a reduction in inflation expectations.31 The results,
however, also suggest that once the economy moves
from high inflation to lower inflation, retum-to-normality elements may become more important. Under
a regime where planned, gradual reductions in the
growth rate of money are announced and pursued,
inflation expectations would seemingly adapt only
slowly. On the other hand, if during periods of de
celerating inflation, expectations become more respon
sive to current experience — as they were during
periods of accelerating inflation — expectations may
well adapt more rapidly. Evidence of strong persist
ence effects over all time periods suggests that break
ing the inflation psychology necessarily involves a
long-term commitment by policymakers to an anti
inflation policy. Once such a policy is announced and
undertaken, any decelerating inflation actually ex
perienced should reinforce the adaptation to lower
inflation expectations.
31This observation should not be interpreted as supporting
incomes-policies since the adoption of price and wage con
trols could be expected to alter the structure of expectations
formation.

Money, Inflation, and Economic Growth:
Some Updated Reduced Form Results
and Their Implications
KEITH M. CARLSON

A HE economic experience of the United States
during the 1950s and 1960s provided an opportunity
to develop and test a number of hypotheses relating
to the performance of the macroeconomy. One such
hypothesis that received empirical support during this
period held that monetary actions, as measured by
movements in the monetary aggregates, have lasting
effects on only nominal variables. This proposition is
an important element in a body of thought called
“monetarism.”1
In contrast to the relative economic tranquility of
the 1950s and 1960s, the decade of the 1970s was
marked by extensive experimentation with wage and
price controls, large supply shocks, proliferation of
government regulations, and worldwide inflation.
These events and developments prompted economists
to question whether or not the performance of the
United States economy during this period was con
sistent with prior hypotheses relating to the lasting
impact of monetary actions. This article is addressed
to that question.
The article focuses on the magnitude of the re
sponse of GNP, output, and the price level to changes
in the money stock, defined as currency plus private
'For an extensive discussion of monetarism, see Thomas Mayer,
et. al., The Structure of Monetarism (New York: W. W.
Norton and Company, 1978).

checkable deposits.2 The magnitudes of these responses
are derived by estimating reduced form equations;
that is, equations in which observations of the rates
of change of economic variables are regressed on cur
rent and lagged values of the rate of change of money
and other suitably chosen exogenous variables. The
sum of the coefficients on the money variable is in
terpreted as a measure of the magnitude of response
during the sample period from which the observations
are drawn.3

THE QUANTITY EQUATION OF
EXCHANGE AND REDUCED FORMS
The underlying framework for the analysis is the
quantity equation of exchange. This equation is an
identity that states the value of all spending for goods
and services in two ways: the product of the stock
of money times its velocity of circulation, and the
-The regressions were run before data were available for the
new definitions of the monetary aggregates. Data for “old”
Ml were used, and ATS and NY NOW accounts were added
after 111/78.
3Whether or not this magnitude of response can be interpreted
statistically as a “long-run” result depends on the length of
the lag relative to the number of observations in the sample
period. A reliable estimate of the long-run response of a
variable that adjusts quickly and completely to an exogenous
shock does not require as many observations as does a slowly
adjusting variable.

APRIL

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

price level times the quantity of aggregate output. In
symbols, this identity is:
(1 ) MV = PX = Y,

where
M = nominal money stock,
V — velocity of circulation,
P = price level,
X = output, and
Y = nominal GNP.

(2 ) e(M,M)M + e(V,M )M + a = e(P,M)M + b
X
+ e(X,M )M + c,

The total differential of equation 2 results in an
expression that relates the elasticities to each other:
1 +

e (V,M)

e (P,M)

The empirical analysis of the impact of monetary
actions on GNP, output, and the price level uses
previous specifications by monetarists as a starting
point and modifies these specifications in light of the
experience of the 1970s.8 After the equations are sum
marized and the variables are defined, the equations
are first estimated using data from 1955 through 1969.
They are then estimated with data from the 1970s.
Of primary interest is the stability of the relationships
when data from the 1970s are incorporated into the
estimates.

Specifications and Definitions of Variables

where £ is the elasticity of the first variable in paren
theses with respect to the second. A dot over a vari
able indicates its compounded annual rate of change.
The constants, a, b, and c, represent the effect of non
monetary influences on V, P, and X, respectively.

(3)

U.S. economy have generally concentrated on Y and
P, although not always in combination.5 Nelson re
cently developed justification for this choice of var
iables by testing the hypothesis that the structure of
the United States economy is recursive, with disturb
ances from GNP flowing to the price level and not
the reverse.6 Consequently, this article focuses on re
duced form estimates of Y and P.7

REDUCED FORM RESULTS

As an identity, the quantity equation of exchange
means little. When combined with assumptions re
lating to the determination of the variables, however,
the equation assumes behavioral content. Writing the
equation in rate of change form, where each of the
variables is allowed to be influenced by money, yields
the following:
M

1980

e (X,M ),

(4 ) 1 + e(V,M ) = e(Y,M ).

The GNP equation is specified as follows:
5

(5 ) Y = ao + Z mi M-i + Z ei E-«,
i= 0
i = 0

where
Y = compounded annual rate of change of nom
inal GNP,
M = compounded annual rate of change of Ml
(plus ATS deposits and NY NOW accounts
after 111/78), and

Equations 3 and 4 indicate the constraints that must
be considered when attempting to estimate these
elasticity parameters. An estimate of either e ( V , M )
or e(Y,M ) implies the other. Given one of these
elasticities, only one of the remaining elasticities —
e(P,M ) or e(X ,M ) — can be estimated. Alterna
tively, estimates of e(P,M ) and e(X ,M ) imply both
e(V,M ) and e(Y,M ).

This equation is essentially the same as that estimated

The elasticity parameters and the constants in equa
tion 2 can be estimated in a variety of ways. Reduced
form equations could be estimated for Y and P, Y
and X, P and X, V and P, or V and X. The choice
is arbitrary only if the error terms for each of these
reduced form equations have exactly the same serial
correlation properties.4 Monetarists researching the

8Charles R. Nelson, “Recursive Structure in U.S. Income,
Prices, and Output,” Journal of Political Economy ( Decem
ber 1979), pp. 1307-27.

4See Yash P. Mehra, “An Empirical Note on Some Monetarist
Propositions,” Southern Economic Journal (July 1978), pp.
154-67.

E = compounded annual rate of change of high
employment federal expenditures.

5For example, see Leonall C. Andersen and Keith M. Carlson,
“A Monetarist Model for Economic Stabilization,” this Review
(April 1970), pp. 7-25, and William G. Dewald and Maurice
N. Marchon, “A Modified Federal Reserve Bank of St. Louis
Spending Equation for Canada, France, Germany, Italy, the
United Kingdom and the United States,” Kredit and Kapital
(1978), pp. 194-212.

7Additional justification for the Y-P combination is found in
Thomas A. Gittings, “A Linear Model of the Long-Run Neu
trality of Money,” Staff Memoranda, Federal Reserve Bank
of Chicago (1979).
8The specifications summarized here are the “preferred” re
sults of estimating a variety of specifications.

FE D E R A L RE SE R V E BANK O F ST LOUIS

APRIL

1980

Table 1
Estimates of Reduced Form Equations with Pre-1970 Data
(Sample Period: I/55-IV/69)1
GNP equation: Y = 3.575 + Zm, M , + Ze. E-,
(3.557)
m0
m,
m2
Uh
m4
m
e
Im i

.275
.430
.345
.139
-.067
-.154
.966

(1.653)
(5.082)
(3.486)
(2.038)
(.837)
(1.679)
(4.054)

.066
.070
.024
-.039
-.086
-.084
-.051

e0
ei
e2
e3
e4
e
-s
Ze,

(1.148)
(2.001)
(.661)
(1.678)
(3.265)
(2.788)
(.561)

R! = .438; S.E. = 3.361; and D.W. = 1.934.

Price equation: P = -.049 + ZniM^i - .030 (Pp - P) + Zfi (P E - P)-i,
(.133)
(.509)
n0
ni
n2
n3
n,
n5
n6
nn*
ns
nJ0

.042
.036
.033
.032
.033
.035
.039
.043
.048
.053
.058

(1.077)
(1.365)
(1.811)
(2.220)
( 2.318)
(2.309)
(2.400)
( 2.631)
(2.995)
(3.463)
( 3.954)

n„
n,2
n,3
nu
n,i
n,s
n1
7
n,s
n,9
naj
Znt

.062
.065
.068
.068
.067
.063
.057
.048
.036
.020
1.008

(4.321)
(4.433)
( 4.293)
(4.014)
( 3.703)
( 3.414)
(3.164)
( 2.953)
( 2.777)
(2.629)
(7.420)

fo
f,
h
U
h
f=
Zf,

-.002
.004
.007
.007
.005
.003
.024

(.062)
(.230)
(.358)
(.381)
(.262)
(.149)
(.279)

R! = .559; S.E. = 1.094; and D.W. = 1.996.
1A polynomial distributed lags are third degree with tail constraint only; figures in paren
11
theses are absolute values of t-statistics; a dot over a variable indicates compounded annual
rate of change.

by Andersen and Jordan in 1968,® but modified so
that the coefficients are constrained on a third degree
polynomial distributed lag with t — 6 = 0 .
The price equation is specified as follows:
20

where
=

compounded annual rate of change of the
GNP deflator,

9Leonall C. Andersen and Jerry L. Jordan, “Monetary and
Fiscal Actions: A Test of Their Relative Importance in
Economic Stabilization,” this Review (November 1968), pp.
11-24.

D2 = decontrol dummy,
PF — compounded annual rate of change of the
food deflator,

•

(6 ) P = b0 + b,D, + b2 + b3 (P p - P) + Z mM-i
D2
i= 0
5
+ Z f , ( P » - P ) - ,,
i = 0

Di = wage and price control dummy,

M = compounded annual rate of change of Ml
(plus ATS deposits and NY NOW accounts
after 111/78), and
PE = compounded annual rate of change of pro
ducer prices for fuels, related products, and
power.
This specification builds on one developed by Karnosky except that it introduces variables designed to
capture the influence of nonmonetary shocks on the

APRIL

F E D E R A L R E S E R V E B A N K O F ST. L O U I S

price level.10 The polynomial distributed lag is third
degree for both money and energy prices with con
straints of t — 21 = 0 and t — 6 = 0, respectively.

Results Using Pre-1970 Data
Table 1 summarizes the estimated equations using
data prior to the onset of the shocks of the 1970s.
For the 1955-69 period, GNP was dominated by
movements in the money stock, and the adjustment to
these changes was essentially complete after five
quarters. The elasticity of GNP with respect to the
money stock, as measured by the sum of the coeffi
cients on money, was not significantly different from
one at the 5 percent level and implied that the elas
ticity of velocity with respect to monev was zero.
10Denis S. Kamosky, “The Link Between Money and Prices —
1971-76,” this Review (June 1976), pp. 17-23.

1980

With the sum of the coefficients on high employment
expenditures not significantly different from zero, the
constant term was an estimate of the trend growth of
velocity. Based on these estimates, the equilibrium
growth rate of GNP during the 1955-69 period was
equal to the growth rate of money plus the trend rate
of change of velocity.
According to the estimated price equation, the rate
of change of the price level was also dominated by
the growth rate of the money stock in the 1955-69
period. Other factors, namely food and energy prices,
were not significant in explaining overall price move
ments during this period, thus confirming Kamosky’s
estimate for essentially the same period. The pattern
of the estimated coefficients indicated that prices ad
just to a monetary shock very slowly, but the total
effect after 20 quarters was an elasticity of the price
level equal to one. Since neither the constant term

Table 2
Estimates of the GNP Equation1
Y = ao + Zmt M-i + ZeiE-!
Coeff.

I/55-IV/69
t

.275

1.653

Cum.2

Coeff.

I/70-IV/79
t

Cum.2

Coeff.

I/55-IV/79
t

.657

2.358

.657

.407

2.968

.407
.815
1.096
1.200

Cum.2

m0
m,

.430

5.082

.275
.704

.376

2.279

1.033

.407

5.344

m2
m
>

.345
.139

3.486
2.038

1.049
1.187

.169
.031

.986
.243

1.201
1.232

.282
.104

3.271
1.782

m4
m5

-.067
-.154

.837

1.120
.966

-.040
-.049
1.144

.242

1.193
1.144

-.052

.752

1.148

1.415
6.115

1.037
.053
.107

1.679
4.054

.282
2.350

Zmi

.966

e0
e,
e2

.066

1.148

.066

.039

.070
.024

2.001

.136

.068

.544
1.041

.661

.159

.079

-.039

1.678

.120

-.086

3.265

.033

-.084

2.788

-.051

Ze.

-.051

3.575

-.111
1.037

.039

.053

1.211

1.248

.106
.186

.055
.023

1.805
.768

.130

.076

1.491

.261

-.021

1.008

.109

.060

1.067

.321

-.054

2.203

.056

.034

.627

.355

-.054

2.064

.001

.561

.355

1.613

.001

.014

3.557

-1.078

.262

3.159

3.437
.410

S.E.

3.361

.272
3.934

3.620

D.W.

1.934

2.331

1.924

.438

1All polynomial distributed lags are third degree with tail constraint only; t-statistics are absolute values; a dot over a vari
able indicates compounded annual rate of change.
-Numbers are the cumulative sum of coefficients.

F E D E R A L R E S E R V E B A N K O F ST . L O U I S

APRIL

1980

Table 3
Estimates of the Price Equation1
P = b„ + biDi + b:D, + b, (P F - P) + Z mM-, + Zf, (P . - P)-,
Coeff.

I/55-IV/69
t

Cum.-

CoefF.

I/70-IV/79
t

Cum.2

Coeff.

I/55-IV/79
t

n0
n,

.042

1.077

.042

.056

1.087

.056

.061

.036

1.365

.078

.087

2.183

.143

.064

1.969
3.006

.033

1.811

.112

.110

3.095

.253

.067

4.360

Cum.2
.061
.125
.192

.032

2.220

.144

.126

3.419

.379

.068

5.300

.260

.033

2.318

.177

.134

3.322

.069

5.303

.329

n5
n«

.035
.039

2.309

.212

3.076

.251

2.794

.784

.069
.068

4.967
4.717

.397

2.400

.137
.134

.513
.650

.043

2.631

.295

.127

2.505

.910

.066

4.625

.465
.531

n8
n»

.048

2.995
3.463

.343

.116

2.211

1.026

.064

4.668

.596

.053

.396

.102

1.909

1.128

.061

4.790

.657

n,0

.058

3.954

.454

.086

1.600

1.215

.058

4.889

nn
ni2

.062

4.321

.516

.069

1.284

.054

4.806

.715
.770

.065
.068

4.433

.582

.052

.967

1.335

.050

4.422

.820

.649

.034

.866

.717

.018

1.370
1.388

3.804

.068

.655
.355

.046

n1
4

4.293
4.014

.041

3.139

.907

n«

.067

3.703

.784

.004

.074

1.391

.036

2.554

.942

11
1®

.063

3.414

.848

-.008

.905

-.017

1.383
1.366

.024

2.085
1.718

.972

3.164

.185
.419

.030

.057

n1
8
H
is

.048

2.953

.953

-.021

.627

1.345

.018

1.432

1.015

.036

.989

no
^
Zn,

.020
1.008

2.777
2.629

-.020
-.013

.811
.971

1.326
1.312

.012
.006

1.208
1.030

1.027
1.033

1.312

1.706

1.033

11.459

-.002

.062

-.002

-.001

.060

-.001

.008

.909

.008

II
fa

.004
.007
.007

.230
.358

.019
.025
.021

3.490
4.195
3.916

.019
.044
.064

.031
.058
.078

.021

.012

1.835

.149

.024

.003

.523

.002

2.179
.469

.089

.076
.079

.024
.026
.020
.011

5.151
5.105
4.971

.005
.003

.381
.262

.003
.009
.016

If.

.024

.279

.079

3.064

.091

5.274

bo
b,

-.049
—

.133
—

-1.522

.345
3.487

-.018

.052

-2.193

-2.256

3.801

-1.655

1.846

-.316

.407

.130

1.833

.060

1.273

f»
u

1.008

7.420

—

-.030

.509
.559

.802

1.094

1.262

1.268

D.W.

1.996

2.180

.091

.819

S.E.

.996

1.735

'All polynomial distributed lags are third degree with tail constraint only; t-statistics are absolute values; a dot over a vari
able indicates compounded annual rate of change; D! and D. are wage and price control and decontrol dummies, respectively.
^Numbers are the cumulative sum of coefficients.

F E D E R A L R E S E R V E B A N K O F ST . L O U I S

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1980

Table 4
Results of Chow Test (I/55-IV/69 vs. I/70-IV/79)
Critical F
GNP equation
Price equation

Calculated F

Conclusion

F.05 (7,86) ==2. 12
=
F.05 (8,60) 2.05

1.20
3.23

Cannot reject Ho1
Reject H
o

’ H is the null hypothesis that the regression equations are equal for the two sample periods.
o

nor the effect of nonmonetary shocks were significantly
different from zero, the equilibrium rate of change of
the price level during this sample period was equal
to the rate of monetary growth.
These two estimated equations implied that the
equilibrium rate of output growth was independent
of the rate of monetary expansion during the 1955-69
period. This implication was derived from an exami
nation of the elasticity estimates in conjunction with
equations 3 and 4; e(Y,M ) = 1 and e ( P , M ) = 1
together implied that e(X ,M ) = 0. In other words,
these estimated reduced form equations substantiated
the hypothesis that monetary actions have lasting ef
fects on only nominal variables.

Updated Results
Tables 2 and 3 present the results using data from
the 1970s. For purposes of comparison, the pre-1970
estimates are also summarized. The Chow test was
used to check the equations for stability.

Estimated Equations — Updated estimates for the
GNP equation are shown in table 2 and for the price
equation in table 3. Results are shown both for the
1970s (I/70-IV /79) and for the extended sample pe
riod (I/55-IV /79).
The sum of the coefficients on money in the GNP
equation was not significantly different from one at
the 5 percent level, either for the 1970-79 period or
for the fully extended sample period 1955-79. Esti
mates of the constant, however, indicated a decline
in the trend growth of velocity when data for the
1970s were included. For the 1970-79 sample period,
the estimated constant was negative but not signifi
cantly different from zero at the 5 percent level. For
the fully extended sample period, however, the con
stant was positive and significantly different from
zero, but the point estimate was less than that for
the 1955-69 period.
The estimate of the price equation for the 1970-79
period showed an increase in the sum of the coeffi

cients on money. However, this sum was not signifi
cantly different from zero at the 5 percent level. For
the fully extended sample period, the sum of the
money coefficients was significantly different from
zero, although not significantly different from one at
the 5 percent level.
Estimates of the remaining coefficients indicate that
nonmonetary factors, namely energy prices and wage
and price controls, influenced price level movements
during the 1970s, and to such an extent that they
were also significant over the full sample period. Esti
mates of the constant term for both the 1970-79 and
1955-79 periods were not significantly different from
zero at the 5 percent level.

Tests for stability — The updated results suggest
some conflicting conclusions. The Chow-test of sta
bility was used to investigate further the appropri
ateness of simply extending the sample period to in
clude the 1970s.11 Table 4 summarizes the results of
applying this test to the GNP and price equations.
The test results show that the hypothesis of stabil
ity for the GNP equation for the two sample periods
was not rejected. However, the hypothesis of stability
was rejected for the price equation. The interpreta
tion of these results is that the GNP equation, as
estimated over the full sample period, can be used to
summarize that relationship. However, the choice of
the estimated price equation depends on the period
that is chosen for analysis.12

Implications of the Results for the
Relationship between Money and Output
One implication of the reduced form results using
data prior to 1970 was that the equilibrium rate of
n Gregory Chow, “Tests of Equality Between Sets of Coeffi
cients in Two Linear Regressions,” Econometrica (July
1960), pp. 591-605.
12These price equations should not be interpreted as long-run
equations, however, because the sample periods are so short.
See footnote 3.

F E D E R A L R E S E R V E B A N K O F ST . L O U I S

output growth was independent of monetary growth.
In other words, trend output was determined by real
factors: namely, growth of the labor force, capital
stock, and technology.
When the reduced form equations were updated
with data from the 1970s, the implication for equilib
rium output was modified. In a strict statistical sense,
the hypothesis that monetary actions have lasting
effects only on nominal variables was not rejected
when data from the 1970s were included in estimating
the relationships. However, when the estimated GNP
equation for the full sample period was combined
with the price equation for the 1970-79 period, the
growth of money appeared to influence the rate of
growth of output. Although e (Y,M) was still approxi
mately one, the point estimate of e(P,M) was 1.31.
Consequently, based on the experience of the 1970s,
the point estimate of e(X,M) was —.31.
The nature of this result, although statistically ten
tative, is summarized in table 5. Underlying the cal
culations in this table is the assumption that non
monetary shocks equal zero. These results, although
they do not demonstrate causality, provide indirect
support for the view that there is a negative relation
between the trend rate of monetary growth (and in
flation) and the trend rate of economic growth.
This contention that inflation adversely affects out
put has received increasing emphasis in the recent
literature.13 One view is that inflation slows growth
by discouraging investment and saving via the exist
ing tax structure.14 The inflation process increases
effective tax rates for both individuals and firms and
lowers after-tax rates of return, thereby reducing in
centives to invest and save.
Another argument stresses the uncertainty associ
ated with inflation.18 If higher and higher inflation
rates also mean greater risks associated with invest
ment planning, saving and investment will be dis
couraged because a given expected rate of return will
be accompanied by a greater variance.
13For general discussions of possible factors contributing to
the slowdown of productivity in the 1970s, see Edward F.
Denison, “Explanations of Declining Productivity Growth,”
Survey of Current Business (August 1979), pp. 1-24; and
John A. Tatom, “The Productivity Problem,” this Review
(September 1979), pp. 3-16.

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1980

Table 5
Relationship between Trend Output
and Money Growth
Rate of growth
of money
0%
2
4
6
8

Rate of growth of output based on:
— --------- —----------------— -------— ----Pre-1970 results1
Updated results1
3.62%
3.54
3.46
3.37
3.29

4.68%
4.13
3.58
3.03
2.48

■These calculations are based on the point estimates of the
parameters in the GNP and price equations and assume
that nonmonetary influences are equal to zero except for
the constant terms.

Still another explanation of the inflation-growth
connection is that the inflation process introduces
“noise” into the price signals that are transmitted from
consumers to producers.16 As a result, the general
efficiency of the price system in allocating resources
is reduced. Such a reduction must be manifested in a
reduced growth rate of output.

SUMMARY
This article presents updated reduced form results
relative to the hypothesis that monetary actions have
a lasting impact on only nominal variables. When
data from the 1970s were included in the sample, this
hypothesis could not be rejected for either the 1970-79
period or the 1955-79 full sample period.
When the reduced form equations were tested for
stability over the entire period, the hypothesis of sta
bility for the GNP equation could not be rejected;
but the null hypothesis for the price equation was
rejected. When the GNP equation for the fully ex
tended sample period was combined with the price
equation for the 1970-79 period, the point estimates
of the coefficients suggested that the rate of growth
of output was negatively related to the growth rate
of money during the 1970s. Even though only sugges
tive, the results provide tentative evidence to support
the notion that real economic gain can be achieved
by reducing the trend growth of money.17

14A recent study providing evidence relating to the effect of in
flation on corporate rates of return is reported in Martin
Feldstein and Lawrence Summers, “Inflation and the Taxa
tion of Capital Income in the Corporate Sector,” National
Tax Journal (December 1979), pp. 445-70.

16Milton Friedman, “Nobel Lecture: Inflation and Unemploy
ment,” Journal of Political Economy (June 1977), pp.
451-72.

16See Stephen L. Able, “Inflation Uncertainty, Investment
Spending, and Fiscal Policy,” Federal Reserve Bank of Kan
sas City Economic Review (February 1980), pp. 3-13.

17Laurence H. Meyer and Robert H. Rasche, “On the Costs
and Benefits of Anti-Inflation Policies,” this Review ( Febru
ary 1980), pp. 3-14.

Full text of Review (Federal Reserve Bank of St. Louis) : April 1980

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