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Vol. 25, No. 3

ECONOMIC REVIEW

FEDERAL RESERVE BANK
OF CLEVELAND

1989 Quarter 3
Vol. 25. No. 3

The Stability of Money
Demand, Its Interest

Sensitivity, and Some

Economic Review

Implications for Money
as a Policy Guide

q uarterly b y the Research

is published

D e p a rtm e n t o f the Federal
R e s e rve B a n k o f C le ve la n d .

b y Jo h n B. C arlson

C opie s of the

Review

are

availa ble through our Public
One common finding of recent empirical research in monetary economics is

A ffa irs an d B a n k Relations

that the interest elasticity of money demand is substantial, and higher than

D e p a rtm e n t, 2 1 6 / 5 7 9 -2 1 5 7 .

many economists previously thought. The evidence seems strongest for M 1
demand in the long run. While interest rates appear to have little or no longrun effect on M 2 demand, the short-run interest elasticity seems higher than
previously thought. This paper examines the recent findings on money

C oordin ating Ec o n o m is t:
Randall W . E b e rts

demand and discusses their implications for monetary policy and rules.
Ed ito rs : Paul J . N ick els
Robin Ratliff
D esign : M ich ae l G a lk a
T y p o g ra p h y : L iz H a n n a

Accounting for the Recent

Divergence in Regional
Wage Differentials

O pin ion s s ta te d in

Review

b y R andall W . Eberts

Economic

are th o s e o f the

a u th ors an d n ot necessarily
those of the Federal R e s e rve

A fter converging for almost half a century, nominal regional wages have

B a n k of C le ve la n d or o f the

diverged since 1980. This paper examines the dispersion of individual worker

Board o f G o ve rn o rs o f th e F e d

wages among the nine census regions. Results show that changes over time

eral R e s e rve S y s te m .

in the value that each region places on worker characteristics account for
much of the switch from wage convergence to divergence. Temporary shocks
from the 1980-82 recessions and the fall in oil prices are probably responsible

M aterial m a y be reprinted pro

for this interruption of the long-term trend of regional wage convergence.

vid e d th a t th e source is credited.
Ple as e send copies o f reprinted
m aterial to the editor.

Why We Don’t Know
Whether Money

2 7

Causes Output
b y C harles T. C arlstrom
and E dw ard N. G am ber
Most economists and policymakers believe that m oney affects real output.
This paper argues, however, that Granger-causality studies that have pur
ported to show this relationship are flawed, and that currently we do not
have enough information to conclude that changes in the m oney supply
cause changes in real G N P . The authors also review different models of bus
iness cycles and show how money can be neutral and yet still appear to
affect real output.

I S S N 0 0 13 -0 2 8 1

The S tability of M oney
Dem and, Its Interest
S e n s itivity, and Som e
Im plications for M oney
as a Policy Guide
by John B. Carlson
John B. Carlson is an economist at
the Federal Reserve Bank of Cleve
land. The author acknowledges help
ful discussions and comments from
Charles Carlstrom, William Gavin,
and George Tavlas. Thanks also to
Christine Dingledine for meticulous
research assistance.

Introduction

The money demand function is one of the most
closely studied relationships in economics. One
reason is that the question of the stability of
money demand has long been central to issues
of monetary theory. This largely reflects the
influential restatement of the quantity theory of
money by Milton Friedman (1956): “The quan
tity theory is in the first instance a theory of
money demand.” Further, he argued, “The quan
tity theorist accepts the empirical hypothesis that
the demand for money is highly stable— more
stable than functions such as the consumption
function that are offered as alternative key
relations.”
Friedman did not specify precisely the mean
ing of “highly stable” or “more stable.” Presum
ably, highly stable implies that the parameters of
the money demand function do not change over
time. Thus, one would expect that any reasona
ble specification of money demand might satisfy
some sort of in-sample stability test (for exam
ple, Chow test) at a minimum. The notion that
money demand is more stable than other “key”
relationships has been interpreted in the context
of a simple IS-LM framework by Poole (1970). In
essence, “more stable” implied that the variance

relatively

of the money demand function was
smaller than the variance of the IS curve.
For years, the question of stability was simply
examined by estimating various specifications of
money demand, including both long-run and
short-run models. It was commonly affirmed that
money demand was a function of relatively few
variables, including income and interest rates. By
the mid-1970s, a consensus seemed to emerge
that money demand was indeed one of the more
stable relationships in economics, reliable enough
to serve as a basis for formulating monetary policy.
Unfortunately, just as a consensus seemed to
develop, many of the estimated relationships
broke down, first around 1974, and again around
1982. By the mid-1980s, it appeared as though
many economists had given up on finding a
specification of money demand that might be
stable, in either the short or the long run.
Recently, however, several researchers have
found evidence that some specifications of
money demand have remained stable through
events of the 1970s and 1980s. One common
conclusion of these studies is that money demand
is highly interest sensitive— more so than many
economists previously thought, particularly in

M l Velocity

The policy implications of the common finding
that money demand is substantially interest sen
sitive are analyzed in sections VI and VII. Section
VIII offers some concluding thoughts.

I. The Demand for M l

Ratio

Before 1980

SOURCE: Board o f Governors o f the Federal Reserve System.

the long run. The magnitude of the interest elas
ticity of money demand has important implica
tions for the role of money in the economy and
hence for the conduct of monetary policy.
Much of the early debate about the role of
money centered on how interest rates affected
the velocity of money. Some analysts argued that
interest-rate changes had little effect on velocity
in the short or long run. Moreover, some pre
sumed that M l velocity had an inherent trend
growth rate of about 3 percent. These assump
tions now appear to be clearly refuted by the
experience of the 1 9 8 0 s.
This paper reviews some recent findings of
the research on money demand and considers
the implications of these findings for monetary
policy and rules. Section I reviews briefly a
common specification of M l demand that misled
many economists about the importance of inter
est rates. Section II examines recent evidence
that long-run equilibrium demand for the nar
row money measure continues to be a stable
function of relatively few variables.
The implications of these findings for the
apparent shift in M l velocity are discussed in
section III. Section IV reviews the evidence that
M2 demand is stable in the short run. In section
V, the findings on M2 demand are reconciled
with evidence that M2 velocity is trend stationary.

Until the 1 9 8 0 s, most attention in the money
demand literature was given to M l— the money
measure that then included currency and noninterest-bearing demand deposits. Focus on this
measure reflected both theoretical and pragmatic
considerations. First, M l was the closest measure
of pure transactions balances and hence con
formed well to the concepts embodied in the
inventory-theoretic model of Baumol (1952) and
the portfolio-choice theory of Tobin (1958).
These approaches essentially explained why
individuals would hold the non-interest-bearing
components of M l instead of interest-bearing
alternatives.
Perhaps more important, the focus on M l
seemed justified on empirical grounds. O f the
various money measures, M l appeared to be
most closely related to economic activity, partic
ularly in the short run. Movements in M l served
as a relatively useful indicator of current and
future changes in economic activity. Moreover,
the velocity of M l exhibited a high degree of
stability. From 1959 to 1980, M l velocity
increased at a trend rate of around 3 percent,
deviating only a few tenths of a percent from
year to year (see figure 1 ).
By the 1970s, a conventional empirical model
for M l demand had evolved. 1 Desired real M l
balances,
were a function of some scale var
iable,
either real income or wealth; and a
measure of the opportunity cost of holding
money,
the level of interest rates:

m *,

(1) m* = a 0 + a xy - a 2r .
Earlier studies used annual data (see Meltzer
[1963], Laidler [1966], and Chow [1966]). In
these studies, the scale variable was typically
some measure of wealth, and the opportunity
cost was most often a measure of the long-term
interest rate. The interest elasticities for M l
ranged between -0.7 and -0.9. 2

■

■2

See, for example, Goldfeld (1973).

For a more complete discussion of earlier studies, see Havrilesky and

Boorman (1978), chapters 7 and 8.

Later studies in money demand used quarterly
data, perhaps motivated by the increasing availa
bility of such data and the development of quar
terly econometric models (see Goldfeld [1973]).
It became more common to use real income as
the scale variable and to use a measure of the
short-term interest rate as the measure of oppor
tunity cost. It was often assumed that in any
given quarter, money balances adjusted only par
tially to their desired (equilibrium) level. The
adjustment process was specified as
(2)

mt - mt _

Disinflation and financial deregulation greatly
affected the opportunity cost of Ml. Disinflation
resulted in sharply falling interest rates, reversing
the secular trend that dated back to the 1950s.
Deregulation allowed banks to compete more
effectively for funds by offering interest-bearing
checking accounts and market rates of interest
on savings and time deposits. The opportunity
cost of most bank deposits fell markedly after
1982 when market rates fell and when banks
priced deposits more competitively.

X(m* - mt _ 1 ),
II. M l Demand Revisited

where A is the speed of adjustment to equili
brium. Substituting equation (1) into (2) yields
(3)

rnt = A.a + k a xy t - X.a2rt + (1 - k)m t _ j .
0

Equation (3) was sometimes estimated in firstdifference form . 3
The speed of adjustment of M l balances to
equilibrium levels was typically estimated to be
between 0.25 and 0.5 per quarter. The estimates
of income elasticities of this specification were
typically around 0 . 2 in the short run and less
than unity in the long run. Estimates for interestrate elasticities were around -0 . 0 2 in the short
run and ranged between -0.05 and -0.15 in the
long run . 4
The estimates of
interest elasticities
seemed lower than the theories predicted and
were substantially lower than earlier estimates.
Given the absence of any evident interest-rate
effects on M l velocity' and the apparent stability
of the short-run specifications through the early
1970s, the smaller estimates of interest elasticity
appeared to have gained greater acceptance.
By the 1980s, however, the quarterly specifica
tions for M l demand failed miserably. This was
evident in the sharp change in the behavior of
M l velocity, which has varied substantially since
1980 and exhibits no clear trend. The break
down in the conventional relationship is
believed to be largely a consequence of disinfla
tion and financial deregulation. 5

long-run

■3

The inclusion of lagged money was also rationalized on an expecta

tion^ basis (see Havrilesky and Boorman).

■4

While attempts have been made to rectify M l
demand in the short run, no consensus appears
to be forming on any particular specification (see
Moore, Porter, and Small [1988]). Many analysts
now question whether a short-run demand func
tion can ever be identified for M l . 6 O n the other
hand, recent studies by Poole (1988) and by
Hoffman and Rasche (1989) suggest that the
long-run (equilibrium) relationship may have
endured through the past decade. Their specifi
cations find that the long-run equilibrium inter
est elasticity of M l demand is substantial.
Poole offers an explanation for why some
economists may have been misled from models
estimated in first-difference form. Such models
often included a constant term, which made it
equivalent to a linear-time-trend specification in
a regression using the levels of the data. He con
cludes that in the postwar period, the constant
term incorrectly picked up the trend in velocity,
which should have been attributed to the post
war trend in interest rates.
This argument fails to explain, however, why
the regressions for M l in levels form (without
time-trend variables) also underestimated inter
est elasticities. Closer inspection of the conven
tional relationships reveals that part of the trend
effect of interest rates on M l may have mistakenly
been attributed to the trend in income. As noted
above, the long-run income elasticity was typically
estimated to be less than one— often around
one-half. This, in turn, implied that over long
periods, velocity would increase at approxi
mately half the rate of increase in income, other
things being equal. Since the conventional esti
mate of income elasticity concurred with the

Some specifications included interest paid on passbook savings depos

its as an additional measure of opportunity cost.

■5

Some economists believe that the breakdown in the conventional rela

tionship w as also a consequence of the change in the Federal Reserve’s oper

■

Poole (1988) discusses the difficulties of identification from a buffer-

stock perspective of money demand and concludes that the econometric prob

ational procedure in October 1979 and the implications of that regime change

lems may well be insurmountable. For a review of the buffer-stock approach

on structural coefficients.

to money demand, see Laidler (1984).

inventory-theoretic models of transactions bal
ances, many analysts accepted the low estimate
as a confirmation of the theory.7
To estimate long-run money demand, Poole
advocates a simple regression of the level of
velocity on the level of a long-term interest rate
using annual data. By excluding income as an
explanatory variable, Poole implicitly constrains
the income elasticity to be unitary; hence, any
potential trend in velocity must be independent
of any trend in income.
Poole’s case for using a long-term interest rate
is predicated on the assumption that equilibrium
money demand would not likely be affected by
changes in interest rates in the long
run. Investment in cash management techniques
is costly and hence only profitable when interestrate increases are sustained. Since long-term
rates are believed to embody expectations about
future short-term rates, a rise in long-term rates is
likely to indicate a more permanent rise in the
general level of interest rates. Thus, Poole con
cludes, long-term rates better measure the
opportunity cost of cash.
Finally, Poole argues that adequate estimates of
a money-demand function cannot be obtained by
using postwar data alone. During this period, both
short- and long-term rates rose secularly. Thus,
he uses an extensive sample period, 1915-1986,
and three different subsamples. He estimates that
the interest elasticity is around -0 . 6 for the
whole period and for various subsamples, which
is substantially larger than conventional estimates.
Hoffman and Rasche obtain estimates of a simi
lar order of magnitude using a different estima
tion and testing method. Unlike Poole, they do
not constrain the income elasticity to be unitary.
Their approach— based on the notion of
cointegration— addresses a potential problem
related to the statistical properties of the varia
bles included in money demand.
As with most economic variables, M l, interest
rates, and income are nonstationary in levels. In
such variables, there is no tendency to systemati
cally return to a unique level or trend over time.
It is now well known that standard regression
analysis can yield spurious relationships between
variables when the variables drift over time.
Methods initially developed by Engle and
Granger (1987) allow one to examine whether
equilibrium relationships exist between nonsta
tionary variables. Such variables are said to be

temporary

cointegrated, if some linear combination of them
is stationary. Thus, cointegration implies a longrun equilibrium relationship between variables,
and one can obtain long-run elasticities from the
cointegrating vector.8
Hoffman and Rasche test for cointegration and
find that 1) real M l balances and real income are
not cointegrated by themselves; 2) real M l, real
income, and the interest rate are cointegrated
with one cointegrating vector; and 3 ) one cannot
reject the hypothesis that the coefficients of real
money and real income in the cointegrating vec
tor are equal in value but opposite in sign. 9
The first result is consistent with the common
finding that M l velocity is nonstationary. Since
both income and money are nonstationary, but
not cointegrated, their difference will be nonsta
tionary. The second result, however, implies a
stable long-run relationship between money,
income, and interest rates. The third result
implies that it is appropriate to interpret the
cointegrating vector as a linear combination of
M l velocity and interest rates or, equivalently,
that the equilibrium real income elasticity of
demand for real balances is unity.
To estimate the equilibrium interest-rate elas
ticity, Hoffman and Rasche consider both a short
term rate (three-month Treasury bill) and a long
term rate (10-year Treasury bond). Like Poole,
they find that the interest elasticity on the long
term rate is about -0 .6 , while somewhat less,
-0.4, for the short-term rate. Moreover, they find
that cointegration holds for either of the long- or
short-term measures. These results are robust
across subsample periods investigated.

III. M l V elo c ity
in the 1 9 8 0 s
The Hoffman and Rasche findings imply that any
observed drift in the velocity of M l should be
proportional to any drift in nominal interest rates.
Thus, any shift in the drift of velocity should be
the mirror image of any shift in the drift of nom
inal interest rates. Rasche (1989) investigates this
last property by examining regressions of the
changes in the log of M l velocity and changes in
the nominal interest rate, each against a constant
and a dummy variable, which is zero through
December 1981 and 1.0 thereafter.

■

For a more precise description of the concepts of cointegration, see

Engle and Granger (1987).
■

Other economic explanations for w hy an income elasticity might be

less than one include improvements in cash management technology.

■

9 All variables are in log form.

The results indicate significant shifts in the
interest-rate equation and in the velocity equa
tion, both in the same direction. Again, the
results hold for both long- and short-term rates;
but, because of the high variance in the short
term rates, the shift is not measured with any
precision. Rasche concludes that the abrupt
change in the pattern of M l velocity in the early
1980s was indeed associated with a coincidental
change in the drift in interest rates.
Rasche further investigates the hypothesis that
the observed change in velocity behavior is a
result of a break in inflationary expectations. He
argues that if the postwar period through 1980 is
characterized by a steady upward drift in infla
tion, then it is reasonable to conjecture that it
has been associated with the observed positive
drift in nominal interest rates. Moreover, he
argues that if inflation expectations stabilized at a
lower rate in the early 1980s, it is reasonable to
conclude that there has been no drift in interest
rates over this period.
As evidence for a break in the drift of infla
tionary expectations, Rasche notes the general
consistency of the Livingston Survey data. These
data, which begin in the late 1940s, provide
annual inflation forecasts formed at the end of
the previous year. The survey reveals a general
upward trend through 1980 and then a break
sharply downward. Rasche notes that since 1982,
the Livingston series has fluctuated without a
trend in the 3 percent to 5 percent range.
To summarize, the recent evidence of large
interest elasticities of M l demand pro
vides a basis for understanding the recent shift in
the trend in velocity. While the evidence points
to a reasonably stable long-run M l demand func
tion, no one yet seems to have identified a satis
factory short-run model. Without a reliable shortrun model of M l, little can be said about Ml
velocity in the short run.

long-run

IV. The Demand for M 2

Recent research on M2 demand provides evi
dence of stable specifications for M2 in the short
run, at least in the postwar period. Moore, Porter,
and Small (1988) estimate a short-run M2
demand function over the period 1964: IQ to
1986:IIQ.10 The model is specified in two parts.
One is an equilibrium money demand function,
similar to equation ( 1 ):

mt -

For further evidence concerning the stability of M 2, see Hetzel and

Mehra (1987).

where
log (M2),
= log (nominal GNP),
and s = log (opportunity cost). Note that the
unitary coefficient on nominal GNP assures that
this also specifies a velocity relationship. 11 The
second component is a dynamic specification
based on an error-correction adjustment:
U

A m t = a + bet_ x + X cjA m t_ i

(5)

+ X
dj A s , _ j + X Ji & y t - i + e / ’
/ =0
i=0

where
_ x is the deviation of money from its
long-run equilibrium value (derived from [4])
and e is white noise.
Equation (5) essentially specifies the short-run
convergence process of M2 to its equilibrium
value. When the coefficient
is negative, con
vergence is assured. Substituting equation (4)
into (5) yields

(6 )

Am t= a - ba - bfist_ x + b (m t X- y t_ x)
U

i =1

c i A m t _ , + X d , A s t- i

i =0

+ X
f i ^ y t- i + v
i=0

Moore et al. estimate a version of equation ( 6 ).
Simulations, both in-sample and out-of-sample,
support the hypothesis that M2 demand has
been and continues to be reasonably stable over
the whole sample period.
One key feature of Moore et al. is the way
opportunity cost is measured. By definition, the
opportunity cost of money is the forgone interest
income of holding a monetary asset. Over the
years, it has been common to use a market yield
on a relatively risk-free asset, such as a Treasury
bill, to measure opportunity cost. For much of
the postwar period, this seemed appropriate for
the narrow money measures, since holders of
currency and demand deposits did not receive
explicit interest payments on these instruments.
Many instruments in the broader monetary
aggregates like M2, however, have yielded
explicit interest. Their yields, when not exceed
ing interest-rate ceilings, responded at least par
tially to market conditions. Moore et al. measure
the opportunity cost of these instruments as the

■

■ 10

mt = a + y t + fis, + e, ,

(4)

Moore et al. include a time index as a regressor to directly estimate

any drift in M 2 velocity. While they find the coefficient to be significant, the
drift is negligible at around .003 percent per year.

difference between their yield and the yield of a
Treasury bill. The opportunity cost of M2 then is
the weighted average of the opportunity costs of
each M2 component, where the weights are
equal to the component’s share of M2.
The response of money demand to changes in
market interest rates in this model requires a
specification of the relationship of deposit rates
to the market rates. 12 Thus, the interest elasticity
of money demand now depends on how rapidly
banks adjust their deposit rates in response to
changing market rates. To illustrate, consider the
extreme case where deposit rates respond instan
taneously to changes in market rates so as to
maintain a constant spread between them. In such
a case, money demand and velocity would be
unaffected by changes in market interest rates
because the opportunity cost of money would
not change.
If, on the other hand, deposit rates adjust
instantaneously but only partially to a change in
interest rates (that is, not point-for-point), then
the interest elasticity would be proportional but
less than the opportunity cost elasticity. Any
trend in interest rates would also be associated
with a trend in the opportunity cost of those
deposits. Equilibrium money demand would
hence be affected, and the trend in velocity
would be proportional to the trend in the oppor
tunity cost of M2.
Finally, consider a case where deposit rates
respond sluggishly to changes in open market
rates. A permanent increase in market interest
rates would initially be associated with an
increase in opportunity cost, as market rates
moved above deposit rates, followed by a
decrease as deposit rates caught up. If the de
posit rates ultimately adjusted point-for-point,
the long-run equilibrium level of opportunity
cost would be unaffected.
Moore et al. specify deposit-rate equations to
be simple linear functions of the federal funds
rate. They assume that competitive forces ulti
mately drive the slope coefficients to equal one
minus the marginal reserve ratio, and the inter
cept to equal some negative value to reflect trans
actions costs that are not recovered as fees
assessed to the depositor. As with M2 demand,
the short run is formulated within an errorcorrection framework. Changes in deposit rates
are assumed to be related to deviations of the

rates from their long-run equilibrium values, and
to changes in the current and past values of
interest rates.
Moore et al. find that for many components of
M2, own rates have been relatively slow to
adjust. This is particularly evident for instruments
with transactions features such as NOW accounts
and, to a lesser extent, money market deposit
accounts. On the other hand, some deposit rates,
such as those on time deposits, have adjusted
relatively quickly and fully to changes in market
rates. 13 However, because a significant share of
M2 deposit rates adjust sluggishly, changes in
market interest rates have substantial short-run
effects on the opportunity cost of M2, and con
sequently on its demand.
Indeed, the model estimated by Moore et al.
suggests that the
interest elasticity of
M2 demand is substantial. What is curious is that
some bank deposits appear more interest sensi
tive than before deregulation. One might expect
just the opposite, as deregulation allows banks to
compete more effectively for funds, even if they
adjust only slowly.
Some analysts have speculated that the in
creased sensitivity of some deposits may reflect
the increased sophistication of most depositholders and the improved communications
technologies that have made funds transfers
more convenient. Even if opportunity costs are
less affected by changes in interest rates now
than before, deposit-holders are much more
aware of alternative assets and therefore are
more likely to respond to changes in the oppor
tunity cost of some deposits. 14

short-run

V. M2 Velocity

The treatment of opportunity cost as distinct
from the market interest rate helps to reconcile
why M2 velocity is trendless despite the
observed trends in interest rates. This is easiest
to understand in the case where deposit rates
ultimately adjust point-for-point with changes in
market rates. In such a case, opportunity cost is
by definition stationary around some trendless
differential, and hence would be independent of
any trend in interest rates. Thus, the velocity of
these deposits would be insulated from chang
ing inflationary expectations.

■ 13

Moore et al. also conclude that deposit-rate adjustments are asym

metric, adjusting more rapidly to upward movements in market rates than to

■ 12

The advantages of measuring opportunity cost as a differential in

downward movements.

yields are in principle greater since deregulation than before. Currently, there
are no interest-rate ceilings on any of M 2’s noncurrency and non-demand-

■ 14

deposit components, which are 83 percent of the total.

ity of the M 2 aggregate after deregulation.

However, there appears to be no shift in the opportunity cost elastic

Interest Rate and
Opportunity Cost of M 2

Percent

SOURCE: Board o f Governors o f the Federal Reserve System.

F I

M 2 Velocity and
Opportunity Cost

Ratio

Percent

However, not all deposits in M2 adjust pointfor-point to changes in interest rates. Reserve
requirements assure some wedge preventing
complete adjustment. Also, since currency pays
no explicit yield, its opportunity cost is essen
tially equal to the interest rate. Thus, if the level
of interest rates exhibits drift, the opportunity
costs of these components of M2 will also exhibit
drift in the same direction. M2 velocity would
not be independent of the level of interest rates.
In practice, however, the drift in the opportu
nity cost of M2 has been highly muted relative to
the drift in interest rates (see figure 2). The
wedge created by reserve requirements is in fact
small— 12 percent or less. Moreover, the share of
currency and resemble deposits amounts to less
than 20 percent of M2; thus, the nonstationary
component of the opportunity cost would be
small and perhaps negligible. Interest-rate
trends, then, would not affect M2 velocity sub
stantially in the long run.
Some evidence indicates that M2 velocity is, in
the long run, independent of interest rates. Engle
and Granger (1987) conclude that nominal in
come and M2 are cointegrated, implying that M2
velocity is a stationary process and hence is unaf
fected by interest-rate trends. Thus, it would
appear that M2 velocity is immune to changing
inflationary expectations in the long run. This
explains why the M2 velocity trend, unlike that of
Ml, was unaffected by the rise and fall of inflation
in the postwar period. In the short run, however,
changes in the opportunity cost of M2 are driven
largely by changes in market interest rates; and,
as figure 3 illustrates, M2 velocity is quite closely
related to the opportunity cost of M2.

8
VI. Money as a Policy
Guide During Disinflation

SOURCE: Board o f Governors o f the Federal Reserve System.

Recent evidence indicating that money demand
is substantially interest sensitive has important
implications for monetary policy. Interest sensi
tivity of money demand poses serious problems
for policies that seek to achieve disinflation.
Poole (1988) concludes, “There is a serious and
probably insurmountable problem to designing
a predetermined money growth path to reduce
inflation...” (p. 97).
Poole offers a clear description of the problem:
If policymakers embark on a credible policy of
disinflation, they should expect that nominal
interest rates will ultimately fall as inflationary
expectations subside. Consequently, they should
expect velocity growth to decline, and perhaps
even become negative, if the policy becomes suc
cessful. Under these circumstances, inflation

Hypothetical M 2 Demand:
Credible Disinflation

Annual percent change

SOURCE: Author’s calculations.

could be reduced without a decline in money
growth, at least initially. Indeed, a decline in
money growth might have a significant depress
ing effect on the economy. He concludes that
the gradualist prescription of predetermined
reductions in money growth would not be politi
cally sustainable, as it would likely be associated
with unnecessary weakness in economic activity.
Poole further argues that this situation poses a
serious dilemma for policymakers. How do they
convince markets of their commitment to disin
flation without a reduction in money growth
rates? Is it not irrational to bet on lower inflation
on the basis of a central bank’s promises, with no
evidence that the central bank is reducing money
growth? Poole concludes that a recession may be
necessary to convince markets that the central
bank is committed to a disinflationary policy.
The problem of targeting money is easy to
appreciate in the context of Ml. After all, few
analysts anticipated the magnitude of the shift in
the drift of Ml velocity. Another reduction in
inflation would likely result in another shift in
the trend in M l velocity. Moreover, no specifica
tion for short-run M l demand seems acceptably
stable at present. On the other hand, there is no
evidence that the trend of M2 velocity has been
affected by the transition to lower inflation in the

1980s. The recent specification by Moore et al.
suggests that the short-run demand for M2 may
be reasonably stable.
A hypothetical example illustrates how the
problem applies to a disinflation policy specified
as a target path for M2. First, assume that on the
basis of a promise alone, markets could be con
vinced of a central bank’s commitment to grad
ual disinflation from current levels to zero infla
tion in 1993- To the extent that disinflation was
perfectly anticipated, we might expect that nom
inal magnitudes such as interest rates, personal
consumption expenditure growth, and nominal
GNP growth would decline smoothly to noninflationary trend paths. 15
If the parameters of the M2 demand function
estimated by Moore et al. are approximately
structural, then we would expect M2 demand to
accelerate initially to growth rates above the
equilibrium rate of nominal GNP growth and
then begin to slow (see figure 4). The additional
money growth would not be for the purpose of
financing future spending, but would reflect a
pure portfolio decision to hold a greater propor
tion of wealth as bank deposits in response to a
sharply falling opportunity cost; hence, the
monetary acceleration could still be associated
with a slowing in nominal spending.
The pattern of M2 growth reflects two key fea
tures of the M2 demand model. First, own rates
on deposits adjust slowly enough to changes in
market rates that the opportunity cost in the
short run is directly related to changes in the
level of interest rates. 16 Second, M2 demand is
substantially sensitive to changes in opportunity
cost. Thus, as interest rates fall with disinflation,
so does the opportunity cost of M2. It is this
decline in M2’s opportunity cost that induces
investors to hold additional bank deposits rela
tive to their spending needs.
This example is hypothetical, of course. If
markets were to maintain an expectation of
gradual disinflation, they would need to under
stand the consequences of a falling opportunity
cost and have confidence that the estimated
M2 demand function was reliable.
Only then might markets reconcile an accelerat
ing money-growth path with a disinflation policy.

short-run

■ 15

W e assume here that in noninflationary equilibrium, growth in nominal

G N P and personal consumption expenditures equals 3 percent, as does the
Treasury bill rate, but that the federal funds rate equals 2 V2 percent.

■

1 6 This, of course, presumes that banks have a rational basis for adjust

ing some deposits more sluggishly than others. Thus, although market interest
rates fully anticipate disinflation, bank deposits would respond with some
delay.

The 22-year estimation period for M2 demand is
relatively short, however, and it is not evident
that deposit-rate pricing has stabilized since
deregulation. It would seem doubtful that
markets could be convinced of such a strategy.
Nevertheless, the evidence of substantial
interest sensitivity of velocity in the short run
suggests that policymakers might sometimes
prefer to accommodate the effects of interest-rate
changes on money demand. During periods of
disinflation, one might then expect wide swings
in money growth. Once a disinflation strategy
becomes credible, velocity could fall substan
tially, if only temporarily, and it would be
appropriate for policymakers to accommodate
the consequent surge in money demand.

VII. Interest Sensitivity
and Monetary Rules

Apart from the problems that arise during disin
flation, the evidence that M2 is more interest-rate
sensitive than previously thought raises some
interesting issues concerning monetary rules. On
the one hand, shocks to money demand would
have smaller real consequences under a
constant-money-growth rule than previously
thought. Consider a positive shock to money
demand. Given an inelastic money supply, inter
est rates would need to rise and output would
need to fall. In conventional macroeconomic
models, interest rates would respond initially.
Higher interest rates would, in turn, tend to slow
economic activity. When the interest elasticity of
money demand is high, smaller interest-rate
changes are required to offset demand shocks,
implying smaller adjustments in output.
O n the other hand, the consequences of non
monetary shocks under a constant-money-growth
rule are less clear when the demand for money
(and hence velocity) is highly interest-elastic.
This longstanding issue is illustrated simply in a
debate between Johnson (1965) and Friedman
(1966). Johnson argued that interest-sensitive
money demand militated against a constantmonetary-growth rule “...because variations in
interest rates generated by the real sector would
make such a rule automatically destabilizing...”
(p. 397). Implicitly, Johnson assumed that varia
tions in interest rates would be a natural by
product of stable output growth; in turn, these
variations would cause procyclical variations in
velocity, which, under the assumption of con
stant money growth, would produce fluctuations
in the rate of nominal income growth.

Friedman acknowledged this potential out
come, but argued that the conditions assumed
by Johnson were highly special. Essentially,
Friedman contended that while velocity would
tend to move with nominal output, a constantmoney-growth rule would nevertheless dampen
output fluctuations relative to “discretionary”
policies. Thus, Friedman was not comparing his
rule to an ideal rule, but to the existing practice
of the central bank.
It is useful to separate this debate into two
issues. The first is the general issue of rules ver
sus discretion. The second is the question of
whether monetary rules (or targets) should
allow for some kind of systematic (that is, auto
matic) feedback to account for interest-rate
changes and, hence, shifts in velocity. More spe
cifically, should a rule or targeting procedure
anticipate changes in interest rates? This first
issue is only indirectly relevant to the question
of interest-rate sensitivity and therefore is not
dealt with here. 1 7 The question of feedback, on
the other hand, is relevant whether a policy
admits some discretion or not.
The feedback issue depends on the kinds of
shocks that occur and on the poorly understood
dynamics of adjustment in the economy. Specifi
cally, it depends on where shocks arise in the
economy, what their relative magnitudes are,
and how they are propagated through the econ
omy. The answers to these questions depend on
the particular model one believes is appropriate
for characterizing the economy. Unfortunately,
no consensus exists or even seems imminent.
One large and influential class of empirical
models, sharing a common propagation mecha
nism, casts some doubt on the efficacy of
monetary-growth rules. In these models,
the inflation process is characterized by an
output-gap accelerationist mechanism:

con

stant

P r P t -i

= ao+ «i (tf* - tf,) + a z t>

where
is the inflation rate,
is the level of
output,
is full-employment output, and
represents other factors. If is constant, a
change in the inflation rate depends on the out
put gap. When output exceeds full-employment
output (that is, when unemployment is below its
natural rate), inflation accelerates. When output
is below full-employment output, inflation
decelerates. Anderson and Enzler (1987) explain
the consequences of such a mechanism for a
monetary rule:

■ 17

For a discussion of the general issue of rules versus discretion, see

Carlson (1988).

It is easy to se e w h y h o ld in g the m o n e y grow th
rate constant might not result in a stable sim ula
tion path for a m a crom od el containin g this m e ch
anism. T he fixed m o n e y grow th path predeter
m ines b o th the rate o f inflation and the price
level consistent with the e c o n o m y ’s steady-state
path at each point o f time. C onsider what
happens if the price level is disturbed upward
from the steady-state grow th path. T he dem a n d
for m o n e y is increased and interest rates rise. This
depresses output and increases un em ploym en t.
T he increased un em ploym en t, in turn, d epresses
the rate o f change o f prices. As lo n g as the price
level remains t o o high, a force is created that
tends to k eep u n em p loym en t a b ove its natural
rate and the rate o f in fla tion con tin u es to fall.
T he d eclin in g rate o f inflation eventually returns
the price level to its steady-state value, and this in
turn allow s the u n em p loym en t rate to return to
the natural rate, but at this p oint in fla tion is to o
lo w to b e consistent with the fixed m o n e y grow th
path and the price level falls through the steadystate level. This redu ces the d em a n d for m oney,
causing interest rates to fall until u n em p loym en t
is b e lo w the natural rate. Inflation then acceler
ates until at so m e p oint it reaches its steady-state
value. But n o w the level o f prices is t o o low . T he
mirror im age o f the p reviou s events takes p lace
and oversh ootin g occu rs again, (p . 2 9 7 )

While the estimated parameters of these models
suggest that the cycle described above eventually
converges, the process is generally only slightly
dampened . 18
Because the estimated interest elasticity of
output in these models is typically relatively
small, it is likely that a higher interest elasticity of
money demand would only attenuate the cycles
of such models. To illustrate this point, consider
again the propagation of the upward price dis
turbance. The higher the interest elasticity of
money demand, the lower the rise in the level of
the interest rate that would result as an effect of
the price shock on money demanded, given an
inelastic supply. However, because the interestrate elasticity of output is low, the consequent
effect on output would be even smaller, and
would hence slow the process that dampens the
shock to inflation. 19
Evidence of a potential for long macroeco
nomic cycles is not a unique consequence for
models with an output-gap mechanism. Indeed,

some simple models linking money and prices
also exhibit long cycles. One example is a recent
single-equation model estimated by Hallman,
Porter, and Small (1989). Theirs is a reducedform model of the relationship between inflation
and M2 that does not explicitly include either
the current level of output or employment as a
variable. 20 While they find rather lengthy adjust
ments to simulated shocks (for example, more
than 1 0 0 years), the cycles of their model are
more damped than those of many large macroeconomic models.
From a deterministic point of view, the Hallman
et al. results suggest that there is a
money-growth path consistent with a relatively
smooth
to equilibrium. As they note,
inflation,
could be controlled at
any constant rate with constant growth of M2.
Notwithstanding the well-known critique of
Lucas (1976), the use of deterministic simulations
as evidence in the debate about an appropriate
policy rule is of only limited value. A critical
issue in this debate is how a rule performs in a
stochastic framework, one that approximates the
of disturbances that have historically
affected the various sectors of the economy. In
this context, the issue is not the selection of an
appropriate policy response to a particular shock,
but the robustness of a contractual commitment
to a policy rule in responding to a
of likely
outcomes arising from a typical distribution.
One sense of robustness has been stressed by
McCallum (1988): that a rule perform well for a
variety of models, preferably ones incorporating
alternative views of macroeconomic relation
ships. It is important to establish robustness (in
this sense) because no structural model of the
economy enjoys sufficiently wide acceptance;
nor does any consensus seem to be evolving.
Thus, to gain acceptance for a proposed rule, the
rule advocate must demonstrate that the rule
would lead to reasonably good outcomes for var
iables of interest
for a variety of models . 21

nonconstant

transition
in equilibrium,

distribution

series

and

■ 20

Nevertheless, the model incorporates estimates of full employment

output and equilibrium velocity as determinants of the equilibrium price level.
In this model, inflation is a function of the gap between the current price level
and its equilibrium level.

■ 18

It should be noted that these models typically do not result in a

trade-off between inflation and unemployment in the long run.

■ 21

One method of simulation designed to address this issue is suggested

by Tinsley and von zur Muehlen (1983). They essentially offer a technique to
generate unplanned disturbances consistent with the error structure observed

■

It is perhaps ironic that these models suggest that a constant-money-

in historical experience. The robustness of a policy rule is tested by multiple

growth rule would result in an interest-rate path that is too smooth to substan

simulations of the performance of the rule over multiyear periods, where each

tially dampen shocks to inflation over reasonably short horizons. Indeed, these

simulation draws a different series or “history” of unplanned disturbances. The

models suggest that rather large and sustained increases in interest rates

horizons are chosen to be long enough to allow significant differences to

would be required to substantially affect the output gap and hence the inflation

emerge among the alternative policies and to assure that policies ultimately

rate. However, it is uncommon to find antagonists of the money-growth rule

stabilize outcomes.

who cite this evidence and also publicly advocate the kind of interest-rate
variation that large models suggest is required to stabilize the inflation rate.

The sum of simulation results provides distributions of outcomes for each of
the model’s variables. For instance, one policy m ay be associated with a wide

Stochastic simulations, however, are costly to
obtain. Moreover, a test for robustness is an
open-ended search, encompassing an endless
variety of both rules and models. As a conse
quence, evidence from this analysis is in only an
embryonic state. Preliminary results by Tinsley
and von zur Muehlen (1983) and Anderson and
Enzler (1987) suggest, however, that monetary
rules do not perform as well as alternative rules
or intermediate targeting procedures. Neverthe
less, the monetary rules and targeting procedures
examined were based on older, less interestsensitive estimates of money demand.
The ongoing debate over the efficacy of a
constant-money-growth rule, when the interest
elasticity of money demand is large, is not likely
to be resolved without some convincing empiri
cal basis. Thus, it would seem appropriate for
policymakers to take account of the conse
quences of expected interest-rate changes on
velocity when choosing target ranges for M2 over
a period of a year or less. That is, it may be
appropriate for M2 growth to slow substantially
when interest rates are rising and expected to
rise further, or to accelerate substantially when
interest rates fall.

VIII. Concluding
Comments

One common finding of recent empirical
research in monetary economics is that the
interest elasticity of money demand is estimated
to be substantial, and higher than many econo
mists previously thought. The evidence seems
strongest for M l demand in the long run. While
interest rates have little long-term effect on M2,
the short-run elasticity seems to be greater than
previously thought.
When the interest elasticity of money demand
is high, velocity can vary widely. This creates a
problem for using money as a policy guide.
Monetary targets should take into account the
consequences of expected changes in interest
rates on money demand. This problem is per
haps most difficult during periods of disinflation,
when changing expectations about inflation
result in large swings in interest rates and hence
in velocity.
range of outcomes for output and interest rates, but with a small range for
prices and money for any given simulation horizon. Another policy m ay be
associated with small ranges for interest rates and money, but with large
ranges for prices and output, or vice versa. Tinsley and von zur Muehlen note,
“ ...the essential contribution of stochastic simulation analysis is the empirical
premise that while individual unplanned disturbances cannot be predicted (by
definition), their ranges of probable outcomes are unlikely to differ significantly
from the dispersions observed in historical experience...” (p. 16).

Finding that a money-demand function is stable
is not a sufficient basis for adopting a constantmoney-growth rule. The rule advocate has the
burden of convincing others that the stabilizing
effects of the monetary rule would outweigh the
potentially destabilizing effects of maintaining
constant money growth when velocity varies sys
tematically with interest rates. Because no con
sensus exists about the best model for the econ
omy, the rule advocate must argue his case in
the context of a variety of models.
The challenge of examining rule robustness
has been recognized and addressed by McCallum
(1988). It is hoped that others will follow his
lead. Recent developments in simulation
methods offer promising approaches for examin
ing the robustness of alternative policy rules.

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25,

Review of Economic Studies,

A ccou nting fo r the
Recent Divergence
in Regional W age
Differentials
by Randall W. Eberts

Randall W . Eberts is an assistant
vice president and economist at the
Federal Reserve Bank of Cleveland.
Comments and suggestions by Brian
Cromwell, Erica Groshen, and Sharon
Smith, and computer assistance by
Ralph Day and John Swinton, are
gratefully acknowledged.

Introduction

Convergence of regional income differentials is
commonly perceived as the natural result of the
gradual development and maturation of regional
economies. One expects that factors such as
improved transportation and communication,
enhanced mobility of capital and labor, and the
shift away from resource-based activities would
lead regions, and their incomes, to look more
and more alike. Indeed, since the 1880s, the
general trend has been toward convergence of
regional per capita income in the United States.
Recently, this trend appears to be reversing.
Browne (1989) shows that since 1979, regional
disparities in per capita personal income have
been on the rise. Furthermore, she concludes,
“...the key to both the converging per capita
incomes of the 1970s and the diverging incomes
of the 1980s was changes in industry earnings”
(p. 38).
According to Nourse (1968), regional income
divergence has happened only once in the last
century, between 1920 and 1940. After 1940,
regional incomes returned to their longer-run
path of convergence. Easterlin (1958) concluded
from that 2 0 -year disturbance in the longer-run

trend that “...it is by no means certain that con
vergence of regional income levels is an inevita
ble outcome of the process of development. For
while migration and trade do appear to exert
significant pressure towards convergence, they
operate within such a rapidly changing environ
ment that dynamic factors may possibly offset
their influence” (p. 325). It appears that the con
clusion Easterlin drew 30 years ago may be rele
vant in today’s situation.
This recent deviation from the general ten
dency toward convergence raises several ques
tions. Why the relatively sudden shift in the
direction of regional income differentials after so
many years of convergence? What are the sources
of this change in regional per capita income?
Have the fundamental forces that shape the
nation’s economy changed direction during the
1 9 8 0 s, or is this merely a temporary digression
from the longer-run trend of convergence?
This paper begins with the observation by
Browne that earnings account for most of the
shift from income convergence to income diver
gence among regions. We identify two basic
sources of regional wage differentials and exam
ine which of them is more responsible for the
shift in wage patterns. The two sources are 1)
regional differences in the return on various

worker attributes and the wage differentials
among industries and occupations, and 2 )
regional differences in the level of worker attri
butes and the distribution of workers among
industries and occupations.
These two sources can be distinguished by
asking whether earnings per worker differ
among regions because of differences in the
attributes of workers, or because of differences
in the value of worker attributes as determined
by the regional labor markets. Explaining con
vergence or divergence of regional wages, there
fore, rests with the ability to explain convergence
or divergence of characteristic prices, levels of
characteristics, or both.
Several studies have explored the relative size
of these two components of wage differentials
between regions, primarily in an attempt to
explain the difference in wages between the
South and other regions of the country. Sahling
and Smith (1983) were among the first to look at
the wages and attributes of individual workers to
examine regional wage differentials over time.
They compared the South with four other regions
in the country: the Northeast, the North Central,
the New York metropolitan area, and the West.
They estimated separate real and nominal wage
equations using a sample of residents from 2 9 of
the largest standard metropolitan statistical areas
(SMSAs) found in these five regions. The workerattribute variables included measures of school
ing, experience, race, occupation, sex, industry,
job status, and union membership. Using two
cross sections of data, from the May 1973 and
May 1978 Current Population Surveys, they con
cluded that much of the variation in wages be
tween the South and the other regions examined
is a result of substantial variation in the real and
nominal rates of return to worker characteristics.
Farber and Newman (1987) extended Sahling
and Smith’s analysis to look explicitly at changes
in characteristic prices over time. In addition to
looking at regional wage differentials in two dif
ferent years, 1973 and 1979, they estimated the
changes in the differentials between the two
years for various pairs of regions. They found
that more than half of the predicted changes in
South/non-South wage ratios can be accounted
for by changing relative returns to worker charac
teristics between the two areas (p. 2 2 3 ).
Other studies, using similar techniques and
micro-level data, do not necessarily agree with
the conclusion that characteristic prices account
for regional wage differentials. Bellante (1979)
and Gerking and Weirick (1983) find that
regional wage differences are due primarily to
differences in the levels of worker characteristics.

These results leave open the possibility that both
prices and levels are likely sources of regional
wage differentials. 1
This paper extends Farber and Newman’s
work in two directions. First, it includes three
time periods in order to examine the sources of
the switch in wage patterns that apparently
occurred at the beginning of the 1980s. Each
time period is constructed by pooling three
years of data: the first period includes the years
1973-75, the second includes 1979-81, and the
third includes 1985-87. The interval between the
first and second periods is characterized by
regional wage convergence, as documented by
Farber and Newman (1987) and Browne (1989).
The interval between the second and third peri
ods exhibits regional wage divergence, as shown
by Browne. The second direction is to look at all
nine U.S. regions as defined by the U.S. Bureau
of the Census, relative to the national average,
instead of comparing pairs of selected regions.
However, unlike the studies by Sahling and
Smith and Farber and Newman, which were con
cerned with comparing wage differentials across
different regions, our purpose is to see whether
the structure that caused a particular region to
converge toward the national average during the
early periods can also account for the divergence
of wages in that same region during the latter
periods. Therefore, it appears that using nominal
wages is sufficient for an initial look at the
sources of the shift in wage patterns. 2

I. Explanations
of Regional Wage
Differentials

One of the longstanding tenets of economics is
that efficient markets result in equal prices across
regions. Indeed, economists have observed for
decades the slow convergence of average wages
among the regions of the United States, where
goods and factors can flow freely. How, then, can
one explain the apparent divergence of wages in
recent years?

■

Dickie and Gerking (1988) provide a very comprehensive and insightful

critique of the literature.

■ 2

Work by Roback (1982) and Beeson and Eberts (1989) shows that

considering nominal wages can be viewed as only a partial-equilibrium analy
sis. Household spatial equilibrium includes not only wages, but also the price
of housing and nontraded local goods. Therefore, focusing only on nominal
wages may introduce estimation bias, especially in the prices of worker char
acteristics, for regions in which housing and other local-goods prices have
changed significantly from the national trend.

International trade theory offers useful insights
into conditions that lead to regional wage con
vergence and divergence. Much of the relevant
literature discusses wage equalization: average
wages across regions are equal if both the prices
of worker characteristics and the composition of
worker characteristics are the same. If the first
condition holds, then wages of identical workers
will be the same across regions. However, unless
the second condition also holds, the average
wages of regions will be unequal.
Within a regional context, conditions for equal
ization of characteristic prices are less stringent
than those for equalization of characteristic
levels. 3 A well-known theorem in trade theory,
the factor-equalization theorem, states that trade
in commodities and factor movements are sub
stitutes. According to this theorem, free trade of
goods leads to equal factor prices among regions,
even when factors of production are immobile.
Therefore, within the United States, which does
not limit trade between regions, one would
expect the unimpaired flow of goods to tend to
equalize wages. It has been this line of thinking,
based on the notion that regions trade because
of differences in factor endowments, that has led
to expectations of regional wage convergence.
Several assumptions, which may or may not be
met, are necessary to reach this conclusion,
however:
a) relative factor endowments are not identi
cal across regions,
b ) regions have identical technologies,
c) regions have identical homothetic
demand,
d) production is characterized by constant
returns to scale,
e) production is characterized by perfect
competition, and
f) there are no domestic distortions in either
region.
Markusen (1983) demonstrates that the rela
tionship between commodity trade and factor
trade varies depending on the specific assump
tions that are retained. By relaxing each of the
assumptions one at a time, he shows that the ini
tial trading equilibrium is not characterized by
factor-price equalization. In each case, factor
prices cannot be equalized between regions until
at least one region is specialized. He concludes
that the notion that trade in goods and factors
are substitutes may be a rather special result,
which is generally true only when differences in
relative factor endowments are the basis for trade
and when no market imperfections exist.

■ 3

Dickie and Gerking (1988) use trade theory to provide a comprehensive

Regions may trade goods for reasons other
than initial differences in factor endowments.
Markusen considers various other bases for trade
between regions in which the initial trade equi
librium is not characterized by factor-price equal
ization. These conditions include
a) differences in production technologies,
b) production taxes,
c) monopolies,
d) external economies of scale (increasing
returns to scale), and
e) factor-market distortions.
If these characteristics hold for regions, then
factor prices will not be equalized, even though
goods may still flow freely among regions. It is
easy to envision regional differences in technol
ogy, taxes, market share, agglomeration econo
mies, and unions— all of which would satisfy
one or more of the above conditions.
Factor-price equalization can be achieved in
these less-specialized cases if factors are mobile.
Factors will flow to the region with the higher
price, until interregional price differentials dis
appear. When trade is based on factors such as
those listed above, factor prices will differ in
such a way that the price will be higher for the
factor that is used intensively in the production
of the export good of that region. Consequently,
the region will be relatively well endowed with
the factor that is more intensively used in the
production of the region’s export good. How
ever, factor flows, particularly labor migration,
are impeded by imperfect information, by mov
ing costs (both monetary and psychic) and, in
the case of labor, by imperfect matches between
labor skills and job requirements.
What does this mean for the second compo
nent of wage changes— the level or composition
of factors? When trade is based on differences in
factor endowments, there will be no migration
based on wage differentials, for the simple rea
son that wages will not differ between regions
because of interregional trade in goods.4 When
trade is based on differences in production
technologies, taxes, or factor-market distortions,
factor-price differentials lead to factor flows, but
these flows will result in different proportions of
factors. Therefore, these models suggest that
average wage levels are very unlikely to be the
same across regions. 5 Even though interregional

■4

Of course, individuals m ay find regions to be attractive for reasons

other than higher wages. Site-specific amenities m ay also influence an individ
ual’s preferences.

■5

W ages will also differ across regions because of compensating differen

assessment of the necessary and sufficient conditions for regional wage

tials for site-specific characteristics, as discussed by Beeson and Eberts

equalization.

(1989).

prices may be equal, as predicted by both m od
els, it is most likely that the composition of the
characteristics will differ among regions.
Dickie and Gerking (1988) summarize the
outcomes of trade theory as they pertain to
interregional wage differentials. First, equaliza
tion of labor-characteristic prices does not
depend on geographic mobility of the entire
labor force. Rather, equalization occurs if enough
markets for goods and factors exist and if those
markets are allowed to clear. Second, when a
combination of commodity trade and factor
mobility guarantees factor-price equalization,
then relative factor supplies end up unequal and
regions tend not to become homogeneous in
factor composition. Third, when labor is hetero
geneous, economic efficiency, as evidenced by
equal factor prices, does not lead to interregional
equality of average wages (pp. 1 0 -1 1 ) . 6
Therefore, it appears that a systematic change
in characteristic prices is a likely source of the
switch from regional wage convergence before
1980 to regional wage divergence after 1980. The
subsequent analysis estimates the two basic
components of regional wage changes and
examines which of them contributes more to
these observed changes.

II. Accounting for
Regional Wage
Differentials

Consider the standard hedonic wage equation in
which the wage (
) of individual living in
region
is a function of the individual’s attri
butes
) and job or workplace characteristics

j
(H'j

(Ctf):

(1 )

Wtj= w(Hit, Cjj).

Assuming perfectly operating labor markets,
prices of each attribute are determined by supply
and demand conditions. Under the assumptions
of perfect information, costless spatial labor
mobility, and zero transactions costs, characteristic
prices will be the same across regions. Conse
quently, workers with the same characteristics will
be paid the same wage regardless of location.
The technique used to account for the two
sources of wage differentials follows the approach
of Oaxaca (1973), with modifications made by

Sahling and Smith (1983) and Farber and New
man (1987). Writing equation (1) in log-linear
form, dropping the individual subscript, and
adding a time subscript yields
(2)

lnwj t = bjtXj t ,

where

j=
t=

regions, and
time periods.

1
1

The parameter vector b -t represents the charac
teristic price and vector XJt represents the levels
of characteristics, both of which can differ among
regions and over time. Using for Inw, we can
write the percentage change in wages between
two regions ( and ) during one time period as

(3)

(yst - yNt) =
(

bSt - bNt)XSt + ( X Sl - XNt)bNt, t=

1 ,...,7 !

The first term on the right-hand side accounts for
the change in characteristic prices between
regions and
For our purposes,
denotes
the national average. The second term denotes
the change in levels of worker characteristics
between the two regions.7 It is clear from equa
tion ( 3 ) that wage differences between regions
result either from differences in prices or from
differences in levels. One can use this frame
work to assess which of the two components
accounts for the larger share of the regional
wage difference.8
The issue of wage convergence or divergence
requires examining how these regional wage dif
ferences change over time. For wages to con
verge toward the national average, the distance
between the regional and national wage level
must narrow over time. Consequently, if the
region starts out with a wage above the national
average, convergence requires that the difference,

y Nt-

0 's, Nt) - Ofc- i "
i>> must be greater
than zero. The same relationship must be nega
tive if the region starts out with a wage below the
national average. The condition for divergence,

■7

A residual term,

(bs

b N )(Xs - X N ),

is omitted for simplicity. Fur

thermore, there is an index problem associated with this technique. Changing
the base to one region or the other will change the values of the components.
Some studies, such as Sahling and Smith (1983), have attempted to avoid the
problem by using averages of the two region’s characteristic levels or prices.
W e instead choose to follow the technique of Farber and Newm an (1987),
which chooses one region as the base. In this w ay, we are better able to
compare our results with theirs.

■

Dickie and Gerking also stress a fourth and important point: if data do

■

A s Farber and Newman point out, the accounting framework relies on

not adequately distinguish between workers with particular characteristics,

the unbiasedness and consistency properties of O L S estimators, and has

then estimated returns will be averages and tests of the interregional wage

avoided the pre-test biases of imposing implicit restrictions on coefficients

equality hypothesis would be biased toward rejection.

found to be statistically insignificant (p. 219).

obviously, would require the opposite signs.9
The relative change over time in regional wage
differentials can be divided into several compo
nents using a variation of the same accounting
scheme adopted in equation ( 3 ) for the static
case. Following Farber and Newman, one can
specify equation ( 3 ) for two different time peri
ods (in this case, periods 1 and 2 ) and then sub
tract one from the other. This technique yields
the following accounting framework:
(4)

( V.v2 - J ^ 2) - 0 ’5I " JWl) =
KX,-2 - * v 2)

XN j)] bN2
+
~ j)( by ~ &s ^
+
- XN1)(bN2 - bN j)
+ Xsl [(bs 2- bN2)
(bsl - (*S i 2

The four components can be interpreted in
the following way. The first term, referred to as
the main effect, reflects how much of the change
in the wage differential is due to changes in the
differences of wage-determining characteristics
between the two regions, evaluated at the
national average characteristic prices. Notice that
this term may be zero even when characteristic
levels differ between region and the national
average in each time period, as long as these dif
ferences are not the same in each time period.
The second term is the price-interaction term
and reflects the effects of absolute changes in
characteristics of workers in region over time.
The third term is the price-interaction effect,
which allows for characteristic prices to change
over time. The last component, the region-time
interaction effect, represents the possibility that
the characteristic prices in the two regions may
change over time at different rates.
These four components of regional wage
changes provide the basis for identifying the rel
ative contributions of intertemporal changes in
characteristic prices and levels to the regional

wage differentials. To construct these wagechange components, separate hedonic wage
equations are estimated for each region in each
time period. For nine census regions and three
time periods, this requires 27 separate regres
sions. The coefficient estimates and the means of
the levels of characteristics are then combined
according to equation (4 ) . 10
Comparing changes in regional wages relative
to the national average partially adjusts for the
general nominal wage increases observed over
the 15-year period between 1973 and 1987. How
ever, any deviations of regional price trends from
the national average will be imbedded in the
various components, particularly in those related
to differences in characteristic prices. Instead of
relying on the national trends to capture regional
price differentials, it would be ideal to adjust
regional wages for differences in the cost of liv
ing. Unfortunately, regional indexes are available
only for metropolitan areas, and even then, there
are no current indexes that can be used to com
pare cost-of-living differences across metropoli
tan areas.

III. Empirical Results
Data

The data used to estimate the wage differentials
are obtained for various years from the Current
Population Surveys (CPS) compiled by the U.S.
Department of Labor, Bureau of Labor Statistics.
The CPS surveys individual workers periodically
regarding hours worked, earnings, worker char
acteristics, employment status, and so forth. Each
time period considered in the analysis consists
of a pooled sample of three years. 11 The first

■ 10

One drawback of this approach, as discussed by Dickie and Gerking

(1988), is the lack of a confidence interval estimate around these various
components, leaving it unclear how the results generalize to the population.

■

Various features of the C P S files have changed over the years

covered in this analysis, which introduces several problems when using these
data to derive a consistent time series of regional wages. First, the method of
collecting wage and worker characteristics has changed. For the years 197378, questions regarding worker wages and characteristics were asked only in
the month of M ay. This poses two problems. First, the sample contains only

■ 9

W e have chosen to compare each region with the national average,

those individuals who were in the second rotation, which, in addition to being

which we feel provides the most clarity when so many regions are being

less representative, reduces the number of respondents. Second, annual wage

compared. This approach m ay introduce two sources of bias, however. The

estimates will reflect wages obtained for only one month of the year.

first is because the national sample is not a region separate from the others,

Starting in 1979, the wage questions were asked of one-quarter of the indi

but is made up of individuals in each region. The second source arises from

viduals in each of the 12 monthly surveys conducted each year. Because of

the finding that the characteristic prices of each region are significantly differ

the difference in the w a y in which information is gathered, the total number of

ent. Consequently, the characteristic prices estimated for the nation m ay not

workers with sufficiently complete records for analysis is much smaller before

represent prices for the national market, but rather the average of prices from

1979 than afterward. Pooling the individual years will ameliorate these prob

each distinctly different regional market.

lems to some extent.

Regression Estimates for the National
Sample of Workers

1 9 7 3 -7 5

Variables

Mean

Full-time (= 1 )
Race (nonwhite = 1 )
Sex (female = 1 )
Experience
Experience squared
Schooling
Schooling squared
(exp) x (sex)
Non-SMSA (= 1)

1 9 7 9 -8 1

Coefficient

.80

Mean

.42
18.72
570.60
1.82
4.03
7.77
.30

Coefficient

.141

.81

.1 0 1

-.040
-.192
.026
-.0004
.130
.007
-.004
-.159

.1 0

1 9 8 5 -8 7

.1 2

-.0 3 2

.46
17.76
521.57
1.98
4.57
7.90
.42

-.1 6 8
.0 2 6

-.0004
.131
.0 0 2

-.004
-.083

Mean

Coefficient

.80
.13
.48
17.59
488.80
2.09
5.00
8.32
.27

.187
-.048
-.133
.029
-.0004
.1 6 2
-.0 0 1

-.005
-.133

occupation
dummy variables)

(1 3

industry
dummy variables)

( 1 2

Dependent variable:
log (earnings/hours)
R2
Number of observations

1.29

1.74

.91

.95

116,298

554,864

2 .0 2

.96
491,510

NOTE: All coefficients are statistically significant at the 99 percent level.
SOURCE: Estimates are derived from the Current Population Surveys. See text for details.

period combines the responses from the May
survey for the years 1973, 1974, and 1975. The
second period pools responses from one-quarter
of the individuals in each of the 1 2 monthly sur
veys for the years 1979, 1980, and 1981. The
third period is derived similarly, except that it
includes the years 1985, 1986, and 1987.
These time periods were chosen because they
correspond to the switch from regional wage
convergence to regional wage divergence as
documented by Browne (1989). In addition,
years were pooled in order that each region con
tained enough workers to ensure reliable esti
mates. The size of the samples ranges from 7,203
workers for the New England census region in
1973-75 to 84,641 workers for the East North
Central region in 1979-81.
Following the human-capital specification of
Hanoch (1967) and Mincer (1974), individual
wages (expressed in logarithms) are specified as
a function of various worker attributes. We include
education level (entered as a quadratic), poten
tial experience (age, minus years of education,
minus six, also entered as a quadratic), and the
interaction between experience and female. We
also include binary dummy variables indicating
whether or not the worker is a full-time em
ployee, female, and nonwhite. Dummy variables

are also used to denote a worker’s occupation,
the industry in which he or she is employed, and
whether the worker resides in an SMSA. Hourly
earnings were computed by dividing average
weekly earnings by average weekly hours. 12
Including the industry-dummy variables is
somewhat inconsistent with the notion that the
human-capital specification captures supply-side
aspects of the labor market. These variables are
included, as they have been in other studies, to
test the popular notion that industrial restructur
ing is a primary source of regional wage changes.
The changing composition of union membership
has also been offered as an explanation for
regional wage changes. 13 Unfortunately, the CPS
did not ask about union affiliation in the 1979-81
surveys.

■

1 2 A n interesting extension of the analysis would be to estimate sepa

rate regressions for males and females and for whites and nonwhites. Sahling
and Smith (1983) found differences in wages between males and females in
the South compared with other regions. Changing norms for women and minor
ities in the workplace m ay lead to regional differences in the characteristic
prices of these groups.

■

However, Farber and Newm an (1987) conclude that while unionization

is an important contributor to the change in the wage differential attributable
to changes in regional differences in worker characteristics, it is not an impor
tant variable in explaining changes in wage ratios between regions (p. 222).

Regional Nominal Wage
Differentials Relative
to the National Average

Percent

everything else being the same. The full-time
wage premium has risen from 1 0 percent in the
first period to 19 percent in the most recent
period. This fairly sizable increase has occurred
even though the percentage of full-time workers
in the sample has remained constant.
The nonwhite wage gap appears to have nar
rowed slightly from 4 percent in 1973-75 to 3-2
percent in 1979-81. However, since that time, the
gap has widened, increasing to 4.8 percent in
1985-87. The female wage gap, on the other
hand, has steadily narrowed, from 19.2 percent
in the first period to 1 3 3 percent in the most
recent period. The wage premium placed on
additional hours of work experience has risen
steadily for both men and women over the three
time periods. Taking into account the interaction
terms and evaluating at the mean level of expe
rience, the elasticity of wages with respect to
experience for men, for example, rose from 2 0 . 6
percent in 1973-75 to 26.4 percent in 1985-87.
The net effect of schooling on wages fell
between the first two periods and then rose in
the third period.

Patterns of Regional Wage
Differentials

SOURCE: Author’s calculations from Current Population Surveys.

Regression Estimates

Separate estimates were obtained for each of the
nine census regions for each time period using
ordinary least squares. F-tests were performed to
test the null hypothesis that the coefficients for
each region are equal to the coefficients for the
national sample. The null hypothesis was
rejected at the 1 percent confidence level for
each time period. Even though coefficients differ
among regions, estimates from the national
sample are displayed and discussed in order to
provide an overall perspective of the results. As
shown in table 1 , all worker-characteristic varia
bles are statistically significant at the 1 percent
level and enter with the expected signs. Full-time
workers (who work 35 hours or more a week)
receive higher wages than part-time workers,

Nominal earnings estimates, using the CPS sam
ple of workers within nine census regions, reveal
a pattern of regional wage convergence followed
by divergence, similar to that found by Browne.
Figure 1 shows the pattern of regional nominal
wage changes relative to the national average.
Nominal wages in all regions, except the New
England and the Pacific regions, converged
toward the national average between 1973-75
and 1979-81.
The standard deviation of the relative wage
differentials fell from 0.086 to 0 . 0 6 8 during this
period. Wages of workers in the Pacific region
increased 2 . 6 percentage points faster than the
national average between the first two periods,
which raised the region’s wage premium to 1 3 - 3
percent. New England, on the other hand, started
out below the national average in 1973-75 and
continued to lose even more ground by 1979-81,
falling from 2 . 1 percent to 5.9 percent below the
national average over this time span.
Between 1979-81 and 1985-87, wages in most
of the regions diverged from the national aver
age. The two exceptions were the New England
and East North Central regions. Wages in the
New England region jumped dramatically during
this period, outpacing the national average by 9.1
percentage points. This spurt in wage growth

closed New England’s wage gap from the pre
vious period and placed its wages 3 . 1 percent
above the national average in 1985-87. Wages in
the East North Central region also came closer to
the national average, but this was achieved by
growing slower than the nation by 3 . 0 percent
age points.
O f the seven regions in which wages diverged
from the national average between 1979-81 and
1985-87, five were below the national average.
The two regions that lost the most ground were
West North Central and East South Central.
Wages in the West North Central region fell from
7.0 percent below the national average in 197981 to 10.9 percent below in 1985-87. Wages in
the East South Central region, which in the first
two periods were the lowest in the country, fell
even further, to 15.2 percent below the national
average.
Wages in the Pacific and Middle Atlantic
regions, on the other hand, increased relative to
the national average. Overall, six of the nine cen
sus regions followed the pattern of wage con
vergence before 1979-81 and wage divergence
after that period. The relative wage gains and
losses across the nine regions combined to in
crease the standard deviation from 0 . 0 6 8 in 197981 to 0.086 in 1985-87, which is roughly the same
level of dispersion found for the first period.

instance, as shown in table 2 , if workers were
identical in all regions (or, at least, if the compo
sition of worker attributes was the same) and
only characteristic prices varied, four of the nine
regions would exhibit a convergence/divergence
wage pattern. These four cases are consistent
with the actual wage patterns of convergence
and divergence. The two regions in which price
differentials did not yield the desired pattern,
even though the actual wage pattern did, were
the West South Central and South Atlantic
regions. In both cases, differences in the charac
teristic levels were consistent with the actual
wage patterns and were large enough to bring
these patterns into line.
Which of the worker characteristics appears to
contribute most to these patterns? Three catego
ries of variables were considered: human capital
variables, industry variables, and occupation vari
ables. The most striking result (which is not
shown in the tables) is that regional differences
in the wage premiums paid in various industries
virtually never emerged as the dominant cate
gory. Rather, human capital dominated in most
cases, being the largest contributor in 1 6 of the
28 cases for the price component, and in 17 of
the 28 cases for the level component.

Components
of Intertemporal
Components of Regional
Wage Differentials

Which of the two components accounts for the
switch from convergence to divergence? One
way to address this question is to consider the
number of cases in which one component or the
other dominated the regional wage differential
for all three periods. This could be interpreted as
indicating that the same “structure” that led to
wage convergence also led to wage divergence.
Looking only at the cross-sectional results, as
shown in table 2, provides a mixed answer. For
the six regions that followed the convergence/
divergence pattern, differences in characteristic
prices dominated the regional/national wage dif
ferential for three regions for all three periods,
differences in characteristic levels dominated
one region, and the effect was split for the
remaining two regions. Tallying up the total
number of cases in which differences in charac
teristic prices dominated the regional wage dif
ferentials results in about the same percentage of
cases— about 6 0 percent.
Another way to evaluate the importance of each
source is to determine the wage patterns gener
ated if only one of the components varied. For

Regional Wage Changes

The previous examination of the sources of
regional wage differentials looked at three sepa
rate cross sections from different time periods.
The next step is to examine how these regional
wage differentials changed over time. As men
tioned earlier, equation (4) provides a frame
work to account for the various components of
this wage change.
Table 3 displays the components of nominal
wage changes for each region between the three
time periods. For example, the 1.6 percent
reduction between the first two periods in the
wages of the East North Central region relative to
the national average can be attributed to primar
ily two effects. The first is the main effect
(column 1 ), which is the change over time in
characteristic levels for the region relative to the
nation. If all other effects were zero, then these
changes in worker characteristics would cause
the regional wages to diverge from the national
average rather than to converge, as they actually
do. The positive sign for this component indi
cates that the difference in the characteristic lev
els that favored this region over the nation was
greater in the second period than in the first.

Components of Regional
Wage Differentials Relative to
the National Average

(1 )

(2 )

( b R- b N ) X N

( X R- X N ) b N

Census
R egion

Year

(3 )
Actual
W age Differe

New England

1973-75
1979-81
1985-87

-.0064
-.0469*
.0 1 9 8 *

-.0096*
-.0123
.0138

-.0208
-.0592
.0305

Middle Atlantic

1973-75
1979-81
1985-87

.0547*
-.0005

.0429
-.0363*
.0504*

.0904
.0327
.0758

1973-75
1979-81
1985-87

.0453
.0117
-.0 0 1 0 *

.0064*

.0490
.0337
.0025

1973-75
1979-81
1985-87

-.0289
-.0137
-.0447

-.0461*
-.0483*
-.0605*

1973-75
1979-81
1985-87

-.0332*
-.0459*
-.0396*

-.0303
-.0027
-.0076

1973-75
1979-81
1985-87

-.0 8 6 1 *
-.0714*
-.1047*

-.0695
-.0264
-.0544

-.1589

1973-75
1979-81
1985-87

-.0915*
-.0496*
-.0471*

-.0176
-.0 0 2 0

-.1078
-.0502
-.0524

1973-75
1979-81
1985-87

-.0

-.0 0 2 1

-.0270

-.0 2 2 0 *
-.0446*

-.0436

East North Central

West North Central

South Atlantic

East South Central

West South Central

Mountain

Pacific

1973-75
1979-81
1985-87

.0 2 2 1

3 1 6

.0 1 0 1

-.0158
.0782*
.1280*
.1253*

.0133*
.0007

-.0 0 0 6

.0495
.0256
.0333

-.0 8 6 1

-.0699
-.1089
-.0 6 2 2

-.0448
-.0463

-.1 0 1 1

-.1524

.0 1 0 6

.1063
.1326
.1427

NOTE: Column 1 is the effect o f differences in characteristic price between the region and the nation; colum n 2 is the effect o f differences in
characteristic levels between the region and the nation. Columns 1 and 2 d o not add up to colum n 3 because o f a residual com ponent not
shown in the table. Asterisks denote the dominant com ponent for each time period and region.
SOURCE: Author’s calculations.

Offsetting the effect of changes in characteris
tic levels are the changes over the time periods
in characteristic prices (column 4). If everything
else remained the same, these changes in inter
temporal prices would result in East North Cen
tral wages converging to the national average by
2 . 8 percent.
In determining which components contribute
most to wage changes, two criteria were used.
First, the signs of the components must be con
sistent with wage convergence between the first
and second periods and with wage divergence
between the second and third periods. Second,

the components should account for a large share
of the total wage change.
The asterisks in table 3 indicate the pairs of
components that are consistent with the conver
gence/divergence wage pattern. For the two com
ponents that are based on the intertemporal
change in characteristic prices (columns 3 and
4), 1 2 of the possible 18 pairs of estimates are
consistent with the convergence/divergence
wage pattern. The components related to inter
temporal changes in characteristic levels (col
umns 1 and 2) contain only five pairs. Further
more, the components related to changes in

Components of Intertemporal Changes
in Regional Wage Differentials
Time

Region

Span

.0 0 2

-.0 0 1

3-2

.0027
.005

.0 1 0
-.0 2 0

-.015
-.0003

.0 1 0

.003

-.030

.013*
-.0 1 2 *

.028*
-.023*

.035*
-.033*

.0 1 6 ’
-.0 3 8 '

.009

.0 1 0

.017'
-.0 0 1 ’

.0 2 0 *
-.0 1 1 *

.0 2 0 *
-.0 1 6 *

.0 6 8 *
-.0 3 6 *

.057'
-.050'

.003

.0 0 6 *

.043

.063

.0 0 2

-.0003*

.0 0 1

.057'
-.0 0 1 ’

.037*
-.015*

-.003

.032

-.0 1 0 *
.038*

-.028

-.0 2 0

3-2

-.003

.0 1 6

2 -1

-.008
-.0 0 1

.014*

.008*
-.0 2 0 *
-.0

1 6

o
o
VO
*

3-2

-.0 0 1

*
*

-.058
.044'
-.0 1 6

2-1

1 1

-.059*
.034*
-.0 1 0

.0
-.0

0 1

-.039
.091

-.0 2 1

3-2

2 -1

.082

-.0 3 6

-.0 2 0

.005
.008

3-2

(6 )

-.014

.023*
-.017*

2 -1

.0 2 0 *
-.004*

.025*

(5)

-.003*
.007*

.007*
-.0 0 1 *

3-2

Pacific

-.005

-.003

.0 6 1

.0 0 6

2 -1

Mountain

-.008*
.017*

.0 0 2 *
-.004*

2 -1

West South Central

-.034

.030

3-2

East South Central

-.003
-.004

.0 0 2

2 -1

South Atlantic

(4)

3-2
2 -1

West North Central

(3)

2 -1

3-2
East North Central

(2 )

Middle Atlantic

(l)

i
b

New England

___________________________________ C om pon ents

i
b
N*J

Census

- .0 1 1

.0 1 6

-.0 2 2

.067’
-.053’
.026
.0 1 1

NOTE: Time spans are denoted as 1 (1973-75), 2 (1979-81), and 3 (1985-87). The notation 2-1 represents the difference between the first two
periods, and 3-2 represents the difference between the latter two periods. The com ponents are (1 ) main effect, (2 ) interaction effects,
(3 ) time-interaction effects, (4 ) regional time-interaction effects, (5 ) the sum o f the four effects, and (6 ) the actual change in the regional
wage differential (relative to the national average) between the two time periods. The asterisks indicate the com ponents that are consistent
with the convergence/divergence wage pattern.
SOURCE: Author’s calculations.

prices (again columns 3 and 4) claim the largest
share, on average, of the total wage changes.
Consequently, it appears (as the trade theory
suggests) that differences in characteristic prices
account for the larger share of nominal regional
wage changes over the three time periods. 14
Therefore, this simple nonparametric test of
counting the number of consistent results sug
gests that intertemporal changes in worker
characteristic prices account for much of the
convergence as well as the divergence of wages.

■

Dickie and Gerking (1988) point out that omitted variables, particularly

the lack of detailed human-capital variables, could bias the accounting method
toward attributing too much importance to characteristic price differences. They
find, using another data set that contained unusually detailed measures of
worker and workplace characteristics, that they could not reject the hypothesis
of equal coefficients across regions. This omission seems less critical for this
study, since we look at the change over time in coefficients of the same set
of variables within the same regions. It would seem that in order for omittedvariable bias to be significant, the relative contributions of each variable would
have to vary substantially over time, which is not supported by the results
from the previous section.

Consequently, basic changes in the way that
worker characteristics were valued by the
regional markets must have occurred around the
turn of the decade. Trade theory suggests various
types of market imperfections as possible candi
dates, including differences in production tech
nologies and factor-market distortions. The backto-back recessions in 1980-82 and the collapse in
oil prices shortly thereafter certainly have taken
their toll on regions such as the West South Cen
tral, while having little effect on others, such as
the Pacific and New England regions. The rela
tive effects of these events among regions can be
partially explained by the slow adjustment of
labor markets and the differential impact of oil
prices between energy-using and energyproducing regions.
Considering the three categories of worker
characteristics defined in the previous section
offers further insight. As before, the industry vari
ables played very little role in accounting for
intertemporal changes in the regional wage dif
ferentials (these results are not shown in the

tables). However, unlike the cross-section analy
sis, occupation variables clearly dominated. For
example, with respect to component four (dif
ferences in prices), occupation variables were
the dominant category in 1 3 of the 18 cases. 15
This result supports some of the speculation
made by various authors about possible reasons
why worker characteristic prices may not be
equal across regions. Farber and Newman
(1987) conjecture that characteristic prices may
not necessarily converge because of occupationspecific demand disturbances. Topel (1986)
shows that disequilibrium in local labor markets
results primarily from stochastic disturbances in
labor demand.

IV. Conclusion

After converging for almost half a century, nom i
nal regional wages have diverged since 1 9 8 0 .
This paper attempts to isolate the source of this
switch in direction either as an intertemporal
change in the market prices for worker attributes
or as an intertemporal change in the levels of
worker attributes. For nine census regions
between the periods 1973-75, 1979-81, and 198587, results using individual workers from the CPS
show that differences in characteristic prices
account for a major share of the change in
regional wages relative to the national average.
Furthermore, virtually all of this intertemporal
change in characteristic prices is found in the
occupation coefficients; industry and worker
characteristic variables account for very little.
Theory suggests that the prices of worker char
acteristics will converge in the presence of free
commodity trade and in the absence of market
imperfections. Various types of market imperfec
tions were suggested as possible sources of the
divergence of regional wages. For example,
incomplete information, a mismatch between
worker skills and job requirements, and institu
tional barriers to mobility can lead to incomplete
adjustments to recent changes in the structural
demand for labor. A recent study estimates that it
takes as much as a decade for local labor
markets to adjust fully to such shocks (Eberts
and Stone [1989]).
Another possibility for nominal wage diver
gence is changes in the regional prices of hous
ing and other nontraded goods that deviate from

■

Farber and Newm an (1987) also find that the worker characteristics

that accounted for much of the cross-sectional accounting of regional wage dif
ferences were different from the worker characteristics that accounted for the
majority of the intertemporal changes in regional wage differentials.

the national average. Because this study did not
adjust for regional cost-of-living differences, it
may be possible that wage differentials simply
compensate workers for higher housing costs.
However, this argument runs counter to the pre
dicted results of free trade among regions, once
equilibrium has been established. If goods are
freely traded, then firms would be hard pressed
to pay higher wages in some regions than in
others, unless employers were compensated by
differences in production technologies and
worker productivity. Therefore, for cost-of-living
differences to explain the results, workers in
areas with higher labor costs coincidentally
would have to be more productive. There are no
compelling reasons why high living costs and
high worker productivity should exist concur
rently in equilibrium.
Two exceptions to this general statement are
possible: First, site-specific attributes could
enhance firms’ productivity. Firms would move
into the more productive region, bidding up the
price of land and the price of labor, everything
else being equal. The second possibility is that
with the slow adjustment to shocks, we are
simply observing these effects in disequilibrium.
The findings that differences over time in
characteristic prices account for a majority of the
changes in regional wage differentials does not
necessarily diminish the importance of migration
in explaining differences in regional growth.
Rather, the analysis suggests that these flows
have not changed the composition of regional
labor forces significantly enough to make them
the dominant factor in explaining changes in
regional wage differentials. The traditional migra
tion patterns of South to North and East to West
are less pronounced now than in the past. For
merly, the primary migration pattern was toward
the West, particularly for college graduates look
ing for job opportunities. More recently, the
South is receiving many younger persons from
the West and North.
If stochastic disturbances have changed the
course of regional wage differentials, then it is
interesting to speculate why these shocks have
had such an impact in a relatively short period of
time, when for so many decades the workings of
efficient markets and equalizing migration flows
seemed to prevail in forcing regional wages to
converge. Several possibilities come to mind:
increased foreign competition, the collapse of oil
prices in the early 1980s, and the severe back-toback recessions of 1980-82.
These recessions hit some regions harder than
others, producing different patterns of change in
regional wage differentials. The West South Cen
tral states of Texas and Louisiana were particularly

hurt as the bottom dropped out of oil prices.
This downturn thwarted the sizable gains that
region had made in previous years in narrowing
its wage gap.
The farming states of the West North Central
region were also severely affected by the reces
sion and the ensuing farm crisis of the early
1980s. After converging toward the national aver
age throughout the 1970s, wages in this region
diverged significantly, falling from 7.0 percent
below the national average at the beginning of
the 1980s to 1 0 . 9 percent below the average
toward the end of the decade. Wages in some
regions continued to grow faster than the
national average in spite of the recession. For
example, the Pacific region, especially California,
was only mildly affected, with its regional wage
differential expanding by a percentage point
between 1979-81 and 1985-87.
Factors other than economic shocks could
also contribute to the wage divergence. One
possibility is state tax policies. The late 1970s
and early 1 9 8 0 s saw the phasing out of substan
tial federal grant programs to states and munici
palities. Many of these programs were designed
to help equalize the fiscal burden across regions.
As these funds dried up, many state and local
governments found it necessary to raise tax rates
to fund the existing programs, while others
decided to curtail the programs. These different
responses could lead to an increase in regional
tax rates, which in turn could affect the location
of firms and ultimately the demand for labor.
Will these factors persist? If history is any
guide, the answer is no. The long-run trend of
regional wage convergence has been interrupted
only once in the last century. That episode lasted
2 0 years, embracing a postwar period and a
much deeper and protracted recession than the
one that greeted this decade. Consequently, it
appears that shocks of this kind will eventually
dissipate as the regions’ economies regain a
more equal footing.
However, many states and localities are not
content to wait the decade or so that it takes for
these forces to play themselves out. Many areas
have pursued vigorous economic development
efforts to help quicken the pace of adjustment.
As long as these efforts attempt to remove
market inefficiencies and strengthen the region’s
comparative advantage, they are socially desira
ble. One would expect that as regions continue
to develop and mature— and barring further
shocks of recent magnitude— the long-run trend
of regional wage convergence will return.

Beeson, Patricia and Eberts, Randall W., “Identi
fying Productivity and Amenity Effects in
Interurban Wage Differentials,”
August 1989
(forthcoming).

Economics and Statistics,

Review of

Bellante, Don, “The North-South Differential
and the Migration of Heterogeneous Labor,”
March 1979,
166-175.

American Economic Review,

69,

Browne, Lynn E., “Shifting Regional Fortunes:
The Wheel Turns,”
Federal Reserve Bank of Boston,
May/June 1989, 27-40.

Review,

New England Economic

Dickie, Mark and Gerking, Shelby, “Interregional
Wage Differentials in the United States: A Sur
vey,” in Alan Schlottmann, et al., eds.,
Boston:
Kluwer Academic Publishers, 1988.

tion and Labor Market Adjustment,

Migra

Easterlin, Richard A., “Long Term Regional
Income Changes: Some Suggested Factors,” in
Gerald AP. Carrothers, ed.,

Papers and Pro
ceedings of the Regional Science Association,
1958, 4, 313-25.

Eberts, Randall W. and Stone, Joe A., “Wage and
Employment Response to Shocks in Local
Labor Markets,” presented at the Western
Economic Association Meetings, Lake Tahoe,
Nev., July 1989.
Farber, Stephen C. and Newman, Robert J.,

“Accounting for South/Non-South Real Wage
Differentials and for Changes in Those Differ
entials Over Time,”
May 1987,
215-23.

Statistics,

Review of Economics and
69,

Gerking, Shelby and Weirick, William, “Com
pensating Differences and Interregional Wage
Differentials,”
August 1983,
483-87.

tistics,

Review of Economics and Sta
65,

Hanoch, Giora, “An Economic Analysis of Earn
ings and Schooling,”
Summer 1967,
310-29.

Resources,

Journal of Human
2,

Markusen, James R., “Factor Movements and
Commodity Trade as Complements,”
Mav 1983,
341-56.

of International Economics,

Journal
14,

Schooling, Experience, and Earn

Mincer, Jacob,
New York: National Bureau of Economic
Research, distributed by Columbia University
Press, 1974.

ings,

Regional Economics: A Study
in the Economic Structure, Stability, and
Growth of Regions, New York: McGraw-Hill,

Nourse, Hugh O.,

References

1968.
Oaxaca, Ronald, “Male-Female Wage Differen
tials in Urban Labor Markets,”
October 1973,
693-709.

Economic Review,

International
14,

Roback, Jennifer, “Wages, Rents and Quality of
Life,”
December
1982
1257-78.

Journal of Political Economy,
,90,

Sahling, Leonard G. and Smith, Sharon P.,
“Regional Wage Differentials: Has the South
Risen Again?”
February 1983,
131-35.

Review of Economics and Statis
65,
Topel, Robert H., “Local Labor Markets,” Journal
of Political Economy, 1986,94, SI 11-43.
tics,

W hy We D o n 't K n ow
W hether M oney
Causes O utp u t
by Charles T. Carlstrom
and Edward N. Gamber

Charles T . Carlstrom is an economist
at the Federal Reserve Bank of
Cleveland. Edward N. Gamber is an
assistant professor of economics at
the University of M issouri-St. Louis
and is a visiting economist at the
Federal Reserve Bank of Cleveland.
The authors wish to thank John
Carlson, Randall Eberts, William
Gavin, William Osterberg, and Alan
Stockman for helpful comments. In
addition, we wish to thank Susan
Black for valuable research
assistance.

Introduction

Macroeconomics has undergone a revolution in
the past 2 0 years, in which significant challenges
have been made to supposedly well-established
theories and facts. Among the most important of
these prevailing theories is the positive correla
tion between money and real output.
Traditionally, most economists and policy
makers have interpreted this correlation to imply
that Federal Reserve open market operations
could affect real output. This interpretation has
persisted in spite of weak and sometimes con
tradictory empirical evidence. Unfortunately, we
cannot attempt to examine all of the existing
evidence on the direction of causality between
money and output. Instead, this paper examines
whether Granger-causality is a valid test for cau
sality and what can be inferred from existing tests
of Granger-causality. The answers to these ques
tions are of paramount importance, since most
policymakers assume that money causes output
in a consistent and reliable way. This correlation
is illustrated in figures 1 , 2 , and 3 using three
measures of money: base, M l, and M2. 1
■

The usual method of distinguishing among
competing economic theories involves econo
metric testing. However, as is well known (see,
for example, Black [1982]), econometric models
indicate correlation, but not causality. Even the
econometric technique of Granger (1969) does
not necessarily identify causality as the term is
commonly understood. We will show in the fol
lowing section that the concept of Grangercausality is not robust to changes in the underly
ing model of the economy .2 In other words, it is
impossible to interpret Granger-causality inde
pendent of theory. Given this, sections II
through IV examine models that try to explain
the correlation between money and output.
Traditionally, this correlation was explained by
assuming some type of nominal rigidity (either
prices or wages). Tobin (1970), however,
showed that the correlation between money and
output could be a result of the Federal Reserve’s
operating procedure and that it did not necessar
ily imply that changes in money caused output
changes. Section III shows that if the Federal
Reserve accommodates increases in output with
a corresponding increase in the money supply,

1 The series is detrended using a Hodrick and Prescott (1980) filter.

Figure 4 illustrates this method as it is applied to real output (G N P ).

■ 2

See also Cooley and LeRoy (1985).

F I

Real G N P and Monetary Base

Percent deviations
2.0

1.5 -

1.0
0.5 —
•.
•
0.0
V. •*'•. L •
V a
%
-0.5
-

1.0

\
\ •/Monetary
v m
*

\V A uul
a

i’

%• # I It\

•/
1
J •M

* %mV

•

N %*
\J +

H
*VJ
•
•
•

: Real
: GNP

•••

2.0

-2.5

# ••

-1.5
-

•••
•

*•"

base

;.
.a frt
1* AII*
; / 1 ** /• v
• r \ •*!/>/•
•/ \l %IVX

' *a -t«
a
Ayv .'A'.
fSr V. 7 V

”
_

%
*•

•
a'a
••

then one would expect to observe a positive
correlation between output and money even
though money is not causing output.
Real business cycle theorists have recently
argued that the correlation between money and
output could be due to reverse causality; that is,
output can cause money independent of the
Federal Reserve’s reaction function. Section IV
examines a model by King and Plosser (1984)
showing that M l and output are correlated
because increases in real output cause increases
in the demand for financial intermediation. This
increased demand leads to the expansion of
broader monetary measures, such as M l and M2,
even though changes in money have no influ
ence on real output.
Section V reviews the empirical evidence
uncovered in these theories to help ascertain the
direction of causality in the money-output corre
lation. Section VI concludes with a discussion of
policy implications.

—l i i i Li i—l i L_i i i i Li i i i Lj i i i 1
L,i .i i i L i

1963

1968

1973

1978

1983

1988

NOTE: Sample period is from 1959: IQ to 1988: IVQ.
SOURCES: Data Resources, Inc., and Board of Governors of the Federal
Reserve System.

I. Granger-Causality

Causality is a very elusive concept. In practice,
most people define x causing to mean that a
change in x leads to a change in
As an anal
ogy, we would implicitly assume that if we could
cause a low-pressure system to appear over a city
(all else remaining constant), then there would
be a high probability that rain would fall. This
causality usually means that if low-pressure sys
tems cause rain, then low-pressure systems must
precede rain.
As can be seen in figure 3, M2 appears to lead
GNP. Does this chronology imply that M2 causes
GNP? The Granger definition of causality
requires two assumptions. As stated by Granger
and Newbold (1986, p. 220):
a) The future cannot cause the past. Causality
can only occur with the past causing the present
or future.
b) A cause contains unique information about
an effect that is not available elsewhere.
According to the first assumption, then, if M2
always leads changes in GNP, we can logically
infer that GNP does not cause M2. Does this
mean that we can conclude the alternative, that
M2 causes GNP? Consider the following example.
Suppose that a group of individuals always
listens to weather forecasts and that these fore
casts are always accurate. Further, suppose that
these people decide to carry umbrellas on days
that rain is forecasted. Clearly, carrying an
umbrella and rain will be correlated, and carry
ing an umbrella will precede a rainstorm.

F I
Real G N P and M l

Percent deviations

F I

Real G N P and M2

Percent deviations
2.0
1.5 -

1.0
0.5

0.0
-0.5
-

,
* •
•
•••

1.0 — \r*

M*
V*
•• I j

I
r

mJ\

v
r

ri*

/•

U'l«
M*

-1.5
“ M2
-

2.0

Real GNP
#I
A' /#
IV t*
il
1 •
1 A ' M
A •:*
I •*, l . ; .
•
1 ,
«
®#
.*
• / a
\
•
•. IV ••
III
•
IIW'* #
•
•
•
•
•
•
t
•
••
•*

I
J

L i i i i Li
-2.5 i i i i Lj i i i Li i i i 1 » ■■* 1 « « ■«
1963
1 9 6 8
1973
1978
1983
1988
NOTE: Sample period is from 1959:IQ to 1988:IVQ.
SOURCES: Data Resources, Inc., and Board of Governors of the Federal
Reserve System.

Logged Real G N P and G N P Trend

According to the first assumption of Grangercausality, rain cannot cause umbrella-carrying.
Yet, clearly, meteorologists would reject the con
clusion that umbrellas cause rain.
The problem with our umbrella and rain
example is that assumption a) is violated. This
assumption is also frequently violated in many
econometric tests. A third variable that uniquely
causes people to carry umbrellas is omitted.
Strictly speaking, rain does not cause umbrellas,
but the
that rain may occur causes
people to carry umbrellas. Expectations are not
formed in a vacuum, however; low-pressure sys
tems in this example could be shown to cause
both umbrella-carrying and rain. Neglecting this
third variable would cause one to conclude that
carrying an umbrella Granger-causes rain.
Because of the importance of expectations in
economics, a variable,
that precedes another
variable,
will frequently not cause
Variable
x may depend on the expected value of
caus
ing x and to be correlated. Since expectations
depend on numerous variables that are, in prin
ciple, observable by the econometrician, one
could conceivably conduct a Granger-causality
test by including all relevant variables. The econ
ometrician, however, would need to have a welldefined model of how expectations are formed.
It is therefore extremely important that Grangercausality tests be interpreted in light of the theory
that one is trying to test.
Consider the formal definition of Grangercausality. Let H , be all the information available
in the universe at time
Let and
be two
random variables within this universe. Granger
says that x causes (does not cause)
if

expectation

Log

yt
y

*
k

(=) ^ O w l n r- **)

for > 1 , where F(.|.) is the conditional prob
ability density function of
given f l o r l) ,
and
is defined to be the universe
less
Suppose that these conditional distribution
functions are equal. If jc and are correlated, it
follows that there must exist a third variable in
O that causes both x and
For example, let
denote the occurrence of rain and let de
note the occurrence of umbrella-carrying. Leav
ing umbrella-carrying out of the information set
does not affect the conditional distribution of
rain or, in other words, weathermen can accu
rately predict rain without seeing whether peo
ple are carrying umbrellas. Because the entire
universe, including low-pressure systems, is
assumed to be in the information set, this exam
ple correctly predicts that umbrella-carrying does
not Granger-cause rain.

x t, Clt - x t
xt.

y t +k

Sims (1972) showed that Granger-causality is
identical to the concept of exogeneity. In other
words, jc Granger-causes if x is exogenous to
and
is not exogenous to x. A variable x is
exogenous to if the occurrence of x is inde
pendent of the occurrence of
Similarly, a var
iable is not exogenous to x if the occurrence
of is dependent on x occurring. Thus, the
occurrence of rain is exogenous to whether
people carry umbrellas: rain will fall regardless
of whether people carry umbrellas. The converse
is not true, however; if it starts to rain, people
will tend to carry umbrellas.
At first glance, Granger-causality or exogeneity
seems to be a reasonable definition of causality.
However, it ignores the case of bivariate causal
ity, where two variables cause each other. For
example, rain causes puddles, and the evapora
tion of puddles causes rain to fall at a later date.
To make Granger-causality operational, the uni
verse of information must be restricted and the
moments of the conditional distribution func
tions must be tested for equality. The universe of
information is restricted by theory. In practice,
the distribution functions are said to be equal if
their first moments (the means) are equal. Test
ing for Granger-causality usually involves the fol
is said to Granger-cause
lowing: A variable
(not Granger-cause) with respect to the
information set if

E (yt+k l7/) ^

(=)

E (yt+kUt - x t ) f o r k >

Because we do not consider all moments of
the distribution, and we do not use all of the
information set, Granger-causality as practiced is
neither a necessary nor a sufficient condition to
determine the direction of causation between a*
and
Consider the case where all the relevant
information in the universe is included in a
Granger-causality test, but only the means are
tested to see if they are equal. If the means were
found to be unequal, then one could logically
infer that x must cause
If the means were
found to be equal, however, then one could not
infer that a; did not cause
Now consider the second assumption in the
case where all the moments can be tested, but
the universe of information is restricted in an ad
hoc manner and an important determinant of
is accidentally omitted. Equality between the
conditional distribution functions necessarily
implies that x does not cause
However, if the
conditional distributions are not equal, then we
cannot infer that jc causes
This is the case in
our example: umbrellas help to predict rain and

thus Granger-cause rain if low-pressure systems
are excluded from the information set.
Since any operational test of causality involves
restricting both the moments of the distribution
functions to be tested and the information set in
the universe relevant to the problem, employing
a Granger-causality test exposes one to the risk
of incorrectly rejecting causality when it is pres
ent and incorrectly rejecting the assumption of
no causality when causality is not present. The
econometrician can seek the direction of causal
ity using a Granger-causality test only by using
theory to determine which variables are helpful
in predicting
However, even after choosing
variables based on some theory, a specification
test should be conducted to help ensure that
important variables have not been omitted.
It should be clear from this discussion that
Granger-causality is neither a necessary nor a suf
ficient test for the existence of true causality.
First, if bidirectional causality exists, then
Granger-causality cannot indicate the presence of
causality. Second, even when bidirectional cau
sality is not present, the Granger-causality test
may fail to identify whether causality is present if
the information set excludes relevant variables or
if all moments of the conditional distributions
are not tested for equality. In addition, Grangercausality is not a useful test for showing the
presence of contemporaneous causality.
Sections II and III present representative theo
ries that have been developed to explain the
money-output correlation. Section IV then inter
prets the econometric evidence that has been
uncovered in light of these theories and the
problems discussed above.

y t+k .

II. Money Causes Output

Most economists currently favor the interpreta
tion that money causes output. They believe that
some nominal rigidities, or price/wage sluggish
ness, allow changes in nominal variables, like
money, to have real effects. These rigidities can
be motivated by nominal wage contracts
(Fischer [1977], Gray [1976]), or by incomplete
information (Lucas [1972, 1977]).
For expositional ease, we consider the nom i
nal wage contracting model as exemplified by
Fischer. In his model, agents in the economy
have rational (model-consistent) expectations,
but wages are “sticky” because of the existence
of long-term nominal wage contracts. Further,
Fischer assumes that employment is demanddetermined; that is, employment is always
chosen so that the real wage is equal to the mar
ginal productivity of labor. Thus, changes in the

money supply that were unexpected at the time
the contract was signed will have real effects.
Unanticipated increases in the money supply
will cause prices to be higher than expected and
will cause the real wage to be lower than
expected. The decline in the real wage lowers
the marginal cost for firms to hire additional
workers, leading to an expansion of employment
and thus output.
Consider a scaled-down version of the model
analyzed by Hoehn (1988). In this example, con
tracts will not be overlapping, and the only
source of uncertainty will be from the moneysupply process. Assume that the aggregate pro
duction function is Cobb-Douglas, that is,
=
where
and
are real output and the
labor supply, respectively. Because wages are
assumed to be demand-determined, we set the
real wage equal to the marginal productivity of
capital. Taking logarithms gives

Nty,

(1 )

wt - p t = In (
wt p t

) -

( 1

y )n t ,

where
,
, and
are the natural logarithms
of wages, prices, and employment. Labor supply
is assumed to be of the following form:
(2 )

n*t = y +

wt ~ P / ) for /J0, /? j >

8 0

Setting labor supply equal to labor demand,
one can solve for the real wage rate that clears
the market. From this equation, it is assumed
that wages are chosen so that the labor market
clears on average.3 This gives the following
equation for nominal wages:
(3)

u'*, = Et _ xp, + [In (

) - (1 - 7)/3 0 ] / ,

where / = [ 1 + 0 , ( 1 - 7 )] To close the model, we must posit a form for
money demand and money supply. Money de
mand is taken to be the simple quantity equation,
that is,
In logarithmic form, it is

Md - KPtYt .

(4)

m dt = p, + y, + k.

For our purposes, this year’s log of money
supply is equal to last year’s money supply plus
a random shock. That is,
=
_, + t,
where the shock
is assumed to be an inde
pendently, identically distributed random varia
ble over time. With these assumptions, output
equals

■ 3

mst mt

Actually, this assumption is not quite true. W ages in Hoehn’s model

are chosen not so that

ENd

= /Vs, but so that

Eln (Nd

) =

End

lnNs

ns.

(5)

y, = A

+ 7 «t ,

A = y[(30 B xln

where
+
( 7 )]/For this simple case, in which contracts do not
overlap and there are no shocks other than those
to the money supply, changes in output depend
only on the shock to this period’s money,
If
one were to randomly determine different reali
zations of t , and were then to graph money
supply and output against time (different realiza
tions of ), one would obtain a picture very
similar to that given in figure 1. In this case,
money causes changes in output. However,
because changes in money and output occur
contemporaneously, money does not Grangercause output.
Equation (5) is also the output equation that
results from a simple linearized version of the
Lucas (1972, 1977) model. Here, workers con
fuse nominal and real shocks. Unanticipated
increases in money result in higher nominal
wages, which workers confuse with higher real
wages. They do not know the extent to which
higher wages reflect an increase in the relative
price of their product or an increase in the gen
eral price level. Unanticipated changes in the
money supply will cause increases in output as
workers rationally mistake this nominal shock for
a change in their real wage.
Models of the type discussed above were orig
inally developed in response to the lack of
empirical and theoretical support for traditional
Keynesian and monetarist models. Both the
Lucas and the Fischer models have recently
come under attack. Barro (1977) shows that con
tracting models such as Fischer’s are inconsistent
with maximizing behavior. He argues that there
is no a priori reason why labor should be
demand-determined in these models.
In addition, economists question why firms
have not indexed their wages, because sticky
wages result in alleged output swings at both the
firm and the macro level. Ahmed (1987) also
presents empirical evidence showing that nom i
nal wage contracting is not important for explain
ing output movements in Canadian data. Although
Lucas’ model is consistent with maximizing
behavior, it also lacks empirical support. Mishkin
(1983) and Boschen and Grossman (1982), for
example, find evidence against the equilibrium
monetary explanation of the business cycle.
The following section shows why the Federal
Reserve’s operating procedure may cause money
and output to be correlated.

et .

III. Post Hoc:
Does The Federal Reserve
Cause Christmas?

Figure 5 plots a scatter diagram of quarterly
changes in the monetary base versus quarterly
changes in output. Fourth-quarter points gener
ally lie to the northeast of the first- through thirdquarter points. Therefore, money and output are
both higher on average in the fourth quarter, or
around Christmastime. One could erroneously
conclude that Federal Reserve policy causes hol
iday spending.
Clearly, causality in this case goes the other
way. Output increases in the fourth quarter be
cause of holiday spending, and the Federal
Reserve, attempting to remove the seasonality
from the interest-rate series, accommodates this
higher output by increasing the money supply.
This is an example of a point given by Tobin
(1970) in his seminal article, “Money and
Income: Post Hoc Ergo Propter Hoc?” meaning
“after this therefore because of it.” Tobin’s
argument was that a positive correlation between
money and output may be the result of the Fed
eral Reserve’s operating procedure and not a
reflection of the common belief that money
causes output.

Real G N P and Monetary Base

Monetary base, not seasonally adjusted

Instead of presenting Tobin’s model, we show
how the operating procedure of the Federal
Reserve can cause one to incorrectly conclude
that the Federal Reserve causes, or at least influ
ences, business cycles. Consider the following
variation of the model presented in the previous
section: Let output be Cobb-Douglas, so that the
log of real wages will again be given by equation
(1). Further, assume that the log of the labor
supply is given by the following equation:
(6 )

n st =

(7)
• IQ
O IIQ

(8)

•

§as$>
m °:°

•

" a

•

-1

-2

. . v

(9 )

L
LI____
.
1L _
,1
J ____ iI____ I____
1_____ I____
1 _____L____
I____ I____

-4

- 3

- 2

- 1

)]/ + J P 2 rt .

rt = r + rjt .

Temporary changes in interest rates, t , can
result because of either shifting tastes or tempor
ary changes in government expenditures. Incor
porating this variable into equation (7), we see
that output depends positively on the innovation
in real interest rates today.

[p0 + jSj/n (
r

■ IIIQ

—

n, =

Real interest rates in the economy are
assumed to fluctuate randomly around a con
stant mean :

A IVQ

O+ (31( w t - p t ) + p 2rt

for 0 O , j8 j , /32 > 0.
This equation differs from equation (2) be
cause the labor supply is also assumed to be
influenced by the real interest rate, rt . Equation
( 6 ) assumes that the labor supply depends posi
tively on the real interest rate, because of the
intertemporal substitution effect. That is, when
interest rates are high, workers transfer consump
tion from today until tomorrow to take advantage
of the high real rate. Consumption is reduced,
thus increasing the marginal utility of consump
tion in the current period. This, in turn, increases
the incentive for agents in the economy to work
additional hours in order to consume more today.
Instead of assuming that there are long-term
nominal wage contracts, this model assumes that
wages vary to clear the market continuously so
that money does not influence output. By equat
ing the real wage in equations ( 1 ) and (5), we
solve for the equilibrium amount of labor sup
plied (demanded) in this economy:

3
•

Real GNP, not seasonally adjusted

yt =

y[p 0+ p jn (y ) +

P2r ] j + y] \32 r j r

To close the model, we assume that money
demand is given by equation ( 4 ) and that the
Federal Reserve follows a nominal interest rate
rule:

(10)

mst = b + k(R t - r ), and A >
Rt - rt Etp t

pt.

where
+
+j Nominal interest rates are assumed to be the
sum of the real rate plus expected inflation over
the next period. Using equations (4), ( 8 ), (9),
and ( 1 0 ), the reduced form for the nominal
interest rate is given by the following equation:
(11)

/ ? , = r + »;, [ ( 1 / ( 1 + A ) )

+ 702/ / (l + A)].
Innovations in the real interest rate are
assumed to be temporary. An increase in the real
interest rate causes policymakers to expand the
money supply in order to stabilize nominal
interest rates. Prices are then temporarily high
and deflation is expected over the next period,
which will offset the increase in the real interest
rate. When A approaches infinity, the nominal
interest rate approaches the long-term real inter
est rate,
That is, when A approaches infinity,
the Federal Reserve is following an interest-rate

pegFrom equation (11), the reduced form of the
money-supply equation is given by
(12)

The above model illustrates how an interestrate target can produce a positive correlation
between money and output. The example was
extremely simple and predicted that money and
output would move contemporaneously One
could likewise construct examples in which
money leads changes in output and would thus
appear to cause changes in output.
For example, consider an economy in which
money has no real effects, but in which agents
are able to predict future output. The prospect of
higher future output will cause agents to borrow
(or save less) in an attempt to smooth their con
sumption stream over time. This increased bor
rowing will boost interest rates. If the effect on
output today from an increase in interest rates is
negligible, then changes in money will occur be
fore changes in output when the Federal Reserve
pursues an interest-rate peg. In this economy,
money leads, but does not cause, output.
The next section discusses another mecha
nism in which output can cause changes in
money. Unlike the model presented in this sec
tion, the mechanism will not come from the
Federal Reserve’s operating procedure, but will
result from the public’s willingness to hold cur
rency versus either demand or time deposits.

m st = b + A [(l/ ( 1 + A))
+ yfi2J / ( l + A)]t 7,.

If one were to randomly determine different
realizations of 7 7 ,, and were then to graph
money supply and output against time (different
realizations of 77 f ), one would again obtain a
picture very similar to that given in figure 1. A
temporary increase in interest rates causes peo
ple to supply more labor today. This occurs
since high real interest rates imply that, on the
margin, individuals greatly value consumption
today, causing them to work longer hours today.
The increase in interest rates also causes the
Federal Reserve to expand the money supply in
order to smooth nominal interest rates, which
causes a temporary rise in prices.
This example implies that, on average, prices
will fall over the next period, leading to a
decline in the nominal interest rate. Unlike the
example given in the previous section, interest
rates in this model cause changes in both output
and money. Thus, money and output are posi
tively correlated. Like the example given in sec
tion III, however, interest rates do not Grangercause output, because interest rates and output
occur contemporaneously.

IV. Output Causes Money

Real business cycle theorists typically assume
that the cause of business cycles is either a shock
to consumer preferences or a shock to real pro
ductivity. 4 Because an indirect measure of these
shocks can be obtained through the use of
Solow residuals (see Solow [1956]), theorists
have tended to concentrate on technology
shocks as a source of business cycle fluctuations.
Real business cycle theory has been successful
in explaining the quantitative aspects of business
cycles. These include the standard deviations
of— and comovements among— real variables
such as output, investment, consumption, and
hours worked. In contrast, monetary-driven bus
iness cycle models have concentrated on
explaining the qualitative aspects of the correla
tion between money and output. 5
Because real business cycle models do not
include a role for money, they have been criti
cized for not explaining the comovements

■ 4

For a thoughtful exposition of real business cycles, see Prescott (1986)

or Stockman (1988).

■

5 A s noted by Stockman (1988, p. 35), “ The large-scale econometric

models do not qualify because they are not true structural models in the sense
of the Lucas critique of econometric policy evaluation....”

Cross-Correlations of Output

Variable

x (t

- 4)

x (t -

)

x (t -

)

x (t

- 1)

Real GNP

.25

.45

Monetary base

.08

.2 0

.29

.39

.1 2

.25

.35

.62

.6 8

.69

.6 8

x (t)

x (t+

)

x (t +

) * ( t + 3)

x ( t + 4)

.87

.6 8

.46

.26

.44

.42

.39

.37

.34

.26

.2 1

.1 6

.62

.48

-.08

-.25

.87

1.0 0

.15

.29

.1 0

Interest rates

-.55

-.36

-.15

.1 0

.34

.47

.51

.49

.45

Real interest rates

-.57

-.41

-.2 0

.07

.30

.40

.44

.43

.41

CPI

-.70

-.75

-.69

-.56

-.40

-.23

-.05

.13

NOTE: Sample period is from 1959:IQ to 1988:IVQ.
SOURCES: Data Resources, Inc., and Board of Governors of the Federal Reserve System.

F I G U R E

Real G N P and Consumer Price Index

Percent deviations

NOTE: Sample period is from 1959. IQ to 1988: IVQ.
SOURCES: Data Resources, Inc., and Board of Governors of the Federal
Reserve System.

among nominal variables such as the price level,
wages, and money (see Summers [1986]). How
ever, as figure 6 and table 1 illustrate, the
comovements among interest rates, prices, and
real output are qualitatively consistent with real
business cycle theory. In particular, interest rates
have been contemporaneously procyclical and
prices have been countercyclical since 1959.6

■

Prior to 1953, prices seem to be more procyclical.

Procyclical interest rates arise in real business
cycle models generated by temporary productiv
ity shocks. A temporary increase in productivity
today, which is expected to lead to higher out
put in the future, causes individuals to borrow
money in order to smooth consumption. Coun
tercyclical prices arise in these models because
the demand for real money balances increases
when output increases. Assuming that the Fed
eral Reserve does not fully accommodate the
increases in interest rates and output, it follows
that prices must fall.
Table 1 provides further evidence that the
Federal Reserve may accommodate increases in
output. Note that the strongest correlations
between the monetary base and output occur
contemporaneously and with money lagging out
put by one quarter. Real business cycle theorists
argue that the correlation between the monetary
base and output is the result of the Federal
Reserve’s operating procedure. They point out
that this correlation is small relative to the corre
lation between output and broader measures of
money, such as M l and M2.
Table 1 shows that while the contemporaneous
correlation between the monetary base (percent
deviations from trend) and real GNP is only .44,
the correlation between M2 (percent deviations
from trend) and real GNP two quarters later is
.6 8 . Although table 1 indicates that the correlation
between M l and real GNP is similar to the corre
lation between the monetary base and real GNP,
the correlation between M l (percent deviations
from trend) and real GNP is .59 if one ignores
the tremendous increase in M l during 1986.
While the monetary base is determined solely
by the Federal Reserve, components of M l and
M2, such as checking accounts, short-term time
deposits, money market accounts, and mutual

funds, are determined by commercial banks and
the public . 7 This suggests an important role for
reverse causality. The public appears to respond
endogenously to future output changes by shift
ing its portfolio from currency to demand and
time deposits. Some mechanism must therefore
serve to link output and deposits.
King and Plosser (1984) develop a model in
which individuals demand both currency and
financial services (demand deposits). In their
model, demand deposits, like other goods, are
produced with capital and labor. They derive a
demand curve for both inside money (financial
services) and outside money (currency). They
assume that the cost of making a transaction
depends negatively on the real amount of inside
and outside money that a person holds. The
demand for both financial services and currency
increases with real output in this model, explain
ing why empirically both real currency and real
demand deposits are correlated with real output.
However, King and Plosser also show empiri
cally that there is a positive correlation between
nominal demand deposits and currency with real
output. If one restricts their cost of transactions
and assumes that with larger purchases (higher
output) there is an extra cost associated with
currency over demand deposits, one can also
generate a positive correlation between nominal
demand deposits and output. This assumption
seems natural because the demand for highticket durable goods is much more procyclical
than for less-expensive purchases such as serv
ices. A model like this can explain the positive
correlation between nominal bank deposits and
real GNP.
An example of reverse causality occurred dur
ing the Great Depression. The monetary base
grew slightly through the period, while the
money supply, defined by M l, declined substan
tially as depositors shifted out of demand depos
its and into currency. The result was a decline in
the currency/deposit ratio as output fell and
banks failed. The ensuing bank failures were
probably both a cause and an effect of the Great
Depression. The decline in the money supply,
therefore, was partly the effect of factors that
caused the Great Depression, although it may
also have been a contributing factor in causing
the financial collapse. 8 Empirical work has not
been able to distinguish this causation.

■ 7

The Federal Reserve currently can control the nonborrowed monetary

base with a fair amount of precision. However, to control total monetary base,
the Federal Reserve would need to alter the current administrative practices of
the discount window and reserve accounting practices. See Laurent (1979).

■

See Friedman and Schwartz (1963).

Real business cycle models have generated a
resurgence in interest to test for the direction of
causality between money and output. The next
section reviews this literature in light of the the
ories presented in sections I through IV.

V. Tests of the MoneyOutput Relationship

To determine the direction of causality between
money and output, economists since Sims
(1972) have employed Granger-causality tests.
The results of these tests are not robust to
changes in the sample period, to changes in the
variables included in the test, or to whether the
data are in log-level or first-differenced form.
Sims finds that money Granger-causes output
in a simple bivariate setting. In a later paper,
Sims (1980) determines that money fails to
Granger-cause output when the commercial
paper rate is included in the test. Litterman and
Weiss (1985) replicate this result and also show
that the nominal commercial paper rate Grangercauses both money and output. They find that
the real interest rate, however, does not Grangercause either output or money.
Eichenbaum and Singleton (1986) replace the
commercial paper rate with the real rate of
return on stocks and the real rate of return on
Treasury bills in their Granger-causality tests.
They find that while the real rate of return on
Treasury bills does not Granger-cause output, the
real rate of return on stocks does. Their model
allows no explanatory power for money once
these variables are included.
Stock and Watson (1989) find that money
Granger-causes output if the rate of return on
stocks is omitted and the nominal rate of return
on Treasury bills is included. Friedman and
Kuttner (1989), however, find that this result is
sensitive to the sample period chosen. They also
determine that money fails to Granger-cause
output (except for one subsample) when the
nominal commercial paper rate is replaced by
the spread between the commercial paper rate
and the Treasury bill rate.
What do these results tell us about the direc
tion of causality between money and output?
First, the inclusion of interest rates seems to
weaken the explanatory power of money. This
seems to be inconsistent with a money-driven
business cycle. McCallum (1983), however,
argues (but does not show) that if the Federal
Reserve attempts to peg the interest rate, then
interest-rate innovations are a better indication of
the influence of money on output than are
monetary innovations. This result is obtained

because monetary innovations that affect output
also cause interest rates to change. There are also
nonmonetary shocks that cause interest rates to
change, leading to changes in output.
Second, different measures of the rate of
return yield drastically different results. The rea
son is probably that some rates of return are a
better proxy for future changes in output than
others. As Friedman and Kuttner indicate, the
primary determinant of the spread between the
Treasury bill rate and the commercial paper rate
is the default risk on corporate securities. The
primary determinant of the default risk of corpo
rate securities is probably the anticipation of
future business conditions, that is, future changes
in output. The real rate of return on stocks in
Eichenbaum and Singleton’s study is probably
also a proxy for future changes in output.
The issue of whether money is significant in
its ability to predict future output when the
spread or return on stocks is included in the
causality test tells us little about the actual direc
tion of causality between money and output.
Money will Granger-cause output whether
money actually causes output or whether future
output causes money, whenever the spread (or
the return on stocks) is a proxy, but an imperfect
proxy for future output. Money would appear to
be significant for both models because it helps
to eliminate some of the noise present in the
spread. Similarly, money will not Granger-cause
output if the spread (or the return on stocks) is a
perfect proxy for future output. The two models,
money causing output and output causing
money, are thus observationally equivalent in
their predictions concerning whether money
Granger-causes output.
This analysis indicates that inferences about
the direction of causality between money and
output cannot be made from the existing
Granger-causality tests. One of the major prob
lems with the existing empirical studies is that
they use M l as their measure of money. As indi
cated in the previous sections, broader measures
of money respond to future business conditions
more than narrow measures of money, such as
the monetary base. It appears that it would be
difficult to distinguish between money causing
output or output causing money when measures
of money containing endogenous components
are used. The same caveat holds for narrow meas
ures of money like the monetary base. These
measures, however, do not seem to respond to
future business conditions to the same degree as
M l or M2.
These results suggest that the use of causality
tests should proceed along the lines indicated by
Sims (1989). He urges that researchers should

concentrate on combining the theoretical tech
niques developed by real business cycle theo
rists and the empirical technique of vector auto
regressions. That is, researchers should proceed
along the lines of Prescott (1986), but should
compare more than simple correlations when
matching simulated data to actual data. Sims
recommends that they compare the results of
Granger-causality tests run on both simulated
data and actual data. This requires models to
pass stricter empirical tests before being judged
as either successful or unsuccessful. Applying
this technique to help determine the direction of
causality between money and output would
require building a real business cycle model
with money and then comparing the vector auto
regressions run on simulated data from both
models with actual data.

VI. Conclusion and Policy
Implications

This paper has shown that Granger-causality tests
alone cannot settle the debate about the direc
tion of causality between money and output.
One reason is the ever-present problem of a
potentially missing third variable. In section I,
we showed how umbrellas could Granger-cause
rain when a variable proxying for the expecta
tion of rain, low-pressure systems, is excluded
from the tests. The above studies seem to affirm
the notion that leaving out variables that proxy
for the expectation of future output could leave
money with explanatory power when no causal
ity is actually present. It should be clear that this
debate is not likely to be settled on the basis of
Granger-causality tests alone. Unfortunately, the
issue can probably never be completely settled
without having the Federal Reserve conduct con
trolled experiments with monetary policy that
would be infeasible.
Causality tests are not necessarily useless,
however. They may provide some information
about the direction of causality, as long as they
are interpreted within the confines of a model.
That is, we must start with the null hypothesis
that a specific model is correct and attempt to
test whether or not we can reject this hypothesis.
This approach is in the spirit of Eichenbaum and
Singleton (1986); however, the suggestions
made by Sims (1989) seem more appropriate.
Many policymakers currently assume that
money causes output in a consistent and reliable
way. Economists have been unable to demon
strate this relationship, however. If money does
cause output, are policies predicated on
such causation benign or harmful? At first glance,

not

it would seem that the effects of current policy
would be benign if money does not cause output.
However, by not being able to pin down the
direction of causality, we cannot rule out other
possibilities. For instance, it may be possible that
inflation or monetary growth decreases output.
Support for this proposition comes from Kormendi and Meguire (1985). Using cross-country
data, they find a negative correlation between
inflation and the growth rate of real output. The
possibility that inflation may lower output
should not be too surprising, given that inflation
is a tax on real cash balances. As is the case with
any other tax, we would expect increases in this
tax to depress output. For example, higher rates
of inflation cause people to engage in wasteful
activities in order to economize on money hold
ings, thus serving to lower output.
Because researchers cannot tell whether
increases in money cause output to increase—
and there is some evidence that increases in the
growth rate of money actually depress output—
how should policymakers proceed? Policy
actions should be analyzed in light of their
potential costs and benefits. Traditional Keynes
ian analysis assumes that all output fluctuations
are inefficient and that policy could improve
economic welfare by stabilizing output. How
ever, as Lucas (1987) points out, the welfare
gains associated with smoothing business-cycle
fluctuations are small and are dwarfed by the
potential gains associated with increasing longrun economic growth.
The costs associated with stabilizing output
may not be small. If unanticipated money
increases output as described by Lucas (1972,
1977), then the real output effects from money
are welfare-reducing. The reason is that the out
put effects of money are generated by misper
ceptions on the part of the public. As Lucas
points out, this analysis prescribes that the Fed
eral Reserve should follow a rule when conduct
ing monetary policy. In Lucas’s model, any out
put changes induced by money are inefficient.
Even if his reasons for why money affects output
are incorrect, it still may be best for policymakers
to follow a rule.
Stockman (1988) also makes the point that
conducting policy as if output fluctuations are
inefficient can be damaging. If the true explana
tion of business cycles turns out to require both
Keynesian and real business cycle elements,
then there may be substantial welfare losses
associated with output stabilization. As argued by
real business cycle theorists, some output
changes are efficient. In addition, it is presently
impossible to distinguish inefficient from effi
cient movements in output. Using monetary pol

icy to offset these shocks could very well leave
us worse off. Therefore, even if money has real
effects, it is not clear how aggressively, if at all,
monetary policy should try to stabilize output.
Policymakers should accept the possibility that
money does not cause output. Instead of con
ducting policy as if money does cause output,
they could base monetary policy on what we
currently know about its costs and benefits. The
preceding analysis leads us to believe that poli
cymakers should be more reluctant to fine-tune
the economy without understanding the ineffi
ciencies present in the economy. Because the
costs of economic stabilization are thought to be
large, while the potential benefits have been
shown to be fairly small, we recommend that
monetary policy be predicated on a rule that is
easy for policymakers to implement and even
easier for the public to monitor.

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