ISSN 1561081-0
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WORKING P
APER SERIES
NO 756 / MA
Y 2007
MAINTAINING LOW
INFLATION
MONEY, INTEREST RA
TES,

AND POLICY ST
ANCE
by Samuel Reynard
In 2007 all ECB
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WORKING PAPER SERIES
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1 The views expressed in this paper do not necessarily reflect those of the Swiss National Bank. This paper was prepared for the
Carnegie-Rochester Conference Series on Public Policy: “Mainstream Monetary Policy Analysis Circa 2006: Are There Reasons for
Concern?”, Pittsburgh PA, November 10-11, 2006. I am grateful to Marvin Goodfriend, Robert Lucas, Ben McCallum, Ed Nelson
and an anonymous referee, as well as CRCSPP, ECB Monetary Analysis Workshop and Econometric Society 2007 Winter Meeting
participants, for helpful discussions and comments. John Cochrane kindly provided me with data on bonds excess returns, and
euro area data were kindly provided to me by the ECB Monetary Policy Stance Division.
2 Swiss National Bank, Research Unit, Boersenstrasse 15, 8022 Zurich, Switzerland; Phone: +41 44 631 3216;
e-mail:

MAINTAINING LOW
INFLATION
MONEY, INTEREST RATES,
AND POLICY STANCE
1
by Samuel Reynard
2
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ISSN 1561-0810 (print)
ISSN 1725-2806 (online)
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Working Paper Series No 756
May 2007
CONTENTS
Abstract
4
Non-technical summary
5
1. Introduction
8
2. Empirical weakness of interest rate rules and
stance measures
14
2.1. Interest rate stance and inflation objective
15
2.2. Implicit vs. realized inflation and
equilibrium interest rate assumption
18
2.3. Implications for monetary policy analysis
and practice
20

3. Money, prices and output
22
3.1. Monetary aggregate choice and
adjustments
22
3.2. Characterizing the money-output-price
empirical relationship
26
3.3. Money usefulness in policy and inflation
dynamics analyses
33
4. Monetary analysis, Phillips curves, and
apparent changes in inflation dynamics
40
5. Conclusions
44
Appendix A: Money demand
46
Appendix B: Equilibrium velocity adjustment
48
References
49
Tables and figures
53
European Central Bank Working Paper Series
69
Abstract
This paper presents a systematic empirical relationship between money and
subsequent prices and output, using US, euro area and Swiss data since the
1960-70s. Monetary developments, unlike interest rate stance measures, are

shown to provide qualitative and quantitative information on subsequent in-
flation. The usefulness of monetary analysis is contrasted to weaknesses in
modeling monetary policy and i nflation with respectively short-term interest
rates and real activity measures. The analysis sheds light on the recent change
in inflation volatility and persistence as w ell as on the Phillips curve flattening,
and reveals drawbacks in pursuing a low inflation target without considering
monetary aggregates.
JEL classification: E52; E58; E41; E3
Keywords: Monetary policy; Monetary aggregates; Inflation; Output; Tay-
lor rule; Equilibrium int erest rate
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Non-Technical Summ ary
No w adays mainstream monetary policy analysis is done without reference to m on-
etary aggregates. M oneta ry policy is described with a short-term in terest rate, as
proposed by Taylor (1993), and it is usually argued that, ev en with a stable money
demand, m onetary aggregates are not useful for monetary policy. In this paper I
discuss the usefulness of monetary aggregates versus interest rates for modeling mon-
etary policy and measurin g mon eta ry policy stance, using stylize d facts observed o ver
the past 30-40 y ear s in the US, the euro area, and Switzerland.
I first show that using in terest rates as a measure of policy stance, i.e. the gap
bet ween th e o bserved 3-mo nth interest rate and t he p r escribed Taylo r r ule interest
rate, does not provide useful i n forma tion regarding subsequent inflation. Focusing on
in terest rate develop m ents relative to a “ neu tral” interest rate is thus not helpful for
centralbankerswhowanttoachieveagiveninflation objective. M oreo ver, the paper
points to em pirical weak nesses of New Keynesian m odels linear ized around a given
trend inflation and w here inflation swings a re attributed to policy o bjectiv e changes.
In con trast, moneta ry developments pro vide qualitative and quantitative inform a-

tion on subsequen t price and output developments. Two elements hav e to be taken
in to account however. First, m on etary aggregates must be adjusted by equilibrium
in terest rates, w hich can be approximated by a b ackw ard -looking filter, to accou nt
for the fact that people hold relatively more real mo ney ba lances w h en in flation and
in terest rates decrease, and vice versa. Not accou nting for these equilibrium velocity
c ha nges blurs the m on ey/p rice relation sh ip an d results in th e less than one-for-on e
(except in short disinflatio n or accelerating inflation samples, where this results in
more than one- for-one) and o ften insignificant relationship s between m o ney grow th
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and inflation rates found in the literature. Second, an important stylized fact is that
in the econ omies and periods considered, in con trast to money levels, p rice levels
do no t d ecrease. This asym m etr ic p rice behavior induces a source of b ias i n l inear
econom etric estimates of studies assessing the effect o f money gro wth on inflation and
comp licates the use of money grow th rates to assess inflation risks. Therefore, a n aly-
ses of money and price lev els are necessary for short-term policy purposes. Findings
are robust to differen t m oney d efinitions and money demand specifications.
It is commonly argued that the long-run relationship between money growth and
inflation stems only from a mon ey demand relationship and is of no r eleva nc e for
the h or izon of interest of central ban ks. It is also claimed that sho r t-term velocit y
mov em ents due to implicitly accommodated m o n ey demand sh oc k s — i.e. through an
in terest rate based policy — or to monetary policy r eactin g to other f un dam ental eco-
nom ic shocks blur the short-term relationship between money and prices, especially
in low inflation econom ies. It is further argued th at, as a result, w ith a su ccessful
inflation targ eting strategy the link between money g rowth a nd in flation should van-
ish. In co ntrast to those claims, the presen t paper sho ws that when the relationship
bet ween p rices and m on ey is characterized in a way that a ccounts for equilibrium
v elocity changes and prices’ asymmetric behavior, significant monetary developments

are in every case follo wed by corresponding price developments. Furthermor e, w e
do not observe significant price movem ents not preceded by corresponding m on etary
movemen ts. The considered velocity “shocks” pro vide informa tion on subsequent
prices and output, pointing to a weakness of m odels that r epresent policy actions
with a short-term interest rate only. Moreover, the quantitative importance of other
economic shocks to inflation is sm a ll in the samples c o nside red . Conseq u ently, a
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successful inflation targeting strategy would result in mon ey (adjusted by poten tial
output) and pr ices gro w ing at the same rate. In s ummary, monetary dev elop m ents
can be used to cha racterize inflationtrendsaswellasfluctuations around these trends,
and provide early information on these inflation developmen ts.
Monetary regularities are t h en used to assess th e forecasting efficienc y of Phillips
curves and to shed light on recent chang es in inflation pattern s, especially on inflation
reduced persistence a nd v olatility as w ell as on the flatt ening of the Phillips curve.
Seen from the angle of monetary aggregates, monetary policies since the early-1990s
have been rather restrictive in term s of lo w money lev els relative to price lev els. Given
theasymmetricpricebehavior,thishaskepttheinflation ra te at a relatively constant
low value while output has m ostly been belo w poten tial, con tributing to a w eak er
relationship between output gaps an d inflation. In other w ords, more liquidity could
have been provided to sustain real ac tivity w itho u t resulting i n significantly h igh er
inflation. Giv en that w e observ e price increases when policy is expansive but do not
observe price decreases when policy is restrictive, a focus on a low inflation target
without considerin g mon etary aggrega tes runs the risk of being too restrictiv e on
averageaspolicyeffects on output appear to be symmetrical.
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1. INTR OD UCTION
There is nowadays a large gap bet ween mainstream monetary policy analysis and
policymakers’ c oncerns. Most models curren t ly used for policy analysis or forecasting
are linearized or no rm alized arou nd an in flation steady state or trend . In these m odels,
the central bank announces an inflation t a rge t, the public believes in th e abilit y of
policymakers to reach this target, a nd central bank ers know ho w to move a short-term
in tere st rate as a function of unobservab le real equilibrium interest rate and economic
shocks in order to remain on that target and conduct optimal cyclical policy. These
“normalized” monetary policy analyses and estimations are in fact focusing on small
inflation deviations from an exogenou sly given steady-state or “trend inflation”.
In ord er to fit the data, which are c haracterized b y substantial and long-lasting
inflation swings, differ ent assum ption s ha ve been ma de regarding “ trend inflation”.
Som etime s, a consta nt steady-state inflation is assu m ed , w ith m ajor inflation fluctu-
ation s “explain ed ” by “sunspot equilibria”. Sometimes , “trend inflation” is modeled
as an exogenous random w alk or is identified as a model residua l once “stru ctural”
restrictions have been imposed on the data, and is in terpr eted as a moving inflation
target with ho wev er no evidence of a correspondence between the resulting “trend
inflation” and a ctual central banks’ objectives. In em pirical w ork, inflation is u su ally
detrended, in a d eterministic o r stochastic wa y. Analyses are thus trying t o explain
only one p art of in flation mo vements, which m o reover ha ve been decomposed in an
arbitrary w ay. At the other extreme of assuming a constant steady-state inflation,
every inflation mo vemen t could be attributed to a c hange in policy target!
An implication of those analyses is th at policymak ers’ preferences can be expressed
in the form of a loss function : cen tr al banks in tha t world car e about m in imizing
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inflation deviations around a giv en target and output deviations around its poten-

tial. Such a loss function has been explicitly deriv ed from theoretical models and is
extensiv ely used in m on etary policy analysis.
Such an analysis is at odds with policymak ers’ concerns and beha v ior. The main
concern of central banks an d o f th e population in general, and what matters for wel-
fare, is not small inflation deviation s aroun d a given steady state but rather a drifting
away from low inflation tow ards higher inflation or deflation. Whether inflation is at
1.7 r a the r than 1 .3 percen t i s not o f mu ch importance. Mon etary policy c anno t
fine-tune and contr ol suc h small orders of magnitudes, a nd inflation is not perfectly
measu red anyway. No wadays, most central ba nks hav e, im p licitly or explicitly, an
adm iss ib le range for inflation, and their concern is to preven t inflation from drifting
substantially and persisten tly above or belo w that range. The position of the inflation
ratewithinthatrangeisnotimportantaslongasitisandisforecastedtoremainin
the desirable ran ge. Th us, the inflation developm ents w hich need to be explained are
the high i nflation of the 1970s, th e subsequen t disinflation, the temporary inflation
increase in the late 1980s / early 1990s, as well as the low and stable inflation there-
after. It is h owe ver evident from policymakers’ pub lic sta tements tha t i t is neith er
clear where the neutral inter est rate is, nor how far one should be from it in a giv en
econom ic situation in order to obtain a desired inflation rate.
Monetary policymakers need to have some quantitativ e guidelines regarding price
developments after policy lags — which a re one re gular ity documented in this p aper —
have taken effect, in order to a void the substan tial and long-lasting inflation swings
c ha racterizin g any coun t ry’s time series da ta. A wait-and-see approach carr ies the risk
of “being behind the curve” or, on the opposite, “overdoing it”. This paper assesses
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the usefulness of m o netary aggregates in prov iding these guidelines and c o ntrasts
mon etary analysis to the current mainstream m on etary policy analysis.
The pa per presents a systematic empirical relationsh ip between mo ney an d su b se-

quent prices and output that man y em pirical studies have claimed to be non-existent,
provides an explanation for these latter results, discusses the usefulness of mon etary
developmen ts as m onetary policy stance m easures, and contrasts monetary analysis
to current mainstream moneta ry policy analysis and inflation dy na m ics m odeling. As
argued by Orphanid es (2003), giv en ou r limited kn owledge of economic dyna m ics and
the resulting fact that various models w ith different im plications f or inflation dynam-
ics coexist in the literature, evaluating stance m easures based on h istorical macr o-
econom ic developments for practical monetary policy purposes requires an an alysis
that is not dependent on specific models. In addition, the stylized facts presented in
this pa per sugge st in he rent instability of r educ ed -form estimated inflation equation s.
Furthermore, as discussed abo ve, e xisting macroeconom ic models that have tried to
incorporate microeconomic foundations are linearized around a giv en “trend infla-
tion”, whic h is not appropriate to address the issu es of interest for t his study. This
analysis is of course no substitute for structur al m odel building, but it pro vid es styl-
ized facts that structural m odels d esign ed to model i nflation dynam ics and address
mon etar y policy issues should be able to replicate.
I use U S, euro area a nd Swiss data. These economies ha v e had different structures
and policy regimes. The Federal Reserve has a dual mand ate with no explicit inflation
target and h as been confronted with very differen t i nflation environments during the
post-war period. The euro area is an aggregation of individual coun tries with different
pre-euro policies and experiences. Finally, the Swiss National Bank had m oneta ry
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targets till the end of the 1990s and has been characterized as a precursor of the
inflation targeting approach (see Bernanke, 1998). The Swiss case is also interesting as
there hav e been several distinct inflationenvironmentseventhoughaverageinflation
has remained one of the lo west in the world. The samples considered are thus from lo w
inflation eco nomies, with howev er significan t changes in inflation environments and

monetar y policy responses. These characteristics allow us t o address critiques t hat
the relationship between money and inflation is w eaker in low e r inflation en vironments
and depends on monetary policy regimes.
In section 2, I first sho w that using interest rates as a measure of policy stance,
i.e. the ga p bet ween the observed 3-mo nth interest rate an d t h e p rescribed Taylor
rule interest rate, does not provide useful inform a tion r egar din g sub sequ ent inflation
rates. Focusing on interest rate dev elopmen ts relative to a “neutra l” rate is thus not
helpful for centr al bankers wh o wan t to ach ieve a given inflation objectiv e. M ore-
o ver, the evidence poin ts to empirical w eakn esses of modeling monetary policy with
a short-term in terest rate. Ana lytically, t he average or steady-state inflation rate in
such models is determined by the centr al bank’s objectiv e specified explicitly in the
Taylor rule. However, the facts presen ted here reveal that observed inflation deviates
substantially a nd persistently from the im plied inflation objective. I n other w ord s,
the equilibrium real in t erest rate that a central bank would ha ve to assume in or-
der for average inflation to equal the inflation target d oes not take plausible values.
Consid eration s on tren d inflationandequilibriuminterestratehavebeenoverlooked
in m oneta ry policy an alyse s. I question the u sua l interpretation of C la rida , G alí a nd
Gertler’s(CGG,2000)results,whichisthatthe1970sintheUSprovideanempirical
example of a high a v erage inflation an d a lo w real in terest rate as a result of too soft
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an in ter est rate reaction to expected inflation increases.
Section 3 presents a systematic empirical relationship between money and sub-
sequent prices and output. In c ontrast to interest rate stan ce measures, monetary
developmen ts pro vide qualitative and quantitative information on subsequent price
level a nd inflation dev elop m ents. Two elements h av e to be taken into account how -
ever. First, monetary aggregates must be adjusted b y equilibrium velocit y chang es,
which can be appro ximated with a backw ard-looking filter, to a ccou nt for the fact

that people decrease their real money balances when inflation and inter est rates in-
crease, and vice versa, inducing money movem ents without corresponding effects on
subsequen t inflation. Second, an importan t stylized fact is that in the economies and
periods considered, in contrast to mo ney levels, price levels do not decrease. T h is
asym m etric p r ice behavior ind uc es a source of bia s in linear econo m etric e stim a tes
of studies assessing the effect of mon ey growth or real activity mea sures on inflation
and c om plicates th e use of m on ey gro w th rates to assess inflation r isks. Ther efore,
analyses of money and price lev els are necessar y for shorter -term policy purposes.
It is com m on ly argu ed that the long-term relation sh ip bet ween m oney growth and
inflation comes only from a money d emand relationship and that, even with a sta-
ble money dem and, money is not useful for horizons of interest to central banks. It
is also claimed that short-term v elocity mov ements due to implicitly accomm odated
money demand shocks — i.e. through an interest rate based policy — or to monetary
policy reacting to other fundamen tal econo micshocksblurtheshort-termrelation-
ship between m o n ey a nd prices, especially in low in flation econ omies. It is furth er
argued that, as a resu lt, with a successful inflation targeting strategy the link be-
t ween money gro wth and inflation should vanish. In contrast to those cla im s, this
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paper s hows that w h en the relationship bet ween prices an d money is characterized in
a way that acc ounts for equilibr ium velocity changes and prices asymmetr ic beha v -
ior, significant monetary dev elopments are in every case followed by corresponding
price d evelopments. Furthermo re, we do not obser ve significant price movemen ts not
preceded b y corresponding monetary mov em ents. Contrary to what is u sua lly argued
and modeled, what are considered as velocity “shoc k s” pro vid e information on subse-
quent price le vels and output, pointing to a wea kness of models that represen t policy
actions with a short-term interest rate only. M oreov er, the quantitativ e importance of
other economic shocks to inflation is small in the samples considered. Consequ ently,

a successful inflation t arg etin g strategy would result in money (adjusted by potential
output) and pr ices gro w ing at the same rate. In s ummary, monetary dev elop m ents
can be used to characterize inflationtrendsaswellasfluctuations around these tr ends,
and provide early information on these inflation developmen ts.
In sectio n 4, monetary regularities are used to assess the forecastin g efficiency of
Phillip s curves and to sh ed light on recent cha nges in inflation pa tterns an d estimated
relationsh ip s, i.e. o n inflat io n reduced persistence and volatility as well as on th e
flatte ning of the Phillips curve. Seen from the angle of m o neta ry aggrega tes, monetary
policies since th e early-1990s h ave been rather restrictive in terms of low money
levels relativ e to price levels. Given the asymmetric price behavior, this ha s kept th e
inflation rate at a relatively constant low value while outpu t has mostly been below
potential, contributing to a w eaker relationship bet ween outpu t ga ps and inflation . In
other words, m ore liquidity could have been provided to sustain real activity without
resulting in sign ificantly higher in flation. This reveals dra wbacks in pursuin g a low
inflation target without considering monetary aggregates: given that we observ e pr ice
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increases when policy is expansive but do not observe price decreases when policy is
restrictiv e, a focus on a lo w inflation t arget without con siderin g monetary aggregates
runs th e r isk of being too restrictive on aver age a s policy effects on output appear to
be symm etrica l.
2. EM PIRICAL W EAKN ESS OF INTEREST R ATE R ULES AND STA NCE
MEASURES
This section presen ts issues with modeling monetary policy with a short-term in-
terest rate and w ith a ssessing m o netar y policy stance with interest rate deviations
from in terest rate rules or from a “neutral” rate. The standard Taylor rule (Taylor,
1993) can be expressed as
i = r

∗
+ π
∗
+1.5(π − π
∗
)+0.5(y − y
∗
) , (1)
where i is a short-term nomina l inter est rate, r
∗
is th e equilibrium real interest rate
assumed b y the m onetary authority, π is the inflation rate, π
∗
is the inflation o bjectiv e
or target of th e cen tral bank, y is (log) real output and y
∗
is (log) real potential output.
Th e timing of variab les differs across studies, which consider past, current or future
deviations from stea dy state or trend .
The usefulness of such a type of rule, for cen tral bank ers as well as economic and
econom etric modelers, depends on the correspond ence between the inflation objectiv e
π
∗
and actual inflation at a horizon relevant for m oneta ry policy. P olicy m akers want
to h ave some g uidan ce on wh ere to set a short-term interest ra te in order t o obtain a
given inflation target at a given horizon. This issue has been o verlooked by focusing
on b usiness cycle analyses arou nd exogenous inflation trends, and by trying to fit
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May 2007
variations of this rule to observed interest rates without considering the relationship
bet ween the imp licit inflation objective π
∗
and actual inflation.
A c entral propert y of New Keynesian models is tha t av era ge i n flation equals th e
chosen inflation target π
∗
if policymakers set r
∗
equal to the equilibrium (averag e) real
in terest rate
1
. A policy rule such as equation (1) thus “closes” New Keynesian m odels
in the sense that it determines avera ge inflation set by the mon eta ry authority. Fo r
examp le, Woodford (2 00 6, p.13), rep lying to a t heo retical argumen t raised by N elson
(2003, sec.2.2), statesthat“thetrendinflation rate is also determ ined within the
system: it c orresponds to the c entral ban k’s target r ate, in corporated i n the policy
rule”. I how ever argu e i n this section tha t there is no useful empirica l r elation ship
bet ween the im plied π
∗
in an in terest rate setting corresponding to equation (1) and
actual in flation, b y analyzing the relationship between these variables under three
different but related angles.
2.1. INTEREST R ATE STANCE AND INFLATION OBJ ECTIVE
The firstapproachistoevaluateinterestratestancemeasuresbycomparingthe
observed n om ina l inter est rate to the Taylor rule rate giv en by equation (1), where
π
∗
is set to 2 percent, and contrasting the difference between the t wo rates to the

evolution o f the o b served i nflation relative to the chosen 2 percent inflation target. A
useful stance m ea sure would imply th at w hen t he observed in terest rate corr esponds
to the Taylor rule, actual inflation should, potentially after a certain lag, be close to
the 2 percent implicit target. When the r ate is abo ve (below ) th e rule, inflation is
expected to go below (above) 2 percent. Moreover, there should be no substantial and
1
See McCallum (2001).
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persistent increa se in inflation above target if the observ ed nomin al inter est rate is at
or above the rule
2
. Figure 1 displays the 3-month T-bill rate (TB3m) together with
the Taylor rule (Taylor) from equation (1) and the Fisherian rate r
∗
+ π
t
(Fisher).
r
∗
and π
∗
are both set equal t o 2 percent as in the original Taylor rule
3
. Realized
inflation th us corr esponds to the Fisher va riab le m inus 2 percentag e points.
Figure 1 su ggests t hat th is stan ce m ea sure p rovides very little inform ation regard-
ing inflation developmen ts. Ov er the 1980s and 1990s, the 3-mon th T-bill rate has

been consistently above th e Taylor rule rate associated w ith a 2 percent inflation.
Despite that fact, inflation reac hed 2 percen t only in the late 1990s. In other words,
inflation has almost alw a ys been abo ve the implied target (2 percent) without the
actual interest rate being below the Taylor rule. There is th u s not a useful relation-
ship between the i mplied inflation target and observed inflation. Moreover, there is
no indication why inflationshouldhavepickedupto4 percent around 1990: the
T-bill rate was even above the rule implying 2 percent inflation before a nd during
this inflation increase. Furthermore, we would h ave expected a strong decrease in
inflation fo llowing the h igh in terest rate relative to the Taylor rule seen in the second
part of the 1990s. There is also no indication wh y inflation bega n to accelerate in
2
My analysis thus goes further than e.g. M cCallum (2000) or Taylor (1999) analyses that assess
whether observed interest rate settings have been loose or tight relative to a rule when compared
to actual inflation outcomes, by relating interest rate deviations from a rule associated with a given
inflation target to subsequent discrepancies of observed inflation from that target.
3
Price series are the GDP price deflator for the US, the harmonized CPI for the euro area, and
the CPI for Switzerland. Inflation rates are year-on-year quarterly rates. Potential output is real
potential GDP (Congressional Budget Office) for the US, HP filtered log real GDP for the euro
area, and is derived from a production function approach (SNB) for Switzerland. Interest rates are
3-month rates. All series except interest rates are seasonally adjusted. The samples considered,
chosen according t o availability of the data series used in the analysis, are 1959Q1-2006Q2 for the
US, 1973Q1-2005Q4 for the euro area, and 1975Q1-2005Q4 for Switzerland. US data are from the
Federal Reserve Bank of St. Louis FRED database and are released by the Federal Reserve Board,
the Bureau of Economic Analysis and the Bureau of Labor Statistics. Euro area data are from the
European Central Bank and Eurostat. Swiss data are from the Swiss National Bank and the Swiss
Federal Statistical Office.
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the mid-1960s, the beginning of the “Great Inflation”, as the T-b ill rate was at o r
above the Taylor prescription just prior to that even t. And finally, in the 1970s, it
is difficult to assess what infla tion observ ed in terest rates would have implied, given
that they have been consistently below the Taylor rule. There is th us neither useful
qualitative nor quantitativ e inform ation in th at m easu re of policy stance
4
.
Swiss interest rates, i.e. the sho rt-term (3-month LIB O R ) as well as the Taylor and
Fisher rates, where r
∗
is set to 1.2% (average o ver the past 3 decades) and π
∗
is set
to 1%, are presen ted in Figure 2. Since 2000 the Taylor rule and the actual in terest
rate hav e ev olv ed close to each other and inflation has fluctuated around 1 percent.
How ever, su ch a rule fails to account for the loose policy stance preced ing th e two
inflationary periods of the early 1980s and early 1990s and pro vides no quantitativ e
information of subsequent price l evels during these episodes. Furthermore, the Taylor
rate is constantly and substan tia lly below the actual interest ra te during th e 1990s
despite the fact that inflation was reduced to and remained around 1 percent. I will
focus the rema ind er of this section on U S d ata given space limitation s.
4
Similar issues arise when the “natural growth rule” (NGR), i.e. ∆i =0.5(π − π
∗
)+
0.5(∆y − ∆y
∗
), discussed by Orphanides (2003) is used to evaluate policy stance. The 3-month
T-bill rate follows the rule relatively well over the 1980s and 1990s while inflation was most of the

time above target. This measure of stance also missed the inflation increase of the late 1980s. Or-
phanides argues that the NGR is equivalen t to a money growth rule. This however is the case only
under his particular assumption that velocity deviations from equilibrium are a function of the inter-
est rate. With a more conventional money demand where velocity itself is a function of the interest
rate, a money growth rule implies that the change of the equilibrium nominal int erest rate appears in
the NGR. Both money demand formulations are equivalent only in t he case of constant equilibrium
nominal interest rate, which is not plausible with data characterized by long-lasting inflation swings.
Moreover, Orphanides disregards the change in the money demand error term, argu ing that short-
term velocity fluctuations are the suggested drawback in considering money. The analysis of this
paper, however, will show that these s hort-term velocity fluctuations contain additional information
for price developments that non-monetary analyses miss.
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2.2. IMP LICIT V S. R EA LIZED I NF LATION AND EQ UIL IBR IUM IN-
TEREST R ATE ASSUMPTION
If devia tion s from a rule a ssociated with a giv en inflation target are not good
signals of inflation going above or below that target, a natural question to ask is what
inflation rate do actual int erest rate settings imp ly. T h e second approach thus assesses
the n om in al ancho r properties of a Taylor rule, i.e. what in flation w e could expect
following a given ob served in terest rate, by plugging th e observed 3-month interest
rate i
t
into the Taylor r ule equation (1) and allowing π
∗
to vary, i.e. comp uting π
∗
t
as

π
∗
t
=2(π
t
+ r
∗
− i
t
)+π
t
+(y
t
− y
∗
t
) , (2)
with r
∗
=2%. I then com pa re the im plied targ et π
∗
t
to the observ ed inflation π
t+k
.
Figu re 3 p rese nts the imp licit in flation target π
∗
t
(Imp licit Target) together with
observed inflation (Inflation)

5
. Implied inflation w as m u ch higher than observ ed in-
flation d uring the 1960s and 1970s, for any reasonable lag, and much lo wer than any
subsequen t in flation value during the disinflation period and in th e 19 80s a nd 1 99 0s.
The discrepancies are substantial and persisten t. Imp lied inflationisonaverage4per-
centage points higher than observed inflation from the mid-1960s to the late-1970s,
and on average more than 4 percen tage poin ts low er during the 1980s and 1990s. This
cannot be attributed to p lausible fluctuations in th e real interest r ate, a s discussed
belo w . A ttrib uting this to econom ic shoc k s seems diffic ult given the persistence and
5
This analysis does not rely on whether or not the Fed was following a Taylor rule in the 1970s.
I adopt a positive perspective relating implicit inflation objective from observed interest rate to
subsequen t inflation, and thus use actual rather than real-time estimated output. I show that there
is a mismatch between implicit and realized inflation both in the 1970s and in the 1980-90s when
the Fed policy has been characterized by Taylor rules. This will be contrasted to a clear relationship
between money and inflation irrespective of whether or not central banks used money in their policies.
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May 2007
patterns o f d eviation s. Potential candida tes would h av e to have had persisten t n eg a-
tive effects of in flation during the 1970s , persistent positiv e effects on inflatio n durin g
the 1980s and 1990s, and positive effects since the early 2000s
6
.
A third but related question is to ask which w ould be the value of the real rate r
∗
t
that wo uld equalize the inflation target π
∗

t
with observed inflation π
t
or (an a verage
of) observ ed future inflation π
t+k
. Figure 4 displays r
∗
t
comp u ted from equation (1)
as r
∗
t
= i
t
− π
∗
t
− 1.5(π
t
− π
∗
t
) − 0.5(y
t
− y
∗
t
),whereπ
∗

t
has been set equal to π
t
.
Setting π
∗
t
equal to leading inflation values instead, e.g. inflation 3 or 5 y ears ahead
(i.e. π
t+12
or π
t+20
), does not affect the evolution of the implied real rate sign ifican t ly,
and the implications from the evolution of r
∗
t
in Figure 4 apply to inflation averages
or trends as well.
A crucial pr operty of New Keynesian models is that if the cen tral ban k appr o-
priately chooses th e equilibrium (av er age) real interest rate r
∗
t
, then actual average
inflation equals inflation target π
∗
t
. For example, Woodford (2006, p.8) states that
“r
∗
t

represents the central ba nk ’s view of the eco nomy’s equilibrium (or n atu ral) real
rate of in terest, and hence its estima te of where the intercept needs to be in order for
this policy rule t o be con sistent with t h e inflation target”. H ow ever, the evolution
of th e implicit real r a te of Figure 4 n eeded to m a tch observed in flation w ith target
does no t look anything like a plausible equilibrium real interest rate, as estimated
e.g. in L a uba ch and W illiam s (2 003), n or to what the Fed could h av e a ssum ed a s a n
equilibrium interest rate. r
∗
t
is c lose to 0% from t he m id-1960 to t he late 1970s, then
jum p s t o almost 10% in the early 1980s, and subsequently decreases to 0% in recen t
6
One could of course perfectly fit objective and realized inflation with high enough inflation
coefficients; every inflation movement would be interpreted as a target change, which is not plausible.
What is needed, and what is missing, is a correspondance between implicit targets and subsequent
inflation developments.
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y ears. Thus, the values that the central bank would have to c hoose as estimates of
the “natural” or equilibrium real interest rate in order for average inflation to equal
target ev olve in an implausible wa y.
2.3. IMPLICATIONS FOR M ONETARY P OLICY ANALYSIS A ND
PRA CTICE
The analysis a bove suggests that assessing mon etary policy stance with in terest
rates does not p rovide usefu l info rm a tion a nd guidance rega rdin g subsequent infla-
tion developmen ts. Moreover, the inflation objective π
∗
t

, supposed to pin dow n “trend
inflation” in New Key nesian models, is not related to o b served inflation for plausible
assumptio ns on equilibrium real interest rates. In other words, t here is n o useful
practical g uid eline for interest ra te settings in order to reach a chosen in flation ob-
jectiv e, and the fact that one has to mak e im p lausible assum ption s regarding the
equilibrium rate in terest rate poin ts to incompleteness or misspecifica tion of New
Key nesian m odels that could come from modeling monetary policy with only a short-
term nom inal interest r a te. The fact that interest rate rules not emp irically related to
inflation objectiv es are describing m oneta ry policy in many models used for analysis
or forecasting sho uld be concerning.
These considerations on mean or trend i nflation a nd equilibrium real interest rat es
have been ov erlooked in moneta ry policy a naly sis. For e xa m p le, CGG argue th at the
Federal Reserv e was reacting less to expected inflation deviations from target before
Vo lk er’s chairmanship period than during and after it. T hey divide the sample in
t wo sub-periods, 1960-79 and 1979-96, and set the equilibrium real interest rate r
∗
equal to the observed sub-sample averages. Althou gh not mentioned in their paper,
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the a verage real rate o ver the 1960-79 period is 0.5%. There are t wo issues with this
low real rate assum p tion .
First, it is unlikely that the monetary authority w ou ld have chosen such a low
value as its assumed r eal r ate d urin g tha t period. Second , the estimated less th an
one-for-one reaction of nom inal in terest rate to inflation deviations from target is o ften
in terpreted as a cause of the high inflation a verage and low observed real interest rate
of the 1 970s. But this lo w real rate is precisely what has already been assumed i n the
rule considered! The assumed real r ate o ver th e 1960-79 period is about 3 percentage
points lo wer tha n for the 1979-9 6 sample, corresponding to the ex-post sub-sam p le

a verages. Moreover, the in flation objective π
∗
for the former period is estimated to
be 4.2%, which appears high for the beginning of the sample as inflation was around
1.5% during the first half of the 1960s and reached that estimated target only in th e
late 1960s when the “Great Inflation” w as already well under w ay
7
. In fact, the ob-
served nom inal interest rate du ring the 196 0-70s can be characterized by an increasing
inflation objective and a higher reaction to infla tion de viation s
8
. A n increasing target
is plausible because the Federal Reserve inflation objectiv e w as probably increasing
during the 1970s as output/inflation trade-off ideas were still widesp rea d. Similarly,
monetary authorities probably d id no t wan t to “kill the econom y” by adopt ing too
7
One estimated inflation target by CGG during the 1960-69 sample is even 7.15%, i.e. on average
about 5 percentage points above observed rates. In contrast, in a similar historical analysis, Taylor
(1999) sets the real interest rate at 2% and estimates an inflation t arget of about 0.5% for the
1960-79 sample, which seems rather low for a period when inflation/output trade-off ideas were still
present, and is below observed inflation during the whole period. Taylor’s findings are awkward in
the sense that the estimated inflation target was lower for the 1960-79 period than for the 1987-97
period, i.e. 0.5% and 1.5% respectively, which represents the Fed in the 1970s as tougher on average
inflation but softer on inflation deviations f rom target.
8
For descriptive purposes, this interpretation can be complementary to Orphanides’ analysis
(2003) — whic h assumes a constant inflation target — resulting in a stronger estimated reaction to
inflation when output gaps are underestimated. For positive purposes, actual rather than estimated
output gaps should be used when comparing implied inflation objective from observed interest rate
with subsequent inflation.

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low an in flation target too early during the disinflation period of the 1980s, and it is
thus plausible to assume a decreasing t arget during that period. Modeling a constant
inflation target d uring t he 1980-90s, as in CGG for exam ple with a target of 3.6%,
while reflecting average inflation, has the unappealing feature of the target being al-
most alwa ys abo ve observ ed inflation after the disin flation episode. T he monetary
analysis of the next section will show that the higher inflation rates of the 1970s are
related to h ighe r m o ne y gr owth, and that inflatio n peaks ha ve alw ays been preceded
b y corresponding money gro wth peaks, casting doubts o n the explanation of self-
fulfilling changes in ex pectations due to a centra l b ank reacting too little to inflation
increases.
3. MONEY, PRICES AND OUTPUT
3.1. MONETARY AGGREGATE CHOICE AND ADJ USTMENTS
Themonetaryvariableconsideredisdefined as
m
∗
t
≡ c + m
t
− y
∗
t
+ βi
∗
t
, (3)
where c is a norm a lization consta nt, whose mea ning a nd usefu lness w ill be discussed

below; m is the observed money lev el; y
∗
is real potential output; β is an estimated
in terest rate semi-elasticit y of a rea l money demand equation where a un itar y income
elasticit y has been i m posed; and i
∗
is a l ow-frequen cy filtered short-term interest
rate or opportunity cost of money
9
. A ll va riables except i nterest rates are in loga-
9
Monetary aggregates are M2- for the US, M2 for the euro area, and M2 for Switzerland. Some
results will also be presented with the euro area M3 aggregate adjusted by portfolio shifts, as the
ECB assigns an explicit role on that aggregate in its strategy. US M2- corresponds to M2 minus
small time d eposits, and includes cash, demand and checking deposits, savings accounts, money
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rithms. Conceptual considerations underlying the computation of m
∗
and the choice
of m on etary aggregate are presented in Reynard (2 006), t hus on ly a brief description
is p rovided in the next paragraphs
10
. M oney demand estimates used for the required
lo w -frequency lev el adjustm ents are presented in appendix A.
I consider an asset as monetary if i t yields an in terest rate belo w th e 3-month
rate and pro vides direct or indirect transaction services. An aggregate composed of
suc h assets is the most likely to exhib it a close and stable relationship to nomin al

GD P. Moreover, such an aggregate gives the right monetary policy stance sign al, i.e.
it in creases when the policy rate decreases and vice versa, as interest rates paid o n
transaction accoun ts are relatively sticky an d mo ve only with persisten t cha nges in
the 3-m onth market rate. B roa der monetary ag gregates do not necessarily provide
the right stance signal, as the additiona l assets included in th em with yields at or
above the 3-month rate are positiv ely correlated with the policy rate
11
.Monetary
market deposit accounts, and retail money market funds. Euro area M2 includes currency, overnight
deposits, deposits with an agreed maturity up to 2 years, and deposits redeemable at a period of
notice up to 3 months. Euro area M3 consists of M2 plus debt securities up to 2 years, repurchase
agreements and money market funds. Swiss M2 includes cash, sight and savings deposits. The
in terest rate used is the opportunity cost of money (3-month rate minus the weighted average of
rates paid on the different monetary assets) when available, i.e. for US M2- and euro area M3, and
the 3-month rate otherwise, i.e. for Swiss and euro area M2.
10
The definition of m
∗
is equivalent to the variable labeled p
∗
in P*-models, initially presented
b y Hallman, Porter and Small (1991), and the difference between m
∗
and the actual price level, i.e.
m
∗
t
− p
t
, corresponds to a measure of excess liquidity used, for example, in analyses of monetary

developments by Fed, ECB and SNB economists (see e.g. Orphanides and Porter (2001), Masuch, Pill
and Willeke (2001), and Peytrignet and Reynard (2004)): using equation (3), the difference between
m
∗
t
and p
t
can be expressed as m
∗
t
−p
t
= m
t
− bm
t
,where bm
t
is the money demand that would prevail
at equilibrium output and interest rate, given the current price level, i.e. bm
t
= −c + p
t
+ y
∗
t
− βi
∗
t
.

The difference between m
∗
t
and p
t
thus represents a measure of excess liquidity, i.e. money in
excess of an estimated long run equilibrium money demand. The interpretation of money and price
developments in this paper however differs from P *-models’ interpretation of excess liquidity and
its relationship to inflation. Moreover, the relative developments of the variables considered, and
thus excess liquidity measures, differ as well given different treatments of equilibrium velocity and in
some instances a different choice of monetary aggregate concept. These differences will be discussed
below.
11
For the euro area, M2 does not exactly correspond to my preferred concept, as it includes some
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time deposits with maturity o ver 3 months. Moreov er, it does not include money market funds,
contrary to M2- in the US. However, whether or not these latter assets are included does not matter
much empirically f o r money demand or the money/price relationship; issues arise mainly when
assets with yields close to checking or transaction accounts are not included, and/or if significant
amounts of assets with yields abo ve the 3-month interest rate are included. Euro area M3 contains
in addition debt securities, which are not related to the transaction concept, but M3 information
value for inflation is considered, as its growth rate is an explicit elemen t of the ECB s trategy.
aggregates defin ed according to this transaction concept are c h aracterized by an es-
timated unitary income elasticity, which is not the case o f broader aggregates. The
latter aggregates are generally associated with an income elasticit y abo ve unity and
samp le-dependent. M y preferred a pp roach reg arding the choice of monetary aggre-
gateisnottoswitchfromoneaggregatetotheotherasapparentinstabilityoccurs,

but rather to choose an aggregate that is closely related to the transaction con cept
and then identify and explain a pp ar ent aggreg ate instabilit y episodes. The aggregates
c ho sen in this paper have been stable o ver the samp le periods considered, except for
two episodes in the US case where aggregate in sta bility is clearly rela ted to c hang es in
extensiv e m argin s of money dem and
12
. A discussion of how to account for instability
is pro vid ed in appendix A. It has been argued that the usefulness of money depends
on a m o ne y dema nd cointegrated relationship holding at a ll times. I d isag ree with this
argument on similar grounds as McCallum (1993). Money demand is a rem arkab ly
stable empirical relationship o ver v ery long time periods, a nd rare money demand
instability episodes should not be arguments for disregarding the clear relationships
bet ween money, output and prices presen ted belo w. T hus, this paper directly ad-
dresses the main recent c riticism s th a t even with a stable mon ey deman d th ere is n o
usefulness of money for m onetary policy.
12
Changes in extensive margins are measured by changes in financial market participation, i.e.
in the fraction of households holding non-monetary assets, like stocks or bonds, as part of their
portfolio. An increase in that fraction means that some households that were holding only monetary
assets decide to in vest part of their financial wealth in non-monetary assets, thus affecting money
demand via the extensive margins. For more details on the measurement, causes and effects of
extensive margin changes, see Reynard (2004).
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