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Federal Reserve Bank of St. Louis
Review
January 1983

In This Issue . . .

This Review contains two articles that represent variations on a common theme.
The theme is that, because “ money matters, ” its influence should be incorporated
explicitly in macroeconomic analysis if better policy decisions are to be made. Both
articles use comparative economic studies to demonstrate the validity o f this
approach.
In the first article, Dallas S. Batten and B. W. Hafer use a modified form o f the
“ St. Louis equation” to assess the relative importance o f monetary and fiscal
actions on econom ic activity in several developed countries. The purpose o f this
cross-country comparison is to determine whether the well-known results for the
United States— that monetary actions have a permanent influence on GNP growth
while fiscal actions have no lasting influence whatsoever— are unique to the
United States, or whether they apply to other economies as well. To adjust for the
importance o f international trade (for the respective economies), Batten and Hafer
modify the St. Louis equation, which relates growth in GNP to monetary and fiscal
influences, by adding a third influence on GNP growth, the growth o f merchan
dise exports.
W hen Batten and Hafer examine the effects o f monetary and fiscal actions on
GNP growth for Canada, France, Germany, Japan, the United Kingdom and the
United States, they find that the U.S. results are generally supported across the
other nations. Monetary actions have a significant and lasting effect on GNP
growth in all six countries. Fiscal actions, on the other hand, are important only in
two countries: France and the United Kingdom.
Further, Batten and Hafer examine the stability o f the money-GNP growth
relationship in each country over the change from fixed to floating exchange rates
in the early 1970s. They find that this international policy shift had no effect on the
significant money-GNP growth relationship in any o f the six countries examined.
The stability o f this relationship in the face o f “ one o f the most significant interna
tional policy shifts in the past two decades” provides evidence o f the robustness of
the money-GNP relationship and demonstrates that the economic relationships
summarized in the “ St. Louis equation” generally describe the economies of
developed nations.
In the second article, Keith M. Carlson and Scott E. Hein compare the long-run
characteristics o f three well-known econometric models — Chase, DBI and Whar
ton — to those o f the St. Louis model. The purpose o f this comparison is to
determine whether the St. Louis model — an explicitly monetarist model —
provides different implications about the long-run effects o f monetary policy from
those generated by non-monetarist econometric models.
The comparisons were based on the impacts o f four alternative monetary policy
scenarios on simulations o f a number o f economic variables — including inflation
rates, real GNP growth and nominal GNP growth. The simulations from the four
models cover the period from 1987 to 1991, which represents the last five years o f a
ten-year simulation for the 1982-1991 period. These simulations were chosen to

In This Issue . . .

represent the “ long-run” policy simulations; differences in the simulations across
the models represent differences in the long-run characteristics o f the models.
These long-run simulations also were compared to the actual relationships b e
tween money growth and the same economic variables over the period from 1955
to 1981 to determine their consistency with the historical record. Significant
deviations from the historical pattern is taken as evidence that there is some
“ problem ” with the m odel’s ability to capture the long-run consequences o f
monetary policy actions.
Carlson and Hein find that none o f the four models consistently matches the
historical record for all o f the relationships assessed. For example, none o f the
large scale models’ simulations o f nominal income growth is generally consistent
with the historical record; only the St. Louis model provides simulations that fit
with past experience. On the other hand, the St. Louis model alone shows
significant long-run variation in real output growth related to different monetary
scenarios. This result runs counter to the historical evidence that long-run money
growth has no lasting impact on real output.
Despite the variation among the models’ long-run characteristics, one particu
larly useful policy conclusion emerges from the comparative evaluation: there are
no long-run econom ic gains from faster money growth. This conclusion holds, in
general, whether the structure o f the model is explicitly “ monetarist” or not.

The Relative Impact of Monetary and
Fiscal Actions on Economic Activity: A
Cross-Country Comparison
DALLAS S. BATTEN and R. W. HAFER

C
o n s i d e r a b l e research has been devoted to
assessing the empirical relationship between both
monetary and fiscal actions and econom ic activity in
the United States. Much o f this research was sparked
by the controversial results obtained from investigat
ing the impact o f monetary and fiscal actions on GNP
using the “ St. Louis equation. ” 1 The St. Louis results
can be summarized neatly: monetary actions have a
significant, permanent effect on nominal GNP growth,
while fiscal actions exert no statistically significant,
lasting influence.

This paper is a shortened version o f an earlier study presented in
seminars at D e Nederlandsche Bank N. V ., Erasmus University and
at the 1982 Southern E con om ic Association meetings. W e wish to
express our thanks to all the participants at these sessions.
'T h e original articles presen tin g the controversial results are
Leonall C . Andersen and Jerry L. Jordan, “ Monetary and Fiscal
Actions: A Test o f Their Relative Importance In E con om ic Stabi
lization,” this Review (N ovem ber 1968), pp. 11-24; and Leonall C.
Andersen and Keith M. Carlson, “ A Monetarist M odel for E co
nom ic Stabilization,” this R eview (April 1970), pp. 7-25.

Substantially less work has been conducted within
this framework for countries other than the United
States.2 Consequently, it is uncertain whether the St.
Louis approach can be used universally in evaluating
the economic impact o f monetary and fiscal actions on
income growth.
This study investigates the generality o f the St.
Louis approach by applying it to other countries.
Based on evidence generated from the study o f six
developed countries — Canada, France, Germany,
Japan, the United Kingdom and the United States —
we conclude that money growth is more important
than fiscal actions in determ ining GN P growth.
Moreover, our results are robust across the “ fixed” and
“ flexible” exchange rate regimes that characterized the
past two decades.

ESTIMATING THE ST. LOUIS
EQUATION ACROSS COUNTRIES
The St. Louis equation typically estimated for the
United States consists o f only three variables: nominal

Early critics include Frank D e Leeuw and John Kalchbrenner,
“ Monetary and Fiscal Actions: A Test o f Their Relative Importance
in E conom ic Stabilization — C om m en t,” this R eview (April 1969),
pp. 6-1 1 ; Richard G. Davis, “ H ow M uch D oes M oney Matter? A
Look at Some Recent E vid en ce,” Federal Reserve Bank o f New
York Monthly Review (June 1969), pp. 119-31; and Edward M.
Gramlich, “The Usefulness o f M onetary and Fiscal Policy as D is
cretionary Stabilization T ools,” Journal o f M oney, Credit, and
Banking (May 1971), pp. 506-32.

^Two exceptions are Michael W . Keran, “ Monetary and Fiscal
Influences on E con om ic Activity: The Foreign E xperience,” this
R eview (February 1970), pp. 16-28; and W illiam G. Dew ald and
Maurice N. Marchon, “ A M odified Federal Reserve Bank o f St.
Louis Spending Equation for Canada, France, Germany, Italy, the
United Kingdom and the United States,” Kredit und Kapital (Heft
2 1978), pp. 194-212.

M ore recent sparring over the same issues is reported in Ben
jamin M. Friedman, “ Even the St. Louis M odel N ow Believes in
Fiscal Policy, ’’ Journal o f M oney, Credit, and Banking (May 1977),
pp. 365-67; Keith M. Carlson, “ D oes the St. Louis Equation Now
Believe in Fiscal Policy?” this Review (February 1978), pp. 13-19;
and R. W . Hafer, “ The Role o f Fiscal Policy in the St. Louis
Equation,” this Review (January 1982), pp. 17-22.

Our approach differs from these and other works in that a) we
focus solely on the growth-rate version o f the St. Louis equation
(see footnote 6); b) w e jettison the com m only used polynomial
estimation technique for unconstrained ordinary least squares (see
footnote 8); c) w e explicitly examine the stability o f the underlying
relationships from each country over time; and d) w e extend the
sample period studied.

FEDERAL RESERVE BANK OF ST. LOUIS

GNP, a variable summarizing monetary actions and
one summarizing fiscal actions. Because the equation
is formulated solely to test the relative efficacy of
monetary and fiscal actions, it is not intended to in
corporate all o f the exogenous forces that affect nomi
nal GNP. Conceptually, therefore, the equation is
misspecified. This conceptual misspecification poses a
statistical problem, however, only if the omitted ex
ogenous variables are correlated with the policy mea
sures used in the equation.3 If, as assumed generally,
the “ missing” exogenous variables are neither policy
variables nor closely correlated with the variables rep
resenting monetary and fiscal actions, their omission
does not pose a serious statistical problem .4
This discussion implicitly assumes that the domestic
economy being analyzed is relatively “ closed” to the
rest o f the world. While this may adequately charac
terize the United States, it is not true for countries
whose exports account for a large proportion o f their
GNP. In addition, because monetary and fiscal actions
obviously affect the foreign sector, the correlation be
tween external and domestic influences on GNP rises
as the economy becomes more open. Consequently,
these external influences should be included in analyz
ing the relative impacts o f monetary and fiscal actions
on GNP in such “ open” economies.
In response both to past criticism o f the St. Louis
equation and the likely interrelation o f domestic and
3For examples o f the specification error argument, see Franco
Modigliani and Albert Ando, “ Impacts o f Fiscal Actions on Aggre
gate Incom e and the Monetarist Controversy: Theory and Evi
d e n ce,” in Jerome L. Stein, e d ., Monetarism , vol. 1, Studies in
M onetary E con om ics (N orth-H olland, 1976), pp. 17-42; and
Robert J. G ordon, “ Com m ents on Modigliani and Ando, ” in M one
tarism, pp. 52-66.
To understand the necessary condition for bias due to misspec
ification, consider the following equation:
(1') Y, = a,i + ai X , + et.

N ow if equation 1' is not the “ true” model, but some other exoge
nous variable, Z, has been om itted, the true m odel is:
(2') Y, = b 0 + b] X, + b 2 Z, + T)t.

Estimating equation 1' instead o f 2' yields an estimate o f a, with an
expected value o f a] +
b 2 where Xj is obtained by estimating
(3') Z, = \() + X] X, + 4),.

Obviously, the estimate o f a, is biased only if X, 4- 0, but X[ equals
r „ (|^ where
rv/ — the sim ple correlation coefficient betw een X and Z , and
S,

— the standard deviation o f i.

Consequently, Xj ^ 0 only if rX7 i= 0; that is, X and Z must be
correlated before the omission o f Z results in a specification error.
4This point also is made in Andersen and Jordan, “ Monetary and
Fiscal A ctions,” p. 24.

JANUARY 1983

external influences on GNP in other countries, the
following modified version o f the St. Louis equation is
used:

(1) Yt

«o

lrij

M t_j

i= 0

Gt_j

i= 0

L
+

es E X t_ j

Et,

i= 0

where Y, M, G and EX represent GNP, narrow money
(M l), federal government expenditures and merchan
dise exports, respectively.5 The dots above each vari
able indicate that the equation is estimated in growth
rate form.6 The appropriate lag lengths (J, K and L) are
determined using an orthogonal regression procedure
with sequential hypothesis testing.'
Finally, one additional modification is made in esti
mating the equation. The St. Louis equation typically
is estimated with each distributed lag’s coefficients
restricted to lie on a fourth-degree polynomial with
endpoints constrained to equal zero. Because these
constraints may not be valid across countries, we esti-

T ’ ven though many countries included in this study do not explicit
ly target the narrow (M l) definition o f m oney, this definition
provides a consistent and com parable set o f explanatory variables
across countries. Also, to rem ove the impact o f cyclical changes,
h igh-em ploym ent governm ent expenditures is the measure o f
fiscal policy action typically included in the estimation for the
United States. Because com parable measures o f governm ent ex
penditures do not exist for the other countries in the sample,
federal governm ent expenditures that are not adjusted for cyclical
changes are used for each country. It should be noted, however,
that using either measure for the United States did not alter the
conclusions reached in this paper.
Furthermore, a criticism frequently leveled at using OLS to
estimate equation 1 is that the right-hand-side variables are not
exogenous with respect to GNP, resulting in simultaneous equa
tion bias. This issue is addressed in an earlier, expanded version o f
this paper through the use o f Granger-type causality tests. These
tests did not indicate any causal relationship from incom e growth to
m oney growth or governm ent expenditure growth in any o f the
countries analyzed. A lternatively, in com e growth appears to
“ cause” export growth in France and the United States, but not in
the remaining countries. Statistically speaking, then, the esti
mated parameters o f equation 1, as specified for the United States
and France, may be biased. This does not appear to b e the case for
the rest o f the sample.
fiCarlson, “ D oes the St. Louis Equation N ow Believe in Fiscal
Policy?” demonstrates that the original first-difference form o f the
m odel, when updated through the 1970s, is plagued by heteroscedasticitv. This problem is not evident in the growth-rate version,
however.
T h is procedure involves a Gram-Schmidt orthogonalization o f the
data and the use o f a testing procedure introduced by Marcello
Pagano and Michael J. Hartley, “ On Fitting D istributed Lag M od
els Subject to Polynomial Restrictions,” Journal o f Econom etrics
(June 1981), pp. 171—98; and extended by Dallas S. Batten and
D aniel L. Th orn ton , “ Polynom ial D istribu ted Lags and the
Estimation o f the St. Louis Equation,” this R eview (forthcoming).

FEDERAL RESERVE BANK OF ST. LOUIS

JANUARY 1983

Table 1

Summary of Estimation Results1
Country and Sample Period
Canada
II/66—IV/81

France
11/65-111/81

Germany
II/63—1/82

Japan
II/60—II/80

United Kingdom
11/66-1/81

United States
II/62-I/82

Constant

—.006
(0.90)

.007
(1.43)

.007
(131)

.010
(1.65)

.001
(0.21)

.007
(194)

,7262
(3.41)

,2892
(1.75)

.5182
(3.50)

.5522
(3.76)

.4192
(2.50)

1,0942
(4.29)

-.011
(0.09)

.1922
(1.90)

-.2 2 5
(1.44)

.006
(0.87)

3452
(2.90)

-.1 9 9
(1.21)

SEX

.5432
(3.04)

.246z
(3.21)

.2762
(2.48)

.067
(1.65)

2092
(3.02)

.114
(1.64)
.41

Coefficient

.49

.82

.29

.19

.59

.006

.008

.011

.016

.013

1.92
(.30)3

2.09

1.91

1.79

2.04

.008
2.24

1Absolute values of t-statistics in parentheses. R2 is the coefficient of determination adjusted for degrees of freedom; SE is the standard error
of the regression; and DW is the Durbin-Watson test statistic.
Statistically significant at the 5 percent level using a one-tailed test.
3Estimate of rho, the first-order serial correlation coefficient.

mate equation 1 using unconstrained ordinary least
squares (OLS) instead o f subjecting the data to poten
tially invalid polynomial restrictions.8
Equation 1 is estimated using quarterly data from
Canada, France, Germany, Japan, the United King
dom and the United States.9 A summary o f the OLS
regression results is reported in table 1. (The detailed
results can be found in the appendix.) The sample
periods differ due to differences in data availability.
The regressions exhibit a relatively wide range o f ex
planatory power in describing GNP growth in the

sFor a discussion o f the possible effects o f using polynomial and
endpoint restrictions, see Peter Schmidt and Roger N. Waud,
“ The Alm on Lag T echnique and the Monetary Versus Fiscal Policy
Debate , ” Journal o f the A m erican Statistical Association (March
1973), pp. 11-19.
The imposition o f polynom ial and endpoint constraints is moti
vated primarily b y the desire to estimate m ore precisely coef
ficients o f highly colinear variables (a com m on characteristic o f
distributed lag models). Our concern, in contrast, is the total or
cumulative impact o f monetary and fiscal actions on G N P growth.
Consequently, OLS will yield estimates o f linear combinations o f
coefficients that are as precise as those obtained by im posing
polynomial and endpoint restrictions. See Henri Theil, Principles
o f Econom etrics (John W iley and Sons, Inc., 1971), pp. 147-52.
W hen estimated for France, equation 1 also contains a dummy
variable representing the student riots and subsequent nationwide
strikes that occurred in II/1968.

different economies; the R2 varies from a high o f .82 in
France to a low o f .19 in Japan. The Durbin-Watson
statistics indicate that the estimates generally are not
plagued by first-order serial correlation problems. In
only one instance, that o f Canada, is a first-order serial
correlation correction technique necessary. As shown
in table 1, this correction (rho is estimated to be .30)
adequately removes the problem.

The United States
The “ standard” results appear to hold for the United
States; that is, they are not affected significantly by our
modifications. The summed impact o f money growth is
significantly positive (t = 4.29) and does not differ from
unity (t = 0.37). This means that a 1 percentage-point
increase in money growth leads to a permanent 1 per
centage-point rise in GNP growth. M oreover, the esti
mated coefficients for the individual lag terms (see
appendix) suggest a large effect o f money on income
during the first three quarters, with a varying impact
throughout the remaining lag terms.
The estimated coefficients for the fiscal measure are
interesting because they indicate only a minor initial
effect on income growth with a mostly negative impact
thereafter. This is supported by the cumulative effect

FEDERAL RESERVE BANK OF ST. LOUIS

JANUARY 1983

o f fiscal policy being negative and negligible (2g =
—0.199), and statistically insignificant (t = —1.21).

actions is smaller than that o f a change in money
growth in each country.

The results obtained for exports are similar to those
for fiscal actions: none o f the individual coefficients are
large in absolute magnitude compared with those o f M
or G, and most are statistically insignificant. M ore
over, the cumulative effect o f export growth on GNP
growth is not statistically significant at any conven
tional level.

The Impact o f Exports

Thus, the standard St. Louis equation results con
tinue to hold for the United States even with the
changes in the specification: money growth exerts a
significant, lasting impact on income growth; govern
ment expenditure growth and export growth have only
transitory influences at best. With these results form
ing the basis for comparison, we will now examine what
the application of this framework produced in the other
countries.

The Impact o f Money
Looking first at the effects o f changes in money
growth, we observe that the qualitative results for each
country are quite similar to those for the United States.
Specifically, changes in money growth have a statisti
cally significant, permanent impact on nominal income
growth in each country.10 The quantitative results,
however, exhibit some differences. The cumulative
impact o f money growth for each country except Cana
da is noticeably smaller than it is for the United States.
For Canada, the cumulative impact is not statistically
different from one (t = 1.29). Thus, while changes in
money growth exert a positive, statistically significant
influence on the growth o f income across all the econo
mies studied, a 1 percentage-point increase in money
growth results in a less than 1 percentage-point rise
in income growth for all o f the countries except the
United States and Canada.

The Impact o f Fiscal Actions
The results of changes in fiscal actions are interesting
because they tend to confirm the U.S. findings. The
cumulative impact of a change in the growth o f govern
ment expenditures on income growth is statistically
significant for the United Kingdom and France. For
the remaining countries, however, the cumulative im
pact is negligible and, for Canada and Germany the
variable takes on an u n expected negative sign.
Moreover, the cumulative impact o f a change in fiscal
10Because the expected cumulative impact o f each variable in equa
tion 1 is positive, one-tailed hypothesis tests are em ployed.

Not surprisingly, export growth is an important fac
tor in explaining GNP growth for the countries in our
sample other than the United States and Japan.11 The
cumulative impact is statistically significant and ranges
in magnitude from 0.54 in Canada to 0.21 in the United
Kingdom. Consequently, it appears that the inclusion
o f export growth is an important modification o f the St.
Louis equation for explaining econom ic activity in
open econom ies.12

IT WORKS, BUT IS IT STABLE?
The comparison o f the empirical results from a vari
ety of countries indicates that the St. Louis equation is
useful in assessing the relative impact o f monetary and
fiscal actions, and that its explanatory power can be
increased with the addition o f export growth as an
explanatory variable. Furthermore, the evidence here
suggests that changes in money growth have a perma
nent and significant influence on GNP growth. The
evidence does not provide a similar conclusion for
fiscal actions, except for the United Kingdom and
France.
The usefulness o f any equation that purports to ex
plain macroeconomic phenomena depends crucially
on the stability o f the estimated relationship. This issue
is even more significant if some o f the right-hand-side
variables in the estim ated equation are p olicy determined. 13 Consequently, it is always important to
u The export results for Japan are not surprising, even though the
general perception o f Japan is that o f a large exporter. Japan’ s
export sector as a percent o f nominal G N P is actually quite low
relative to other countries in our sample. For example, in 1980
Japan’s exports accounted for only 12 percent o f GNP. In com pari
son, the figures for the other countries are; United States (8
percent); Canada (27 percent); United Kingdom (21 percent);
France (18 percent); and Germ any (24 percent).
12W hen equation 1 is estimated excluding the distributed lag o f
export growth, the qualitative results for France are the only ones
affected. In that case, the cumulative impact o f a change in m oney
growth is no longer statistically significant (even at the 10 percent
level). Furtherm ore, there is little change in the quantitative
results concerning the cumulative impacts o f either monetary or
fiscal actions. This finding is com forting given the discussion in
footnote 5.
I3The argument is that if estimated parameters change with policy
changes, then there is no stable foundation upon which policy
makers may project the outcom e o f today’s actions into the future.
This argument is presented in Robert E. Lucas, Jr., “ Econom etric
Policy Evaluation: A C ritique,” in Karl Brunner and Allan A.
Meltzer, eds., The Phillips C u rve and L a b or M arkets, vol. 1
(1976), The Carnegie-Rochester C onference Series on Public
Policy, Supplement to the Journal o f M onetary Econom ics, pp.
19-46.

FEDERAL RESERVE BANK OF ST. LOUIS

examine the statistical stability o f the estimated param
eters across alternative policy rules if the equation is
being used in policy analysis.
Although the determination o f each policy shift in
each country is a task well beyond the scope o f this
paper, there is a single event common to all o f the
countries that can be used to assess the stability o f the
estimated relationships. That event, which occurred
during the early 1970s, is the collapse o f the Bretton
W oods system. In general, the period before the
second quarter o f 1973 is viewed as a fixed exchange
rate regime while the period since then usually is
characterized as a floating exchange rate period.14
While one may quibble about this characterization, the
early 1970s would seem to mark a significant turning
point in the implementation o f domestic monetary and
fiscal policies for the open economies in our sample.
Consequently, this apparent policy shift provides a
useful point to test the stability properties o f the esti
mated income relationships.15
It is essential to understand that we are investigating
the stability o f the relationship that explains the trans
mission o f changes in money growth and government
expenditure growth, however determined, to changes
in GNP growth. W e are not concerned with how or
why a change in money growth or government expen
diture growth occurs; we simply wish to determine the
extent to which these variables affect the growth of
nominal GNP. Consequently, the use o f the exchange
rate regime change does not require monetary or fiscal
actions to have any greater or lesser effect on GNP
growth after the break than before. The change in

14The break points for the United Kingdom and Canada tested are
slightly different from the L/1973 point. See text.
15It is typically thought that during a fixed exchange rate regim e the
reserve currency country determ ines monetary policy for the rest
o f the world. I f this w ere the case, the measured influence o f
monetary actions on econ om ic activity during the Bretton W oods
period actually w ould indicate actions motivated by the reserve
currency country, not by the dom estic monetary authorities. To
test this proposition, w e perform ed G ranger-type causality tests
to see if changes in U.S. m oney growth “ caused” changes in
foreign m oney growth during the fixed exchange rate period.
These tests results did not indicate any systematic relationship
betw een U.S. m oney growth and m oney growth in any o f the
countries included in our sample. O ur results support those o f
Edgar L. Feige and James M. Johannes, “ Was the United States
Responsible for W orldw ide Inflation U nder the Regim e o f Fixed
Exchange Rates?” Kyklos (Fasc. 21982), pp. 263-77; and Edgar L.
Feige and Kenneth J. Singleton, “ Multinational Inflation Under
Fixed Exchange Rates: Som e Empirical E vidence From Latent
Variable M o d e ls ,” The R eview o f E con om ics and Statistics
(February 1981), pp. 11-19. Consequently, connecting observed
m oney growth with monetary policy decisions in these countries,
even during the fixed exchange rate period, appears to have some
empirical support.

JANUARY 1983

Table 2

Stability Test Results
Absolute values
of t-statistics
Country

Canada

0.26

0.40

France

1.44

1.08

Germany

1.65

0.68

Japan

0.70

1.55

United Kingdom

0.07

2.241

United States

0.61

1.35

'Statistically significant at 5 percent level.

exchange rate regimes is chosen as a likely break in the
income equations primarily because o f its universality.
To examine the stability o f the estimated income
relationships, (0,1) dummy variables are used to form
multiplicative slope-dum m y terms for the money
growth and government expenditure growth variables.
Stability is investigated by testing the hypothesis that
the cumulative impact o f each dummied variable’s dis
tributed lag is significantly different from zero.16 If the
resulting t-statistic is less than a predetermined critical
value, the null hypothesis that these coefficients are
stable across exchange rate regimes cannot be re
jected.
The calculated t-statistics for each variable’s stability
test are reported in table 2. The break point for the
United States, France, Germany and Japan is 1/1973,
the widely accepted timing o f the breakdown o f the

16This approach is suggested by Dam odar Gujarati, “ Use o f D um m y
Variables in Testing for Equality Between Sets o f Coefficients in
Linear Regressions: A Generalization,” The A m erican Statistician
(D ecem ber 1970), pp. 18-22. W e em ploy this m ethod by con
structing a slope-dummy; term for each variable in the distributed
la g o fM a n d o fG (e .g ., D M , = D -M ,w h e re D = 0 in the fixed-rate
period and 1 in the floating-rate period). The hypothesis that the
cumulative impact o f M has changed with the m ovem ent o f float-

K
ing exchange rates is then investigated by testing

.
D M t_, = 0.

i= 0
A similar procedure is used for G.
This approach is chosen over the m ore com m only used C how
test, because the C how test examines the stability o f the entire
relationship. Thus, the coefficients o f one variable may change
dramatically over tim e, while the C how test will not reject the
hypothesis o f stability if that variable’s explanatory pow er is weak
relative to that o f other variables w hose coefficients are relatively
stable. The dum m y variable approach circum vents this potential
problem .

JANUARY 1983

FEDERAL RESERVE BANK OF ST. LOUIS

Smithsonian extension o f the Bretton W oods system.
Because the United Kingdom and Canada had refused
earlier to peg the value o f their currencies to the U.S.
dollar, the break points tested are 11/1972 and 11/1970
for the United Kingdom and Canada, respectively.
The results reported in table 2 support the hypothesis
that in each country the cumulative impact o f a change
in money growth is stable across the break in exchange
rate regimes. The cumulative impact o f a change in the
growth of government expenditures exhibits instabil
ity only for the United Kingdom.
The results for the United Kingdom indicate that the
estimated equation does not reliably capture the rela
tionship between changes in the growth o f government
expenditures and GNP growth. Furthermore, a shift in
the trend rate o f velocity growth (captured by the
constant term) is detected. To correct for both o f these
deficiencies, equation 1 is re-estimated for the fullsample period with the coefficients o f government ex
penditure growth and the constant term allowed to
take on different values during the two exchange rate
periods. The re-estimated United Kingdom equation
is (absolute value o f t-statistics in parentheses):
11

0.024 D1 + 0.679 X M, j
(1.90)
(2.12) i = 0

Y = 0.008 (1.05)

2
2
- 0.043 2 C L , + 0.530 2 GfL j
(0.19) i = 0
(3.39) i = 0
2
+ 0.200 2 EXt_
(2.95) i = 0
R2 = 0.66

SE = 0.012

DW = 2.15

These results indicate that, after separating the in-

fluence of government expenditures and the constant
term into the two periods, the cumulative effect of
changes in British money growth increases in magni
tude and remains positive and significant and now is
not statistically different from one (t = 1.00).

Digitized for 10
FRASER

This suggests that the failure to incorporate the secular
decline in the trend rate o f velocity growth since 1973
seriously understated the initially estimated impact o f
changes in money growth. Export growth continues to
influence GNP growth significantly, although the sum
med coefficient indicates a slight decline.
The United Kingdom estimates indicate that the
government expenditure results in table 1 are captur
ing the post-II/1972 effects. For the period 11/1966 to
11/1972, fiscal actions have no significant lasting effect
on income growth. The post-II/1972 results, on the
other hand, point to a significant and fairly substantial
fiscal effect. The post-II/1972 results indicate that in
creasing the growth o f government expenditures by 1
percentage point will permanently increase income
growth by about one-half as much. Thus, in contrast to
the evidence presented for the other countries ex
amined, the cumulative impact o f fiscal actions is high
ly significant only in the United Kingdom, and then
only after 11/1972.

SUMMARY
The results in this paper demonstrate that the St.
Louis equation can be applied to a variety o f other
countries and that monetary actions dominate fiscal
actions in determining the pace o f economic activity in
these countries. Estimating a modified St. Louis equa
tion for six different countries, our results indicate that
changes in money growth have a significant and lasting
impact on nominal income growth in all six cases. O f
equal importance, the money-GNP link was stable in
each country across one o f the most significant interna
tional policy shifts o f the last two decades — the move
from fixed to floating exchange rates.
In contrast, fiscal actions are significant only in the
United Kingdom and France. Moreover, this effect
does not appear to be stably related to income in the
United Kingdom where fiscal actions have exerted a
lasting impact on income growth only during the re
cent floating exchange rate period.

FEDERAL RESERVE BANK OF ST. LOUIS

JANUARY 1983

Appendix
Detailed Estimation Results1
Constant
-.0 0 6 (0.90)

cn
"tf;
CVJ
CO

DW = 2.09

.246 (3.21 )3
.202
.045
- .0 1 7
-.0 1 8
.064

(4.71 )2
(1.16)
(0.45)
(0.49)
(1.45)

R2 = .29
SE = .011
DW = 1.91

.276 (2.48)3

.013
.161
.289
-.1 2 0
.209
.552

(0.13)
(1.44)
(2.54)2
(1.03)
(1.83)
(3.76)3

.006 (0.87)

.067 (1.65)

- .007
.335
.069
-.2 7 4
.190
-.1 1 3
-.0 4 1
.108
.160
-.1 6 9
-.0 1 6
.177
.419

(0.07)
(3.31 )2
(0.64)
(2.76)2
(1.81)
(1.07)
(0.38)
(1.04)
(1.45)
(1.60)
(0.15)
(1.75)
(2.50)3

.274 (3.11 )2
—.094 (1.24)
.165 (2.19)2

.156 (4.86)2
.117 (3.42)2
- .0 6 4 (1.81)

.067 (1.65)

R2 = .19
SE = .016
DW = 1.79

.001 (0.21)

SE = .008

cvj

United Kingdom
Lag 1
Lag 2
Lag 3
Lag 4
Lag 5
Lag 6
Lag 7
Lag 8
Lag 9
Lag 10
Lag 11
Sums

.518 (3.50)3

(0.53)
(0.66)
(1.46)
(0.56)
(1.50)
(2.09)2
(1.44)

(1.64)
(1.16)
(1.83)
(0.03)
(0.83)
(0.89)
(1.53)

DW = 1.92 (,30)4

ICC

.010 (1.65)

.022
-.0 2 8
-.0 6 4
- .0 2 4
-.0 6 2
-.0 6 9
-.2 2 5

.192 (1.90)3

.066
.035
.052
.001
.024
.025
.043

SE = .006

Japan
Lag 1
Lag 2
Lag 3
Lag 4
Sums

.087 (0.67)
.024 (0.16)
.407 (3.06)2

(1.47)
(0.08)
(0.10)
(1.55)
(1.78)
(2.48)2
(2.00)2
(1.43)

(2.73)2
(4.36)2
(0.94)
(0.00)
(1.03)
(2.68)2
(0.92)
(1.31)
(1.88)
(0.12)
(0.85)
(2.64)2
(1.00)
(3.04)3

CVJ

.007 (1.31)

-.0 3 9
-.0 0 2
.003
.042
.047
.065
.049
.027

.063
.124
.025
.000
.029
.076
.025
.036
.051
-.0 0 3
.021
.073
.023
.543

ICC

Germany
Lag 1
Lag 2
Lag 3
Lag 4
Lag 5
Sums

-.0 1 1 (0.09)

(0.57)
(2.01 )2
(0.98)
(0.43)
(0.37)
(1.17)
(0.19)
(0.77)
(1.08)
(1.75)3

-.0 3 6
.132
.075
-.0 3 4
.030
.088
.015
-.0 5 8
.077
.289

(0.31)
(1.48)
(0.25)
(0.39)
(0.16)
(1.92)

Summary statistics

.007 (1.43)

.006
-.0 3 5
-.0 0 7
-.0 1 1
-.0 0 5
.041

(2.51 )2
(3.15)2
(2.03)2
(0.51)
(3.05)2
(2.25)2
(2.00)
(1.00)
(1.73)

.726 (3.41 )3

France
Lag 1
Lag 2
Lag 3
Lag 4
Lag 5
Lag 6
Lag 7
Lag 8
Sums

.142
.205
.131
-.0 3 3
.215
.154
-.1 3 4
-.0 6 9
.115

ICC

Canada
Lag 1
Lag 2
Lag 3
Lag 4
Lag 5
Lag 6
Lag 7
Lag 8
Lag 9
Lag 10
Lag 11
Lag 12
Sums

SE = .013

DW = 2.04

.345 (2.90)3

.209 (3.02)3

(continued on next page)

FEDERAL RESERVE BANK OF ST. LOUIS

JANUARY 1983

Appendix Continued1
Constant
United States
Lag 1
Lag 2
Lag 3
Lag 4
Lag 5
Lag 6
Lag 7
Lag 8
Lag 9
Lag 10
Lag 11
Sums

.007 (1.94)

M
.709
.425
.380
-.2 5 5
.204
-.3 6 9

(4.14)2
(2.70)2
(2.64)*
(1.74)
(1.29)
(2.08)2

1.094 (4.29)3

1See notes accompanying table 1.
Statistically significant at the 5 percent level using a two-tailed test.
Statistically significant at the 5 percent level using a one-tailed test.
4Estimate of rho, the first-order serial correlation coefficient.

Digitized for 12
FRASER

G
.065
.055
-.1 2 1
.030
- .0 6 3
- .0 4 9
.079
-.0 2 8
-.0 7 6
-.0 9 1

(1.22)
(1.04)
(2.28)2
(0.56)
(1.17)
(0.93)
(1.49)
(0.49)
(1.28)
(1.61)

.022
.015
.005
.000
-.0 0 9
.006
- .009
.015
-.0 1 6
.015
.030
.040 (2.41 )2
-.1 9 9 (1.21)
.114

(1.28)
(0.86)
(0.31)
(0.01)
(0.54)
(0.36)
(0.51)
(0.87)
(0.91)
(0.84)
(1.73)
(1.64)

Summary statistics

R2 = .41
SE = .008
DW = 2.24

Four Econometric Models and Monetary
Policy: The Longer-Run View
KEITH M. CARLSON and SCOTT E. HEIN

O
NE key element in the making o f an informed
economic policy decision is the accuracy with which
policymakers can gauge the longer-run consequences
o f their policy actions and strategies. Crucial to such
attempts to grasp these policy consequences is the use
o f econometric models. Whether current econometric
models are useful in this respect depends upon their
“long-run” characteristics; unfortunately, until recent
ly, there had been virtually no study o f the compara
tive long-run properties o f the major econom etric
models currently in use. Most analyses instead have
dealt with how well these models forecast a few quar
ters ahead.
This situation changed with the publication o f a re
cent study by the Joint Economic Committee (JEC) o f
Congress that focused explicitly on the econom ic im
pact o f alternative long-run monetary strategies using
three well-known econometric m odels.1 Missing from
the JEC study, however, was an econometric assess
ment using an explicit monetarist model. The purpose
of this paper is to extend the JEC study by comparing
their results with those obtained for the St. Louis
model. Analysis o f the St. Louis model according to
criteria used in the JEC study is informative for two
reasons. First, it indicates whether a monetarist
framework provides additional insight into the longrun effects o f monetary policy. Second, it provides
policymakers the opportunity to compare the long-run
properties o f a monetarist model with those o f the
major nonmonetarist models.

FEATURES OF THE JEC STUDY
The JEC study examined the simulated perfor
mance o f certain key macroeconomic variables under
four different long-run monetary strategies. Three
large-scale econometric models were analyzed: those
o f Chase Econometrics, Data Resources Incorporated
1Robert E. Weintraub, T hree Large Scale M odel Simulations o f
F ou r M oney G row th Scenarios, a staff study prepared for the use o f
the Subcomm ittee on Monetary and Fiscal Policy o f the Joint
E conom ic Com m ittee o f Congress (G overnm ent Printing Office,
1982).

(DRI) and Wharton, the best-known and most widely
used models.
Four separate monetary strategies were considered
over a 10-year simulation period (1982 through 1991),
using the fourth quarter o f 1981 and an M l growth rate
o f 5.8 percent as points o f departure;
(1) a sudden deceleration of M1 growth to zero percent
in one year, and then held at zero;
(2) gradual deceleration of M 1 growth to zero percent
over a five-year period, and then held at zero;
(3) sudden deceleration o f M l growth to 3 percent in
one year, and then held at 3;
(4) gradual acceleration of M l growth to 10 percent
over a five-year period, and then held at 10.

In addition, each m odel’s proprietor was asked to run a
baseline projection with freedom to choose the mone
tary strategy.2

2The baseline simulations thus represented each m odel’s assump
tion about the future course o f monetary policy as o f March 1982.
These assumptions w ere as follows:
M l Growth Rate:
1982-91
Chase
DRI
Wharton

6.3%
4.5
5.2

The m odel proprietors w ere further instructed to simulate each
o f the four monetary strategies twice: first, without making any
judgmental adjustments, and second, making any adjustments
deem ed necessary to ensure consistency and generate results that
were considered sensible. These adjustments w ere at the discre
tion o f the individual m odel proprietor and involved no contact
with the JEC staff. The JEC labeled these two sets o f simulations
“ pure” and “ managed. ”
The JEC study concluded, on the basis o f the pure simulations,
that none o f the models can b e used b y themselves to decide among
the monetary strategies. The results o f these pure simulations w ere
term ed “ puzzling,” because the links betw een the m oney growth
and the key m acroeconom ic variables ran counter to historical
experience.
The JEC conclusions about the managed simulations w ere m ore
positive. W hile there still remained som e inconsistencies with
historical relationships, the managed simulations w ere ju dged to
provide a better basis for considering the longer-run policy im
plications o f alternative monetary aggregate growth strategies.
Thus, in the discussion to follow, only the managed simulation
results from the large scale models are considered.

FEDERAL RESERVE BANK OF ST. LOUIS

JANUARY 1983

The St. Louis Model
The basic structure o f the St. Louis model, de
veloped in the late 1960s, has remained essentially
unchanged since then.1 The model consists of five
equations and two identities (see appendix). The
foundation o f the model and the basis for its mone
tarist label is the GNP equation. The growth rate o f
GNP is specified as a function o f current and lagged
values o f M l growth and current and lagged values
o f the growth o f high-employment federal expendi
tures. The monetarist label stems primarily from
the estimated coefficients: the sum o f the coef
ficients on money growth is about unity and the sum
o f the coefficients on high-employment expenditure
growth is about zero.

The price equation relates the rate-of-change o f
prices to current and lagged values o f demand pres
sure, current and lagged values o f changes in the
relative price o f energy, and a measure o f antici
pated price change. Demand pressure is defined as
the growth o f output relative to the growth o f highemployment output. Anticipated price change is a
weighted sum o f past price changes with the weights
obtained by estimating the corporate Aaa rate as a
function o f past inflation. Output growth (real GNP)
is determined residually via the GNP identity;
nominal GNP growth is the sum o f real GNP growth
and the rate o f change o f prices.

'Leonall C. Andersen and Keith M. Carlson, “ A Monetarist
M odel for E conom ic Stabilization,” this Review (April 1970),
pp. 7-25. M inor changes which have been made include: (1) a
respecification in rate-of-change form from the original first
difference form; (2) the addition o f energy prices as an exoge
nous variable; and (3) a change in estimation procedure from
ordinary least squares to generalized least squares for those
equations in which serial correlation is evident. See Keith M.
Carlson and Scott E. H ein, “ An Analysis o fa M odified St. Louis
M od el,” a paper prepared for the Spring C onference on C om
paring the Predictive Performance o f M acroeconom ic M odels
at Washington University in St. Louis (April 20, 1982).

The model’s remaining equations provide esti
mates o f three other macroeconomic variables. Un
employment is estimated as a function o f the gap
between actual output and high-employment out
put. The Aaa bond rate is a function o f past inflation.
The 4-month commercial paper rate is a function
of contemporaneous M l growth and current and
lagged values o f changes in the relative price o f
energy, output and prices.

Though the instructions were specified in terms o f
M l, none o f the models permitted direct control o f this
monetary aggregate. Both Chase and DRI specify the
control o f money growth through nonborrowed re
serves. Thus, nonborrowed reserves were manipu
lated to achieve the desired M l growth.3 For the
Wharton model, the target variable is M2 instead of
M l. The Wharton simulations were conducted using
M2 target rates o f 4 percent, 7 percent and 14 percent,

respectively, whereas the JEC specified M l targets of
zero percent, 3 percent and 10 percent.4

3D RI has an iterative procedure that allowed them to hit M 1 targets
exactly as specified by the JEC. Chase, on the other hand, used a
trial and error procedure, and was unable to achieve M l targets
precisely.

Simulation o f the St. Louis model for the long-run
monetary strategies outlined in the JEC study re
quired assumptions about other exogenous variables:
potential output was assumed to grow 2.5 percent per
year, high-employment expenditures to increase at a
steady 8 percent rate, and the change in the relative
price o f energy to be zero. To determine a baseline
strategy, an average o f the baseline strategies for the
large-scale m odels was con stru cted . W hat this
amounted to was a gradual reduction in M l growth
from a 5.8 percent rate in fourth quarter 1981 to 5.0
percent in 1991.

Since the simulations w ere run in March 1982, Chase E con
ometrics has revised their m odel to incorporate a new monetary
sector to reflect changes in Federal Reserve policy procedures in
O ctober 1979. At the time the simulations w ere run, the Chase
m odel used an index o f credit rationing as the primary channel o f
monetary influence.

4M 1 is an endogenous variable in the m odel, however, so there is a
basis for com paring the W harton m odel with the other m odels. The
resulting M l growth rates w ere generally, but not precisely, con
sistent with the JEC s instructions.

FEDERAL RESERVE BANK OF ST. LOUIS

PROPERTIES OF THE MODELS AS
REVEALED BY THE SIMULATION
RESULTS
This study follows the general format o f the JEC
study, using the U.S. econom ic experience from 1956
through 1981 as a guide in comparing the models. If
certain systematic relationships among key variables
have held over the past 26 years, the simulation results
for the next 10 years should be roughly consistent with
that experience if one is to place much faith in the
model. Deviations from historical experience place the
burden o f explanation on the individual model pro
prietor.
Simulation results relating money growth to (1)
nominal GNP growth, (2) inflation and (3) real output
growth are considered first. Then, the relationships
between real output growth and unemployment, and
between nominal interest rates and inflation are evalu
ated. Since the longer-run relationships are o f primary
interest and since short-run adjustments make the re
sults difficult to interpret, the results for the last five
years o f the simulations, 1987-91, are investigated.

GNP, Money and Velocity
With simulations o f the four long-run monetary
strategies and a baseline simulation, five observations
characterizing the 1987—91 period were generated for
each model, providing a basis for examining the rela
tionship between money growth and nominal GNP
implicit in each. This relationship is referred to con
ventionally as the velocity o f money. The well-known
equation o f exchange portrays this as
M V = Y, o r V =

where M is money stock, Y is nominal GNP, and V is
the velocity o f money. In its growth rate form,

M + V = Y.
Although velocity growth is influenced by many
variables, it has shown considerable stability during
the 1956-81 period. The implication o f this stability is
that, in the long run, nominal GNP growth is related
closely to the growth o f M l. The stability o f velocity
growth further suggests that a 1 percent change in rate
of growth o f money should coincide generally with a 1
percent change in the rate o f growth o f nominal GNP.
The large-scale econometric models do not specify
GNP as a direct function o f money. In these models,

JANUARY 1983

money affects GNP indirectly via interest rates and
wealth or real balance effects. Despite this, the large
models still yield systematic relationships between
money and GNP.
Chart 1 summarizes the money-GNP simulation re
sults. Each model is summarized by plotting the aver
age growth o f simulated nominal GNP for the 1987-91
period against the average growth rate o f M 1 for the
same period. Each point represents model results for a
particular long-run monetary strategy.5 As noted
above, these strategies are stated in terms o f M l
growth, and include (1) a sudden deceleration to zero
percent, (2) a gradual deceleration to zero percent, (3) a
sudden deceleration to 3 percent, (4) a gradual accel
eration to 10 percent, and (5) a baseline strategy chosen
by the model proprietor.
The historical line is derived by regressing the fiveyear average growth rate o f nominal GNP on the fiveyear average growth rate o f M l. The parallel lines
depict the regression estimate plus or minus one stan
dard error o f the equation. If velocity growth is totally
independent o f money growth, then the slope o f the
historical line would be 45 degrees. The estimated
slope, in fact, is not significantly different from 45
degrees.
Comparing the different models with historical ex
perience suggests that none o f the large-scale models is
generally consistent with the actual past. Only four of
the 15 simulated cases for these models fall within the
historical band. The DRI and Chase simulations indi
cate that velocity growth is related negatively to money
growth, so that higher rates o f money growth do not
yield proportionally higher nominal GNP growth. On
the other hand, simulation results for the Wharton
model indicate that higher money growth results in
more than a proportional increase in GNP growth. This
result, however, follows from the nature o f the finan
cial sector in the Wharton model. On the basis o f M2,
which is Wharton’s actual monetary target variable,
velocity growth is related negatively to money growth
as in the Chase and DRI models.
Not surprisingly, the St. Louis model falls clearly
within the historical band; after all, the GNP equation

5For the M l growth rate associated with each strategy, refer to the
accompanying table. The points on the chart are connected for each
m odel in ascending order o f M l growth. Consequently, the results
for the Chase and W harton m odels are not charted with the JEC’ s
slowest growth strategy farthest to the left. See also footnote 3.

FEDERAL RESERVE BANK OF ST. LOUIS

JANUARY 1983

C h a rt 1

Table 1

M oney and GNP
Y

(Percent)

GNP, Money and Velocity (1987-91)

(Percent)

Average Annual Results
Model and Strategy

M
(Percent)

is constructed to be consistent with this historical
experience.6 The proprietors o f the other models offer
no explanation as to why their models predict that
velocity behavior in the future will be different from
the past.1

Inflation and Money
Economists generally agree that, over the long run,

fT h e St. Louis m odel simulations do show a weak positive rela
tionship betw een velocity growth and m oney growth. This result
occurs because the estimated sum o f the coefficients on M in
the G NP equation is slightly greater than unity.
7The JEC study suggests that the reason the large-scale m odels run
contrary to historical velocity experience is that they are built to
short-run specifications, that is, their focus is on forecasting for
short periods into the future. Such an explanation might be
appropriate for the Chase m odel, but the D R I and W harton models
are annual models. The results suggest that something more fun
damental is awry. In addition, the St. Louis m odel, which is a
quarterly m odel, does not exhibit any departure from historical
long-run velocity behavior.

Digitized for 16
FRASER

Chase
1
2
3
4
Baseline

3.0%
1.1
2.8
10.6
6.4

8.1%
8.0
8.3
11.5
9.4

5.1%
6.9
5.5
1.0
3.0

DRI
1
2
3
4
Baseline

0.0
0.0
3.0
10.0
4.1

7.2
7.3
9.1
13.5
9.6

7.2
7.3
6.0
3.2
5.3

Wharton
1
2
3
4
Baseline

3.0
1.5
3.2
6.5
4.9

5.8
6.4
7.5
12.5
9.8

2.8
4.8
4.2
5.7
4.6

St. Louis
1
2
3
4
Baseline

0.0
0.1
3.0
9.9
5.2

2.8
2.9
6.2
14.0
8.7

2.8
2.8
3.1
3.7
3.3

inflation is related directly to money growth.8 In terms
o f the equation o f exchange, with rates o f change o f
prices and output ( P + X ) substituted for Y ,
M + V = P + X.
A justification o f the money-inflation relationship is
that V and X are not related systematically to M over
the long run. Consequently, variations in M eventually
are reflected in P .
To evaluate the money-inflation relationship for the
different models, the simulation results are summa-

8For example, Barro and Fischer introduced their 1976 survey o f
monetary theory with the follow ing statement:
“ Perhaps the most striking contrast between current views o f
money and those o f 30 years ago is the rediscovery o f the endogeneity
o f the price level and inflation and their relation to the behavior o f
m oney.”

Robert ]. Barro and Stanley Fischer, “ Recent D evelopm ents in
Monetary Theory, ” Journal o f M onetary Econom ics (April 1976),
p . 133.

FEDERAL RESERVE BANK OF ST. LOUIS

JANUARY 1983

C h o rt 2

M o n e y a n d In fla tio n

Table 2

Inflation and Money (1987-91)

(P e r c e n t)

Average Annual
Results

Model and Strategy

12
11

M is average a nnual rate fo r 1987-91; P is fo r
1991.

Final Year

4.8%
4.9
5.2
7.8
6.3

4.9%
4.4
4.8
7.9
5.9

Chase
1
2
3
4
Baseline

3.0%
1.1
2.8
10.6
6.4

DRI
1
2
3
4
Baseline

0.0
0.0
3.0
10.0
4.1

4.0
4.0
6.1
10.4
6.5

3.6
3.6
5.8
9.8
6.2

Wharton
1
2
3
4
Baseline

3.0
1.5
3.2
6.5
4.9

2.9
3.4
4.2
9.8
6.6

2.1
2.3
3.8
10.3
6.2

St. Louis
1
2
3
4
Baseline

0.0
0.1
3.0
9.9
5.2

-2 .7
-0 .9
1.6
10.0
5.2

-1 .7
- 1 .9
2.8
12.8
6.0

H isto rica l re la tio n sh ip :
P = - 1.46 + 1.36 M
(2.05)

(9.70)

R2 = 0.82
SE = 1.22

(Percent)

rized in chart 2. Without exception, all four models
show a direct relationship between monetary growth
and inflation. There is substantial variation, however,
in the degree o f sensitivity among the models. The
Chase model shows a difference in inflation forecasts of
only 3.5 percent betw een the slowest and fastest
monetary growth strategies. DRI shows a 6.2 percent
age point differential and Wharton a differential o f 8.2
percentage points. The St. Louis model shows the
largest differential o f 14.5.
To provide a basis for historical comparison, the
inflation rate was regressed on the average o f money
growth over the previous five years for the 1956-81
period. Comparing the simulation results o f the four
models with this historical line suggests that there is
some bias in each. The Chase and DRI models exhibit a
sensitivity o f inflation to money growth that appears
too low, while the Wharton and St. Louis models show

a sensitivity that appears too high. W hile the models
generally are inside the historical band for money
growth rates in the neighborhood o f the 1956-81 aver
age o f 4.7 percent, a wide range o f results occurs for
monetary strategies that lie at the extremes o f his
torical experience.9
9An explanation o f these diverse results w ould require a detailed
analysis o f the inner workings o f each m odel. For the most part, the
large-scale models estimate the price level primarily by marking up
som e measure o f labor costs. Consequently, the insensitivity o f
inflation to m oney growth developm ents in the Chase and D RI
m odels might b e related to the stickiness o f wages. This explana
tion does not seem to explain the W harton results, however. The
Wharton m odel shows considerable sensitivity in the 3 percent to 7
percent range for m oney growth, yet the price determination
process apparently is similar to that for Chase and D RI. The St.
Louis m odel differs from the large-scale m odels in that prices are
determ ined directly b y dem and pressure and past prices. The
influence o f past prices tends to capture effects operating through
wages, yet inflation remains sensitive to m oney growth throughout
the full range.

FEDERAL RESERVE BANK OF ST. LOUIS

JANUARY 1983

C h a rt 3

Table 3

M on ey and Real GNP

Real GNP Growth and Money (1987-91)

(Percent)

71---------

Average Annual Results

Model and Strategy

H istorical relationsh ip

(

1956- 81 )

M and X are average annual rates fo r 1987-91.
Historical relationship:
X = 3.87 - 0.07M
R2 =
0.02
(7.42) (0.72)
SE = 0.89
_L_

_L_

_l_

M
(P e rce n t)

Real GNP and Money
A corollary to the long-run, money-inflation rela
tionship is the hypothesis that the trend growth o f real
GNP is not systematically related to long-term money
growth. Money may affect the growth o f real GNP in
the short run, but if inflation rises one-for-one with
accelerated money growth, as the equation o f ex
change indicates, there are no cumulative effects on
real GNP.
Chart 3 summarizes the money-real GNP rela
tionship from the simulations o f the four models. The
three large-scale models all show real GNP growth
rates in the neighborhood o f 3 percent, regardless o f
which monetary strategy is considered. The St. Louis
model, on the other hand, shows greater variation of
real GNP growth among the strategies. This is because
the dynamic lag structure o f the St. Louis model is such
that, after 10 years, the model is still a considerable
time away from steady-state equilibrium in growth
Digitized for 18
FRASER

Chase
1
2
3
4
Baseline

3.0%
1.1
2.8
10.6
6.4

3.1%
3.0
2.9
3.4
3.0

DRI
1
2
3
4
Baseline

0.0
0.0
3.0
10.0
4.1

3.0
3.2
2.9
2.8
2.9

Wharton
1
2
3
4
Baseline

3.0
1.5
3.2
6.5
4.9

2.8
2.9
3.2
2.5
3.0

St. Louis
1
2
3
4
Baseline

0.0
0.1
3.0
9.9
5.2

5.6
3.9
4.5
3.7
3.3

terms. Given more time to adjust, the St. Louis model
tends to approach about 3 percent real growth, regard
less o f money growth.
The historical line in chart 3 is based on five-year
growth rates o f both money and real GNP. The slope of
the line is not significantly different from zero, and the
standard error is quite large relative to the mean. The
results for the three large-scale models are virtually
identical. Relative to the large-scale models, the St.
Louis model is the outlier, though four o f the five
simulated observations are well within the historical
band; only the strategy o f sudden deceleration o f M l to
zero yields real output growth that is outside the his
torical band. Again, this makes sense because o f the
long adjustment process in the St. Louis model; very
weak output growth in the early years under the zero
money growth strategy is offset by very strong output
growth in the 1987—91 period.
In general, the simulation results suggest that
money has a neutral effect on real output growth in the

FEDERAL RESERVE BANK OF ST. LOUIS

JANUARY 1983

Table 4

C h a rt 4

R eal G N P a n d U n e m p lo y m e n t R ate
AU

Real GNP Growth and Unemployment
AU

(1987-91)
Model and Strategy

(P o r te n t)

long run. A sustained change in the money growth rate
has little or no effect on the long-run growth rate o f real
GNP.

Real GNP and Unemployment
Another relationship o f interest in macroeconomics
is the one between real GNP growth and the unem
ployment rate. All three o f the large-scale models show
essentially the same rates o f real growth for each o f the
monetary strategies. Thus, Okun’s law, which relates
unemployment to deviations o f actual from potential
output, suggests that the change in the unemployment
rate would be approximately equal for all strategies.10
Such is not the case. Each o f the large-scale models
shows considerable variation in the change in the un

10Arthur M. Okun, “ Potential GNP: Its M easurem ent and Signifi
can ce,” 1962 Proceedings o f the Business and E conom ic Statistics
Section o f the Am erican Statistical Association, pp. 98-104.

Average Annual Rate

Change in U:

1986-91

Chase
1
2
3
4
Baseline

3.1%
3.0
2.9
3.4
3.0

0.0%
0.5
0.1
- 2 .3
- 1 .3

DRI
1
2
3
4
Baseline

3.0
3.2
2.9
2.8
2.9

-1 .5
-1 .9
-0 .9
0.0
- 0 .6

Wharton
1
2
3
4
Baseline

2.8
2.9
3.2
2.5
3.0

-1 .9
-1 .4
- 3 .2
1.4
- 1 .0

St. Louis
1
2
3
4
Baseline

5.6
3.9
4.5
3.7
3.3

- 6 .6
- 2 .9
- 4 .5
- 3 .0
- 2 .0

employment rate despite near-equal rates o f real GNP
growth. What is not known, o f course, are the assumed
growth rates for the labor force and other determinants
o f potential output in these models. Nevertheless,
when the strategies are compared across models, the
results o f a sudden deceleration o f M l growth to zero
range from no change in the unemployment rate for
the Chase model to a 1.9 percentage point decline for
the Wharton model. The results for the opposite ex
treme, gradual acceleration o f M l to 10 percent, show
even greater variation— from a 2.3 percentage drop in
the unemployment rate for the Chase model to a 1.4
point increase for the Wharton model.
The St. Louis model also shows considerable varia
tion in the change in unemployment across monetary
strategies; however, this is due to substantial variation
in the growth rate o f real GNP. All the unemployment
changes are negative, because the simulated real
growth rates exceed the assumed growth rate o f 2.5
percent for potential GNP. Moreover, because the St.

JANUARY 1983

FEDERAL RESERVE BANK OF ST. LOUIS

mmmmmmmm^mmm

C h a rt 5

Table 5

In fla tio n a n d Long-Term Interest Rate
(P e rc e n t)

Percent)

Inflation and Interest Rates (1987-91)
Model
and Strategy

St. Louis

Historical relationship
( 1956 - 8 1 )
is average annual rate fo r 1987-91; RL is MA
corporate bond rate fo r 1991.
H istorical rela tion sh ip:
RL = 2.68 + 1.03 P
(5.28) (10.04)

R2 = 0.83
SE = 1.09

i____I____I____I____I____ I___

(P e r c e n t)

Louis model simulates very strong 1987-91 real output
growth in conjunction with the sudden deceleration of
money growth to zero, sizable reductions in unem
ployment go hand in hand with such a policy.
The historical line in chart 4 is estimated by regress
ing the change in the unemployment rate over fiveyear periods on the five-year growth rate o f real GNP.
The historical band encompasses only one observation
from the 20 that are charted. The models’ failure to
replicate history may not be as bad as appears in the
chart, however. Potential output supposedly grew
faster in the 1956-81 period than it is assumed to be
growing in 1987-91. The simulation results suggest an
implied growth rate o f potential output o f 2.5 percent
to 3.0 percent for 1987—91, instead o f the 3.6 percent
rate calculated for 1956-81. Nevertheless, the largescale models show the inverse relationship between
real growth and unemployment suggested by Okun’s
law. In contrast to the St. Louis model, however, the
degree o f sensitivity is not well defined.
Digitized for 20
FRASER

Average Annual Results
M

Chase
1
2
3
4
Baseline

3.0%
1.1
2.8
10.6
6.4

DRI
1
2
3
4
Baseline

0.0
0.0
3.0
10.0
4.1

Wharton
1
2
3
4
Baseline
St. Louis
1
2
3
4
Baseline

Final Year
RS

11.5%
11.5
9.5
11.6
10.0

16.3%
15.8
10.6
9.0
8.4

10.7%
11.6
8.7
12.7
9.6

4.0
4.0
6.1
10.4
6.5

10.1
10.1
11.1
14.8
11.4

8.0
7.8
9.5
12.4
10.0

9.5
9.5
10.7
14.1
10.9

3.0
1.5
3.2
6.5
4.9

2.9
3.4
4.2
9.8
6.6

8.8
8.1
10.7
16.0
12.3

6.5
6.2
8.6
13.8
9.4

6.9
7.4
9.2
16.5
11.7

0.0
0.1
3.0
9.9
5.2

- 2 .7
- 0 .9
1.6
10.0
5.2

5.6
7.6
8.4
14.0
11.3

1.9
2.8
4.9
11.3
7.3

4.6
5.8
8.5
16.1
11.5

4.8%
4.9
5.2
7.8
6.3

Inflation and Interest Rates
The relationship between inflation and nominal in
terest rates is the final relationship considered. The
inflationary experience o f the last 15 years provides an
ample basis for examining the nature o f this rela
tionship.
Monetary theory suggests that nominal interest
rates reflect inflationary expectations. These expecta
tions can be modeled as a function o f past inflationary
experience. The question examined here is whether
the econ om etric m odels incorporate such a rela
tionship.
Chart 5 summarizes graphically the simulation re
sults for inflation and long-term interest rates. The
Chase model does not appear to show any consistent
relationship between inflation and long-term interest
rates. The Wharton model displays a peculiar kink at
relatively low rates o f inflation, while the DRI and St.
Louis models display a strong positive relationship.

JANUARY 1983

FEDERAL RESERVE BANK OF ST. LOUIS

C h a rt 6

C h a rt 7

Inflation an d Short-Term Interest Rate

M is e ry In d e x
p+u

P +U
(P e r c e n t)

(P e r c e n t)

M
( P e r c e n t)

What is most obvious from the chart is the incon
sistency with historical experience. The slopes o f the
simulation results are roughly consistent, but the
general level is vastly different. For the St. Louis
model, the inconsistency arises because o f the use of
the serial correlation adjustment in the simulations.
With long-term rates in late 1981 well above the infla
tion rate, this differential only gradually disappears
during the simulation period. It appears that the largescale models are following a similar procedure. In this
regard, it seems that most o f the models would do
much better at predicting the change in long-term
rates, rather than the level itself.
Chart 6 plots the simulation results for inflation and
short-term interest rates. Again, with the exception of
the Chase model, the models demonstrate substantial
similarities. The St. Louis model tends to simulate the
lowest level o f short-term rates for a given rate of
inflation. The historical line, as in the case o f long-term
rates, is below all the model results, but the discrepan

cy is not as great as that for long-term rates. All the
models, with the exception o f the Chase model, in
corporate an inflation premium into short-term rates,
suggesting that the lower the inflation rate, the lower
short-term interest rates will be.

THE POLICY IMPLICATIONS OF
THESE SIMULATION RESULTS
The discussion above emphasized the long-run
properties o f econometric models as revealed by the
simulation results. What remains to be determined are
the implications o f these results for long-run monetary
policy. From this longer-run perspective, do the mod
els’ simulation results favor a strategy o f slow M l
growth, fast M l growth or something in between?
To aid in this assessment, a crude index, called a
“ misery index,” is constructed to summarize the re
sults. The index is simply the sum o f the inflation rate
21

FEDERAL RESERVE BANK OF ST. LOUIS

JANUARY 1983

Table 6

Misery Index (1987-91)
Average
Annual Result
Model and Strategy

Misery Index

Final Year
P

P + U

Chase
1
2
3
4
Baseline

3.0%
1.1
2.8
10.6
6.4

4.9%
4.4
4.8
7.9
5.9

DRI
1
2
3
4
Baseline

0.0
0.0
3.0
10.0
4.1

3.6
3.6
5.8
9.8
6.2

6.5
6.4
6.3
6.6
6.5

10.1
10.0
12.1
16.4
12.7

Wharton
1
2
3
4
Baseline

3.0
1.5
3.2
6.5
4.9

2.1
2.3
3.8
10.3
6.2

7.6
7.6
5.5
9.1
6.1

9.7
9.9
9.3
19.4
12.3

St. Louis
1
2
3
4
Baseline

0.0
0.1
3.0
9.9
5.2

- 1 .7
-1 .9
2.8
12.8
6.0

3.9
6.2
3.9
1.7
4.9

2.2
4.3
6.7
14.5
10.9

and the unemployment rate at some point in tim e.11
Construction o f such an index is, o f course, simplistic,
yet it provides general information for evaluating the
effect o f the alternative monetary strategies.
Chart 7 summarizes this misery index for the 198791 period for the four econometric models. In general,
the simulation results indicate that there is a long-run
payoff from following a slow M l growth strategy; the
results from the Chase model provide the only excep
tion. There seems to be little basis for choosing be
tween sudden and gradual deceleration to zero money
growth, however, because the misery index differs
little when these strategies are compared. An evalua
tion o f these strategies would involve a more detailed

10.5%
9.8
8.8
2.3
5.0

15.4%
14.2
13.6
10.2
10.9

analysis o f the adjustment path o f inflation and unem
ployment.
The general levels o f the misery index for the four
models indicate substantial variation in the predicted
effects o f alternative monetary strategies. For the slow
M l growth scenarios, the St. Louis model is by far the
most optimistic, and the Chase model is the most
pessimistic. For the fast M l growth strategy, Chase is
most optimistic and Wharton is most pessimistic.
Thus, using this set o f results, a policymaker is con
fronted with a disturbing diversity o f opinion. Yet,
three o f the four models show a definite payoff from
following a strategy o f slow to moderate growth o f M l.

SUMMARY AND CONCLUSIONS
n This simple index originated with the late Arthur Okun, although
he called it a “ discom fort index. ” The term “ misery index” is used
b y Jerome L. Stein, M onetarist, Keynesian and N ew Classical
Econom ics (N ew York University Press, 1982), p. 159.

This article, extending recent work by Robert Weintraub at the Joint Economic Committee, has compared
simulation results from various econometric models to

FEDERAL RESERVE BANK OF ST. LOUIS

the historical record o f the last 26 years. The emphasis
is on the longer-run econom ic impact o f alternative
money growth scenarios. No single model was found to
be consistent with the historical record on all counts.
The simulation results generally show, however, the
positive consequences o f following a slow M 1 growth
strategy. Higher rates o f money growth are associated
with higher rates o f spending growth, which eventual
ly are reflected in higher inflation rates. Using a simple
social loss function called the misery index, three o f the
four models indicate that, over the long run, unem

JANUARY 1983

ployment gains, if any, are insufficient to offset the
increase in inflation.
Consequently, this article — like the JEC study
before it — concludes that there are no long-run eco
nomic gains from higher rates o f money growth. This is
true even though the models run counter to historical
experience in some important aspects. Moreover, the
results indicate that higher inflation rates are associ
ated with higher levels o f both short- and long-term
interest rates, so that interest rates tend to be higher
when the faster monetary strategies are followed.

Appendix
Revised Form of St. Louis Model
The version o f the St. Louis model used for the
simulations in this article is summarized in table 1,
with the coefficients given in table 2. Equations 1-4 are
estimated with Almon constraints on the coefficients.

Equation 5 is estimated with ordinary least squares.
Three characteristics differentiate this model from the
original version published in 1970: (1) most variables
are entered in rate-of-change form rather than firstdifference form; (2) the demand slack variable is en
tered in real rather than nominal terms; and (3) where
relevant, the m odel’s equations have been corrected
for serial correlation problems.

Table 1

The Model
(1) Y, = C1 +

4
4
2 CM| (Mt _i) + 2 CEi(E,_i) + e1,
i= 0
i= 0

4
5
(2) P, = C2 + 2 CPE, (PE, ,) + 2 CD,(Xt l - XF,*_,)
i= 0
i= 0

Table 2

In-Sample Estimation: 1/1955—IV/1981
(absolute value of t-statistic in
parentheses)

+ CPA (PA,) + CDUM1 (DUM1)
+ CDUM2 (DUM2) +

e2,

(1) Y, = 2.81 + 1 . 1 3
(3.11)
(6.91)

20
(3) RL, =

2 CPRLi (Pt . ,) + e3t
i= 0

R2 = 0.40

2 CPERSi (PE,_,) + CMRS (M,)
i= 1

SE = 1.28

(9) X, = ((X,/X,_,)4 - 1) 100
(10) P, = ((P ./P ,-,)4 - 1) 100
(11) GAP, = ((XF, - X,)/XF,) 100
(12) XF,* = ((XF,/X,_1)4 - 1) 100
Y
M
E
P
PE
X
XF
RL
RS
U
UF

=
=
=
=
=
=
=
=
=
=
=

nominal GNP
money stock (M1)
high employment expenditures
GNP deflator (1972 = 100)
relative price of energy
output in 1972 dollars
potential output (Rasche/Tatom)
corporate bond rate
commercial paper rate
unemployment rate
unemployment rate at full employment

DW = 2.13

DW = 2.00

p = 0.16

(3) RL, = 0.87 2 P,_i
(3.50) i = 0
e5,

R2 = 0.12

SE = 0.32

DW = 1.76

p = 1.00
16

(4) RS, = 0.05 2 PE,_i -0 .0 8 M, + 0.77
i= 1
(2.84)
(3.22)

2
i=

(7) Y, = (P./100) (X.)
(8) Y, = ((Y,A,,_ 1)4 - 1) 100

(0.06)

2 CPRSi (P,_i) + e4,

21
2 CPRLi (P,_i)
i= 1

SE = 3.72

R2 = 0.76

i= 0

(6) PA, =

+ 1.13 PA, - 0.80 DUM1, + 1.72 DUM2,
(11.44)
(1.33)
(2.79)

(5) U, - UF, = CG (GAP,) + CG1 (GAP,_,) +

5
(2) P, = 1.12 + 0.06 2 PE, , +0.08
2 (X, , - XFt*_,)
(3.27)
i= 1
(5.00) i = 0

16
+ 2 CXRSi(X,_i)
i= 0
+

2 E,_,

2
(4) RS, =

2 M,_| - 0.01

+ 0.97
(5.62)
R2 = 0.32

2 P,_,
i

=0
SE = 0.90

DW = 1.83

p = 0.89

(5) U, - UF, = 0.29 GAP, + 0.14 GAP,_,
(14.85)
(6.84)
R2 = 0.70

SE = 0.19

p, = 1.33

p2 = -0.44