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S C I E N C E- / ^ D D
I RI REECC T *.

ELSEVIER

Journal of
MONETAEY
ECONOMICS-

Journal of Monetary Economics 50 (2003) 1029-1059
www.elsevier.com/locate/econbase

The future of monetary aggregates in
monetary policy analysis^
Edward Nelsona’*
a Monetary Policy Committee Unit, Bank o f England, Threadneedle Street, London, EC2R 8AH, UK
Received 22 November 2002; received in revised form 3 March 2003; accepted 3 March 2003

Abstract
This paper considers the role of monetary aggregates in modem macroeconomic models of
the New Keynesian type. The focus is on future model developments that are suggested by the
monetarist literature, and that in addition seem justified empirically. Both the relation between
money and inflation, and between money and aggregate demand, are considered. Regarding
the first relation, it is argued that both the mean and the dynamics of inflation in present-day
models are governed by money growth. This arises from a conventional aggregate-demand
channel; claims that an emphasis on the link between monetary aggregates and inflation
requires a direct channel connecting money to inflation, are wide of the mark. The relevance of
money for aggregate demand, in turn, comes not via real balance effects (or other justifications
for money in the IS equation), but on money serving as a proxy for the various substitution
effects of monetary policy that exist when many asset prices matter for aggregate demand.
This role for monetary aggregates is supported by empirical evidence and enhances the value
of money to monetary policy.
© 2003 Elsevier B.V. All rights reserved.
JEL classification: E52; E58
Keywords: Taylor rules; Inflation; Money; Monetary aggregates; Monetary policy; Transmission mechanism

^F or detailed comments on the whole of the paper, I am indebted to Milton Friedman, Peter Ireland,
David Laidler, Bennett McCallum, Allan Meltzer, Anna Schwartz, and Lars Svensson. For specific
comments and feedback on earlier drafts, I thank participants at the Carnegie-Rochester Conference,
22-23 November, 2002, seminar attendees at the Bank of England and the European Central Bank, and
Michael Bordo, Paul De Grauwe, William Dewald, Charles Goodhart, Amit Kara, Stuart Lee, and
Magdalena Polan. I thank Kosuke Aoki for providing code and for helpful discussions. The views
expressed in this paper should not be interpreted as those of the Bank of England or the Monetary Policy
Committee.
*Corresponding author. Tel.: +44-207-601-5692; fax: +44-207-601-3550.
E-mail address: ed.nelson@bankofengland.co.uk (E. Nelson).
0304-3932/$ - see front matter © 2003 Elsevier B.V. All rights reserved,
doi: 10.1016/S0304-3932(03)00063-1



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E. Nelson I Journal o f Monetary Economics 50 (2003) 1029-1059

1. Introduction
The paper by Taylor (1993) was pivotal in shaping the conduct of monetary policy
analysis. Monetary economists had long recognized that central banks in practice
treated the nominal interest rate rather than the monetary base or a reserves
aggregate as their policy instrument. They had also acknowledged that interest-rate
rules that responded to nominal variables in an appropriate manner could deliver
low and stable inflation, even if these rules did not respond directly to movements in
the money stock.1 But Taylor put these elements together with an empirical insight,
namely, that actual monetary policy decisions could be usefully approximated by a
simple interest-rate rule that responded to observed movements in a small set of key
variables—inflation and detrended output. Taylor’s insight has facilitated the use of
small-scale models that analyze monetary policy, the business cycle, and inflation
with interest-rate rules (see e.g. the papers in Taylor, 1999).
In itself, the use of a Taylor rule for monetary policy analysis is neutral on the
issue of the importance of monetary aggregates. The fact that actual policy is well
characterized by a rule with no explicit money term does not preclude a role for
monetary aggregates in the transmission of monetary policy or the analysis of
inflation. Nevertheless, the literature that has found the Taylor rule a useful way of
characterizing monetary policy has also endorsed the use of New Keynesian models
that feature no explicit reference to monetary aggregates (e.g. Clarida et al., 1999,
pp. 1686-1687; Rotemberg and Woodford, 1997, p. 309).2 It is not difficult to see
why this development has taken place: if policy actions can be characterized in terms
of movements in interest rates, it is convenient to trace the transmission of policy
effects through the reaction of aggregate demand to interest rates. Moreover, some
analysts who reject Taylor rules as a useful description of actual monetary policy
behavior have nevertheless supported the movement away from the use of monetary
aggregates in monetary policy analysis (e.g. Svensson, 2003).
This paper aims to answer four questions about the future of monetary aggregates
in monetary policy analysis, two on the relationship between money and inflation,
and two on the transmission mechanism of monetary policy. The questions are:
(a) Do the new Keynesian models referred to above imply that inflation in the
long run is governed by money growth, as stressed by the quantity theory of
money?
(b) Can inflation dynamics in these models be given a conventional quantity-theory
interpretation?
(c) Is the basic transmission mechanism of monetary policy in these models the same
as that in pre-1990s models, which apparently gave a more explicit role to
money?
^ e e e.g. Artis (1993), Goodhart (1987), McCallum (1981), and Walters (1988).
2It remains standard for money to be included in VAR studies (e.g. Christiano et al., 1999; Leeper et al.,
1996). This, however, can be motivated by the fact that policymakers responded to money during the
estimation period, and need not imply an explicit role for money in the behavioral equations of the private
sector.




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1031

(d) Finally, are there aspects o f the transmission mechanism of monetary policy
present in the pre-1990s work that could usefully be added to new Keynesian
models?
Throughout, my investigation of these questions will be with the aim of determining
whether the behavior of monetary aggregates deserves attention in the decision­
making of inflation-targeting central banks that use an interest-rate operating
instrument.
At a conference in July 1992, Taylor made his own position clear. While observing
that “interest rates are likely to remain the preferred operating instrument of
monetary policy”, Taylor (1992, p. 12) advised: “The evidence that the large swings
in inflation are related to money growth indicates, however, that money should
continue to play an important role in monetary policy formulation in the future.”
The subsequent decade of monetary policy formulation, however, has seen a move
away from this prescription, with continuing de-emphasis of money on the part of
the Federal Reserve and other central banks, and with the European Central Bank’s
assignment of a prominent role to money being the basis for sharp criticism from a
number of economists (e.g. Begg et al., 2002; Gall, 2002; Rudebusch and Svensson,
2002; Svensson, 1999a, b, 2002). Such criticism, on the surface, appears to be
justified by current models for monetary policy—which, a variety of observers claim
(see Section 2 below), give money much-diminished importance compared to its role
in the quantity theory.
In answering the above questions, I make two departures from much recent work
on money. First, while money demand behavior is an important element of my
discussion, I do not focus on the issue of formal stability of the money demand
function. One reason for this is that, as stressed by Rudebusch and Svensson (2002),
a stable money demand function does not preclude the optimality of monetary policy
arrangements which proceed without any reliance on data on the money stock.
Another reason, noted by Lucas (1980), is that numerical stability of money demand
neither implies nor is implied by a close relationship between money growth and
inflation. A further reason is that observed instability of empirical money demand
functions may reflect omission of important determinants of money demand; but the
dependence of money on these determinants gives it an indicator role that may be a
reason for continuing to monitor money.
This last reason leads me into the second major departure from other recent
approaches to the role of money. Much of this work has highlighted novel properties
of models that include a term involving money, either in the policy rule or in the
structural equations. For example, Christiano and Rostagno (2001) show how a
strategy that includes a monitoring range for money growth serves as an insurance
policy against undesirable multiple equilibria. Other studies have evaluated the size
of cross-derivative terms involving money in households’ utility functions (Andres
et al., 2001; Ireland, 2001a; McCallum, 2000; Woodford, 2003). My approach is
different. I endeavor to determine whether money in current models has the role
advanced for it in the work of Milton Friedman, Anna Schwartz, Karl Brunner, and
Allan Meltzer. It was, after all, largely the work of these authors that was the basis




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for the “monetarist counter-revolution” (Friedman, 1970) in the 1960s that changed
macroeconomists’ views regarding the potency of monetary policy and the
importance of monetary aggregates.3 Focusing on their work helps identify the
distinguishing features of current models for monetary policy.4
Various combinations of answers to the above questions are possible. One is that
current models represent a decisive rejection of the earlier quantity-theory-based
analysis, but that this rejection is theoretically and empirically justified. In that case,
the answers to (a)-(d) above are all “no”, and, insofar as there is a role for money in
monetary analysis, it must be based on a new justification different from those
advanced by monetarists. Another answer is that the differences between current
models and their monetarist antecedents are more apparent than real, and so an
eclectic interpretation of current models indicates that they have standard monetarist
properties. Then questions (a)-(c) should be answered with “yes” , and (d), “no.”5
The conclusion suggested by the analysis in this paper, however, is that while
current models are partially monetarist, further insights from monetarist analysis
could be fruitfully added to New Keynesian models. I argue in Section 2 that present
models are consistent with quantity-theory or monetarist approaches regarding their
modeling of inflation. The relation between monetary policy and aggregate demand
in New Keynesian models is discussed in Section 3, and I argue that, in basic terms,
the transmission mechanism is a special case of that in monetarist models. New
Keynesian models lack, however, an important element of most monetarist analysis.
This is the notion that a spectrum of yields matters for the determination of
aggregate demand and money demand. The implication of this model feature is that
money conveys information about monetary conditions not summarized by the
short-term interest rate.6 I argue that there is support for adding this model feature
3As well as being the tenth anniversary of the conference-presentation and publication of the Taylor
rule paper, 2002-2003 is the 40th anniversary of the NBER Conference on the State of Monetary
Economics, held on April 13-14, 1962, whose proceedings (published February 1963) included Friedman
and Schwartz (1963a). According to Brunner (1971a, p. 35), this conference “alerted the profession to a
change in the intellectual climate.” It also featured the first four-way meeting of Friedman, Schwartz,
Brunner, and Meltzer. Like the conference that introduced the Taylor rule, the 1962 conference was held at
Carnegie Mellon University (then known as the Carnegie Institute of Technology).
4For space reasons, I restrict the scope of this paper in several respects. I do not consider the fiscal
theory of the price level (e.g. Woodford, 2001) or liquidity-trap issues. And I do not discuss financial
intermediation, in order to focus on properties of money that remain valid even for narrow definitions
such as currency or high-powered money.
5Considering these questions explicitly seems preferable to the approach of Alvarez et al. (2001), who
endorse the empirical validity of the quantity theory, claim that current models reject the quantity theory,
then propose their own “new theory” for monetary analysis. Clearly, the validity of the quantity theory
hardly justifies a “new theory.” And insofar as current models lack worthwhile elements of the quantity
theory, it is preferable to isolate those elements directly.
6Beside my (2002) paper (discussed in King, 1999; Svensson, 1999b), recent discussions of the multiple
channels of monetary policy, and the implications for the significance of money, include Clouse et al.
(2000) and Goodfriend (2000). Clouse et al. attribute these ideas to Meltzer (2001) and Tobin (1982);
Goodfriend attributes them to Friedman and Meltzer. My own view is that they should be jointly
attributed to Brunner, Meltzer, Friedman, and Schwartz, on account of their all having advanced
such ideas in the 1960s; e.g. Brunner (1961, p. 53), Brunner and Meltzer (1963, p. 322), Friedman (1961a,




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1033

to New Keynesian models. In total, the analysis suggests answers of “yes” to (a)-(d)
above.

2. Money and inflation
Taylor (1992, p. 12) concluded that “there is ample evidence in many of the recent
experiences with inflation and disinflation to support Friedman’s (1992) point that
‘substantial inflation is always and everywhere a monetary phenomenon.’” Milton
Friedman’s famous statement that “inflation is always and everywhere a monetary
phenomenon” (appearing originally in Friedman, 1963, p. 17)—referred to here for brevity
as the AEMP proposition—forms a useful way of organizing the discussion of current
views on the relationship between money growth and inflation. Taylor’s conclusion
appears to have been widely shared in the early 1990s, with McCallum (1990, p. 965)
expressing confidence that “there is little professional disagreement with Friedman’s
position”, and Robert Lucas claiming that “a macroeconomic consensus [has been]
reached... on the monetary sources of inflation” (quoted in Snowdon et al., 1994, p. 226).
Policymakers still appear to adhere to the AEMP proposition. Endorsements of
the proposition appear not only in the recent outline by Issing et al. (2001) of the
ECB’s monetary policy strategy, but also in statements by policymakers outside the
euro area. For example, King (1997, p. 441) states that “inflation is assuredly a
monetary phenomenon in the medium term”; Meyer (2001a, p. 5) argues that “[f]ew
economists would disagree that inflation is, as Milton Friedman taught us long ago,
always and everywhere a monetary phenomenon”, and Hubbard (2002, p. 739)
observes: “Nobel laureate Milton Friedman once remarked that ‘inflation is always
and everywhere a monetary phenomenon.’... [T]his is true.”
But there have been suggestions that theoretical developments and empirical work
of the last decade have shattered support for the AEMP proposition. Alvarez et al.
(2001, p. 219), for example, describe the “consensus [that] has emerged” as “a
rejection of the quantity theory.” After providing a brief outline of the proposition
(Section 2.1), in Section 2 .2 ,1 discuss the long-run relations between money growth
and inflation suggested by current theory, and in Section 2.3, turn to recent empirical
work that claims to find that inflation is not a monetary phenomenon. Other issues
relating to money growth and inflation are taken up in Sections 2.4 and 2.5, with
Section 2.6 providing some conclusions.
2.1. Outline o f the AEM P proposition
Here I provide an outline of the proposition that inflation is always and
everywhere a monetary phenomenon.7 Discussions of the AEMP proposition
(footnote continued)
pp. 461-463), Friedman and Schwartz (1963a). (The key passage describing these ideas cited in
Goodfriend’s fn. 32, which he attributes solely to Friedman, is joint work by Friedman and Schwartz
(1963a, pp. 59-63).) One reason for not associating such views with Tobin is that he denied that the extra
transmission channels gave additional significance to money as an indicator; see Nelson (2002, fn. 31).
7In this paper, I also refer to this proposition as the “quantity-theory explanation of inflation”.




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E. Nelson / Journal of Monetary Economics 50 (2003) 1029-1059

available in the literature that endorse AEMP include those in Friedman’s work (e.g.
1963, 1970), McCallum (1990, pp. 965-966), Meltzer (1977, p. 183), and the many
editions of Mishkin (2001); the following is based closely on these interpretations.
The proposition amounts to the claim that for the central bank to allow a
sustained change in inflation of g percentage points, it must allow the steady-state
money growth rate to change by g percentage points. In addition, fluctuations in
inflation around its steady-state value are largely explicable by movements in money
growth.8
There are several qualifications, discussed in greater detail below. First, it is a
proposition about inflation, not the price level. Once-and-for-all price-level shocks
occur—e.g. from falls in the level of potential GDP.9 In addition, to establish the
money growth/inflation relationship, one must allow for a lag from money growth to
inflation. And significant discrepancies between money growth and inflation can
occur during periods of lasting shifts in the opportunity cost of holding real
balances—from changes in the own rate on money, and as real balances recover in
the adjustment to a new low-inflation, lower nominal interest rate regime.
Velocity growth is formally equivalent to monetary growth in its implications for
nominal spending growth and inflation. An increase in velocity growth implies lower
growth in demand for real money balances per unit of output, which with an
unchanged growth in nominal money per unit of output, implies a higher inflation
rate. The AEMP proposition does not deny that changes in velocity growth occur
over both short and long periods. However, the longer-term changes (excluding
those from the Fisher effect) tend to be determined by a set of factors (demographics,
innovations in the financial system, etc.) that bear no necessary relationship to the set
of factors commonly advanced as non-monetary determinants of inflation (such as
8Some readers might object to the use of terms such as “explicable by” or “governed by” money
growth, given that the discussion here is intended to include the realistic case where money growth is not a
univariate exogenous process. I would contend, however, that money growth can still be thought of as
“explaining” or “governing” inflation in such cases, in the same sense that in Woodford’s (2003) “neoWicksellian framework” for monetary analysis, the gap between the real interest rate and natural rate is
regarded as governing or explaining inflation behavior. Both monetary variables (money growth and the
rate gap) are endogenous. But both variables are nonetheless responsive to monetary policy actions. And
whether the central bank permits money growth or the rate gap to respond to a shock is a useful guide to
whether that shock has major implications for the ongoing inflation rate. Furthermore, as argued below, a
positive correlation between money growth and (future) inflation would tend to arise even if nominal
money demand were completely insensitive to current and expected future nominal price levels, which is
inconsistent with an interpretation of the correlation as reflecting a passive adjustment of nominal money
to price behavior.
9A s price-level shocks, King (1997, p. 438) mentions changes in commodity prices, Meltzer (1977,
p. 183), one-time changes in the degree of monopoly power, and Friedman (1992, p. 204) and
McCallum (1990, p. 965), movements in the terms of trade. It is important to emphasize in each case that
the permanent effect on the price level, for an unchanged nominal money stock, comes from the fact that
potential output has been changed, not because particular items in the price index directly respond to the
shock. King (1997) further mentions indirect tax changes and Meltzer (1981, p. 21), “the imposition or
elimination of the distorting influence of price controls.” Abstracting from effects on potential output,
these events can be regarded as affecting the price level by introducing measurement error into recorded
price indices.




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union “wage-push” or world inflation). It follows that non-monetary factors must
affect the growth of the nominal quantity of money to have a systematic effect on
inflation.
2.2. Long-run relations: theory and implications for policy
Let us first consider the validity of the AEMP proposition as a steady-state
property. It is convenient, as in McCallum (2001) and Meyer (2001b), to write down
the standard New Keynesian setup of an IS equation, an expectations-augmented
Phillips curve, and a Fisher equation:
yt = E ^+i -

grt

+ vt9

(1)

n, = pEtnt+l + x(yt - y*),

(2)

R t = rt + Etjit+i.

(3)

Here R t is the short-term nominal interest rate, rt the short-term real interest rate, y t
log output, y f log potential output, nt quarterly inflation, and the parameters satisfy
a > 0, a > 0, and 0 < /?< 1. The variables R t, ru and nt are expressed as deviations
from constant steady-state values; y t and y f, as deviations from a common steadystate growth path.
McCallum (2001, pp. 146-147) argues that while no explicit term involving money
appears in the above model, and the solution expression for inflation would be
unchanged by adding a money demand equation to the system, inflation nevertheless
can still be regarded as pinned down in the long run by the economy’s steady-state
nominal money-growth rate (relative to the output growth rate). His demonstration
is not repeated here; I will argue in Section 2.3 that this demonstration of money’s
steady-state role, while valid, understates the closeness of this model to the standard
quantity theory.
McCallum’s derivation helps address a question raised by Gall (2002, Section 3.3).
Gall contends that as the long-run money growth/inflation relation is one among
several steady-state relations between nominal variables—the Fisher relation
between nominal interest rates and inflation being another—it deserves no “special
attention.” But Gall’s analysis takes as given that the average value of inflation is
equal to target. In empirical work on inflation dynamics or the theoretical study of
optimal stabilization policy, it can be legitimate to abstract from the determination
of the average or steady-state inflation rate.10 But, as Gall notes, central banks have
to be concerned with setting the steady-state rate of inflation, not just minimizing the
variability of inflation around its steady-state value. And it is for the former purpose
that explicit attention to the long-run inflation/money growth relationship may be
10Phillips curves such as Eq. (2) describe the dynamics of inflation around a steady-state value.
Empirically, this steady-state value is taken into account via the inclusion of an intercept term (as in Gall
and Gertler, 1999) or by removal of a time-varying mean from the data prior to estimation (Coenen and
Wieland, 2002). The theoretical studies of Clarida et al. (1999) and Svensson (2003) describe welfaremaximizing policy in a model where inflation is expressed as a deviation from its steady-state value.




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valuable. Gall treats this relation as only one of several long-run conditions, but
there is a key distinction between the money/inflation link and other conditions, such
as the Fisher condition. The Fisher relation has a direct counterpart in the equations
describing inflation dynamics, namely Eq. (3); there is no extra information from the
steady-state Fisher relation. The money growth/inflation link, by contrast, has no
counterpart in the equations describing inflation dynamics. Rather, this long-run
relation is “buried” in the constant terms of the structural relations that underlie
Eqs. (l)-(3), and so is suppressed altogether in the dynamic equations that are
expressed in terms of deviations from the steady state. Consequently, the steady-state
link between monetary growth and inflation does have a special status that deserves
separate consideration from other long-run relations.11
A more legitimate basis for not taking the long-run money growth/inflation
relationship into account in policymaking would be if the short-run model (l)-(3)
were a reasonable description of the data in the presence of moderate changes in the
mean of inflation.12 The money growth/inflation relation would still demand special
attention for contemplating and understanding large changes in the mean of
inflation, but the short-run model might be adequate for much policy analysis.
Finally, it should be noted that McCallum’s steady-state analysis refers to a system
that includes a conventional money demand function of the form:
(m - p)t = c0 + c\yt + c2R t + rjt,

(4)

where (m —p)t is log real money balances, rjt is a money-demand disturbance, and
ci > 0 ,c 2<0. I will argue in Section 3 that a less conventional money demand
function, in which the long-term interest rate and other yields appear, is appropriate.
This modification, however, would not overturn the model’s steady-state property of
a unitary link between nominal money growth and inflation.
2.3. Long-run relations: recent empirical evidence
What of the empirical evidence on money and inflation in the long run? Both Begg
et al. (2002, p. 21) and Svensson (2002) refer to the recent study by De Grauwe and
Polan (DP) (2001) as providing decisive evidence against AEMP. DP’s exercises
include both cross-country and panel regressions of inflation on money growth using
1970-1999 annual data from “low-inflation” (i.e., less than 10% average) countries.
Finding that the estimated coefficient on money growth is low relative to 1.0 and
11The steady-state growth rate of money relevant for policy may change over time. For example, Bordo
and Jonung (1990, p. 167), Brunner (1997, p. 82), Friedman and Schwartz (1982, p. 150), and Meltzer
(1987, p. 30) all recognize that changes in financial structure can alter the trend growth of velocity, and
that the money-growth rate relevant for analysis of inflation is one adjusted in light of changes in the
velocity trend. The recognition that the steady-state relation can undergo shifts should be distinguished
from the claim that the long-run relation deserves no attention in policymaking.
12For example, if moderate changes in the mean of inflation have little effect on the length of nominal
contracts in the economy, the assumption of a constant value of a in Eq. (2) would remain valid across
different mean inflation rates.




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statistically insignificant, DP conclude that “there is no evidence for this statement
[i.e., AEMP] in relatively low inflation environments.”
A serious omission, however, is that while DP review the empirical literature, they
provide no discussion of previous attempts (such as those cited in Section 2.1 above)
to interpret the AEMP statement itself. Moreover, no paper by Milton Friedman
which uses the AEMP phrase is cited or discussed.13 I suggest that, under the
interpretations offered in these papers, DP’s rejection of the proposition is
unjustified. Reconsidered in light of Friedman’s work in the area, their study has
limitations regarding data, dynamics, and the theoretical interpretation of the
AEMP proposition.
The first misinterpretation of AEMP pertains to DP’s main evidence for the lowinflation economies, namely regressions based purely on cross-country averages.
With each country represented in the regression by single 30-year means of money
growth and inflation, DP find no relationship between the two series. Note first that
such cross-country regressions have no implications for whether inflation and money
growth are closely related over time in each country. The only issue, therefore, is
whether the AEMP proposition is intended to account for cross-country differences
in inflation in the manner that DP specify. DP’s cross-country regressions implicitly
impose the restriction that the steady-state growth rate of desired real balances
relative to income is constant across countries. But advocates of AEMP clearly did
not make this claim (see e.g. Brunner, 1997, p. 96; Friedman, 1983, p. 4; Meltzer,
1987, p. 30). Rather, the benchmark noninflationary steady-state money-growth rate
was accepted as varying by country, on account of different velocity trends implied
by each economy’s financial structure. DP’s cross-country results for low-inflation
economies—which Begg et al. (2002) focus upon—therefore have no bearing on the
AEMP proposition.14
Regarding data, DP use Ml and M2 growth rates computed from International
Financial Statistics annual series. These money definitions have a large deposit
component, and IFS data on these aggregates are subject to numerous statistical
breaks, including those due to reclassification of nonbank deposits as bank deposits,
nondeposit liabilities as deposits, and time deposits as demand deposits. In addition,
variations in the payment of interest on deposits tend to produce jumps in particular
monetary aggregates. Sympathizers with and critics of the quantity theory would
surely grant that the conceptual definition of money is one that is invariant to these
breaks, and so the appropriate monetary aggregate in empirical work is one that
either adjusts for the breaks or excludes the affected components of money. For this
reason, Friedman and Schwartz (1970, p. 145) recommended using currency as
the definition of money in cross-country studies. This recommendation remains

13The AEMP phrase does not appear in Friedman and Schwartz (1963b), the only work authored or
coauthored by Friedman that is cited by De Grauwe and Polan (2001).
14A similar judgement pertains to the earlier work of Haldane (1997, pp. 86-89) who, like DP, used 30year averages of inflation and money growth and found that the money growth/inflation correlation was
weaker for low-inflation countries.




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E. Nelson / Journal o f Monetary Economics 50 (2003) 1029-1059

compelling today, and so DP’s failure to consider results for currency is a serious
drawback.
Regarding dynamics, Friedman’s long-held position is that the peak response of
inflation to money growth is with a lag of over a year (see Batini and Nelson, 2001).
DP’s panel regressions, however, are of inflation on same-period money growth. Nor
do their regressions that use multi-year averages of inflation and money growth
allow for lags in a satisfactory manner.15 The material effect of allowing for lags is
shown below.
A final issue regarding interpretation is that DP take a negative correlation
between money growth and velocity growth (observed in the low-inflation countries)
as ipso facto inconsistent with AEMP. Such negative correlations can be inconsistent
with AEMP under certain circumstances. For example, if monetary policy has no
effect on aggregate demand, then a monetary policy easing leads both to a rise in
money growth and a fully offsetting and permanent movement of velocity growth.
Such a feature of the data would rule out any role for monetary policy in controlling
inflation, let alone any attention to monetary aggregates.16 But other factors
consistent with the AEMP proposition can produce a negative money growth/
velocity growth correlation. Most notably, a protracted fall in nominal interest rates,
associated with the aftermath of a disinflation, reduces the cost of holding real
balances and so generates data characterized by higher money growth, slower
velocity growth and unchanged inflation. Such a pattern of money/velocity behavior
is, as Wicksell (1906, p. 152) observed, “in complete agreement with the Quantity
Theory.” The cost dimension to velocity behavior was noted explicitly in Barro’s
(1982, p. 101) and McCallum’s (1990, p. 966) expositions of the AEMP proposition.
De Grauwe and Polan (2001) reject interest rates as the source of the negative
money growth/velocity growth correlation, on the grounds that “the liquidity effect
of an increase in the money growth... occurs only in the short run” and cannot
account for patterns that affect a 30-year dataset. The problem here is a
concentration on falls in the nominal interest rate from the liquidity effect—which
would be transitory in nature—at the expense of falls from the Fisher effect, which
would be permanent, and—in the case of a protracted and erratic disinflation—could
easily leave an imprint on long runs of annual data. Declining nominal yields due to
the Fisher effect, and the resulting lowered cost of holding real balances, readily
account for negative money growth/velocity growth correlations, for as Friedman
(1985) notes, “[a] break in the trend of velocity... has been observed whenever and
wherever accelerating inflation has been succeeded by disinflation.”

15DP’s panel regressions using multi-year averages take means of inflation and money growth over
synchronous periods. Clearly, a regression of the average of inflation from years t —j \ o t + j o n money
growth over the same period regresses inflation on future money growth as much as it does on past money
growth. In fact, the situation is worse than that, because IFS data on money are end-of-year while prices
data are year-averages, so period-^ prices data in effect lead the period-* money data.
16As Friedman and Schwartz (1982, p. 207) note, this view of monetary policy was prevalent in the UK
prior to the 1970s (and also the US; see Hetzel, 1998; Meltzer, 1998, for recent discussions), but surely has
no following today, even among critics of monetary aggregates.




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1039

Let us now consider the empirical inflation/money growth relationship in light of
the above points. Using Batini and Nelson’s (2001) data for the US, a regression of
annual CPI inflation (n f ) on contemporaneous annual M2 growth (juf) produces:
n f = 0.036 + 0.211 n f, R2 = 0.052,
(0.009) (0.118)

(5)

(Sample period January 1970-August 2001; Newey West standard errors in
parentheses.) The money-growth coefficient, while positive and nearly significant,
is far from unity, in that respect apparently supporting DP’s conclusions. But if one
instead allows explicitly for lags by regressing inflation on M2 growth two, three,
and four years earlier, the result is:
n f = -0.006 + 0.257 (if_24 + 0.376
(0.012) (0.108)
(0.131)

+ 0.182 nf_4i, R 2 = 0.555,
(0.168)

(6)

with a coefficient sum of 0.814 (s.e. 0.190) on money growth, decidedly more
favorable to the quantity theory.17 Allowing for dynamics moves the results for the
UK in a similar, though less striking, manner: a regression of annual consumer price
(RPIX) inflation on contemporaneous base money growth18 for January 1970August 2001 produces a coefficient of 0.910 (0.318), while that of inflation on base
growth two years earlier delivers 1.097 (0.205).19
If one uses annual base money growth in the US case, a regression of inflation on
contemporaneous money growth delivers a slope coefficient of —0.438 (s.e. 0.163).20
Replacing current money growth with growth two years earlier, and including an
intercept dummy from 1982 to capture the average effect of disinflation on velocity
growth, lead to a coefficient on money growth that is positive, but only 0.221 (s.e.
0.118). Other evidence for the US establishes, however, that money base growth is
significant in predicting aggregate demand (Nelson, 2002); and that there was a high
degree of stability in the demand function for the base in the twentieth century
(Anderson and Rasche, 2001; Meltzer, 1998)—indeed, probably more so than for
M2. This evidence suggests that changing opportunity cost of holding base money,
due to adjustment to a noninflationary regime, has been a pervasive feature of the
final 20 years of the sample, disguising the underlying unitary relationship between
base growth and inflation. The resulting discrepancies between base growth and
17Batini and Nelson (2001) and Leeper and Roush (2002) document the resilience to sample period of
the correlation between inflation and prior M2 growth. Batini (2002) reports similar results using euro area
data.
18For the UK, base money is the preferred measure of money in empirical work for precisely the
Friedman-Schwartz (1970) reasons mentioned earlier, and is endorsed by Brunner (1997, p. 136) on the
same grounds.
19Allowing for lags in the UK case has a more important impact if a longer span of data is considered.
Using annual data for 1834-2000 on inflation and base money growth, a regression of inflation on current
money growth produces coefficient 0.493 (0.141), while a regression of inflation on the prior two years’
base growth yields coefficient sum 0.755 (0.167).
20Again, the Batini-Nelson data, which employ the Anderson-Rasche (2001) domestic base series where
available, are used.




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inflation are, as argued above, not inconsistent with the AEMP proposition, and
reflect a property of velocity behavior noted by Wicksell a century ago.
2.4. Inflation dynamics: the Phillips curve
“Of course, it is not money as such which drives up prices.” This observation of
Karl Brunner (1969, p. 26) has been restated constantly in recent criticism of
monetary aggregates. Typically, the criticism has taken the form of noting that
current models, like earlier non-optimization based models, have Phillips-curve
specifications in which prices are adjusted in light of current and prospective market
conditions. These conditions are expressed in terms of the output gap or marginal
cost; no explicit term involving money appears. The implication would appear to be
that those who advocate using money in the analysis of inflation must believe that
money enters these price-setting specifications directly, and should provide empirical
evidence to that effect. Thus Svensson (1999a, p. 114) states that a “rational role for
monetary aggregates” in an inflation-targeting framework is as indicators “whose
usefulness exclusively depend[s] on their performance in predicting inflation.” To
this end, he points to the evidence of Estrella and Mishkin (1997) that “money has
essentially no predictive power beyond lags of inflation and output in forecasting
inflation.” Similarly, Gall (2002, Section 3.4) maintains that “a rationale for the
emphasis on monetary aggregates and inflation” requires “a direct link between
money and inflation.”
But quantity theorists recognized, as Gall and Svensson do, that in a sticky-price
world, monetary actions operate via effects on real aggregate demand.21 Accord­
ingly, a structural price-setting equation in which the sole forcing process is a
measure of excess demand or cost pressures is in harmony with a quantity-theory
account. As Artis and Lewis (1985, p. 213) put it: “There is no necessary
contradiction between allowing a substantial role to ‘money’ in inflation and
describing its determinants in the conventional way [i.e. using Phillips curves or
markup equations].”22 Put differently, using a Phillips curve to describe inflation
dynamics is entirely consistent with inflation being a monetary phenomenon.23
Once it is recognized that the route from money growth to inflation is not a direct
one, it is less compelling to regard inflation as related to money growth in the long
run only. By amalgamation of the money demand function, Phillips curve, and
21 The case where the marginal utility of consumption depends on real money balances provides only a
partial exception. Ireland (2001a) and Woodford (2003) show that this modification introduces a term in
money into the Phillips curve. This term appears because money now enters the expression for potential
GDP. As in the standard case, there is no term in money in the Phillips curve once the output gap is
defined appropriately, i.e. as the percentage difference between actual and fiexible-price real GDP.
22Batini and Nelson (2001, p. 391) provide references giving similar statements. See also Friedman
(1970, p. 15), Friedman and Schwartz (1982, pp. 60-61), Laidler (1982, p. 13), Harrington (1983, p. 65),
and Meyer (2001b, p. 4).
23 As Milton Friedman observes in October 31, 2002 comments on the preceding paragraphs, “What
would it mean for money of itself to drive up prices?... What drives up prices is spending by the holders of
money, driven by many factors, of which the quantity of money that they happen to have at the moment
is one.”




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1041

policy rule, it is possible to obtain a reduced-form expression for the dynamics of
inflation in which money-growth terms appear prominently.24 No direct role for
money is required; rather, money growth can be considered, as in Harrington (1983,
pp. 65-66), Walters (1988, p. 279) and Batini and Nelson (2001, p. 387), a “quantityside” indicator of the monetary conditions induced by central-bank policy. Open
market operations by the central bank raise money growth and lower nominal yields;
with inflation persistence, real yields fall in the short run and produce variations
in real aggregate demand relative to potential GDP, and so in inflation. This
perspective provides a counterexample to Svensson’s (1999b, p. 215) contention that
the correlation between money growth and inflation emerges only from the long-run
money demand function having a unit coefficient on prices. Variations in the
opportunity-cost variables that enter both the money demand function and the
economy’s IS function are associated with movements in both real money and real
aggregate demand, and so help in generating a money growth/inflation correlation.25
One can agree with Svensson’s (1999b, p. 215) observation that “M2 has no direct
role in the transmission mechanism” , without sharing his conclusion that money
growth and inflation are uncorrelated “at the horizon relevant for monetary policy.”
Money growth thus explains inflation dynamics via the effect of monetary policy
on real aggregate demand relative to potential GDP. The ability to view inflation
dynamics in this way underlies the traditional analysis of the accommodation issue—
that is, the implications for inflation of a nonmonetary event (such as an increase in
government spending or an oil price increase). Textbook treatments (e.g. Lipsey and
Chrystal, 1999, pp. 512-516) characterize these events as producing ongoing
inflation only if the monetary authority “accommodates”, permitting a rise in money
growth. So, for example, an oil shock permanently raises the price level via the
reduction in potential output, but only leads to ongoing inflation if the central bank
follows policies that allow nominal money growth (relative to output growth) to rise
permanently following the oil shock. Other pressures on the price level can be treated
analogously. The same analysis says that a shift in the level of government spending
alongside unchanged money growth can affect the price level permanently via its
effect on potential output and by producing a one-time change in the opportunity
cost of holding real balances, but cannot produce ongoing inflation.26
More recent expositions (e.g. Clarida et al., 1999) instead characterize the
accommodation issue directly in terms of central banks permitting a move in the
output gap, avoiding any analysis of money. In principle, this approach is
unambiguously more useful, since velocity movements distort growth in nominal
money per output unit as an indicator of inflationary pressure. But this superiority
may be less clear in practice: deviations of measured output gaps from their
24See Rotemberg (1996, p. 512, Eq. (11)). A similar representation would result if Rotemberg’s
framework was generalized to incorporate an interest-elastic money demand function and a Taylor rule to
describe policy behavior.
25This issue is taken up in Section 3 below.
26For permanent changes in government spending, one would not expect large effects on the
opportunity cost of holding money, as the natural real interest rate is insensitive to such changes in
infinite-horizon models.




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conceptual counterparts may be as quantitatively important as velocity movements.
A key reason for this, even abstracting from difficulty in measuring the trend in
GDP, is that the cyclical component of potential output responds to unobserved real
shocks. Indeed, a dichotomy in Clarida et al.’s (1999, p. 1687) analysis is that “large
unobservable shocks to money demand” are advanced as a reason for “not even
bothering] to include a money aggregate” in modeling; yet their analysis of optimal
monetary policy is framed in terms of whether policy should accommodate certain
real shocks—which are, of course, in practice large and unobservable, with an
unknown mapping between these shocks and potential GDP.27 Certainly, estimates
of these real shocks should be constructed, as Clarida et al. (1999, pp. 1684-1685)
recommend; but once problems in measuring potential are acknowledged, the
advantage of conducting analysis of accommodation issues without reference to
money is less obvious. In short, policymakers’ knowledge of output-gap behavior
may not be superior to their knowledge of velocity behavior, and so they may find it
useful to consult money-growth data in evaluating whether they are following
policies consistent with maintenance of inflation on target.
To reemphasize the main point, however: the quantity theory does not claim, and
the importance claimed for monetary aggregates in the determination of inflation
does not rest on, a direct channel linking money growth and inflation. Accordingly, I
would not expect the money growth terms in Eq. (6) to remain significant once terms
in the output gap were added to the specification.28 And I would interpret the
evidence in Estrella and Mishkin (1997) that money does not matter in inflation
equations, conditional on real-activity terms, as simply reaffirming evidence against
flexible-price models, not as evidence against the monetary origins of inflation.
Conversely, the evidence in Gerlach and Svensson (2002) that money terms do
provide explanatory power for inflation over and above that contained in measured
output gaps, suggests measurement error in the latter, as well as a positive
correlation between money growth and the true output gap. What is clear is that
tests of the significance of terms in money in inflation equations that include outputgap terms are not a valid basis for evaluating the quantity theory or for judging
whether there should be a role for money in monetary policy decisions.
2.5. Inflation and the monetary regime
Svensson (2002, p. 2) argues that:
“the well-known high long-run correlation between money growth and inflation...
is often misunderstood. Since it is a correlation between two endogenous
variables, it says nothing about the direction of causality... Indeed, the direction
of causality is determined by the nature of the monetary policy pursued. For
instance, under successful strict money-growth targeting, money growth would be
stable and in a sense exogenous to inflation. Then one can argue that endogenous
27Problems in measuring this cyclical component of potential GDP would remain even if the errors in
conventional real-time measures of the output gap, stressed by Orphanides (2003), could be reduced.
28This includes leads of the output gap, which matter via the expected future inflation term in Eq. (2).




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1043

inflation is caused by exogenous money growth. However, under successful strict
inflation targeting, inflation would be stable and in a sense exogenous to money
growth. Then one could argue that endogenous money growth is caused by
exogenous inflation.”
I do not feel that such a regime-dependent interpretation of the money growth/
inflation relationship is necessary. Certainly, monetarists in the 1960s acknowledged
that actual policy made money growth a state of the economy, yet they found it
useful to regard inflation as governed by money growth behavior.29 In this spirit, the
AEMP proposition can be applied symmetrically across regimes. For example, the
following features have characterized conditions in the US and the UK for most of
the last half-century:
(i) Under all monetary policy regimes, inflation has been an endogenous variable
that is dependent on developments in potential output, aggregate demand, etc.
(ii) Monetary aggregates such as the monetary base, Ml or M2, have never been
used as the policy instrument, which has instead been primarily a short-term
nominal interest rate; and the regime in force has always been one that implies
that money growth expands or contracts in response to real shocks hitting the
economy.
(iii) The fact that money has not been used as the policy instrument has not, of
course, implied that the path of money growth is invariant to monetary policy
decisions. On the contrary, these decisions imply a pattern of money-growth
behavior. For example, for a given path for real shocks, an open market
operation undertaken with the aim of raising the policy rate will also slow
money growth—in the case of the monetary base, both because the growth rate
of reserves is reduced directly, and because households are discouraged from
adding to their currency holdings by the higher nominal interest rate. In that
sense, the money stock or money growth can be regarded as a “quantity-side”
indicator of the monetary conditions put in place by central-bank policy, even
when money is not the policy instrument.30 Of course, fluctuations occur in
money growth not related to interest-rate movements; and some of these—e.g.
due to changes in the own rate on money or to money demand shocks—will not
be of interest to policy, and tend to weaken the value of money as an index of
monetary conditions. But other fluctuations—e.g. due to changes in current or
29Among many examples, see Brunner (1969, p. 27), Friedman and Schwartz (1963b, p; 581), and
Schwartz (1969, p. 4). Notably, in comments on the present paper, Milton Friedman writes, “under a
flexible exchange rate, money can be exogenous, but again that depends on the monetary policy pursued.”
30As Goodhart (1987, p. 254) puts it, “a particular level and path for the monetary base impl[y] a given
level and path for interest rates, and vice versa.” One can cast this relationship in terms of impulse
response functions. A contractionary monetary policy shock leads to a declining profile for the impulse
response for the money stock and a rising profile for the interest-rate response, regardless of whether the
policy rule uses money or the interest rate as the instrument. Similarly, for real shocks that affect the
natural rate of interest, one can characterize whether monetary policy is “accommodating” either in terms
of the response of money or the response of interest rates to the shock. For example, monetary policy
accommodation of a positive IS shock can be characterized either as a flat interest-rate response or as a
rise in the money stock.




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prospective movements in aggregate demand or, as argued in Section 3, to
changes in yields on alternatives to money beside short-term securities—will
tend to improve the value of money as an indicator.
Based on (i) above, the characterization of inflation targeting as corresponding to
“exogenous inflation” seems inappropriate; the target may be exogenous, and
inflation will be stable ex post if the target is met, but the target is met through
monetary policy decisions, which determine inflation endogenously by offsetting
shocks to the output gap and other variables.31 And from (ii) and (iii), we need not
regard money-growth targeting as the only regime in which money growth can serve
as a measure of policy stance.
Seemingly anomalous episodes also become explicable under the above quantitytheory interpretation. Woodford (2001, p. 674) characterizes the Korean War period
as one where the Federal Reserve had an interest-pegging regime in the face of fiscal
deficits. He argues that “the government budget affects the general level of prices,
and only because prices change does it also affect the money supply (as higher prices
result in higher [nominal] money demand, which the Fed passively accommodates
under such a regime). Thus one cannot explain the change in the price level as being
due to the increase in the money supply.” One could say with equal validity: “Under
the interest-rate pegging regime, the Fed offsets upward pressure on interest rates by
money creation, and only because the regime is one that permits the money supply to
expand do fiscal deficits create significant inflation.” Interest-rate pegging is simply a
special case of an interest-rate rule. And the relationship between money and
inflation that emerges under an interest-rate rule is just a special case of the quantity
theory. As usual, the money-supply path observed is a consequence of central-bank
policy.32
One final illustration of the pitfalls of reinterpreting the AEMP statement
according to monetary regime is provided by Germany’s interwar hyperinflation.
During that period, the Reichsbank Governor publicly regretted that the authorities
were not creating money at the rate required by the needs of trade (Robbins, 1979,
p. 57). No doubt, much of the monetary expansion that occurred once the German
hyperinflation was in effect could be regarded as accommodation by the authorities
of higher quantity of nominal money demanded by the private sector. But surely noone would disagree that the hyperinflation and its continuation were the result of
runaway monetary growth.33
31While, as Poole (1994, p. 95) and Svensson note, a successful strict inflation-targeting regime should
lead to a zero correlation between money growth and inflation, there are several grounds for expecting
positive and significant correlations between money growth and inflation under inflation targeting in
practice (see Batini and Nelson, 2001, p. 388). As discussed in Section 2.3 above, the conclusion that the
two series are uncorrelated empirically in low-inflation countries is unwarranted.
32As Allan Meltzer puts it (in October 10, 2002 comments): “For most issues we want to address (as
opposed to estimation), it matters very little whether I say: ‘The central bank created too much money
growth,’ or ‘The central bank held the interest rate too low for too long and this induced excess money
growth.’” See also Meltzer (1976, p. 612).
33Milton Friedman (correspondence October 31, 2002) comments that “a comparable and in some
ways clearer example is the gold standard”, a regime which (as discussed in Friedman and Schwartz, 1982,




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2.6. Money and inflation: conclusions
1. The proposition that inflation is always and everywhere a monetary phenomenon
(AEMP) remains valid in present-day models, and can be applied both to the
analysis of inflation dynamics and of the determination of steady-state inflation.
2. The AEMP proposition can be given a similar interpretation irrespective of
monetary policy regime.
3. The quantity theory neither justifies, nor relies upon, the presence of explicit terms
involving money in the economy’s price-setting relations. Evidence that money
growth enters significantly when added to empirical Phillips curves suggests
misspecification or mismeasurement problems for those equations, rather than a
structural role for money.
4. The long-run relation between inflation and money growth is of relevance to
central banks in considering the implications of their policies for the steady-state
rate of inflation; and this long-run relation does deserve special attention as it has
no direct counterpart in the key equations governing inflation dynamics.
The above conclusions are closer to those of Taylor (1992) quoted in the
introduction than to most of the recent literature’s discussion of money. There is
agreement with McCallum (2001) that current models imply a steady-state role for
money in the determination of inflation, and, in contrast to Gall’s (2002) conclusion,
I argue there are grounds for highlighting that role. But McCallum understates the
extent to which current models allow inflation dynamics to be modeled using money
growth; the inflation dynamics in these models does not amount to a rejection of the
quantity theory. Rotemberg and Woodford’s (1997, p. 309) description of money as
having “no role” in determining inflation in New Keynesian models refers to the
absence of explicit terms in money in the IS and Phillips curves; it remains the case
that whether policy allows nonmonetary shocks to affect money growth is decisive in
determining whether those shocks shift inflation.
Nevertheless, most of the disagreement expressed here with recent discussions of
money and inflation is more with the letter than the spirit. Advocates of current
models have exaggerated the contrast with an approach that analyzes inflation in
terms of money growth. But insofar as a key message of Gall (2002), McCallum
(2001), Svensson (1999a, 2002), and others is that the control of inflation around its
steady-state value can be accomplished by a monetary policy framework that does
not respond explicitly to monetary aggregates, I would not disagree.34 There is no
merit in Alvarez et al.’s (2001, p. 219) claim that a “new theory” is required to
provide an underpinning for the inflation-targeting frameworks observed in practice.
It has been argued above that recent rejections of the AEMP proposition reflect
misinterpretations. The AEMP proposition indicates what a central bank must allow
(footnote continued)
pp. 325, 626) implies an endogenous money stock, but not a clear-cut direction of causality between money
and nominal income.
34 As argued above, ensuring that the actual steady-state value of inflation corresponds to the target rate
does lend itself to a role for money.




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E. Nelson / Journal of Monetary Economics 50 (2003) 1029-1059

to happen to money growth in order for inflation to proceed. It does not require a
belief that money demand is perfectly stable or that monetary aggregates play, or
should play, an explicit role in either price-setting or policy decisions. Appropriately
interpreted, it is an uncontroversial proposition, which explains why Mishkin (2001,
pp. 671-672)—a critic of giving monetary aggregates a role in policymaking (see
Estrella and Mishkin, 1997)—can conclude: “Recognizing that by inflation we mean
a continuing increase in the price level at a rapid rate, most economists agree with
Milton Friedman that ‘inflation is always and everywhere a monetary phenomen­
on,”’ and why Harry Johnson (1975, p. 14) observed of the quantity-theory
explanation of inflation, “the monetarists do not have a simple model, they have
truth.”

3. Money and the transmission mechanism
This section discusses the relationship between monetary policy and aggregate
demand, and the implied role for money. Section 3.1 establishes that real balance
effects are not an issue of dispute, then Section 3.2 turns to the crucial issue, namely
the role that money can play when both aggregate demand and money demand are
functions of several interest rates. Section 3.3 provides a brief demonstration of the
implications of this role for money in a modified New Keynesian model, while
Section 3.4 provides some conclusions.
3.1. Real balance effects
It was argued in Section 2 that the relevance of monetary growth for inflation did
not depend on the presence of explicit terms involving the money stock in the Phillips
curve. In considering the role of money in the transmission mechanism, we can
therefore focus on the aggregate demand side of macroeconomic models. I first
consider the following issue: Do theories that emphasize the significance of money
for aggregate demand require that terms involving the money stock should be added
to the IS function (1)?
Many discussions of monetarist vs. nonmonetarist views of the transmission
mechanism do proceed on this basis. As Brunner (1971b, p. 56) observed: “One
frequently encounters arguments which juxtapose the Keynesian view centered on
the interest rate mechanism with an alternative view centered on the money supply.”
In particular, both in the literature that Brunner described, and in more recent
discussions, many analysts attribute to monetarists a belief in the quantitative
importance of the real balance effect, i.e. the stimulus to consumption or aggregate
demand from the increment to real financial wealth that occurs when the real
monetary base increases. Walsh (1998, p. 213), for example, argues that “[d]uring the
Keynesian/monetarist debates of the 1960s and early 1970s, some monetarists argued
for a direct wealth effect that linked changes in the money supply directly to
aggregate demand.” More recently, Andres et al. (2001), Ireland (2001a), McCallum
(2000, p. 883) and Woodford (2003, Chapter 2) have looked at the dependence of the




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1047

marginal utility of consumption on real money balances.35 These studies uniformly
find that the role for money in the IS equation that arises from nonseparable utility is
quantitatively negligible. Similarly, work on the traditional real balance effect in
macroeconomic models established that it was unimportant (e.g. Dornbusch and
Fischer, 1994, p. 126), owing to the negligible contribution of base money to
financial wealth.
Since theory and evidence do not provide support for an important real-balances
term in the IS function, is the monetarist view of the transmission mechanism
rejected? A careful reading of the work by key monetarists indicates that the answer
is no. In this regard, an important distinction must be made between arguing that
there are many transmission channels of monetary policy—as Friedman, Schwartz,
Brunner, and Meltzer certainly did36—and claiming importance for the real balance
effect—which they did not. Friedman (1972, p. 947) stated unambiguously, “I never
have believed that the real balance effect is of much empirical significance”, while
Brunner and Meltzer’s model of the transmission mechanism was one in which
monetary policy can stimulate the economy through means other than short-term
interest rates, and “does not depend on the real-balance effect” (Brunner and
Meltzer, 1968, p. 29).
In fact, not only was the traditional real balance effect not central to monetarist
work, but monetarists also did not claim that terms involving money appeared
directly in the structural equations describing aggregate demand determination.
Brunner (1971b, p. 56) noted of his model: “The money supply does not even occur
as a variable in the system”—i.e., his IS equation contained no explicit term
involving money—and this view of the transmission mechanism was shared by other
monetarists. Thus Mayer (1978, pp. 7-8), reviewing the monetarist literature, noted
that “one can reformulate the monetarist story in terms of the interest rate” , while
Friedman and Schwartz (1982, p. 58) described monetary expansion as “rais[ing] the
price of assets and reducing] interest rates”, their difference with Keynesian analysis
being that “market rates... [are] only a small part of the total spectrum of rates that
are relevant” for aggregate demand. The significance of the money stock emerges in
this analysis not via a direct real balance effect on aggregate demand, but because
money can serve as an index of the “spectrum of rates”—or, as Meltzer (2001,
p. 125) puts it, “real money balances capture the many channels of monetary
transmission.”37
Before discussing this role of money in more detail, the key point should be
emphasized that a “monetarist” model does not require either the existence of the
real balance effect or any explicit term involving the money stock in the IS equation.
Similarly, evidence that nonseparability in utility is unimportant does not provide
35Woodford (2003) interprets this dependence as the counterpart in an infinite-horizon model to the real
balance effect. Ireland (2001b), however, derives a distinct real balance effect in an infinite-horizon
optimizing model that does not require nonseparability in utility.
36As Artis (1993, p. 238) notes, “[t]he monetarist literature of the 1960s is full of suggestions to [the]
effect” that “the focus on a narrow set of interest rates unduly restricts the perception of what monetary
policy can (and does) do.” For specific references, see footnote 6 above.
37See also Friedman and Schwartz (1970, p. 126).




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relevant evidence against monetarist views of the transmission mechanism. And the
proxy role for money arises from its ability to serve as an index of substitution
effects, rather than wealth effects of monetary policy. This emphasis on substitution
rather than wealth effects is consistent with present models.
It might nevertheless be noted that the fact that only a single interest rate appears in
the IS function, Eq. (1), itself constitutes a rejection of monetarist views of the
transmission mechanism. I would, however, argue against this interpretation. Eq. (1)
is only a baseline specification; plausible generalizations, such as detailed modeling of
physical capital formation, would mean more asset prices appearing explicitly in the
model structure. More generally, use of models in which only the short rate appears
should not be regarded as a rejection of the empirical importance of multiple
transmission channels. Consider, for example, Dombusch’s (1980, p. 71) view that
monetary policy has “effects through changes in explicit or implicit real interest rates
on aggregate demand.” This is a clear endorsement of Friedman and Schwartz’s
(1963a, p. 61) outline of the transmission mechanism, according to which the interest
rates relevant for aggregate demand are a “broad construct, covering explicit or
implicit rates on the whole spectrum of assets.” Yet in Dornbusch and Fischer’s (1994,
Chapter 4) exposition of the transmission mechanism, the only interest rate relevant
for aggregate demand is the yield on short-term securities. This simply illustrates the
principle that, while recognizing many distinct assets “is clearly correct for some
purposes..., disaggregation provides benefits but also costs, so two-asset models will
often prove convenient and satisfactory” (McCallum and Nelson, 1999a, pp. 298299).38 For this reason, some monetarist work specifies only a single rate in the IS
equation—e.g. Brunner et al. (1980), where the focus is on aggregate supply behavior.
Another important respect in which Eq. (1) is consistent with the basic
transmission channels stressed by monetarists comes through its forward-looking
nature. The expected-future-output term in (1) renders expectations of future real
short rates—and so the real long rate—relevant for the private sector’s current
spending decision. In this respect, the model’s transmission mechanism is broader
than textbook IS-LM analysis in which only the short rate is relevant for spending
decisions, and represents a shift in the direction advocated by monetarists. Indeed,
this forward-looking property of aggregate demand allows a potentially important
role for money as an indicator of macroeconomic conditions. This role for money,
however, cannot be separated from the issue of the specification of the money
demand function in present models. As I now discuss, this is one area where current
models do differ sharply from the specification advocated by monetarists.
3.2. The monetarist transmission mechanism
Accepting that monetary policy exerts effects on aggregate demand by influencing
a variety of yields does not, by itself, imply attaching greater significance to the
38 This is also the position of Brunner (1989, p. 210). Anna Schwartz (in December 11, 2002 comments)
notes that modern two-asset models do distinguish between nominal and real interest rates, which
represents an advance on much of the policy discussion that monetarists criticized in the 1960s and 1970s.




E. Nelson I Journal o f Monetary Economics 50 (2003) 1029-1059

1049

money stock. Under what conditions will monetary aggregates have the properties
claimed of them by monetarists—namely that they are a good index of the
movements in yields that drive the economy? It is here that New Keynesian models
do differ sharply from monetarist analysis, and where the former could most benefit
from modification. This section lays out the argument, then Section 3.3 demonstrates
its potential quantitative importance by applying the optimal-indicator framework
of Aoki (2002) and Svensson and Woodford (2002).
I argue that a vital element of monetarist analysis absent from current models is
the money demand function of Friedman (1956), where a spectrum of yields enters
the money demand function. This is in contrast to the LM function both of
traditional textbook analysis and current models, in which the return on short-term
nominal securities is the sole opportunity-cost variable. A Friedman-style money
demand function can produce the property that money summarizes monetary
conditions not contained in short-term interest rates. Essentially, if the same
spectrum of yields enters both the IS and the LM equations, then the behavior of
money could be a useful proxy for the yields.
In the most broad specification of Friedman’s demand function, the yields that are
relevant for money demand include yields beside those observed in securities
markets, such as the returns on physical assets like property (e.g. Friedman and
Schwartz, 1982, pp. 39-40, 261; Laidler, 1982, p. 113). Empirically, this is likely to be
an important advantage of money, since monetary aggregates are probably more
directly observable than the complete set of yields that matter for aggregate demand.
For the present discussion, however, it is useful to concentrate (as in Nelson, 2002)
on a version of Friedman’s money demand function that differs from the standard
LM relation only in emphasizing the nominal return on long-term securities rather
than the short-term return as the cost variable.39 A money demand specification of
this form was the baseline empirical specification used by Meltzer (1963), while
Brunner (1983, p. 50) argued that the fact that “[ajspects of term structure are
explicitly recognized” in Friedman’s analysis is a key reason why “[h]is formulation
is not subsumable under a Keynesian view of the transmission mechanism.”
The Friedman money demand function is decidedly out of favor in current
theoretical analysis. Analysis of money demand functions based on optimizing
analysis, such as McCallum and Goodfriend (1987) and Lucas (1988), rejects
Friedman’s specification both in its general form and in the specific form where the
long-term interest rate is a relevant opportunity-cost variable. McCallum and
Goodfriend argue that Friedman’s analysis did not constitute a “formal theory of
money demand” (1987, p. 779), and, from their analysis of optimizing behavior in
the Sidrauski-Brock model, find the current short rate to be the relevant
opportunity-cost variable. Lucas (1988, pp. 142, 150-151) similarly concluded that
the only cost variable for money demand should be the current short rate, and that a
money demand function incorporating other yields would be nonstructural. Yet this
theoretical expectation has been contradicted by the empirical findings of Anderson
and Rasche (2001) and Meltzer (1998), who document a close relationship between
39Early Keynesian work also focussed on the long-term rate, as King (1999, p. 39) notes.




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E. Nelson / Journal o f Monetary Economics 50 (2003) 1029-1059

monetary base velocity and the long-term interest rate in the United States over the
twentieth century. These results have been buttressed by Gerlach and Svensson’s
(2002) finding that the long-term interest rate enters a money demand equation
estimated on euro area data. All in all, empirical work documents a robust role for
the long-term interest rate in the LM relation.
In fact, a money demand function in which the long-term interest rate is the most
relevant opportunity-cost variable can be justified by optimizing analysis. Modest
portfolio adjustment costs imply dynamics in money demand adjustment; and, in an
optimizing model, such dynamics imply that expected future short rates, and so the
long rate, are relevant for today’s money demand decision. The model used below
features such a money demand function.
3.3. Application: the value o f money to monetary policy
In Nelson (2002), I showed that a general demand function of the Friedman/
Meltzer form conferred on money significant information in predicting output not
contained in short-term interest rates.40 Here I reconsider the information content in
money by reexamining my model in light of recent work by Aoki (2002) and
Svensson and Woodford (2002) on optimal monetary policy when current privatesector shocks are not observable to the central bank. This focus on the efficient use
of information sheds light on the short-run role of money in monetary policy.
Stabilization of inflation around target without reference to money is feasible, but is
it desirable? Or does attention to money provide information that aids stabilization?
Coenen, Levin and Wieland (CLW) (2001) and Dotsey and Hornstein (DH) (2003)
consider the information content of money using the Svensson-Woodford methods
in an environment where current output is not observed. In contrast to these papers,
I investigate the optimal commitment policy. There are also fundamental differences
between the model specification and information structure employed here and those
in CLW and DH. CLW’s model, particularly its IS-LM block, is not based on
optimizing behavior. In addition, CLW assume symmetric information on the part
of the private sector and monetary authority which, as discussed below, is
problematic in an optimization-based model. DH assume asymmetric information
and their model is optimization-based, but they employ a conventional money
demand function such as Eq. (4), according to which the quantity of money
demanded is a static or backward-looking function of short-term nominal interest
rates and output. Variation in money not associated with current or prior short-rate
and output movements is uninteresting noise—money demand shocks—that
undermines the value of money as an indicator.41
Suppose, however, that the true money demand function is of the FriedmanMeltzer type. Then some of the variation in money not explicable using standard
40In a formal multivariate analysis, Leeper and Roush (2002) produce additional support for this result.
41Similarly, the role advocated by Soderstrom (2001) for money growth depends on money being a
linear combination solely of current (or current and lagged) values of the nominal interest rate and
nominal GDP.




E. Nelson / Journal o f Monetary Economics 50 (2003) 1029-1059

1051

money demand functions reflects movements in yields beside current short-rate
movements, as well as reactions to expected future income. These variations in
money, rather than being noisy money demand shocks, are useful to policymakers
because they are informative about future movements in output. I now demonstrate
the impact of using a Friedman-Meltzer type money demand specification on the
value of money to policymakers.
The model includes Eqs. (l)-(3). The structural equations of the model are
completed by the money demand function
( m - p ) t = Hi E,(m - p)t+i + n2(m - p)t_ i + nyy t + nRR t + 1]„

(6)

where the forward-looking terms and lags arise from portfolio adjustment costs.
Because money does not appear in Eqs. (l)-(3), the model continues to have the
standard property of New Keynesian models that money does not enter explicitly as
a state variable in the solutions for output and inflation unless policymakers respond
to money. Other methods of putting the long-term interest rate into the money
demand function would, however, imply an explicit term in money in the
households’ optimality conditions for optimal bond-holding, and so also in the
solution expressions. Suppose we introduced explicit long-term government
securities as in Woodford (2001, Section 1.3) and, furthermore, allowed for
imperfect substitutability between assets. To be specific, suppose that, for prudential
reasons, households were unwilling to acquire long-term securities without
simultaneously adding to their holdings of base money by a fraction of the increase
in bond holdings.42 Then the expression for wealth in the household’s period budget
constraint would be augmented by a term such as f ( M t/Bf+l), where/i(®) > 0, M t is
the household’s nominal money holding at the end of period t, and Bf+l denotes
nominal long-term bond holdings carried over into t+ 1; and derivatives of this
function would appear in the household’s first-order conditions for money and long­
term bond holdings. Analogous assumptions could be made about household
acquisition of equity, foreign exchange, or other assets. Such self-imposed “reserve
requirements” on households’ asset acquisition have the dual effect of bringing these
asset yields into the money demand function, as in Friedman (1956), and putting
terms involving money into the arbitrage conditions governing asset-price behavior.
Thus, a Friedman-style money demand function makes “risk premia” for long-term
government debt or foreign exchange dependent on the quantity of money, as noted
by Brunner (1989, pp. 209-210), King (1999, pp. 39-41) and Meltzer (1999, p. 274).
However, to emphasize that the value of money to policymakers does not depend on
42 That money might serve such a prudential function is in keeping with Friedman and Schwartz’s
argument that money has a role as a temporary abode of purchasing power separate from its function of
facilitating current-period transactions (e.g. Friedman, 1961b, p. 263; Friedman and Schwartz 1970,
pp. 112, 125, 137; 1982, pp. 24, 39, 262). In an interview with the present author on January 22, 1992,
Friedman expressed the view that the temporary-abode function was more important than the medium-ofexchange function, citing as an example the increases in households’ desired real quantity of money during
wartime emergencies. This perspective was also clear in a 2001 press interview (Campbell, 2001) in which
Friedman observed, “there’s no doubt that one of the effects of September 11 will be to increase the
demand for cash balances.”




E. Nelson I Journal o f Monetary Economics 50 (2003) 1029-1059

1052

its presence in the structural equations, I do not make use of this extension and
instead use model (l)-(3) plus (6). For present purposes, it is not necessary to depart
from the assumption of perfect asset substitutability, as Eq. (6) takes us sufficiently
close to a general Friedman-style demand function.
As in Aoki (2002), I use the social loss function:
00

(7)
which is consistent with private sector utility maximization (see Woodford, 2003).43
With private-sector behavior given by Eqs. (l)-(2) and private-sector shocks
known to the central bank, complete stabilization of the output gap and inflation is
possible. This can be achieved if monetary policy reacts to lagged information and
current shocks in such a way as to make the real rate rt coincide with its natural value
each period. When, however, current shocks are not observable to the monetary
authority, complete stabilization is infeasible, as discussed by Aoki (2002) and
Svensson and Woodford (2002). The asymmetric-information assumption used in
these papers is an attractive one in a representative-agent model where shocks arise
from the private sector. Since, as Aoki notes, innovations in potential output y*
reflect shocks to private productive capacity, it follows from the representativehousehold setup that the aggregate potential GDP shock is known to the private
sector. And the IS disturbance vt should certainly be known to private agents, if
interpreted as a shock to the household’s period utility function.44
Following Aoki (2002), I assume that the central bank in period t does not observe
current shocks but does have accurate observations on all lagged data and shocks,
and, in addition, observes a vector Z t of “noisy” observations on certain period-?
data. In Aoki’s framework, Z t consists of error-ridden observations y ° and n ° on
current log output y t and inflation nt. I augment this information set by assuming
that the central bank can observe current-period nominal money growth Amt. Its
observation on this variable is without error, but, since the money demand function
(6) contains a money demand shock term rjt, money growth is “noisy” from the
perspective of extracting information about variables beside money.
As Aoki shows, in this environment, the optimal monetary policy under
commitment takes the form
4 • Rt —4 •

+ r(Zt —

(8)

where 4 • R t is the annualized nominal interest rate, r*t_x is the period t — 1
expectation of the period-? natural real interest rate,45 A is a vector of response
coefficients to the lagged Lagrange multipliers (f>t_x that appear in the central bank’s
first-order conditions under commitment, and r is a vector of optimal responses to
the indicators.
43Utility from real balances is neglected in calculating welfare.
44See McCallum and Nelson (1999a, b) for a derivation of Eq. (1) that implies this interpretation of vt.
45An explicit expression for r* (in terms of current vt, y* and expected next-period y f) is obtained by
evaluating Eq. (1) under price flexibility.




E. Nelson / Journal o f Monetary Economics 50 (2003) 1029-1059

1053

Table 1
Optimal coefficients on indicators in interest-rate rule (8)
Coefficient in r response vector on

o
II
Hi = 0.47

0.262
0.262

1
o-s1

(x? -

3.631
3.631

(Am, - Amr(,_i)
0.170
0.235

Note: Numbers in the table give the optimal monetary policy responses to news in data on inflation,
output, and nominal money growth, both in the case of a standard money demand function (jix = 0) and a
function incorporating Friedman-Meltzer features (n\ > 0).

In calibrating the model, I set the money demand adjustment coefficients to jix =
0.47 and n2 = 0.48, in line with my 2002 paper. I set the remaining coefficients to
imply long-run scale and interest elasticities of 1.0 and —0.5, and assume a whitenoise money demand shock rjt with standard deviation 1%. I follow Aoki in setting
the Phillips curve parameters to /? = 0.99 and a = 0.024, and the weight a in the
welfare function (7) to 0.047. However, Aoki’s calibration of the intertemporal
elasticity of substitution (<r), based on Rotemberg and Woodford (1997), implies
extremely interest-sensitive aggregate demand—out of line with most empirical
estimates, and too high to respect a cross-equation restriction which links the IS and
money demand elasticities. I use a more moderate value of a = 0.5. For the vt and y f
processes, I assume AR(1) parameters of 0.33 and 0.99, respectively, with
corresponding innovation standard deviations 1.1% and 0.7%—again, more in line
with econometric estimates than are Aoki’s choices (see e.g. Ireland, 2001a;
McCallum and Nelson, 1999b). Following Aoki, y f and n f are assumed to differ
from y t and nt by white-noise measurement errors with standard deviations 0.89%
and 0.35%, respectively.
Using Aoki’s (2002) fixed-point algorithm, I obtain the optimal responses in rule
(8) to the indicators both in the case
= 0 and 0.47.46 These cases have the same
impact income and short-rate elasticities for money demand, but in the
> 0 case,
money demand also depends on the long rate, and so on an additional interest rate
relevant for aggregate demand. The results are given in Table 1. Relative to the
Hi = 0 case, the optimal response of policy to money growth rises by about a third.
In effect, a model specification in which money serves as a proxy for yields beside the
short rate has enhanced the value of money to monetary policy, even though this
specification has not added money to the structural IS or Phillips curve relationships.
In the words of Brunner (1971b, p. 57): “The role of the money stock as an indicator
is thus shown to be totally independent from its occurrence as a variable in the
system.”

46 An appendix (available on request) describes the generalization of Aoki’s solution procedures
required to accommodate the endogenous state variable (m —p)t_x.




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E. Nelson / Journal o f Monetary Economics 50 (2003) 1029-1059

3.4. Money and the transmission mechanism: conclusions
1. In contrast to the case of inflation dynamics, where there is no theoretical
expectation that money has explanatory power for inflation given the output gap,
there are grounds for expecting money to have information about aggregate
demand for given short-term interest rates.
2. This expectation is based on the possibility that money might serve as a
proxy for a variety of yields that matter for aggregate demand. This
indicator or proxy role for money is consistent with monetarist models
of the Brunner-Meltzer or Friedman-Schwartz variety. Those authors
were clear that in their framework, the structural equations for aggregate
demand determination had many relative prices and yields, but no explicit
money term.
3. In particular, monetarist models do not insist on the importance or presence of a
real-balance or wealth effect of money on aggregate demand.
4. Equally, models in which the only effect of monetary policy is via a
short-term interest rate are, by themselves, not inconsistent with the quantity
theory, although they may neglect empirically important channels of monetary
policy.
5. A key modification to current models that would enhance the role of money is to
generalize money demand functions so that, as in Friedman (1956), they include
opportunity-cost variables beside the nominal short rate. Such a modification is
consistent with empirical work on money demand.

4. Conclusions
The detailed conclusions of this paper are given in Sections 2.6 and 3.4
above. Here I simply observe that for cyclical analysis the most fruitful area in
which money can play a greater role is as a proxy for yields that matter for aggregate
demand, some of which do not have a ready counterpart in securities-market interest
rates. Associated with this is a more general specification of New Keynesian models
to include, as in Friedman (1956), a spectrum of cost variables in households’
money-holding decision. This proposed modification does not overturn the
legitimacy of concerns about the problems of measuring money in practice. But
measurement and instability problems are not isolated to relationships involving
money; the IS and Phillips curve relations also involve unobservable shock terms,
and it is likely that both the shock processes and the structural parameters in these
equations exhibit some nonconstancy. Nor does the contention—which the analysis
above has endorsed—that money does not appear explicitly in either the Phillips
curve or IS function, justify not bothering to model money. The information
imparted to money by its relationship to yields that matter for aggregate demand,
gives money value to monetary policy, even when money is absent from the key
structural relationships.




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1055

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