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1996 Quarter 2
The Benefits of Interest Rate Targeting:
A Partial and a General Equilibrium Analysis
by Charles T. Carlstrom and Timothy S. Fuerst

MZM: A Monetary Aggregate
for the 1990s?
by John B. Carlson and Benjamin D. Keen

Economic Review 1996 Q2


1996 Quarter 2
Vol. 32, No. 2

The Benefits of Interest Rate
Targeting: A Partial and a General
Equilibrium Analysis


by Charles T. Carlstrom and Timothy S. Fuerst
The authors of this paper explore some of the benefits of interest rate targeting in both partial equilibrium and general equilibrium environments.
They find that an interest rate peg is desirable because such a policy mitigates the distortions that arise in a monetary economy. In order to achieve
the interest rate peg, money growth should be procyclical. This increase in
output variability is actually welfare-improving.

MZM: A Monetary Aggregate
for the 1990s?


by John B. Carlson and Benjamin D. Keen
Deregulation and financial innovation have wreaked havoc on the relationship of traditionally defined money measures with economic activity and
interest rates. In this article, the authors present some tentative evidence
that an alternative measure of money—MZM—has endured these events
reasonably well. MZM is broader than M1 but essentially narrower than
M2, comprising all instruments payable at par on demand. Since 1974,
MZM has exhibited a fairly stable relationship with nominal GDP and with
its own opportunity cost, suggesting that the aggregate has a potential role
for policy.

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The Benefits of Interest
Rate Targeting: A Partial
and a General Equilibrium
by Charles T. Carlstrom and Timothy S. Fuerst

One of the oldest debates in monetary economics concerns the appropriate target for monetary policy. Two distinct camps emerge from
this debate—those who favor interest rate targets and those who favor money growth targets. Poole (1970) first addressed this question
in an aggregate demand framework of the ISLM type. He showed that an interest rate rule is
preferable if money demand shocks are more
numerous than IS shocks, while a money
growth rule is preferable in the opposite case.
Yet, to obtain this answer Poole assumed that
the monetary authorities would choose the
money supply rule that minimized the variability of output. This assumption, however, begs
the question of whether such stabilization is
indeed optimal.
This article revisits Poole’s original question.
It argues that there are clear benefits to interest
rate targeting, independent of what types of
shocks hit the economy. Furthermore, these
benefits arise even though money growth must
be procyclical in order to keep interest rates
constant, which increases the variability of output. The reason a constant interest rate will be
optimal is that interest rates act like a tax on

Charles T. Carlstrom is an economist at the Federal Reserve Bank of
Cleveland, and Timothy S. Fuerst
is an associate professor of economics at Bowling Green State
University and a consultant at the
Federal Reserve Bank of Cleveland.

labor, and constant taxes are preferable to variable taxes. This is true whether the alternative
to an interest rate target is a constant money
growth rule or some general money growth
specification. However, this paper places special emphasis on analyzing Poole’s original
question—the optimality of money growth
versus interest rate rules.
We use both a partial equilibrium model and
a monetary general equilibrium model with
sluggish portfolio adjustments to analyze the
benefits of interest rate targets. The general
equilibrium analysis shows that an interest rate
target will undo the distortion caused by sluggish portfolios. This occurs because, to keep
interest rates constant, the monetary authority
will supply the reserves that would have been
supplied by households in a frictionless environment. Even if private savings cannot respond
to current economic conditions, an interest rate
target will enable output and employment to
respond to them efficiently. Which rule will a
benevolent central banker prefer—a constant
money growth rate or an interest rate peg?
Unlike Poole’s analysis, which suggests that the
optimality of an interest rate rule depends on
the source of the shock affecting the economy,
this paper concludes that an interest rate peg




Supply and Demand for Labor



SOURCE: Authors’ calculations.

will be the benevolent central banker’s choice,
whatever one’s view about the types of shocks
most likely to buffet the economy.
We proceed as follows: Section I sets out a
partial equilibrium model of the labor market in
order to discuss the benefits of an interest rate
peg, and section II does the same for the credit
market. Section III integrates these partial equilibrium analyses into a general equilibrium
framework. Section IV discusses how the economy will behave with both interest rate targets
and money growth targets. It demonstrates that
if the economy is buffeted by supply shocks,
interest rate rules will dominate any other policy
rule. Section V extends this analysis by assuming that the economy is subject to demand
shocks. Section VI discusses further possible
extensions, and section VII concludes.

I. A Partial
Equilibrium Analysis
of the Labor Market

sonable because there is a lag between the time
when workers are paid and when a firm receives payment for its product. This means that
firms cannot use cash from sales of their product to pay their workers, but must borrow funds
in order to obtain the necessary cash. Sales
receipts are then used to repay these loans.
This friction leads to a key distortion in the
economy. Since firms must borrow money to
pay their wage bill, the nominal interest rate
(and hence inflation) acts like a tax on a firm’s
ability to hire workers. For example, assume
that the demand for labor is perfectly elastic,
that is, the marginal productivity of labor is
constant at the pre-tax market wage, Z. Thus,
L hours of work translates into Z * L units of
output, where Z can be thought of as a productivity shock term that is assumed to be random over time. A firm that needs cash to pay
its workers can borrow Z * L /R dollars (where
R > 1 is the gross nominal rate of interest) in
order to generate Z * L units of output after paying off its loan. Defining (1–t) = 1/R, we see
that a nominal interest rate of R translates into
a wage tax of t = 1 – 1/R.
What are the benefits of a constant interest
rate? Such a rate implies that the resulting wage
tax, t, will be constant over time. A constant
money growth rule, by contrast, may imply a
fluctuating interest rate, and hence a fluctuating
wage tax. To understand the conditions under
which a constant interest rate—that is, a constant wage tax—is preferred, see figure 1,
which plots the supply and demand for labor.1
Labor supply is standard and is assumed to
have a constant elasticity of h. The deadweight
loss associated with the CIA constraint is given
in figure 1 by triangle D. The average distortion
from the inflation (wage) tax is approximately2
(1) D = 21 hE [Zt Lt (tt )2 ].
A constant tax rate is usually preferred to a
variable tax rate over time.3 Since positive
nominal interest rates act like a wage tax, this
suggests that constant interest rates will prove
superior to a policy that allows interest rates to

This section develops the partial equilibrium
analogue of the general equilibrium economy
contained in the third section. We investigate a
model economy where money is introduced by
imposing a cash-in-advance (CIA) constraint on
market transactions, so that consumers must
hold cash in order to purchase consumption
goods. We also assume a CIA constraint on the
part of firms, which must hold cash in order to
pay their workers. This assumption seems rea-

■ 1 It may seem peculiar to look at the inflation-tax distortion in the
labor market rather than the money market, but it can be measured in
either. However, one cannot count the distortion in both markets, because
to do so would be double counting.

■ 2 By definition, D L = h w and Lt = htt L t .
Therefore, D » D Ltt Z = Lt Z(tt )2.


■ 3 See Sandmo (1974) and Barro (1979, footnote 7).




Supply and Demand for Loans





SOURCE: Authors’ calculations.

vary. Why one might suspect that constant tax
rates and interest rates are preferable to variable
ones is apparent in figure 1 and equation (1).
The distortion from a tax is triangle D in figure
1 and is thus proportional to the square of the
tax. Therefore, a tax that stays at 15 percent
over time will usually be better than one that
fluctuates from zero to 30 percent. With a constant 15 percent tax, the associated loss is proportional to 15 squared, or 225; however, the
loss with a tax that is either zero or 30 percent
is proportional to either zero (zero squared) or
900 (30 squared). If both of these are equally
likely, the average loss associated with a timevarying tax rate is 450 (versus 225 for a constant tax).

II. A Partial
Equilibrium Analysis
of the Credit Market
Although intuitive, this partial equilibrium
analysis is incomplete. It ignores the general
equilibrium effects that the labor market has on
other markets—and vice versa. For example,
the distortion in the labor market spills over
into the credit market because a higher interest
rate lowers a firm’s demand for labor, which in
turn decreases the firm’s demand for loans.
Thus, these two markets become intimately
linked. The general equilibrium section shows
that this link is crucial if we are to understand
the costs and benefits of interest rate rules.

Before developing this general equilibrium
model, it is useful to discuss the market for
loans, because it is so closely connected with
the labor market. Besides the wage-tax distortion caused by the CIA constraint, another
important friction in the economy is that households can adjust their consumption and savings
decisions only sluggishly in response to new
conditions. This is the so-called “sluggish portfolio adjustment” or “limited participation”
assumption, first proposed by Lucas (1990) and
further analyzed by Fuerst (1992).4 This friction
affects the loan market directly, but, as we will
show, it also spills over into the labor market.
We employ this assumption because it predicts that monetary surprises will increase output and lower nominal interest rates.5 Both of
these predictions are crucial to understanding
how the Federal Reserve operates. For example, if the Fed wishes to lower interest rates
and stimulate economic activity, it increases
money growth. Despite the nearly universal
agreement that faster money growth lowers
nominal interest rates in the short term, very
few economic models generate this prediction.6
However, models with sluggish portfolio
adjustments (households’ inability to immediately adjust their consumption and savings
decisions to shocks) can cause a liquidity
effect. In these models, the key assumption is
that households adjust their portfolios more
slowly than firms do. Christiano, Eichenbaum,
and Evans (1996) present evidence that there is
a liquidity effect and that households do indeed
adjust their portfolios more slowly than firms.
By plotting the supply and demand for loans
(equilibrium in the credit market), figure 2 helps
illustrate why sluggish portfolios may produce
a liquidity effect. The demand for loans slopes
downward, meaning that as interest rates decrease, the quantity demand for loans increases.
This occurs because a rise in the nominal interest rate is equivalent to an increase in the wage
tax; its result is less employment and thus a reduction in the demand for loans. However, the
supply of loans is perfectly inelastic because
sluggish portfolio adjustments imply that the
■ 4 For an eminently readable paper that provides a detailed discussion of this economy, see Christiano (1991).
■ 5 The ability of surprise monetary injections to lower nominal interest rates is called the liquidity effect. For empirical evidence of a liquidity
effect, see Christiano, Eichenbaum, and Evans (1996).
■ 6 Even dynamic optimizing versions of sticky-price models cannot
generate the liquidity effect. While real interest rates may decrease with
monetary expansions, this decline is not large enough to undo the increase
in the expected inflation component of the nominal interest rate.


supply of credit (savings by households) is
predetermined. That is, households cannot
adjust their savings decisions in response to
changes in either money growth (interest rates)
or productivity.
When the Fed increases the money supply,
it injects reserves into the financial system,
thereby shifting the supply of loans outward.
With sluggish portfolios, this results in lower
interest rates, which in turn induce firms to
expand employment and boost output.7 If
portfolios were not sluggish, this increase
would be completely offset because households would save less, thereby shifting the supply of loans inward.
To understand the distortion caused by sluggish portfolios, consider the effects of a positive
productivity shock. A productivity increase (in
figure 1, an increase in Z ) induces firms to hire
more workers. The greater demand for workers
in turn shifts out the demand for loans in figure
2. In an economy without portfolio rigidities,
households respond to a productivity shock by
saving more. Their extra savings increase the
cash that intermediaries have on hand to loan
out to firms, thereby shifting out the supply of
credit (loans) as well.
However, when savings behavior is sluggish,
the supply of credit does not increase. It can do
so only if the monetary authority steps in and
supplies extra reserves, which by assumption
would not be forthcoming if money growth
were constant. The effective supply curve with
an interest rate peg is therefore perfectly elastic
(horizontal) at R. With constant money growth,
however, the supply curve is completely inelastic, so that interest rates must increase substantially with productivity shocks in order to clear
the loan market. With sluggish portfolios, keeping money growth constant is especially costly,
because it implies that interest rates must be
quite variable in order to clear the loan market.
With an interest rate peg, the credit for loans
to firms is supplied by the monetary authority
rather than by the private sector. That is, in
order to keep interest rates from rising, the
monetary authority supplies reserves to the
banking sector, enabling firms to borrow more
and thereby increase their employment. This
allows the economy to respond more efficiently
and quickly to potential economywide shocks,
like productivity shocks. Analogous to revenues
and losses in the labor market, the same variables can be measured in the loan market instead. One can calculate the deadweight loss
from the CIA constraint in either the labor market or the loan market, but not in both.

The next section combines the major features
of the partial equilibrium models discussed
above into a general equilibrium model where
firms must borrow cash to pay their workers,
and households can adjust their savings decisions only sluggishly. The first of these distortions, which arises from the firm’s CIA constraint, implies that if the nominal interest rate is
positive, there will be too little labor supplied
(or, equivalently, too little savings or loans
demanded) in equilibrium. The second distortion results from the sluggish portfolio assumption, which implies that interest rates will vary
too much and that this variability is bad precisely because the interest rate is acting like a
wage tax (or a tax on the demand for loans).
We show that the benefit of an interest rate
peg is that it essentially eliminates the distortion
caused by sluggish portfolios. The real sides of
two economies—one with portfolio rigidities
and an interest rate peg, the other with an
interest rate peg and instantaneous portfolio
adjustments—will be identical. However, there
will also be a cost associated with pegging
interest rates. Because of the precautionary
demand for savings, variability in interest rates
will tend to increase savings. This increase
spills over into the labor market, mitigating the
distortion caused by the CIA constraint. Despite
these costs and benefits, we show that a constant interest rate will still be preferable to a
policy that allows interest rates to vary.

III. The General
Equilibrium Analysis
The model economy consists of four different
types of agents: households, firms, financial intermediaries, and the government. At the beginning of each period, all money in the economy
is in the hands of households, which accumulated it in the previous period from labor, dividend, and interest earnings. Households decide
how much of this money they wish to save
(loan to the financial intermediary) for future
consumption, and how much they wish to pay
to firms in order to consume today. We assume
that households must hold money in order to
purchase consumption goods.
As discussed earlier, portfolio adjustments
are assumed to take time. The simplest way of
■ 7 This is a partial equilibrium story, so we have obviously ignored
the roles of price adjustments and expected inflation, which are crucial to
understanding the whole story. Readers interested in the conditions under
which a liquidity effect arises in a general equilibrium model with sluggish
portfolios are encouraged to see Christiano (1991).


modeling this sluggishness is by positing that
households make consumption and savings
decisions before they identify the various
shocks that buffet the economy. This less-thanperfect flexibility is meant to reflect that continually changing one’s behavior with every bit of
new information would be prohibitively costly.
We first consider the case of productivity
shocks (supply shocks). We then examine the
case where there are shocks to government
spending (demand shocks).
After households make their consumption
and savings decisions, the productivity shock,
Z, occurs and is costlessly observed by everyone.8 Under an interest rate peg, the monetary
authority then injects money into the economy
through the financial intermediary, so that the
productivity shock does not change nominal
interest rates. Therefore, money growth will be
endogenous, responding as necessary to keep
the nominal interest rate from changing. With a
constant money growth regime, there will be a
fixed injection to the financial intermediary,
and interest rates will respond endogenously.
The model’s details are spelled out below.
Since the purpose of this paper is to provide a
simple example of the benefits of an interest
rate peg, we abstract from capital accumulation
and assume particular functional forms for utility and production. In addition, the productivity
shock is assumed to be independently identically distributed (i.i.d.) over time. As Carlstrom
and Fuerst (1995) show, none of these abstractions affects our results.

Preferences are standard in that households
derive utility from consumption,ct , and disutility over labor, Lt , to maximize discounted
expected utility subject to the CIA constraint
and the resource constraint:9

worker’s wage earnings (which are paid in
cash) and the fraction of period t money holdings left after the saving partner visits the financial intermediary to deposit Nt dollars.
The second constraint states that the cash
sources the household carries into t + 1 include
interest on savings, dividends that the household receives from the firm Ft , and dividends it
receives from the intermediary Dt . Since the
household is an atomistic part of the economy,
dividend payments are outside its control and
are equivalent to lump-sum payments. Financial intermediaries’ profits arise because of the
monetary injection they receive. Firms’ profits
arise because a worker’s average productivity is
greater than his marginal productivity. The sum
in parentheses is the cash that is not spent
when the consumption market closes. In equilibrium, this will be zero.

The economy consists of one representative
firm owned by a representative household. The
firm produces one consumption good according to the production function

yt = K + Zt L tD .

The variable L tD is labor demand at time t,
while Zt is the productivity shock, which we
assume to be i.i.d. over time. The unusual
aspect of this production function is K, which
measures the contribution of capital to production and is assumed to be fixed. We have fixed
capital entering additively in the production
function because we wish to capture the
observed phenomenon that labor increases
with positive productivity shocks.10 This feature arises in more complicated models with
capital accumulation, where capital affects the
marginal productivity of labor.


max E 0 t S
b t [ln(ct ) – AL ts ], subject to

Pt Ct < Mt – Nt +Wt L ts


Mt + 1 < Rt Nt + Dt + Ft
+ (Mt – Nt +Wt L ts – Pt Ct ).

The variables Mt , Pt , Ct , Wt , and L ts are the
time t money holdings, nominal price level,
consumption, nominal wage, and labor supply
(or hours worked). The first constraint is the
CIA constraint, which says that consumers must
have enough cash on hand to finance consumption expenditures. This cash consists of the

■ 8 The modeling fiction used is that households consist of a
“worker–shopper” and a “saver” to conduct financial transactions. The
assumption of sluggish portfolios implies either that the saver does not
observe the shock contemporaneously, or that he leaves for the bank
before Z is realized. After Z is realized, the worker–shopper leaves for work
and then purchases consumption goods on the way home.
■ 9 The assumption that the disutility of working is linear in labor
supply is equivalent to assuming that labor supply is indivisible. See
Rogerson (1988) or Hansen (1985) for details.
■ 10 Without this assumption, the income and substitution effects of
a productivity shock will cancel one another out, so that labor supply will
be constant in equilibrium. Interest rates will also be constant, with or
without portfolio rigidities.


Because firms are also subject to a CIA constraint, at the beginning of periodt they borrow enough from the financial intermediary to
finance their nominal labor costs,Wt L tD. Every
firm then uses the proceeds from selling its
consumption goods to pay off the labor loan
that it took out when the period began,R tWt L tD.
Since the firm is owned by the representative
household, it maximizes


5 S 3b

t +1

4 6

Uc,c, tt ++ 11 D subject to (2),
Pt + 1
RtWt L tD

where Dt = Pt yt –
The term in the square brackets above is a
shareholder’s marginal utility of a dollar received at the end of period t. Therefore, a dollar of a dividend received in period t can be
transformed into 1/Pt + 1 units of consumption
in period t + 1, where Uc, t + 1 reflects the household’s marginal valuation of each additional
unit of consumption.

The Financial
There is also a representative but competitive
financial intermediary, owned by the representative household, that is completely passive in
our analysis. It accepts deposits from households, Nt , and receives lump-sum transfers
from the government equal to the seigniorage
the government receives from money creation,
Mt + 1 – Mt , then loans these funds out to firms.
Therefore, in equilibrium, the supply of loans
must equal the demand for loans:
Wt Ht = Nt + (Mt + 1 – Mt ). Because governments
distribute their seigniorage to intermediaries,
intermediaries make a profit, which is distributed to households as a lump-sum payment.11
This dividend payment is given by
(3) Ft = Rt (Mt + 1 – Mt ).

The Monetary
For most of this section, we consider two different operating procedures for the monetary
authority. The first is pursuit of an interest rate
target, where reserves are supplied to the banking sector in such a way that the interest rate in
the economy is constant at R. Note that money
growth, Gt = Mt + 1/Mt , is not constant under this
procedure and responds endogenously to support the interest rate target. The second operat-

ing procedure that we analyze, money growth,
Gt = G, is constant. In this case, the interest rate
R t is not constant and will respond endogenously to productivity shocks.

In equilibrium, the labor (4), loan (5), and
goods (6) markets must all clear and the CIA
constraint (7) must be satisfied.

Lts = L Dt = Lt


nt + Gt – 1 = wt L Dt


Yt = K + Zt Lt = Ct


ptCt £ 1 – nt + wt Lt ,

where wt = Wt , pt = Pt , and nt = Nt .12
Since this model does not include capital,
equation (6) states that the goods market clears
when consumption equals output. Equation (7)
is the household’s CIA constraint which, when
combined with (5), states that, in equilibrium,
tomorrow’s money stock must equal the value
of consumption today.
Equilibrium also consists of households
maximizing utility13

A = p Ct
t t

and firms maximizing profits

Zt .
pt = Rt

This last condition says that the equilibrium
real wage rate will equal the marginal productivity of labor deflated by the gross nominal
■ 11 Therefore, revenues from money creation are essentially redistributed to households in a lump-sum manner instead of being used by the
government to help finance deficit spending. This assumption is made for
simplicity and does not affect the results of our analysis.
■ 12 As long as nominal interest rates are strictly positive, that is,
R > 1, (7) will be satisfied with equality. All equations with nominal variables are divided by the beginning-of-period money supply so that they are
■ 13 There is actually one more equation that is necessary in equilibrium. This is the household’s intertemporal first-order condition, which
determines its choice of nt . After simplification, this first-order condition is
Es(G1 ) = bEs (G G t ). For the sluggish portfolio model, s = t – 1, since
t t +1
savings nt are chosen at time t – 1. With fixed capital and independent
technology shocks, this implies that savings will be constant, nt = n . With
flexible portfolios s = t, indicating that nt can be chosen conditional on
time t innovations.


interest rate; that is, the real wage equals the
after-tax marginal productivity of labor. This
equation also gives the demand curve for labor.
Combining (5), (6), (7), and (9) implies
the following expression for equilibrium

Ct =

1 – Rt st

nt +Gt – 1
where st =
, Rt = R for an interest
rate peg, and st = s when money growth rates
are pegged.
The variable st is interpreted as the share of
the money stock held by the intermediary. As
the next equation indicates, this share will
determine equilibrium labor, and thus output,
for the economy. Using (5) and (8) gives the
following expression for labor in equilibrium:

Lt =

st .

The disadvantage of letting money growth
be constant is apparent in (11). With sluggish
portfolios and i.i.d. technology shocks, n is constant (see footnote 7). Therefore, when money
growth rates are pegged, the share of money in
the hands of the intermediary will also be constant, st = s . This implies that with constant
money growth, labor will also be constant.
However, with an interest rate peg, money
growth is endogenous, so that the share of
money held by intermediaries is not constant.
The next section analyzes how money growth
must respond in order to keep interest rates

IV. Interest Rate
Targets versus
Money Growth
The Benefit of an
Interest Rate Peg
In order to understand how money growth will
behave to support an interest rate peg, combine (6), (10), and (11) to obtain the relationship between the share of cash held by intermediaries, st , and productivity:
(12) st =

Zt – AK R .
Zt R

To keep nominal interest rates constant,
the share of cash held by financial intermediaries must increase as productivity rises. Then,
from the definition of st , money growth must
also increase with productivity (since nt = n ).
Equation (12), however, will hold regardless
of whether portfolios are rigid. The only difference between an economy with portfolio rigidities and one without them is how the increase
in st is achieved. With sluggish portfolios, since
savings n are predetermined, the private sector
cannot supply the credit necessary to make this
occur. Therefore, in order to keep interest rates
constant, the monetary authority must step in
and supply reserves to the banking system,
which lowers the real rate of interest. In appendix 1, we show that with portfolio rigidities,
money growth (G tpr ) and savings will be of the
following form:
b ,
G tpr = a + Zt
where a, b > 0 and ntpr = nss .
Without portfolio rigidities, private savings
are not fixed; that is, they can respond to current economic conditions. This reverses the role
of private savings versus government credit creation. When there are no portfolio rigidities
(npr), money growth G tnpr is constant, while private savings respond to productivity increases:
G tnpr = Gss and ntnpr = c – Zd ,

where c, d > 0. The relationship between the
two economies is E (ntnpr ) = nss , E ( G pr ) = G .14


The important variable governing the economy’s behavior is st , the share of cash held by
financial intermediaries. With an interest rate
peg, this share is the same regardless of whether portfolios are sluggish. Therefore, from equation (11) we know that hours worked will also
be the same. Since the share of cash held by intermediaries increases with positive productivity
shocks, equilibrium labor will respond quickly
and efficiently to technology shocks whether or
not portfolios are sluggish. The only difference
between the two economies is whether the private sector or the government is supplying the

■ 14 With flexible portfolios, there are many possible money growth
rules that support an interest rate peg (see footnote 13). Another rule that
will support an interest rate peg is i.i.d. money growth shocks.


credit.15 Without portfolio rigidities, a constant
money growth rule can support an interest rate
peg. Households are now supplying the intermediary with the savings that the monetary
authority supplied when portfolios were rigid.
The advantage of an interest rate peg is that
it eliminates the distortion caused by sluggish
portfolios. However, it does not eliminate the
distortion caused by the CIA constraint, which
persists as long as nominal interest rates are
positive. With a constant money growth rule,
both distortions will be present. Despite this,
however, we are in a second-best environment
and cannot conclude that an interest rate peg
will necessarily dominate a constant money
growth rule. The reason is that sometimes two
distortions are preferable to one (for example,
if one distortion mitigated the other). Indeed,
we will show that this occurs to a limited
extent: Variable interest rates increase savings,
partially mitigating the distortion caused by the
CIA constraint.
We do know, however, that the Friedman
rule of setting the nominal interest rate to zero,
R = 1, will be unambiguously better than a
money growth rule or any other rule that
achieves a zero nominal interest rate on average. This is because all distortions in the economy are eliminated when the nominal interest
rate is pegged to zero.

Portfolios: Constant
Money Growth
versus Constant
Interest Rates
When money growth is constant, equilibrium
will still be characterized by equations (10) and
(11) above. The difference is that in equation
(12), st , the share of cash in the hands of financial intermediaries, will be constant, while the
nominal interest rate will vary. With constant
money growth and sluggish portfolios, this
share is also constant, since neither money
growth nor private savings can change:

Rt =

sZt + AK

This equation shows that with constant
money growth, interest rates and technology
shocks covary positively with one another. A
rise in productivity increases loan demand,
which in turn increases interest rates, because
credit is fixed. Equation (11) tells us that interest
rates will increase until equilibrium labor does
not change. Labor’s inability to respond to

technology shocks will prove especially costly.
An equivalent way to look at this cost is through
the sharp interest rate movements required to
ensure that the loan market always clears.
Under an interest rate peg, labor can respond
to productivity changes because money growth
is procyclical. However, for the same reason,
many economists and policymakers believe that
an interest rate peg would be counterproductive. They reason that if money growth were
procyclical, output (and hence consumption)
would also be more variable. They consider this
undesirable because, holding everything else
constant, consumers prefer a less variable consumption stream.
Yet everything else is not held constant.
Allowing labor to respond efficiently to productivity shocks may increase the variability of
consumption, but it also increases average consumption. To see this, assume that the average
distortion is the same for an interest rate peg as
it is for a money growth peg. That is, we assume that 1/R = E (1/Rt ) or, equivalently, that
E(st ) = s (from equation [12¢]).
From (10) and (12¢), the standard deviation
of consumption when interest rates are pegged

sR =

sZ .

From the goods-market-clearing condition,
the standard deviation of consumption when
money growth is constant equals

sG = A Z .

Since s < 1/R, it is easy to see that consumption is more variable under an interest rate
peg.16 This occurs because money growth is
allowed to move with output when interest
rates are constant, thus increasing the variability
of both output and consumption. Why is an
interest rate peg beneficial under these circumstances? Mean consumption will also be higher
under an interest rate peg than it is with constant money growth.

■ 15 If all real variables are the same, the real rate of interest will
also be the same. Since nominal interest rates are the same by assumption, the expected rate of inflation is also the same for an economy with
and without portfolio rigidities. Yet with portfolio rigidities, money growth
increases with productivity shocks. However, this increase leads to a onetime rise in the price level and does not affect “expected” inflation, since
with portfolio rigidities, the expectation is formed prior to realization of the
productivity shock.
■ 16

From (12), we know that s = 1/R – AKE (1/ Zt ). This implies

that s < 1/ R .


From equation (6), the goods-market-clearing
condition, we obtain
(15) EtC tR – E tC Gt = cov(LtR, Zt ).
Average consumption is higher under an interest rate peg precisely because labor responds
optimally to technology shocks. Therefore, the
same economic force that increases output’s
variability when interest rates are pegged also
increases average consumption. With constant
money growth, however, labor supply is constant. Variable labor is preferred because it allows workers to truncate the effect of bad
shocks by working less and to accentuate the
effect of good shocks by working more.
Despite increased variability in consumption,
households would gladly trade off this extra
variability for the extra consumption it provides
on average. Using (13) we have
(16) EU R – EU G = ln ( 1 ) – E ln( 1 ) > 0.17
This expression is positive, since utility is
concave and, by assumption, E (1/Rt ) = 1/R. Recalling that 1/Rt = (1 – tt ), this expression is the
general equilibrium equivalent of the result that
a constant tax rate is preferred to a variable one.
To compare an interest rate peg with a constant money growth rule, something must be
held constant across the two regimes. The
analysis above assumes that the average distortion is the same for both economies. An alternative variable that could be held constant
across both regimes is the amount of seigniorage collected under each. Although 1 – 1/R
measures the distortion in the economy, the
effective rate at which taxes are collected is
1 – 1/G.18 These two differ because, even if
inflation is zero, there still exists the distortion
caused by workers’ inability or unwillingness to
obtain direct payment in real goods after production. Therefore, an alternative way to compare constant money growth rates and constant
interest rates is to choose money growth so that
1 .
G = bE (Rt – 1) = E (Gt ) = bR This is equivalent to setting interest rates in the two economies to be equal on average. In appendix 2, we
show that for any two policies in which average
seigniorage is the same, a constant interest rate
will be preferred to a variable one.19 As a special case, this implies that an interest rate rule is
preferred to a constant money growth rule.
The intuition about the advantages and
disadvantages of a constant money growth
rule versus a constant interest rate rule is this:
The cost of a money growth rule is that with

sluggish portfolios, it greatly increases interest
rate variability and thus the variability of the
equivalent wage tax. However, there is also a
benefit to having a constant money growth rate,
that is, letting interest rates be variable: Since
interest rates are the same on average, the
inverses of the interest rates are not the same; in
particular, 1/R > E (1/Rt ). Therefore, to obtain
equal revenue, the average distortion is greater
with an interest rate peg. Variable interest rates
help mitigate the distortion caused by the CIA
constraint, because they increase savings. From
equation (12), we derive E (st ) > s or nG > n R.
This increase in savings spills over into the labor
market, implying more employment, thus mitigating the distortion caused by the CIA constraint. Unless this distortion is extremely large
(R > 2), the gains from reducing it are less than
the potential gains from stabilizing interest rates
and hence wage taxes.

V. Interest Rate
Rules and
Spending Shocks
Up to this point, our analysis has assumed that
all shocks to the economy are productivity
shocks. Poole’s original study suggested that an
interest rate rule is preferred when money demand shocks are more numerous than IS
shocks, while a money growth rule is preferred
when IS shocks are more numerous. The meaning of IS and LM shocks is ambiguous in general
equilibrium models. Nonetheless, one might
expect an interest rate rule to be desirable, because we assume that all shocks to the economy are supply shocks.

■ 17 Since E (st ) = s , equilibrium labor is the same on average.
Therefore, given the assumption that utility is linear in leisure, we are simply left with the difference in the utility from consumption, which from (13)
simplifies to (16).
■ 18 We define seigniorage for the two policies in terms of how
many labor units the government can hire with the revenue. This is
because we think of the government as using seigniorage to hire labor in
order to produce a public good. Therefore, seigniorage (in labor units)
equals (Mt + 1 – Mt )/Wt = (Gt – 1)/(A *pt *Ct ) = (Gt – 1)/(A *Gt ). If government production is not subject to the same high-frequency technology
shocks as the private sector, the average amount of public goods produced
will be the same for any two policies where E (1/Gt ) is the same for both
policies. For simplicity, however, the actual model in the text continues to
assume that these revenues are given right back to the households as a
lump-sum transfer. That is, the government robs Peter to pay Peter.
■ 19 Actually, an interest rate target will be preferred only if R < 2.
That is, the nominal interest rate must be less than 100 percent annually.


To analyze the effect of demand shocks, we
introduce government spending shocks into
our framework.20 The question now is whether
a benevolent monetary authority should accommodate government spending shocks to support an interest rate peg. The answer is yes.
Government spending that is financed with
lump-sum taxes can be introduced quite simply by redefining output and consumption as
yt = (K + ess ) + ZLt
Ct = Kt + ZL t ,
where Kt = (K + ess ) – et .
The only difference in the definition of consumption is that K is no longer constant but
can vary randomly over time. In particular, we
assume that Kt is i.i.d. over time, which corresponds to the assumption that government
spending shocks are i.i.d. A large value of K is
equivalent to government spending below its
mean (et < ess ), while small values of K represent government spending shocks above its
mean (et > ess ).
The first-order conditions are the same as
before, except that in equations (10)–(12), Zt
is assumed to be constant while K is allowed
to vary:
(17) Ct = 1 – R s ,
t t
nt + Gt – 1
where st =
, Rt = R for an interest rate
peg, and st = s when money growth rates are

Lt = At


Rt =

(19¢) st =

(money growth rule)
sZ + AKt
Z – ARKt
(interest rate rule).

With a money growth rule, interest rates
increase to clear the loan market so that equilibrium labor is constant once again. When
interest rates are pegged, however, labor will
increase with positive government spending
shocks (K is small). This increase is brought
about as the money supply increases in order
to keep the interest rate from rising. An interest
rate peg will still undo the distortion caused by
sluggish portfolio adjustments.
To understand the dynamics of the model, it
is useful to look at the labor market again. The

demand curve for labor, given by equation (9),
is completely elastic at the marginal productivity of labor deflated by the nominal interest
rate, Z /Rt . Labor supply is obtained by combining (8) and (6). For a money growth peg,
labor supply equals
1 (wt ) – Kt .
(20) L ts = As
A positive shock to government spending
(small K ) has the immediate impact of reducing today’s private consumption relative to
tomorrow’s. As the marginal utility of consumption rises, workers want to increase the number
of hours worked in order to boost their consumption. Thus, labor supply (20) shifts outward. This increases firms’ demand for both
labor and loans. In order to clear the loan market, interest rates are driven up, thereby shifting
labor demand (9) down. In equilibrium, the
nominal interest rate increases until the real
wage in (20) declines, so that equilibrium labor
does not change.
Therefore, with a money growth rule, output
(private consumption plus government spending) is constant, implying that private consumption is crowded out completely. With an interest rate peg, however, money growth increases
in order to prevent the nominal rate from rising
(19¢), thereby allowing both labor and output
to increase. Combining (2) and (19), private
consumption is constant (C tR = Z ), so that
equilibrium output rises by the amount of the
increase in government spending.
If we choose an interest rate target such that
Est = s , it is easy to see that mean consumption
is the same with either operating target. But an
interest rate target is preferred, since private
consumption is less variable (that is, constant).
However, equation (16) will still hold, implying
that an interest rate target will be preferred to
any other rule where 1/R = E (1/R t ). As with
productivity shocks, seigniorage is higher for a
money growth peg if 1/R = E (1/R t ). However,
as appendix 2 makes clear, if 1/G = E (1/Gt ), an
interest rate rule will be preferred to a money
growth peg.

■ 20 In some ways, it is misleading to call government spending
shocks “demand shocks,” since they act like a drain on resources.


VI. Extensions
The foregoing analysis illustrates an important
implication of an interest rate target: It completely eliminates the distortion caused by
households’ inability to readjust portfolio holdings quickly following either technology or
government spending shocks. But there is
nothing special about these shocks. The result
of this analysis would be true for any type of
shock, including preference shocks. For example, the same arguments would apply if A or
even b were allowed to vary over time.
We also assume that these shocks are i.i.d.
over time. In an earlier paper (Carlstrom and
Fuerst [1995]), we show that this assumption is
also unnecessary. Under a money growth rule,
consumption and labor will depend on last
period’s shocks and not on today’s innovations. In contrast, an interest rate rule will once
again allow labor and consumption to respond
to today’s information. As before, this option
value will be welfare-improving.
The other assumption used in our model —
that portfolios are rigid for exactly one period
—is also nonessential. Suppose that households adjust their portfolios slowly because of
convex adjustment costs, as in Christiano and
Eichenbaum (1992). Equation (12¢) will still
determine the share of cash held by intermediaries. Therefore, labor and output will also be
the same. The only difference will be how fast
money must grow in response to various
shocks in order to support the interest rate target. Besides allowing the economy to respond
efficiently to current shocks, the interest rate
rule also has the advantage of enabling households to avoid the costs associated with adjusting their nominal portfolio holdings.
Yet monetary authorities typically do not
keep interest rates constant over the course of
a business cycle. One reason often given is that
procyclical money growth may make output
more variable, but it has already been refuted in
this paper: It is efficient to allow the economy
to respond to shocks, although output variability increases. A second reason is fear of the
long-run inflationary consequences of an interest rate peg. In the model presented here, longterm inflation is pinned down by the nominal
interest rate, but short-term inflation can be
quite variable under an interest rate peg. The
long-run inflation rate will be pinned down by
Fisher’s equation. The real federal funds rate has
averaged approximately 2 percent per year
since the beginning of the century; thus, if one
wants inflation to average zero over time, one
should choose a funds rate peg of 2 percent.

Similarly, if one wants inflation to average 3 percent, the nominal interest rate peg should be 5
percent. As for increased short-run inflation variability, it is far from clear why this is costly.21
According to one argument, there are costs
to changing prices, so stable prices would be
beneficial. If these costs result simply from having to reprogram price scanners and change
price tags on products, it is uncertain that prices
will change more frequently with variable inflation, given that inflation is positive. In addition,
similar savings are associated with an interest
rate target, since it has the advantage of allowing households to avoid the costs associated
with adjusting their nominal portfolio holdings.

VII. Conclusions
This paper explores some of the benefits of
interest rate targeting. An interest rate peg is
desirable because such a policy eliminates any
distortion caused by sluggish portfolios. That is,
an interest rate peg allows labor—and thus
output and consumption—to respond optimally to economic shocks. An equivalent way
to think about the benefits of an interest rate
peg is that it minimizes the “inflation tax” distortion. Nominal interest rates are a tax on noninterest-bearing assets and mimic the effect of
wage taxes. With sluggish portfolios and constant money growth, interest rates can be quite
variable. Eliminating this variability is welfareimproving.
Our analysis also suggests that, in order to
achieve an interest rate peg, money growth
should be procyclical. This implies that the variability of output will also be higher when interest rates are pegged. Despite popular wisdom
to the contrary, this increase in variability is
optimal. With productivity shocks, this is so
because mean consumption is higher. With
government spending shocks, it is so because,
although output is more variable, private consumption is less variable.

■ 21 It is obvious why increased inflation uncertainty would be costly.
However, inflation would not be more uncertain, since money growth, and
hence inflation, would respond to publicly observed shocks. If nominal
wage contracts had been made prior to these shocks, this variability would
have real costs.


Appendix 1

From footnote 13, we obtain

Rigidities and
an Interest
Rate Rule


Using the definitions of nt , st , and equation
(12) yields

With portfolio rigidities, money growth (Gtpr )
and savings will be of the form
Gtpr = a + Zt

where a, b > 0 and ntpr = nss .
Given that money growth is of this form,
using the first-order condition for nt (footnote
13), we obtain
Et – 1 ( G 1

1 = 1 .

) = Et – 1 (a + Zt b+ 1 ) = bR1 .

t +1

This expression uses the assumption that
technology shocks are i.i.d. Taking a secondorder approximation, we obtain
1 ,
(A1) a + Zb + b2 sZ2 = bR

where Z and sZ2 are the mean and variance of
Zt , respectively.
From equation (15), the definition of st ,
and our assumed form for money growth,
we obtain
(A2) 1 + (nss – 1)a + (nss – 1)b = 1 – AK
Using the method of undetermined coefficients, we have
a =

(R – 1)
bR [(R – 1) + RAK (1 + sZ2 )]

b =

b[(R – 1) + RAK (1 + sZ2 )]

nss = 1 + b(1 – R ) – bRAK (1 + sZ2 ).

No Portfolio
Rigidities and an
Interest Rate Rule
If portfolios are not fixed, we assume that
money growth and savings have the following
Gtnpr = Gss and ntnpr = c – Z
where c, d > 0, E (ntnpr ) = nss , and E 1pr = 1 .



( ) = R1

(A4) 1 + (c – 1) – d 1
Gss Zt

– AK .

Using the method of undetermined coefficients, we have
c = 1 + b(1 + R )
d = – bRAK
Gss = bR.
Therefore, E (ntnpr ) = nss , and E 1pr = 1 ,
as the text of this paper asserts.




Appendix 2


The Desirability
of an Interest
Rate Peg

Barro, R.J. “On the Determination of the Public Debt,” Journal of Political Economy, vol.
87, no. 5, part 1 (October 1979), pp. 940–71.

This appendix shows that if seigniorage is on

Carlstrom, C.T., and T.S. Fuerst. “Interest
Rate Rules vs. Money Growth Rules: A Welfare Comparison in a Cash-in-Advance Economy,” Journal of Monetary Economics, vol.
36, no. 2 (November 1995), pp. 247–67.

average equal, interest rate rules will dominate
a money growth rule. Equal revenues imply
E ( 1R ) = G1 , or E (Rt ) = R.


Christiano, L. “Modeling the Liquidity Effect of
a Monetary Shock,” Federal Reserve Bank of
Minneapolis, Quarterly Review, vol. 15, no. 1
(Winter 1991), pp. 3–34.

Money Growth Rule:
1 AK
s =R – Z
s ~ 1 + Rr3 – AK – AK3 sZ2 .

( )

Interest Rate Peg:
st = 1 –
E (st ) ~ 1 – AK – AK3 sZ2 .



We know that consumption is equal to
C Rt = Z t
Ct = t

, and M. Eichenbaum. “Liquidity
Effects and the Monetary Transmission Mechanism,” American Economic Review, vol. 82,
no. 2 (May 1992), pp. 346–53.
, and C. Evans.
“The Effects of Monetary Policy Shocks: Evidence from the Flow of Funds,” Review of
Economics and Statistics, vol. 78, no. 15
(February 1996), pp. 16–38.
Fuerst, T.S. “Liquidity, Loanable Funds, and
Real Activity,” Journal of Monetary Economics, vol. 21, no. 1 (February 1992), pp. 3–24.

and labor is Lt = st .
The difference in utility is therefore
EU Rt – EU Gt = E ln(Rt ) – ln(R ) + s – E (st )



» 1 3 – 1 2 sR2 > 0.
If R < 2, that is, if the nominal interest rate is
less than 100 percent, then an interest rate peg
is preferred to a money growth peg. Actually, a
stronger result holds. Nothing in the proof
assumes that money growth is constant. The
proof compares an interest rate peg to a policy
where the interest rate varies (with average revenues in labor units equal). An interest rate peg
will be preferred to any other policy unless the
distortion caused by the CIA constraint is
extremely large.

Hansen, G.D. “Indivisible Labor and the Business Cycle,” Journal of Monetary Economics,
vol. 16, no. 3 (November 1985), pp. 309–27.
Lucas, R.E., Jr. “Liquidity and Interest Rates,”
Journal of Economic Theory, vol. 50, no. 2
(April 1990), pp. 237–64.
Poole, W. “Optimal Choice of the Monetary
Policy Instrument in a Simple Stochastic
Macro Model,” Quarterly Journal of Economics, vol. 84, no. 2 (May 1970), pp. 197–216.
Rogerson, R. “Indivisible Labor, Lotteries, and
Equilibrium,” Journal of Monetary Economics, vol. 21, no. 1 (January 1988), pp. 3–16.
Sandmo, A. “A Note on the Structure of Optimal Taxation,” American Economic Review,
vol. 64, no. 4 (September 1974), pp. 701–06.


MZM: A Monetary
Aggregate for the 1990s?
by John B. Carlson and Benjamin D. Keen

The Humphrey–Hawkins Act of 1978 requires
the Federal Open Market Committee (FOMC) to
specify annual growth ranges for money and
credit early each year. These ranges are reconsidered at midyear, and preliminary ranges are
specified for the upcoming calendar year. In
the past, financial market participants paid
close attention to the announcement of the
monetary aggregate growth ranges in order to
assess the intentions of the FOMC, the policymaking arm of the Federal Reserve System.
Large deviations from range midpoints were
often associated with policy actions designed to
bring money growth back to its intended path.
In recent years, however, the reliability of
various money measures as useful indicators on
which to base policy has become seriously
compromised. Consequently, the role of money
in policy decisions has greatly diminished. In
July 1993, Federal Reserve Chairman Alan
Greenspan reported that “... at least for the time
being, M2 has been downgraded as a reliable
indicator of financial conditions in the economy, and no single variable has yet been identified to take its place.”1

John B. Carlson is an economist at
the Federal Reserve Bank of Cleveland, and Benjamin D. Keen is a
graduate student of economics at the
University of Virginia. The authors
thank Thomas Hall, Robert Hetzel,
Dennis Hoffman, Robert Rasche, and
E.J. Stevens for helpful comments
and suggestions.

The breakdown of M2 as a monetary policy
guide may sound familiar to those who have
followed policy closely over the past two decades.2 In the 1980s, the relationship between
M1 and the economy became questionable.3 As
evidence grew that the aggregate had become
an unreliable indicator, policymakers turned
their attention to M2, which appeared to be
immune to the effects that had undermined M1.
Recently, in response to the M2 breakdown,
some analysts have been monitoring MZM, a
measure of money that includes assets redeemable at par on demand. Interestingly, the relationship between MZM and economic activity
appears to have stabilized in recent years, suggesting that the aggregate has a potential role
■ 1 See 1993 Monetary Policy Objectives: Summary Report of the
Federal Reserve Board, July 20, 1993, p. 8.
■ 2 For a complete analysis of the breakdown of M2, see Miyao
■ 3 Although Hoffman and Rasche (1991) present evidence that M1
continued to have a stable long-run relationship with interest rates and
income throughout this period, no short-run relationship was found to be
sufficiently reliable for policy. Lucas (1994) also presents some evidence
of a stable M1 demand relationship using annual data from 1900 to 1985.




Measures of Money
M1 =

Demand deposits
Other checkable deposits
Traveler’s checks

M2 =

Savings deposits (including MMDAs)
Small time deposits
Retail MMMFs


Institutional MMMFs
Small time deposits

M3 =

Large time deposits
Institutional MMMFs

for policy. This article describes MZM, discusses
its relationship with economic activity, and presents evidence that it has maintained a stable
relationship with nominal GDP and interest
rates. Some implications for MZM’s usefulness
as a policy guide are also briefly discussed.

I. What Is MZM?
Poole (1991) first coined the term MZM when
he proposed a measure of money encompassing all of the monetary instruments with zero
maturity. He based this distinction on Friedman
and Schwartz’s (1970) principle that money is a
“temporary abode of purchasing power.” Assets
included in MZM are essentially redeemable at
par on demand, comprising both instruments
that are directly transferable to third parties and
those that are not (see box 1). This concept
excludes all securities, which are subject to risk
of capital loss, and time deposits, which carry
penalties for early withdrawal. Motley (1988)
had earlier proposed such a measure, but
called it nonterm M3.
On the spectrum of monetary aggregates,
MZM is broader than M1 but essentially narrower than M2. Like M2, it encompasses M1,
savings deposits (including money market
deposit accounts [MMDAs]), and retail money
market mutual funds (MMMFs). It does not,
however, include small time deposits (such as
retail certificates of deposit), which are in M2.
On the other hand, MZM does cover institutional MMMFs, while M2 does not.4 In sum,

MZM includes all types of financial instruments
that are, or can be easily converted into, transaction balances without penalty or risk of capital loss. The MZM measure that we use in this
paper does not include overnight wholesale
repurchase agreements (RPs) or overnight
eurodollars, components of the originally proposed measure.5

II. Why MZM?
One of the basic motives for holding monetary
assets is uncertainty. Inventory-theoretic models
of money demand such as those of Baumol
(1952), Tobin (1958), and Miller and Orr (1966)
stress the uncertainties related to cash flow.
Earlier, Keynes (1936) had noted the importance of uncertainty regarding future interest
rates as a determinant of money balances. In
proposing the nonterm distinction for a money
measure, Motley states that “if there were no
uncertainty about future rates of interest, the
present and all future values of securities also
would be known, and hence an investor would
have no incentive to hold money.” Holding
money is thus a hedge against potential capital
losses if an unanticipated need for liquidity
occurs. The demand for money arises because
wealth holders cannot anticipate their transaction needs in the face of uncertainty.
Motley also discusses the importance of
transaction costs in exchanging non-money
assets for money. These costs include not only
brokerage fees, but also the implicit costs associated with inconvenience, sometimes called
shoe-leather costs. Uncertainty about the future
need for liquid funds thus creates incentives
apart from interest rate uncertainty. The consequences of such behavior are captured in the
inventory-theoretic models of money demand.
Whether predicated on transaction costs or on
interest rate uncertainty, money demand models generally indicate that the amount of money
demanded varies directly with income and
inversely with the opportunity cost of money.
To link the MZM measure to its theoretical
conception, Motley (1988, p. 39) argues that
“each of the motives for holding wealth in the
form of ‘money’ is more closely related to
■ 4 Retail money funds are those with minimum initial investments
under $50,000; institutional money funds have a required minimum initial
investment of $50,000.
■ 5 Technically, these are both term instruments, albeit of short duration. Whitesell and Collins (1996) find little evidence of substitution between these instruments and demand deposits in recent years. Data on
overnight RPs and eurodollars are no longer available.




MZM Velocity and
Opportunity Cost

SOURCES: Board of Governors of the Federal Reserve System; and U.S.
Department of Commerce, Bureau of Economic Analysis.

B O X 2
Calculation of MZM’s
Rate of Return
+ (RMF + IMF) x RR & IMF]


Rate of return on MZM deposits
Other checkable deposits
Rate of return on other checkable deposits
Savings deposits
Rate of return on savings deposits
Retail MMMFs
Institutional MMMFs
Rate of return on retail and institutional MMMFs

money’s being a nonterm asset, that gives more
or less immediate command over goods and
services, than to its being the medium of
exchange. All are motives for holding liquid
assets in general, and not only assets that are a
means of exchange.” Thus, the zero-maturity
criterion for selecting assets to be included in a
measure of money has its basis in principle.

III. The Demand
for MZM
Developing theoretical underpinnings for
money demand is one thing; finding a stable
empirical relationship is another. Estimated
money demand relationships are notoriously

unstable. The literature is replete with examples of estimated models that fail the test of
time. Most fall victim to the effects of financial
innovation, if not of regulation and deregulation. Financial innovation, for example, can
lead to the development of new instruments
like MMMFs, first introduced in the mid-1970s.
Generally, such instruments are not included in
the official money measures until an empirical
basis becomes well established. MMMFs were
first included in the 1980 redefinition of M2.
Structural change in the demand for an
aggregate is usually evident in the time series of
its velocity, especially in relation to interest
rates. Figure 1 illustrates MZM velocity in relation to its opportunity cost (the difference
between a market yield and the yield on MZM).
In principle, MZM opportunity cost is a measure of the forgone income from holding MZM.
It is calculated here as the difference between
the three-month Treasury bill rate and the
share-weighted average of yields paid on MZM
components (see box 2).6
The movements in MZM velocity can be separated into two distinct periods. Prior to 1975,
velocity seemed to trend continually upward
with little regard for changes in the aggregate’s
opportunity cost. Since then, however, velocity
appears to be relatively trendless in the long
run, but varies systematically with changes in
opportunity cost in the short run.
Poole argues that the upward trend in MZM
velocity before 1975 is the likely result of financial regulations, especially Regulation Q,
which placed ceilings on interest rates paid by
depositories. We find this argument compelling. During periods of high and rising market
interest rates, such ceilings create strong incentives for deposit holders to economize on their
cash balances.7
Although interest rate ceilings were not
totally eliminated until the early 1980s, they
were often rendered ineffective by revisions of
Regulation Q that started in the mid-1970s. For
example, ceilings were sometimes raised once
■ 6 Ideally, the opportunity cost measure would include all returns to
holding deposits (such as gifts for opening an account and service credits)
and subtract service charges. These data are not available, which may
explain why some empirical specifications fail.
■ 7 It is interesting to note that MZM velocity appears to ratchet up.
When the aggregate’s opportunity cost rises, its velocity also rises, but
when opportunity cost falls, velocity does not. This is reminiscent of the
experience of M1 in the 1970s. Porter, Simpson, and Mauskopf (1979)
argue that this pattern reflected incentives for adopting cash management
technology. Specifically, when interest rates breached old thresholds, balance holders adopted techniques that allowed them to economize on their
M1 holdings. These techniques reduced the need to hold M1 even when
interest rates fell.


they became effective. Moreover, depositories
were periodically allowed to introduce new
accounts whose interest rates were tied to those
paid on U.S. Treasury bills. Finally, MMMFs,
first introduced in 1973, provided balance holders with a zero-maturity instrument that effectively yielded a market rate. These instruments
appeared to serve as a refuge from regulated
yields. Because MMMFs attracted at least part of
the depository outflows related to effective
interest rate ceilings, such substitutions were
internalized in the MZM aggregate.8

IV. An MZM Demand
We consider a specification of MZM demand
similar to that proposed by Moore, Porter, and
Small (1990; hereafter MPS) for the M2 demand
model. They apply methods developed by
Engle and Granger (1987) that distinguish longrun and short-run determinants. Our long-run
relation follows the form

Mt = AYt S gt ,

where M is the measure of money, A is the
scale parameter, Y is nominal GDP, and S is
equal to one plus the opportunity cost of
money.9 Note the implicit constraint that the
elasticity of M with respect to Y is equal to
one.10 The parameter g is the elasticity of
opportunity cost. An implication of all money
demand theories, of course, is that the sign of
g is negative.
Equation (1) can be rewritten as

Yt /Mt = Vt = A –1S t–g ,

where V is the income velocity of money.
Thus, the long-run relation embeds the simple
relationship between MZM velocity and opportunity cost evident in figure 1.
Because the model is estimated in log form,
we rewrite the long-run relations as

mt = a + yt + gst + et , or


vt = –a – gst – et ,

where lower-case variables denote the natural
log. The variable e is introduced to account for
any potential deviation between the actual level
and long-run equilibrium.
Estimation of (1¢) or (2¢) requires careful
analysis. It is widely known that most aggregate

economic time series are nonstationary in levels. In such variables, there is no tendency to
systematically return to a unique level or trend
over time. Moreover, when these variables
exhibit drift, standard regression analysis can
yield spurious relationships. Table 1 presents
evidence that natural logarithms of MZM velocity and opportunity cost are nonstationary both
in the whole sample period and after 1974.
Methods developed by Engle and Granger
(1987) and Johansen (1988) allow us to examine whether equilibrium relationships exist
between two or more nonstationary variables.
Such variables are said to be cointegrated if
some linear combination of them is stationary.
Thus, cointegration implies a long-run relationship between variables, and we can obtain estimated long-run elasticities from the cointegrating vector. However, cointegration between
two or more variables requires that each be stationary in a differenced form. The evidence
presented in table 1 tends to confirm that the
first differences of MZM velocity and opportunity cost are stationary.11
To test if MZM velocity and opportunity cost
are cointegrated, we estimate a chi-squared statistic proposed by Johansen (1988).12 Specifically, this approach tests the hypothesis that
there are, at most, r cointegrating vectors. The
results presented in table 2 are mixed. These
tests fail to reject the hypothesis that there is no
cointegrating vector involving MZM velocity and
opportunity cost over the whole sample. Since
1974, however, evidence supports the hypothesis that there is one cointegrating vector. Thus, a
stable equilibrium relationship linking MZM
velocity and opportunity cost appears to have
■ 8 The existence of reserve requirements has given banks an incentive to “sweep” transaction balances into nonreservable and usually nonmaturing assets like MMDAs. Thus, this form of regulation avoidance is
also internalized in the zero-maturity measure.
■ 9 The units are not in percentage terms. Hence, a 3 percent rate for
opportunity cost would appear as 1.03. We found that this specification is
more robust than the simple log of opportunity cost. Since the model is
estimated in log form, this variable approximates a semilog form for
opportunity cost. MPS include the log of opportunity cost in their model,
but use a linear approximation when the value is small.
■ 10 Although the Baumol (1952) model of money demand indicates
an income elasticity of 0.5, it assumes that money bears no interest. MZM
largely comprises interest-bearing components.
■ 11 Unlike the whole-period findings, these test results are not uniformly concordant. The augmented Dickey–Fuller test for stationarity in
the first difference of MZM is not significant at the 10 percent level, but the
Phillips–Perron test is significant at the 5 percent level.
■ 12 For any n variables there may be n cointegrating vectors. We are
concerned here with finding one cointegrating vector for two variables.




Stationarity Test Results
Sample: 1961:IQ to 1994:IVQ

Sample: 1975:IQ to 1994:IVQ

Test Statistics

Lag truncation:

Constant, no trend
Dickey–Fuller ta
Phillips–Perron ta
Constant, trend
Dickey–Fuller ta
Phillips–Perron ta
Variable (1st diff.)
Lag truncation:

Constant, no trend
Dickey–Fuller ta
Phillips–Perron ta
Constant, trend
Dickey–Fuller ta
Phillips–Perron ta

Critical Value
















–3.34 –3.64
–7.15 –9.90
–76.9 –101.7




–3.68 –3.66
–7.11 –9.86
–75.1 –100.7





Test Statistics

Lag truncation:

Constant, no trend
Dickey–Fuller ta
Phillips–Perron ta
Constant, trend
Dickey–Fuller ta
Phillips–Perron ta

Critical Value







–2.69 –1.81
–2.18 –1.23
–8.95 – 4.10






– 41.5

–2.66 –2.46
–7.93 –5.37
–67.4 – 42.7



– 41.9

–2.69 –2.47
–7.93 –5.37
–67.0 – 43.2



Variable (1st diff.)
Lag truncation:

Constant, no trend
Dickey–Fuller ta
Phillips–Perron ta
Constant, trend
Dickey–Fuller ta
Phillips–Perron ta





NOTE: Regressions are of the form Dyt = a 0 + a1 yt – 1 + a2t + S gj Dyt – j + et , except when the trend is omitted. The test statistics are for
H 0: a1 = 0. Thus, when the test statistic exceeds the critical value, we cannot reject the hypothesis that the series is nonstationary. Lag length is
determined by the highest significant lag order from the autocorrelation or partial autocorrelation function. Critical values are interpolated from
tables 4.1 and 4.2 in Banerjee et al. (1993).
SOURCE: Authors’ calculations.



Cointegration Test Results
Johansen Trace
Test Statistics









5% Critical Values Trace Test

NOTE: If the test statistic is greater than the critical value, we can reject the
hypothesis that there are, at most, r cointegrating vectors. The results are based
on four lag specifications.
SOURCE: Authors’ calculations.

emerged beginning in 1975. It is important to
note that this latter period includes extensive
deregulation of depositories, an acceleration in
financial innovation, a substantial disinflation,
and three relatively unique business cycles.

V. An ErrorCorrection
One implication of the cointegration test results
is that et in equations (1¢) and (2¢) has been
stationary since 1974. Stationarity in et allows
us to obtain consistent estimates of the parameters of the long-run relationship over the latter
period. One estimation procedure is to embed
et – 1 in a short-run relation that describes the
adjustment path to equilibrium. This relation is
commonly called the error-correction process.
We propose a streamlined version of the MPS




MZM and M2 Prediction Errors

SOURCES: Board of Governors of the Federal Reserve System; and authors’


From this form, the long-run opportunity cost
elasticity, g, can be easily recovered. Equation
(3¢) is estimated using ordinary least squares,
with the results presented in box 3.
It is most interesting to note that the longrun opportunity cost elasticity of MZM is –4.33,
an unusually high estimate. A one-percentagepoint increase in MZM opportunity cost from its
current level would reduce equilibrium MZM
demanded by more than 4 percent. This indicates that the lion’s share of MZM variation
(and the variation in its velocity) reflects a systematic effect due to interest rates. To verify
that the velocity specification is appropriate, we
test the restriction that the income elasticity
equals one. This test fails to reject a unitary
income elasticity at the 5 percent significance
level. In sum, MZM demand since 1974 is relatively well explained by the few variables
included in our framework.


Regression Results

VI. MZM in
the 1990s

Dmt = – 0.095 – 0.132 (mt – 1 – yt – 1) – 0.572 st – 1 + 0.248 Dmt – 1
(2.97) (3.35)

It is widely held that the demise of M2 as a reli-

– 0.438 Dst – 0.742 Dst – 1 – 0.114D831t + et
NOTE: Adj. R2 = 0.83, SSE = 0.0098, Box–Ljung statistic Q(12) = 18.35,
F1,72 = 3.20 (test on restriction: mt – yt = 0), and estimation period = 1975:IQ
to 1994:IVQ.
SOURCE: Authors’ calculations.


Dmt = b0 + b1et – 1 + b2 Dmt – 1 + b30 Dst
+ b31Dst – 1 + b4 D831 + et ,

where D denotes the first difference of a variable, et – 1 is the deviation of money from its
long-run equilibrium value in the prior period,
e is white noise, and D831 is a qualitative variable that equals zero in all quarters except
1983:IQ, when it equals one. We include the
final variable to account for transitory effects
related to the introduction of MMDAs.
Solving for et in (1¢) and substituting into
(3) yields a form that allows the parameters to
be estimated jointly:

able policy guide resulted largely from the proliferation of mutual funds in capital market
instruments, particularly bond funds (see Duca
[1995], Darin and Hetzel [1994], Collins and
Edwards [1994], and Orphanides, Reid, and
Small [1994]). This view is summarized succinctly by Darin and Hetzel (p. 39): “In the early
1990s, the combination of 1) low rates of return
on bank deposits relative to capital market
instruments and 2) the decreased cost of operating bond and stock mutual funds diminished
the public’s demand for saving in the form of
bank deposits.” The historical relationship
between M2 and economic activity broke down
as depositors redirected these savings flows
from bank deposits to stock and bond mutual
funds. This unraveling is evident in the cumulative out-of-sample projection errors of a version
of the MPS model specification (see figure 2).
To investigate the robustness of the MZM
specification during the proliferation of bond
and equity funds, we estimate the model
through 1989 and use out-of-sample simulations
to 1996:IQ.13 This simulation reveals no significant cumulative error. Indeed, more than five
years after the sample period, MZM is essentially

(3¢) Dmt = b0 – b1a + b1(mt – 1 – y t – 1)
– b1gst –1 + b2 Dmt – 1 + b30 Dst
+ b31Dst – 1 + b4 D831 + et .

■ 13 Because we are examining only the robustness of parameters,
we use actual values for exogenous variables. However, the simulation is
dynamic. Hence, values of MZM are model projections during the simulation period.


on track. It appears that the rapid growth of
mutual funds came largely at the expense of
small time deposits, and that the zero-maturity
distinction is an important and durable dividing
line for aggregating monetary assets.
MZM also fares well when compared to the
narrower aggregates. One factor that has recently been depressing growth in the narrow
aggregates is the widespread emergence of
sweep accounts. Banks are initiating these programs to economize on their reserves, which
earn no return. These arrangements “sweep”
excess household checkable deposits, which
are reservable, into MMDAs (also of zero maturity), which are not reservable, thereby reducing
a bank’s required reserves. Over the past few
months, depository institutions have stepped
up their efforts to initiate sweep programs,
leading to sharp declines in checkable deposits
and total reserves and thereby depressing both
M1 and the monetary base. Because there is little or no reason to believe that the development of sweep accounts has had any measurable impact on aggregate economic activity,
the related weakness in the narrow money
measures is misleading. Since MZM includes
MMDAs, the effects of the sweep program are
internalized. Thus, MZM’s relationship to economic activity is unaffected.

a Policy Guide
The estimated interest sensitivity of MZM
demand has implications for the aggregate’s
usefulness as a policy guide. For example, normal interest rate fluctuations over a business
cycle may imply relatively sharp movements in
the level of MZM demanded. When choosing
monetary targets, policymakers typically
attempt to project changes in money growth
due to demand and set target ranges to accommodate such growth. Because interest rate
changes are largely induced by unforeseen circumstances, it would be difficult, if not impossible, to anticipate the appropriate growth rate
for MZM in the year ahead. Thus, the aggregate
does not seem well suited to being a monetary
target, particularly when real shocks to the
economy result in desired changes in equilibrium interest rates.
Nevertheless, policymakers may find it useful to monitor MZM. Specifically, MZM could
play an important complementary role in
assessing the indicator properties of the other
monetary aggregates, especially M2. Because
MZM was immune to the effects of mutual fund

development while M2 was not, we can reasonably infer that M2 weakness was largely a
portfolio phenomenon—reflecting the substitution of mutual funds for time deposits—and
not a signal of inherent weakness in the economy. Monitoring MZM thus allows us to gain
some insight into potential problems associated
with M2. Moreover, given the widespread implementation of sweep accounts, narrower aggregates such as M1 have become less reliable.

VIII. Conclusion
Deregulation and financial innovation have
wreaked havoc on the relationship of traditionally defined money measures with economic
activity and interest rates. Surprisingly, perhaps,
we have found that an alternative measure of
money, MZM, has endured these events quite
well. Over the last 20 years, the aggregate has
exhibited a stable relationship with nominal
GDP and with its own opportunity cost.
Our estimated model of MZM demand is
based on the framework proposed by MPS to
estimate M2 demand. Out-of-sample predictions in the 1990s reveal that the MZM demand
relationship is immune to innovations in the
mutual fund industry that led to the demise
of M2. In addition, because MZM includes
MMDAs, it has not been affected by the advent
of sweep accounts, which continue to confound the interpretation of narrower money
measures such as M1 and the monetary base.
The relative stability of MZM demand tends
to confirm Motley’s (1988) and Poole’s (1991)
conjecture that zero maturity is an important
theoretical distinction for determining which
assets should be included in a measure of
money. Interestingly, Poole invoked the “temporary abode of purchasing power” principle
advocated by Milton Friedman, while Motley
drew on the notion of “liquidity preference”
proposed by Keynes. Nonetheless, both argue
that zero-maturity instruments tend to be better
insulated from the effects of deregulation and
financial innovation.
We find that MZM demand is quite sensitive
to changes in opportunity cost. This complicates MZM’s usefulness for policy purposes
because policymakers may choose to accommodate such changes in demand. The upshot
is that MZM is not particularly well suited to
being an intermediate target. Nevertheless, it
could play a complementary role in monitoring
the other monetary aggregates.


Finally, we would like to acknowledge our
own reservations about making too much out
of empirical relationships estimated over spans
of 20 years or less. Clearly, experience has
shown that many macroeconomic relationships
hold up well for such periods, only to break
down miserably once they are taken seriously.
What is different about our model of MZM
demand is that it has endured a period of
tumultuous change that laid waste to most
other measures of the money supply.

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