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The “Rationality” of Survey-Based
Inflation Forecasts
R. W. HAFER and DAVID H. RESLER

1 HE notion that economic agents rationally form
their expectations about future economic events has
emerged as a critically important hypothesis with pro
found implications for macroeconomic policy. For ex
ample, modern hypotheses relating to the Phillips
curve emphasize that it is the departure of actual
inflation from expected inflation that cause any shortrun trade-off that may exist between inflation and
unemployment. Consequently, empirical tests of many
macrotheoretic models require the identification not
only of directly observable phenomena, such as infla
tion and unemployment, but also of expectations or
anticipations of these phenomena.
The measurement of generally nonobservable phe
nomena, such as inflation expectations, poses a diffi
cult challenge in constructing empirical tests for
macro models that include such variables. It is first
necessary to identify an inflation expectations proxy
that is consistent with the assumptions of the under
lying model. As a result, tests of theories, such as the
natural rate hypothesis, that employ proxy measures
for inflation expectations (such as autoregressive pro
cedures) are joint tests of both the underlying theory
and the validity of the expectations proxy.
Presumably, autoregressive procedures are used
because they are less costly than opinion surveys.
When survey-based data on inflation expectations

are readily available, this cost argument loses some of
its force. Nevertheless, it is important to determine
which of the two measures is appropriate for test
ing various economic theories; that is, whichever
measure conforms most closely to the requirements
of the underlying theory becomes the measure of
choice. For instance, tests of rational expectations
models should first establish that the measures of
expectations conform to the criteria of rationality. This
paper examines whether one particular set of survey
data — the Livingston data — meets specified criteria
of rationality.1
JFor examples of studies dealing with the measurement and
effects of inflation expectations, see John A. Carlson, “A Study
of Price Forecasts,” Annals o f Econom ics and Social Measure
ment (Tune 1977), pp. 27-56; Stephen Figlewski and Paul
Wachtel, “The Formation of Inflationary Expectations,” R e
view o f Econom ics and Statistics (forthcoming); Rodney L.
Jacobs and Robert A. Jones, “Price Expectations in the United
States: 1947-1975,” American E conom ic R eview (June 1980),
pp. 269-77; Edward Kane and Burton G. Malkiel, “Autore
gressive and Nonautoregressive Elements in Cross-Section
Forecasts of Inflation,” Econom etrica (January 1976), pp.
1-16; Donald J. Mullineaux, “On Testing for Rationality: An
other Look at the Livingston Price Expectations Data,” Jour
nal o f Political Econom y (April 1978), pp. 329-36; Douglas
K. Pearce, “Comparing Survey and Rational Measures of
Expected Inflation: Forecast Performance and Interest Rate
Effects,” Journal o f Money, C redit and Banking (November
1979), pp. 447-56; James E. Pesando, “A Note on the Ration
ality of the Livingston Price Expectations Data,” Journal o f
Political E conom y (August 1975), pp. 849-58; and Stephen
J. Tumovsky,^ “Empirical Evidence on the Formation of Price
Expectations,” Journal o f the American Statistical Association
(December 1975), pp. 1441-54.

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

Tests of Rational Expectations
The hypothesis of rational inflation expectations,
pioneered by John Muth, holds that expectations
about future inflation are formed in a manner that
fully reflects all currently available and relevant in
formation.2 Stated somewhat differently, the observed
rate of inflation differs from the expected rate of
inflation only by some random error. Thus, the ration
ality hypothesis can be stated algebraically as:
( 1 ) TT, = ,-t u? +

U t,

where Ttt is the actual rate of inflation during period
t, t-iTt? *s the rate of inflation expected at time t-1 for
period t, and ut is a random variable with mean zero
and variance cr,V3
Expressed in this form, i.e., inflation expectations
are unbiased estimates of observed inflation, the ra
tionality hypothesis can be tested empirically by esti
mating the equation,
(2 )

TT,

= Bo + B,

+ u ,,

where t-i^t represents the survey-based expected in
flation rate for period t made at period t-1. The notion
of rational expectations, then, corresponds to the joint
hypothesis that B0 = 0 and B, = 1. In addition, u.
should exhibit no evidence of autocorrelation.
Pesando and Figlewski and Wachtel subjected the
Livingston expectations series to this test of rational
ity.4 Pesando was unable to reject the joint hypothesis
using consensus inflation forecasts from each survey
for the periods 1959-1969 and 1962-1969. Figlewski
and Wachtel, however, were able to reject the null
hypothesis using a pooled time series/cross-section
sample of 1,864 individual forecasts for the period
1947-1975.
An additional criterion for rationality requires that
inflation forecasts be efficient; in other words, the
process by which inflation expectations are formed
should be identical to the process that actually gener
ates observed inflation. Consequently, any evidence
suggesting that some of the relevant information set
is not being fully (i.e., efficiently) utilized would
indicate rejection of rationality. Pesando tested this
notion of rationality by hypothesizing that both the
expectations of inflation and inflation itself are de
scribed by the history of inflation. Mathematically,
2John F. Muth, “Rational Expectations and the Theory of Price
Movements,” Econom etrica (July 1961), pp. 315-35.
Alternatively, equation ( 1 ) can be rewritten as ( tt, - ,-iH?)
= Ut; that is, any departure of actual from expected inflation
is a random variable with mean zero and variance, 05.
4Pesando, “A Note on the Rationality . . .
and Figlewski and
Wachtel, “The Formation of Inflationary Expectations.”

NOVEMBER

1980

this interpretation of rationality can be expressed as:
(a)

IT, =

(3 )

1=1

B i TT, i +

(in

□

(b )

,-,H ? =

12=1 B ,'

Ttt- i +

LU, .

Efficiency requires that Bj = B/ for all i, . . . , n.
Pesando, Carlson, and Mullineaux directly tested the
efficiency of the Livingston inflation forecasts by esti
mating equation (3 ) and then applying an F-test to
the sum of the squared residuals.5 Pesando was not
able to reject the efficiency criterion at standard confi
dence levels for the period 1959-1969. Carlson, using
the same time period but a revised version of the
Livingston data, found that the inflation forecasts do
not satisfy the efficiency criterion.6
Mullineaux, on the other hand, demonstrated that
the error variances of equations (3a) and (3b ) esti
mated by Pesando and Carlson are not homogeneous.
Consequently, the F-test used by Pesando and Carlson
is inappropriate.7 Mullineaux proposed an alternative
efficiency test that involves estimating the equation,
(4 )

FEt

(tt,

, .it?)

b„ +

i= l

b , Tt t - i

where £, = [ilt _ ^i2t. The forecast error (F E t) is re
gressed on past inflation rates known at the time the
forecast was made.8 Efficiency requires that F E t be
5See Pesando, “A Note on the Rationality . . .
This approach
to testing for rationality is generally referred to as a “weakform” test because it employs only information contained in
the history of inflation. It should be noted, however, that fail
ure to meet the weak-form requirements of rationality sug
gests that the forecast would also fail stronger forms of the
test. For a discussion of weak-form and other types of tests,
see John Rutledge, A M onetarist M odel o f Inflationary E xpec
tations (Lexington: Lexington Books, 1974). In addition,
equation (3 ) does not specify either the exact length of the
lag on past inflation or the length of the period over which
the inflation is observed. Pesando, Carlson, and Mullineaux
each used a 5-period lag on observed 6-month inflation rates.
This lag length will also be used in this paper.
'■Carlson has noted that the numbers published by Livingston
have been judgmentally revised. To circumvent this possible
source of error, Carlson constructs a forecast series that is
based on the actual responses received by Livingston. See
Carlson, “A Study of Price Forecasts,” for a more detailed
discussion of his construction procedures.
7The Chow test used by Pesando and Carlson requires that the
error terms H,, and
be independently and identically dis
tributed. If the error terms are not identically distributed
(homogeneous variances), the Chow test is inappropriate.
Mullineaux tests for variance homogeneity by using Bartlett’s
test statistic and finds that the hypothesis of homogeneous
variances is rejected at the five percent level of significance.
See Mullineaux, “On Testing for Rationality . . . ,” pp. 331-32.
8Equation (4 ) is derived by subtracting equation (3 b ) from
(3 a ). That is, b, = Bi — B| for all i. Following Mullineaux,
equation ( 4 ) is estimated with a constant term (bo) instead
of subsuming it into the error structure as Pesando and Carl
son did.

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

unrelated to any information known at the time ( t-1)
the forecast was formed. In other words, all the in
formational content of past inflation rates is fully
utilized in forming expectations. Thus, the null hypoth
esis is that b0 = 0 and bj = 0 for all i, . . . , n. In
addition, efficiency requires that the error term be
serially uncorrelated, or Cov (£ t, £i) = 0 for t / i.9
Using Carlson’s version of the Livingston data, Mullineaux was unable to reject the efficiency hypothesis
for the period 1959-1969.10
Pearce, using Carlson’s data set and another test of
efficiency, concluded that “the survey respondents did
not efficiently use the information in the past history
of the Consumer Price Index (C P I) when forming
their expectations of inflation.”11 Thus, it appears that
efficiency tests of the Livingston inflation expectations
data are sensitive to the type of tests used, to the
version of the Livingston data used, and to the time
period examined.
This article demonstrates that these test results are
also sensitive to assumptions about the length of the
forecast horizon. Therefore, it is particularly impor
tant to determine the actual period over which Liv
ingston respondents are making their' forecasts. The
nature of this problem can be illustrated by a careful
review of the survey method.

The Forecast Horizon and the Forecast Error
Livingston conducts his survey each spring and fall,
requesting respondents to indicate their predictions
about a number of economic indicators including the
CPI. For example, in the spring survey they are asked
to predict what the level of the CPI will be in the
following December and June. Because the question
naires are mailed in April and usually are returned in
May, two interpretations can be made about the fore
cast horizon. If, as Carlson assumes, the survey re
spondents know only the April CPI, then they are
implicitly predicting an 8-month rate-of-change ( April
to December) and a 14-month rate-of-change (April
9It should be noted that, although the heterogeneous variance
problem that plagued the Chow tests of Pesando and Carlson
is alleviated here, the procedure employed does require the
maintained hypothesis of independent errors.
10Mullineaux also found that for the data set used by Pesando
(i.e., inflation forecasts inferred from the originally published
versions of Livingston data), the hypothesis of efficiency is
rejected.
11Pearce, “Comparing Survey and Rational Measures . . .
p. 451. Pearce statistically analyzes the forecast errors ob
tained by using either the Livingston forecasts or forecasts
generated from a continuously updated moving average
model [M A (1)] of the monthly CPI series.

NOVEMBER

1980

to June of the following year). Alternatively, Jacobs
and Jones argue that a more reasonable assumption
is that the respondents actually know or have an ac
curate estimate of the May CPI.12 This, of course,
means that the forecast CPI implies a 7-month (or
13-month) rate of inflation.
The choice of the forecast horizon can affect the
results of the bias and efficiency tests, especially if
the forecast is interpreted loosely as a prediction of a
steady inflation. Mullineaux and Resler each made this
assumption; i.e., they assume that the prediction is a
constant rate-of-change for any period within a given
forecast horizon.13 This assumption is often conven
ient and may not be inappropriate when the investi
gation focuses on the process that generates the fore
cast. It may pose problems, however, when efficiency
tests, such as those represented by equation (4 ), are
conducted.
Because the survey respondents are, in fact, fore
casting an inflation rate over a 7- or 8-month horizon,
it is desirable to evaluate equation (4 ) by calculating
the forecast error over that time horizon. For example,
F E t should be calculated by taking the difference be
tween the actual rate of inflation occurring between
April (or May) and December and the rate of infla
tion predicted for that period. This forecast error
should be regressed against lagged inflation rates
known to the forecaster as of April (or May). This
approach differs from Mullineaux’s procedure in which
F E t was computed as of the time the next forecast was
made (i.e., October). This approach seems inappro
priate for evaluating the efficiency of the forecasts,
especially since the forecasts exhibit expectations of
accelerating inflation. The next section reevaluates the
tests for bias and efficiency in light of these new tim
ing assumptions.

Empirical Results
To investigate the importance that assumptions
about the forecast horizon have on tests for bias and
12Jacobs and Jones, “Price Expectations in the United States:
1947-1975.”
13This essentially requires that inflation forecasts are linear.
Thus, changes from one point to another within the fore
cast horizon will not be distinguishable. If, however, infla
tion expectations are not linear over different time horizons
(e.g., 6 or 8 months), then the assumption of a steady rate
of inflation prediction is vitiated. The fact that the 14-month
forecasts are greater than the 8-month forecasts in 38 out
of 40 observations from 1959-1978 suggests that the assump
tion of a constant rate of inflation within the 8- or 14-month
periods may not be appropriate. See Mullineaux, “On Test
ing for Rationality,” fn. 3. See also, David H. Resler, “The
Formation of Inflation Expectations,” this Review (April
1980), pp. 2-12.

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

efficiency (and hence rationality), the three alternative
forecast horizons discussed in the preceding section
are utilized in direct empirical comparisons. Based on
these forecast horizons, three forecast error series are
calculated and employed in the efficiency tests re
ported below. To reiterate, these alternative F E t series
are determined by assuming an April-October fore
cast horizon (Mullineaux), a May-December fore
cast horizon ( Jacobs-Jones), and an April-December
forecast horizon. All tests use Carlson’s version of the
Livingston data (i.e., sample average CPI forecasts
from which the expected inflation rate is generated).
To facilitate a comparison with previous research, the
following sample periods are used: 1959-1969, 19591978, and 1959-1978 excluding the 1971-1973 period of
price controls of various phases.14
To test for bias in the inflation forecasts, equation
(2 ) is estimated and an F-test on the joint hypothesis
that B0 = 0 and Ba = 1 is conducted for each of the
alternative forecast horizons.15 The F-values calcu
lated for this test are presented in table 1, and allow
rejection of the null hypothesis at the 1 percent level,
irrespective of the sample period chosen. This result
contrasts directly with Pesando’s but is consistent with
the findings of Figlewski and Wachtel, who found
the Livingston data to be biased.16 An examination of
the individual coefficients, B,, and B,, indicated
that the joint hypothesis is rejected primarily be
cause B, exceeds unity for all the sample periods.
Nevertheless, the results indicate a tendency for B,
to decline toward unity as more recent observations
are added to the sample, suggesting that forecasters
gradually adjusted to the accelerating inflation of the
1960s and early 1970s.17
Table 2 presents additional information on the
accuracy of the inflation expectations series. Although
the root-mean-squared error and mean error statistics
14This truncated 1959-1978 sample period was chosen to ex
clude observations of forecasts errors that occurred during
the period of wage and price controls. It seems reasonable
that forecasters would have encountered considerably more
difficulty in forecasting inflation during this period, since the
controls were applied unevenly and gradually relaxed at
unpredicted intervals.
15To facilitate computation of the appropriate F-statistics,
equation ( 2 ) was modified slightly. Specifically, subtracting
t-iTt? from each side of (2 ) produces:
(2') Ut — t-illt = B„ + (B , — 1 ) t-ilT? + u,.
The null hypothesis then implies that the estimated slope
and intercept of equation (2 ') be jointly equal to zero.
1GPesando, “A Note on the Rationality . . . ” and Figlewski
and Wachtel, “The Formation of Inflationary Expectations.”
17In studies of the process by which inflation forecasts are gen
erated, more definitive evidence indicates that this process
has changed over time. For more detail about this evidence,
see Donald J. Mullineaux, “Inflation Expectations and Money

NOVEMBER

1980

Table 1

Bias Test for “Short-Run”
Inflation Forecasts1
F-Values
Period
Forecast
horizon

1959-1969

1959-1978

1959-1978-

April-October

15.242

15.723

14.401

May-December

12.660

15.487

14.411

April-December

28.367

18.144

17.439

F(2,20)

F(2,38)

F(2,35)

Critical

3.49

3.25

3.27

F-values 1%

5.85

5.21

5.27

'Test based on joint hypothesis that B0 = 0 and Bi =
in equation (2 ’).

2This period excludes the 1971-1973 price control years.

vary only slightly between forecast horizons, the
Theil statistics indicate that the fraction of forecast
error due to bias is reduced somewhat by using the
May-December horizon. It is interesting to note that,
of all of the horizons examined, the April-December
assumption continually yields statistics suggesting
greater problems with bias than variance or covari
ance in the forecasts.18
Although unbiased forecasts satisfy one criterion
for rationality, it is common to find properties of bias
in other non-survey-based inflation forecasts. For in
stance, Lombra and Moran note that, while the
Federal Reserve Board staff’s forecasts of nominal
GNP are unbiased, its forecasts of GNFs real and
inflation components show evidence of systematic
errors.19
It is possible that inflation forecasts can show evi
dence of systematic bias yet still be characterized as
Growth in the United States,” American Econom ic Review
(March 1980), pp. 149-161, and Resler, “The Formation of
Inflation Expectations.”
18For a description of this methodology, see Henri Theil, Ap
plied Econom ic Forecasting (Amsterdam: North Holland
Publishing Co., 1971), pp. 26-32.
19Raymond Lombra and Michael Moran, “Policy Advice and
Policy Making at the Federal Reserve,” Carnegie-Rochester
C onference Series on Public Policy 13, 1980, p. 20. For evi
dence that other forecasts similarly underestimate inflation
and over-estimate real output, see V. Zarnowitz, “An Analysis
of Annual and Multiperiod Quarterly Forecasts of Aggregate
Income, Output, and the Price Level,” Journal o f Business
(1 9 7 9 ), p. 133.

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

NOVEMBER

1980

Table 2

Analysis of the “Short-Run” Forecast Errors1
Forecast
horizon
assumption

Sample
period

April-October

May-December

April-December

Theil statistics

RMSE

Mean
error

1959-69

1.383

0.911

1959-78

2.151

1.324

1959-78-’

2.053

1959-69
1959-78
1959-782

0.434

0.360

0.206

0.379

0.226

0.394

1.270

0.383

0.223

0.394

1.344

0.858

0.408

0.347

0.246

2.317

1.414

0.372

0.252

0.375

2.214

1.356

0.375

0.252

0.373

1959-69

1.307

0.934

0.513

0.344

0.143

1959-78

2.101

1.355

0.416

0.210

0.374

1959-782

1.962

1.261

0.413

0.203

0.384

'RM SE is the root-mean-squared error, Um is the Theil bias coefficient, U” the variance coefficient, and Uc the covariance
coefficient.
2Omits the 1971-1973 price control years.

“weakly” rational in the sense that the forecasters
efficiently utilize all information contained in the his
tory of inflation. To implement this efficiency test, FE,
is calculated for each forecast horizon and used to
estimate equation (4 ).

ably from those of Mullineaux, and thev highlight the
importance of specifying the time period over which
FE, is calculated. If FE, is evaluated at the end of the
period over which the respondents were forecasting
inflation (e.g., December), the efficiency hypothesis is
rejected in all but one instance. The results for the
three different time periods are now discussed in
greater detail.

Because acceptance of the efficiency hypothesis in
the present context requires that bi = 0 for all i ( i = l ,
. . . , n) and that the estimated relationships indicate
no evidence of serial correlation, the statistics of pri
mary interest are the reported F-values and the Durbin-Watson and Durbin-h statistics. The reported
F-value is pertinent for testing the joint hypothesis that
all the bi (i = 1, . . . ,5) are concurrently zero. Both
the Durbin-Watson and Durbin-h statistics test for the
presence of serial correlation. Although the DurbinWatson statistic is usually appropriate, Durbin has
shown that the h statistic is more efficient when the
set of independent variables includes a lagged de
pendent variable.20 Because Mullineaux has interpreted
equation (4 ) as containing a lagged dependent vari
able, both statistics are reported.

Turning first to the 1959-1969 period, the reported
F-statistic for the May-December and the AprilOctober forecast horizons indicates that the efficiency
criterion is satisfied. Recalling that the April-October
horizon corresponds to the assumption made bv
Mullineaux, these results are essentially consistent
with his. The Durbin-h statistic for the April-October
horizon, however, indicates the presence of negative
serial correlation, even though the Durbin-Watson
statistic falls within the indeterminate range.21 Since

Ordinary least squares estimates of equation (4 ),
using the alternative F E t series and sample periods,
are presented in table 3. These results differ consider-

+ 0.050tt<-4 + 0.083tt,
(0.25)
(0.48)

20See James Durbin, “Testing for Serial Correlation in Least
Squares Regression When Some of the Regressors are Lagged
Dependent Variables,” E conom etrica (May 1970), pp.
410-21.

21For purposes of comparison, Mullineaux’s estimation results
are presented here:

(it,- t-iTrf) = -0.232 + 0.237tt,., -0.051tt,-2 + 0.251n„„
(1.91) (1.44)
(0.27)
(1.36)

R 2 = 0.102, h = 1.89, F = 1.48.
The difference between Mullineaux’s results and those in
table 3 may well be due to the use of different computer
algorithms. As such, the difference between the Durbin-h
values may not be representative of true differences in the
respective residual processes.

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

NOVEMBER

1980

Table 3

Efficiency Test Results1
CoefficientsForecast
horizon

b„

Summary statistics3

R-’

D.W ./h

S.E.E.

F ° (.05, .01)

1959- 1969
April-October

-0.244
(0.46)

0.244
(1.48)

-0.049
(0.26)

0.254
(1.37)

0.050
(0.26)

0.083 '
(0.48)

0.11

2.61/-2 .2 6

1.00

1.54

May-December

-0.493
(1.02)

0.193
(1.19)

0.114
(0.61)

0.215
(1.10)

0.114
(0.58)

0.041
(0.22)

0.24

2.25/-0.91

0.92

2.36

April-December

-0.345
(0.88)

0.218
(1.79)

0.051
(0.36)

0.295
(2.16)

0.019
(0.13)

0.061
(0.47)

0.38

1.85/0.43

0.74

3.52

April-October

0.695
(1.53)

0.397
(2.82)

0.003
(0.02)

-0.100
(0.55)

-0.261
(1.44)

0.102
(0.71)

0.20

2.14/-0.97

1.54

2.92

May-December

0.442
(1.01)

0.435
(3.29)

0.133
(0.81)

-0.113
(0.64)

-0.436
(2.43)

0.200
(1.40)

0.37

1.98/0.12

1.47

5.68

April-December

0.717
(1.74)

0.368
(2.88)

0.035
(0.22)

-0.058
(0.35)

-0.362
(2.21)

0.160
(1-23)

0.26

1.77/1.01

1.40

3.76

2.85, 4.44

19 59-1978

2.49, 3.51

19 59-1978
(Omitting 1971-73)
April-October

0.649
(1.44)

0.300
(2.06)

0.062
(0.35)

-0.052
(0.28)

-0.257
(1.41)

0.082
(0.56)

0.14

2.21 / - 1 .22

1.51

2.16

May-December

0.414
(0.96)

0.340
(2.43)

0.175
(1.06)

-0.051
(0.29)

-0.412
(2.31)

0.155
(1.07)

0.34

2.01/-0.05

1.50

4.43

April-December

0.668
(1.69)

0.269
(2.11)

0.098
(0.63)

-0.009
(0.06)

-0.361
(2.26)

0.140
(1.10)

0.24

1.80/0.90

1.33

3.14

2.54, 3.73

iT e s t results based on equ ation ( 4 ) .

-Values in parentheses represent absolute values of t-statistics.
3R- is the coefficient of determination corrected for degrees of freedom; D.W. is the Durbin-Watson statistic; h is the Durbin-h statistic; S.E.E. is the standard error of the equation; F is the calculated F-value to test the joint hypothesis that all
bi (i = 1, . . . , 5 ) equal zero; and F ° represents the relevant critical F-value.

efficiency requires no serial correlation among the
residuals, the hypothesis of efficiency for the AprilOctober horizon remains unresolved. Unlike these two
forecast horizons, however, the results based on using
the April-December assumption clearly permit rejec
tion of the efficiency hypothesis.22
In contrast to the results for the 1959-1969 period,
the hypothesis of efficiency is unambiguously rejected
at the 5 percent level for each forecast horizon ex
amined during the entire 1959-1978 sample period.
The hypothesis is also rejected at the 1 percent level
for the May-December and April-December horizon
22It should be recalled that the April-December forecast hori
zon does not require the special assumptions necessary to
construct the competing forecast error series. We know that
Livingston supplies the April CPI to the survey recipients
and specifically asks for their D ecem ber CPI forecast.

periods. Based on these test results, the period from
1959-1978 does not appear to be one in which
Livingston forecasters, on average, efficiently utilized
the information contained in the history of observed
inflation rates.
Similarly, when the period of wage price controls
is excluded, the efficiency criterion is not satisfied if
the forecast error is calculated at the end of the fore
cast period (e.g., in December). For instance, when
the forecast error is measured at the end of the pe
riod over which the forecast is made, the F-test per
mits a rejection of the efficiency hypothesis at the
5 percent level.23 The efficiency hypothesis is not re23The efficiency hypothesis cannot be rejected, however, at the
1 percent level when the 8-month (April-December) fore
cast horizon is employed.

NOVEMBER

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

jected only when the forecast error is evaluated in
October (as in Mullineaux).

1980

_________________________

Table 4
Efficiency of the 12-Month Forecasts
Most previous analyses of the Livingston inflation
forecasts focus on the short-run (8-month) forecasts.
Because the respondents are asked at each survey date
to predict the level of the CPI for the following De
cember and June, the forecasts embody both an 8month and a 14-month (long-run) prediction of the
inflation rate. This section examines the rationality
of the 14-month forecasts.

Bias Test for 14-Month
Inflation Forecasts1
F-Values
Sample
period

June
forecast

December
forecast

Critical F
(.05, .01)

1959-1969

16.130

20.800

4.26, 8.02

1959-1978

9.533

5.188

3.55, 6.01

10.599

4.592

3.63, 6.23

1959-19782

The methodology used here slightly modifies the
approach used for the 8-month forecasts. Specifically,
the lagged inflation rates in equation (4 ) are now
interpreted as occurring over 12-month periods ( again,
observed in either April or October). This assump
tion requires that the estimation of these equations
for the 14-month forecasts be modified.
Because the forecasts are made at 6-month intervals,
this new interpretation means that the first lagged
term in equation (4) contains information that over
laps from the previous period, if all available observa
tions are included in the estimation procedure. Such
overlapping observations may introduce serial corre
lation into the equation.24 To avoid this problem,
separate estimations of equations (2) and (4 ) are
made for each semiannual observation of the 14month forecast; that is, each sample period is split
into two data sets, one consisting only of the June
forecasts and the other consisting only of the Decem
ber forecasts. With these modifications, equations (2)
and (4 ) are estimated for the three time periods used
in the previous section.
The analysis first examines the 14-month forecasts
for bias. F-statistics were computed from the regres
sions of equation (2) for each semiannual forecast
series over each sample period. These F-values, re
ported in table 4, again indicate that the forecasts
are biased. Table 5 provides the statistics for Theil’s
analysis of the forecast errors. These results also show
that .33-54 percent of the forecast error is due to bias.
Nevertheless, as with the “short-run” forecasts, the
portion due to bias declines as new data are added.
The efficiency test is then applied to the 14-month
forecast errors. The forecast errors are consistently
24Introduction of serial correlation tends to bias the efficiency
test toward rejecting the null hypothesis. Recall that an
additional criterion for efficiency is that the estimation be
free of autocorrelation.

'Test based on joint hypothesis that B» ~ 0 and B, — 1
in equation (2 ’).
2Oniits the 1971-1973 price control years.

measured as of the end of the period over which the
forecast was made. The F-statistics and the DurbinWatson statistics for these equations are reported in
table 6.-5 In contrast to the 8-month ( April-December) inflation forecasts, the results for the 14-month
forecasts do not permit rejection of the efficiency
hypothesis. Because halving the sample period severely
reduces the degrees of freedom, these results should
be interpreted with considerable caution. Nevertheless,
the F-statistics suggest that the errors in the 14-month
forecasts are not correlated with observations of past
inflation available at the time the forecast was made.
The Durbin-Watson statistics, however, indicate that
the hypothesis of no serial correlation can neither be
rejected nor accepted. Thus it appears that, based
on the F-test, the 14-month forecasts comply with the
efficiency criterion.
These contrasting results for the 8-month and 14month forecast horizons cast some doubt on the find
ings that the Livingston forecasts are not formed
efficiently. This disparity may indicate that forecasters
are better able to anticipate longer-term movements
in economic variables, such as inflation, relative to
explaining the short-term vagaries of the time series.
For instance, if the actual rate of inflation is accelerat
ing within the 14-month period, the forecaster may be
able to forecast efficiently the overall rate of change
but not be able to forecast the rate within shorter
sub-periods.
25The Durbin-h statistic is not appropriate for small samples
(n < 3 0 ). On this point, see J. Johnston, Econom etric M eth
ods, 2nd ed. (New York: McGraw-Hill, 1971).

F E D E R A L R E S E R V E B AN K O F ST. LO UI S

NOVEMBER

1980

Table 5

Analysis of 14-Month Forecast Errors1
Forecast
horizon
assumption

Sample
period

June

December

Mean
error

RMSE

Theil statistics
---------------------------------------Um
U*

1959-69

1.120

0.824

0.540

0.337

0.123

1959-78

1.964

1.298

0.436

0.208

0.356

1959-782

2.022

1.383

0.468

0.222

0.310

1959-69

1.182

0.782

0.438

0.474

0.088

1959-78

2.085

1.190

0.326

0.198

0.477

1959-782

1.976

1.133

0.329

0.194

0.477

1RMSE is the root-mean-squared enror; Um is the Theil bias coefficient; Us the variance coefficient; and Uc the covariance
coefficient.
2Omits the 1971-1973 price control years.

Table 6

Efficiency Test Results: 14-Month Forecasts1
Sample period

June forecasts
D.W.

1959-69

0.426

December forecasts
N

1.38

D.W.

F *(.05, .01)

1.344

2.25

5.05, 10.97

1959-78

1.049

1.88

2.029

1.87

2.96, 4.69

1959-782

0.875

1.34

1.993

2.30

3.11, 5.06

*N is the respective sample size; F is the calculated F-statistic; D.W. is the Durbin-Watson test statistic; and F * represents
the relevant critical F-value.
2Omits the 1971-1973 price control years.

Summary
This paper has reexamined the rationality of the
inflation forecasts contained in the Livingston survey
data by emphasizing that the inflation forecast error
should be calculated in a manner consistent with the
forecast horizon used by the survey respondents.
Specifically, empirical tests for bias and efficiency of
the forecasts were employed to determine the effect
that changes in the assumption about the forecast
horizon have on the conclusions of previous investiga
tions. The test for bias indicated that, regardless of
the forecast horizon or the sample period used, the
Livingston forecasts exhibited characteristics of bias.
The “efficiency” test suggested by Mullineaux was
also employed. These test results indicate that over

the period, 1959-1969, only one forecast horizon
( April-December) could be judged unambiguously
inefficient. When the 1959-1978 period is examined,
however, the results for each forecast horizon allow
rejection of the efficiency hypothesis. When the period
of wage-price controls is deleted from this sample
period, only the April-October forecast horizon is
judged efficient.
These findings imply that conclusions regarding the
forecast efficiency (and, therefore, rationality) of the
Livingston inflation expectations are sensitive to the
period over which the forecast error is evaluated.
Because the survey respondents are asked specifically
to predict the level of the CPI for the following
June or December, it seems appropriate that tests of

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

efficiency be formulated to measure the forecast error
only after the actual value of the predicted CPI be
comes known. When this approach is used in con
junction with the assumption of either a May-December or April-December forecast horizon, the results
indicate that the forecasters did not efficiently use the
information available at the time of the survey in five
out of six samples. This conclusion contrasts sharply
with that reached when the forecast error is calcu
lated at the time the forecasts are made ( i.e., April or
October).
Finally, evidence about the bias and efficiency of
the 14-month forecasts indicates that these longer
forecasts are efficient, even though, like the 8-month
forecasts, they are apparently biased. Although the
apparent disparity in the efficiency tests between the
“short-” and ‘long-run” forecasts is somewhat puz
zling, it suggests that the forecasters are more efficient

NOVEMBER

1980

at predicting longer term inflation trends than short
term movements in the series.
The evidence presented here indicates that Carlson’s
sample average forecasts of the rate of CPI inflation
in the Livingston data do not conform to two criteria
of rationality. Consequently, the use of these data in
empirical investigations of rational expectations mod
els appears to have serious limitations. In addition,
the observation that these survey-based inflation ex
pectations fail to conform to rationality criteria sug
gests that adjustments in expectations evolve slowly.
This further implies that, even if inflation forecasts
are ultimately rational, fully anticipated short-run
monetary policy actions may have important economic
effects since inflation expectations adapt slowly. These
and other possible implications of the apparent non
rationality of survey-based expectations deserve fur
ther study.

We would like to thank Don Mullineaux and Doug Pearce for their helpful com
ments on an earlier draft of this paper. Their contributions in no way imply complete
agreement with the opinions expressed herein.

Monetary Aggregates as
Monetary Indicators
KEITH M. CARLSON and SCOTT E. HEIN

1 HE monetary aggregates are being relied upon rently being taken by monetary authorities.
more and more as indicators of the thrust of mone
Early this year, the Federal Reserve Board an
tary policy actions on aggregate economic activity.1
nounced a redefinition of the monetary aggregates. In
To be useful as a monetary indicator, a monetary ag
some cases, the differences between the old and new
gregate should satisfy at least two criteria. First, it
money measures are quite substantial. While the re
must be sensitive to policy actions taken by the
lationship between the old monetary aggregates and
Federal Reserve — such as open market operations
economic activity has received much attention in the
and changes in reserve requirements, the discount
economic literature, the usefulness of the new mone
rate, and Regulation Q ceilings; it must not be sensi
tary aggregates as monetary indicators has yet to be
tive to influences other than Federal Reserve actions.
examined in detail. This article reports some results
If the monetary aggregate is responsive to nonpolicy
bearing on this issue.
forces, it will provide erroneous signals as to the
thrust of monetary policy.2
The analysis focuses primarily on the relationship
of the new MIA, M1B, and M2 measures to economic
Second, a monetary aggregate should be both con
activity. To provide historical continuity, the results
sistently and predictably related to the pace of eco
are compared with those derived from analyses of the
nomic activity. If it is not, changes in the monetary
old M l, M2, and M3 aggregates.
aggregate will not “indicate” what will happen to
aggregate economic activity as a result of actions cur

THE NEW MONETARY AGGREGATES
1For a general discussion of monetary indicators, see Albert E.
Burger, “The Implementation Problem of Monetary Policy,”
this R eview (March 1971), pp. 20-30.
2This criterion explains why many argue against the use of
market interest rates as monetary indicators. See Albert E.
Burger, “The Implementation Problem . . . ,” where he argues
that market interest rates are poor monetary indicators be
cause they are sensitive to nonpolicy impulses, such as factors
that affect the demand for credit.

Components of the new MIA, M1B, and M2 mone
tary aggregates are listed in table l.3 MIA is identical
3For a detailed description of the new
see R. W. Hafer, “The New Monetary
view (February 1980), pp. 25-32; or
“The Redefined Monetary Aggregates,”
letin (February 1980), pp. 97-114.

monetary aggregates,
Aggregates,” this R e
Thomas D. Simpson,
F ederal Reserve Bul

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

to old M l, except that it excludes demand deposits
due to foreign commercial banks and official institu
tions. The new M1B aggregate, a broader transaction
measure, is equal to M l A, except that it includes
newly developed interest-bearing transaction deposits.
These latter deposits include negotiable order of with
drawal (NOW ) accounts, automatic transfer system
deposit (ATS) accounts, and credit union share
drafts. NOW accounts were legalized in certain New
England states early in the 1970s, and such legaliza
tion will extend nationwide as of December 31, 1980.4
Commercial banks have been permitted to offer indi
vidual ATS accounts since November 1, 1978.
Chart 1 presents compounded annual rates of
change of old M l, MIA, and M1B for the period II/
1959 through IV/1979.5 The chart shows that the ex
clusion of demand deposits held by foreign commer
cial banks and institutions has had little effect on the
growth rates of the monetary aggregates. Growth
rates of new MIA closely resemble those of old M l.
Furthermore, the growth rates of MIA and M1B
differ little prior to early 1974 and, although M1B
growth usually exceeds that of MIA over the period
1/1974 through III/1978, the disparity between these
aggregates is quite small. It is only after the nation
wide introduction of ATS accounts in late 1978 that
the growth rates of these new aggregates show any
marked divergence.
While the new MIA and M1B measures are similar
in scope to old M l, the new M2 measure is quite
different from old M2. In fact, the new M2 measure
is more closely related to the old M3, which included
savings and small time deposits of thrift institutions;
old M2 did not include such deposits. Because the
monetary aggregates are no longer differentiated on
the basis of institutional considerations, old M2 does
not have a counterpart among the new measures.
As shown in table 1, there is essentially only one
component of the old M3 measure — large time de
posits (other than large negotiable CDs) at commer
cial banks and thrift institutions — that is not included
4For a description of the New England experience with NOW
accounts, as well as a discussion of how their legalization will
affect other parts of the country, see William N. Cox III,
“NOW Accounts: Applying the Northeast’s Experience to the
Southeast,” Econom ic R eview of the Federal Reserve Bank of
Atlanta (September/October 1980), pp. 4-10; and Patrick J.
Lawler, “NOW Accounts in the Southwest: A Break for Con
sumers, an Entry from S&L’s, and a Test for Banks,” V oice
o f the F ederal R eserve Bank o f Dallas (October 1980), pp.
5The historical series for the new monetary aggregates begins
in 1/1959.

NOVEMBER

1980

Table 1

The New Monetary Aggregates
Component

M1A

M1B

Currency in circulation

Demand deposits at commercial
banks and thrift institutions,
exclusive of deposits due to
foreign commercial banks and
official institutions

NOW and ATS accounts and
credit union share drafts
Overnight RPs

Savings deposits at commercial
banks and thrift institutions

Small time deposits (less than
$100,000) at commercial banks
and thrift institutions

Overnight Eurodollar deposits
issued by Caribbean branches of
member banks and held by
U.S. nonbank residents

Money market mutual fund shares

in the new M2 measure. On the other hand, a num
ber of the changes that have been made make new
M2 even more comprehensive than old M3. In addi
tion to the interest-bearing transaction deposits in
cluded in M1B, the new M2 measure also includes
overnight BPs at commercial banks, money market
mutual funds, and overnight Eurodollar deposits is
sued by Caribbean branches of member banks and
held by U.S. nonbank residents.6
Chart 2 depicts the compounded annual rates of
change of new M2, old M2, and old M3. Growth rates
of the new M2 and old M3 aggregates were similar
from the 11/1959 through 11/1973 period; growth rates
of old M2, on the other hand, generally were much
slower than these aggregates. The similarity in the
growth rates of old M3 and new M2 breaks down in
late 1973, however, when overnight BPs, money mar
ket mutual funds, and the overnight Eurodollar de
posit component of new M2 became increasingly
popular.
6Timothy Q. Cook and Jeremy G. Duffield, “Short-Term In
vestment Pools,” E conom ic Review of the Federal Reserve
Bank of Richmond ( September/October 1980), pp. 3-23. The
authors have recently argued that there are many other in
vestment pools, similar to money market mutual funds, which
should be included in the new M2 measure.

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

Chart 1

Compounded A n n u a l Rates of Change of
M l(o ld ), M I A and M1B

L a te st d a ta p lo tte d : M l (o ld ) - 4 th q u a r te r 1 979; O th e rs-2 n d q u a rte r 1980

C h a rt 2

Compounded A n n u a l Rates of Change of

L a te st d a ta p lo tte d : M 2(new )-2nd q u a rte r 1 98 0; O th e rs -4 th q u a rte r 1979

NOVEMBER

1980

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

NOVEMBER

1980

C h a rt 3

C om pounded A n n u a l Rates of C hange of
M 2 ( n e w ) and M1B
Percent

1959 6 0

Percent

79 1980

S h a d e d a re a s re p re s e n t p e r io d s d u r in g w h ic h th e th re e -m o n th tre a s u ry b ill ra te w a s a t le a s t 100 b a s is p o in ts a b o v e
th e c e ilin g ra te o n c o m m e rc ia l b a n k s a vin g s d e p o s its .
L a te s t d a ta p lo tte d : 2nd q u a r te r 1 980

Finally, chart 3 presents the compounded annual
rates of change of the new M1B and M2 aggregates.
This chart illustrates the differential growth rates of
narrow versus broad money measures.7 Note the dif
ference in average growth rates; new M2 growth is
usually above that of M1B. The average growth rate
of new M2 over the 11/1959 through IV/1979 period
is 8.4 percent, compared to 5.0 percent for M1B.
The differential between the two growth rates
sometimes varies. The chart indicates a definite pat
tern in the relative growth rates. Over the periods
II/1959-IV/1965, III/1970-I/1973, and I/1975-I/1978,
growth rates of new M2 are substantially above those
of M1B. In the intervening periods, the differential
between growth rates of these two aggregates is very
small.
Historical experience indicates that the growth rate
of the broad money stock measure is sensitive to
the differential between market interest rates and
Regulation Q ceilings. This is clearly indicated by the
7M1A is excluded for simplification purposes; prior to late 1978,
quarterly growth rates of MIA were very similar to those of
M1B (see chart 1). Further, while only the new aggregates
are shown, old M l and M2 display a similar pattern.

shaded areas in chart 3, which depict periods of two
quarters or more during which the three-month treas
ury bill rate was at least 100 basis points above the
ceiling rate on commercial bank savings deposits.8
Redefining this broader monetary aggregate has not
made it insensitive to nonpolicy influences. Nonpolicy
factors that affect the supply or demand for credit
and, as a result, change market interest rates will
clearly influence the growth of new M2 just as they
affected the growth of old M2 and M3. The sensitivity
of new M2 to such nonpolicy factors thus reduces its
usefulness as an indicator of monetary policy actions.

THE RELATIONSHIP BETW EEN
ECONOMIC ACTIVITY AND THE
MONETARY AGGREGATES
The relationship between economic activity and
the new monetary aggregates is investigated with
8The chart indicates that the most recent period of disinterme
diation, IV/1977-II/1980, has not had the same effect in re
ducing new M2 growth relative to M1B as observed in pre
vious periods of disintermediation. However, at least part of
this phenomenon is explained by the rapid growth of over
night RPs and Eurodollar deposit holdings and, more recently,
by money market mutual funds.

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

reference to nominal GNP. Nominal GNP is chosen
because this is the apparent channel by which mone
tary policy variables directly affect the economy.9 The
general form of the relationship to be estimated is:
(1 )

Yt — C + 2 mi M u
1=0

+ Z e, E t l + |at
I=0

where Y is the compounded annual growth rate of
nominal GNP, M is the compounded annual growth
rate of the given monetary aggregate, E is the com
pounded annual growth rate of high-employment ex
penditures, and p is a random error term.10 This re
lationship is estimated using the new MIA, M1B, and
M2 aggregates and the old M l, M2, and M3 measures.
The relationships are estimated with the ordinary
least squares estimation technique.
The investigation subjects the six different relation
ships to a number of statistical tests. The strategy is
first to find the optimal lag structure for the different
relationships over the sample period, III/1962 through
III/1977. After investigating the in-sample stability of
the relationships and the likelihood of simultaneous
equation bias problems, these estimated relationships
are then used to project nominal GNP over the post
sample period, IV/1977 through IV/1979, to deter
mine which relationship would have yielded the most
accurate forecasts for this period. This period was
chosen because of the divergent growth rates for the
various aggregates, as shown in the preceding charts.

Sample Period Relationships
The first concern in estimating the general relation
ship given in equation (1) is to determine the ap
propriate values of f and g, the number of lags on
the monetary and fiscal variables. Lag values of 0,
4, and 8 were considered for each of the six relation
ships. Interestingly enough, F-tests for each of the
equations indicated that the appropriate lag value was

9See Milton Friedman, “A Theoretical Framework for Mone
tary Analysis,” in Milton F riedm an s Monetary Fram ew ork:
A D ebate with His Critics, ed. R. J. Gordon (University of
Chicago Press, 1974), pp. 1-63; and Charles R. Nelson, “Re
cursive Structure in U.S. Income, Prices, and Output,” Journal
o f Political Econom y (December 1979), pp. 1307-27.
10This relationship is similar to the original Andersen-Jordan
equation. Such a relationship has been estimated more re
cently by Keith M. Carlson, “Money, Inflation, and Eco
nomic Growth: Some Updated Reduced Form Results and
Their Implications,” this Review (April 1980), pp. 13-19.
Usually, the relationship is estimated assuming that the lag
coefficients lie along a polynomial of a given degree. No
such constraints are imposed here.

NOVEMBER

1980

4 for each of the separate monetary aggregates, as
well as for the fiscal variable.
Table 2 provides the sample period coefficient esti
mates and summary statistics for the six different
equations, where the relationships are estimated with
ordinary least squares and four lags on the fiscal and
monetary variables are assumed. There is very little
difference between the sample period fit provided by
the various aggregates. In all cases, the standard error
of the estimating equation (S E E ) is less than onethird the size of average GNP growth over the sample
period (9.61 percent).
While the pattern of the distributed lag effects of
both the fiscal and monetary variables is similar across
equations, the size of the coefficients is clearly de
pendent on the comprehensiveness of the monetary
aggregate employed. In general, the more comprehen
sive the aggregate, the smaller the size of any lagged
monetary coefficient. The sum of the money coeffi
cients is close to 1.0 for both MIA and M1B.11 On the
other hand, the sum of the money coefficients for new
M2 is close to 0.7. Begardless of the aggregate used,
the sum of the high-employment expenditures coeffi
cients is close to zero.

Stability Tests
A question to be considered with these estimation
results is whether the relationships reported in table
2 are structurally stable (i.e. whether the regression
coefficients change significantly with time). The hy
pothesis of structural stability was investigated with
the use of the Chow test. The formal hypothesis
tested is whether the regression coefficients estimated
for the III/1967 through IV/1969 sample period differ
significantly from those obtained for the same equa
tion in the 1/1970 through III/1977 period. The null
hypothesis is that the coefficients are equal in each
of these periods. The midpoint of the sample was
chosen as the breakpoint because it maximizes the
power of the test.12
Table 3 lists the F-statistics for each of the various
equations. None of the cases considered provide eviu The results reported for the narrow aggregates are similar
to those found by Keith M. Carlson, “Money, Inflation and
Economic Growth . . . ,” where a third degree polynomial
with tail constraints was employed in the estimation.
12See John U. Farley, Melvin Hinich, and Timothy W. Mc
Guire “Some Comparisons of Tests for a Shift in the Slopes
of a Multivariate Linear Time Series Model,” Journal of
Econom etrics (Volume 3, No. 3, 1975), pp. 297-318.

F E D E R A L R E S E R V E BAN K O F ST. LO UI S

NOVEMBER

1980

Table 2

Relationships Between GNP and The Monetary Aggregates
Yt =

C +

mi Mt-i +

Z ei Et-i + jit

1=0

(Sample Period, III/1962-III/1977; absolute value of t-statistic in parenthesis)
Monetary aggregates
Old

New

M1A

M1B

2.94
(2.00)

0.56
(0.32)

0.90
(0.54)

2.35
(1.56)

2.20
(1.49)

1.30
(0.85)

0.58
(2.97)

0.38
(2.03)

0.16
(0.81)

0.61
(3.20)

0.60
(3.18)

0.13
(0.74)

0.02
( 0.10)

0.14
(0.59)

0.26
(0.90)

0.03
(0.13)

0.05
(0.24)

0.39
(1.67)

0.20
(0.83)

0.12
(0.52)

0.08
(0.27)

0.32
(1-36)

0.31
(1.35)

-0.07
(0.28)

m»

0.56
(2.28)

0.43
(1.82)

0.49
( 1.68)

0.36
(1.53)

0.38
(1.62)

0.44
(1.85)

-0.54
(2.67)

-0.19
(0.99)

-0.30
(1.48)

-0.35
(1.75)

-0.35
(1.79)

- 0.22
(1.28)

0.04
(0.89)

0.05
(0.98)

0.08
(1.74)

0.05
(1.18)

0.05
(1.19)

0.08
(1.95)

0.12
(2.67)

0.10
(2.15)

0.13
(2.80)

0.12
(2.55)

0.12
(2.59)

0.12
(2.80)

-0.07
(1.54)

-0.07
(1.61)

-0.08
(1.81)

-0.08
(1.82)

-0.08
( 1.88)

0.02
(0.42)

0.01
(0.23)

0.02
(0.34)

0.02
(0.35)

0.01
(0.31)

0.02
(0.43)

XX1
( 0.02)

- 0.02
(0.43)

- 0.01
(0.28)

0.01
(0.13)

xxi
(0.04)

- 0.01
(0.23)

0.49

0.46

0.49

0.48

0.49

0.51

SEE

2.96

3.05

2.95

2.98

2.90

1.78

1.87

2.00

1.82

1.89

2.03

Mess than 0.005

Table 3

Calculated F-Statistics for Test of Break In Relationships
(111/1962-IV/1969 vs. 1/1970-111/1977)
Monetary aggregates
Old

F (1 1,39)1

New

M1A

M1B

1.52

1.11

0.64

1.64

1.62

0.61

1The 5 percent critical level is 2.05; the 10 percent critical level is 1.73.

NOVEMBER

F E D E R A L R E S E R V E BANK O F ST LOUIS

dence to reject the null hypothesis at traditional levels
of significance.13

Simultaneous Equation Bias Tests
A further question with regard to the estimation
results reported in table 2 is whether or not they are
subject to significant simultaneous equation bias.
Equations such as those reported in table 2 can be
estimated reliably with ordinary least squares methods
only if the independent variables are exogenous. A
major criticism of equations of this type is that the
monetary aggregates are not exogenous with respect
to GNP.14
Sims has recently suggested a test to examine
whether the independent variables in a distributed
lag relationship, such as equation (1 ), can be said to
be statistically exogenous.15 The test procedure in
volves adding leading values of the independent vari
ables to the basic distributed lag equation. If the
regression coefficients of the leading values of the
13A break in the relationship in 1/1974 was also considered.
With the exception of the new M2 relationship, there is evi
dence, at traditional levels of significance, to suggest a break
in all the relationships. With regard to the inability to reject
the stability of the new M2 relationship, it should be noted
that none of the separate subperiod money coefficients dif
fered from zero.
The fact that all other equations break is evidence of the
specification error. There appear to be two likely candidates
for omitted variables. First, none of the relationships include
a variable to capture the impact of the oil shock which oc
curred near 1974. Second, there is no variable to capture a
shift in money demand if, as many argue, money demand
shifted in 1974. (For example, see Stephen M. Goldfeld,
“The Case of the Missing Money,” Brookings Papers on
Econom ic Activity (3 :1 9 7 6 ), pp. 683-730.)
Since we are primarily concerned with the coefficients on
the money variables, either of these specification errors will
cause a problem only to the extent that the excluded vari
able is correlated with the independent variables. It is only
when such correlation exists that the estimated coefficients
will be biased. Regardless of whether either or both of the
above specification errors exist, it is unlikely that this bias
problem will result. Both of the suggested specification errors
resulted because shock variables were excluded. For evi
dence of the “shock” view of money demand, see R. W.
Hafer and Scott E. Hein, “The Dynamics and Estimation of
Short-Run Money Demand,” this Review (March 1980),
pp. 26-35. By definition, these shock variables should not
be correlated with the included independent variables. The
out-of-sample simulation results to be reported later in this
aper indicate that there is little evidence of a significant
ias in these simulations.
,4See Frank de Leeuw and John Kalchbrenner, “Monetary and
Fiscal Actions: A Test of Their Relative Importance in Eco
nomic Stabilization — Comment,” this R eview ( April 1969),
pp. 6-11.
15Christopher A. Sims “Exogeneity and Causal Ordering in
Macroeconomic Models,” in New M ethods in Business Cycle
R esearch: Proceedings from a C onference (Federal Reserve
Bank of Minneapolis, 1977), pp. 23-44.
Digitized for18
FRASER

1980

independent variable are not different from zero, the
null hypothesis of exogeneity is supported. On the
other hand, statistical significance of leading coeffi
cients suggests that simultaneous equation bias prob
lems would result if the equation were estimated with
ordinary least squares.
To test for the presence of simultaneous equation
bias, four leads on both the fiscal and monetary vari
ables were added to the basic equation as follows:
(2 )

Y, ~ C + £ in , M ,-, +
1=0

Z e , E, , + Zm! M „,

1=0

1 =1

+ Z e( E „ i + Ht.

i-i

Since the Sims test depends crucially on the statistical
significance of regression coefficients, every effort was
made to assure the absence of serially correlated error
terms. This was accomplished by following Sims’ re
commendation of filtering the data prior to estimation.
In most cases, the filter employed was the first order
linear filter (1-K L ), where L is the lag operation and
K is a constant. The value of K was determined by
iterating over values from 0 to 1, at intervals of 0.1.
The first value of K which yielded no evidence of a
relationship between the contemporaneous residual
and residuals lagged, first two and then four periods,
was chosen as the appropriate value.10
This search procedure removed the problem of
serially correlated disturbances in all relationships ex
cept that using old M l. In this case, the fourth lagged
residual always remained statistically significant in an
autoregressive error structure in the residuals. Thus,
in the case of old M l, the filter employed was
(1-KL4).
Table 4 lists the F-statistics testing the null hypo
theses; (1 ) mf = 0 for i = 1, 2, 3, 4; (2 ) e,' = 0 for
i = 1, 2, 3, 4; and (3 ) m| = e[ = 0 for i = 1, 2,
3, 4. In none of the cases considered were F-statistics
large enough to reject the null hypothesis at the 5
percent level, thus suggesting the absence of any
simultaneous equation bias problems associated with
the estimation results reported in table 2.17
16A similar search procedure was employed by Yash P. Mehra
and David E. Spencer, “The St. Louis Equation and Re
verse Causation: The Evidence Reexamined,” Southern E co
nomic Journal (April 1979), pp. 1104-20.
17This conclusion is somewhat different than that obtained by
Mehra and Spencer, “The St. Louis Equation. . . .” In esti
mating a relationship similar to equation ( 1 ) , they found
evidence of simultaneous equation bias problems. However,
their study differed in three important ways. First, the only

FEDERAL. R E S E R V E BAN K O F ST. LO UI S

NOVEMBER

1980

Table 4

F-Statistics for Simultaneous Equation Bias Tests
Monetary aggregates
Null hypothesis1
(degrees of freedom)

Old

New

m,' = 0 (4,42)2

1.62

0.57

e,' = 0 (4,42)2

0.22

0.47

m,' = e,' =

0.94
0.10

0 (8,42)3

Value of K

M1A

M1B

0.85

0.23

0.25

2.20

0.12

0.14

0.13

0.27

0.37

0.44

0.23

1.18

0.10

0.20

0.10

*i = 1, 2, 3, 4 in all cases.
2The 5 percent and 10 percent critical values for F (4 ,4 2 ) are 2.60 and 2.09, respectively.
3The 5 percent and 10 percent critical values for F (8 ,4 2 ) are 2.17 and 1.82, respectively.

Two qualifications to this conclusion are required.
These qualifications concern the regressions employ
ing old M l and new M2. While the F-statistics re
ported in table 4 do not allow the rejection of the
null hypothesis at the 5 percent level, there were
individual lead money coefficients in these two cases
that were different from zero at certain levels of sig
nificance; thus, there is some evidence to reject the
null hypothesis at lower significance levels. For ex
ample, in the case of old M l, the regression coefficient
on the one-quarter lead of money was 0.64. The tstatistic associated with this individual coefficient was
2.32, indicating that the estimate was statistically dif
ferent from zero at the 5 percent level. In this regard,
there is some evidence of “reverse causation” — an
increase in economic activity “causing” an increase in
future money growth.18 This result generates some
concern about the regression estimates reported for
the equation using old M l in table 2.
It is interesting to note that the redefinitions of the
monetary aggregates, although not directly concerned
with this simultaneity problem, have done much to
resolve it. None of the individual leading money
coefficients were close to being statistically different
from zero when the MIA aggregate was employed.
Together, these findings suggest that the simultaneous

equation bias, to the extent it exists, is due to the
inclusion of demand deposits held by foreign institu
tions or commercial banks.
In the case of new M2, the coefficient on the money
variable led two quarters was -0.50; and its abso
lute t-statistic of 1.83 was significantly different from
zero at the 10 percent level. In addition, the joint
hypothesis that all leading money coefficients are zero
had to be rejected at the 10 percent level. This again
suggests the possibility of a simultaneous equation
bias problem. However, it is important to recognize
that the problem does not appear to be a result of a
;positive association between current economic activ
ity and future money growth, as traditionally sug
gested. Rather, in this case, this regression coefficient
suggests that current economic activity is negatively
associated with new M2 growth two quarters in the
future.19
This negative relationship should not come as a sur
prise in light of the evidence of the impact of disin
termediation on new M2 growth. An increase in eco
nomic activity, by causing market interest rates to
rise above Regulation Q ceilings, will be associated,
other things being equal, with a reduction in future
new M2 growth.
In summary, it appears that the redefinitions of the

monetary variable they consider is the monetary base. Sec
ond, they include high-employment receipts, as well as highemployment expenditures, in their relationship. Finally, they
focus on a diiferent time period (I/1952-1V/1974).
18More formally, if one were willing to use the 25 percent
significance level, the null hypothesis that the leading M l
coefficients are equal to zero must be rejected.

19In this regard, it is to be noted that when old M3 is used,
the coefficient on money variable led two quarters is also
negative. However, the coefficient is not different from zero
even at the 10 percent level. Thus, it appears that including
overnight RPs, overnight Eurodollars, and money market
mutual funds in new M2 has compounded the simultaneity
problem.

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

NOVEMBER

1980

Table 5

Summary Measures of Out-of-Sample
(IV/1977-IV/1979) GNP Predictions
Monetary aggregates
Old

New

-2.17

-2.67

-2.60

4.05

4.55

4.62

0.29

0.34

0.32

due to variation

0.29

0.36

0.31

0.20

0.47

0.17

due to covariation

0.42

0.29

0.38

0.64

0.53

0.56

Mean error
Root mean squared error

M1A

M1B

-0.02

-2.57

4.04

3.68

5.03

0.16

0.00

0.26

-1.61

Fraction of error1
due to bias

lNeed not sum to unity as a result of rounding.

monetary aggregates have removed possible problems
associated with simultaneity as far as the narrow
transaction aggregates are concerned. However, there
still remains a question concerning simultaneity with
regard to the more comprehensive measure.

Prediction Results
How well do the relationships presented in table
2 simulate nominal GNP over the IV/1977 through
IV/1979 period? Table 5 indicates that the equation
using the new M1B aggregate performs the best in
simulating GNP growth over this period, regardless
of the criteria considered. The strength of this equa
tion is most evident in the lack of bias in the pre
dictions. The other aggregates underpredict GNP
growth over this period, on average, by approximately
2.5 percent. In comparison, the average prediction
error for M1B is a trivial -0.02 percent.
It is also appropriate to note that the bias in pre
diction errors is smaller for new MIA than for old
M l. Removing demand deposits held by foreign com
mercial banks and institutions did not reduce the
variance of forecast error; it did, however, reduce the
average error and the bias in the forecast.
The fact that the more comprehensive monetary
aggregates (old M2, old M3, and new M 2), which
include savings deposits subjected to Regulation Q
ceilings, underpredict GNP growth by more than
the transaction aggregates is again consistent with the
Digitized for2 0FRASER

view that disintermediation has adversely affected the
growth of these deposits. The whole period from
IV/1977 through IV/1979 has been characterized by
market interest rates well above Regulation Q ceilings.
This has led to a relative slowing in the growth of
these regulated deposits. As a result, equations using
these aggregates have underpredicted economic ac
tivity since IV/1977.

SUMMARY
The monetary aggregates were redefined early this
year. The purpose of this article was to examine these
new aggregates in terms of their usefulness as mone
tary policy indicators. Two criteria for judging the
usefulness of the monetary aggregates as indicators
were suggested. First, to serve as an indicator, the
aggregate should reflect the policy actions of the
monetary authority and not be highly sensitive to
nonpolicy influences. Second, the aggregate should be
consistently and predictably related to economic
activity.
Although the first criterion was not considered for
mally, examination of the rates of change of the new
monetary aggregates indicated that redefining M2 did
not remove the influence of nonpolicy forces. In par
ticular, the movement of market interest rates relative
to Regulation Q ceilings has had an adverse effect
on new M2 growth (relative to the narrowly de
fined aggregates), as it did with the old M2 and M3
aggregates.

F E D E R A L R E S E R V E BANK O F ST. LO UI S

The second criterion was examined more extensively
by regressing nominal GNP growth on the growth of
the various monetary aggregates and a fiscal variable
( growth rates of high-employment expenditures).
These relationships were checked for structural sta
bility, simultaneous equation bias, and out-of-sample
prediction accuracy. Of the new monetary aggregates,
only M2 showed any evidence of simultaneous equa
tion bias. This problem is felt to be closely related
to the impact of Regulation Q ceilings. In out-ofsample simulations, M1B performed better than any
of the other new aggregates analyzed, indicating that
it had a closer relationship to economic activity than
did the other new aggregates.
In light of the criteria suggested for judging the
usefulness of the new monetary aggregates as mone

NOVEMBER

1980

tary indicators, M1B was thus found to best satisfy
these requirements. It appears to be relatively insen
sitive to nonpolicy influences ( a characteristic it
shares with M IA ), and it is more predictably and
consistently related to movements of nominal GNP
than MIA or new M2.
On the other hand, new M2 was found to be par
ticularly unreliable as a monetary indicator. Growth
in this aggregate was found to be sensitive to non
policy forces. While proposed actions under the Finan
cial Institutions Deregulation and Monetary Control
Act of 1980 should eventually resolve this type of
problem, new M2 growth will likely remain a poor
monetary indicator in the seven-year transition period,
especially in light of the absence of any reliable his
torical relationship with economic activity.

EIGHTH F E D E R A L .. R E S E R V E

DI S T R I C T

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H e a d O f f ic e

B r a n c h O f f ic e s o f th e FRB, St. Louis

o f th e FRB, St. Louis

S ta n d a rd M e tr o p o lita n S ta tis tic a l A re a s

P laces

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(§)

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P o p u la tio n is b a s e d
on th e 1970 census.

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961

S ca le in M ile s

F e d e ra l R eserve B a n k o f St. L o u is

DECEMBER 1975