Full text of Economic Review (Federal Reserve Bank of San Francisco) : Summer 1981 : Monetary Policy and Interest Rates

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M onetary Policy and
Interest Rates

I.

Introduction and Summary

5

7

II. Why Have Interest Rates Been So Volatile?
Paul Evans
. The 1979 change in monetary policy produced only about 30 percent of the
increased volatility in long-term interest rates, and the rest came from sources
not directly under Federal Reserve control.

III.

Liability Management, Bank Loans and
Deposit “Market” Disequilibrium
John P. Judd and John L. Scadding

21

. . . Large swings in bank loans, induced primarily by the Special Credit Restraint
Program, were the major source of money’s variability in 1980.

IV.

45

The Response of Real Output and Inflation
to Monetary Policy
Rose McElhattan
. . . Both inflation and real GNP respond quickly to a change in monetary policy,
with the major effects occurring within two years of the initial change.

Editorial committee for this issue:
Hang-Sheng Cheng, Brian Motley, and Kenneth Bernauer

October 6, 1979 may represent one of the
key dates in the nation's monetary history,
along with December 23, 1913 (the passage of
the Federal Reserve Act) and March 4, 1951
(the signing of the "Accord" which removed
Treasury domination of central-bank policy).
On that October day, the Federal Reserve
began to improve its monetary control by
changing its operating techniques - that is, by
controlling the quantity of bank reserves
rather than by tightly pegging the cost of those
reserves (the Federal-funds rate). The Fed
subsequently has been broadly successful in
meeting its monetary-control objectives, but
its operational shift also has been accompanied
by increased volatility in both interest rates
and the monetary aggregates. This issue of the
Economic Review examines these several
aspects of post-1979 monetary policy, and also
analyzes the response of major economic
variables to policy changes.
Paul Evans investigates how much of the
recent increase in interest-rate volatility stemmed from the October 1979 change in monetary policy. He finds that this policy change
produced only about 30 percent of the
increased volatility in long-term interest rates,
and that the rest came from sources not
directly under Federal Reserve control.
"Almost all of this 30 percent resulted from
the Fed's adherence to its monetary targets; by
itself, the freeing of the funds rate had little to
do with the increased rate volatility."
Evans' findings thus indicate that the
Federal Reserve has been responsible for only
a small part of the increase in interest-rate
volatility. Citing a number of national and
international political events of the period, he
argues, "Clearly, none of these events was a
direct consequence of the monetary-policy
change. Furthermore, future years may see a

return to normalcy, with a sharp reduction in
interest-rate volatility."
Continuing, he argues that the Federal
Reserve's decision to move the Fed-funds rate
more in response to monetary surprises entails
more volatility of both long- and short-term
interest rates. "It probably also helps the
Federal Reserve to hit its targets for money
growth and hence for inflation. For this
reason, the increased volatility - and the
resultant reduction in capital formation and
redirection of capital towards shorter-lived
assets - may be the price that must be paid to
hit these targets."
Turning to the surprisingly high variability
of the monetary aggregates in the post-1979
environment, John Judd and John Scadding
have developed a monthly money-market
model which explains this phenomenon. The
model shows how certain types of financialmarket disturbances, such as sharp changes in
bank loans, can affect the money supply and
thus cause problems of monetary control. The
evidence indicates that large swings in bank
loans; induced primarily by the Special Credit
Restraint Program, were the major source of
money's variability in 1980.
Conventional money-market models reflect
the view that the monetary aggregates are
determined primarily by the public's demand
for money. The Judd-Scadding model reflects
an alternative view - that the monetary
aggregates are determined in the short-run primarily by the supply of money, which rises out
of the behavior of banks and the public in
credit markets On the markets for bank loans
and banks' liabilities like large certificates of
deposit}. As evidence, they note that banks'
demand for reserves responds to its financialmarket determinants with very short lags, consistent with the typical speed of adjustment in
5

level of real money balances reach their
respective long-run values, while real output
continues to adjust until it equals the level of
potential output and is growing at the rate of
potential output. Most other reduced-form
models focus only upon the adjustment of
rates of change in prices and output to a monetary disturbance. In contrast with these,
McElhattan's model provides results which are
consistent with the neutrality of money, which
is one of the most generally accepted properties regarding economic behavior. It holdg:that
changes in the money supply ultimatelyaff~.ct
only nominal variables, such as prices a~d
wages, leaving all real quantities, such as
goods and services, unchanged.
In McElhattan's model, both inflation and
real GNP respond quickly to a change in
monetary policy, with the major stimulative or
deflationary phase occurring within two years
of the initial change. Her findings thus conflict
with most of the published literature, which
suggests that output and prices require about
five years to respond to a change in money
growth.
McElhattan thus provides an alternative to
the viewpoint that it will take a long time to
bring down the inflation rate, and that we risk
an economic recession in the process.
"Changes in monetary growth, at least since
the mid-1960's, !lPparently have acted fairly
rapidly upon inflation - and hence upon
aggregate demand as well. Thus, since a monetary contraction is likely to bring inflation
down faster than previously anticipated, less of
the brunt of that contraction need be borne by
real GNP, so that a major decline or loss of real
income need not result when we adopt a policy
which gradually reduces monetary growth."

credit markets, but not with the typical sluggishness of money demand. Also, bank loans
had a potent influence on the monetary
aggregates in 1980, as their model predicts.
Finally, they note that the market for money is
often characterized by disequilibrium in the
short-run: money-supply shocks temporarily
push the public off its short-run moneydemand curve, which allows the money supply
to exert a large short-run influence on the
stock of money observed in the economy.
The Judd-Scadding results imply that policy
makers should pay close attention to financialmarket developments, especially when signs
appear of a shift in the conventional moneydemand function. They cite in particular the
second quarter of 1980, when conventional
models severely overpredicted the money
stock. "Evidence of a downward shift in the
money-demand relationship would imply that
the money supply should be allowed to fall
commensurately to avoid an overly expansionary monetary policy. On the other hand, our
model explains the decline in money as supply
shock, induced by the decline in bank loans
that followed from the Special Credit Control
Program of 1980. Such a conclusion implies
that monetary-control efforts should be
directed toward more rapid money-supply
growth to avoid an overly contractionary
policy. "
Next, Rose McElhattan presents a small
model of the U.S. economy for estimating the
response of inflation and real output to a
change in monetary policy. Measures obtained
from the model's reduced-form equations provide estimates of the complete adjustment
paths of inflation and real output to a monetary
disturbance. In her model, prices continue to
change until both the inflation rate and the

6

I
Paul Evans·
On October 6, 1979, the Federal Reserve
announced that henceforth it would tightly
control the money supply while letting the
Federal-funds rate respond freely to market
forces. The Federal Reserve hoped that this
policy change would help it to stabilize
employment and real income while bringing
inflation down to a tolerable level.
The Federal Reserve did indeed free the
Federal-funds rate - the rate clearly was
much more volatile after October 6, 1979
than it was before that date, as can be seen
from Panel a of Figure 1. That action,
however, has produced no clear victory against
inflation, and 1980 could hardly be considered
a year of great stability in the real economy.
Furthermore, both short-term and long-term
interest rates have become much more
volatile, as panels band c of Figure 1 demonstrate.
Volatile interest rates - especially volatile
long-term rates - may impose burdens on the
real economy. Savers may find their portfolios
riskier, and may therefore save less and shift
from long-term to short-term securities.!
Purchasers of houses, plant and equipment,
and other long-lived physical assets may then
be forced to finance their purchases with shortterm debt, thus making these purchases

riskier. If the additional risk reduces long-term
investment as well as saving, the economy will
experience less capital formation, and a
smaller portion of that capital formation will go
into long-lived assets. As a result, the economy's growth rate will slacken.
This paper investigates how much of the
recent increase in interest-rate volatility
stemmed from the change in monetary policy of
October 6, 1979. It finds that this policy
change produced only about 30 percent of the
increased volatility in long-term interest rates,
and that the rest came from sources not
directly under Federal Reserve control.
Almost all of this 30 percent resulted from the
Fed's adherence to its monetary targets; by
itself, the freeing of the funds rate had little to
do with the increased rate volatility.
Therefore, panel c of Figure 1 gives a misleading picture of the new monetary policy's
impact on rate volatility and hence on investment and growth. The actual effect was substantially smaller.
The next section of this paper formulates a
model of interest rates, and Sections II and III
discuss the estimates resulting from the fitting
of this model to weekly U.S. data. Next, Section IV decomposes the recent increase in
interest-rate volatility into several components, and discusses each of those components. Finally, Section V summarizes the
paper and draws some policy conclusions.

• Assistant Professor, Stanford University, and Visiting
Scholar (Spring semester), Federal Reserve Bank of San
Francisco. Brian Dvorak provided research assistance on
this article.

7

Figure A
Federal Funds Rate
Percent

October 1979

20
18
16
14
12
10
8
6
4
0

1977

1978

1979

1980

I. Formulation of an Empirical Model
in response to new information, a savvy investor could use that information accurately to
predict future capital gains or losses. Being
able to make accurate predictions would be a
veritable license to print money, because the
investor could hold bonds when they were
going to rise in price and sell them short when
they were going to fall in price. For example, if
the investor knew that government deficits
raise interest rates gradually, he or she would
react to an unusually low deficit by buying
bonds and to an unusually high deficit by seiling them short. By the time the interest rate
actually changed, he or she would probably
have made a fortune.
The efficient-markets hypothesis essentially

To begin, we formulate a model based on
the hypothesis that the securities markets are
efficient. 2 Simply speaking, the efficientmarkets hypothesis claims that readily available information is so efficiently processed t4at
no market participant can do systematically
better than any other participant.
Samuelson (1965) and Sargent (1976) have
shown that, to a close approximation, interest
rates in an efficient market respond
immediately and completely to any new information reaching the bond markets. The reason
is that interest-rate changes generate capital
gains or losses, which dominate the shortperiod returns to all but the shortest-term
bonds. 3 If interest rates in fact changed slowly
8

used in the empirical analysis. Then, if bondmarket participants knew Z(-1), the value of Z
in the previous period, they would predict Z as
AZ(-1), where A is a matrix of coefficients
obtained by regression Z on Z(_1).4 Therefore,
E, the vector of new information about Z, is
simply the error vector in the equation

assumes that a large number of savvy investors
participate in the securities markets.
Therefore, when these investors think, on the
basis of new information, that interest rates
will rise and hence that bond prices will drop,
their efforts to sell their bonds immediately
will drive up interest rates. In principle, the
rise will be so rapid that no one can manage to
sell a single bond before interest rates rise as
far as they are going to rise.
The efficient-markets hypothesis implies
that DR, the interest-rate change, is given
approximately by
DR

=

K

+

BE

+

V,

Z

= AZ(-1) + E.

(2)

Note that E is serially uncorrelated, because
past values of E are known by assumption and
serial correlation would imply (contrary to
assumption) that past values of E are useful in
predicting current values of E. Similarly, V in
equation (1) should be serially uncorrelated
because it, too, is new information that should
not depend on such information as its own past
history.
Equations (1) and (2) suggest the following
strategy. First, collect some series that are
readily available (say, from government publications). Then estimate prediction equations,
like (2) , for these series and obtain the
residuals, which are consistent estimates of E.
Finally, regress changes in various interest
rates on these residuals to obtain consistent
estimates of K and B in equation (1). If the
efficient-markets hypothesis is correct, past
information should not change interest rates.
Therefore, this hypothesis is refuted if any lagged E's have statistical significance in equation
(1) or if V is serially correlated.

(1)

where K is a parameter, B is a vector of
parameters, E is a vector of new information
used in the empirical analysis, and V is an error
term that captures the effects of all other information and that moves independently of E.
The longer the term to maturity of the bond,
the better is the approximation.
By definition, new information is that part of
current information that was not known in the
past. In order to give content to this definition,
we must add an hypothesis about knowledge
- namely, that one part of currently available
information can be predicted from past information with the use of standard econometric
techniques, and the other part (to be called
"new information") cannot be so predicted.
Specifically, let Z be the vector of variables

II. Prediction Equations
Bond-market participants surely pay attention to a great many series of data - such as
real GNP, the inflation rate, the government
deficit, corporate credit demands, and monetary-policy variables. However, many of these
series cannot be used here, because they are
not available on a weekly basis. Moreover,
since this paper is mainly concerned with the
impact of monetary policy on interest rates, we
limit the analysis to appropriate monetary
series.
We assume that GM, the growth rate of the
(unadjusted) 5 money supply (M -1 B) , and

DFFR, the change in the Federal-funds rate,
adequately characterize monetary policy. To
extract the new information from these series,
one must estimate prediction equations that
relate them to past information known by
bond-market participants. Essentially, one
must estimate an equation system of the form
(2) - first for the sample period extending
from the first full week of 1977 to the last full
week before October 6, 1979, and again for the
sample period extending from the first full
week after October 6, 1979, to the week ending on October 22, 1980. 6 Using the

9

+ 3.05 DR12MO( -2)

methodology advocated by Box and Jenkins
(1976),7 we obtained the following results for
the sample period before October 6, 1979 (the
figures in parentheses are standard errors):

+

GM = GM(-52)

+

.006013, R

2

S.E.

=

.1361, R

2

=

where DR3MO is the weekly difference in the
three-month Treasury-bill rate, DR12MO is
the weekly difference in the twelve-month
Treasury-bill rate, and DRI0YR is the weekly
difference in the ten-year Treasury bond rate.
Even though equations (3) and (4) or equations (5) and (6) may not look like the equation system (2), it is easy to show that they
take that form. 8 This is because EM and EFFR
in equations (3) - (6) are unknown only until
GM and DFFR become known.
Equations (3) and (5) imply that only three
kinds of effects are relevant in determining the
money-supply growth rate in any given week.
First, if all other effects are zero, GM equals
GM(-52), the value that it assumed in the
same week of the previous year 9• Thus, GM
tends to keep any weekly seasonal pattern it
has assumed. Second, the term EM combines
all of the influences on the money growth rate
that could not have been predicted in the previous week. Third, the terms in lagged values
of EM determine how GM will tend to move
the year after EM has assumed a non-zero
value.
To illustrate, suppose that EM rises by one
percentage point in the first week of January
some year, but is left unchanged in all other
weeks. Equation (3) implies that the money
growth rate is one percentage point higher in
the first week ofJanuary of that year, .673 percentage points lower in the second week of
January, .232 percentage points higher in the
first week of April, .156 percentage points
lower in the second week of April, and is
unchanged in all other weeks of the year. At
year's end the money supply is .403 (= I .673 + .232 - .156) percentage points higher
than at the end of the previous year. Consequently, the average annual money growth
rate rises by .403 percentage points. Moreover,

= .357;

+ EFFR
(4)

.042;

where EM is a residual from the regression for
the money growth rate, EFFR is a residual
from the regression for the Federal-funds rate,
and ( - i) attached to a symbol indicates that it
is lagged i weeks.
For the sample period after October 6,1979,
we obtained

GM

=

.000413 + EM
(.001201)
.290 EM( -1) + .587 EM( -13)
(.137)
(.175)
(-52)

+

- .170EM(-14)
(.110)

+

.493 EM(-26)
(.233)

- .143EM( -27),
(.122)
S.E. = .007767,R
DFFR = .074

+

2

=

+ EFFR,

2

(3)

DFFR = .0515 + 4.72EM(-l)
(.0114) 0.89)

(6)

S.E., = .7158, R = .478;

.232EM( -13)
(.085)

-.156EM( -14),
(.057)
=

- 2.07 DRI0YR( -2)
(0.67)

.00126 + EM
(.000203)

- .673 EM( -1)
(.063)

S.E.

(0.68)

(5)

.443;

37.2 EM( -2)

(.100) (13.8)

- 0.93 DR3MO( -2)
(0.35)
10

since money growth will follow this same
scenario in future years - note that GM
(- 52), the growth rate one year earlier,
appears in the right-hand member of equation
(3) - average money growth also rises by .403
percentage points in every future year.
A similar calculation using equation (5)
yields a money growth rate that is one percentage point higher in the first week of January,
.290 percentage points lower in the second
week of January, .587 percentage points higher
in the first week of
J 70
points lower in the second week of April, .493
percentage points higher in the first week of
July, and .143 percentage points lower in the
second week of July. The money growth rate
also follows this same pattern in every future
year; the average rate rises by 1.477 (= 1 .143) percen.290 + .587 - .170 + .493
tage points.
It is important to note that a monetary
surprise (EM;z!'O) permanently changes the
growth rate of the money supply and not just
its level. A positive surprise raises the growth
rate; a negative surprise lowers the growth
rate.
The results suggest that the Federal
Reserve, before October 6, 1979, would have
responded to a monetary surprise of one percentage point by raising the Federal-funds rate
only about 4.72 basis points. (See equation
(4).) No other variable was helpful in predicting changes in the funds rate. Surprises in the
funds rate were usually small: about two-thirds
of them were between -13.61 and + 13.61
basis points. This fact demonstrates that the
Federal Reserve more or less pegged the
Federal-funds rate and responded sluggishly to
monetary surprises.
The results also suggest a quite different
Federal Reserve response since October 6,
1979 (See equation (6).) In this period, the
Federal-funds rate responded to monetary
surprises with a two-week lag rather than a
one-week lag, and the response was much
larger. Furthermore, lagged interest rates
began to affect the funds rate.
The two-week lags in equation (6) have
special significance. For a number of years,

reserve requirements have been lagged two
weeks, rather than imposed contemporaneously. This institutional feature implies
that an increase in the money supply, and
hence deposits, generates an increase in
demand for reserves two weeks later. For this
reason, the Federal-funds rate will tend to rise
two weeks later unless the Federal Reserve
completely accommodates this increase in
demand. Therefore, because EM ( - 2) had no
statistically significant effect on the funds rate
Ocllobl;lr6, 1979, the Federal Reserve in
that period must have largely accommodated
changes in the demand for reserves. Since
then, however, the Federal Reserve has
apparently let the banks largely fend for themselves, for EM ( - 2) has a latge and statistically
significant coefficient in equation (6).
The two-week lag on the interest-rate terms
suggests that these rates affect the Federalfunds rate by operating first on the demand for
reserves. For example, a change in bond rates
might drive businesses to borrow more from
the banks, and this in turn would push up the
demand for reserves two weeks later. This
explanation, however, would lead to the conclusion that business-loan demand is roughly
independent of the level of interest rates
(-0.93 + 3.05 - 2.07 is roughly zero), but
rises when the term structure becomes more
humped (the twelve-month Treasury-bill rate
rises relative to the three-month Treasury-bill
rate and the ten-year Treasury-bond rate.)
Equations (4) and (6) provide one more
insight. Since October 6, 1979, the Federal
Reserve has evinced a much greater willingness to tolerate large movements in the
Federal-funds rate: the standard error rises
from .1361 percent a year in equation (4) to
.7158 percent a year in equation (6). The
"T~."t" .. movement in the funds
as well as
the Federal Reserve's apparent willingness to
let the banks bear some of the brunt of adjustment in the market for reserves, suggests only
one conclusion: the Federal Reserve tried
much harder to contol the money supply after
October 6, 1979 than it ever did before.
Nevertheless, the short-term variability of the
money supply has also risen (the standard
11

error of equation (5) is larger than that of
equation (3) ). Moreover, movements in the
money supply have become more persistent,

as we have seen in our analysis of equations
(3) and (5).

III. Interest-Rate Equations
ing on Saturdays. This complication, and two
others discussed below, imply that the
appropriate equation is:

The residuals EM and EFFR represent
"new information" about monetary policy. In
this section, we estimate how bond markets
have used this new information in setting
interest rates, and then test whether these
markets are efficient.
In Equation (1), DR referred to changes in
end-of-period (say, end-of-week) interest
rates. Our interest-rate data, however, are not
end-of-week data, but rather averages of daily
data for weeks beginning on Sundays and end-

DR

=

k

+

+

bEM(-1)
dEFFR( + 1)

+ cEM(-2)
+ eEFFR +

V,

where DR is the difference in the bond rate
averaged over weeks beginning on Sundays
and ending on Saturdays; k, b, c, d and e are
parameters; and V is an error term. In this

Figure B
Three-Month Treasury Bill Rate

16

(7)

Percent

October 1979

14

12

10
8

6

4

01..------......-----1..----..&....
. . . - ---.
...
1977
1978
1979
1980
12

equation, EM ( -1) , EM ( - 2) , EFFR( + 1)
and EFFR take the place of E, and the error
term V is serially correlated, unlike its counterpart in equation (1). To be specific, V
should be a first-order moving
average. 10 The Federal Reserve generally
releases M-IB data with an eight-or nine-day
lag. Moreover, these data are averages of daily
data for weeks ending on Wednesdays rather
than Saturdays. For this reason, the bond
markets know only EM ( - 2) during the first
few days of any week, and then learn
EM ( -1) . 11 Therefore, both EM (-1) and
EM ( - 2) belong in equation (7).
The Federal-funds rate data used to fit equations (4) and (6) are averaged over weeks ending on Wednesdays. Since bond-market participants probably keep track of the funds rate

on an hour-to-hour (or even minute-tominute) basis, they already know part ofEFFR
before the week begins on Sunday, and then
learn part ofEFFR( + 1) before the week ends
on Saturday. Therefore, including EFFR( + 1)
and EFFR in equation (7) is appropriate. 12
We used Treasury-bill and Treasury-bond
rate data, as well as the residuals from equations (3) - (6), to fit equation (7) for the sample periods before and after October 6, 1979.
According to the efficient-markets hypothesis,
including EM(-3), EM(-4), EFFR(-l),
EFFR( - 2), etc., in equation (7) - or specifying its error term to be a second (or higher)
order moving average - should add no
statistically significant explanatory power. We
have found this hypothesis to be true for the
long-term interest rates. The regressions for

Figure C
Twenty-Year Treasury Bond Rate
October 1979

11

10

9

8

-----.1...--------"1..--__......--'

0 .....

1977

1978

1979

13

1980

.....

some of the short-term interest rates,
however, improved somewhat when we
lengthened their lags or error-term structures. 13 Tables 3 and 4 report the best regressions. 14 Table 1 summarizes those results,
which have the following implications.
1. Unexpected monetary increases tend to
raise interest rates, and unexpected monetary
decreases tend to lower them - contrary to a
common belief among economists. In that
popular view, if the Federal Reserve increases
the money supply and nothing else happens,
the public will hold more money than it wants.
In the short run, incomes and goods prices will
not change very much; therefore, interest
rates must fall to make the public content to
hold the increased money supply. That
analysis is faulty, however, perhaps because it
assumes that the stock of money rises because
the Federal Reserve consciously chooses to
increase it. Suppose instead that the money
stock rises because of a rise in the quantity of
money demanded at prevaiting interest rates.

If the Federal Reserve does not entirely
accommodate the increased demand, interest
rates must rise to make the public content to
hold less money than desired at the initial
interest rates. Incidentally, if this analysis is
valid, monetary surprises are primarily due to
changes in money demand rather than in
money supply.
2. Since October 6,1979, the bond markets
have responded about ten times as much as
before to weekly money-supply data.
Specifically, a monetary surprise of one percentage point tended to raise interest rates
only 3-7 basis points before October 6, 1979,
but tended to raise them 31-86 basis points
after that date. Since interest rates respond to
monetary surprises as useful economic indicators, bond-market participants must believe
that monetary surprises tell them more now
about the future state of the economy than
they used to do. Apparently, the monetarypolicy change has increased the information
content in weekly money-supply data (or at

Table I
Cumulative Interest-Rate Effects
of Various Surprises*

Security

Three-month Treasury Bill
Six-month Treasury Bill
Twelve-month Treasury Bill
Three-year Treasury Bond
Five-year Treasury Bond
Seven-year Treasury Bond
Ten-year Treasury Bond
Twenty-year Treasury Bond

Effect of One-Percentage-Point Increase in
Money Supply
Federal Funds Rate
Before 10/6/79 After 10/6/79 Before 10/6/79 After 10/6/79

5.62
(2.94)
6.60+
(2.14)
6.98+
(1.94)
6.77+
(1.76)
5.99+
(1.46)
4.76+
(1.32)
4.02+
(1.24)
3.11 +
(1.02)

85.7+
(13.3)
83.0+
(11.5)
61.2+
(15.6)
54.0+
(10.5)
44.6+
(9.2)
38.4+
(8.4)
35.7+
(7.2)
31.2+
(6.4)

61.2+
(13.3)
57.6+
(9.9)
49.7+
(8.6)
34.4+
(7.8)
22.7+
(6.5)
19.1+
(5.8)
16.6+
(5.5)
13.5+
(4.5)

'The effects are measured in basis points. The figures in parentheses are standard errors.

+ Statistically significant at the .05 level.

14

35.0+
(22.8)
26.0+
(21.4)
29.2+
(10.7)
28.0+
(11.3)
18.6+
(10.0)
14.0+
(8.l)

14.0+
(7.8)
10.7+
(6.9)

surprises have affected short-term interest
rates much more than long-term rates.
Apparently, when nonborrowed reserves are
used as the operating instrument, as they are
today, changes in money demand exert their
greatest effects on the economy almost
immediately.
5. Surprises in the Federal-funds rate have
affected short-term interest rates much more
than they have long-term rates. For example,
before October 6, 1979, a surprise of one percentage point would have raised the threemonth Treasury-bill rate 61 basis points, while
raising the twenty-year bond rate by only 14
basis points. Presumably, surprises in the
funds rate tell the bond markets less about the
far future than about the near future.
6. Surprises in the Federal-funds rate have
affected interest rates less since October 6,
1979, than before. In particular, a surprise of
one percentage point raised interest rates by
14-61 basis points before October 6,1979, but
only by 11-35 basis points since then.
Apparently, letting the Federal-funds rate respond freely to market forces has reduced the
information content of rate surprises for predicting the future state of the economy. 15

least has made the market believe so).
3. Before October 6, 1979, monetary
surprises affected short-term interest rates
more than long-term interest rates, and
affected intermediate-term rates even more
than short-term rates. To explain this finding,
suppose that a security's term to maturity indicates the type of new information to which its
interest rate is most sensitive. For instance,
the three-menth Treasury-bill rate is most
sensitive to new information about what the
economy will do in the next three months,
whereas the ten-year Treasury-bond rate is
sensitive to new information about what the
economy will do for the next ten years. It then
follows that, before October 6, 1979, monetary
surprises conveyed relatively more information about what the economy would do six
months to a year in the future (intermediateterm) than about what it would do for the next
six months (short-term) or after a year (longterm) . Apparently, during the period when the
Federal-funds rate was pegged, changes in
money demand (which produce monetary
surprises) took six months to a year to exert
their greatest effects on the economy.
4. After October 6, 1979, monetary

Table 2
Percentage Decomposition of Increase
in Volatility of Interest Rates
Source of Increased Volatility
Increased Coefficients on
Surprises in
Increased Variances of Surprises in
Security

Three-month Treasury Bill
Six-month Treasury Bill
Twelve-month Treasury Bill
Three-year Treasury Bill
Five-year Treasury Bond
Seven-year Treasury Bond
Ten-year Treasury Bond
Twenty-year Treasury Bond

Money Supply

Federal Funds Rate

Money Supply

Federal Funds Rate

Nonfinancial Factors

28.2
35.0
27.1
28.1
25.7
24.5
27.8
27.4

-1.9
-9.7
-18.2
-5.0
-3.2
-3.4
-2.2
-2.4

7.2
8.9
7.1
7.3
6.7
6.4
7.2
7.0

21.3
21.6
23.8
12.5
8.3
7.0
6.7
5.7

45.2
44.2
58.2
57.1
62.6
65.6
60.5
62.3

15

Table 3
Interest-Rate Regressions
for Period Before October 6, 1979

Security

EM(.1)

Three-month Treasury Bill

0.97
(2.12)

Six-month Treasury Bill

2.39
(1.54)

Twelve-month Treasury Bill

2.39
( 1.39)
2.63+
(1.26)

Three-year Treasury Bond
Five-year Treasury Bond
Seven-year Treasury Bond

2.57+
(1.04)
2.25+
(0.94)

Ten-year Treasury Bond

1.57
(0.89)

Twenty-year Treasury Bond

1.34
(0.73)

Coefficients
EM(-2) EFFR(+1)
.389+
4.65+
(.093)
(2.03)
.425+
4.21+
(.070)
0.48)
.392+
4.59+
(1.35)
(.060)
.286+
4.14+
(.055)
0.23)
.203+
3.42+
(1.02)
(.046)
.170+
2.51+
(.041)
(0.92)
2.45+
.136+
(.039)
(0.87)
1.77+
.116+
(0.71)
(.032)

Moving-Average
Coefficients*
of*
Lag 1
Lag 2' Constant·
EFFR
-.349+ .0402+
.223+
-.080
(.082) (.0075)
(.095)
(.082)
-.246+ .0381+
.151 + -.009
(.086)
(.086) (.0070)
(.070)
.105+
.0343+
.131
(.061)
(.086)
(.0092)
.200+
.0242+
.058
(.085)
(.0089)
(.055)
.230+
.0196+
.024
(.085)
(.0076)
(.046)
.176+
.0168+
.021
(.0065)
(.041)
(.086)
.185+
.0148+
.030
(.0062)
(.039)
(.086)
.254+
.0123+
.019
(.0054)
(.084)
(.032)

R2

S.E.

Q(12)"

.211

.1551

7.3

.254

.1103

9.6

.310

.0971

10.8

.275

.0883

5.5

.255

.0733

8.8

.217

.0661

8.5

.185

.0624

8.7

.203

.0514

8.5

*The standard error of each coefficient appears below it in parentheses.
**Q(2) is the Box-Pierce statistic, a measure of serial correlation. None of the entries in this column indicates significant
serial correlation at any conventional significance level.
+ Statistically significant at the .05 level.

Table 4
Interest-Rate Regressions
for Period After October 6, 1979
Moving-Average
Coefficients'

Coefficients of'

Sec...1ty

EM(-1) EM(-2) EM(-3)EFFRI+1) EFFR EFFR(-1)EFFRI·2)EFFR(.3)EFFRI·4) Lag1 Lag2

Three-month Treasury Bill

26.1+
0.8)

Six-month Treasury Bill

2S.1+
(6.S)

Twelve·month Treasury Bill 21.S+
0.0)
26.3+
Three·year Treasury Bond
0.4)
22.0+
Five-year Treasury Bond
(6.S)
20.2+
Seven-year Teasury Bond
(6.01
19.9+
Ten-year Treasury Bond
(S.I)
Twenty-year Treasury Bond I7.S+
(4.S)

36.6+
OS)

23.0+ ·.070
181
(7,8) (099) CI 10)
3S.F 22.2+ -.079
137
(6.8) (67) C08S) (096)
26.9+ 12.8+ .143 .149+
0.4) 0.2) (077) C07S)
27.F
132 .148
(080) (080)
0.4)
22.6+
.126 .060
(6.S)
C07l) C07l)
18.2+
.094 .046
(064) (064)
(S.9)
IS.8+
.087 .OS3
(S.I)
COS5) C05S)
13.7+
.042 .06S
(049) (049)
(4.S)

-.020 .224+ .226+
CliO) CI04) (094)
-.007
116 .199+
C09S) (089) (082)

Constant·

-.191+ .321+ .641 + .01S
(089) C13I) CI32) CI06)
.420+ .S64+ 009
-,106
C07S) CI39) CI40) C09l)
.170 .314+ .043
CI48) (.]SS) (073)
.046
.OSO
O.SS)

(OSS)

.198
US])
.174
CI52)
.098

.OSI
COS6)
.049
COSO)
.048
(040)
.OSO
C03S)

CIS4)

.092
CIS3)

R2 S.E.

0(12)**

.736 .3832

7.2

.763 .324S

12,3

.S60 .3603

4.6

.441

.38S4

7.3

.431

.3399

4.6

.393 .3090

3.6

.419 .2646

3.0

.395 .2364

3.S

'The standard error of each coefficient appears below it in parenthe6es.
"Q( 12) is the Box-Pierce statistic. a measure of serial correlation. None of the entries in this column indicates significant serial correlation at any conventional significance level.
+Statistically significant at the .OS level.

16

IV. Decomposition of the Increase in Rate Volatility
In this section, we attempt to explain why
interest rates have become much more volatile
since October 6, 1979, than they were previously.
Equation (7) implies that VR, the volatility 16
of the bond rate R, is
VR

=

(b 2 + c 2)VEM
+ (d 2 + e 2) VEFFR

2 has no economic content by itself. To give it
content, we have made four specific assumptions, as follows.
1. The nonmonetary component is independent of monetary policy. If the money supply
and the Federal-funds rate provide a sufficiently complete characterization of monetary
policy, and if equations (3)-(6) adequately describe that policy, this assumption follows
immediately.
2. Changes in monetary policy have little
effect on· the variance of monetary surprises.
This variance presumably reflects the weekly
variance of money demand or of bank-loan
demand, as Judd and Scadding argue
elsewhere in this issue of the Economic
Review. Monetary policy may well be able to
control the money supply closely over periods
as long as a quarter or two, but has little control on a weekly basis. In other words, a shift in
monetary policy can change the coefficients in
an equation like (3) or (5), but can have little
effect on the standard error.
3. The coefficients band c rose because the
equation generating the money supply
changed from (3) to (5), and because the
Federal Reserve raised the coefficient on EM
substantially (see equations (4) and (6».
These changes were part of the Fed's effort to
target the money supply. Since stricter targeting makes monetary surprises more informative, interest rates responded much more to
monetary surprises after October 6, 1979 than
before.
4. The coefficients d and e fell because of a
rise in the variance of surprises in the funds
rate. This increased variance reduced •the
information contained in monetary surprises,
thereby causing interest rates to respond less
to any given surprise.
Given these assumptions, the decomposition procedure (Table 2) suggests several
important implications. First, factors beyond
the Federal Reserve's direct control accounted
for most of the increased volatility of interest
rates. Nonfinancial factors accounted for about
45 percent of the increased volatility of short-

+ VV,

where VEM, VEFFR and VV are the variances
of surprises in money, the Federal-funds rate,
and the error term; and b, c, d and e are the
coefficients of EM (-1), EM (- 2),
EFFR( + 1) and EFFR. To a first approximation, differencing this equation then yields
DVR

=

(D(b 2 + c 2»VEM
+ (b 2 + c 2) DVEM
+ (D(d 2 + e 2»::::':V=E=F=ER=+ (d 2 + e 2)DVEFFR + DVV

(8)

where DVR, D(b 2 + c 2), DVEM, D(d 2 + e 2),
DVEFFR and DVV are the differences in VR,
b 2 + c 2, VEM, d 2 + e 2, VEFFR and VV between the two sample periods; and VEM, (b 2
+ c2), VEFFR and (d 2 + e 2) are the average
values ofVEM, b 2 + c 2, VEFFR and d 2 + e 2 in
the two sample periods.
One can decompose the increase in volatility
of each interest rate into five components due
to 1) larger coefficients on monetary surprises;
2) larger variance of monetary surprises; 3)
larger coefficients on the surprises in the
Federal-funds rate; 4) larger variance of
Funds-rate surprises; and 5) a more variable
error term. Since the first four terms are supposed to capture the effects of monetary
changes, the last term may be called the nonmonetary component.
We have used equation (8) and the empirical results reported in Tables 3 and 4 to calculate the fraction of the interest-rate volatility
attributable to each component. 17 The results
appear in Table 2. Since equation (8) approximates an identity, the decomposition in Table
17

variance of surprises in the Federal-funds rate
after October 6, 1979 would have reduced
interest-rate volatility, but significantly so only
for short-term rates. For example, preventing
the variance of surprises in the funds rate from
rising would have reduced the volatility of the
three-month Treasury-bill rate by 19.4 percent
(=21.3 - 1.9), but would have reduced the
volatility of the twenty-year Treasury-bond
rate by only 3.3 percent (=5.7 - 2.4).

term interest rates, and for up to 65 percent of
the volatility of intermediate-and long-term
rates. Factors causing monetary surprises contributed about 7 percent more, so that all
sources together accounted for 52-72 percent
of the increased volatility. Second, making the
Federal-funds rate more sensitive to monetary
surprises generally resulted in 25-30 percent of
the increased interest-rate volatility. Third,
any Federal Reserve attempt to reduce the

V. Summary and Conclusions
The efficient-markets hypothesis implies
that interest rates adjust immediately to new
information. Our empirical results support this
hypothesis for long-term interest rates, since
they suggest that bond markets quickly use
new information about the money supply and
the Federal-funds rate.
The Federal Reserve's October 6, 1979
change in monetary policy altered the way that
bond markets set interest rates. Previously, a
monetary surprise of one percentage point
raised interest rates by 3-7 basis points, and a
surpris~ of one percentage point in the
Federal-funds rate raised rates by 14-61 basis
points. After October 1979, such surprises
would have raised interest rates by 31-86 and
11-35 basis points, respectively. Clearly,
monetary surprises have become rather important, while surprises in the Federal-funds rate
have become substantially less important.
Analysis of the decomposition of rate
volatility suggests that 52-72 percent of the
increased volatility resulted from factors not
under the Federal Reserve's direct control.
About 25-30 percent of the increased volatility
resulted from making the Federal-funds rate
respond to monetary surprises. The rest came
from freeing the Federal-funds rate to respond
to nonmonetary market forces; this source was
responsible for as much as 20 percent of the
increased volatility of short-term rates, but for
as little as 3 percent of the increased volatility
of long-term rates.
These findings suggest several public-policy
implications - primarily, that the Federal
Reserve has not been responsible for most of

the increase in interest-rate volatility. The
post-October 1979 period has seen many
unexpected events that could have changed
interest rates or shifted the demand for money.
For example, militant students seized hostages
in Iran, the Russians invaded Afghanistan,
decontrol of oil prices began, President Carter
authorized credit controls, the silver market
collapsed, and the U.S. underwent a radical
change in political direction. Clearly, none of
these events was a direct consequence of the
monetary-policy change. Furthermore, future
years may see a return to normalcy, with a
sharp reduction in interest-rate volatility.
Second, the Federal Reserve's decision to
move the Federal-funds rate more in response
to monetary surprises entails more volatility of
both long-and short-term interest rates. It probably also helps the Federal Reserve to hit its
targets for money growth and hence for inflation. For this reason, the increased volatility and the resultant reduction in capital formation and redirection of capital towards shorterlived assets - may be the price that must be
paid to hit these targets. The price has certainly
proven to be higher than many believed before
October 6, 1979. Whether this price has been
too high depends on how important it is to hit
monetary targets, and how much the increased
volatility reduces savings and changes the
composition of investment.
Finally, Federal Reserve intervention in the
market for reserves to eliminate surprises in
the Federal-funds rate would mean only a
slight reduction in the volatility of long-term
interest rates. If the Federal Reserve inter18

vened, however, it would simply replaceprivate agents as the speculator in that market.
This paper has established no presurnption
that the Fed is a better speculator than private
agents - and even if it were, it would not need
to intervene directly itself. A timely and credi-

ble public announcement of the Fed's superior
information would make the market as efficient as it could ever be - simply because efficient securities markets make optimal uSe of
an the information available to them.

FOOTNOTES
Then

1. For example, see Herman (1981).

Z = AZ(-1)

2. See Fama (1970) for a discussion of the efficientmarkets hypothesis and for a review of some empirical work supporting it.
3. Mishkin (1980) has shown that one-quarter holding-period yields of long-term bonds are indeed dominated by capital gains and losses.

where
A=

4. Clearly, I am assuming here that a linear predictor
is best.
5. I have used unadjusted data, because I believe
that the method by which the Federal Reserve obtains
its seasonally adjusted data does more harm than
good.
6. Henceforth, I shall refer to these sample periods
as "before October 6, 1979" and "after October 6,
1979."
7. This methodology entails examining the sample
autocorrelations and partial autocorrelations of these
series, identifying univariate processes for each
series, fitting these processes, subjecting each fitted
process to tests of model adequacy, crosscorrelating
the residuals of these processes, identifying the
bivariate process generating the two series, fitting
this bivariate process, and testing whether the fitted
process is adequate. See Box and Jenkins (1976)
and Granger and Newbold (1977) for a complete
description of this methodology.
8. For example, equations (3) and (4) take the form
(jgnoring the constant term)

9. This statement ignores the constant term and
assumes that a year has exactly 52 weeks.
10. To keep the analysis as simple as possible, I
assume that

where dril is the change in the bond rate from the end
of day i-1 of week t to the end of day i of week t (day 0
of week t is day 7 of week t - 1), and Vit is a serially
uncorrelated error term. This equation implies that
DR lt, the change in the bond rate from the end of day i
of week t - 1 to the end of day i of week t, is

7
i
DR It = IVjt-1 +IVjl
i+1 i+1
1
Averaging this equation then yields
(*) DR

z = H(L)e,
where z is a vector composed of GM -GM(-52) and
DFFR; e is a vector composed of EM and EFFR:and
H(L) is a 2x2 matrix in polynomials in the lag operator
L, which is defined such that LiZ = ZH). Since H(L) is
invertible,
W

+ E,

J1
J2
J3
100
0
I
0
o 0
I

= U(j-1) Vil-1

+

~(8-j)vj/7

Therefore, DR and DR (-1) have the nonzero
covariance
(**) [}(8-iHi-1 )Var VIt-]/49

1 (L)z=e.

and DR and DR(-j), i> 1, have a zero covariance, it
follows that DR is the first-order moving average. Note
that DR has the representation

Suppose that
.
W 1 (L) = I-J 1L - J 2L 2 Then z = J 1z(-1) + J 2 z(-) +
+ e.
Let Z be the vector obtained by stacking z, z(-1), ... ,
and let E be the vector with EM in the first entry, EFFR
in the second entry, and zeros in the remaining
entries.

DR = U

+ g U(-1),

where U is a serially uncorrelated error term and g is
a parameter. The parameter g and the variance of U

19

Similarly, the probability limit of the least-squares
estimator b2 of the coefficient on X2 is
plim (b 2 = (1-0:) 13
Hence
plim (b 1 + b2 ) = 13

are chosen so that DR has the samevarianceas(·)
implies and DR and DR(-1) have the covariance (••).
11. It is hard to be more specific about when EM(~1)
affects the bond markets, because M~1 B data may
leak out before its official release date. I assUme,
however, that leakage occurs after the beginning of
the week.
12. The sum of the coefficients on EFFR(+1) and
EFFR consistently estimates the coefficient that one
would obtain using Federal-funds rate data averaged
over weeks ending on Saturdays. First, let Xl be
EFFR(+1), X2 be EFFR, Y be DR, and X be the EFFR
that would be used if the right data were available.
Next, let Zl and Z2 be the parts of X that Xl and X2
give to the bond markets, and let E1 and E2 be defined
by

13. Strictly speaking, the efficient-markets
hypothesis only rules out long lag structures in the
equations for long-term interest rates. I therefore
conclude that the data support the efficient-markets
hypothesis.
14. If the error term V is a first-order moving average,
it takes the form
V = U + g U(-1),
where U is a seriaily uncorrelated error term and g is
a parameter. If V is a second-order moving avarage,
V= U + gU(-1) + hU(-2),

Xl =Zl +E 1
X2 =Z2+ E2
X =Zl +Z2
By construction, Zl' Z2' E1 and E2 are mutually
orthogonal and Xl' X2 and X have the same variance.
Then, let be 0: the fraction of the variance of X contributed by Zl and 1-0: be the fraction contributed by
Z2' Finally, let
Y = 13K + V,
where V is orthogonal to Z l' Z2' E1 and E2' Then
Y =f3(X 1 +X 2 ) +V -f3(E 1 + E2 ).
Since Xl and X2 are orthogonal, the least-squares
estimator b1 of the coefficient on Xl is

where h is a parameter. The columns labeled Lag 1
and Lag 2 provide the estimates of g and h.
15. Since October 6, 1979, the Federal-funds rate
has conveyed more information about supply and
demand in the market for reserves, even though it has
conveyed less information about the aggregate economy.
16. I define the volatility of an interest rate to be the
variance of its weekly differences.
17. Some of the equations reported in Tables 1 and 2
have longer lag structures than equation (8) recognizes. For these equations, I have modified equation
(8) appropriately.

IX 1Y/IX¥.
Its probability limit is therefore
plim (IX 1 l/3(X 1 + X2 ) + V - f3(E 1 + E2 ))/IX¥)
=13 + 13 plim (IX 1 X2 /IX¥)
+plim (IX 1V/IX 12) -f3plim (IX1(E1E2)/IX12)
=13 - 13 plim (I (Zl + E~)(El + E2 )/IX 1 )
= (1-plim (IE 12/IE 1 IIX 1 2 ))f3
=(1-var E1lvar X1 )f3
=0:13

REFERENCES
Box, G.E.P. and G.M. Jenkins. Time Series Analysis:
Forecasting and Control. San Francisco:
Holden-Day, 1976.

Mishkin, F.S. "Monetary Policy and Long-Term
Interest Rates: An Efficient Markets Approach,"
NBER Working Paper 517 (July 1980).

Fama, E.F. "Efficient Capital Markets: A Review of
Theory and Empirical Work," Journal of Finance
25 (1970),383-417.

Samuelson, P.A. "Proof That Properly Anticipated
Prices Fluctuate Randomly," Management
Review 6 (Spring 1965), 65-81.

Granger, C.W.J. and P. Newbold. Forecasting Economic Time Series. New York: Academic, 1977.

Sargent. T.J. "A Classical Macroeconometric Model
for the United States," Journal of Political Economy 84 (April 1976), 207-237.

Herman, T. "Volatile Interest Rates Dry Up Bond Trading," Wall Street Journal (Feburary 10, 1981),
25.

20

John P. Judd and John L. Scadding*
High rates of inflation during the past
decade have increasingly focused the attention
of policy makers and the general public on the
importance of bringing the monetary aggregates under control. The Federal Reserve
System now has an official goal of slowly
reducing growth rates in the monetary aggregates over the next few years in order to lower
rates of inflation gradually. Since October
1979, the Fed has attempted to improve
monetary control by focusing its short-run
operations on achieving targets for bank
reserves, and by letting the Federal-funds rate
vary more widely than previously had been the
1
case.
Despite these procedural changes, the
monetary aggregates gyrated widely in 1980,
and were significantly above or below the
Fed's longer-run targets at various times during the year. This paper discusses a monthly
money-market model which provides an
explanation for the surprisingly high variability
of money in 1980. The model shows how certain types of financial-market disturbances,
such as sharp changes in bank loans, can affect
the money supply and thus cause problems of
monetary control. The evidence indicates that
large swings in bank loans, induced primarily
by the Special Credit Control Program, were
the major source of money's variability in
1980.
This explanation has no role in conventional
models, which view the supply of deposits as
being determined by the public's demand,

given short-term rates of interest, income and
prices. 2 With a conventional model, unexpected movements in the monetary aggregates
often reflect changes in the past relationship
between the public's demand for money and
its determinants - that is, reflect a "shift" in
the demand function for money. There is little
doubt, in retrospect, that such a downward
shift occurred in 1975-76, when historically
high interest rates induced the public to
3
economize on money balances. In far greater
doubt, however, are assumed subsequent
"shifts" of shorter duration, such as the one in
the second quarter of 1980. The present paper
argues that the rapid monetary deceleration in
the second quarter of 1980 (as well as the rapid
growth in the first and third quarters) was
caused, not by a money-demand shift, but by a
money-supply "shock" induced by changes in
bank loans. This is a crucial distinction for
policymakers. A downward shift in the
demand for money makes a given money supply more expansionary. Thus the appropriate
policy is to lower the money supply. On the
other hand, a downward money-supply
"shock" for a given demand for money makes
policy more contractionary. Thus the appropriate policy response is to offset the money-supply "shock" through faster growth in bank
reserves.
Whereas conventional models emphasize
the demand for money, the model in this paper
emphasizes the supply of money, with banks
playing an important role in determining that
supply. In particular, it explicitly incorporates
bank loans and banks' management of nondeposit liabilities into the determination of
4
transaction deposits. In this approach, banks
maximize profits by satisfying the public's

'The authors are Senior Economists, Federal Reserve
Bank of San Francisco. Lloyd Dixon and Steven Kamin
provided research assistance for this article.

21

demand for loans with funds raised with the
least costly mix of managed liabilities (such as
large certificates of deposit and repurchase
agreements). The outcome of this process is
an aggregate "supply" of transaction deposits,
which varies inversely with the Federal-funds
rate and directly with the commercial-paper
rate and with bank loans.
The model treats money as a buffer stock in
the public's portfolio. Loan-induced increases
in the money supply thus exert an especially
powerful impact on the monetary aggregates in
the model. When the public demands additional bank loans, it temporarily absorbs the
deposits that are created in the process without
significant interest-rate changes in the shortrun: Le., money-supply shocks induced by
bank-loan movements can put the market for
money into temporary disequilibrium. This
means that changes in bank loans have a large
short-run effect on the public's money holdings and a relatively small effect on interest
rates.
The model therefore provides a theoretical
rationale to explain why changes in the supply
of money can dominate short-run movements
in the monetary aggregates. The empirical sec-

tion provides three pieces of evidence consistent with this hypothesis. They involve the
speed with which banks adjust reserves when
interest rates change, with the contribution
that bank-loan changes make to explaining
movements in money, and with the extent to
which money-supply shocks temporarily shift
the public's demand curve for money.
Section I of the paper describes the theoretical model. Here we show how the model determines the stock of transaction deposits, total
reserves, and the Federal-funds and commercial-paper rates. Section II reports the results
of estimating the model on lunar-monthly data
(four-week blocks) for the sample period July
1976 to September 1979. This section also
considers the results of simulating the model
both over the sample period and out of sample
over the post-October 1979 period - the
period marked by the Federal Reserve's adoption of a new reserve-operating procedure.
Section III uses the simulation results to assess
the cause of the volatility in the monetary
aggregates in 1980. Section IV summarizes the
conclusions and the policy implications of the
model.

I. Theoretical Model
below, demands for and supplies of these
instruments - expressed as functions of own
and substitute yields as well as the sizes of the
banks' and public's portfolios - are sufficient
to determine the banking system's mix of
liabilities between deposits and nondeposits.
The level of deposits implied by this mix constitutes the banking system's "supply" of
transaction deposits. Note that in Stage I, the
"supply" of deposits is defined as a function of
the Federal-funds rate, and therefore abstracts
of conditions in the market for reserves.
Stage 2 introduces the Federal Reserve by
adding to the analysis the market for bank
reserves. The banking system's desired mix
between nondeposit liabilities and deposits
determined in Stage I, together with the
reserve-requirement ratios on these categories
of bank liabilities, define the banking system's

The model is designed to analyze the
behavior of the commercial banks, nonbank
public and Federal Reserve in the markets for
transaction deposits and bank reserves. Thus
the primary variables determined by the model
include the stock of transaction deposits and
the commercial-paper rate in the deposit
market, and the stock of reserves and the
Federal-funds rate in the reserves market. The
underlying characteristics of the model are described in three distinct stages, which are summarized in Table 1. Each stage includes the
preceding stage(s), so that by stage 3, the
model is complete. A formal specification of
the model is presented in Appendix A.
Stage 1 analyses the markets in which commercial banks sell nondeposit liabilities (such
as large certificates of deposit and repurchase
agreements) to the nonbank public. As shown

22

Stage 1: Nondeposit Liabilities
The analysis begins with the description of
the portfolio behavior of an individual bank
(Figure 1). A minimum of seven categories of
bank assets and liabilities is necessary to
preserve the model's usefulness as a foundation for empirical research. These categories
are total reserves, R; bank loans, BL; private
transaction deposits (including demand, ATS
and NOW accounts), DB; other deposits (primarily small time and savings), TB; managed
liabilities less security holdings, 1MB; 5
member-bank borrowing, RB; and net Federal
funds purchased and repurchase agreements,
FF IRP. The last three items together constitute what we call nondeposit liabilities.
The short-run problem of a representative
bank involves financing a given stock of loans.
Banks consider loans to be exogenous on a
monthly basis, because the short-run demand
is relatively interest inelastic - and because
banks often respond sluggishly in altering their
loan rates when their marginal costs of funds
change, waiting for signs that such cost
changes are not transitory.
Part of the bank's loan portfolio is financed
by transaction and other deposits, which it

demand for total reserves. The supply of
reserves comes from 1) the amount of borrowing from the Federal Reserve, and 2) the
amount of nonborrowed reserves supplied by
the Fed. The addition of the supply of reserves
allows the reserves market to clear at
equilibrium values of the funds rate and total
reserves. In Stage 2, both the reserves and
nondeposit-liabilities markets clear. Hence the
supply of deposits at this stage is consistent not
only with the banks' preference among
liabilities, but also with the banks' and the
Fed's desired level and composition of
reserves.
Stage 3 introduces the public's demand for
transaction deposits. The interaction of this
demand with the supply of deposits determined in Stage 2 completes the solution of the
model. Here it is not strictly accurate to speak
of market equilibrium because the market for
deposits allows for short-run disequilibrium.
Nevertheless, since the model defines the
source and size of that disequilibrium, the deposit market can determine the stock of deposits and the commercial-paper rate. The
remainder of this section describes each stage
in more detail.

Table 1
Stages of the Model
Markets
Stage I

Stage 2

Banks' nondeposit
liabilities

Bank reserves

Behavioral
Relations

Variables or Relations
Solved For

1. Banks' supplies of

a. Supply of
deposits-1

nondeposit liabilities
2. Public's demand for
nondeposit liabilities

b. Banks demand
for total reserves
c. CD Rate

1. Banks' demand

a. Supply of

for total reserves
2. Federal Reserve's
supply of reserves
Stage 3

Transaction
deposits

1. Supply of
deposits-2
2. Public's demand
for deposits

23

deposits-2
b. Funds Rate
c. Total Reserves

a. Stock of
deposits
b. Commercial
paper rate

Variables
Affecting Solution

i) Funds rate
ii) Commercial
paper rate
iii) Discount rate
iv) Bank loans
i) Nonborrowed reserves
target
iii Commercial
paper rate
iii) Discount rate
iv) Bank loans
i) Nonborrowed
reserves target
ii) Discount rate
iii) Bank loans
iv) Personal income

regards as exogenous in the short run. The
bank adjusts implicit deposit rates sluggishly
- as it does the loan rate - viewing the quantity of deposits in the short run as being essentially determined by the public's demand.
Banks must finance the excess of loans over
deposits by selling nondeposit liabilities to the
public. The individual bank's short-run
portfolio choice involves choosing the structure of nondeposit liabilities - among 1MB,
FFIRP and RB.
The bank's portfolio choices are the outcomes of maximizing expected profits subject
to the balance-sheet constraint. In the very
short run, only 1MB, FF IRP and RB can be
adjusted. The factors influencing expected
profits include, among other things, the
explicit interest costs of each of three liability
items - the rate on longer-term managed
liabilities (such as CDs), denoted by io; the discount rate, iB; and the Fed-funds rate, iF. As
well, expected profits depend on the risk and
liquidity characteristics of assets and liabilities,
so that the marginal returns or costs of each
portfolio item include a marginal non-interest
element in addition to the explicit interest
cost. 6 For example, banks' borrowings from
the Federal Reserve depend not only on the
discount rate, but also on banks' traditional
"reluctance to borrow" from the Fed. Given
these variables - as well as the (exogenous)
size of the portfolio to be financed, (BL + R DB - TB) - individual banks sell optimal
quantities ofIMB, FF/RP and RB to the noncommercial-bank sectors.
The quantities of these instruments actually
observed depend on the interaction of the
banks' supplies of various types of nondeposit
liabilities with the nonbank public's demands
for them. The latter depends upon relative

yields and other characteristics (e.g., risk) of
the bank and nonbank assets in the public's
portfolio, together with the overall size of that
portfolio. 7
The interaction between the banks and the
nonbank public in the markets for banks' nondeposit liabilities is critical to the model,
because equilibrium in these markets determines the "supply" of deposits created by the
banking system. Equilibrium is depicted in
Figure 2 by the curve EQ. This curve represents all combinations of the funds rate and
bank nondeposit liabilities (IMB + FF/RP)
which are consistent with equilibrium between
the banks' supplies of and the public's
demands for 1MB and FF/RP (for expositional
purposes we assume that RB = 0).
Movements along EQ are determined in the
following manner. Assume that the funds rate
rises. Since banks consider FF/RP a substitute
for 1MB as a source of funds, they will respond
8
by raising their offer rates on IMB. Since rates
on both 1MB and FF/RP have risen, the public's demand for the total of those instruments
would also have risen, with the net inflow of
funds having been drawn from nonbank
instruments (such as commercial paper),
whose rates had not increased. Thus an
increase in the funds rate induces an increase
in io, which results on balance in a rise in
banks' total nondeposit funds.
The increased purchases of 1MB + FFIRP
extinguish demand deposits as the public
draws down its checking accounts to pay for
them. This process ensures that the banks' balance sheets will be in equilibrium. If banks
attract more nondeposit funds, their need for
deposits decreases, given the size of the loan
portfolio to be financed. The destruction of deposits that accompanies the inflow of noo-

Figure 1
Representative Bank Balance Sheet
Assets
Reserves:

Loans:

R
BL

Depos.its and Nondeposit Liabilities
Transaction deposits

Other deposits
Managed liabilities less security holdings
Net Fed funds purchased plus repurchase agreements
Member bank borrowing

24

DB

IB
1MB
FF/RP

RB

the public's demand for bank nondeposit
liabilities as they shift funds into commercial
paper. Banks will respond by raising offer rates
on nondeposit liabilities, but this will be
insufficient to stem completely the exodus of
funds. As a result, banks will end up supplying
more transaction deposits, which they create
as they buy back managed liabilities from the
nonbank public.
A rise in SCALE also shifts DBs-l to the
right. A rise in bank loans, for example,
increases the size of the portfolio banks must
finance, with a consequent increase in SCALE.
For given iF and io, the amount of nondeposit
liabilities is fixed by the public's demand for
these liabilities. Consequently, the supply of
bank deposits must increase by the increase in
loans if rates are not to change. These deposits
constitute the proceeds of loans, which are
spent by the initial borrower and flow into the
accounts of his suppliers, employees and the
like.
Stage 2: Reserves
The deposit-supply function of Stage 1 was
defined as a function of the funds rate. In Stage
2, we add the reserves market; this determines
the funds rate along with a more comprehensive definition of the supply of deposits,
s
denoted DB ·2, which includes the influence
of the Federal Reserve's conduct of monetary
policy.
The right-hand diagram of Figure 3 shows
DBs_l from Stage 1. In the left-hand diagram,
Rd plots the amounts of required reserves the
banking system would need to hold for each
point on DBs_I. This will depend upon the
required-reserve ratio for transaction deposits.
(For expositional purposes, only transaction
deposits are considered reservable.) The
higher the level of transaction deposits supplied, the larger are required reserves. Hence
lower funds rates, which are consistent with a
larger quantity of deposits supplied, are in turn
associated with a greater need or "demand"
for reserves. The graph of all such combinations of funds rates and required reserves
therefore can be thought of as defining the
banking system's demand function for
reserves, depicted in Figure 3 as Rd.

Figure 2
Equilibrium in the Markets for
Banks' Nondeposit Liabilities

IMB+FF/RP

deposits ensures that the new mix of liabilities
is consistent with the banking system's
portfolio needs. Thus the combination of EQ
- which describes the nondeposit funds sup·
plied by the public for each level of the funds
rate - and the bank's portfolio constraint
implicitly defines the stock of deposits which is
consistent with both the banks' and public's
preferences for nondeposits.
The combinations of iF and DB that satisfy
both EQ and the bank's portfolio constraint
constitute the Stage 1 supply of deposits (DB
1). A higher funds rate leads to fewer deposits
being supplied. This occurs because the inflow
of nondeposit funds to banks resulting from
the funds-rate increase causes banks to
extinguish deposits as their need for them des
clines. DB . 1 is also a function of the nonfinancial commercial-paper rate (representing
the rate on the public's nonbank instruments)
and the banking system's portfolio scale variable, BL + R - TB (referred to as SCALE
below).
DBs-l is positively related to the nonfinancial commercial-paper rate, which means that
its curve shifts to the right when icprises. The
public regards commercial paper as a
substitute for bank liabilities like RPs and large
CDs. Hence a rise in the paper rate will reduce
S

_

25

The description of the factors determining
the total amount of reserves available - the
supply of reserves - is conditional on the
Federal Reserve's choice of operating. procedure. We assume the current procedure,
whereby the Federal Reserve determines a
target for nonborrowed reserves; in Figure 3
one such target is illustrated by the vertical line
RU*.
Total reserves available can be larger than
RU*. Banks may borrow reserves from the
Federal Reserve on a temporary basis, instead
of borrowing in the Federal-funds market.
Consequently, a higher funds rate leads banks
to switch from the Fed-funds market to the
Federal Reserve's discount window, adding to

the aggregate stock of reserves in the system.
The amount borrowed will also depend on the
discount rate (iJ, the rate charged by the Fed
for such borrowing. At funds rates below the
discount rate, banks have little incentive to
borrow, so that total reserves are roughly equal
to nonborrowed reserves (this accounts for the
vertical portion ofRsbelow the "kink" at iF =
iJ. But as the funds rate rises- above the discount rate, banks respond to a profit incentive
and expand their borrowing from the Fed.
However, the amount of this borrowing is
limited by the banks' reluctance to borrow,
which effectively determines the slope of RSat
funds rates above the kink. Since the reluctance to borrow tends to rise as the level of

Figure 3
Derivation of Stage 2 Deposit Supply

R

I
I

- II -

DB

26

induces a lower equilibrium quantity ofIMB +
FF IRP, and thus a larger supply of deposits.
An increase in bank loans also has a positive
s
effect on DB _2. When bank loans rise, banks'
managed liabilities and deposits rise at
unchanged interest rates: i.e., both R d and
s
DB _2 shift to the right. The increased demand
for reserves causes the funds rate to rise, as
banks are "forced" to the discount window for
a larger quantity of reserves when nonborrowed reserves are held constant. The higher
funds rate eliminates part of the increase in
banks' reserves demand and deposit supply,
but on balance both quantities rise.
Note that the influence of bank loans on deposit supply depends heavily on the behavior
of the Federal Reserve. If, for example, the
Fed held the funds rate constant in the face of
an increase in bank loans, the partial offset of
s
the increase in DB _2 could not occur. As a
consequence, the impact of a bank-loan
increase would be larger than in the case where
the Fed held nonborrowed reserves constant
and allowed the funds rate to rise. By an
analogous argument, the Fed could reduce
nonborrowed reserves to such an extent that a
change in bank loans would have no influence
on the quantity of deposits supplied.
Stage 3: Transaction Deposits
Only in the last stage is the public's demand
for transaction deposits introduced. This
demand is used in conjunction with the Stage 2
deposit supply to solve for the commercialpaper rate and the stock of transaction deposits. The model allows for the possibility of
market disequilibrium by distinguishing two
concepts of deposit demand. The first - shortrun equilibrium demand - is the conventional relationship in which deposit demand is
a function of short-term interest rates, income
and lagged deposits. We include lagged deposits in this function to allow for incomplete
adjustment of the public's demand in the
short-run to changes in interest rates and
income.
Conventional practice treats this short-run
equilibrium demand as equal to the actual
stock of deposits: Le., it views the public as
always being on its demand function. The pre-

borrowing rises, R S becomes more steeply
sloped at higher funds rates. 9 In Figure 3, discount-window borrowing as a function of the
funds rate is added to the nonborrowedreserves target to obtain total reserves available, or what we call reserves supply, R s.
The interaction of reserves supply, reserves
demand and DBs_l determine market-clearing
levels for the funds rate, total reserves and the
S
Stage 2 supply of deposits (DB -2). As noted
earlier, DBs-l is defined for different funds
s
rates, whereas DB _2 is co-determined with the
funds rate for any given level of the Federal
Reserve's monetary-control instrument. Point
A in the upper two graphs of Figure 3 illustrates the determination of DB at stage 2 for
the case in which the Fed uses nonborrowed
reserves as its instrument. 10
The movement from A to B shows the effect
on Stage 2 DB of an increase in the commercial-paper rate. As seen from the discussion of
Stage l, a rise in the commercial-paper rate
shifts DBs-l to the right. This shift, shown in
the NE diagram of Figure 3, is associated with
an increase in the demand for reserves in the
NW diagram. The increased demand for
reserves puts upward pressure on the funds
rate. Hence the increase in icp causes both
iF and DB to rise from A to B. Levels of Stage 2
deposits are plotted against the commercialpaper rate in the SE diagram, and denoted by
s
DB -2.
An increase in the Federal Reserve's nonborrowed-reserves operating instrument
s
causes DB -2 to rise. For example, a larger
stock of nonborrowed reserves puts downward
pressure on the funds rate. As a result, borrowed reserves fall, offsetting part of the
increase in RU. In addition, the lower funds
rate induces banks to cut the rates they pay on
other nondeposit liabilities, so that the public
reduces its holdings of these instruments, causing banks to create more deposits.
The net effect in the reserves market is a
movement down along the R d curve, with a
lower funds rate and a higher level of total
reserves. In the deposit market, the Stage 2
supply curve shifts to the right. For any given
commercial-paper rate, a lower funds rate

27

sent model, however, allows for temporary
disequilibrium in the deposit market, in which
the commercial paper rate does not adjust to
make the actual stock equal to the short-run
equilibrium demand at each moment oftime. II
Actual deposits are therefore identified with
the second concept of short-run demand - the
disequilibrium demand for deposits. This
differs from its equilibrium counterpart to the
extent that market disturbances originating in
certain types of shifts in the Stage 2 money
supply temporarily force the public off the
equilibrium demand curve. This approach
makes an important distinction between the
demand for money and the demand for credit.
Changes in the quantity of bank loans, for
example, are assumed to be in accordance with
equilibrium in the bank-loan market.
However, these loan changes have an important by-product: the creation or destruction of
deposits. Since changes in credit demand are
not necessarily associated with equal changes
in deposit demand, the public ends up temporarily holding deposits it does not want: Le.,
it only accepts the deposits because this is a
necessary part of accepting the credit it does
want.
The important question is whether the public remains in disequilibrium for a long enough
time to permit this effect to show up in
monthly observations. The persistence of disequilibrium will depend, in part, upon the size
of transaction costs involved in adjusting
money balances to desired levels, and will vary
among classes of depositors. Transaction costs
may be relatively small for large businesses,
who have at their disposal a number of highly
liquid financial instruments (e.g., repurchase
agreements) with which to adjust deposit holdings. In contrast, households and others could
face relatively large transaction costs. Inflows
of "unwanted" deposit balances do not lead
them to make immediate portfolio adjustments by the full amount necessary to restore
equilibrium.
Disequilibrium in the deposit market could
persist longer than it takes an individual depositor to adjust to desired balances. One depositor's equilibrium may be another deposi-

tor's disequilibrium. To the extent that depositors reduce their unwanted balances by
purchasing goods and services and securities
from other members of the public, the latter's
deposit balances may exceed desired levels.
This process of spending and respending persists until the unwanted deposits are "sold"
back to banks for nondeposit liabilities (reducing deposit supply) and/or income and prices
rise enough (raising deposit demand) to
restore equilibrium to the deposit market.
Finally, the actions" of the Federal Reserve
can significantly influence disequilibrium in
the deposit market. If the Fed moves RU so as
to peg the funds rate, for example, it would in
effect allow the full impact of bank-loan
changes on deposit supply to be felt in the deposit market. If, on the other hand, the Fed
hits its nonborrowed reserves targets and lets
the funds rate vary, the impact of bank loans
on deposit-market disequilibrium will be
muted. Furthermore, under such a reservescontrol procedure, the Fed could be an important source of disequilibrium itself. Assume,
for example, that the Fed exogenously
increased total reserves in excess of required
reserves. Banks might lend out these excess
reserves by purchasing Treasury securities

Figure 4
Effect of Deposit Supply "Shock"
on Observed Deposits

DB

28

cated by the equilibrium-demand function. At
s
d
point B, DB differs from DB by some fraction
s
It of the initial DB "shock". This disequilibrium reduces interest-rate variability in
response to deposit-supply disturbances such
as changes in bank loans. (The same may also
be true for changes in nonborrowed reserves
when they are a source of deposit-market disturbances.) Graphically, the process of the
move back to equilibrium can be thought of as
s
made up of 1) movements along DB as
interest rates adjust,. and 2) leftward shifts in
d
d
DB (shown by DB ) as income and prices
change until equilibrium is reached at D.
The theoretical model is completed with the
addition of descriptions' of the public's
demands for currency (C) and other deposits
(TB) as functions of income, the commercialpaper rate and other variables. These equations will be described in more detail in the
next section.

from the public. The Treasury-bill rate would
fall enough to induce the public to sell bills,
but the associated increase in deposits (i.e.,
the proceeds of the bill sales) would not
necessarily be demanded in the equilibrium
sense in the short-run. The deposit market
would be in (temporary) disequilibrium to the
extent that this occurs.
The process by which bank loans influence
the deposit market is illustrated in Figure 4.
d
The curve DB denotes the short-run
equilibrium demand for deposits as a function
of the commercial-paper rate, icp , with
nominal income, Y, held constant. A decrease
in bank loans is illustrated by a leftward shift in
the deposit-supply function by the horizontal
s
distance, IlDB • This disturbance causes the
public to end up holding fewer deposits than
the equilibrium-demand curve would indicate.
d
In the short-run, icp and DB move from point
A to point B rather than to the point C indi-

II. Empirical Model
We summarize the empirical version of the
theoretical model in Table 2, and report the
corresponding estimation results in Table 3.
(Appendix B contains a glossary of variable
names.) The empirical version of the model
recapitulates, with modifications, the theoretical model, but it also includes additions to explain other components of MIB besides
demand deposits, and to account for the other
important uses of reserves besides those held
against demand deposits and nondeposit
funds. (A fuller accounting for the uses of
reserves, along with a more complete description of some of the modifications discussed
below, can be found in Appendix C). But more
importantly, the empirical model includes
modifications to the core equations dictated by
the fairly complex structure of reserve requirements in the real world.
Two of the equations from the theoretical
model carryover with minor changes. They
are the banks' aggregate demand for reserves
against demand deposits and nondeposit
funds, denoted RA and described in equation

(2.1), and the banks' demand for borrowed
reserves described in equation (2.3). Reserves
demand now includes the discount rate, iB,
which had previously been assumed to be constant, and the reserve ratio against nondeposit
liabilities, rio which had been assumed to be
zero. Equations (2.1), (2.3), the specification
of the Federal Reserve's supply of nonborrowed reserves (equation (2.11)) and the supply of deposits (2.12) together constitute the
empirical version of Stage 2 of the model,
which is used to solve for the funds rate, the
s
quantity of reserves, and DB - 2.
The empirical counterpart of Stage 3 is used
to solve for the commercial-paper rate and the
quantity of demand deposits. This version consists of the public's demand for demand deposits, equation (2.5), and the corresponding
S
supply of demand deposits (DB - 2). The latter relationship is where the empirical version
departs most significantly from the theoretical
model.
In the theoretical discussion, the derivation
of deposit supply in Stage 2 was trivial: the

29

Table 2
Empirical Model
Behavioral Relations
Description

Estimated
Equation
(see Table 3)

Banks, Thrifts and Public
-

+ ...

+

+

(2.1)

Banks' demand for
reserves

(2.2)

Banks' demand for
reserves (two week lag)

(2.3)

Borrowing from Federal
Reserve

RB

(2.4)

Multiplier

DB/RAt+v, = MULT(r D , r l , SCALE, (LTB/DB)t_l)

(2.5)

Public's demand for
demand deposits

DBd = DBd(li cp , IY, .6.BL)

(2.6)

Public's demand for
savings deposits

SB = SBO cp , Y, DUM(.), SB t_l )

(2.7)

Public's demand for
small time deposits

STB = STBO cp , Y, DUM(.), STBt_l)

(2.8)

Public's demand for
currency

(2.9)

Public's demand for
checkable deposits
at banks

OCDB = OCDB(OCDB t_l , OCDB t_2)

(2.10)

Public's demand for
other checkable
deposits at banks
and thrifts

OCD = OCD(OCD t_1 ' OCD t_2 , OCD t_3)

(3.1)

RA = RA OF' icp , iB , SCALE, r D , r l)

(3.2)
+

+

RBO F , iB , ARU, RB t_l )

=

-

-

+

+

(3.3)
?

-

(3.4)

+

(3.5)

+

+

(3.6)
+

0.7)

0.8)

Federal Reserve
Supply of Nonborrowed Reserves

RUO F*, Rd)

(2.11a)

Funds rate operating
procedure

RU

(2.11b)

Reserves operating
procedures

RU = RU'

(2.12)

Supply of demand
deposits

DB= MULT. RAt+v,= O!(r D + rl(LTBIDB»)RA1+v,

(2.13)

Total reserves

R = RA

(2.14)

M-IA

MIA = DB + C

(2.15)

M-IB

MIB = MIA + OCD

(2.16)

Excess reserves

RE=

(2.17)

Reserves against
thrift deposits

RTH =

RIB

(2.18)

Treasury deposits at
commercial banks

DBG =

DBG

=

Identities

+ r D DBG t_l12 + rT(SB t-il2 + STBt_il2 + OCDB t_I12 ) + RTH + RE

RE

30

0.9)

0.10)

the discount rate) did not. Since large CDs
(LTB) accounted for almost all of the reserve
requirements against nondeposit funds, we
used the lagged ratio of large CDs to demand
deposits to help predict the multiplier, as
shown in equation (2.4). We then multiplied
this prediction by RA t + 1/2 to obtain the deposit-supply function for Stage 2.
Estimation Results
All equations were estimated in seasonallyadjusted lunar-monthly observations (fourweek periods) from 1976:Lunar 8 (begins July
21, 1976) through 1979:Lunar 10 (ends October 3, 1979). The ending date coincided with
the Federal Reserve's adoption ofa monetarycontrol procedure which focuses primarily on
reserves in day-to-day operations. We chose
the beginning date to avoid entangling the
estimation of the model with the bias inherent
in the (mid-1974 to mid-1976) shift in money
demand. (Now that the model has been estimated over a fairly "clean" sample period, we
are working to extend the sample back to
1973.)
We aggregated seasonally-adjusted weekly
figures (where available) to give lunar-month
observations, or interpolated where only
calendar-month data were available. Both the
funds rate and commercial-paper rate are
endogenous in the model, so that we used twostage least squares wherever these rates
appeared as explanatory variables in a regression equation. Even though the funds rate was
a policy variable under the Fed's pre-October
1979 operating regime, it was not strictly
exogenous. The Fed adjusted the rate when
money deviated from target,13 and because
money is one of the endogenous variables in
the model, this practice effectively made the
funds rate endogenous as well. We corrected
for first-order serial correlation where the
autocorrelation coefficient was significant at
the 10-percent level.
The results of estimating the reservesmarket equations and the demand-deposit
multiplier are reported in Table 3 as equations
(3.0 to (3.4). Recall that reserves demand is
viewed as reflecting primarily the behavior of
deposit supply. The latter in turn is regarded as

reserves-demand function was simply multiplied by the inverse of the required-reserve
ratio against demand deposits. This approach
implicitly assumed that changes in deposits
were fully reflected contemporaneously in
reserves, and that only demand deposits were
reservable. In the real world, neither is true.
With lagged reserve accounting, changes in
deposits do not show uf in reserves demand
1
until two weeks later. Even with monthly
data, reserves of the current month only
partly reflect contemporaneous deposit
changes. The full effect of deposits shows up in
reserves centered two weeks later: i.e., in the
average of the last two weeks of this month
and the first two weeks of next month. Clearly,
if we want to predict deposits from reserves,
we must use this measure of reserves, i.e.,
reserves shifted forward half a month.
Hence, two estimates of reserves demand
are needed for the empirical model. The first,
RA or contemporaneous reserves, is used to
explain the funds rate, and is described by
equation (2.1). The second, RA t + l12 , or
reserves shifted forward half a month, is used
to predict the supply of deposits for Stage 2,
and is described by equation (2.2). To make a
uniform two-week lag from deposits to
reserves, we must respecify all of the data in
the model in lunar months of four weeks each.
Predicting the multiplier is also no longer
trivial. The complication arises not because
nondeposit funds are reservable, but because
the requirement is not uniform across all types
of such funds. Consequently, the average
reserve-requirement ratio is a function not
only of the split between demand deposits and
nondeposit funds, but also of the allocation of
the latter among reservable and nonreservable
categories. As a result, the arguments of RA,
which explain the split only, are not
necessarily suited to predicting the average
reserve-requirement ratio and hence its
inverse, the multiplier. Preliminary estimation
indicated that the SCALE variable of RA (a
measure of the aggregate size of banks'
portfolios) helped to explain the multiplier,
but that the interest-rate arguments of RA
(the funds rate, the commercial-paper rate and
31

Table 3
Estimated Equations
Equation

(3. 1) InRA~= 3.8 - .360ni F I - Ini cp t) - .071ni BI-I + .23InSCALEt
(9.27)(1.93)'
. (1.83) . (4.62)
+ 1.041nr D t - .231nr I t + .53U t_1
(5.49)
. 0.67) . (4.06)

IF = .98
SEE = .0069
DW= 1.89
(3.2) InRA~+1/2= 3.1- .51 Oni FI - Ini cPI )
(6.2) (2.6)'
,
-.121ni B,t_1 + .301nSCALEt + .701nr D,t+112 - .131nrl,t+1I2 +.36U t_if1
(3.0)
(4.9)
(3. I)
(1.0)
(2.5)

IF = .96
SEE = .0087
DW= 1.85
(3.3) RBt = .008 + .64 (iF.t - i B/
(0.19) (4.61)

h

Zl - .54.6.RU t·ZI + .59 RBt_1
(7.44)
(6.14)

ZI = I when iF,t >i B.t

owhen iF.I~iB,t
IF = .92
SEE= .14
DW= 1.84
(3.4) InMULT t = .01 - .075In(LTB t./DBt_l ) - .04InSCALEI
<0.6) (3. j)
(2.6)
- .801nr D ,t - .13lnrl,t + .73U t_1
02.1)
(2.7)
(7.0)

IF = .97
SEE = .0026
DW = 1.99
6
(3.5) InDB t - .8InDBI_I = .17 + .66 .6.lnBL t + 1 a j Ini cp .
(1.42)(2.16)
i=O
l-i
6
3
3
- .8 1a; Ini cp t-I-i + 1 bjlnY t_j - .81 bjlnY t_l _j •
i= 0
'
i= 0
i= 0
where
.016 0.24)
.015 (2.Q2)
.014 (2.75)
.012 (2.39)
.010 (1.81)
.008 (1.46)
.006 (1.22)

bO = .33 (1.67)
b l = .19 (4.36)

1 = - .081 (2.75)

1 = .64 (7.47)

ao =
al =
a2 =
a3 =
a4 =
as =
a6 =

-

b2 = .100.57)

b 3 = .02 <0.3 I)

R 2 = .88
SEE = .0038
DW = 1.74

32

Table 3 (continued)
(3.6) InSBt == .44 +.11 (l!iept) + .BlnYt + .65InSBt_1
(3.07)(2.44)
,
(4.07)
01.03)
.02MMCDUM t - .BBUSDUM t - .02ATSDUM t + .56U t. 1
(2.63)
(2.78)
(5.21)
(4.36)

IF= .998
SEE = .0024
SW= 1.76
(3.7) InSTBt = -0,05 + .160/iCpt )
(.20) (1.54)
,

.150/iCpt )MMCDUM t + .l61nY1-,
(2.63)'
(2.52)

+ .77lnSTB t _1 + .03MMCDUM t + .008ATSDUM t + .007SPRDUM t + .19U t _l
03.93)
(2.92)
(4.69)
0.02)
0.29)

IF = .999
SEE = .0029
DW= 2.19
8
0.8) InC t = - 1.64 + 1 ajlnY t• j + .87U t _1
(12.2) i= 0
(11.5)
where
a o = .12
a l = .12
a 2 =.12
a 3 = .11
a4 =.11

(1.62)
(2.95)
(8.07)
(17.92)
(5.14)

as =
a6 =
a7 =
ag =

.09 0.20)
.07 (2.42)
.05 (2.01)
.04 (1.75)

1 = .83 (46.34)

IP = .999
SEE = .0016
DW = 1.57
(3.9) OCDB t = .03 + 1.000CDBt. 1 + .55 aOCDB t _1
(1.43) (60.83)
0.96)

lP = .989
SEE = .254
DW= 1.99
0.10) OCD t + .80 + 1.570CDt_l - .73 OCD t.2 + .12 OCD t•3
(2.02) (5.32)
(1.39)
(0.40)

lP = .986
SEE = .473
DW= 2.11
NOTE:
t-statistics are in parentheses.
Estimation method is two-stage least squares with Cochrane-Orcutt adjustment where indicated by the variable Ut • l . Instrumental variables used for iF and icp , Sample period was 1976: Lunar 8 - 1979: Lunar 10. Distributed lags in 0.5) and (3.8)
are second-degree Almon with the tail tied to zero.

33

ventional models produce the result that deposits (and thus reserves) respond to interest
rates with long lags and low elasticities.
Next, we present the model's representation
of the supply of total reserves. Under the
funds-rate regime of the estimation period,
total reserves supply is simply equal to banks'
demand for total reserves, Rd. The only
remaining issue concerns what part of this
demand is supplied through borrowed and
what part through nonborrowed reserves. The
estimated member-bank borrowing function is
reported in Table 3 equation (3.3). Its arguments are the square root of the differential of
the funds rate over the discount rate (defined
to be zero when the funds rate is below the discount rate), changes in nonborrowed reserves,
and lagged borrowing. It was observed that,
when the funds rate fell below the discount
rate, member-bank borrowing shrank to a
small frictional amount. Thus, we
hypothesized that banks borrow from the
Federal Reserve primarily when there is sufficient incentive in the form of a positive funds
rate/discount rate differential. Tests of this
hypothesis were strongly confirmed. As a consequence, we imposed the constraint on the
estimated equation that borrowing responds
only to positive differentials.
We used the square root of the differential
to reflect the increasing administrative pressure and/or reluctance to borrow accompanying a rise in the spread (and therefore in RB).
With the square root, the RB equation has the
property that RB's responsiveness to a given
change in the spread declines as the level of
the spread rises.
We also hypothesized that because of lagged
reserve accounting, changes in nonborrowed
reserves would have a transitory effect on borrowing. Under lagged accounting, required
reserves this week are fixed, being determined
by deposits of two weeks ago. A reduction in
nonborrowed reserves therefore forces banks
in the short-run to replace them with borrowed
reserves, because the total demand for reserves
is unchanged. Thus we should observe a negative relationship between changes in nonborrowed and borrowed reserves.

being determined by the aggregate size of
banks' portfolios, measured by SCALE, and
by the fraction financed by nondeposits, which
is a function of icp , iF, and iB• Hence RAd depends on the same variables and is influenced
in the same direction by them. In particular,
higher iF and iB would be expected to lower
RAd, while increases in SCALE and icp would
raise it. Also, increases in the required-reserve
ratios, rD and rj, should raise RAd.
The first two lines report the results for the
two estimates of reserves demand. Both equations fit the data quite well. All the estimated
coefficients have the right signs, and all pass a
test of significance at the 95-percent confidence level, except for the coefficients on rl .
Both measures of RAd are relatively elastic
with respect to the funds rate, especially
RA t+ l/2, which determines the elasticity of
demand-deposit supply. The RAt measure of
reserves demand should be less responsive to
its arguments than is RA t+l/ 2' which in fact is
true. The reason is that RAt reflects only a partial response of demand deposits to changes in
the funds rate and the other arguments,
because it excludes the requirements against
deposits created in the last half of the month.
RA t+ l12 on the other hand includes reserves
against all deposits of the current month, and
therefore more accurately measures their
response to interest rates and SCALE.
The two versions of reserve demand adjust
rapidly to their explanatory variables, with full
adjustment occurring in one month. Although
we tried a number of distributed-lag specifications, lagged effects of the explanatory variables were consistently insignificant. These
findings - rapid speeds of adjustment and
relatively large interest elasticities - are consistent with one of our central hypotheses: the
supply of deposits results from the interaction
of banks and the public in various credit
markets, where participants actively maximize
profits on a day-by-day and hour-by-hour
basis. As noted earlier, this part of the model
differs from conventional models, which view
deposit supply as accommodating the public's
demand for deposits. Since many deposit
holders inactively manage their balances, con34

money-supply shocks. Disequilibrium caused
by past shocks is worked off at a rate of (I -p)
per month, so that a fraction p oflast month's
disequilibrium persists into the current period.
At the same time, the fraction X of this
month's shock is held temporarily, and thus
adds to the measure of current disequilibrium.
Observed deposits therefore can be written,

In .. the. borrowing equation, .first,all
explanatory variables have. the expected signs
and are highly significant. Second, the speed of
adjustment is again relatively fast - the mean
lag is 1.4 lunar months. However, even this
relatively quick adjustment seems surprisingly
slow when compared to the even faster adjustment in the reserves-demand equations noted
earlier. Third, the implied contemporaneous
response of borrowing to the funds rate is very
large, especially when the spread is very low.
Thus a 10-basis-point rise in the funds rate
increases borrowing by $64 million when the
spread is 25 basis points. When the spread rises
to 50, 100 or 200 basis points, a lO-basis-point
increase in the funds rate produces $45, $32
and $22 million of additional borrowing,
respectively. The long-run responses are about
21J2 times larger.
To complete the banking side of the model,
we need a prediction of the supply of deposits.
This we obtain by multiplying the equation for
RA t+ l12 (equation (3.2» by the estimate of
the multiplier in equation (3.4). The multiplier
is simply a weighted average of the reserverequirement ratios on demand deposits and
nondeposit funds. For reasons explained in
Appendix C, large certificates of deposit (LTB)
are the only significant reservable "nondeposit" liability. Hence, the multiplier can be
written as lI(r D + r,(LTB/DB) ). For reasons
discussed above, the ratio LTB/DB is approximated as a function of its lagged value and
SCALE. Hence we estimated the multiplier as
a function of these two variables and the
required-reserve ratios. The coefficients on
the latter had the correct negative signs. The
coefficient on SCALE was also negative,
indicating perhaps that as banks' portfolios
increased, they raised nondeposit rates to
attract more funds, causing the ratio of CDs to
demand deposits to rise.
The demand for demand deposits can be
viewed as a disequilibrium process in which
deposit-supply shocks move the public away
from its equilibrium demand. Over the sample
period of this study, bank loans were found to
be the major source of money-supply shocks. 14
Changes in bank loans therefore can proxy for

The short-run equilibrium demand function
for deposits, DBd, is a function of icP and
nominal income (Y) - which determine the
long-run equilibrium dema"nd for deposits and lagged values of DBd represent partial
adjustment of money demand in the short-run
to the long-run equilibrium level. Since we
d
cannot directly observe DB - it does not
equal DB when there is disequilibrium - we
solve for it in terms of interest rates and
income by successive substitution, Le.,

Substituting this result into (0 and rearranging we have l5
InDB t = Iai Inicp,t_i - plai Inicp,t_l_i
+ Ibi InYt_i - plbJnYt-1-i
+ plnDBt_1 + XlllnBL t

(3)

Estimates of the demand-deposit demand
equation are shown in (3.5). The long-run
elasticities on income and the commercialpaper rate are highly significant, and their
values are in the "normal" range for traditional money-demand equations. Second, the
change in the bank-loan variable is significant,
with the expected positive sign. Third, the
coefficient on IllnBL is relatively large. For
example, the decline in BL in May 1980 is estimated to have held observed demand deposits
to a I/2-percent growth rate, compared to the
I3-percent growth which would have otherwise occurred. Fourth, the estimate of p at .8

35

indicates that deposit-market'disequilibrium
induced by bank loans persists with a mean lag
of four months.
Equation (3.8) presents the public's demand
for currency as a function of a distributed lag
on nominal GNP. The commercial-paper rate
could theoretically enter this equation, but did
not do so significantly during, the sample
period. The combination of DB and Cd provides the model with the stock ofMIA.
In order to determine MIB, we must explain
MIA plus total other checkable deposits
(OCD). The latter includes deposits both at
banks and thrifts, although thrift deposits were
relatively small, being confined to NOW
accounts at institutions in Northeastern states.
The major component ofOCD during the sample period was commercial-bank ATS (automatic transfer from savings) accounts. These
deposits were introduced in November 1978;
hence the growth in OeD represents almost
entirely the public's accumulation of desired
stocks of ATS accounts. This'stock adjustment
in the public's demand was modelled most
effectively as a function of past OCD. (3.10)
The model includes three more demands by
the public for bank liabilities: banks' other
checkable deposits, equation (3.9); small time
deposits, equation (3.7); and passbook savings
deposits, equation 0.6). These variables

enter the model because banks are required to
hold reserves against them. Other checkable
deposits at banks (OCDB), like OCD, is
modelled as a time series. For savings (SB)
and small time deposits (STB) , the public's
demands determine their quantities. The arguments of these functions include personal
income, the commercial-paper rate, and a
number of (dummy) variables capturing the
effects of various regulatory changes during
the sample period (see Appendix B for definitions) .
Simulation Results
While Table 3 shows how the estimated
equations perform individually, it does not
indicate how well all of the model's equations
and identities simultaneously predict the
endogenous variables of the system. Consequently, we made a full-model static simulation of the sample period, using actual values
for lagged dependent variables and applying
autocorrelation corrections to preceding
month's errors. Table 4 presents the results of
this simulation for the four major variables of
the model (MIA, MIB, R, icp ).
The model fits the in-sample data for the
monetary and reserve aggregates quite well,
producing root-mean-squared errors (RMSE)
ranging from 0.21 to 0.30 percent of the
average levels of MIA, MIB, and R. As is typi-

Table 4
Model Simulations
Root Mean Squared Errors

MIA
MIB
Total reserves
Commercial
paper rate

In_Sample 1
1978/lS - 1979/l1 0
(Static)

Out-of-Sample 2
1979/l11 - 1980/l11
(Dynamic)

$883 million
(0.21 percent)
$1,016 million
(0.30 percent)'
$108 million
(0.24 percent)
14 basis points
(1.7 percent)

$2,238 million
(0.60 percent)
$2,166 million
(0.55 percent)
$169 million
(0.45 percent)
195 basis points
05.9 percent)

'Fe(jer~lI-lUtnds rate exogenous. All exogenous variables set at actual values.
2Nonborrowed reserves exogenous in 1979/Lll-1980/L5, and 1980/LlO-1980/LlI. Federal-funds rate exogenous in 1980/
L6-1980/L9. All exogenous variables set at actual values.

36

caloflnoney-market models, the interest-rate
forecasts are less accurate than the monetary
and •reserve-aggregate· forecasts. The RMSE
for the commercial-paper rate is 1.7 percent,
which amounts to 14 basis points.
The right-hand column of Table 4 shows
RMSEs for the same four variables from a
dynamic out-of-sample simulation over 1979/
LII - 1980/L11. In this simulation, lagged dependent variables took on values predicted by

thel110del in previous periods, and serial correlation adjustments were applied only to the
error in the final in-sample ·l11onth. Not
surprisingly, the RMSEs from this experiment
are larger than the in-sampleresuits -- for the
aggregates, they range from 0.45 to 0.60 percent, while for the commercial-paper rate the
RMSE is 15.9 percent. In view of the extreme
volatility of the post-October 1979 period compared to the earlier estimation period, we may

Figure 5
Out-of-Sample Predictions of
M-tB and the Commercial Paper
Rate: Post-October 6, 1979

$ Billions
410
405
400
395
390
385
380
375

o •","'_ ......_eL..._.........I_...._

......_eL......I..........._

......_..&.._&-....._

.....

Percentage Points
17
Commercial Paper Rate

15

13

11

9
0_....I_..A._...I-_..........._..L._eL........IL........_...I-_..........._..L._.1
3
4
5
6
7
8
9
10
11
11
12
13
2
1980

1979

37

Lunar Months

take the out-of-sample results as a measure of
the model's success.
Even more encouraging is the success of the
model at predicting the turning points during
the period. As shown in Figure 5, the model
was able to simulate the rather wild gyrations

of MIB, whereas a wide variety of more traditional models missed these turning points. 16
The model did not do quite as well on icp ,
specifically missing the large drop in 19801L5.
In other months, however, the simulation
tracked reasonably well.

III. Why Were the Aggregates So Volatile in 1980?
Analysis of the model's exogenous variables
indicates that changes in bank loans were by
far the most important contributor to MIB's
rapid growth in the first and third quarters of
1980 - and also to its rapid second-quarter
decline. Evidence for this conclusion is presented in Figure 6, which compares two
dynamic simulations of MIB. The solid line is
a full dynamic simulation - i.e., the same one
shown in Figure 5. The dashed line is a simulation with bank loans constant, but identical in
every other respect to the full simulation. This

experiment indicates that without the post1979 volatility in bank loans, MIB would not
have gyrated as it did.
What accounts for the erratic pattern of
bank-loan movements in 1980? The most
plausible explanation is the Special Credit
Control Program of March 1980, which put
binding constraints on bank-credit growth. In
the first quarter of 1980, the financial press
had reported that businesses were anticipating
credit controls. This probably contributed to
the rapid growth of loans in that quarter, as

Figure 6
Simulation of the Effect of
Bank Loans on M-1 B:
Post-October 6, 1979

$ Billions
410
405
400

Dynamic Simulation with
Bank Loans Constant at its
1979/L10 Level
"

395

385

380r

37St0:

L._ . L -......_
11
12

.............._
13

.....-.I'_-'--.lI......,jII....-'-_...
' _
3
4
5
6
7
8
2

1980

1979

38

...........-

...

9

11

10

Lunar Months

spurted in the summer period as firms
attempted to make up for the lack of loans in
the preceding quarter.

firms attempted to obtain bank credit while it
was still available. In the second quarter, loans
declined absolutely in response to the binding
constraints of the credit controls. Finally, loans

IV. Conclusions
Conventional money-market models reflect
the view that the monetary aggregates are
determined primarily by the public's demand
for money. The money-market model presented in this paper reflects an alternative view
- that the monetary aggregates are determined in the short run primarily by the supply
of money, which arises out of the behavior of
banks and the public in established financial
markets. Several pieces of evidence support
this hypothesis. First, the money supply responds to its financial-market determinants
with very short lags, consistent with the typical
speed of adjustment in financial markets, but
.not with the typical sluggishness of money
demand. Second, bank loans can have - and
in 1980, did have - a potent influence on the
monetary aggregates. Third, the market for
money is often characterized by disequilibrium
in the short-run. Money-supply "shocks"
temporarily push the public off its short-run
money-demand curve, which allows the
money supply to exert a large short-run influence on the stock of money observed in the
economy.

These results have important implications
for Federal Reserve monetary policy. First,
policy makers should pay close attention to
financial-market developments, which can influence the growth of money in a quick and
potent fashion. Second, policy makers should
be especially careful to evaluate financialmarket developments when signs appear of a
shift in the conventional money-demand function. A good case in point is the second quarter
of 1980, when conventional models severely
overpredicted the money stock. Evidence of a
downward shift in the money-demand relationship would imply that money supply
should be allowed to fall commensurately to
avoid an overly expansionary monetary policy.
On the other hand, the model in this paper
explains the decline in money as a supply
shock, induced by the decline in bank loans
that followed from the Special Credit Control
Program of 1980. Such a conclusion implies
that monetary-control efforts should be
directed toward more rapid money-supply
growth to avoid an overly contractionary
policy.

Appendix A
Formal Representation of the Model
The model describes the portfolio behavior
of the Federal Reserve, commercial banks and
the nonbank public over monthly observations. The balance sheets of commercial banks
and the nonbank public are shown below. See
Appendix B for definitions of variables.

Commercial Banks
Assets 1 Liabilities
DB

RI

BL

39

Nonbank Public
Assets
Liabilities
DB
NW

TB

TB-DBG

BL

!MB

1MB

OL

I

FF/RP

I

RB

FF/RP
OA
C

NW = DB + TB - DBG - BL
+ FF/RP + OA - OL

The Federal R~serve is assumed to control
RU = R - RB and i B, making them
exogenous. In addition, the model takes as
exogenous BL and Y. BL is exogenous because
the public's demand for loans is unresponsive
to the contemporaneous (monthly) loan rate,
while Y is exogenous because the lag between
monetary policy and Y is greater than one
month. In addition, individual banks take deposits (DB and TB) as determined entirely by
the public's demand for deposits. Since the
yields banks pay on these assets are legally
held below market-clearing levels, individual
banks will supply any quantity demanded by
the public. Finally, it is assumed that any
quantity of currency demanded by the public
will be supplied. Given these assumptions and
the profit-maximizing behavior described in
Section I of the text, the following structural
model may be specified.
IMBS = IMBS 00 , iF, iB, BL - DB - TB + R)
IMB d = IMB d 00 , iF, icr, Y)
FF/Rps = FF' 00 , iF, i B, BL - DB - TB + R)
FF/Rpd = FFd 00 , iF, icp , Y)

RB d

=

RB

OF, i B)

OA d 0 0 , iF, icp , Y) - OLsO o , iF, icp , Y)
DBd

=

DB d OcP, Y)

Cd =

=

TBd 00, iF, icr, Y)
Cd 00 , iF, icr, Y)

Rd - RB d = RD s
Rd = rDDB

(J)
(2)
(3)
(4)

(6)
(7)

DB - DBd = DBSH (~DBS)
TEd

0

(13)

Only twelve of these thirteen equations are
independent, and thus anyone of them can be
dropped from the solution of the model's
reduced form. We chose to drop equation 6.
The remaining twelve equations can be solved
for the following twelve unknowns: 1MB, FF/
RP, DB, DBd, TB, C, R, RB, NW, io, iF, icp .
In Section I of the text, the model is solved
in three stages as follows. In Stage 1, equations
1,2,3,4,5 and 12 are solved for 1MB, FF/RP,
RB, i o, DB and R as functions of iF, icp, iB, (BL
- TB), Y and other variables. The sum of the
equations for 1MB, FF/RB, and RB provides
the EQ equation of the text. The equations for
DB and R are the Stage 1 deposit-supply and
reserves-demand equations.
In Stage 2, equation 11 is added to the Stage
1 equations, to provide solutions for 1MB, FF/
RP, RB, io , DB, R and iF, as functions of icp ,
and iB, (BL - TB), Y and other variables. The
equation for DB is the Stage 2 deposit-supply
equation.
In Stage 3, equations 7 and 8 are added to
the Stage 2 equations, providing solutions for
d
1MB, FF/RP, RB,i o, DB, R, iF, and DB and
icp, as functions of iB, (BL - TB) Y and other
variables. Finally, the model can be completed
by using equations 9, 10, and 13 to provide
solutions for C, TB, and NW.

(5)
=

+ C + 1MB

(8)
(9)

l

(I 0)
(II)
(I2)

Appendix B
Glossary of Symbols
ATSDUM
BUSDUM

C
DB
DBG
DUM(.)

Dummy variable for the introduction of ATS accounts at commercial banks:
Inl, In2, In3, ... , In13, during 1978/Lll-1979/LlO.
Dummy variable for the introduction of business and state-and-Iocal government saving deposits at banks: In20, In21, In22, ... , In26, during 1976/L71976/Ll2, and In26 during 1976/Ll3-1979ILIO.
Currency in the hands of the public
Private demand deposits at commercial banks.
U.S. Treasury demand deposits at commercial banks.
Institutional changes affecting the public's demand for SB and STB; includes
ATSDUM, BUSDUM, MMCDUM and SPRDUM.

40

FF/RP
1MB
LTB
iB
i cp
iF
io
iSB

BL
MMCDUM
M1B
MULT
NW
OCD
OCDB
OA

pL
R
RA
RB
RE

RR
RU

ro
rT

SB
SCALE
SPRDUM

STB
TB
y

Zl

Net federal funds purchased plus security repurchase agreements at commercial banks.
Total nondeposit funds plus time deposits in denominations of $100,000 or
more, less total holdings of securities at commercial banks, less FFIRP.
Time deposits in denominations of $100,000 or more.
Federal Reserve discount rate.
Three-month nonfinancial commercial-paper rate.
Federal-funds rate.
Ninety-day large negotiable certificate-of-deposit rate.
Passbook-savings rate at commercial banks.
Total loans at commercial banks.
Dummy variable for the introduction of six-month money market certificates
at commercial banks: 1 during 1978/L7-1979/L10; 0 elsewhere.
C + DB + OCD.
DB/RA t + l12
Net worth of the nonbank public = DB + TB
DBG - BL + C + 1MB +
FF/RP + OA - OL.
Other checkable deposits at commercial banks and thrift institutions.
Other checkable deposits at commercial banks.
Other assets of the nonbank public.
Other liabilities of the nonbank public.
Total member-bank reserves, adjusted for Regulations D and M.
Reserve requirements against demand deposits and managed liabilities,
adjusted for Regulations D and M.
Borrowed reserves from the Federal Reserve.
Member bank excess reserves.
Member bank required reserves, adjusted for Regulations D and M.
Member bank nonborrowed reserves, adjusted for Regulations D and M.
Reserve-requirement ratio against demand deposits.
Reserve-requirement ratio against time deposits in denominations of$100,000
or more.
Reserve-requirement ratio against 1MB.
Reserve-requirement ratio against SB, STB and OCDB.
Passbook-savings deposits at commercial banks.
1MB + FF/RP + RB + DB - RA = BL
TB + (R-RA).
Dummy variable for the elimination of the 25-basis-point spread between
yields on money-market certificates at thrift institutions over commercial
banks: 1n1, 1n2, ... , 1n7 during 1979/L4-1979/LlO.
Time deposits in denominations of less than $100,000 at commercial banks.
Other deposits = DBG + OCDB + SB + STB.
Personal income in current dollars.
Zero when funds rate below or at discount rate. Unity when funds rate above
discount rate.
41

Appendix C
Other Reserve Requirements
(DUM (.)).19 The resulting estimates are
multiplied by the corresponding reserve ratio
to predict the amount of reserves held against
them. Estimates of the public's demand for
other checkable deposits at banks (equation
2.9) are used in the same way to estimate the
reserves held against them.
Recognizing that both demand deposits and
some non-deposit liabilities are reservable
makes the analysis of the multiplier somewhat
more complicated than our theoretical discussion would indicate. In that discussion, we
could think of demand deposits alone as having reserve requirements, which meant that
the multiplier - the ratio of demand deposits
to reserves - was simply the reciprocal of the
demand-deposit required-reserve ratio, rD'
With managed funds also reservable, we must
also take account of the fact that part of RA
will not be available to support demand deposits. The larger the amount of reserves
absorbed in requirements against nondeposit
liabilities, the smaller will be the amount of
demand deposits outstanding per doilar of RA,
i.e. the smaller will be the multiplier.
Not all nondeposit liabilities are reservable.
For all intents and purposes, large time deposits (LTB) are the only significant ones that
are. This is because the model uses a reserve
series that abstracts from changes in Regulations D and M, which define reserve requirements. That is, the measure removes discontinuities in the reserves numbers caused by
changes in required-reserve ratios. If a liability
item has incurred reserve requirements only
part of the time, its reserves will not show up
in the smoothed series because its benchmark
ratio is zero. Most reserve requirements on
nondeposits have been on-again, off-again (on
Eurodollar borrowing, for example) and
therefore are not included in our reserve
series. The important exception is reserves
against LTB, which are included because these
large CDs have always been covered by
reserve requirements.

The theoretical model focuses on the way
that portfolio decisions of banks and the public
affect the stock of demand deposits, and
through them, the demand for reserves. In
reality, other items besides demand deposits
are reservable. Small time and savings deposits
(SB and STB), government deposits (DBG),
other checkable deposits (OCDB), and certain
nondeposits also have reserve requirements,
and therefore affect the amount of required
reserves. 17 In addition, required reserves contain the reserves that thrift institutions must
hold (RTH) with the phasing in of the universal reserve requirements mandated by the
Monetary Control Act. 18 And finally,
measured reserves also include the small
amount of excess reserves (RE) that banks
hold.
The behavioral relationship underlying
reserves demand is framed in terms of demand
deposits and nondeposit liabilities only. Hence
the other components of reserve requirements
must first be stripped away before reserves
demand can be estimated. This refined version
is called adjusted reserves, RA; its relation to
total reserves, R, is shown in the reserves
identity (equation 2.13 of Table 2 in the text.)
The other components of total reserves
must still be accounted for. This is done in two
ways. Excess reserves and requirements
against thrift deposits and Treasury deposits
are treated as constants over the sample period
(equations 2.16, 2.17, and 2.18), since they
are small and exhibit only slight variation. The
others are treated by estimating the quantities
of corresponding deposits and multiplying
them by the appropriate reserve ratio. For
small time and savings deposits, the public's
demands are viewed as determining their
quantities, because the banks' scope for altering rates is constrained by interest-rate ceilings. Thus the public's demands for SB and
STB are estimated as functions of interest
rates, income, and a number of variables
representing institutional changes
42

Hence our adjusted reserves series, RA, is
essentially composed of required reserves
against demand deposits and large time deposits. The multiplier therefore depends not

only on r D but as well on LTB (relative to DB)
and its reserve ratio, rl' In the empirical model,
the multiplier is estimated as a function of
these variables.

FOOTNOTES
growing importance of Federal funds and repurchase
agreements as alternatives to managed liabilities.
9. See Murray E. Polakoff and William L. Silber,
"Reluctance and Member Bank Borrowing: Additional
Evidence," Journal of Finance, March 1967, pp. 8892.

1. John P. Judd and John L. Scadding, "Conducting
Effective Monetary Policy: The Role of Operating
Instruments," Economic Review, Federal Reserve
Bank of San Francisco, Fall 1979, pp. 23-37.
2. See Thomas D. Thomson, James L. Pierce and
Robert T. Parry, "A Monthly Money Market Model,"
Journal of Money, Credit and Banking, November
1975, pp.411-431.
3. Richard D. Porter, Thomas D. Simpson, and Eileen
Mauskopf, "Financial Innovation and the Monetary
Aggregates," Brookings Papers on Economic
Activity, 1:1979, pp. 213-224.
4. The money-supply part of the present model is in
the spirit of the model in Franco Modigliani, Robert
Rasche, and J. Philip Cooper, "Central Bank Policy,
the Money Supply, and the Short Term Rate of
Interest," Journal of Money, Credit and Banking,
May, 1970, pp. 166-217.

10. Until October 6, 1979, the Fed used the funds
rate as its operating instrument. To achieve its
targets, the Fed set RU so that the funds rate which
cleared the reserves market equalled the funds-rate
target. This procedure makes DBs-1 and DBs-2
empirically indistinguishable. However, the theoretical distinction noted above still applies: DBs-2
includes Fed behavior, whereas DBs-1 remains the
same no matter what the Fed's operating procedures
are.
11. This approach is in the tradition of the following
research: Jack Carr and Michael R. Darby, "The Role
of Money Supply Shocks in the Short-Run Demand
for Money," U.C.L.A. Discussion Paper, No. 98, September 1978 (forthcoming, Journal of Monetary Economics); Warren L. Coats, "Modeling the Short-Run
Demand for Money with Exogenous Supply," unpublished paper, Board of Governors of the Federal
Reserve System, 1979; Michael R. Darby, "The
Allocation of Transitory Income Among Consumers'
Assets," American Economic Review, December
1972, pp. 928-941; Dennis R. Starleaf, "The
Specification of Money Demand/Supply Models
Which Involve the Use of Distributed Lags," Journal
of Finance, September 1970, pp. 743-760; and D.
Tucker, "Macroeconomic Models and the Demand for
Money Under Market Disequilibrium," Journal of
Money, Credit and Banking, February 1971, pp. 5783. For a discussion of the conventional approach
see Gregory C. Chow "On the Long-Run and ShortRun Demand for Money", Journal of Political Economy, April 1966, pp. 111-131.

5. Managed liabilities and security holdings are combined because they serve basically the same function
in banks' balance sheets - they provide liquidity. See
Jack Beebe, "A Perspective on Liability Management
and Bank Risk," Economic Review, Federal Reserve
Bank of San Francisco, Winter 1977, pp. 12-25.
6. Ernst Baltensperger, "Alternative Approaches to
the Theory of the Banking Firm," Journal of Monetary
Economics, January 1980, pp. 1-38. He distinguishes
the following non-interest costs: for liabilities, their
associated costs of liquidity management (e.g.,
differences in withdrawal risk) and costs of producing
and maintaining deposit contracts; on the asset side,
risks of default, and information and transaction costs
associated with extending different types of credit.
Baltensperger also includes differences in the cost of
acquiring or disposing of an asset or liability.
7. The nonbank public's balance-sheet constraint is
derived from the following balance sheet.
Assets
Liabilities
Currency
C
Loans from Banks BL
Demand Deposits
DB
Other Liabilities
OL
NW
Other Deposits
TB-DBG Net Worth
Managed liabilities of
bank (net of bank
securities holdings) 1MB
Net Federal Funds lent
plus repurchase
agreements
FF/RP
Other assets
OA
8. Thomas D. Simpson, "The Market for Federal
Funds and Repurchase Agreements," Board of
Governors of the Federal Reserve System, Staff
Studies, Number 106, July 1979, has detailed the

12. See Warren L. Coats, "Lagged Reserve Accounting and the Money Supply Process," Journal of
Money, Credit and Banking, May 1976, pp. 239-246,
and Daniel E. Laufenberg, "Contemporaneous Versus
Lagged Reserve Accounting," Journal of Money,
Credit and Banking, May 1976, pp. 239-246.
13. See Paul DeRosa and Gary H. Stern, "Monetary
Control and the Federal Funds Rate," Journal of
Monetary Economics, April 1977, pp. 217-230.
14. There is no theoretical reason why this must be
so. Rather, the importance of bank loans presumably
reflects in part the fact that the Federal Reserve used
a Federal-funds instrument to try to control money
during the sample period. As discussed in the
theoretical section, this procedure allowed bank

43

17. Reserve-requirement ratios include the effects
of the proportion of each deposit type held at member
banks: I.e., ro = rm(DM/DB), where rm is the average
ratio imposed on member banks, DM is member-bank
demand deposits subject to reserve requirements,
and DB is all bank demand deposits. Weekly data are
available for DM/DB. Member-to-total bank ratios of
.70 and .63 were used for SB and STB throughout the
sample period. The member-to-total bank series for
LTB was calculated for each month as the residual
from the above data and assumptions, and from currently available reserve-requirement data.
18. J. A. Cacy and Scott Winnin9ham, "Reserve
Requirements Under the Depository Institutions
Deregulation and Monetary Control Act of 1980,"
Economic Review, Federal Reserve Bank of Kansas
City, September - October 1980, pp. 3-16.

loans the fullest scope to affect the supply of money.
But during the simulation period (1980) - despite the
Fed's reserves-control procedure - bank loans
remained an important source of disequilibrium
because of the very large impact of the Special Credit
Control Program.
15. Equation 3 resembles an autoregressive
transformation of a conventional short-run depositdemand function, in which actual deposits are identified with short-run equilibrium demand. This
transformation is frequently used in conventional
estimates of short-run money-demand functions
because of evidence of significant serial correlation
in the residuals. The disequilibrium specification (1)
suggests that there is a structural explanation for this
serial correlation: namely, the process by which
equilibrium is restored in the money market. As well,
however, the disequilibrium specification differs from
the conventional by a term which measures the effect
on money demand of current money-supply disturbances.
16. See David Lindsey and others, "Monetary Control Experience Under the New Operating Procedures," Federal Reserve Staff Study - Volume II,
New Monetary Control Procedures, February 1981 .

19. These consist of the following: the introduction
of business and state and local government
passbook-savings deposits; the introduction of sixmonth MMCs at banks; the introduction of ATS
accounts; and the removal of the 25-basis-point thrift
differential on MMCs.

44

Rose McElhattan*
This paper presents a small model of the
economy for estimating the response of
inflation and real output to a change in monetary policy. Measures obtained from the
model's reduced-form equations provide estimates of the complete adjustment paths of
inflation and real output to a monetary disturbance. By complete adjustment we mean that
the response of each variable to a change in
monetary policy continues until the variable's
level and rate of change have both reached
their respective long-run values. In other
words, prices will continue to change until
both the inflation rate and the level of real
money balances reach their respective longrun values, while real output will continue to
adjust until it equals the level of potential output and is growing at the rate of potential output. Most other reduced-form models focus
only upon the adjustment of rates of change in
prices and output to a monetary disturbance.
In contrast with these, our model provides
results which are consistent with the neutrality
of money, which is perhaps one of the most
generally accepted properties regarding economic behavior. It holds that changes in the
money supply ultimately affect only nominal
variables, such as prices and wages, leaving all

real quantities, such as goods and services,
unchanged.
Our empirical estimates provide the adjustment patterns of both real GNP and inflation
to their respective long-run values implied by
the neutrality property. Notably these time
patterns show a relatively quick, short-run
response of both inflation and real GNP to a
change in monetary growth, with those
responses completed within about two years'
time. This contrasts with conventional model
estimates which range from three to five years.
Our results suggest that a monetary contraction is likely to bring inflation down faster with
less adverse affect upon real economic activity
than previously anticipated.
In the next section we describe the model
and detail its long- and short-run properties,
emphasizing the expected lag pattern between
changes in monetary policy and changes in the
level and rates of change of prices and real output. In the following section, we estimate the
reduced-form equations of the model, utilizing
an estimation technique suggested by John
Scadding (see Appendix 1). Using this
method, we are able to place restrictions on
both the steady-state level of a variable and its
rate of change. The final section provides
policy implications and conclusions.

I. Model of Real Output and Inflation
aggregate-demand and aggregate-supply equation shown in Table 1. Each of the variables is
measured in terms of its natural logarithm.
Aggregate demand, which is stated in terms
of the level of output relative to its potential,
(YIYP)d, is inversely related to the rate of
inflation, dP t • This occurs because - given the
rate of growth in the nominal money supply,
dM t - a reduction in the rate of inflation raises

The structure of the model is concerned
directly with behavior in the markets for
goods, money and labor. Each market is
characterized by fairly standard economic relationships which are detailed in Appendix 2,
and which may be combined to provide the
*Economist, Federal Reserve Bank of San Francisco. The
author wishes to acknowledge the advice of John Scadding and the research assistance provided by Duane Seppi.

45

real money balances at each level of output.
Higher real balances lead to a fall in real
interest rates, which in turn increases interestsensitive spending. By the same line of reasoning, aggregate real demand declines when the
inflation rate increases.
However, demand is positively related to
expected changes in the rate of inflation, as
indicated by the positive sign associated with
the coefficient a!2' For example, if people anticipate an increase in the inflation rate, their
demand for goods and services will increase in
the current period as they take advantage of
this period's relatively lower prices. The negative value associated with the coefficient au
indicates that demand is inversely associated
with changes in the government-budget
surplus. For example, an increase in government revenues relative to spending acts to depress aggregate demand. Also, past increases
in the real-GNP gap tend to reduce current
real growth. This may occur, for instance,
when past increases in income tend to increase
current saving more than investment. Finally
Wit represents the random disturbance or error
term in estimating aggregate demand. It captures the sometimes sizable but unsystematic
effect upon aggregate demand of many factors
whose total impact over time averages zero.
For instance, the impact of both labor troubles
and unusual weather would generally be
included in this term.
The aggregate-supply equation states that
deviations of output from potential are determined by unexpected changes in the current
inflation rate and by past deviations of output
from potential. Since these past deviations can
in turn be related to past unexpected price
changes, the supply equation indicates that the
impact of unexpected inflation will persist for
some time.! The equilibrium condition states
that aggregate demand equals supply in any
given period of time.
The specification of inflation expectations
for the current and subsequent periods, dP;
and dP;+b completes the model. The
hypothesis used here, following John Muth,
states that expectations are informed predictions of future events, based on the available

information and the relevant economic theory
at the time the expectations are formed. This is
the well-known "rational expectations
hypothesis.,,2 We win leave the detailed
specification of inflation expectations for later.
For now, these general comments are sufficient to begin analysis of the model under
steady-state and long-run conditions.
Long-run Behavior
Certain economic conditions characterize an
economy in its steady-state or long-run
equilibrium. In summary, they indicate that
money is neutral in the long-run with respect
to the level and rate of change of output.
First, there are no surprises regarding peopie's expectations. Therefore, the actual
money-supply growth rate and actual inflation
rate are both equal to their respective anticipated rates.
Second, actual GNP is equal to potential
GNP, as can be seen from the aggregate-supply equation in Table 1. In the long-run, unanticipated inflation is zero (dP - dP* = 0), and
therefore the logarithm of the real GNP gap,
YNP, is zero.
Third, in the long-run, the inflation rate is
determined by the excess money supply - by
the growth rate of the money supply less the
amount of money the public demands to
finance the changing quantity of output. This
result may be derived by considering the
market conditions underlying aggregate
demand which are stated in equations (I)
through (5) in Appendix 2. In the long-run,
several terms in those equations are zero, and
we are left with the following specification for
the inflation rate:
dP t = dM t -a 6dYP t
where a6 represents the income elasticity of
money demand.
Fourth, in the long-run, changes in the
money-supply growth rate are fully reflected in
changes in the inflation rate: one percentage
point more (less) monetary growth means one
percentage point higher (lower) inflation. This
result is represented in the above equation by
the one-to-one relationship between those two
rates - dP t and dM t - and by the earlier

46

also provide useful "rules-of-thumb" regarding average economic behavior over spans of
time. For instance, over long enough periods
of time, the average rate of GNP will approach
the economy's potential growth rate as determined by its labor-forc;e productivity growth.
Similarly, the average rate of inflation will
approach the rate of excess money supply.

assumption that potential GNP is exogenous
with respect to the variables in our model.
Some critics argue that the long-run is an
inappropriate state in which to analyze economic behavior; in other words, the economy
is so frequently shocked away from its steady
state that that state may never in fact be
attained. However, long-run conditions may

Table 1
Summary of the Model
Aggregate Demand

(YIYP)~ = ko - a l1 (dP t - dM t) + a I2 (dP\+1 - dP*t) -a13dGt
- c1B(L) d(YIYP)t-1 + (YIYP)t-1 + Wit
Aggregate Supply
(Y /YP)~ = alO(dP t - dP*t)

+ J(L)

(YIYP)t-l + W2t
Equilibrium Condition

(YIYP)~ = (YIYP)~

(0)

OI)
(2)

where the coefficients and weights of the polynomials are combinations of the coefficients and
weights in the structural equations 0) - (7) in Appendix 2*.
The unknown variables are Y~, Y~, dP\, dP*t+h and dP t.
list of Variables
G

Y
YP
YIYP
M

P
P*

Federal government real high-employment surplus, measured as the ratio of revenues
to expenditures,
Real GNP,
Real potential GNP,
Real GNP gap,
Money supply,
GNP implicit price deflator,
Expected GNP implicit price deflator.

Each of the variables is measured in terms of its natural logarithm. Therefore, the change in real
GNP, dY, is a measure of the rate of change in real GNP, and YIYP is a measure of real GNP as a
percent of potential. The variables G, YP, UN and M are exogenous variables.
*C 1 = a/(a7
alO

=

+ a4a6)

a9ag

all = ai (a7 + a4a 6)
au = a4a/ (a7 + a4a6)
a 13 = aSa/(a7 + a 4a 6)
ko = (-d YP t - c1B(L) dYP t-)

47

Short-run

Adju!!~tm,enlts

Chart 1

In the
we focus on the transition period after a monetary change as the
economy tends to move from one steady state
to another. We emphasize the short-run
adjustment paths of real GNP, inflation and
real money balances which result from an
increase in the money-supply growth rate.
Similar reasoning may be applied to a decrease
in monetary growth.
Any such monetary stimulus would lead
initially to the creation of excess real money
balances in the hands of the public. (This can
be shown in the aggregate-demand equation
by increasing the money-growth rate, dM t ,
while leaving all other variables unchanged.)
Individuals now will attempt to reduce those
balances by increasing expenditures. Whether
this increased demand will be met with greater
production, higher
or some combination of the two depends upon aggregate supply
behavior. If both employers and labor expect
an increase in prices equal to the increased
monetary growth, and if no contractual
impediments exist, prices and wages will adjust
quickly. Accordingly, there will be no change
in the rate of output growth, and the increased
in price and
monetary stimulus will result
nominal-wage increases.
These results may be shown graphically with
the use of the aggregate demand and supply
equations. To simplify, we assume no change
in fiscal policy and in the level of potential output, but a continued change in expected inflation. In addition, we assume zero weights for
both polynomial functions, (B(L) and ](L», in
the aggregate demand and supply equations.
With these assumptions, we can specify
aggregate demand and supply with the following two simplified equations, each written with
the inflation rate on the left-hand side.

Inflation and Output
Adjustment to Increase
in Money-Growth Rate:
Immediate Adjustment
in Price Expectations
Inflation Rate

m,

Potential

Real Output

We begin with the economy in equilibrium
for some time, illustrated in Chart 1 by the
intersection of aggregate demand, ADo, and
aggregate supply, AS o, at point Eo. At that
point, the level of real output is equal to potential and the rate of inflation is equal to the
money-supply growth rate, "mo", on the vertical axis. Now, let the money growth rate
increase to m b which shifts aggregate demand
upward by the full amount of that increase to
AD!, according to equation (10). If price
expectations increase by the same amount as
money growth, aggregate supply will shift
upward by the same amount as aggregate
demand, to AS!. The intersection of AS! and
AD! at point E! provides the new solution: the
change in money growth leads only to an equal
increase in the inflation rate - without any
change in the quantity of output - as inflation
expectations change at the same time and by
the same amount as the permanent change in
money growth.
However, empirical evidence suggests that
prices and inflation expectations do not adjust
3
quickly to their new long-run values. Working
in the face of uncertainty, individuals appear to
rely heavily on observations of past behavior

dP t = -l/a ll (Y IYP)~ + kola ll + dM t
+ lIa ll (YIYP)H
Aggregate Demand (l 0.1)
dP t = dP*t + lIa lO (Y IYP)~
Aggregate Supply (ILl)

48

and other relevant information in forming
expectations of the future. These expectations,
although rational in the sense of being wellinformed and based upon the relevant information, nevertheless provide imperfect predictions of the future at any
time. As a
consequence, each increase in the moneygrowth rate may be followed by an increase in
both real GNP and inflation.
in
2, the initial
equilibrium position is again marked as point
Eo. Let the rate of money growth increase to
M t. The aggregate-demand function will again
shift upward to ADj, and aggregate supply
probably will also shift. But since we anow for
inflation expectations which do not adjust
immediately and completely to their new longrun value (m t on the vertical axis), the supply
shift is smaller than the demand shift. For purposes of illustration, assume that aggregate
supply shifts upward to AS I . The new, shortrun equilibrium is then at point B, which indicates an initial increase of both real output and

inflation in response to the
increase.
At the beginning of the next period, aggregate demand will shift upward again, according
to equation 10, as past real income increases
from the level associated with point Eo to that
of point B. Also, aggregate supply will shift
upward again as market participants reevaluate
price expectations in light of information not
available.
of
aggregate demand and supply at point C illustrates the new short-run equilibrium position.
It is important to note that inflation
increases from the level m o to a rate close to its
new equilibrium rate, m l , and then overshoots
that value as continued adjustments in aggregate demand and supply lead to a new, shortrun equilibrium at point C. Changes in price
expectations (in light of revised forecasts) influence the shifts in supply, while past income
and real money balances produce adjustments
in aggregate demand. This characteristic overshooting property - "the
element in
monetary theories of cyclical fluctuations,"
according to Milton Friedman - is a widely
4
noted economic phenomenon.
The inflation pattern is associated with a particular adjustment in real GNP, as shown in
Chart 2. After the initial increase in monetary
growth, real GNP increases above its potential
level, and continues to increase as
as the
inflation rate is below its new equilibrium rate,
mi' This occurs because as long as inflation
increases more slowly than money growth
(m t), real money balances will increase and,
accordingly, stimulate aggregate demand.
Once the inflation rate starts to overshoot its
new equilibrium level, real money balances
will begin to decline. As a result of this contractionary force, real GNP begins to decline
from its previous value.
The adjustments of real output, inflation
and real money balances continue until each
reaches a new, long-run value associated with
the permanent increase in money-supply
growth (Chart 3). First consider the response
of inflation to an increase in the money rate,
from m to mt(Chart 3A). Initially, the inflation rate increases by less than the change in

Chart 2
Inflation and Output
to Increase in
Money-Growth Rate: Lagged
Adjustment in Price Expectations
Inflation Rate

Potential

Real Output

49

money growth each period, but completes its
initial adjustment phase at time T j • At that
time, the inflation rate will equal the long-run
rate of change in money growth, although
price expectations and real income will still not
have made a complete adjustment. Subsequent
to T j, inflation overshoots and then returns to
its long..run rate. In our illustration, we depict
inflation as gradually returning to its new
equilibrium position, although alternatively, it
may exhibit a damped cyclical adjustment to its
long-run value.
Next consider the response of real money
balances to an increase in the money growth
rate (Chart 3B). In the initial equilibrium,
individuals hold a certain desired proportion of
income in that form. For some time after
money-supply growth increases, prices
increase less rapidly than the nominal money
supply in each period. As a result, real money
balances increase and reach a maximum when
the inflation rate initially reaches its long-run
rate at time T j • Subsequently, these balances
steadily decline toward their new, long-run
level, which we have shown to be equal to
their initial leveL With any sensitivity to
interest rates, however, the level of real balances in the new equilibrium will be lower than
initially. In the U.S., money demand generally
moves inversely with interest rates. Therefore,
we would expect that, after a permanent
increase in monetary growth, real money balances will ultimately be slightly less than
before the change.
Finally consider the response of real GNP to
a change in the money growth rate (Chart 3C).
In this adjustment process, the level of real
output returns to its long-run path after rising
above potential for some time. Meanwhile, the
rate of change in real GNP increases and then
declines in response to an increase in monetary growth, and finally increases again before
approaching its long-run rate of change (Chart
3D). This pattern of growth is consistent with
the adjustment in the level of GNP shown in
Chart 3C.
In summary, a change in money-supply
growth may have no significant effect on real
output, at least as long as prices and price

Chart 3
Response of Selected Variables
to Permanent
Increase in Money-Growth Rate
Inflation Rate

m~-------------Real Money Balances

~ equilibrium level
Real Output

Real Output
Growth Rate

T*

T,

Time

expectations adjust immediately. In other
words, the entire change in money may be
absorbed by a change in prices. In contrast, if
there is no immediate price adjustment, monetary changes may be accompanied by changes
in both inflation and real output. The key
feature in the adjustment process is the cyclical
response of both output and inflation After a
permanent increase in money growth, inflation will increase, overshoot, and then decline
towards its long-run value. The real-output
growth rate will at first increase, then decline,

50

and may increase again as the level of output
returns to potential.

changes.) Particularly important is the process
or rule by which the public forecasts future
rates of change in the money supply and in
Federal-budget surpluses. We assume that
people forecast these values by considering
their past history, and that they update their
forecasts each period as new information
becomes available. Consequently, expected
inflation is determined by the past history of
the money supply, Federal-budget surpluses
and the GNP gap.
The derived specifications for expected
inflation (shown in the appendix) can next be
used to obtain the final equations for inflation
and real GNP. However, changes in the processes by which the public predicts future
monetary and fiscal policies will lead to
changes in the parameters of the estimated
equations. Consequently, those equations will
provide appropriate means of forecasting real
GNP and inflation as long as the public does
not change the rule bl which it predicts future
government policies.

Formation of Inflation Expectations
Before deriving the final model equations,
we must first express the functional forms for
expected inflation. These will then be
substituted into the aggregate demand and
supply equations, which in turn can be solved
for the final equations for real GNP and inflation.
To obtain the specifications for expected
inflation, we follow a procedure suggested by
Sargent and Wallace (1975). The mathematics
are shown in Appendix 3. Given the rationalexpectations feature of the model, expected
inflation depends upon the public's forecasts
of future monetary and fiscal policies, as well
as the past history of deviations of output from
its potential level. (These deviations directly
affect current inflation, due to the lagged
response of prices to past money-supply

II. Solution of the Model: Reduced·form Equations
In this section, we provide the reduced-form
equations for the inflation rate and real GNP
which are solutions of the system (equations
10,11,12, plus equations 16.1 and 17.1 from
Appendix 3), and which serve as the basic
equations estimated in the next section.
First, we obtain the equation for real GNP,
which will be stated in terms of the GNP gap,
YIYP, by substituting the specifications for
inflation and expected inflation - provided by
equations (13) and (14) in Appendix 3 - into
the aggregate-supply equation.

Also, we have assumed a finite length of the
lags, N. The equation thus states that the cyclical movement in real GNP is determined by
distributed lags on unanticipated changes in
money-supply growth and in the Federalbudget surplus. (An unanticipated change is
defined as the actual less the expected value of
a variable.)
"'mw = allZ
MJi = allZJ i, i = 0, 1, 2, .,.

N

(Recall that J; are the weights of the
polynomial J(L) in the aggregate supply equation.)

(Y IYP) t = Imjj(dM - Et-1-;dM) t-i
;-0

N

- Igjj(dG - Et-I-;dG)t-i
;-0

(18)

where the coefficients mJi and gli are combinations of the coefficients in equations (1)
through (9) in Appendix 2. '"

gw=a l3 Z
gjj = a l3 ZJ;, i

51

= 0, 1,2, ...

estimate the level of GNP relative to its
potential and
derive the rate of growth of
real GNP from that equation. We do this
because the level specification possesses the
desirable property that the long-run values of
both the level and rate change will be independent of the initial conditions of the
forecast.
After a monetary shock, our real GNP estimates eventually return to their long-run
values. This long-run property does not hold
for conventional reduced-form equations,
which estimate rates of change in real GNP
directly. In such cases, the long-run value of
income equals the initial level of income times
the subsequent rate of change in potential
GNP. As a result, those equations predict a
persistent gap in real output equal to the initial
gap at the time of the monetary shock. By
so, the
specifications
ignore the economic impact resulting from
deviations of unemployment
its natural
rate. Consequently, these specifications may
produce biased estimates of the impact of
monetary growth upon real GNP.
To obtain the reduced form for the inflation
rate, we substitute equations 06.1) and 07.0
into equation (13) in Appendix 3, and collect
terms.
J

K

dP t

=

i-O

-

+ y/YIYP)t-l

Ig dGr-j
i-a 2i

availability of M-lB data and the length of
the estimated lag distribution in the equations.
The estimation period ends in 1978.1, to permit a relatively sizable time span outside the
sample period for assessing the model's performance. The estimation results are shown in
Box 1.
In estimating these equations, we applied a
method suggested by John Scadding and
det.ail(ld in
1. The method enllbl~lS
us to place restrictions on both the steady-state
level.of a variable and its range of change. For
example, we can impose the restriction of the
long-run neutrality of money, with respect to
both the level and growth rate of real GNP.
Similarly, in the inflation equation the restrictions may be imposed that the elasticity of the
inflation rate with respect to the growth rate of
money is unity, and that the level of prices is
consistent with the level of money, given the
demand for money.
In the real-GNP equation, we have added a
lagged GNP-gap term to the reduced-form
specification, equation 18. The equation then
may be interpreted as estimating a rational distributed lag between the dependent variable
and the M andE variables. In addition, in the
inflation equation we have added two variables, D Iand D 2, to capture the possible impact
of Nixon-era wage and price controls. These
same variables, although significant in the
inflation equation, had no significant impact
upon real GNP and are therefore not included
in that equation.

+ c'

N

- I Y2JY/YP)t-I-i
i-I

(9)

where the coefficients are combinations of the
coefficients in the equations (1) to (9) and of
the money-supply and fiscal-policy processes. *
The equation states that the rate of inflation
is determined
1) a distributed lag on current
and past rates of growth in the money supply,
2) a distributed lag on current and past changes
in the Federal surplus, and 3) past values of
l1
the cyclical component of GNP, YIYP.

K

*Im 2i dM t- i = [wIHI(L)
i=O

+ W2 H 3(L) + W4] dM t

Ig 2i dGt - i = [w 1H 2(L)
i=O

+ w2H4(H) + ws] dG t

N

IY2i
i-O

J<.:ulpiric:al Results

Following the above speCifications, we estimated equations for real GNP and the inflation
rate over the sample period 1966.2-1978.1.
The starting date was dictated by the

52

=

qJl

+ (WI + w 2 )k 3 /0 -

WI)

Both the real GNP and inflation regressions
account for over 80 percent of the variation in
the dependent variables. The adjusted coefficient of determination, R 2, is .89 in the case of
real GNP and .83 for inflation. The DurbinWatson statistic (D.W.) indicates support for
the hypothesis of no serial correlation in the
error terms. Thus, on the basis of the relevant
T -statistics, the explanatory variables in each
equation have a statistically significant impact
upon the determination of the dependent
variables.
According to the estimated real-GNP equation, money is neutral in the long run with
respect to the level of real GNP and its rate of
change. These findings follow from several
characteristics of the equation. First, in the
long run, both unanticipated money and unanticipated federal expenditures equal zero. Second, the constant term does not significantly
differ from zero, and the coefficient on the lagged gap term is less than unity, assuring the
stable long-run result of a zero value for the
log of Y IYP.
According to the Scadding method, the
coefficient on the current change in unanticipated money, M t, in the real GNP equation
provides an estimate of the total short-run
effect of such a change. The estimate of .187
indicates that a one-percentage-point increase
(decrease) in unanticipated money growth
leads to a small transitory gain (loss) in real
GNP. Since economic theory does not indicate
an expected value of the transitory impact, we
have left unconstrained the coefficient on the
current value of unanticipated monetary
growth.
The estimates also indicate that unanticipated increases in Federal expenditures, E, will
at first lead to increases in real GNP, but after
14 quarters will have no significant impact
upon either the level or rate of growth of real
GNP. This result follows from the estimated
sum of - .068, which is not significantly
different from zero.
With regard to the inflation equation, we
constrained the coefficient of dM t to be unity,
after testing for the appropriateness of that
constraint. Consequently, in the long run,

changes in money growth are fully reflected in
changes in the inflation rate. The coefficient
on the second difference of money, according
to our estimadon procedure, is equivalent to
the long-run elasticity of the price level with
respect to a change in the money-supply
growth rate. In other words, the coefficient is
equivalent to the long-run elasticity of real
money balances with respect to money (with
the signs reversed) .6
Our estimate indicates that real money balances, in the long-run, will decline by .21 percentage point when money growth increases
by one percentage point each quarter. This
value appears consistent with estimates for the
long-run elasticity of money demand for our
7
sample period. Accordingly, we did not constrain the estimate to take on any particular
value. Together the two coefficients indicate
that the inflation equation is consistent with
the long-run neutrality of money. In the first
instance, changes in the money growth rate are
fully reflected in prices; and in the second, the
price level is consistent with the level of
money, given the demand for money in the
steady state.
Only unanticipated changes in Federal
spending significantly affected the inflation
rate. There was no effect in the long run,
because unanticipated changes are zero in that
case. The results, however, indicate a shortrun or transitory impact from spending
changes which are initially unanticipated.
Finally, the sum of coefficients on the lagged gap measure was not significantly different
from zero, so that we constrained their sum to
that value. The estimated coefficients on the
first difference of the gap indicate that a positive widening of the gap in period t-l will lead
to a small negative effect upon the current
quarter's inflation rate. Thereafter, the positive impact of the lagged-gap values offset the
initial negative effect upon inflation.
Next, consider the response patterns of real
GNP and inflation to changes in the moneysupply growth rate. These patterns may be
obtained from the empirical estimates by
"unscrambling" the estimated coefficients,
according to the method outlined in Appendix

53

54

1. This "unscrambling" may be done either
directly, through algebraic manipulations of
the estimated coefficients - or by obtaining
estimated lag patterns from dynamic multiplier
simulations of the equations.
These computer simulations essentially
solve the estimated equations for a given rate
of money growth, and then repeat the solution
with another rate of money growth exactly one
percentage point higher in each and every
period. The difference between the results in
each period provides the estimate of the
response of the dependent variable (such as
real GNP or the deflator) to the specified
increase in money growth. In these dynamic
simulations, the lagged dependent variables
are solutions of the model after the initial
period.

Real GNP Estimates
Our model has been able to capture the
complete adjustment paths of both the level
and rate of change in real GNP to the change
in monetary policy. This can be seen from the
similarity between the empirical multiplier
estimates (Charts 4A and 4B), and the
expected estimates from the theoretical model
(Charts 3C and 3D).
If we begin, say, with an initial equilibrium
situation in which the level of real GNP is
equal to potential (Chart 4A), an increase of
one percentage point in the money growth rate
will lead to a small initial response in the level
of real GNP (Table 2).
After a rise of seven quarters, ouput reaches
a peak .66 percentage point higher than potential, but it then returns to its potential level

55

cline, and reaches its initial rate after the end
of two years. Following a further decline, the
growth rate increases again in the final phase of
adjustment, settling at its long-run rate of 3.2
percent in about 10 years' time.
With this adjustment pattern, the initial
stimulus to real GNP is almost matched by an
equivalent contraction of real GNP in the final
phases of economic adjustment. As a result,
the monetary change leads to a small but transitory gain in real output. However, in the long
run, these gains disappear as real GNP returns
to its potential path regardless of the rate of
money growth. Moreover, most of the

around the 14th quarter after the money
change. The stimulus to real GNP thus appears
toen<.1within about two years, although the
final adjustment does not end until about ten
years after the initial change.
The growth rate of real GNP follows a cyclical pattern over time in response to a permanent increase in money growth. For instance,
frornan initial position of equilibrium with real
GNP rising at a steady 3.2 percent rate each
quarter, aone-percentage point rise in money
growlhwould raise GNP growth to 3.7 percent
within a half-year of the initial monetary
change. The growth rate then begins to de-

Chart 4
Response of Selected Variables to
Permanent Increase in Money-Growth Rate
Percentage
Points

.8

4A

Real-GNP Gap Multiplier*

.6

.4

.2

r----=====----------

or----.. . . .

-.2

-.4
-.6 I..--""_......._ ......_ ......-""_......_ ......_ ..........._ ......_ ......_L-......I._..L--A
o
10
30
70
20
40
50
60
Period
Percentage

Points
.6

48

Real-GNP Growth-Rate Multiplier**

.4

.2

ol---~--.....,.'--_..::==:::=::JiiiI_---------_
-.2
-.4

-.6
-.8

-......11.-......_

o

10

......_

......_

...._ 1 . . _......._

20

30

....._ . . & . _......_"-.....11...-......_

40

50

60

....._

...

70

Period

'Percentage-point change in level of GNP relative to potential after a permanent one-percentage-point increase in the
money growth rate, measured in natural logs.
"Percentage-point change in growth rate of real GNP after a permanent one-percentage-point increase in money
growth rate, measured in natural logs.

56

stimulative effect of an increase in monetary
growth appears to end within two years of the
initial stimulus.
Our estimates capture the systematic
changes in real GNP, although not the sharp
saw-toothed variations characteristic of this
series (Chart 5). The standard error of the
quarterly estimates of GNP, at annual rates, is
2.92 percent within the estimation period
0962.2-1978.1) and 3.30 percent outside that
period 0978.2-1980.4).8

Percentage
Points
1.8

Inflation Estimates
Our model, again, permits us to estimate the
complete adjustment of the level of prices and
the rate of inflation to a change in money
growth. This can be seen from the conformity
of the estimated lag patterns in Charts 4C and
4D to those anticipated in Charts 3A and 3B.
In the long-run, the change in the rate of
inflation equals the change in the rate of
money growth. By the end of the first year, the
inflation rate exhibits about 50 percent of its

Inflation-Rate Multiplier *

4C

1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
0

10

20

30

40

50

70

60

Period
Percentage
Points
1.4

Real-Money-Balances MUltiplier **

40

1.2
1.0
0.8
0.6
0.4
0.2
0.0
-0.2
-0.4
0

10

20

30

40

50

60

70

Period

*Percentage-point change in inflation rate after a permanent one-percentage-point increase in money growth rate,
measured in natural logs.
**Percentage-point change in level of real money balances after a permanent one-percentage-point increase in money
supply, measured in natural logs.

57

Table 2
ResponseofR. .1GNP to Permanent Percentlilge-Polnt Incr..se In Money-Supply Annul1llGrowthRate

Percentage-Point Change In
Rate of Growth of Real GNP

Percentage- Point Change In
Level of Real GNP
Estimate
Lag

o

Estimate

Lag

.09

25

2

.20
.32

3

.43

4
5
6

.53
.60
.64

7

.66

26
27
28
29
30
31
32

8

.63
.59

1

9
10

11
12
13
14
15
16
17
18
19
20
21

.52
.43
.32
.21
.08

Estimate
Lag

of mil
-.22
-.19
-.16
-.14
-.12
-.11
-.09
-.08
-.07
-.06
-.05
-.03
.00

33
34
35
40
50

o
1

2
3
4
5

6
7
8
9
10

11
12

13

-.40
-.39
-.37

14
15
16
17
18
19
20
21

22

-.33

22

23
24

-.29

23
24

-.11
-.24

-.33
-.38

-.25

Estimate
.38
.46
.48
.46
.39
.30
.18
.05
-.09
-.20
-.29
-.37
-.45

Lag

25

.13

26
27
28
29
30
31
32

.12
.10
.09
.08
.07
.06
.05
.04
.04
.03
.02
.00

33
34
35
40
50

-.48
-.54
-.78
-.56
-.37
-.21
-.08
.03
.10
.15
.18
.15

Table 3
Response of Inflation Rate and Real Money Balances to
Permanent Percentage-Point Increase In Money Supply Annual Growth Rate
Percentage Change in
Real Balances

Percentage Change In
Inflation Rate
Lag

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

Estimate
-.02
-.02
.16
.32
.47
.60

.72
.84
.95
1.06
1.16
1.24
1.33
1.39
1.46
1.49

Lag

16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
35
40
50
60

Estimate

Lag

1.52
1.54
1.49
1.46
1.34
1.37
1.23
1.20
1.17
1.14
1.10
1.07
1.04
1.01
.99
.93
.95
.99
1.00

0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15

58

Estimate

.24
.48
.69
.85
.98
1.07
1.14
1.18
1.19
1.17
1.13
1.07
.99
.89
.77
.66

Lag
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
35
40
50
60

Estimate
.53
.39
.27
.16
.07
-.02
-.08
-.13
-.17
-.20
-.23
-.25
-.26
-.26
-.26
-.19
-.12
-.07
-.05

towards their new long-run value - about .05
percentage-point lower after a one-percentagepoint annual rate of increase in money growth.
Within the estimation period, 1966.21978.1, our equation follows the general
movements in the inflation rate fairly closely
(Chart6). The model makes no adjustment for
supply shocks, other than for the episodes of
price control and decontrol, which sharply
affected short-run inflation estimates. Within
the sample period, the standard error is 1.24
percentage points, at an annual rate, or 22 percent of the mean inflation rate of 5.6 percent.
Outside that period, from 1978.2-1980.4, the
standard error is 1.8 percentage points, at an

ultimate change, and within two years exhibits
a 1OO-percentchange (Table 3). But over the
next two years, it overshoots its ultimate
change by about 50 percent. For instance, with
a one-percentage-point increase in money
growth .associated with an inflation-rate
increase from 7.0 percent to ultimately 8.0 percent, we expect to see inflation rise from 7.0 to
8.0 percent within two years, rise further to 8.5
percent within four years, and then slowly des9
cend to 8.0 percent by the end of 10 years.
Real money balances at first increase
steadily in response to the monetary change,
reaching a maximum at the end of two years
(Chart 4D). Thereafter, they generally decline

Chart 5
Rate of Change in Real GNP
Percent

12.5

Outside
estimation
period

10.0
7.5
5.0
2.5
0
-2.5
-5.0
-7.5
-10.0

1966

1968

1970

1972

1974

59

1976

1978

1980

balances begin to decline -- that is, around the
eighthqllarter after the. initial monetary
change-- the level of output begins to decline,
falling below itspotentialarollndthefifteenth
quarter. The rate of inflation then declines
arollndtheseventeenth· quarter..• Finally, both
realGNP andinflation virtually cornpleteJheir
adjustments around 10 years after the initial
monetary shock.

annual rate, or 20 percent of the meaninflaHon rate of 9.0· percent.
Consistency.ofthe Estimates
Our· estimates of real GNP and inflation
appear generally consistent. .As long as real
money>balances increase, the level of real
GNP also increases. Once the inflation rate
overshoots its long-run value and real money

Chart 6
Rate of Inflation

Percent

16
Outside
estimation
period

14
12
10

8
6
4
2
0
-2

1966

1968

1970

1972

1974

60

1976

1978

1980

UI. Policy Implications
Monetaryp()licy makers often have tried to
counteract the business cycle, with either
stimulative or deflationary policies. In this
paper, we have concentrated upon the effects of
a stimulative policy. For a deflationary policy,
the response patterns for real GNP and inflation will be the same, but with the signs
reversed. Let us consider such a policy especially one where the decrease in money
growth is at first unanticipated.
Within the first year, inflation declines by
about half of the decrease in money growth,
and by the end of two years, by 100 percent of
that change. Some overshooting then occurs,
followed by a gradual and slow adjustment, so
that inflation returns to its long-run value
within 7 to 10 years. Thus, in the long-run, the
permanent decrease in inflation matches the

permanent decrease in the money growth rate.
Our results show a more substantial and
rapid change in inflation than we are
accustomed to expect from standard inflation
models. According to conventionalmoqels,
the initial inflation adjustment to a change in
monetary growth takes about five instead of
two years to complete. However, these standard models do not estimate the complete
adjustment of prices. Asa result, they fail to
capture a period of overshooting, which is
essential if the model is to capture the long-run
effect of money on both the rate of inflation
and the level of prices.
Recognizing this shortcoming, several
authors have recently devised models which
incorporate the long-run neutrality of money
(as we have done), but with methods which
are far more complicated than the Scadding
10
method. Nonetheless, in each case, the
intitial adjustment period for inflation is much
shorter than estimated from the standard
model - from six to eight quarters for the U.S.
(Giddings), and about five quarters on average
for eleven developing countries (Khan).
These results suggest that the inflation
response has been relatively faster than what
has been captured in standard-type estimates.
Our results also indicate that the major contraction in real GNP will be completed within
two years following an unanticipated decrease
in monetary growth. Within another year or
two it will have returned to its initial level.
Thereafter, the level of output will overshoot
and, tracing a cyclical pattern, will return to its
permanent level within about 10 years of the
initial monetary change.
Point A in Chart 7 represents the initial position of the economy, where output equals
potential and where the inflation rate is stable.
In response to a one-percentage point decrease
in monetary growth, which is initially not anticipated, in one year's time inflation decreases
by about .5 percentage points and real GNP
falls .5 percent below what it otherwise would
have been (point 1). By the end of the second
year, inflation declines 1.0 percentage points

Chart 7
Response of Inflation Rate
and Real GNP to a
Permanent Decrease of 1
Percent in Money-Growth Rate
Change in
Inflation Rate (%)

A

o
-0.2
-0.4
-0.6

-0.8
-1.0
-1.2

5

-1.4
-1.6
-B

-B

-A

-2

0

2
A
GNP Gap (%)*

* (GNP-Potential) /Potential

61

billion annually for three years to bring inflationdown by one percentage point, again in
1972 dollars. Similarly, our results indicate a
$27~billion anntialloss during the first 15 quarters after the initial shock, but the loss is partiallyoffsetandis .reduced to· $16 billion
indicated).bytheend.ofthe adjustment period.
Separately, we can compare the results of
two different policy assumptions - holding
moneY growth constant at 7.5 percent a
the averageofthe past three years - or reducing money growth gradually from 6.0 to 3.5
percent over the next half-decade - essentially what the Reagan Administration
assumes. The results, shown in Chart 8, portray
the consequences of the monetary assumptions
but of no other outside shocks.
The policy of constant 7.5-percent money
growth should raise real GNP from 1.5 percentage points below potential in 1980 until it
equals potential GNP by the end of 1983.
Thereafter some cyclical response occurs, producing some over-and undershooting, but not
enough to lead to any recession. The inflation
rate meanwhile should drop to around 7.0 percent by the end of 1982 and thereafter stay
close to its long-run value of 7.3 percent.
In contrast, the policy of gradual reduction
of money growth should hold real GNP below
potential until mid-1988, and after some overshooting, should help the economy reach (and
maintain) potential by 1991. With this
approach, inflation should decline from
around 6.5 percent by the end of 1982 to
around 3.5 percent in 1985, and after some
overshooting, should reach its permanent
level of 3.5 percent in 1991.
The gradualpolicy could lead to $115 billion
less output than the stable money-growth
policy, in 1972 prices - or approximately 6
percent of the average level of potential over
the 1980-91 period. Nonetheless, we may be
able to obtain a gradual reduction in inflation
without having to incur a recession in the process. But this gradual reduction in inflation
generally would be associated with only
moderate rates of real growth - averaging 3.9
percent in 1984 but thereafter remaining close
to its potential rate of 3.2 percent.

and real GNP declines a maximum ofabout .7
percentage points below potential. Thereafter
inflation overshoots its long-run value, while
real GNP begins to approach potential after
temporarily overshooting that level. Between
thethird··alldfourth years, real output .has
returned to • its initial level. Between the
seventh. and tenth years, both the inflation rate
and real GNP virtually attain their permanent
values.
. The cost of a deflationary policy in terms of
lost output occurs within the first four years of
the policy change. After that, real GNP overshoots potential and some gain occurs. On balance, we estimate that the short-run loss of
real GNP exceeds the cumulative gain specifically by a net $16 billion when real GNP
equals $1540 billion (potential in 1981.1) at
point A, in 1972 prices.
George Perry (Brookings Institution) argues
that real GNP would have to decline by $33

Chart 8
Comparison of Inflation
and GNP Gap:
Steady Growth vs. Gradual
Reduction in Monetary Growth
Inflation Rate (%)

10.0
9.0
8.0

I' 7.5% Policy

• 84

7.0

6.0
5.0
4.0
3.0

2.0

87 88

0.0 ................._ ......_ ......_ ......_ ....._ .....-2.0 -1.5 -1.0
-.5
0
.5
1.0
GNP Gap (%)*
* (GNP-Potential) IPotential

62

IV. Summary and Conclusions
the level of output as a percent of its potential.
For both variables, and also for the rates of
change in real GNP and real money balances,
our results indicate a cyclical response to a permanent change in money growth. Notably,
both inflation and real GNP respond quickly to
a change in monetary policy, with the major
stimulative or deflationary phase occurring
within two years of the initial change. Our findings thus conflict with most of the published
literature, which suggests that output and
prices require about five years to respond to a
change in money growth.
Some analysts suggest that it will take a long
time to bring down the inflation rate, and that
we risk an economic recession in the process.
Our results offer an alternative viewpoint.
Changes in monetary growth, at least since the
mid-1960's, apparently have acted fairly
rapidly upon inflation - and hence upon
aggregate demand as well. Thus, since a monetary contraction is likely to bring inflation
down faster than previously anticipated, less of
the brunt of that contraction need be borne by
real GNP, so that a major decline or loss of real
income need not result when we adopt a policy
which gradually reduces monetary growth.

In this paper, we consider the output and
price effects of a permanent increase in the
money-supply growth rate which is at first
unanticipated. Initially, inflation steadily
increases but by less than the permanent
increase in money. During this period, real
money balances expand, providing the
stimulus for increases in real demand and real
GNP.
Yet in the long-run, an increase in money
growth apparently does not affect the level or
the rate of growth of real GNP, at least to a
first approximation. Consequently, the level of
real money balances also should remain
generally unchanged, since these are held in
desired proportion to income. Interest rates
could also be a determining factor, however, at
least in this country. The desired level of real
balances could be somewhat less in the new
situation than before the monetary increases
occurred, because the rate of interest can be
expected to increase with the higher rate of
'inflation.
Our model of economic behavior is consistent with the behavior of real GNP and inflationjust discussed. We have estimated reducedform equations of the model for both the rate
of inflation and the real GNP gap, defined as

63

Appendix I
John Scadding*
Simple Technique for imposing Restrictions on Sums of
PDl coefficients
In estimating polynomial distributed lags,
researchers typically are not so much
interested in the individual coefficients as they
are in certain sums of the coefficients. In many
problems, for example, considerable importance attaches to whether the total sum of
coefficients is unity or not. This appendix is
designed to illustrate a simple method for
estimating directly the sum of coefficients, or
alternately for imposing on it any point restriction. The method illustrated can also be used
to impose or estimate more complicated
restrictions, and an illustration is given in the
example below.
Suppose we take the familiar PDL relationship between money growth (measured as first
differences in the log of money) and inflation
(measured by first differences in the log of
prices):

Thus W o gives the contemporaneous response
of inflation to a one-percentage-point increase
in money .growth, WI measures how much
higher inflation will be in the next period
(compared to the rate before monetary expansion increased), and so on. The last coefficient, wN, measures the steady-state response
of inflation to an increase in the rate of monetary growth. It is usual to inquire whether this
long-run response is unity - Le., whether
ultimately changes in the rate of monetary
expansion are fully reflected in the rate of
inflation. The usual way to answer this question is to estimate (I) and sum the estimated
a's. An alternative is to rearrange (0 in such a
way that W Ncan be estimated directly. To do
that, we intergrate (I) by parts to obtain
N-l

.1logP t = I wj .1 2 10gMt-j + wN':llogM t _ N,
j~O

N

.1 log P t =I aj .1logM t _ j
)~o

, a j = 0, for j ~ N.

(0

Interest usually focuses on how inflation
adjusts to a permanent change in the rate of
monetary growth. The answer to that question
is given by the sequence of coefficients

(2)

2

where .1 denotes second differences. Adding
and subtracting W N from each of the terms in
the first summation yields
N-l

10gP t = I (w j

W N)

-

.1 2 10gM t-j

j=O

N-l

+ wN .1logM t - N+ w NI.1 2 IogMt-j
j=O

N-l

.1logP t = I (w j

-

wN ) .1 2 logMt-j + wN.1logM t

j=O

N-l

= I

)=0

'Senior Economist, Federal Reserve Bank of San Francisco.

64

w.1
j

(3)

2 IogM

I_ j

+ wN.1log Mt;

Define the following coefficients:

Thus it is possible to rewrite the distributed lag
as another distributed lag in second differences
of log M, plus a term in the contemporaneous
growth rate of money whose coefficient is the
sum of distributed-lag coefficients. Hence W N
can be directly estimated; alternatively any
restriction on W N can be imposed simply by
taking the last term in (3) over to the left-hand
side of the question.
To illustrate how the method can be used to
impose more complicated restrictions, consider the question of whether a change in the
rate of monetary expansion permanently
affects the level of real money balances. Sufficient conditions that the level of real balances
be unchanged in the new steady state (i.e. that
the long-run elasticity of the level of prices
with respect to money is unity) are:

v o=

Wo

Next, integrate (3) by parts again to obtain
N-2

1l10gP t = I

j=O

(4a)

(Vj-

v N) 1131 0gM t _ j + wNlllogM t

Hence it is possible to rewrite the distributed
lag as yet another distributed lag, this time in
third differences of log M and two other terms
- a term in contemporaneous money growth,
and a term in first differences of money
growth. The coefficients on these two variables
provide estimates respectively of the long-run
elasticity of the inflation rate (w N) and of the
price level (v N) with respect to money. Alternatively, equation (5) allows assumptions
about either or both of these elasticities to be
easily imposed.

(4b)

65

Appendix 2
Model of Real Output·and Inflation
The structure of the model is concerned
directly with behavior in the goods, money and
labor markets. Each market is characterized by
simplified and highly aggregative relationships, and labor is the only factor market
directly considered. The terms long-run,
steady-state and potential are used
interchangeably.

l:urrent and past changes in real income, F(L)
dYt, and the change in the high-employment
Federal-government budget surplus, dG t. The
expression F(L) is a polynomial so that
F(L)dYt represents a polynomial distributed
lag of the variable dY, and F(L)dYt = fodY t +
f1dY t- 1 + f2dYt- 2 + ... +. Equation (2)
relates changes in real investment expenditures to changes in the real rate of interest,
which in turn is represented by the change in
the nominal rate of interest, R, minus the
change in the expected rate of inflation. Equation (3) expresses equilibrium in the goods
market.
From equations (I) - (3) we derive the IS
function which expresses the equilibrium conditions in the goods market.

List of Variables
S
Total real savings in the nationalincome accounts;
Total real investment in the
national-income accounts;
Federal government real highG
employment surplus, measured as
the ratio of revenues to expenditures;
Real GNP,
Y
Real potential GNP;
YP
Real GNP gap;
Y!yP
Nominal rate of interest;
R
Money supply;
M
GNP implicit price deflator;
P
Unemployment rate;
U
Natural rate of unemployment;
N
Unemployment gap;
U/UN
Expected GNP implicit price
P*
deflator.

dY t =

- B(L) dY t- 1
- a4 (dR t - (dP\+l - dP*t» - asdG t
IS function (3a)

where the weights of the polynomial, B(L),
and the coefficients, a4 and as, are combinations of the coefficients in the structural equations (1) - (3).

(4)
(5)

With the exception of R, the nominal rate of
interest, each of the variables is measured in
terms of its natural logarithm. Therefore, the
change in real GNP, dY, is a measure of the
rate of change in real GNP, and dP is a
measure of the inflation rate. The variables G,
YP, UN and M are exogenous variables.
Goods Market
dS t = F(L) dY t + a 2 dG t
dI t = a3(dR t - (dP\+l - dP*J)
dS t = dI t

Equation (4) states that the demand for real
money balances (dM~ - dP t) is positively
related to current income and declines with
increases in nominal interest rates. Equation
(5) states the equilibrium conditions in the
money market, that nominal money
demanded equals nominal money supplied in
any given period. From equations (4) and (5),
we derive the LM function, which expresses
the equilibrium conditions in this market.

(1)

(2)
(3)

dM t = dP t + a6 dY t - a7 dR t

Equation (1) indicates that the change in
total savings depends upon a distributed lag in

LM function (Sa)

66

Factor Market
(U/UN)t = ag(dP t - dP*t)
+ J(L) (U/UN)t-l
(YIYP)t = a9(UIUN)t

information about labor-purchased items.
Unemployment is linked to levels of output
via the production function, which is represented in the model as a type of Okun's Law
equation, equation (7).
The specification of inflation expectations
completes the model. Our hypothesis, following John Muth's proposal, states that expectations are informed predictions of future
events, based on the available information and
the relevant economic theory at the time the
expectations are formed. This implies that
expected inflation can be represented by the
conditional mathematical expectation of inflation, dP t, based on the economic model and all
the information assumed to be available as of
the end of period (t -1) . Inflation expectations
may then be represented with the following
equations:

(6)
(7)

Equation (6) states that deviations in
unemployment from its natural level are determined by unexpected changes in the current
inflation rate and by past deviations of
unemployment from its natural rate, J(L)(UI
UN)t-l' Since these past deviations of
unemployment can in turn be related to past
unexpected price changes, equation (6) indicates that the economic impact of unexpected
inflation will persist for some time into the
future. The reasoning here is that, in labor
markets, suppliers of labor and of goods
bargain with respect to the expected real price
of the product they supply. Suppliers of goods
initially interpret unexpected increases in
inflation as an increase in the relative price of
the product which is being supplied. This
increases the derived demand for labor, and
places upward pressure on nominal wages.
Labor interprets the unexpected demand for
its services and the increase in its nominal
wage as an increase in real wages. This occurs
initially because labor receives price information about labor-supplied items faster than

(8)

dP\ = Et- 1 dP t
dP\+I = Et- 1 dP t+1

(9)

where the E operator signifies expectations
conditional on information available as of the
end of period (t - 1). This hypothesis regarding the formation of expectations has become
popularly known as "rational expectations."

Appendix 3
Formation of Inflation Expectations
inflation rate, dP t. The expectations operator,
b is then applied recursively to that equation to yield the equations for inflation expectations.
This procedure results in the following
equations. First, the solution for the inflation
rate is,

Before the final equations for the inflation
rate and real GNP can be derived from the
model, we must express the functional forms
IdP t and Et-1dP t +b
for expected inflation,
equations (8) and (9) of the model. These will
then be substituted into the aggregate demand
and supply equations, which in turn can be
solved for the final equations for the inflation
rate and real GNP.
To obtain the specifications for expected
inflation,
IdP t and E t-ldP t+ b we follow a
procedure suggested by Sargent and Wallace
(I 97 5). The first step is to obtain the solution
of the system of equations (8) -0 2) for the

E t-

dP t = wIEt-1dP t + w2Et-IdPt+I
N

+ w3 (YIYP)t-I + rqj(YIYP)t.j
1-2

67

00

where the coefficients are functions of the
parameters of the equations (0-(9):*
Applying the E operator to equation 13, we
obtain,

Et-ldPt+1

i-a

i-O

.N

i=J
00

-vsIv\dG t+Hi + Iv\k l
i-a

N

i-O

where the coefficients are combinations of the
coefficients in equation (13).**

Iqi(Y IYP) (-i
i-2

N

Applying equations (14) and (15) recursively
and then gathering terms yields the solution
for expected inflation,
E,_ldP t = V2 Iv\Et-IdM,+i+ v 3I v\(YIYP)t-l
1=0

I v\I (qJO-w l» (YIYP)t-i
i-2
-vsIv\dGt+i+ Iv\k l
-

i-O

i-a

'-a

- I v\ I (q;lO-wj)) (YIYP)t-i

- Iq/Y IYP) t-l-i + w4E t- 1dM t+1
i-I
wsE t- 1dG'+1 + Co

ooi=O

v 2I V\Et-IdMt+i+1 + V3 I V\(YIYP)t-1
00

Et-IP t = wIEt-IdP t + w2 E t-l dP t+1

+ W3(Y IYP) t-I -

=

i-a

In equations (6) and (7), expected inflation for time t and time t+ 1 formed at time
t-l will depend upon the predictions formed
at time t-l for the exogenous variables, dM
and dG, for all future periods. Particularly
relevant, then, is the process or rule by which
the public forms expectations of these variables. There are a number of alternatives for
specifying such rules or processes. For instance, we may postulate a model which relates
expected future monetary growth and fiscal
policy to a set of predetermined variables relative to the model, or we may choose to postulate an ARIMA process for each variable. In
the latter case, only past values of a variable
are used to predict future values of the same
variable. For now, we assume that the public
forecasts future values of changes in M and G
by considering the past history of these variables.
In addition, we assume that expectations
regarding future policy variables are updated
each period, as new information becomes
available, in accordance with the theorem of
optimal least-squares learning and expectations formation stated by Benjamin Friedman.
This updating process is fully optimal in the
sense of meeting the information-exploitation
assumptions of Muth's rational-expectations
hypothesis. We may write the expectation of
future variables as a polynomial distributed lag

**v = w/(I - WI)
V2 = wJ(1 - w)
V 3 = w/O - WI)
V s = w/O - WI)
k l = colO - WI)

68

of past values of that variable. Expected future
money growth is then specified as follows:

+ V3 I

Et-]dM t = Fo(L) dM t
Et-]dM t+ 1= F 1(L) dM t+ 1
or, in general

vi (y NP) t-I

i-O

N

-

Ivi I (q/O-w l » (YNP)t-2
i-O
i-2

Et-IdM t+j = Fj(L) dMt+j

06.0

where Fj(L) indicates a polynomial in the lag
operator, and j = 0, 1, 2, .... Similar
specifications can be written for the fiscal
variable, dG.
These specifications for expected monetary
growth and fiscal policy may next be
substituted into the expected inflation equations (6) and (7). Expected inflation thus
depends upon linear combinations of past
monetary growth and past fiscal-budget
changes. We may gather terms and write the
expected inflation equations as polynomials in
past exogenous variables and the lagged
endogenous variables, as is done in the following equations.

Et-]P t+ 1 = H 3(L) dM t - HiL) dG t

+ V3 I

vi (YNP)t-1

i-O

N

- I vi I (q/O-wI» (YNP) t-i
i-O

i-2

07.0
Equations 06.0 and 07.0 represent the
final equations for expected inflation. The
model now may be represented by the equations shown in Table 1 of the text and quotations 16.1 and 17.1.

FOOTNOTES
RCBPASS = rate on commercial-bank passbook deposits, annual effective yield;
Y = nominal GNP;
P = GNP price deflator
The long-run elasticity of money demand with respect
to the treasury-bill rate is -.0232. According to that
estimate, and assuming that nominal interest rates in
the long-run fully reflect a change in the money
growth rate, the expected change in real money balances with respect to a change in the level of interest
rates would be .34. Our estimate is .21, which is not
significantly different from .34 at the 1O-percent level
of significance. On the other hand, Throop's estimate
appears lower than Goldfeld's estimate of -.048 for
the long-run elasticity of money demand with respect
to the commercial-paper rate. This implies a .8
elasticity of real money balances with respect to a
change in the level of short-term rates, and indicates
that our estimate may be on the low side, given
Goldfeld's estimate.
8. These estimates were obtained from dynamic
simulations in each sample period, in which only the
initial lagged-dependent variable is the actual value,
and actual money and Federal expenditures appear
as the right-hand side of the equation.
9. Our estimates of the inflation mUltipliers shown in
Table 3 and Chart 4C reflect what I shall call the "full
effect" of a permanent change of 1.0 percentage
point in the money growth rate upon the inflation rate.
By "full effect" I mean that two effects are considered
in deriving those multipliers: (1) the "direct" effect of

1. For similar models, see Thomas J. Sargent and
Neil Wallace and Roque B. Fernandez.
2. For a discussion of rational expectations, see
Benjamin Friedman.
3. For discussion of alternative models of the inflation-adjustment process, see Robert J. Gordon
(1980), George Perry, David H. Resler and Keith M.
Carlson.
4. See Milton Friedman (1969), pages 1 - 14.
5. See Sargent and Wallace for an early discussion
of this point.
6. This is shown in AppendiX 1.
7. From 1960.4 - 1980.1, the money-demand equation estimated in first-difference form by Adrian
Throop, (Federal Reserve Bank of San Francisco) is:
On M1 BIP t) = .00133 + .585 In (M1 Bt-l/P t )
(-1.60)
(6.29)
- .00965 In RTB t
(-1.73)
- .00654 In RCBPASS t
(-1.03)
+ .264 In (YIP t)
(3.72)

IP = .576
OW. = 2.00 S.E. = .00490
The variables are defined as:
RTB = rate on three-month Treasury bills, annual
effective yield;

69

changes in money on the inflation rate, and (2), the
indirect effects of money as they work their way
through changes in the GNP gap (since lagged gap
values also appear in the inflation equation). We
derived these multipliers from dynamic simulation of
both the GNP and price equations. If we do not take
into consideration the indirect effects, we may easily
obtain estimates for the inflation multiplier and the
standard errors associated with those multipliers, as
shown below. The reader will notice that the multipliers are slightly different from those reported in Table
3 in the text. For example, the initial adjustment period
is moved up by one-to-twoqvartersto the seventh
quarter following the initial change in monetary
growth when the indirect effect is not considered.
Also, In the latter Instance, the total length of the lag is
22 quarters rather than about 10 years. When the
indirect effects are considered, then, they add a considerable period of time in which slow adjustment
continues. Importantly, the small size of the standard
errors indicates that the estimated multipliers are
statistically significant, and that the overshooting property of inflation is highly significant.

Period

o
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21

Inflation
Multiplier
-.019
.008
.224
.424
.605
.768
.914
1.042
1.152
1.244
1.319
1.376
1.415
1.437
1.440
1.426
1.394
1.345
1.277
1.192
1.089
1.127

Standard

Error
.098
.098
.078
.062
.050
.043
.041
.042
.044
.046
.048
.048
.048
.046
.045
.045
.048
.055
.066
.082
.102
.105

10. See Gittings and Khan.
REFERENCES
Khan, Mohsin S., "Monetary Shocks and the
Dynamics of Inflation," International Monetary
Fund Staff Papers (June 1980), pp. 250-284.

Carlson, Keith M. "Money, Inflation, and Economic
Growth: Some Updated Reduced Form Results
and Their Implications," Federal Reserve Bank
of St. Louis Review, Vol. 62, No.4, (April 1980).

Laidler, David. "Money and Money Income: An Essay
on the 'Transmission Mechanism,''' Journal of
Monetary Economics 4, (1978), pp. 151-191.

Fernandez, Roque B. "An Empirical Inquiry on the
Short-run Dynamics of Output and Prices,"
American Economic Review, (September 1977),
pp. 595-609.

Lucas, R.E., "Some International Evidence on Output,
Infiation Tradeoffs," American Economic
Review, (June 1973), pp. 326-34.

Friedman, Benjamin M. "Optional Expectations and
the Extreme Information Assumptions of
'Rational Expectations, Macromodels," Journal
of Monetary Economics, 5(1979), 23-41.

Perry, George L. "Inflation in Theory and Practice,"
Brookings Papers on Economic Activity, 1,
(1980).

Friedman, Milton. The Optimum Quantity of Money,
and Other Essays. Chicago, 1969.

Sargent, Thomas J. and Neil Wallace. "Rational
Expectations, the Optimal Monetary Instrument,
and Optimal Money Supply Rule," Journal of Political Economy, (April 1975), 241-254.

Gittings, Thomas A., "A Linear Model of the Long-Run
Neutrality of Money," Staff Memorandum,
Federal Reserve Bank of Chicago, 79-6.

70