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________ Review________
Vol. 68, No. 7




August/September 1986

5 The Discount Rate and Market Interest
Rates: Theory and Evidence
22 A M icroeconom ic System-Wide
Approach to the Estim ation o f the
Demand for Money

T h e Review is p u b lis h e d 10 tim e s p e r y e a r by th e R e se a rch a n d P u b lic In fo rm a tio n D e p a rtm e n t o f
th e F e d e ra l Reserve R a n k o f St. Lo uis. S in g le-cop y s u b s c rip tio n s a re availab le to th e p u b lic f r e e o f
charge. M a il req u ests f o r s u b s c rip tio n s , ba ck issues, o r a d d re s s ch a n g e s to: R e se a rch a n d P u b lic
In fo rm a tio n D e p a rtm e n t, F e d e ra l Reserve R a n k o f St. Louis, P.O. Rop 442, St. Lo uis, M is s o u r i 63166.
T h e views e x p re sse d a re th o se o f th e in d iv id u a l a u th o rs a n d d o n o t n e ce ssa rily re fle c t o ffic ia l
p o s itio n s o f th e F e d e ra l R eserve R a n k o f St. L o u is o r th e F e d e ra l Reserve System. A r t ic le s h e re in m ay
be r e p r in te d p r o v id e d th e s o u rc e is cre d ite d . Ple a se p ro v id e th e R ank's R e se a rch a n d P u b lic
In fo rm a tio n D e p a rtm e n t w ith a co p y o f r e p r in te d m aterial.




Federal Reserve Bank of St. Louis
Review
August/Septem ber 1986

In This Issue . • .




In the first article in this Review, “The D iscount Rate an d Market Interest Rates:
Theory and Evidence,” Daniel L. Th orn ton d iscu sses the theoretical links
betw een the Federal Reserve’s d iscou n t rate an d market interest rates and
p resents som e em pirical evidence on the extent of this link. He finds that, both in
theory an d p ractice, the direct relationship betw een the d iscou n t rate an d m oney
market rates is extrem ely weak. Consequently, any observed relationship betw een
these rates m ust be due to an exp ectation s effect o r to a ch an ge in Federal Reserve
behavior. If the latter is co rre ct, however, there should have been a stron ger
association betw een the d iscou n t rate and m oney m arket rates following the
Federal Reserve’s ch an ge in operating p ro ced u re in the fall of 1982. Th orn ton
finds, how ever, that, if anything, this relationship h as b eco m e w eaker.

In the seco n d article in this Review, "A M icroecon om ic System -W ide A pproach
to the Estim ation of the D em and for M oney,” Salam K. Fayyad d escribes h ow the
m icro eco n om ic system -w ide ap p roach to m on ey d em an d differs from th e usual
m oney d em an d specifications. Using a neoclassical utility function defined over
five expend iture categories, two of w hich are p resu m ed to cap tu re th e flow of
“m onetary services,” he d em o n strates how the m icro eco n o m ic system -w ide
ap p roach can be im plem ented. Fayyad th en exam ines in-sam ple p red iction s of
budget shares for exp en d itu res on m o n etaiy services an d the o th er expen d itu re
categories estim ated by this ap p ro ach over the 1/1969—
1/1985 period. His results
indicate that the m icro eco n om ic system -w ide ap p ro ach to m o n ey dem an d
estim ation yields p red iction s that closely track the actu al behavior of the flow of
m on etary services over this period.

3




FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

The Discount Rate and Market
Interest Rates: Theory and
Evidence
Daniel L. Thornton

T

A . HE relationship betw een the Federal Reserve’s
discou n t rate and m oney m arket interest rates c o n ­
tinues to be a topic of m u ch interest and even m ore
confusion. A significant nu m b er of m oney m arket an a­
lysts and som e in public service believe that the dis­
co u n t rate is an im portant tool through w hich the
Federal Reserve exerts its influence over the econ om y
— particularly m arket interest rates. This view ap ­
pears to have gathered strength from recen t evidence
that discoun t rate changes have a statistically signifi­
can t effect on m arket interest rates an d from the
presu m ed effects of a 1982 change in the Federal
Reserve’s operating p ro ced u re.1 Consequently, the
long-standing d iscrep an cy betw een w hat eco n om ic
th eoiy says about the relationship betw een the dis­
co u n t rate and market interest rates an d the view
am ong m any m oney m arket analysts ap p ears to have
b ecom e larger. The purpose of this article is to narrow
the gap by pointing out that, both in theoiy and in
p ractice, changes in the Federal Reseive’s d iscou n t
rate, p e r se, have essentially no effect on m arket inter­
est rates. At best they “signal’’ chan ges in the Federal
Reserve’s use of o th er m ore powerful tools of policy.
Any im pact of a discou n t rate ch an ge on market in ter­
est rates is due to changing exp ectatio n s o r to a
change in Federal Reserve operations following the
discount rate change.

Daniel L. Thornton is a senior economist at the Federal Resen/e Bank of
St. Louis. Rosemarie Mueller provided research assistance.
'See Thornton (1982) for a summary of some of the usual sources of
confusion; Thornton (1982), Sellon and Seibert (1982) and Smirlock
and Yawitz (1985) for empirical estimates of a change in the dis­
count rate on market interest rates; and Batten and Thornton (1984,
1985) and Hakkio and Pearce (1986) for empirical estimates of an
impact of a discount rate change on the foreign exchange market.




THE MARKET ANALYST’S VIEW
Figure 1 illustrates a com m on ly held view of the
relationship betw een a cu t in the d iscou n t rate and
the response of m arket interest rates; it show s the
hypothetical time path of market interest rates before
and after a hypothetical cu t in the Federal Reserve
discou n t rate at tim e t„, and it reflects the p ercep tion
that a cu t in the d isco u n t rate ca u ses m arket interest
rates to be perm an en tly low er than they otherw ise
w ould have been. This cau se-and-effect relationship is
p u rely qualitative. It is not cle a r w h e th e r a 1
p ercen tage-p oin t cu t in the discou n t rate will low er
market rates by 1 p ercen tage point o r only a few basis
points, it m erely is asserted that m arket rates will be
lower.
The view that the discou n t rate is preem inent in the
m oney m arket co n trasts sharply with e co n om ic th e­
ory and the p ercep tion of m any eco n om ists that the
discount rate is the least powerful of the Federal
Reseive’s tools for influencing the m oney stock and
interest rates. Before turning to this analysis in detail,
it is instructive to co n sid er som e casual evidence
against the idea that the d iscou n t rate is preem inent
in the m oney market. Chart 1 show s the th ree-m o n th
Treasury bill, federal funds an d d iscou n t rates weekly
for the period from O ctober 1982 to Ju n e 1986. W hat
do th ese data show about the effect of a d iscou n t rate
ch an ge on m arket interest rates? First, in a n u m b er of
instances, d iscou n t rate ch an ges are followed closely
by a leveling off of m arket interest rates o r by a m ove­
m ent in the opposite d irection. While this does not
rule out the possibility that m arket rates w ould have
been higher (lower) if the d iscou n t rate h ad n ot been
cu t (raised), it does suggest that the m arket analyst

5

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

view is not su p p o rted by a simple analysis of interest
rate behavior.
Second, nearly all discount rate ch an ges follow,
rath er than lead, m ovem ents in m arket interest rates
in the sam e direction.- It w ould seem that ch an ges in
m arket interest rates m otivate d iscoun t rate ch an ges
rath er than the reverse. F u rth erm ore, even w hen m ar­
ket rates declined (increased) following a d iscount
rate cu t (increase), it is particularly difficult to d eter­
m ine w h eth er m arket rates w ould have m oved in the
sam e or sim ilar fashion in the ab sen ce of a ch an g e in
the d iscou nt rate. While all of this is inconclusive, it
provides w eak and often co n trary evidence of a dis­
co u n t rate/m arket interest rate line of causation, and
provides little com fort to those w ho believe the view
illustrated by figure 1.

F ig u re 1

Hypothetical Response to a Discount Rate Cut

THE DISCOUNT RATE AND MARKET
RATES IN THEORY
B ecau se the interest rate is the price of credit, any
im pact of d isco u n t rate ch an ges on m arket interest
rates m ust com e via their effect on the supply of o r the
d em an d for credit. In this regard, th ree distinct —
though not n ecessarily m utually exclusive — effects of
a d iscou n t rate ch an ge can be identified. These are
illustrated in figure 2. Prior to the d iscou nt rate cut,
the credit m arket is in equilibrium at an interest rate of
R,,, co rresp on d in g to the intersection of the initial
supply and dem and curves, S„ and D„, respectively.

The Direct Effect
The first effect, called the direct (or substitution)
effect, cau ses a shift in the supply of credit. D iscount
w indow borrow ing is one m eth od depository institu­
tions use to adjust their reserve position. Alternatively,
they ca n buy federal funds o r sell governm ent secu ri­
ties directly in the m oney m arket.3 Since these altern a­
tives are close substitutes, the d em an d for borrow ed
reserves d ep en ds on the spread betw een m arket inter­
est rates, especially the federal funds rate, and the
d iscou n t rate. As the federal fu n d s-d iscount rate
spread increases, borrow ings from the Federal Re­
serve tend to increase and vice versa. Thus, the level of
d iscount w indow borrow ings usually is exp ressed as:
(1) Borr = a(Rf—R(l),

a > 0,

2
This is true of other periods as well; see Thornton (1982), p. 14.
depository institutions also can call in loans or carry the deficiency
over into the next reserve period. They rarely, if ever, use these
alternatives, however.

Digitized6for FRASER


w here Borr den otes the aggregate level of ind eb ted ­
ness of depository institutions to the Federal Reserve
and Rf and R(l denote the federal funds an d discount
rate, respectively.
To illustrate the direct effect of a ch an ge in the
discou n t rate on m arket interest rates, assu m e that the
discount rate is cut. In response, d ep ositoiy institu­
tions increase their borrow ings an d red u ce their use
of alternative so u rces of reserves. The in crease in
borrowings p ro d u ces an increase in the m on etary
base and, in turn, the supply of credit — illustrated in
figure 2 by a shift from S„ to S,. Thus, a d iscou n t rate cu t
has a direct effect, causing m arket interest rates to
decline from R„ to R,. The effect of an in crease in the
discount rate w ould be sym m etric.

The Announcement Effect
Additionally, discou n t rate ch an ges ca n have an
“an n ou n cem en t effect.” If a change in the discou n t
rate is interpreted as a “signal” that the Federal Re­
serve will alter its policy w ith resp ect to the grow th of
reserves and the m oney stock, the m arket m ay react in
anticipation of a policy ch an ge. A cu t in the discou n t
rate usually is thought to be a signal that the Federal
Reserve is going to p u rsu e an easier m on etary policy
so the m arket reacts in anticipation of Federal Reserve

AUGUST/SEPTEMBER 1986

FEDERAL RESERVE BANK OF ST. LOUIS

C h a rt 1

Selected Interest Rates

1982

1983

1984

open m arket operations that will increase the supply
of credit.4 Consequently, there is an im m ediate shift in
the supply of credit, relative to dem and, in an ticip a­
tion of further m onetary ease. If the an n ou n cem en t
effect o ccu rs, it is over and above the direct effect of a
discount rate change, and is illustrated by the shift
from S, to S, in figure 2:'

The Policy Effect
Finally, there could be a “policy effect” if the Federal
Reserve actually changes its policy and in creases the

"This is not the only possible interpretation for the market. See Batten
and Thornton (1984) and Smith (1963) for a discussion of this point.
5
This also could have been illustrated by a reduction in the demand
for credit, but was illustrated as a shift in supply to keep the figure
simple.




19 8 5

19 8 6

grow th rate of reserves. 1'his also can be illustrated by
the shift from S„ to S,. If the m arket co rrectly antici­
pates the direction and m agnitude of the policy effect,
market interest rates will rem ain p erm anently low er at
R2. Of course, this requires that the m ark et’s e x p e cta ­
tions be co rrect, both in term s of the actu al ch an ge in
Federal Reserve policy and in term s of the im p act of
that policy change on the market." As the Federal
Reserve p u rch ases m ore securities, sp ecu lators sell off
those acquired in anticipation of the policy ch an ge. If
the market overanticipates Federal Reserve actions,
however, m arket rates first will fall below an d then

6
This brief discussion gives rise to several issues not analyzed in this
paper, such as the effectiveness of policy and the credibility of the
central bank. For a general discussion of the credibility issue, see
Cukierman (1986).

7

FEDERAL RESERVE BANK OF ST. LOUIS

subsequently rise to th eir long-run equilibrium. F u r­
therm ore, if th e m ark et’s expectation s are in correct
an d Federal Reserve policy rem ains u nch an ged , inter­
est rates will rise back to R, — the only im p act of a
d iscou n t rate ch an ge w ould be the d irect effect.

AUGUST/SEPTEMBER 1986

F ig u re 2

Three Possible Effects o f a Discount Rate Cut on M arket Intere st Rates

DISCOUNT WINDOW BORROWINGS
AND THE FED’S OPERATING
PROCEDURE
Some have argued that the policy effect h as b ecom e
m ore im portant sin ce the O ctober 1982 ch an ge in the
Federal Reserve’s operating p ro ced u re. At that time,
the Board sw itched from a n onborrow ed reserve to a
borrow ed reserve operating p ro ced u re. It is now
widely believed that the Federal Reserve operates to
achieve a certain average level of borrow ed reseives
(called the initial borrow ing assum ption) over a given
tim e period.7 The m ech an ics of this operating p ro ce ­
dure can be illustrated by tracin g the reaction of the
Federal Reserve to an u n exp ected in crease in the
d em an d for reserves. O ther things u n chan ged , an in­
crease in the d em an d for reserves tend s to cau se both
borrow ings and the funds rate to rise, as depository
institutions attem p t to satisfy their d em an d for re ­
serves in the m on ey m arket and at the Federal Reserve
d iscou n t w indow . As borrow ings increase relative to
the borrow ing assum ption, the Fed in creases th e su p ­
ply of nonb orrow ed reserves via open m arket p u r­
ch ases of governm ent secu rities; in respon se, both
borrow ing an d the federal funds rate fall.
A cu t in the d iscou n t rate, not accom p an ied by a
ch an ge in the initial borrow ing assum ption, w orks
analogously. If the Federal Reserve cu ts the d iscou n t
rate, th e d em an d for borrow ed reseives will increase
at all levels of th e federal funds rate, cau sing b orrow ­
ings to in crease relative to the initial borrow ing a s­
sum ption. If the initial borrow ing assu m p tion is u n ­
ch an g ed , th e F ed m u st in crease th e supply of
nonborrow ed reserves through open m arket o p era­
tions until the federal funds rate h as declined by
enough to retu rn borrow ings to th e level of the bor­
rowing assum ption.
The above implies that equation 1 can be w ritten as:
(21 Borr* = a(Rf- R d
),
w here Borr* d en otes th e Federal Reserve's initial b o r­
row ing assum ption. Equation 2 implies a co n stan t
sp read betw een the federal funds an d d iscou n t rates.

7
For a discussion of this, see Roley (1986), Wallich (1984) and
Federal Reserve Bank of New York (1986).


8


Any ch an ge in the d iscou n t rate will be m a tch e d by an
equal change in the federal funds rate, providing th ere
is no co m p en satory ch an ge in th e borrow ing a s­
sum ption.
It should be em p h asized that it is not the d iscou n t
rate change p e r s e that affects m arket interest rates,
but the subsequent policy effect if the Fed eral Reserve
strictly ad h eres to an operating p ro ced u re th at a t­
tem p ts to m aintain the level of borrow ings assu m ed
by its cu rren t policy directive. If th e m arket perceives
this behavior, it cou ld also stren gth en an y a n n o u n ce ­
m ent effect.

The Importance o f the Liquidity Effect
All of the potential effects of a ch an ge in th e dis­
co u n t rate on m arket interest rates (but, in particu lar,
the policy effect) d ep en d on the so-called "liquidity
effect” — the ch an ge in interest rates asso ciated w ith
an u n an ticip ated in crease in the grow th rate of the
m on ey supply. W hile su ch an effect is w idely tou ted in
theoretical discussions, th ere is little em pirical evi­
d en ce to su p p ort it. Yet, w ithout a liquidity effect o r at
least the exp ectatio n of a liquidity effect, ch an g es in
the d iscou n t rate cou ld n ot have an im p act on a broad
sp ectru m of m arket interest rates*
8
This, of course, ignores the possible effect of changes in expecta­
tions of inflation on interest rates. See Brown and Santoni (1983),
Cagan and Gandolfi (1969) and Melvin (1983) for a review of the
direct evidence on the liquidity effect.

FEDERAL RESERVE BANK OF ST. LOUIS

Which Market Interest Rates?
M uch of the d iscussion thu s far has been carried
out in term s of the federal funds rate. In reality, there
are a large num ber of different rates: the: rates on
federal funds, T reasury bills, notes an d bonds, co m ­
m ercial bank loans, m ortgages, etc. H ence, the array of
credit m arket assets should be divided into those that
are closely related to the d iscou n t rate an d those that
are less closely related to it.
The m arket for federal funds is one segm ent of the
credit m arket that is particularly sensitive to d iscou n t
rate ch anges an d to ch anges in Federal Reserve o p era­
tions. Federal funds are sim ply the reserve assets of
one depository institution that are sold (lent) to an ­
o th er for the purp ose of achieving both institutions'
desired reserve positions. B ecau se su ch funds are
close substitutes for reserves supplied by the Federal
Reserve, including those supplied through the dis­
co u n t w indow, ch an ges in the d iscoun t rate o r F ed ­
eral Reserve policy should initially affect the federal
funds rate and subsequently o th er market rates. (See
page 10 for a d iscussion of the relationship betw een
the discoun t rate and the prim e rate.)

Borrowings and the Rate Spread
The relationship betw een the d iscount rate and
m arket interest rates rests, in one w ay o r an other, on
the strength of the relationship betw een borrow ings
an d the rate spread. Equations 1 an d 2, however, imply
that borrow ings d epend on m ore than the spread
betw een the market and d iscount rates. To see this,
assum e that there are no im pedim ents to borrow ing
so th at dep ository institution s ca n b orrow any
am ount they desire at the d iscoun t w indow . If this
w ere the case, borrow ings w ould rise w hen ever m ar­
ket rates w ere above the d iscou n t rate an d fall w h en ­
ever the discou n t rate is above the market rate. If we
ab stract from problem s of inflation and inflationary
expectation s, the m arket rate w ould always equal the
discount ra te :’ But if R, = R(l, however, equation 1
implies that borrow ings w ould be zero.
The d ata in ch art 2, w hich show weekly adjustm ent
borrowings and the federal funds rate/d isco u n t rate

9
Under this arrangement, one can envision the Federal Reserve
pushing down interest rates by lowering the discount rate. As this is
done, hovyever, money growth will accelerate and so will inflation.
As a result, nominal interest rates will rise and money will grow even
faster. Hence, even if the discount window were completely "open,”
the Federal Reserve would be unable to control interest rates with
the discount rate in anything but the short run.




AUGUST/SEPTEMBER 1986

sp read from O ctober 1982 to Ju n e 1986, ind icate that
the d iscount an d federal funds rates are seldom
equal.1 M oreover, w h en th e rates are equal, borrow ­
"
ings are not zero. This is p rim a fa c ie evidence that
borrow ing is not explained solely by the interest rate
spread. Indeed, Federal Reserve regulations, w h ich set
forth the conditions u n d er w h ich dep ository institu­
tions m ay u se the d iscou n t w indow , m ake it cle a r that
borrow ing is a privilege an d explicitly state that it is
inappropriate to borrow “to take advantage of a differ­
ential betw een the d iscou n t rate an d the rate on
alternative so u rces of funds.”1
1
A visual inspection of ch a rt 2 show s that th ere is
usually a positive relationship betw een borrow ings
an d the rate spread, that is, that increases in borrow ­
ings tend to be associated w ith in creases in the spread
and vice versa. T here are, how ever, som e m arked d e­
p artures from this relationship. The m ost obvious of
these o ccu rre d w ith the sh arp in crease in borrow ings
in M ay-Ju n e 1984 an d November 1985. Both of these
events w ere accom p an ied by special circu m stan ces.
The form er is associated w ith heavy d iscou n t w indow
borrow ings by Continental Bank of Illinois an d the
latter with the largest single-day borrow ing from the
Federal Reserve w hen th e Bank of New York (BONY)
exp erienced a co m p u te r failure on November 21,
1985.1 Even w hen these outliers are ignored, however,
2
there are instances w hen borrow ings and the spread
m ove in opposite d irections. M oreover, th ere is co n ­
siderable variation in the relationship betw een the
average level of borrow ings an d the average level of the
spread. The m ost obvious of these is the period from
Ju n e 13, 1984, through O ctober 3, 1984, w hen the
sp read averaged over 200 basis points and borrow ings
averaged less than a billion dollars, as co m p ared to an
average sp read of 70 basis points an d average borrow ­
ings of $.7 billion over the entire p eriod .1
3
The strength of the relationship betw een borrow -

'“Borrowing from the Federal Reserve is divided into three categories:
adjustment borrowing, seasonal borrowing and extended credit
borrowing. The borrowing assumption, however, pertains only to
adjustment and seasonal borrowings; see Partian, Hamdani and
Camilli (1986).
"This is called the “reluctance of banks to borrow from the Federal
Reserve,” and at one time there was considerable discussion over
whether this reluctance was “inherent” or “induced.”
1 See Federal Reserve Bank of New York (1986) for a discussion of
2
the BONY borrowings.
1 lt could be that depository institutions became more reluctant to
3
borrow from the Federal Reserve in light of the large borrowings by
Continental Bank.

9

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

The Discount Rate and the Prime Rate
One possible reason for the hypothesized strong
effects of discoun t rate ch an ges on interest rates is
the fact that d iscou n t rate ch an ges an d ch an ges in
the com m ercial bank prim e rate often o c c u r to ­
geth er and are usually acco m p an ied by a great deal
of publicity. Both of th ese rates are adm inistered
rates that do not ch an ge daily w ith m arket forces,
but change less frequently an d by fairly large
am ounts.
Because ch anges in the prim e rate often follow
on the heels of ch an ges in the d iscou n t rate, it m ay
lead som e to co n clu d e incorrectly the latter cau sed
the form er. B ecau se both are adm inistered rates,
however, they are likely to respo n d similarly but not
precisely coterm inously, to market rates. F or exam ­
ple, as market interest rates fall relative to these
adm inistered rates, th ese rates b eco m e in creas­
ingly out of line with the m arket. Hence, there is an
incentive for the Federal Beserve to cu t the dis­
co u n t rate and for com m ercial banks to cu t their

Prime rate
Date effective

prim e rate. If the Federal Beserve cu ts the d iscou n t
rate first, banks m ay feel additional p ressu re to cut
their prim e rate, but this does n ot im ply th at the
form er cau sed the latter. R ather both rates are
m erely responding to m arket forces.
The table above show s that on four o ccasio n s
since O ctober 1982 d iscou n t rate and prim e rate
ch an ges w ere effective on the sam e day. In each
instance, the an n ou n cem en t of a cu t in the prim e
rate followed the an n ou n cem en t of the d iscou n t
rate change. F o r the rem aining five ch an g es in the
d iscount rate, ch an ges in the prim e rate followed
d iscount rate ch an ges by a week o r m ore. Also,
there w ere a n u m b er of ch an ges in the prim e rate
that w ere n ot even rem otely asso cia te d w ith
ch an ges in the discou n t rate. It w ould ap p e a r that
changes in m arket interest rates are prim arily re­
sponsible for ch an ges in both of th ese adm inistered
rates.

Discount rate
Change

October 7, 1982

13% to 12%
12% to 11.5%

January 11,1983
February 25, 1983
August 8, 1983
March 19, 1984
April 5, 1984

11.5% to 11%
11% to 10.5%
10.5% to 11%
11% to 11.5%
11.5% to 12%

May 8, 1984
June 25,1984
September 27,1984
October 16, 1984
October 29, 1984
November 8,1984

12% to 12.5%
12.5% to 13%
13% to 12.75%
12.75% to 12.5%
12.5% to 12%
12% to 11.75%

November 28, 1984
December 19,1984

11.75% to 11.25%
11.25% to 10.75%

January 15,1985
May 20, 1985
June 18,1985
March 7, 1986
April 21, 1986

10.75% to 10.5%
10.5% to 10%
10% to 9.5%
9.5% to 9%
9% to 8.5%

Change

13.5% to 13%

October 13,1982
November 22, 1982

Date effective

October 12, 1982
November 22, 1982
December 14, 1982

9.5% to 9%
9% to 8.5%

April 9, 1984

8.5% to 9%

November 21,1984

9% to 8.5%

December 24,1984

10



10% to 9.5%

8.5% to 8%

May 20, 1985

8% to 7.5%

March 7,1986
April 21, 1986

7.5% to 7%
7% to 6.5%

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

C h a rt 2

A d ju s tm e n t plus S easo nal B o rro w in g s from F e d e ra l Reserve
an d F ed eral F u n d s -D is c o u n t R ate Spread

1

i— i— i— i— *
—

O N D J

J— i— i— i— i— * * i—
— —

F M A M J

1982

— * i— '— i— i— i— i— i— i— i— i— — i— i— 1 i— * 1 i— i— * * i— — i— i— i— i — i— i - i
—
—
— —
— —

J A S O N D J

F M A M J J A S O N D J

1 9 83

1984

ings and the sp read can be estim ated statistically by
considering the equation:
(3) Borr, = a„ + a,(R f—Rd + u,.
)
The term u, is a rand om d isturban ce that can be
thought of as cap tu ring the effect of all factoi-s oth er
than the rate spread that d eterm ine deviations in
borrow ing from its average level. From a statistical
point of view, the variation in borrow ings can be d e ­
com p osed into two so u rces: the proportion explained
by the rate spread and that explained by all o th er
factors. (Since the factors that go into u, are not exp lic­
itly identified, this is called “unexplained variation.’’)
Equation 3 is estim ated with ordinary least squares,
using the weekly d ata show n in ch art 2. The outliers
for the weeks ending May 16 to Ju n e 6, 1984, and
N ovember 27, 1985, w ere deleted.'4 The results are
,4lf these outliers are not removed, the R2falls to about .15.




F M A M J

J A S O N D J

19 8 5

I M A M

J

1986

p resen ted in the first row of table 1. The coefficient of
determ ination, d en oted R3, m easu res the proportion
of the variation in borrow ings explained by the rate
spread, and 1-tT is the p roportion of variation e x ­
plained by all o th e r factors. The R3 ind icates that only
35 p ercen t of the variation in borrow ings is a cco u n te d
for by the spread, leaving 65 p ercen t to be acco u n te d
for bv o th e r factors.
T he fit can be im proved by putting in a du m m y
variable that takes on the value one for the p eriod from
the week ending Ju n e 13, 1984, to O ctober 3, 1984,
w hen the sp read w as unusually high, an d zero else­
w here. The results of including a d u m m y variable are
show n in the secon d row of table 1. While including
the du m m y variable b oosts the R2 som ew hat, it does
n ot explain this anom aly. Nevertheless, even after a c ­
cou n tin g for this ap p aren t shift in the borrow ing fu n c­
tion, the spread and the d u m m y variable explain only

11

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

extent of the shift in th e supply of cred it an d the
interest sensitivity of the d em an d for credit, so it is
possible, in principle, to determ in e the effect of an
exogenous ch an ge in the m on ey stock on interest
rates.

Table 1
Estimates of Equation 3
Intercept

Dummy variable

.368*
(12.21)

-.410*
(4.03)

R2

SE

.291*
(10.04)

.420*
(14.74)

Spread

.35

.28

.419*
(9.94)

.40

.27

"Indicates the variable is statistically significant at the 5 percent
level.

40 p ercen t of the total variation in borrow ings, leaving
the bulk of the variation to be explained by o th er
facto rs.1
5

IN SEARCH OF THE DIRECT EFFECT:
SOME EMPIRICAL ESTIMATES
Separating the three possible effects of d isco u n t rate
ch an ges on m arket interest rates — the direct, policy
an d a n n o u n cem en t effects — is difficult. The results
in table 1, how ever, provide a basis for estim ating the
likely direct effect of a d isco u n t rate ch an ge on interest
rates. From the seco n d row of table 1, w e see that a 1
p ercen tage-p oin t (100 basis-point) decline in th e dis­
co u n t rate will cau se borrow ings to in crease by $.419
billion. All o th er things th e sam e, this will in crease the
m on etary base (in the form of borrow ed reserves) by
the sam e am ou nt. Given an M l-m o n etary base m ulti­
plier of 2.7, this will p ro d u ce a $1.13 billion in crease in
M l.1 Such ch an ges in the m on ey stock shift the supply
6
of cred it to the right, cau sing m arket interest rates to
fall. The effect of this on m arket rates d ep en ds on the

1 Because borrowings fluctuate with market interest rates, they can
5
be a source of cyclical variation in the money stock. Because of this,
some have suggested that the discount rate be tied to some market
interest rate. Opponents of this view have argued that no single
interest rate adequately represents the appropriate opportunity cost
for all institutions. If this were true, rates other than the federal funds
rate might explain borrowings. To test this, the second equation on
table 1 was reestimated with the difference between the threemonth Treasury bill and federal funds rates added as a separate
regressor. The coefficient on the difference between these rates
was not statistically significantly different from zero at the 5 percent
level (t-ratio = 1.26). Hence, it appears that the federal funds rate is
the primary interest rate on which borrowing depends.
1 The M1 multiplier averaged much less than this during all of the
6
period under consideration, i.e., 2.7 is approximately its current
level.

12



The largest estim ates of this liquidity effect co m e
from estim ated sh o rt-ru n m on ey d em an d equations.
F o r exam ple, usual estim ates suggest that a $1.13
billion ch an ge in M l w ould p ro d u ce a 67 basis-point
initial ch an ge in the th ree-m o n th T reasu ry bill rate,
but only a six basis-point effect in the lon g-ru n equilib­
rium ra te .1 It is well known, how ever, th at su ch eq u a­
7
tions have u n reasonably large estim ates of th e liquid­
ity effect.1 O ther studies, w hich attem p t to estim ate
"
the liquidity effect directly, sh ow only sm all an d tra n ­
sient effects of u n an ticip ated ch an ges in m o n ey on
interest rates. Using th ese estim ates, a $1.13 billion
ch an ge in the m oney stock w ould p ro d u ce about a
one basis-point ch an ge in the T-bill rate initially, w ith
no long-run effect w hatsoever.I
U
Put into an o th er perspective, sin ce O ctob er 1982 the
average, absolute w eekly ch an ge in M l h as b een $1.77
billion, m ore than one an d one-half tim es th e esti­
m ated $1.13 billion ch an ge in M l associated w ith a full
1 p ercen tage-p oin t ch an ge in th e d isco u n t rate. Thus,
the direct effect of a ch an ge in the d isco u n t rate on
m arket interest rates, all o th er things co n stan t, is likely
to be small.

Technical Fs. Nontechnical Changes in
the Discount Rate
Alternatively, estim ates of the m agnitude of th e di­
rect effect can be obtained by classifying d iscou n t rate
changes accord in g to th e reaso n they w ere m ade.
Some d iscou n t rate ch an ges are m ad e solely as te ch n i­
cal adjustm ents, designed to align the d iscou n t rate
with market interest rates. Other’s are m ad e for- policyre la te d re a so n s. T h ese a re called n o n te ch n ica l
changes.

1These estimates are based on current levels of M1 and interest
7
rates. Using a short-run interest elasticity estimate from the
“nominal-adjustment” specification of the short-run demand for
money of - .015 and a money stock of $670 billion, the percentage
change in the interest rate would be about 11 percent. A T-bill rate of
6 percent translates into a 67 basis-point change in market interest
rates. The long-run effect was calculated under the assumption of a
long-run elasticity of about - .14 ( - .015/.11). These estimates are
in line with the results from Thornton (1985).
1 See Carr and Darby (1981).
8
1 See Brown and Santoni (1983). Similar estimates would be ob­
9
tained from Cagan and Gandolfi (1969) and Melvin (1983).

FEDERAL RESERVE BANK OF ST. LOUIS

Since the response of borrow ings to a d iscou n t rate
change should be the sam e regardless of the reason
for the change, ce teris paribus, the direct effect of a
discou nt rate change on m arket interest rates should
be the sam e for all ch an ges in the d iscou n t rate.-"
Fu rtherm ore, there should be no ch an ge in the m ar­
ket’s p ercep tion of policy w hen d iscou n t rate changes
are purely tech n ical ad ju stm ents. F or n on tech n ical
changes, however, not only is there a direct effect due
to th e im p act on borrow ings and th e supply of credit,
but a potential an n ou n cem en t effect, w hich m ay or
m ay not be validated by subsequent Federal Reseive
actions. If the d iscoun t rate ch anges th at are m ade
purely as tech n ical ad ju stm ents do n ot affect m arket
interest rates, this is fu rth er evidence that there is
essentially no direct effect of d iscou n t rate ch anges.
Any interest rate effects co m e through an an n o u n ce ­
m ent effect o r subsequent policy chan ges.
It should be noted that the fact that the Federal
Reserve changes the d isco u n t rate from tim e to time
solely to bring it in line w ith m arket interest rates is
itself p rim a fa c ie evidence that the link betw een bor­
rowings an d the federal funds/discount rate spread is
not the sole d eterm inant of depository institution
borrowing. If it w ere, the Federal Reserve should never
have to make su ch tech n ical adjustm ents, but this is
not the case. Of the nine d iscou n t rate ch an ges from
O ctober 1982 to Ju n e 1986 listed in table 2, three w ere
stated to have been m ade solely for technical reasons
and three of the rem aining six m entioned tech n ical
co n ce rn s as one of the reasons for the ch an ge.2
1
Recent em pirical work provides strong evidence
that only d iscount rate ch an ges m ade for policy rea­
sons affect m arket interest rates.2- This work is u p ­
dated here by estim ating the equation:
10

(4) AR, = a„ +

X

a,A R ,, + 0ADR, + u„

i= 1

“ This discussion assumes that the Federal Reserve is not trying to
control the money stock, and in particular, it is not using a monetary
base or total reserves target. If it were, any change in the discount
rate would have no direct effect on interest rates because the effect
of such a change would be neutralized by compensatory open
market operations.
2 The classification used is based upon the Federal Reserve's an­
1
nounced statement of intentions as used by Thornton (1982) and
Batten and Thornton (1984, 1985). Smirlock and Yawitz (1985)
investigate alternative schemes, but find that the one employed
here works best. Their results are supported by Hakkio and Pearce
(1986).
“ See Thornton (1982), Batten and Thornton (1984, 1985), Smirlock
and Yawitz (1985) and Hakkio and Pearce (1986).




AUGUST/SEPTEMBER 1986

w here AR den otes the o ne-d ay ch an ge in a m arket
interest rate, and ADR d en otes the ch an ge in the
d iscou n t rate.23 This equation w as estim ated using
daily d ata from O ctober 1 ,1 9 8 2 , to Ju n e 1 1 ,198G, using
both the federal funds and th ree-m o n th T reasury bill
rates. The T-bill rate w as selected to rep resen t m arket
interest rates in general. E stim ates of th e coefficient on
ADR and som e sum m ary statistics are p resen ted in
table 3.2J The results indicate that a ch an ge in the
d iscou n t rate has a positive, significant effect on both
the federal funds and T-bill rates on the n ext m arket
day. The effect on the federal funds rate is roughly 2.5
tim es that on the T-bill rate.
W hen the d iscou n t rate ch an ges are partitioned
into those m ade for tech n ical reason s (ADRT) and
those m ade for n on tech n ical reason s (ADRNT), the
results indicate th at d iscou n t rate ch an ges m ad e
solely for tech n ical reason s h ad no significant effect
on the federal funds rate. The results for the T-bill rate
are less clear. The coefficient on d isco u n t rate ch an ges
m ad e solely for tech n ical reason s is sm aller th an that
for policy-related reason s, but is statistically signifi­
can t at the 5 p ercen t level. A clo ser look, how ever,
reveals that only o ne of the th ree d iscou n t rate
ch an ges m ad e solely for tech n ical reason s is a sso ci­
ated with m ovem ent in the T-bill rate in the exp e cte d
d irection. The h alf-percent decline in the d isco u n t
rate on O ctober 1 2 ,1 9 8 2 , is associated w ith a 37 basispoint decline in the T-bill rate. In co n trast, the half­
p ercen t increase on April 9 ,1 9 8 4 , is asso ciated w ith a 9
basis-point decline in the T-bill rate an d th e half­
p ercen t d ecrease on April 21, 1986, is associated with
no change in the T-bill rate.
W hen d iscou n t rate ch an ges m ad e for p urely te ch ­
nical reason s are partitioned into the one m ad e on
O ctober 12, 1982 (ADRTO), and the o th e r tw o (ADRT),
the results indicate that significance of tech n ical
ch an ges on th e th ree-m o n th T reasu ry bill rate is due
to the change on O ctober 12. Fu rth erm ore, the effect
on the federal funds rate is significant at th e 10 p e r­

?3
ADR takes on the value of the discount rate change on the day that
the change became effective. The one exception is the change that
was announced on November 21, 1984, effective immediately.
Since the announcement was made at 4:15 p.m. EST after the
market closed, the ADR takes on a value on November 23. (The
federal funds rate declined by 35 basis points between November
21 and 23 and increased by 4 basis points between November 20
and 21).
2 The coefficients on the distributed lag of the dependent variable are
4
not reported because they are intended only to capture the effect of
all previously known information on these interest rates and are not
of importance themselves.

13

AUGUST/SEPTEMBER 1986

FEDERAL RESERVE BANK OF ST. LOUIS

Table 2
Discount Rate Changes, October 1982 to June 1986
Date effective

Change

Classification

Reason

October 12,1982

10% to 9.5%

T

Action taken to bring the discount rate into closer alignment with short­
term market interest rates

November 22,1982

9.5% to 9%

P

Action taken against the background of continued progress toward greater
price stability and indications of continued sluggishness in business
activity and relatively strong demand for liquidity

December 14,1982

9% to 8.5%

P

Action taken in light of current business conditions, strong competitive
pressures on prices and further moderation of cost increases, a slowing of
private credit demands and present indications of some tapering off in
growth of the broader monetary aggregates

April 9, 1984

8.5% to 9%

T

Action taken to bring discount rate into closer alignment with short-term
interest rates

November 21,1984

9% to 8.5%

P

Action taken in view of slow growth of M1 and M2 and the moderate pace
of business expansion, relatively stable prices and a continued strong
dollar internationally

December 24,1984

8.5% to 8%

P

Essentially the same as before plus to bring the discount rate into more
appropriate alignment with short-term market interest rates

May 20,1985

8% to 7.5%

P

Action taken in the light of relatively unchanged output in the industry
sector stemming from rising imports and a strong dollar. Rate reduction is
consistent with declining trend in market interest rates

March 7,1986

7.5% to 7%

P

Action taken in context of similar action by other important industrial
countries and for closer alignment with market interest rates. A further
consideration was a sharp decline in oil prices

April 21, 1986

7% to 6.5%

T

Action taken to bring discount rate into closer alignment with prevailing
levels of market rates

P = policy related
T = technical
Source: Federal Reserve Bulletin, paraphrased from statem ents in various issues, and the Wall Street Journal.

cen t level w hen th ese data are partitioned in this way.
This is the only instance w hen a tech n ical ch an ge in
the d iscou n t rate had a significant effect on m arket
rates.2’ The p rep on d eran ce of evidence suggests that
d iscou n t rate ch an ges m ade solely for tech n ical re a ­
sons have no statistically significant effect on market
interest rates.2 This result is co n sisten t w ith o u r pre6

2 This change was announced two days after the Federal Reserve de­
5
emphasized M1 as a monetary target. (See Thornton (1983) for a
discussion of this period.) While there was no immediate announce­
ment of the decision to de-emphasize M1, there were leaks to this
effect, so the market may have interpreted the October 12 decrease
in the discount rate as an indication that the Federal Resen/e would
move toward an easier policy. There were leaks to the press on
October 7 that the Federal Reserve would pay more attention to
interest rates and less to M1 growth. See BNA’s Daily Report for
Executives, October 8,1982.
“ This finding has been reiterated by Thornton (1982), Smirlock and
Yawitz (1985) and the results presented in table 5 for the money

14



vious finding that there is little, if any, direct effect of a
d iscount rate change on m arket interest rates.
It cou ld be, how ever, that d iscou n t rate ch an ges
m ade solely for tech n ical reason s are m ore readily
an ticip ated than those m ad e for policy reason s.2 If
7
this w ere the case, and if the m arket perceived the
effect of the corresp on d in g ch an ge in th e m o n ey su p ­
ply on interest rates, m arket rates w ould ch an ge p rior
to the ch an ge in the d iscou n t rate so th ere w ould be
no statistically significant effect following th e a n ­
n ou n cem en t of a d iscou n t rate ch an ge. Hakkio and
Pearce (1986) report that d iscou n t rate ch an g es m ade
for tech n ical reason s are n o m ore readily fo recasted
than those m ade for n on tech n ical reason s. H ence, this
market, and by Batten and Thornton (1984, 1985) and Hakkio and
Pearce (1986) for the foreign exchange market.
2 This conjecture is offered by Batten and Thornton (1984).
7

AUGUST/SEPTEMBER 1986

FEDERAL RESERVE BANK OF ST. LOUIS

Table 3
Estimates of Equation 4 for Technical and Nontechnical
Discount Rate Changes
Constant

ADR

ADRNT

ADRT

ADRT0

R2

SE

.20

.35

.20

.35

.20

.35

.03

.08

.03

.08

.04

.08

Federal funds rate
-.011
(0.94)

.690*
(2.95)

(0.91)

.827*
(2.90)

.412
(1.02)

-.010
(0.87)

.829*
(2.91)

-.009
(0.02)

-.010

1.289
(1.81)

Treasury bill rate
-.000
(0.12)

.267*
(4.74)

-.000
(0.10)

.299*
(4.32)

.204*
(2.08)

.000
(0.02)

.297*
(4.33)

-.066
(0.56)

.789*
(4.55)

'Indicates statistical significance at the 5 percent level.

alternative interp retation ap pears to have little m erit

The Discount Rate jIs a Penalty Rate
A nother w ay of estim ating the direct effect of a
d iscou n t rate change on m arket interest rates conies
from noting that dep ository institutions have little
incentive to borrow from the Federal Reserve w hen
the d iscou n t rate is a “penalty rate,” that is, w hen it is
above th e federal funds rate. D epository institutions
th at borrow from the Federal Reserve w hen the d is­
cou n t rate is a penalty rate are assu m ed to do so for
reason s o th er than to m inim ize the explicit co st of
obtaining reserve-adjustm ent funds. C hanges in the
discou n t rate that co m e w hen the d iscou n t rate is a
penalty rate — especially ch an ges that leave the dis­
co u n t rate at penalty levels — should have no effect on
borrow ing and, h en ce, no direct effect on m arket in­
terest rates.-0 If estim ates indicate that d iscou n t rate

2 Their “forecasts," however, are based on in-sampie results and are
8
not true ex ante forecasts.
^While this idea is common in the literature, e.g., Broaddus and Cook
(1983) and Sellon and Seibert (1982), it is sometimes presented in
such a way that it appears that the only effect is the direct effect. In
this case, any finding of a significant effect of a discount rate change
on market interest rates implies that it is produced via the direct
effect. We have shown, however, this is not the case.




ch an ges m ad e w hen the d iscou n t rate is n ot a penalty
rate do not have an effect on m arket rates, while those
m ad e w hen the d isco u n t rate is a penalty rate do have
a significant effect, this w ould be fu rth er evidence that
there is no direct effect of a d isco u n t rate ch an ge on
m arket interest rates.
To test this hypothesis, d iscou n t rate ch an g es w ere
partitioned into those w hen the d iscou n t rate w as a
penalty rate (ADRP) p rior to th e an n o u n cem en t and
those w hen the d iscou n t rate w as not a penalty rate
(ADRNP).3 The results, rep orted in table 4, indicate
'1
that ch an ges m ade w hen the d isco u n t rate w as a
penalty rate are statistically significant.3 F u rth erm ore,
1
“ The partition used was based upon whether the discount rate was a
penalty rate with respect to the federal funds rate. There was only
one instance when the discount rate was a penalty with respect to
the T-bill rate. Such a partition is of little interest, however, since the
evidence in footnote 15 indicates that the federal funds rate is the
relevant opportunity cost variable.
3 Sellon and Seibert (1982) performed a similar analysis on data for
1
the period from February 1980 to August 1982 and found that
discount rate changes made when the discount rate was a penalty
rate had no statistically significant effect on market interest rates or
borrowings. During this period, however, such discount rate
changes were primarily those made for technical reasons; thus it
appears that the Sellon and Seibert result is due to this fact and not
to the fact that the discount rate was at a penalty level at the time of
the change. See Thornton (1982) for the technical vs. nontechnical
results over a similar period.

15

FEDERAL RESERVE BANK OF ST. LOUIS

ch an ges m ad e w h en the d iscou n t rate w as not a
penalty rate w ere not statistically significant. These
results are precisely the opposite of those th at should
have been obtained if the effect of a d iscou n t rate
change, rep orted in table 3, w ere due to a d irect effect.

Evidence on the Announcement and
Policy Effects
The evidence indicates that d iscou n t rate changes
do n ot directly affect m arket interest rates. C on se­
quently, the effect on m arket rates indicated in table 3
m u st be due to an a n n o u n cem en t effect, a policy effect
o r both. B ecau se the effect m easu red in table 3 o ccu rs
on the day following the an n o u n cem en t of a ch an g e in
the d iscou nt rate an d ch anges m ad e for tech n ical
reasons have no effect on m arket rates, this strongly
suggests that it is, at least in part, an an n o u n cem en t
effect, ft is im possible to determ ine, how ever, w heth er
the exp ectation s w ere subsequently validated by
ch an ges in the rate at w hich the Federal Reserve
supplied reserves.3
2
Attem pts m ade to test directly for a policy respon se
following a d iscoun t rate ch an ge w ere incon clu sive.1
1
Nevertheless, som e evidence b ears on the policy ef­
fect, at least in term s of its im plications for th e period
following the O ctober 1982 change in the Federal
Beserve’s operating p roced u re. First, if the Fed's new
operating p ro ced u re attem p ts to m aintain a co n stan t
sp read betw een the federal funds and d iscoun t rate,
borrow ings always should be close to their assu m ed
level. Chart 3 plots the actu al level of ad ju stm ent plus
seasonal borrow ings an d th eir assu m ed level for
weekly d ata from O ctober 6, 1982, through D ecem ber
1985. As the ch art shows, the actual level of borrow ing
often deviates from the initial borrow ing assum ption,

AUGUST/SEPTEMBER 1986

Table 4
Estimates of Equation 4 for Penalty and
Non-Penalty Discount Rate Changes
Constant

ADRP

ADRNP

R2

SE

.20

.35

.03

.08

Federal funds rate
-.010
(0.93)

.741*
(2.58)

.588
(1.46)
Treasury bill rate

-.000
(0.04)

.372*
(5.41)

.060
(0.62)

‘ Indicates statistical significance at the 5 percent level.

som etim es by a considerable m agnitude. Two of the
m ost notable deviations, of co u rse, o ccu rre d in mid1984 and November 1985. Even w h en th ese unusual
periods are ignored, the average absolute deviation of
borrow ings from the initial borrow ing assu m p tion is
$226 million, over 40 p ercen t of th e average level of the
initial borrow ing assu m p tion during the period.
Fu rtherm ore, there is a ten d en cy for the initial b or­
row ing assu m p tio n to follow, ra th e r th a n lead,
changes in actu al borrow ings. It ap p ears th at the
federal funds/discount rate sp read is m aintained
w hen the borrow ing assu m p tion ch an g es; the d e ­
m and for borrow ed reserves is not forced to conform
to the borrow ing assum ption.

“ Alternatively, Smirlock and Yawitz (1985) allow for the change in the
discount rate to impact market interest rates with a lag of up to five
days. Because they cannot reject the hypothesis that effects past
the initial day are significant, they conclude that the rapid adjustment
is consistent with market efficiency. Because the market rates
nearly always return to levels prior to discount rate changes, how­
ever, it is possible to find no statistically significant long-run effect
simply by making the lag “long enough” or a permanent effect (as
they found) by making it “short enough.”

Second, if the policy effect is strong, the resp o n se of
m arket interest rates, especially th e federal funds rate,
to a change in the d iscou n t rate should be larger since
the O ctober 1982 change in the o peratin g p ro ced u re.
To test this, equation 4 w as reestim ated for the period
from O ctober 1, 1979, to Ju n e 11, 1986, and the re ­
sp on se of m arket interest rates to n on tech n ical
changes in the d iscou n t rate w as allow ed to be differ­
ent for the periods O ctober 1, 1979, to O ctober 5 ,1 9 8 2 ,
and O ctober 6, 1982, to Ju n e 11, 1986. The results are
rep orted in table 5 w ith the coefficients for th e prea n d p o s t - O c t o b e r 1 9 8 2 p e r i o d s d e n o t e d by
ADBNTPBE82 and ADBNTPOST82, respectively.M

“ Several attempts to directly test various hypotheses were con­
ducted, but the results were unsatisfactory. For example, discount
rate changes that indicate a change in policy — regardless of the
reason given for the change — should be followed by a sharp
change in the growth of nonborrowed reserves. Hence, statistical
tests of nonborrowed reserve growth before and after discount rate
changes were undertaken. Because the nonborrowed reserve data
only are available biweekly, the tests were also done using weekly
M1 data. The results indicated no statistically significant change in
the growth rate of either nonborrowed reserves or M1; however, the
data were highly variable and the observations few. Hence, these
tests should be considered inconclusive.

^Because of the differences in the variation of the dependent vari­
ables between the periods, the equation was estimated adjusting for
heteroskedasticity. Also, the pre-October 1982 period includes a
surcharge variable because Thornton (1982) has shown the results
are sensitive to this modification. While not reported here, the
surcharge coefficient is nearly identical to that reported by Thornton.
The coefficient on ADRNTPRE82 differs from that reported by
Thornton primarily because of a difference in the sample period;
however, all of the qualitative conclusions are the same.

16



FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

C h a rt 3

A d ju s tm e n t plus S easo n al B o rro w in g s from F e d eral Reserve
a n d In itia l B o rro w in g A ssum ption
Billioas of dollars

Billiots of dollars

5 ,------------- ---------------

5

A c tu a l b orrow in gs

The results sh ow that th e responsiveness of the
federal funds rate to ch an g es in th e d iscou n t rate w as
essentially the sam e during the two periods. Indeed,
an F -test of the equality o f the two coefficients does
not reject the hypothesis that the respon se w as the
sam e. There is a statistically significant difference in
the responsiveness of th e T-bill rate; however, it has
b ecom e less, not m ore, responsive to ch an ges in the
d iscount rate. The evidence suggests th at the shift in
the F ed ’s operating p ro ced u re has not increased the
initial response of m arket interest rates to d iscou n t
rate ch an ges; if anything it appeal's to have low ered it.
Finally, there is one additional p iece of evidence on
the an n ou n cem en t vs. policy effect of a d iscou n t rate
ch an ge. The effect of th e d iscou n t rate o n m arket
interest rates, especially the policy effect, im plies c a u ­
sality running from the federal funds rate to o th er
m arket interest rates. In o rd er to investigate this, tests



of “G ranger cau sality” w ere co n d u cte d using both
daily an d w eekly d ata for th e federal funds an d threem o n th Treasu ry bill rates. T h ese tests are designed to
determ in e w h eth er ch an g es in o ne rate p reced e or
follow ch an ges in th e oth er. (Details an d results are
p resen ted in the appendix.) The results using th e daily
d ata ind icate th at ch an g es in th e T-bill rate p r e c e d e
ch an ges in the federal funds, the reverse of w h at the
policy-effect hyp oth esis w ould m ost strongly imply.
T h e results using w eekly d ata are less definitive, indi­
catin g that at tim es eith er rate p re ce d e s th e other.
While this result is not particularly surprising, the fact
th at the stro n ger (m ost statistically significant) effect is
from the T-bill rate to th e federal funds rate is in co n ­
sistent w ith a stron g policy effect.
While th ese results are disquieting to those w ho
su p p ort the policy effect, th ey are n ot conclusive. The
im p ortan ce o ne assigns to the a n n o u n ce m e n t o r pol­

17

AUGUST/SEPTEMBER 1986

FEDERAL RESERVE BANK OF ST. LOUIS

Table 5
Estimates of Equation 4 with the Discount Rate Partitioned into the Pre- and
Post-October 1982 Periods
Dependent
Variable
Federal funds rate

Treasury bill rate

Constant

ADRT

ADRNTPRE82

ADRNTPOST82

-.006
(0.54)

(139)

.824*
(2.85)

.779*
(2.71)

-.001
(0.23)

.129
(1.68)

.686*
(6.57)

.292*
(4.43)

.382

F-Test'
.013

10.206*

R2

SE

.14

1.01

.04

1.00

’ Indicates statistical significance at the 5 percent level.
’Test of the hypothesis that the coefficients on ADRNTPRE82 and ADRNTPOST82 are equal.

icy effects d ep en ds on th e interpretation of a d isco u n t
rate ch an ge. If it is believed th at d iscou n t rate ch an ges
are prim arily signals that th e Federal Reserve is going
to con tin u e its p resen t policy of ease o r restraint, the
policy effect should be nil. If, on th e o th er hand,
d iscou n t rate ch an ges typically signal a ch an ge in the
rate at w hich the Federal Reserve is going to supply
reserves to the system , the extent to w h ich o ne b e­
lieves this ch an ge will affect m arket interest rates
d ep en d s on o n e’s view of th e liquidity effect. If the
liquidity effect is believed to be w eak an d transient —
as m ost em pirical w ork suggests — the resp o n se of th e
m arket to su ch ch an ges is essentially noise, w ith no
real significance for the future co u rse (or level) of
m arket interest rates. In su ch instances, d iscoun t rate
cu ts th at are followed by m o re exp an sion ary m o n e­
tary policy ultim ately m ight be followed by higher, not
lower, interest rates if su ch a policy ch an ge gives rise
to exp ectatio n s of h igher inflation. On the o th er hand,
if one believes th at th e liquidity effect is stron g an d
lasting, ch an ges in the d isco u n t rate will be thought to
have p erm an en t effects on m arket interest rates, but
only if followed by a ch ange in Federal Reserve policy.

the a n n o u n ce d ch an ge in th e d isco u n t rate; an d (3)
the "policy effect,” the im p act of a subsequent ch an g e
in Federal Reserve activity on th e m arket. Special a t­
tention w as given to th e hyp oth esis th at th e im p act of
d iscou n t rate ch an ges on m arket interest rates b e­
cam e stro n ger following the Federal Reserve’s sw itch
from a n onborrow ed reserve to a b orrow ed reserve
operating p ro ced u re in O ctob er 1982.
The evidence sh ow ed a statistically significant effect
of a ch an ge in the discou n t rate on both the federal
funds an d Treasu ry bill rates im m ediately following
the d iscou n t rate ch an ge. A series of tests provided
evidence, con sisten t with the theory, that th e direct
effect of a discou n t rate ch an ge is nil. Consequently,
the im pact of a d iscou n t rate ch an ge on m arket rates is
due to an an n ou n cem en t effect, a policy effect o r both.
The rapidity with w hich m arket rates resp o n d to the
d iscou n t rate ch an g e suggests th at th e an n o u n cem en t
effect is operative. F u rth erm ore, som e ind irect tests of
th e policy effect p ro d u ced results th at are in con sis­
tent w ith it, suggesting th at d iscou n t rate ch an ges
have h ad n o p erm an en t effect on m arket interest rates.

CONCLUSIONS
REFERENCES
This article w as intend ed to clarify th e relationship
betw een th e Federal Reserve’s d isco u n t rate an d m ar­
ket interest rates. T hree distinct, thou gh n ot m utually
exclusive, potential effects of a d isco u n t rate ch an ge
on m arket interest rates w ere outlined: (1) th e “direct,
ce te ris paribus, effect,” w hich ab stracts from market
reaction s to the d iscoun t rate ch an ge an d any su b se­
quent ch ange in Federal Reserve operation s; (2) the
"an n o u n cem en t effect,” w h ich reflects the changing
exp ectatio n s of th e Federal Reserve’s activity b ased on

18


Batten, Dallas S., and Daniel L. Thornton. “Discount Rate Changes
and the Foreign Exchange Market,” Journal of International Money
and Finance (December 1984), pp. 279-92.
_________“The Discount Rate, Interest Rates and Foreign Ex­
change Rates: An Analysis with Daily Data,” this Review (February
1985), pp. 22-30.
Broaddus, Alfred, and Timothy Cook. “The Relationship Between
the Discount Rate and the Federal Funds Rate Under the Federal
Reserve’s Post-October 6, 1979 Operating Procedure,” Federal
Reserve Bank of Richmond Economic Review (January/February
1983), pp. 12-15.

AUGUST/SEPTEMBER 1986

FEDERAL RESERVE BANK OF ST. LOUIS
Brown, W. W., and G. J. Santoni. “Monetary Growth and the Timing
of Interest Rate Movements,” this Review (August/September
1983), pp. 16-25.
Cagan, Phillip, and Arthur Gandolfi. “The Lag in Monetary Policy as
Implied by the Time Pattern of Monetary Effects on Interest
Rates,” American Economic Review (May 1969), pp. 277-84.
Carr, Jack, and Michael R. Darby. “The Role of Money Supply
Shocks in the Short-Run Demand for Money,” Journal of Monetary
Economics (September 1981), pp. 183-99.
Cukierman, Alex. “Central Bank Behavior and Credibility: Some
Recent Theoretical Developments,” this Review (May 1986), pp.
5-17.
Daily Report for Executives, The Bureau of National Affairs, Inc.,
Washington (October 8,1982), L12.
Federal Reserve Bank of New York. “Monetary Policy and Open
Market Operations in 1985,” Quarterly Review (Spring 1986), pp.
34-53.
Hakkio, Craig S., and Douglas K. Pearce. “Exchange Rates and
Discount Rate Changes,” Federal Reserve Bank of Kansas City
working paper 86-06 (1986).
Melvin, Michael. “The Vanishing Liquidity Effect of Money on Inter­
est: Analysis and Implications for Policy,” Economic Inquiry (April
1983), pp. 188-202.
Partian, John C., Kausar Hamdani, and Kathleen Camilli. "Re­
serves Forecasting for Open Market Operations,” Federal Re­
serve Bank of New York Quarterly Review (Spring 1986), pp. 1933.




Roley, V. Vance. “Market Perceptions of U.S. Monetary Policy
Since 1982,” Federal Reserve Bank of Kansas City Economic
Review (May 1986), pp. 27—
40.
Sellon, Gordon H., and Diane Seibert. “The Discount Rate: Experi­
ence Under Reserve Targeting,” Federal Reserve Bank of Kansas
City Economic Review (September-October 1982), pp. 3-18.
Smirlock, Michael, and Jess Yawitz. “Asset Returns, Discount Rate
Changes, and Market Efficiency,” The Journal of Finance (Septem­
ber 1985), pp. 1,141-158.
Smith, Warren L. “The Instruments of General Monetary Control,”
National Bank Review (September 1963), pp. 47-76.
Thornton, Daniel L. “The Discount Rate and Market Interest Rates:
What’s the Connection?” this Review (June/July 1982), pp. 3-14.
_________“The FOMC in 1982: De-emphasizing M1,” this Review
(June/July 1983) pp. 26-35.
________ . “Money Demand Dynamics: Some New Evidence,”
this Review (March 1985), pp. 14-23.
Thornton, Daniel L., and Dallas S. Batten. “Lag-Length Selection
and Tests of Granger Causality Between Money and Income,”
Journal of Money, Credit and Banking (May 1985), pp. 164-78.
Wallich, Henry C. “Recent Techniques of Monetary Policy,” Fed­
eral Reserve Bank of Kansas City Economic Review (May 1984),
pp. 21-30.

(See appendix on next page.)

19

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

Appendix

w here A d en otes the first difference o perator, i.e., ARfl
= R„ — Rn ,, an d H, an d RTd en ote the federal funds an d
three-m on th Treasury bill rates, respectively. T h e p ro ­
ced u re co n sists of testing the hypothesis th at p., = |x,
= . . . = |xK = 0. If this hyp oth esis is rejected , it is said
the “causality” runs from the federal funds rate (R() to
the th ree-m on th Treasury bill rate (R,.). To test for
causality running from the Treasu ry bill rate to the
federal funds rate, the equation

Tests o f Granger Causality
T ests of “G ranger cau sality” are really tests of tem ­
poral ordering of time series. The test of causality
running from the federal funds rate to the T reasury
bill rate is perform ed by estim ating, using ordinary
least squares (OLS), the equation
K

K

K

AR,, = a. + X 8,AK„ , + 2 (jl,AR„ ,,
i= 1

K

ARf, = 0„ + 2 XAR„. + 2 eiARn ,
i= 1

i= 1

i= 1

Table A.1
Granger Causality Results for ARf and ART: Daily Data
Tests of jjl’s = 0
Lags of ARr
Lags of
AR,

1

2

3

4

5

6

7

8

9

10

11

12

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

.342
.624
.570
.678
.775
.707
.718
.494
.339
.267
.238
.211

.355
.610
.524
.647
.739
.682
.706
.480
.325
.242
.227
.208

.358
.616
.481
.617
.707
.666
.696
.457
.305
.223
.217
.205

.382
.646
.519
.677
.741
.713
.751
.492
.311
.223
.220
.218

.377
.646
.526
.681
.715
.709
.754
.473
.291
.197
.198
.199

.378
.647
.527
.682
.716
.704
.746
.471
.292
.198
.199
.200

.346
.583
.486
.651
.672
.695
.650
.462
.317
.250
.237
.217

.346
.585
.497
.662
.685
.704
.653
.436
.284
.216
.213
.199

.338
.575
.498
.660
.683
.694
.634
.439
.246
.171
.178
.176

.342
.586
.512
.675
.675
.686
.645
.428
.218
.185
.178
.168

.342
.587
.513
.675
.676
.686
.646
.429
.218
.184
.172
.159

.341
.585
.512
.675
.675
.684
.639
.423
.219
.186
.172
.163

8

9

10

11

12

.059
.031*
.068
.084
.145
.174
.166
.220
.299
.381
.435
.424

.061
.032*
.070
.087
.149
.178
.168
.222
.301
.382
.434
.425

.057
.026*
.058
.071
.125
.146
.135
.177
.246
.317
.381
.384

.060
.026*
.055
.064
.114
.132
.116
.152

Tests Of e’S = 0
Lags of AR,
Lags of
ART

1

2

3

4

5

6

7

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

.681
.837
.597
.640
.524
.625
.673
.686
.770
.792
.850
.787

.379
.581
.372
.409
.288
.382
.476
.526
.620
.634
.714
.633

.304
.419
.469
.462
.302
.385
.480
.552
.648
.654
.734
.649

.195
.249
.386
.540
.293
.360
.466
.540
.641
.659
.740
.628

.173
.167
.300
.453
.437
.474
.590
.676
.765
.799
.859
.745

.107
.097
.198
.310
.397
.524
.639
.733
.809
.835
.878
.777

.102
.054
.117
.166
.256
.338
.377
.482
.563
.638
.707
.658

'Indicates significance at the 5 percent level.

20



.098
.050*
.106
.147
.235
.303
.315
.408
.477
.560
.627
.579

.213
.276
.343
.319

AUGUST/SEPTEMBER 1986

FEDERAL RESERVE BANK OF ST. LOUIS

Table A.2
Granger Causality Results for ARf and ART: Weekly Data
Tests of ( ’s = 0
x
Lags of ART
Lags of
AR,

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

1

2

3

4

5

6

7

8

9

10

11

12

.269
.538
.291
.325
.209
.025*
.028*
.038*
.061
.074
.092
.099

.258
.505
.337
.374
.248
.031*
.034*
.047*
.074
.088
.109
.117

.242
.493
.423
.512
.352
.053
.056
.077
.115
.136
.161
.170

.314
.580
.466
.602
.501
.086
.084
.113
.162
.169
.205
.215

.319
.570
.477
.613
.535
.086
.085
.112
.161
.170
.210
.209

.312
.564
.453
.584
.531
.051
.066
.088
.130
.147
.192
.207

.361
.615
.501
.617
.549
.066
.092
.108
.158
.185
.241
.265

.415
.673
.536
.648
.590
.077
.108
.131
.187
.216
.275
.294

.352
.649
.567
.677
.648
.058
.085
.117
.162
.225
.293
.346

.339
.632
.482
.607
.593
.056
.085
.116
.164
.225
.297
.356

.341
.635
.485
.606
.596
.057
.087
.118
.166
.228
.299
.361

.434
.736
.525
.632
.544
.058
.087
.118
.161
.221
.292
.370

Tests Of

e ’S

=

0

Lags o f AR,
Lags of
ART

1

2

3

4

5

6

7

8

9

10

11

12

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

.073
.181
.043*
.027*
.045*
.040*
.045*
.027*
.044*
.062
.044*
.063

.031*
.097
.029*
.016*
.024*
.022*
.027*
.017*
.027*
.036*
.028*
.041*

.022*
.070
.008*
.005*
.007*
.009*
.012*
.007*
.013*
.014*
.013*
.020*

.039*
.115
.021*
.015*
.018*
.021*
.027*
.017*
.028*
.030*
.026*
.038*

.041*
.123
.024*
.018*
.021*
.024*
.031*
.018*
.030*
.033*
.027*
.041*

.038*
.115
.020*
.015*
.015*
.021*
.028*
.016*
.027*
.030*
.025*
.037*

.046*
.134
.024*
.017*
.017*
.024*
.032*
.019*
.030*
.034*
.028*
.042*

.041*
.123
.029*
.022*
.022*
.030*
.044*
.029*
.045*
.049*
.041*
.059

.046*
.137
.080
.069
.063
.071
.103
.101
.149
.144
.115
.150

.045*
.136
.078
.071
.065
.073
.107
.104
.153
.141
.109
.143

.042*
.128
.077
.065
.066
.067
.103
.107
.158
.157
.110
.146

.054
.157
.087
.071
.111
.167
.161
.103
.138
.108
.146
.183

'Ind ica te s significance at the 5 percent level.

is estim ated and the hypothesis that e, = e., = . . . = eK
= 0 is tested. If the hypothesis is rejected , the cau sal­
ity runs from the T reasu ry bill rate to the federal funds
rate. If the hypotheses co n cern in g the jjl ’ s an d the e's
are both rejected, there is said to be bidirectional
causality betw een the rates. If n eith er is rejected, the
series are said to be independent.
The tests w ere perform ed using both daily and
weekly data. B ecause the test results are quite sen si­
tive to the ord er of the lag, K, the tests w ere perform ed
on all orders up to K = 12.' The significance levels
1
For a discussion of this procedure, see Thornton and Batten (1985).




corresp on d in g to the F -statistics for all ord ers are
presen ted in tables A.l and A.2 for the daily and
weekly data, respectively.
The tests using daily d ata show unidirectional c a u ­
sality from R, to R,, the opposite of w hat is required for
policy actions to be tran sm itted from the federal funds
rate to o th e r m arket interest rates. It should be noted
that the daily federal funds rate series exhibits co n sid ­
erably m ore variability than the T-bill rate series. W hen
these data are sm ooth ed by averaging over a week, the
tests indicate bidirectional causality; how ever, the
stron ger relationship ap p ears to be running from the
T-bill rate to the federal funds rate.

21

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

A Microeconomic System-Wide
Approach to the Estimation of the
Demand for Money
Salam K. Fayyad

A

STABLE d em and-for-m oney relationship is a
n ecessary condition for the viability of a m on etary
policy based on the use of m on etary aggregates as
interm ediate policy targets. In recen t years, stan d ard
m oney-dem and form ulations have exhibited large
shifts that rem ain largely u nexplained today despite
extensive research efforts devoted to determ ining the
reasons for these shifts.
This p ap er p resen ts an alternative to the stan d ard
single-equation m ethod of estim ating the d em and for
m oney. The alternative, called the m icro eco n om ic
system -w ide ap p roach to dem an d analysis, differs in
several fundam ental wavs from the usual m onevd em an d specification. The p u rp ose of this article is to
show how the system -w ide ap p roach can be applied
to estim ating the d em an d for m oney. The results indi­
cate that in-sam ple prediction s m ade using this ap ­
p ro ach closely track the actu al data over the 1969-85
period.

THE STANDARD MONEY DEMAND
FORMULATION: A BRIEF REVIEW
Over the past three d ecad es, m ost dem and-form oney studies have em ployed sim ilar specifications.
Typically they use incom e (as a tran saction variable)
an d one o r m ore (typically two) interest rates (to c a p ­

Salam K. Fayyad is an assistant professor at Yarmouk University
(Jordan) and a former visiting scholar at the Federal Reserve Bank of
St. Louis. The author is intellectually indebted to his teacher, William A.
Barnett. Laura A. Prives provided research assistance.


22


ture the effect of the opp ortun ity co st of holding
money) as explanatory variables; the d ep en d en t vari­
able is generally the stock of real M l b alances.
The w ide a cce p ta n ce of the stan d ard m on ey d e­
m and specification is understandable. It em bodies a
proposition, w hich, sin ce K eynes’ G eneral Theory, has
co n stitu ted a key tenet of the received w isdom o n the
d em an d for m oney: the desire to hold m on ey balan ces
is directly related to th e n eed to co n d u ct tran sactio n s
and inversely related to the opp ortun ity co st of h old ­
ing m oney b alances. In addition, it perform ed rem ark­
ably well in a statistical sense. The coefficients of the
explanatory variables h ad “sensible” signs an d m agni­
tudes, and the estim ated m odel fit the d ata very well.
The disquietude accom p an yin g Goldfeld’s (1976)
d iscovery th at his sta n d a rd fo rm u lation of the
d em and-for-m oney function began in 1973 to system ­
atically overpredict th e real m on ey b alan ces u n d e r­
scores the im p ortan ce th at h as been a tta ch e d to the
stability, and h en ce predictability, of the d em an d for
m oney. It is not surprising th at the rep o rted shift in
Goldfeld’s specification, o r w hat, after 1976, b ecam e
generally known as the “ca se of the m issing m o n ey,”
instigated a seem ingly tireless search for a verifiable
explanation of w hat hap p ened .'
A review of the vast literature devoted to finding the
reason s for the shift in m oney d em an d reveals that
these studies are largely u n su ccessfu l in a cco u n tin g

1 recent study suggests that the demand-for-money function has
A
undergone shifts in the periods 111/1962, IV/1973, IV/1979, and I/
1980. See Mizrach and Santomero (1986).

FEDERAL RESERVE BANK OF ST. LOUIS

for it. F o r exam ple, Laidler has co m m en ted that:
T h e first th in g to be said . . . is w h atev er e lse th e y do,
th e y d o n o t re s c u e th e d e m a n d fo r M , fu n ctio n from
th e su s p ic io n o f in stab ility . . . . [T]he o ften u n s a tis fa c ­
to ry re su lts . . . in d ic a te th at fu rth e r w o rk is req u ired ,
ra th e r th a n th a t th e lin e o f inqu iry th at th e y re p re s e n t
sh o u ld be a b a n d o n e d .2

The inconclusiveness of the evidence on w hat cau sed
the stan d ard m on ey-d em and specification to shift in
1973 ca n be viewed as an indication that exam ining
alternative ap p roach es to the dem an d -for-m on ey for­
m ulation might be useful. The alternative offered h ere
is derived from a m icro eco n o m ic system -w ide a p ­
p ro ach to d em an d analysis.

A NEW APPROACH TO MODELING
MONEY DEMAND: THE MICROECONOMIC SYSTEM-WIDE
APPROACH
The basic prem ise w hich underlies any m icro th eo ­
retic ap p ro ach to co n su m e r d em an d analysis is that
the co n su m er m axim izes a n eoclassical utility fu n c­
tion subject to a budget co n strain t.1 A m odel co n sis­
tent with both the principles of m icro eco n om ic theory
and aggregation theory yields specific behavioral im ­
plications w hich can be tested using available data
aggregated over goods and co n su m ers. (Some criti­
cism s of including m oney in this ap p roach ap p ear on
page 24.)
This study uses a neoclassical utility function
defined over five expen d itu re categories, two of w hich
are presu m ed to cap tu re the “m on etary services” in
the U.S. econ om y. By restricting the analysis to five
expenditure categories, this study assu m es the exist­
en ce of a m acro utility function that is weakly sep ara­
ble in these categories.4
T he solution to the co n su m er ch o ice problem w hen
the utility function is defined over five goods is a
system of five d em an d equations. In each equation,
the quantity d em an d ed of a specific good is expressed
as a function of the total am ou nt available for' sp en d ­
2
See Judd and Scadding (1982), p. 1014.
3 neoclassical utility function is one that is continuously twice
A
differentiable and quasiconcave with positive marginal utility every­
where.
4 neoclassical utility function is weakly separable in a block of goods
A
if and only if the marginal rate of substitution between any two goods
inside the block is independent of consumption outside that block.
While this separability assumption may seem overly restrictive, it is
actually less restrictive than that maintained by studies in which
money is considered to be the sole argument in the utility function.
See, for example, Ewis and Fisher (1984).




AUGUST/SEPTEMBER 1986

ing on all five goods, and (in the general case) of their
prices. Naturally, th e exact specification of these d e ­
m an d equations will d ep en d on the specific form of
the utility function ch o sen . This study, how ever, uses
a general d em an d system co n sisten t with the m axim i­
zation of an arbitrary neoclassical utility function.
Thus, while the system is subject to all the restrictions
that eco n o m ic theory implies, the results are invariant
to the functional form of the utility function being
m axim ized. This ch o ice avoids the loss of generality
w hich m ay result if a p articu lar functional form is
specified an d perm its testing of h yp oth eses about the
stru ctu re of the utility function itself.
The m icro eco n om ic system -w ide ap p roach to d e­
m and analysis deals with the allocation of total sp en d ­
ing am ong the individual goods co n sid ered . Thus, for
the specific set of goods ch osen , the exp lan atory vari­
ables in the d em an d system are th e am ou nt available
for spending and the p rices of these goods. This a p ­
p roach provides a convenient m ean s for acquiring
detailed inform ation about utility-based attributes of
goods; this inform ation is readily available by in sp e ct­
ing the signs (and, of cou rse, the statistical an d e co ­
nom ic significance) of estim ated incom e, own- and
cross-p rice param eters.
The d em an d m odel u sed in this study, th e absolute
p rice version of the R otterdam m odel, w as ch o sen
primarily b ecau se the theoretical restriction s are
readily exp ressed in term s of the m o d el’s p aram eters.
This makes it relatively easy to im pose and to test the
validity of these restrictions.3 A nother attractive fea­
ture of the Rotterdam m odel is that it ca n be used to
provide predictions of the value (budget) sh ares of the
goods included in the analysis. These p red iction s can
be u sed to co m p u te m easures of inform ational in a c­
cu racies useful in assessing the p erfo rm an ce o f the
dem and system as a w hole and the individual d e ­
m and equations as well.
The m on etary variables u sed are the real flow of
m on etary services provided by various m on etary a s­
sets, not the sim ple sum of the real stocks of m on etary
aggregates generally u sed in stan d ard m on ey-d em an d
analysis. A m easure of the m onetary-service flows w as
obtained by evaluating the stocks of m on etary assets
at th eir corresp on d in g u ser-co st p rices (see the dis­
cussion of the data below). T he u ser-cost price of each
m on etary asset is the difference betw een the interest

5 the aggregated-over-consumers version of the model derived by
ln
Barnett (1979), the macro parameters are subject to the same
restrictions as their micro counterparts. (See footnote 9.)

23

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

Can Money Be Included in a Microeconomic
System-Wide Demand Model?
The applicability of the theoretical restrictions in
the general case of d em and for m oney and goods
h as been questioned. In fact, if, as in the Samuelsonian tradition, the utility-based analysis of the
dem an d for m oney is handled by putting m oney
an d prices in the utility function, then, by the
strong results p ro d u ced by Sam uelson and Sato
(1984), the restrictions in question, as they pertain to
the d em a n d f o r go o d s, are sim ply unattainable.
While potentially disquieting, the Sam uelson-Sato
results are not unqualifiedly binding. Indeed, these
results are founded in th e view, long esp oused by
Sam uelson, that, in co n n ectio n w ith the inclusion
of m on ey in the preferen ce stru ctu res, m oney is
w anted solely for the p u rp oses of facilitating tran s­
actions. As Sam uelson (1983), p. 117, states:
In th is c o n n e c tio n , I have re fe re n c e to n o n e o f th e
te n u o u s c o n c e p ts o f m o n ey , a s a n u m e ra ire c o m ­
m od ity, o r as a c o m p o s ite co m m o d ity , b u t to m o n ey
p ro p er, th e d istin g u ish in g fe a tu re s o f w h ic h a re its
in d ire c t u se fu ln e ss, n o t fo r its o w n sake but fo r
w h at it c a n buy, its a c ce p ta b ility , its n o t b e in g "u s e d
u p ” b y u se , etc., e tc .

This is the rationale behind S am uelson’s inclusion
of p rices and m oney in the utility function specified
to be h om ogeneous of degree zero in both m oney
an d p rices. It is precisely this form ulation to w hich
the Sam uelson-Sato results pertain.
One could argue that S am uelson’s view of w hat
m oney is w anted for is unduly restrictive. In fact, of
the assets currently regarded as potential so u rces
of m on etary services in the U.S. eco n om y (see table
1), only a few are “generally accep tab le in e x ­
ch an g e.”1 Fu rtherm ore, the supposition, based on
Sam uelson’s view, that m oney can n o t properly be
treated like o th er com m od ities can also be ques-

'In this study, the Federal Reserve’s definition of monetary assets
was taken as given. The use of the Fed’s definitions does not
mean that the list of assets which appears in table 1 includes all
assets that provide monetary services in the U.S. economy or, for
that matter, that all assets included in the list provide such
services.

Digitized 24 FRASER
for


tioned. H ouseholds co n su m e the services provided
by various expen d itu re categories ostensibly be­
cau se of the utility they derive from these exp en d i­
ture categories: in general, little, if any, effort is
d irected tow ard d eciphering the n atu re of the util­
ity involved in those cases. By the sam e token, it can
be m aintained that m oney is held b ecau se of the
utility it provides, w ithout having to sp ecu late as to
w h eth er that utility derives from m oney's ‘general
acceptability in exch an g e,” the serenity its h olders
exp erience by holding it, o r from any o th er knowable o r even unknow able attribute.2 Indeed, if
m oney ca n be treated like o th er goods, then it can
be includ ed in the utility function in precisely the
sam e m an n er as any o th e r good. In that case, the
Sam uelson-Sato results w ould not apply, an d one
cou ld thus im pose o r test for any of the restriction s
implied by eco n om ic theory.
Interestingly, even w ithin the Sam uelson-Sato
framework, the theoretical restriction s w ould not
be unattainable if the utility function w ere weakly
separable in the block of goods (see Sam uelson an d
Sato (1984), pp. 5 9 2 -9 5 ). Hence, it is legitim ate to
im pose o r test for any of the restriction s im plied by
th eoiy if one assu m es, or, even better, tests for an d
(where applicable) im p oses blockw ise w eak sep ara­
bility in goods. The la tte r w as d on e in this study,
since weak separability in the block of goods could
not be statistically rejected .3

2 course, this amounts to suggesting that money is held for the
Of
“moneyness” of it. While tautological, this statement can be
made operational by hypothesizing that, on the margin, the extent
to which income is forgone when monetary assets are held is a
measure of the moneyness that these assets possess. The gain
that is realized by adopting this hypothesis is considerable; not
only does it play a key role in the measurement of the flow of
monetary services in terms of readily observable data, it also
inherently captures the various degrees of moneyness provided
by various monetary assets.
3
The manner in which weak separability was tested for is dis­
cussed at length in Fayyad (1986), chapter 4. A preliminary draft
of a paper on this subject is available on request.

AUGUST/SEPTEMBER 1986

FEDERAL RESERVE BANK OF ST. LOUIS

rate paid on that asset and the m axim u m available
holding-period yield.0

THE MODEL
F o r n goods, the (discrete-tim e) absolute p rice ver­
sion of the Rotterdam m odel is given by
n
(1) w^Dx,, = ^D m ,* + 2 Tr^Dp,, + eM
i= i

i = l , ..., n.7

The x ’s and p ’s denote the quantities and p rices of the
various goods, respectively, an d the subscript t in­
dexes time. D is the log-change operator; thu s Dxh =
Adog x„). W; den otes the expend iture (value) share of
the ith good, w* = (w,
+ w h)/2 is that g o o d ’s average
value share over two su ccessive tim e periods. Thus,
the d ependent variables in the m odel are the (average)
share-w eighted grow th rates of the quantities of
goods. The explanatory variables are the grow th rates
of real incom e (mt ) and prices.8 The last term in the
*
system of dem and equation 1, e„ d en otes the dem an d
d isturbance. The p roperties of this term are discu ssed
in appendix A in con ju n ction w ith the estim ation
p ro ced u re em ployed in this study.
The p aram eters of th e m od el are
(xf ( = p,

an d

tt m
.

is the m arginal budget sh are of the ith

PiPi dxi
good. T ( = ---- 1 — , (j =
r.j

°

^

1

m dpi

i.
1, ..., n ) ) is the ith good s

p rice coefficient. U nder the stan d ard assu m p tions of
eco n o m ic theory, if the co n su m er m axim izes a n eo ­
classical utility function subject to a budget co n ­
straint, then the above p aram eters satisfy the follow­
ing co n strain ts:
(2) E |x, = 1 ,

i
(3) 2

ttm =

0 ,

i

6
The maximum available holding-period yield is the highest yield of
those available either on the monetary assets or on Baa-rated
bonds.
7 detailed discussion of the model’s derivation and applications can
A
be found in Theil (1971, 1975, 1976, 1980), Barten (1969), and
Barnett (1979,1981).
8 this study, the terms “expenditure” and “income” are used
ln
interchangeably. When the latter is used, however, it means “full
income,” that is, income augmented by expenditure on the mone­
tary assets that are included in this study. In the estimation proce­
dure employed in this study, Dm* is replaced by Dx„ where Dx, =
2 wj Dx„. See Theil (1971), pp. 331-32.




(4) [T ji) is sym m etric an d negative sem idefinite.8
T
In the estim ation p ro ced u re em ployed in this study,
the co n strain ts
= 1, 2,iTn = 0, an d [Tri(] = [iTn] w ere
im posed. The negative sem idefiniteness of th e [irM
]
m atrix w as not im posed; how ever, it w as ch eck ed for.

THE DATA
The d ata con sist of U.S. quarterly tim e series of
exp en d itu res on, an d p rices of, food, nondurables,
services and two blocks of m on etaiy assets for the
period 1/1969-1/1985. Together, the two blocks of m o n ­
etary assets, M l and ABM1, com p rise the 27 assets that
the Federal Reserve Board cu rren tly recognizes as
potential so u rce s of m o n etaiy services in the U.S.
econ om y. M l is the n arrow m o n etaiy aggregate, co n ­
sisting of cu rre n cy and total checkable deposits. ABM1
co n sists of the n on -M l m o n etaiy assets show n in
table 1.
Data on the first three com m od ity grou p s (food,
nondurables an d services) w ere obtained as follows: A
tim e series on the p rice of e a ch co m m o d ity grou p (ph)
w as gen erated from available tim e series on cu rren tdollar an d (1972) co n stan t-d ollar co n su m p tio n ex­
pen d itu res (ph q„ an d p i7, qi| respectively) an d the
(
identity (ph ii7 = (p,, qT i72 q„). P er-cap ita co n stan t/p J
1
/p
dollar exp en d itu res in ea ch q u arter w ere th en ob­
tained by dividing th e aggregate co n stan t-d ollar e x ­
p e n d itu re s by th e c o r r e s p o n d in g m id -q u a rte r
population size (N,). Thus, in term s of the variables
1
w hich ap p ear in the estim ated system , x„ = — pl 7, q„.
One ca n gen erate the d ata on th e quantities and
p rices of M l an d ABM1 m on etary services as follows:
(1) Convert the nom inal balan ces of m on etaiy assets
into real b alan ces by deflating the form er by the
"tru e cost-of-living ind ex.” In this study, this index
w as the geom etric m ean of the C on su m er Price
Index and the C om m erce D ep artm en t's implicit

9 question may arise as to whether these restrictions are applicable,
A
given that the data are aggregated over both goods and consumers.
Insofar as goods are concerned, Hicks’ composite commodity theo­
rem can be used, assuming that each of the commodity groups is an
elementary good. Resolving the more formidable issue of aggrega­
tion over consumers requires using the aggregation results pro­
duced by Barnett (1979). In his aggregated-over-consumers abso­
lute price version of the Rotterdam model, Barnett treats the
macrocoefficients, n and it, as population versions of weighted
average microcoefficients, with the weights proportional to corre­
sponding incomes. He then shows that the macrocoefficients have
the same properties as their micro counterparts, p and -nir
.,

25

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

dexes for M l an d ABM1 for the entire sam ple
period.

Table 1
Potential Monetary Assets
Asset Description

Component
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27

Currency and traveler's checks
Demand deposits held by households
Demand deposits held by business firms
Other checkable deposits less Super NOW
accounts
Super NOW accounts at commercial banks
Super NOW accounts at thrifts
Overnight repurchase agreements
Overnight Eurodollars
Money market mutual fund shares
Money market demand deposit accounts at
commercial banks
Money market demand deposit accounts at thrifts
Savings deposits less MMDAs at commercial
banks
Savings deposits less MMDAs at savings and
loans
Savings deposits less MMDAs at mutual savings
banks
Savings deposits less MMDAs at credit unions
Small time deposits and retail repurchase
agreements at commercial banks
Small time deposits and retail repurchase
agreements at thrifts
Small time deposits at credit unions
Large time deposits at commercial banks
Large time deposits at thrifts
Institutional money market mutual funds
Term repurchase agreements at commercial
banks and thrifts
Term Eurodollars
Savings bonds
Short-term Treasury securities
Banker’s acceptances
Commercial paper

p rice d eflator for p erso n al co n su m p tio n
p enditures.

ex­

(2) Evaluate the real balan ces of each m o n etary asset
in the base period at its real u ser-cost p rice to
obtain the real exp en d iture on th at asset during
the base period."'
(3) Sum the exp en d itu res th u s obtained over the co m ­
pon en ts of M l an d ABM1.
(4) C om pute the Tornqvist-Theil Divisia quantity in-

'°The user-cost price of money was derived by Barnett (1978). See
also Barnett (1986) and (1981), chapter 7.


26


(5) Set the b ase-period exp en d itu res obtained in (3)
equal to the respective quantity ind exes co m p u te d
in (4) an d interpolate to acquire co m p lete series on
the real exp en d itu res on th e m o n e ta iy services
provided by M l and ABM1.
(6) C on stru ct Tornqvist-Theil Divisia p rice ind exes of
the u ser-cost p rices of the respective co m p o n en ts
of M l and ABM1.

THE ESTIMATION RESULTS
The m axim um likelihood estim ates of the p aram e­
ters of th e absolute p rice version of the R otterdam
m odel and the associated incom e and price elastici­
ties are rep orted in table 2 ." E stim ates of the incom e
coefficients ((A are all positive an d statistically signifi­
,)
can t at usual significance levels, indicating that the
five com m od ity groups includ ed in this study are
norm al goods.
The incom e elasticity of d em an d for M l show n in
table 2 (0.53) is sim ilar to those rep o rted in o th er
studies. M oreover, it co rresp o n d s closely to its th e o ­
retical value of 0.50 im plied by the Baum ol (19 5 2 )Tobin (1956) inventory — th eo retic m odel of the tra n s­
action s dem an d for m oney.
The own- and cross-p rice coefficients (ttm are g en er­
)
ally estim ated w ith less p recision than the incom e
coefficients. C onsistent w ith the stan d ard a ssu m p ­
tions of eco n o m ic theory, estim ates of the (Slutsky)
ow n-price coefficients are negative, although n ot all
are statistically significantly different from zero at
usual significance levels.1
3

"The income elasticity of demand for the ith commodity group, (x
,,
is given by | , =
jl

This result can be verified by a simple manipu­

lation of the definition ix =
,

dm

On the other hand, the Hicks-Alien

price elasticity of demand for the ith group, (i,,, is given by

jjl,
,

=

which can also be verified by a simple manipulation of the definition
,

1
1

=

m apj'

1 Negativity of the own-price coefficients, the diagonal elements in the
2
[iiij matrix, is a necessary, but not sufficient, condition for it to be
negative semidefinite; a matrix is negative semidefinite if and only if
all of its characteristic roots are nonpositive, and at least one root is
zero. This property, which was not imposed in this study, was
examined by computing the characteristic roots of the estimates of
the [tt,,] matrix in table 2. The computed characteristic roots are
(0.0000,0.0000, -0.0022, -0.0097, -0.1743); thus, the negativ­
ity condition is satisfied.

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

Table 2
Maximum Likelihood Estimates of the Absolute Price Version of the Rotterdam Model
Equation

M
i
Food

Nondurables

ABM1

Services

M
1

Food

0.187083
(6.682878)

-0.116241
(-7.380222)

0.058199
(4.867328)

0.057593
(3.167629)

0.000352
(2.913345)

0.000097
(1.779196)

Nondurables

0.291246
(9.685506)

0.058199
(4.867328)

-0.034326
(-1.918331)

-0.024572
( - 1.228305)

0.000549
(2.129760)

0.000150
(1.319010)

0.467938
(10.304847)

0.057593
(3.167629)

-0.024572
(-1.228305)

-0.034144
(-1.135707)

0.000882
(1.596066)

0.000242
(1.686502)

ABM1

0.042172
(2.090867)

0.000352
(2.913345)

0.000549
(2.129760)

0.000882
( 1.596066)

0.001399
(-2.558969)

0.000384
( -1.832747)

M1

0.011561
(3.043011)

0.000097
(1.779196)

0.000150
(1.319010)

0.000242
(1.686502)

- 0.000384
(-1.832747)

-0.000105
-0.276950)

Services

Note: t-ratios are in parentheses.
Average Income Elasticities
Food

Nondurables

Services

ABM1

M1

0.828044

1.390072

0.942341

1.027321

0.525813

Average Hicks-Allen Elasticities
Food
Food

Nondurables

-0.514493

0.257394

0.254911

Services

ABM1

M1

0.001560

0.000428
0.000718

Nondurables

0.277775

-0.163834

-0.117278

0.002619

Services

0.115982

-0.049483

-0.068760

0.001775

0.000487

ABM1

0.008585

0.013365

0.021474

-0.034071

-0.009354

M1

0.004394

0.006841

0.010991

-0.017464

-0.004763

The Model’s In-Sample Predictive
Performance
As stated earlier, the R otterdam m odel can tie used
to provide predictions of the value (budget) shares.
The m odel's implied prediction of the sh are of the ith
good at time t is given by
Wi,1+1 = w h - eH,
w here w„ is the actual value share of the ith good, and
eh is the residual of the ith dem an d equation at tim e t.
The in-sam ple predictive p erform ance of the R otter­
d am m o d el c a n be ev alu ated in te rm s of its
inform ation-theory results; a general discussion of
this m eth od of assessing prediction a ccu ra cy is p re­
sented in appendix B. C om puted m easu res of infor­
m ation (prediction) in accu racies from the m odel are
rep orted in table 3, along w ith inform ation -in accu racy
m easures for a naive (no-change) extrapolation of the



value shares. The rep orted m easu res show substantial
red u ction s in inform ation in accu racies w hen the
m o d e l re s u lts a re c o m p a r e d w ith th e n aiv e
p red iction s.1
3
F u rth er insight into the m o d el’s in-sam ple p red ic­
tions m ay be gained by plotting the; actual and p re­
dicted shares; this is done in ch arts 1 -5 . An inspection
of these ch arts reveals that the m o d el’s in-sam ple
predictions track the data extrem ely well; this is esp e­
cially true for the M l equation despite considerable
variability in the actual sh ares of M l. These results
suggest that the dem an d for M l, as derived in this

1 ln fact, in view of the greater variability of the shares of M1 and
3
ABM1 relative to the shares of the other goods and services shown
in charts 1-5, it is not surprising that predictions from the money
equations “beat” the naive model by a larger margin than predic­
tions from the other equations. In the presence of high period-toperiod variation in the actual shares, the no-change naive model will
always perform poorly.

27

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

Table 3
Average Information Inaccuracies1
Rotterdam Model

Naive

System Results
Uncorrected information inaccuracy
Information inaccuracy with d.f. correction
Percent reduction from naive

14.40
14.82
96.73%

452.60

3.505
71.22%
4.141
65.35%
5.943
82.79%
5.083
98.67%
0.646
98.74%

12.18

Single Equation Results
Food information inaccuracy
Percent reduction from naive
Nondurables information inaccuracy
Percent reduction from naive
Services information inaccuracy
Percent reduction from naive
ABM1 information inaccuracy
Percent reduction from naive
M1 information inaccuracy
Percent reduction from naive
'The information inaccuracies are to be multiplied by 10-4.

C h a rt 1

Actual vs. Predicted V alue Shares of Food


28


11.95
34.54
381.30
51.30

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

C h a rt 2

Actual vs. Predicted Value Shares of Nondurables

C h a rt 3

Actual vs. Predicted Value Shares of Services




29

FEDERAL RESERVE BANK OF ST. LOUIS

Actual vs. Predicted Value Shares of ABM1

C h a rt 5

Actual vs. Predicted Value Shares of M l


30


AUGUST/SEPTEMBER 1986

AUGUST/SEPTEMBER 1986

FEDERAL RESERVE BANK OF ST. LOUIS

study, was m ore stable than the d em an d for o th er
goods, services and financial assets over the sam ple
period.

CONCLUDING REMARKS
This study has d iscu ssed an ap p roach to the esti­
m ation of the dem an d for m oney that relies on a
m ethodology m arkedly different from that em ployed
in the conventional m oney d em an d analysis. The a p ­
p roach is explicitly derived from the principles of
m icro eco n om ic th eoiy and em p h asizes the im p or­
tance of interaction am ong goods. Th e m odeling p ro ­
cess is not influenced by a search for “goodn ess of fit”;
instead the em phasis is p laced on the m od el’s co n sist­
en cy with explicit utility-m axim izing conditions.
The em pirical results p ro d u ced in this study show
that it is possible to specify a m odel of m oney dem and
that closely tracks the actual behavior of the flow of
M l’s m on etary services despite its considerable varia­
bility over this period. Thus, there seem s to be nothing
m ysterious about that variability; it can be explained
in term s of ch an ges in relevant eco n o m ic variables.
T hese results indicate that m oney dem and has been
considerably m ore stable over the past two d ecad es
than stan d ard m oney d em an d analysis has suggested.

________and Kenneth Singleton. “The Microeconomic Theory of
Monetary Aggregation,” New Approaches to Monetary Economics
(Cambridge University Press, forthcoming).
Barten, A. P. “Maximum Likelihood Estimation of a Complete De­
mand System,” European Economic Review, Vol. 1 (1969), pp. 773.
Baumol, William J. “The Transactions Demand for Cash: An Inven­
tory Theoretic Approach,” Quarterly Journal of Economics (Novem­
ber 1952), pp. 545-56.
Ewis, Nabil A. and Douglas Fisher. "The Translog Utility Function
and the Demand for Money in the United States,” Journal of
Money, Credit, and Banking (February 1984), pp. 34-52.
Fayyad, Salam K. “Monetary Asset Component Grouping and Ag­
gregation: An Inquiry into the Definition of Money” (Ph.D. disserta­
tion, The University of Texas at Austin, 1986).
Goldfeld, Stephen M. “The Demand for Money Revisited," Brook­
ings Papers on Economic Activity (3:1973), pp. 577-646.
_________ “The Case of the Missing Money,” Brookings Papers on
Economic Activity (3:1976), pp. 683-739.
Judd, John P. and John L. Scadding. “The Search for a Stable
Money Demand Function: A Survey of the Post-1973 Literature,”
Journal of Economic Literature, Vol. 20 (1982), pp. 993-1023.
Mizrach, Bruce and Anthony M. Santomero. “The Stability of Money
Demand and Forecasting through Changes in Regimes,” The
Review of Economics and Statistics (May 1986), pp. 324-28.
Samuelson, Paul A. Foundations of Economic Analysis (Harvard
University Press, 1983).
________ and Ryuzo Sato. "Unattainability of Integrability and
Definiteness Conditions in the General Case of Demand for Money
and Goods,” American Economic Review (September 1984), pp.
588-604.
Theil, Henri. Economics and Information Theory (North-Holland,
Amsterdam, 1967).
_________Principles of Econometrics (Wiley, 1971).
_________ Theory and Measurement of Consumer Demand, Vol. 1
(North-Holland, Amsterdam, 1975).

REFERENCES
Barnett, William A. “The User Cost of Money," Economics Letters,
Vol. 1 (1978), pp. 145-49.
_________ “Theoretical Foundations for the Rotterdam Model,”
Review of Economic Studies, Vol. 46 (1979), pp. 109-30.
_________ Consumer Demand and Labor Supply (North-Holland,
Amsterdam, 1981).




_________ Theory and Measurement of Consumer Demand, Vol. 2
(North-Holland, Amsterdam, 1976).
_________The System-Wide Approach to Microeconomics (Uni­
versity of Chicago Press, 1980).
Tobin, James. “ The Interest Elasticity of Transactions Dem and for
Cash,” Review of Economics and Statistics (August 1956), pp.
241-47.

(See app en dixes A and 1 on following pages)
5

31

FEDERAL RESERVE BANK OF ST. LOUIS

AUGUST/SEPTEMBER 1986

Appendix A
In o rd e r to e stim a te th e fu n ctio n a l form o f th e d em an d
eq u atio n s, a s to c h a s tic v ersio n o f th a t form sh o u ld b e s p e c ­
ified a n d th e d is tu rb a n ce te rm s in te rp re te d . T h e sy ste m o f
d em a n d e q u a tio n s c a n b e w ritte n as follow s,
5
2

(1) X„ = m x , +

t1
t,,

P| + e„,
t

/I ,

" 't

w h e re X„ ( = w*, Dx,,) is a T -d im e n sio n a l v e cto r o f o b serv a­
tio n s o n th e le ft-h a n d -sid e v ariables o f th e ith co m m o d ity
group, PM = D ph) is a T -d im e n sio n a l v e cto r o f th e lo g -ch a n g e
(
in th e p rice o f th e ith co m m o d ity grou p , |x, is th e m arginal
b u d g et s h a re o f th e ith co m m o d ity gro u p , I t t J is a 5 x 5
5

matrix of the price coefficients, and X, ( =

2

w *

Dxh) is a

i= t
T -d im e n sio n a l v e cto r o f th e (bu d get-sh are) w eig h ted su m o f
th e lo g -ch an g e in e x p e n d itu re s on th e five co m m o d ity
grou p s.
T h e last term in e q u a tio n 1, e m, is th e d is tu rb a n ce term o f
th e ith d em an d e q u atio n . T h e d is tu rb a n c e te rm s, [ e j , are
a ssu m e d to c a p tu re th e ran d o m e ffe cts o f all v ariab les o th e r
th a n in c o m e a n d all p ric e s . T h e d is tu rb a n c e te rm s are
fu rth e r a ssu m e d to be n o rm ally d istrib u te d w ith m e a n ze ro
a n d a v a ria n ce-co v a ria n ce m atrix 2 (x) I„ s u c h th at
e

m
)

=

a u

(3) a n d E (eis, eit) = 0

f o r s = t,
fo rs^ t,

w h ere (x) is th e K ro n e ck e r p ro d u c t, I, is a T x T id en tity
m atrix, a n d cr*, is th e i, jth e le m e n t o f th e 5 x 5 m atrix, S .
A n o th er p ro p e rty o f th e d e m a n d -d is iu rb a n c e te rm s is
th at th e ir su m v an ish es w ith u n it p ro b ab ility (see B arten
(1969), p. 16 an d T h e il (1971), p. 333). A p o te n tia lly tro u b le ­
so m e im p lica tio n o f th is p ro p erty is th at
2(7^ = E(eit(eM+ ... + e j ) = 0.
i
Thus, th e c o v a ria n ce m atrix, 2 , is sin g u lar, a n d as s u c h ,
c a n n o t have a rank th at is larg er th a n n — 1. In w h at follow s,
it is a ssu m e d th at th e ran k o f 2 is e x a ctly n —1. In o rd e r to
circu m v e n t th e c o m p lic a tio n s p o se d by th is sin g u larity
p ro b lem , o n e e q u a tio n o f th e sy stem (1) is d ele te d . T h e
leg itim acy o f th is p ro ced u r e c a n be v erified easily by s u m ­
m in g over i an y fo u r o f th e five e q u a tio n s o f th e sy stem and
u sin g th e p ro p e rtie s o f th at sy ste m in o rd e r to re co v e r the
d ele te d e q u atio n . In fact, a m a jo r ad van tage o f th e e s tim a ­
tio n m e th o d u se d in th is study, full in fo rm atio n m ax im u m
lik elih o o d (FIML), is th at th e p a ra m e te r e stim a te s it p ro ­
d u c e s are invariant to th e e q u a tio n d e le te d (see B arten
(1969), pp. 2 5 -2 7 ).

32



For notational convenience, the system of demand equa­
tions (II may be written as follows,
(4) y, = g(x„0) + e ,,

i= i

(2) E(£is,

Formulation o f the Likelihood Function

where y, are the vectors of the left-hand-side variables of (1),
x, are the vectors of the right-hand-side variables, e, are the
vectors of the demand-disturbance terms, and 0 is the
vector of the parameters |x and tt^. Since the additive distur­
,
bance vectors e , = ( e ,„ ..., e 41), t = l, ..., T, are assumed to be
independently normally distributed with mean 0 and
variance-covariance matrix 2, it follows that the vectors y,
must also be independently normally distributed with
mean g(x„ 0 ) and variance-covariance matrix 2 . In arriving
at the vector-valued function g, it is assumed for notational
convenience that prior restriction on the parameters has
already been eliminated by substitution.
Given the observed data on y = (y„ ...,yr)a n d x = (x„ ...,x.r),
the log-likelihood function on 0 and 2 is given by
(5) L (0, 2 ;y , x) = —(T(n —1)/2) log 2 it

- 1 /2

l2 l

T
1
2 f(y, ~ g (x„ 0 ) ) ' 2 (y, —g (x, 2))].
t= i

This function is to be maximized with respect to the ele­
ments of the parameter vector 0 and the elements of the
variance-covariance matrix, 2 . For computational conven­
ience, however, and since the asymptotic distribution of 2
is not at all needed, a stepwise-optimization procedure is
used. This procedure involves first maximizing the loglikelihood function (5) with respect to the elements of 2, for
a given value of 0 , to obtain an expression for 2 in terms of
the elements of 0 . Thus, for 0 = 0 *, the value of 2 that
maximizes (5) is given by
1 1
(6) 2 * (0 *;y , x) = — 2 (y ,-g (x„ 0 ) )(y ,-g (x„ 0 ) )'.
t= l
Substitution of 2* into (5) yields
1
(7) L (0;y, x) = - (T(n - l)/2) log 2 tt l2 (0 ;y , x) I - “ ( T ( n - l) ),
which is the concentrated likelihood function.
The second step in the optimization procedure becomes
immediately clear when one recognizes that maximizing
the log-likelihood function (5) is equivalent to minimizing
the determinant of 2 in (7). The latter is accomplished by
searching the feasible parameter space for the value of 0 at
which I2 I is minimized. The values of the elements of ©
thus obtained,©, are the maximum likelihood estimates of

FEDERAL RESERVE BANK OF ST. LOUIS

the system (1). T h e a sy m p to tic co v arian ce m atrix o f© is o b ­
tained by invertin g th e m atrix - [ ff- L ], w h ic h is n u m e ri-

d&d&'

AUGUST/SEPTEMBER 1986

m atrix p e rta in o n ly to th e e stim a te d p a ra m e ters. T h e a s ­
y m p to tic co v a ria n ce m atrix o f th e e n tire v e cto r o f (e sti­
m ated as w ell as co m p u ted ) p a ra m e te r e stim a te s is derived
in Fayyad (1986).

cally ev alu ated at (n = (n N aturally, th e e le m e n ts o f that
)
).

Appendix B
Available resu lts from in fo rm a tio n th e o iv ca n lie u se d to
develop m e a su res by w h ic h th e p e rfo rm a n c e o f e a c h o f the
estim a te d e q u a tio n s as w ell as th at o f th e sy ste m as a w h o le
can be gau ged .' C o n sid e r an in fin ite sim a l c h a n g e in th e
bu d get sh a re o f th e ith co m m o d ity ' w = p.x/m l:

xi ,

Pi ,

PA .

dw: = - dp, + — dx, — — r dm ,
m 1
m
nv
from w h ic h it follow s that
(1) dw, = w, d log f), + w, d log x, — w, d log m .
T h e fin ite -ch a n g e an alo g o f e q u a tio n 1 is given by
(2) Aw,, = w*, I)p,, + w*t Dx,, - w*, Dm,.
S in ce Dm, = Dx, + Dp,, it follow s th at e q u a tio n 2 c a n be
rew ritten as
(3) Aw,, = w* Dx,, + w*, (Dp,, — Dp,) — w*, Dx,.
O bseiv e th at the first te rm on the rig h t-h a n d -sid e o f e q u a ­
tion 3, to b e in te rp re te d as th e q u a n tity c o m p o n e n t o f the
ch a n g e in th e bu d get sh a re o f th e ith good, is th e d e p e n d e n t
variable o f th e ith d em a n d e q u a tio n o f th e e stim a te s sy stem .
T h u s, given the lo g -ch a n g es in real in c o m e a n d relative
p rices, th e R o tterd am m o d el c a n be u sed to provide c o n d i­
tion al fo re c a sts o f w*. Dx,, and , th ro u g h e q u a tio n 3 o f A w,,.
S in ce th e p re d ictio n o f wf, Dx,, is equ al to th e rig h t-h an d sid e o f th e ith d em an d e q u a tio n w ith th e d is tu rb a n c e term
d eleted , it follow s th at
w lil+, = w„ - e ,, ,
w h ere w lil+, is th e im p lied p re d ictio n o f w i t , a n d e ,, is th e
re sid u al o f th e ith d em an d e q u a tio n in p e rio d t.
In view o f the fact th at th e b u d g e t sh a re s are p o sitive an d
ad d up to unity, th e y m ay be view ed as p ro b a b ilitie s. A
m e a su re o f the m o d e l fit c a n be a c q u ire d b y d ete rm in in g
the e x p e c te d gain in in fo rm a tio n from th e a c tu a l sh a re s,
w h ic h ca n be view ed as p o s te rio r p ro b a b ilitie s, w h e n th e
'See Theil (1967), pp. 1-48; (1971), pp. 646-50, and Barnett (1981),
pp. 149-54.




im p lied p re d ic tio n s (or th e fitted values) o f th e s e s h a re s are
view ed as p rio r p ro b a b ilitie s. T h a t m e a su re is given by

(4) f, =

■

n
2

.

i= t

w Mlog

Y
V
w ,,

,

"

w h e re I, is the in fo rm a tio n in a c c u ra c y o f th e p re d ictio n s
prov id ed by th e sy stem o f d e m a n d e q u a tio n s. It is to be
n o te d th a t not o n ly is th is m e a su re o f in fo rm a tio n in a c c u ­
racy ad ditive over g o o d s, as is in d ic a te d by th e e x p re ssio n
in (4), but it is also ad ditive o v er tim e. T h u s, it is p o ssib le to
c o n s tr u c t an average in d e x o f in fo rm a tio n in a c cu ra cy , 1,
over th e p erio d from t, to t, by u sin g th e follow ing form u la

(5) I =

2 I, .
______!_____
t. - ». + 1 t = t,

O b seiv e th at the in fo rm a tio n -in a c cu ra c y m e a s u re s p re ­
se n te d above p e rta in to th e p re d ic tio n s w h ic h are prov id ed
by th e sy stem o f d e m a n d e q u a tio n s as a w h o le. It is p o ssib le
to a c q u ire a sin g le -e q u a tio n m e a su re o f in fo rm a tio n in a c ­
c u ra c y by u sin g th e fo rm u la
(6) I,, = w it log ^ + (1 —w„) log J_ ^1!,
_
w„
1 —w„
w h e re 1 —w Mis th e c o m b in e d b u d g et s h a re o f all c o m m o d i­
ties o th e r th a n th e ith. As b efo re, th e average (over tim e)
in d ex o f a sin g le -e q u a tio n in fo rm a tio n in a c c u ra c y c a n be
o b ta in e d by u sin g fo rm u la 5.
In o rd e r to provide co m p a ra b ility o f the in fo rm atio n
in a c c u ra c y a c ro ss m o d e ls, a c o r re c tio n (ad ju stm e n t) facto r
sh o u ld be a p p lied to th e s e m e a s u re s (see T h e il (1971), pp.
t>.r l - 5 2 , a n d B a rn e tt (1981), p. 150). A d ju stm e n t w as
i
ach iev e d in th is stu d y by m u ltip lyin g th e in fo rm a tio n -in a c cu ra c y m e a su re in e a c h c a s e by a fa c to r o f ML/1ML-K),
w h e re M is th e n u m b e r o f jo in tly e stim a te d e q u a tio n s, L is
th e n u m b e r o f tim e p e rio d s (qu arters), a n d K is th e n u m b e r
o f u n re s tr ic te d p a ra m e te rs. Clearly, th is p ro c e d u re is
clo s e ly akin to the d eg re e s-o f-fre e d o m a d ju s tm e n t o f the
c o rre la tio n c o e fficie n t.

33