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June/July 1980
Vol. 62, No. 6

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2 Eurodollars and the U .S. Money Supply
13 Dynamic Forecasting and the
Demand for Money
24 Financing Constraints and the Short-Run
Response to Fiscal Policy

Eurodollars and the U.S. Money Supply
ANATOL B. BALBACH and DAVID H. BESLEB

INTRODUCTION
J t is frequently asserted that the Eurodollar mar
ket has contributed substantially to worldwide infla
tion and general economic instability. Eurodollars
allegedly move with ease from country to country,
disrupting national credit and money markets and
creating fears about the inflationary consequences for
the U.S. economy if all these “dollars” pour back into
the U.S. banking system.
Inflation results when spending grows faster than
real output. If excess spending occurs because the
quantity of money grows faster than people’s desire
to hold money, then Eurodollar transactions can in
crease inflation only if they reduce the growth of
output, reduce people’s desire to hold money, or in
crease the amount of money in existence. There is no
theoretical or empirical evidence that Eurodollar trans
actions have reduced output growth. The extent to
which the Eurodollar market has reduced the de
mand for domestic currencies remains uncertain. Con
sequently, if the Eurodollar market contributes to in
flation, it does so either by increasing the amount of
money in existence or impeding control of domestic
money stocks. The extent to which the Eurodollar mar
ket has independently contributed to an expansion of
the world money supply has been the focus of a num

ber of studies.1 Despite this research effort, serious
questions remain about whether or not the volume of
Eurodollar balances should be included in any aggre
gation of the world money stock.
This article, however, addresses a different but re
lated question by focusing on the relationship be
tween the Eurodollar market and monetary control.
It assumes throughout that the Federal Reserve Sys
tem does not engage in Eurodollar transactions or
alter its monetary policy as a result of such transac
tions. The first section of the article describes the
Eurodollar market. The second section illustrates,
through the use of balance sheets, how Eurodollar
transactions may affect the U.S. money supply. The
third section investigates the effects of Eurodollar
transactions on the U.S. money supply in the context
of a money multiplier model.
!F o r representative studies on this question that make use of
a multiplier framework, see John H. Makin, “Identifying a Re
serve Base for the Eurodollar System,” Journal of Finance
(June 1973), pp. 609-17; and Boyden E . Lee, “The Eurodollar
Multiplier,” Journal of Finance (September 1 9 7 3 ), pp. 86774. Fo r an alternative portfolio balance approach that chal
lenges the relevance of the multiplier framework as applied
to the Eurodollar market, see John Hewson and Eisuke
Sakakibara, T he Eurocurrency Markets and their Implications
(Lexington, Mass.: Lexington Books, 19 7 5 ).

FED E R A L. R E S E R V E B A N K O F ST. L O U IS

A Brief Descriptive History of the
Eurodollar Market
A Eurocurrency market consists of banks that ac
cept deposits and make loans in currencies other than
those of their own country.2 The modem Eurodollar
market evolved from the special circumstances of
the post-World War II international finance system.3
Early in this period, many foreigners found it con
venient to deposit dollar balances with banks in Eu
rope. As in the post-World War I period, these funds
were generally repatriated to the U.S. as European
banks acquired dollar assets directly through the U.S.
money market.4 By the end of the 1950s, however,
Eurobanks began lending dollar-denominated funds,
and this activity spawned the modern Eurodollar
market.
The primary reason for this market’s development
and subsequent expansion is that, like other financial
market innovations, it reduces the costs of inter
national trade by offering traders an efficient means
of economizing on transaction balances in a world
where most trade is denominated and transacted in
dollars. Regulation Q ceilings and differential reserve
requirements for various categories of U.S. bank lia
bilities also contribute to further Eurodollar inter
mediation. U.S. banks periodically encounter difficulty
in attracting and retaining corporate deposit balances
because of effective Regulation Q interest rate ceil
ings.5 Foreign branches of U.S. banks, however, do
not face these restrictions. Consequently, as interest
rates rise and the yield differential between Eurodol
lar and domestic deposits widens, corporate depositors
channel funds into Eurodollar accounts. Foreign
branches of U.S. banks then can re-lend the funds
back to the parent institution. In this way, many U.S.
banks are able to mitigate some of the consequences
of the disintermediation that accompanies periods of
2Although U.S. banks are prohibited from accepting deposits
or making loans in currencies other than U.S. dollars, banks
in other countries, including foreign branches of U.S. banks,
are not.
3Fo r a detailed discussion of the history of this market see
Paul Einzig, T he Eurodollar System, 5th ed. (N ew York: St.
Martin’s Press, 1973).
4Some authors have attributed a special role in the develop
ment of the Eurodollar market to Communist bloc countries.
It is argued that these countries feared that their assets
would be frozen by the U.S. government as part of Cold W ar
political strategy.
5The emergence of the large denomination certificate of de
posit (C D ) market can be traced to the early 1960s, when
corporate financial officers began managing cash positions
more carefully to take advantage of the higher interest rates
offered on short-term time deposits. (Banks have not been
permitted to pay explicit interest on demand deposits.)

JU N E/JU LY

1980

rising U.S. interest rates.6 Finally, differences in re
serve requirements across bank liabilities often rein
force U.S. banks’ incentive to secure funds from Euro
dollar sources.

The Eurodollar Banking System
Because Eurobanks intermediate between lenders
and borrowers, the Eurodollar market, like any other
fractional reserve banking system, can expand the
amount of Eurodollar liabilities. Since not all deposi
tors will withdraw their funds simultaneously, Euro
banks can lend these deposits, and the transferral of
these funds from one bank to another produces a
multiple expansion of deposits and credit. In national
banking systems, this multiple expansion is limited by
the extent to which banks hold required or precau
tionary reserves. The potential expansion of dollardenominated credit occurring through the Eurodollar
system is limited only by the amount of precautionary
reserves that Eurobanks hold in order to meet their
short-term liquidity needs.
Eurobanks do not issue demand deposits, even
though some deposits are of very short duration —
frequently overnight — and can be transferred from
one individual to another easily and conveniently.
Despite this rapid transferability, Eurodollars are not
generally acceptable as payment for goods and serv
ices in any country and therefore are excluded from
current definitions of money.7 Borrowers of Eurodol
lars who wish to buy goods and services with the
proceeds of a loan must first convert them into some
national currency.8 Viewed in this light, Eurodollar
deposits are similar to savings and time deposits that
serve as a “temporary abode of purchasing power.”
In summary, the Eurodollar system can expand
credit by some multiple of its reserves, but it cannot
create money since its liabilities, unlike those of banks,
are not generally acceptable as a means of payment.
Although the Eurodollar market does not create
money directly, it may generate some important in
direct effects if Eurodollar transactions affect domestic
money stocks.
6Until these borrowings by U.S. banks were subjected to re
serve requirements, banks had an additional incentive to
acquire such funds.
7The Federal Reserve Board of Governors does include “over
night Eurodollars held by U.S. residents other than banks at
Caribbean branches of member banks” in its current defini
tion of M2. This article, however, focuses on the transactionbased definitions of money — old M l and the newly defined
M IA and M1B.
8This process is analogous to that which occurs when an indi
vidual borrows from a savings and loan institution. Before
spending these funds, he too must first convert the loan into
currency or demand deposits at a commercial bank.

JU N E/JU LY

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

Transaction 1.

Conversion of Demand Deposits into Eurodollars

Public
Assets

Liabilities

U.S. banks
Assets

D D P —$100
ED -f-$100

Can Eurodollar Transactions
Affect the U.S. Money Stock?
The Eurodollar market and the U.S. monetary sys
tem are linked by those transactions in which holders
of U.S. dollar-denominated assets deposit dollars in
Eurobanks, or in which holders of Eurodollars spend
these funds in the United States. The majority of such
transactions involves the exchange of short-term as
sets. For example, an individual or a corporation that
owns demand deposits, certificates of deposit, repur
chase agreements, Treasury bills, or commercial paper
may convert these assets into Eurodollars. Similarly,
holders of Eurodollars, or borrowers in the Eurodol
lar market, may convert these funds into domestic
financial instruments or buy goods and services
outright.
In the following discussion, four transactions are
used to typify the relationship between the Eurodollar
and U.S. money markets.9 Transactions 1 and 3 in
volve the conversion of demand deposits into Euro
dollars. Transaction 1 assumes that Eurodollar insti
tutions hold their reserve assets in the form of
demand deposits at U.S. banks; transaction 3 assumes
that these reserve assets are held in the form of bal
ances “due from” U.S. banks. Transactions 2 and 4
involve conversion of other U.S. bank liabilities such
as certificates of deposit into Eurodollars. Transactions
2 and 4 maintain the same assumptions as transac
tions 1 and 3, respectively, about the form in which
Eurodollar institutions maintain their reserves.
For convenience, two additional assumptions are
made. First, the Federal Reserve System continues to
supply the monetary base at some predetermined con
stant rate. This assumption is necessary to distinguish
the effect of Eurodollar transactions from policyinduced changes in money stock. Second, the required
reserve ratio is assumed to be 10 percent on demand
deposits and 5 percent on other bank liabilities.
9Although they do not exhaust all possible asset substitutions,
these four transactions are representative of the way in which
Eurodollar-related transactions affect the U.S. money stock.

1980

Eurobanks

Liabilities

Assets

Liabilities

D D E+$100
D D P — $100

D D E+$100

ED +$100

In transaction 1, a holder of demand deposits at a
U.S. bank transfers $100 million into Eurodollar depos
its at a Eurobank.10 On the public’s balance sheet,
demand deposits (DDP) decline and Eurodollar de
posits (ED ) rise by the same amount. At the Euro
bank, the individual’s account is credited and the
bank’s Eurodollar liabilities rise by $100 million. When
the check clears, the U.S. bank’s demand deposit lia
bility to the public (DDP) declines and the demand
deposit liability to the Eurobank (D D E) increases.
The Eurobank’s balance sheet will record this trans
action as an increase in assets.
The impact of this transaction on the U.S. money
stock depends on how money is measured. Using the
old definition of money (M l), which includes foreign
commercial bank demand deposits at U.S. banks, the
money supply is unaffected since DDP declined and
DDE rose by the same amount. Because DDP and
DDE have the same reserve requirements, excess re
serves are not affected and no further contraction or
expansion of loans and deposits in the U.S. is possible.
On the other hand, if money is measured either by
MIA or MIB (which exclude foreign bank demand
deposits at U.S. banks), then the money supply de
creases by the amount of the transaction since DDP
declines while the increase in DDE is not counted.
Because excess reserves are still unaffected, there will
be no further change in the money stock. Thus, the
initial effect of deposit outflows into the Eurodollar
market lowers the money stock, as currently mea
sured, by an amount equivalent to the size of the
transaction.
It is important to note that in this transaction Euro
banks collectively are assumed to hold total reserves
(in the form of demand deposit balances at U.S.
banks) equal to the initial dollar outflow from U.S.
banks. If, in the extreme, Eurobanks hold no reserves
at all, the U.S. money stock, however defined, will be
10This Eurobank may be a foreign branch of some U.S. bank
or an unafBliated foreign bank.

JU N E/JU LY

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

Transaction 2.

Conversion of Certificates of Deposit into Eurodollars

Public
Assets

Liabilities

U.S. banks
Assets

C D — $100
ED +S100

unaffected.11 However, to the extent that Eurobanks
hold some precautionary reserves in the form of de
mand deposits at U.S. banks, the qualitative effect of
the Eurodollar transactions is the same as outlined
above.
In transaction 2, the owner of a certificate of deposit
(CD) at a U.S. bank fails to renew a maturing CD
and deposits the funds as a Eurodollar deposit at
some foreign bank. On the public’s balance sheet,
CDs fall and Eurodollar deposits rise. At the Euro
bank, Eurodollar liabilities increase and, when the
transaction clears, the foreign bank’s deposits at the
U.S. bank rise. At the U.S. bank, domestic CDs fall
while liabilities to foreign banks rise. If money is
measured as Ml, then the increase in DDE implies
an immediate increase in the money supply. On the
other hand, if M1B (or MIA) is used, the money
stock does not change since neither CDs nor DDEs
are included in the definition of money. In both cases,
however, bank excess reserves decline. Because the
DDE reserve requirement is 10 percent and the CD
reserve requirement is 5 percent, an increase in DDE,
offset by an equivalent decrease in CDs, raises banks’
required reserves by 5 percent of the transaction.
Since banks must contract loans and deposits, the
money stock will decline. Thus, in the case of Ml,
the net effect is an expansion (an immediate increase
in Ml plus a subsequent, less than fully offsetting,
contraction caused by a decrease in excess reserves).
In the case of M1B, there is a net contraction (no
immediate change in M1B — only the subsequent
contraction).
These results are derived from the assumption that
the Eurodollar banking system maintains precautionu The Eurobank would create a new loan equal to the full
amount of D DE, thereby drawing down such balances. The
borrower would have to acquire a U.S. demand deposit be
fore he could spend the proceeds of this loan. This transac
tion then restores the balance sheet of the U.S. bank to its
original position. Note that this intermediation through the
Eurodollar market generates a greater extension of credit
than would have occurred if generated through the U.S.
banking system only.

1980

Eurobanks

Liabilities

Assets

Liabilities

C D — $100
D D E+$100

D D E+$100

ED +$100

ary reserves in the form of demand deposit balances
at U.S. commercial banks.12 The effect of Eurodollarrelated transactions on the U.S. money stock will be
somewhat different if Eurobanks hold their precau
tionary reserves in a different form. For instance, the
Eurobank receiving the initial deposit transfer from
a U.S. bank will, on the day of the transaction, actu
ally receive a credit referred to as balances “due
from” the U.S. bank. The U.S. bank initially carries
the transaction as balances “due to” a foreign bank.
This part of the transaction is analogous to the initial
book entries made by domestic banks when funds
transferred between them are in the process of col
lection. Transactions 1 and 2 assume that these “col
lection balances” are cleared quickly with offsetting
changes to U.S. demand deposit balances of the Euro
banks. This assumption is appropriate if the Eurobank
wishes to lend to non-bank borrowers.
On the other hand, if the Eurobank continues to
carry the “due from” item on its balance sheet, the
U.S. bank will record a corresponding liability item
“due to” a foreign branch or commercial bank in
stead of recording a demand deposit.13 The Federal
Beserve defines the net amount of these “due tos”
(gross “due tos,” less the U.S. bank’s “due froms”) as
Eurodollar borrowings.14 In this case, Eurodollar bor
rowings increase and, because these borrowings are
subject to different reserve requirements than demand
12In the event that the Eurodollar banking system held no
reserves, the final effect of this second transaction would be
to increase the money stock under any definition of money.
13The Eurobank may consider these funds to be either pre
cautionary reserve balances or an earning asset like any
other loan, depending on the nature of its relationship with
the U.S. bank and on whether the “due from” credit ex
plicitly earns interest and is of some specific duration.
Whether these funds are regarded as reserves or an earning
asset, their impact on the U.S. money stock is the same as
described in the text.
14For foreign commercial banks that are not branches of U.S.
banks, only those gross “due to” balances not designated as
demand deposits are treated as Eurodollar borrowings. For
branches of U.S. banks, all gross balances “due to” the
branch enter into the calculation of Eurodollar borrowings.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

Transaction 3.

U.S. banks

Liabilities

Assets

D D P —$100
ED +$100

deposits, the money stock is affected differently. The
two transactions outlined above are now re-examined
under the assumption that the Eurobank chooses to
carry an asset in the form of a “due from.”
In transaction 3, as in transaction 1 above, $100 mil
lion in demand deposits at a U.S. bank are converted
into Eurodollars. Balance sheet entries in the public’s
account are identical to those in transaction 1. Unlike
that example, however, the Eurobank records its assets
from the transaction as balances “due from” (DF) U.S.
banks. At the U.S. bank, DDP declines and funds “due
to” (DT) its own branch or other foreign banks rise by
$100 million. This transfer has two immediate effects.
First, Ml, MIA, and M1B decline by $100 million
since DDP falls by $100 million and DT is not in
cluded in either measure of the money stock. Second,
since banks are assumed to hold reserves equal to 10
percent on demand deposits and 5 percent on all other
liabilities, including Eurodollar borrowings, the U.S.
bank’s excess reserves rise by $5 million. These excess
reserves permit an expansion of loans and deposits,
partially offsetting the initial decline in the money
supply.
In transaction 4, the U.S. public converts $100 mil

Transaction 4.

Liabilities

Assets

Liabilities

D T+$100
D D P — $100

D F+$100

ED +$100

lion in CDs into a Eurodollar deposit at a foreign
bank. The change in the public’s balance sheet is
identical to transaction 2. Eurobank liabilities rise by
$100 million, as do balances “due from” the U.S. bank.
Upon clearing the transaction, U.S. bank liabilities in
the form of CDs fall, while funds “due to” its foreign
branch rise by $100 million. Since neither CDs nor
DTs are included in the definitions of money and
since both, by assumption, have the same reserve re
quirement, the money stock is unaffected.
As this discussion illustrates, Eurodollar transac
tions can affect the U.S. money supply even when the
monetary base remains constant. The extent to which
Eurodollar transactions affect the money stock de
pends partially on how money is measured.15 Differ
ential reserve requirements combine with Eurodollar
flows to produce an additional effect on the money
stock. The transactions outlined here, however, have
essentially the same impact on the money stock as
do transfers from demand deposits into domestic
time deposits or other near-money assets. Conse
quently, the problems that such transfers might create
for monetary control are not unique to Eurodollar
transactions.

U.S. banks
Liabilities

Assets

C D — $100
ED +$100

1BAdditional transactions would have to be examined if the U.S.
money supply is measured by broader aggregates, such as
M2. Fo r instance, if the demand deposit transfer outlined
in transaction 1 were channeled to a Caribbean branch of a
U.S. bank, M IA and M lB would decline as before, but M2
would not change. An increase in the magnitude of such
transfers might suggest the desirability of redefining trans

Eurobanks

Conversion of Certificates of Deposit into Eurodollars

Public
Assets

1980

Conversion of Demand Deposits into Eurodollars

Public
Assets

JU N E/JU LY

Eurobanks

Liabilities

Assets

Liabilities

C D — $100
D T+$100

DF+$100

ED +$100

action balances. On the other hand, to the extent that such
transfers occur because differential reserve requirements en
courage banks to raise funds in this way, the differential
effects on the various monetary aggregates could be elimi
nated by uniformly applying reserve requirements to branch
Eurodollar deposits of non-bank institutions.

JU N E/JU LY

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

EFFECTS OF EURODOLLAR
TRANSACTIONS
Although the foregoing analysis of balance sheets
can illustrate the effects of a single transaction, it
overlooks other portfolio changes that often accom
pany the transaction. The transactions described above
involved a change in preferences for Eurodollar de
posits relative to domestic bank deposits. By holding
other asset balances constant, however, these transac
tions also implicitly altered preferences for all other
assets relative to demand deposits (or Eurodollars).
An alternative analytical model provides a more
convenient framework for investigating the effect of
relative shifts in preferences between only two assets.
A money multiplier model can analyze directly the
effect on the U.S. money stock of a change in port
folio preferences between any two assets while hold
ing constant the relative preferences for all other as
sets. The next section develops such a model and
provides some quantitative estimates of the impact of
Eurodollar transactions on the U.S. money stock.

A Multiplier Model
The money multiplier framework can be used to
analyze how changes in the portfolio decisions of
commercial banks and the public affect the domestic
money supply. Such changes are typically described
by changes in the various ratios that comprise the
money multiplier. For instance, a shift in the public’s
preferences for time deposits relative to demand de
posits is characterized by a change in the desired
t-ratio.16 Money multipliers for three definitions of
money — Ml, MIA, and M1B — are derived in the
appendix and reproduced here.

/ n\ mi. _— —^—
1+ k,
(2)

where A = rd [(1 + f-fd ) + n] + rtt -f- rec + rhh -f
e -{- k.17 These multipliers provide the framework for
16When the initial substitution results in a reduction in demand
deposits, all other actual ratios will rise momentarily. Be
cause its desired ratios for other assets have not changed,
the public will reduce its holdings of other liabilities to
restore these ratios to their desired levels. An increase in
the t-ratio, for example, will be accompanied by an increase
in time deposits and a reduction in demand deposits, cur
rency, etc.
17The denominator ( A ) of each multiplier includes four differ
ent required reserve ratios, in contrast to the simplifying
assumption of two reserve requirements made in the preced
ing section. This approach makes the analysis more realis-

1980

Table 1
Definitions of Ratios Used in the Money
Multipliers
Ratio
symbol

Ratio of the following items to demand
deposits of the non-bank public
(the demand deposit component of M IA )

Large denomination certificates of deposit

Demand deposits of the U.S. Treasury at
commercial Danks

Excess reserves

Demand deposits of foreign commercial banks
and official institutions at U.S. commercial banks

Net Eurodollar borrowings

Currency held by the non-bank public

Interest-bearing checkable deposits
(ATS and NOW accounts, and share drafts at
credit unions)

Time and savings deposit component of the
money stock

Reserve ratios against various bank
liabilities (j = c , d, h, and t )

examining the implications of various Eurodollar trans
actions. For convenience, table 1 defines the ratios that
comprise the multipliers.
Eurodollar transactions may affect the multiplier
either through domestic banks’ net balances “due to”
its own branches and to other Eurobanks (i.e., through
Eurodollar borrowing) or through foreign commer
cial banks’ deposits with U.S. banks. Shifts in pref
erences toward Eurodollars similar to those described
by transactions 1 and 3 are represented in the multi
plier model either by changes in the ratio of foreign
commercial bank deposits to domestic demand de
posits (the f-ratio) or by changes in the ratio of
Eurodollar borrowing to domestic demand deposits
(the h-ratio). Asset shifts like those detailed in trans
actions 2 and 4 entail a shift in preferences from cer
tificates of deposit to Eurodollars. Thus both the ratio
of CDs to domestic demand deposits (the c-ratio)
and either the f- or h-ratio change simultaneously.
Changes in the portfolio decisions of the public and
commercial banks affect the money stock. These effects
can be analyzed by differentiating these multipliers
with respect to changes in the relevant preference
ratios. These partial differentials can be translated
easily into elasticities.
tic. Nevertheless, the present model retains the assumption
that all checkable deposits are subject to a single, uniform
reserve requirement. Under current regulations, checkable
deposits are subject to different reserve requirements, de
pending on bank size and the type of deposit.

JU N E/JU LY

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

Table 2
Elasticities of Money Multipliers with
Respect to Changes in Selected
Preference Ratios
Multiplier

f-ratio

h-ratio

c-ratio

£ f 1
1
TA I------l mi ri JJ

h
~ Th~K

c
~ r' A

f
" rd A

h
" rh A

c
- rc A

mib

f
- r<1A

h
- rh A

o|<
£
I

Elasticities were determined for each multiplier
with respect to changes in the f-, h-, and c-ratios and
are presented in table 2. Because the elasticities for
MIA and MIB are identical, only the analysis for
MIB — the broader measure of transactions balances
— is discussed below.
In transaction 1, the public’s shift from U.S. demand
deposits toward Eurodollars was associated initially
with an increase in foreign commercial banks’ demand
deposits at U.S. banks. In the multiplier framework
this transaction would be characterized by an increase
in the f-ratio. This change assumes that Eurobanks
hold precautionary reserve balances in the form of
demand deposits at U.S. banks and that these reserves
are proportional to the total volume of Eurodollar de
posits.18 The initial deposit shift toward Eurodollars
increases Eurodollar reserves, thereby allowing an ex
pansion of Eurodollar loans and deposits. Although
Eurobanks have not changed their desired ratio of
Eurodollar reserves as a share of total Eurodollar d e
posits, Eurodollar reserves as a percent of U.S. de
mand deposits have risen.
Table 2 indicates that the sign of the elasticity of
the M l multiplier (mt ) with respect to changes in the
f-ratio depends upon the relationship between m, and
the average reserve ratio against demand deposits
(rd). Over the past two decades, mt has rarely fallen
below 2.5, and the highest marginal reserve require
ment has never exceeded .17. Clearly then, for even
these extreme values of rd and m,, the elasticity of
18This simplifying assumption probably overstates the extent
to which such deposits serve as reserves for the Eurodollar
system and consequently overstates the effect that Euro
dollars have on the U.S. money stock.

http://fraser.stlouisfed.org/
8
Federal Reserve Bank of St. Louis

1980

m, with respect to the f-ratio is positive. That is, an
increase in f is associated with an increase in the U.S.
money stock as measured by Ml. In contrast, the
elasticity of the MIB multiplier (mu) with respect
to changes in the f-ratio is negative. The difference
between the mj and mlb elasticities results from ex
cluding foreign commercial bank deposits from the
new measures of the U.S. money stock. Further, for
plausible values of mx and rd, the absolute value of
the elasticity of mi with respect to f exceeds that of
mlb.
Changes in the h-ratio reflect a preferential shift in
the composition of U.S. bank liabilities toward Euro
dollar borrowing. As shown in table 2, elasticities for
each multiplier with respect to the ratio of Eurodollar
borrowing to domestic demand deposits (h) are iden
tical. Thus, changes in Eurodollar borrowing by U.S.
banks have a similar effect on the money stock re
gardless of how money is defined. (Note that if rh is
zero, as is currently the case, these elasticities are
zero.)
A shift in the preferences of the U.S. non-bank pub
lic away from domestically issued CDs is represented
by a change in the ratio of CDs to domestic demand
deposits (c). If this shift is accompanied by an off
setting change in either the f- or h-ratio, then the im
pact on the U.S. money stock will be the result of the
combined elasticities of the multipliers with respect to
the c- and f- (or c- and h-) ratios. This is the multiplier
counterpart to transactions 2 and 4 above. As shown
in table 2, all multipliers have the same negative
elasticity with respect to the c-ratio.
Table 3 reports numerical values for these elastici
ties, calculated from monthly data over the period

Table 3
Calculated Elasticities of Money
Multipliers with Respect to Changes in
Selected Preference Ratios (1973-1979)
Multiplier
m,

f-ratio

h-ratio1

c-ratio
- .0 4 4

.021

-.0 0 4

- .006

- .004

- .044

mib

- .006

- .004

- .044

1Based on the period from 1973 through September 1978,
during which Eurodollar borrowings were subject to re
serve requirements. Federal Reserve action announced in
August 1978 lowered reserve requirements against such
borrowings to zero, beginning in October 1978.

JU N E/JU LY

FED E R A L. R E S E R V E B A N K O F ST. L O U IS

from January 1973 through December 1979.19 These
elasticities indicate that a 1 percent increase in the
f-ratio would cause a .021 percent increase in m, and
a .006 percent decline in both mla and mlb. Further,
these calculations reveal that, although the multipliers
are more sensitive to fluctuations in the c-ratio, even
those elasticities are small. Therefore, unless changes
in the ratios are large, they would have little impact
on the money stock. For instance, suppose that mlb is
2.5, that the monetary base is $160 billion, and that
M1B is $400 billion. Holding the base constant, a 1
percent increase in the c-ratio would lower M1B by
approximately $176 million, while a 1 percent increase
in the f-ratio would lower M1B by only $24 million.

Interest Rate Effects
Since these ratios are intended to reflect the port
folio behavior of the public and the commercial bank
ing system, they should vary with interest rates. Thus,
if the ratios reflecting Eurodollar activity are suffi
ciently interest-sensitive, changes in interest rates will
change the money stock.20
The interest-sensitivity of Eurodollar flows depends
upon the extent to which Eurodollars are substitutes
for domestic deposits. Term Eurodollars are Eurodol
lar liabilities of a specified maturity, usually 90 davs
or less. The relative attractiveness of these deposits
should vary with their interest rate differential against
domestic CDs. If both assets were perfect substitutes,
they would require the same yield. On the other hand,
if depositors considered domestically issued CDs to be
safer or more convenient, Eurodollar deposits would
yield a higher interest rate, implying that a positive
interest rate spread would prevail even in equilibrium.
Any momentary widening of this spread would attract
funds to the Eurodollar market. Thus, Eurodollar
flows should vary directly with changes in the equi
librium interest rate spread.
The equilibrium spread itself will vary with changes
in market interest rates if U.S. bank liabilities are
subject to different reserve requirements. For example,
as U.S. banks bid competitively for funds, the mar
19The elasticity expressions from table 2 were calculated for
each month in the sample and then averaged over the period.
For the f-ratio elasticities, a 9 percent average reserve re
quirement against demand deposits was assumed. For the
h- and c-ratios, actual marginal reserve requirements in
effect during each month were used.
20The positive (and larger) elasticity of the M l multiplier,
with respect to the f-ratio, suggests that M l would fluctuate
more than either M IA or M1B when the f-ratio changes. If
the f-ratio is interest-sensitive, then M l would show greater
volatility due to interest rate changes than would either of
the new definitions of money.

1980

ginal effective cost of funds from various sources tends
toward equality. (For convenience, this discussion
focuses on only two bank liabilities — U.S. CDs and
borrowings from Eurobanks.) Under current regula
tions, CDs are subject to a higher marginal reserve re
quirement than are Eurodollar borrowings.21 Assum
ing no reserve requirement against Eurodollar
borrowing, the cost of these liabilities to U.S. banks
is equalized when the following condition is satisfied:
/ A\ . __

iu.s.

TT77’

where iD.s., 1e, and rc are, respectively, the domestic
CD rate, the Eurodollar interbank lending rate, and
the marginal reserve requirement against CDs.22
The spread, S, between Eurodollar and U.S. interest
rates is defined as:
( 5 ) S — iE —iu.s.,

which upon substitution from equation (4) produces
I*
—5— ) iu.s.. If U.S. interest rates rise, the spread between Eurodollars and domestic CDs will widen. Dif
ferentiating equation (5) with respect to iu.s. yields

(6)

a lu. s.
1 - rc
j*
Since -—-— is positive, an increase in U.S. market inJ- ~ rc
terest rates will be associated with an increase in the
Eurodollar/U.S. interest rate differential which, in
turn, will stimulate a flow of funds from domestic CDs
to the Eurodollar market.
Equation (6) implies that the elasticity of the in
terest rate spread with respect to the level of U.S.
interest rates should be ( . T‘—) -Tj,K . Using the U.S.
1

I*c

certificate of deposit rate as the representative U.S. in
terest rate, this elasticity was estimated to be 1.08 over
the period from 1973 through 1979.23 This value did
not differ significantly from unity, indicating that a 1
percent rise in the level of U.S. interest rates is asso21Both domestic CDs and net Eurodollar borrowings, as part
of a bank’s “managed liabilities,” were subject to a marginal
reserve requirement on the total amount of managed liabil
ities above some base. This reserve requirement was im
posed, in addition to any other reserve requirements, against
the liability. At present, this separate reserve requirement is
zero against net Eurodollar borrowings and is 6 percent
against domestic CDs.
--If there are reserve requirements against Eurodollar borrow
ing, the equal cost condition becomes

— =
1 - rh

,lp's' .
1 - rc

- aThis elasticity was also estimated using the U.S. Treasury
bill rate by regressing the logs of the spread against a con
stant and the logs of the interest rate. Results were similar.

JU N E/JU LY

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

dated with a 1 percent increase in the spread. In
other words, the spread was some constant fraction
of the level of U.S. interest rates.
Over much of this period, reserve requirements
against CDs and Eurodollars were identical, implying
that any observed spread would correspond to some
risk or preference premium on Eurodollar deposits.
Thus, the estimated unitary elasticity of this premium,
with respect to the level of U.S. interest rates, sug
gests that the risk premium varies directly with in
terest rate levels. Interestingly, for the subperiod from
September 1978 through December 1979, after reserve
requirements against Eurodollar borrowings were low
ered to zero, the estimated interest rate spread elas
ticity of 1.57 differed significantly from unity at the
10 percent confidence level. This result is consistent
with the effective risk spread remaining a constant
ratio to the level of U.S. interest rates.
If the money multipliers are more interest-sensitive
due to Eurodollar activity, the Fed’s ability to restrain
money and credit expansion could be affected, as some
critics of the Eurodollar market have asserted. For
example, if Federal Reserve policy temporarily raises
domestic interest rates, the volume of CDs could be
expected to decline relative to Eurodollar borrowings
by U.S. banks. Such Eurodollar-related flows would
affect both the c- and h-ratios and, consequently, the
multipliers. The net impact on the U.S. money stock
depends on both the interest elasticities of these ratios
and the elasticities of the multipliers with respect to
changes in the ratios.

POTENTIAL IMPACT OF
EURODOLLAR TRANSACTIONS
ON THE U.S. MONEY STOCK
Two critically important results are evident in the
foregoing discussion. First, Eurodollar transactions
affect the behavior of the U.S. money supply primarily
through their impact on the money multipliers.24 Sec
ond, Eurodollar transactions respond to changes in
interest rate differentials that are related to interest
rate levels. The behavior of the three relevant ratios
is examined to assess the importance of these Eurodollar-related effects for the 1973-79 period.
Table 4 reports the annual averages (of monthly
data) for the f-, h-, and c-ratios from 1973-79. The
24Even if these Eurodollar transactions have a sizeable impact
on the money stock, they would not pose an insurmountable
barrier to controlling the money stock. To the extent that
such effects are predictable, the monetary authority could
offset them in its conduct of monetary policy.

1980

Table 4
Values of Selected Preference Ratios
(Annual Averages of Monthly Data)
Year

f-ratio

h-ratio

c-ratio

1973

.029

.038

.299

1974

.037

.045

.386

1975

.036

.026

.402

1976

.038

.019

.313

1977

.042

.004

.278

1978

.043

.008

.347

1979

.039

.096

.359

f-ratio, ranging from .029 to .043, shows the least
amount of year-to-year variation, while the c- and
h-ratios are more volatile. Using annual averages of
the c- and h-ratios, however, masks much of their
intra-year variability. For instance, despite an appar
ent increase in 1979 over its 1978 value, the c-ratio
actually declined substantially during most of the year
and, by year end, was 11 percent lower than it had
been at the beginning of the year. The h-ratio, on the
other hand, began to rise sharply after Federal Re
serve Board action in August 1978 lowered the reserve
requirement on net Eurodollar borrowing to zero in
August 1978.25
Table 5 reports the estimated interest elasticities of
these ratios and provides another perspective on their
behavior over the past eight years.26 All interest elas
ticities are positive and differ significantly from zero at
least at the 10 percent confidence level. The estimated
interest elasticities for both the f- and h-ratios exceed
that of the c-ratio, reinforcing the view that the pres
ence of differential reserve requirements induces more
25Fo r a discussion of the extent to which Eurodollar borrow
ings are substituted for domestic CDs, see David H. Resler,
“Does Eurodollar Borrowing Improve the Dollar’s Foreign
Exchange Value?” this Review (August 1 9 7 9 ), pp. 10-16.
26Data reported in table 5 were computed by estimating equa
tions or the general form In x = a« + ai In i + u, where x
designates the ratio, i the market yield on three-month
Treasury bills, and u a random error term. This equation was
estimated by a Cochrane-Orcutt iterative regression tech
nique to correct for the presence of serially correlated re
siduals in the ordinary least squares regression. Fo r the cross
elasticities, In c was substituted for In i in this general
expression. Although it would be desirable to estimate the
elasticities of these ratios with respect to the interest rate
spread, such estimates would require the specification of a
full structural model. Consequently, the estimates provided
here should be considered to be crude approximations of the
interest elasticities that are useful for a rough determination
of the importance of Eurodollar activity in the U.S. money
supply process.

JU N E/JU LY

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

Table 5
Elasticities of Selected Preference
Ratios (1973-79)1
Ratio

W ith respect to:
Interest rates

c-ratio

.196 (2 .0 1 7 )

- .0 8 1 ( - . 4 4 8 )

.715 (1 .9 6 6 )

- .4 4 1 ( - . 6 4 9 )

.147 ( 2.5 3 4 )

U-statistics appear in parentheses.

substantial Eurodollar flows during periods of rising
interest rates.27
Table 5 also reports estimates of the cross elastici
ties of the h- and f-ratios against the c-ratios. Although
these elasticities were of the predicted sign, they did
not differ significantly from zero, indicating that sub
stitutions between Eurodollar transactions and domes
tic CDs have not had an important effect on these
ratios during the period.
The potential effect of interest-induced Eurodollar
transactions on the money stock can be evaluated by
using estimates reported in tables 3 and 5. Assuming
a constant monetary base of $160 billion, the potential
effect that Eurodollar transactions would have on Ml
and M1B was calculated for a 1 percent change in the
level of interest rates (10 basis points if interest rates
are initially 10 percent).28 These calculations indicate
that if old Ml were used to measure money, the U.S.
money stock would be about $68 million higher than
it would have been otherwise. On the other hand, if
measured by M1B, the money stock would have been
only about $44 million higher. In each case, these
changes are less than two one-hundredths of 1 percent
of the money stock. Even a 10 percent monthly in
crease (100 basis points) in domestic interest rates
would result in an average monthly money stock
27Elasticity estimates for the h-ratio were derived indirectly.
Since calculations of the elasticities were based on logarith
mic transformations of the actual ratios and since the h-ratio
was negative during some months of the sample period, it
was necessary to first transform the h-ratio by adding one
to all values for h. The estimated elasticity of 1 + h was
then converted into an elasticity for h by multiplying the
estimated coefficient of (1 + h) by (1 + h )/h , evaluated
at the mean values of h over the sample period.
28These calculations were based on average values of the mul
tipliers and the estimated elasticities of the three ratios, even
though the t-statistics for some coefficients did not differ
significantly from zero.

1980

(M l) that would be less than 0.2 of 1 percent higher.
Because the assumptions used in this analysis exag
gerate the effect that Eurodollar transactions have on
the money stock, it is apparent that Eurodollar trans
actions have only a small effect on the U.S. money
supply. Further, the Federal Reserve could easily
offset this effect with appropriate open-market
transactions.

Summary and Conclusions
This article has examined the extent to which
Eurodollar transactions can affect the U.S. money
supply, as measured by current and past Federal Re
serve Board versions of narrowly defined money. Us
ing both T-accounts and a money multiplier frame
work, Eurodollar transactions were shown to affect
the U.S. money stock in two ways. First, regardless
of the chosen definition of money, Eurodollar flows
may affect the U.S. money stock indirectly through
their impact on the portfolio composition of U.S.
banks’ liabilities. Changes in this portfolio composi
tion, whether due to Eurodollar flows or simply do
mestic asset shifts, may affect the money supply
through differential reserve requirements. Second,
Eurodollar flows may affect foreign commercial bank
demand deposits at U.S. banks. To the extent that
these deposits serve as reserves for the Eurodollar
system, they will vary directly with flows between the
U.S. Eurodollar and the U.S. money markets. Because
these deposits are excluded from the new definitions
of money, but not from the old M l definition, Euro
dollar flows will affect the various transactions-based
definitions differently. Analysis based on the multi
plier model indicated that old Ml would be slightly
more sensitive to Eurodollar flows than either MIA
or M1B.
Since Eurodollar transactions have some impact on
narrowly defined money, the question of whether such
transactions impair the monetary authorities’ control
of monetary aggregates merits investigation. The mul
tiplier framework presented in this paper was used to
examine systematically Eurodollar-induced effects on
the money stock. Based on estimates over the period
for 1973-79 — a period of rapid growth in the Euro
dollar market — Eurodollar flows were shown to have
only minor effects on the U.S. money stock. This evi
dence warrants the conclusion that the Eurodollar
market does not pose a serious threat to the ability of
the Federal Reserve to control the money supply.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

JU N E/JU LY

1980

APPENDIX: Derivation of Money Multipliers
(8 ) ICD = n D p

A. Definitions of Symbols
Ratio
as to
Variables DP

Description
Bank Liabilities
Time Deposits
Demand Deposits
Government
Non-bank public
Foreign Commercial bank
Large CDs
Net Eurodollar borrowings
Interest-bearing checking
deposits
NOW accounts
Credit union drafts
ATS accounts

Relevant
reserve
ratios

(10) C = k D p
(11) R = rd (D P + D t + Dg + [IC D ]) + r, T

—

d
1
f
c
h

rd
rd
rd
rc
rh

ICD
NOW
DCU
ATS

DP
Dr
CD
H

+ r= CD +

Substituting into equation
through (10) produces:

—

Source base

Money Stock Measures

Ml
MIA
M IB

Thus (1) can be rewritten as:

where A equals the bracketed term on the right hand
side of (13).
Similarly, the three money definitions can be written
as ratios to D p :

(1 ) B = R + C

DCU + ATS

(1 + f + k) D p

MIA =

(1 + k ) D p

M IB =

(1 + k + n) D p

The three multipliers are derived by dividing all expres
sions in (14) by (13) producing:

1+f

(1 5 )

( 4 ) Dg = d Dp
( 5 ) D f = f Dp
(6 ) CD = c Dp
( 7 ) H = h Dp

(3)

+ rcc + rhh + e] Dp

(14) M l

(3 ) T = tD ,

from equations

(12) R = [rd (1 + f + d + n) + rt t

B. Derivations
Dp + D , + C
DP + C
Dp + C + NOW
+ ICD

(11)

+ rcc + rhh + e + k] D p = ADP

(2 ) M l = m, B =
M IA = mi, B =
M IB = nil, B =
= DP + C

H + E

(13) B = [rd (1 + f + d + n) + r,t

Currency held by public

Excess reserves

(9 ) E = e F p

m„
i
and mib =

1+ k
1 -f- k + n
. ,
------- ^ ------ , as in the text.

Dynamic Forecasting and the Demand
for Money
SCOTT E. HEIN

ERRATA:Change Y to Y i n eq. 4 & 11;
p. 16, c o l . 1 , l i n e 9 ; p. 16, c o l .
2 , l i n e 20.

Change Yt + 2 -Y-j-+2 to

yt + 2 - Y t + 2 . P- 17, c o l . 2 , l i n e 2.

I V I u C H of the statistical evidence on the break
down in the short-run demand for money relationship
in the United States results from poor dynamic outof-sample simulations over the post-1974 period.1 How
ever, this evidence must be regarded cautiously be
cause the dynamic forecasting procedure lacks a firm
econometric foundation.

drawn from such an investigation.2 Next, the dynamic
forecasting procedure is contrasted, in general terms,
with the more widely understood static forecasting
technique. This analysis provides a framework for
reevaluating conclusions about the breakdown in the
money demand relationship.

This paper reexamines the conclusions that have
emerged from these inadequate dynamic money de
mand forecasts. First, it presents a conventional money
demand relationship and its post-1974 dynamic fore
casts, along with a restatement of the conclusions

The review demonstrates that certain inferences
drawn from dynamic forecasts of money demand over
the post-1974 period are incorrect and misleading. In
general, the pattern and the degree of breakdown in
the money demand relationship has been obscured by
reliance on this forecasting procedure. The shifts are
neither as large nor as frequent as suggested by the
dynamic forecast errors.

1Since only ex post forecasting is discussed in this paper, the
terms “forecasts” and “out-of-sample simulations” are used
interchangeably. In addition, this paper discusses the stability
of a relationship in the statistical sense: a relationship is said
to be stable if the regression coefficients are statistically in
variant with time.

A Conventional Demand for Money
Relationship and Its Dynamic Forecasts

The following studies rely heavily on dynamic forecasting
performance in their analysis of the stability of the demand
for money relationship: Stephen M. Goldfeld, “The Case of
the Missing Money,” Brookings Papers on Economic Activity
( 3 :1 9 7 6 ) , pp. 683-730; Jared Enzler, Lewis Johnson, and John
Paulus, “Some Problems of Money Demand,’ Brookings Papers
on Economic Activity ( 1 :1 9 7 6 ) , pp. 261-79; Michael J. Ham
burger, “Behavior of the Money Stock: Is There a Puzzle?”
Journal of Monetary Economics (No. 3, 1 9 7 7 ), pp. 265-88;
Gillian Garcia and Simon Pak, “Some Clues in the Case of
the Missing Money,” American Economic Review, Papers and
Proceedings (M ay 1 9 7 9 ), pp. 330-34; and Richard D. Porter,
Thomas D. Simpson, and Eileen Mauskopf, “Financial Inno
vation and the Monetary Aggregates,” Brookings Papers on
Economic Activity (1 :1 9 7 9 ) , pp. 213-29.

The money demand relationship considered here is
given by:
(1 )

In ( M t / P t ) = « „ + « ! In T B R t + cc2 In RCB,
+ a 3 In GNPRt + a 4 In (M .-./P .-i) + £,,

where M is measured by old M l balances, P is the
2With the exception of Michael J. Hamburger and Gillian
Garcia and Simon Pak, all of the above studies obtained poor
out-of-sample money demand simulations for the post-1974
period. For an alternative view on the stability suggested by
Hamburger and Garcia-Pak, see R. W . Hafer and Scott E.
Hein, “Evidence on the Temporal Stability of the Demand
for Money Relationship in the United States,” this Review
(Decem ber 1 9 7 9 ), pp. 3-14.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

implicit GNP deflator (1972 = 100), TBR is the
treasury bill rate, RCB is the commercial bank pass
book rate, GNPR is real GNP (1972 dollars), and Et
is a random error term.3 This relationship was esti
mated for the sample period IV/1960 — 11/1974 with
ordinary least squares, after correcting for serial cor
relation in the error terms.4 The estimated coefficients
and summary statistics are as follows:5
( 2 ) In ( M t/P .) = - 0 .9 7 8 - 0 .0 1 2 In TBR , - 0 .0 4 4 In RCB, +
(4 .0 1 ) (1 .9 5 )
(2 .3 3 )
0.208 In GNPR, + 0.542 In (M ,-,/P « >)•
(4 .0 0 )
(4 .0 6 )
R2 = 0.964
S E E = 4 .6 8 E -0 3
D W = 1.63; Durbin-h = 9.79
RHO = 0.57

All estimated coefficients have the anticipated sign,
are significantly different from zero, and are similar
in magnitude to those found by others. The coefficient
of determination corrected for degrees of freedom, R2,
shows that a substantial portion of the variation in
real money balances is explained by the independent
variables on the right-hand side of the equation.
This estimated equation was used to dynamically
forecast the dependent variable, In (Mt/Pt), for the
post-sample period III/1974 — IV/1979. With the ex
ception of the lagged dependent variable, actual values
of the independent variables were used to perform
this dynamic simulation. For the first forecast, III/
1974, the actual value of the lagged dependent variable
was used; thereafter, the previous period’s forecast
for this variable was utilized. The dynamic money
3This relationship and sample period were chosen for compar
ison purposes. The relationship is similar to money demand
specifications estimated by Goldfeld and Porter, et. al. Both
studies, however, deflate the lagged money term on the righthand side of the equation by the contemporaneous price level.
In this study, the lagged money term is deflated by the
lagged price level so that the relationship has a true lagged
dependent variable. This simplifies the procedure used to ob
tain dynamic forecasts. The sample period used in the study
coincides with that investigated by Porter, et. al.
4This author, in a paper co-authored with R. W . Hafer, “The
Dynamics and Estimation of Short-Run Money Demand,” this
Review (M arch 1 9 8 0 ), pp. 26-35, argues that directly esti
mating the relationship described in equation ( 1 ) will yield
inconsistent estimates; the relationship should be firstdifferenced before estimation. When this estimation procedure
is employed, the supposed breakdown in the relationship is
no longer evident. This present paper, however, follows the
more widely accepted practice of estimating equation ( 1 )
directly, with the Cochrane-Orcutt technique.
5The Durbin-h statistic, which is appropriate to test for serial
correlation in the disturbances when a lagged dependent vari
able is present, indicates the existence of first-order autocorre
lation, even after the Cochrane-Orcutt technique is used. This
is a serious problem, indicating that more attention should be
devoted to the actual estimation technique employed. How
ever, since this specification and estimation technique is
widely used in money demand studies, no attempt to correct
this problem is made here. It should be noted that the esti
mation results reported by Porter, et. al., are subject to the
same criticism.

Digitized for14
FRASER

JU N E/JU LY

1980

demand forecasts and resulting forecast errors pre
sented in table 1 (columns 3 and 4, respectively) are
in general agreement with those found by others.
Real money balances are consistently overpredicted
and by increasing proportions (table 1, column 6). For
example, by the second quarter of 1978, prior to the
introduction of nationwide ATS accounts and New
York NOW accounts, real money balances were fore
casted to be approximately $27 billion above the
actual level for that period.6
The inability to accurately simulate the movement
of real money balances over this period led to the
general conclusion that the money demand relation
ship shifted. In reviewing the evidence, Kimball
states: “As these overpredictions continued and in
creased in size through 1975 and 1976, many econo
mists concluded that the money demand function had
shifted during 1974 by a substantial amount and that
this shift placed in doubt the usefulness of (old) Ml as
either an indicator of GNP or as a policy instrument.”7
This summary statement pinpoints three separate
conclusions drawn from the errors associated with dy
namic out-of-sample simulations of money demand.
First, there is the contention that the relationship was
subject to some sort of shift in or around 1974. The
forecast errors suggest that this shift was quite sizable.
Second, the dynamic forecasting errors suggest that
the relationship has been shifting ever since late 1974
(column 3, table 1). This view is consistent with the
notion of a negative drift in money demand over the
period.8 Finally, the evidence of a shift and subse
quent drift has raised a question about the usefulness
of this money measure as an indicator of monetary
policy.

Static Versus Dynamic Forecasts:
A General Comparison
Although the dynamic forecasting procedure has
been a primary tool used to evaluate the statistical
breakdown in the money demand relationship, it has
received little, if any, attention in the econometric
literature. This section attempts to partially fill the
(iIt is felt that the introduction of these interest-bearing “check
ing deposits” has led to a shift out of conventional demand de
posits. Evidence of this type of shift is provided subsequently.
"Ralph C. Kimball, “W ire Transfer and the Demand for
Money,” Federal Reserve Bank of Boston New England E co
nomic Review (M arch/A pril 1 9 8 0 ), p. 14.
8See for example, Porter, et. al., “Financial Innovations and the
Monetary Aggregates,” p. 214. In that article, table 1 indicates
that quarterly real balances grew at an annualized rate of
nearly 4 percent below that suggested by the estimation equa
tion for the period III/1 9 7 4 -IV /1 9 7 6 . Also, see “Inflation and
the Destruction of Monetarism,” (New York: Goldman Sachs
Economics, November 1 9 7 9 ), pp. 5-12.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

JU N E/JU LY

1980

Table 1
Post-Sample Dynamic Forecasts of Money Demand (111/1974-IV/1979)
Dynamic
forecast
error

Dynamic forecast
error as
percent of
dependent variable

Dynamic forecast
error in billions
of real
money balances1
$ -5.28

Date

Actual
In (M ,/P t)

Dynamic
forecast of
In (M t/P t)

111/1974

0.8645

0.8865

-0.0220

-2.54

IV/1974

0.8462

0.8872

-0.0410

-4.84

-9.75

1/1975

0.8260

0.8851

-0.0591

-7.16

-13.91

-0.0620

-7.51

-14.61
-15.61

11/1975

0.8260

0.8880

111/1975

0.8264

0.8925

-0.0661

-8.00

I V / 1975

0.8187

0.8975

-0.0788

-9.63

-18.59

1/1976

0.8213

0.9071

-0.0858

-10.44

-20.37

11/1976

0.8258

0.9129

-0.0871

-10.55

-20.78

111/1976

0.8246

0.9178

-0.0932

-11.31

-22.28

IV/1976

0.8283

0.9233

-0.0950

-11.47

-22.82

1/1977

0.8320

0.9310

-0.0990

-11.90

-23.91

11/1977

0.8319

0.9371

-0.1052

-12.65

-25.49

111/1977

0.8415

0.9425

-0.1009

-11.99

-24.65

IV /1977

0.8442

0.9452

-0.1010

-11.96

-24.72

1/1978

0.8455

0.9470

-0.1015

-12.00

-24.88

11/1978

0.8429

0.9519

-0.1090

-12.93

-26.75

111/1978

0.8451

0.9549

-0.1098

-12.99

-27.02

IV /1978

0.8350

0.9574

-0.1224

-14.66

-30.01

1/1979

0.8092

0.9584

-0.1492

-18.44

-36.14

11/1979

0.8071

0.9619

-0.1548

-19.18

-37.52

111/1979

0.8107

0.9591

-0.1484

-18.31

-35.99

IV /1979

0.8032

0.9550

-0.1519

-18.91

-36.60

Summary Statistics
Mean error:

-0.097

Root-mean-squared-error:

0.103

Theil’s inequality coefficient:

0.124

Fraction of error due to:
(A )

Bias:

0.890

(B )

Variation:

0.015

(C )

Co-variation:

0.095

‘Calculated as actual real money stock, less the exponential of the predicted logarithm of real money balances.

void by focusing on dynamic forecasting as a basis
for evaluating the temporal stability (i.e., the con
stancy of the coefficients) of an economic relationship.

hypothesized to influence the contemporaneous value
of the dependent variable. Specifically, assume that

To facilitate understanding, the static forecasting
procedure is discussed first. Consider a general rela
tionship in which the lagged dependent variable, as
well as an additional explanatory variable, X, are

is the “true” model for t = 1, 2, .. . , T. In this equation,
X is a non-stochastic independent variable, st are in
dependent and identically normally distributed ran
dom variables with mean zero and variance o2, and

( 3 ) Y t = oto + % Xt + cc2 Yt-i + Et

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

the parameters a 0, a 1; a 2 are non-stochastic and
known with certainty.9
Under these conditions the traditional static fore
cast for Yt .i, conditioned on knowledge of X T+i and
Y t, is
(

Y t+ i ~

CCo +

OCi X t + i -I- (Xi Y t .

According to the maintained hypothesis of structural
stability, equation (3 ) is appropriate for period T + l .
As a result, a forecast error (Y t+i - YTti ) is expected
and this error is equal to s T+1. The expected value of
the forecast error, E ( e t+1), is zero by assumption. It
is important to recognize that this result can be gen
eralized for any time period for which equation (3 )
is valid and a static forecast is developed. Specifically,
for any time period for which equation (3 ) is true,
a forecast error can be expected and this error will be
a random variable with a zero expected value and a
constant variance, a 2 (table 2 ).
Provided the variance of the disturbances ( a 2) is
known, the static forecast errors can be used to de
termine whether the relationship is temporally stable
(i.e., whether equation (3 ) holds after T ) . The static
forecast error should, by hypothesis, behave as a nor
mally distributed random variable with mean zero
and variance a 2. Contradictory evidence, such as
static forecast errors that are large relative to a 2,
would suggest that equation (3 ) does not characterize
the post-sample period. Consistently one-sided static
forecast errors (e.g., under- or overpredictions)
would also support such a conclusion. Using similar
reasoning, Brown, Durbin, and Evans have developed
formal tests to ascertain whether a relationship such
as that described by equation (3 ) remains valid over
an extended time period.10
The difference between these static forecasts and the
dynamic forecasts used in money demand studies is

JU N E/JU LY

1980

simple and relatively straightforward; dynamic fore
casts use previously forecasted values of the lagged
dependent variable instead of actual values. In other
words, the forecaster is assumed to know the actual
value of all the explanatory variables on the righthand side of the equation, except for the lagged de
pendent variable.11 Consequently, in dynamic fore
casting, an estimate of the lagged dependent variable
— specifically, the value forecasted for the previous
period — must replace the actual value of the variable
that would be used in static forecasting. In this re
spect, the dynamic forecasts are developed as part of
a recursive system.
To better understand the dynamic forecasting pro
cedure, assume equation (3 ) holds for t = l , . . . T,
and dynamic forecasts for periods beyond T are de
sired.12 The actual value of YT is used to form the
initial dynamic forecast of Yt+i. Thus, the dynamic
forecast for T + l, Yt+i> is equal to the static forecast,
YT+1:
(5 )

Y t+ i —

CCo “I" OCi X t + i +

0C2 Y t .

The resulting dynamic forecast error (YT+, - YT+1) is
St+i — identical to the forecast error that occurred in
the static forecasting procedure. Consequently, every
thing said about the first static forecast error holds for
the dynamic forecast error as well.
However, in forecasting Y for the subsequent pe
riod (T + 2 ), the forecasted value of YT+1, rather than
the actual value, is used to develop the dynamic fore
cast. Thus, the T + 2 dynamic forecast is represented
by:
(6 )

Y t.: =

oc„ +

a , X t ,= +

OC; Y T+,.

Using the equation for the previous period’s dynamic
forecast error,
(7 )

Y t , i - Y t +i =

E t +1

( —>

Y t +i =

Y t +i — £ t +i )■

equation (6) can be rewritten as:
9The assumption that the parameters are known with certainty
makes the analysis simpler and, more importantly, doesn’t
effect the central conclusions drawn in this section. The reader
is referred to Henri Theil, Applied Economic Forecasting,
(Chicago, North-Holland, 1 9 6 6 ), pp. 5-8, for a discussion of
the case where the parameters in ( 3 ) are ordinary least
square estimates. The analysis in this paper, based on the
assumption that the parameters are known with certainty,
will underestimate the variance of the forecast error if the
forecasts are actually based on parameters that are obtained
from ordinary least squares.
10R. L. Brown, J. Durbin, and J. M. Evans, “Techniques for
Testing the Constancy of Regression Relationships Over
Time,” Journal of the Royal Statistical Society (Vol. 37
19 7 5 ), pp. 149-92. In one sense, the test the authors de
scribe is more general than that discussed here. Specifically,
they investigate the stability of a relationship when the
right-hand side parameters are actually random variables,
and when o' is unknown. However, they do not consider
the specific case in which a lagged dependent variable is in
cluded as an additional explanatory variable.

( 8 ) Y t +2 =

OCo +

oti Xt+2 +

0C2 ( Y t+ i - E m ) .

u Dynamic forecasting appears to be particularly appropriate
for studying an equation that has a lagged dependent vari
able and that is part of a larger model. If the right-hand
side variables, other than the lagged dependent variable,
were all exogenous, dynamic forecasting would give a valid
indication of the “sturdiness” of that relationship. However,
in the case of money demand, all of the right-hand side
variables would be endogenous in a fuller model and thus
should be forecasted as well. In this respect, it is strange
that dynamic forecasting has become so popular in money
demand studies, while true ex ante forecasting (in which all
of the right-hand side variables are forecasted) would pro
vide better insight into the problems associated with actually
forecasting money demand. Ex ante forecast errors would
provide a better understanding of the actual problems facing
policymakers in forecasting the demand for money.
12RecalI the assumption that the parameters a», a ,, and 0C2
are assumed to be known with certainty.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

JU N E/JU LY

1980

Figure 1
A l t e r n a t i v e D i s t r i b u t i o n s of S ta tic a n d
D y n a m ic Forecast Errors

If equation (3) continues to hold for T+2, the actual
value of the dependent variable will be given by
( 9 ) Y t +2 — OCo “t“ OCl X t +2 +

0C2 Y t +1 +

£ t +2.

Subtracting equation (8) from equation (9) yields
the following dynamic forecast error for T+2:
(

10)

Y t +2 — Y t +2 —

E t +2 “ 1
“ OC2 £ t+ i,

which can be compared with the static forecast error
for the same period:
(

11)

Y t +2 -

Y t +2 — - £ t+ 2.

These alternative forecast errors are statistically
similar in one sense, but quite different in another.
Since, according to the null hypothesis of stability, the
expected value of each disturbance, et (t = 1, . . .),
is zero, the expected value of both the static forecast
error and the dynamic forecast error will be zero. In
this respect, there would be no reason to prefer one
forecasting procedure over the other, since both will
yield unbiased forecasts.
The variance of these two forecast errors, however,
is quite different. The variance of the static forecast
error is the variance of the error, eT+2, which is simply
a 2. Equation (10) shows that the variance of the dy
namic forecast error will be larger than this for all
cases in which a 2 is non-zero. If the errors are

independent, as has been assumed, the variance of
the dynamic forecast error, var (YT+2 - YT+2), is
a- [1 + oc2]2.13
Figure 1 compares the two alternative distributions
under the assumption that both oc2 and a 2 equal unity.
The distribution associated with the static forecast
error is clearly more concentrated about the mean of
the distribution than the dynamic forecast error.
Since the standard deviation of the static forecast error
is equal to one, it is smaller than the dynamic forecast
error, which is equal to v/2* ( *1.414). In the statis
tical sense, the dynamic forecasting procedure can be
considered inefficient relative to the static forecasting
framework. This means that there is a higher prob
ability of observing a dynamic forecasting error on the
far tail ends of the distribution than there is with a
static forecast. As a result, the investigator should be
less confident in the former type of forecast.
In terms of evaluating the temporal stability of a
relationship such as that presented in equation (3),
the relatively larger variance associated with the dy
13The variance of the dynamic forecast error, Var ( Y t + 2 - Y 1 + 2 ) ,
equals Var ( s T+2 + CC2ET+1) according to equation ( 10) . This
latter term, by assumption of independence in the disturb
ances, equals Var (e T+:) + Var (ochEt+i), which finally
equals a 2 + odcr.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

JU N E/JU LY

1980

Table 2
Static and Dynamic Forecasts Errors
Time

Static
Variance of
forecast
static
error
forecast error

Dynamic
forecast
error

Variance of
dynamic
forecast error

T+l

Et+i

o’

Et+i

T+2

Et+»

Et+s + OC2 Et+i

d2 ( l + o c 2)

T+3

Et+»

Et+3 + Otj Et+s + a , Et+i

o3 ( 1+oci + otj)

T+K

Et+K

cr*

K 0 -1)
Z a 2 Et+k-<i -i )
1=1

a3 [

namic forecasting procedure indicates that, for any
given confidence interval, a larger dynamic forecast
ing error (than that associated with the static fore
casting procedure) is required before the null hy
pothesis of temporal stability can be rejected.
Table 2 presents static and dynamic forecast errors
and the variance of these respective errors for periods
T + l through T+3. In addition, these particulars are
generalized for the Kth period beyond the end of the
sample period, T. The generalization shows that the
dynamic forecasting procedure becomes increasingly
inefficient relative to the static forecasting procedure,
the further the forecast is from the end of the sample
period. As long as a 2 is less than unity, however,
increments in the variance of the dynamic forecast
error will diminish with time.
The table also shows the interesting fact that the
dynamic forecast error for any given period can be
calculated based on the knowledge of the parameter,
a 2, and on the static forecast errors for that same period
and prior periods; that is, the dynamic forecast error
for T +K is simply a weighted average of the static
forecast errors, £T, eT+1, . . ., £t+k, with the weights
determined by a 2. The essential contribution of the
dynamic forecasting procedure is its unique weight
ing scheme for current and past static forecast errors.
If the investigator is interested in determining the
long-run forecasting accuracy of his model, the
weighting scheme of the dynamic forecasting method
ology is uniquely appropriate.
It is further evident from table 2 that the weighting
scheme depends crucially on the parameter a 2 (the
coefficient on the lagged dependent variable). Other
things being equal, the researcher developing dynamic
forecasts will prefer a smaller value for this para
meter, because it is the mechanism by which past
18FRASER
Digitized for

K-l
<!>’
Z a3 ]
1=0

forecast errors are fed through the system. The smaller
the coefficient on the lagged dependent variable, the
less impact its value will have on subsequent fore
casts. The table also shows that, if a 2 exceeds unity,
the dynamic forecasting framework becomes explo
sive: Past static forecast errors are given increasing
weight as the forecast period is extended.
Finally, in terms of the question of the temporal
stability of a relationship, table 2 indicates that the
static and dynamic forecast errors will yield different
patterns as a result of a shift in the relationship. For
example, suppose a once-and-for-all intercept shift in
equation (3) occurs at T + l, such that
(1 2 ) Y, =

(oto + 6 ) + otiXt + oc2 Yt_i + et

holds for all t> T + l. If static forecasts are developed
under the erroneous assumption that equation (3)
presents the correct relationship, the resulting fore
cast error will be £t+ 6 (for all t > T + l ) . As a result,
there will be a bias in the forecast of the size, 8,
that will persist irrespective of the time for which the
forecast is made ( table 3).
In the case of dynamic forecasting, the path of the
forecasts errors that occurs in the face of this same
intercept shift is considerably different. With dynamic
forecasting, the forecast will deviate from the actual
level not only because the intercept shift is not built
into the forecast, but also because the lagged de
pendent variable is inaccurately forecast for inter
vening periods. Since the dynamic forecasting frame
work is a recursive system, these latter inaccuracies
will cumulate over time.
Figure 2 compares the path (i.e., the expected
value) of the static and dynamic forecast errors for a
once-and-for-all, 5-sized intercept shift with a para
meter value of a 2 = 0.7. Although the hypothesized
shift in the relationship is the same in both cases, the

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

JU N E/JU LY

1980

Fi gure 2

Expected V a lu e of Static a n d D y n a m ic Forecast
Errors U n d e r Assum p tion of a 6 - S i z e d
O n c e - A n d - F o r - A I I Intercept Shift

expected path of the two alternative forecast errors
is quite different. Even an astute investigator could
easily misjudge the once-and-for-all intercept shift in
the relationship, if the only information provided is
the pattern of the dynamic forecast errors. The re
searcher would probably perceive the shift as a con
tinuing phenomenon, rather than a once-and-for-all

occurrence. In addition, if the researcher is provided
only the dynamic forecast errors, the shift in the re
lationship is likely to be judged larger than it actually
is. In the above example, the relationship was hypoth
esized to have shifted up by 5, but all the dynamic
forecast errors after T + l exceed this magnitude by
ever-increasing amounts.

Table 3
Static and Dynamic Forecast Errors Under the
Assumption of an Intercept Shift (5)

Time

Static
forecast
error

Bias in
static
forecast

T+l

£ t+i + 8

T+2

£ t+2 + 5

+8
Et+2 + 8 + a ; ( Et-h + 8 )

T+3

ET+3 + 6

Et+3

£ t*i

+ 8 + 0(2 (Et+i + 8 ) +

2
OC2 ( £t*i
T+K

Et+k + 8

Bias in
dynamic
forecast
error

Dynamic
forecast
error

K
Z a2
i= l

8
8 ( l + a 2)
8

( 1 + a* + a 2)

+8)
( et+k- u d + 8 )

K-l 1
8 ( Z cc2)
i= 0

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

JU N E/JU LY

1980

Table 4
Post-Sample Static Forecast of Money Demand (111/1974-IV/1979)

Date

Actual
In ( M ,/P ,)

Static
forecast of
In (M ,/P ,)

Static
forecast
error

111/1974

0.8645

0.8865

-0.0220

IV/1974

0.8462

0.8753

1/1975

0.8260

0.8629

11/1975

0.8260

111/1975

Static forecast
error as
percent of
dependent variable

Static forecast
error in billions
of real
money balances'

-2.54

$ -5.28

-0.0291

-3.44

-6.88

-0.0369

-4.47

-8.59

0.8560

-0.0300

-3.63

-6.96

0.8264

0.8589

-0.0325

-3.93

-7.54

I V / 1975

0.8187

0.8617

-0.0430

-5.26

-9.96

1/1976

0.8213

0.8644

-0.0431

-5.24

-10.01

11/1976

0.8258

0.8665

-0.0406

-4.92

-9.49

111/1976

0.8246

0.8706

-0.0461

-5.59

-10.74

IV/1976

0.8283

0.8728

-0.0445

-5.38

-10.42

1/1977

0.8320

0.8795

-0.0475

-5.71

-11.18

11/1977

0.8319

0.8835

-0.0516

-6.21

-12.17

111/1977

0.8415

0.8855

-0.0439

-5.22

-10.44

IV /1977

0.8442

0.8905

-0.0463

-5.49

-11.02

1/1978

0.8455

0.8923

-0.0468

-5.53

-11.16

11/1978

0.8429

0.8969

-0.0540

-6.41

-12.89

111/1978

0.8451

0.8959

-0.0508

-6.01

-12.13
-14.96

I V / 1978

0.8350

0.8979

-0.0629

-7.53

1/1979

0.8092

0.8921

-0.0829

-10.25

-19.41

11/1979

0.8071

0.8811

-0.0740

-9.16

-17.22

111/1979

0.8107

0.8752

-0.0646

-7.97

-14.99

IV/1979

0.8032

0.8747

-0.0715

-8.90

-16.55

Summary Statistics
Mean error:

-0.048

Root-mean-squared-error:

0.051

Theil’s inequality coefficient:

0.061

Fraction of error due to:
(A )

Bias:

0.914

(B )

Variation:

0.002

(C )

Co-variation:

0.084

‘Calculated as actual real money stock, less the exponential of the predicted logarithm of real money balances.

Static Versus Dynamic Forecasts
of Money Demand
Given this analysis, it is useful to question whether
the conclusions based on dynamic forecasts of the
demand for money are valid. Of specific concern are
the conclusions that the money demand relationship
shifted down in 1974 and that this downshift has been
progressively increasing ever since.
Digitized for
20FRASER

Static out-of-sample forecasts over the period, III/
1974 — IV/1979, were developed for the same money
demand relationship given in equation (2). These
forecasts, along with summary statistics, are presented
in table 4.
Like the dynamic forecasts, the static money de
mand forecasts differ by large amounts from the actual
values observed. Real money balances are consistently

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

overpredicted and by fairly sizable amounts through
out the post-1974 period. The root-mean-squared-error
for the static forecasts over the period III/1974 — IV/
1979 is approximately ten times the sample period’s
standard error of the equation, suggesting that some
thing in the relationship has indeed changed over the
post-1974 period.14

While the static forecast results support the conclu
sion that the money demand relationship has shifted,
they do not corroborate other inferences drawn from
dynamic forecast errors. Reliance on the dynamic
forecasting technique has seriously exaggerated the
magnitude of the breakdown in the relationship. For
example, the 11/1978 dynamic forecast of money de
mand overestimates real money balance by almost $27
billion. Many studies suggest that this forecast error
is an estimate of the magnitude of the “downshift” in
the money demand relationship.
When the same estimated relationship is statically
rather than dynamically simulated, however, a much
smaller estimate of the downshift emerges. In the case
of static forecasts, real money balances are projected
to be “only” $13 billion above the actual level in
11/1978. The reason for the significant difference in
these forecast errors is that the dynamic forecast error
is simply a weighted average of current and past static
forecast errors. As table 4 shows, the static forecast
errors in money demand have been consistently one
sided (overpredicted) since III/1974. Consequently,
the dynamic forecast error for any period thereafter
has always exceeded the static forecast error.
Although the dynamic forecasting procedure indi
cates how errors can cumulate over the long-run, it
provides a p oor basis for measuring the extent o f the
“shift” in the relationship. Again, consider the $27 bil

lion dynamic forecast error for 11/1978. This error
tells the policymaker the extent to which forecasts of
real money balances would have been inaccurate if
equation (2) had been used in 11/1974 to project II/
1978 money demand, assuming that he had full infor
mation about the actual course of interest rates and
real income but no knowledge of the course of actual
real money balances over the four-year intervening
period. On the other hand, the $13 billion static fore
cast error for 11/1978 tells the policymaker how inac
curate his prediction of real money balances would
have been if he had used the coefficients in equation
(2) but had full knowledge of the 1/1978 level of
14This conclusion is further supported by a Chow test, which
leads to the rejection of the hypothesis of coefficient equality
over the p re-III/1974 and p ost-III/1974 periods. The F statistic for 5, 69 degrees of freedom, is 5.23. Thus, the null
hypothesis can be rejected at the 1 percent level.

JU N E/JU LY

1980

real money balances. Thus, over one-half of the dy
namic forecast error for 11/1978 is due to the error in
predicting real money balances in the previous period
and should not be considered part of the “shift” in
the relationship.
One example of improperly using dynamic forecast
errors to measure the extent of the money demand
shift is provided by the work of Tinsley and Garrett.15
These authors argue that the introduction of immedi
ately available funds (IF ) in the mid-1970’s was
largely responsible for the downshift in money de
mand. To support the argument that the introduction
of these financial assets have displaced a portion of
conventional demand deposits, they compare the size
of IF with the dynamic forecast errors for a demand
deposit equation: “There is, of course, a striking simi
larity between the magnitude of IF . . . and the size
of the dynamic (emphasis added) forecast error of
demand deposits . . .”18
If, as these authors argue, economic agents simply
substituted IF for demand deposits in their portfolios,
the dynamic forecast error should have increased
at a faster rate than the growth of IF. This would
occur because the dynamic forecast for periods be
yond T + l would differ from the actual observation
by the magnitude of the shift in funds plus a weighted
average of previous forecast errors for demand de
posits. It is precisely this latter portion of the fore
cast error that many investigators ignore. Thus, rather
than providing support, the similarity in magnitude
between IF and the dynamic forecast errors actually
casts doubt on the Tinsley-Garrett argument.
The use of the dynamic forecasting technique has
also masked the pattern of the shift in the money de
mand relationship. As suggested at the outset, dynamic
forecasts of money demand have led some researchers
to conclude that there has been a continuous down
shift in the relationship following 11/1974, because the
dynamic forecast errors have been increasing over
time (figure 3 ).17 Obviously, the argument that this
pattern of dynamic forecast errors implies a contin
uous shift in the relationship is invalid.
In contrast to the view of a continuous drift in the
relationship, the static forecast errors suggest three
15P. A. Tinsley and Bonnie Garrett, with M. E . Friar, “The
Measurement of Money Demand,” Special Studies Paper, No.
133 ( Board of Governors of the Federal Reserve System
19 7 8 ).
1(iP. A. Tinsley, et. al., “The Measurement of Money Demand,”
p. 15.
17For this view see Porter, et. al. “Financial Innovations and
the Monetary Aggregates.” Fo r a more elementary approach,
see’ “Inflation and the Destruction of Monetarism,” pp. 5-12.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

JU N E/JU LY

1980

Figure 3

Static a n d D y n a m i c Forecast Errors of M o n e y
D e m a n d Equations

separate intercept shifts.18 The first shift — equal to
approximately -0.03 (table 4, colmun 4 ) — occurred
in III/1974. There is, however, little evidence to sup
port the notion that any further significant shifts oc
curred prior to IV/1975. All of the static forecast
errors that occurred over the period IV/1974 — III/
1975 are within two standard errors of the estimated
equation (SE E ) on either side of -0.03.
Another discrete shift in the relationship in IV/1975
is apparent from the jump in the static forecast error
from III/1975 to IV/1975. Again, while there is a
slight drift in the relationship, it does not appear to
change significantiy over the subsequent three-year
period; from IV/1975 to III/1978, the static forecast
error fluctuates around -0.05. Static forecast errors
over this period are within two standard errors of the
estimated equation on either side of this point. Finally,
in IV/1978, another downshift is indicated by the dis
crete jump in the static forecast error.19 But, again,
18Fo r support of this notion of selected shifts in the money de
mand relationship, see Michael R. Darby, “The International
Economy as a Source of and Restraint on United States In
flation,” Working Paper No. 347 (Cambridge, Mass.: National
Bureau of Economic Research, Inc., January 1 9 8 0 ).
19Note that this latter point coincides with the introduction of
nationwide ATS accounts and New York NOW accounts.

Digitized 22
for FRASER

the forecast error subsequently stabilizes around this
higher level.
The pattern of breakdown suggested by the static
estimation procedure differs greatly from that de
duced from the ever-increasing dynamic forecast errors
shown in figure 3. The static forecasting procedure
isolates the periods III/1974, IV/1975, and IV/1978
as the specific shift points that require further study.
The analysis also suggests that, as far as short-run
forecasting is concerned, the best the researcher can
do in the future is to assume that any statistically
significant shift in the relationship is a once-and-forall occurrence.

CONCLUSION
This paper demonstrates that the magnitude of the
recent downward shift in the money demand rela
tionship has been exaggerated and the pattern of the
precise shifts has been obscured by reliance on the
dynamic forecasting procedure to evaluate the tem
poral stability of the money demand relationship.
The magnitude of the shift is much smaller (in fact, insig
nificant) if M IB is used in place of M l as the monetary
aggregate measure.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

The pattern of ever-increasing dynamic forecast
errors has led some investigators to conclude that
money demand has been subject to a downward drift
since III/1974, and, as a result, they argue that money
is no longer a useful policy instrument or indicator.
On the contrary, the evidence in this paper supports
the notion of discrete once-and-for-all shifts in the re
lationship, and isolates the periods of late III/1974,
IV/1975, and IV/1978 as specific periods of these
shifts.
By rejecting the notion of a constantly shifting
money demand relationship, this paper reaffirms the
usefulness of money as a policy instrument. By using
the conventional money demand equation considered
here, a policymaker, unaware of the financial inno
vations occurring over the recent period, would have
made only three significant errors in forecasting the
growth rate of real money balances. Consequently,
only on these three separate occasions would the
linkage between money and prices have been other
than expected.

JU N E/JU LY

1980

Finally, although this paper has presented longrange (dynamic) forecasts of money demand which
are in serious error, this evidence should not be inter
preted as highly critical of a long-range policy of
money control, such as Friedman’s X-percent rule.
The period considered in this paper, III/1974-IV/1979,
was one of ever-accelerating monetary growth, which
resulted in a higher rate of inflation, as well as higher
interest rates. These high interest rates, in turn, have
led to financial innovations (e.g., ATS accounts, NOW
accounts, and money market mutual funds) designed
to circumvent Federal Reserve regulations (primarily
Regulation Q interest rate ceilings). To the extent
that these financial innovations have been responsible
for the shifts in money demand, the ultimate precur
sor of the shifts has been the excessive growth of
money over this period. In other words, it is legitimate
to question whether money demand would have been
subject to the few shifts experienced had monetary
growth not accelerated over the past decade.

Financing Constraints and the
Short-Run Response to Fiscal Policy
LAURENCE H. MEYER

j^^|[oNETARISTS have long emphasized that the
impact of an increase in government expenditures
depends on how the increase is financed. In particu
lar, they have suggested that a bond-financed increase
in government expenditures has only minimal effects
on aggregate demand and income, because the gov
ernment borrowing necessary to finance the additional
public expenditures may “crowd out” a roughly equiv
alent amount of private spending and borrowing. This
view is summarized as follows:
“Fiscal policy provides additional spending in a
world of sparse spending opportunities. But it does
not provide a new source of finance in a world where
spending is constrained by sources of finance. The
government expenditures are financed in debt markets
in competition with private expenditures. The case
least favorable to fiscal policy is that in which the
additional government borrowing simply crowds out
of the market an equal (or conceivably even greater)
volume of borrowing that would have financed pri
vate expenditures.”3

This paper presents a framework for analyzing fiscal
policy that incorporates the interaction between gov
ernment and the private sector in their spending and
borrowing decisions. It shows that ambiguity sur
rounding the income-multiplier for increased govern
ment expenditures results from the failure to model
correctly the stock repercussions of changes in govern
ment spending and private investment. Specifically,
the ambiguity is caused by failure to allow for changes
in the supply of capital (or private financial secu
rities issued to finance the capital stock) that arise in
ijohn M. Culbertson, Macroeconomic Theory and Stabilization
Policy (N ew York: McGraw-Hill, 1 9 6 8 ), p. 463.

24 FRASER
Digitized for

response to debt-financed fiscal policy. When the
analysis is amended to correctly incorporate the financ
ing of private and public expenditures and to develop
the relationship among saving, the deficit, and crowd
ing out, the initial impact of an increase in govern
ment expenditure on aggregate demand and income is
unambiguously positive.

FOUR MODELS OF THE SHORT-RUN
RESPONSE TO FISCAL POLICY
Four models of the response to fiscal policy are
analyzed in detail. Each model includes the equilib
rium conditions in the commodity and money mar
kets (which correspond to the IS and LM curves in
standard income-expenditure analysis) and the defini
tion of disposable income, as shown in equations (1)
through (3). The demand for output depends on in
come and the interest rate [equation (1)]; the money
supply is exogenous, and the demand for money de
pends on the interest rate, income, and end-of-period
value of household wealth [equation (2 )].2 Dispos
able income is simply national income minus taxes net
of transfers [equation (3)].
2The model includes a wealth effect in the money demand
function but not in the consumption function. This was done
primarily to simplify the analysis, since the major concern
involves the portfolio effects of fiscal policy. In addition, the
relevant wealth variable in a consumption function is beginning-of-period wealth, and this is predetermined in the sub
sequent analysis. The only way a wealth effect in the con
sumption function could affect the conclusions is through an
interest-induced wealth effect. Including an interest-induced
wealth effect would be equivalent to making consumption
( saving) depend on the interest rate. Such a modification is
discussed later in the analysis.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

Models 1-4

{

( 1 ) X = CyY + I rr + C + I + G

Model I:
1-3
with La — 0

( 2 ) m = L + L*X + L rr + L .a

(3 ) Y = X - T
Model II:
1-3 + 4, 5

1(4) a = m + b + K
1 ( 5 ) Ab = D_, + AG - AT - Am

Model III:
1-3, 5-7

(6) a = m + b + d
( 7 ) Ad = I_i + AI = I-i + I rAr

Model IV:
1-3, 8, 9

j(8) a = a + S

Notation:

1 ( 9 ) S = Y - C = Y - ( C + C yY )

X = output or national income
Y = disposable income
r = interest rate
m = money supply
a = end-of-period wealth of households
T = net taxes ( taxes net of transfers)
b = end-of-period supply of government bonds
D-i = deficit inherited from the previous period
d = end-of-period supply of private securities
I-i = ( net ) investment in the previous period
a = beginning-of-period wealth of households
S = saving
G = government expenditures on goods and services
C, I = autonomous private expenditures on consumption
and investment
Cy, I r, L x, L r> La = model parameters
Parameter restrictions:
1 > Cy > 0

-oo < Ir < 0
L, > 0
-oo < L r < 0
1 > L„ > 0

Model I, the traditional textbook model associated
with the income-expenditure view, assumes La = 0
and includes only equations (1) through (3). It also
corresponds, however, to Friedman’s representation of
a common framework that would be acceptable to
both monetarists and nonmonetarists.3

Alternative Approaches to Modeling
Wealth Determination
Models 2 through 4 include the determination of
household wealth, and it is the modeling of wealth
3See, for example, Milton Friedman, “A Theoretical Fram e
work for Monetary Analysis,” Journal of Political Economy
(M arch/A pril 1 9 7 0 ), pp. 193-238.

JU N E/JU LY

1980

that is critical to the analysis in this article. Two defi
nitions of wealth can be used to complete the model:
Both are equally correct and yield identical results
when the definitions are specified properly. The sum
of the assets measure defines wealth as the sum of the
assets that are held in household portfolios. The per
petual inventory measure defines wealth as the sum of
last period’s wealth and saving, where saving is mea
sured as the change in wealth between last period and
this period.4 The sum of the assets approach links
wealth to the rest of the model by using financing
constraints that link the supply of money and bonds
to spending decisions of the government and private
sectors. The perpetual inventory approach links wealth
to the rest of the model by adding a saving equation
to the model.
Model 2 is an extension of Model 1 and incorpo
rates both a wealth effect in the demand for money
(0 < La < 1) and a government financing constraint
[equation (5)]. The government financing constraint
(GFC) requires that government expenditures (G)
be financed by some combination of taxes net of trans
fers (T ) and issue of money and government bonds
(Am and Ab, respectively).8 Equation (5) rewrites
this restriction in terms of the inherited deficit (D_i)
and changes in government expenditures and taxes (AG
and AT, respectively). The inherited deficit plus any
increase in government spending in the present period
relative to the previous period must be financed by
increases in tax revenue net of transfers or by issue
of money or government bonds.
Wealth is defined, according to equation (4), as the
sum of money, government bonds, and the capital
stock.6 Both money and the capital stock are assumed
to be constant, and the supply of government bonds
is determined via the GFC. Since all four models as
sume an exogenous money supply, increases in gov
4Peter E. Kennedy, “Direct Wealth Effects in Macroeconomics
Models: The Saving vs. the Definitional Approach,” Journal
of Money, Credit and Banking (February 19 7 8 ), pp. 94-8.
5The integration of the government financing constraint into
macroeconomic models was advanced by the work of Carl
Christ. See, for example, Carl F . Christ, “A Simple Macroeco
nomic Model with a Government Budget Constraint,” Journal
of Political Economy ( January/February 1 9 6 8 ), pp. 53-67.
eThe author assumes throughout that government bonds are
part of net wealth and this assumption presumes the absence
of “tax discounting.” The evidence on tax discounting is mixed.
For a review of the theory and evidence on tax discounting,
see Willem H. Buiter and James Tobin, “Debt Neutrality: A
Brief Review of Doctrine and Evidence,” Cowles Foundation
Discussion Paper No. 497 (Yale University, September 15,
1978) . For an empirical investigation which finds no evidence
of tax discounting, see Jess B. Yawitz and Laurence H. Meyer,
“An Empirical Investigation of the Extent of Tax Discount
ing,” Journal of Money, Credit and Banking (May 19 7 6 ),
pp. 247-56.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

ernment expenditures are financed by increasing the
government debt. This common assumption allows us
to focus on debt-financed fiscal policy.
The critical assumption in Model 2 is that the capi
tal stock is also exogenous. Although this assumption
is common in short-run models of income determina
tion, it presents serious difficulties for modeling the
portfolio repercussions of fiscal actions.7
Models 3 and 4 further refine the analysis of fiscal
policy by relaxing the assumption that the capital
stock is fixed. These models introduce properly speci
fied but alternative definitions of wealth. Model 3 es
sentially retains the wealth definition used in Model
2 but endogenizes the capital stock by defining the
end-of-period capital stock as the sum of the beginning-of-period capital stock and investment over the
period. All capital is assumed to be held by firms and
purchased with external funds acquired by selling se
curities to the household sector. Thus, households can
be viewed as indirectly holding the capital stock via
their holdings of private securities, and the net wealth
of the household sector can be rewritten as the sum
of money, government bonds, and private securities
[equation (6)], where the supply of private securities
is determined via the investment financing constraint
[equation (7 )].8 The simple structure of the model
can be maintained by assuming that government debt
and private securities are perfect substitutes in house
hold portfolios.9 The supply of private securities is
determined by the investment financing constraint
(IF C ), the private sector counterpart to the GFC.
The IFC [equation (7)] links changes in the supply
of private securities directly to (net) investment (ex
pressed as last period’s investment plus the change in
investment from last period to the current period) and
thus links private spending and financial decisions.
7Models embodying the assumption of a fixed capital stock have
been used to investigate the portfolio repercussions of fiscal
policy by Silber, Meyer, and B. Friedman. See William L.
Silber, “Fiscal Policy in IS-LM Analysis: A Correction,”
Journal of Money, Credit and Banking (November 1 9 7 0 ), pp.
461-72; Laurence H. Meyer, “The Balance Sheet Identity, the
Government Financing Constraint, and the Crowding-Out E f
fect,” Journal of Monetary Economics (January 19 7 5 ), pp.
65-78; and Benjamin Friedman, “Crowding-Out or CrowdingIn: Economic Consequences of Financing Government Defi
cits,” Brookings Papers on Economic Activity ( 1 9 7 8 : 3 ) ,
pp. 593-641.
8Equations ( 4 ) and ( 6 ) correspond to two different ways of
defining wealth: net private wealth and net wealth of house
holds. Net private wealth equals the capital stock (the econ
omy’s tangible or real assets) plus outside financial assets of
the private sector (outside money and government bonds).
Net wealth of households includes only the outside financial
assets of the household sector (assuming all capital assets are
held by businesses). The two are identical, provided capital
in net private wealth is valued at its market value as defined
by the value of the financial claims to that capital stock held
in household portfolios.
9Firms finance acquisition of capital via private bonds, equities,

http://fraser.stlouisfed.org/
26
Federal Reserve Bank of St. Louis

JU N E/JU LY

1980

Properties of the Framework
These four models have a common framework:
They are fixed price/variable output, one-good, twoasset models of the short-run response to fiscal policy.
Additionally, Models 3 and 4 employ an end-of-period
specification of asset market equilibrium.
The fixed price/variable output framework is appro
priate for studying the response of output to policy ac
tions in a disequilibrium setting where price flexibility
is insufficient to sustain continuous full equilibrium.10
Its suitability, however, is confined to developing in
sights about the short-run response to fiscal actions.
The framework described in this article extends the
one-good, two-asset IS/LM model that is widely used
in macroeconomics. The two assets included in the
models are money and bonds. Both government and
private debt are included in Models 3 and 4 and, in
order to retain the two-asset framework, they are as
sumed to be perfect substitutes in household port
folios. To further simplify the analysis, households are
assumed to hold all the financial assets and, in Models
3 and 4, firms are assumed to finance all investment
externally.
The models are developed to yield one-period mul
tipliers only. Models 2, 3, and 4 are intrinsically dy
namic since the supply of bonds continues to increase
as long as the government runs a deficit and, in Mod
els 3 and 4, as long as saving and investment occur.
The GFC, for example, requires that government
expenditure increases be financed not only in the ini
tial period but during all future periods as long as
the deficit continues. The models, however, investi
gate the impact of the increase in government spend
ing during the initial period only.
To model the financial repercussions of spending
decisions in a one-period framework, an end-of-period
(EOP) specification of asset market equilibrium is
and internal funds. To maintain the model’s simple structure
and allow every possibility for substantial portfolio effects
associated with government deficits, all investment is assumed
to be financed externally by emitting a single financial instru
ment which is a perfect substitute for government bonds in
wealth owners’ portfolios. In principle, the models employed in
this article should distinguish between private debt, equity,
and government debt. But the approach used here only makes
the portfolio effect of deficit financing larger and the conclu
sion that there is an unambiguous one-period multiplier more
noteworthy. Fo r a three-asset version that is otherwise similar
to the approach taken in this paper, see James Tobin and W il
lem Buiter, “Fiscal and Monetary Policies, Capital Formation,
and Economic Activity,” in George von Furstenburg, ed., The
Government and Capital Formation (Cambridge: Ballinger
Publishing Co., 1 9 8 0 ), pp. 73-151.
10For a rationalization of this approach, see Robert J. Barro
and Herschel I. Grossman, Money, Employment, and Infla
tion (Cambridge: Cambridge University Press, 19 7 6 ).

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

used in Models 3 and 4.11 In discrete time models, the
concept of simultaneous equilibrium in stock and flow
markets is subtle. Since flows are defined as rates over
the unit interval and stocks are defined at a point dur
ing the interval, there is no natural way of defining
simultaneous equilibrium.12 For the following analy
sis, it is convenient to define simultaneous equilibrium
as corresponding to flow equilibrium over the period
and to stock equilibrium at the end of the period. By
defining stocks at the end of the interval used to de
fine the flow variables, the financing of expenditure
flows over the period is allowed to affect the supplies
of bonds outstanding, thereby allowing the model to
include both the effect of the increase in expenditures
and the effect of the associated increase in the supply
of bonds.

MODEL 1: THE TEXTBOOK MULTIPLIER
AND HICKSIAN CROWDING OUT
The textbook IS/LM multiplier identifies a single
source of crowding out, labeled by Modigliani and
Ando as “Hicksian crowding out.”13 Model 1 includes
neither a wealth effect in the demand for money
(L a = 0) nor any financing constraints. It is generally
associated with the income-expenditure approach and
has been widely criticized by monetarists. The multi
plier for an increase in government expenditures in
u Fo r a discussion of the modeling of simultaneous stock and
flow equilibria in period models, see Duncan K. Foley, “On
Two Specifications of Asset Equilibrium in Macroeconomic
Models,” T he Journal of Political Economy (April 1 9 7 5 ),
pp. 303-24.
12One way to eliminate the ambiguity is to reduce the unit
interval of the period analysis until the beginning and the
end of the period converge. This results in a continuous
analysis in which flows at instantaneous rates and stocks can
both be measured simultaneously. However, since this anal
ysis focuses on capturing the stock repercussions of flow
decisions, the end-of-period, discrete framework is particu
larly appropriate. Most continuous models are used to solve
for either instantaneous or steady-state values of multipliers.
Discrete models, on the other hand, are the most convenient
approach when the analysis is to be carried out over a dis
crete interval, short of the time required to achieve full
steady-state equihbrium. Fo r example, Tumovsky notes:
“While many macroeconomic models are formulated using
discrete time, much of macroeconomic theory is formulated
using continuous time. Both kinds of models have their place,
and the choice between them is often dictated by conven
ience. If one is interested in analyzing short-run effects, dis
crete time models tend to be more useful. On the other hand,
for steady-state and stability analyses, continuous models are
usually more practical.” Stephen J. Tumovsky, Macroeco
nomic Analysis and Stabilization Policies (Cambridge: Cam
bridge University Press, 1 9 7 7 ), p. 43.
13Franco Modigliani and Albert Ando, “Impacts of Fiscal Ac
tions on Aggregate Income and the Monetarist Controversy:
Theory and Evidence,” in Jerome Stein, ed., Monetarism
(Amsterdam: North-Holland Publishing Company, 1 9 7 6 ),
pp. 17-42. The terminology, “Hicksian crowding-out,” reflects
the origins of the IS-LM framework in the writing of J. R.
Hicks. See, for example, J. R. Hicks, “Mr. Keynes and the
Classics: A Suggested Interpretation,” Econometrica (April
1 9 3 7 ), pp. 145-59.

JU N E/JU LY

1980

this model is:
(i) M = _______ I_______
AG

1 - Cj + ( L , / L r)Ir

V---------r ------ J

Hicksian crowding out

This multiplier has several properties: (1) In the
absence of extreme values of the parameters, the multi
plier is unambiguously positive, confirming the in
come expenditure view about the response to fiscal
policy. (2) The multiplier does not allow for any effect
of government borrowing on the response of output to
the fiscal operation. Since money and taxes are held
constant, the multiplier implicitly corresponds to a
bond-financed fiscal action. Despite the absence of
any effect associated with the increase in government
borrowing, partial crowding out occurs via the income-induced rise in the interest rate. As income
increases, the demand for money increases relative to
the fixed supply of money. The resulting excess de
mand for money (and excess supply of bonds) exerts
upward pressure on the interest rate which, in turn,
restricts the interest responsive portion of aggregate
demand (investment, in this model). However, as
long as Lr < 0 and Ir > -oo, AX/ AG remains positive
and investment declines by less than the increase in
government expenditures. The magnitude of Hicksian
crowding out (or negative feedback) is controlled by
the last set of terms in the denominator of equa
tion (1).
Thus, although some investment is crowded out by
government spending, the fiscal multiplier is never
theless unambiguously positive. Of course, this does
not guarantee that the multiplier is large. Monetarists
have generally argued that, even in this framework,
fiscal policy will have a minimal effect due to the ac
tual magnitude of Hicksian crowding out resulting
from the small absolute value of the Lr parameter and
the large absolute value of the Ir parameter.14

MODEL 2: THE GFC AND THE WEALTH
EFFECT: PORTFOLIO CROWDING OUT AND
THE AMBIGUOUS FISCAL MULTIPLIER
To generate an ambiguous sign on the fiscal multi
plier in this framework, the financing of government
spending via the increase in the supply of government
bonds must affect the interest rate and income. This
requires that a wealth effect be added to the demand
for money (1 > La > 0) and that both the definition
of wealth given by equation (4) and the GFC [equa
tion (5)] be included in the analysis.
14See, for example, Milton Friedman, “Comments on the
Critics,” Journal of Political Economy ( September/October
19 7 2 ), pp. 906-50.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

The resulting fiscal multiplier is:
portfolio
crowding out
A

I9\

AX _

( ' AG

1 -

(L a /L ,)Ir

where the denominator, Q, is the same as in the first
multiplier. The fiscal operation now has two direct
impacts, indicated by the two terms in the numerator
of equation (2 ): The increase in G directly increases
aggregate demand (the direct fiscal impact, also op
erative in Model 1) and the accompanying increase
in the supply of bonds exerts upward pressure on
interest rates, thereby reducing aggregate demand
(the direct portfolio im pact). The net effect of these
two direct impacts — and, hence, the multiplier — is
ambiguous. Thus, while Hicksian crowding out can,
at most, induce partial crowding out, “portfolio
crowding out” can, at least in this model, induce com
plete or even more than complete crowding out, as
suggested by the quote at the beginning of this article.
Note that if La = 0, the multiplier collapses to the
multiplier derived for Model 1. Income-expenditure,
macroeconometric models typically use a transactionsbased model of the demand for money (where La =
0), while monetarists generally prefer portfolio mod
els of the demand for money (where La > 0). If
La = 0, wealth owners want to retain the entire incre
ment in wealth in the form of bonds; in this case, the
increase in the supply of bonds does not induce an
excess supply of bonds and, therefore, does not exert
upward pressure on the interest rate. On the other
hand, if La > 0, wealth owners want to diversify their
portfolios and, hence, to split any increase in wealth
between increased holdings of money and bonds. In
this case, an increase in the supply of bonds and
wealth will increase the demand for bonds by less
than the increase in the supply of bonds, resulting
in an excess supply of bonds and upward pressure on
the interest rate.

MODEL 3: ADDING THE INVESTMENT
FINANCING CONSTRAINT: RETURNING
TO AN UNAMBIGUOUS MULTIPLIER
Models 1 and 2 are useful as simple models which
yield income-expenditure and monetarist results, re
spectively, but both are incomplete. Models 3 and 4
refine the analysis presented in Models 1 and 2 in
different but equivalent ways. Although each com
bines portfolio crowding out with Hicksian crowding
out as did Model 2, they yield unambiguously positive
fiscal multipliers as did Model 1.

JU N E/JU LY

1980

In order to allow for portfolio crowding out, it is
necessary to continue assuming that 1 > La > 0. The
problem with Model 2 is that it accounts for the fi
nancing of government spending but ignores the fi
nancial repercussions of private spending. Model 3,
therefore, respecifies the definition of wealth to in
clude private securities along with government debt,
and the IFC is added in order to link investment to
the supply of private securities. Thus, Model 3 in
cludes dual financing constraints: End-of-period
wealth is now the sum of end-of-period supplies of
money and bonds, and the GFC and IFC are used to
determine end-of-period supplies of government and
private securities, respectively.
By redefining wealth, Model 3 refines the definition
given in Model 2, where the capital stock was treated
as fixed even though net investment was occurring.
Consequently, Model 2 failed to address the portfolio
repercussions of investment. Increases in the capital
stock associated with investment must be absorbed
into private portfolios, just as increases in government
debt associated with government deficits must be
absorbed.
The multiplier for Model 3 is:
direct
fiscal
impact

direct
portfolio impact

AX J T - [ L . / ( L , + L a p ] I,
1 ' AG
Q'

where Q' =r 1 - Cy + [LX/(L,. -f La I,)] Ir. The two
terms in the numerator reflect the two direct impacts
associated with the fiscal operation. The direct fiscal
impact is the dollar-for-dollar increase in aggregate
demand associated with the increased government ex
penditure. The direct portfolio impact is the effect
on investment associated with the increase in the sup
ply of government bonds. The multiplier has a form
similar to that of Model 2: A positive direct fiscal im
pact and negative portfolio impact are contained in
the numerator. However, in the case of Model 3, it
can be demonstrated that the direct portfolio impact
is unambiguously smaller than the direct fiscal impact
so that the multiplier is unambiguously positive. The
numerator is positive because the terms in the direct
portfolio impact can be combined to form a ratio less
than unity [LaIr/(Lr + LaIr) < 1],
The multiplier given by Model 3 implies that, al
though investment declines in response to an increase
in government spending, the decline in investment in
duced by the increase in supply of government bonds
is less than the increase in government expenditures.
The increase in government debt raises the interest
rate because it results in an increase in the supply

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

relative to the demand for bonds. If the decline in
investment due to the rise in the interest rate were
to exceed the increase in government spending, the
decline in private bonds (associated with the decline
in investment) would exceed the increase in the sup
ply of government bonds so that the total supply of
bonds would fall rather than rise.15 This situation, of
course, would be contradictory since investment de
clines only if the interest rate rises. Because the de
cline in investment slows the rise in the interest rate,
the resulting portfolio crowding out can be only par
tial. Although Hicksian crowding out occurs in re
sponse to the rise in income, it cannot alter the con
clusion that the fiscal policy multiplier is unambigu
ously positive.

MODEL 4: A SIMPLIFIED SOLUTION WITH
THE PERPETUAL INVENTORY DEFINITION
OF WEALTH
Model 4 underlies Modigliani and Ando’s conclu
sion that the short-run response to fiscal policy is posi
tive: “Clearly r cannot rise unless [a] rises; but [a]
cannot rise unless saving increases, which requires a
rise in X!”16 Model 4 uses a perpetual inventory defi
nition of wealth [equation (8)] that is equivalent but
alternative to that employed in Model 3. End-ofperiod wealth is defined in this case as beginning-ofperiod wealth plus saving over the period.17 The AX/
AG multiplier for this model is:
(4 ) M = __________________ 1__________________
AG
1 - CjT + [(Luc + L« (1 - C , ) ) / L r ] Ir
V

both Hicksian and portfolio crowding out

This multiplier, like that for Models 2 and 3, includes
both Hicksian and portfolio crowding out and it is
identical to that in Model 3 even if it doesn’t appear
to be.18 As in Model 3, portfolio crowding out can be
only partial.
15The statement that a decline in investment induces a de
cline in the supply of private bonds requires clarification.
As long as net investment is positive, the supply of bonds
will be increasing. The bond financing of government ex
penditures raises the interest rate, lowers investment, and
lowers the supply of bonds relative to what it would have
been in the absence of the policy action. The multiplier
AX/AG, in turn, indicates how income differs from what
it would have been in the absence of the policy action. The
multiplier, therefore, has a different interpretation than the
usual comparative static multipliers derived from IS/LM
models without financing constraints. Such multipliers indi
cate the change in income between the old and the new
equilibrium levels of income. One-period multipliers in
models with financing constraints, in contrast, only indicate
how income differs from what it would have been in the
absence of the policy change.
1''Modigliani and Ando, “Impacts of Fiscal Actions on Aggre
gate Income and the Monetarist Controversy,” p. 17.
17Capital gains have been ignored in order to simplify the
analysis.
18To show that Models 3 and 4 are identical, put the numer
ator of equation ( 3 ) in terms of a common denominator,

JU N E/JU LY

1980

Multiplier 4 resembles multiplier 1 but it contains
an additional term in the numerator of the fraction
in the denominator of the multiplier. This term,
La( l - Cy), represents the effect of the increase in
wealth (via saving) on the demand for money. Since
the money supply remains unchanged, all additional
wealth is implicitly held in the form of bonds. To
induce the private sector to increase its holdings of
bonds relative to money, the Treasury must offer a
higher interest rate. But, as Modigliani and Ando have
noted, portfolio crowding out is activated by the in
crease in wealth that is associated with an increase in
saving and, hence, income.19 Therefore, portfolio
crowding out can restrain but not reverse the increase
in income associated with the increase in government
spending.
Model 4 highlights the role of saving in the analysis
of crowding out. The increase in government bonds
can be absorbed into private portfolios either by an
increase in wealth (i.e., induced saving g en era ted by
the fiscal action) or by displacing (i.e., crowding out)
private debt. Saving can be defined as the sum of the
deficit and investment; the deficit can be defined as
the difference between saving and investment. Any
increase in the deficit must be offset, therefore, by a
combination of increased saving (allowing absorption
of increased government bonds) or decreased invest
ment (replacing private securities with government
bonds).
Model 4 analyzes the response to fiscal actions
without directly including either the GFC or the IFC.
Models 2 and 3 include the financing constraint in
order to determine the end-of-period supplies of gov
ernment and private bonds. The bond market is the
redundant market in the analysis, and the perpetual
inventory definition of wealth does not use end-ofperiod supplies of bonds. Consequently, Model 4 does
not explicitly contain the supply of bonds or require
the financing constraints in order to solve for the re
sponse to fiscal actions.

REFINEMENTS AND COMPLICATIONS
This section discusses the implications of relaxing
L r + L ,I r; then multiply the numerator and denominator by
L r + Lalr; then divide the numerator and denominator by
L r. The equivalence of Models 3 and 4 can also be seen by
comparing the two definitions of wealth: Model 3 defines
the change in wealth as the sum of the deficit and invest
ment, and Model 4 defines the change in wealth as equal
to saving. Since S = I + D is an equilibrium condition,
the multipliers for Models 3 and 4 will be identical.
18The “increase in wealth” in the above statement refers to
the increase in wealth relative to what it would have been
in the absence of the policy action. As long as saving is
positive, wealth will increase. The policy action induces an
increase in wealth only if it induces an increase in saving.

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

some of the assumptions employed in Models 1
through 4. First, some considerations relevant to an
analysis of the longer-run response to fiscal actions
are discussed. Second, two modifications that intro
duce the possibility that bond-financed fiscal policy
may “pull in” rather than crowd out investment are
considered. Finally, a modification that allows for an
ambiguous short-run fiscal multiplier in Models 3 and
4 is discussed.

Longer-Run Considerations: Price Flexibility
and Cumulative Stock Effects
Models 1 through 4 yielded only one-period multi
pliers. The longer-run response to fiscal actions is
affected also by price flexibility and the cumulative
effects of financing continuing deficits associated with
once-and-for-all changes in government expenditures.
The models employed above assumed prices were
fixed and were justified as simple disequilibrium mod
els along lines developed by Barro and Grossman.
However, they apply only to the analysis of the shortrun response to fiscal actions. In the long run, price
flexibility insures a unique equilibrium level of the un
employment rate via the Phillips Curve. Although fis
cal policy may temporarily increase output and em
ployment, most models yield zero long-run multipliers
for the response of output and employment to policy
actions.20
Another factor that affects the longer-run response
to fiscal actions is the continuing increase in the sup
ply of bonds associated with a once-and-for-all in
crease in government expenditures. The implications
of the continued financing of deficits associated with
once-and-for-all increases in government expenditures
for the long-run response of income have been in
vestigated by Blinder and Solow.21

Pulling In: Income-Induced Investment
and Multiple Assets
In each of the models developed above, an increase
in government expenditures reduced investment. The
question they addressed was whether investment fell
by more or less than the increase in government
expenditures. Two simple modifications introduce the
20See, for example, Modigliani and Ando’s discussion of pol
icy simulations with the MPS model in “Impacts of Fiscal Ac
tions on Aggregate Income and the Monetarist Controversy.”
21Alan S. Blinder and Robert M. Solow, “Does Fiscal Policy
Matter?” Journal of Public Economics (November 19 7 3 ),
pp. 319-37.

JU N E/JU LY

1980

possibility that bond-financed increases in government
expenditures may encourage rather than discourage
investment. These modifications include adding in
come as an argument in the investment function and
allowing government debt and private securities to
be imperfect substitutes.
If investment depends on the level of income, in
vestment may rise even though the fiscal operation
raises the interest rate. Hendershott has referred to
this phenomenon as pulling in rather than crowding
out investment.22
In the two-asset model employed above, increased
supply of government debt restrains investment, in
part, because government and private securities are
assumed to be perfect substitutes. If the model is
refined to allow for at least three assets — money, gov
ernment debt, and, for example, equities — the port
folio response to the increase in the supply of govern
ment debt becomes ambiguous. Tobin and Tobin and
Buiter have used three-asset models to study the re
sponse to policy actions.23 In the two-asset model, an
increase in government debt creates excess supply in
the securities market and upward pressure on “the”
interest rate. The three-asset model involves two
rates: The rate on government bonds and the rate on
equities. The models generally focus on the rate on
government debt and the price of equities, and they
designate investment as a positive function of the
price of equities.
An increase in government debt increases the rate
on government bonds thereby inducing substitution
out of equities into government debt. This substitu
tion effect reduces the demand for equities and de
presses their price (thus raising their rate of return).
Wealth is also increasing, and wealth owners may
wish to diversify their portfolios and hold some of
their increased wealth in equities. This wealth effect
increases the demand for equities, as well as their
price. The net impact of the substitution and wealth
effects is ambiguous. Equity prices and, hence, invest
ment may rise or fall. In this three-asset example, if
La = 0, an increase in the supply of government debt
unambiguously raises equity prices and stimulates
investment.
22Patric H. Hendershott, “A Tax Cut in a Multiple Security
Model: Crowding-Out, Pulling-In and the Term Structure
of Interest Rates,” Journal of Finance (September 1 9 7 6 ),
pp. 1185-99.
23James Tobin, “An Essay on Principles of Debt Management,”
in Fiscal and D ebt Management Policies, Commission on
Money and Credit (Englewood Cliffs, N .J.: Prentice-Hall,
1 9 6 3 ), pp. 143-218; and Tobin and Buiter, “Fiscal and Mon
etary Policies, Capital Formation, and Economic Activity.”

F E D E R A L R E S E R V E B A N K O F ST. L O U IS

Interest-Responsive Saving

JU N E/JU LY

1980

likely that this effect is quantitatively small.24

There is one modification of the models that permits
a negative short-run response to fiscal policy — mak
ing saving a positive function of the interest rate
(and consumption a negative function of the interest
rate). This modification would not alter the quali
tative results of Model 1, although it would, of course,
increase Hicksian crowding out and reduce fiscal mul
tipliers. In Models 3 and 4, however, it results in a
theoretically ambiguous sign on the fiscal multiplier.
The explanation of the effect of this modification will
be most easily understood with respect to Model 4.
In that model, the key to the unambiguous result is
the positive relation between income and saving: The
wealth effect in the demand for money is activated
by an increase in wealth which in turn requires an
increase in income. If saving depends on the interest
rate as well as income, however, saving can increase
even if income falls. Saving has generally been con
sidered unresponsive to interest rates, but recent work
by Boskin has revived the belief that saving may be
significantly interest-responsive, although it remains

Increased sales of government securities necessary
to finance increased government expenditures can be
purchased either from the increased saving that is
generated by the fiscal action or by the crowding out
of private security purchases. In order to fully model
the response to fiscal policy, it is essential to capture
the relationships among the deficit, saving, invest
ment, government, and private debt. This paper has
developed two alternative ways of analyzing these re
lationships, both of which utilize end-of-period speci
fications of asset market equilibrium. The first ap
proach includes both government and private sector
financing constraints in the model; the second ap
proach relates changes in wealth to saving behavior in
the model. Both approaches yield positive impacts of
increased government expenditures on aggregate de
mand and income as the first-period fiscal effect. At
least in the short-run, fiscal policy actions matter
because complete crowding out does not occur.

24See, for example, Michael J. Boskin, “Taxation, Saving and

the Rate of Interest,” Journal of Political Economy (April
1 9 7 8 ), pp. S3-S27.

CONCLUSION