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THE IRRELEVANCE OF TESTS FOR BIAS IN
SERIES OF MACROECONOMIC FORECASTS
Roy H. Webb

Many economists have recently examined time
series of macroeconomic
forecasts or surveys of
expectations for statistical bias.’ A partial listing
of prominent writings includes articles by Brown and
Maital [ 19811, de Leeuw and McKelvey [ 19811,
Figlewski and Wachtel [ 19811, Friedman [ 19801,
Gramlich [ 19831, Hafer [ 19851, Holden and Peel
[ 19851, Lakonishok [ 19801, McNees [ 19781, Pearce
[ 19841, Urich and Wachtel [ 19841, and Zarnowitz
(19851.
The standard test for bias in a series of forecasts
begins by estimating coefficients in the following
equation:
(1)

A, = (Y + P ,-,P, + et

where A, is the actual value at time t of the variable
predicted, ,-,P, is the prediction made at time t-l for
the value at time t, a! and /3 are coefficients estimated
by least squares, and E, is an error term that is
assumed to be from a series of independent and
identically distributed normal random variables with
zero mean. An F-test can then be used to test the
joint hypothesis that (Y = 0 and fl = 1. If that
hypothesis is rejected, the standard interpretation is
that the series of forecasts is biased.
Most of the authors apparently believe that by
examining the statistical bias of those time series, they
are testing an important component of the new
classical economics,
the hypothesis of rational
expectations. As Hafer put it, “Because [wealthmaximizing] agents presumably will not make

forecasts that are continually wrong in the same
direction, rational forecasts should be statistically
unbiased.“2
The assertion that bias is not consistent with
rational expectations is examined below. First, two
meanings of the term rational expectations will be
presented. Several difficulties with interpreting the
test for bias are discussed next; several limit the
relevance of the test for the more important definition of rational expectations. Even if that test is
interpreted as applying to the less important definition (a technical requirement adopted for analytical
convenience), it is argued that the authors cited above
have failed to consider several possible explanations
for their results that do not contradict rational
expectations. It is concluded that tests of macroeconomic predictions for statistical bias have not
yielded useful information about the rationality of
expectations.
Rational Expectations

The author gratefully acknowledges helpful comments from
Timothv Cook. Michael Dotsev. leffrev Fuhrer. Thomas
Humphrey, Jia-Yuan Lin, Yash kehra, and Susan Dolman
Webb. Views and opinions are those of the author and should
not be attributed to the Federal Reserve Bank of Richmond nor
to the Federal Reserve System. An earlier version of this paper
was presented to the Western Economic Association in July
1987.

The term rational expectations has become widely used; different authors, however, may attach different meanings to the term. This paper will focus
on two ideas, one that is a general principle and the
other a highly restricted form of the first. The general
principle is that the actions of optimizing individuals
lead to an absence of rents in equilibrium (in other
words, profitable opportunities will be exploited). An
important implication is that costly information will
be used efficiently. This “informational efficiency”
idea is crucial to economists often labeled as rationalexpectations analysts. The restricted form of informational efficiency that is often used is “certainty
equivalence,” which implies that a representative
individual’s optimally predicted value of an economic
magnitude can be identified with the mathematical
expectation of a specific linear function that correctly describes the operation of the economy. The
assumption of certainty equivalence helps economists

r An even larger literature exists in finance, where tests for bias
have been stimulated by the efficient markets hypothesis.

2 Hafer, page 3.

FEDERAL RESERVE BANK OF RICHMOND

build theoretical models that are mathematically
tractable; as the passages below indicate, however,
it is not a critical idea for economists who have
pioneered the use of rational expectations.
The [rational expectations]
hypothesis
asserts three
things: (1) Information is scarce, and the economic
system generally does not waste it. (2) The way expectations are formed depends specifically on the structure
of the relevant system describing the economy. (3) A
in the sense of Grunberg and
“public prediction,”
Modigliani,
will have no substantial
effect on the
operation of the economic system (unless it is based
on inside information).
. . . For putposes of ana&sis,
we s/ka// use a speciak-ed form of th hypothesis. In particular, we assume: (1) The random disturbances are
normally distributed. (2) Certainty equivalents exist for
the variables to be predicted. (3) The equations of the
system,
including the expectations
formulation,
are
linear. Muth 119611, p. 348. (Emphasis added.)
But it has been only a matter of analytical convenience
and not of necessity that equilibrium models have used
. . . the assumption that agents have already learned the
probability distributions they face. [It] can be abandoned,
albeit at a cost in terms of the simplicity of the model.
Lucas and Sargent [1979], p. 13.
[The rational expectations] approach says that if people
do not observe something directly-such
as the current
price level-then
they form the best possible estimate of
this variable, given the information that they possess. In
other words people make efficient use of their limited
data, so as not to commit avoidable errors. Barro [1984],
pp. 468-69.

As Muth noted, the strong requirement of certainty
equivalence was adopted for analytical convenience.
Without certainty equivalence it is not necessary
that optimal predictions are mathematical expectations. Also, note that the authors stress that individuals make the best possible use of information
they possess-not
that individuals have perfect
information.

SEVEN REASONS
WHY OPTIMAL
FORECASTS
CAN SHOW BIAS

This section explains why a series of predictions
could appear biased even though they were originally
prepared optimally. Many of the explanations have
the common thread of asymmetric information. In
some cases, the ex post reviewer uses more information than was actually available to forecasters when
the forecasts were made. In others, the process of
reviewing forecasts ignores relevant data that was
available to forecasters. Failure to properly account
for either of those informational asymmetries limits
4

the relevance of tests for bias. The first four reasons
below question the relevance of tests for bias as a
test for both informational efficiency and certainty
equivalence; the last three only apply to the strict
requirements of certainty equivalence.
1.

Unequal Data Availability: Real-Time
Forecasts versus Ex Post Evaluation

In many cases economists have tested for biased
predictions by comparing recorded forecasts with the
latest available data. The data on which the forecasts
were based, however, have often been revised
substantially by the agencies that compile and report
the data. In fact, it is possible that the ex post bias
found in forecasts could be due to the reviewer
having access to data revisions that were unavailable
to real-time forecasters (that is, those who actually
issued forecasts before the fact).3
Lupoletti and Webb [ 19861 noted that preliminary
data on the rate of change of the GNP implicit price
deflator were at one time biased predictors of the final
data released. Since most findings of biased fore-casts
or surveys of expectations refer to the inflation rate,
the biased original inflation data could explain many
biased forecasts without contradicting their rationality.
To see whether early reports of the percentage
change in the implicit price deflator were biased,
consider:
(2)

A, = a + @P, + et

where A, is the actual value4 at time t of the percentage change in the implicit price deflator from ‘the
previous quarter, P, is the first data officially released for that percentage changes, CYand fl are
3 It is implicitly assumed that forecasters attempt to predict the
true value that is estimated in official-reports, and that successive
revisions are usually closer to the true value than initial reports.
The first assumption may not always be valid; consider a bond
trader who is concerned about market changes in the first few
minutes following a preliminary report.
4 The actual data are index numbers, based on 1982 = 100. They
reflect all revisions through early 1987.
5 Approximately
fifteen days after the beginning of each
calendar quarter (t + 1) the Commerce Department released its
preliminary estimate of the implicit price deflator for the previous
quarter (t). At that time a forecaster would also have had a value
for the deflator two quarters earlier (t - l), which would have
been revised twice since its preliminary release. At the beginning of quarter t + 1, therefore, the first official estimate of
the change in the deflator between quarter t and quarter t - 1
becomes available. It is that first official estimate that is used
as the early series P, in this section.
Due to the benchmark revision of 1976, which changed the
base year of the index from 1958 to 1972, there is a discontinuity in late 1975 for the original data. To adjust for the
base period change, data before the revision were multiplied by

ECONOMIC REVIEW, NOVEMBER/DECEMBER

1987

coefficients estimated by least squares, and et is an
error term that is assumed to be from a series of independent and identically distributed normal random
variables with zero mean. If the preliminary value
P, is an unbiased predictor of the latest revised value
A,, then the estimate of the coefficient CY
should be
0 and the estimate of fl should be 1.
Table I contains regression results for equation (2)
over the 1970s. The hypothesis of no bias is decisively rejected by a conventional F-test. Forecasters
in the 197Os, therefore, should not be assumed to
have had unbiased data on which to base their
forecasts, given the subsequent revisions in the implicit deflator.
The implicit deflator is not the only measure of
prices that has been studied. Leonard and Solt [ 19863
noted that the consumer price index diverged from
other measures of consumer prices before 1983 due
to the CPI’s treatment of mortgage interest payments
(which has been criticized by many analysts). They
found that survey data which other authors had found
to be biased were unbiased when compared against
a better estimate of consumer prices.
The problem of biased initial data that is later
revised is not confined to prices. Mork [ 19871 found
that early releases of real GNP growth from 1968
through 1984 were biased. Since it is widely believed that real GNP is the best single statistic for
describing the economy’s performance,
Mark’s
finding is particularly disturbing. Certainly many
0.68187, the ratio of the deflator for the last two quarters of
1975 with 1972 = 100 to the deflator for those two quarters with
1958 = 100. Visual inspection of the series, before and after
rebasing the earlier data, did not reveal any distortion. Also,
residuals from the regression reported in Table I were not unusual
in late 1975.

Table

I

REGRESSION
RESULTS:
IN PRELIMINARY
A, = 2.95
(.65)

TESTS FOR BIAS
DATA

+ 0.67
t.09)

Time span: 7O:l to 79:4
R2 = .57
DW = 2.18
F-statistic
(for CY = 0 and P =
F. o,,z,m = 5.26
Notes:

P,

1) = 11.9

A is the actual inflation rate, measured with latest data.
P is the inflation rate, based on the preliminary
data
release.
Standard errors are in parentheses.

economists’ expectations of other variables would be
affected by the reported growth rate of real GNP.
Zarnowitz [ 19821 has not only found evidence of
biased initial data releases for many time series, but
also found “extraordinary divergences” among various
data series describing real economic activity in
1973-74. Since most studies of forecasts or expectations include that period, confusion at that time
could have a strong impact on the results of ex post
studies.
None of the studies cited in the introduction
attempt to determine the extent to which their results
might be due to bias in the data available to
forecasters at the time forecasts were prepared.
Pearce (19841 and Zarnowitz [1985], however, do
mention the problem of data available to forecasters.
2.

Difficulty of Improving Real-Time
Forecasts

It may seem that a biased series of forecasts would
indicate that forecasters did ignore an easy method
of improving forecasts: simply removing that bias.
That, at least, is apparently the assumption of most
of the articles cited.
Now suppose that a series of forecasts was found
to be biased-that
is, after the coefficients in equation (1) were estimated, the joint hypothesis of
(Y = 0 and p = 1 was rejected. As Theil [ 1966) has
noted, a more accurate series of forecasts P’ could
then be constructed by adjusting the series P:
(3)

P,’ = & + BP,

where & and fi are estimates of the coefficients (Yand
p from equation (1). For example, if the predicted
series was expressed in percentage points and a
forecaster was on average one percentage point too
high (& = -l), then the adjusted forecast would subtract one percentage point from that forecaster’s
prediction. This would be an almost costless way of
improving forecasts. Failing to use it would therefore
seem to waste information.
The flaw in that argument is that it assumes that
the coefficients of equation (3) were known to
forecasters at the time of forecast. In fact, those
coefficients could have been estimated only after the
forecasts were issued. Now if the coefficients were
stable over time, one could reasonably impute their
knowledge to a forecaster, since after a few years the
forecaster could have recognized the bias and
estimated the coefficients. But if the coefficients were
to change over time, then using historic data to
estimate them would not necessarily improve
forecasts, since estimates of (Yand fi would no longer
be relevant.

FEDERAL RESERVE BANK OF RICHMOND

5

In other words, the analyst studying a sample of
forecasts has more information than did the forecaster
when the forecasts were prepared. Just because
using some of the additional information could improve forecasts does not show that forecasters ignored
potentially valuable data.
For example, Table II contains regression results
for equation (l), using quarterly growth rates of the
implicit price deflator from 1970 to 1984 as the
actual series and the published forecast of Wharton
Econometric Forecasting Associates as the forecast
series. An F-test shows statistical bias; moreover, the
residuals were significantly autocorrelated.
Could
Wharton have produced more accurate forecasts by
using the Theil adjustment mechanism shown by
equation (3)?
To answer that question, the first 25 observations
were used to estimate equation (l), and the estimated
coefficients were used to adjust the forecast as in
equation (3). Next, one observation was added, equation (1) was reestimated,
and the next quarter’s
forecast was adjusted. That process was repeated
until 32 adjusted forecasts were obtained.6 The
adjusted forecasts had a slightly larger root mean
squared error (1 S6.5) than did Wharton’s published
series (1 S38). It therefore appears that Wharton did
not waste the information from their past forecast
errors even though a sample of its historic forecasts
now appear biased.
Wharton’s inflation forecasts therefore provide a
counterexample
to the idea that a retrospective
finding of bias proves that information was wasted.7
Of course, an author might still be able to show that
other information-that
was available to Wharton
when its forecasts were prepared-could
have improved its forecasts. The point is, that author would
have to specifically identify the useful information
that was wasted. A simple test for bias does not iden
6 Although serially correlated residuals were apparent in the
whole data range, standard tests revealed no significant serial
correlation in the partial ranges that ended before 1981. The
coefficients in the earlier ranges were therefore estimated by
OLS. When serial correlation became significant, a first-order
autoregressive process was assumed and-maximum likelihood
estimates were made for the coefficients in (1) and for rho. The
estimated rho value was then also used to adjust the Wharton
forecasts.
7 The general usefulness of the The&type bias correction is an
unresolved issue. It is possible that the Wharton counterexample is simply a small-sample happenstance.
It is also
possible that findings of bias themselves are often small-sample
happenstances with little predictive value. In any particular case,
actually testing the bias correction method gives an indication
of its ability to improve forecast accuracy; unfortunately, such
tests are rarely performed.

6

Table

REGRESSION
FROM

RESULTS:
WHARTON

A, = 3.23
t.941

+ 0.60

II

INFLATION
FORECASTS
ECONOMETRICS
,,P,

Time span: 7O:l to 84:l
R2 = .52
DW = 2.01
F-statistic
(for a! = 0 and p =
F. 01,2,54 Notes:

+ 0.37

(. 14)

ut-,

(. 13)

1) = 6.29

5.04

A is the actual inflation rate, measured with latest data.
P is the Wharton Econometrics
forecast for the inflation
rate, prepared at the end of the previous quarter.
Standard errors are in parentheses.

tify that information; moreover, any process that identified wasted information would probably make a test
for bias superfluous. None of the authors cited in the
introduction specifically identify the wasted information that could account for findings of bias.
3.

Average versus Marginal

In many cases it is marginal behavior that determines economic outcomes. Studies of surveys of expectations, however, often focus on average behavior.
The relevance of such studies was questioned by
Mishkin [1981, p.295]:
Not all market participants have to be rational in order
for a market to display rational expectations.
The behavior of a market is not necessarily the same as the
behavior of the average individual. As long as unexploited
profit opportunities are eliminated by some participants
in a market . . . then the market will behave as though
expectations
are rational despite irrational participants
in that market.

Mishkin tested the same survey data that were
found to be inconsistent with rationality by Friedman. By focusing on marginal behavior, he found the
data to be consistent with rationality. To explain
Friedman’s results, he suggested that the survey data
did not accurately describe actual behavior in the
bond market.
Other studies of expectations also focus on average
behavior. None of the authors cited in the introduction who study surveys of expectations examine
whether their conclusions would change if they examined marginal behavior.

ECONOMIC REVIEW, NOVEMBER/DECEMBER 1987

4.

Uninformed Opinions of Irrelevant
Aggregates

Although most economists could state an opinion
for the future time path of macroeconomic variables,
not all would be willing to bet money on their predictions. Equivalently, it is a trivial matter to put a
number on a survey form; if an important decision
were to be based on the data, however, careful and
thoughtful analysis would probably precede any
forecast.
Surveys of expectations do not necessarily measure
solid analyses or even informed opinions that affect
real decisions. Instead, it is quite possible that they
contain relatively uninformed opinions of persons
who will not make important decisions based on their
expectations and accordingly have little incentive to
acquire costly information. The relevance of any
findings of bias in such surveys is questionable.

5.

6.

Nonstationary Data

Suppose that a data series z is generated
following random walk:
(4)

hypothesis of no bias was rejected at the 5 percent
level, and in an additional 139 cases it was rejected
at the 10 percent level. That is, investigators would
have found bias in many instances due to the inappropriate choice of a test statistic.
Once the possibility of nonstationary
data is
recognized, the burden of proof should be on the
author to demonstrate that F-tests are valid.9 For
example, Schwert [ 19871 discusses procedures that
could be used to test time series for stationarity. In
addition, Nelson and Plosser [1982] and Schwert
have presented evidence that many macroeconomic
time series appear to be empirically indistinguishable
from random walks. Yet none of the authors cited
in the introduction test for stationarity in the actual
data series employed. That is especially troubling for
those authors that examined predicted stock prices,
since stock indexes are widely believed to follow random walks.

by the

zt = z,+ + e,

where e, is from a series of independent and identically distributed normal random variables with zero
mean. The mathematical expectation of zt at time
t-l is therefore z,+. But a sample of such forecasts
could be found to be statistically biased if the coefficients of equation (1) were estimated, assuming that
A, = zt and ,-,P, = zel. That is, equation (1) is
misspecified if the actual data-generating process is
given by (4)s. Significance tests from a misspecified
equation can of course be misleading.
A Monte Carlo study illustrates that point. Equation (4) was used to generate 101 observations of z,,
where z1 =0 and values of e, were randomly drawn
from a normal distribution with a zero mean and a
unit variance. Using z,+ as the forecast for zt, since
E,-l[z,] = zrTl, equation (1) was estimated and an
F-test performed for bias. The procedure was then
repeated 999 times, thereby testing 1000 random
walks of 100 observations each for bias. By construction there was no bias; yet in 189 cases, the
8 To see why equation (1) would be misspecified, note that it
assumes the existence of a fixed constant term, which is not consistent with the assumed random walk. A random walk can often
drift far from the origin without ever crossing the origin in a
fixed sample. In that case, a regression equation such as (1) will
find a significant constant term and slope coefficient different
from unity. Those findings, however, have no meaning for the
future behavior of the random walk.

Peso Problems

If an unlikely event would make a dramatic impact
on predicted outcomes, that event’s likelihood can
affect optimal forecasts, even if the event did not occur during a particular intervallO. In effect, the
forecast contains a risk premium for the unlikely yet
dramatic event. For example, if Russian investors in
1916 assigned a positive probability to a Bolshevik
Revolution, stock prices of Russian firms in 1916
might appear lower than could be explained by observable factors such as earnings, dividends, and interest rates. In hindsight, such a forecast appears
eminently rational. Krasker [1980] has noted that
such peso problems can invalidate usual tests of
efficiency in the foreign exchange market.
In studying macroeconomic forecasts, a particularly
important event to consider is the possibility of a
major policy regime change. The acknowledged
possibility of a regime change could account for
statistical bias over almost any specific interval. For
example, downward-biased forecasts of inflation could
be due to a positive probability placed on the Federal
Reserve’s adopting a monetary policy emphasizing
price stability. Even if such a policy were not adopted
during a particular time period, a forecaster’s subjective probability of such a policy being adopted may
have been correct.
9 Indeed, even with stationary data that is highly autocorrelated,
Mankiw and Shapiro (19861 have shown that conventional
F-tests will reject true models too frequently.
lo This is labeled a peso problem due to a lengthy period when
the Mexican peso traded in forward markets at a rate below the
fiied spot rate, due to the widespread belief that a devaluation
of the peso would eventually occur.

FEDERAL RESERVE BANK OF RICHMOND

7

Although it is not possible to completely rule out
peso problems, it is feasible to see whether plausible anticipated policy changes could account for
findings of statistical bias. None of the authors cited
in the introduction makes the attempt.
7.

Representative Individual’s Utility
Function

Zellner [ 19861 has noted that, for many utility functions, an individual’s optimal forecast can be biased.
In particular, by accepting some bias it may be possible to lower the standard error of a point predictor
and thereby lower the mean squared error of a series
of forecasts. Also, if the loss of utility from an overprediction does not precisely equal the loss of
utility from an underprediction
of the same
magnitude, then an unbiased forecast may not
maximize
utility. Zellner
provides
a specific
example to illustrate the latter point. Stockman
[ 19871 derives a loss function for forecast errors from
an agent’s exact decision problem, finding that in
general such loss functions will not value over- and
underpredictions
equally.
None of the studies cited in the introduction provide evidence that a representative
individual’s
utility function is maximized by an unbiased forecast.
That key point is simply assumed.

Barro, Robert J. Macrveconomh. New York: Wiley, 1984.
Brown, Bryan W., and Shlomo Maital. “What Do Economists
Know? An Empirical Study of Experts’ Expectations.”
Econometrica 49 (March 1981): 491-504.
de Leeuw, Frank, and Michael J. McKelvey. “Price Expectations of Business Firms.” Bmokings Papers on Economic
Activiry (1: 1981), pp. 299-314.
Figlewski, Stephen, and Paul Wachtel. “The Formation of Inflationary Expectations.” Rev&~ of Econot~~ics Statistics 63
and
(February 1981): l-10.
Friedman, Benjamin. “Survey Evidence on the ‘Rationality’ of
Interest Rate Expectations.” Journal of Monetary Economics
6 (October 1980): 453-65.
Gramlich, Edward M. “Models of Inflation Expectations Fory;;Io;;.” J~malofMoney, Credit, andBanking 15 (May 1983):

Hafer, R. W. “A Look at the ASA-NBER Inflation Forecasts:
Tests of Rationalitv and Formation.” Federal Reserve Bank
of St. Louis Research Paper 85-003. 1985.
Holden,. K., an! D. A. Peel. ,,“An Evaluation ?f Quarterly
F;;y;l
Instrtute Forecasts. hurnalofForeastrng4
(1985):

Krasker, William S. “The ‘Peso Problem’ in Testing the Efficiency of Forward Exchange Markets.” Journal of Monetaty
Economics 6 (April 1980): 269-76.
Lakonishok, Josef. “Stock Market Return Expectations:
General Properties.” JounudofFinance 3.5 (September
921-31.

CONCLUSION

Many authors have tested for bias in surveys of
macroeconomic
expectations
or time series of
forecasts. Although the authors believed they were
testing the rationality of expectations, there are many
reasons why they could have found bias. Seven
reasons are listed above that are seldom examined,
that are likely to affect the results of conventional
tests, and that have little relevance to important
economic questions. Some of the reasons are due
to the reviewer using information that was not
available to forecasters.
Others are due to the
reviewer not using relevant information that was
available to forecasters. Since any finding of bias could
be due to at least one of the reasons given above,
the relevance of such tests is questionable.
The convenient assumption of certainty equivalence can be appropriately
tested, once careful
attention is given to data available to real-time
forecasters. The fundamental idea of informational
efficiency is much harder to test. It has not been,
and almost certainly cannot be, properly examined
by simple tests for biased expectations or forecasts.
8

References

Some
1980):

Leonard, David C., and Michael E. Solt. “Recent Evidence
on the Accuracy and Rationality of Popular Inflation Forecasts.” Joumaf ofFinan&~Rtxea~h 9 (Winter 1986): 281-90.
Lucas, Robert E., and Thomas J. Sargent. “After Keynesian
Macroeconomics.” Federal Reserve Bank of Minneapolis,
Qaafler4 Rewie~~3 (Spring 1979): 1-16.
Lupoletti,

William M., and Roy H. Webb.

“Defining

and

Improving the Accuracy of Macroeconomic Forecasts:
Contributions
from a VAR Model.” .I&mal
59, part 1 (April 1986): 263-85.

of BusinRc

Mankiw, N. Gregory, and Matthew D. Shapiro. “Do We
Reject Too Often?” Economics &ten 20 (1986): 139-4.5.
McNees, Stephen K. “The ‘Rationality’ of Economic Forecasts.” American Economic R&
68 (May 1978): 301-S.
Mishkin, Frederic S. “Are Market Forecasts Useful?” American
Economic Review 71 (June 1981): 295-306.
Mork, Knut Anton. “Ain’t Behavin’: Forecast Errors and
Measurement Errors in Early GNP Estimates.” Joamal of
Business and Economic Statistics 5 (April 1987): 165-75.
Muth, John F. “Rational Expectations
and the Theory of
Price Movements.” Econome&a 29 duly 1961): 3 15-35.

ECONOMIC REVIEW. NOVEMBER/DECEMBER

1987

Nelson, Charles R., and Charles I. Plosser. “Trends and
Random Walks in Macroeconomic
Time Series: Some
Evidence and Implications.” Journal of Monetary Economics
10 (September 1982): 139-62.

Urich, Thomas, and Paul Wachtel. “The Structure of Expectations of the Weekly Money Supply Announcement.”
Journal of Monetary fionomics 13 uanuary 1984): 183-94.
Zarnowitz, Victor. “On Functions, Quality, and Timeliness
of Economic Information.” Journal of Business 5.5 (January
1982): 87-l 19.

Pearce, Douglas K. “An Empirical Analysis of Expected
Stock Price Movements.” Journal of Money, Credit, and
Banking 16 (August 1984): 317-27.

-.

“Rational
Expectations
and Macroeconomic
Forecasts.” Journal of Bushess and Economic Stahics 3
(October 1985): 293-3 11.

Schwert, G. William. “Effects of Model Specification on
Tests for Unit Roots in Macroeconomic
Data.” Journal
of Monetary Economics 20 (July 1987): 73-103.

Zellner, Arnold. “Biased Predictors,
Rationality and the
Evaluation of Forecasts.” Econo&cs L.eters 21 (1986): 45-48.

Stockman, Alan C. “Economic Theory and Exchange Rate
Forecasts.” Int~ati~a~JournolofForecasting 3 (1987): 3-15.
The&
Henri. Applied Economic Forecasting. Amsterdam:
North-Holland,
1966.

Economic

Review

Index

Volume
Federal
January/February

lntraday

Credit:

Risk, Value,

73,

Reserve

Bank of Richmond

1987

David L. Mengle,
David B. Humphrey,
and Bruce J. Summers

and Pricing

Stephen

A. Lumpkin

The Agricultural
Outlook for 1987
. . . Financial Turnaround Unlikely

Raymond

E. Owens

The Theory of Multiple Expansion of Deposits:
What It Is and Whence It Came

Thomas

The Equilibrium

Alan C. Stockman

Repurchase

March/April

and Reverse

Approach

IPC or Total Deposits?
May/June

Swiss and United
The Effect

An Overview
July/August

States

Policy:

Rate Variation

and the Measurement
Policy .

and Neoclassical

Has Monetarism

on U.S.

Textile

of Economies
Past,

Present,

The Fed’s Anti-Inflationary

Strategy:

The Case for Rules in the Conduct

The Irrelevance
Money

of Monetary

and High Nominal

Thomas

Tariffs

E. Owens

L. Hetzel
M. Humphrey

John R. Walter and
David L. Mengle

1986

Robert

P. Black

of the Reserve

Rates

FEDERAL RESERVE BANK OF RICHMOND

Example

Bennett

T. McCallum

Michael

Policy: A Concrete

Interest

Chmura

Raymond

and Future

of Tests for Bias in Series of Macroeconomic

Growth Volatility

Christine

David B. Humphrey

in Banking

Is It Adequate?

The Australian Money Market and the Operations
of Australia: A Comparative
Analysis
November/December

Imports

Robert

in the Fifth District,

L. Welker

Georg Rich

Failed?

and Apparel

Roots of the Theory of Optimum

A Review of Bank Performance

M. Humphrey

Donald

Is a Difference!

Monetary

of Agricultural

Rates

Henry Thornton: Seminal Monetary Theorist
and Father of the Modern Central Bank
Classical

September/October

Agreements

to Exchange

There

of Exchange

Cost Dispersion

Repurchase

Dotsey

Bank

Forecasts

Roy H. Webb
Yash Mehra

MONEY GROWTH VOLATILITY AND
HIGH NOMINAL INTEREST RATES

On October 6, 1979, the Federal Reserve announced a change in its operating procedures aimed
at improving control of the monetary aggregate Ml.
Since then, however, Ml growth has become highly
volatile.’ Furthermore,
the increased volatility of
money growth was accompanied early by increased
levels as well as volatility of nominal interest rates.
Nominal interest rates rose and remained at significantly high levels through mid-1984, despite the
sharp reduction in actual inflation which occurred
between 1979 and 1982. Since mid-1984, however,
nominal interest rates have declined significantly.
Some analysts contend that the high nominal
interest rates of the 1979-86 period were due to increased volatility of money growth* caused by the
Federal Reserve’s new operating procedures. The
main argument is that the increased money growth
volatility induced by policy raised uncertainty about
the direction of Federal Reserve monetary policy.
A rise in uncertainty resulted in an increased demand
for money which-in
the absence of an accommodative Federal Reserve policy-caused
nominal
interest rates to rise. Nominal interest rates have
declined sharply since mid-1984, even though Ml
growth continues to be highly variable. This argument, if correct, attributes such a decline to a more
accommodative
Federal Reserve monetary policy
stance adopted since then.
This article reexamines the foregoing hypothesis.
The period since 1979 has been marked by a new
round of financial deregulation including the introduction nationwide of interest-bearing NOWs in 1981
Economist and Research Officer, the Federal Reserve Bank
of Richmond. The views expressed are those of the author and
do not necessarily reflect the views of the Federal Reserve Bank
of Richmond or the Federal Reserve System.
l

I In the late fall of 1982, the
its operating procedures. The
clined somewhat since then.
mained quite variable during

Federal Reserve again modified
volatility of Ml growth has deHowever, Ml growth has rethe 1982 to 1986 period.

2 Mascaro and Meltzer (1983) and Hall and Noble (1987).
10

and Super NOWs in 1983. It is now widely recognized3 that these developments may have played
an important role in causing shifts in money demand
and in raising the volatility of money growth over the
1980s. Hence, when testing the validity of the
hypothesis of money growth volatility, it is essential
to control for such effects of financial deregulation.
The empirical work reported here suggests that
not all of the increase in the volatility of Ml growth
should be attributed to Federal Reserve operating
procedures. The recent round of financial deregulation has caused shifts between the types of assets
the public wants to hold, shifts manifested by
movements into and out of Ml that made Ml growth
more volatile. Evidence supports this conclusion; for
while the volatility of Ml did increase significantly
after the change in procedures, the volatility of a
broad monetary aggregate, M2 or M3, was not
significantly greater than before. If all of the increased volatility of M 1 growth was policy-induced,
the volatility of M2 and M3 also should have increased, ceteris paribus.
It is also concluded that money growth volatility
does not exert an independent
influence on the
public’s demand for real money balances, so that the
increased volatility of Ml growth did not contribute
to high nominal interest rates through the money demand channel. Nevertheless, M 1 demand has shifted
upward during the 198Os, and the major source of
this shift appears to be financial deregulation. Hence,
high nominal interest rates observed early in the
1979 to 1986 period could have been caused in part
by an increase in the demand for money. Apparently, too, deregulation has raised the magnitude of
the response of the nominal interest rate to expected
inflation, which could explain part of the high levels
of nominal interest rates observed in recent years.
3 Simpson (1984), Mehra (1986), Kretzmer and Porter (1986),
Wenninger (1986), Trehan and Walsh (1987), and Hetzel and
Mehra (1987).

ECONOMIC REVIEW, NOVEMBER/DECEMBER 1987

The remainder of the article contains an evaluation of the money growth volatility hypothesis and
the empirical results that underlie the conclusions
reached here.

Chart

VARIABILITY

la

OF Ml GROWTH*
1963-1966

Percent

I.
Money Growth Volatility Hypothesis
This section presents and evaluates
growth volatility hypothesis.

the money

Background
Analysts who contend that the Federal Reserve’s
new operating procedures caused money growth to
be highly volatile usually point to a sharp increase
in the variability of Ml growth since 1979. As shown
in Chart la, the variability increased sharply between
1979Q4 and 1982522, declined somewhat thereafter,
and has remained high since then.4 Chart 2 depicts
the behavior of the nominal interest rate over the
same period. As shown in Chart 2, the nominal interest rate, measured here by the yield on one-year
Treasury bills, rose to high levels between 1979 and
1982 when the new monetary control procedures
were in force. The nominal interest rate persisted
at fairly high levels through the first half of 1984 and
since then it has trended downward. It is a widely
held view that the behavior of the nominal interest
rate since 1979 could not be readily predicted from
its past relationship with inflation, money growth,
cyclical pressure, and fiscal policy variables.5

0.0

II’...‘...“..’

‘.‘...‘...’

Chart

VARIABILITY

’

’

‘1

1b

OF M2 GROWTH*
1963-1986

Percent

6.0 CL1
5.0

/

-___

4.0

2.0
3.0 ;JJf-

b

---

r

--

b

-

_\i!

b

L

/

1.0

0.0 1

64 66 68 70 72 74 76 78 80 82 84 86

Money Growth Volatility Hypothesis Stated
Mascaro and Meltzer (1983) instead have attributed the above noted behavior of nominal rates to
an increase in the degree of monetary instability,
which, they allege, was caused by the Federal
Reserve’s new monetary control procedures. They
reason that in a less stable, more variable environment, people choose to hold more money and less
of other assets such that there is a positive associ-

.‘-..I

64 66 68 70 72 74 76 78 80 82 84 86

Chart

VARIABILITY

lc

OF M3 GROWTH*
1963-1986

Percent

h

7.0
6.0
5.0
4.0

4 Variability is here defined as the eight-quarter moving average
of the standard deviation of quarterly growth rates of actual
money stock. This measure is similar in spirit to measures used
in other studies although some of those deal with unexpected
portions of the growth rate of the money stock.
0.0

5 For example, Clarida and Friedman (1984) using a vector
autoregression
model reach the conclusion that short-term
interest rates in the United States have been “too high” since
October 1979. The standard estimated Fisher-type interest rate
regressions used in several interest rate studies, including Wilcox
(1983) Peek (1982), Tanzi (1980), and Makin (1983), tend to
underpredict the nominal interest rate in the post-1979 period.

I."...'...'...'.

.'.

.'...I...'...'..

'...I...1

64 66 68 70 72 74 76 78 80 82 84 86
* Variability of money growth is measured as the eight-quarter
moving average of the standard deviation of quarterly growth rates
of actual money stock.

FEDERAL RESERVE BANK OF RICHMOND

11

Chart 2

NOMINAL INTEREST RATE
,ONE-YEAR TREASURY BILL RATE
1963-l 986
Percent
15.0

Criticism of the Money Growth
Volatility Hypothesis

10.0

5.0

0.0

64 66 68 70 72 74 76 78 80 82 84 86

ation between variability and the demand for money.
Assuming further that an increase in the demand for
money raises short-term nominal interest rates, it
follows that there is also a positive association
between monetary variability and the level of the
nominal interest rate.
The assumptions which underlie their hypothesis
can be clarified further using the IS-LM model.
Consider first the simple IS-LM model which contains two assets-money
and capital-and
in which
the demand for money depends positively upon the
degree of monetary instability. In such a model an
increase in the degree of monetary instability raises
money demand which, in turn, results in a higher
short-term nominal interest rate, provided the real
supply of money remains fixed. The latter assumption implies either that the price level does not
adjust or that the Federal Reserve does not accommodate the increase in money demand.
In case there are more than two assets, the effect
of an increase in the degree of monetary instability
on short-term interest rates is ambiguous. Mascaro
and Meltzer (1983) consider the IS-LM model in
which there are three assets-money,
short-term
bonds, and capital. If one continues to assume that
the demand for money depends positively on the
degree of monetary instability, then increased instability could cause people to hold more of both
money and short-term bonds that are close substitutes for money. In that case, even though an increase
in the demand for money raises the short-term
interest rate, higher demand for substitute short-term
bonds depresses the nominal interest rate, so that
the net impact of an increase in the degree of
monetary instability on the short-term
rate is
uncertain.

12

The empirical work reported in Mascaro and
Meltzer, however, shows that the short-term nominal
rate does rise in response to an increase in the
variability of M 1 growth. Moreover, they also report
evidence suggesting a positive association between
the variability of Ml growth and the demand for
money.

The major objection to the money growth volatility
hypothesis questions the empirical validity of the
underlying assumptions of (1) a positive association
between degree of monetary instability and demand
for money, and (2) the supposition that the increased monetary instability was due entirely to the
Federal Reserve’s monetary policy operating procedures. The empirical evidence supporting these
assumptions is not very persuasive because it does
not control for the potential effects on money demand of financial deregulation.
An alternative hypothesis receiving considerable
support in several recent money demand studies,
including Simpson (1984), Mehra (1986), Kretzmer
and Porter (1986), Trehan and Walsh (1987), and
Hetzel and Mehra (1987), is that Ml demand has
been stronger and more volatile in the 1980s than
before because M 1 now contains interest-bearing
assets such as NOWs and Super NOWs. The inclusion in Ml of NOWs and Super NOWs has reduced the opportunity cost of holding money, thereby
inducing the public to hold more of it. Moreover,
the public has also been willing to substitute more
than before between the interest-bearing deposits included in Ml on the one hand and the substitute,
savings-type deposits included in M2 and M3 on the
other.
A bit of evidence that supports the above mentioned shifts in money demand is reproduced below.
It consists of out-of-sample prediction errors of the
conventional money demand regression that uses
alternative measures of money-Ml,
M2, and M3.
A standard money demand regression that uses these
measures is estimated over the common sample
period 1963521 to 1979Q3 and simulated out-ofsample over 1979Q4 to 1986Q4. The resulting
errors are reported in Table I. The percentage error
in predicting the level of nominal money demand is
reported in columns A 1, and the error in predicting
its quarterly growth rate is reported in columns A2
(only second- and fourth-quarter observations are
reported). RMSE statistics are also reported in
Table I. For Ml, prediction errors are large and
positive and the RMSE value is high, implying that
Ml demand had been strong and highly variable in

ECONOMIC REVIEW, NOVEMBER/DECEMBER 1987

TableI
Simulation Results, Percentage Error in Predicting Nominal Money Demand
Quarterly Data 1979Q4 to 1986Q4
Measure

of Money

Used

in the

Ml

Year/Quarter

Level

Demand

Regression

M3

M2
A2
Quarterly
Growth Rate

Al

Money

1979Q4

-.4

-1.5

1980Q2

-2.9

Al
Level

-10.6

198064

-1.5
-1.9
-3.5
-2.5
.7

-.6

1.3
10.9

-4.1
-1.5

1.9
-.8

1982Q2
1982Q4

-.o
-.O

1.1

198182
1981Q4

A2
Quarterly
Growth Rate

.2

- .o

.6
.O

A2
Quarterly
Growth Rate

Al
Level

-.9
- 1.0

5.4
.7

.5
.8

.8
-5.1
-.l
2.9
1.2

1.6

2.7

2.9

1.0

5.7
4.9

.9
- 1.8

4.1

-.6

3.5
3.2

-1.8
.8

2.5
3.9

3.9
.7

1983Q2

3.5

6.4

1983Q4
1984Q2

4.7
4.4

.O
1.1

3.5

- 1.1

1984Q4

4.4

-.o

3.9

1.6

1985Q2

6.6

4.9

3.3

-3.9

1985Q4

10.6

5.6

3.0

-2.3

1986Q2
1986Q4

15.4
22.6

11.9
14.2

3.2
4.0

2.4
2.5

2.3
2.5

1.3
1.4

7.6

5.9

3.1

3.0

2.6

2.3

RMSE

3.9

2.0

2.6

-4.6

1.9

-1.8

Notes: The values reported in columns Al above are the percentage errors in predicting the level of the nominal money demand, whereas
those reported in columns A2 are the (annualized) quarterly growth rate errors (only second- and fourth-quarter
observations are reported).
The predicted values are from the money demand regressions estimated over 1963Ql to 1979Q3.
The underlying money demand
regression is of the form
ln(M,/P,)

= a +

z

s=o

b,

lny,,

+

z

s=o

c, lnR,-,

+ D74

where M is,either Ml or M2 or M3, y is real GNP, R is the 4-6 month commercial
paper rate, and P is the implicit GNP deflator.
Estimation
IS by Hildreth-Lu
procedure, and simple distributed lags are used. D74 is the zero-one dummy variable, taking values 1
In 1974Q2-1976Q4 and zero otherwise.
RMSE is the root mean, squared error, calculated
using the errors over the 1979Q4 to
1986Q4 period.

the 1980s. However, there is a sharp reduction in
the magnitudes of prediction errors if M2 or M3 is
used. For example, the RMSE values of the quarterly
growth rate prediction errors are 5.9, 3.0, and 2.3
percent for Ml, M2, and M3, respectively. These
estimates, therefore, support the presence of increased substitutions by the public between assets
included in Ml on the one hand and M2 and M3
on the other.
The alternative
explanation
of Ml demand
behavior has several implications for the validity of
the money growth volatility hypothesis. First, one
may find divergence in the volatility of monetary

aggregates. Deregulation-induced substitutions could
produce an increase in the volatility of Ml growth
accompanied by little or no change in the volatility
of broad aggregates .6 This is confirmed further by
6 Formally, this point can be explained as follows. Consider the
following expressions for the variance of the broad aggregates
Var M2 = Var Ml t Var (MZ-Ml) t 2 COV (Ml, MZ-Ml)

(a)

Var M3 = Var Ml t Var (M3-Ml)

(b)

t 2 COV (Ml, M3-Ml)

where (M’2 -Ml) is the non-Ml component of M2; (M3 -Ml),
the non-Ml component of M3; Var, the variance; and COV,
the covariance of the relevant variables. If the increase observed in the variance of Ml is policy-induced, then variances

FEDERAL RESERVE BANK OF RICHMOND

13

the evidence reported in Charts lb and lc and
Table II. Charts lb and lc display the variability of
broad aggregates, M2 and M3, and Table II reports
mean standard deviation values of money growth
computed over the two sample periods, 196 1Q 1 to
1979Q3 and 1979Q4 to 1986Q4. As can be seen
by comparing Charts la through lc, the broad
measures of money--M2 and M3- have not since
1979 displayed the variability of the Ml measure.
The same is true if one compares the mean standard
deviation values reported in Table II.7
The implication of all this is that not all of the increase observed in the variability of M 1 growth should
be attributed to the adoption by the Federal Reserve
of new monetary control procedures. A part has been
due to an increase in the variability of Ml demand.
A second implication is that the money growth
volatility hypothesis should be reexamined using
broad measures of money. The broad measures of
money are likely to internalize the above mentioned deregulation-induced
substitutions. Hence
they should provide a sharper test of the joint
hypothesis that the increased volatility of money
growth was policy-induced and contributed to high
nominal interest rates via raising money demand.
If financial deregulation is at the source of the
observed strength in money demand, then another
important consequence is a potential increase in the
magnitude of the response of the nominal interest
rate to inflation. The basic argument here is as
follows. Most empirical studies of interest rate determination have found that fully anticipated inflation
has less than a one-for-one effect on the nominal interest rate. Thus, expected inflation reduces real rates
of return on financial assets (bonds). Some analysts
attribute this result to the existence of legal restrictions on the payment of explicit interest on money.8
According to their argument, optimizing individuals
tend to hold money and financial assets to the point
of the broad measures of money should also increase. However,
if part of the increase observed in the variance of Ml is due to
increased substitution by the public between assets included
in Ml on the one hand and assets included in (M2 -Ml) or
(M3-Ml)
on the other, then the broad measures-M2
and
M3-should
be relatively less variable, as higher variance terms
in (a) and (b) above are offset by large, negative covariance terms.
7 Two aspects of this data, reported in Table II, warrant
underscoring. First, whereas the mean values of the standard
deviation of broad measures of money exceeded that of the
narrowly defined measure Ml in the early sample period,
1961Ql-1979Q3,
this ordering is reversed in the later sample
period, 1979Q4-1986Q4. Second, while the variability of Ml
growth increased most over the 1979524 to 1986Q4 period, that
of M2 growth showed only a modest rise, and that of M3 fell.
* Carmichael and Stebbing (1983) and Fried and Hewitt (1983).

14

Table

II

Volatility of Monetary Aggregates
Mean Values of the Standard Deviation
of Quarterly Growth Rates
Monetary
Sample

Period

Ml

Aggregate
M2

M3

1961Ql-1979Q3

1.88

2.18

2.10

1979Q4-1986Q4

4.15

2.73

1.67

Notes: Volatility is defined as the eight-quarter
moving average of
the standard deviation of quarterly growth rates of actual money
stock. The values reported above are mean values of the
standard deviation of monetary aggregates.

at which their (after-tax) yields are equal. Inflation
reduces the equilibrium real rate of return on money,
which, in the presence of the prohibition of the
payments of explicit interest on money, is just the
negative of the rate of inflation. If one assumes further that financial assets are closer substitutes for
money than for capital, 9 then an inflation-induced
fall in the equilibrium real rate of return on money
forces a corresponding fall in the real rate of return
on ,financial assets as investors substitute out of
money into financial assets.
The introduction nationwide since 198 1 of interestbearing NOWs, Super NOWs, and Money Market
Deposit Accounts together with the gradual lifting
in recent years of the remaining regulatory interest
rate restrictions on several components of money and
money substitutes’0 means that a rise in anticipated
inflation does not reduce equilibrium real rates of
return on money and money substitutes as much as
it did before. The presence of this effect tends to
enhance the response of the nominal interest rate to
expected inflation.
9 Several analysts including Carmichael and Stebbing (1983) and
Fried and Hewitt (1983) have emphasized that money and financial assets are likely to be highly substitutable ac the margin.
This is so because, apart from the medium of exchange function, money and financial assets are almost identical; they are
both nominal stores of value, they have very similar liquidity
and risk characteristics, and so on.
10 The maximum rate payable on NOWs was initially set at
5% percent. As of January 1986 this restriction has been
removed. The maximum races payable on passbook savings
accounts and several time deposits have also been completely
deregulated. However, the explicit nominal rate payable on
demand deposits held by businesses is still fixed at zero.

ECONOMIC REVIEW, NOVEMBER/DECEMBER 1987

II.
Empirical Evidence
In this section I present empirical evidence on the
relative roles of money growth volatility and financial deregulation in explaining the recent behavior
of the nominal interest rate.
Specification of the Testable Hypothesis
The major thrust of the money growth volatility
hypothesis is that the degree of monetary instability
is an important determinant of nominal interest rates.
A policy-induced increase in monetary instability
tends to raise the level of the nominal interest rate,
because such an increase raises uncertainty which,
in turn, raises money demand. A simple way to test
these implications is to estimate the following interest
rate and money demand regressions:
i, = a0 + aJI, - a2MG, + aJX,
+ a4VOL,
(MIPJ

(1)

= bo + by, - bzR,
+ bJM,,/P,)
+ b‘,VOL,.

(2)

Equation (1) is the Fisher type interest rate regression in which i is the nominal interest rate, II is expected inflation, MG is money growth, X is the
variable measuring shift in exogenous aggregate demand, and VOL is the variable that measures the
degree of monetary instability. Equation (2) is the
standard money demand regression that includes real
income (y), the short-term nominal interest rate (R,),
lagged real money balances (M,-JP,), and money
growth volatility (VOL) as the explanatory variables.
The money growth volatility hypothesis posits that
coefficients a4 and b4 attached to the VOL measure
in regressions (1) and (2) are positive and significantly
different from zero.
The alternative hypothesis is that financial deregulation is at the source of the strength in Ml
demand. Furthermore,
as a result of financial
deregulation, the magnitude of the response of the
nominal interest rate to expected inflation should
have increased over the 1980s. In order to control
for these effects of financial deregulation, consider
the following expanded interest rate and money demand regressions
i, = a0 + aJIt - a2MG, + aaX,
+ a4VOL, + a5D81 *II,
WP3

(3)

= bo + by, - MC + MM-Apt)
+ b4VOL, + b$HIFT,

(4)

where all variables except D81 and SHIFT are as
defined before. D8 1 is the zero-one dummy variable
that takes values unity in the post-1981 period and
zero otherwise. D8 1 *II is formed by taking the product of D81 and expected inflation II. SHIFT is a
variable that captures the effect of financial deregulation on money demand. In empirical work this
effect is captured by broadening the measure used
in defining money. If the money growth volatility
hypothesis is valid, then coefficients a4 and b4 should
continue to be significant in (3) and (4).
It should, however, be pointed out that the
aforementioned
interest rate and money demand
regressions (3) and (4) provide a test of the joint
hypothesis that money growth volatility affects the
nominal interest rate through the money demand
channel. But money growth volatility could affect
the nominal interest rate through other channels as
well. In particular, increased money growth volatility also generates inflation uncertainty, which could
directly change the real rate by influencing saving,
investment, and real output. In general, the impact
of inflation uncertainty on the equilibrium real rate
is indeterminate. But, as shown in Makin (1983),
inflation uncertainty could directly raise the real rate
if it depresses saving more than investment.rr With
respect to the empirical tests proposed above, this
point implies that the money growth volatility variable
could be significant in the nominal interest rate regression (3) but not necessarily so in the money demand
regression (4). Hence one must be careful in interpreting results from the tests conducted in this article.
Empirical Results
This section presents estimates of the interest rate
and money demand regressions (3) and (4). All
regressions are estimated over the common sample
period, 1963-86. The interest rate regressionI is
estimated by the instrumental variable estimation
rr This impact may be enhanced if higher inflation uncertainty
also depresses real output.
I2 Since the measure of expected inflation used in the interest
rate regressions is based on the Livingston Survey inflation
forecasts, the regressions are estimated using semiannual observations that correspond to the survey data collected each June
and December. The variables included in the regressions are
measured as follows: i is the average market yield on a one-year
Treasury bill (June and December observations), IT is the
Livingston Survey forecast of inflation over the 14-month
horizon, and MG is the annualized growth rate of the nominal
money stock over the last six months minus its annualized growth
rate over the last three years (second- and fourth-quarter observations are used). The interest rate regression estimated here
is in essence similar to the ones given in Carlson (1979), Peek
(198’2) Wilcox (1983), and Mehra (1985).

FEDERAL RESERVE BANK OF RICHMOND

1.5

procedure, correcting estimated standard errors for
the presence of any heteroscedastic
disturbance
term.13 The money demand regression is estimated
by the Hatanaka two-step estimation procedure that
corrects for the presence of first order serial correlation.i4’is The interest rate regressions are presented first, followed by money demand regressions.

Evidencefim the InterestRate Equation. Table III
reports interest rate regressions that include money
growth volatility and inflation interaction dummy
variables. Regressions 3.1 and 3.2 indicate that the
volatility variable based on the M 1 measure of money
is highly significant in explaining the nominal interest
rate. The Ml volatility variable continues to appear
statistically significant in the interest rate regressions
that also included the inflation interaction dummy
variable (see equation 3.2 in Table III).
Contrariwise, volatility variables based on broad
measures of money do not do as well in these interest rate regressions (see equations 3.3, 3.4, 3.5,
and 3.6 in Table III). In these the coefficient on the
volatility variable remains positive but generally not
13 Estimation treats MG endogenous with the instruments
used including the contemporaneous
and lagged values of the
expected inflation rate, volatility, and inflation-interaction dummy
variables and the lagged values of the nominal interest rate and
money growth. The standard errors of the regression estimates
were corrected for the presence of heteroscedasticity,
using
estimated covariance matrix as outlined in White (1980).
Actual estimation was carried out by using the procedure outlined
in RATS, Chapter 18, Section 3. It should be pointed out that
the interest rate regressions reported in Table III of the text were
also estimated by-using ordinary least squares. Except for the
coefficient on the variable MG. ordinary least squares estimates
of other parameters are not different from the -ones generated
by the instrumental variable estimation procedure. Hence, the
inference regarding the impact of volatility on the nominal
interest rate is not sensitive to the estimation procedure chosen
here.
I4 The money demand regressions are estimated using quarterly
observations. The measures of nominal money used are Ml,
M2, and M3. The scale variable used is real GNP, and the
opportunity cost of holding money is measured by the commercial paper rate (R). The degree of monetary instability is
measured by the eight-quarter moving average standard deviation of the quarterly growth rates of actual money stock.
1s The use of the lagged dependent variable in the money demand regression is subiect to several well-known criticisms, as
reviewedrecently
in Mehra (1986). Since this is the specification orieinallv renorted in Mascaro and Meltzer (1983) I chose
the same, so that results could be compared. in view of the
presence of a lagged dependent variable as well as serially
correlated errors in the money demand regressions, the Hatanaka
two-step estimation procedure, rather than the commonly
employed Cochrane-Orcutt procedure, is used. The use of the
Cochrane-Orcutt procedure can result in biased estimates of the
parameters (Hatanaka (1974)). Nevertheless, the money demand
regressions were also estimated by ordinary least squares, correcting standard errors for the presence of first-order serial correlation in the residuals. These estimates imply results similar
to the ones based on the Hatanaka procedure.
16

statistically significant. Instead, the inflation interaction dummy variable usually appears significant in
these regressions.
Nominal interest rate regressions that included
volatility variables were also estimated over the 1963
to 1979 period. None of these volatility variables
were significant however (these regressions are not
reported).
At best, these estimates provide only a mixed support for the money growth volatility hypothesis. True,
it appears that the heightened volatility of M 1 growth
is highly correlated with the nominal interest rate in
the 1963 to 1986 period. But this correlation does
not appear to indicate the presence of a systematic
relation between the two variables. Money growth
volatility variables are never significant in interest rate
regressions estimated over the period excluding the
1980s. Furthermore, even over the sample period
1963-86 volatility variables based on broad measures
of money are generally not significant in explaining
the behavior of the nominal interest rate.16’17
The evidence from the money demand regression
reviewed below further casts doubt on the validity
of the money growth volatility hypothesis.

Evidence Ji-om the Money Demand Equation. An
important
assumption implicit in the volatility
hypothesis is that an increase in monetary instability raises the demand for money. The money demand regressions reported in Table IV provide a
direct test of this contention. Equation 4.1 (Table
IV) is the standard money demand regression that
includes the Ml volatility measure estimated over
the period 1963-86. The coefficient on the volatility variable is of the hypothesized
sign and
statistically significant. This regression indicates that
the degree of monetary instability is an important
determinant of money demand.
16 Kantor and O’Brien (1985) report a similar conclusion.
17 As noted in the text, the interest rate regressions reported
here included, in addition to volatility measures, other variables
intended to capture the effects on the interest rate which are
due to changes in expected inflation and monetary accelerations.
Rises in expected inflation (II) are found to raise interest rates
while accelerations in money growth (MG) lower them (see Table
III). Other variables such as&pply shocks, lagged real income
growth and changes in the exogenous components of aggregate
demand were also tried and found generally insignificant in these
interest rate regressions. In particular, I found no significant effect of the fiscal deficit on the level of the nominal interest rate.
The interest rate rearessions similar to those reported in Table
III were reestimated including, in addition, the fiscal deficit
variable (measured bv the ratio of federal deficits to GNP). The
,
coefficient that appears on this fiscal deficit variable is negative
and generally insignificant.

ECONOMIC REVIEW, NOVEMBER/DECEMBER 1987

Table
III
Estimates of the Interest Rate Equation
Semiannual Data, 1963.06-1986.12
Dependent
Independent
Variables

constant

Eq. 3.1

VOL(il1)

Treasury

Bill Rate

Eq. 3.4

Eq. 3.5

(2.6)

1.4

2.0

(3.1)

(3.0)

.9 (8.5)

.8 (10.8)

2.5

(3.7)

.8 (7.6)

1.0

(9.7)

-31.2

(2.0)

.l

1.0

t.6)

2.5

(3.7)

1.3

(3.9)

-33.0

(9.8)

(3.2)

1.0

(2.6)

-24.0

(1.8)

.4 (1.8)

-38.7

MG

One-Year

Eq. 3.3

Eq. 3.2

.8 (10.7)

I-I

Variable:

.l

.2

-2
R

-8.2

(6.6)

-7.1

(3.1)

.8 (7.6)
-32.2

(2.1)

(4.6)

VOL(il3)

cc

2.1

l.5)

-33.8

VOL(il2)

D81*rI

Eq. 3.6

(5.1)

.6 (5.5)

.5 (5.2)

(1.7)
-.8

(5.5)

-3.6

(4.2)

.82

.84

.59

.80

SER

1.24

1.18

1.87

1.13

DW

1.62

1.70

.59

1.51

.3 (1.3)

-6.1

(5.9)

-4.6

.78

.58
1.89
.61

(4.7)

1.37
1.50

Notes: The nominal interest rate equation is estimated
by instrumental
variable procedure,
and t values (absolute values reported in
parentheses)
have been corrected for the presence of heteroscedacity
(see footnote 13). II is the expected inflation proxy (measured
here by the Livingston Survey forecast of inflation), MG is the annualized growth rate of the nominal money stock (Ml or M2 or M3)
over the last six months

minus

its annualized

growth

rate over the last three

years,

and VOL (h;l) is the moving-average

standard

deviation of quarterly changes in the money stock. VOL&l)
is based on Ml measure of money; VOL&l2),
on M2; and VOL@3),
on M3. D81*lI
is formed by taking the product of II and a dummy variable that takes values 1 in 1981-86 and zero otherwise.
CC is the credit control dummy taking value unity in 1980.06
and zero otherwise. Estimation treats the variable MG endogenous,
and the instruments used included the contemporaneous
and lagged values of the expected inflation rate, volatility, and inflation-interaction
dummy variables and the lagged values of the nominal interest rate and money growth.

But this conclusion is quite fragile. The regression
4.1 (Table IV) is the standard money demand regression estimated in level form and including a lagged
dependent variable. When this regression is estimated
either in the first difference form or with simple
distributed lags, the volatility variable (VOL(M1))
becomes insignificant. Likewise, that variable is no
longer significant in the money demand regression
estimated over the early sample period, 1963-79
(these regressions are not reported).
The money demand regression 4.1 (Table IV) does
not allow for evaluation of the alternative hypothesis
that Ml demand during the 1980s was affected by
the inclusion in Ml of interest-bearing NOWs and
Super NOWs. In particular, as explained before,
broad measures of money, since they internalize
deregulation-induced substitutions from components

of Ml to components of M2 and M3, provide a more
stringent test of the money demand channel of the
volatility hypothesis. Hence the regression 4.1 (Table
IV) is reestimated using instead the M2 and M3
measures of money as the left-hand-side dependent
variable. The result (see equations 4.2 and 4.3 in
Table IV) is that Ml volatility variable is no longer
statistically significant. 18 On balance, these results
do not support the contention that money growth
volatility is a significant determinant of the public’s
demand for real money balances.19
r8 It should also be pointed out that money growth volatility
variables based on broad measures of money are not statistically significant in such regressions.
i9 Hall and Noble (1987) use Granger-causality tests to show
that volatility influences velocity. However, this causality result
is also shown not to be very robust (Mehra (1987)).

FEDERAL RESERVE BANK OF RICHMOND

17

Table

IV

Estimates of the Money Demand Equation
Quarterly Data, 1963Ql-1986Q4
Dependent
Equation
Ml

Independent
Variables

-.38

constant

.05

Yt
R,
Mt.-APt

4.1

(3.4)

.002

(1.4)

-.81
.14
-.Ol

(4.4)
(4.6)

.OOl (1.5)
.OOl (1.1)
- .ooo (1.1)

.OOOl (1.2)

D742

Equation
M3

4.2

-.03
(7.1)
.84 (22.5)

(2.1)

- .002

D74

- 1.01
.19

(4.2)

-.02
(4.9)
.99 (36.8)

VOL(fGll)

Variable

Equation
M2

4.3

(2.7)
(2.9)
(3.0)

.90 (25.2)

- .ooo
.ooo
.ooo

1.1)
l.2)

Cl)

-2

R
SER
DW

.00615
2.0

.ll

Rho

.00487
2.2

(1.2)

.43

Notes: The money demand regression
is of the following form:
In (MAP,)

= b, + bI lny,

where y is real GNP,

-b,

(5.1)

estimated
lnR,

R is the commercial

.00477
1.70
.75 (10.3)

by the Hatanaka

+ b, ln(M,,/P,)
paper rate,

procedure

+ b,VOL(Ml)
P is the implicit

GNP deflator, and VOL(M1) is the measure of Ml volatility. D74 is the
dummy variable that takes value 0 through 1974Q1,
1 in 1974Q1,
incrementing
by ones until it reaches 11 in 1976Q4 and remaining at
11 thereafter.
0742 is the sauare of D74. In is the natural logarithm.
Parentheses
contain absolute values of t statistics.
The regr&sion
is
estimated
using Ml, M2, and M3 as the dependent variable, but the
VOL variable used is based on Ml.

III.
Concluding

Remarks

If one focuses primarily on the behavior of M 1-the
narrowly defined measure of money-then
the
evidence reviewed here supports the contention that
the volatility of money growth did increase during
the period that followed the change in monetary control procedures. Since then Ml demand has also been
stronger than predicted from its past relationship with
real income, the price level, and the nominal interest
rate. Furthermore, some specifications of interest rate
and money demand equations suggest that the increased volatility of money stock raised money demand and thus contributed to high levels of nominal
interest rates in the 1979-86 period.
An entirely different set of inferences emerges if
one focuses on the behavior of broad monetary aggregates. The error in predicting money demand over
this period is sharply lower when a broad definition
of money is used in the money demand regression,
18

suggesting that M 1 demand had in fact been affected
by changing asset preferences of the public. If one
controls for this effect and uses the broad definition
of money in measuring volatility, then the evidence
reported here does not support the hypothesized
causal link between the degree of monetary instability
and the level of the nominal interest rate. Money
stock volatility does not exert an independent influence on the public’s demand for real money
balances.
An increase in the demand for money not caused
by increased money stock volatility could have contributed to high nominal interest rates in the 1979
to 1986 period. Also the nominal interest rate now
moves more in line with expected inflation than
before. This consideration too could explain part of
the high levels of interest rates observed in recent
years.
What do the results presented imply for monetary
policy? An important issue raised by changes in
Federal Reserve operating procedure is whether

ECONOMIC REVIEW, NOVEMBER/DECEMBER 1987

money stock volatility matters enough to receive an
independent
weight in policy decisions. Some
analysts contend it does matter enough, because it
induces interest rate volatility and generates uncertainty about monetary policy. This uncertainty then
supposedly raises the general level of interest rates,
with adverse consequences for the performance of
the economy.20 If so, the Federal Reserve should
pay serious attention to the volatility of the growth
path of the money stock, in addition to focusing on
money’s growth rate.

2o Evans (1984) and Tatom (1985).

The empirical work reported in this article,
however, provides mixed support for the above view.
A policy-induced
rise in the volatility of money
growth is likely to be associated with a rise in the
volatility of the interest rate since accelerations or
decelerations in the growth rate of the money stock
influence nominal interest rates in the short run. This
result is due to the so-called liquidity effect of money
on interest. However, the evidence presented to support the hypothesis that money stock volatility
exerts an independent influence on the level of the
nominal interest rate is not robust. Thus it is not clear
that money stock volatility ought to be given an
independent weight in monetary policy decisions.

References
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Mehra, Yash. “Inflationary Expectations, Money Growth, and
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Carmichael, J., and P.W. Stebbing. “Fisher’s Paradox and the
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Clarida, Richard H., and Benjamin M. Friedman. “The Behavior
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Evans, Paul. “The Effects on Output of Money Growth and
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FEDERAL RESERVE BANK OF RICHMOND

19