View original document

The full text on this page is automatically extracted from the file linked above and may contain errors and inconsistencies.

Short-Run Effects of Money
When Some Prices Are Sticky
Lee E. Ohanian and Alan C. Stockman

M

uch of the literature in macroeconomics is concerned with the
effects of monetary disturbances on the real economy, particularly
the role of money in business cycles. Monetary shocks can have
important real effects in “Keynesian” models because this class of models
generally involves nominal rigidities in prices or wages. In sharp contrast, a
broad neoclassical tradition in macroeconomics (including real business cycle
theory) typically assumes prices are completely flexible, although there have
been some recent attempts to combine these traditions, as in Kydland (1987),
Cho and Cooley (1990), and King (1990).
While there is much evidence that certain types of goods have sticky nominal prices, there is also evidence of frequent price changes for other types of
goods, such as the relatively homogeneous commodities sold on near-auction
markets, food, automobiles (transactions prices), and computers. Typically,
Keynesian macroeconomic studies postulate a sticky price level, so that a
change in the nominal money supply is (in the short run) a change in the real
money supply. These studies generalize from the evidence that some prices
are sticky to the hypothesis that the general price level is sticky. In contrast,
neoclassical studies often assume flexible prices, so that the price level adjusts
immediately to changes in the nominal money supply. These studies typically
ignore or discount the evidence that certain prices are sticky.
Studies presenting evidence that certain nominal prices are “sticky” include
Stigler and Kindahl (1970), which found evidence of infrequent changes in
transactions prices in product markets, and Carlton (1986), which extended the
Stigler-Kindahl study and documented slow changes in nominal transactions
Lee E. Ohanian is assistant professor of economics at the University of Pennsylvania, and
Alan C. Stockman is the Marie C. and Joseph C. Wilson Professor of Economics at the
University of Rochester. They would like to thank Tim Cook, Mike Dotsey, Tom Humphrey,
and Peter Ireland for very helpful comments, and Mark Gertler for very helpful discussions
on an earlier draft. The views expressed are those of the authors and do not necessarily reflect
those of the Federal Reserve Bank of Richmond or the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 80/3 Summer 1994

1

2

Federal Reserve Bank of Richmond Economic Quarterly

prices for producers’ goods even without long-term relationships between buyers and sellers and showed that delivery lags and other product characteristics
often change before or in place of changes in nominal prices. Carlton’s result
(1989, p. 921) that the degree of price rigidity differs greatly across industries (with the average period between price changes ranging from 5.9 months
for household appliances to 19.2 months for chemicals) is one motivation for
our assumption below that sectors differ in their speed of price adjustment.
Other papers include Cecchetti’s (1986) study of stickiness in nominal magazine prices, Kashyap’s (1991) study showing substantial price sluggishness
in three major mail-order catalogs (even when new catalogs are published),
Rees’s (1961) study providing evidence that catalog prices and retail-store
prices have similar properties, and Blinder’s (1991) survey that found that
most firms change nominal prices one time or less in a typical year. Other
evidence for nominal price sluggishness includes the well-known fact that prices
are seldom formally indexed to a price index and the fact that real exchange
rates (exchange rate-adjusted ratios of price indexes across countries) vary
much more under floating exchange rate systems than under pegged exchange
rate systems (see Stockman [1983], Mussa [1986], and Baxter and Stockman
[1989]). This evidence strongly suggests that the exchange rate system affects
international relative-price variability, a fact that is easy to explain with models
in which some prices are sticky and much harder to explain in flexible-price
models. Related evidence appears in Engel (1991). On the other hand, many
sectors of the U.S. economy appear to have very flexible prices—with nominal
prices that often change weekly, daily, or every few minutes.
This article studies a hybrid model in which some nominal prices are
sticky and others are flexible. This model turns out to have several interesting
properties. Unexpected changes in the money supply change the relative prices
of sticky-price and flexible-price goods, so the real effects of monetary disturbances can differ across sectors. With certain parameter configurations, the
model has the ability to produce endogenous price sluggishness in the flexibleprice sector because the equilibrium response of those prices to a change in
money is small in the short run. With other parameter configurations, the
response of flexible nominal prices to a monetary disturbance is sufficiently
large that the change in real money balances is small, as are monetary effects
on the real economy working through the standard Keynesian transmission
mechanism. In that case, however, a monetary disturbance has large effects on
relative prices and induces different responses of output in different sectors of
the economy. Monetary shocks, in this way, may contribute to sectoral shifts
in the economy. Nominal price sluggishness also affects the short-run response
of the economy to real disturbances (e.g., to changes in technology), even in
sectors of the economy with flexible prices.
Because there is currently no well-established theory to explain nominal price stickiness, we follow Svensson (1986), Lucas (1991), Lucas and

L. E. Ohanian and A. C. Stockman: Short-Run Effects of Money

3

Woodford (1992) and Cho and Cooley (1990) in assuming that nominal prices
in the sticky-price sector are set one period in advance.1 (We assume that
the implications of sluggish price adjustment are largely independent of the
source of that sluggishness.) In contrast to those models, however, the economy we study also has a flexible-price sector with trading at Walrasian prices.
An interesting feature of our more general theory (to coin a phrase) is that
it encompasses the standard Keynesian model (in one of its guises) and the
flexible-price neoclassical model as special cases.
We study two versions of the model. The first version is developed in the
spirit of Barro and Grossman (1976): when nominal prices cannot adjust to clear
markets, some agents are rationed and output is determined by the minimum of
the quantity demanded and the quantity supplied. In this case positive money
shocks result in excess demand, with households rationed, and negative money
shocks result in excess supply, with producers constrained. The second version
we study assumes that output is determined by the quantity demanded. This
version of the model is more consistent with recent sticky-price literature such
as Blanchard and Kiyotaki (1987), who assume monopolistic competition so
that small, positive money shocks leave the sticky-price sector in a situation
of demand-determined output and do not imply rationing of buyers as in the
Barro-Grossman model. (Instead, firms supply more of the good as long as price
exceeds marginal cost.) We show that the effects of positive money shocks differ across the two versions of the model, though the effects of negative money
shocks are similar in both versions.
This article does not attempt to match closely the implications of the model
with data. Instead, its purpose is to analyze the properties of a simple model
with sticky- and flexible-price sectors and to examine how its properties depend
on basic parameter values. Consequently, the analysis we present below focuses
on the effects of isolated, exogenous monetary disturbances.

1.

A SIMPLE COMPETITIVE EQUILIBRIUM MODEL

We begin with a simple flexible-price equilibrium model that we have also
examined in Ohanian and Stockman (1994) and (in a two-country framework)
in Stockman and Ohanian (1993). The model has two consumption goods, X
and Y, and labor. We introduce money through a cash-in-advance constraint,
intended to stand in for a more general transactions model of money. We assume, for simplicity, that there are complete asset markets. The representative
household maximizes utility:

1 In contrast to Lucas and Woodford, we simply assume the level at which nominal prices
are predetermined in the sticky-price sector rather than deriving an endogenous distribution of
prices.

4

Federal Reserve Bank of Richmond Economic Quarterly

∞

βt

max E0
t=0

1
αxt(σ−1)/σ + (1 − α)yt(σ−1)/σ
(1 − ρ)

[σ/(σ−1)]·(1−ρ)

− v(LXt + LYt )

(1)

subject to the two constraints
δ
nt−1 + τt + PX,t−1 kX,t−1 Lδ
X,t−1 + PY,t−1 kY,t−1 LY,t−1 − Mt

+ νt (qt + dt ) − νt+1 qt = 0

(2)

and
Mt − PXt Xt − PYt Yt ≥ 0

(3)

each period. Equation (2) is a budget constraint for period t asset markets and
(3) is the cash-in-advance constraint which applies to period t product markets
(which immediately follow period t asset markets as in Lucas [1982]). The
terms x and y refer to consumption of goods X and Y, LX and LY refer to labor
hours producing goods X and Y, 0 ≤ δ < 1 is a parameter of the production
function, kX and kY are exogenous productivity parameters, nt−1 refers to the
household’s money holdings at the end of period (t−1) product markets (which
is the slack in inequality [3] from the previous period and equals zero in our
equilibrium), τ refers to a lump-sum transfer of money to the household from
the government, PX and PY are nominal prices, Mt is the nominal money the
household chooses as it leaves period t asset markets and enters period t product
markets, and νt is a vector of other assets the household owns at the beginning
of period t, with dividend vector d and ex-dividend price-vector q.2
Several important parameters that we will focus on later appear in (1) and
(2). First, α is a parameter describing tastes. Because α helps determine the
equilibrium share of good X in total output, we will vary it in “The Size of the
Sticky-Price Sector” subsection of Section 2 to discuss changes in the relative
sizes of the X and Y industries. Next, ρ is the inverse of the intertemporal
elasticity of substitution; an increase in ρ means households are less willing to
trade current consumption for future consumption (that is, they are willing to
2 One

can also think of kX and kY as fixed levels of the capital stock. However, adding
capital accumulation to the model would change its implications in several ways. The most obvious change would occur in the dynamics of adjustment to equilibrium following a disturbance.
In addition, changes in the rate of capital accumulation would provide an additional margin of
substitution for the economy that could tend to smooth consumption over time and thereby reduce
the response of interest rates to exogenous disturbances. By abstracting from capital accumulation,
the current article greatly simplifies the analysis. The benefit of this simplicity is that it facilitates
understanding; the cost is that it may lead to slightly different quantitative results than a more
complicated model with capital accumulation. We are currently extending the model to include
capital and will report on the results in a forthcoming paper.

L. E. Ohanian and A. C. Stockman: Short-Run Effects of Money

5

pay more for a more constant consumption stream). The subsection “The Size of
Intertemporal Substitution” explains how the size of ρ affects our results. Third,
σ is the elasticity of substitution between goods X and Y; a larger σ means
the goods are better substitutes. The impact of the size of σ on our results is
the subject of the subsection “The Size of Intratemporal Substitution.” Finally,
δ determines the curvature of the production function, with lower values of δ
indicating higher degrees of diminishing returns to labor; the subsection “The
Degree of Curvature in Production” discusses the impact of this parameter on
our results.3
We assume that the cash-in-advance constraint (3) holds as an equality,
kX = kY = 1 for all t, and that τ ≡ 0. The flexible-price perfect foresight
equilibrium for this simple production economy satisfies
M s = PXt Lδ + PYt Lδ ,
t
Xt
Yt
PXt λt = αLδ(σ−1)/σ + (1 − α)Lδ(σ−1)/σ
Xt
Yt
PYt λt = α(σ−1)/σ Lδ + (1 − α)Lδ(σ−1)/σ
Xt
Yt

(4)

(1−ρσ)/(σ−1)

(1−ρσ)/(σ−1)

αL−δ/σ ,
Xt

(5)

(1 − α)L−δ/σ ,
Yt

(6)

v = βPXt δLδ−1 λt+1 ,
Xt

(7)

v = βPYt δLδ−1 λt+1 ,
Yt

(8)

and

where M s is the (exogenous and constant, because τ = 0) money supply at
t
the end of period t asset markets and λ is the current-value Lagrange multiplier
on constraint (2). (It is easy to show that λ = γ, the multiplier on the cash-inadvance constraint, because of the first-order condition for the choice of Mt .)
It is also easy to show that the nominal interest rate on a one-period nominal
asset satisfies the usual pricing condition:
1 + it =

2.

λt
.
βλt+1

(9)

EQUILIBRIUM WHEN SOME PRICES ARE STICKY

This section examines the implications of the basic model when prices in one
sector are predetermined (for one period) at the expected market-clearing level.
We assume for now that output is determined by the minimum of quantity demanded and quantity supplied. We return to this assumption later and modify
it so that output is always demand determined.
3 The

other parameters in equation (1), β and v, have no important effects on our results.

6

Federal Reserve Bank of Richmond Economic Quarterly

We introduce short-term price stickiness into the model by assuming that
sellers must choose PX,t one period in advance (that is, at the end of period
t − 1). We assume, however, that the nominal price of Y, PY , adjusts instantaneously to clear markets at each date. We examine the effects of a permanent,
unanticipated change in the money supply starting from a nonstochastic steadystate equilibrium in which the money supply is constant and PX is fixed at its
expected equilibrium level. The money supply change occurs at the beginning
of period t. Real variables dated at t +1 and later are unaffected by this change,
but real variables at date t are affected because PX,t is predetermined.
First consider the excess-supply case. Suppose the money supply falls permanently by 1 percent at date t, with PX,t fixed for one period. When PX,t is
above its equilibrium level, the quantity of X supplied exceeds the quantity
demanded, so output of X will be demand determined. As a result, equation (7)
(describing the supply of X) does not hold. That is, people would like to work
more in the X industry and sell more of product X, but the price is predetermined
at a level above the equilibrium, so the quantity demanded is insufficient to
satisfy supply. Instead, sellers are rationed (equally in equilibrium). So we have
equations (4)–(6) and (8) in the four variables LX,t , LY,t , PY,t , and λt , (with λt+1
taking its new steady-state value).
Because a change in the money supply has no steady-state effect on x, y, or
LX , equation (5) implies that the change in money has no effect on PX,t+1 λt+1
in the new equilibrium. But the fall in the money supply reduces PX,t+1 by 1
percent, so it must raise λt+1 by 1 percent.
Our first result is the following: a fall in the money supply reduces PY , and
the percentage fall in PY is less than the percentage fall in the money supply if
and only if the elasticity of substitution in consumption, σ, exceeds one. This
means that if X and Y are good substitutes (relative to the Cobb-Douglas case
of σ = 1), then exogenous price stickiness in the X sector causes endogenous
price stickiness in the Y sector. The overall price level also adjusts sluggishly
in this case.
Our second result is that a fall in the money supply causes a rise in the oneperiod nominal interest rate if and only if the degree of relative risk aversion,
ρ, exceeds one, that is, if and only if the elasticity of intertemporal substitution
(1/ρ) is less than one.
Next, consider the excess-demand case. Suppose the money supply rises
permanently by 1 percent at date t, with PX,t fixed for one period. When PX,t is
below its equilibrium level, the quantity of X demanded exceeds the quantity
supplied, so output of X is supply determined. As a result, equation (5) (describing the demand for X) does not hold. Instead, buyers are rationed (equally in
equilibrium) and we have equations (4) and (6)–(8) in the (same) four variables
LX,t , LY,t , PY,t , and λt , (with λt+1 taking its new steady-state equilibrium value).

L. E. Ohanian and A. C. Stockman: Short-Run Effects of Money

7

Our first result for the excess-demand case is that the equilibrium response
of PY to a rise in the money supply, is:
sX
d ln PY
,
=1+
d ln M
1 − sX

(10)

where sX is the share of good X in total spending. This means that a rise in the
money supply raises the nominal price of Y by more than it would if the price
of X were fully flexible and that this “overshooting” of PY is increasing in the
share of the economy with sticky prices.
Our second result in the excess-demand case is that the overshooting of PY
necessarily implies an inverse effect of money on interest rates. To see why,
consider the pricing relationship for a one-period nominal bond:
Uy,t+1 Py,t
1
=β
,
(1 + i)
Uy,t Py,t+1

(11)

where Uy,t denotes marginal utility of good y at date t. Two factors affect the
nominal interest rate: the marginal rate of substitution between Y today and
Y tomorrow and the rate of change of the nominal price of Y. In the excessdemand case, both factors tend to decrease the interest rate. First, note that
households are rationed in purchasing X, so substitution into Y today raises the
marginal rate of substitution, which reduces the interest rate. Second, Py,t overshoots the new equilibrium level, Py,t+1 , which results in (expected) deflation
in the Y sector, which also tends to reduce the nominal interest rate.
As long as δ < 1, which means that there are diminishing returns to labor,
the changes in labor inputs in response to a positive money shock are
d ln LY
sX
=
d ln M
1 − sX

1
1−δ

(12)

and
−1
d ln LX
=
.
d ln M
1−δ

(13)

In this case a positive monetary disturbance moves labor from the sticky-price
sector (X) to the sector with the rising relative price (Y). Because output is
supply determined, it is interesting to note that the elasticity of substitution between the two goods does not affect the sectoral reallocation of labor between
the X and Y industries.
Effects of a Fall in the Money Supply
The analytic results available for this model are limited, so we now turn to
a numerical analysis of the model. Consider a permanent 1 percent fall in
the money supply (from 10 to 9.9), starting from a steady-state equilibrium.
Table 1 shows the results when α = 0.5, σ = 2, δ = 0.64, v = 1, β = 0.96,

8

Federal Reserve Bank of Richmond Economic Quarterly

Table 1 Baseline Model
Variable

Old SS

SR

New SS

Ratio

Labor in X
Labor in Y
Total labor
Output of X
Output of Y
GNP
Price of Y
CPI
Interest rate

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.925
7.925
4.167

0.4761
0.489
0.9651
0.6219
0.6326
1.255
7.858
7.891
4.771

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.846
7.846
4.167

−2.21
0.43
−0.89
−1.42
0.27
−0.58
0.15
0.58
0.60

and ρ = 2.4 (We analyze permanent changes in the money stock to eliminate
labor-supply responses that reflect temporary inflation tax considerations.)
The first column of Table 1 shows the variables: labor inputs in the X and
Y industries, total labor, output in each industry (x and y) and total real GNP
(evaluated at equilibrium prices and production shares), the nominal price of
good Y (the nominal price of X in the old steady state and the short run equals
the old steady-state price of good Y, and the new steady-state prices are also
equal), the economy’s consumer price index, and the nominal interest rate (in
percent per period). The next column shows the old steady-state (“Old SS”)
levels of the variables, before the change in money. The “SR” column shows
the short-run effects of the fall in money (while the nominal price of X is fixed
at its previous level). The “New SS” column shows the new steady state. The
column labeled “ratio” shows the percentage by which each variable in the
short run exceeds its new steady-state level—except for the interest rate row
in which the “ratio” shows the absolute difference between the interest rate in
the short run and in the long run.
With the parameter values in Table 1, the sticky-price sector (X) represents
one-half of output in the economy. Half of all labor is employed in the stickyprice sector. A permanent 1 percent fall in the money supply is neutral in
the long run (with a 1 percent fall in nominal prices and no effects on real
variables). But in the short run, with pX predetermined, real GNP falls about
0.58 percent. This fall in total GNP masks major differences across sectors:
4 The value of β in Table 1 is appropriate if prices in the X sector are sticky for about one
year. If, instead, they are sticky for about one quarter, then a more appropriate level of β is 0.99.
An unexpected change in the money supply of about 1 percent per quarter with prices sticky
for one quarter has nearly the same effects as an unexpected change of about 1 percent per year
when prices are sticky for a year.

L. E. Ohanian and A. C. Stockman: Short-Run Effects of Money

9

output in the sticky-price sector falls 1.4 percent, while output in flexible-price
industries rises 0.27 percent.5 The fall in money reduces the nominal price of
Y, which raises the relative price of X. This leads to a fall in the quantity of
X demanded and creates excess supply in the X industry. Output of X is determined by the minimum of the quantity demanded and the quantity supplied,
so output of X falls. But consumers substitute (partly) into purchases of Y, so
output of Y rises. Notice that the nominal price of Y falls by almost exactly
the amount it would fall if the price of X were flexible (it falls by almost 1
percent—to about one-seventh of 1 percent above its new steady-state level).
Because the nominal price of Y responds almost proportionally to the change
in the money supply while the nominal price of X is fixed and because each
sector represents one-half of the economy’s output, the CPI falls about halfway
to its new long-run level.
As in standard Keynesian models, the fall in the money supply has a
short-run “liquidity effect” on the nominal interest rate. In Table 1, the interest
rate rises 60 basis points from 4.17 percent to 4.77 percent in the short run.
This increase is slightly higher than the estimates reported by Christiano and
Eichenbaum (1992), who estimate that a lower bound for the liquidity effect is
that a 1 percent fall in the money supply raises the federal funds rate by about
27–53 basis points (within one to two quarters). Because expected inflation is
negative (the CPI is expected to fall another 0.6 percent), this represents a rise
in the real interest rate (measured in terms of the output bundle) of about 120
basis points. Notice that the liquidity effect occurs despite the introduction of
money through a cash-in-advance constraint, which (when binding as in these
examples) builds in a zero interest elasticity of the demand for money. Ohanian
and Stockman (1994) examine the question of how much price stickiness is
necessary to generate a liquidity effect of money on interest rates of realistic
size and find that only a small sticky-price sector can be sufficient to produce
interest rate effects of the magnitude found in the data.
Table 1 provides an initial answer to one of our central questions: Are
nominal prices in flexible-price sectors “sluggish” in response to monetary
and real disturbances—so that relative prices remain close to their equilibrium
levels—or do nominal prices in flexible-price sectors change more than proportionally to monetary disturbances—so that the overall price level adjusts to
equate the supply of and demand for money? The answer provided by Table 1
is a compromise between these two possible responses: PY is not endogenously
sluggish, but neither does it change more than proportionally to the monetary
disturbance. As a result, the overall price level exhibits a degree of sluggishness

5 Because the capital stock and technology are fixed in this experiment, the marginal product of labor rises in the sticky-price sector (as employment in that sector falls) and rises in the
flexible-price sector (as employment in that sector rises).

10

Federal Reserve Bank of Richmond Economic Quarterly

at the same time the monetary disturbance contributes to a change in relative
prices.6
The Size of Intertemporal Substitution
Raising the degree of relative risk aversion from two to three (i.e., lowering the
elasticity of intertemporal substitution from one-half to one-third) raises labor
effort and output (and lowers nominal prices) in the steady state. However,
Table 2 shows that the responses of the economy to a fall in the money supply
are virtually unchanged, except for a larger liquidity effect on the interest rate.
With ρ = 3, a 1 percent fall in the money supply raises the nominal interest
121 basis points in the short run, roughly double the response when ρ = 2.
The other responses of the economy are virtually unaffected. A reduction in
the elasticity of intertemporal substitution raises the size of the liquidity effect
for a simple reason. A fall in the money supply raises the interest rate in the
short run because households become cash constrained: with the smaller money
supply, PX fixed at its old level, and PY roughly at its new equilibrium level,
households cannot afford to buy as many consumption goods as they did before
the fall in money or as many as they will buy after all nominal prices adjust.
Households attempt to smooth consumption intertemporally by borrowing. The
equilibrium real interest rate is bid up as all households attempt to borrow. The
higher real interest rate induces households to accept the temporary reduction in
consumption. However, the smaller the elasticity of intertemporal substitution,
the larger the increase in the real interest rate required to induce households to
accept the temporarily low level of consumption. So increases in ρ raise the
interest rate response to a monetary disturbance.
The Size of Intratemporal Substitution
We have assumed that outputs of the two sectors are substitutes in the sense
that the elasticity of substitution σ exceeds one. Now suppose that σ = 0.5
rather than 2. Table 3 shows that reducing the elasticity of substitution from
two to one-half has several effects on the economy’s response to a monetary disturbance. First, output in the flexible-price sector now falls along with
6 The

effects of increases in productivity in this model differ from the effects in either
standard Keynesian models or neoclassical models. Suppose productivity rises permanently by 1
percent in each sector: output is 1 percent higher for each level of labor input. In the long run,
this reduces nominal prices and employment in each sector and raises output in each sector, with
no permanent effect on the interest rate. (Labor input is constant in response to a productivity
change if we assume log utility, in which case income and substitution effects are offsetting.) But
with the nominal price PX fixed in the short run, the relative price of X rises as the nominal price
of Y falls. As a result, an economy-wide rise in productivity can reduce output in the sticky-price
sector in the short run. It also raises output in the flexible-price sector more in the short run than
in the long run and temporarily raises nominal and real interest rates.

L. E. Ohanian and A. C. Stockman: Short-Run Effects of Money

11

Table 2 Baseline Model, ρ = 3
Variable

Old SS

SR

New SS

Ratio

Labor in X
Labor in Y
Total labor
Output of X
Output of Y
GNP
Price of Y
CPI
Interest rate

0.718
0.718
1.436
0.5959
0.5959
1.192
6.964
6.964
4.17

0.7078
0.7199
1.428
0.5827
0.5985
1.181
6.905
6.934
5.38

0.718
0.718
1.436
0.5959
0.5959
1.192
6.894
6.894
4.17

−1.42
0.27
−0.58
−2.21
0.43
−0.89
0.15
0.58
1.21

Table 3 Baseline Model, σ = 0.5
Variable

Old SS

SR

New SS

Ratio

Labor in X
Labor in Y
Total labor
Output of X
Output of Y
GNP
Price of Y
CPI
Interest rate

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.925
7.925
4.167

0.4814
0.4856
0.967
0.6263
0.6298
1.256
7.838
7.881
4.64

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.846
7.846
4.167

−1.13
−0.28
−0.70
−0.73
−0.18
−0.45
−0.10
0.46
0.47

output in the sticky-price sector. Second, output in the sticky-price sector falls
much less when σ = 1⁄2 than when σ = 2. The reason for these differences is
straightforward. When a fall in the money supply reduces the nominal price of
Y but not the price of X, households substitute out of consumption of X into
consumption of Y. When X and Y are good substitutes, there is a large increase
in the demand for Y and a large decrease in the demand for X, which raises
equilibrium output of Y and causes output of X to fall by a large amount. If,
however, the goods are complements in the sense that an increase in consumption of one of the goods raises the marginal utility of the other good, then the
fall in equilibrium consumption of Y reduces the marginal utility of consuming
X. Instead of rising, the demand for X falls and equilibrium output of X also
falls. The fall in demand for Y is smaller in this case, and equilibrium output of
Y falls less than it would if X and Y were good substitutes. This also explains
why, with σ = 1⁄2, the price of Y falls more (overshooting its new equilibrium
level), whereas if σ = 2, PY falls only partway to its new equilibrium level.

12

Federal Reserve Bank of Richmond Economic Quarterly

The Degree of Curvature in Production
Table 4 presents the results of the same experiment as in Table 1, but with
δ = 0.9 rather than δ = 0.64. This means that the economy experiences only a
small degree of diminishing returns to labor. The assumption that δ = 0.64 is
more appropriate based on long-run studies of aggregate production functions,
but some time-series estimates suggest a higher value of δ in the short run.
While the steady state of the economy with δ = 0.9 differs from that presented
in Table 1, the response of the economy to a monetary disturbance is similar.
Total employment falls less, because changes in employment do not so quickly
result in diminishing returns. Employment in the sticky-price sector falls less
for the same reason. Because output of the flexible-price good rises more in
this case, the price PY falls less.

Table 4 Baseline Model, δ = 0.9
Variable

Old SS

SR

New SS

Ratio

Labor in X
Labor in Y
Total labor
Output of X
Output of Y
GNP
Price of Y
CPI
Interest rate

0.6429
0.6429
1.286
0.6719
0.6719
1.344
7.441
7.441
4.167

0.6324
0.646
1.278
0.662
0.6748
1.337
7.37
7.406
4.715

0.6429
0.6429
1.286
0.6719
0.6719
1.344
7.367
7.367
4.167

−1.64
0.48
−0.58
−1.47
0.43
−0.53
0.05
0.53
0.55

The Size of the Sticky-Price Sector
Now consider changing the relative sizes of the two sectors of the economy.
Table 5 takes the same parameter values as in Table 1 except α = 0.2 rather than
0.5. This implies that the sticky-price sector is about 21 percent of aggregate
GNP and accounts for 11 percent of employment. A permanent 1 percent fall
in money reduces the nominal price of Y by almost 1 percent immediately and
reduces employment in the sticky-price sector by 2.86 percent and output by
1.8 percent in the short run. Real GNP falls 0.1 percent and total employment
falls 0.23 percent, as output in the flexible-price sector rises 0.07 percent. The
liquidity effect (inverse effect of money on interest rates) in Table 5 is smaller
than in Table 1, but reaches the lower end of the range estimated by Christiano
and Eichenbaum (1992) if the elasticity of intertemporal substitution is reduced
to one-third instead of one-half (that is, if ρ = 3 rather than 2), in which case
the interest rate rises 31 basis points in the short run. The fall in α also
raises the percentage response of labor in the sticky-price sector to a monetary

L. E. Ohanian and A. C. Stockman: Short-Run Effects of Money

13

Table 5 Baseline Model, α = 0.2
Variable

Old SS

Labor in X
Labor in Y
Total labor
Output of X
Output of Y
GNP
Price of Y
CPI
Interest rate

SR

New SS

Ratio

0.1015
0.7797
0.8813
0.2313
0.8528
1.025
10.380
9.754
4.167

0.09862
0.7806
0.8792
0.2271
0.8534
1.024
10.280
9.665
4.324

0.1015
0.7797
0.8813
0.2313
0.8528
1.025
10.270
9.656
4.167

−2.86
0.11
−0.23
−1.84
0.07
−0.10
0.04
0.10
0.16

disturbance, because it reduces the absolute size of that sector. Similarly, it
reduces the percentage response of labor in the flexible-price sector because it
raises the absolute size of that sector. With a smaller sticky-price sector, households are less cash constrained by a fall in the money supply, so the interest
rate response is smaller. And the smaller the sticky-price sector, the smaller the
effect of that sector on the nominal price PY . Ohanian and Stockman (1994)
examine these issues in greater detail and show that a change in the money
supply can have a substantial “liquidity effect” on nominal and real interest
rates in the short run even if only a small fraction of the economy has sluggish
prices.
Costly Time-to-Move Labor Across Industries
The results discussed above involve substantial short-run movements of labor
across industries in response to monetary shocks. Because labor is often costly
to reallocate across industries in the short run, we now modify the model so
that rapid labor mobility is costly. We assume it takes one period to move labor
across sectors unless the worker pays a utility cost of moving equal to
v2

lyss
ly
−
ly + lx lyss + lxss

2

+ v2

lxss
lx
−
ly + lx lyss + lxss

2

,

(14)

where lxss and lyss are the original steady-state levels of employment in the X
and Y industries and v2 is a nonnegative parameter. We assume v2 = 10 and
the same parameters as in Tables 1 and 3. Tables 6 and 7 present the results of
this experiment.
First, compare Table 6 to Table 1: the costly time-to-move assumption
results in a much smaller increase in employment and output in the flexibleprice sector; output in that sector is roughly constant (rising only 0.02 percent).
Total labor supply falls more than in Table 1, as does GNP. Nominal prices in
the flexible-price sector fall less than in Table 1: PY remains 0.32 percent above

14

Federal Reserve Bank of Richmond Economic Quarterly

its new equilibrium level in the short run. If the equilibrium price response in
the flexible-price sector is small, as in this case, studies such as Blinder (1991)
that search for “menu costs” or similar reasons for “price-stickiness” in these
markets would fail to uncover them because that price sluggishness would reflect an equilibrium response to the fact that other nominal prices are sticky. In
fact, it is interesting that Blinder’s survey found little or no evidence of “menu
costs” in changing prices. Instead, firms reported that the reason they change
nominal prices infrequently is that they are concerned about their product price
relative to those of their “competitors.” If we interpret “competitors” to include
goods in the sticky-price sector, this observation may be consistent with the
results in Table 6.7
Next, compare Table 7 to Table 3: the costly time-to-move assumption
results in a much smaller fall in employment and output in the flexible-price
sector; output in that sector is roughly constant (falling only 0.02 percent rather
than 0.18 percent). Total labor supply falls less than in Table 3, as does GNP.
Nominal prices in the flexible-price sector fall more than in Table 3: PY falls
1.3 percent and overshoots its new equilibrium level by 0.3 percent. The timeto-move assumption in this case reduces the response of interest rates by about
10 basis points. As before, the size of the liquidity effect is governed by the
size of intertemporal substitution: if it is one-third rather than one-half, the
nominal interest rate rises twice as much as in Tables 6 and 7.
Sticky Wages with Flexible Prices
We have assumed up to now that nominal stickiness in the X sector occurs
mainly in product markets. We now modify the model so that nominal rigidities in the X sector have their origin in labor markets. We assume nominal
wages in the X sector are predetermined for one period, while nominal product
prices in both sectors (and nominal wages in the Y sector) are flexible. Table
8 presents the results of the same experiment as in Table 1 (with the same
parameter values), but with sticky wages rather than sticky prices. We assume
the nominal wage rate in the X sector is set one period in advance equal to
the expected nominal marginal product of labor, which equals the steady-state
marginal product multiplied by the original steady-state nominal price, PX . In
this sticky-wage economy, employment in the X industry is demand determined
in the case of negative money shocks and supply determined in the case of
positive money shocks.
7 It

is interesting that most of the reasons given by firms for sluggish nominal prices in
Blinder’s study deal with relative prices. For example, some firms said that price is only one
component of an overall package that matters to buyers; others spoke of implicit contracts and
so on. These reasons by themselves are not sufficient to explain sticky nominal prices. But if
some nominal price is exogenously fixed, then these reasons could help explain the “spread” of
stickiness to other nominal prices.

L. E. Ohanian and A. C. Stockman: Short-Run Effects of Money

15

Table 6 Baseline Model, v2 = 10
Variable

Old SS

SR

New SS

Ratio

Labor in X
Labor in Y
Total labor
Output of X
Output of Y
GNP
Price of Y
CPI
Interest rate

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.925
7.925
4.167

0.4768
0.4871
0.9638
0.6225
0.631
1.253
7.871
7.898
4.859

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.846
7.846
4.167

−2.08
0.03
−1.03
−1.34
0.02
−0.66
0.32
0.67
0.69

Table 7 Baseline Model, σ = 0.5, v2 = 10
Variable

Old SS

SR

New SS

Ratio

Labor in X
Labor in Y
Total labor
Output of X
Output of Y
GNP
Price of Y
CPI
Interest rate

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.925
7.925
4.167

0.4818
0.4868
0.9686
0.6267
0.6308
1.257
7.822
7.873
4.531

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.846
7.846
4.167

−1.05
−0.03
−0.54
−0.67
−0.02
−0.35
−0.31
0.35
0.36

The results in Table 8 differ slightly from those in Table 1, but the main
differences are quantitative rather than qualitative. Wage and price stickiness
have similar results because the main effect of wage stickiness is to keep the
marginal cost of production constant in nominal terms in the short run. This
reduces the effect of money on equilibrium nominal product prices in the X
sector. As a result, the economy resembles a sticky-product-price economy but
with some nominal price movement, and equilibrium responses to money are
smaller than in the sticky-product-price economy. Wage stickiness results in
less aggregate labor movement—and less sectoral reallocation than does price
stickiness. Total labor falls 0.50 percent in the sticky-wage economy, while it
fell by 0.89 percent in the sticky-price economy. Employment in each sector
changes by only about half as much in the sticky-wage case as in the stickyprice case. The sticky wages endogenously generate sluggish nominal prices:
PY , the price of output in the sticky-wage sector, falls immediately by an amount
equal to 44 percent of its long-run fall. In this sense, wage stickiness induces

16

Federal Reserve Bank of Richmond Economic Quarterly

Table 8 Baseline Model with Sticky Wages
Variable

Old SS

SR

New SS

Ratio

Labor in X
Labor in Y
Total labor
Output of X
Output of Y
GNP
Price of X
Price of Y
CPI
Interest rate

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.925
7.925
7.925
4.167

0.4809
0.4881
0.969
0.6259
0.6319
1.258
7.89
7.852
7.871
4.502

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.846
7.846
7.846
4.167

−1.23
0.24
−0.50
−0.79
0.15
−0.32
0.56
0.09
0.32
0.3352

partial price stickiness. This induced price stickiness is even more pronounced
if goods X and Y are less substitutable; Table 9 shows the results of a 1 percent
fall in money in the sticky-wage model when σ = 0.5 (as in Table 4). In this
case the short-run fall in PX is only 28 percent of its long-run fall.
As δ → 1, the sticky-price and sticky-wage economies become equivalent.
This occurs because a linear production function (with marginal-cost pricing
of factors) implies that competitive payments to labor exhaust production.
The relative similarity between the sticky-price and sticky-wage economies
is consistent with Lucas’ (1989) conjecture that the effect of money shocks on
sticky-price and sticky-wage economies should be similar.

Table 9 Baseline Model with Sticky Wages, σ = 0.5
Variable

Old SS

SR

New SS

Ratio

Labor in X
Labor in Y
Total labor
Output of X
Output of Y
GNP
Price of X
Price of Y
CPI
Interest rate

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.925
7.925
7.925
4.167

0.483
0.486
0.9689
0.6277
0.6301
1.258
7.902
7.84
7.871
4.503

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.846
7.846
7.846
4.167

−0.81
−0.20
−0.50
−0.52
−0.13
−0.32
0.72
−0.07
0.32
0.34

Increases in the Money Supply
Increases in the money supply have qualitatively different effects on the economy because it generates excess demand in the sticky-price sector (because
increases in nominal prices in the flexible-price sector reduce the relative price

L. E. Ohanian and A. C. Stockman: Short-Run Effects of Money

17

of sticky-price goods). As a result, output in the sticky-price sector is determined by the quantity supplied rather than the quantity demanded. Table 10
shows the effects of a permanent 1 percent rise in the money supply (from 10
to 10.1), starting from a flexible-price steady state and with the same parameter
values as in Table 1.

Table 10 Baseline Model with Money Rising One Percent
Variable

Old SS

SR

New SS

Ratio

Labor in X
Labor in Y
Total labor
Output of X
Output of Y
GNP
Price of Y
CPI
Interest rate

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.925
7.925
4.167

0.4736
0.5002
0.9738
0.6199
0.6419
1.262
8.082
8.004
2.304

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
8.004
8.004
4.167

−2.73
2.73
0.00
−1.75
1.74
0.01
0.97
−0.01
−1.86

Table 10 shows that a 1 percent rise in the money supply causes the nominal
price of Y to overshoot its new steady-state value. The price of Y rises nearly
2 percent in the short run in response to the 1 percent increase in money. This
overshooting of the price of Y leads the overall price level to respond rapidly
to the increase in the money supply: nearly all of the long-run response of the
CPI to the increase in money occurs immediately. The model therefore implies
that the overall price level responds much more rapidly to a rise in the money
supply than a fall (even though the price of X is assumed to be sticky upwards
as well as downwards). It is interesting to note that this result is consistent
with empirical work presented by Fischer (1981) that inflation is positively
associated with periods of high relative-price variability. Also, Cody and Mills
(1991) (among others) find that spot commodity prices are important predictors
of future inflation in U.S. data. This is consistent with the two-sector model
economy in that the immediate sharp increase in the price of flexible goods
is a “leading indicator” of future changes in prices of sticky goods. Finally,
this asymmetric response of prices is consistent with the widely held view that
prices are more sticky in a downward direction than in an upward direction. Our
model, however, generates this result even though individual prices are either
flexible or sticky in both directions. This shows how an observer who looks
only at the overall price level rather than individual prices could mistakenly
conclude that some underlying friction allows prices to rise but not to fall.
While an increase in money raises output and employment in the flexibleprice sector, it reduces output and employment in the sticky-price sector.

18

Federal Reserve Bank of Richmond Economic Quarterly

Aggregate GNP rises only slightly and total labor supply is fixed: the increase in
money induces sectoral reallocation of employment and output. The increase in
money also causes a large fall in the interest rate: the interest rate falls 186 basis
points in response to the 1 percent rise in money. This result suggests that there
may be an asymmetry in the size of the liquidity effect of money on interest
rates depending on whether the money supply rises or falls. There is also an
asymmetry with respect to the effects of intertemporal substitution on the size of
the liquidity effect: when the money supply rises, the elasticity of intertemporal
substitution has very small effects on the size of the liquidity effect.
Table 11 shows the effects of adding time-to-move labor to Table 10, with
v2 = 10. In this case a 1 percent increase in money has little effect on output or
employment in either sector, though it again causes considerable overshooting
of PY and a large (though smaller) liquidity effect: the nominal interest rate
falls 105 basis points in response to a 1 percent rise in money. Notice that
this interest rate response is smaller than without the time-to-move assumption;
in contrast, we found above that adding the time-to-move assumption reduced
the inverse effect of money on interest rates in response to negative monetary
disturbances.

Table 11 Baseline Model with Money Rising One Percent, v2 = 10
Variable

Old SS

SR

New SS

Ratio

Labor in X
Labor in Y
Total labor
Output of X
Output of Y
GNP
Price of Y
CPI
Interest rate

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
7.925
7.925
4.167

0.4864
0.4874
0.9738
0.6305
0.6313
1.262
8.083
8.004
3.114

0.4869
0.4869
0.9738
0.6309
0.6309
1.262
8.004
8.004
4.167

−0.10
0.10
−0.00
−0.06
0.06
0.00
0.99
−0.00
−1.05

Increases in the Money Supply with Monopolistic Competition
A number of recent papers have studied economies with sticky prices and
firms that have market power (Blanchard and Kiyotaki 1987; Mankiw 1985;
Svensson 1986). In these papers, an increase in the money supply does not
necessarily lead to rationing of consumers (as in our version of the BarroGrossman model with excess demand). Instead, firms willingly supply output
equal to the quantity demanded, provided that the fixed product price exceeds
the marginal cost of production. (If marginal cost does exceed price, consumers
are rationed and output is supply determined.) While the implications of a negative money shock are similar in both setups (in either case, firms would like

L. E. Ohanian and A. C. Stockman: Short-Run Effects of Money

19

to sell more than is demanded at the fixed price), the effect of an unexpected
increase in the money supply differs across these two sticky-price models.
This section discusses the effects of an increase in money in our model
economy modified so that output in the X industry is always determined by
quantity demanded. This amounts to assuming that the X sector is monopolistically competitive, with price exceeding marginal cost. Rather than solving for
the explicit equilibrium of a monopolistic-competition model, we can consider
an experiment in which steady-state PX is set above its market-clearing level. In
this case, a small positive money shock leads to an expansion in output in the
X industry. The results of this experiment are nearly identical, with a change in
sign, to the results reported earlier for reductions in the money supply (creating
a case of excess supply).
Increases in money have strikingly different effects on the economy depending on whether output in the sticky-price sector is demand determined (as
it is here) or supply determined (as in the experiments reported earlier). In both
cases, there is a sectoral reallocation of labor. In the supply-determined case
discussed earlier, a positive money shock causes labor to move from the stickyprice sector (X) to the flexible-price sector (Y), which has a rising nominal (and
relative) price. With monopolistic competition (where output is demand determined even in the case of a positive money shock), labor moves in the opposite
direction: labor flows from the flexible-price sector to the sticky-price sector. In
addition, fluctuations in output and interest rates due to monetary shocks in the
monopolistic competition case are symmetric (in contrast to the asymmetric
results reported above) because demand determines production regardless of
the sign of the disturbance.
Without taking a stand on the market structure in sticky-price industries in
the U.S. economy, these models suggest some interesting tests. Do monetary
disturbances affect industries identically? Do they have asymmetric effects on
the economy, depending on whether the disturbances are positive or negative?
What are the characteristics of the sectoral flow of labor over the business
cycle? Kretzmer (1989) provides evidence related to the first question: he finds
that monetary shocks affect different industries differently. Using unanticipatedmoney regressions for individual industries, his evidence suggests that output
and employment initially decline in response to a positive money shock in almost 40 percent of the industries.8 This finding could be consistent with either
of the market structures discussed above; to distinguish between the two structures, we would need to know whether the industries that contract in response
to a positive money shock are sticky-price or flexible-price industries. Cover
(1992) and Thoma (1992) present aggregate evidence on the second question:

8 See

Kretzmer’s Table 2 (p. 288). He reports that 13 of 30 impact coefficients in his hours
equations and 11 of 30 impact coefficients in his output equations are negative.

20

Federal Reserve Bank of Richmond Economic Quarterly

they find that positive and negative money shocks affect the economy differently. In particular, it appears that negative money shocks precede economic
declines, but positive money shocks do not suggest significant increases in
future output. This is consistent with our two-sector model with output determined by the short side of supply and demand, but not with the two-sector
monopolistic-competition model. (Ball and Mankiw [1992] modify a one-good
monopolistic-competition model so that positive trend inflation combined with
menu costs triggers price adjustments that depend on the sign of the monetary
shock.)
Comparison of Results to a One-Sector Model
It is interesting to contrast the implications of this two-sector model to those
of a one-sector model. Recall that a one-sector model is a special case of our
model, with the parameter α = 1. The utility function becomes
U=

c1−ρ − 1
− vL,
1−ρ

(15)

where L is labor supply. Perhaps the most interesting comparisons are the effects of money on interest rates. If money falls unexpectedly and permanently,
output is demand determined and (assuming the cash-in-advance constraint
binds) output and consumption fall proportionally with the decrease in money.
The interest rate is
Pt
Pt+1

ρ−1

1
= 1 + i.
β

(16)

With ρ = 2, the interest rate rises one for one with the fall in money.
That is, a 1 percent fall in the money supply raises the nominal interest rate 1
percent, which is more than in the two-sector model. In the excess-demand case
(resulting from an unexpected permanent increase in money), the differences
are even more striking. In the one-sector model, labor supply falls in percentage
1
terms by 1−δ d ln m, which implies that output also falls proportionally to the
change in money in the excess-demand case. Because money has increased,
the cash-in-advance constraint clearly does not bind. As a result, the interest
rate falls to zero for any increase in money.

3.

CONCLUSIONS

There is considerable evidence that the nominal prices of some goods change
very infrequently, while nominal prices of other goods change on a daily
basis. This article presents a simple two-sector monetary economy with production in which the degree of price flexibility differs by sector. In the excessdemand/excess-supply setup, the model predicts that unanticipated monetary

L. E. Ohanian and A. C. Stockman: Short-Run Effects of Money

21

shocks cause (1) asymmetric changes in output and employment that depend
on whether money has increased or decreased, (2) changes in relative prices
over the cycle, (3) sectoral reallocation of labor, and (4) a significant liquidity
effect of money on interest rates. In a related paper (Ohanian and Stockman
1994) we show that only a small amount of price stickiness is needed in this
economy to generate a liquidity effect of reasonable size. The asymmetric
effects of money in the model are consistent with recent empirical studies
(Cover 1992; Thoma 1992), and the model is also consistent with the finding
reported by Fischer (1981) that periods of significant inflation are associated
with high relative-price variability. The model also reproduces the empirical
finding documented by Cody and Mills (1991) that changes in the prices of
flexible-price goods (spot commodities) predict future aggregate price changes
and the empirical finding by Kretzmer (1989) that output and employment in a
significant fraction of U.S. industries decline initially in response to a positive
money shock. In the case that X and Y are good substitutes, the model also
has the interesting implication that the price level is “sticky” downwards as an
equilibrium phenomenon.
In our continuing work, we hope to show that even very short-term price
stickiness can set into motion forces that lead to longer-lasting effects on real
interest rates, output and employment, and nominal price changes. To study
this, we are currently studying the effects of adding capital to the basic model
described here. Our extension of this model to a two-country world in Stockman
and Ohanian (1993) examines the effects of monetary disturbances on domestic
and world interest rates, exchange rates, and domestic and foreign output, and
shows that the effects of monetary disturbances are highly non-linear in open
economies. In future work we intend to use the model to study the effects of
alternative exchange rate systems, devaluations, and optimal currency areas.

REFERENCES
Ball, Lawrence, and N. Gregory Mankiw. “Asymmetric Price Adjustment
and Economic Fluctuations,” Working Paper. Boston: Harvard University,
1992.
Baxter, Marianne, and Alan Stockman. “Business Cycles and the ExchangeRate Regime: Some International Evidence,” Journal of Monetary
Economics, vol. 23 (May 1989), pp. 377–400.
Barro, Robert J., and Herschel I. Grossman. Money, Employment, and Inflation.
New York: Cambridge University Press, 1976.
Blanchard, Olivier, and Nobu Kiyotaki. “Monopolistic Competition and the
Effects of Aggregate Demand,” American Economic Review, vol. 77
(September 1987), pp. 647–66.

22

Federal Reserve Bank of Richmond Economic Quarterly

Blinder, Alan. “Why Are Prices Sticky? Preliminary Results from an Interview
Study,” American Economic Review, vol. 81 (May 1991, Papers and
Proceedings, 1990), pp. 89–96.
Carlton, Dennis W. “The Theory and the Facts of How Markets Clear: Is
Industrial Organization Valuable for Understanding Macroeconomics?” in
R. Schmalensee and R. Wilig, eds., Handbook of Industrial Organization,
Vol. 1. Amsterdam: North-Holland, 1989.
. “The Rigidity of Prices,” American Economic Review, vol. 76
(September 1986), pp. 637–58.
Cecchetti, Steve. “The Frequency of Price Adjustment: A Study of the
Newsstand Prices of Magazines,” Journal of Econometrics, vol. 31
(August 1986), pp. 255–74.
Cho, Jang-Ok, and Thomas Cooley. “The Business Cycle with Nominal Contracts,” Working Paper 260. Rochester: Rochester Center for Economic
Research, 1990.
Christiano, Larry, and Martin Eichenbaum. “Liquidity Effects, Monetary Policy
and the Business Cycle,” Working Paper. Evanston, Ill.: Northwestern
University, 1992.
Cody, Brian J., and Leonard O. Mills. “The Role of Commodity Prices in
Formulating Monetary Policy,” The Review of Economics and Statistics,
vol. LXIII (May 1991), pp. 358–65.
Cover, James P. “Asymmetric Effects of Positive and Negative Money Supply
Shocks,” Working Paper. Tuscaloosa, Ala.: University of Alabama, 1992.
Engel, Charles. “Is Real Exchange Rate Variability Caused by Relative Price
Changes? An Empirical Investigation,” Working Paper. Seattle: University
of Washington, 1991.
Fischer, Stanley. “Relative Shocks, Relative Price Variability, and Inflation,”
Brookings Papers on Economic Activity, 2:1981, pp. 381–431.
Kashyap, Anil. “Sticky Prices: New Evidence from Retail Catalogs,” Working
Paper. Chicago: University of Chicago, 1991.
King, Robert. “Money and Business Cycles,” Working Paper. Rochester:
University of Rochester, 1990.
Kretzmer, Peter. “The Cross-Industry Effects of Unanticipated Money in an
Equilibrium Business Cycle Model,” Journal of Monetary Economics, vol.
23 (September 1989), pp. 275–96.
Kydland, Finn. “The Role of Money in a Competitive Model of Fluctuations,”
Working Paper. Pittsburgh: Carnegie-Mellon University, 1987.
Lucas, Robert E., Jr. “The Effects of Monetary Shocks when Prices Are Set in
Advance.” Unpublished paper. University of Chicago, 1989.

L. E. Ohanian and A. C. Stockman: Short-Run Effects of Money

23

. “Interest Rates and Currency Prices in a Two-Country World,”
Journal of Monetary Economics, vol. 10 (November 1982), pp. 335–60.
, and Michael Woodford. “Real Effects of Monetary Shocks in an
Economy with Sequential Purchases.” Unpublished paper. University of
Chicago, 1992.
Mankiw, N. Gregory. “Small Menu Costs and Large Business Cycles: A
Macroeconomic Model,” Quarterly Journal of Economics, vol. 100 (May
1985), pp. 529–39.
Mussa, Michael. “Nominal Exchange Rate Regimes and the Behavior of Real
Exchange Rates,” Carnegie-Rochester Conference Series on Public Policy,
vol. 25 (Autumn 1986), pp. 117–214.
Ohanian, Lee E., and Alan C. Stockman. “How Much Price Stickiness Is
Necessary for Reasonable Liquidity Effects?” Working Paper. Rochester:
Rochester Center for Economic Research, 1994.
Rees, Albert. “Alternative Retail Price Indexes for Selected Non-Durable
Goods, 1947–59,” in G. Stigler, ed., The Price Statistics of the Federal
Government. New York: National Bureau of Economic Research, 1961.
Stigler, George, and J. Kindahl. The Behavior of Industrial Prices. New York:
National Bureau of Economic Research, 1970.
Stockman, Alan. “Real Exchange Rates Under Alternative Nominal Exchange
Rate Systems,” Journal of International Money and Finance, vol. 2
(August 1983), pp. 147–66.
, and Lee E. Ohanian. “Short-Run Independence of Monetary
Policy Under Pegged Exchange Rates and Effects of Money on Exchange
Rates and Interest Rates,” Working Paper 4517. New York: National
Bureau of Economic Research, 1993.
Svensson, Lars E. O. “Sticky Goods Prices, Flexible Asset Prices, Monopolistic
Competition, and Monetary Policy,” Review of Economic Studies, vol. 3
(July 1986), pp. 385–405.
Thoma, Mark A. “Subsample Instability and Asymmetries in Money-Income
Causality,” Working Paper. Eugene, Ore.: University of Oregon, 1992.

A Shift-Adjusted
M2 Indicator for
Monetary Policy
Robert Darin and Robert L. Hetzel

T

he Federal Reserve System influences the economy through its control
of fiat money (currency and bank reserves) and the monetary aggregates.
This influence is more predictable and is easier to observe when there
is a stable relationship between the monetary aggregates and the public’s dollar
expenditure or output. The monetary aggregate M2 in particular has exhibited
a long-term stable relationship with dollar output (Hetzel 1989, 1992; Ireland
1993). In the early 1990s, however, this relationship apparently disappeared.
Over the three-year period 1990Q4 through 1993Q4, nominal GDP grew at an
annualized rate of 5.2 percent, while M2 grew at an annualized rate of only
2.0 percent.
We first review regulatory and technological changes affecting financial
intermediation that could be reducing the public’s demand for M2. Specifically, we review the events that have encouraged bank depositors to place their
funds in bond and stock mutual funds, which are not part of M2. We then
investigate whether a version of M2 that adjusts for net flows into bond and
stock mutual funds can reestablish the previous stable relationship with nominal
output growth. This latter aggregate, “shift-adjusted” M2, consists of regular
M2 plus cumulative net inflows from households into bond and stock mutual
funds. The article concludes with a discussion of the likely future stability of
money demand.
The views expressed are those of the authors and not necessarily those of the Federal Reserve
Bank of Richmond or the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 80/3 Summer 1994

25

26

1.

Federal Reserve Bank of Richmond Economic Quarterly

MUTUAL FUNDS

From 1990Q4 through 1993Q4, total bank deposits declined by $25.1 billion,
while bond and stock mutual funds rose by $506.7 billion. (All the figures
here are for open-end mutual funds, that is, funds whose shares are continuously issued and redeemed.) A regular flow of news stories provides anecdotal
evidence that individuals are taking funds out of small retail CDs, which are
included in M2, and placing them in bond and stock mutual funds, which are
not included in M2. For example, a story in the American Banker (3/22/93)
states:
Banks that sell mutual funds face a major test of their marketing mettle next
month when a huge batch of certificates of deposit reaches maturity. As much
as $110 billion in CDs will be up for grabs, and with interest rates at the
lowest level in a generation, many customers won’t be looking to roll over
the investments. If recent history is any indication, depositors will pour much
of that money into mutual funds. . . . [C]ustomers are becoming convinced
that rates will remain low for a while and are ready to seek alternatives. . . .
Now they are saying, “I’ve got to get some income.”
(P. 1)

Money Market Mutual Funds
The recent growth of bond and stock mutual funds is reminiscent of the growth
of money market mutual funds in the late 1970s. Competition from the mutual
fund industry for bank deposits began in earnest with the cyclical pickup in
money market rates in 1977. Prior to that time, a large rise in market rates would
cause Reg Q ceilings on the rates financial institutions could pay on time and
savings deposits to become binding. Holders of small deposits had difficulty
fleeing to money market instruments like commercial paper because of the
large denominations of those instruments. By 1977, however, the availability
of money market mutual funds, which pool funds from numerous individuals
for investment in short-term financial assets, allowed depositors to avoid Reg
Q and still hold assets that were available in small denominations and that
could be bought and sold with low transactions costs. A good example was
Merrill Lynch’s Cash Management Account, a checkable money market account
introduced in 1977.
Money market mutual funds not only collected deposits from investors, but
also bought the commercial paper of corporations. Large corporations, often
with better credit ratings than banks, found raising funds in this way cheaper
than borrowing from banks. Intermediation that formerly went through banks
now bypassed them completely. The ability of investors to circumvent Reg Q
made inevitable its elimination, beginning with the introduction of all-savers
certificates in June 1978 and ending with the elimination of the ceiling on
savings deposits in April 1986. The introduction of money market deposit
accounts (MMDAs) in 1982Q4 allowed banks to compete directly with money

R. Darin and R. L. Hetzel: Shift-Adjusted M2 Indicator

27

market funds. The decline in bank intermediation, however, led to a decline in
the public’s demand for M2 defined exclusive of money market mutual funds.
Through the early 1980s, most of the growth in mutual funds occurred
in money market mutual funds. Like other M2 deposits, the shares of money
market mutual funds are available in small denominations. Also, because these
funds hold only short-term securities, their shares are redeemable at par. That
is, they do not fluctuate in value with changes in interest rates. (The weightedaverage maturity of money market mutual funds cannot be greater than 90
days.) As a consequence, including the shares of money market mutual funds
in M2 was straightforward and restored the long-run stable relationship between
M2 and the public’s dollar expenditure and output.
Bond and Stock Mutual Funds
Table 1 shows net inflows into bond and stock mutual funds. These funds, as
opposed to money market mutual funds, first began to grow significantly in
1984. They grew fairly strongly from the middle of 1985 through the middle
of 1987, grew very little from the second half of 1987 through early 1990, and
then began to grow rapidly toward the middle of 1991. The growth of bond
and stock mutual funds in the mid-1980s is not associated with instability in
the relationship between M2 and nominal output. Most of the growth in this
period occurred in bond rather than stock funds and was heavily concentrated in
mortgage-backed securities and, to a lesser extent, in junk bonds. Apparently,
the investors financing this growth in bond funds were drawing funds from
large CDs and money market instruments not included in M2.

Table 1 Annual Inflows
Fourth Quarter over Fourth Quarter

Year

Total
Bank
Deposits

Total
Money Market
Mutual Funds

Total
Stock and Bond
Mutual Funds

1984
1985
1986
1987
1988
1989
1990
1991
1992
1993

228.38
187.11
184.70
122.29
177.04
97.60
11.51
−0.57
−15.25
−9.29

39.44
22.26
53.11
16.44
19.71
91.02
60.79
60.24
16.40
−18.47

20.63
71.09
135.54
45.72
−23.46
3.07
22.94
96.65
168.90
241.12

Source: For data on bank deposits and money market mutual funds, the Board of Governors of
the Federal Reserve System; for mutual fund data, the Investment Company Institute.

28

Federal Reserve Bank of Richmond Economic Quarterly

In the early 1990s, two forces combined to encourage the large-scale transfer of funds from bank deposits to bond and stock mutual funds. (See Duca
[1992, 1993], Simpson and Scanlon [1993], and Reid and Small [1993].) First,
the ongoing telecommunications and computer revolution continued to lower
the cost to mutual funds of pooling cheaply the savings of investors. The resulting competition from mutual funds for bank deposits prompted a relaxation
by regulators of the constraints imposed by Glass-Steagall, which prevents
banks from underwriting securities. In the early 1990s, that relaxation allowed
banks to market actively bond and stock mutual fund shares. The second force
encouraging deposit outflows was the depressed state of the loan market, which
prompted banks to pay low rates on their deposits, both absolutely and relatively
to the returns available on stocks and bonds.
The first force, advances in communications and computer technology, reduced the cost of maintaining records on purchases and sales and on income
and distributions. It also helped with the recordkeeping required to keep track
of gains and losses for tax purposes. Vanguard Group introduced a series of
U.S. government securities funds that charged a maximum annual operating fee
of 15¢ per $100 (Business Week, 1/18/93), compared with the 23¢ per $100 of
deposits charged for FDIC insurance alone. Also, mutual funds were offered as
families of different kinds of funds, within which investors can easily switch
by telephone. The increased ease in selecting mutual funds was exemplified
in Charles Schwab’s combined offering of almost 250 no-load mutual funds
that do not charge brokers’ fees. The New York Times (3/20/94) described
this concentration of funds in one place as “a financial Wal-Mart that enables
investors to trade funds as easily as stocks” (Sec. 3, p. 1).
In the last part of the 1980s, regulators, concerned about the ability of banks
to compete for the public’s savings, increasingly allowed banks to become
involved in the marketing of mutual funds. The Glass-Steagall Act prevents
banks from underwriting mutual fund shares. That is, banks cannot buy the
underlying securities, repackage them in the form of mutual funds shares, and
distribute those shares to the ultimate investors. By the early 1990s, however,
banks or their affiliates had acquired the right to perform most of the other
services needed to maintain a mutual fund. They could serve as the investment
adviser. That is, they could select the particular stocks or securities specified by
the fund’s stated objectives. Banking organizations could also serve as transfer
agent and custodian. That is, they kept records of ownership and of the collection and distribution of interest and dividend income. They also settled the
accounts between buyers and sellers.
In the early 1980s, regulators allowed banks to establish a discount brokerage service not subject to the geographical limitations of the McFadden Act.
In 1992, the Federal Reserve Board allowed bank holding companies to
provide investment advice along with brokerage services. In 1993, the Office
of the Comptroller of the Currency permitted Dean Witter and a subsidiary of

R. Darin and R. L. Hetzel: Shift-Adjusted M2 Indicator

29

NationsBank to form a partnership to sell mutual funds and other securities in
the branch offices of NationsBank. Also, in April 1993, the Federal Reserve
Board allowed Mellon Bank Corporation, which had already teamed up with the
mutual fund company Dreyfus, to buy The Boston Company, which provided
administrative and advisory services to 84 different mutual funds.
In 1991, a fall in the rate of interest paid on bank deposits, combined
with the ongoing technological and regulatory changes that were facilitating
the creation of mutual funds, encouraged the large-scale transfer of funds from
bank deposits to bond and stock mutual funds. Many retired investors used the
income from bank CDs to support themselves. Especially with the sharp fall
in short-term rates that began at the end of 1990, they moved out of CDs into
bond and stock mutual funds, which promised a steadier cash flow (at the risk
of capital fluctuation). The Wall Street Journal (2/12/93) wrote:
[The yield on] Treasury bills plunged 37% last year. “That was the great T-bill
crash of 1992,” says Laurence Siegel. . . . Investors usually think of stocks
as very risky and bonds as moderately risky. Meanwhile, T-bills, certificates
of deposit, money market funds and other short-term debt instruments are
seen as virtually risk-free. That’s certainly the case, if all you care about is
fluctuations in price. But if your concern is getting a steady stream of income,
then holding T-bills and rolling them over as they mature is much more risky
than holding stocks or bonds.
(P. C1)

By fall 1992, the rate paid on six-month CDs had fallen to about to 3.25
percent, where it remained until early 1994. For all of 1992, the 30-year bond
rate averaged 7.67 percent, while three-month CDs averaged 3.62 percent, an
unusually wide difference of four percentage points. As of February 1994,
savings deposits at commercial banks and savings banks paid on average 2.43
percent (Board of Governors of the Federal Reserve System statistical release
H.6, “Monthly Survey of Selected Deposits,” March 24, 1994). That level of
short-term rates produced a transfer of funds out of bank deposits into higheryielding bond and stock mutual funds.
The immediate cause of the disintermediation from financial institutions
was the low rates paid on deposits, which in turn reflected weakness in loan
demand. In addition, the need to rebuild capital forced many financial institutions to restrict their asset growth and, indirectly, their deposit growth.
Finally, the well-publicized problems of financial institutions with debt
defaults, especially in real estate, beginning in 1989 altered the perception
of investors with small amounts of capital that bank deposits were the primary
safe form of saving apart from savings bonds and Treasury bills. Mutual funds,
in contrast, experienced no such bad publicity.
A survey by the Board of Governors (1993) documented the change in
emphasis in the 1990s by banks from solely attracting deposits to retail
marketing of mutual funds. The Board surveyed 56 large banks nationwide.
All but four of these banks marketed mutual funds to their retail customers.

30

Federal Reserve Bank of Richmond Economic Quarterly

Three-quarters of the banks that marketed mutual funds had sales representatives at their branches. Forty percent of the banks had sales forces with over
50 people. By 1993, customers of Wells Fargo could buy and sell mutual funds
through automated teller machines (The Economist, 9/4/93).

2.

SHIFT-ADJUSTED M2

Shares in bond and stock mutual funds possess many of the characteristics of
the deposits in M2. They are liquid and available in small denominations, and
they can be bought and sold with low transactions costs. The existence of these
common characteristics suggests adding shares in bond and stock mutual funds
to M2 to create a more inclusive monetary aggregate that would be unaffected
by transfers between these funds and M2. Bond and stock mutual funds, however, are not complete substitutes for the time deposits in M2. Fluctuation in
their capital value presents a risk not present with bank time deposits. Also,
they are not suitable for regular small transactions in that each sale of a mutual
fund share creates a capital gain or loss that is taxable.
Fluctuation in capital value makes bond and stock mutual funds unsuitable
for inclusion in a broad monetary aggregate. Consider, for example, the anomaly
that could arise if bond and stock mutual funds were added to M2 to create a
new, more inclusive monetary aggregate. Assume that a rise in money growth
creates an expectation of a future rise in inflation. That expectation would
produce a rise in bond yields, which would depress the value of bonds. The
value of an inclusive definition of money would then fall and give a misleading
message about the thrust of monetary policy. Money growth would fall when
nominal output growth rose.
One way to offset the distortions in M2 produced by bond and stock mutual
funds is to construct a shift-adjusted M2: M2 plus cumulative net inflows into
bond and stock mutual fund shares not coming from institutional investors
and not held in IRA/Keogh accounts. The exclusion of institutional holdings
is consistent with the definition of M2, which excludes money market funds
held by institutions. Similarly, the exclusion of IRA/Keogh accounts reflects the
exclusion of these accounts in M2. The shift-adjusted measure also excludes
reinvested dividends. The use of dollar inflows to adjust M2 avoids the problem
of changes in the capital value of bonds and stocks.
This construct should not be thought of as a conventional monetary aggregate. The divergence between its growth and M2 growth, however, suggests a
measure of the extent of shifts in the public’s demand for M2. By taking account
of these shifts, it is possible that M2 could again be used as an indicator of the
thrust of monetary policy. Shift-adjusted M2 is analogous to the shift-adjusted
M1 the Fed used in 1981 (Bennett 1982). At that time, an adjustment to M1 was
needed because the incorporation of interest-bearing NOW (negotiable order
of withdrawal) accounts in the definition of M1 in 1980 and the introduction

R. Darin and R. L. Hetzel: Shift-Adjusted M2 Indicator

31

of these accounts nationwide in 1981 produced an inflow of funds into M1
from deposits not formerly included in M1. Shift-adjusted M1 subtracted an
estimate of these inflows. Analogously, the suggested shift-adjusted M2 adds
in an estimate of outflows from M2 into bond and stock mutual funds. Table 2
lists figures for conventional M2 and shift-adjusted M2. In 1991 the difference
in their growth rates was only 1.4 percent, but that figure rose to 1.9 percent
in 1992 and 2.4 percent in 1993.

3.

SHIFT-ADJUSTED M2 AS AN INDICATOR

How well does shift-adjusted M2 predict the impact of monetary policy
actions? Shift-adjusted M2 predicts better than unadjusted M2; however, it
does not eliminate all of the unusual reduction in the public’s demand for M2.
Figure 1 uses shift-adjusted M2 per unit of output to predict the price level. (M2
is shift-adjusted starting in 1991.) Assuming that M2 velocity is stable over
time, that is, the ratio of dollar output to M2 fluctuates around an unchanged
value, M2 divided by real output should move with the price level over long
periods of time. (See Humphrey [1989] for a history of the use by quantity

Figure 1 Money per Unit of Output as a Predictor of the Price Level

1.75
1.50

Shift-Adjusted M2 per Unit of Output
Price Level

1.25
1.00
0.75
0.50
0.25
0.00
1955

60

65

70

75

80

85

90

+Notes: Data are quarterly observations of shift-adjusted M2 divided by real GDP and of the

implicit price deflator. Both series are logarithms of the index numbers created by dividing each
series by its 1955Q1 value. Shift-adjusted M2 is M2 plus cumulative net inflows starting in 1991
from households into bond and stock mutual funds (non-IRA/Keogh accounts).

32

Federal Reserve Bank of Richmond Economic Quarterly

Table 2 Growth of M2 and Shift-Adjusted M2
Monthly
Quarterly
Annualized
Annualized
ShiftMonthly
Growth
Quarterly
Growth
Adjusted Annualized
ShiftAnnualized
ShiftAdjusted
Growth
Adjusted
M2
M2
Growth
Year Month (billions) (billions)
M2
M2
M2
M2
(1)
1991

1992

1993

(2)

(3)

(4)

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

3363.53
3380.02
3398.11
3409.00
3418.86
3426.64
3426.42
3427.40
3427.51
3432.33
3445.36
3455.25

3365.40
3384.65
3405.88
3419.30
3432.99
3444.01
3447.19
3453.14
3458.72
3469.06
3486.11
3501.98

3.85
6.04
6.62
3.91
3.52
2.77
−0.08
0.34
0.04
1.70
4.65
3.50

4.54
7.08
7.79
4.83
4.91
3.92
1.12
2.09
1.96
3.65
6.06
5.60

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

3464.09
3483.61
3486.28
3481.94
3482.07
3477.77
3480.72
3489.43
3496.58
3507.46
3510.53
3509.04

3519.20
3547.02
3555.74
3554.52
3560.23
3562.72
3572.35
3587.62
3599.00
3610.43
3617.26
3624.41

3.12
6.97
0.92
−1.48
0.04
−1.47
1.02
3.05
2.49
3.80
1.05
−0.51

6.06
9.91
2.99
−0.41
1.94
0.84
3.29
5.25
3.87
3.88
2.29
2.40

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

3502.78
3494.21
3494.83
3497.99
3521.86
3528.70
3533.56
3535.69
3543.59
3545.09
3556.19
3563.11

3624.12
3621.75
3630.23
3641.85
3674.52
3687.19
3700.11
3712.65
3727.09
3735.63
3753.27
3765.99

−2.12
−2.90
0.21
1.09
8.50
2.36
1.66
0.73
2.71
0.51
3.82
2.36

−0.10
−0.78
2.85
3.91
11.32
4.21
4.29
4.14
4.77
2.79
5.82
4.14

(5)

(6)

3.89

4.47

4.53

5.64

1.05

2.46

2.02

3.84

3.97

6.45

0.30

2.11

0.96

3.09

2.32

3.51

−1.33

0.89

2.18

4.77

2.46

5.05

1.96

4.20

R. Darin and R. L. Hetzel: Shift-Adjusted M2 Indicator

33

theorists of money per unit of output as a predictor of the price level.) As shown
in Figure 1, M2 per unit of output and the price level do gravitate around each
other. In 1992, however, M2 begins to underpredict the price level, even with
the shift adjustment. By 1993Q4, the underprediction reaches 5 percent.
Figure 2 shows the normally positive relationship between M2 velocity
and the financial market opportunity cost of holding M2. The latter variable is
measured by the difference between the commercial paper rate and a weighted
average of the explicit rates of return paid on the components of M2 (Hetzel
1989). An increase in the cost of holding M2 raises M2 velocity by lowering
the demand for M2, and conversely. The shift-adjustment does not restore for
the early 1990s the normal positive relationship between M2 velocity and the
financial market opportunity cost of holding M2. Shift-adjusted M2 velocity
should have fallen, but did not.
Figure 3 shows quarterly observations of quarterly rates of growth of shiftadjusted M2 and nominal output (GDP) over the recent period of instability in
M2 demand. The two series exhibit some common fluctuations. The correlation
between growth in nominal output and growth in M2 is .35. When M2 growth
is lagged one quarter, the correlation is .41. The rise in nominal output growth
Figure 2 The Relationship Between Shift-Adjusted M2 Velocity and the
Financial Market Opportunity Cost of Holding M2

1.80

6
M2 Velocity (left scale)
Cost of Holding M2
(right scale)

1.75

5

1.70

4

1.65

3

1.60

2

1.55

1

1.50

0
1950

55

60

65

70

75

80

85

90

Notes: The financial market opportunity cost of holding M2 is the difference between the rate
on six-month commercial paper and a weighted average of the explicit rates of interest paid on
+
the components of M2. Shift-adjusted M2 is M2 plus cumulative net inflows starting in 1991
from households into bond and stock mutual funds (non-IRA/Keogh accounts). Shift-adjusted M2
velocity is nominal GDP divided by shift-adjusted M2.

34

Federal Reserve Bank of Richmond Economic Quarterly

Figure 3 Shift-Adjusted M2 and Nominal Output Growth
10
9
8

M2 Growth
GDP Growth

Percent

7
6
5
4
3
2
1
0
1990Q1

91

92

93

+
Notes: Data are quarterly observations of quarterly annualized growth. Shift-adjusted M2 is M2
plus net household inflows into stock and bond mutual funds beginning in 1991.

during the economic recovery, however, is not matched by the usual rise in
M2 growth. It appears that shift-adjusted M2 continues to contain some useful
information about the effect of monetary policy actions on nominal output, but
less than M2 does before 1991.
Shift-adjusted M2 appears to account for somewhat less than half of the
unusual decrease in the demand for M2. Over the three-year period 1990Q4
through 1993Q4, the annualized rate of growth of nominal output was 5.2
percent, while the annualized rate of growth of M2 was only 2 percent. Over
this same period, the cost of holding M2 (the financial market opportunity cost
shown in Figure 2), fell about 1 percent. In the past, that decline would have
produced somewhat faster growth in M2 than in nominal output (a fall in M2
velocity). Appendix B makes these figures more precise by comparing the prediction errors from a money demand regression estimated with conventionally
defined M2 and with shift-adjusted M2. Using conventionally defined M2, the
overprediction in the rate of growth of real M2 for the years 1991, 1992, and
1993 is 2.6, 3.2, and 4.2 percent, respectively. Using shift-adjusted M2, the
overprediction in each year falls to about 2 percent.
It is possible that there is an explanation for the leftward shift in M2
demand that does not focus on the desire of the public to shift its savings
from the deposits of financial institutions to capital market instruments. The
explanations offered, however, have not proven satisfactory. One explanation
offered was that the closing of thrifts by the Resolution Trust Corporation

R. Darin and R. L. Hetzel: Shift-Adjusted M2 Indicator

35

extinguished thrift deposits that had been included in M2. The Resolution Thrift
Corporation, however, stopped closing insolvent thrifts after March 1992 because of lack of funds. Despite this fact, M2 continued to grow slowly relative
to nominal output. The other explanation offered was that the public was using
M2 balances to reduce its debt. Consumer installment credit, however, began to
grow strongly in 1992Q3. Adding home equity loans to consumer installment
credit results in a typical growth in consumer credit for a period of economic
recovery. This growth implies that the public no longer considered its debt level
excessive. M2 growth, however, did not subsequently revive.
It appears that the leftward shift in M2 demand derives from the public’s increased desire to save with capital market instruments rather than bank deposits.
This change in behavior is driven by the reduction in the transactions cost of
buying and selling capital market instruments and by the availability of these
instruments in small denominations made possible by the pooling of investors’
savings in mutual funds. The failure of the shift-adjustment to account fully
for the leftward shift in M2 demand evidently arises from a failure to account
fully for the outflows of M2 deposits to other sources. Indirect confirmation
of this conjecture comes from the Board of Governors’ Surveys of Consumer
Finances (Kennickell and Starr-McCluer 1993, p. 3). Between the 1989 and
1992 surveys, bank deposits as a fraction of households’ financial assets fell
from 31.9 to 26.1 percent, or 5.8 percentage points. Mutual fund holdings,
however, rose only 3.2 percentage points, from 14.6 to 17.8 percent. The direct
purchase of stocks and bonds apparently accounted for the remainder of the
decline. Duca (1993) also points out that in 1992 sales of U.S. savings bonds
held for under five years surged when money market rates fell below the floor
of 4.16 percent paid on these instruments. It is likely that much of the inflows
into these savings bonds came from M2 deposits.
Finally, shift-adjusted M2 does not account for the increase in the use of
tax-sheltered forms of savings in the early 1990s. Governor Lindsey (1994)
reports that in 1993 tax-sheltered forms of income, particularly pension fund
and life insurance reserves, accounted for 70 percent of the net acquisition of
financial assets. This tax shifting was probably undertaken in response to the
increase in marginal tax rates in 1991 and 1993. Because the shift-adjustment
made here to M2 does not include deposit inflows to IRA/Keogh accounts
or deposit inflows from institutional investors, it does not capture the decline
in M2 that occurs when an individual withdraws funds from a time deposit
included in M2 and places them in a tax-sheltered investment. The increased
importance of tax-sheltered savings can be seen by comparing mutual fund
inflows in the mid-1980s and in the early 1990s. Over the three years 1985 to
1987, 43 percent of the inflows into bond and stock mutual funds went either
into accounts held by institutional investors like life insurance companies or
into IRA/Keogh accounts. This figure rose to 61 percent over the three-year
period 1991 to 1993 (see Table 3 in Appendix A).

36

4.

Federal Reserve Bank of Richmond Economic Quarterly

WILL M2 DEMAND BECOME STABLE AGAIN?

Will the behavior of the public’s demand for M2 become predictable again? In
particular, will the Fed again be able to set targets for M2 growth that can be
reliably related to the desired rate of growth of the public’s dollar expenditure?
The admittedly equivocal answer is, “It could.” The distressed condition of
banks in the early 1990s and the associated low rates of interest on bank deposits are not likely to recur. After the completion of the current rechanneling
of saving from the indirect intermediation provided by banks in favor of the
direct intermediation of Wall Street, it is possible that mutual funds will grow
steadily enough to avoid destabilizing M2 demand.
A somewhat different question is whether the Fed will be able to use
M2 again as an indicator of the impact of its policy actions on the behavior
of the public’s dollar expenditure. Even if the public continues to shift funds
between bank deposits and bond and stock mutual funds, a shift-adjusted M2,
by offsetting the resulting fluctuations in M2 demand, could become a useful
measure of the impact of monetary policy. Assuming that a primary reason that
shift-adjusted M2 does not fully account for the leftward shift in M2 demand
is the move toward tax-sheltered savings instruments, then, in the absence
of major future changes in the tax code, shift-adjusted M2 should become a
useful monetary indicator. It could become particularly useful in the event of
a financial disturbance causing a large, sudden outflow from mutual funds. In
that event, the resulting large changes in conventional M2 would be primarily
noise.
The future usefulness of the monetary aggregates as targets or indicators
also depends upon the tax and regulatory environment that banks will face. The
computer technology that made mutual funds possible also makes it possible
for banks to take deposits off their books in ways that can make it difficult to
measure money accurately. Banks will have an incentive to pursue this technology as long as they face tax and regulatory obstacles to collecting deposits
that are not incurred by other organizations competing for the public’s savings.
Two major handicaps that banks suffer in competing for the public’s savings are
the prohibition of payment of interest on demand deposits and the imposition
of a tax in the form of noninterest-bearing reserve requirements. (Goodfriend
and Hargraves [1983] discuss the role that reserve requirements have played
as a tax.) These two institutional features create incentives for banks to lower
the amount of demand deposits and other checkable deposits on their balance
sheets in ways that distort measurement of the monetary aggregates.
In particular, sweep accounts allow banks to avoid the prohibition of
the payment of explicit interest on demand deposits and the tax imposed by
noninterest-bearing reserve requirements. For example, on March 21, 1994, a
large bank advertised in The Wall Street Journal for an account that “automatically sweeps your excess cash into preselected investments daily.” In one

R. Darin and R. L. Hetzel: Shift-Adjusted M2 Indicator

37

version, the bank sweeps balances from a NOW account above a specified
amount into an MMDA account. Whenever the NOW account falls below a
specified minimum level, the bank transfers funds from the MMDA back into
the NOW account. (All funds are transferred back in with the sixth transfer
to avoid exceeding the legal limit of six automatic transfers per month from
an MMDA account.) Reid and Small (1993) state that “about a quarter of the
banks selling mutual funds provide retail sweep accounts whereby funds in
a depositor’s account in excess of a predetermined amount are automatically
invested in a money market mutual fund or some other uninsured investment
vehicle” (p. 12).
A group that helps banks design sweep accounts reports the benefits of
offering sweep accounts (Treasury Strategies 1994, pp. 24 and 26):
Reduced Reserves—Money market funds and trust sweeps move customer
funds off balance sheet. Reserves of those deposits are eliminated and the
amount of assets available for investment is increased.
Reduced FDIC premiums—Again, by moving funds out of insured depository
accounts, FDIC premiums are eliminated. This .23% savings is also a benefit
in which both the customer and bank can share.
Banks interested in encouraging fee payment for services and/or removing
demand balances from their balance sheets set target balances and minimum
sweep amounts at zero.

If a bank sweeps funds above a target balance into an MMDA, it does
not affect the behavior of M2, but it does reduce measured M1. M1 has not
been useful as a measure of money in the 1980s because of its high degree of
sensitivity to changes in market interest rates (Hetzel and Mehra 1989). In the
absence of a good measure of the interest sensitivity of the public’s demand
for M1 balances, when interest rates have changed, it has been hard to estimate
how M1 was changing relative to the public’s demand for it. The additional
observations made possible by the passage of time could make this econometric
problem manageable in the absence of sweep accounts. As Figure 4 shows, the
variations in M1 velocity are related to the cost of holding it. In time, it might
be possible to estimate again a reliable M1 demand function. In the future,
with a high degree of substitutability between shares in bond and stock mutual
funds and the time deposits in M2, a narrow aggregate like M1 could well be
more stably related to the public’s expenditure than M2.
Computer technology is making it easier to avoid the tax imposed by
noninterest-bearing reserve requirements. In principle, the Fed could solve the
problem by paying interest on required reserves. Such proposals were advanced
in discussions of the 1980 Monetary Control Act, but they were politically
unacceptable. Alternatively, the Board of Governors could reduce reserve requirements. It is, however, limited by the legal minimum reserve requirement
of 8 percent.

38

Federal Reserve Bank of Richmond Economic Quarterly

Figure 4 Annual M1 Velocity and the Opportunity Cost of Holding M1

7.25

16
M1 Velocity (left scale)

7.00

14

Cost of Holding M1 (right scale)

12
6.75
10
6.50
8
6.25
6
6.00

4
2

5.75
1980 81

82

83

84

85

86

87

88

89

90

91

92

93

+
Notes: M1 velocity is nominal GDP divided by M1. The opportunity cost of holding M1 is the
six-month commercial paper rate minus a weighted average of the rates paid on the components
of M1 (zero for currency and demand deposits).

Depending upon where “swept” funds are placed, sweep accounts can reduce measured M1 or M2. To an extent, the kind of shift-adjustment proposed
here could reduce the resulting mismeasurement of the monetary aggregates.
However, the data necessary to make such adjustments are never likely to
be complete and are available only with a lag. Bank intermediation bears the
burden of a large variety of regulations not imposed on other forms of financial
intermediation. It seems likely that in the future the ability to define monetary
aggregates that are useful for monetary policy will depend upon whether banks
have a continuing incentive to adapt to special taxes and regulations.

5.

SUMMARY

The growth of mutual funds that began in earnest in 1978 has increasingly
directed financial intermediation away from banks and directly into the money
and capital markets. Initially, growth occurred in money market mutual funds.
Because shares in these funds are redeemable at par, they could be included
in the definition of M2. Redefined to include money market mutual funds, M2
retained its long-run stable relationship with nominal output. Beginning in the
mid-1980s, growth in mutual funds has been concentrated in bond and stock
mutual funds. Because shares in these funds exhibit fluctuation in capital value,
they cannot be included in an expanded definition of M2 in a satisfactory way.

R. Darin and R. L. Hetzel: Shift-Adjusted M2 Indicator

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. M2 velocity rose as depositors redirected
savings from time deposits to bond and stock mutual funds. In principle, a
shift-adjusted M2, defined as M2 plus cumulative dollar inflows into bond and
stock mutual funds, could maintain the same relationship to the public’s dollar
expenditure as conventional M2. The shift-adjustment, however, accounts for
only about half of the unusual rise in M2 velocity that began in 1991. The
remainder to the rise in M2 velocity is probably caused by the use of bank
time deposits to purchase stocks and bonds directly and to make tax-sheltered
investments.

APPENDIX A
CONSTRUCTION OF SHIFT-ADJUSTED M2
Tables 3, 4, and 5 detail the construction of shift-adjusted M2 from the
Investment Company Institute (ICI) data contained in the monthly release
“Trends in Mutual Fund Activity.” As shown in Table 3, the first step is
to subtract redemptions (including exchanges out of bond and stock mutual
funds) from sales (including exchanges into bond and stock mutual funds but
excluding reinvested dividends) of mutual funds to derive total net inflows.
Subtracting net inflows due to institutions and net inflows into IRA/Keogh
accounts then yields the net inflows due to households that are assumed to be
coming out of deposits in M2. These net inflows are cumulated and added to
conventionally defined M2 to derive shift-adjusted M2. Unfortunately, there
are no direct measures of net inflows due to institutions or of net inflows into
IRA/Keogh accounts. Tables 4 and 5 explain the derivation of these two series.
ICI publishes figures on the dollar values of institutional and IRA/Keogh
accounts. Dollar inflows into these accounts can be calculated by subtracting
capital gains from the changes in their dollar value. The capital gains (losses)
for these accounts are assumed proportional to the capital gains (losses) for
all types of mutual fund accounts. Figures on the level of mutual fund assets
held in IRA/Keogh accounts are available monthly, while the figures for institutional accounts are only available for December of each year. Therefore, it
is necessary to interpolate monthly asset levels for institutional accounts from
year-end figures.

Table 3 Calculation of Household Net Inflows to Mutual Funds
Billions of dollars
Sales of
Mutual Funds
(excludes
reinvested
dividends)

1984

1985

1986

1987

Qtr.

1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4

Redemptions

Net Inflow
Due to
Institutions

Net Inflow
into IRA/
Keogh
Accounts

Net Inflow
Due to
Households
(3)−(4)−(5)

Annual
Totals

(1)

Year

Total
Net Inflow
(1)−(2)

(2)

(3)

(4)

(5)

(6)

(7)

15.49
13.84
16.05
15.69
24.35
32.36
35.22
44.11
58.92
66.67
68.40
74.54
94.17
76.20
61.88
48.03

9.61
9.12
8.91
11.54
12.48
13.41
15.86
16.17
22.51
31.67
37.13
39.18
46.57
68.37
63.99
69.61

5.88
4.72
7.14
4.15
11.87
18.95
19.36
27.94
36.41
35.00
31.26
35.36
47.60
7.83
−2.11
−21.58

1.39
1.74
2.19
1.20
2.01
3.64
4.58
8.07
11.06
11.85
11.00
13.03
10.66
0.35
−2.99
−8.16

1.11
1.00
1.22
0.69
2.03
3.29
1.69
2.74
5.53
5.83
2.89
2.67
7.10
7.31
0.63
−1.29

3.38
1.97
3.72
2.26
7.84
12.02
13.09
17.13
19.82
17.32
17.38
19.66
29.84
0.16
0.25
−12.13

11.33

50.08

74.18

18.12

1988

1989

1990

1991

1992

1993

1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4

42.03
41.28
30.87
33.23
37.06
41.99
44.48
49.10
52.58
51.98
45.77
44.80
61.82
71.68
77.92
94.14
115.06
106.57
113.12
119.03
148.38
150.13
161.92
171.71

44.65
44.83
40.02
41.09
42.27
39.52
39.98
41.96
45.73
40.77
46.96
40.34
45.87
48.53
46.27
58.12
70.03
62.33
69.04
79.17
87.61
88.99
98.02
114.01

−2.62
−3.55
−9.14
−7.86
−5.21
2.47
4.50
7.14
6.85
11.21
−1.19
4.46
15.95
23.16
31.65
36.01
45.02
44.25
44.07
39.85
60.77
61.14
63.90
57.70

−1.12
−1.33
−2.78
−2.41
−1.36
0.79
1.58
2.22
4.63
5.88
1.64
2.87
5.87
9.41
10.42
12.75
19.17
18.00
17.54
15.08
27.15
28.35
30.02
29.41

0.87
0.43
0.82
0.49
−0.52
1.24
1.81
1.96
4.36
3.15
0.44
−0.46
1.95
4.83
4.72
6.84
5.38
10.30
9.49
10.32
12.90
12.58
7.26
8.42

−2.37
−2.64
−7.19
−5.94
−3.34
0.44
1.11
2.96
−2.14
2.18
−3.27
2.04
8.13
8.92
16.51
16.42
20.47
15.95
17.04
14.46
20.73
20.21
26.62
19.87

−18.13

1.17

−1.17

49.98

67.92

87.43

Notes: All data are from the Investment Company Institute. Sales include exchanges into stock and bond mutual funds; redemptions include exchanges out
of stock and bond mutual funds. Quarterly data are sums of monthly figures. Annual totals are sums of quarterly data from the previous column.

Table 4 Aggressive-Growth Stock Funds
Net Inflows into IRA/Keogh Accounts, 1991
Millions of dollars
All accounts, including IRA/Keogh

1991
1992

Month

December
January
February
March
April
May
June
July
August
September
October
November
December

Total
(1)

Year

Monthly
Change
(2)

63287.3
65474.8
68050.4
66136.0
65941.1
67847.9
66295.1
69545.6
67472.7
68160.4
72134.5
78842.4
83365.3

2187.5
2575.6
−1914.4
−194.9
1906.8
−1552.8
3250.5
−2072.9
687.7
3974.1
6707.9
4522.9

IRA/Keogh accounts

Net Inflow

Capital
Gain (Loss)
(2)−(3)

(3)

(4)

2180.7
1555.3
1872.0
1050.4
1075.0
951.1
430.2
812.1
−214.7
414.7
543.3
2753.9
2276.0

632.2
703.6
−2964.8
−1269.9
955.7
−1983.0
2438.4
−1858.2
273.0
3430.8
3954.0
2246.9

Total

Monthly
Change

Capital
Gain (Loss)
[(5)÷(1)]×(4)

Net Inflow
(6)−(7)

(5)

(6)

(7)

(8)

18528.3
19425.1
19426.0
19691.8
19547.4
19844.0
19292.7
20205.9
19507.6
19608.1
20769.8
22596.5
23893.3

896.8
0.9
265.8
−144.4
296.6
−551.3
913.2
−698.3
100.5
1161.7
1826.7
1296.8

187.6
200.9
−882.8
−376.4
279.5
−577.1
708.5
−537.2
78.5
987.8
1133.2
644.0

709.2
−200.0
1148.6
232.0
17.1
25.8
204.7
−161.1
22.0
173.9
693.5
652.8

R. Darin and R. L. Hetzel: Shift-Adjusted M2 Indicator

43

Table 4 illustrates the estimation of net inflows into IRA/Keogh accounts
for aggressive-growth stock mutual funds. We repeat these calculations for
the other 18 categories of bond and stock mutual funds in order to arrive
at aggregate data. Column (1) of Table 4 lists monthly figures for the dollar
value of all aggressive-growth funds, and column (2) shows changes in
column (1). Column (3) shows monthly net inflows into aggressive-growth
funds. Capital gains (4) are the difference between the change in dollar value
in column (2) and net inflows in column (3). Column (5) lists the monthly
dollar values of aggressive-growth funds held in IRA/Keogh accounts, and
column (6) shows changes in (5). Column (7) shows estimated monthly capital
gains of IRA/Keogh accounts. It is derived by multiplying capital gains for all
aggressive-growth funds from column (4) by the percentage of all assets held in
IRA/Keogh accounts, which is column (5) divided by column (1). The resulting
capital gain for IRA/Keogh accounts (7) is then subtracted from the change
in the dollar value of IRA/Keogh accounts in column (6) to derive a monthly
figure for the net inflow into aggressive-growth funds held in IRA/Keogh accounts, which is shown in column (8). Summing these figures across all types
of mutual funds yields the figure in column (5), Table 3.
Table 5 illustrates the estimation of net inflows into institutional accounts.
Part 1 shows year-end figures for the dollar value of total and institutional
aggressive-growth funds. Column (c) shows the percentage held in institutional
accounts. In Part 2, column (1) shows the dollar value of total aggressivegrowth funds. The dollar amount held in institutional accounts, column (3), is
estimated as the product of column (1) and the fraction held in institutional
accounts, column (2), interpolated from the figures shown in column (c), Part
1. Column (4) shows monthly changes in these figures. Column (5), which
is copied from column (4) of Table 4, shows capital gains for all bond funds.
Capital gains for institutional accounts, column (6), is estimated by multiplying
capital gains for all accounts, column (5), by the percentage of assets in institutional accounts, column (2). Net inflows into institutional accounts, column (7),

Table 5 Aggressive-Growth Stock Funds, Institutional Accounts—
Part 1
Millions of dollars

1991
1992

Month

December
December

Institutional
Accounts

Percentage in
Institutional
Accounts

(a)

Year

All
Accounts

(b)

(c)

63287.3
83365.3

21035.0
24283.3

33.2%
29.1%

Table 5 Aggressive-Growth Stock Funds, Institutional Accounts—Part 2
Millions of dollars

1991
1992

Month

December
January
February
March
April
May
June
July
August
September
October
November
December

All
Accounts

Institutional
Accounts
(1)×(2)

Change in
Institutional
Accounts

(1)

Year

Interpolated
Fraction
Institutional
Accounts
(2)

(3)

(4)

63287.3
65474.8
68050.4
66136.0
65941.1
67847.9
66295.1
69545.6
67472.7
68160.4
72134.5
78842.4
83365.3

33.2%
32.9%
32.6%
32.2%
31.9%
31.5%
31.2%
30.8%
30.5%
30.2%
29.8%
29.5%
29.1%

21035.0
21537.9
22152.1
21302.5
21014.0
21389.3
20672.8
21448.3
20578.0
20554.4
21505.8
23235.8
24283.3

502.9
614.3
−849.6
−288.5
375.4
−716.5
775.5
−870.3
−23.6
951.5
1729.9
1047.5

Capital
Gain (Loss)
All Accounts

Capital
Gain (Loss)
Institutional
Accounts
(2)×(5)

Net Inflows
Institutional
Accounts
(4)−(6)

(5)

(6)

(7)

632.2
703.6
−2964.8
−1269.9
955.7
−1983.0
2438.4
−1858.2
273.0
3430.8
3954.0
2246.9

208.0
229.0
−955.0
−404.7
301.3
−618.4
752.0
−566.7
82.3
1022.8
1165.3
654.5

294.9
385.2
105.3
116.1
74.1
−98.1
23.5
−303.6
−106.0
−71.4
564.6
393.0

R. Darin and R. L. Hetzel: Shift-Adjusted M2 Indicator

45

is the difference between the change in the dollar amount in column (4) and
capital gains for institutional accounts, column (6). Summing across all types
of mutual funds yields the aggregate net inflow figure used in column (4),
Table 3.
Because mutual fund data are end-of-month figures while M2 data are
daily-average figures, the end-of-month figures are averaged to derive the
monthly mutual fund data series.

APPENDIX B
AN ESTIMATED M2 DEMAND REGRESSION
The estimated M2 demand regression below uses shift-adjusted M2 for the years
1991, 1992, and 1993. It is a regression of percentage changes in real M2 on
a dummy for the Korean War, percentage changes in real GDP, a contemporaneous and lagged value of changes in the financial market opportunity cost of
holding M2, and second differences of percentage changes in nominal output.
The last term is an estimate of the nominal rate of return on physical assets,
which is used by Friedman and Schwartz in their money demand regressions.
See Friedman and Schwartz (1982, Sec. 6.6.3) and Hetzel (1992). Estimation
of the following regression using shift-adjusted M2 rather than conventionally
defined M2 results in a reduction of the overprediction of real M2 of 23 percent
in 1991, 55 percent in 1992, and 47 percent in 1993.
M2 Demand Regression, 1950 to 1993
∆ ln rM2t = −3.0 ∗ Korea + .93 ∆ ln rGDPt − 1.1 ∆(Rt − RM2t )
(2.9)
(11.9)
(4.8)
ˆ
−1.2 ∆(Rt−1 − RM2t−1 ) − .51∆2 ln GDPt + et
(4.5)
(6.3)
CRSQ = .64

SEE = 1.6

DW = 1.4

DF = 39

Notes: Observations are annual averages. M2 is shift-adjusted for the years 1991, 1992, and
1993. rM2 is per-capita M2 deflated by the implicit GDP deflator. rGDP is real per-capita gross
domestic product. R is the four- to six-month commercial paper rate expressed as a decimal.
RM2 is a weighted average of the own rates of return paid on components of M2. Korea is a
shift dummy with a value of one in 1951, 1952, and 1953 and zero otherwise. Before 1959, M2
is M4 in Table 1 of Friedman and Schwartz (1970). From 1991 on, M2 includes inflows from
households into non-IRA/Keogh bond and stock mutual funds. ln is the natural logarithm and ∆
the first-difference operator. CRSQ is the corrected R-squared; SEE the standard error of estimate;
DW the Durbin-Watson statistic; and DF degrees of freedom. Absolute value of t-statistics are in
parentheses. Estimation is by ordinary least squares.

46

Federal Reserve Bank of Richmond Economic Quarterly

REFERENCES
American Banker. “Bank Mutual Funds Target Big Batch of Maturing CDs,”
March 22, 1993, p. 1.
Bennett, Barbara A. “ ‘Shift-Adjustments’ to the Monetary Aggregates,”
Federal Reserve Bank of San Francisco Economic Review, Spring 1982,
pp. 6–18.
Board of Governors of the Federal Reserve System. “Senior Financial Officer
Survey on Retail Mutual Funds,” May 12, 1993.
Business Week. “The Power of Mutual Funds,” January 18, 1993, p. 66.
Duca, John V. “Should Bond Funds Be Included in M2?” Research Paper
9321. Dallas: Federal Reserve Bank of Dallas, June 1993.
. “The Case of the ‘Missing M2,’ ” Federal Reserve Bank of Dallas
Economic Review, Second Quarter 1992, pp. 1–24.
The Economist. “Hole in the Wall,” September 4, 1993, p. 72.
Friedman, Milton, and Anna J. Schwartz. Monetary Trends in the United States
and the United Kingdom. Chicago: University of Chicago Press, 1982.
. Monetary Statistics of the United States. New York: National
Bureau of Economic Research, 1970.
Goodfriend, Marvin, and Monica Hargraves. “A Historical Assessment of
the Rationales and Functions of Reserve Requirements,” Federal Reserve
Bank of Richmond Economic Review, vol. 69 (March/April 1983),
pp. 3–21.
Hetzel, Robert L. “How Useful Is M2 Today?” Federal Reserve Bank
of Richmond Economic Review, vol. 78 (September/October 1992),
pp. 12–26.
. “M2 and Monetary Policy,” Federal Reserve Bank of Richmond
Economic Review, vol. 75 (September/October 1989), pp. 14–29.
, and Yash Mehra. “The Behavior of Money Demand in the 1980s,”
Journal of Money, Credit, and Banking, vol. 21 (November 1989), pp.
455–63.
Humphrey, Thomas M. “Precursors of the P-Star Model,” Federal Reserve
Bank of Richmond Economic Review, vol. 75 (July/August 1989), pp. 3–9.
Ireland, Peter N. “Price Stability Under Long-Run Targeting,” Federal Reserve
Bank of Richmond Economic Quarterly, vol. 79 (Winter 1993), pp. 25–45.
Kennickell, Arthur, and Martha Starr-McCluer. “Mutual Fund Ownership in the
1989 and 1992 SCF.” Memorandum, Board of Governors of the Federal
Reserve System, June 25, 1993.
Lindsey, Lawrence. “The Best of Times—the Worst of Times.” Remarks
made to the Baltimore Chapter of the Commercial Finance Association,
March 7, 1994.

R. Darin and R. L. Hetzel: Shift-Adjusted M2 Indicator

47

The New York Times. “The Next Giant in Mutual Funds?” March 20, 1994,
Sec. 3, p. 1.
Reid, Brian, and David Small. “Bank Involvement in the Mutual Fund
Industry.” Mimeograph, Board of Governors of the Federal Reserve
System, June 17, 1993.
Simpson, Thomas D., and Martha Scanlon. “Some Implications of the Growing
Importance of Mutual Funds.” Mimeograph, Board of Governors of the
Federal Reserve System, June 25, 1993.
Treasury Strategies. “Treasury Strategies’ 1994 Commercial Banking Sweep
Account Survey Results.” Chicago: Treasury Strategies, February 1994.
The Wall Street Journal. “T-Bill Trauma and the Meaning of Risk,”
February 12, 1993, p. C1.

The Role of Interest Rate
Swaps in Corporate Finance
Anatoli Kuprianov

A

n interest rate swap is a contractual agreement between two parties
to exchange a series of interest rate payments without exchanging the
underlying debt. The interest rate swap represents one example of a
general category of financial instruments known as derivative instruments. In
the most general terms, a derivative instrument is an agreement whose value
derives from some underlying market return, market price, or price index.
The rapid growth of the market for swaps and other derivatives in recent years has spurred considerable controversy over the economic rationale
for these instruments. Many observers have expressed alarm over the growth
and size of the market, arguing that interest rate swaps and other derivative
instruments threaten the stability of financial markets. Recently, such fears
have led both legislators and bank regulators to consider measures to curb the
growth of the market. Several legislators have begun to promote initiatives
to create an entirely new regulatory agency to supervise derivatives trading
activity. Underlying these initiatives is the premise that derivative instruments
increase aggregate risk in the economy, either by encouraging speculation or by
burdening firms with risks that management does not understand fully and is
incapable of controlling.1 To be certain, much of this criticism is aimed at many
of the more exotic derivative instruments that have begun to appear recently.
Nevertheless, it is difficult, if not impossible, to appreciate the economic role
of these more exotic instruments without an understanding of the role of the
interest rate swap, the most basic of the new generation of financial derivatives.
The views expressed herein are those of the author and do not necessarily represent the
views of either the Federal Reserve Bank of Richmond or the Board of Governors of the
Federal Reserve System. The motivation for this article grew out of discussions with Douglas
Diamond. Michael Dotsey, Jeff Lacker, Roy Webb, and John Weinberg provided thoughtful
criticism and helpful comments.
1 For

a review of these stated concerns, recent policy initiatives, and pending legislation, see
Cummins (1994a, 1994b), Karr (1994), and Rehm (1994).

Federal Reserve Bank of Richmond Economic Quarterly Volume 80/3 Summer 1994

49

50

Federal Reserve Bank of Richmond Economic Quarterly

Although the factors accounting for the remarkable growth of the swaps
market are yet to be fully understood, financial economists have proposed a
number of different hypotheses to explain how and why firms use interest rate
swaps. The early explanation, popular among market participants, was that
interest rate swaps lowered financing costs by making it possible for firms to
arbitrage the mispricing of credit risk. If this were the only rationale for interest
rate swaps, however, it would mean that these instruments exist only to facilitate a way around market inefficiencies and should become redundant once
arbitrage leads market participants to begin pricing credit risk correctly. Thus,
trading in interest rate swaps should die out over time as arbitrage opportunities
disappear—a prediction that is at odds with actual experience.
Other observers note that the advent of the interest rate swap coincided with
a period of extraordinary volatility in U.S. market interest rates, leading them
to attribute the rapid growth of interest rate derivatives to the desire on the part
of firms to hedge cash flows against the effects of interest rate volatility. The
timing of the appearance of interest rate swaps, coming as it did during a period of volatile rates, seems to lend support to such arguments. Risk avoidance
alone cannot explain the growth of the swaps market, however, because firms
can always protect themselves against rising interest rates simply by taking
out fixed-rate, long-term loans or by bypassing credit markets altogether and
issuing equity to fund investments.
Recent research emphasizes that interest rate swaps offer firms new
financing choices that were just not available before the advent of these instruments, and thus represent a true financial innovation. This research suggests
that the financing choices made available by interest rate swaps may help to
reduce default risk and may sometimes make it possible for firms to undertake
productive investments that would not be feasible otherwise. The discussion
that follows explains the basic mechanics of interest rate swaps and examines
these rationales in more detail.

1.

FUNDAMENTALS OF INTEREST RATE SWAPS

The most common type of interest rate swap is the fixed/floating swap in
which a fixed-rate payer promises to make periodic payments based on a fixed
interest rate to a floating-rate payer, who in turn agrees to make variable payments indexed to some short-term interest rate. Conventionally, the parties to
the agreement are termed counterparties. The size of the payments exchanged
by the counterparties is based on some stipulated notional principal amount,
which itself is not paid or received.
Interest rate swaps are traded over the counter. The over-the-counter (OTC)
market is comprised of a group of dealers, consisting of major international
commercial and investment banks, who communicate offers to buy and sell

A. Kuprianov: The Role of Interest Rate Swaps

51

swaps over telecommunications networks. Swap dealers intermediate cash flows
between different customers, acting as middlemen for each transaction. These
dealers act as market makers who quote bid and asked prices at which they
stand ready to either buy or sell an interest rate swap before a customer for
the other half of the transaction can be found. (By convention, the fixed-rate
payer in an interest rate swap is termed the buyer, while the floating-rate payer
is termed the seller.) The quoted spread allows the dealer to receive a higher
payment from one counterparty than is paid to the other.
Because swap dealers act as intermediaries, a swap customer need be
concerned only with the financial condition of the dealer and not with the
creditworthiness of the other ultimate counterparty to the agreement. Counterparty credit risk refers to the risk that a counterparty to an interest rate swap
will default when the agreement has value to the other party.2 Managing the
credit risk associated with swap transactions requires credit-evaluation skills
similar to those commonly associated with bank lending. As a result, commercial banks, which have traditionally specialized in credit-risk evaluation and
have the capital reserves necessary to support credit-risk management, have
come to dominate the market for interest rate swaps (Smith, Smithson, and
Wakeman 1986).
The discussion that follows largely abstracts from counterparty credit risk
and the role of swap dealers. In addition, the description of interest rate swaps
is stylized and omits many market conventions and other details so as to focus
on the fundamental economic features of swap transactions. For a more detailed description of interest rate swaps and other interest rate derivatives, see
Kuprianov (1993b). Burghardt et al. (1991) and Marshall and Kapner (1993)
provide more comprehensive treatments.
Mechanics of a Fixed/Floating Swap
The quoted price of an interest rate swap consists of two different interest rates.
In the case of a fixed/floating swap, the quoted interest rates involve a fixed and
a floating rate. The floating interest rate typically is indexed to some marketdetermined rate such as the Treasury bill rate or, more commonly, the threeor six-month London Interbank Offered Rate, or LIBOR.3 Such a swap is also
known as a generic, or plain-vanilla, swap.
The basic mechanics of a fixed/floating swap are relatively straightforward.
Consider an interest rate swap in which the parties to the agreement agree to
2 An increase in market interest rates, for example, increases the value of a swap agreement
to the fixed-rate payer, who will subsequently receive higher interest rate payments from the
floating-rate payer.
3 The London Interbank Offered Rate is the rate at which major international banks with
offices in London stand ready to accept deposits from one another. See Goodfriend (1993) or
Burghardt et al. (1991) for a detailed description of the Eurodollar market.

52

Federal Reserve Bank of Richmond Economic Quarterly

exchange payments at the end of each of T periods, indexed by the variable
t = 1, 2, . . . , T. Let rs denote the fixed rate and rs (t) denote the floating
interest rate on a fixed/floating swap. Payments between the fixed- and floatingrate payers commonly are scheduled for the same dates, in which case only net
amounts owed are exchanged. The net cost of the swap to the fixed-rate payer
at the end of each period would be rs − rs (t) for each $1 of notional principal.
If the swap’s fixed rate is greater than the variable rate at the end of a period
(i.e., rs > rs (t)), then the fixed-rate payer must pay the difference between
the fixed interest payment on the notional principal to the floating-rate payer.
Otherwise, the difference rs −rs (t) is negative, meaning that the fixed-rate payer
receives the difference from the floating-rate payer. The net cost of the swap
to the floating-rate payer is just the negative of this amount. For the sake of
notational convenience, the discussion that follows assumes that all swaps have
a notional principal of $1, unless otherwise noted.
Uses of Interest Rate Swaps—Synthetic Financing
Firms use interest rate swaps to change the effective maturity of interest-bearing
assets or liabilities. To illustrate, suppose a firm has short-term bank debt outstanding. At the start of each period this firm refinances its debt at the prevailing
short-term interest rate, rb (t). If short-term market interest rates are volatile, then
the firm’s financing costs will be volatile as well. By entering into an interest
rate swap, the firm can change its short-term floating-rate debt into a synthetic
fixed-rate obligation.
Suppose the firm enters into an interest rate swap as a fixed-rate payer. Its
resulting net payments in each period t = 1, 2, . . . , T of the agreement are
determined by adding the net payments required of a fixed-rate payer to the
cost of servicing its outstanding floating-rate debt.
Period t cost of servicing outstanding short-term debt
+ Period t cost of interest rate swap payments

rb (t)
rs − rs (t)

= Period t cost of synthetic fixed-rate financing

rs + [rb (t) − rs (t)]

Thus, the net cost of the synthetic fixed-rate financing is determined by the
swap fixed rate plus the difference between its short-term borrowing rate and
the floating-rate index.
Banks often index the short-term loan rates they charge their corporate
customers to LIBOR. Suppose the firm in this example is able to borrow at
LIBOR plus a credit-quality risk premium, or credit-quality spread, q(t).
Suppose further that the swap’s floating-rate index is LIBOR. Then,
rb (t) − rs (t) = [LIBOR(t) + q(t)] − LIBOR(t)
= q(t).

A. Kuprianov: The Role of Interest Rate Swaps

53

The period t cost of synthetic fixed-rate financing in this case is just rs + q(t),
the swap fixed rate plus the short-term credit-quality spread q(t).
Now consider the other side to this transaction. Suppose a firm with outstanding fixed-rate debt on which it pays an interest rate of rb enters into a swap
as a floating-rate payer so as to convert its fixed-rate obligation to a synthetic
floating-rate note. The net period t cost of this synthetic note is just the cost of
its fixed-rate obligation plus the net cost of the swap:
Period t cost of synthetic floating rate note = rs (t) + (rb − rs ).
The cost of synthetic floating-rate financing just equals the floating rate on the
interest rate swap plus the difference between the interest rate the firm pays
on its outstanding fixed-rate debt and the fixed interest rate it receives from its
swap counterparty.
Thus, interest rate swaps can be used to change the characteristics of a
firm’s outstanding debt obligations. Using interest rate swaps, firms can change
floating-rate debt into synthetic fixed-rate financing or, alternatively, a fixedrate obligation into synthetic floating-rate financing. But these observations
raise an obvious question. Why would a firm issue short-term debt only to
swap its interest payments into a longer-term, fixed-rate obligation rather than
just issue long-term, fixed-rate debt at the outset? Conversely, why would a firm
issue long-term debt and swap it into synthetic floating-rate debt rather than
simply issuing floating-rate debt at the outset? The next two sections explore
the rationales that have been offered to explain the widespread use of interest
rate swaps.

2.

INTEREST RATE SWAPS, ARBITRAGE, AND THE
THEORY OF COMPARATIVE ADVANTAGE

The rapid growth of the swaps market in recent years strongly suggests that
market participants must perceive significant benefits associated with the use of
such instruments. The rationale most frequently offered by market participants
is that interest rate swaps offer users an opportunity to reduce funding costs.4
Bicksler and Chen (1986) present what is perhaps the best-known exposition
of this viewpoint, which is based on the principle of comparative advantage.
In international trade theory, the principle of comparative advantage explains
the economic rationale for international trade by showing how different countries facing different opportunity costs in the production of different goods
can benefit from free trade with other countries. According to Bicksler and
Chen, differential information in different markets, institutional restrictions,
and transactions costs create “some market imperfections and the presence
4 For

example, see Rudnick (1987).

54

Federal Reserve Bank of Richmond Economic Quarterly

of comparative advantages among different borrowers in these markets” (p.
646). These market imperfections, according to Bicksler and Chen, provide the
economic rationale for interest rate swaps.
The Quality-Spread Differential
All firms pay a credit-quality premium over the risk-free rate when they issue
debt securities. These credit-quality premiums grow larger as the maturity of
the debt increases. Thus, whereas a firm, call it firm A, might pay a creditrisk premium of 50 basis points over the risk-free rate on its short-term debt
obligations, the credit-quality premium it is required to pay on longer-term
debt, say ten-year bonds, might rise to 100 basis points.
Not surprisingly, firms with good credit ratings pay lower risk premiums
than firms with lower credit ratings. Moreover, the credit-quality premium rises
faster with maturity for poorer credits than for good credits. Thus, if firm B
has a poorer credit rating than firm A, it might pay a credit-risk premium of
100 basis points on its short-term debt while finding it necessary to pay 250
basis points over the risk-free rate to issue long-term bonds. The quality spread
between the interest rate paid by the lower-rated firm and that paid by the
higher-rated firm is only 50 basis points in the short-term debt market, but
rises to 150 basis points at longer maturities. The quality-spread differential,
the difference in the quality spread at two different maturities, is 100 basis
points in this example. Firm A has an absolute cost advantage in raising funds
in either the short- or long-term debt markets, but firm B has a comparative
advantage in raising funds in short-term debt markets.
To explore this line of reasoning in more detail, suppose firms A and B
both need to borrow funds for the next two periods, t = 1, 2. Let rf (t) denote
the period t short-term (one-period) risk-free interest rate and rf the long-term
(two-period) fixed risk-free rate. The period t cost of short-term debt to firm A
is the short-term risk-free rate plus the credit-quality spread qA (t). To issue longterm fixed-rate debt, firm A would be required to pay rf + qA , where qA denotes
the long-term quality spread. Define qB (t) and qB analogously. Assuming firm
A has the better credit rating,
qA (1) ≤ qB (1), and
qA ≤ qB .
An increasing quality spread means that
qB (1) − qA (1) < qB − qA .
Conditions Necessary for Arbitrage to Be Feasible
Under certain assumptions, both firms could lower their funding costs if firm
A were to issue long-term debt, firm B were to issue short-term debt, and they

A. Kuprianov: The Role of Interest Rate Swaps

55

swapped interest payments. To see how this would work, assume A and B enter
into an interest rate swap with B as a fixed-rate payer and A as the floating-rate
payer. As above, let rs denote the fixed swap rate for a two-period agreement.
To minimize the notational burden, assume that the swap floating rate is just
the risk-free rate of interest, rf (t). The resulting period t (t = 1, 2) net cost of
synthetic fixed-rate financing to firm B is:
Period t cost of servicing short-term, floating-rate debt
+ Period t cost of interest rate swap

rf (t) + qB (t)
rs − rf (t)

= Period t cost of synthetic fixed-rate financing

rs + qB (t)

The synthetic fixed-rate financing will be less costly for firm B than actual
fixed-rate financing in each period t if and only if
rs + qB (t) ≤ rf + qB ,
which implies
rs − rf ≤ qB − qB (t).
The term on the left-hand side of the last expression is the swap fixed-rate
credit-quality spread, or risk premium, over the risk-free long-term interest
rate. Thus, the quality spread associated with the swap fixed rate must be less
than the increase in the credit-risk premium firm B would need to pay to issue
long-term debt. Otherwise, synthetic fixed-rate financing will not be cheaper
than actual fixed-rate financing.
Now examine the transaction from the vantage point of firm A, the floatingrate payer. The cost of synthetic floating-rate financing is determined by the
cost of servicing fixed-rate debt plus the net cost of the swap:
Period t cost of servicing fixed-rate debt
+ Period t cost of swap

r f + qA
rs (t) − rs

= Period t cost of synthetic floating-rate financing

rs (t) + (rf + qA − rs )

Period t synthetic floating-rate financing will cost less than actual floating-rate
financing for firm A if
rs (t) + (rf + qA − rs ) ≤ rs (t) + qA (t),
which, in turn, requires that
qA − qA (t) ≤ rs − rf .
That is, the increase in the credit-quality premium firm A must pay when
issuing long-term fixed-rate debt must be smaller than the risk premium it
receives from the swap’s fixed-rate payer.

56

Federal Reserve Bank of Richmond Economic Quarterly

Combining results, firm A will have a comparative advantage in issuing
long-term debt and firm B in issuing short-term debt if
qA − qA (t) ≤ rs − rf ≤ qB − qB (t),

t = 1, 2.

For the floating-rate payer, synthetic floating-rate financing is cheaper than
actual short-term financing if the interest rate swap quality spread (which the
floating-rate payer receives) is greater than the added interest expense of longterm debt. For the fixed-rate payer, synthetic fixed-rate financing is less costly
than issuing long-term bonds if the premium of the fixed swap rate over the
two-period risk-free rate is less than the difference between its long-term and
short-term quality spreads. Both parties will enjoy gains from trade if the swap
floating-rate payer charges the fixed-rate payer a smaller credit-quality spread
than the fixed-rate payer would be forced to pay in the bond market.
The astute reader will notice that the conditions outlined above require the
parties to the agreement to know future values of qA (t) and qB (t). Both firms
know their current short-term quality spreads along with qA and qB at the start
of period 1. But it is unrealistic to assume that firms will know their future
short-term quality spreads with certainty. Bicksler and Chen (1986) implicitly
assume that firms expect the above relations to hold (at least on average) based
on the past behavior of the quality-spread differential.
There is empirical evidence that long-term quality spreads for lower-rated
counterparties are lower in the interest rate swap market than in credit markets
(Sun, Sundaresan, and Wang 1993). Smith, Smithson, and Wakeman (1988)
and Litzenberger (1992), among others, note that the expected loss to a swap
counterparty in the event of a default is much less than that associated with
holding a bond because interest rate swaps are not funding transactions and involve no exchange of principal. Moreover, swaps receive preferential treatment
under the Bankruptcy Code in the event of a default. Under these conditions
it may not seem surprising to find that quality spreads do not increase as
rapidly in the swap market and that the cost of synthetic fixed-rate financing
often seems lower than that of actual long-term financing. But while interest
rate swaps might offer firms a way around paying increasing quality-spread
differentials, synthetic fixed-rate financing does not offer firms the proverbial
“free lunch.” As the following discussion will show, the risks responsible for
increasing quality-spread differentials do not disappear when firms use interest
rate swaps.
Criticisms of the Comparative Advantage Rationale
Smith, Smithson, and Wakeman (1986, 1988) argue that observed behavior in
the swap market is not consistent with classic financial arbitrage of the type
described by proponents of the comparative advantage rationale. The use of
interest rate swaps to arbitrage quality-spread differentials, they argue, should
increase the demand for short-term loans among firms with poor credit ratings

A. Kuprianov: The Role of Interest Rate Swaps

57

while reducing demand for “overpriced” long-term loans. Eventually, such a
process should reduce quality-spread differentials and therefore reduce demand
for interest rate swaps. In fact, Bicksler and Chen (1986) did report evidence
of declining quality-spread differentials as interest rate swaps came into widespread use. But trading activity in interest rate swaps has shown no sign of
abating even as quality-spread differentials have declined. To the contrary, the
market for interest rate swaps has grown exponentially since these instruments
were first introduced in the early 1980s. According to the International Swap
and Derivatives Association, the total notional principal amount of interest rate
swaps outstanding has risen from $683 billion in 1987 to just over $3.8 trillion
as of year-end 1992.
Smith, Smithson, and Wakeman (1986, 1988) observe that much of the
apparent savings from the use of swaps can be attributed to the absence of a
prepayment option on generic swaps. Fixed-rate bonds typically carry a prepayment option that allows the borrower to call and refund a debt issue should
market interest rates fall. The cost of this option is incorporated into the interest
rate the firm is required to pay on such bonds. In contrast, the generic interest
rate swap carries no such prepayment option. Early termination of a swap
agreement requires the value of the contract to be marked to market, with any
remaining amounts to be paid in full. A borrower can buy a “callable” swap,
which permits early termination, but must pay an additional premium for this
option. Thus, to be fair, the cost of actual long-term debt should be compared
to the cost of callable synthetic fixed-rate financing, which would reduce the
measured cost advantage resulting from the use of interest rate swaps.
Another problem with the comparative advantage rationale, noted by Smith,
Smithson, and Wakeman (1988), is that it does not address the underlying
reason for the existence of quality-spread differentials between short- and longterm debt. Loeys (1985) notes that short-term creditors implicitly hold an option
to refuse to refinance outstanding loans. He attributes the difference in quality spreads between short- and long-term debt to the value of that implicit
option.5 But while this option is valuable to lenders, it increases the risk of
a future funding crisis to the borrowing firm, thereby increasing the risk of
bankruptcy proceedings. The risk that lenders will refuse to refinance outstanding short-term debt is known as liquidity risk, or rollover risk. From the
firm’s perspective, added liquidity risk represents an implicit cost of short-term
financing.
Bansal, Bicksler, Chen, and Marshall (1993) compare the cost of synthetic
fixed-rate financing with the cost of actual fixed-rate financing when the hidden
costs noted above are taken into account. They control for the cost of liquidity
5 Wall and Pringle (1987) note that Loeys’ hypothesis is only consistent with increasing
quality-spread differentials if the ability of short-term debtholders to refuse to renew outstanding
debt makes it easier to force reorganization of a financially distressed firm.

58

Federal Reserve Bank of Richmond Economic Quarterly

risk by adding in the expense of a bank standby letter of credit in which a bank
guarantees that it will assume a firm’s outstanding debt if the firm finds itself
unable to roll over a commercial paper issue. To take account of the value of a
prepayment option, they add the premium on a callable swap into the total cost
of synthetic fixed-rate financing. Finally, they also take account of transactions
and administrative costs. The cost advantage of synthetic fixed-rate financing
disappears once these costs are taken into account. Bansal et al. conclude that
“a significant part of the reputed gains from swaps . . . were illusory, stemming
from the way the gains have been calculated in practice” (p. 91).

3.

ALTERNATIVE EXPLANATIONS

Smith, Smithson, and Wakeman (1988) hypothesize that the rationale for interest rate swaps lies with their usefulness in creating new synthetic financial
instruments for risk management. The early 1980s brought unprecedented
interest rate volatility, exposing firms to the risk of fluctuating funding costs.
Rawls and Smithson (1990) argue that these events led to an increased demand
for risk-management services on the part of firms. Smith, Smithson, and Wakeman (1988) argue that the growth of the swaps market effectively increased
market liquidity for forward interest rate contracts, citing rapidly falling bidask spreads for interest rate swaps as evidence.6 Thus, they argue, trading in
interest rate swaps has helped to complete forward markets and to lower the
cost to firms of managing their exposure to interest rate risk.
The Role for Hedging in the Theory of Corporate Finance
The foregoing discussion has focused on increased volatility in financial markets as the major factor behind the growth of the derivatives market in recent
years. That firms would wish to hedge against the risk of such volatility simply
has been assumed. But as Smith, Smithson, and Wilford (1990) note, much
of textbook portfolio theory suggests that not hedging might be a firm’s best
policy. The well-known Modigliani-Miller theorem states that a firm’s financing
decisions have no effect on its market value when (1) a firm’s management and
outside investors share the same information about the returns accruing to all
investment projects; (2) transactions costs are negligible; (3) a firm’s tax bill is
not affected by its financing decisions; and (4) the costs of financial distress are
inconsequential. Under these assumptions, portfolio theory holds that individual
investors can efficiently diversify away volatility in individual firm profits at
6 An

interest rate swap can be viewed as a bundle of forward contracts (see Smith, Smithson, and Wakeman [1988]). Sun, Sundaresan, and Wang (1993) find that bid-ask spreads in the
interest rate swap market are smaller than those in the underlying market for long-term, fixed-rate
corporate debt.

A. Kuprianov: The Role of Interest Rate Swaps

59

least as well as the firms themselves. If so, there is no reason for firms to
expend resources hedging against volatility in future cash flows.
When these assumptions are relaxed, however, financing decisions may
affect a firm’s value. First, a firm’s managers can be expected to know more
about the risks and returns to different investment projects than outside
investors. Second, the existence of transactions costs makes some kinds of
financing decisions more costly than others. Third, a volatile cash flow stream
can make a firm more susceptible to financial distress and bankruptcy, which
can be extremely costly as well as threatening management with loss of control.
Fourth, existing tax laws favor certain forms of funding over others. Firms are
permitted to treat interest payments on debt as a tax-deductible expense, but
not dividend payments to shareholders. Moreover, tax laws sometimes favor
the use of certain derivative instruments to restructure cash flows. For all these
reasons, firms will sometimes have incentives to hedge their cash flows.
Agency Costs as a Rationale for Interest Rate Swaps:
Incentives to Undertake Synthetic Fixed-Rate Financing
Miller (1977) stresses the tax advantages of debt to explain why firms finance
their investments with a combination of debt and equity. As Jensen and
Meckling (1976) note, however, firms issued debt long before corporate income taxes came into existence. As an alternative rationale for debt, Jensen
and Meckling emphasize the difficulty outside investors face in evaluating
the performance of managers. As defined by Jensen and Meckling, an agency
relationship is “a contract under which one or more persons (the principal(s))
engage another person (the agent) to perform some service on their behalf which
involves delegating some decision making authority to the agent” (p. 308). If
principals could always costlessly monitor the behavior of their agents, they
could ensure that agents would always act in their best interests. Monitoring
the behavior of agents is costly, however, and requires principals to expend
resources. Thus, the agent might be required to incur certain bonding expenditures. Finally, if principals cannot ensure that agents will always act in their
best interests despite monitoring and bonding, there may be some deadweight
residual loss. Jensen and Meckling define “agency costs” as the sum of these
expenditures. They show that debt finance can reduce overall agency costs for
a firm, but their analysis does not consider the problem of interest rate volatility
and the question of whether a firm should issue short-term or long-term debt.
Interest rate volatility would not affect the investment or financing decisions of firms if revenues were always perfectly correlated with changes in
market interest rates, because revenues would vary along with debt servicing
costs in this case. Revenues typically are not perfectly correlated with market
interest rates, however. As a result, interest rate volatility can increase the risk
of financial distress. If financial distress is costly (because of the administrative

60

Federal Reserve Bank of Richmond Economic Quarterly

costs of bankruptcy proceedings), or if the firm’s management values its right
to exercise control over the affairs of the organization, management will have
an incentive to mitigate such risks. Ideally, then, a firm would wish to schedule
repayment of its capital financing costs to match the realization of revenues
from its investments (Myers 1977). If a firm’s revenues are completely uncorrelated with market interest rates, it could minimize the risk of future financial
distress by funding long-term investments with long-term, fixed-rate debt and
short-term investments with short-term debt.
Long-term lending carries substantial risks from an outside investor’s viewpoint, however. A borrower’s financial condition can deteriorate substantially
over the term of the loan. Moreover, as Jensen and Meckling (1976) note,
management has an incentive to take actions that benefit shareholders at the
expense of creditors once a firm has received the proceeds of the loan. As
an example, management can pursue high-risk strategies or otherwise attempt
to dissipate the organization’s assets by paying excessive dividends. Creditors
could prevent such behavior if (1) they always knew as much about a firm’s
investment opportunities as its managers and (2) they could monitor management’s behavior costlessly. But such actions are prohibitively costly for most
creditors, if even feasible, for they would involve duplicating essentially all
the functions of management. For these reasons, bondholders often demand
loan covenants that limit management’s discretion in deploying loan proceeds.
Typically such covenants give creditors the right to exercise greater control
over the firm when a condition of the loan is violated or in the event of a
material deterioration in its financial condition. To be certain, enforcement of
loan covenants still requires some monitoring on the part of creditors. Jensen
and Meckling (1976) argue that these monitoring costs are ultimately borne by
borrowers through higher interest rates.
Wall (1989) argues that the existence of agency costs is one reason that
quality spreads widen with debt maturity. He notes that while established firms
with good credit ratings and access to low-cost credit have incentives to limit
risks, newer and smaller firms do not have the same incentives. Like Loeys
(1985), Wall gives special emphasis to the influence creditors can exercise
over borrowers when renegotiating short-term loans. Wall was among the first
to observe that synthetic fixed-rate financing carries different incentives for
borrowers than actual fixed-rate financing. To understand why this might be
so, notice that the interest rate lenders charge a borrower when renewing a
short-term loan can change for two reasons: (1) a change in market interest
rates or (2) a change in the firm-specific credit-quality risk premium. Interest
rate swaps compensate the borrower only for changes in market rates, and not
for changes in the short-term quality spread. Thus, as noted earlier, the cost
of synthetic fixed-rate financing is rs + [rb (t) − rs (t)], the swap fixed rate plus
the quality spread between the rate the firm pays on its short-term debt and
the swap floating-rate index. A firm that chooses synthetic fixed-rate financing

A. Kuprianov: The Role of Interest Rate Swaps

61

faces the risk that the quality spread [rb (t) − rs (t)] might rise if lenders realize
that management has increased the firm’s riskiness. In extreme cases, the firm
might even find itself unable to roll over its outstanding short-term debt and
be forced into bankruptcy proceedings.
Wall’s (1989) rationale for interest rate swaps lies with the observation
that synthetic fixed-rate financing should discourage management from pursuing risky investment strategies.7 According to this argument, interest rate swaps
lower funding costs by controlling the adverse incentives a firm’s management
might have to increase the risk assumed by the firm to the detriment of creditors.
Thus, interest rate swaps do make it possible for firms to reduce financing costs
in Wall’s theory. But the savings attributable to the use of swaps result from
lower agency costs and do not constitute arbitrage in the sense that term is
normally understood.
The Problem of Adverse Selection:
More Incentives to Borrow Short and Swap into Fixed
Flannery (1986) and Diamond (1991) investigate the determinants of debt maturity by focusing attention on the incentives borrowers have to signal information
to lenders about their financial condition. Their analysis is based on the assumption that outside investors have imperfect information about firms, and so are
unable to discriminate perfectly between safe firms and relatively risky firms.
If outside investors cannot perfectly discriminate between risky and safe firms,
they will demand default-risk premiums on long-term debt that may appear
excessively high to relatively safe borrowers. Conversely, the managers of a
risky firm recognize that there is a high probability that the organization’s
financial condition will deteriorate, leading them to prefer long-term debt over
short-term debt.
Firms that lenders can identify as risky borrowers have difficulty securing
long-term loans and are forced to issue short-term debt that matures before the
returns to an investment are realized. Often such firms must obtain their credit
lines from banks, which specialize in credit evaluation and are well positioned
to monitor the firm’s activities. In the event that a firm’s financial condition
deteriorates, lenders can demand a higher interest rate upon refinancing, can
further restrict the discretion of management, can engage in more intensive
monitoring, can take some combination of these actions, or can even refuse to
refinance outstanding debt. A firm that defaults on its outstanding debt obligations can be forced into bankruptcy proceedings.
If a firm’s management believes that default premiums on long-term loans
are excessive, it might choose a short-term funding strategy. By voluntarily
7 Diamond

(1984) makes a similar observation regarding the optimal hedging behavior of
firms, although he does not discuss the rationale for interest rate swaps per se.

62

Federal Reserve Bank of Richmond Economic Quarterly

taking on liquidity risk, management can signal that it does not expect the
firm’s condition to deteriorate in the future. Over time a firm that consistently
demonstrates its ability to meet its financial obligations develops a reputation as
a safe firm. Thus, a safe firm might employ a short-term funding strategy until
it can convince creditors to extend long-term loans on better terms (Diamond
1991).
One drawback to such a strategy is that it can leave the firm’s cash flows
unhedged. Arak, Estrella, Goodman, and Silver (1988) stress that interest rate
swaps are not redundant securities, but offer firms new financing choices that
were not previously available in credit markets. Like Wall (1989), Arak et al.
note that synthetic fixed-rate financing requires the borrower to bear the risk of
changes in the short-term credit-risk premium. Their hypothesized rationale for
interest rate swaps differs somewhat from that of Wall, however. They hypothesize that firms may have an incentive to bear rollover risk when management
is more optimistic about a firm’s future prospects than the market. If a firm’s
management is optimistic about its financial condition, it may choose to issue
short-term debt in the expectation that the quality spread will fall in the future.
In effect, the firm speculates on its own quality spread while using swaps to
immunize itself against market risk.
Titman (1992) and Minton (1993a) derive conditions under which a firm’s
best strategy is to use interest rate swaps in conjunction with short-term financing. Like Flannery (1986) and Diamond (1991), Titman and Minton emphasize
that firms may have an incentive to bear the liquidity risk associated with
short-term debt finance as a means of signaling management’s belief that the
firm’s financial prospects will improve. Titman finds conditions under which
synthetic fixed-rate financing gives firms an incentive to undertake safer investments. Minton finds that giving firms the option of using interest rate swaps
can reduce default risk and, in doing so, increase the capacity of firms to undertake productive long-term investment. Both Titman and Minton find plausible
conditions under which interest rate swaps reduce financing costs, albeit not
through the channels of financial arbitrage.
Notice that the basic logic of the adverse selection rationale runs closely
parallel to that of Wall’s (1989) agency cost rationale. While borrowers in
Titman and Minton’s models choose short-term financing to signal management’s belief that the firm is creditworthy, the act of taking on short-term debt
mitigates incentives to take on added risk once loan proceeds are received, just
as Wall predicts.
Incentives to Borrow Fixed and Swap into Floating
The preceding discussion has focused on the incentives firms might have to
enter into a swap as a fixed-rate payer. But every swap agreement must also
have a floating-rate payer. Wall (1989) and Titman (1992) hypothesize that

A. Kuprianov: The Role of Interest Rate Swaps

63

floating-rate payers share in the gains fixed-rate payers receive from synthetic
fixed-rate financing. Litzenberger (1992) notes at least two reasons why highly
rated firms may be able to lower funding costs by issuing callable fixed-rate
debt and then swapping into synthetic floating-rate debt. First, like Wall and
Titman, he hypothesizes that floating-rate payers essentially act as financial
intermediaries that earn income in return for managing a diversified portfolio
of risky contractual obligations. The total exposure resulting from this activity is small, he argues, because (1) the credit risk associated with an interest
rate swap is much smaller than that associated with actual lending; (2) most
swap agreements take place among parties with at least single A credit ratings
(lower-rated counterparties are rejected or required to post collateral); and (3)
a diversified swap portfolio has little risk of a large credit loss.
Second, Litzenberger also notes that the highly rated AAA firms that typically become floating-rate payers often issue callable fixed-rate notes, and
then sell the prepayment options on these notes by selling callable swaps to
swap dealers. He argues that such transactions can create synthetic floating-rate
financing at a modest savings in cost because the prepayment options attached
to fixed-rate debt tend to be underpriced, probably because of a past history
of non-optimal exercises on such options. Thus, Litzenberger attributes at least
part of the incentive to become a floating-rate payer to arbitrage opportunities
created by the mispricing of prepayment options for corporate bonds.
Smith, Smithson, and Wakeman (1988) emphasize that interest rate swaps
can help to conserve on transactions costs. As an example, they note that it
can be cheaper to sell an interest rate swap than to call and refund outstanding
fixed-rate debt.

4.

A COMPARISON OF INTEREST RATE FUTURES AND
INTEREST RATE SWAPS

A discussion of the economic role of interest rate swaps would not be complete
without at least some mention of interest rate futures. Interest rate futures can
be used to create synthetic fixed-rate debt in much the same way as interest rate
futures. In particular, selling a “strip,” or sequence, of Eurodollar futures with
successive maturity dates can be compared to buying an interest rate swap.
To see how interest rate futures can substitute for an interest rate swap,
recall that the buyer (fixed-rate payer) of an interest rate swap receives a net
payment from the seller whenever the floating-rate index exceeds the swap
fixed rate. In the case of a generic swap with a floating rate indexed to some
maturity of LIBOR, the buyer receives the difference in interest on the notional principal amount whenever the specified maturity of LIBOR exceeds the
swap fixed rate. When LIBOR is below the fixed rate, the buyer must pay the
difference in interest to the seller.

64

Federal Reserve Bank of Richmond Economic Quarterly

Selling a strip of Eurodollar futures creates a similar pattern of returns
and payments. The seller of a Eurodollar contract receives the difference in
interest on the notional principal ($1 million) when the futures rate negotiated
at the outset of the agreement turns out to be less than the value of three-month
LIBOR prevailing on the contract maturity date. Otherwise, the seller must pay
the difference in interest to the buyer. Thus, selling a strip of Eurodollar futures
produces a return stream comparable to that of a generic interest rate swap.
Because of this similarity, an implied swap rate can be derived from Eurodollar
futures rates.8 Minton (1993b) finds evidence that the behavior of swap market
rates is closely related to this implied swap rate.
These observations suggest that much of the rationale for interest rate swaps
discussed above must also apply to interest rate futures—in particular, to Eurodollar futures. The foregoing discussion has focused on interest rate swaps
because the growth of trading in Eurodollar futures in recent years appears
to have been driven by the growth of the swap market. Although trading in
Eurodollar futures predates the advent of the interest rate swap, trading was
limited to contracts extending two years into the future at the time of the first
widely publicized interest rate swap in 1982. As a result, Eurodollar futures
were not as well suited for use in creating synthetic long-term financing as
were interest rate swaps. More recently, the Chicago Mercantile Exchange has
begun listing Eurodollar futures for delivery as far as ten years into the future.
Burghardt et al. (1991) attribute the recent expansion of trading in Eurodollar
futures to the growth of the interest rate swap market. Swap dealers in particular often use Eurodollar futures to hedge their commitments. Thus, although
interest rate futures contracts can substitute for interest rate swaps, it was the
growth of the swap market that had the greatest effect on corporate finance.
Kawaller (1990) and Minton (1993b) discuss the factors influencing the
choice between interest rate futures and interest rate swaps. Kawaller emphasizes transactions costs and other practical considerations of managing a futures
position as key factors influencing the choice between interest rate futures and
interest rate swaps. The main benefit of a swap is that it can be custom-tailored
to the needs of an individual firm, so that managing an interest rate swap is
relatively easy compared to managing a futures market position. A firm that
enters into an interest rate swap faces a set schedule for receiving or making
its payments. As long as nothing happens to change the firm’s underlying
exposure to interest rates—that is, as long as nothing has happened to change
the reasons the firm decided to create synthetic fixed- or floating-rate financing
in the first place—managing an outstanding swap position merely requires the
firm’s treasurer to make or collect scheduled payments.

8 For

more detailed expositions, see Burghardt et al. (1991) and Kawaller (1990).

A. Kuprianov: The Role of Interest Rate Swaps

65

The principal disadvantage of interest rate swaps relative to interest rate
futures lies with counterparty credit risk. Exchange-traded instruments such
as interest rate futures are backed by a system of margin requirements, along
with the guarantee of the exchange clearinghouse (which, in turn, is jointly
backed by the paid-in capital of the clearinghouse member firms). This system
of safeguards removes virtually all risk of default in the futures market. In
contrast, a counterparty to an interest rate swap is exposed to the risk that the
other counterparty might default. To be certain, most interest rate swaps take
place between relatively creditworthy counterparties. Nonetheless, credit risk
is a greater concern with interest rate swaps than with futures contracts.
The very factors that make interest rate futures safer also make managing
a futures position somewhat more challenging than managing a swap commitment, however. First, a party to a futures contract is required to post margin
before being permitted to buy or sell a futures contract. Second, the futures
exchanges mark all outstanding positions to market at the end of each trading
session, adding any realized gains or subtracting any realized losses from each
trader’s margin account. While this procedure minimizes default risk, it exposes any party with an open futures position to the risk of margin calls. As a
consequence, payments are less predictable in the short run with a futures position than with an interest rate swap. Third, futures contracts are standardized
agreements. Contract standardization, along with the clearinghouse guarantee,
facilitates trading in futures contracts. Futures markets tend to be more liquid
than OTC markets (and actual cash markets for that matter) as a result, lowering
transactions costs. But while contract standardization facilitates trading, it also
means that an interest rate futures contract will almost never be perfectly suited
to the needs of any one trader.9 Thus, an interest rate futures position requires
greater monitoring and can be more difficult to execute unless a firm maintains
a staff devoted to trading futures contracts.
While the factors that determine the choice between interest rate futures
and interest rate swaps is of great interest to practitioners, it has not received
a great deal of attention in the academic finance literature. Minton’s (1993a)
model of the hedging behavior of firms is a noteworthy exception. Minton finds
that relatively safe firms—firms that expect their future credit-quality spreads
to fall—may have an incentive to choose swaps over futures contracts so as to
avoid the cost of margin requirements.

5.

CONCLUDING COMMENTS

The reasons for the extraordinary growth of the swap market in recent years are
not yet fully understood. But there seems to be a consensus that the market has
9 For

(1993a).

a more detailed description of futures exchanges and interest rate futures, see Kuprianov

66

Federal Reserve Bank of Richmond Economic Quarterly

developed because interest rate swaps offer firms financing choices that were
not available before the advent of these instruments. In this respect, interest
rate swaps represent a true financial innovation.
The early rationale offered for the existence of the market—that firms used
interest rate swaps to arbitrage credit market inefficiencies—cannot by itself
explain the exponential growth of the market over the past decade. By the same
token, it is unlikely that firms would use interest rate swaps if they did not lower
financing costs in some way. Recent research suggests at least two reasons why
firms use interest rate swaps. First, in cases where a firm’s management expects
its financial condition to improve, interest rate swaps make it possible for firms
to hedge against changes in market interest rates while avoiding excessive
fixed-rate quality-spread premiums. Second, interest rate swaps make possible
financial arrangements that reduce the incentives of borrowing firms to take on
added risk at the expense of creditors.
Conceived in the wake of unprecedented interest rate volatility brought
about by a decade of accelerating inflation, the interest rate swap was born of
necessity. In a period of low interest rate volatility, the choice between shortand long-term borrowing was primarily a choice between fixed and floating
credit-quality spreads. With rising interest rate volatility, however, the ability
to separate the effects of changes in market rates from changes in credit-quality
spreads became more valuable, leading firms to experiment with alternative
financing schemes. Based on the results of recent research, it appears that
interest rate swaps have helped firms to weather the uncertainties of volatile
financial markets by reducing default risk and facilitating increased productive
investment.

REFERENCES
Arak, Marcelle, Arturo Estrella, Laurie S. Goodman, and Andrew Silver. “Interest Rate Swaps: An Alternative Explanation,” Financial Management,
Summer 1988, pp. 12–18.
Bansal, Vipul K., James L. Bicksler, Andrew H. Chen, and John F. Marshall.
“Gains from Synthetic Financing with Interest Rate Swaps: Fact or
Fancy?” Continental Bank Journal of Applied Corporate Finance, vol. 6
(Fall 1993), pp. 91–94.
Bicksler, James, and Andrew H. Chen. “An Economic Analysis of Interest
Rate Swaps,” The Journal of Finance, vol. 41 (July 1986), pp. 645–55.
Burghardt, Belton, Luce, and McVey. Eurodollar Futures and Options.
Chicago: Probus Publishing Company, 1991.

A. Kuprianov: The Role of Interest Rate Swaps

67

Cummins, Claudia. “Gonzalez Moving Legislation on Derivatives to Front
Burner,” American Banker, May 4, 1994a.
. “OCC Eyes Lid on Swaps,” American Banker, April 21, 1994b.
Diamond, Douglas W. “Debt Maturity and Liquidity Risk,” The Quarterly
Journal of Economics, vol. CVI (August 1991), pp. 709–37.
. “Financial Intermediation and Delegated Monitoring,” Review of
Economic Studies, vol. 51 (August 1984), pp. 393–414.
Flannery, Mark J. “Asymmetric Information and Risky Debt Maturity Choice,”
The Journal of Finance, vol. 41 (March 1986), pp. 19–37.
Goodfriend, Marvin. “Eurodollars,” in Timothy Q. Cook and Robert K.
LaRoche, eds., Instruments of the Money Market, 7th ed. Richmond:
Federal Reserve Bank of Richmond, 1993, pp. 48–58.
Jensen, Michael C., and William H. Meckling. “Theory of the Firm: Managerial Behavior, Agency Costs and Ownership Structure,” The Journal of
Financial Economics, vol. 3 (October 1976), pp. 305–60.
Karr, Albert R. “Bank Regulator Signals Move on Derivatives: Comptroller
Voices Concern over For-Profit Trades and Internal Oversight,” The Wall
Street Journal, April 21, 1994.
Kawaller, Ira G. “A Swap Alternative: Eurodollar Strips,” in Carl R. Beidleman,
ed., Interest Rate Swaps. Homewood, Ill.: Business One Irwin, 1990, pp.
390–404.
Kuprianov, Anatoli. “Money Market Futures,” in Timothy Q. Cook and Robert
K. LaRoche, eds., Instruments of the Money Market, 7th ed. Richmond:
Federal Reserve Bank of Richmond, 1993a, pp. 188–217.
. “Over-the-Counter Interest Rate Derivatives,” in Timothy Q.
Cook and Robert K. LaRoche, eds., Instruments of the Money Market, 7th
ed. Richmond: Federal Reserve Bank of Richmond, 1993b, pp. 238–65.
Litzenberger, Robert H. “Swaps: Plain and Fanciful,” The Journal of Finance,
vol. 47 (July 1992), pp. 831–50.
Loeys, Jan G. “Interest Rate Swaps: A New Tool for Managing Risk,” Federal
Reserve Bank of Philadelphia Business Review, May/June 1985, pp. 17–25.
Marshall, John F., and Kenneth R. Kapner. Understanding Swaps. John Wiley
and Sons: New York, 1993.
Miller, Merton H. “Debt and Taxes,” The Journal of Finance, vol. 32 (May
1977), pp. 261–75.
Minton, Bernadette. “Interest Rate Derivative Products and Firms’ Borrowing
Decisions: The Case of Interest Rate Swaps and Short-Term Interest Rate
Futures Contracts.” Manuscript. University of Chicago, December 1993a.
. “An Empirical Examination of U.S. Dollar Swap Spreads.”
Manuscript. University of Chicago, November 1993b.

68

Federal Reserve Bank of Richmond Economic Quarterly

Myers, Stewart C. “Determinants of Corporate Borrowing,” Journal of
Financial Economics, vol. 5 (November 1977), pp. 147–75.
Rawls, S. Waite III, and Charles W. Smithson. “The Evolution of Risk
Management Products,” Journal of Applied Corporate Finance, reprinted
in Robert J. Schwartz and Clifford W. Smith, Jr., eds., The Handbook
of Currency and Interest Rate Risk Management. New York: New York
Institute of Finance, 1990.
Rehm, Barbara A. “Trio of Heavyweights Sees No Swaps Crisis,” American
Banker, May 11, 1994.
Rudnick, Linda T. “Discussion of Practical Aspects of Interest Rate Swaps,” in
Conference on Bank Structure and Competition. Chicago: Federal Reserve
Bank of Chicago, 1987, pp. 206–13.
Smith, Clifford W., Charles W. Smithson, and Lee Macdonald Wakeman. “The
Market for Interest Rate Swaps,” Financial Management, vol. 17 (1988),
pp. 67–73.
. “The Evolving Market for Swaps,” Midland Corporate Finance
Journal, vol. 3 (Winter 1986), pp. 20–32.
Smith, Clifford W., Charles W. Smithson, and D. Sykes Wilford. “Financial
Engineering: Why Hedge?” Intermarket, vol. 6 (1989), pp. 12–16.
Sun, Tong-Sheng, Suresh Sundaresan, and Ching Wang. “Interest Rate Swaps:
An Empirical Investigation,” Journal of Financial Economics, vol. 34
(August 1993), pp. 77–99.
Titman, Sheridan. “Interest Rate Swaps and Corporate Financing Choices,”
Journal of Finance, vol. 47 (September 1992), pp. 1503–16.
Wall, Larry D. “Interest Rate Swaps in an Agency Theoretic Model with
Uncertain Interest Rates,” Journal of Banking and Finance, vol. 13 (May
1989), pp. 261–70.
, and John J. Pringle. “Alternative Explanations of Interest Rate
Swaps,” in Conference on Bank Structure and Competition. Chicago:
Federal Reserve Bank of Chicago, 1987, pp. 186–205.

John Wheatley’s
Theory of International
Monetary Adjustment
Thomas M. Humphrey

O

f the bullionist writers who advocated restoration of the gold convertibility of England’s currency during the Bank Restriction period
1797–1821, few are as little known today as John Wheatley. Certainly
his name is not as familiar as those of David Ricardo, Henry Thornton, Thomas
Malthus, Francis Horner, William Huskisson, and other bullionists. Yet in some
respects he was the most original of the group. His Essay on the Theory of
Money and Principles of Commerce (1807) spelled out the logic and implications of the strict bullionist position more forcefully and systematically than any
document before Ricardo’s High Price of Bullion: A Proof of the Depreciation
of Bank Notes (1810).
To Wheatley belongs much of the credit for expounding at least four
hard-line bullionist propositions often attributed to Ricardo. First, money-stock
changes have no effect on output and employment. Second, exchange rate depreciations, a high price of gold, and specie drains stem solely from an excess
issue of currency. Third, being purely monetary phenomena, exchange rate
changes, gold price movements, and specie drains are immune to real shocks
operating through the balance of payments. Fourth, exchange rate depreciation
and the excess of market over mint price of gold constitute proof and measure
of overissue in inconvertible paper regimes. To these can be added a fifth contribution: his demonstration that monetary expansion and price inflation can
continue indefinitely on a given gold base if all countries expand in step.
Wheatley derived these propositions from an analytical model characterized by sharp dichotomization of real and monetary sectors. He sought to show
that monetary shocks do not affect real variables nor real shocks monetary

The author is greatly indebted to his colleagues Tim Cook, Mary Finn, Bob Hetzel, and Peter
Ireland for their penetrating criticisms of earlier drafts of this article. The views expressed
are those of the author and do not necessarily represent those of the Federal Reserve Bank
of Richmond or the Federal Reserve System.

Federal Reserve Bank of Richmond Economic Quarterly Volume 80/3 Summer 1994

69

70

Federal Reserve Bank of Richmond Economic Quarterly

variables. To do so, he partitioned his real and monetary variables into separate
compartments and allowed little or no interaction between the two. Neutrality,
block exogeneity, and absence of reverse causality—these were the hallmarks
of his analysis. They allowed him to contend that his monetary indicators were
uncontaminated by real disturbances. As such, they signaled overissue pure and
simple and so constituted an unambiguous measure of the need for monetary
contraction to correct the excess issue. More than most economists before or
since, he took the extreme position that monetary shocks affect only monetary
variables and real shocks real variables.1
Despite Wheatley’s originality, his work has suffered from neglect. Ignored
in his own time because of a labored, archaic expository style and a hypercritical, vitriolic attitude toward his fellow economists, he has also been underrated
in ours.2 Modern commentators, when they mention him at all, typically focus
exclusively on certain striking aspects of his work rather than on his complete
analytical model. Thus Schumpeter (1954) concentrates on his crude version of
the quantity theory of money. Einzig (1962), Frenkel (1978), Officer (1984), and
Wu (1939) emphasize his purchasing power parity doctrine. Fetter (1942) and
Viner (1937) spotlight his assumption of price and exchange rate invariance to
real shocks. Metzler (1948), Morgan (1943), O’Brien (1975), and Viner (1937)
accent his income-expenditure theory of unilateral transfers. Chipman (1983)
criticizes his theory of gold price determination. None, however, mention his
integration of these elements into a consistent theory of how an open economy
responds to real and monetary disturbances.
The result is a gap in our knowledge of Wheatley’s theory of the international adjustment mechanism. This gap is all the more regrettable because
it contributes to the notion of a monolithic classical theory based on David
Hume’s account of the price-specie-flow mechanism. In fact, Wheatley’s
theory differs from Hume’s. It emphasizes continuous purchasing power parity,
gold market arbitrage, and unilateral payments accomplished through income
changes rather than through price adjustments. It demonstrates that there is
more than one classical theory of the international mechanism.
This article represents an effort to fill the gap and to give Wheatley his
due. First, it specifies the basic building blocks of Wheatley’s model. Second,
it shows how he used these components to explain international adjustment to
monetary disturbances under convertible and inconvertible currency regimes.
Third, it shows how he modified his model to handle real disturbances and in
so doing contributed to the theory of international transfers. Fourth, it outlines

1 Wheatley’s strong real-nominal dichotomy has its closest modern counterpart in the work
of the contemporary real business cycle school founded by Kydland and Prescott (1982) and Long
and Plosser (1983).
2 On Wheatley’s expository style and attitude toward his fellow economists, see Chipman
(1983), pp. 7 and 49–50, and Hollander (1911), p. 464.

T. M. Humphrey: International Monetary Adjustment

71

some policy implications of his analysis. Last, it evaluates his place in classical
monetary thought.

1.

BASIC BUILDING BLOCKS

The first task is to sketch the chief components of Wheatley’s model. These
consist of (1) the quantity theory of money, (2) the purchasing power parity
doctrine, and (3) a theory of gold arbitrage. Together, they trace out a causal
chain in which money determines prices, prices determine exchange rates, and
exchange rate movements trigger specie drains under metallic and convertible
currency regimes and currency depreciation under inconvertible paper regimes.
Of the three components, the quantity theory employs closed-economy propositions; the parity and arbitrage doctrines, open-economy ones.
Quantity Theory
Wheatley adheres to a particularly strict or rigid version of the quantity theory.
This version embodies the notions of (1) proportionality of money and prices,
(2) money-to-price causality, (3) neutrality of money, (4) monetary rather than
real theory of prices, and (5) exogeneity of the nominal stock of money.
On the proportionality postulate, Wheatley (1807) declares that “all prices
are in proportion to the quantity of money.” “This principle,” he writes, “appears
so obvious, that it would be superfluous to enter into the proof of its validity;
and I shall assume it as a postulate that would be universally conceded” (p.
12). In symbols, P = kM, where P is the home country’s price level, M is its
money stock, and k is a constant coefficient equal to the ratio of the circulation
velocity of money to real output—both variables (velocity and output) treated
as fixed constants by Wheatley. A similar equation holds for the foreign
country in Wheatley’s two-country model. That is, P∗ = k∗ M∗ , where the asterisks denote foreign country variables. Thus, “if the currency of one country is
relatively greater than the currency of another, its price will be proportionally
higher” (1819, p. 24), or P/P∗ = K(M/M∗ ), where K is the ratio of the constants
k and k∗ .
As for the notion of money-to-price causality, Wheatley endorses it in no
uncertain terms. “Prices,” he says, “are determined by the quantity of money”
(1819, p. 24). Thus a money-stock expansion has “no other operation than to
raise the price of produce” (1807, p. 38). It “has no other effect than to cause
its own depression” in purchasing power 1/P (p. 37). In his view, money drives
prices through a direct expenditure mechanism. A monetary expansion raises
the ratio of cash to nominal transactions above the fraction people desire to
hold. Cash holders spend the excess money immediately and mechanically in
an effort to work off the unwanted balances. The increased spending raises
prices and the volume of nominal transactions. The process ends when the
desired cash ratio is restored and the new money is willingly held.

72

Federal Reserve Bank of Richmond Economic Quarterly

Having asserted direct causality, he implicitly rejects the notion of reverse
causality running from prices to money. Reverse causality might arise in metallic currency regimes if an exogenous fall in the price level, by raising the goods
value of gold, induces an increase in the supply of specie flowing either from
the mines or from abroad through the balance of payments. It also might arise in
a fiat paper regime if the central bank validates exogenous price increases with
monetary expansion. Wheatley, however, says nothing about such mechanisms.
He does, however, expand at length on the quantity theory’s neutrality
proposition. He argues that money-stock changes exert no influence, temporary
or permanent, on real output and employment. Perfect wage-price flexibility,
he claims, ensures as much. Such flexibility means that nominal wages and
prices adjust instantaneously and equiproportionally to monetary shocks. The
result is that the real wage rate and thus the output and employment variables
it determines are invariant to such shocks. Thus, contrary to the popular notion
that “an increase of currency gives a stimulus to industry by the elevation
of prices,” the truth is that “no greater stimulus can in reality exist” (1807,
p. 40). For “the wages of labour are augmented only in proportion to the
increase [of money and prices], and purchase no greater quantity of produce
after the addition than before it” (p. 40). Wheatley concludes: “[A]n increase of
money . . . has no effect like an increase of produce to augment the wealth of
a nation” (p. 37). It has “no other operation than to raise the price of produce,
and augment the nominal incomes of all, without making any addition to their
real opulence” (1807, p. 38). One can hardly find a clearer statement of the
neutrality proposition in the entire classical literature.
Wheatley’s neutrality proposition states only that monetary shocks affect
prices and not real variables. It does not deny that real determinants might also
drive the price level. To rule out this possibility, Wheatley asserts that price
changes stem exclusively from monetary rather than real disturbances. “There
is no other cause,” he writes, “than a relative excess of currency which makes
prices higher” (1819, p. 24). True, he notes that real shocks might depress
output and so the demand for money, thereby rendering the existing money
stock excessive. But he argues that any resulting price increase must be attributed to the monetary excess and not to the real shock. Likewise, he denounces
as “imbecilic” Sir James Steuart’s view that the same real forces of “demand
and competition” that determine relative prices also drive the general price
level (1807, p. ix). Not so, says Wheatley. Money-stock movements govern
the general price level. He also asserts that secular inflations emanate from
excessive paper money growth rather than from output contractions and a
shortage of goods.
Finally, Wheatley posits money-stock exogeneity, which he sees as a
corollary of the proposition that money is the independent causal factor governing prices. He realizes that if money were an endogenous variable responding
passively to prior changes in the economy, he could not claim it plays the

T. M. Humphrey: International Monetary Adjustment

73

active initiating role in raising prices. For this reason, he treats gold coin and
paper notes as exogenous variables emanating autonomously from “the fertility
of mines, and the general publication of state and bank paper” (1807, p. 60).
He ignores the feedback effect of prices on the profitability of mining and the
production of gold. By dismissing such real determinants of commodity money,
he essentially treats it as fiat currency.

Purchasing Power Parity Doctrine
The purchasing power parity doctrine forms the second building block in
Wheatley’s model of international adjustment. In what is the clearest and most
complete account of the doctrine before Gustav Cassel’s statement in the 1920s,
he enunciates it in both its absolute and relative versions.
The absolute version says that the exchange rate E—defined as the domestic currency price of a unit of foreign currency—equals the ratio of domestic
to foreign general price levels. This condition renders the purchasing power
of money expressed in terms of a single currency everywhere the same. In
symbols, E = P/P∗ or, equivalently, P = EP∗ . As Wheatley (1807) puts it,
“the course of exchange is exclusively governed by the relative state of prices,
or the relative value of money, in the different countries between whom it is
negotiated” (p. 85). It “approximates the price of their produce to a general
level” (p. 45). He sees price-level parity P = EP∗ as emanating from the law
of one price. That law, of course, states that abstracting from tariffs, transport
costs, and other impediments to trade, the price of any given traded good is
the same in all locations when quoted in the same currency. Since Wheatley
assumes that all goods are traded and that identical commodities bear the same
weight in each country’s price index and product mix, he essentially treats
them as a single composite commodity. In his composite-commodity model,
the law of one price applies to aggregate price levels as well as to the prices
of individual goods. Therefore, the real exchange rate, or commodity terms of
trade, between two nations equals unity, or EP∗ /P = 1. In Wheatley’s words,
“the state of exchange must uniformly coincide with the state of prices, or
the interchange of produce could not be transacted on equal terms” (1819,
p. 21). A unitary value of the terms of trade permits “any given quantity” of
the composite commodity to “exchange for the same value in every part of the
world” (1807, p. 46).
He gives an equally lucid statement of the doctrine’s relative version, according to which the percentage change of the exchange rate is the differential
between the percentage changes of the price levels. “The exchange between
London and Hamburgh,” he says, “is at any given moment five percent against
London, only because the general prices at Hamburgh are at that time five
percent lower than the general prices of London” (1807, p. 63). Here is his

74

Federal Reserve Bank of Richmond Economic Quarterly

description of the relationship e = p − p∗ , where the lowercase letters denote
percentage changes in their uppercase counterparts.
Wheatley saw the parity doctrine as an extension of the quantity theory
to the open economy. It is therefore not surprising to find him treating the
exchange rate as a purely monetary phenomenon determined by relative national money stocks operating through national price levels. “Nothing can
alter the state of the exchange,” he wrote, “that does not alter the state of
prices, and nothing can alter the state of prices, the quantity of produce being the same, that does not alter the state of currency” (1819, p. 27). In
terms of the quantity theory equations presented above, Wheatley held that
E = P/P∗ = kM/k∗ M∗ = K(M/M∗ ). From this equation derives his conclusion
that “there is no other cause than a relative excess of currency, which makes
the exchange unfavourable” (1819, p. 24). Thus “the course of exchange is the
exclusive criterion of how far the currency of one country is increased beyond
the currency of another” (1803, p. 207).
Wheatley comments at length on key propositions of the doctrine. Regarding causality, he asserts it runs unidirectionally from price levels to exchange
rates. Regarding the transmission mechanism, he posits rational expectations.
He argues that agents, observing price-level changes and anticipating the compensating exchange rate correction, incorporate those anticipations into the
rate and so make them a reality.3 The result is that exchange rates adjust
instantaneously to price levels.4 Regarding deviations from purchasing power
parity, he denies their occurrence. Rational expectations maintain the exchange
rate at parity equilibrium. Therefore, currencies cannot be temporarily over- or
undervalued on the market for foreign exchange. Finally, regarding neutrality,
he argues that because exchange rates are always at parity, their fluctuations
cannot affect real trade balances or the terms of trade in the least. His treatment
of these issues is among the more extreme and uncompromising in the classical
literature.

3 According to Wheatley, the exchange rate attains purchasing power parity equilibrium so
swiftly as to bypass trade-balance effects. Other classical economists, notably Henry Thornton
(1802, p. 198), had suggested that a rise in one country’s prices relative to another’s could only
exercise its self-correcting influence on the exchange rate through the trade balance. In their view,
a rise in home prices relative to foreign prices would, by spurring imports and checking exports,
cause a trade deficit and a corresponding excess demand for foreign exchange to finance it. This
excess demand in turn would bid up the exchange rate, thereby equalizing common-currency
price levels. But Wheatley thought such intermediate steps unnecessary. In his view, the exchange
rate adjusts immediately.
4 “But immediately that the prices of one country become relatively higher than the prices
of another, the course of exchange . . . will note the difference, and become unfavourable to the
same extent” (Wheatley 1819, p. 24). “The instant that the variation occurs it is announced by
the exchange, and a credit given in conformity to the difference” (Wheatley 1807, p. 64).

T. M. Humphrey: International Monetary Adjustment

75

Gold Price Arbitrage
Wheatley’s theory of gold arbitrage constitutes the third building block of his
model. It explains how countries eliminate their excess or deficient money
stocks under metallic and convertible currency regimes.
His theory is simplicity itself. It says that arbitrageurs will ship gold from
where its monetary value is low to where its monetary value is high. Comparison of fixed domestic and foreign mint prices of gold quoted in a single
currency at the rate of exchange reveals these respective monetary values. Let
a rise in the exchange rate—that is, a depreciation of the home currency relative to the foreign currency—raise the common-currency value of gold abroad
over its value at home. The result will be to precipitate a specie export. For
arbitrageurs will find that they can convert domestic paper into gold at the fixed
mint price, sell the gold abroad at its foreign mint price, convert the proceeds
at the given exchange rate into more domestic currency than they started with,
and thus buy more gold than they had before. They will continue to engage in
this sequence of transactions as long as gold’s geographical value differential
yields arbitrage profits.
At this point, Wheatley introduces transport costs into the analysis. Instead
of abstracting from such costs as in the case of goods, he argues that these costs
are too substantial to neglect in the case of gold. In particular, he estimates that
specie transport costs amount to at least 3 percent of gold’s value. Consequently,
arbitrageurs will find it profitable to export specie only when the exchange rate
exceeds relative mint prices by more than enough to cover such costs. In
symbols, E > (1 + s)Pg /P∗ , where Pg and P∗ are the domestic and foreign
g
g
mint prices of gold and s is gold’s shipping cost expressed as a percentage of
the domestic mint price. Rewriting this condition as EP∗ − Pg > sPg yields
g
the profitability criterion for gold exports: such exports are profitable when the
foreign-to-domestic gold price differential exceeds the cost of transit. It follows
that “when the exchange becomes unfavourable to . . . the extent of five, ten,
or fifteen percent, gold will find its way out.” For arbitrageurs will reap “as
a profit what remains after the charge of transit, which is . . . three percent”
(1819, pp. 24–25).
Symmetrically, Wheatley argues that gold imports become profitable when
the exchange rate falls below mint par by more than transit costs, or E <
Pg /P∗ (1 + s). Then the home price of gold exceeds the foreign price by more
g
than the cost of transit, or Pg − EP∗ > sEP∗ . Arbitrageurs, secure that their
g
g
profits will not be eaten up by shipping costs, will import gold to realize the
differential. In short, Wheatley specifies certain critical values of the exchange
rate that trigger gold inflows and outflows. These values of course are the
famous specie points of the trade literature.

76

2.

Federal Reserve Bank of Richmond Economic Quarterly

ADJUSTMENT MECHANISMS

Armed with the foregoing concepts, Wheatley explains how an open economy adjusts to real and monetary shocks under alternative currency regimes.
According to Wheatley, monetary shocks trigger specie redistributions under
metallic and convertible currency regimes and exchange rate changes under
inconvertible paper regimes. Adjustment ceases and equilibrium reigns when
the common-currency prices of goods and gold are the same worldwide. By
contrast, real shocks prompt changes in real incomes and expenditures but leave
nominal exchange rates and specie flows unchanged. Adjustment ends when
the income and spending changes re-equilibrate the real balance of payments.
In the following paragraphs, it will be useful to consider Wheatley’s analysis of monetary shocks first. Such shocks take the form of exogenous increases
in the domestic money stock. He examines the resulting responses in purely
metallic, convertible currency, and inconvertible currency regimes. In all cases,
money’s influence is confined to nominal variables. No real variables change
except for gold’s relative price EP∗ /Pg , which moves to its export point.
g
The Process of Adjustment to Monetary Shocks in a
Purely Metallic Regime
Consider first a metallic or 100 percent reserve gold-standard regime. Let an
exogenous increase in the quantity of specie attributable to “the fertility of the
mines” occur in the home country. The monetary expansion produces an immediate, equiproportional rise in the domestic price level. With perfect wage-price
flexibility, nominal wages rise in step with prices, leaving real wages and thus
employment and output unchanged. Here is the first strict bullionist or Ricardian
proposition, namely, that money is neutral in its effect on real activity.
Turning to the market for foreign exchange, Wheatley argues that agents
there observe the rise in domestic prices and anticipate the compensating exchange rate depreciation. They incorporate those anticipations into the rate,
which depreciates immediately. The resulting equiproportional rise in the price
level and the exchange rate leaves the terms of trade or relative price of goods
at home and abroad, EP∗ /P, unchanged. With no terms-of-trade improvement
to induce a trade deficit, none occurs.
Instead, adjustment occurs in the market for monetary gold. Given the fixed
foreign and domestic mint prices of gold, P∗ and Pg , it follows that the rise in
g
the exchange rate raises gold’s common-currency price abroad, EP∗ , above its
g
price at home, Pg , or EP∗ − Pg > 0. Still, the exchange rate may not depreciate
g
enough to raise the gold price differential EP∗ − Pg above the cost of transit
g
sPg . If so, nothing further happens.
But let the exchange rate rise above mint par by more than the cost of
transporting gold and arbitrage becomes profitable. Agents then have an incentive to ship specie abroad to realize the gold price differential. By contracting

T. M. Humphrey: International Monetary Adjustment

77

the domestic money stock and deflating the domestic price level, the resulting
loss of specie will restore the exchange rate to mint parity, thus putting a
stop to further gold drains. In this way, the efflux of gold will have restored
the natural distribution of specie required for national (and world) monetary
equilibrium. The upshot in Wheatley’s small-open-economy case is that (1) P
and E are the same as before, (2) the specie increment is dispersed abroad
where it is too small to affect the world money stock and world price level,
and (3) P∗ accordingly remains unchanged. Wheatley (1807) summarizes:
“In every instance, therefore, where a relative excess of currency caused the
same sum to measure a less value in one country than it measured in others,
the course of exchange would become unfavourable, and by leading to the
departure and general distribution of the surplus specie, maintain inviolable the
level of money” (pp. 66–67).
Wheatley Versus Hume
Here was a new theory of the adjustment mechanism. It differed from David
Hume’s celebrated account of the price-specie-flow mechanism enunciated in
his 1752 essays “Of Money” and “Of the Balance of Trade.” In his first essay,
Hume maintains that increases in the stock of metallic money temporarily
stimulate real activity before raising prices proportionally. Wheatley’s model
permits no such temporary nonneutrality. And in the second essay, Hume implies that the rise in domestic prices produces no fully offsetting rise in the
exchange rate. The result is an increase in the relative price of home to foreign goods, which, by rendering imports cheap and exports dear, precipitates a
trade deficit. Wheatley’s model allows no such terms-of-trade or trade-balance
effects.
Moreover, since the exchange rate in Hume’s model is fixed (or at least
remains below the export point), it cannot depreciate sufficiently to produce the
gold price differential that triggers specie arbitrage. True, gold moves abroad
in his model to equalize commodity prices. But it does so passively just to
finance the trade deficit rather than actively in search of a higher price abroad.
Thus, while Hume’s model achieves the same equilibrium distribution
of specie as Wheatley’s model, it does so through a different process. In
short, Hume’s account features exchange rate fixity, terms-of-trade variation,
trade deficits, continuous gold price parity, and no gold arbitrage. By contrast,
Wheatley’s account stresses exchange rate variation, continuous purchasing
power parity, no trade deficits, and temporary gold price differentials that
activate specie arbitrage. Evidently there is more than one classical theory
of the adjustment mechanism.
Adjustment to Monetary Shocks in Convertible Currency Regimes
Wheatley notes that a process similar to that described above works to eliminate
excess money supplies in convertible currency regimes wherein paper is freely

78

Federal Reserve Bank of Richmond Economic Quarterly

convertible into gold at a fixed price upon demand. Now, however, correction
is achieved through retirement of excess notes as well as through specie drains.
Let an exogenous increase in the “publication of state and bank paper”
occur in the home country (1807, p. 60). Money, prices, and the exchange rate
rise equiproportionally maintaining relative prices EP∗ /P and the trade balance
unchanged. When the exchange rate depreciates to the point where gold export
becomes profitable, arbitrageurs present paper notes to banks for conversion
into gold at the official mint price. The resulting specie drain obliges banks to
contract the note issue to protect their gold reserves. Such contraction causes
the price deflation that restores the exchange rate to mint par and puts a stop to
specie drains.5 Indeed, Wheatley contends that central bankers’ knowledge of
this process disciplined them to contract as soon as the exchange rate signaled
overissue.6
Wheatley also pioneered the distinction between small and large openeconomy models. He was the first to point out that a small economy’s excess
issue, being a negligible fraction of the world money stock, could have no perceptible influence on that stock or world prices. By contrast, a large economy’s
excess issue could affect both. The large economy would, after working off its
excess balances, retain its relative share of the enhanced world money stock
and its price level would be higher than before. By contrast, adjustment would
leave the small economy’s price level unchanged.
In this connection, he also observes that all nations expanding in concert
could do what no single nation could do alone, namely, generate an unlimited
rise in money and prices. “Paper,” he writes, “might be increased in any given
country to any extent, provided that the currency of other nations were augmented in a similar ratio to preserve the equivalency” (1807, p. 28). For if all
countries expanded in step, none would be conscious of an excess of currency.
Although money and prices would rise in each country, there would be no exchange rate depreciation, no rise in the market price of gold, no drain of gold
reserves from one country to another to limit expansion. Each country’s paper,
no matter how greatly augmented, would retain its value relative to gold and
to other currencies. Wheatley was the first economist to enunciate this point.
5 “When the over-issue of paper made the prices of this country higher than the prices of
others . . . and the course of exchange marked the difference, bullion, which is foreign money
. . . sold at a correspondent premium . . . together with the charges of transit. . . . Bank paper,
therefore, was pressed upon the Bank to be exchanged for guineas, that the guineas might be
converted into bullion, to be . . . sent abroad. By this process, Bank paper was reduced in amount
. . . and . . . its contraction lowered our prices to a level with prices of other countries . . . and
restored the exchange to par” (1819, pp. 39–40).
6 “The unfavourable exchange, which naturally resulted from a partial redundance, constituted the exclusive check to the issues of the Bank of England throughout the whole of the
preceding century, and prevented the publication of a greater sum than that proportion, which
was adequate to circulate the produce of this country at par with the produce of others” (1807,
pp. 68–69).

T. M. Humphrey: International Monetary Adjustment

79

Adjustment to Monetary Shocks Under Inconvertible Currency Regimes
Wheatley was also among the earliest to analyze the operation of an inconvertible paper currency, which he saw as introducing a new twist to his model.
Under inconvertibility, money cannot leak out into foreign trade. An excess
issue cannot be worked off through specie drains as it can under metallic
and convertible currency regimes. Instead, the exchange rate eliminates the
redundant currency by devaluing it in proportion to its excess.
As before, Wheatley begins his analysis by introducing an exogenous monetary disturbance into his model. He assumes the banking system, desiring to
reduce its reserve ratio, injects additional paper notes into an economy initially
in monetary equilibrium with the exchange rate at mint par. He then traces out
the ensuing sequence of events.
As in the convertible currency case, the overissue of inconvertible paper
generates immediate and proportional rises in the prices of goods and foreign
exchange. Together, these increases operate to maintain the real terms of trade
EP∗ /P unchanged, thus forestalling trade deficits.
At the same time, the depreciating exchange rate raises gold’s relative price
abroad EP∗ /Pg . But as long as that increase does not exceed the cost of transit,
g
gold remains a non-traded good that sells domestically at its unchanged market
(and mint) price.
Let the exchange rate rise by more than the cost of transit, however, and
gold becomes a traded good and therefore subject to the law of one price. As
a result, market and mint price diverge. No longer tied to the mint price by
convertibility, gold now fetches a price equal to its common-currency price
abroad, EP∗ , minus the cost of transit.7 And since that common-currency price
g
varies one for one with the exchange rate, it follows that gold commands a
premium over its old mint price equal to the percentage rate of depreciation of
the exchange rate. As this percentage rate is also the rate of expansion of the
money stock, Wheatley arrives at the Ricardian or strict bullionist proposition
that the percentage premium on gold constitutes proof and measure of overissue
under inconvertibility.
The gold premium also prohibits specie exports. For the same law-of-oneprice condition that equalizes gold’s value worldwide precludes arbitrageurs
from making profits on shipping the metal. Wheatley’s (1807, p. 70) exposition
of this point is both seminal and definitive. Under inconvertibility, arbitrageurs
cannot obtain gold from the central bank. If some coin remains in circulation,
however, they can obtain it from domestic coin holders. To induce the latter
to part with their gold, arbitrageurs must pay the asking price. But coin holders themselves have the option of shipping their gold abroad, selling it at the
7 In

Wheatley’s words, specie annexes a premium and “resiliates to a level with its value
abroad” (1807, p. 367).

80

Federal Reserve Bank of Richmond Economic Quarterly

foreign mint price, and converting the proceeds net of transit cost into domestic
currency at the rate of exchange. Consequently, arbitrageurs must pay a perounce price of Pg = EP∗ − sPg for domestic gold, to which must be added
g
the cost of shipping it sPg . But this sum EP∗ − sPg + sPg leaves no arbitrage
g
profits to induce gold exports. For it just equals EP∗ , exactly what gold fetches
g
abroad.
Since no profits can be made by exporting gold, none is exported. Instead,
exchange rate changes rather than gold drains eliminate excess money stocks.
Exchange depreciation devalues money in proportion to its excess. Such devaluation keeps demand-adjusted money stocks everywhere the same, as international monetary equilibrium requires. Let k∗ M∗ be the foreign demand-adjusted
money stock and kM/E its domestic counterpart measured in terms of a common
currency. Then world monetary equilibrium requires that k∗ M∗ = kM/E. Any
excess of kM will be offset by compensating rises in E to maintain the equality.
In Wheatley’s words, “the course of exchange has no other means” of working
off an excess supply of inconvertible currency “than to reduce it to a discount
in proportion to its excess” (1807, p. 69).
In short, Wheatley argues that exchange rates bear the full burden of adjustment under inconvertibility. Specie movements do not occur. To explain
why specie does not move, he appeals to the law of one price. He also appeals
to the idea of comparative cost. He argues that inconvertibility renders gold
just another commodity whose price during inflation rises identically with all
commodity prices. But identical rises in the prices of goods and gold imply that
gold cannot be cheap in terms of goods. And not being the relatively cheap
commodity, it cannot qualify for exportation on comparative cost grounds.
Therefore it is not exported. For that reason, specie does not move when inconvertibility reigns. Instead, it leaves adjustment to the exchange rate.

3.

ADJUSTMENT TO REAL SHOCKS

Having argued that exchange depreciation, gold price premia, and specie drains
constitute proof and measure of overissue, Wheatley had to show that those
same phenomena could not also arise from real shocks operating through the
balance of payments. For if his monetary variables registered real disturbances
as well as monetary overissue, they could hardly be unambiguous indicators of
the latter alone. Candidate real shocks included domestic crop failures, subsidies
and loans to Britain’s allies in the war against Napoleon, and the expenses of
maintaining troops on the continent. He had to show that these disturbances
propagated their effects through non-monetary channels and could not affect
his monetary variables in the least.
To do so, he posits a demand-shift, income-expenditure mechanism. In the
case of domestic crop failures, he sees adjustment occurring through shifts in

T. M. Humphrey: International Monetary Adjustment

81

reciprocal demands. Jacob Viner explains. Wheatley, he says, insisted that “the
demand of England and the rest of the world for each other’s product would
necessarily so immediately and completely adjust themselves . . . as to result
under both a metallic and an inconvertible paper standard in the maintenance of
equilibrium in the balance of payments without the aid of specie movements,
changes in the relative level of prices in the two areas, or movements of the
exchange rate” (Viner 1937, p. 142).
Let a home harvest failure depress domestic income. Imports, a function
of income, therefore fall. The resulting decline in the foreign country’s export sales induces it to cut back its purchases from the home country. Home
exports consequently fall to match home imports. The trade balance remains
unchanged, as do the exchange rate and the ratio of national price levels—
provided, of course, that the central bank eradicates that portion of the money
stock rendered redundant by the fall in income. In terms of Marshallian reciprocal demand schedules or offer curves, the curves of both nations shift inward
by equal amounts to intersect the unchanged terms-of-trade vector at a smaller
volume of trade. Exchange rate movements and specie flows are not required.
Wheatley uses the same demand-shift, income-adjustment mechanism to
resolve the transfer problem. He argues that foreign remittances—loans and
subsidies to Britain’s allies plus military expenditures abroad—are effected
by a transfer of goods without disturbing price levels, exchange rates, or the
distribution of specie. Causation runs from remittances to incomes to import
demands to the export surplus that transfers the goods. The home government,
say, taxes domestic citizens and gives the proceeds to the foreign country as a
subsidy. The subsidy reduces home income and raises foreign income by equal
amounts. Imports as a function of income fall in the home country and rise
in the foreign country. The result is a home-country export surplus that, if the
propensities to import in the two countries just add up to one as Wheatley assumes, precisely equals the amount of the subsidy.8 Here is Wheatley’s special
case in which income shifts accomplish the goods transfer with no help from

8 By definition, the home country’s real trade balance B is the difference between its real
exports X and its real imports I, or B = X − I. Also by definition, home exports X are the foreign
country’s imports, I∗ , so that the trade balance may be expressed as the difference between foreign
and domestic imports, each a function of real national income, or B = I∗ (Y ∗ ) − I(Y). Differentiating the trade balance with respect to the subsidy T yields dB/dT = (dI∗ /dY ∗ )(dY ∗ /dT) −
(dI/dY)(dY/dT). Since Wheatley assumes the recipient’s and the payer’s incomes increase and
decrease, respectively, by the exact amount of the subsidy—that is, dY ∗ /dT = −dY/dT = 1—the
expression simplifies to dB/dT = (dI∗ /dY ∗ ) + (dI/dY), where the right-hand side is the sum of
the marginal propensities to import. If this sum is one, as Wheatley assumes, then dB/dT = 1,
or dB = dT, and the trade balance moves into surplus by exactly the amount of the subsidy.
In the final analysis, the subsidy is paid in goods. Hence he concludes that “the superiority of
our exports above imports must nearly correspond with the amount of our foreign expenditure”
(1807, p. 219).

82

Federal Reserve Bank of Richmond Economic Quarterly

monetary variables or the terms of trade.9 Here too is his formulation of the
Ricardian or strict bullionist doctrine that monetary phenomena are invariant
in response to real shocks to the balance of payments.
Wheatley’s income-shift theory differed from the dominant gold-flow,
price-adjustment theory of his contemporaries (see Fetter [1968], pp. 65–69).
They held that real transfers are accomplished through price changes and specie
flows prompted by the initial financing of the transfer. Such financing requires
the paying country to obtain the recipient country’s currency to make the cash
payment. The resulting increased demand for foreign exchange bids up the
exchange rate. Given national price levels, the rising exchange rate lowers the
relative price of goods P/EP∗ in the paying country, thus spurring its exports
and checking its imports. Net exports get an extra boost when the exchange
rate reaches its specie point and the resulting gold drain and monetary contraction deflate the paying country’s price level. With deflation and depreciation
lowering relative prices, the export surplus expands to effect the transfer in
goods.
The view that transfers operate through monetary variables was, of course,
anathema to Wheatley, who omits such channels from his model. Transfers were
real phenomena. As such, they were entirely independent of monetary phenomena. To dramatize this independence, Wheatley argued that even as the paying
country was making massive unilateral transfers abroad, it could still enforce
specie inflows to any extent simply by contracting paper issues and deflating
prices until the exchange rate fell to its import point.10 Foreign payments, in
other words, had nothing to do with exchange rates and specie flows.

4.

POLICY IMPLICATIONS OF WHEATLEY’S WORK

Although Wheatley’s analysis was primarily theoretical, it had some practical
policy implications.11 First, exchange rates, gold prices, and specie movements
offer infallible indicators of overissue. When they signal monetary excess, it
must be occurring since they respond to nothing else. Their invariance to real
disturbances means that such disturbances cannot distort their signal and render
it ambiguous.
A second implication is that persistent inflation is less likely to occur in
convertible than in inconvertible currency regimes. Under convertibility, inflation is self-correcting. It automatically precipitates gold drains and forces
9 “Foreign payments . . . have no effect to alter the state of our currency, they have no effect
to alter the state of the exchange” (1819, p. 29).
10 “A due compression of our paper circulation would have led to its [gold’s] influx at the
very moment, that the loan was in payment, and would have glutted the country with specie”
(1807, p. 193).
11 On Wheatley’s policy views, see Fetter (1942), pp. 368–74.

T. M. Humphrey: International Monetary Adjustment

83

banks to contract their note issue to protect their gold reserves. The resulting
shrinkage of the money stock ends the inflation. No such corrective drains
occur under inconvertibility when gold, if available at all, commands a price
that renders specie exports unprofitable. It follows that convertibility offers the
stronger safeguard to overissue.
A third implication of Wheatley’s work is that price-level stability can be
achieved by monetary means. A staunch advocate of such stability, Wheatley
stressed the evils of price fluctuations. They arbitrarily redistributed income and
wealth among the social classes and provoked social discontent. Avoiding such
evils meant removing their monetary causes. To this end, Wheatley advocated
(1) ending the suspension of specie payments and restoring convertibility of the
British pound, (2) eliminating small notes which he saw as the most unstable
component of the money supply, and (3) removing the note-issuing privilege
from competing private banks and lodging it with the Bank of England.12 These
reforms, he thought, would prevent or minimize sharp variations in the money
stock that constituted the primary obstacle to price stability.
A fourth implication of Wheatley’s work is that indexation can immunize
real payments from unanticipated movements in nominal ones. In this connection, he proposed price-level indexation of long-term contracts to compensate
for fluctuations in the value of money. “Some criterion,” he said, “should be
assumed for the purpose of providing a graduated scale of the value of money”
so that nominal incomes could be adjusted “in conformity to the result.” Of
the candidate criteria, a general price-index series such as that constructed by
Sir George Shuckburgh Evelyn would be “the least objectionable” (1807, pp.
328–29). Earlier writers had advocated stabilizing real incomes by adjusting
nominal incomes according to changes in the price of a single commodity such
as rye or corn. But Wheatley was the first to recommend a general price-level
index number for that purpose. The modern notion of indexation originates
with him.

5.

WHEATLEY’S PLACE IN CLASSICAL
MONETARY THOUGHT

Even at its best, Wheatley’s Essay on the Theory of Money could hardly match
the subtlety and insight of Henry Thornton’s Paper Credit of Great Britain. Nor
could it match the power, brilliance, and lucidity of David Ricardo’s High Price
of Bullion. Still, if originality is any criterion, Wheatley’s name belongs in the
12 Unlike

other bullionists, Wheatley was unwilling to exonerate private banks from overissue. By perversely varying their reserve ratios, such banks overissued notes independently of
the central bank. He denied that the Bank of England controlled such banks through their reserves
or that overissue was prevented by the operation of an interregional price-specie-flow mechanism.

84

Federal Reserve Bank of Richmond Economic Quarterly

front rank of classical monetary theorists. He formulated the strict bullionist
model, which dichotomizes real and monetary sectors and posits neutrality and
exogeneity in the short run as well as the long. True, this model looks primitive
compared to Thornton’s sophisticated schema. But its ultra-simplicity entails
certain positive strengths. The model yields clear-cut policy conclusions. And
it avoids confusion between real and nominal variables. It emphasizes money’s
permanent price effects but ignores transitory output and employment effects
that might distract the central bank from pursuing its primary goal of price
stability. Ricardo, for one, found these properties desirable. He employed a
version of the strict bullionist model after Wheatley first presented it.
Nor should Wheatley’s other contributions go overlooked. He established,
three years before Ricardo, the theoretical underpinnings of the Ricardian definition of excess (see O’Brien [1975], p. 148). This definition says that if (1) the
exchange rate is depreciated, (2) gold is selling at a premium, and (3) specie
(under convertibility) is leaving the country, then the currency is by definition
excessive and must be contracted. Here was the tool strict bullionists needed.
With it they could counter antibullionists’ and moderate bullionists’ claims
that such phenomena might well originate in real shocks so that monetary
contraction was not required.
Beyond these ideas were his specific contributions to international monetary theory. He presented the clearest and most complete statement of the
purchasing power parity doctrine before Gustav Cassel. He was the first to
use the rational expectations argument to explain why the terms of trade
is always in equilibrium. He originated the distinction between large- and
small-open-economy models in which a large country’s note issue perceptibly
influences world money and prices whereas a small country’s issue does not.
Likewise, he introduced the notion that all nations expanding in step in a
convertible currency regime can do what no single nation can do alone, namely,
generate an unlimited rise in money and prices. And his demand-shift, incomeexpenditure theory of unilateral transfers anticipated the subsequent contributions of Mountifort Longfield, J. E. Cairnes, C. F. Bastable, J. S. Nicholson,
and Bertil Ohlin.
Perhaps his most outstanding contribution, however, was his specification
of the link between exchange rates, gold prices, and gold flows. In an explanation superior to any before Ricardo, he showed that in metallic and convertible
currency regimes gold is not simply a means of discharging international payments. Rather it is a commodity that flows across nations to capture arbitrage
profits created when exchange rate movements generate gold price differentials.
A related contribution was his use of the law of one price to show that gold
ceases to move across nations when its common-currency value is equalized
worldwide such that no arbitrage profit can be realized by shipping it. He
showed that money’s purchasing power parity over gold, not its purchasing
power parity over goods, is what halts gold movements. These contributions,

T. M. Humphrey: International Monetary Adjustment

85

together with his indexation proposal, were the products of an original mind.
They identify Wheatley as a creative scientific economist who deserves a
prominent rank in the classical pantheon. Above all, his ideas identify him
as the most monetarist, or strictly quantity theoretic, of all the classical writers.
Wheatley took three key ideas—(1) the quantity theory of money, (2) the
purchasing power parity doctrine, and (3) the notion of gold arbitrage—and
endowed them with sharp analytical content. He then combined these concepts into a powerful framework capable of tracing the effects of monetary
disturbances produced by England’s suspension of convertibility during the
Napoleonic Wars. To analyze the effects of real disturbances produced by the
wars, he developed a separate demand-shift, income-expenditure mechanism.
His achievements merit recognition from economists today.

REFERENCES
Chipman, John S. “Balance of Payments Theory from Locke to Ricardo.”
Manuscript. University of Minnesota, 1983.
Einzig, Paul. The History of Foreign Exchange. London: Macmillan, 1962.
Fetter, Frank W. “The Transfer Problem: Formal Elegance and Historical
Realism,” in C. R. Whittlesey and J. S. Wilson, eds., Money and Banking
in Honour of R. S. Sayers. London: Oxford University Press, 1968.
. “The Life and Writings of John Wheatley,” Journal of Political
Economy, vol. 50 (June 1942), pp. 357–76.
Frenkel, Jacob A. “Purchasing Power Parity; Doctrinal Perspective and
Evidence from the 1920s,” Journal of International Economics, vol. 8
(1978), pp. 169–191.
Hollander, J. H. “The Development of the Theory of Money from Adam Smith
to David Ricardo,” Quarterly Journal of Economics, vol. 25 (1911), pp.
429–70.
Hume, David. “On Money” and “On the Balance of Trade,” in E. Rotwin, ed.,
Writings on Economics. Madison: University of Wisconsin Press, 1955.
Kydland, Finn, and Edward C. Prescott. “Time to Build and Aggregate
Fluctuations,” Econometrica, vol. 50 (November 1982), pp. 1345–70.
Long, J. B., and C. I. Plosser. “Real Business Cycles,” Journal of Political
Economy, vol. 91 (February 1983), pp. 39–69.
Metzler, Lloyd A. “The Theory of International Trade,” in A Survey of
Contemporary Economics, Vol. 1. Philadelphia: The Blakiston Company,
1948.

86

Federal Reserve Bank of Richmond Economic Quarterly

Morgan, E. V. The Theory and Practice of Central Banking, 1797–1913.
London: Cambridge University Press, 1943.
O’Brien, D. P. The Classical Economists. London: Oxford University Press,
1975.
Officer, Lawrence. Purchasing Power Parity and Exchange Rates. Greenwich,
Conn.: JAI Press, 1984.
Ricardo, David. The High Price of Bullion: A Proof of the Depreciation of
Bank Notes. London: Murray, 1810, reprinted in Piero Sraffa, ed., The
Works and Correspondence of David Ricardo, Vol. 3, Pamphlets and
Papers, 1809–1811. Cambridge: Cambridge University Press (for Royal
Economic Society), 1951.
Schumpeter, J. A. History of Economic Analysis. New York: Oxford University
Press, 1954.
Thornton, Henry. An Enquiry into the Nature and Effects of the Paper Credit
of Great Britain. 1802. Edited with an introduction by F. A. von Hayek.
London: Allen and Unwin, 1939.
Viner, Jacob. Studies in the Theory of International Trade. New York: Harper,
1937.
Wheatley, John. Report on the Reports of the Bank Committees. Shrewsbury,
England: W. Eddowes, 1819.
. An Essay on the Theory of Money and Principles of Commerce,
Vol. 1. London: Cadell and Davies, 1807.
. Remarks on Currency and Commerce. London: Cadell and Davies,
1803.
Wu, C-Y. An Outline of International Price Theories. London: Routledge,
1939.


Federal Reserve Bank of St. Louis, One Federal Reserve Bank Plaza, St. Louis, MO 63102