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Vol. 73, No. 6

November/December 1991

3 T h e 1990 Oil P ric e H ike in
P e r s p e c tiv e
19 A lte rn a tiv e M e asu res o f the
M o n e t a r y Base: W h a t A r e the
D iffe r e n c e s and A r e T h e y
Im portant?
36 A M ic r o e c o n o m e t r ic A p p r o a c h to
Estim ating M o n e y D em an d: T h e
A s y m p to tic a lly Ideal M o d e l
52 M ic r o s tr u c tu r e T h e o r y and the
F o re ig n E xch an ge M a r k e t

THE
FEDERAL
J RESERVE
JU BANK of
ST.IjOI IS

Federal R eserve Bank of St. Louis
R e v ie w

November/December 1991

In This Issue . . .

When oil prices doubled in 1990 as a result of Iraq's invasion of
Kuwait, the economic effects of oil price shocks became central to dis
cussions o f the economic outlook and economic policy. In the first arti
cle in this Review, “The 1990 Oil Price Hike in Perspective,” John A.
Tatom discusses several popular but misleading perceptions about the
changing effects of oil price shocks on the U.S. economy and policymak
ers’ response to such changes in the past.
The author explains that the principal channel of influence of higher
energy prices is a loss in economic capacity and productivity. Other
channels of influence arise through the oil import bill or changing ener
gy efficiency. Tatom compares the recent experience with the two
previous oil price shocks and finds that there was little reason to expect
the effects of the 1990 oil price shock to be much smaller.
The most significant difference in the latest shock, says the author, is
that it was more clearly temporary, so that the doubling of oil prices
from July to October 1990 was virtually eliminated by offsetting move
ments from October to March 1991. As a result, Tatom concludes, the
adverse effects of the oil price shock should be reversed almost as
quickly as they occurred.
* * *
In the second article in this issue, “Alternative Measures of the Mone
tary Base: What Are the Differences and Are They Important?” Michelle
R. Garfinkel and Daniel L. Thornton explore the differences in two
measures of the adjusted monetary base, one constructed by this Bank,
the other constructed by the Federal Reserve Board. Noting that these
two indicators of monetary policy can and frequently do give conflicting
impressions of monetary policy, the authors briefly review the basic
idea behind the adjustment for reserve requirement changes. They then
discuss differences in the construction of the two measures and go on
to explore the importance of these differences empirically. Because the
differences in their construction are arbitrary and technical in nature,
there is little reason to prefer one measure over the other. The authors
suggest that, when the difference is important, the measure that ap
pears to perform best for the problem at hand should be used.
* * *
In the third article in this Review, “A Microeconometric Approach to
Estimating Money Demand: The Asymptotically Ideal Model,” Piyu Yue
presents an advanced approach to estimating money demand called the
“Asymptotically Ideal Model” or AIM. She briefly reviews alternative
microeconometric approaches to money demand, then estimates the
AIM using U.S. quarterly monetary aggregate data. Dynamic simulations

NOVEMBER/DECEMBER 1991

of the growth rate of the various aggregates and consumption suggest
that the model performs well. Among other things, she concludes that
the failure of conventional money demand equations may result from
the inability of linear equations to approximate the behavior of non
linear demand functions.
*

In recent years, a number of articles discussing the theory of securi
ties market microstructure have appeared in economics and finance
journals. The study of market microstructure deals with the behavior of
participants in securities markets and the effects o f information and in
stitutional rules on the economic performance of securities markets.
Although a large and growing number of such articles have appeared,
relatively few have attempted to model the foreign exchange market.
In the fourth article in this issue, "Microstructure Theory and the For
eign Exchange Market," Mark D. Flood reviews the theoretical literature
on market microstructure to see what lessons it holds for the foreign
exchange market. Microstructure theory is of interest to students of the
foreign exchange market, says the author, because it can yield insights
into dealers’ behavior and the impact of institutional arrangements. Con
versely, the foreign exchange market is o f interest to students of
microstructure, because it combines two very different methods of
matching buyers and sellers—bank dealers trade both directly and
through brokers.
*

FEDERAL RESERVE BANK OF ST. LOUIS

John A. Tatom
John A. Tatom is an assistant vice president at the Federal
Reserve B ank o f St. Louis. James P. Kelley provided research
assistance.

The 1990 Oil Price Hike in
Perspective

J . ' HE ECONOMIC EFFECTS of the sharp rise
in oil prices in 1990 were, for a while, the cen
tral issue in discussions of the economic outlook
for 1990 and 1991. Iraq’s maneuvers to raise
the world price of oil late in July 1990 and
their invasion of Kuwait less than a week later
led to a doubling of oil prices. As a result, oil
price shocks and the appropriate economic
policy response to such shocks became subjects
of renewed speculation.
One of the most popular hypotheses to emerge
at the time was that, since the economy was
different in 1990 than it had been when previ
ous large oil price increases occurred, the 1990
price rise should not affect the economy to the
same extent.1 It still was widely believed, how
ever, that the principal and most immediate
effect would be the onset o f a recession. In
response, many analysts believed that the Fed
eral Reserve would ease monetary policy be
cause they thought it had done so at the outset
of previous oil shocks.
This article outlines the potential channels of
influence o f a rise in the price of oil and the ex
tent to which the purported differences in eco

nomic conditions in 1990 could account for
differences between the economic effects of the
1990 oil price surge and those in earlier, com
parable episodes.

W HY DO OIL PRICES MATTER?
One usually encounters two principal argu
ments in assessing how oil and energy price
changes affect the economy. First, since energy
resources are used to produce other goods and
services, a change in their price affects how
much of the goods are produced as well as the
mix of resources that will be used to produce
them. This argument focuses on the supply side
of the markets for goods and services. It sug
gests that the output losses associated with
higher energy prices are permanent, so that
changing economic policies or shifting market
prices cannot replace the loss.
A second argument focuses on the effects on
the demand for a country’s output. It suggests
that output losses are cyclical or transitory, so
that adjustments in wages and prices, or in eco
nomic policy, can reverse the loss in output.

1Fieleke (1990) was one of the first to develop this a rg u
ment. Am ong the reasons he cites are differences in the
size of the shock, the sensitivity of oil consum ers to oil
price changes, the state of the econom y before the oil
shock and differences in available policy options. The
Council of Econom ic Advisers (1991) provides a more ex
tensive discussion consistent w ith this view.

NOVEMBER/DECEMBER 1991

Each argument suggests which characteristics of
the economy determine the effects of an energy
price shock, as well as how changes in these
characteristics would alter these effects. Each
also provides a different conclusion about the
potential for economic policy to ameliorate the
adverse influences of energy price shocks.

Energy Prices and Econom ic Ca
pacity: The Permanent Effects o f
an Energy Price Shock
Energy resources are used to produce most
goods or services. As such, a rise in their price
will (1) raise the total cost of an efficient pro
ducer’s output, (2) alter the most efficient means
for producing output, (3) lower the profit-maxi
mizing level of output, (4) raise the long-run
equilibrium price of output and (5) reduce the
capacity output of each firm ’s existing stock of
capital.2 Capacity output declines when energy
prices rise because firms reduce their use of
energy and energy-using capital, some capital
becomes obsolete, and firms use labor and capi
tal to economize on energy costs—that is, they
generally switch to less energy-intensive p ro
duction methods. The shaded insert on pages
6 and 7 b riefly explains the microeconomic
foundations of this capacity effect.
The economy’s aggregate supply is the sum of
the supply decisions o f the nation’s firms. Thus,
the effect of energy prices on the typical firm’s
economic capacity determines the effect on the
economy’s natural output and its aggregate sup
ply. The influence of a rise in the price of ener
gy on aggregate supply is shown in figure 1.
The aggregate supply curve indicates the output
that producers will supply at various levels of
the aggregate price level, given other factors
influencing this decision. The supply curve typi
cally is derived from a given production func
tion, which relates output to the employment of
resources such as labor and capital. An initial
level of nominal wages, the supplies of labor
2T his discussion draw s upon Rasche and Tatom (1977a)
and (1981); Karnosky (1976) was one of the first to argue
that a rise in the price of energy reduces capacity and
raises th e price level. H ickm an, H untington and Sweeney
(1987) sum m arize th e sim ila rities and differences o f e m piri
cal estim ates of the effects of energy price shocks in 14
prom inent m acroeconom ic m odels. All of these m odels
show a perm anent o utput loss due to an oil price increase;
in six of these m odels, th is loss is e xp lictly cited as a
decline in potential output.
The Council of Econom ic Advisers (1991) suggests that
any effect on capacity is transitory. O thers who have been

FEDERAL RESERVE BANK OF ST. LOUIS

and capital goods and the relative price of
energy resources are assumed to be given in
deriving a particular aggregate supply curve.
Suppose that the price level, P0 in figure 1,
results in a real wage (nominal wage deflated
by the price level) at which a given supply of
labor resources is fully employed. At this level
of employment, which often is referred to as
natural employment, the economy produces its
capacity or natural output level, X°. Given the
nominal wage level, the real wage is lower
when prices are higher than P0, so firms would
desire to produce more output and demand
more employment. Workers would be unwilling
to work more at a lower real wage, however,
so neither output nor employment could rise.
Indeed, to maintain output and employment, the
nominal wage must rise proportionately with
the price level to keep the real wage unchanged.
Thus, the aggregate supply curve is vertical at
X" for prices above P0. At a lower price level
than P0, the real wage is too high for firms to
employ as much labor or produce as much out
put as at X"; output and employment are below
their natural counterparts along this upwardsloping portion of the aggregate supply curve.
A rise in the relative price of energy, given
the short-run supply of capital and labor re
sources, will reduce capacity output from X" to
X^, and raise the aggregate level o f prices as
sociated with this output from P° to P1. The
percentage decline in capacity output and the
rise in price level associated with each 1 per
cent rise in the relative price of energy gener
ally are equal and proportional to the share of
energy in the cost of outpu t.3 In this case, al
though real output has fallen, the level of nomi
nal spending on output at point B in figure 1
will be the same as at point A. Thus, if output
is measured by the nation’s real GNP, then real
GNP is lower at point B than at point A, but
nominal GNP is the same.
Aggregate output and the price level are de
termined by the interaction o f aggregate supply
critical of the significance o f the capacity e ffect include
Berndt (1980), Berndt and W ood (1987), Denison (1979)
and (1985), D arby (1984) and O lson (1988).
3The conditions required to obtain the eq u ality of these out
com es are discussed in Rasche and Tatom (1977a) and
derived in Rasche and Tatom (1981). The shaded insert to
this article provides a sum m ary of th e analysis.

Figure 1
The Effect of a Higher Price
of Energy on Output and
the Price Level

and demand. Aggregate demand indicates the
quantity o f output demanded at various price
levels and is inversely related to the general
price level. The aggregate demand curve in
figure 1 passes through both points A and B. At
these points, nominal GNP (the product o f the
price level and output) is the same, indicating
that a rise in the price level is associated with
an equal proportionate decline in real output.
Thus, the nominal value of aggregate demand is
unaffected by the price level.
This assumption simplifies the analysis with
out reducing its generality. The higher price
level reflects the permanent decline in natural
output, with no cyclical loss of output or em
ployment; the smaller natural output level is
produced by an unchanged level of natural em
ployment. Only a further reduction in output
would fit the notion o f a cyclical loss associated
with cyclical unemployment.
For cyclical output and employment losses to
arise from an energy price increase, either (1)

4Tatom (1981) indicates th a t tem porary cyclical effects oc
cur for the third reason above; that is, they are short-run
dynam ic variations as the econom y m oves from point A to
point B. In this analysis, sticky prices keep the price level
from rising instantaneously. Inventories and increased em
ploym ent initially are used to m eet unchanged sales and
partially offset the productivity loss. W ithin a short tim e,
however, firm s begin to reduce output because sales fall

aggregate demand must be more responsive to
a rise in the price level (flatter than that drawn
in figure 1), (2) an increase in the relative price
of energy must cause the aggregate demand to
shift to the left, or (3) there is some short-run
dynamics o f price and output adjustment not
shown in the movement from A to B. For exam
ple, if the price level adjusts upward slowly be
cause of temporary rigidities in the prices of
goods and services, then a rise in energy prices
will lead producers to reduce employment tem
porarily, reducing output by more than the
decline in natural output. When output prices
rise sufficiently to reduce real wages by the
extent of the permanent decline in labor pro
ductivity, employment will be restored to its
natural level and output will have fallen only to
the extent of the capacity loss.4 Thus, even if
the principal effects o f an energy price rise are
a permanent decline in capacity and a rise in
the price level, some transitory recessionary
declines in output and employment are likely to
occur.

Energy Prices and Aggregate
Dem and
The second channel of influence above indi
cates that a rise in the relative price o f energy
would shift aggregate demand to the left, reduc
ing output and/or the level of prices. These ef
fects are transitory, or cyclical, however, in
contrast to the permanent output loss arising
from reduced capacity. When output is less
than its natural level, employment is as well.
Thus, wages and rental prices of capital goods
will tend to fall, shifting the upward-sloping
portion of the aggregate supply curve and the
price level down until output is restored to its
natural level.
Aggregate demand will fall if a rise in oil
prices raises expenditures on oil and total im
ports and thereby lowers net exports. In effect,
the rise in the oil import bill acts like a tax on
domestic income, reducing aggregate demand.
For such a shift in aggregate demand, the de
cline in output and employment are propor-

m ore as prices begin to rise; cyclical losses in output and
em ploym ent occur. Em pirical evidence indicates that, after
about a year, the price level has adjusted fu lly (to P, in
fig u re 1), so producers step up production and em ploy
m ent to th e ir natural levels (point B).

NOVEMBER/DECEMBER 1991

The Effect of a Higher Price of Energy on Eco
nomic Capacity
The effect of a rise in the price of energy
on a firm ’s cost structure is illustrated in the
accompanying figure, which shows the longand short-run average cost of output and
how they are affected by a rise in the price
o f energy. The long-run average cost curve
(LACq) indicates the minimum cost per unit of
output for the firm. This curve is derived
from the least-cost combination of resources
that produces the indicated quantity of out
put, given available technology and the prices
of the resources used to produce the firm ’s
output. The long run refers to a period over
which the firm is free to vary the quantity of
all resources used in production.
In the figure, the long-run average cost
curve is horizontal, or unaffected by the level
o f output. The long-run average cost could
decline over some range of output, indicating
what are called “economies of scale,” or it
could rise over some range indicating “dis
economies of scale.” When the curve is hori
zontal, as in the figure, the firm ’s production
exhibits constant returns to scale so that, for
any initial output level, proportional increases
or decreases in output can be obtained from
equiproportional changes in the employment
o f each resource. In this case, long-run cost
varies equiproportionately with output, so
that the long-run average cost is unaffected
by the output level the firm chooses to pro
duce. With constant returns to scale, the
long-run average cost also indicates the longrun marginal cost, the minimum additional
total cost o f producing an additional unit
of output.1
The short run is characterized by the inabil
ity to vary the use of some resources. In par
ticular, firms have difficulty in varying their
capital stock—their plant and equipment—to
produce more or less output in the short
run. Thus, a given size of capital stock would
be freely chosen to allow least-cost produc
tion at only one level of output. At a larger
’ The m ost general case is often illustrated with a Ushaped long-run average cost curve, w hich exhibits in
creasing returns to scale over the range of relatively
low o utput levels and decreasing returns to scale at

FEDERAL RESERVE BANK OF ST. LOUIS

The Effect of a Higher Price
of Energy on a Firm’s Cost,
Capacity and Price

O u tp u t p e r
p e rio d

(smaller) output, more (less) capital would be
used to minimize the cost o f production. The
output level at which the existing stock of
capital would be selected is called the eco
nomic capacity o f the firm ’s capital stock. At
this output, the long-run and short-run total
and average cost of output are the same.
Should the firm desire to produce more or
less output, it could not do so as cheaply in
the short run as it could in the long run be
cause the capital stock cannot be varied in
the short run. Higher-cost methods of pro
duction, which use relatively more labor or
other variable resources, must be used until
the capital stock can be altered. Since the
total cost of producing any level o f output
other than the capacity level (XQ) is higher in
the short run than the long run, the shortrun average cost (SAC0) is also higher.
When the price of energy rises, the longrun and the short-run average cost of output
rise (LACi and SACt, respectively). The size of
relatively high levels of o utput. A t the m inim um longrun average cost, there are constant returns to scale.

the rise depends, in part, on the size of the
increase in energy prices and the share of
energy resources in total cost. The effect on
the firm's economic capacity depends on how
the optimal long-run mix o f resource employ
ment changes. The higher price of energy
will cause the firm to reduce its use of
energy to produce a given level o f output
(say X0) and increase the use of some re
sources whose prices have not changed. The
use of some other resources could also be
reduced along with energy.2 As drawn in the
figure, the capacity output of the firm falls to
X , since the short-run average cost rises
more than the long-run average cost at out
put X0.
2T he effect of a rise in the price of one resource on the
e fficient level of em ploym ent of another is assessed by
the “ e lasticity of su b stitu tio n ” between the two
resources, w hich m easures the percentage change in
one resource associated w ith each 1 percentage-point
rise in the price of the other, holding o utput constant. If
the e lasticity o f substitution between energy and some
o ther resource is positive, a rise in the price of energy
raises the em ploym ent of th e other resource. In this
case, energy and the other resource are said to be
substitutes. W hen this e lasticity of substitution is nega
tive, energy and the other resource are “ com
ple m e n ts.”
3Some analysts describe production as “ p utty-clay,”
m eaning that, in the short run, the capital stock re
qu ire s fixed proportions of oth er resources. In this
case, the elasticity of substitution between energy and
capital is zero in the short run, so that capacity is un
affected. O ver tim e, a capacity loss w ould be realized
as obsolete capital is replaced w ith capital that uses

tional to the rise in the oil price and the share
of oil imports in GNP. In this case, the net oil
import status of a country determines the ef
fects o f an energy price shock.5 Countries that
export oil face larger aggregate demand when
oil prices rise; world aggregate demand and out
put are redistributed from oil importers to ex
porters when oil prices rise, and conversely
when oil prices fall.6
5Feldstein (1990) and the Council of Econom ic Advisers
(1991) provide recent restatem ents of th is shift in ag
gregate dem and and the price-level-induced m ovem ent
along the aggregate dem and curve as the central chan
nels of influence of an oil price hike. The Council of Eco
nom ic Advisers also em phasizes a decline in real
consum ption expenditures as a result of an oil price hike.
Perry (1991) argues that the oil price hike had little effect
on the econom y in 1990, because it did not reduce real in
com e m uch (operating through the aggregate dem and
channel above), nor did it induce the Fed “ to raise interest

Whether capacity output falls, rises or is
unaffected by a rise in the price of energy
depends on the relationship between capital
and energy resources in production. When
these resources are substitutes, a rise in en
ergy prices would lead the firms to substitute
capital for energy in producing XQ. Thus, the
existing capital stock would be chosen to
produce a smaller output level (XJ.3 If capital
and energy are independent or complements,
the higher short-run and long-run average
cost level will be identical at the same or
higher level of output, respectively. Energy
and capital are substitutes, however, which
implies that economic capacity will fall when
energy prices rise.4
less energy. See C orcoran (1990), for exam ple. Evi
dence cited in the text suggests that putty-clay con
siderations are not dom inant in the short run.
4The size of the fall in econom ic capacity is proportional
to the share o f energy in fa cto r cost and th e elasticity
of substitution and inversely proportional to the expen
diture elasticity of the capital stock (or fixed resources
generally). The ela sticity of capacity equals ( —ake/rjk)
se, w hich reduces to - se, th e share of energy in total
cost, if the expenditure e lasticity of capital, >jk, and the
e lasticity of substitution, oke, are one; these elasticities
are each one for a broad class of fu n ction s used in em
pirical analysis. The form er e lasticity is the response of
desired capital use to an increase in expenditures on
all resources. For increases in the relative price of
energy, instead of the nom inal price, the share of ener
gy in the expressions here and above is replaced by
(se/1 - s e).

Monetary P olicy and Oil Price
Shocks
The appropriate monetary policy response to
a rise in the relative price o f energy depends on
its dominant channel of influence. If the higher
energy price only lowered aggregate demand,
policymakers could take offsetting actions to
neutralize this shift by increasing the money
rates to fig h t in fla tio n ” as, he argues, it had in th e past.
6A change in the relative price of energy could also affect
a ggregate dem and by altering investm ent in plant, equip
m ent and housing. Such an effect can account for a
d ecline in the real interest rate, which is incom patible with
a conventional m odel of aggregate dem and. Reinhardt
(1991) d iscusses the effects of energy price shocks on in
terest rates.

NOVEMBER/DECEMBER 1991

supply, which would shift the aggregate de
mand curve back to the right.
If an energy price increase affects aggregate
supply, however, both raising the price level
and reducing natural output, policymakers could
attempt to offset the price level rise by reducing
the money stock to reduce aggregate demand.
This would result in a cyclical loss in output
and employment as the economy’s output fell
short of its lower natural output level until the
price level declined sufficiently.
Alternatively, policymakers could attempt to
offset the reduction in output by raising ag
gregate demand. Raising demand could not re
store the economy’s natural output, however; it
would not replace the energy and capital re
sources that firms can no longer afford to pur
chase or use. Instead, it would further raise the
aggregate level of prices associated with the
smaller level of capacity output.7
Thus, there is no real policy dilemma posed
by oil price increases. Raising the money stock
cannot offset a loss in natural output, while
reducing the money stock can only offset a
price level increase at the cost of a further loss
in output and a cyclical rise in unemployment.
Moreover, it is virtually impossible to alter mon
etary policy enough to fully offset the price
level surge because of the time it takes for a
change in the money stock to affect the price
level and because of the relatively small size of
the initial price response to changes in mone
tary policy.8 An unchanged growth rate for the
money stock is a policy that accepts the perma
nent output and price level consequences de
scribed above without compounding one or the
other loss.

HAVE THE ECONOMIC EFFECTS
OF OIL PRICE SHOCKS
CHANGED?
Many analysts argued that the rise of oil
prices in 1990 would have substantially less im
7Kahn and Ham pton (1990) contrast three m onetary policy
options, which include tightening to offset the price level
effect, easing to offset the cyclical effects and a neutral
policy which “ m aintains constant m onetary or nominal
GNP g ro w th .” Feldstein (1990) endorses the third option,
nom inal GNP targeting, and he also equates this w ith un
changed m oney stock growth.
8See Tatom (1981) and (1988a), for exam ple, for evidence
on the relative size and lag lengths for energy price and
m onetary policy effects on prices and output.

FEDERAL RESERVE BANK OF ST. LOUIS

pact on the U.S. economy than earlier oil price
hikes. There were two versions of this argu
ment. The first was that the adverse effects of
an oil price rise are proportional to the share of
oil imports in the economy and that this share
had fallen since the earlier oil price shocks. The
second argument was that the effects of an oil
price rise are proportional to the use of energy
per unit of output and that this dependence on
energy also had fallen.9

D oes a Smaller Im port Share
Reduce the Adverse Effects o f an
Oil Price Hike?
If the share of oil imports in GNP has fallen,
then the first argument above implies that the
economy’s aggregate demand and output have
become less sensitive to a rise in oil prices.
Figure 2 shows expenditures on petroleum im
ports as a percent of nominal GNP since 1970.
In mid-1990, this share was about 1 percent,
less than half its level in early 1979, but above
its 0.6 percent share in 1973. Thus, the share
had fallen below its level preceding only one of
the previous two oil price shocks.
The import share argument has other short
comings. First, it suggests that oil-exporting
countries, including Canada in 1974 or the
United Kingdom in 1979, should gain when oil
prices rise, because net exports and aggregate
demand should rise. In each instance, however,
output did not rise nor was there other evi
dence of a cyclical expansion following the
previous oil price shocks. The argument also
suggests that countries that import a relatively
small share of their oil, like the United States,
will be less affected than countries that import
relatively more o f their oil, like Germany or
Japan. The earlier experience with oil price
shocks indicates that, especially in 1973-74, both
the temporary rise in inflation and the perma
nent loss in output were larger in Japan than in
9See C ouncil of Econom ic Advisers (1991), Kahn and
Ham pton (1990), Anderson, Bryan and Pike (1990), Brinner
(1990), “ How Big An Oil S hock” (1990), "S h o cke d A g a in "
(1990), May (1990), Y anchar (1990) and Fieleke (1990) for
analyses that em phasize one or both of these argum ents.
Fieleke, Kahn and Ham pton, May and Y anchar emphasize,
to varying degrees, that the expected effects also are
sm aller because of a sm aller expected rise in the price of
oil.

Figure 2
Petroleum Imports as a Percent of GNP

the United States, but that these effects were
smallest in Germany.10
There are three other major difficulties with
the import share argument. First, it is difficult
to reconcile the relatively large economic effects
of oil price hikes with the relatively small size
o f the petroleum import share. Second, an ag
gregate demand reduction in the face of an oil
price hike implies only a cyclical decline in out
put, not a permanent one. The failure of real
GNP per worker and real wages to return to
their previous growth trends in virtually all na
tions after the two previous OPEC price hikes is
not consistent with the pattern expected for a
purely cyclical loss. Third, the trade-based ag
10See Rasche and Tatom (1981), Tatom (1987) and Tatom
(1988a) for reviews of this international evidence. In 1973,
the share of petroleum im ports in GNP equaled 1.7 per
cent in G erm any and 1.6 percent in Japan, m uch more
than the 0.6 percent in the United States. S im ilarly, in
1978, this share was 2.7 percent in Japan, 2.5 percent in
G erm any and 1.9 percent in the United States.
11See Tatom (1988b) for a discussion of the theory and evi
dence supporting such contrary effects. C onsistent with

gregate demand story predicts a decline in net
exports and the currency value of a large oil
importer after an oil price shock. At least for
the United States, however, exports rose rela
tive to imports so that both net exports and the
exchange rate rose after each earlier oil price
shock. Indeed, the only periods of positive net
exports since 1970 occurred in 1974-75 and
1979-82, following the earlier oil price hikes.11

D oes Increased Energy Efficiency
Reduce the Adverse Effects o f an
Oil Price Hike?
The second argument for less adverse effects
of the 1990 price hike is based on a decline in
th is rise in net dem and for U.S. goods, th e trade-weighted
value of the dollar rose in IV/1973 and 1/1974, and was
higher over the rest of 1974 than it had been in the two
quarters preceding the oil price rise. In the second quarter
of 1979, the value of the d o lla r also rose slightly. Over the
next four quarters, the value of the dollar was only 0.6 per
cent lower than in the two quarters before the oil price
hike.

NOVEMBER/DECEMBER 1991

Figure 3
E nergy Use per Unit of Real GNP
(Thousands of BTUs per dollar of real GNP, 1982 prices)
25

0
1970

energy use per unit of output. According to this
argument, energy is less important to a firm ’s
production than in the past, so a rise in oil
prices is expected to have a smaller effect on
prices and production today than in the past.
Figure 3 shows total U.S. energy use per unit
of output (measured in BTUs per unit of real
GNP) from 1970 to 1988, the latest year availa
ble on this basis.12 Energy use per unit o f out
put has fallen sharply since 1973: BTUs used
per unit of real GNP were about 31 percent
lower in 1988 than in 1973 and about 22 per
cent lower than in 1979. This rise in output per
unit of energy is not surprising given the rise in
the relative price of energy since 1973, but it is
not relevant in assessing the importance of
energy as a resource or in assessing whether
12T he energy expenditures and quantity data used for
figures 2 and 3 are from the Energy Inform ation A dm inis
tration, State Energy Price a nd Expenditure Report, 1988
(Septem ber 1990).

FEDERAL RESERVE BANK OF ST. LOUIS

1988

the effects of an energy price boost have
declined in magnitude.
While energy use per unit of output is lower
than earlier, the responsiveness of prices or out
put to a change in a resource’s price are pro
portional to the share of the resource’s cost in
total cost, not to the share of its quantity in out
put. Consider the familiar case of labor produc
tivity. Labor employment per unit of output in
the business sector declined by nearly one-third
from 1955 to 1973, as output per worker rose
from $21,084 to $31,142 (1982 prices). Thus, the
economy became less dependent on labor over
these 18 years—in exactly the same sense and
to nearly the same extent as some have sug
gested about energy resources over the past 18
years. Nevertheless, the share o f labor in total

Figure 4
Energy Expenditures as a Percent of GNP
Percent

cost was about the same: 65.3 percent in 1973
and 64.8 percent in 1955. For a given share of
labor in cost, a percentage point rise in the wage
rate will raise the cost of an additional unit of
output and price in proportion to this share.13
Analysts who emphasized the increased pro
ductivity of energy are unlikely to espouse the
equivalent view that a 10 percent rise in wages
has a smaller effect on unit costs or product
prices today than in 1973 or 1955. As discussed
previously, the response of capacity and price
to changes in a resource’s price depends on the
share of the resource in cost, not on its produc
tivity or output per unit.
Figure 4 shows how the share of energy ex
penditures as a percent of GNP has changed
from 1970 to 1988. Following each energy price
hike, expenditures rose sharply relative to GNP;
as energy prices fell beginning in 1982 (on an

13A typical discussion of the relationship between wages,
productivity and prices can be found in Fischer, Dornbusch and Schm alensee (1988), pp. 566-67. Shin (1991)

annual basis), the share fell. By 1988, the share
nearly had returned to its 1970-73 level. These
data suggest that the share of energy in the
cost of the economy’s output has not fallen be
low its level before the earlier oil price changes,
especially the 1973-74 rise. Thus, these data do
not support the view that a doubling of the
price of oil should be expected to have smaller
effects in 1990 than it had earlier, especially in
1973-74, because the share of energy in total
cost has not declined.

RECENT OIL AND ENERGY PRICE
DEVELOPMENTS
The economic effects of an energy price shock
depend on the size of the price change as much
as they depend on the responsiveness of mea
sures o f economic performance to a given

discusses o ther shortcom ings of using the energy-output
ratio for analytical or policy purposes,

NOVEMBER/DECEMBER 1991

change in energy prices. Table 1 shows the
monthly average price o f oil purchased by re
finers since June 1990. Following the Iraqi inva
sion of Kuwait and the subsequent U.N. embargo
of crude oil exports from both countries, the
price of oil doubled within three months. The
1990 oil price rise was comparable in magnitude
to the two earlier OPEC price hikes in 1973-74
and 1979-80. In each of these previous cases, oil
prices nearly doubled. In the second instance,
oil prices rose again sharply in the first quarter
of 1981.
A rise in the price of oil is likely to raise the
cost of production of competing energy sources
and raise the demand for competing forms of
energy, as consumers substitute other fuels for
oil. For both reasons, the prices of competing
sources of energy change along with the price
of oil. Thus, an oil price shock can be consi
dered more generally an energy price shock.
Figure 5 shows the relative price of crude
petroleum—measured by the producer price
index for crude petroleum deflated by the busi
ness sector implicit price deflator—and the rela
tive price o f energy—the producer price o f fuel,
power and related products relative to the same
deflator.14 The relative price affects economic
performance because producers of goods and
services assess the cost o f energy relative to the
goods and services produced using it. From the
third quarter o f 1973 to the third quarter of
1974, the relative price o f crude oil nearly dou
bled. Measured in 1990 prices, the composite
refiner acquisition cost of crude oil rose from
$10.67 per barrel in 1973 to $21.28 in 1974, or
99.4 percent.15 In the second OPEC oil price
shock, from early 1979 to the second quarter of
1980, this relative price of oil nearly doubled
14A logarithm ic scale is used because differences in
logarithm s show percentage changes; an equal-sized in
crease or decrease in figure 5 reflects equal percentage
changes. For exam ple, a rise from 50 to 100, or 100 to
200 represents a doubling of the relative price and the
respective distance in each case is the sam e in figure 5.
15The rise in the relative price of oil shown in the figure ac
tu a lly begins in early 1973, but this earlier increase largely
reflects partial and tem porary relaxation of U.S. price con
trols on dom estic crude oil prices. The m uch larger OPEC
price increases followed the Yom Kippur W ar in O ctober
1973. The 1947 oil price shock is not discussed here. The
producer price for crude petroleum m easures prices paid
to dom estic producers, w hich were controlled from 1971 to
early 1981. O ver m ost of th is period, the com posite refiner
acquisition cost was higher, but was representative of oil
p rices paid by dom estic purchasers.
,6The total output o f Kuwait and Iraq fell about 4 m illion bar
rels per day in A ugust 1990 from its M ay-July 1990 aver-

FEDERAL RESERVE BANK OF ST. LOUIS

Table 1
The Composite Refiners Acquisition
Cost of Crude Oil (dollars per barrel)
Date

Price

Date

Price

June 1990

$14.98

Ja n u ary 1991

$22.90

July

16.15

February

19.02

A ugust

23.57

March

17.89

Septem ber

30.01

April

18.43

O ctober

33.18

May

18.60

Novem ber

30.61

June

17.98

Decem ber

26.21

again, rising from $22.35 per barrel to $41.82
per barrel. A further surge in early 1981 put
the price up to $50.75 per barrel.
From the second quarter o f 1990 to the
fourth quarter of 1990, the price of oil rose
from $16.10 per barrel to $30.00 per barrel, an
86.3 percent rise that is almost as large as the
near-doubling in the previous two oil shocks.16
If the effects of oil price hikes are proportional
to their size, then the effects of the 1990 in
crease should be about the same as in the two
previous instances. The relative price of energy
rose about 50 percent during the previous two
energy price shocks. From the second quarter
of 1990 to the fourth quarter o f 1990, however,
the rela tive price of e n e rg y rose 29.6 percent,
about 60 percent o f the earlier magnitudes.17
Thus, on this basis, the recent energy price
shock is somewhat smaller.
age; by Novem ber and D ecem ber 1990, it was down 4.6
m illion from th e e arlier average. The latter reduction
equaled 7.6 percent of w orld production and 19 percent of
OPEC output. In com parison, the reductions in the total of
Iran and Iraq production from 1978 to its lowest annual
average level in 1981 was som ew hat larger, 5.4 million
barrels per day, but this was 18.2 percent of O PE C ’s 1978
production.
17Em pirical estim ates suggest th a t the relative price of ener
gy adjusts contem poraneously and w ith a one-quarter lag
to changes in the relative price o f oil; thus, one reason for
the relatively sm aller rise in the energy price is the fact
that the relative price of crude oil fell 20.6 p ercent in the
second quarter of 1990. W hen expressed in logarithm s,
each 1 percentage-point rise in the relative price o f crude
oil is estim ated to result in about a one-half percent rise in
the relative price of energy. See Tatom (1987b).

Figure 5
Relative Price of Energy and Crude Petroleum
Index (1975 to 1978 average equals 100)
250

50
1950

1990

There were two other important differences
between the recent rise and the previous two.
First, the recent rise occurred much more
quickly—in two quarters instead of four or six.
Second, the recent increase did not persist.
Nevertheless, producers did not know at the
time whether, or by how much, oil prices might
decline in the future. This article assumes that
producers treat price changes as permanent, in
the sense that the expected price they use for
economic decisions is the current price. It also
focuses only on the effects of the recent price
increase. To the extent that producers did not
anticipate having to face the price increase, the
effects of the price shock should be smaller.

as a temporary acceleration in inflation and a
temporary reduction in output growth. More
over, temporary rigidities in nominal prices and
lags in the adjustments that firms and con
sumers make in response to large price changes
were likely to give rise to temporary movements
in employment, including a recessionary decline
in employment, although past experience sug
gests that such a change occurs with a delay of
about one year. These effects should be expected
to have been somewhat smaller than those fol
lowing previous oil shocks, because the rise in
the relative price of energy in the 1990 episode
was only about 60 percent as large as the previ
ous increases.

THE EXPERIENCE IN PREVIOUS
OIL PRICE SHOCKS

Following the sharp rise in the relative price
of energy in 1973-74 and 1979-80, the loss in ca
pacity and adjustment to a higher price level, as
discussed earlier in reference to figure 1, were
reflected in a temporary acceleration in the in
flation rate. In each case, output growth slowed,
reflecting both the permanent decline in natural
output and a transitory loss in output. Produc

The previous discussion of energy price ef
fects indicates that the 1990 oil price hike should
be associated with a lower level of natural out
put and productivity and a rise in the price
level. These changes were likely to be revealed

NOVEMBER/DECEMBER 1991

tivity (and real wages) fell.18 Generally, the per
manent loss in output and productivity and the
rise in prices were experienced first, with the
temporary surge in inflation (as measured by
the GNP deflator) delayed about two quarters.19
Employment declined much later and for only a
few quarters. Cyclical unemployment associated
with an oil price rise peaked about six quarters
later, before quickly dissipating.
Table 2 shows these developments for the
three most recent large energy price hikes. For
periods surrounding each oil price hike, the ta
ble provides real GNP growth, productivity (bus
iness sector output per hour) growth, the rate
o f increase in the GNP deflator, civilian employ
ment growth, the average unemployment rate
for the civilian labor force and money stock
(M l) growth. Each measure is provided for the
year before and the first four consecutive twoquarter periods following the shock. Two-quarter periods are used to simplify the data presen
tation, although the timing of energy price
effects facilitates the usefulness o f this proce
dure. OPEC1 refers to the first oil price shock
which began in IV/1973. OPEC2 begins in 11/1979
and IRAQ begins in III/1990.
As table 2 indicates, real GNP growth slowed
following the two previous oil price hikes, but
did not become negative on a two-quarter basis
until after the first two quarters (OPEC1) or
after a year (OPEC2). The slowing in output
growth reflects both the decline in natural out
put and, principally later, a temporary cyclical
loss in output. Table 2 also shows that the ex
pected productivity decline (negative growth) oc
curred more quickly than the decline in real
GNP in the previous two cases; it began in the
first two quarters of the energy price shock in
18These developm ents were observed in nearly all countries.
The notable exception was that incom e policies im peded
the reductions in real wages (and, therefore, in labor
productivity) in some countries, especially in 1973-74, so
that the effective supply of natural em ploym ent fell, further
reducing natural output. See Rasche and Tatom (1977a),
(1977b) and (1981), Tatom (1988a) and (1987). Ham ilton
(1983) also provides em pirical evidence supporting the
perm anent effect on U.S. real GNP. Helliw ell, Sturm , Jarrett and Salou (1986) provide international evidence on the
e ffect on natural output.
19See, for exam ple, Tatom (1981) and (1988a). The lag for
the PCE d eflator and CPI is shorter (one quarter) and the
m agnitude is larger for these consum er price series, be
cause the share o f energy cost in expenditures is larger
for consum er expenditures than for GNP as a whole.
Thus, the effect of a given rise in oil prices is larger for
consum er price inflation m easures. The effects on
producer prices o ccu r even fa ste r and are even larger.

FEDERAL RESERVE BANK OF ST. LOUIS

each case. Both productivity and output growth
show a sharp cyclical acceleration in the last
two-quarter period.
The most recent energy price shock, like the
earlier two, was accompanied by an immediate
decline in productivity and a slowing in output
growth.20 Output growth became negative earlier
than in the previous two cases. Since the recent
energy price hike occurred over only two quar
ters, the period of decline in productivity and
output growth should be correspondingly shorter
than in the previous two instances. The slight
rise in productivity growth in the second twoquarter period is consistent with this expectation.
In the previous two instances, the decline in
productivity and natural output was reflected,
with about a two-quarter lag, in a sharp and
temporary acceleration in the rate o f price in
crease as measured by the GNP deflator. Thus,
in the second two-quarter period in OPEC1, in
flation accelerated sharply and only temporarily,
reflecting the one-time adjustment in the price
level. The same acceleration occurs in OPEC2,
but with a one-quarter lag; the data for the
two-quarter period ending one quarter later are
shown in parentheses. As table 2 shows, how
ever, in the first two-quarter period, the rate of
increase in the GNP deflator rose (OPEC1) or
was unchanged (OPEC2); in the latest instance,
it declined.21
In the previous two cases, the delayed acceler
ation in the rate of price increase persisted for
about four quarters (five quarters for OPEC2),
about as long as the period of sharp increases
in energy prices. There is also an acceleration
in the recent second two-quarter period (1/1991
and 11/1991). Since the latest price hike occurred
over half as many quarters as in the previous
“ Productivity growth had declined m ore rapidly in the year
before the recent oil price shock than it did in the initial
tw o-quarter period, so pro d u ctivity grow th did not actually
slow in the second half of 1990.
21The initial decline in the rate of price increase in the first
tw o-quarter period is not out of line. In each of the previ
ous initial tw o-quarter periods, th is rate was m uch lower in
at least one of the two quarters. In particular, in the first
quarter of 1974, the rate of increase of the d eflator fell to
a 5.6 percent rate; in 1979, it fell from 9.5 percent in the
first quarter to a 9.2 percent rate in the second quarter
and to 8.5 percent in the th ird quarter of 1979.

Table 2
Economic Performance Surrounding Three Energy Price Shocks
Previous Year
Real GNP growth rate
OPEC1
OPEC2
IRAQ
Productivity growth rate
OPEC1
OPEC2
IRAQ

4 .4%
5.3
1.0

1.5
0.6
-0 .6

First TwoQ uarter Period

Second TwoQ uarter Period

0.7%
1.6
- 0 .1

- 2.0%
1.6
-1 .7

-1 .3
-2 .6
-0 .2

- 2 .1
0.4
0.2

Third TwoQ uarter Period

Fourth TwoQ uarter Period

- 5.6%
-4 .5

5.5%
6.6

0.9
0.4

6.8
3.7

Rate of price increase
OPEC1
O PEC 21
IRAQ

7.1
8.9
4.0

Civilian em ploym ent
growth rate
OPEC1
OPEC2
IRAQ

3.5
3.9
0.9

3.3
1.6
- 1 .1

0.9
1.7
-1 .0

-3 .9
-1 .9

1.8
2.7

Average unem ploym ent
rate
OPEC1
OPEC2
IRAQ

5.0
5.9
5.3

5.0
5.8
5.7

5.4
6.1
6.7

7.4
7.5

8.7
7.4

M1 growth rate
OPEC1
OPEC2
IRAQ

7.0
7.4
4.0

6.0
10.3
3.6

3.7
5.1 (1.5)1
6.8

3 .7 '
5.8

6.9
8.0

7.7
8.9 (8.4)
3.2

11.5
8.5 (9.1)
4.9

10.9
9.4 (10.7)

7.8
11.4 (8.7)

Period
OPEC1
OPEC2
IRAQ

111/1972 to 111/1973
1/1978 to 1/1979
11/1989 to 11/1990

II and 111/1974
IV/1979; 1/1980
I and 11/1991

IV/1973; 1/1974
II and 111/1979
III and IV/1990

IV/1974; 1/1975
II and 111/1980

II and 111/1975
IV/1980; 1/1981

1Data in parentheses are for the two quarters ending one quarter later.

two, the acceleration would be expected to be
reversed in the third two-quarter period, even
without any effect from the decline in energy
prices in 1/1991 and 11/1991. It remains to be
seen whether inflation will decline as abruptly
as it did following earlier oil price shocks.22
The delayed cyclical response to an energy
price hike is seen most clearly by looking at the
22The rate of increase in the CPI rose from a 3.8 percent
rate in the second quarter of 1990 to about a 7 percent
rate in the third and fourth quarters of 1990. Sim ilarly, the
rate of increase of the producer price index rose from a
0.3 percent rate in the second quarter of 1990 to a 6.6
percent rate and a 10.8 percent rate in the third quarter

growth o f civilian employment. In the two pre
vious instances, employment growth slowed, but
did not become negative until a year after the
energy price shock began. Moreover, this de
cline occurred in only one two-quarter period
(the third one), when employment fell at a rela
tively rapid pace. Thus, the typical recessionary
characteristic o f falling employment did not ocand fourth quarters of 1990, respectively. The rate of in
crease of the latter two price m easures fell sharply in the
first half of 1991, reflecting the quicker response of these
m easures to a rise in energy prices as well as to th e ir sub
sequent decline.

NOVEMBER/DECEMBER 1991

cur until a year after the onset of the two pre
vious energy price hikes.
The unemployment rate also did not rise im
mediately after the two previous adverse energy
price shocks. In 1973-74, it fell slightly in the
fourth quarter of 1973, rose only 0.8 percen
tage points by the third quarter of 1974, then
peaked 3.3 percentage points higher three quar
ters later.23 The unemployment rate peaked six
quarters after the initial surge in energy prices,
in the last period shown in the table. In the
second quarter of 1979, the initial quarter of
OPEC2, the unemployment rate also fell slightly,
then rose gradually for the next three quarters
so that it was only 0.4 percentage points higher
in 1/1980 than it was before the energy price
shock. The unemployment rate then rose 1.4
percentage points to a peak in III/1980, six quar
ters after the initial energy price surge.24
In the most recent case, the unemployment
rate rose immediately, climbing from 5.5 per
cent in July 1990 to 7 percent in June 1991.
Such a rise is substantially different from the
pattern in the initial stages of the previous en
ergy price shocks.
Its behavior might better be understood in the
context of the slowing in U.S. economic activity
that began in 1988. For example, civilian em
ployment actually began declining sharply in
March 1990, five months before the energy
price hike; civilian employment fell at a 0.9 per
cent rate from March to July 1990 and declined
further at a 0.5 percent rate from July to Oc
tober 1990, when energy prices peaked; from
October 1990 to August 1991, such employment
fell at a 1.3 percent rate. Thus, the path of eco
nomic activity downward into recession had
begun well before energy prices rose.25

23One explanation for the initial decline in the unem ploy
m ent rate when oil prices rise relies on the capacity loss
and “ stic k y ” prices. The initial fall in productivity and ini
tial absence of a price-related decline in aggregate de
mand when oil prices rise require that producers raise
em ploym ent to offset some of th e output loss and avoid
larger-than-desired depletion of inventory. See Tatom
(1981) and O tt and Tatom (1986) for discussions of this ef
fect. Rasche and Tatom (1977a) show that em ploym ent
rose during th e first three quarters of the 1973-74 oil
shock and did not fall until five quarters later.
24ln th is second instance, a further rise in energy prices late
in 1980 and early in 1981 contributed to a fu rth e r rise in
the unem ploym ent rate about a year later, from IV/1981 to
11/1982.
250 th e r analysts have em phasized this point. See W eidenbaum (1990) and Erceg and Leovic (1990), for exam ple.
26After late 1982, m onetary policym akers placed relatively
m ore em phasis on M2 instead of M1. Another m easure,

FEDERAL RESERVE BANK OF ST. LOUIS

A Comparison o f Changes in M o n e
tary P olicy Actions
Each of the two previous oil shocks were fol
lowed by changes in monetary policy actions.
There is no clear initial pattern, as money
growth slowed in the initial two quarters in
1973-74 but accelerated in 1979. As shown at
the bottom of table 2, however, in each case,
M l growth then slowed sharply during the se
cond two-quarter period, at the same time that
the rate of price increase temporarily accelerat
ed.26 Then, in each instance, M l growth acceler
ated sharply in the fourth two-quarter period
following the sharp rise in the unemployment
rate.
The expectation that the economy would
quickly experience a recessionary rise in unem
ployment because of the 1990 oil price rise was
widespread. There were equally widespread
warnings against repeating the "typical” policy
response o f easing monetary policy to combat
this unemployment.27 While there is evidence of
rising unemployment and subsequent accelera
tions in M l growth following previous oil price
surges, these changes came more than a year
after the initial oil price rise. These changes also
occurred after the substantial slowing of M l
growth and the transitory inflation rate hike
that are more closely associated with the oil
price increases.
In the most recent case, money (M l) growth
slowed from a 4.8 percent rate from IV/1989 to
11/1990 to a 3.7 percent rate in III/1990 and to a
3.5 percent rate in IV/1990. Money growth
quickly reversed course, however, accelerating
to a 6.8 percent rate, as the unemployment rate
continued to rise in the first half of 1991. This

the adjusted m onetary base, is often a convenient sum
m ary m easure of m onetary policy actions. H igher energy
prices sig n ifica n tly raise relative currency dem and one
q uarter later, reducing m onetary aggregates relative to the
adjusted m onetary base; see Tatom (1990). Thus, m one
tary base growth is less useful as an indicator of m onetary
policy d u ring energy price shocks. Bullard (1991) d iscuss
es these and o ther indicators o f m onetary policy and the
potentially co n flictin g signals they offer.
27For exam ple, according to T rehan (1990), “ Researchers
have generally concluded that the Fed eased policy to
overcom e the reduction in o utput caused by the oil em bar
g o ” and " ... the Fed’s initial response to the second oil
shock also was sim ilar to its response to the first oil
sh o ck.” See also, C ouncil o f E conom ic A dvisers (1991),
w hich indicates that policy was excessively stim ulative p ri
or to the previous oil shocks so that it lacked credibility,
m aking e fforts to ease ineffective. The C ouncil of Econom
ic Advisers (p. 80) suggests such te m porary actions would
be appropriate and effective today.

acceleration in M l growth occurred earlier than
it had following the previous oil price hikes,
although it did follow both a previous slowing
in M l growth and a recessionary rise in the un
employment rate, just as had similar accelera
tions in M l following the two previous energy
price increases.28

growth that had been under way since late in
1988. Thus, the expected productivity decline
and temporary surge in inflation were accompa
nied by a continuing decline in employment and
cyclical output loss. While these developments
were uncharacteristic of the initial effects of
previous oil price hikes, monetary growth slowed
in the second half of 1990 anyway.

CONCLUSION

There were other distinguishing features as
sociated with the 1990 oil price hike. Foremost
among them was its brevity: it occurred over a
three-month period and was nearly reversed in
another five months. Thus, while the response
of output, productivity and prices appears con
sistent with the capacity-loss-induced effects as
sociated with previous oil price doublings, the
subsequent decline in oil prices from October
1990 to March 1991 can be expected to result
in offsetting price, output and employment
movements.

The rise in oil prices from August to October
1990 set in motion renewed concern and confu
sion over both the effects o f oil price hikes and
the appropriate monetary policy response. Three
views achieved widespread acceptance. First, the
economy was believed to be less sensitive to oil
price hikes than it had been earlier. Second, it
was widely believed that the principal and most
immediate effect would be a cyclical decline in
output and employment. Third, analysts believed
that the Fed would ease policy, as it had when
faced with this problem in the past.
These views are at odds with previous ex
perience. In 1990, the share of oil imports in
GNP and energy per unit of GNP had not fallen
to the level before the first oil price shock in
1973. Moreover, the relevant parameter, the
share of energy in cost, had not fallen below its
1973 level either. Thus, U.S. economic perfor
mance should not have become less sensitive to
oil price shocks than it was before. In addition,
negative employment growth and an accelera
tion in money growth had not characterized the
initial year of previous energy price shocks.
Earlier evidence suggests that the principal
cost of an energy price hike is the loss in capac
ity output and productivity. A counterpart of
this loss is a one-time surge in the general level
of prices, which follows the energy price hike
relatively closely. The adverse cyclical conse
quences of past shocks occurred later. The prin
cipal policy response following previous oil price
hikes was a slowing in money growth. Later,
when inflation declined and the unemployment
rate rose sharply, money growth accelerated.
The 1990 oil price rise occurred against the
backdrop of a slowing in money and output
28M2 shows the same pattern. It grew at a 2.5 percent rate
from 11/1990 to IV/1990, down from a 4 percent rate in
11/1990 or the 5.1 percent rise in the tw o-quarter period
ending in 11/1990. In the first half of 1991, M2 growth also
rose, but only to a 4.2 percent rate. Bullard (1991) indi
cates that Fed decisionm akers were keenly aware of the
policy dilem m a and chose to pursue a course o f neither

REFERENCES
Anderson, G erald H., M ichael F. Bryan, and C hristopher J.
Pike. “ Oil, the Econom y and M onetary Policy,” Federal
Reserve Bank of Cleveland Econom ic Com mentary
(Novem ber 1, 1990).
Berndt, Ernst. “ Energy Price Increases and the Productivity
Slowdown in United States M anufacturing,” The Decline in
Productivity Growth, Federal Reserve Bank of Boston Con
ference Series, no. 22 (1980), pp. 60-89.
Berndt, Ernst R., and David O. Wood. “ Energy Price Shocks
and Productivity Growth: A Survey,” in Robert C. Gordan,
et. al., eds., Energy: M arkets a nd Regulation, Essays in
Honor o f M.A. Adelman (MIT Press, 1987), pp. 305-67.
Brinner, Roger E. “ Finding Keys to Turn,” U.S. Forecast
Sum mary (DRI/M cG raw Hill, O ctober 1990).
Bullard, Jam es B. “ The FOM C in 1990: O nset of Reces
sion,” this Review (May/June 1991), pp. 31-53.
Corcoran, Patrick J. “ ‘P utty’ and ‘C lay—A Parable for
Potential GNP,” Prudential Economics, The Prudential
(February 15, 1990), pp. 6-9.
Council of Econom ic Advisers. “ Oil Price Shocks and Eco
nomic Policy,” chapter 3 in Econom ic Report o f the Presi
dent (1991), pp. 79-110.
Darby, M ichael R. “ The U.S. Productivity Slowdown: A Case
of Statistical Myopia,” Am erican Econom ic Review (June
1984), pp. 301-22.
Denison, Edward F. Trends in Am erican Econom ic Growth,
1929-1982 (The Brookings Institution, 1985).
________ . “ Explanations of Declining Productivity Growth,”
Survey o f Current Business (August 1979, Part II), pp. 1-24.
Erceg, John J., and Lydia K. Leovic. “ The O utlook After the
Oil Shock: Between Iraq and a Soft Place,” Federal
Reserve Bank of Cleveland Econom ic Com m entary (O c
tober 15, 1990).

easing nor tightening. He indicates that there was a con
cern for a ctual inflationary pressures late in 1990, but con
cern for the cyclical consequences of the oil price hike
was fram ed only in term s of the potential risk.

NOVEMBER/DECEMBER 1991

Feldstein, M artin. “ The Fed Must Not Accom m odate Iraq,”
Wall Street Journal, August 13, 1990.
Fieleke, Norm an S. “ Oil S hock III?” New England Econom ic
Review (Septem ber/O ctober 1990), pp. 3-10.
Fischer, Stanley, R udiger Dornbusch, and Richard
Schm alensee. Economics, 2nd ed. (M cGraw Hill Book
Company, 1988).
H am ilton, Jam es D. “ Oil and the M acroeconom y since World
War II,” Journal of Political Economy (April 1983), pp.
228-48.
Helliwell, John, Peter Sturm , Peter Jarrett, and Gerard Salou.
“ T he Supply Side in the O EC D ’s M acroeconom ic M odel,”
OECD Econom ic Studies (Spring 1986), pp. 75-131.
Hickm an, Bert, Hillard G. H untington, and Jam es L.
Sweeney. M acroeconom ic Im pacts o f Energy Shocks (North
H olland Press, 1987).
“ How Big An Oil Shock,” The Econom ist (August 11, 1990),
pp. 12-13.
Kahn, G eorge A., and Robert Ham pton, Jr. “ Possible M one
tary Policy Responses to th e Iraqi Oil Shock,” Federal
Reserve Bank of Kansas C ity Econom ic Review (Novem
ber/D ecem ber 1990), pp. 19-32.
Karnosky, Denis S. “ The Link Between M oney and
P rices— 1971-76,” this Review (June 1976), pp. 17-23.
May, Todd Jr. “ Oil Prices W on’t Bring a Recession,” For
tune Forecast/Special Report, Fortune (Septem ber 10,
1990), pp. 51-52.
Olson, Mancur. “ The P roductivity Slowdown, The Oil Shocks
and The Real Cycle,” Journal o f Econom ic Perspectives
(Fall 1988), pp. 43-69.
Ott, M ack, and John A. Tatom. “Are E nergy Prices Cyclica \T 'E n e rg y Econom ics (O ctober 1986), pp. 227-36.
Perry, G eorge L. “ The Anom alous Recession,” The Brook
ings Review (Spring 1991), p. 51.
Rasche, Robert H., and John A. Tatom. “ Energy Price
Shocks, A ggregate Supply and M onetary Policy: The The
ory and the International Evidence,” in Karl B runner and
Allan H. Meltzer, eds., Supply Shocks, Incentives a n d Na
tional Wealth, C arnegie-R ochester C onference Series on
Public Policy (N orth Holland, 1981), pp. 9-93.

FEDERAL RESERVE BANK OF ST. LOUIS

________ . “ The Effects of th e New Energy Price R egim e on
Econom ic Capacity, Production and Prices,” this Review
(May 1977a), pp. 2-12.
________ . “ Energy Resources and Potential GNP,” this
Review (June 1977b), pp.10-24.
Reinhart, Vincent. “ Reading the Effects of an Energy Shock
in Financial Markets,” Journal o f Econom ics and Business
(1991), pp. 115-32.
Shin, David. “ International C om parisons of Energy-G ross Na
tional Product Ratios,” A m erican Petroleum Institute Dis
cussion Paper 68 (June 1991).
“ Shocked Again,” The Econom ist (August 11, 1990), p. 23.
Tatom, John A. “ The Effects of Financial Innovations on
C heckable Deposits, M1 and M2,” th is Review (July/August
1990), pp. 37-57.
________ . “Are T he M acroeconom ic Effects of Oil Price
C hanges S ym m etric?” in Karl B runner and Allan H. M elt
zer, eds., Stabilization Policies a nd Labor Markets,
C arnegie-R ochester C onference Series in Public Policy
(North Holland, 1988a), pp. 325-68.
________ . “ M acroeconom ic Effects of the 1986 Oil Price De
cline,” Contem porary Policy Issues (July 1988b), pp. 69-82.
________ . “ T he M acroeconom ic Effects of the Recent Fall in
Oil Prices,” th is Review (June/July 1987), pp. 34-45.
________ . “ Energy Prices and Short-Run Econom ic Perfor
mance,” this Review (January 1981), pp. 3-17.
Trehan, Bharat. “ Lessons from the Oil Shocks of the
1970s,” Federal Reserve Bank of San Francisco Weekly Letter
(Novem ber 9, 1990).
W eidenbaum , Murray. “ Recessionary Signs Were Evident
Even Before Oil C risis,” Christian Science Monitor, October
16, 1990.
Yanchar, Joyce. “A Look at Oil Market Fundam entals,” Spe
cial Study, DRI/M cG raw-Hill U.S. Review (August 1990),
pp. 25-31.

Michelle R. Garfinkel and
Daniel L. Thornton
M ichelle R. Garfinkel, an assistant professor at the University
o f California at Irvine, was a senior econom ist a t the Federal
Reserve Bank of St. Louis while this p a p er was written. Daniel
L. Thornton is an assistant vice president at the Federal
Reserve Bank of St. Louis. R ichard I. Jako provided research
assistance.

Alternative Measures of the
Monetary Base: What Are the
Differences and Are They Im
portant?
HE MONETARY BASE, adjusted for changes
in reserve requirements, is a measure intended
to summarize the net effect of all Federal Re
serve actions on the money stock.1 As such, it
serves as an indicator of the effects o f monetary
policy actions on the money stock.
Because of the Federal Reserve Bank o f St.
Louis' long-standing interest in monetary policy,
it began publishing a series on the adjusted
monetary base in August 1968.2 Nearly 11 years
later, the Federal Reserve Board began publish
ing an alternative series. While the objective of

1The idea of adjusting th e m onetary base to reflect changes
in reserve requirem ents was proposed initially by Karl
B runner (1961) in an effort to fo rm u la te an “ e m pirically
significant th e ory” of the m oney supply process. B runner
called this adjustm ent “ liberated reserves.” He was the
first to com pile data on the adjusted m onetary base and
em pirically investigate the relationship between his m eas
ure and the m oney supply. T his research agenda was pur
sued by both him and Allan M eltzer in a num ber of articles
dealing with the m oney supply process and m onetary policy.
2See Andersen and Jordan (1968).
3One of the m ost dram atic changes in the structure of
reserve requirem ents occurred with the im plem entation of

the Board’s series is the same, it has always
differed from the series constructed by the St.
Louis Fed in a number of respects. These differ
ences have changed over time with changes in
the structure of reserve requirements and, thus,
changes in the methods of calculating the re
spective series.3
The two series have been used separately
and, on occasion, jointly to address a number of
issues of importance in monetary theory and
policy. Occasionally, they have yielded signifi
cantly different results.4 Moreover, at times

the M onetary Control Act of 1980 (MCA). G arfinkel and
Thornton (1989) discuss the changes in the structure of
reserve requirem ents brought about by the phase-in o f the
MCA. G arfinkel and T hornton (1991) discuss the effects of
the MCA on the m oney supply process and the usefulness
of the m onetary base as an indicator of th e effect of m on
etary policy on the m oney stock. See Burger and Rasche
(1977) and G ilbert (1987) for tw o significant changes in the
calculation of the St. Louis adjusted m onetary base.
“ See Friedm an (1988), M cCallum (1988a,b), Haslag and
Hein (1990) and M uelendyke (1990) for some exam ples of
differential perform ance.

NOVEMBER/DECEMBER 1991

Figure 1
Levels of the STL-AMB and BOG-AMB,
Seasonally Adjusted
Billions of dollars

Billions of dollars

Data plotted from January 1959 thru April 1991.

they have presented conflicting pictures of mon
etary policy.
Because of changes in their calculation and
the recent conflicting results, now seems to be
an appropriate time to re-examine these series
to see how and why they differ, both historically
and currendy. W e can also investigate whether
they are likely to continue to behave differently
in the years ahead and whether their differential
performance is attributable to fundamental differ
ences or merely to arbitrary differences in their
construction. Finally, we will provide preliminary
evidence on whether the existing difference is
potentially important for money stock control.

THE DIFFERENCE BETWEEN THE
TW O ADJUSTED MONETARY BASE
MEASURES
The adjusted monetary base series constructed
by the St. Louis Fed (hereafter labeled STL-

FEDERAL RESERVE BANK OF ST. LOUIS

AMB) and that constructed by the Board of
Governors of the Federal Reserve System (here
after labeled BOG-AMB) were designed for the
same purpose. Each is intended to isolate the ef
fects of monetary policy actions—that is, changes
in the supply of reserves and changes in reserve
requirements—in a single measure. Neverthe
less, the two series are quite different.

H o w D o They Differ?
The difference in their behavior can be seen
in figure 1, which shows both adjusted mone
tary base measures, seasonally adjusted, from
January 1959 to April 1991. Although the two
measures behave similarly throughout the sam
ple period, STL-AMB is always larger than BOGAMB and the spread between them increases
over time. As will be discussed later, much of
this spread can be attributed to differences in
the reserve requirement measure used to calcu
late the two series. Currently, this difference is

Figure 2
Difference Between the Growth Rates of STL-AMB and
BOG-AMB
Percent
0.10

Percent

0.10

0.05

0.00

- 0 .0 5

-0 .0 5

0.10

1960

0.10

1990

Data plotted from February 1959 thru April 1991.

due to the weight each assigns to the level of
transaction deposits. As a consequence, the re
cent widening in the spread between the two
AMB series is driven by the growth of deposits.5
Although the difference in the level of the
two series gets larger over time, figure 2 shows
that the difference in the monthly compounded
annual growth rates of the two adjusted mone
tary base measures does not exhibit a signifi
cant trend. Indeed, although the monthly dif
ference in the growth rates ranges from -8.4
percent to 8.6 percent, the average difference
5Thus, the series should be strongly cointegrated. Haslag
and Hein (1990), using data from 1959 through 1989, find
that the two adjusted m onetary base m easures are coin
tegrated. T heir results, based on a procedure suggested
by Engle and G ranger (1987), indicate that th e null hypoth
esis of no cointegration can be rejected at the 5 percent
level. This hypothesis, however, cannot be rejected at the
1 percent level. Nevertheless, alternative tests for coin
tegration, using a procedure developed by Johansen
(1988), add fu rth e r support to the notion th a t the two ser

in their growth, 0.18 percent, is not significantly
different from zero at the 5 percent significance
level (the t-statistic is 1.35). Thus, over a suffi
ciently long period, the growth rates of the two
series are nearly identical.
Over shorter periods, however, the differ
ences in the growth rates of these aggregates
persist, as illustrated by a six-month moving
average of the difference between the growth
rates of the two series—presented in figure 3.
The six-month moving average, which ranges
from -3.6 percent to 3.4 percent, shows that,
ies are cointegrated [This procedure and others are dis
cussed in Dickey, Jansen and T hornton (1991).] The chisquare statistic for the null hypothesis that there is one
cointegrating vector is 74.5, com pared w ith a critical value
at the 1 percent significance level o f 22, w hich provides
evidence that the two m onetary base series are cointegrat
ed, as expected.

NOVEMBER/DECEMBER 1991

Figure 3
A Six-Month Moving Average of the Difference Between
the Growth Rates of STL-AMB and BOG-AMB
Percent

Percent

1960

1990

Data plotted from July 1959 thru April 1991.

for periods as long as six months, the two ad
justed monetary base measures can give con
siderably different pictures of monetary policy.
In fact, as an examination of figure 3 shows,
the growth rates of the two series can differ
significantly even for fairly long periods o f time.
For example, the six-month moving average of
the difference in the growth rates was strictly
positive before April 1969 and nearly always
negative after August 1984. The difference in
the monthly growth rates averaged 0.60 percent
during the former period and -0.32 percent
during the latter, and both differences are
statistically significant (the t-statistic is 7.96 in
the former period, 7.04 in the latter).
6O nly the STL refers to th is adjustm ent as RAM — short for
reserve adjustm ent m agnitude. For expository conve
nience, th is article also w ill refer to th e BO G ’s adjustm ent
for reserve requirem ents as RAM.

FEDERAL RESERVE BANK OF ST. LOUIS

Why D o They Differ?
Much of the difference in the two series is at
tributable to the method of adjusting for reserve
requirement changes. Each adjustment creates
an index o f reserves that would have been held
during some “base period.” The magnitude of
this adjustment, hereafter referred to as RAM,
reflects the reserves that are absorbed (released)
if the reserve requirements w ere higher (lower)
than those in effect during the base period.6
When the STL series was first created, a
bank’s reserve requirements depended on its lo
cation, the type of deposits it held (transaction
vs. non-transaction) and whether it was a mem-

ber of the Federal Reserve System.7 The adjust
ment for reserve requirement changes was made
by multiplying the deposits in a given reserve
category by the difference between that cate
gory’s reserve requirement in the base period
and its corresponding reserve requirement in
the current period. The initial base period used
was from August 1935 to July 1936.8
In contrast, the BOG has always used the cur
rent period as the base period in calculating its
reserve adjustment. Thus, each time reserve
requirements change, the BOG revises the his
torical data to reflect the “current” system of
reserve requirements. For example, when re
serve requirements are reduced, the BOG calcu
lates the amount of reserves that would have
been required had the lower reserve require
ment been in effect previously. The actual level
of required reserves in past periods are multi
plied by the ratio of the new average reserve
requirement to the old, thereby creating a new,
counterfactual “adjusted reserve” series. In this
example, the new historical series for adjusted
reserves would be lower than the previous
historical series. The lower level of the "new ”
historical series relative to the current period’s
levels reflects a hypothetical release of reserves
in the past brought about by the decrease in re
quirements in the current period.
In essence, both the STL and BOG methods cre
ate counterfactual series for adjusted reserves. For
STL, the counterfactual series is the reserves
that would have been held if the historical re
serve requirements w ere in effect today. Hence,
if reserve requirements have been reduced
(raised), actual reserves would be lower (higher)
than adjusted reserves. For the BOG, the coun
terfactual series is the reserves that would have

7Prior to MCA, non-m em ber banks did not have to m aintain
reserves w ith the Federal Reserve System . At the tim e the
Federal Reserve A ct was passed, reserve requirem ents
were diffe re n t for “ central reserve c ity ,” “ reserve c ity ”
and “ c o u n try” banks. This d istinction was not based ex
p licitly on the size of the institution, but on the location of
the bank at the tim e the Federal Reserve A ct was passed.
O ver tim e, th is classification system becam e less m eaning
ful, with m any large banks classified as country banks.
8See Burger and Rasche (1977), G ilbert (1980) and Tatom
(1980).

been held in the past if the current reserve re
quirements w ere in effect. Actual reserves held
in the past would be higher (lower) than ad
justed reserves if reserve requirements were
reduced (raised) in the current period.
With the STL approach, it is not necessary to
revise the historical monetary base series each
time reserve requirements are changed. As not
ed above, the BOG series, in contrast, requires
that all historical data be revised, which means
there is a delay in the availability of data. Con
sequently, the STL approach has a comparative
advantage for empirical research over the BOG
approach because it produces a series that is
readily available at the time it is most needed—
when there is a change in reserve requirements.9
Beyond this advantage, the base-period distinc
tion between these approaches appears to be
unimportant.

A Recent Change in the Construc
tion o f the STL Series
In 1987 the STL adjusted monetary base ser
ies was revised in response to fundamental
changes in the structure of reserve require
ments associated with the Monetary Control Act
(MCA) of 1980. Currently, the series is obtained
by splicing two adjusted monetary base series
with RAMs based on different systems of
reserve requirements. Before November 1980,
RAM is based on average ratio of reserves to
deposits, for transaction and non-transaction
deposits, during the period from January 1976
to August 1980. After November 1980, RAM is
based on the structure of marginal reserve re
quirements on transaction deposits in effect un
der the MCA. These series are spliced together
at the first reserve maintenance period (Novem-

d ifficu lt or im possible to continue using the o riginal base
period. A t these tim es, the historical data were revised.
The first of these changes occurred in 1977 when Burger
and Rasche (1977) altered the series by both changing the
m ethod used to calculate RAM and adjusting the series to
account for th e sig n ifica n t ch ange in the structure of
reserve requirem ents in Novem ber 1972. The next oc
curred in D ecem ber 1980 w hen the base period was
changed to the period from January 1976 to A ugust 1980.
The m ost recent, discussed next, was in 1987.

9Although reserves absorbed or released by changes in
reserve requirem ents typ ica lly are offset through open
m arket operations so that there is no m arked change in
the adjusted m onetary base, RAM does change sig n ifica n t
ly. It should be noted, however, th a t the base period for
the St. Louis series has changed when fundam ental
changes in the structure o f reserve requirem ents m ade it

NOVEMBER/DECEMBER 1991

ber 19, 1980) under the new reserve require
ments imposed by the MCA.10
At the splice date, the second part o f the ser
ies is calculated under the assumption that the
marginal reserve requirements on reservable
categories of time and savings deposits are
zero.11 Reserve requirements on all non-transaction deposits w ere eliminated in December
1990. Consequently, after November 1980, the
STL series utilizes the present structure of re
serve requirements for its base period. Because
the base period for the BOG’s series is always
the current one, the "base-period” distinction
between the two series has been virtually elimi
nated for the period since November 1980.12
This distinction remains relevant for the preNovember 1980 data, however.
Another distinction remains, however. STL
calculates its RAM using the marginal reserve
requirement on transaction deposits, 12 percent,
while the BOG uses the average reserve require
ment ratio at the time of the last change in
reserve requirements. Currently, this ratio is
about 8 percent for transaction deposits.13 As a
result, the level of STL-AMB is larger than that
of BOG-AMB.

DETERMINING THE SOURCE OF
THE DIFFERENCES BETWEEN THE
TW O SERIES
Although the difference in adjustment methods
for reserve requirement changes accounts for
much of the difference exhibited by the two
monetary base series, it is not the entire source
of their differential behavior. There are two
other potentially significant sources: the treat

10The procedure scales th e “ o ld e r” part of the series down
to the level of the “ new er” part of the series to reach the
level consistent w ith the post-M CA base period. The growth
rates of the data before the splice date are unaffected by
the change in the base-period for the level data. See G il
bert (1987), p. 26, for a detailed discussion o f the
procedure.
" T h is was done because the data necessary for m aking a
RAM adjustm ent for non-transaction deposits were not
available. See G ilbert (1987).
12The only base-period d istinction that rem ains is due to the
fact that the G arn-St. G erm ain Depository Institutions Act
of 1982 requires that a certain level of transaction deposits
at each depository institution be subject to a reserve re
quirem ent of zero and that this rate be adjusted upward
with the rise in total reservable liabilities.
13Because the average ratio of reserves held against tran s
action deposits to transaction deposits for th e period from

FEDERAL RESERVE BANK OF ST. LOUIS

ment of vault cash and the seasonal adjustment
methods used. Each of these three sources and
their empirical importance is discussed below.
(A more detailed discussion of the current con
struction o f the two series and their differences
appears in the appendix.)

The Treatment o f Vault Cash
Currently, the two adjusted monetary base
series start with slightly different “raw ” data.
Both unadjusted monetary base measures,
roughly speaking, are the sum o f reserve
balances held by depository institutions at Fed
eral Reserve Banks and currency in circu
lation—in other words, currency held by the
public, including depository institutions. The
differences in these raw data lies primarily in
the treatment of vault cash—that is, cash held
by depository institutions in their vaults. The
BOG, in contrast to STL, adjusts its series for
the timing of reserve requirements as satisfied
by depository institutions with vault cash.
To get a better understanding o f this differ
ence, it is helpful to review briefly the Federal
Reserve’s system of reserve requirements. Un
der the current system, depository institutions
are required to hold reserves in the form of
vault cash and/or reserve balances at the Feder
al Reserve equal to a fixed percentage of their
reservable deposit liabilities—specifically, trans
action deposits held by the public, government
and foreigners.14 A depository institution’s re
quired reserves are calculated on the basis of
the transaction deposits it holds during a twoweek period ending every other Monday. An in
stitution can satisfy its requirements with de
posit balances at the Federal Reserve during the
two-week reserve-maintenance period ending

January 1976 to A ugust 1980 was 0.12664, the use of the
m arginal reserve requirem ent, rather than the average ra
tio of reserves to deposits previously used, m inim izes the
difference between the " o ld e r ” and “ new er” series at the
splice date.
14There are low er reserve requirem ents on a tranche of
deposits for each depository institution. Also, depository in
stitu tio ns are required to m aintain reserves against th e ir
net checkable deposits with o ther institutions. Aggregated
over all institutions, however, the net deposits are zero.
Consequently, in the aggregate, no reserves are held
against checkable deposits w ith other depository in stitu
tions. Because reserve balances held against such
deposits do not net out to zero for individual institutions,
however, reserves held against net “ in te r-b a n k” checkable
deposit lia bilities affects the d istribution of required
reserves am ong these institutions.

two days after the period used in computing its
reserves, and with vault cash held during a
two-week period ending 30 days before the end
of the maintenance period. Vault cash used to
satisfy statutory reserve requirements is called
"applied vault cash.”
The BOG's adjustment for vault cash involves
a distinction between "bound" institutions, whose
statutory reserve requirements exceed their
holdings o f vault cash, and "non-bound” institu
tions, whose vault cash exceeds their statutory
reserve requirements. Another important dis
tinction is between weekly reporting institutions,
called EDDS, and quarterly reporting institu
tions, called QEDS. In the BOG’s adjustment for
vault cash, the difference between current vault
cash and lagged (applied) vault cash of bound
EDDS (see appendix) is excluded from the BOG's
raw monetary base series. Hence, the STL and
BOG unadjusted, not-seasonally-adjusted series
effectively differ by the change in vault cash of
bound EDDS.15
What is the empirical importance of this differ
ence? Because of limited data availability, an exact
measure o f the magnitude of the BOG's adjust
ment to vault cash cannot be obtained over the
entire sample. As a proxy, the difference be
tween the STL source base and the BOG’s notbreak-adjusted monetary base (with no seasonal
adjustments) is used.16 This measure, denoted
here by ATVC, is depicted in figure 4 for the
full sample period from February 1959 to April
1991. As the figure shows, the difference in the
treatment of vault cash fluctuates between
-$2.3 billion to $1.7 billion, but is positive for
most of the sample period. Indeed, ATVC aver
ages $.15 billion over the period. While this
average is small, both in absolute terms and
relative to the difference in the two base meas
ures, it is statistically significant from zero at
the 5 percent level (the t-statistic is 7.82).
As discussed in more detail below, the differ
ence in the treatment of vault cash has a pro
15They also d iffe r because of “ as-of” adjustm ents, w hich the
BOG m akes but STL does not, and because the BOG in
cludes “ required clearing ba la n ces” in its not-breakadjusted series.
The rationale for the BO G ’s adjustm ent to vault cash is
not entirely clear. A recent Board m em o states that the ad
justm ent is made on th e belief that current vault cash con
strains the lending activities of non-bound institutions,
w hile lagged vault cash is the relevant constraint for
bound institutions.
16As noted in the appendix, required clearing balances and
“ as-of” adjustm ents are included in the B oard’s not-break-

nounced seasonal pattern, which has become
more amplified over time. Thus, although the
difference in the treatment of vault cash con
tributes relatively little to the "low-frequency”
(quarterly or annual) variation in the difference
between the two series, it contributes somewhat
to the "high-frequency” (monthly) variation.

The R eserve Adjustment
Before November 1980, there are two basic
differences between the adjustments that STL
and the BOG use on the raw data for reserve
requirement changes. First, as noted previously,
STL uses a fixed, historical period, while the
BOG uses the current period as the base period.
Because the average ratio of required reserves to
deposits was substantially higher during this
period than it is today, the STL adjustment be
fore November 1980 is significantly larger than
the BOG’s. Second, the BOG makes an additional
adjustment for changes in reserve requirements
on applied vault cash (see appendix for details).
These two differences continue to be relevant
after November 1980. Because STL uses the
marginal reserve requirement o f 12 percent,
which is larger than the average ratio of re
serves to deposits used by the BOG to calculate
its RAM, the levels o f the series are quite differ
ent even after this date. As in the period before
November 1980, the BOG makes, as part of its
break-adjustment procedure, a separate adjust
ment to applied vault cash. In addition, since
February 1984, with the switch to contempora
neous reserve accounting, the BOG makes a
separate break adjustment to its adjustment for
lagged vault cash of bound EDDS.
The difference between the STL adjusted
monetary base and the BOG’s break-adjusted
monetary base can be used to measure the em
pirical magnitude of differences in the method
of adjusting for reserve requirement changes.
ATVC is added to this measure to isolate the efadjusted m onetary base series, but not in the source base.
(See table A1 of the appendix for details). Required clear
ing balances and these “ as-of” adjustm ents, however, are
not included in the B o a rd 's break-adjusted series and,
thus, play no role in explaining the d ifference between the
two adjusted m onetary base measures. To isolate the ef
fect of the d ifference in the treatm ent of vault cash on the
difference between the two series, required clearing
balances and the as-of adjustm ents (when these data are
available) are rem oved from the difference between the
two unadjusted base series.

NOVEMBER/DECEMBER 1991

Figure 4
Difference in the Treatment of Vault Cash ATVC
Billions of dollars

Billions of dollars

1960

Data plotted from January 1959 thru April 1991.

feet of the difference in RAM from that o f the
BOG’s different treatment of vault cash. The
resulting series, denoted here by ARAM, and the
difference between the two seasonally adjusted,
adjusted monetary base measures, denoted by
AAMBSA, are presented in figure 5. The figure
shows that most of the difference between the
levels of the two seasonally adjusted bases is, in
fact, explained by differences in the method
used to adjust for reserve requirement changes.

Seasonal Adjustment
To remove regular variations in the AMB ser
ies due to seasonal factors, both series are sea

17See Zeller (1972). Also, see G ilbert (1985) fo r a discussion
of the change in seasonal adjustm ent associated with the
sw itch to contem poraneous reserve accounting.

FEDERAL RESERVE BANK OF ST. LOUIS

sonally adjusted. For monthly and quarterly
data, STL adjusts its monetary base series by
simply applying the standard X -ll seasonal ad
justment program to its not-seasonally-adjusted
series. Weekly data are seasonally adjusted with
a separate program that inputs unadjusted weekly
data and seasonally adjusted monthly data.17
The BOG seasonally adjusts weekly data using
a model-based approach; it then obtains season
ally adjusted monthly and quarterly data from
the seasonally adjusted weekly data.18 In con
trast to STL, the components o f the base are
seasonally adjusted separately: break-adjusted
required reserves against transaction deposits,
the break-adjusted measure of surplus vault

18See Pierce, G rupe and C leveland (1984) and Farley and
O ’ Brien (1987) for a discussion of the seasonal adjustm ent
procedures used by the Board.

Figure 5
Difference Between STL-AMB and BOG-AMB and
the Difference Between Their Reserve Adjustments,
AAMBSA and ARAM
Billions of dollars

Billions of dollars

Data plotted from January 1959 thru April 1991.

cash used by the BOG, and currency held by
the nonbank public.19
The difference in the two series due to differ
ent seasonal adjustment procedures is presented
in figure 6. This difference, denoted by ASAM,
is measured by subtracting the BOG’s seasonal
adjustment (the difference between the seasonally
adjusted and the not-seasonally-adjusted, breakadjusted monetary base) from STL’s seasonal ad
justment (the difference between the seasonally
adjusted and the not-seasonally-adjusted, adjust
ed monetary base). Not surprisingly, the average
difference in the series due to differences in
seasonal adjustment is essentially zero over the
sample period.20 Nevertheless, ASAM ranges

19AII com ponents of the m onetary base, excluding excess
reserves, are adjusted as a whole before the switch to
contem poraneous reserve accounting. For the series after
the switch, the w eekly series is adjusted by com ponent us
ing a m odel-based procedure and then is m odified to be
m ade consistent with the m onthly series.

from -$1.6 billion to $2.6 billion, suggesting
that differences in the seasonal adjustment are
a source of high-frequency variation in the dif
ference between the two series.

The Relative Im portance o f These
Differences O ver Time
As indicated by figures 4 and 6, the contribu
tion of the differences in the treatment of vault
cash and the seasonal adjustment have become
more variable starting shortly after the MCA,
especially around 1984. Moreover, after 1984,
both differences have large seasonal compo
nents. ATVC becomes larger and more variable,
perhaps because the BOG's adjustment for lagged

20The average difference is $.025 billion, with a t-statistic of
1.14 for the test of the null hypothesis th a t the difference
is zero.

NOVEMBER/DECEMBER 1991

Figure 6
Difference in the Seasonal Adjustment ASAM
Billions of dollars
3

Billions of dollars
3

-1

-2
1960

1990

Data plotted from January 1959 thru April 1991.

vault cash at bound EDDS does not change with
the Fed's move from lagged to contemporaneous
reserve accounting. Separate break adjustments
are made to this series and to lagged vault cash
at QEDS starting in February 1984, however.
The difference due to seasonal adjustments
becomes larger with higher frequency variation
about this same time. This may be the result of
the Board’s changing its seasonal adjustment
method in February 1984.21
The seasonal variations in these two series
tend to offset each other so that the difference
between STL-AMB and BOG-AMB does not have
21As noted above, the BOG seasonally adjusts its breakadjusted m onetary base as a whole for data before the
sw itch to contem poraneous reserve a ccounting in February
1984. Thereafter, it has used a m odel-based approach to

FEDERAL RESERVE BANK OF ST. LOUIS

a large seasonal component. Indeed, ATVC and
ASAM are highly negatively correlated after
1984—the simple correlation between changes
in the two series after January 1984 is - .84.
As shown in table 1, which reports the vari
ances of AAMBSA, ARAM, ATVC, ASAM and
(ATVC + ASAM) for various subperiods, the varia
bility in AAMBSA has also increased over the
entire sample period. The subperiods corre
spond to various reserve requirement regimes.
The full sample is broken at the time of the im
plementation of the MCA and the time of its ef
fective completion, which coincides with the
switch to contemporaneous reserve accounting.
seasonalize the com ponents of the base separately for
w eekly data. In addition, as discussed by G ilbert (1985),
th e seasonal factors used by the St. Louis Fed also
changed around that tim e.

Table 1
The Variances of Changes in the Difference between STL-AMB
and BOG-AMB and Changes in its Sources_________________
AAMBSA

ARAM

1959.02-1991.04

.093

1959.02-1980.11
1980.12-1991.04
1980.12-1984.01
1984.02-1991.04

Period

ATV C + ASAM

ATVC

ASAM

.034

.245

.290

.104

.033
.216

.023
.058

.016
.725

.019
.858

.025
.269

.120
.258

.072
.051

.069
1.011

.119
1.181

.094
.346

Table 2
Simple Correlations between Changes in the Difference between
STL-AMB and BOG-AMB and Changes in its Sources________
Period

ARAM

ATVC

ASAM

ATV C + ASAM

1959.02-1991.04

.206

.175

.334

.826

1959.02-1980.11
1980.12-1991.04

.563
.022

.233
.177

.488
.333

.614
.887

1980.12-1984.01
1984.02-1991.04

.528
-.1 5 6

.227
.180

.421
.334

.669
.925

As the table shows, the variance of changes in
the differences of the two seasonally adjusted
AMB series has increased throughout the sam
ple period, especially since February 1984, when
the variances of both ATVC and ASAM sharply
increase. Because these series are negatively
correlated, however, this increased variability is
not reflected in a similar rise in the variance of
these combined series (ATVC + ASAM). Neverthe
less, the simple correlations between changes in
AAMBSA and both changes in ARAM and changes
in (ATVC + ASAM) presented in table 2 show that
more of the month-to-month changes in AAMBSA
is attributable to changes in ATVC + ASAM since
January 1984.

ALTERNATIVE MEASURES OF THE
MONETARY RASE: ARE THE
DIFFERENCES IMPORTANT?

22G arfinkel and Thornton (1991) have shown that the relationship between th e m oney supply and the adjusted
m onetary base has weakened since the MCA. More im por-

tant, they argue that the usual linear relationship between
the m oney su p p ly and the m onetary base, as a m odel of
the m oney supply process, fa ils to perform well since then.

Since the adjusted monetary base is intended to
be a summary measure of the policy actions of
the Federal Reserve, an important question arises:
are the differences in the STL and BOG measures
of the adjusted monetary base important?22 Over
a sufficiently long period of time, the answer to
this question is an emphatic, “No!” As noted earli
er, over sufficiently long periods of time, the
average difference in the growth rates of the two
series is negligible. Nevertheless, over shorter

NOVEMBER/DECEMBER 1991

Table 3
Estimate of Changes in M1 on Changes in Alternative Measures
of the Adjusted Monetary Base Monthly Results____________
St. Louis
Period

Constant

AAMB

1959.02-1980.10

.080
(0.89)

1980.11-1984.02

Board
R2

D.W .

Constant

AAMB

2.210*
(13.86)

.424

1.69

.169
(1.75)

.730
(0.96)

2.025*
(3.37)

.210

2.11

1984.03-1991.04

.344
(0.53)

2.135*
(6.11)

.299

1984.03-1990.11

- 1 .1 5 6
(1.56)

3.244*
(7.32)

.396

D.W .

2.237*
(11.81)

.348

1.53

.444
(0.51)

2.594*
(3.23)

.195

2.15

1.12

-.0 3 9
(0.05)

2.480*
(5.51)

.257

1.03

1,27

- 2 .2 3 9 *
(2.64)

4.139*
(7.58)

.414

.81

* Indicates statistical significance at the 5 percent level.

periods, the two measures could lead to different
interpretations of monetary policy.
The adjusted monetary base has been used fre
quently in theoretical and empirical models of
money stock control. Hence, one way to assess
whether the difference in the two AMB measures
is important is to see if either measure explains
more of the movements in the money stock, M l.23
Some preliminary evidence on the relative per
formance of these alternative measures in con
trolling the money stock can be obtained by
regressing changes in M l on changes in the alter
native base measures. Estimates of these equa
tions using monthly data are reported in table
3.24 The results are reported for three subperiods
from February 1959 to April 1991 based on impor
tant changes in the construction of the two ser
ies. The results indicate that, in all cases, there
there is a statistically significant relationship be23M2 is not included in the analysis because, since Decem
ber 1990, there is no d irect relationship between th e nonM1 com ponents of M2 and policy actions. M2 can only be
controlled directly through its M1 com ponent. Equations
sim ilar to those reported here, using M2, produce results
broadly sim ilar to those here, except w here noted below.
24These equations are sim ple and are not intended to be the
specification of the m oney su p p ly process over the tim e
period. M oreover, as G arfinkel and T hornton (1991) have
shown, such a sim ple specification of the m oney supply
function is inappropriate since February 1984. The strong

FEDERAL RESERVE BANK OF ST. LOUIS

tween changes in M l and changes in each of the
base measures.25 The relationship between M l
and either adjusted monetary base appears to
have deteriorated since the effective implementa
tion of the MCA in February 1984. This result ap
pears to be due, however, to the sharp rise in
depository institutions’ holdings of excess reserves
following the December 1990 elimination of
reserve requirements on non-transaction deposits
and the sensitivity of ordinary-least-squares
regression analysis to outliers. When the last five
months of data are deleted, the adjusted R-squares
are similar to those obtained over the first
period—indeed, the adjusted R-square for the
BOG’s measure rises by nearly 20 percent.26
The relationship between M l and the adjusted
monetary base is somewhat tighter when the STL
measure is used for all three periods; this is not
the case when the last five months are deleted
serial correlation of the residual since then is evidence of
th is m isspecification using either base m easure. For these
reasons, the results here are intended to be illustrative.
25The equations were also estim ated using the growth rates
of M1 and th e two AM B m easures. In all instances, the ad
justed R-squares were sm aller when grow th rates were
used. Q ualitatively, the results are the sam e as those in
th e te xt when q u arterly and annual data are used.
26As expected, after February 1984, there is no sta tistically
significant relationship between M2 and e ith e r base m eas
ure, at the m onthly or q uarterly frequency.

Table 4
Estimates of Changes in M1 on Changes in Alternative Measures
of the Adjusted Monetary Base Quarterly and Annual Results
St. Louis
Period

Constant

Board

AAMB

D.W ,

Constant

AAMB

D.W .

QUARTERLY RESULTS
.151
(0.75)

2.254*
(16.77)

.774

1.52

I/80-I/84

- 1 .2 5 0
(0.50)

3.086*
(4.18)

.507

2.32

11/84-1/91

.850
(0.23)

2.148*
(3.02)

.231

II/84-III/90

- 8 .0 9 6 *
(2.14)

4.406*
(5.34)

.524

II/59-IV/79

2.266*
(14.99)

.732

1.41

- 1 .8 5 8
(0.58)

3.678*
(3.45)

.406

2.54

.37

1.892
(0.47)

2.014*
(2.44)

.156

.41

.42

- 7.089
(1.55)

4.360*
(4.15)

.394

.46

- .8 2 9
(0.26)

2.85*
(8.75)

.716

.428*
(2.06)

ANNUA L RESULTS
1959-90

-2 .3 2 1
(0.77)

2.794*
(9.72)

.757

.82

.77

* Indicates statistical significance at the 5 percent level.

from the last period.27 Overall, the two meas
ures appear to differ little in their relationship
to monthly M l growth.
Because the difference in the growth rates of
the two AMB series declines at lower frequen
cies, the equations also were estimated using
quarterly data and annual data for the period
from 1959 to 1990. These results are summa
rized in table 4. The quarterly estimates are
similar to the monthly ones; the overall perfor
mance is better, however, using quarterly data
during the first period and somewhat worse
during the last. Again, much of the deteriora
tion in the last period is due to including the
quarters during and immediately after the elimi
nation of reserve requirements on non-transaction deposits.
For quarterly data, the St. Louis measure al
ways explains somewhat more of the variation
in M l growth. Estimates using annual data pro
vide a similar result, with the STL series ex
plaining about 4 percent more than the BOG
series of the annual variation in M l.

CONCLUDING REMARKS
While no formal tests of the difference in the
performance of the two base measures for money
stock control have been made here, the differ
ences might be statistically significant. Indeed,
this has been the case in other applications. For
example, Haslag and Hein (1990) have reported
statistically significant differences in the explan
atory power of the two monetary bases for
nominal GNP. More importantly, Friedman (1988)
and McCallum (1988a,b) report substantive dif
ferences in the performance of the two meas
ures for monetary policy analysis.
The problem is that the two measures differ
by their reserve adjustments, their treatment of
vault cash and their methods of seasonal adjust
ment. While differences in the reserve adjust
ment procedures account for the bulk of the
discrepancies, differences arising from the treat
ment of vault cash and seasonal adjustments
have become more important in explaining
short-run variations between the two series in
the 1980s. Because there is little objective rea-

27Also, the B O G ’s m easure produces a higher adjusted
R-square than does the STL m easure in the last period
w hen m onthly growth rates are used.

NOVEMBER/DECEMBER 1991

son to prefer one method of technical adjust
ment over the other, there is little basis for
choosing one measure over the other in empiri
cal studies, when the two measures produce
substantially different results.
In instances where the results are qualitative
ly the same but quantitatively different, such as
the results reported here or by Haslag and Hein,
the researcher must be content to choose the
measure that performs "best” for the problem
at hand. If the problem is money stock control,
the preliminary evidence presented here sug
gests that the St. Louis measure holds an edge.

G arfinkel, M ichelle R. and Daniel L. Thornton. “ The M ultiplier
Approach to The Money S upply Process: A Precautionary
Note,” this Review (July/August 1991), pp. 47-64.
________ .“ The Link Between M1 and the M onetary Base in
the 1980s,” th is Review (S eptem ber/O ctober 1989),
pp. 35-52.
G ilbert, R. Alton. “A Revision in the M onetary Base,” this
Review (August/Septem ber 1987), pp. 24-29.
________ . “ New Seasonal Factors for the Adjusted Monetary
Base,” this Review (Decem ber 1985), pp. 29-33.
________ . “ C alculating the Adjusted M onetary Base under
C ontem poraneous Reserve Requirem ents,” this Review
(February 1984), pp. 27-32.
________ . “ Two M easures of Reserves: W hy Are They Dif
ferent?” this Review (June/July 1983), pp. 16-25.
________ . “ Revision of the St. Louis Federal Reserve’s
Adjusted M onetary Base,” this Review (D ecem ber 1980),
pp. 3-10.

REFERENCES
Andersen, Leonall C. and Jerry L. Jordan. “ The M onetary
Base-Explanation and Analytical Use,” th is Review (August
1968), pp. 7-11.
Brunner, Karl. “A Schem a for the S upply T heory of Money,”
International Econom ic Review (January 1961), pp. 79-109.
Burger, Albert E. “Alternative Measures of the M onetary
Base,” this Review (June 1979), pp. 3-8.
Burger, Albert E., and Robert H. Rasche. “ Revision of the
Monetary Base,” this Review (July 1977), pp. 13-28.
Dickey, David A., Dennis W. Jansen and Daniel L. Thornton.
“A Prim er on C ointegration w ith an A pplication to Money
and Income,” this Review (M arch/April 1991), pp. 58-78.
Engle, R obert T., and C. W. J. Granger. “ Co-Integration and
Error C orrection: Representation, Estimation and Testing,”
Econom etrica (March 1987), pp. 251-76.
Farley, Dennis E., and Yueh-Yun C. O ’Brien. “ Seasonal Ad
justm ent of the M oney Stock in the United States,” Journal
o f O fficial Statistics (1987), pp. 223-33.
Friedm an, B enjam in M . “C onducting M onetary Policy by

C ontrolling C urrency Plus Noise: A Com m ent,” CarnegieRochester Conference Series on Public Policy (Autumn
1988), pp. 205-12.

Haslag, Joseph H., and Scott E. Hein. “ U.S. M onetary Policy
M easures: Are They Roughly Equivalent?” m imeo, Federal
Reserve Bank of D allas (1990).
Johansen, Soren. “ Statistical Analysis of C ointegration Vec
tors,” Journal o f Econom ic Dynam ics and Control
(June/Septem ber 1988), pp. 231-54.
M cCallum , Bennett T. “ R obustness Properties of a Rule for
M onetary Policy,” Carnegie-Rochester Conference Series on
Public Policy (Autum n 1988a), pp. 173-204.
________ . “ Reply to Com m ents by Benjam in Friedm an,”
Carnegie-Rochester Conference Series on Public Policy (Au
tum n 1988b), pp. 213-14.
M eulendyke, Ann-M arie. “ Possible Roles for the M onetary
Base,” in Intermediate Targets a nd Indicators for M onetary
Policy: A C ritical Survey (Federal Reserve Bank of New
York, July 1990) pp. 20-66.
Pierce, David A., M ichael R. G rupe, and W illiam P. Cleve
land. “ Seasonal Adjustm ent of the W eekly M onetary Ag
gregates: A M odel-Based Approach,” Journal o f Business
a n d Econom ic Statistics (July 1984), pp. 260-70.
Tatom, John A. “ Issues in M easuring an Adjusted M onetary
Base,” this Review (Decem ber 1980), pp. 11-29.
Zeller, Louis. “ W eekly Seasonal Adjustm ent Program for the
IBM S/360 Computer,” unpublished m anuscript, Board of
Governors of the Federal Reserve System (February 15,
1972).

Appendix
The Construction of the T w o Adjusted Base Meas
ures Since February 1984
This section discusses how each series, not
seasonally adjusted, is constructed in two steps:
the raw data series (called "source base” by STL

them. Similarly, table A2 shows the adjustments
made to each series and their differences.

The R aw Data

and "not-break-adjusted monetary base” by the
BOG) and the adjustment for reserve require
ment changes. Table A1 shows the construction
of the STL source base and the analogous BOG
series and summarizes the differences between

FEDERAL RESERVE BANK OF ST. LOUIS

The St. L o u is Series. The STL source base
measure is the sum of reserve balances at Fed
eral Reserve Banks and currency in circula
tion—i.e., currency held by the public. As shown
in panel A of table A l, reserve balances are de

Table A1
Calculating the St. Louis Source Base and the Board’s Not-Seasonally-Adjusted,
Not-Break-Adjusted Monetary Base (since February 1984)
A. STL:

$290,759

= RESERVE BALANCES
= total reserve balances
- required clearing balances
+ CU RR ENCY IN CIRCULATIO N
= currency held by th e nonbank public
+ current total vault cash

34.090
(-)

35.714
1.624

256.669
223.000
33.669

B. BOG:

$292,131

= TO TAL RESERVES
= total reserve balances
- required clearing balances
+ applied vault cash
+ CU RR E N C Y HELD BY THE NO N BA N K PUBLIC
+ SUR PLUS VAULT CASH (BOG)
= current total vault cash
- applied vault cash at non-bound banks
- applied vault cash at bound QEDS
- current vault cash at bound EDDS
+ REQUIRED CLEARING BALANCES
+ FLOAT-PRICING AS-OFs

62.931
(-)

35.714
1.624
28.841

223.542
3.550
(-)
(-)
(-)

33.619
3.331
.196
26.543

(-)

26.543
25.314

1.624
.484

C. S T L - B O G

- $ 1 .3 7 2 1

= - A D JU STM EN T FOR LAGGED VA U LT CASH AT BOUND EDDS
= current vault cash at bound EDDS
- applied vault cash (lagged) bound EDDS
-R E Q U IR E D CLEARING BALANCES
-F L O A T -P R IC IN G AS-OFs

- .8 7 9
(-)

(-)
(-)

- 1 .2 2 9

1.624
.484

NOTE: Exam ple data are for January 1990. C olum ns m ight not add due to rounding errors.
'T h is d ifference does not equal the sum of colum n 2, section C, because the B O G ’s figure for currency held by the nonbank
p ublic and vault cash used in ca lcu la tin g th e ir adjusted m onetary base differ from th e ir published series. The published
data are m onthly averages of daily figures, w hile the m onthly data used to ca lculate th e ir m onetary base are obtained by
prorating data averaged over reserve m aintenance periods.

fined as total reserve balances net of required
clearing balances of depository institutions.1
The B o a rd o f G o v ern o rs’ Series. As shown
in panel B o f table A l, the BOG’s not-breakadjusted monetary base is essentially the same
as the STL source base. Roughly speaking, the
not-break-adjusted monetary base is the sum of
total reserves and currency. Total reserves used
in the calculation is defined as the sum of total

'R e q uire d clearing balances are deposit balances that
depository institutions are required to m aintain at the Fed
eral Reserve to ensure that the dollar volum e of their
check clearings and other transfers of funds through the
Federal Reserve System are covered. These balances are
subtracted from total reserve balances since they do not
satisfy statutory reserve requirem ents and, hence, do not

reserve balances, net of required clearing bal
ances, and applied vault cash.2 Required clearing
balances plus currency held by the nonbank
public and surplus vault cash are added to the
measure of reserves. In constructing this mone
tary base series, the BOG defines "surplus vault
cash” as current vault cash net of lagged (applied)
vault cash held by both non-bound and bound
depository institutions that report quarterly

constrain a depository in stitu tio n ’s expansion of deposit
liabilities explicitly.
2As noted in the m ain text, applied vault cash refers to the
vault cash held by depository institutions during the twoweek period ending 30 days before the end of the current
m aintenance period.

NOVEMBER/DECEMBER 1991

Table A2
Calculating the St. Louis Adjusted Monetary Base and the Board’s Break-Adjusted
Monetary Base, Not Seasonally Adjusted (since February 1984)
$299,961

A. STL in period t - s :

290.759
9.202

= SO URCE BASE ( t - s )
+ RESERVE A D JU STM EN T M AG NITUDE ( t - s )
= rT(b) x transaction deposits (t - s)
- required reserves (t - s)
$277,636

B. BOG:
= N O T-BR EAK-ADJUSTED M O NETARY BASE ( t - s )
- FLOAT-PRICING AS-OFs ( t - s )
- REQUIRED CLEARING BALANCES ( t - s )
- REQUIRED RESERVES AG A IN S T EUR OD OLLARS ( t - s )
+ AD JU STM EN T FOR THE BREAK IN REQUIRED
RESERVES ( t - s )
= rT (t) x transaction deposits (t - s)
- rT (t - s) x transaction deposits (t - s)
- A D JU STM EN T FOR BREAK IN APPLIED VAULT CASH
+ A D JU STM EN T FOR THE BREAK IN LAGGED VA U LT CASH
AT BO UND EDDS AND BO UND QEDS
C. S T L -B O G :
= RAM (STL)
- A D JU STM EN T FOR
+ A D JU STM EN T FOR
- A D JU STM EN T FOR
EDDS AND BOUND
- A D JU STM EN T FOR

(-)
(-)
(-)
(+ )

292.131
.484
1.624
1.347
- 1 2 .4 4 0

(-)

- 1 .4 9 2

(+)
$22,325'

THE BREAK IN REQUIRED RESERVES
THE BREAK IN APPLIED VA U LT CASH
THE BREAK IN LAG GED VAULT CASH AT BOUND
QEDS
LAGG ED VA U LT CASH AT BO UND EDDS

-.0 8 8
21.467

(-)
(+ )

9.202
- 1 2 .4 4 0
-1 .4 9 2

(-)
(-)

-.0 8 8
- 1 .2 2 9

NOTES: Exam ple data are for January 1990. The series are constructed for periods i = t,t —1,t —2 ..... t - s ..... w here t is the
most recent period. rT(b) is the reserve requirem ent in the base period (12 percent). rT(i) is the average reserve
requirem ent on transaction deposits in period i. As in table A1, the colum ns m ight not add due to rounding errors.
’ This does not equal the sum of colum n 2, section C.

(QEDS) and net of current vault cash held by
bound institutions that report weekly (EDDS).3
As shown in panel C of table A l, the key
difference between the STL source base and the
BOG's unadjusted base measure is the treatment
of vault cash held by bound EDDS. In particu
lar, the two measures are essentially identical
except that the Board’s measure excludes the
surplus vault cash of bound EDDS—i.e., current
vault cash net of lagged applied vault cash at
bound EDDS. The two base series also differ in
that the BOG’s measure does not remove re
quired clearing balances and includes floatpricing "as-ofs.” As noted in the main text and

3The m easure of surplus vault cash reported on the
B oard's H.3 release is not the m easure used in th is com
putation. R ather than using current vault cash of all
depository institutions, th e surplus vault cash in the H.3
release includes lagged vault cash of only those institu

FEDERAL RESERVE BANK OF ST. LOUIS

below, however, required clearing balances and
float-pricing as-ofs are removed when the Board
calculates its break-adjusted series.

Adjustments f o r R eserve R equ ire
ment Changes
The St. Lou is Series. Panel A of table A2
shows the computation of the STL reserve ad
justment magnitude, RAM, which is simply ad
ded to the source base. RAM is the difference
between actual required reserves and the re
serves that would have been required, given the
actual level and composition of deposits held at
depository institutions, under the reserve re-

tions subject to reserve requirem ents. In addition, rather
than subtracting cu rre n t vault cash o f bound EDDS, the
surplus vault cash reported in the H.3 release subtracts
applied vault cash of these institutions.

quirements of a chosen base period. The reserve
requirement ratio on transaction deposits cur
rently used for the base period is 12 percent,
the marginal reserve requirement in effect since
the full implementation of the MCA.4
This adjusted base measure indicates what the
monetary base would have been given the cur
rent level of currency held by the nonbank
public and the current level and composition of
deposits under the base period's system of re
serve requirements. If the required reserve ratio
were to be reduced in any period, the adjust
ment would increase.5 In this case, the source
base would not change initially, but the adjusted
monetary base measure would increase as RAM
increased, reflecting a release o f reserves into
the system available to expand deposit liabilities.6
The B oard o f G o v e rn o rs’ Series. The BOG
adjusts the series for breaks in reserve require
ments historically. In particular, it treats the
most current period as its base period so that
the break-adjusted series and the unadjusted
series are identical. Reserves are adjusted with
4The actual average reserve ratio is low er than 12 percent
because, fo r the individual bank, the reserve ratio is only
3 percent for transaction deposits below the reserve tranch
and 12 percent fo r deposits in excess of that tranch. Even
before last ye a r’s elim ination o f reserve requirem ents on
personal tim e and saving deposits, which was com pleted
in tw o steps starting in the m iddle of D ecem ber 1990 and
ending after the first m aintenance period in January 1991,
th e STL-RAM assum ed that base period requirem ents on
non-transaction deposits w ere zero. It should also be not
ed that both RAM s assum e that the base period require
m ents on Eurodollar deposits is zero since February 1984.
5For example, the recent e lim ination of reserve require
m ents on non-transaction d eposits released about
$13.6 billion during the two (two-week) m aintenance peri
ods starting in the m iddle of December.
6Typically, however, the Fed offsets the release of reserves
generated by a reduction in reserve requirem ents, at least
partially, by rem oving reserves from the banking system.
Such a defensive m easure would prevent the m oney sup
ply from accelerating in response to the reserve require-

a ratio method. For any period in which the
system of required reserves differs from that in
the current period, required reserves held against
these deposits are multiplied by the ratio of cur
rent required reserves to what reserves would
have been required under the old system, given
the current composition of deposits. As shown
in panel B of table A2, this adjustment simplifies
to a measure similar to the STL-RAM, where
the base-period reserve requirements are re
placed by the most recent reserve requirements.
An adjustment for breaks in applied vault cash
is subtracted and an adjustment for breaks in
lagged vault cash at bound EDDS and QEDS is
added.7 In addition, reserves held against Eu
rodollar deposits are excluded from this series
after the switch to contemporaneous reserve ac
counting.8
As summarized in panel C of table A2, the
main difference between these series (not sea
sonally adjusted) revolves primarily around the
treatment o f vault cash and the method of re
serve adjustment.9
m ent change. Nevertheless, the change in reserve require
m ents would a ffect the adjusted m onetary base provided
that the resulting release of reserves were not perfectly
offset by such a defensive measure.
H 'he adjustm ent fo r the lag in applied vault cash at bound
EDDS is not break-adjusted before the sw itch to contem
poraneous reserve accounting. After the switch, the BOG
also started to m ake the break-adjustm ent to lagged vault
cash at QEDS.
8Because the STL-RAM assum es that the base period
reserve requirem ents on E urodollar deposits are zero, the
B oard’s exclusion of reserves held against these deposits
plays no role in explaining the difference between the two
AM B series.
9lt should also be noted that the B oard’s series is adjusted
for the annual increase in the reserve tranch as if the
change were being phased in gradually over the whole
year. In contrast, the St. Louis m easure adjusts for the
change when it occurs. See M eulendyke (1990), p. 59.

NOVEMBER/DECEMBER 1991

Piyu Yue
Piyu Yue, a research associate at the 1C2 Institute, University
o f Texas as Austin, was a visiting scholar a t the Federal
Reserve B ank o f St. Louis when this article was written. Lynn
Dietrich provided research assistance. The au tho r wishes to
thank Professor Leon Lasdon for the GRG2 Fortran code and
Professor Douglas Fisher for providing the data. Estim ations
that appear in this article were calculated at the University o f
Texas at Austin a n d are the responsibility o f the author.

A Microeconometric Approach
to Estimating Money Demand:
The Asymptotically Ideal
Model

X HE DEMAND FOR MONEY plays a critical
role in macroeconomics. In conventional money
demand analysis, the demand for real money
balances is typically expressed as a function of
such variables as real income, the expected rate
of inflation and the nominal interest rate.1 Em
pirical investigations using these variables have
not been particularly useful in predicting the
demand for money or in formulating and evalu
ating monetary policy.2
More recently, a number of researchers have
attempted to estimate money demand in a man
ner consistent with microeconomic foundations.

’ See Friedm an (1956) for one of the m ost com prehensive
discussions of th e m oney dem and function.
2These fu n ction s have been subject to several unexplaina
ble shifts and often im ply a larger liq u id ity effe ct than is
typ ica lly experienced. Perhaps the most dram atic exam ple
of this phenom enon occurred in the early 1980s w ith the
yet unexplained break in the incom e velocity of M1. For
this and other exam ples, see G oldfeld (1976), Friedm an
(1984), Lucas (1988) and Rasche (1990).

FEDERAL RESERVE BANK OF ST. LOUIS

Even in these cases, however, the empirical
results have been largely discouraging.3
This paper reviews the general micro-econometric approach to estimating the demand for
money, culminating with an advanced microeconometric model, called the Asymptotically
Ideal Model (AIM). AIM is applied to U.S. timeseries data and the results are compared briefly
with those from previous studies. AIM results
are consistent with microeconomic theory and
provide insight into the behavior of money de
mand in the 1970s and 1980s.

fr e q u e n tly , th e estim ated own price e la sticitie s of dem and
for m onetary assets are positive, im plying th a t th e ir de
mand curves slope upward. For exam ple, see Serletis
(1988), Fisher (1989) and Moore, Porter and Sm all (1990).

MICROECONOMIC MODELING
As a result of developments in macroeconomic
theory over the past two decades, "almost all
macroeconomists agree that basing macroeco
nomics on firm microeconomic principles should
be higher on the research agenda than it has
been in the past.”4 Problems arise, however,
when aggregate, macroeconomic data are used
to estimate microeconomic-based models of
money demand. Some of these problems are il
lustrated by a simple example that uses two ap
proaches to microeconomic modeling: the
demand function approach and the utility func
tion approach.5

The Dem and Function Approach
Consider an economy where the representa
tive consumer allocates income between a com
posite consumer good, A, and a monetary asset,
M, that yields monetary services. The consumer's
objective is to maximize the utility function
(subject to a budget constraint), given the price
of the composite commodity and the user cost
of the monetary asset. Let P, u and E denote
the price level (the price of A), the nominal user
cost of holding one real unit of M and total ex
penditures (or income), respectively.6 The con
sumer’s decision problem is expressed by

cision problem yields ordinary demand functions
for A and M. In this case, the demand functions
are:
(1) A = rE/P = r/(P/E) = G,(u/E, P/E, r), and
(2) M = (1 -r)E/u =(l-r)/(u/E) = G2(u/E, P/E, r).
The demands for A and M are functions, Gj and
G2, respectively, o f E, P, u and the unknown
parameter r. Because the budget constraint is
linear in P and u, the normalized price, P/E, and
user cost, u/E, can replace P, u and E. In gener
al, demand functions can be expressed by nor
malized prices (including the user cost) and the
unknown parameter. This parameter can be es
timated by simultaneously fitting equations (1)
and (2) using data on real quantities o f A and M
and the normalized price and user cost.
This approach is called the “demand function”
approach because estimation begins after de
mand functions are specified. For this approach
to yield meaningful estimates, however, the
specified system of demand functions must cor
respond to the neoclassical utility function from
which they were derived. Consequently, the
conditions for estimating the system of demand
functions are fairly restrictive. For instance, the
Rotterdam model (a well-known demand system
used in empirical studies) requires specific forms
for demand functions and specific constraints
on parameters during estimation.8

Max f(A, M) = ArM l r,
subject to PA + uM = E.7
For simplicity, the utility function, f, is CobbDouglas, where r, an unknown parameter,
characterizes the consumer’s taste or prefer
ence. The optimal solution to the consumer’s de
4M ankiw (1990), page 1658.
5Som e econom ists argue that aggregate data cannot be ap
plied to m icroeconom ic m odels w ithout considering the
problem s of aggregation. A ggregation problem s are not
discussed in this paper, although the aggregation error
m ight be one source of the unsatisfactory perform ance of
conventional m oney-dem and functions.
6The user cost of holding a unit of a real m onetary asset is
com puted by the form ula,
u = p*(t) [R (t)-i(t)]/[1 + R (t)], w here p *(t) is the “ tru e ” cost
of living index defined as the geom etric average of the
consum er price index and the consum ption goods deflator,
R(t) is the benchm ark interest rate or the m axim um rate in
the econom y at each period and i(t) is the interest rate on
the m onetary asset. The form ula is derived from a widely
applicable consum er decision m odel.

Even if these conditions are satisfied, however,
the Rotterdam model is still highly restrictive
because the assumed underlying utility function
(either Cobb-Douglas or CES) is a member of a
narrow class o f utility functions with constant
elasticities of substitution.9
s u m e r’s u tility function along with real consum ption. In the
o th er approach, m oney is viewed as in trinsically worthless;
consum ers hold it only to finance current and future con
sum ption. As a result, real m oney balances do not enter
the consum er’s u tility fu n ction per se. Instead, the liquidity
cost o f holding real m oney balances is taken into account
in the budget constraint. Feenstra (1986) shows that these
tw o approaches are equivalent.
8For an application of the Rotterdam m odel to the moneydem and system, see Fayyad (1986). For the theory of the
Rotterdam m odel, see Barnett (1981).
9lt is easy to e n counter d ifficu ltie s using the dem and fu n c
tion approach. T he failure to specify fu n ction s correctly or
im pose relevant restrictions can result in biased or ineffi
cient param eter estim ates.

7D istinct views about m oney have resulted in tw o ap
proaches to analyzing consum er dem and for m oney. In the
first approach, m oney is viewed as a com m odity which
provides a m onetary service flow to holders. Thus, real
balances of the m onetary assets directly e nter the con

NOVEMBER/DECEMBER 1991

The Utility Function Approach
The utility function approach to demand esti
mation also has been used in empirical studies.
To understand this approach, reconsider the
consumer's decision problem and the demand
functions shown in equations 1 and 2. In the
utility function approach, demand functions for
A and M are substituted into the utility func
tion, f(A, M), to obtain the indirect utility
function,
h(v1; v2, r) = f[A(v1; v2, r), M (v„ v2, r)],
where v1 = P/E, v2 = u/E. Because the indirect
utility function has properties that are the in
verse of those for the utility function, it is more
convenient to use the reciprocal o f the indirect
utility function,
F(v,, v2, r) = l/h(va, v2, r).10
By definition, demand functions can be ex
pressed in terms of their expenditure shares,
Sj = AP/E and s2 = Mu/E. That is,
A = s jv 1 and M = s2lv2.ri
In this way, demand functions can be ob
tained without solving first-order conditions.
Consequently, no matter how complicated the
utility function might be, the derivation o f share
equations and demand functions is straight
forward.
Of course, if the utility function is relatively
simple and well-behaved (for example, when the
Cobb-Douglas function is used), there is no need
to use the utility function approach. However, if
the utility function includes more than two goods
or is sufficiently complicated, the Lagrange mul
tiplier procedure cannot be used to derive de
mand functions.

THE SEMI-NONPARAMETRIC
METHOD FOR ESTIMATING THE
DEMAND SYSTEM
The critical step in applying the utility func
tion approach is the specification of the proper
,0The d u a lity theory states that if the reciprocal of the in
direct u tility function, F, is nondecreasing and quasi
concave w ith respect to norm alized prices, the respective
u tility function, f, m ust be nondecreasing and quasi
concave with respect to qu a ntity variables. In this sense,
th e u tility fu n ction is equivalent to its reciprocal indirect
u tility function.
"E x p e n d itu re s shares can be obtained by using the modi-

FEDERAL RESERVE BANK OF ST. LOUIS

reciprocal indirect utility function, F. To simpli
fy the terminology, the term “utility function”
will indicate “the reciprocal of the indirect utili
ty function” in the following discussion.

Flexible Functional Form Modeling
Cobb-Douglas and CES functions have been
used extensively in theoretical and applied work
because of their relative simplicity. Despite their
apparent successes, however, such use has been
criticized. For example, if there are more than
two goods, the CES utility function can only
generate demand systems when each pair of
goods has the same constant elasticity of substi
tution.12 Unless there is prior information to the
contrary, however, the elasticities of substitu
tion should be determined by the data rather
than restricted by the specification of the utility
function. This limitation has motivated research
ers to look for utility functions that are more
flexible and allow for data-determined elastici
ties of substitution.
Flexible functional form models have attracted
considerable attention in economics literature
since the early 1970s, when it was proposed
that the translog and generalized Leontief func
tions should replace neoclassical utility func
tions. It was recognized that the values of the
elasticities of substitution are determined by the
value of the utility function and the values of its
first- and second-order derivatives are evaluated
at its extreme point. Consequently, if the values
of the utility function and these derivatives can
be estimated, so too can the elasticities of sub
stitution. This idea forms the basis for the flexi
ble functional form approach.
A functional form is said to be flexible if its
level and the first- and second-order derivatives
at a point in its domain are allowed to reach
the respective values of the "true” utility func
tion at that point. The true utility function is as
sumed consistent with the properties of the
data, so that, in principle, elasticities of substitu
tion consistent with the data can be estimated.
fied R oy's identity from d u a lity theory. That is,
s, = (Vj dF/dv,)/V'VF(V,r), i = 1 ,2 ,
w here the vector V ' = (vn, v 2) and the gra d ie n t vector
V F(V,r) = (dF /dv1t dF/dv2)'. See Diewert (1974).
12See Uzawa (1962).

One flexible functional form is derived from a
Taylor series expansion where all terms greater
than second-order are eliminated, that is,
(3) F = a0 +

+ Z^aijXiXi.13

This approximation is flexible because it has
enough free coefficients, a0, ai( a,,, to allow for
any desired value of the first- and second-order
derivatives of function F.
Two frequently used flexible functional forms,
the translog and generalized Leontief functions,
are given by simple substitution into equation 3.
For the translog function,
F = ln(f(x)) and x, = ln(q),
where f denotes the utility function and q,
represents the quantity of good i. The general
ized Leontief function is attained by letting
F = (fix))* and x, = (q )‘\
The coefficients in these functional forms can
be estimated and, in turn, the demand system
and the elasticities of substitution can be
derived.

Caveats F or Flexible Functional
Form s
Theoretically, the second-order Taylor approx
imation can attain flexibility only at a single
point or in an infinitesimally small region.
Hence, estimates of the elasticities of substitu
tion are valid only for the range of observations
covered by the sample data. Therefore, the
second-order Taylor series approximation
should be viewed as "locally flexible."
Such models are also subject to another,
potentially more serious, problem. Experience
has demonstrated that regularity conditions are
frequently violated! Therefore, the restrictions
that microeconomic theory imposes on con
13T his equation is w ritten in general form , w here a0 denotes
all the constants (that is, the function evaluated at the
point of interest and the partial derivatives evaluated at the
same point). The use of this general form to estim ate
these equations is one o f the p rocedure’s lim itations be
cause the point about which th e expansion is made is esti
mated by the data, rather than being specified by the
researcher. Hence, there is no guarantee that this point
w ill necessarily correspond with the m axim um value of the
function itself.

sumer behavior are not embedded in these flex
ible functional forms. This point is illustrated
later in the empirical section of this paper.
In an attempt to solve these problems, micro
economists have developed a variety of flexible
functional forms that maintain their flexibility
and have larger regularity regions.14 A family of
such flexible functional form models has been
proposed (for example, Barnett's (1981) minflex
Laurent model).15 To gain global regularity,
however, additional constraints are imposed on
the parameters which result in a loss of local
flexibility. This tradeoff between flexibility and
regularity is characteristic of flexible functional
form modeling. None of these models is both
globally regular and globally flexible.16

Semi-nonparametric M ethod
Gallant (1981) created the "semi-nonparametric
method” to remove the local flexibility limita
tion. His method specifies a series of models
that approximate the underlying utility function
at every point in the function’s domain. Hence,
the models are globally flexible.
The "semi-nonparametric method” is built upon
a well-known result in mathematics: a Fourier
series expansion can converge to any continu
ous function.17 In contrast to the local conver
gence of the flexible functional forms, the
Fourier series can approximate a continuous
function in the entire domain. Gallant proposed
to use the Fourier series expansion to specify a
series of utility functions that can converge to
any neoclassical utility function. Because neoclas
sical functions are a subset of continuous func
tions, the property of the Fourier series expan
sion will guarantee asymptotic convergence to
an u n d erly in g neoclassical u tility function.

Fourier series modeling consists of a series of
expansions of models, with succeeding models
nested in the preceding one. When the sample
size increases, higher-order models can be speci15lnstead o f th e Taylor series expansion, B arnett used the
Laurent expansion to enlarge the regularity region and
m aintain enough param etric freedom to satisfy require
m ents for fle xib ility. See Barnett (1983).
16See Diewert and W ales (1987).
17T he function m ust be integrable or, more generally, it must
lie in a H ilbert space. See Telser and Graves (1972).

14The regularity region is the subset of the dom ain of the
utility function in which all regularity co n ditions are
satisfied.

NOVEMBER/DECEMBER 1991

fied by simply adding more terms of the compo
nent functions. For instance, the first-order
model is defined by the utility function,
F = a0 + I^ q , +

+ ZibiCoslQq,)

+ ZjdjSinfQq,).
The jth-order model is defined by the utility
function,
F = a0 + S.afl, + 1,1,3,.qq, + X,Xjbiicos(jQqi)
+ lilidijSinfjQq).

Asymptotic3lly, the model contains 3n infinite
number of terms 3nd unknown parameters.
Therefore, asymptotic inference based upon the
Fourier series expansion models is free from
functional-form specification error. This is its
principal advantage.
In empirical work, however, the number of
terms must be finite. Consequently, the proper
ties of lower-order Fourier models become deci
sive. The harmonic component functions, such
as sines and cosines which are frequently used
in engineering and physics, are not suitable in
economic applications because they do not satis
fy the usual regularity conditions, such as
monotonically increasing and strictly quasi
concave. This means that lower-order Fourier
series models can violate regularity conditions.18
Nevertheless, Gallant's approach permitted
micro-econometric models to achieve both global
regularity and global flexibility.

The A IM Dem and System
To solve the problems of Fourier series
models, another infinite function series, called
the Muntz-Szatz series, is adopted. A typical
form of the series is expressed as:
f = a0 + S.a1q|/2 + I,a,2q;A + 1,3? q* +...

+ 1,1,3,; q‘/;qj4 + I,I,a2q*q'f +...
+ S.Ijb,} qr qf + Ijljb.f q*q* +...
The Muntz-Szstz series expansion converges
to 3 continuous function, and any continuous
function can be approximated by the Muntz18M oreover, the Fourier series m odels can easily overfit the
noise of the data. Usually, the m easurem ent errors of eco
nom ic variables can be decom posed into a pure white
noise plus some high-frequency periodic functions. These
latter functions m ight be m istaken for useful inform ation if
th e ir frequencies are close to that of the sine and cosine
fu n ction s in the Fourier series m odels.

FEDERAL RESERVE BANK OF ST. LOUIS

Szatz series.19 Consequently, this series C 3 n be
used to approximate 3 neocl3ssic3l utility func
tion asymptotically.20
The Muntz-Szstz series is 3 linear combin3tion
of 3 set of specisl power functions. In contrast
to the Fourier series, the component functions
of the Muntz-Sz3tz series, q)2, q|4, ... , q; =qj*, ... ,
sre neoclassical functions. In other words, they
are monotonically incressing and quasi-conc3ve
with respect to variables q, and q,. The MuntzSzstz series is necessarily neoclassical, however,
only if sll of the coefficients, 3j; 3,, , b,- , ... , sre
non-neg3tive, becsuse only positive linear combinstions of the neoclsssicsl component functions
sre necesssrily neoclsssicsl. As a result, the coefficient-restricted Muntz-Szatz series can ap
proach a neoclassical function but may not
approach any continuous function. Imposing
these restrictions guarantees that the estimated
function will not violate regularity conditions.
The Muntz-Szatz series is used in place of the
Fourier series in Gallant’s semi-nonparametric
method. A series o f models can be defined by
increasing degrees of the Muntz-Szatz approxi
mations. Under the parameter constraint, these
models are globally regular; the respective utili
ty functions are neoclassical everywhere in their
domain. When the sample size increases, higherorder models can be specified with more free
parameters to best fit the data and derive the
elasticities o f substitution that the data suggest.
Hence, the Muntz-Szatz series gives rise to a
model that is asymptotically globally flexible.
Even a low-order approximation requires a fairly
large number of parameters to be estimated,
however. Hence, while the model is asymptoti
cally globally flexible, finite samples will limit
the researcher’s ability to fully utilize this
property.
The model has two additional features that
make it particularly attractive for applied work.
First, although there are a relatively large num
ber of free parameters to be estimated, it is im
possible to overfit the noise in the data. Because
movements due to measurement errors are ir
regular and cannot be expressed by the neoclas
sical component functions, the model simply
19O nce again, the function m ust be integrable or, more
generally, lie in a Hilbert space. See T elser and Graves
(1972).
20See Barnett and Jonas (1983).

ignores them. Also, because the component
functions are not periodic, the high-frequency,
periodic movements in the data are likewise
ignored.
Consequently, models based on the MuntzSzatz series expansion are globally regular and
are asymptotically globally flexible. This is why
they are called Asymptotically Ideal Models
(AIMs).21

ESTIMATION OF THE AIM MONEY
DEMAND SYSTEM
Four subaggregated goods are included in the
empirical work presented here: a consumer
good, A4, and three monetary assets, A 1; A2 and
A3. A4 is an aggregate good of consumer dura
bles, nondurables and services and its respective
aggregate price is denoted by p*. A1 consists of
currency, demand deposits of households and
other checkable deposits; A2 is composed of sav
ings deposits at commercial banks and thrifts,
super NOW accounts and money market deposit
accounts; and A3 is small time deposits at com
mercial banks and thrifts.22 For each subset, an
aggregate quantity is defined as a sum of per
capita real balances of the component monetary
assets.23 The opportunity cost of holding a unit
of a real monetary asset is measured by its user
cost, a quantity-share-weighted sum of the in
dividual user costs that compose it. The user
cost of A; is denoted by U;.
The representative consumer solves an op
timal allocation problem by selecting real con
sumption, A4, and real balances of the monetary
assets, A 1( A2 and A3, to maximize the utility
function f(A 1( A2, A3, A4), subject to the budget
constraint, given p*, ut, u2, u3 and the total ex
penditure, E. Following the utility function ap
proach and using the first-order AIM model, we
specify the reciprocal indirect utility function
for the four goods case as:
21See Barnett and Yue (1988) and Barnett, G eweke and Yue
(1991).
22This division of m onetary assets is proposed in Fisher
(1989), who has perform ed separability tests over a variety
of deposit categories included in M2. He found that this d i
vision (A ^ A2, A3, A 4) is w eakly separable in term s of the
General Axiom of Revealed Preference (GARP) test. The
weak separability condition offers theoretical assurance
that A ,, A 2, A 3 and A 4 are m eaningful aggregate goods by
the definition of econom ic aggregation theory. However,
the partition, [(A,, A 2, A 3), A4] did not pass the GARP test
for weak separability. This raises the question of the exis
tence o f the m onetary aggregate, M2 (M 2 sA t + A 2 + A 3). If

F(v,a) = ajV/2 + a2v2,/2 + a3v3‘/2 + a4v4'/2
+ a5v 1'/4v2,/! + a6va,/2v3,/2 + a7v 1'4v4'4
+ a8v2'!v3,/! + a9vz,/2v4'/2
+ aioV3'"v4'2 + a11v1,/2v2,/2v3,/2
+ a12v 1*v2,/iv4,/i + a13v 1,/2v3,/2v4,/2
+ a14v2'iv3'!v4,J + alsv a,/!v2'/!v3‘/!v4,/;,
where v 1; v2, v3 and v4 are the normalized prices,
and a1; a2, ..., and a15 are the parameters of the
indirect utility function.
The share equation for each good is derived
from equations 3 using the modified Roy’s iden
tity. These are
sa = S^S, s2 = S2/S, s3 = S3/S, and s4 = (1 — s,
- s2 - s3), where
51 = a1v 1l/I + a5v1'sv2,i + a6v,'/2v3'/2 + a7v1’iv4Vi
+ aiav 1,/iv2,-'2v3'/- + aa2v1,/!v2,/!v4,/‘
+ a13v 1'!v3''!v4l! + a15v 1'/!v2,/,v3’/,v4,/2,
52 = a2v2'/! + a5va,/2v2’'2 + a8v2'2v3'/2 + a9v2,/2v4'/2
+ aiiv,l/2v2,/2v3‘/' + a12v 1,/!v2,/2v4,/2
+ a14\2 v3 \4 + air,v, v2 v3 v.,' .
53 = a3v3’/2 + a6v 1'/!v3,/2 + a8v2'2v3'2 + a10v3,2v4"2
+ a11v 1,/2v2,/2v3,/2 + a13v 1'/2v3'/2v4l/2
+ a14v2,/2v3'2v4'2 + a15v 1'2v2'2v3'!v4'2 and
S = a ^ / 2 + a2v2’/! + a3v3’2 + a4v4,/2 + 2a5v ,’/2v2'/2
+ 2a6v 1'/2v3'/2 + 2a7v1'2v4,/! + 2a8v2l/2v3l/2
+ 2a9v2'4v4'/2 + 2alu\3 v4 + 3a11v1'/2v2'/!v3‘/2
+ 3a12v 1'2v2'2v4'2 + 3a13v 1'2v3'2v4l2
+ 3a,,\2 v3 v,

+ 4aj5v j1/2v21/2v31/2v4,/!.

Only the first three share equations are in
dependent and can be written generally as:
(4) Sj = S/S = g;(v,a) for i = 1, 2, 3.
When the additional parameter normalization a,
+ a2 + a3 + a4 = 1 is imposed, one parameter,
for example a4, can be eliminated by substitu
t e s is the case, the dem and system of consum ption and
the subaggregate M2 m onetary assets are the appropriate
way to study dem and for m oney in term s of the econom ic
aggregation theory.
23The reader is cautioned that these results are not directly
com parable with those using conventional m oney dem and
specifications because the latter em ploy conventional
m onetary aggregate data that d iffe r in several respects
from those used here. First, business dem and deposits are
excluded from the data used here, so that M1 is not equal
to A, and M2 is not equal to A, + A 2 + A 3. M oreover, un
like the conventional m onetary aggregates, each of the
sub-aggregates is seasonally adjusted separately.

NOVEMBER/DECEMBER 1991

tion. Hence, in the case of four goods, the firstorder AIM system contains 14 free parameters.24

global optima was reduced, however, by an ex
tensive search of the parameter space.26

The share equations are nonlinear with respect
to the normalized prices and hence, to income
and prices as well. By the definition of expendi
ture shares, demand functions can be expressed
as Aj = Sj/vj. The complicated nonlinearity of the
share equations, however, makes it impossible
to derive a closed-form expression for the de
mand functions, such as the conventional linear
or log-linear functions of income, prices and in
terest rates. Fortunately, the estimated
parameters and share equations can be used to
compute the income and price elasticities for
consumer goods and monetary assets.

All parameters are subject to non-negativity
constraints to guarantee that global regularity
conditions are satisfied. Because inequality con
straints limit the applicability of the existing the
oretical sampling distribution theory, the usual
methods for testing hypotheses cannot be
used.27

Estimation o f the A IM Dem and
System
The AIM model is estimated by a maximum
likelihood procedure under the assumption that
each share equation in (4) has an additive error
term, £it. That is,
(5) Si = gi(v,a) + £it, i = 1,2,3.
The disturbances are assumed to be indepen
dent and identically distributed multivariate nor
mal random variables with zero mean and
covariance matrix X. The sample disturbance
covariance matrix, X, is defined as
£ = (

£,£’t)/N,

Incom e Elasticities and Price
Elasticities
Because the share equations are so complex,
AIM does not yield explicit functional forms for
demand functions. This is the consequence for
correctly embedding utility maximization into an
econometrically estimable demand system that
can be used to compute economically meaning
ful income and price elasticities.
The Allen Partial elasticities of substitution
and income elasticities are defined and ex
pressed by the following formulas:28
for i # j,
_

d Aj Pj

£ti = s( - g, (v,a), for i = 1, 2, 3.
Maximizing the likelihood function for the sys
tem is equivalent to minimizing the generalized
variance, |X|.25
The estimation was accomplished using a non
linear program (GRG2). To find a global optima,
an extensive search over a large range of initial
conditions was conducted. Because of the com
plex nonlinearity o f the AIM demand system,
the true maximum likelihood estimates are
difficult to obtain. The possibility of missing the

s| ( 1

0PjA-

3 s,
—
+ -)
3E
Pi

EVjVj

for i = j,
oH=-

9 A? pj _

dp,A?
where N is the sample size, and the sample dis
turbance, £„ is computed by

1 3Sj

1 3 S;

•Vi 3 Pi

v,Pi

S; j 1

3sj

Ev2

s2.

where pj are the prices (and user costs), Af
denotes the in com e-com pensated dem and fu n c

tions for the ith asset, s, denotes th e expen ditu re
shares and E denotes total expenditures. T h e
elements, oip constitute a symmetrical matrix
called the Allen Partial matrix.
The income elasticities are defined by
>1i0 =

3 A,E

3 s; E

3E A.

3E sf

+ 1,

and the uncompensated price elasticities are
denoted by

24The higher-order AIM system contains m any m ore
unknow n param eters; see Barnett and Yue (1988).

27See Dufour (1989), Kodde and Palm (1986), W olak (1989)
and Barnett, Geweke and Yue (1991).

25See Barnett (1981).

28See Diewert (1974) and Barnett and Yue (1988).

26To estim ate param eters, a: \ = 1, 2, 3, 5, . . , 15, initial
values of the unknow n param eters were assigned. A num
ber of diffe re n t initial values of a,, 0.01, 0.03, 0.05, 0.08,
0 . 1, 0.2 ..... 1.0 , 2 .0 ,..., 10.0 were used.

FEDERAL RESERVE BANK OF ST. LOUIS

_9APi
nn =

Sj*7iO<

a PiA,

where A, are the ordinary or uncompensated
demand functions. The connection between com
pensated and uncompensated demand functions
is stated by the usual Slutsky equation.
Gross substitutability and complementarity is
provided by the off-diagonal terms of the un
compensated price elasticity matrix. If rjit is posi
tive, good i and good j are substitutes; in other
words, when the price of good i rises, demand
for good j increases to replace a cutback in de
mand for good i. If it is negative, they are com
plements—an increase in the price of good i (or j)
causes the demand to fall for both goods.
Similarly, the pure substitution effects are de
fined by the Allen Partial matrix. If the utility
function obeys regularity conditions, the own
compensated price elasticities (s ^ ) and (aif),
must be negative. Hence, the compensated price
elasticity matrix represents potential movements
along the consumer's indifference curves and
can be used to examine whether the estimated
underlying utility function satisfies regularity
conditions.
The computed elasticities of the AIM demand
system are compared with other money demand
systems in the next section. Because of the com
plexity of share equations, a numerical method
is used to compute the partial derivatives of the
expenditure shares with respect to prices and
income that occur in the elasticity formula. The
computation of elasticities is calculated using
the estimated share equations. Time series of
the elasticities are produced by substituting time
series of normalized prices and respective par
tial derivatives into the elasticity formula.

EMPIRICAL RESULTS OF THE AIM
MONEY DEMAND SYSTEM
In this section, the AIM demand system is esti
mated and the income and substitution elasticities
are compared with those for the translog and
Fourier demand systems. In addition, charac
teristics of monetary assets relative to consumer
goods are analyzed.
29Douglas Fisher provided all of the data used to estim ate
the AIM dem and system. He had previously used these
data to estim ate the translog and the Fourier dem and sys
tems. Hence, the em pirical results presented here can be
com pared d irectly with his. See Fisher (1989).

Table 1
Estimates of Coefficients of the AIM:
1970.1 to 1985.2
ai

.0000

.0122

34
.9878

35
.2225

a6
.2857

^7
.2299

as
.4466

39
.3568

3l0
.0515

311
.4446

312
.3961

313
.4056

314
.4535

3is
.4489

Table 2
Income and Substitution Elasticities
Allen Partial Matrix
Income

.502
(.005)

- 1 6 .5 6 4
(1.880)

.512
(.008)

2.693
(.213)

-15.450
(2.649)

.521
(.003)

5.553
(.721)

5.312
(.609)

-31.375
(6.944)

1.045
(.007)

.364
(.009)

.378
(.008)

.170
(.009)

-.0 3 0
(.005)

NOTE: Standard deviations in parentheses.

Estimates o f Parameters and In
com e and P rice Elasticities
Table 1 displays the coefficient estimates from
the AIM demand system derived by U.S. quar
terly data from 1970.1 through 1985.2.29 These
parameters represent the consumer's taste or
preference and determine the utility function
that underlies the estimated AIM demand sys
tem. Because the taste parameters are assumed
to be constant, the consumer's utility function
and preference did not change over time. The
estimates o f at and a2 were zero due to the
non-negativity constraint.30
The estimated Allen Partial elasticities of sub
stitution and income elasticities are reported in
table 2. The numbers represent the averages
30To this extent, the AIM m odel is at odds with the data be
cause the estim ated param eters w ould have been negative
if unconstrained.

NO VEMBER/DECEMBER 1991

Table 3
Income and Substitution Elasticities
T ra n s lo g
In co m e

_________ F o u rie r
a3

0.542

0.106

3.669

- 0 .4 9 0

- 0 .9 6 7

2.741

0.323

2.192

- 0 .2 6 2

A»

0.737

- 0 .1 5 0

0.805

0.428

- 0 .6 7 2

and their standard deviations (in parentheses)
over the sample period. Table 3 displays the es
timated substitution and income elasticities from
the translog and the Fourier series models
previously reported by Fisher (1989, page 103).
Table 4 presents the average uncompensated
price elasticities and their standard deviations
over the sample period for AIM. The cor
responding elasticities for the other two models
are not available.

What’s W rong with the Translog
and Fourier Dem and Systems?

In co m e

0.879

-3 .8 5 1

2.714

1.258

- 8 .1 0 4

2.803

1.119

2.876

- 1 .5 9 0

0.898

0.171

0.412

- 0 .2 2 4

Problems in the Fourier series demand system
cannot be seen in table 3 because the numbers
reported there are the average values of these
coefficients. According to Fisher, however, ex
cept for >7 40, the income elasticities and Allen
Partial elasticities of substitution changed signs
frequently over the period.31 For example, in
1970, o12 was significantly negative, implying
complementarity; in 1971-1972, it was signifi
cantly positive, implying substitutability; and
then in 1974-1975, it became negative again.
Figure 1 displays a o12-comparison of the Fourier
and AIM money demand systems. It is inexplica31See Fisher (1989), pp. 105-06.

FEDERAL RESERVE BANK OF ST. LOUIS

- 0 .0 4 2

Table 4
Uncompensated Price Elasticities
A,

-.5 3 4
(.004)

.075
(.010 )

.084
(. 011 )

- .1 2 6
(.009)

.069
(.005)

- .5 3 7
(.007)

.080
(. 010 )

-.1 2 3
(.007)

.157
(.005)

.162
(.009)

- .5 1 8
(.004)

-.3 2 2
(.004)

- .0 2 3
(.005)

- .0 1 5
(.003)

- .9 8 5
(.003)

A„

In the translog demand system results (shown
in table 3), the positive sign of
indicates that
the regularity condition is violated. This result
suggests that the higher the opportunity cost of
holding currency and demand deposits, the
greater their demand. Given this violation of the
"law o f demand,” the results from the translog
demand system must be considered suspicious
at best and, at worst, unreliable.

-.0 2 2
(.003)

NOTE: Standard deviations in parentheses.

ble that currency and demand deposits, A 1( and
savings deposits and money market deposit ac
counts, A2, should be complements during some
periods and substitutes during others.

Empirical Inference o f
Characteristics o f M onetary Assets
b y the A IM Dem and System
The anomalies observed with the translog and
the Fourier series demand systems do not occur
in the AIM demand system. The own-price
elasticities are negative and all estimated elastici
ties maintain their signs over the entire sample
period. Moreover, their smaller standard devia
tions indicate that they are more stable; this can
also be seen in figure 1. In the Allen Partial
matrix, the diagonal elements are all negative

F ig u re 1
T h e A lle n P artial E la s tic ity o f A 1 a n d A 2

while the off-diagonal elements are positive.
This implies that the three monetary aggregates
and aggregate consumption are substitutes for
each other in the presence of income compensa
tion. Moreover, the pure substitution effect be
tween each pair o f the three aggregated
monetary assets is much greater than between
the consumption good and monetary assets.
The income elasticities in table 2 are all posi
tive, with the income elasticity of the consump
tion good about unity, and the income
elasticities of the three monetary assets roughly
equal to 0.5.32 These results suggest that con
sumption goods and monetary assets are normal
goods.
Table 4 shows that the uncompensated crossprice elasticities of (A1( A2), (A1; A3) and (A2, A3)
are positive, implying that these monetary assets
are gross substitutes. The uncompensated cross
price elasticities of (A1( A4), (A2, A4) and (A3, A4)
are negative, indicating that consumption goods
and monetary assets are gross complements.
These results show that, if the user costs of
savings deposits (or money market deposit ac
counts, or small time deposits) rise, consumers
will shift their funds to demand deposits (or to
32T his may not be ju stifie d by the unity incom e e lasticity in
the reduced form of the aggregate m oney-dem and function. As pointed out in the text, no reduced form dem and
fu n ction s are estim ated in our study and the incom e
e lasticity is defined by the m icroeconom ic approach.
Because their incom e elasticities are sign ifica n tly less
than one, the m onetary assets in our study are not “ luxury
goods,” as has been claim ed in some previous research.
See Serletis (1988).

checkable deposits or currency). An opposite
shift of funds will take place if the user costs of
currency, demand deposits and checkable
deposits should rise. If these user-cost changes
are sufficiently large, ignoring the cross-price
effects among monetary assets will produce
large errors in their demand functions.
Monetary services and consumer goods are
consumed jointly. If a consumer increases the
consumption of commodities for some reason,
the demand for monetary assets is also in
creased. This is consistent with the idea that
consumers hold monetary assets to finance cur
rent and future consumption. Also, the negative
rjj4 indicates that price inflation will reduce de
mand for monetary assets.
Not surprisingly, the own price elasticities of
monetary assets are greater than their cross
price elasticities. Similarly, it is not surprising to
see that the cross-price effects o f a change in
the price of consumption goods on the demand
for monetary assets are greater than the crossprice effects of a change in the price of mone
tary assets on consumption. Consequently, em
pirical results from the AIM demand system
provide a reasonable quantitative analysis of the
characteristics of monetary assets—characteris
tics that are broadly consistent with conventional
views o f demand for money.

A DYNAMIC ANALYSIS BY THE
AIM DEMAND SYSTEM
Constructing a dynamic model of demand for
money has been difficult because the current
state of economic knowledge about dynamic be
havior is incomplete; the dynamics of money de
mand are still very much a "black box” mystery.33
Unlike most multivariate time series models,
the AIM model is static. It does not consider
specific dynamic effects among monetary assets
and consumption goods. The utility function is
not intertemporal and its parameters are timeinvariant—the consumer's preference is not per
mitted to change over time.
33This situation occurs in a recent debate in econom ic literature; see Hendry and Ericsson (1991) and Friedm an and
Schwartz (1991).

NOVEMBER/DECEMBER 1991

Figure 3
Uncompensated Own Price Elasticities

F igure 2
Incom e Elasticities E ,, E2, E3 and E4 for A ,, A2,
A 3 and A 4

- 0.54
- 0.55

1970

1985

Nevertheless, a simple dynamic analysis can
be used to examine the AIM demand system.
Time series of income and price elasticities can
be computed using estimated share equations.
Movements in these elasticities reflect both
changes in user costs and the consumer's reac
tions to such changes. Both of these are reflected
in the shares, S;. In this way, the dynamics of
the AIM demand system can be investigated even
though demand for money is stable by
assumption.
This dynamic analysis is displayed in figures
2, 3 and 4. Figure 2 shows that the income
elasticities of the three monetary assets are rela
tively constant over the entire sample period. In
contrast, the price elasticities (shown in figures
3 and 4), exhibit sizable fluctuations. Major shifts
in price elasticities occurred during 1973.1-1974.4
and 1978.2-1982.2. During these periods, a num
ber of studies have reported that demand for
monetary aggregate M l was "erratic.”34
Price and user cost elasticities moved drasti
cally during these periods. In the second period
(1978.2-1982.2), the cross price elasticity, rj12,
rose by 50 percent of its 1977 level, implying
that demand for Aa (currency plus demand de
posits, plus checkable deposits) became much
more sensitive than it was previously to changes
in the opportunity cost of holding A2 (savings
deposits and money market demand accounts).
Meanwhile, there was a sharp rise in the user
34See Goldfeld (1976) and Friedman (1984).

FEDERAL RESERVE BANK OF ST. LOUIS

Figure 4
U ncom pensated Cross Price Elasticities

cost of A2. These factors would appear to ac
count for the major shift of funds from A2 to A,
during the period.
The opposite price elasticity, r]21, also rose by
20 percent. Nevertheless, it was less than 80
percent of the value of rj12 and the rise in the
user cost of A1 was more modest than that of
A2. It was observed that the opportunity cost of
A2 increased much faster than that of A,. Hence,
the actual flow of funds from A, to A2 might not
be significant.
The cross price elasticity, r)13, dropped 30 per
cent in 1979, implying that the demand for A,

was less sensitive to changes in the user cost of
A3. Hence, the shift of funds from A3 to Aj
should have been moderate despite a substantial
increase in the user cost of A 3.

Figure 5
G row th Rates o f A g greg ate A 1 A ctual vs. Sim ulation

These results are roughly consistent with de
velopments during the period. In November 1978,
commercial banks w ere authorized to offer au
tomatic transfer service (ATS) from savings ac
counts to checking accounts. Other interest
ceiling-free accounts were also introduced in
the early 1980s. In January 1981, NOW ac
counts were introduced nationwide. These finan
cial innovations should have encouraged
consumers to shift funds from savings accounts
and money market deposit accounts in A2 into
NOW accounts in A x. This may have increased
the interest sensitivity of demand for A,.35

Simulating the Growth Rates o f
Monetary Aggregates

F ig u re 6
G ro w th R a te s o f A g g re g a te A 2 A c tu a l v s . S im u la tio n

A further investigation of the behavior of mon
etary aggregates can be made by a dynamic
simulation. For example, suppose that demand
for A; has been derived by utility maximization
and expressed by the ordinary demand func
tions of price and user costs and total expen
diture
(6) Aj = G, (uu u,, u3, u4, E).
The total differentiation of (6) results in
(7) dAj = X dGj/du, du, +dG/dE dE.
i=i
Dividing both sides of (7) by (6) and using defi
nitions of the uncompensated price elasticities
and the income elasticity gives
(8) dAj/Aj = I

Figure 7
G row th Rates o f A g greg ate A 3 Actual vs. Sim ulation

Kjij (du/u;) + r),„ (dE/E).

i- i

Using time series of the elasticities and the
growth rates o f price and user costs and total
expenditure, the right-hand sides of the equa
tions in (8) are computed. In this way, the
growth rates of demand for A, can be
"simulated."
The actual and simulated growth rates of de
mand for monetary aggregates and consumption
are displayed in figures 5 through 8. The simu
lations match the actual growth rates fairly
well, especially for consumption. The simulation
rates of monetary assets had large fluctuations
35See Thornton and Stone (1991) for a discussion of this
possibility.

NOVEMBER/DECEMBER 1991

Figure 8
Growth Rates of Aggregate A4 Actual vs. Simulation

around the actual growth rates in the periods
1972.4-1975.1 and 1978.2-1982.2. Fluctuations in
interest rates and inflation rates were substan
tial during each period, causing corresponding
fluctuations in growth rates of user costs.36
These changes are reflected directly in the sim
ulation rates.
Because the AIM model is static, sharp changes
in user costs are necessarily reflected in cor
respondingly sharp changes in the simulated
growth rates of aggregates. Hence, it is not sur
prising that the simulation errors are large dur
ing periods when there are sharp changes in
user costs. Nevertheless, figures 5 through 8
suggest that the AIM demand system has cap
tured many of the characteristics of the U.S.
m on etary system du rin g the sample period.

Can the A IM Dem and System Ex
plain the Case o f the Missing
M oney?
Although the simulation o f the growth rate of
A! indicates that the AIM model produced rela
tively large errors during the period of "missing
money” (1973.4-1976.2), an analysis of the AIM
results might provide a clue.37 During this peri
od, there was a sharp decline in demand for
36Some term s are essentially zero and can be ignored. The
follow ing grow th rate equations are accurate enough to
produce the sim ulation:

dA-|/Ai = f7ndui/ui + i7i2du2/u2 + f]i3du3/u3 + ^44du4/u4
+ rj10dE/E
dA 2/A 2 = rj22du2/u 2 + 7723d u 3/u 3
dA 3/A 3 = J733du3/u3
= r)42d u 2/u 2 + ^ 43du 3/u 3 + K)44du 4/u 4 + rjiodE/E.
In the equation fo r A, th e re are m ore affecting elements;
the own and cross-price effects of A2, A 3 and A 4 are im

FEDERAL RESERVE BANK OF ST. LOUIS

M l; conventional money demand equations con
sistently overpredicted demand.
A potential explanation can be obtained by
considering figures 9 and 10. Figure 9 shows
the partial derivative of demand for A1 with
respect to its own user cost. Figure 10 shows
the partial derivative of demand for A, with
respect to the user costs of A2, A 3, A4 and E.
Figure 9 shows a sharp rise in the rate of change
in demand for A, with respect to a change in
its user cost. Indeed, figure 11 shows that the
user cost o f Aj increased relative to the price
level. Hence, the demand for A 1 should have
declined by a proportionately larger amount
than the rise in its user cost. Conventional
linear money demand equations with fixed
regression coefficients could not accommodate
this nonlinearity because, in such linear demand
systems, the coefficients (derivatives) are assumed
to be constant. However, figures 9 and 10 clear
ly suggest that this is not the case. Moreover,
ordinary least squares is relatively sensitive to
"outliers.” Consequently, there will be substan
tial changes in the estimated regression coeffi
cients when the equations are estimated over
periods when these derivatives change signifi
cantly.
Conventional money demand equations may
be misspecified for another reason, as well.
Usually they include a single short-term interest
rate intended to reflect the opportunity cost of
holding money. AIM analysis indicates that the
demand for money does not depend on a single
“representative” interest rate, but on its user
cost and the user costs of “close” substitutes
(recall that the demand for A1 was sensitive to
changes in the user costs of A2). Hence, conven
tional money demand equations may produce
misleading results when interest rates change
relative to the user costs of M l or relative to
the user costs of close substitutes for M l.
Therefore, the case of “missing money” and
“unexplained” parameter shifts in conventional
money demand functions may result from the
fact that they are essentially linear approximaportant in sim ulating the growth rate of A ,. T he growth
rates of dem and for the oth er tw o m onetary aggregates,
however, are determ ined m ainly by th e ir own price effects
and cross-price effect, rj23. T his suggests that ignoring the
substitution effects of non-M1 com ponents of M2 m ight be
one of the factors that d iscre d it reliability of the conven
tional M1 dem and function.
37See G oldfeld (1976).

Figure 9
The First Derivative of A, w ith Respect to Own User Cost

1970

1985

F igu re 10
T h e First D e riv a tiv e s o f A t w ith R e s p e c t to U s e r C osts,
Price and In c o m e

d a 13

—

d a 14
- 10

- 20

-3 0

S 'N s - n d a e

1970

..... ................................
.- ::
....
71
72
73
74
75
76

F igure 11
U ser Cost o f A, vs. Price of A4

1985

tions to nonlinear demand functions. If so, they
intuitively will provide much poorer approxima
tions during periods when there are dramatic
changes in user costs.

Is The M on ey Demand Function
Stable?

ble.”38 Others have asserted that money demand
is stable based on the observed stability of the
consumption function.39
The AIM demand system integrates demand
for both consumption and money and then esti
mates them simultaneously. These estimates sug
gest that, while the own price and cross price
elasticities show considerable variation due to
changes in the price level and user costs, they
change little on average over the period (see
figures 3 and 4).40 Moreover, the estimated in
come elasticities for all three monetary aggre
gates are nearly constant (see figure 2). Of course,
these results are obtained from a model where
the estimated parameters are time-invariant,
that is, the preference function is constant.
Because of this, it is necessarily true that de
mand functions are "stable." Nevertheless, the
relatively good performance of AIM provides
some promise that, like consumption, the de
mand for money will ultimately be shown to be
a stable function of a relatively few economic
variables—in this case, income and user costs.

CONCLUSION

The erratic behavior of conventional money
demand functions and, more recently, the in
come velocity of M l, have led many researchers
to assert that the demand for money is “unsta

Two distinctly different micro-econometric de
mand system approaches to the demand for
money were presented and discussed. An ad
vanced AIM demand system was presented and
estimated using U.S. time-series data. Unlike

38For a discussion of the velocity of M1 and an analysis of
som e of the explanations, see Stone and Thornton (1987).

ing. However, no form al tests of stationarity were per
form ed in this study.

39For example, see Friedm an (1956) and Lucas (1988).
40ln the parlance of modern tim e-series analysis, these
elasticities are said to be stationary, that is, mean revert

NOVEMBER/DECEMBER 1991

other utility function-based approaches, AIM es
timates are consistent with microeconomic the
ory. Dynamic simulations of the growth rates of
various monetary aggregates and consumption
suggest that the estimated AIM model performed
well; nevertheless, the largest simulation errors
occurred in periods when there were relatively
sharp swings in user costs or inflation. This is
perhaps not too surprising given the static na
ture of the AIM analysis.
An analysis of changes in income and cross
price elasticities are suggestive of portfolio shifts
among monetary aggregates in the 1970s and
1980s consistent with the observed behavior of
these aggregates. The results of AIM suggest
that the reported failure of conventional linear
(or log-linear) money demand equations may
result from trying to fit fundamentally non
linear functions with linear ones. The results
shown here suggest that this problem will be
particularly acute whenever there are sharp
changes in user costs. Unfortunately, these are
precisely the times when AIM performance was
also poor. The key to solving this problem in
AIM, however, is to find a way to make AIM ex
plicitly dynamic. It may not be necessary to
assume that consumer preferences are unstable.
The sampling distribution theory for AIM has
not been worked out at this time, so relevant
hypothesis tests cannot be conducted yet. Also,
because the time series on the relevant user
costs o f monetary aggregates is limited, the
available data cover a relatively short sample
period. These factors, coupled with the fact that
even low-order (first-order) AIM systems require
a relatively large number of estimated parame
ters, place severe limits on attempts to evaluate
the performance o f AIM using out-of-sample
forecasts. Despite these problems, the estimated
AIM system appears to have captured many of
the characteristics of monetary assets and offers
some useful explanations to puzzling empirical
issues. Hence, these results are encouraging to
those who believe that microeconomic princi
ples, such as utility maximization, can be ap
plied usefully to macroeconomic problems.

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FEDERAL RESERVE BANK OF ST. LOUIS

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Lucas, R obert E., Jr. “ M oney Dem and in the United States: A
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Moore, George R., Richard D. Porter, and David H. Sm all.
“ M odeling the Disaggregated Dem ands for M2 and M1:
The U.S. Experience in the 1980s,” in Peter Hooper and
others, eds., Financial Sectors in Open Econom ies: Em piri
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Federal Reserve System, 1990), pp. 21-97.
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Money and Debt,” in Peter Hooper and others, eds., Finan
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System, 1990), pp. 113-61.

Swofford, Jam es L., and G erald A. W hitney. “ Flexible Func
tional Forms and the U tility A pproach to the Dem and for
Money: a N onparam etric Analysis,” Journal o f Money,
Credit and Banking (August 1986), pp. 383-89.
Telser, Lester G., and Robert L. Graves. Functional Analysis
in M athem atical Econom ics (The U niversity of Chicago
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T hornton, Daniel L., and C ourtenay C. Stone. “ Financial Inno
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Mervyn K. Lewis, eds., Current Issues in M onetary Analysis
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Uzawa, H irofum i. “ Production Functions with Constant
Elasticities of Substitution,” Review o f Econom ic Studies
(October 1962), pp. 291-99.
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NOVEMBER/DECEMBER 1991

Mark D. Flood
M ark D. Flood is an econom ist at the Federal Reserve Bank of
St. Louis. David H. Kelly provided research assistance.

Microstructure Theory and
the Foreign Exchange Market

GROWING BODY OF theoretical literature,
known as the study of securities market microstructure, deals with the behavior of participants
in securities markets and with the effects of in
formation and institutional rules on the economic
performance of those markets. These institu
tional factors may arise from technology, tradi
tion or regulation. Microstructure and its impact
are important, because of the vast amounts of
wealth which pass through securities markets —
including the foreign exchange market —
every day.
Microstructure is of interest to students of the
foreign exchange market: microstructural analy
ses of other markets have yielded insight into
traders’ behavior and the effect of various insti
tutional arrangements. Conversely, the foreign

'S im ila r arrangem ents exist for other se cu ritie s— for exam
ple, the federal funds m arket and the secondary m arket
fo r T reasury securities— but these too have been relatively
neglected in the literature.
2The shaded insert on the opposite page provides a context
in which the m icrostructural approach can be com pared
with m ore traditional approaches to m arket efficiency.
Follow ing some early articles by Dem setz (1968), Tinic
(1972) and T inic and W est (1972), G arm an (1976) per
form ed the crucial task of defining m arket m icrostructure
as an independent area o f th e literature, th u s focusing the
debate. Since then, m arket m icrostructure has burgeoned,
led by Cohen, Maier, Schw artz and W hitcom b (1978a,
1978b, 1981, 1983), Am ihud and M endelson (1980, 1986,
1988), Stoll (1978, 1985, 1989) and Ho and Stoll (1980,
1981). See also Beja and Hakansson (1977), Cohen,
Hawawini, Maier, Schw artz and W hitcom b (1980), Cohen,
Maier, Ness, O kuda, Schwartz and W hitcom b (1977), A m i
hud, Ho, and Schwartz (1985), Schreiber and Schwartz
(1986), Schwartz (1988) and Cohen and Schw artz (1989).

FEDERAL RESERVE BANK OF ST. LOUIS

exchange market is also of special interest to
students o f microstructure, because it combines
two very different arrangements for matching
buyers and sellers — bank dealers trade with
one another both directly and through foreign
exchange brokers.1
Standard models of exchange-rate determina
tion concentrate on relatively long-run aspects,
such as purchasing power parity. While micro
structure theory cannot address these issues
directly, it can illuminate a more narrowly fo
cused array of institutional concerns, such as
price information, the matching of buyers and
sellers, and optimal dealer pricing policies. De
spite the substantial literature on microstructure,
little attention has been paid to the particular
microstructure of the foreign exchange market.2

Cohen, Maier, Schw artz and W hitcom b (1979, 1986) and
Stoll (1985) have surveyed th e m icrostructure literature.
In addition to the early note by Allen (1977), very recently
there have appeared some m icrostructural studies of the
foreign exchange m arket: Bossaerts and Hillion (1991),
Lyons (1991), Rai (1991) and Flood (1991). There is also
an em pirical literature m easuring the determ inants of the
bid-ask spread in the foreign exchange m arket. See Black
(1989), W ei (1991) and Glassm an (1987) as well as the
references therein. Because th e focus of this article is on
m icrostructure theory, such em pirical studies receive little
attention here.
Finally, although a consideration of the results of laborato
ry experim ents would expand th e scope of th is paper to
unw ieldy dim ensions, th e ir role in establishing the sensitiv
ity of m arket behavior to in stitutional fa cto rs m ust at least
be acknow ledged; see Plott (1982, 1991) fo r an in
troduction.

Price Efficiency in a Heterogeneous Marketplace
Implicit in most microstructural models is a
presumption that participants in any given
market are heterogeneous, that is, that they
differ in certain key determinants of econom
ic behavior: information, beliefs, preferences
and wealth. Although this assumption con
sumes little attention in the microstructure
literature — it is taken for granted — it is
valuable to discuss it in the more familiar
theoretical context of market efficiency.
The standard definition o f price efficiency
is: fm(p,|lmt_i) = f *(pt1 1 ,_ In other words, the
joint distribution over future prices, fm(pt), as
sessed by the monolithic market (or a repre
sentative agent in that market) and made
conditional on the current information, Iml_„
available to the market is equal to the “true"
joint distribution, f*(p t), made conditional on
all current information, I,_,. Roughly speak
ing, the market sorts things out as accurately
as possible.1
This approach breaks down in a microstructural analysis. First, the simplifying as
sumption of homogeneous participants is
abandoned. Although it is widely recognized
“that investors do not show the homogeneity
of beliefs which characterize our theories,"
the benefits o f realism (i.e., the heterogeneity
assumption) are often outweighed by other
criteria (e.g., testability, tractability, etc.).2 Em
phasizing testability, Ross offers a standard
rejoinder, namely that “since a single ex post
distribution of returns is observed by all,
over time one would not expect to observe
systematic and persistent differences.” This is
a rational expectations argument, which de
pends crucially on the stationarity o f the
returns distribution and which ignores the ef
fect o f differences in opinions and beliefs,
which go beyond differences in information.
1See Fama (1976), ch a p te r 5, for the de fin itive presentation.

In general then, at the level of detail involved
in microstructural studies, the homogeneity
assumption is not an excusable flaw; in a
homogeneous market why — let alone how —
would anyone trade?
More fundamentally, the notion of a “true”
price must be questioned. In the context of
the literature on price efficiency, the intro
duction o f a “true” distribution as a theoreti
cal conceit leads to joint testing problems, as
the “true” distribution is ipso facto unobserva
ble. More fundamentally, positing a “true”
distribution confuses the chain of causality; it
presumes that future prices are drawn from
some exogenous probability distribution and
that investor behavior is concerned with ac
curately estimating that distribution.
In fact, investor behavior in the market
place determines the distribution o f future
prices, not the other way around. This fact in
no way depends on the ultimate basis or mo
tivation for investor behavior. In an explicit
model of price discovery, the assertion o f an
ex ante exogenous equilibrium price is mean
ingless. As Schreiber and Schwartz put it,
“the fact that security analysts assess the
value o f a stock for their own portfolios does
not imply that they undertake a treasure
hunt to find some golden number which one
might call an intrinsic value.”3 In sum, the
standard theory of efficient markets is illsuited to the modeling of price discovery. In
comparing observed prices to an imputed
“true” distribution, studies o f market efficien
cy ignore more immediate concerns — for ex
ample, how well the institutional structure
transmits information, whether arbitrage op
portunities occur, and how well the market
allocates assets among investors. These con
cerns are the focus o f microstructural analysis.
3See S chreiber and S chw artz (1985), p. 22.

2See Ross (1978), pp. 889-90. See Varian (1989) for a
more thorough review of the theoretical issues involved
in the heterogeneity assum ption.

NOVEMBER/DECEMBER 1991

This paper examines the extant literature on
market microstructure to determine how it
might be applied to the foreign exchange
market.
The paper begins with a brief description of
the foreign exchange market. Aspects of the
literature concerned with institutional details
are addressed second, noting how such details
can affect the performance of the market. Next,
the literature dealing with behavioral details, es
pecially the communication and interpretation
of price information, is considered. Finally, the
interaction of institutional and behavioral fac
tors, notably the bid-ask spread, is discussed.

Figure 1
Spot Market Volume by
Transactor (4/89)

INSTITUTIONAL BASICS OF THE
FOREIGN EXCHANGE MARKET
The foreign exchange market is the interna
tional market in which buyers and sellers of
currencies "meet.”3 It is largely decentralized:
the participants (classified as market-makers,
brokers and customers) are physically separated
from one another; they communicate via tele
phone, telex and computer network. Trading
volume is large, estimated at §128.9 billion for
the U.S. market in April 1989. Most of this trad
ing was between bank market-makers.4
The market is dominated by the market-makers
at commercial and investment banks, who trade
currencies with each other both directly and
through foreign exchange brokers (see figure l).5
Market-makers, as the name suggests, "make a
market” in one or more currencies by providing
bid and ask prices upon demand. A broker ar
ranges trades by keeping a "book” of marketmaker’s limit orders — that is, orders to buy (al
ternatively, to sell) a specified quantity of for
eign currency at a specified price — from which
he quotes the best bid and ask orders upon re
quest. The best bid and ask quotes on a broker’s
book are together called the broker's "inside
spread.” The other participants in the market
are the customers of the market-making banks,
w ho generally use the market to com plete
transactions in international trade, and central
banks, who may enter the market to move ex3For m ore thorough descriptions of the w orkings of the for
eign exchange m arket, see Burnham (1991), C hrystal
(1984), Kubarych (1983) and Riehl and Rodriguez (1983).
4See Federal Reserve Bank of New York (1989a) and Bank
fo r International S ettlem ents (BIS) (1990). E xtending this
fig u re over 251 trad in g days per year, this im plies a trad
ing volum e of roughly $32 trillio n for all of 1989. Volum e

FEDERAL RESERVE BANK OF ST. LOUIS

- Interbank Direct
(55.0%)
- Interbank Brokered
(39.9%)

change rates or simply to complete their own
international transactions. Market-makers may
trade for their own account — that is, they may
maintain a long or short position in a foreign
currency — and require significant capitalization
for that purpose. Brokers do not contact cus
tomers and do not deal on their own account;
instead, they profit by charging a fee for the
service o f bringing market-makers together.
The mechanics of trading differ substantially
between brokered transactions and direct deals.
In the direct market, banks contact each other.
The bank receiving a call acts as a market-maker
for the currency in question, providing a twoway quote (bid and ask) for the bank placing
the call. A direct deal might go as follows:
M o n go b a n k : '‘Mongobank with a dollar-mark
please?”
(Mongobank requests a spot market quote
for U.S. dollars (USD) against German marks
(DEM).)
has roughly doubled every three years fo r the past
decade.
5Federal Reserve Bank of New York (1989a) lists 162
m arket-m aking institutions (148 are com m ercial banks) and
14 brokers; an earlier study, Federal Reserve Bank of New
Y ork (1980), lists 90 m arket-m aking banks and 11 brokers.

Loans 'n Things: “20-30”
(Loans n’ Things will buy dollars at 2.1020
DEM/USD and sell dollars at 2.1030 DEM/USD
—the 2.10 part of the quote is understood.)
M ongobank: “Two mine.”
(Mongobank buys $2,000,000 for DEM
4,206,000 at 2.1030 DEM/USD, for payment
two business days later. The quantity traded
is usually one of a handful of "customary
amounts.”)
Loans ’n Things:

“My marks to Loans 'n
Things Frankfurt."
(Loans n' Things requests that payment of
marks be made to their account at their
Frankfurt branch. Payment will likely be
made via SWIFT.)6

M ongobank:

“My dollars to Mongobank New
York. ”
(Mongobank requests that payment of dol
lars be made to them in New York. Payment
will most likely be made via CHIPS.)7

Spot transactions are made for “value date”
(payment date) two business days later to allow
settlement arrangements to be made with cor
respondents or branches in other time zones.
This period is extended when a holiday inter
venes in one of the countries involved. Payment
occurs in a currency's home country.
The other method o f interbank trading is
brokered transactions. Brokers collect limit
orders from bank market-makers. A limit order
is an offer to buy (alternatively to sell) a speci
fied quantity at a specified price. Limit orders
remain with the broker until withdrawn by the
market-maker.
The advantages of brokered trading include
the rapid dissemination o f orders to other
market-makers, anonymity in quoting, and the
freedom not to quote to other market-makers
on a reciprocal basis, which can be required in
the direct market. Anonymity allows the quoting
bank to conceal its identity and thus its inten
tions; it also requires that the broker know who
is an acceptable counterparty for whom. Limit

6The Society for W orldw ide Interbank Financial Telecom m u
nication (SWIFT) is an electronic m essage network. In this
case, it conveys a standardized paym ent ord e r to a Ger
man branch or correspondent bank, which, in turn, effects
th e paym ent as a local interbank transfer in Frankfurt.

orders are also provided in part as a courtesy
to the brokers as part of an ongoing business
relationship that makes the market more liquid.
Because his limit order is often a market-maker’s
first indication of general price shift, Brooks
likens the posting of an order with a broker "to
sticking out the chin so as to be acquainted
with the moment that the fight starts.”8 Schwartz
points out that posting a limit order extends a
free option to other traders.9
A market-maker who calls a broker for a quote
gets the broker’s inside spread, along with the
quantities of the limit orders. A typical call to a
broker might proceed as follows:
M ongobank: “What is sterling, please?”
(Mongobank requests the spot quote for
U.S. dollars against British pounds (GBP).)
Fonm eister: “I deal 40-42, one by two.”
(Fonmeister Brokerage has quotes to buy
£1,000,000 at 1.7440 USD/GBP, and to sell
£2,000,000 at 1.7442 USD/GBP)
M ongobank: “I sell one at 40, to whom?”
(Mongobank hits the bid for the quantity
stated. Mongobank could have requested a
different amount, which would have re
quired additional confirmation from the bid
ding bank.)
Fonmeister: [A pause while the deal is reported
to and confirmed by Loans ’n
Things] "Loans 'n Things London.”
(Fonmeister confirms the deal and reports the
counterparty to Mongobank. Payment ar
rangements will be made and confirmed
separately by the respective back offices. The
broker's back office will also confirm the
trade with the banks.)
Value dates and payment arrangements are the
same as in the direct dealing case. In addition to
the payment to the counterparty bank, the banks
involved share the brokerage fee. These fees are
negotiable in the United States. They are also
quite low: roughly $20 per million dollars trans
acted.10

8See Brooks (1985), p. 25.
9See Schw artz (1988), p. 239.
10See Burnham (1991), p. 141, note 16, and Kubarych
(1983), p. 14.

H ’he C learing House for Interbank Paym ents System
(CHIPS) is a private interbank paym ents system in New
Y ork City.

NOVEMBER/DECEMBER 1991

The final category o f participants in the fo r
eign exchange market is the corporate cus
tomers of the market-making banks. Customers
deal only with the market-makers. They never go
through brokers, who cannot adequately monitor
their creditworthiness. Typically, a customer
transacts with a bank with which it already has a
well-established relationship, so that corporate
creditworthiness is not a concern for the bank's
foreign exchange desk, and trustworthiness is not
an issue for the customer. The mechanics of cus
tomer trading are similar to those of direct deal
ing between market-makers. A customer requests
a quote, and the bank makes a two-way market;
the customer then decides to buy, sell or pass.
The chief difference between this and an inter
bank relationship is that the customer is not ex
pected ever to reciprocate by making a market.
Participants in the foreign exchange market also
deal for future value dates. Such dealing com
poses the forward markets. Active forward mar
kets exist for a few heavily traded currencies and
for several time intervals corresponding to active
ly dealt maturities in the money market. Markets
can also be requested and made for other ma
turities, however. Since the foreign exchange
market is unregulated, standard contract speci
fications are matters o f tradition and con
venience, and they can be modified by the
transacting agents.
Forward transactions generally occur in two
different ways: outright and swap. An outright
forward transaction is what the name implies, a
contract for an exchange of currencies at some
future value date. “Outrights” generally occur
only between market-making banks and their
commercial clients. The interbank market for out
rights is very small, because outright trading im
plies an exchange rate risk until maturity of the
contract. When outrights are concluded for a
commercial client, they are usually hedged im
mediately by swapping the forward position to
spot. This removes the exchange rate risk and
leaves only interest rate risk.
A swap is simply a combination of two simul
taneous trades: an outright forward contract and
an opposing spot deal. For example, a bank might
"swap in” six-month yen by simultaneously buying
spot yen and selling six-month forward
" H e d g in g an o utright purchase of currency with an oppos
ing swap deal still leaves an open spot purchase of the
currency. This can be easily covered in the spot m arket.

FEDERAL RESERVE BANK OF ST. LOUIS

Figure 2
Market-Maker Volum e by
Type (4/89)

yen. Such a swap might be used to hedge an out
right purchase of six-month yen from a bank cus
tomer.11 In effect, the swapping bank is
borrowing yen for the six months of the outright
deal. The foreign exchange market-maker swaps
in yen — rather than simply borrow yen on a
time deposit — because banks maintain separate

foreign exchange and money market accounts for
administrative reasons. Swapping is generally the
preferred means of forward dealing (see figures 2
and 3).
In practice, the vast majority of foreign ex
change transactions involve the U.S. dollar and
some other currency. The magnitude of U.S. for
eign trade and investment flows implies that, for
almost any other currency, the bilateral dollar ex
change markets will have the largest volume.
Consequently, the dollar markets are the most li
quid. The possibility of triangular arbitrage en
forces the law of one price for the cross rates.
The upshot is that liquidity considerations out
weigh transaction costs. A German wanting

Figure 3
Broker Volume by
Type (4/89)
Options
(3.5%)

erature is that institutional differences can af
fect the efficiency of pricing and allocation.
As described above, the foreign exchange
market combines two disparate auction struc
tures for the same commodity: the interbank
direct market and the brokered market. Defying
a naive application of institutional Darwinism,
whereby only the fitter of the two systems
would survive, these trading methods appear to
coexist comfortably.12 The direct market can be
classified as a decentralized, continuous, openbid, double-auction market. The brokered mar
ket is a quasi-centralized, continuous, limit-book,
single-auction market. The meanings of these
classifications are explained below.

Centralization

Spot
(56.8%)
-Outright Forward
(0.3%)

pounds, for example, will typically convert
marks to dollars and then dollars to pounds,
rather than trading marks for pounds directly.
Though this is especially true in the American
market, it holds for foreign markets as well.

CLASSIFYING MARKETS
The microstructure literature is by nature
market-specific, and much of it concerns U. S.
equity markets. This specificity has the advan
tage of realism, but it makes the immediate ap
plicability of some microstructural models to the
foreign exchange market questionable. The first
task is to define some basic microstructural con
cepts, identifying where the foreign exchange
market fits into the context they provide. Such
a taxonomy is important, because one of the
fundamental lessons of the microstructure lit
12A sim ilar situation obtains on the New Y ork Stock Ex
change, where specialists act as either brokers or marketmakers, depending on the level of a ctivity in the market.
13See W olinsky (1990), p. 1. He goes on to analyze theoreti
ca lly the difference in the price discovery process between
centralized and decentralized m arkets. Schw artz (1988),
pp. 426-35, refers to centralization as “ spatial consoli
d a tio n.”

In a centralized market, “trades are carried
out at publicly announced prices and all traders
have access to the same trading opportunities.”
In a decentralized market, in contrast, “prices
are quoted and transactions are concluded in
private meetings among agents.”13 A New York
Stock Exchange’s (NYSE) specialist system is a
centralized market; the interbank direct market
for foreign exchange is a decentralized one.
The distinction between centralized and de
centralized markets might seem to provide a
neat dichotomy of possible market structures.
The multiplicity of brokers in the foreign ex
change market violates this simple taxonomy,
however. Each foreign exchange broker accum
ulates a subset of market-makers’ limit orders.
This network of “brokerage nodes” is as dif
ferent from a fully centralized system as it is
from a fully decentralized one. This arrange
m ent is labeled h ere as "qu asi-centralized.”

Most microstructural studies have confined
themselves to centralized markets, especially the
NYSE’s specialist system and the National Associ
ation of Securities Dealers Automated Quotation
(NASDAQ) System on the over-the-counter (OTC)
market.14 Although there are a number o f im
portant decentralized markets, including the in
terbank direct foreign exchange market, rela14For m odels o f specialist system s, see Dem setz (1968), Tinic (1972), G arm an (1976), Bradfield (1979), Am ihud and
M endelson (1980), Conroy and W inkler (1981), Glosten
and M ilgrom (1985) and S irri (1989). For studies of the
OTC m arket, see Tinic and W est (1972), Benston and
Hagerm an (1974), Ho and M acris (1985) and Stoll (1989).

NOVEMBER/DECEMBER 1991

tively few studies have focused on the impact
o f decentralization.
There is some evidence that differences in
the degree of centralization between various
markets cause differences in market perfor
mance. Garbade, in studying the largely decen
tralized Treasury securities market, concludes
that because brokerage tends to centralize
trading and price inform ation, it "uses time
more efficiently,” “eliminates the most important
arbitrages,” and benefits dealers by ensuring that
orders are executed according to price priority.15
The efficiency gains of centralized price infor
mation may imply economies o f scale and, thus,
a natural monopoly for brokers in securities
markets. This is entirely consistent with the text
book presentation of the relatively greater opera
tional efficiency of centralized markets.16 Thus,
the fact that a number of brokers service the
foreign exchange market seems to represent a
discrepancy between theory and reality. Brokers
do communicate among themselves, however, to
eliminate the possibility of arbitrage between
limit order books. While this helps explain the
multiplicity of brokers, it does not fully resolve
the issue o f decentralization in the interbank
direct market.

Temporal Consolidation
The distinction between a continuous market
and a call market involves what Schwartz refers
to as the degree of "temporal consolidation.”17
In a call market, trading occurs at pre-appointed
tim es (the "calls”), w ith arriving transaction ord
ers detained until the next call for execution. In
continuous markets, like the foreign exchange
market, trading occurs at its own pace, and
transaction orders are processed as they arrive.
A range of intermediate arrangements falls be
tween these two extremes.
15See G arbade (1978), p. 497.
16The textbook argum ent counts trips to m arket. Briefly, if
there are N traders, then a total of N trips to a central
m arketplace are required for each to haggle with everyone
else; to pair them bilaterally requires a total of N(N-1)/2
trips. If trips are costly, then centralization is more ef
ficient.
17See Schw artz (1988), pp. 435-47. G arm an (1976), pp. 25758, also describes continuous and call m arkets; he refers
to these as asynchronous and synchronous markets,
respectively.
18See Hahn (1984), Negishi (1962), Beja and Hakansson
(1977), as well as the references therein.
19A continuous m arket cannot be viewed as a continuum of
in fin ite sim a lly lived call m arkets. C learing supply and de-

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Most microeconomic models assume call mar
kets. In a Walrasian tatonnement model, for ex
ample, an auctioneer calls out a series of prices
and receives buy and sell orders at each price.
When a price is found for which the quantities
supplied and demanded are equal, all transactions
are consummated at that price. Interestingly
enough, Walras based this price discovery
model on the mechanics of the Paris Bourse.
Temporal consolidation can affect the perfor
mance of a market. Theoretical work indicates
how continuous trading can alter allocations,
the process of price discovery and even the ulti
mate equilibrium price.18 The basic thrust of
these arguments is that, with continuous trading,
earlier transactions satisfy some consumers and
producers, causing shifts in supply and demand
that affect prices for later transactions. As a
result, the Pareto-efficiency characteristic of
Walrasian equilibria does not necessarily obtain
in continuous markets.19
On the other hand, the periodic batching of
orders that occurs in a call market also has dis
advantages. The difference in time between ord
er placement and execution can impose real
costs on investors. A recurring argument in the
literature is the willingness of investors to pay
more — a liquidity premium — for the ability to
trade immediately. Similarly, periodic calls delay
any information conveyed by prices until the
time of the call, introducing price uncertainty in
the period between the calls.
In sum, a trade-off exists between the allocational efficiency of the nearly Walrasian call
market system and the informational efficiency
and immediacy of the continuous market sys
tem.20 It is not clear whether the microstruc
ture of the foreign exchange market represents
a globally optimal balance of these relative admand in each such call m arket would require an infinite
trading volum e over the course of a day. Cohen and
Schw artz (1989) recom m end an e lectronic order-routing
system for the stock exchanges, to fa cilita te the placem ent
and revision o f orders. T his would encourage additional
trading volum e, m aking m ore frequent calls feasible.
20See Stoll (1985), p. 72, and especially S chw artz (1988),
pp. 442-53, for a m ore thorough exposition o f the pros and
cons of tem poral consolidation. Interm ediate arrangem ents
are also possible. For exam ple, Schw artz argues that
m any of the problem s caused by infrequent batching in a
call m arket m ig ht be overcom e by expanding access to
the m arket with co m p u te r technology, w hereby the in
creased num ber of traders w ould allow for m ore frequent
calls.

vantages. A persistent deviation from optimality
might be explained, for example, by arguing
that the allocational benefits of a call market
system are a public good.

Communication o f Prices
The terms "open-bid” and "limit-book” refer to
ways in which price information is communi
cated. In an open-bid market — the open outcry
system on the futures exchanges, for example
— offers to buy or sell at a specified price are
announced to all agents in the market. At the
opposite extreme, in a sealed-bid market, orders
are known only to the entity placing the order
and perhaps to a disinterested auctioneer.
Direct trading in foreign exchange approxi
mates the standard open-bid structure. The
salient difference between the foreign exchange
market and the standard arrangement is the
bilateral pairing of participants in the foreign
exchange market. In principle, any participant
can contact a market-maker at any time for a
price quote. The bilateral nature of such con
tacts and the time consumed by each contact
together imply, however, that all participants
cannot be simultaneously informed of the cur
rent quotes of a market-maker. This practical
constraint on the dissemination of price infor
mation is significant: it introduces the possibility
of genuine arbitrage, that is, of finding two
market-makers whose current bid-ask spreads
do not overlap.
The limit order book, which is used by both
foreign exchange brokers and stock exchange
specialists, is another intermediate form of price
communication. Although it would be possible
in principle for foreign exchange brokerage
books to be fu lly open fo r pu blic inspection, in
practice only certain orders — namely, the best
bid and ask on each book — are revealed to
market-makers, while the others remain con
cealed. As in the direct market, market-makers
must contact brokers bilaterally to get these "in
side spreads.” Knowledge of the concealed limit
orders would be of speculative value to marketmakers, because an imbalanced book suggests
that large future price movements are more
likely in one direction than the other.
More generally, price communication is inti
mately related to the role of market-makers as

21This term is due to Dem setz (1968), p. 35. Tinic (1972),
p. 79, calls in “ liquidity se rvices.”

providers of "predictable immediacy.”21 Market
participants are willing to pay a liquidity pre
mium, usually embedded in a market-maker’s
spread, for the reduction in search costs im
plied by constant access to a counterparty. The
costs of "finding” the other side of a transaction
can be further broken down into the liquidity
concession, the cost o f communicating the in
formation and the cost of waiting for potential
counterparties to respond.22 Other things equal,
an efficient system o f price communication is
one that minimizes such transaction costs. While
the communication of price information is a
central function of securities markets, the fact
that the systems of price communication in the
foreign exchange market are not fully central
ized suggests that these systems do not represent
a cost-minimizing arrangement.

Structure o f Prices
The terms "double-auction” and "single-auction”
refer to the nature o f the prices quoted. In a
double-auction market, certain participants pro
vide prices on both sides of the market, that is,
both bid and ask prices. Participants providing
double-auction quotes upon demand are known
as market-makers, and they must have sufficient
capitalization to back up their quotes. In a single
auction market, prices are specified either to
buy or to sell, but not both. In the foreign ex
change market, market-makers provide double
auction prices, while brokers try to aggregate
single-auction quotes into tw o-w ay (inside)
spreads. A broker's book may occasionally be
empty on one or both sides. Rather than make
a market in such cases, the broker provides,
respectively, a single-auction quote or n on e at all.
Thus, whether double or single-auction prices
are quoted depends largely on w hether the
agent quoting prices is providing market-making
services or simply attempting to acquire (or sell)
the commodity. This issue is related to the
degree o f centralization in the market. The
absence of market-makers in a single-auction
market, together with the presence of search
costs, results in a tendency toward centraliza
tion of price information, thus facilitating the
search for a counterparty. Inversely, decentrali
zation of price information leads to a tendency

22See Logue (1975), p. 118.

NOVEMBER/DECEMBER 1991

toward double-auction prices, again to facilitate
the search for a counterparty.23

MODELING TRADERS’ REHAVIOR
The microstructure literature extends well be
yond a simple description of market institutions.
Modeling the behavior of market participants is
central to almost all discussions o f microstructure. Although numerous approaches to
such modeling have been taken, two common
concerns are of special interest. These are the
treatment of price information by market par
ticipants, and determination of the bid-ask spread.
The latter raises the interrelated issues of inven
tory and quantity transacted.

Price Expectations
Modeling the interpretation of price informa
tion is a crucial step in constructing microstructural models of price discovery.24 Many diverse
approaches have been taken in such modeling.
An almost universal simplification is to model
securities markets in partial equilibrium, so that
prices are not determined endogeneously in the
traditional general equilibrium sense. This allows
the modeler to focus on the microstructure's
finer details. Another common simplification is
to assume that agents ignore the impact o f their
own behavior on the market.25
Rather than explicitly model such forces as
general equilibrium or recursive beliefs, models
posit probability distributions that produce the
prices of orders in the market. Modelers have
included randomness at one or both of two lev
els, depending on their focus. First, order
prices can be generated by objective distribu
tions, that is, by stochastic processes exogenous
23Note that the converse does not appear to hold. T hat is,
centralization does not tend to elim inate double-auction
quoting. For exam ple, the NASDAQ system on the OTC
stock m arket centralizes price inform ation w hile still sup
porting num erous m arket-m akers for every stock.

24Notably, the term “ p rice ” is generally too inexact in a
m icrostructural context. One m ust often distinguish at a
m inim um between quoted prices, transaction prices and
equilibrium prices. There are also reservation prices,
m arket-clearing prices and closing prices (see Schwartz
(1988), chapter 9, for the d istinction between equilibrium
and clearing prices). If unspecified here, the intended defi
nition should be clear from the context.
25The alternative, w hich dates at least to Keynes' “ beauty
c o n test,” is recursive beliefs, in which an agent considers
the feedback of her own actions on the beliefs of others,
and thence how the behavior on the other agents m ight af
fect her own beliefs, etc. See Keynes (1936), p. 156. The
lim iting case— an infinite recursion of beliefs— presum es

FEDERAL RESERVE BANK OF ST. LOUIS

to the market. For example, there may be a
stochastic process that generates the “ tru e”
equilibrium price. Second, probability models of
participants’ subjective beliefs about prices can
be used. Conroy and Winkler, for example, at
tribute subjective normal price distributions to
market-makers, who use Bayesian updating to
learn about the prices of incoming limit orders.26
Objective processes can coexist with subjective
beliefs about those processes. Harsanyi suggests
a consistency requirement for the subjective
price distributions of multiple agents; these dis
tributions are each equated with a conditional
distribution of a single distribution known to all.27
Models can be further classified according to
how they relate supply and demand. In particu
lar, there are both models with single price
processes and with dual price processes. In dual
price models, purchase orders (whether market
or limit orders) are generated by one process,
while sale orders are generated by another.28
The salient point here is that purchase and sale
orders come from independent distributions.
This independence is especially clear in Conroy
and Winkler, where the distributional assump
tions are explicit; there, independence implies
that any sequence of buy orders, regardless of
their prices and quantities, has no effect on the
subjective probability of a sell order at any price.
Statistical independence implicitly restricts the
ways in which orders can be generated. Pur
chase and sale orders are somehow motivated
independently, although the cause o f this
separation is not always specified. Statistical in
dependence is not a necessary component of a
dual price process, however. Cohen, Maier,
Schwartz and Whitcomb (1981), for example, as
sume that actual market bid and ask prices are
extrem e inform ational and com putational resources on the
part of agents, and m odels based on it are usually intrac
table. Interm ediate approaches allow ing a finite degree of
recursion m ust som ehow ju stify the truncation of recursive
beliefs, just as the standard m odel of atom istic agents al
lows no beliefs about beliefs and is ju stifie d by an as
sum ption on the relative size of individual agents.
26See shaded insert on opposite page.
27See Harsanyi (1982), especially chapter 9, and the refer
ences therein. His consistency requirem ent identifies a
unique e q uilibrium for the game.
28A m arket order is an order to trade at the best price avail
able; a lim it ord e r specifies a price. These m odels
represent a strain of the literature that was pioneered by
Dem setz using straightforw ard supply and dem and sched
ules (see shaded insert on page 63). S im ila r approaches
were later taken by G arm an (1976), Am ihud and Mendelson (1980) and Conroy and W inkler (1981), am ong others.

Bayesian Learning of Price Inform ation
Conroy and Winkler (1981) developed a
Bayesian model of market-maker price expec
tations, which is outlined here. Consider an
expected-profit-maximizing, monopolistic
market-maker who faces streams o f buy and
sell limit orders from investors.1 All orders
are for a single round lot. Assume that the
market-maker believes that reservation prices
of buy orders, pd, are generated by a normal
distribution, Fd(pd:^d,od); reservation prices of
sell orders, ps, are generated by a second, in
dependent, normal distribution, Fs(ps:/is,os).
That is, the market-maker has two indepen
dent, normal, subjective price distributions
(with corresponding densities fd and fs). Fur
ther assume that the market-maker currently
holds his desired inventory level. How should
he set his spread?
The inventory condition implies that the
chosen bid and ask rates, B and A, must
satisfy the constraint, FS(B) = l - F d(A), so that
the expected change in inventory is zero.2
Given this constraint, the expected profit per
period is: E(tt) = (A -B ) FS(B) = (A -B ) ( l - F d(A)).
Maximizing this over B and A yields: B* =
M - os<D(B')/0(B') and A* = M + odO(A')/<£(A'),
where M - (od^s+ osfid)/(od+ o5), B' = (B-pts)/os,
A ' = (A -/^d)/od, and <£(•) and 0(0 are the stan
dard normal density and distribution func
tions. It can be shown that this optimal
spread shrinks (i.e., A * - B * decreases), ceteris
paribus, as the subjective variances, os and od
decrease.
The important aspect of this study is that it
provides an explicit mathematical model for a
market-maker’s interpretation o f price infor
mation. The market-maker is assumed to
behave in a Bayesian fashion, using the
observed prices on incoming limit orders to
'C o n ro y and W in kle r (1981) also consider a risk-averse
m arket-m aker and the inform ation conveyed by a m ar
ket order, w hich does not specify a price. They do not
incorporate the im pact of inventory on p ricing, nor do
they generalize beyond the unrealistic assum ption of
norm ally distributed prices.

Profit Per Pair of Trades and
Expected Number of Trades
Per Unit Time
f d(p„)

Profit per pair
of trades

Expected num ber
of sell trades

*1
N— Expected num ber
of buy trades

refine the parameters o f his subjective
distributions. For example, assume that the
market-maker views purchase prices as com
ing from a normal distribution gd(pd:^d,od), but
is unsure about the mean of this distribution.
Represent this uncertainty by a normal prior
density h'(^d:m',v') over the possible values
for the mean, ptd. Given this, the marginal
subjective density over the prices of incoming
limit orders, fd(pd) = Jgd(pd)’h'(^d), is normal
with mean m' and variance (od2+ v '2). Follow
ing a sample of n buy orders with mean
price m, the market-maker is able to refine
his subjective distribution of the mean. The
posterior parameters o f h"(^d:m ",v") are m "
= (m'/v'2+ nm/od2)/(l/v'2 + n/od2) and v " =
l/(l/v'2 + n/od2). The upshot of this refined es
timate is that the variance of the marginal
subjective price density, fd(p), is now smaller,
and the market-maker's optimal spread,
(B*, A*), is narrower.
the interval from B to A, and the inventory constraint is
satisfied w hen the two shaded ta ils have equal area.
T heir optim ization problem is sim ilar in sp irit to that of
Allen (1977), although the latter does not consider
learning.

2T his is depicted in the figure above, w here price is on
the horizontal axis, and the relative frequency of orders
is on the vertical axis. The m arket-m aker’s spread is

NOVEMBER/DECEMBER 1991

independent Poisson processes and give inves
tors joint subjective distributions over those
prices. For the latter distributions, probabilistic
independence of bid and ask prices is not ex
plicitly required. Black (1989) models quantities
(independent o f prices) of market orders. Quan
tities supplied and demanded are drawn from
different distributions, but the distributions are
constrained to have the same mean. Garbade
(1978), on the other hand, assumes a single,
unknown and fixed equilibrium price, around
which market-makers set their spreads. Incom
ing buy and sell orders arrive via random
processes whose mean arrival rates depend on
the difference between the quoted bid (or ask)
price and the exogenous equilibrium price and,
thus, are not independent.
The most common alternative to separate pur
chase and sale processes is to model prices as
some function of a single scalar process. This
approach is in the spirit of the efficient markets
literature, which posits a unique value for a
security conditional on the available informa
tion. Ross (1987) points out that this approach
can be regarded conceptually as a special case
of the dual price process, with supply and de
mand infinitely elastic at a common price. Many
authors reveal their theoretical roots by using
terminology drawn from the literature on effi
cient markets. Thus, for example, Barnea des
cribes a stock’s "intrinsic value,” which follows a
random walk.29 Similarly, Copeland and Galai
posit a "'true' underlying asset value ... known
(ex ante) to all market participants.”30 In con
trast, Garbade’s (1978) exogenous equilibrium
price is unknown.
It is possible to extend the single price ap
proach beyond the efficient markets tradition
by modeling the value of a security subjectively
rather than as an objective fact. Glosten and
Milgrom (1985), for example, begin with an ex
ogenous random value representing the consen
sus value of a stock given all public information.
Investors do not act on this exogenous value
directly; instead, they act on their expectation
of it, conditional on their information set. Ho
and Stoll personalize price expectations in a
similar fashion:31

29See Barnea (1974), pp. 512-14.
30See Copeland and Galai (1983), p. 1458.
31See Ho and Stoll (1981), p. 48. For a sim ilar exam ple, see
Stoll (1978), especially p. 1136.

FEDERAL RESERVE BANK OF ST. LOUIS

We take the dealer's opinion of the "true’’ price of
the stock to be exogenously determined by his in
formation set and ask how the dealer prices rela
tive to his "true” price...
This subjectivization of the pricing process is
significant, because it allows for heterogeneous
expectations and thus for more realistic model
ing of price discovery.
Research into the microstructure o f the for
eign exchange market should presume such het
erogeneity among market-makers. There are
numerous market-makers for foreign exchange:
The Federal Reserve Bank of New York (FRB-NY)
(1989a) lists 162 dealing institutions in the U.S.
interbank market. There would be little point in
such superfluity if all market-makers were iden
tical. Furthermore, it is well known that “taking
a view/’ that is, speculating on future prices, is
routine for many participants.32 To omit this
heterogeneity from a model is to ignore an im
portant characteristic of the market.
The large proportion o f market-makers in the
foreign exchange market has another important
modeling implication. It implies that a single
price process is more appropriate as a theoreti
cal representation of agents’ expectations. Market-makers consistently face other market-makers,
who can hold positive or negative inventories of
foreign currency with equal ease. A quote that
is “o ff the market” on the high side will be hit
(i.e., traded upon) just as surely as a quote that
is o ff on the low side. This is also true of cus
tomers, who normally enter the market with a
predilection to either buy or sell. As Burnham
notes:33
The customer knows that if the first marketmaker
is too far off the market price, he can unexpected
ly take the other side of the quote and resell the
position to a second marketmaker.
The point is that the market-maker must expect
to be penalized for underestimating as well as
overestimating his counterparty’s valuation of
the currency. From the perspective of the mar
ket-maker, who quotes a spread and observes a
response, the forces determining short-run ef
fective demand and supply are not merely re
lated, but indistinguishable.

32See, for exam ple, Kubarych (1983), p. 29, or Burnham
(1991), p. 139.
33See Burnham (1991), p. 136.

Dealer Services and the Bid-Ask Spread
Traditional wisdom refers to the
bid-ask spread as the “jobber’s
turn/’ suggesting that it provides
compensation to the dealer for the
provision of services.1 Demsetz
(1968) formalized this rationale for
the spread, defining the particular
service provided as “predictable im
mediacy” and offering a simple
model to describe the spread.

Market Buy and Sell Curves with and
without the Provision of Immediacy
Price

Consider a continuous market
with aggregate supply (sell) and de
mand (buy) schedules, S and B, for
a security (see figure at right). In
an idealized world, investors would
come together simultaneously, and
the market would clear at price P*
and quantity Q*. In this market
place, however, such coordination
o f trading is impossible. By assump
tion, the market is continuous, and
there is no mechanism (e.g., a limit
order book) for holding orders
over time. Thus, S and B do not
represent standard static supply
and demand schedules, but rather time rates
of supply and demand. At any given instant,
there may be no orders on either side.
Instead, we introduce a monopolistic mar
ket-maker who allows the trading to occur by
standing in as a counterparty to all trades. In
the process, he provides a service to investors
that Demsetz labels “predictable immediacy.”
The market-maker knows the aggregate sup
ply and demand propensities. The supply and
demand curves that he presents to the public,
S' and B', however, are both shifted leftward.

Investor purchases clear for price Pa, at the
intersection o f the market demand schedule,
B, with the market-maker’s supply schedule,
S'. Similarly, investor sales clear at the inter
section o f S and B', for price Pb. The differ
ences: Pa- P * and P * - P bare liquidity premia.
In the figure, the quantities, Q r, purchased
and sold by the market-maker happen to be
equal, so that no market-maker inventory is
accumulated. His profit thus equals QT(Pa- P b);
this is th e "jo b b er's tu rn .”

1See, for exam ple, Keynes (1936), p. 158, or Stigler
(1964), p. 129.

A market-maker's constant contact with other
well-capitalized market-makers implies that this
is not a theoretical fine point. In the words of
one market-maker:34
Ninety percent of what we do is based on percep
tion. It doesn’t matter if that perception is right or

wrong or real. It only matters that other people in
the market believe it. I may know it’s crazy. I may
think it’s wrong. But I lose my shirt bv ignoring it.
In other words, as a direct implication of their
readiness to buy or sell, market-makers must
strive first to achieve a price consensus. The im-

34Jam es Hohorst, as quoted by M ossberg (1988), p. 29R.
Mr. Hohorst directed foreign exchange trading in North
A m erica for M anufacturers Hanover.

NOVEMBER/DECEMBER 1991

perative o f arbitrage avoidance must be re
garded as the first priority in individual marketmaker pricing, to which all other factors (e.g.,
purchasing power parity) must be subordinated.

Market-m akers’ Bid-Ask Spreads
The bid-ask spread has attracted considerable
interest in the literature on market microstructure. The complexity of modeling the spread is
largely because it requires incorporating a sub
stantial amount of institutional detail. At a facile
theoretical level, a market-maker's spread appears
to be a direct violation of the law of one price,
since it assigns tw o prices to the same com
modity. Several explanations have been offered
to resolve this seeming inconsistency. They can
be roughly categorized as involving the cost of
dealer services, the cost of adverse selection and
the cost o f holding inventory.35
The dealer services argument can be traced
back at least as far as Stigler (1964), who argues
that stock exchange specialists charge a "job
ber’s turn” as compensation for the costs of act
ing as a specialist. The analysis o f dealer services
was formalized bv Demsetz (1968), who identi
fied "predictable immediacy” as the particular
service for which investors are willing to pay.
This identification hints at the complex question
of what liquidity is and where it comes from. In
a busy market, liquidity is a public good: a con
tinuous stream of buyers and sellers generates
predictable immediacy as a by-product of their
trading.
The determinants o f the level of compensation
are themselves a topic of debate. Stigler argues
that, because centralization of exchange limits
fixed costs and aggregates separate transaction
orders into less risky actuarial order flows, it
implies economies of scale and thus a natural
monopoly for market-making.36 Smidt (1971)
counters that barriers to entry among NYSE
35This is essentially the sam e taxonom y as provided by Barnea and Logue (1975), although they use the term s
“ liquidity th e ory,” “ adversary th e o ry,” and “ dynam ic
price/inventory adjustm ent th e o ry,” respectively.
36See S tigler (1964), p. 129.
37See Sm idt (1971), p. 64.
38For exam ple, in the context of the OTC stock m arket, Benston and Hagerm an (1974), p. 362, conjecture that, “ deal
ers may face positively sloped m arginal cost curves which
shift down as industry o utput in creases.” The idea is that
m arket-m aking per se is not a natural m onopoly, even

FEDERAL RESERVE BANK OF ST. LOUIS

specialists allow them to exact monopoly rents
from other investors. In his view, the natural
monopoly argument, while used as an apology
for barriers to entry, remains unsupported em
pirically: “There is no empirical evidence to sup
port the proposition that [market-making] is, in
fact, a natural monopoly.”37 Indeed, if marketmaking is a natural monopoly, barriers to entry
should be unnecessary.
The foreign exchange market has no apparent
barriers to entry other than the need for suffi
cient capitalization. It also has no apparent bar
riers to exit. The market supports a large and
increasing number o f competing market-makers.
Unless it can be shown that there is some sub
tle restriction in the foreign exchange market
that prevents consolidation of the market-making
function, one must conclude that market-making
per se is not a natural monopoly.38 The multi
tude of market-makers also implies that they
cannot earn monopoly rents by embedding a
premium fo r predictable immediacy in the
spread, although the spread may still cover the
costs of processing orders.
Other research suggests that a market-maker’s
job is m ore complex than the m ere sale o f
counterparty services. A second explanation for
the bid-ask spread — adverse selection — can
be traced to Bagehot (1971). He starts with
“ liquidity-motivated transactors” who pay the
market-maker the price o f the spread in ex
change fo r the service o f predictable immedi
acy. The market-maker also confronts traders
who have inside information, however, and who
can therefore speculate profitably at the expense
of the market-maker.39 The market-maker must
charge everyone a wider spread to compensate
for losses to the information-motivated traders.
Because of the relatively abstract nature of
currencies as commodities, it is difficult to con
struct examples o f “ inside” inform ation on
foreign exchange rates. One exception is money
supply announcements, which, if known before
though the industry as a whole experiences econom ies of
scale. Ham ilton (1976) also addresses th e natural m onopo
ly question; Reinganum (1990) provides evidence on li
qu idity prem ia for NYSE vs. NASDAQ stocks.
39This situation is called adverse selection, because, in a
m arket with com peting m arket-m akers, the one who gets
the in sider’s business is a loser rather than a winner.
Bagehot also posits a th ird class of investors, who only
th in k they have inside inform ation; th e y speculate, but lose
on average, and are in d istinguishable to the m arket-m aker
from the liquidity-m otivated traders.

publicly distributed, might provide a basis for
profitable speculation. Another form of informa
tion that can be construed as inside information
is knowledge of an arbitrage opportunity. Con
sider a hypothetical market in which there are
numerous decentralized market-makers who do
not quote spreads, but single prices at which
they are willing both to buy and sell. Unless
there were a perfect consensus among the mar
ket-makers on the value of the foreign currency,
all of them would be vulnerable to arbitrage. A
decentralized market makes a perfect consensus
difficult to achieve. Without centralizing price
information, it is impossible to know if no arbi
trage opportunities exist. A bid-ask spread, in
contrast, allows a market-maker to include an
error tolerance in her prices, thus facilitating a
price consensus: it is easier to get bid-ask
spreads to overlap than to get scalar prices to
coincide. The spread also provides the m ar
ket-maker with some degree o f protection
from adverse selection in the form of arbitrage.
The bid-ask spread is also affected by invento
ry considerations. This idea dates back at least
as far as Barnea and Logue (19 75).40 The notion
of a desired inventory level for the marketmaker underlies all o f these models. In the
simplest case, the desired level is set at zero,
and a constant spread is shifted up and down
on a price scale to equalize the probability of
receiving a purchase order with that of receiv
ing a sale order. The result is that the expected
change in inventory is always equal to zero, and
(with all trades for one round lot) the inventory
level follows a simple random walk.
An undesirable implication of random-walk
models of inventory is the inevitable bankruptcy
of the market-maker. Finite capitalization levels
for market-makers impose upper and lower
bounds on allowable inventories. Because inven
tory follows a random walk, with probability
one it will reach either its upper or lower bound
in a finite number of trades.41 The dynamic op
timization models of Bradfield (1979), Amihud
and Mendelson (1980) and Ho and Stoll (1981)
resolve this problem. They conclude that a
market-maker, optimizing his bid and ask prices
40Barnea and Logue a ttribute it to Sm idt (1971), although
S m id t’s paper does not explicitly develop the connection
between the m arket-m aker’s inventory and his spread. For
mal m odels of the relationship between inventories and
spreads can be found in Stoll (1978), Am ihud and M endel
son (1980), Ho and Stoll (1981) and Sirri (1989), am ong
others.
41See, for exam ple, Ross (1983), pp. 106-07.

over time in the face of a stochastic order flow,
will shift both bid and ask rates downward (up
ward) and increase the width of the spread when
a positive (negative) inventory has accumulated.42
We should expect two of these three ration
ales for the spread to apply to market-makers’
bid-ask spreads in the foreign exchange market.
Because there are numerous market-makers,
competition should eliminate their ability to earn
monopoly rents by charging a premium for pre
dictable immediacy per se. The adverse selec
tion argument does apply in the foreign ex
change market, however, since the spread allows
market-makers some protection against arbit
rage opportunities. Arbitrage opportunities can
be construed as a form of inside information in
a market where price information is not cen
tralized. In accordance with the dynamic optimi
zation models, a market-maker’s inventory level
should affect the spread, widening and shifting
it as inventories accumulate.

B rok ers’ Spreads
So far, the discussion of the bid-ask spread
has focused on models in which bid and ask
prices are set by individual market-makers. The
dual role o f the stock exchange specialist sug
gests that this is only part of the story. Spreads
are produced in two fundamentally different
ways. It is only when limit orders are sparse
that a NYSE specialist must step in as a marketmaker to provide an “orderly market.”43 When
limit order volume is sufficient, the specialist
acts as a broker, accounting for incoming limit
orders on the limit order book, and pairing
market orders against them. Cohen, Maier,
Schwartz and Whitcomb (1979) note that inade
quate attention has been given to the fact that
not all prices are market-maker spreads. The
market often makes itself without specialist as
sistance, through the aggregation o f limit ord
ers on the book.
The foreign exchange market differs from the
NYSE in that the market-making and brokerage
roles are separated: market-makers do not act
as brokers, and brokers do not make markets.
42See shaded insert on page 66.
43The NYSE defines this role in rule 104: “ the specialist
should m aintain a continuous m arket w ith price continuity
and close bid and asked prices, and m inim ize the e ffect of
tem porary d isparity between public supply and d em and.”
See Leffler and Farwell (1963), pp. 211-12.

NOVEMBER/DECEMBER 1991

Dynamic Price-Inventory Adjustment Models
Amihud and Mendelson (1980, 1982) pro
vide a model of market-maker spread-setting
that takes inventory into account. Assume
that a market-maker faces order flows of buy
and sell market orders that arrive according
to independent Poisson processes. The buy
and sell arrival rates (i.e., process intensities),
d and s, respectively, depend on the ask and
bid prices, P., and Pb, that the market-maker
quotes: d = D(P.,) and s = S(P1}). Denote the
inventory level by k € {-Z ,...,A }, where X
and A are the largest allowable short and
long positions, respectively. Let dkand skde
note the order arrival rates when prices are
set as functions of the inventory level: dk =
D(Pa(k)) and sk = S(Ph(k)).

' <dk+ sk)

= dk • Pa(k) - sk • Ph(k).
The market-maker's objective is to maximize
the expected profit per unit time, given by:

„ =

0 kQ(k).

k= - X

Where 0 is the probability of being at inven
tory level k. The solution to this optimization
problem gives the values for Pa(k) and Pb(k),
which are depicted in the figure below. The
market-maker controls inventory by adjusting
prices up (down) to make an investor sale
(purchase) more likely when inventory is low
(high). The spread must widen as the invento
ry nears its bounds, in order to avoid the
problem o f a random walk for inventory; at
the extremes, d x = sA = 0.

The expected sojourn at k (i.e., the time un
til an order arrives) is given by the Poisson
processes known as l/(dk+ sk). The probability
that the next order will be a buy order is
dk/(dk+ sk), and the probability that it will be a
sell order is sk/(dk+ sk). Thus, the expected cash
flow per unit time at position k is given bv:

Optimal Prices and Bid-Ask Spread
as a Function of Inventory Position

Price

Therefore, it is even more appropriate to model
brokered spreads as determined in a fundamen
tally different way from market-maker spreads.
The separation of roles also has other implica
tions for modeling foreign exchange brokerage.
A brokered spread is the combination of the
best bid and best ask, received by the broker as

FEDERAL RESERVE BANK OF ST. LOUIS

k -1

In v e n to ry
Po sitio n

separate limit orders. This arrangement might
be modeled as a pair of extreme order statistics
from independent distributions of purchase and
sale limit orders. The distribution of these statis
tics would have to he conditional on limit order
volume and on the fact that the best ask must
always exceed the best bid, since crossing ord

ers transact immediately and are removed from
the hook.44 Perhaps because of its complexity,
such a derivation has not been attempted.
Cohen, Maier, Schwartz and Whitcomb (1979)
model limit orders as generated by ' vawl” distri
butions. These distributions satisfy three heu
ristics for the incentives of investors placing
limit orders.45 The heuristics are motivated by a
notion of the centralized exchange as a market
for immediacy; placers of limit orders produce
immediacy, and placers of market orders con
sume it. This relationship between limit and
market orders is formalized in Cohen, Maier,
Schwartz and Whitcomb (1981), where each half
of the brokered spread is assumed to be gener
ated by a compound Poisson process. A mini
mum brokered spread results: if the limit order’s
bid (ask) price is sufficiently close to the special
ist’s ask (bid), the benefit to the investor of being
able to specify the price of a limit order is over
whelmed by the cost of foregone immediacy.
Because models of the informational content
of brokered spreads are few, the literature
offers little guidance in modeling brokered
quotes in the foreign exchange market. The
yawl distribution is the only explicit distribu
tional form for brokered spreads in the litera
ture. Unfortunately, its heuristic basis cannot be
transferred directly to the foreign exchange
market, because market-makers there differ
from stock market investors. Indeed, this may
be an instance in which the foreign exchange
market informs microstructure theory rather
than the other way around. The extant ap
proaches to brokerage treat it as a service
facilitating predictable immediacy. This aspect of
brokerage is redundant in the foreign exchange
market, because of the multitude of marketmakers, each providing immediacy. This red u n
dancy suggests instead that foreign exchange
brokerage serves some other function.
One motive for trading through a foreign ex
change broker is to maintain anonymity — the
name of the bank placing a limit order is not
revealed unless a deal is consummated and then
only to the counterparty.46 Anonymity is valu
able, because revealing a need to buy or sell a

44An order statistic is defined as follows: the sam ple realiza
tions of a fin ite num ber of independent random variables
are ranked in increasing order, and the kth order statistic
is the kth num ber in that list. For the foreign exchange
m arket, the m odeling is still m ore com plex, since brokers
com pare books am ongst them selves in the sense that in
com ing orders can cross against any book.

currency puts a market-maker at a bargaining
disadvantage. In addition, anonymity can help
pair market-makers who ordinarily would not
contact each other directly. These issues have
not been explored at a theoretical level. Until an
adequate microstructural model of the strategic
benefits of anonymity is developed, the theoreti
cal understanding of foreign exchange broker
age will be limited.

CONCLUSIONS
Students of the foreign exchange market can
draw several lessons from the literature on
market microstructure. The most fundamental
of these is that the institutional details of ex
change in a market can affect all aspects —
price, allocational, informational and operational
— of the market’s efficiency. A multitude of
market-makers who can provide liquidity, or
predictable immediacy, arises in response to the
decentralization of the market. As a result,
search costs are reduced relative to a world
without market-makers, because finding one of
many market-makers amounts to finding a
counterparty. Brokerage also reduces search
costs by achieving a degree of centralization in
price information.
An unanswered question is why the specific
combination of trading structures characteristic
of the foreign exchange market — a decentral
ized, open-book, direct arrangement and a
quasi-centralized, limit-book, brokered arrange
ment — should coexist. Apparently, each struc
ture has relative advantages, but a full analysis
of these advantages is lacking. Is there a single
microstructure that would combine the relative
advantages of the direct and brokered arrange
ments? Put another way, why does the microstructure of the foreign exchange market differ
from that of the stock exchanges, the futures
pits and the OTC stock market? Answering these
questions will require a fuller specification of
the objectives of a trading system and a better
understanding of the impact of microstructural
arrangements on those goals.
These issues provide a motive for deeper in
vestigation of the behavior o f the foreign ex-

45The yawl distribution, named for its resem blance to a sail
boat, is a probability d istribution contrived for m odeling the
generation o f buy (or sell) lim it orders. See Cohen, Maier,
Schwartz and W hitcom b (1979, 1983, 1986) for details.
46See Kubarych (1983), p. 16, Burnham (1991), p. 141, and
Federal Reserve Bank of New York (1989b), p. 41-3.

NOVEMBER/DECEMBER 1991

change market and its participants. Marketmakers are the crucial element: they provide all
transaction prices in the market and are in
volved in at least one side of every deal. The
microstructure literature has developed numer
ous models of the interpretation and setting of
prices by traders. The diversity of expectations
models used in the literature illustrates the im
portance of tailoring such models to the specific
environment confronted by market participants.
Given that a foreign exchange market-maker’s
double-auction quote can be hit on either side
(bid or ask) with equal ease, he must try to
maneuver his spread to bracket the market’s
consensus valuation of the foreign currency. In
other words, suppliers and demanders of cur
rency are indistinguishable to the market-maker
ex ante. The inability to separate the forces de
termining effective demand from those de
termining effective supply in the very short run
imply that a single-price expectations process
(rather than a dual-price process) is appropriate
in modeling market-makers in the foreign ex
change market.
A market-maker’s bid-ask spread serves several
purposes. Competition among market-makers in
the foreign exchange market implies that they
should be unable to charge a monopoly premi
um for the service of predictable immediacy. In
stead, the spread obviates the need for perfect
price consensus by giving the market-maker
some protection from arbitrageurs with superior
price information. While arbitrage avoidance
must be considered a primary goal in setting a
market-maker’s bid and ask quotes, the spread
provides flexibility elsewhere. Just as a rbitrage
avoidance is concerned with accurately estimat
ing current prices, speculation is concerned
with estimating future prices. By changing in
size and shifting up or down, the spread can
control stochastically the market-maker’s foreign
currency inventory in the face of random order
flows. Systematic empirical study of the effect
of inventories on market-makers’ spreads is still
needed, however.
The brokered spread is less well understood
than the market-maker’s spread, and certain
areas are ripe for further research. Theoretical
models of brokered spreads are few. The exist
ing rationales for brokerage maintain that it
provides liquidity services. In the foreign ex
change market, however, numerous marketmakers make the liquidity services provided by
brokerage superfluous. Descriptions of the for
eign exchange market suggest instead that

FEDERAL RESERVE BANK OF ST. LOUIS

anonymity is an important motive for trading in
the brokered market. Yet the strategic value of
anonymity in foreign exchange quoting is not
well understood at a theoretical level. In addi
tion, there is not a clear understanding of the
differences in price information between a
market-maker’s spread and a broker’s spread;
this too remains a topic for future research.
From a broader perspective, a better under
standing of institutional choice and change as
regards securities market microstructure is
necessary. Most microstructural research has
been devoted to analyzing the impact of microstructural factors on important economic vari
ables, such as price and allocation. Relativ ely
little attention has been paid to the effect of
economic factors on the choice of an institution
al microstructure.

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FEDERAL RESERVE BANK OF ST. LOUIS
REVIEW INDEX 1991

JANUARY/FEBRUARY

JULY/AUGUST

Ft. Alton Gilbert, “ Do Bank Holding Companies
Act as ‘Sources of Strength’ for Their Bank Sub
sidiaries?”

Cletus C. Coughlin, “ U.S. Trade-Remedy Laws:
Do They Facilitate or Hinder Trade?”

Cletus C. Coughlin, “ A C onsum er’s Guide to
Regional Economic M ultipliers”
Keith M. Carlson, The Future of Social Security:
An Update”
James B. Bullard, Learning, Rational Expecta
tions and Policy: A Summary of Recent
Research”

MARCH/APRIL
John A. Tatom, “ Should Government Spending
on Capital Goods Be Raised?”
Alison Butler, “ A Case for a Bilateral Trade
Deficit”
Mark D. Flood, “ An Introduction to Complete
Markets”
David A. Dickey, Dennis W. Jansen and Daniel L.
Thornton, “ A Primer on Cointegration with an
Application to Money and Incom e”

Jeffrey D. Karrenbrock, “ The Behavior of Retail
Gasoline Prices: Symmetric Or Not?”
M ichael T. Belongia, “ Monetary Policy and the
Farm/Nonfarm Price Ratio: A Comparison of Ef
fects in Alternative M odels”
Michelle R. Garfinkel and Daniel L. Thornton,
“ The M ultiplier Approach to the Money Supply
Process: A Precautionary Note”
Cletus C. Coughlin and Thomas B. Mandelbaum,
“ Measuring State Exports: Is There a Better
W ay?”

SEPTEMBER/OCTOBER
Keith M. Carlson, “ The U.S. Balance Sheet:
What Is It and W hat Does It Tell Us?”
Piyu Yue and Robert Fluri, “ Divisia Monetary Ser
vices Indexes for Switzerland: Are They Useful
for Monetary Targeting?”
Steven Russell, “ The U.S. Currency System: A
Historical Perspective”

NOVEMBER/DECEMBER
MAY/JUNE
John A. Tatom, “ Public Capital and Private Sec
tor Perform ance”
R. Alton Gilbert, “ Supervision of Undercapitalized
Banks: Is There a Case for Change?”
James B. Bullard, “ The FOMC in 1990: Onset of
Recession”
Allan H. Meltzer, “ U.S. Policy in the Bretton
Woods Era”

FEDERAL RESERVE BANK OF ST. LOUIS

John A. Tatom, “ The 1990 Oil Price Hike in Per
spective”
Mark D. Flood, “ M icrostructure Theory and the
Foreign Exchange M arket”
Piyu Yue, “ A M icroeconom ic Approach to Es
tim ating Money Demand: The Asym ptotically
Ideal M odel”
Michelle R. Garfinkel and Daniel L. Thornton, “ Al
ternative Measures of the Monetary Base: W hat
Are the Differences and Are They Im portant?”

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Full text of Review (Federal Reserve Bank of St. Louis) : November/December 1991

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