Is Quantity Theory Still Alive?∗

Pedro Teles

Banco de Portugal, Universidade Catolica Portuguesa, and CEPR

Harald Uhlig

Dept. of Econ., Univ. of Chicago, NBER and CEPR

Joao Valle e Azevedo

Banco de Portugal and Nova School of Business and Economics

This revision: July 9, 2015

Abstract

This paper investigates whether the quantity theory of money is still alive. We demon-

strate three insights. First, for countries with low inflation, the raw relationship between

average inflation and the growth rate of money is tenuous at best. Second, the fit markedly

improves, when correcting for variation in output growth and the opportunity cost of money,

using elasticities implied by theories of Baumol-Tobin and Miller-Orr. Finally, a subsample

characterized by the adoption of inflation targeting shows considerably less inflation variability,

worsening the fit of a one-for-one relationship between money growth and inflation.

Keywords: quantity theory, money demand, money demand elasticity, inflation targeting

JEL codes: E31, E41, E42, E50

∗The addresses of the authors are Pedro Teles and Joao Valle e Azevedo, Banco de Portugal, DEE, 1150-165,Lisbon, e-mails: pteles@fcee.ucp.pt, azevedojv@gmail.com, and Harald Uhlig, Univ. of Chicago, Dept. of Economics,1126 East 59th Street, Chicago, IL 60637, U.S.A, huhlig@uchicago.edu. Uhlig’s research has been supported by theNSF grant SES-0922550 and by a Wim Duisenberg fellowship at the ECB. Teles gratefully acknowledges the financialsupport of FCT. Uhlig has an ongoing consulting relationship with a Federal Reserve Bank, the Bundesbank andthe ECB. The views here are entirely our own.

1

1 Introduction

One of the most established folk wisdoms in monetary economics is a relationship, which in its

practical version for monetary policy might be stated as follows: long run inflation is related one-

for-one with long-run money growth. This “quantity theory” relationship seems firmly established

at least since Friedman (1956) and Lucas (1980).

This paper takes a cross-section of countries from 1970 to 2005 and re-investigates the relation-

ship between money growth and inflation. We demonstrate three insights. First, for countries with

low inflation, the raw relationship between average inflation and the growth rate of money is tenuous

at best. Second, the fit markedly improves, when correcting for variation in output growth and the

opportunity cost of money, using elasticities implied by money demand theories of Baumol-Tobin

and Miller-Orr. Finally, the sample after the implicit or explicit adoption of inflation targeting (IT)

shows considerably less inflation variability, worsening the fit of a one-for-one relationship between

money growth and inflation but maintaining a low residual variance.

To demonstrate these insights, we provide a series of graphs and tables. We start by showing

that, for countries with moderate inflation, the raw relationship between money growth and inflation

is tenuous or even nonexistent. Quantity theory suggests to take into account the growth rate of

real GDP. Additionally, monetary theory points out the dependence of velocity on yields. The

correction for GDP growth alone turns out not to help. However, the correction for a yield effect has

a remarkable impact. Indeed, one would expect a rise in nominal yields to increase the opportunity

cost of holding money, and thus lead to a reduction in the real quantity of money per real unit

of output. This should translate to either lower nominal money growth or higher inflation. Lucas

(2000) has documented a rather tight fit of the ratio of the real quantity of money to real output

vis-a-vis the yield on government bonds, which furthermore is close to a relationship predicted

by theories on the transaction demand for money, see Baumol (1952), Tobin (1956), Miller and

Orr (1966). Taking into account the relationship suggested by Lucas, we demonstrate that the

fit between money growth and inflation indeed markedly improves. An even better fit is obtained

when using the (lower) elasticity value suggested by Miller and Orr (1966). We finally estimate the

relationship and find just a small improvement over the Miller-Orr specification.

2

The estimation of money demand has been under debate recently. The 90s and 2000s have been

testing decades for it, see in particular the discussion in e.g. Ball (2001), Carlson et al. (2000),

Coenen and Vega (2001), and Teles and Zhou (2005), Ireland (2009), Sargent and Surico (2011),

Lucas and Nicolini (2013). Motivated mostly by Ireland (2009) and Sargent and Surico (2011), we

split the data into two parts, choosing as split point for each country the dates coinciding with the

implicit or explicit adoption of inflation targeting.1 We also consider 1990 as an alternative breaking

point, which could reflect changes in financial arrangements and regulation. Teles and Zhou (2005)

and Lucas and Nicolini (2013), consider 1980 as a data break for the US, focusing on the effects

on monetary aggregates of banking deregulation introduced after 1980.2 Those changes together

with the financial innovation in the 1990s associated with the development of electronic payments

suggest that M1 might not be the most appropriate monetary aggregate to use in the later part of

the sample.

The relationship between money growth and inflation has become hard to pin down during the

second part of the sample. Generalized inflation targeting at low inflation rates, by considerably

reducing the dispersion of inflation across countries, has made it virtually impossible to establish

the one-to-one relationship between average inflation and the growth rate of money implied by the

Quantity Theory. This has also been argued by Sargent and Surico (2011) using US time series

data, in a recount of Whiteman’s (1984) arguments.

Another feature of the second part of the sample is that the interest elasticity of the money

demand is also harder to estimate and is lower than in the earlier sample. One of the reasons

for the difficulty in the estimation is the lower variability in interest rates. Reasons for the lower

elasticity are beyond the scope of this paper. They could involve the shape of the money demand

as in Ireland (2009) or the choice of the monetary aggregate as in Teles and Zhou (2005) or Lucas

and Nicolini (2013). As it turns out, the issues with the estimation of the interest elasticity in

the second part of the sample are not relevant for the purposes of our exercise. Given the lack of

variation in inflation and interest rates, the interest elasticity of the money demand does not make

a significant difference.

1We thank a referee for this suggestion.2The Depository Institutions Deregulation and Monetary Control Act of 1980 and the Garn-St Germain Deposi-

tory Institutions Act of 1982.

3

Investigating international cross-sections of countries to analyze the evidence on the quantity

theory of money has obviously been done before, notably by McCandless and Weber (1995), restated

in Lucas (1996). We build up on that literature. More recent literature such as Assenmacher-

Wesche and Gerlach (2006), using information on the interest rate, and Benati (2009) find a long

run relationship between money growth and inflation for several countries, but do not exploit the

cross section evidence as we do.

The outline of the paper is as follows. Section 2 provides a basic perspective on the cross-

country data. Section 3 describes a simple model that allows for additional “corrective” terms.

Section 4 examines the issue of subsample instability. The data is described in appendix A. An

online appendix and a .zip file provide further graphs and tables, as well as the data used and the

programs for calculating all results.

We conclude that quantity theory is still alive. Whether it should be used as a guide to long-term

monetary policy is more debatable, and it is certainly beyond the scope of this paper. Woodford

(2008) has argued that there is no independent role for tracking the growth rate of money, if

a central bank is already willing and able to stabilize inflation rates at short and medium-term

horizons, without making an explicit use of monetary aggregates. The practice of central banks

seems to be reassuring, that it is possible to keep inflation low using, as it appears to be the case,

some form of interest rate feedback rule. However, theory is more sceptical about that capacity,

pointing out that local determinacy does not imply uniqueness (see e. g. Benhabib, Schmitt-Grohe

and Uribe, 2001). In particular an interest rate feedback rule could be ineffective in raising inflation

from very low inflation at the zero bound. The tracking of money supply could be a means of

avoiding that policy trap (see also Atkeson, Chari and Kehoe, 2010, as well as the analysis in

Fischer et al., 2006).

2 The World

Teachers of intermediate macroeconomics may have consulted Barro (1993 or 2007) in order to

teach students the relationship between money growth rates and inflation. His figure 7.1 in the

1993 edition shows a large sample of countries, and plots this relationship, having calculated the

4

growth rates of money and prices from, typically, the fifties to 1990. The figure is reproduced here

as figure 1: one apparently gets a nice fit to the 45 degree line.

Figure 1

0 20 40 60 800

10

20

30

40

50

60

70

80

Money growth in Percent

Infla

tion

in P

erce

nt p

er y

ear

Money versus Inflation per year

This figure, which just restates figures drawn in Barro (1993, 2007), McCandless and Weber (1995) or Lucas (1996)

shows the relationship between average monetary growth rates and average inflation in a sample of 79 countries.

The data is from Barro (1993). Also drawn is the 45 degree line: it seems that, indeed, long-term monetary growth

is synonymous with long-term inflation.

However, that picture turns out to be misleading and mainly driven by high inflation countries.

Concentrating on the subset of countries we analyze, whose inflation rates were all below 12 percent,

the points no longer assemble nicely around a straight line, but produce a rather randomly looking

scatter plot with all the points below the 45 degree line, see figure 2. The question is thus: is the

relationship between money growth and inflation too loose to be of any relevance for low inflation

countries?

These pictures should be considered disturbing by anybody who believes in a tight relationship

between money growth and inflation and bases monetary policy advice on such a belief. Additional

issues may be of relevance at low rates of inflation, however. In particular, GDP growth, changes

5

Figure 2

AU

AT

CADK

FIN

FR

DE

IE

IT

JP

KR

NL

NZ

PT

ES

CHUK

US

02

46

810

Infla

tion

0 5 10 15 20Money Growth

Not Corrected1970*−2005

This figure is similar to figure 1, but restricts attention to only those countries in our sample whose average

inflation rate was below 12 percent in the period 1970-2005. The inflation measure is Consumer Price Index (CPI)

inflation and the monetary aggregate is M1. Average CPI inflation is plotted vis-a-vis average M1 growth.

Averages of the variables are from 1970 (or later if data is unavailable) until 2005. Instead of a tight relationship

between monetary growth and inflation, one can just see a cloud below the 45 degree line.

in interest rates, technological progress in transaction technologies as well as production may make

a difference. We next discuss how these can be taken into account.

3 Correcting the Quantity Theory relationship

In deriving an equilibrium money demand relationship, we follow the simple analysis in Attanasio,

Guiso and Jappelli (2002).3 A (representative) agent needs transaction services proportional to real

consumption ct, which are produced with time st and real money balances mt = Mt/Pt, according

to

st = l(A−1t ct,mt), (1)

where At measures progress in the transactions technology.

3See also Lucas (2000).

6

Given ct, the agent will want to minimize the cost of transactions, wtst + Rtmt, subject to (1),

where wt is the wage rate and Rt is the opportunity cost of holding money, the nominal interest

rate. The marginal condition

−wtlm(A−1t ct,mt) = Rt (2)

will have to hold.

Let the transactions function l be

l(c,m) = ηcamb (3)

for some η, a and b, with b < 0 and η > 0. When a = 1 and b = −1, the form for the transactions

technology can be justified by assuming, inspired by Baumol (1952) and Tobin (1956), that the

consumer spends cash holdings intended for the purchase of the good at a constant rate ct per unit

of time. ctmt

is the number of times cash balances for transactions of the good are exhausted and

must be restored, the number of trips to the bank. This time cost is a constant η. The Miller-Orr

(1966) specification amounts to l(c,m) = η(

cm

)2, i.e. a = 2 and b = −2.

The marginal condition (2) can be written as −ηbwtA−at catm

b−1t = Rt. In logs, the condition is

logmt = B − 1

1− blogRt +

a

1− blog ct +

1

1− blogwt −

a

1− blogAt, (4)

with B = log(−ηb)1−b

.

To make contact with the data, we wish to examine a panel of countries i = 1, . . . , N and a time

period t = 1, . . . , T . For a country i and a variable xi,t, generally denote the sample growth rate of

that variable between time one and time T with ∆xi =

log xi,T−log xi,1

T.

Equation (4) implies

∆Mi −∆P

i = − 1

1− b∆R

i +a

1− b∆c

i +1

1− b∆w

i − a

1− b∆A

i , (5)

in which ∆Mi is the average growth rate of the stock of nominal money in country i and ∆P

i is the

average inflation in that country. This suggests that the long run relationship between money and

7

prices ought to be corrected by the variation of nominal interest rates and by the growth rates of

consumption, as a measure of transactions, real wages and technical progress in transactions. There

are implications from the transactions technology for the relevant elasticities. For instance, for the

Baumol-Tobin, with a = 1 and b = −1, the interest elasticity would be one half, and so would be

the elasticity to the growth rate of consumption. For the Miller-Orr technology (a = 2 and b = −2),

the two elasticities are one third and two thirds, respectively.

Before taking the theoretical relationship to the data, we take two further steps. The first is to

use balanced growth to impose that the average growth rate of consumption is equal to the growth

rate of real wages, and to the growth rate of output, ∆yi ,

∆ci = ∆w

i = ∆yi . (6)

Notice that with this assumption, the relationship between money and prices is to be corrected by

the growth rate of output with an elasticity of 1+a1−b

. This long run elasticity is equal to one for both

Baumol-Tobin and Miller-Orr technologies.4

The second step is to assume that the cross-country level shift in the transactions technology

can be captured by a random fixed effect,

a

1− b∆A

i = ϵi, (7)

where we assume, and this is a strong assumption, that ϵi is independent of ∆yi and ∆R

i . With this

assumption as well as with (6), we obtain the empirical specification5

∆Mi −∆P

i = γ∆yi − α∆R

i − ϵi, (8)

where

γ =1 + a

1− band α =

1

1− b. (9)

4The unit elasticity of the money demand to output in typical formulations of the money demand, as in Lucas(2000), is a feature of long run growth.

5The specification in (8) is log-log in contrast to a semi-log specification. See the discussion in Bailey (1956) andIreland (2009).

8

One can now either proceed to estimate (8), noting that the two structural parameters a and b

are identified per (9), or one can directly measure the fit of that equation for given specifications of

the transaction technology. In particular, we note that

∆Mi −∆P

i = ∆yi −

1

2∆R

i − ϵi (10)

for the Baumol-Tobin specification and

∆Mi −∆P

i = ∆yi −

1

3∆R

i − ϵi (11)

for the Miller-Orr specification.

3.1 Data and Results

For our investigation, we have used data for all OECD countries, drawing on statistics of the IMF,

the OECD, the European Commission, the ECB and other sources. We excluded countries with

average inflation above 12 percent, transition countries and countries with missing data. We focus

on annual data from 1970 until 2005. The reason not to include data after 2005 is to avoid the zero

bound episode in the aftermath of the financial crisis. At zero interest rates, money and bonds are

perfect substitutes and the demand for money is not uniquely pinned down. Put differently, if we

are to find changes in the relationship between money growth and inflation within our sample, they

will not be due to zero bound considerations. We used CPI inflation, short rates as well as M1 for

all countries.6 We agree that more appropriate aggregates, with instruments more closely related to

transactions motives, such as Money Zero Maturity (MZM) could be used. Unfortunately, they are

not readily available and are reliable only in a few countries. The same applies to divisia indices,

see, e.g., Barnett (1988) and Barnett and Apostolos (2000). More information on the data as well

as explanations for the short codes used to denote countries are in appendix A.

Figure 3 “corrects” the money growth rate by subtracting the GDP growth rate. The points

scatter loosely below the 45-degree line. Figure 4 removes the yield effect with the coefficient of

6In earlier versions of this paper we also experimented with M2 and M3, as well as long rates: the data problemsthere were generally greater, but preliminary results looked rather similar to the results documented here.

9

0.5 on the interest rate change as suggested by the Baumol-Tobin specification (10), as well as

suggested by Lucas (2000) and close to the one estimated for Italy by Alvarez and Lippi (2009).

The correction with the yield considerably improves the fit, shifting the data points upwards, that

now line up nicely along the 45-degree line.

Figure 5 contains the result for the Miller-Orr specification, while figure 6 finally contains the

correction implied by estimating (8) with γ = 1 and including a constant, using as variables the

averages from 1970 until 2005, per ordinary least squares.7 Information about the quality of fit, by

calculating an R2 and the variances of ϵi is in table 1, including results for subsamples, see section 4.

The results from the regression imposing γ = 1 are in table 2, including results for subsamples, see

also section 4. Full results with γ unrestricted can be found in the online appendix. The estimated

interest rate elasticity is below the Baumol-Tobin and Miller-Orr values. For the full sample, the

Baumol-Tobin fits worse compared to the other three specifications that control for yields, all of

which provide essentially the same quality of fit.

We complement this analysis with the estimation of the following panel cointegration model:

log(Mit

Pit

) = α0,i + α1t+ γ log(Yit)− α log(Rit) + uit

with ∆

(log(Yit)

log(Rit)

)= λ0,i + vit

where ∆ is the first-difference operator. wit := (uit, vit)′ is possibly serially correlated but assumed

independent across i = 1, ..., N . (1,−γ, α) is a cointegrating vector and the equilibrium error

(log(Mit

Pit) − γ log(Yit) − α log(Rit)) is allowed, in its most general configuration, to have country-

specific fixed effects and a common time trend. Interestingly, panel tests indicate clearly that

log(Mit

Pit), log(Yit) and log(Rit) are integrated of order one and cointegrated.8 Next, we consider

several variations of the Dynamic OLS (DOLS) and Fully Modified OLS (FMOLS) panel estimators,

see e.g., Phillips and Moon (1999), Pedroni (2000, 2001), Kao and Chiang (2000) and Mark and Sul

7We provide results including a constant, which would not be motivated by the theory above but instead by thedesirability to control (if one thinks in the equation in levels) for movements in velocity not captured by changes inthe interest rates, due, e.g., to financial innovation.

8We employ the tests implemented in E-views due to Levin, Lin and Chu (2002), Breitung (2000), Im, Pesaranand Shin (2003), Maddala and Wu (1999), Choi (2001) and Hadri (2000) to test for unit roots and those due toPedroni (1999), Pedroni (2004), Kao (1999) and Maddala and Wu (1999) for cointegration.

10

(2003). Using DOLS the uit are allowed to be correlated with at most pi leads and lags of vit, which

controls for the possible endogeneity one hardly can get rid of in the simple regression setting. For

all the details and full results of this exercise, see the online appendix. Partial results obtained

with the restriction γ = 1 are in table 3. In this setting, the estimates of α obtained within the

1970-2005 sample are in the range 0.10-0.29, i.e., below the 0.33 of the Miller-Orr specification.

11

Figure 3

AU

AT

CADK

FINFR

DE

IE

IT

JP

KR

NL

NZ

PTES

CH UK

US

05

1015

Infla

tion

0 5 10 15Corrected Money Growth

Corrected for GDP growth1970*−2005

Corrected money growth rate here is average M1 growth minus average real GDP growth. Average CPI inflation is

plotted vis-a-vis corrected money growth. For each country, the average of the variables is from 1970 (or later if

data is unavailable) until 2005. The points scatter loosely around, but mostly below the 45-degree line.

12

Figure 4

AU

AT

CADK

FINFR

DE

IE

IT

JP

KR

NL

NZ

PTES

CH UK

US

05

1015

Infla

tion

0 5 10 15Corrected Money Growth

Corrected for yield − Baumol−Tobin1970*−2005

Baumol-Tobin: Corrected money growth rate here is average M1 growth minus average real GDP growth plus the

average growth of a nominal interest rate, divided by two, following (10). Average CPI inflation is plotted vis-a-vis

corrected money growth. For each country, the average of the variables is from 1970 (or later if data is unavailable)

until 2005. The correction with the yield improves the fit to the 45-degree line.

13

Figure 5

AU

AT

CADK

FINFR

DE

IE

IT

JP

KR

NL

NZ

PTES

CH UK

US

05

1015

Infla

tion

0 5 10 15Corrected Money Growth

Corrected for yield − Miller−Orr1970*−2005

Miller-Orr: Corrected money growth rate here is average M1 growth minus average real GDP growth plus the

average growth of a nominal interest rate, divided by three, capturing the transactions technology model due to

Miller and Orr (1966). Average CPI inflation is plotted vis-a-vis corrected money growth. For each country, the

average of the variables is from 1970 (or later if data is unavailable) until 2005. The fit around the 45 degree line is

better than the Baumol-Tobin specification.

14

Figure 6

AU

AT

CADK

FINFR

DE

IE

IT

JP

KR

NL

NZ

PTES

CH

US

05

1015

Infla

tion

0 5 10 15Corrected Money Growth

Corrected for yield − estimated1970*−2005

Corrected money growth rate here is average M1 growth minus average real GDP growth plus the average growth

of a nominal interest rate, multiplied by an estimated elasticity, minus a regression constant. Average CPI inflation

is plotted vis-a-vis corrected money growth. For each country, the average of the variables is from 1970 (or later if

data is unavailable) until 2005. The fit around the 45 degree line is similar to the Miller-Orr specification.

15

4 Subsamples

4.1 The Quantity Theory with inflation targeting

We now draw attention to the results before and after the implicit or explicit adoption of inflation

targeting (IT). For each country we split the full sample in IT and non-IT periods and consider this

splitting to calculate averages, run regressions with these averages or consider (unbalanced) panel

cointegration regressions. The specific dates and justification for these choices are in appendix A.

Starting with the corrections to average money growth, we note that in all samples the Miller-Orr

specification as well as the estimated specifications, which point to a lower interest rate elasticity,

clearly fit better than the Baumol-Tobin specification. But what is more striking is that while the fit

for all specifications in the non-IT part of the sample is essentially as good as for the whole sample,

the fit, as measured by an R2 is much worse for the IT part of the sample, as table 1 shows. Also,

not including a constant in the regression, i.e., not controlling for movements in velocity (through

a linear trend) not attributable to movements in the short rate deteriorates dramatically the fit in

the more recent sample.

Table 1Measures of fit and error dispersion

Period Benchmark Corrections Regression Based Corrections

Not GDP Baumol- Miller- γ = 1, α est. γ = 1, α est.corrected growth Tobin Orr with Constant No Constant

1970*-2005 R2 -2.79 0.31 0.37 0.62 0.65 0.64s.d.(ϵi) 4.76 2.04 1.94 1.51 1.45 1.46

s.d.(∆ log(M/P )) 2.451970*-IT R2 -1.18 0.52 0.23 0.56 0.69 0.66

s.d.(ϵi) 4.47 2.10 2.65 2.00 1.67 1.77s.d.(∆ log(M/P )) 3.02

IT-2005 R2 -6.45 -0.93 -0.18 0.10 0.43 0.10s.d.(ϵi). 5.59 2.94 2.29 2.01 1.59 2.01

s.d.(∆ log(M/P )) 2.12

R2 is calculated as 1− SSR/SST , where SSR is the sum of squared residuals, where the residuals are the differences between average

inflation and (possibly adjusted) average money growth and SST is the total variation in real money growth). s.d.(ϵi) is the estimated

standard deviation of the residuals. s.d.(∆ log(M/P )) is the standard deviation of real money growth. Averages of the variables are

from 1970 (or whenever data is available) until 2005, denoted 1970*-2005; from 1970 (or whenever data is available) until IT adoption,

denoted 1970*-IT and from IT adoption until 2005, denoted IT-2005. Countries included: AU, AT, CA, DK, FIN, FR, DE, IE, IT, JP ,

KR, NL, NZ, PT, ES, CH, US (17 observations). 1970*-IT does not include DE and CH. IT-2005 does not include JP.

The figures provide an even more revealing story. Figure 7 shows the results for the Baumol-

Tobin specification across samples, figure 8 for the Miller-Orr specification, and figure 9 shows the

16

Table 2Regression results

Period Benchmark No constant Constant includedPreferred spec.

γ = 1 γ = 1α R2 α Const. R2

1970*-2005 0.26 0.64 0.34 -0.44 0.65(0.07) (0.14) (0.77)

1970*-IT 0.18 0.66 0.26 -0.74 0.69(0.08) (0.10) (0.59)

IT-2005 0.33 0.10 -0.01 2.51 0.43(0.08) (0.13) (0.88)

Regression of (averages of) real money growth on real output growth and the nominal interest rate. Standard errors below the

estimates. R2 is calculated as 1 minus (sum-of-squared of residuals divided by total variation of real money growth). Averages of the

variables are from 1970 (or whenever data is available) until 2005, denoted 1970*-2005; from 1970 (or whenever data is available) until

IT adoption, denoted 1970*-IT and from IT adoption until 2005, denoted IT-2005. Countries included: AU, AT, CA, DK, FIN, FR,

DE, IE, IT, JP , KR, NL, NZ, PT, ES, CH, US (17 observations). 1970*-IT does not include DE and CH. IT-2005 does not include JP.

Table 3Panel cointegration regression results

Estimation-DOLS Constant Constant and common trendPreferred specification

Period benchmark γ = 1 γ = 1

Grouped Pooled Grouped Pooledα α α α

1970*-2005 0.24 0.18 0.13 0.10(0.02) (0.01) (0.02) (0.01)

1970*-IT 0.26 0.20 0.25 0.19(0.04) (0.02) (0.04) (0.02)

IT-2005 0.25 0.17 0.06 0.02(0.02) (0.01) (0.02) (0.01)

Estimation-FMOLS Constant Constant and common trend

Period benchmark γ = 1 γ = 1

Grouped Pooled Grouped Pooledα α α α

1970*-2005 0.24 0.29 0.14 0.20(0.02) (0.02) (0.02) (0.02)

1970*-IT 0.25 0.24 0.25 0.19(0.03) (0.03) (0.03) (0.03)

IT-2005 0.22 0.34 0.05 0.13(0.02) (0.05) (0.01) (0.05)

Estimation by DOLS and FMOLS considering country fixed-effects only and country fixed-effects and a common time trend in the

cointegration equation. In each setting we consider Grouped and Pooled (weighted) estimation of the panel. Pooled (weighted)

estimation considers cross-section estimates of the error covariances. With FMOLS we consider heterogeneous first-stage long-run

coefficients. Using DOLS the uit are allowed to be correlated with at most pi leads and lags of vit. We choose pi according to the AIC

criterion. HAC standard errors are below the estimates. For each country, data is from 1970 (or whenever available) until 2005, denoted

1970*-2005; from 1970 (or whenever data is available) until IT adoption, denoted 1970*-IT and from IT adoption until 2005, denoted

IT-2005. Countries included: AU, AT, CA, DK, FIN, FR, DE, IE, IT, JP , KR, NL, NO, NZ, PT, ES, CH, US. 1970*-IT does not

include DE and CH

17

results for the estimated specification.

Results for the simple regression with averages are in table 2 and those for the panel cointegration

regression imposing a unitary output elasticity (γ = 1) are in table 3. More complete versions of

the results, including choosing 1990 as the split point, can be found in the online appendix.9 We

should mention that, in our view, the most appropriate specifications include a constant in the

simple regression and, additionally, a trend in the cointegration equation.10

We want to stress two points here. The first is that the estimated interest elasticity is lower for

the IT part of the sample. This result has been observed in the literature on the stability of the

money demand using time series data, as for example in Ireland (2009). Part of the explanation for

the low elasticity is the increasing role of money substitutes that are not included in M1, as argued

by Teles and Zhou (2005), and recently also by Lucas and Nicolini (2013).

The second result, more important for our purposes, is the apparent poor fit of a money growth-

inflation relationship in the IT part of the sample compared to the non-IT part of the sample or

the whole sample, see table 1. It is still the case, however, and very importantly, that the residual

variance, or variability around the 45 degree line in the inflation-(adjusted) money growth plots, is

comparable to the other samples.

The reason for the apparent poor fit of the quantity theory relationship in the IT sample is

that inflation is nearly the same across countries. Without variation in inflation there can be no

one-to-one relationship between inflation and money growth. Examining figures 7, 8 and 9 makes

this point in a striking way. The explanation is simple. Central banks have increasingly focused

on achieving a low and roughly common target for the inflation rate. Apparently, they have been

successful in achieving this goal. Central banks choose a money growth rate that offsets shocks

to the money-inflation relationship, in order to achieve their common target. There is residual

dispersion in money growth, probably due to differing experiences in deregulation and innovation

in transactions technologies, but not enough to question the tightness of the relation as measured

by the residual variance.

9The main messages do not change if we consider that alternative split point.10This way we control, even if in a crude way, for movements in velocity not attributable to changes in interest

rates or output. Not including a constant in the regressions (or a trend in the cointegration equation) has a bigimpact in the estimated elasticities for the IT-2005 sample due to the fact that these movements are being attributedto the fall in interest rates over this period. This is a typical bias due to the omission of deterministics.

18

The fact that the Quantity Theory one-to-one relationship between money growth and inflation

cannot be found in the data does not mean that it is not a feature of a model that generates

comparable data. In the simple model of section 3, if inflation was equal to 2% for every country

and if interest rates were constant over time (possibly equal to 4%), that would make it impossible

to identify the relationship in the data generated by the model, regardless of the interest elasticity.

Even if the relationship is indeed a feature of the model. In this sense, the model can trivially be

used to explain the subsample instability.

Interestingly, the recent work of Sargent and Surico (2011) makes similar points using the time

series evidence for the US, also used in Lucas (1980). They argue that part of the difficulty in

establishing a relationship between money and inflation in the US in the more recent data is due to

the policy of inflation targeting. This has reduced the intertemporal variability of inflation, making

it hard to find a one-to-one low-frequency relationship between money growth and inflation in the

US time series.

19

Figure 7

AU

AT

CADK

FINFR

DE

IE

IT

JP

KR

NL

NZ

PTES

CH UK

US

05

1015

Infla

tion

0 5 10 15Corrected Money Growth

Corrected for yield − Baumol−Tobin1970*−2005

AU

AT

CADKFIN

FR IE

IT

JP

KR

NL

NZ

PT ES

UK

US

05

1015

Infla

tion

−5 0 5 10 15Corrected Money Growth

Corrected for yield − Baumol−Tobin1970*−IT

AUATCA DK

FINFR

DEIE

ITKRNLNZ

PTES CH

UK

US

05

1015

Infla

tion

−5 0 5 10 15Corrected Money Growth

Corrected for yield − Baumol−TobinIT−2005

Baumol-Tobin: Corrected money growth rate here is average M1 growth minus average real GDP growth plus the

average growth of a nominal interest rate, divided by two, following 10 as well as the suggestion of Lucas (2000).

Average CPI inflation is plotted vis-a-vis corrected money growth. For each country, the average of the variables is

from 1970 (or whenever data available) until 2005, denoted 1970*-2005; from 1970 (or whenever data is available)

until IT adoption, denoted 1970*-IT and from IT adoption until 2005, denoted IT-2005.

20

Figure 8

AU

AT

CADK

FINFR

DE

IE

IT

JP

KR

NL

NZ

PTES

CH UK

US

05

1015

Infla

tion

0 5 10 15Corrected Money Growth

Corrected for yield − Miller−Orr1970*−2005

AU

AT

CA DKFIN

FR IE

IT

JP

KR

NL

NZ

PT ES

UK

US

05

1015

Infla

tion

0 5 10 15Corrected Money Growth

Corrected for yield − Miller−Orr1970*−IT

AUATCA DK

FINFR

DEIE

ITKRNLNZ

PTES CH

UK

US

05

1015

Infla

tion

0 5 10 15Corrected Money Growth

Corrected for yield − Miller−OrrIT−2005

Miller-Orr: Corrected money growth rate here is average M1 growth minus average real GDP growth plus the

average growth of a nominal interest rate, divided by three, capturing the transactions technology model due to

Miller and Orr (1966). Average CPI inflation is plotted vis-a-vis corrected money growth. For each country, the

average of the variables is from 1970 (or whenever data available) until 2005, denoted 1970*-2005; from 1970 (or

whenever data is available) until IT adoption, denoted 1970*-IT and from IT adoption until 2005, denoted IT-2005.

The fit around the 45 degree line is better when compared to the Baumol-Tobin in all the samples.

21

Figure 9

AU

AT

CADK

FINFR

DE

IE

IT

JP

KR

NL

NZ

PTES

CH

US

05

1015

Infla

tion

0 5 10 15Corrected Money Growth

Corrected for yield − estimated1970*−2005

AU

AT

CA DKFIN

FR IE

IT

JP

KR

NL

NZ

PT ES

US

05

1015

Infla

tion

0 5 10 15Corrected Money Growth

Corrected for yield − estimated1970*−IT

AUATCA DK

FINFR

DEIE

ITKRNLNZ

PTESCHUS

05

1015

Infla

tion

−5 0 5 10 15Corrected Money Growth

Corrected for yield − estimatedIT−2005

Corrected money growth rate here is average M1 growth minus average real GDP growth plus the average growth

of a nominal interest rate, multiplied by an estimated elasticity, minus a regression constant. Average CPI inflation

is plotted vis-a-vis corrected money growth. For each country, the average of the variables is from 1970 (or

whenever data available) until 2005, denoted 1970*-2005; from 1970 (or whenever data is available) until IT

adoption, denoted 1970*-IT and from IT adoption until 2005, denoted IT-2005. The fit around the 45 degree line is

similar to the Miller-Orr specification.

22

5 Conclusions

A cross section of long term averages for inflation and money growth plotted one against the other as

in e.g. McCandless and Weber (1995) has those averages line up nicely along a 45 degree line. In his

Nobel lecture, Lucas (1996) claims that there is no sharper evidence in monetary economics.11 But

the evidence is by no means as sharp when the sample excludes countries with very high inflation.

For countries with moderate inflation, the overwhelming evidence is just not there.

We use a cross section of countries with moderate inflation to reestablish the one-to-one close

relationship between long term inflation and money growth. For that we need to take into account

the effect of long term movements in nominal interest rates, according to elasticities that match

the ones suggested by both theory on transactions technologies, as in Baumol (1952), Tobin (1956),

Miller-Orr (1966), and estimation using time series data for the US and other countries. Once we

take into account the effect of movements in interest rates for the whole sample, between 1970 and

2005, what appeared to be a random scatter of points is now a 45 degree line through the origin.12

The data is split into two subsamples with the data break coinciding with the explicit or implicit

adoption of inflation targeting. We find that for the later part of the sample the one-to-one relation

between inflation and money growth seems to deteriorate. Such deterioration is only apparent since

the residual variance is comparable to the one found for the full sample. The reason for all this is

moderate dispersion in money growth coupled with successful inflation targeting at a low common

rate. In the later sample the variability of inflation is indeed considerably reduced. The points

seem to form an horizontal line at low inflation. With very low variability of inflation it is hard

to find any relationship between inflation and money growth. A similar difficulty was described by

Whiteman (1984) and met by Sargent and Surico (2011) in their review of Lucas (1980). Sargent

and Surico also find that inflation targeting around low inflation, reducing its variability, made it

hard to extract from the more recent US data the one-to-one relationship that Lucas found. Our

results here complement their findings, using a cross-country analysis compared to their US time

11”(...)Central bankers and even some monetary economists talk knowledgeably of using high interest rates tocontrol inflation, but I know of no evidence from even one economy linking these variables in a useful way, let aloneevidence as sharp as that displayed in figure 1. The kind of monetary neutrality shown in this figure needs to be acentral feature of any monetary or macroeconomic theory that claims empirical seriousness.(...)”

12For the line to be through the origin, the effect of output growth must also be taken into account.

23

series analysis.

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27

A Data Description

The list of countries included in the regressions starts from the OECD countries excluding Chile,

Iceland, Israel, Mexico and Turkey, due to high inflation during relevant parts of the sample.

We furthermore excluded Luxembourg (as it is a financial hub in small country), the UK in the

regression but not in several plots (as it became a large financial hub during this period, with the

consequence that it is an extreme outlier in all the exercises), Japan for the sample IT-2005 to avoid

zero bound considerations and the transition countries (since there is no useful data for the purpose

of the analysis here from 1970 and 1990). For all other countries, we attempted to obtain as much

reliable data as possible, dropping Belgium, Greece, and Sweden due to missing data. In the end, 19

countries remain in the sample for at least part of the calculations. Table 4 lists the country codes.

An Excel file containing all the data as well as detailed remarks regarding sources and corrections

is available as part of an online appendix to the paper. Likewise, the E-Views and Stata programs

that perform all the calculations and produce the graphs as part of an online appendix to the paper.

An original version of the data used was collected by Jan Auerbach, an undergraduate RA in

Berlin 2006, using EcoWin, a commercial data base, which was available and existent then. Ding

Xuan, an undergraduate RA in Chicago 2012, corrected a few entries, using IMF and World Bank

Data. A number of further issues then were dealt with by the authors. In a nutshell, the latest

version of annual CPI and real GDP data is in most instances from the IMF-IFS. As for the short

nominal interest rate the main source is also the IMF-IFS. Data from the OECD, the ECB and

from St. Louis Fed’s FRED database is also used. As for M1, we rely on FRED, the IMF-IFS and

the ECB. Euro zone countries do not have an independent series for M1 for the whole sample, but

data for their contribution to M1 is provided by the ECB from 1980 onwards. For Germany, the M1

as well as the real GDP series was ”spliced” across unification, per extending the series backwards

using the growth rates of West Germany. Details can be found in table 6. Since the paper at

hand focusses on prices, M1, real GDP and short-term interest rates, the data regarding M2, M3

and long-term rates would need further corrections before full use, but appears to be sufficient to

provide a “first pass” at the results.

28

Code CountryAU AustraliaDK DenmarkDE GermanyFI FinlandFR FranceIE IrelandIS IcelandIT ItalyJP JapanCA CanadaKR S.KoreaNZ New ZealandNL NetherlandsNO NorwayAT AustriaPT PortugalCH SwitzerlandES SpainUK United KingdomUS US

Table 4Country Codes

Country Year of IT adoption Source and/or justificationAU 1993 Gill Hammond (2012)DK 1995 Nominal interest rate reaches average of subsequent periodDE 1970 Very low inflation throughout the sampleFI 1993 Bank of Finland statementFR 1999 Adoption of the Euro; no previous statement or low πIE 1999 Adoption of the Euro; no previous statement or low πIT 1999 Adoption of the Euro; no previous statement or low πJP 2001 Gill Hammond (2012)CA 1991 Gill Hammond (2012)KR 1998 Gill Hammond (2012)NZ 1989 Gill Hammond (2012)NL 1999 Gill Hammond (2012)NO 2001 Gill Hammond (2012)AT 1999 Adoption of the Euro; no previous statement or low πPT 1999 Adoption of the Euro; no previous statement or low πCH 1970 Very low inflation throughout the sampleES 1994 Bank of Spain statementUK 1992 Gill Hammond (2012)US 1984 Onset of great Moderation, common break point

Table 5Beginning of inflation targeting dates

29

Series

Fre

q.

Countries

Sourc

eSam

ple

Desc

ription

and

Note

s

P Consu

merPriceIn

dex,All

Item

s,2010=100

Annual

All

IMF

IFS

1970-2

005

Data

forW

est

Germ

any

before

1991,

Seriesexte

nded

backward

sis

ourcalculation

Y RealGDP,in

dex

2010=100,SA

Annual

All

exc.DE

and

PT

IMF

IFS

1970-2

005

RealGDP

at2010

Mark

etprices

Annual

PT

EC

AM

ECO

1970-2

005

RealGDP

at2010

Mark

etprices

Annual

DE

EC

AM

ECO

1970-2

005

Data

forW

est

Germ

any

before

1991,

Seriesexte

nded

backward

sourcalculation

R Nomin

alIn

tere

stRate

:DiscountRate

Annual

AT

IMF

IFS

and

ECB

1970-2

005

ECB

rate

from

1999

onward

s,Dec.31

valu

eand

ECB

Main

Refinancin

gOpera

tionsra

teDepositRate

Annual

CA

IMF

IFS

1971-2

005

Moneta

ryPolicy

Inte

rest

Rate

Annual

DK

IMF

IFS

1970-2

005

Nomin

alIn

tere

stRate

:DiscountRate

Annual

FIN

IMF

IFS

and

ECB

1970-2

005

ECB

rate

from

1999

onward

s,Dec.31

valu

eand

ECB

Main

Refinancin

gOpera

tionsra

teNomin

alIn

tere

stRate

:3-m

onth

T-b

illra

teAnnual

FR

IMF

IFS

and

ECB

1970-2

005

ECB

rate

from

1999

onward

s,Dec.31

valu

eand

ECB

Main

Refinancin

gOpera

tionsra

teNomin

alIn

tere

stRate

:Short

Rate

,T-b

illra

teAnnual

DE

OECD,IM

FIF

Sand

ECB

1970-2

005

OECD

short

Rate

from

1970-1

974,T

-Billfrom

1975-1

998,

and

ECB

Main

Refinancin

gOpera

tionsra

teECB

rate

from

1999

onward

s,Dec.31

valu

eNomin

alinte

rest

rate

:DiscountRate

Annual

ISIM

FIF

S1970-2

005

and

ECB

Main

Refinancin

gOpera

tionsra

teNomin

alinte

rest

rate

:Discountra

teAnnual

IEIM

FIF

S,OECD

and

ECB

1970-2

005

IMF

Discountra

teuntil1999,1992

filled

by

Dec1992

OECD

Short

rate

,and

ECB

Main

Refinancin

gOpera

tionsra

teECB

rate

from

1999

onward

s,Dec.31

valu

eNomin

alinte

rest

rate

:DiscountRate

Annual

IT,PT,ES

IMF

IFS

and

ECB

1970-2

005

ECB

rate

from

1999

onward

s,Dec.31

valu

eand

ECB

Main

Refinancin

gOpera

tionsra

teNomin

alinte

rest

rate

:DepositRate

Annual

JP

IMF

IFS

1970-2

005

Nomin

alinte

rest

rate

:DepositRate

Annual

KR

IMF

IFS

1970-2

005

Nomin

alinte

rest

rate

:Call

Money

Rate

Annual

NL

Sta

tisticsNL

and

ECB

1970-2

005

Sta

tisticsNeth

erlandsDecembervalu

es

and

ECB

Main

Refinancin

gOpera

tionsra

teECB

rate

from

1999

onward

s,Dec.31

valu

eNomin

alinte

rest

rate

:Short

rate

and

T-b

illra

teAnnual

NZ

IMF

IFS,OECD

1973-2

005

Short

Rate

OECD

1973-1

977,T-b

illfrom

1978

onward

s,hole

for1985

filled

by

Dec.valu

eofOECD

short

rate

Nomin

alIn

tere

stRate

:3

month

T-b

illra

teAnnual

GB

FRED

INTGSTGBM

193N

1977-2

005

Decembervalu

esfrom

month

lyse

ries

Nomin

alIn

tere

stRate

:3

month

T-b

illra

teAnnual

US

FRED

TB3M

S1970-2

005

Decembervalu

esfrom

month

lyse

ries

M Moneta

ryaggr.

M1,NationalCurrency,SA

Annual

US,KR

IMF

IFS

1970-2

005

Moneta

ryaggr.

M1,NationalCurrency,SA

Annual

AU

FRED

MANM

M101AUA189S

1970-2

005

Dec.valu

esfrom

month

lyse

ries

Moneta

ryaggr.

M1,NationalCurrency,SA

Annual

CA

FRED

MANM

M101CAA189S

1970-2

005

Dec.valu

esfrom

month

lyse

ries

Moneta

ryaggr.

M1,NationalCurrency,NSA

Annual

CH

FRED

MANM

M101CHA189N

1970-2

005

Dec.valu

esfrom

month

lyse

ries

Moneta

ryaggr.

M1,NationalCurrency,NSA

Annual

DK

FRED

MANM

M101DKA189N

1970-2

005

Dec.valu

esfrom

month

lyse

ries

Moneta

ryaggr.

M1,NationalCurrency,NSA

Annual

GB

FRED

MANM

M101GBA189N

1986-2

005

Dec.valu

esfrom

month

lyse

ries

Moneta

ryaggr.

M1,NationalCurrency,NSA

Annual

ISFRED

MANM

M101IS

A189N

1970-2

005

Dec.valu

esfrom

month

lyse

ries

Moneta

ryaggr.

M1,NationalCurrency,NSA

Annual

NO

FRED

MANM

M101NOA189N

1970-2

005

Dec.valu

esfrom

month

lyse

ries

Moneta

ryaggr.

M1,NationalCurrency,NSA

Annual

NZ

FRED

MANM

M101NZA189N

1970-2

005

Dec.valu

esfrom

month

lyse

ries

Moneta

ryaggr.

M1,NationalCurrency,SA

Annual

JP

FRED

MANM

M101JPA189S

1970-2

005

Dec.valu

esfrom

month

lyse

ries

Moneta

ryaggr.

M1,NSA

Annual

AT,DE

IMF

IFS

and

ECB

1970-2

005

Data

from

ECB

startin

gin

1980,using

Dec.valu

esfrom

origin

alm

onth

lyse

ries;

exte

nded

backward

susing

gro

wth

rate

sofIM

FIF

SAnnualData

Moneta

ryaggr.

M1,NSA

Annual

ES

IMF

IFS

and

ECB

1970-2

005

Data

from

ECB

startin

gin

1980,using

Dec.valu

esfrom

origin

alm

onth

lyse

ries;

exte

nded

backward

susing

gro

wth

rate

sofIM

FIF

SAnnualData

.Use

May

2005

instead

ofDec.dueto

very

larg

esp

ike

Moneta

ryaggr.

M1,NSA

Annual

FR

IMF

IFS

and

ECB

1977-2

005

Data

from

ECB

startin

gin

1980,using

Dec.valu

esfrom

origin

alm

onth

lyse

ries;

exte

nded

backward

susing

gro

wth

rate

sofIM

FIF

SAnnualData

Moneta

ryaggr.

M1,NSA

Annual

FIN

,IE

,IT

,ECB

1980-2

005

Dec.valu

esfrom

origin

alm

onth

lyse

ries.

IEwith

larg

esp

ikein

Jan

2003.

PT,NL

Wese

tJan

2003=Dec2012

and

exte

nd

serieswith

subse

quentgro

wth

rate

s

Tab

le6

DataDescription

30