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Journal of Business & Economic Statistics

ISSN: 0735-0015 (Print) 1537-2707 (Online) Journal homepage: http://www.tandfonline.com/loi/ubes20

Stock Market Downswing and the Stability of
European Monetary Union Money Demand
Kai Carstensen
To cite this article: Kai Carstensen (2006) Stock Market Downswing and the Stability of
European Monetary Union Money Demand, Journal of Business & Economic Statistics, 24:4,
395-402, DOI: 10.1198/073500106000000369
To link to this article: http://dx.doi.org/10.1198/073500106000000369

Published online: 01 Jan 2012.

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Date: 12 January 2016, At: 23:35

Stock Market Downswing and the Stability of
European Monetary Union Money Demand
Kai C ARSTENSEN
Kiel Institute for the World Economy, Duesternbrooker Weg 120, 24105 Kiel, Germany
(kai.carstensen@ifw-kiel.de)
This article analyzes the question whether money demand in the euro area underwent a structural change
in the end of 2001 when M3 money growth started to considerably overshoot the reference value set by the
European Central Bank. It is found that conventional specifications of money demand have in fact become
unstable, whereas specifications that are augmented with equity returns and volatility remain stable. Using
such an augmented specification, it turns out that the high M3 growth rates have not led to excess liquidity
and thus do not pose a measurable threat to price stability.

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KEY WORDS: Cointegration; Excess liquidity; Inflationary pressure; Stability test.

1. INTRODUCTION
On May 8, 2003, the European Central Bank (ECB) announced a revision of its monetary policy strategy (European
Central Bank 2003b). Most observers interpreted the revision
as a weakening of the monetary pillar (de Grauwe 2003; Belke,
Kösters, Leschke, and Polleit 2003). It might have been motivated in part by the fact that M3 reference growth rates had
been continuing to exceed the reference value of 4.5% by more
than 2.5 percentage points since the end of 2001. At the same
time, the ECB lowered its key interest rate from 4.25% on August 31, 2001 to 2% on June 6, 2003, even though the monetary
developments suggested a raise in the interest rate.
The ECB attributed the strong money growth to portfolio
shifts from equities to safe and liquid assets induced by the recent stock market downswing and the increased financial uncertainty and predicted that it would be reversed once stock
prices rose again and uncertainty diminished (see, e.g., European Central Bank 2003a). From this perspective, the recent
money growth does not seem to pose a particular threat to price
stability. It might, however, indicate that the relationship between money and prices has become unstable and hence that
money growth is not a well-suited tool for analyzing prospective inflation and support monetary policy decisions. Then it
would have been natural for the ECB to have reduced the weight
of the monetary pillar.

Because it is generally assumed that money and prices are
related through a money demand function, the preceding discussion raises the question of whether European money demand
has recently become unstable. Numerous papers have dealt with
estimating money demand functions of the European Monetary
Union (EMU) and testing their stability. Most used exclusively
synthetic data for the pre-EMU period (e.g., Gottschalk 1999;
Hayo 1999; Bruggeman 2000; Clausen and Kim 2000; Coenen
and Vega 2001; Funke 2001; Müller and Hahn 2001; Golinelli
and Pastorello 2002) or the period up to the first year of the
EMU (Brand and Cassola 2000; Calza, Gerdesmeier, and Levy
2001) and cannot reject stability. Extending the dataset until the
third quarter of 2001, Kontolemis (2002) found evidence for instability of the conventional money demand function at his very
last observation due to the strong growth of M3 beginning in
this period.
In a comprehensive stability analysis, Bruggeman, Donati,
and Warne (2003) applied the fluctuation and Nyblom-type

stability tests proposed by Hansen and Johansen (1999) and obtained mixed results, but finally concluded that some specifications of money demand seem stable. However, because their
dataset ends with the fourth quarter of 2001 and the excessive
money growth did not start until the second quarter of 2001, it is

possible that their limited dataset prevented the statistical tests
from indicating nonstability.
This article adds to the literature by first using an updated
dataset for the period from the first quarter of 1980 to the second
quarter of 2003, which provides more observations with excessive money growth at the end of the sample, and second, supplementing the battery of existing stability tests with a new family
of stability tests proposed by Andrews and Kim (2003) that fits
the purpose of this article perfectly because it is designed to detect breakdown of cointegration at the end of a sample. Because
it is found that a conventional money demand specification became unstable in 2001, an alternative money demand function
is considered that is augmented by stock market variables. This
money demand function exhibits structural stability and can be
used to assess the importance of stock market developments
on M3 growth rates. We provide evidence that the recent high
M3 growth rates did not reflect excess liquidity that would have
posed a threat to price stability.
The remainder of the article is organized as follows. Section 2 discusses the specification of the EMU long-run money
demand function. Section 3 outlines various stability tests for
cointegrated time series, and Section 4 presents the empirical
estimation and testing results. Finally, Section 5 concludes.
2. SPECIFICATION OF LONG–RUN
MONEY DEMAND

There already exists a large body of literature on specifying and estimating long-run European money demand functions
and testing their stability. Detailed surveys have been provided
by Fagan and Henry (1998) and Golinelli and Pastorello (2002).
Concerning the specification issue, real money demand is generally modeled as depending on real GDP as a scale variable,

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© 2006 American Statistical Association
Journal of Business & Economic Statistics
October 2006, Vol. 24, No. 4
DOI 10.1198/073500106000000369

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Journal of Business & Economic Statistics, October 2006

whereas there seems to be no consensus as to which opportunity
cost measure should be included. Typical choices are a longterm (government bond) rate (Golinelli and Pastorello 2002),

a short-term (money market) rate (Brand and Cassola 2000;
Funke 2001; Kontolemis 2002), or a spread between long-term
and short-term rates, with the latter used to approximate the
own rate of M3, that is, the rate of return on M3 (Gottschalk
1999; Clausen and Kim 2000; Müller and Hahn 2001). Calza
et al. (2001) argued that it would be better to construct a direct measure of the own rate and use the spread between a
short-term rate and this own rate, an approach also followed
by Bruggeman et al. (2003). A few authors have included additional variables, such as the inflation rate (Coenen and Vega
2001) or real stock prices (Kontolemis 2002; Bruggeman et al.
2003).
In this article we follow Calza et al. (2001) and consider the
baseline long-run money demand function
mpt = β1 yt + β2 (rts − rto ) + ut ,

(1)

where mpt = mt − pt denotes real M3, yt is real GDP, rto is the
own rate of M3, rts is the short-term interest rate, and ut is the
disequilibrium. This choice of an opportunity cost variable is
motivated by two factors. First, it has been successfully applied in the most recent work (Calza et al. 2001; Bruggeman

et al. 2003); second, Calza et al. (2001) obtained an insignificant effect of the spread between a long rate and the own rate
on money demand. A comprehensive analysis of different possible specifications reported in an earlier version of this article
(available from the author on request) found that the spread between the short rate and the own rate is an appropriate choice
in terms of significance and economic interpretation.
Concerning the stability of European money demand, most
authors apply informal techniques, such as recursive estimation
and out-of-sample forecasting or Chow tests with critical values
valid only for stationary relationships. In contrast, Funke (2001)
used the SupF test of Hansen (1992) designed for cointegrating
regressions, and Bruggeman et al. (2003) used the fluctuation
and Nyblom tests of Hansen and Johansen (1999) developed
for cointegrated vector autoregression (VAR) models. Rather
surprisingly, there seems to be consensus that European money
demand functions are remarkably stable (see, e.g., Calza and
Sousa 2003 for a discussion of this result). However, the samples analyzed so far generally end before the recent start of excessive money growth rates. Two notable exceptions are those
reported by Kontolemis (2002), who found signs of instability
at his last observation 2001Q3, and Bruggeman et al. (2003),
who could not reject stability in a sample ending in 2001Q4 but
obtained a strong rise in the money overhang in 2001Q4.
In fact, the persistently high money growth rates since 2001

might indicate instability of a money demand function that neglects stock market influences. This view is supported by an
empirical analysis of the ECB (2003a), which reveals that shifts
of risky assets into funds that are part of M3 compose a large
fraction of money growth. The coincidence of excessive money
growth and stock market turmoil suggests that there might be a
relationship between money demand and stock prices.
Friedman (1988) argued that stock markets should affect
money demand in several ways; for instance, real stock prices
should have a positive wealth effect, stock returns should have

a negative substitution effect, and stock market risk should have
a positive risk-avoidance effect given risk-averse agents. For
the United States, Friedman can support these claims empirically. Choudhry (1996) and Carpenter and Lange (2002) also
found evidence in favor of a long-run influence of stock market variables on U.S. money demand. Caruso (2001) extended
this work to a panel of 25 countries and obtained a significant
wealth effect. For EMU money demand, Kontolemis (2002)
found a significant long-run influence of stock prices, whereas
Bruggeman et al. (2003) did not obtain significant of effects
either real stock prices or stock market volatility. The latter result stands in contrast to the argument of the ECB (2003a) that
the increased uncertainty in equity markets has led to portfolio

shifts from equities to safe and liquid assets, which are part of
M3, and hence to the excessive M3 growth. Moreover, Cassola
and Morana (2002) found that real stock prices play an important role in the monetary transmission mechanism.
To analyze the impact of stock market variables on money
demand, the “stock market” specification
mpt = β1 yt + β2 (rts − rto ) + β3 (rte − rto ) + β4 vt + ut

(2)

rte

is used, where
denotes equity returns and vt denotes stock
market volatility. (Again, a more comprehensive analysis of different stock market specifications is available on request.) Theoretically, the stock market variables should reflect expectations
of investors who decide whether they want to hold money or
equity. However, there does not seem to be a well-suited expectation variable for the period since 1980. Using realized future
returns instead would not only impose rational expectations on
stock market investors, but also would necessitate generalized
method-of-moments GMM estimation, which is not readily
available for a cointegrated VAR model. Therefore, backwardlooking variables are included, with the obvious problem that

past outcomes might not be an optimal predictor of the future
outcomes with which investors are concerned. There are, however, two observations that may justify this choice in addition to
the simple availability rationale. First, if stock market variables
behave like a random walk, then current values are as good as
any predictor. Second, historical performance measures play a
significant role in stock market practice. In particular, it seems
that the recent stock market downturn has had a protracted impact on money demand, which may be explained by investors
revising their expectations only gradually over time as more information is observed. Moreover, from an econometric perspective, the long-run analysis should be invariant to using realized
current versus expected future variables as long as the difference between them is stationary.
3. TESTS FOR LONG–RUN
STRUCTURAL STABILITY
It has long been recognized that the variables entering the
long-run money demand functions (1) or (2) can be modeled as
integrated I(1) processes. Therefore, stability of a money demand function requires at a minimum that it constitute a cointegration relationship. It is by now a well-established empirical
finding that the European money demand function is stable and
cointegrated at least for the sample 1980Q1–1998Q4, which we
will call the baseline sample here. Therefore, it is particularly

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Carstensen: Stability of EMU Money Demand

interesting to test whether this stability has been lost since then,
especially in the time since M3 started its excessive growth. Toward this end, tests for long-run stability are applied, as briefly
reviewed in what follows.
Long-run stability means that the parameters of the cointegration relationship are invariant over time. To allow valid
inference, the stability tests must take into account the nonstationarity of the single variables. For cointegrated VAR models,
Hansen and Johansen (1999) suggested applying a fluctuation
test to the nonzero eigenvalues of the reduced-rank matrix and
a Nyblom test to the cointegration parameters. The fluctuation
test is in the spirit of Ploberger, Krämer, and Kontrus (1989)
and rejects stability when the recursively estimated eigenvalues
fluctuate excessively. It can be applied either to the eigenvalues λi themselves, giving rise to the test statistic Sup λ, or to
the transformation ξi = log(λi /(1 − λi )), giving rise to the test
statistic Sup ξ . The Nyblom test statistics MeanQ and SupQ
are obtained by applying the mean and supremum operators,
respectively, to the recursively estimated likelihood maximum
(LM) statistics for structural stability of the cointegration parameters. Hansen and Johansen (1999) used a first-order approximation to the relevant score function to calculate the LM
statistic, whereas Bruggeman et al. (2003) used the score function itself, which yields the test statistics MeanQs and SupQs .
Bruggeman et al. (2003) and Warne (2005) suggested that the
MeanQs and SupQs tests are superior to the MeanQ and SupQ
tests because the latter suffer from numerical problems in simulation exercises, leading to small-sample distributions that are
far away from the limit distributions. Therefore, the results of
the MeanQ and SupQ tests should be taken with caution.
Usually, it is deemed a particular strength of all of these tests
that they do not require a prespecified break date, but rather
test the null hypothesis of structural stability against the alternative that there is a structural break at some unknown point
in the sample. For the present situation, this strength may turn
out to be of less value, because stability in the pre-EMU period
is well documented (Calza and Sousa 2003), whereas there are
two known dates later in the sample when instability may show
up, namely the start of EMU in 1999Q1 and the start of excessive M3 growth around 2001Q4. Although the former date
is clearly identified exogenously, one can argue that the latter
is not, and that it cannot be unambiguously fixed to exactly
one quarter. On the other hand, there is ample evidence from
newspapers, ECB reports, commentators, and other sources that
something was happening on around this date. Therefore, tests
that use the information that there was a break at the end of the
sample, probably around 2001Q4, might be better suited than
tests that abstract from any a priori knowledge.
Unlike the fluctuation and Nyblom tests, the cointegration
breakdown tests proposed by Andrews and Kim (2003) are
particularly well suited to the situation of a potential break at
the end of the sample. The cointegration breakdown tests are
generalizations of the well-known Chow stability test and can
be applied to any estimation procedure, such as fully modified ordinary least squares (FM–OLS) proposed by Phillips
and Hansen (1990) and full information maximum likelihood
(FIML) proposed by Johansen (1988, 1991). Moreover, critical
values and p values can be obtained from parametric subsampling, which circumvents the use of asymptotic distributions.

397

This article applies the Pc and Rc statistics that Andrews and
Kim (2003) found to have stable sizes and good power properties for detecting the breakdown of a cointegration relationship
at the end of a sample, due to either a shift in the parameter
vector of the cointegration relationship or a change in the distribution of the cointegration residuals from being stationary to
being integrated, I(1).
4. EMPIRICAL ANALYSIS
This section presents and compares the empirical results for
the baseline and the stock market specifications of the euro area
money demand function. First, cointegration and long-run stability tests are used to determine a stable long-run money demand relationship. Then the question is analyzed whether the
recent strong money growth has created excess liquidity in
the euro area. The sample runs from 1980Q1 to 2003Q2, with
the first four observations reserved as presample values. The
construction of the variables is explained in the Appendix.
4.1 Cointegration and Long-Run Stability
The cointegration properties of the baseline and stock market
specifications in both the baseline and the full sample are analyzed by Bartlett-corrected trace tests (Johansen 2002). Toward
this end, VAR models with an unrestricted constant were estimated. (The results are robust to adding a linear trend restricted
to the cointegration space.) For both models, a lag order of two
was picked by the Schwarz and Hannan–Quinn information criteria, which was sufficient to obtain uncorrelated residuals, as
indicated by LM tests for first- and fourth-order autocorrelation.
Table 1 reports the trace test results along with p values derived
from the asymptotic distribution. Using bootstrapped p values
instead did not lead to any important changes, however. At the
10%, but not at the 5%, level, the variables mpt , yt , and rts − rto
of the baseline specification exhibited one cointegration relationship in the baseline sample; however, the null of no cointegration could not be rejected in the full sample. This can be
taken as a first sign of the long-run instability of this specification. In contrast, the variables mpt , yt , rts − rto , rte − rto , and vt
of the stock market specification were clearly cointegrating in
both samples.
Imposing a cointegration rank of 1, the long-run parameters can be estimated by FIML. As a cross-check, FM–OLS
Table 1. Cointegration of the Long-Run Money Demand Specifications

Specification

Sample end

Baseline

1998Q4

Baseline

2003Q2

Stock market

1998Q4

Stock market

2003Q2

5

Bartlett-corrected trace statistics
4
3
2
1

82.03
(.004)
75.97
(.015)

45.64
(.080)
31.79
(.624)

29.09
(.060)
22.30
(.282)
16.03
(.710)
15.01
(.779)

9.51
(.320)
5.08
(.800)
6.97
(.581)
2.88
(.972)

.01
(.904)
.01
(.906)
.02
(.896)
.04
(.836)

NOTE: The baseline and stock market specifications are given in (1) and (2). The Bartlettcorrected trace statistics proposed by Johansen (2002) are obtained from a VAR model with two
lags, which is sufficient to guarantee uncorrelated disturbances. The asymptotic p values of the
trace tests are given in parentheses. The computations are performed using Anders Warne’s
program Structural VAR 0.24.

398

Journal of Business & Economic Statistics, October 2006

Table 2. Estimation of the Long-Run Money Demand Specifications
Estimated parameters
Specification
Baseline

Sample end

Estimation method

β1

β2

1998Q4

FM–OLS

1.37
(.049)
1.32
(.036)
1.40
(.099)
1.09
(.083)

−.54
(.367)
−.94
(.279)
−.72
(.821)
−3.40
(.697)

1.30
(.043)
1.24
(.030)
1.29
(.035)
1.25
(.024)

FIML
2003Q2

FM–OLS
FIML

Stock market

1998Q4

FM–OLS
FIML

2003Q2

FM–OLS

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FIML

β3

β4

−1.40
(.412)
−2.06
(.308)

−.09
(.047)
−.17
(.040)

0
(.011)
.04
(.011)

−1.60
(.308)
−1.87
(.218)

−.12
(.024)
−.14
(.020)

.02
(.006)
.04
(.006)

NOTE: The baseline and stock market specifications are given in (1) and (2). FM–OLS denotes fully modified least
squares. The nonparametric correction is calculated using a Parzen kernel with associated automatic bandwidth selection as proposed by Hansen (1992). FIML denotes the full information maximum likelihood estimator (Johansen
1988, 1991) with lag length 2 to obtain uncorrelated residuals and cointegration rank 1. Standard errors are reported in
parentheses.

estimates are reported in Table 2 as well. First, consider the
baseline specification. The FIML estimates changed from 1.32
(baseline sample) to 1.09 (full sample) for β1 and from −.94
(baseline sample) to −3.40 (full sample) for β2 . Again, this
finding informally indicates long-run instability. Although the
FM–OLS point estimates remained rather stable, the estimated
standard errors increased considerably, again pointing to potential stability problems. The estimated parameters of the stock
market specification changed much less than the parameters
of the baseline specification, especially when taking estimation uncertainty into account. Except for the FM–OLS estimate
of β4 in the baseline sample, all parameters were highly significant and correctly signed. The income elasticity of slightly
below 1.30 is in the range obtained in previous studies, whereas
the interest rate semielasticity is rather large in absolute terms.
Moreover, in line with findings of Friedman (1988), long-run
money demand is negatively related to equity returns and positively related to stock market volatility.
After imposing a cointegration rank of 1, the stability of
the two specifications was analyzed by the eigenvalue fluctuation and Nyblom tests. The p values of these tests were derived from a parametric bootstrap, which provides stable sizes
in small samples, as documented by Warne (2005) in an extensive Monte Carlo study. Toward this end, the VAR was estimated using the cointegration rank of 1, which yielded the
ˆ and the estimated covariance maestimated mean parameters B
ˆ
trix
. In each bootstrap replication, normally distributed disˆ were drawn.
turbances with mean 0 and covariance matrix

(A bootstrap procedure that resamples directly from the residuals led to virtually the same results.) Then the bootstrap disturˆ were used
bances, the actual initial values, and the parameters B
b
to generate a bootstrap sample, Yt , t = 1980Q1, . . . , 2003Q2,
from which a bootstrap test statistic was calculated. Bootstrap p
values for each actual test statistic were based on 999 bootstrap
replications, as suggested by MacKinnon (2002).
The results of the stability tests are displayed in Table 3. For
both the baseline specification and the stock market specification, stability cannot be rejected using any test. Note that the

MeanQ and SupQ statistics are very large, indicating that the
numerical problems found by Warne (2005) also show up here.
Nevertheless, because the remaining four tests do not reject
stability either, the test results suggest that either both specifications are stable or the null hypothesis of stability cannot be
rejected because of low power, as would be typical of situations
in which the break occurs at the end of the sample.
More evidence can be gained from the cointegration breakdown tests of Andrews and Kim (2003), which were applied
to FIML and FM–OLS estimation of the cointegration parameters. Three different test setups were evaluated. First, a break
after the start of EMU 1999Q1 was tested in a reduced sample that ends at 2001Q3, that is, before the M3 growth rates
become extremely large. Thus a potential break after 2001Q3
did not affect the test. The results reported in Table 4 clearly
show that the start of EMU did not induce a break for any of
the two specifications. Next, the break after the start of EMU
was tested in the full sample ending at 2003Q2 and thus including the excessive M3 growth rates. In this case, stability of the
baseline specification was rejected by the tests applied to FM–
OLS at the 10% level and FIML at the 1% level, indicating that
Table 3. Nyblom and Fluctuation Tests of the Long-Run Money
Demand Specifications
Specification

Sup λ

Sup ξ

MeanQ

SupQ

MeanQ s

SupQ s

Baseline

1.51
(.168)
1.23
(.440)

1.28
(.173)
1.24
(.604)

4.69
(.170)
3.00
(.329)

79.07
(.192)
64.17
(.271)

.20
(.458)
.17
(.930)

.99
(.286)
.80
(.807)

Stock market

NOTE: The baseline and stock market specifications are given in (1) and (2). MeanQ and
SupQ denote the Nyblom tests based on a first-order Taylor expansion of the score function
as proposed by Hansen and Johansen (1999), MeanQ s and SupQ s denote the related Nyblom
tests based directly on the score function as proposed by Bruggeman et al. (2003). Sup λ and
Sup ξ denote the fluctuation tests based on the largest eigenvalue λ1 and the transformation
ξ1 = log (λ1 /(1 − λ1 )), as proposed by Hansen and Johansen (1999). All test statistics are computed from a VAR model with two lags and cointegration rank 1. The first 16 observations are
used as the base period, as done by Hansen and Johansen (1999, p. 316). Bootstrapped p values calculated with Anders Warne’s program Structural VAR 0.24 are given below the test statistics.

Carstensen: Stability of EMU Money Demand

399

Table 4. Cointegration Breakdown Tests of the Long-Run Money Demand Specifications
Specification
Baseline

Stock market

Sample end

Break

Pc (FM)

Rc (FM)

Pc (FIML)

Rc (FIML)

2001Q3
2003Q2
2003Q2
2001Q3
2003Q2
2003Q2

1999Q1
1999Q1
2001Q4
1999Q1
1999Q1
2001Q4

.968
.055
0
.936
.964
.753

.999
.073
0
.999
.655
.662

.952
0
0
.613
.655
.156

.999
0
0
.323
.200
.052

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NOTE: The baseline and stock market specifications are given in (1) and (2). Pc and Rc are the cointegration breakdown tests proposed by Andrews and Kim (2003). They are based either on estimation of a VAR with two lags and
cointegration rank 1 (FIML) or on fully modified least squares with Parzen kernel and associated automatic bandwidth
selection (FM). Only the simulated p values are reported, because the simulated critical values change from case to
case so that the test statistics themselves are difficult to interpret.

the break occurred at the end of the sample after 2001Q3. This
can be confirmed be testing the break point of 2001Q4 in the
full sample. All four tests reject stability of the baseline specification at the 1% level. In contrast, at the 10% level, stability
cannot be rejected for the stock market specification except for
the Rc (FIML) test, which has a p value of .052 and thus is a
borderline case.
Hence, from the tests of long-run stability it can be concluded
that there are strong signs of instability for the baseline specification that neglects any stock market influence on EMU money
demand. On the other hand, the extended specification that includes equity yields and stock market volatility is stable by all
of the criteria applied.
4.2 Excess Liquidity
The strong rise in money growth in the euro area in recent
years has provoked the concern that excess liquidity has built
up, with the possible consequence that inflation will start to rise
in the near future. This concern is based mainly on a particularly simple measure of excess liquidity, namely the difference
between the actual money growth rates and the reference value
of 4.5% announced by the ECB (1999). Because actual money
growth rates have permanently exceeded 4.5% since the end
of 2001, this approach indicates that there is enormous excess
liquidity in the euro area. The reference value was derived by
the ECB from the quantity equation using the desired inflation
rate and assumed long-run growth rates in output and velocity
that resemble the historical averages before the monetary union;
however, there is no reason why historical averages should be
good indicators for the current situation.
An alternative measure of long-run excess liquidity is the
money overhang. Money overhang is defined as the difference
between the observed money balance and the estimated equilibrium money demand and thus is derived from an equilibrium
concept that takes the current situation into account (Masuch,
Pill, and Willeke 2001; Nicoletti-Altimari 2001). Figure 1 compares two measures of money overhang, the first estimated from
the baseline specification and the second estimated from the
stock market specification. In both cases, the FM–OLS estimates were used because they are more stable in the baseline specification. It turns out that neglecting the stock market
influence would indicate that there has been a strong money
overhang since the end of 2001, peaking at nearly 8% in
2003Q2. This number compares well with the results of other
authors who neglected stock market influences (e.g., Belke et al.

2004). However, the strong money overhang may simply reflect
the cointegration breakdown of the baseline specification after
2001. In fact, money overhang is negligible if the money demand function includes the stock market variables. This finding
is consistent with the view that the recent excessive M3 growth
rates can be attributed to the stock market downswing. Once
stock market developments are taken into account, there is no
indication that there is excess liquidity and, thus, serious inflationary pressure in the euro area.
5. CONCLUSION
This article has analyzed the stability properties of two
money demand specifications for the euro area. Using, inter alia, cointegration breakdown tests recently introduced by
Andrews and Kim (2003), the hypothesis of structural stability had to be rejected when stock market influences were neglected in long-run money demand. The tests indicate that the
break point was probably at the end of the year 2001, when
M3 growth increased and stock market conditions deteriorated.
However, including equity returns and stock market volatility in
the long-run money demand equation improved stability considerably.
The presence of excess liquidity was analyzed by means of
the money overhang, defined as the difference between the observed money balances and the estimated long-run money demand. It turns out that the conventional measure, which neglects

Figure 1. Money Overhang From 1990Q1 to 2003Q2 (
specification;
stock market specification).

baseline

400

Journal of Business & Economic Statistics, October 2006

were updated by adding log changes to the last observation of
the Calza et al. (2001) dataset. Again, the EMU enlargement
break was eliminated by using log changes of EMU-11 before
enlargement and of EMU-12 after enlargement. The short-term
and long-term interest rates were updated with the 3-month
money market rate and the 10-year government bond yield. Finally, the own rate of M3 was constructed from the rates of return to the components of M3 as outlined by Calza et al. (2001).
The data for M3 and the interest rates from 2000Q1 to 2003Q2
were taken from the ECB website, and the data for GDP and the
GDP deflator were taken from Eurostat, through Datastream.
Nominal stock prices were approximated using the German
DAX30 for 1980–1986 (because no euro-denominated European stock price index is available for this period) and the Dow
Jones Euro Stoxx50 for 1987–2003. The data were downloaded
from Datastream. The DAX30 was rescaled such that the value
on December 31, 1986 equaled the value of the Euro Stoxx50
on January 1, 1987. Equity returns were constructed as follows. First, the annualized log difference of average quarterly
stock prices were calculated, which yielded a very volatile series. Therefore, a 3-year average of the equity returns was computed. This rather long-term yield measure was used to mimic
the fundamental yield path and exclude erratic short-term yield
changes, which probably do not affect long-run money demand.
Because there are clearly many ways to obtain a smooth quarterly series of equity returns from daily data, the following alternatives were checked: a 3-year average of quarterly returns
calculated as the quarterly average of daily returns, and a 2-year
and a 2- 12 –year average instead of a 3-year average. In all cases,
the estimation results remained largely unaffected.
Stock market volatility was constructed as the 2-year average
of the conditional variance estimated from a leverage generalized autoregressive heteroscedasticity (GARCH) model with

the influence of the stock market variables, indicates an alarmingly high money overhang, whereas the more appropriate measure incorporating the influence of the stock market variables
does not indicate any noteworthy excess liquidity. This result
corroborates the view put forward by the ECB that the recent
money growth poses no exceptional threat to price stability.
Overall, the results demonstrate that measures of excess liquidity produce different results depending on whether stock
market variables are included. Because the official 4.5% money
growth target was derived without taking stock market influences into account, it is no wonder that this target is misleading
in the current environment. It was perhaps due to this realization that the ECB decided to downweight the monetary pillar in
their May 2003 policy revision.

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ACKNOWLEDGMENTS
The author thanks, without implicating, Don Andrews, Paul
Kramer, Joachim Scheide, Anders Warne, Beatrice Weder, the
editor, Torben Andersen, three unknown referees, and the participants of the Freitagsseminar at the Bundesbank for helpful
comments and suggestions.
APPENDIX: CONSTRUCTION OF THE DATA
The dataset published by Calza et al. (2001), which contains data for M3, GDP, the GDP deflator, the long-term and
short-term interest rates, and the own rate of M3 for 1980Q1 to
1999Q4, was updated until 2003Q2. To not induce a break in
the data series, their construction of variables was closely mimicked. M3 was updated with flows adjusted for any changes that
did not arise from transactions. This implies in particular that
the break induced by EMU enlargement in 2001 was eliminated
from the data. In a similar manner, GDP and its price deflator
(a)

(b)

Figure 2. The Stock Market Variables From 1980Q1 to 2003Q2. (a) Equity returns. (b) Stock market volatility.

Carstensen: Stability of EMU Money Demand

401

Table A.1. Univariate Unit Root Tests

Test

Optimal lag length
BIC
LM test

M3 money balances mpt
ADF
1
DFGLSu
Real GDP yt
ADF
1
DFGLSu
Interest rate spread rts − rto
ADF
1
DFGLSu

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Stock return spread rte − rto
ADF
1
DFGLSu
Volatility vt
ADF
1
DFGLSu

1

Lags for autocorrelation correction
2
3
4

12

2

−1.67
−1.81

−1.54
−1.70

−1.78
−1.92

−1.62
−1.75

−2.21
−2.36

1

−1.42
−1.44

−1.35
−1.48

−1.53
−1.77

−1.98
−2.25

−1.53
−2.01

1

−1.45
−1.46

−1.00
−1.02

−1.05
−1.07

−1.16
−1.17

−1.04
−.81

12

−1.54
−1.57

−1.46
−1.51

−2.14
−2.10

−2.12
−2.06

−1.93
−1.71

1

−.33
−.62

−.48
−.79

−.44
−.74

−.48
−.91

.18
−.35

NOTE: ADF is the augmented Dickey–Fuller test, and DFGLSu is the Dickey–Fuller test with GLS detrending proposed by Elliott (1999).
The test regressions for mpt and yt were estimated with a constant and a linear trend. The corresponding 5% critical values are −3.45 for
ADF and −3.17 for DFGLSu. The test regressions for rt t s − rto , rte − rto , and vt were estimated with a constant. The corresponding 5% critical
values are −2.89 for ADF and −2.73 for DFGLSu. The optimal lag length of the ADF model was determined both by the Bayesian information
criterion (BIC) and by successively increasing the lag length until the null of no autocorrelation could not be rejected using an LM test (LM).

t-distributed innovations, applied to daily returns of the nominal stock price index. Using averages makes the volatility index
less erratic and better reveals the underlying movement in risk
perception, which again seemed a better measure to include in
a long-run money demand function. Further, the sensitivity of
the results was also rechecked, with the degree of smoothing
changed to 2- 12 –year and 3-year averages. The estimation results remained unaffected. The two stock market variables are
displayed in Figure 2.
The presence of unit roots is a necessary condition for a variable to enter a cointegration relationship. Because standard unit
root tests fail to reject the unit root assumption for all variables
in Table A.1, we treat these variables as integrated of order 1.
The volatility measure in Table A.1 was constructed from a
GARCH model with a nearly nonstationary conditional variance equation, hence the result of the unit root tests is no surprise. (For a discussion of the nonstationarity of interest rate
spreads, see Calza et al. 2001; Evans and Lewis 1994.)
[Received April 2005. Revised April 2006.]

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