Modern Economy, 2012, 3, 534-541 Published Online September 2012 (
The Eurozone’s Equilibrium Real Exchange Rates
Antonin Rusek
Department of Economics, Susquehanna University, Selinsgrove, USA
Received May 15, 2012; revised June 18, 2012; accepted June 25, 2012
The equilibrium real exchange rate is the one of the key concepts in the macroeconomic and policy analysis. The im-
portance of this concept yet increases in a currency union. In general, the real exchange rate misalignments are per-
ceived to be the causes of the loss of a competitiveness, growth slowdowns and currency crises in cases of overvalua-
tion, overheating and inflation in cases of undervaluation, sectoral misallocations of resources and global economic im-
balances. In a case of a currency union the divergent dynamics of real effective exchange rates in the individual coun-
tries—both the actual and an equilibrium—will exacerbate both economic and political tensions (in addition to above
mentioned problems) and may lead to the collapse of not only the monetary union per se but the underlying integration
processes as well. This paper employs the estimation of the BEER (behavioral equilibrium exchange rate) for the seven
Eurozone countries: Germany, France, Italy, Spain, Greece, Portugal and Ireland for the 1999:1-2011:3 period. The
purpose is to compare the performance of the Eurozone “powerhouses” (Germany and France) with the countries on the
Mediterranean littoral plus Ireland (so called “troubled periphery”). Those estimates are then used to calculate the de-
gree of Euro’s misalignment and the magnitude, persistence and the direction of dynamic tendencies within the Euro-
zone itself.
Keywords: Real Exchange Rate; Equilibrium; Misalignment
1. Introduction
The real exchange rate is among the most important cate-
gories in the both macroeconomic and the international
economics analysis. The dynamics of the real exchange
rate influences (and is in turn influenced by) the dynam-
ics of both real and financial sectors of all economies.
Empirically, the real exchange rate misalignments are
perceived to be the causes of the loss of competitiveness,
growth slowdowns and currency crises in cases of over-
valuation, an overheating and inflation in cases of under-
valuation, sectoral misallocations of resources and global
economic imbalances.
In the case of a currency union which includes sover-
eign countries, the dynamics of the real exchange rate
takes on an additional importance. The divergent dynam-
ics of real effective exchange rates in the individual coun-
tries—both the actual and an equilibrium—will exacer-
bate both economic and political tensions and may lead
to the collapse of not only the monetary union per se but
the underlying integration processes as well.
The reason is that the members of a currency union
loose both the monetary policy to influence domestic
economic dynamic and the nominal exchange rate as a
tool to influence unfavorable developments vis a vis the
rest of the global economy.
That, indeed, places an increased burden on the remain-
ing economic policy tools, namely the microeconomic
policies (which encompass both regulations in general
and labor markets policies) and the fiscal policy in all its
aspects. But the use of the both microeconomic and fiscal
policies to deal with unfavorable economic developments
more often than not leads to an economic pain, which
then results in the government unpopularity and the ris-
ing political and social tensions.
Under those circumstances individual governments at-
tempt to influence the common monetary (and hence the
exchange rate) policy in their favor. But because indi-
vidual countries face different economic circumstances
(and, in fact, may have governments with different eco-
nomic preferences), attempts to influence the central mone-
tary authority may (and will) lead to a rising tensions and
disagreements between countries. This may eventually
endanger the existence of the monetary union itself.
Whether a currency union is in the process of an in-
creasing economic cohesion or an increasing divergence
is, indeed, the empirical question. After all, in the entity
like EMU (European Economic and Monetary Union,
commonly called Eurozone) a degree of difference among
member states is natural. It is the consequence of differ-
ent historical, economic and political traditions, as they
express themselves in differing legal systems, regulations,
opyright © 2012 SciRes. ME
A. RUSEK 535
labor markets, social welfare and economic policy insti-
tutions. Removing those differences is a very long run
In the medium term the “cohesion” processes are sup-
posedly facilitated by the processes of removing the ob-
stacles to the movement of goods and services and capi-
tal among the Eurozone (and EU) member nations, by
the harmonization of the of the goods, services, capital
and labor markets regulations among these states and by
a harmonization of public taxes and public services (i.e.
the fiscal policy area). And whereas a large progress was
made here in 1990s, the process itself slowed down radi-
cally after the Euro introduction in 1999 (Tilford, [1]).
That raises the question: did the introduction of the
common currency resulted in an increased cohesion among
the Eurozone countries? Or did it lead to increasing di-
vergences (as the discussion above hinted is certainly
Dynamics of the real exchange rates may indicate pos-
sible answers. Even if the nominal exchange rate is the
same for all Eurozone participants, the real exchange rates
may differ. The reasons are the differing dynamics of the
unit labor costs in the individual countries and the dif-
ferent trade patterns generating different weights in the
calculations of the “effective” real exchange rates.
However, one would assume that as the Eurozone co-
hesion increases (i.e. it gradually becomes single eco-
nomic area) the real effective exchange rates should con-
verge as well—or at least not to diverge. And this proc-
ess should be observable not only for the actual real ef-
fective exchange rates, but, perhaps more importantly,
for their “equilibrium” values as well.
The objective of this paper is to analyze the long term
dynamics of the real exchange rates in the several indi-
vidual Eurozone countries and to estimate their “equilib-
rium” values. It is today increasingly recognized that the
diverging real exchange rates (i.e. the diverging competi-
tiveness) between the Eurozone members are at the root
of the current crisis. But the equilibrium real exchange
rate dynamics during the common currency existence is
seldom analyzed and compared, especially as far as the
different groups of countries (and/or different areas within
the Eurozone) are concerned. This paper aims to contrib-
ute to filling this gap.
Therefore, the questions this paper seeks to answer are:
1) Do the “equilibrium” real exchange rates for the
“core” (represented here by Germany and France) and
“periphery” (Greece, Italy, Spain, Portugal and Ireland)
of the Eurozone converge or diverge?
2) Are the actual real exchange rates for the individual
analyzed countries in the Eurozone overvalued or under-
valued with respect to the individual countries equilibria?
The discussion is divided into six parts. The next part
provides the basic overview of the “equilibrium” real
exchange rate concepts and literature. The third part then
provides the basic discussion of the McDonald’s BEER
(behavioral equilibrium exchange rate) concept, which is
then used in the further analysis. Part four reports econo-
metric results which are then discussed in the part five.
Part six concludes.
2. “Equilibrium” Real Effective Exchange
Rate: Modeling Concepts and Literature
A misaligned real exchange rate is commonly thought of
to be the one of the main reasons for economic disequi-
libria. However, it is obvious that the notion of “mis-
alignment” of the real exchange rate requires the idea of
the “equilibrium” real exchange rate.
But the latter one is not a simple concept, because the
real exchange rate affects not only a single market (or a
single economic sector) but the multitude of markets and
sectors—both real and financial.
But even if the “equilibrium” real effective exchange
rate can be defined theoretically, the complexity of this
concept generates difficulties in operationalizing the equi-
librium real effective exchange rate notion for the pur-
poses of the empirical estimation and study.
The current economic and econometric approaches gen-
erally follow one of the three basic analytical models
developed in the economic literature. Chronologically
first is the FEER (fundamental equilibrium exchange
rate). The variants of this approach were applied for a
variety of the real effective exchange rates involving a
multitude of countries. (Examples of work in the FEER
tradition are Baffles et al. [2], Bayoumi et al. [3], Cline
and Williamson [4], Feyzioglu [5], Wren-Lewis [6], this
approach is analyzed and compared to others by Siregar
and Rajan, [7]).
This model is derived from the (rather standard) eco-
nomic assumption that the equilibrium real effective ex-
change rate is the one which is compatible with both the
internal and external equilibria.
In the empirical work, the small multi-equation mac-
roeconomic model is specified and estimated using ob-
served values of the relevant economic variables. Equi-
librium real effective exchange rate is then calculated
using presumed long term (equilibrium) values of the
economic variables.
(That is why some call this approach an equilibrium
calculation, not estimation.) The degree of the misalign-
ment is then calculated by comparing the actual real effec-
tive exchange rate with its calculated equilibrium values.
This approach is critiqued in two areas. First, the use
and the implied need to estimate that the multi-equation
macroeconomic model introduces possible inconsistencies
and hence biases into the values of estimated coefficients.
This comes from the fact that the number of variables in
even relatively small models is often large relative to the
Copyright © 2012 SciRes. ME
number of available observations. That makes the direct
and consistent estimation of the multi-equation model
unfeasible. Hence, the single equation estimations must
be used, tying them together by methods like seemingly
unrelated regressions and trying to restore the coefficient
consistency with subsequent calibrations. This technique,
even if necessary under circumstances (the lack of suffi-
ciently long reliable data), casts a shadow over the “es-
timated” coefficients and hence over the reliability of the
calculated equilibrium real effective exchange rate itself.
Second, the specifications of both internal and external
equilibria are often controversial. This is less so as far as
the internal equilibrium is concerned, where concepts as
the output at its potential level or the NAIRU level of
unemployment are generally accepted as the internal equi-
librium indicators. But even here the things are sometime
controversial, given the demographic and preference dy-
namic, changing the retirement age, changing work par-
ticipation rates etc.
The specification of an external equilibrium is the more
disputed subject. It is generally recognized that the as-
sumption of a zero external balance in the medium term
is rather unrealistic, given the both domestic savings –
investment nexus and the medium term fiscal nexus. In
these circumstances the assumptions regarding the me-
dium term “external equilibrium” contain a strong nor-
mative element, which then affects the calculation of the
equilibrium real effective exchange rates.
NATREX (Natural real exchange rate) class of models,
first elucidated by Jerome Stein [8], reflects an effort to
address some of the perceived shortcomings of the FEER
approach. Here the assumption of the internal equilib-
rium is preserved, usually approximated by the NAIRU
concept. However, the external position is modeled as a
dynamic interaction between the long term values of
domestic savings and investments, which then determine
the current account and hence the long term capital flows.
Both long term dynamic of domestic savings and invest-
ments is determined by economic fundamentals (relative
productivity, relative wealth, rate of return differentials
etc). Short term and cyclical influences are excluded
from the determination of the equilibrium real effective
exchange rate. Due to its construction the NATREX
model is stock flow consistent.
The real effective exchange rate determined by the
NATREX class of models is sometimes described as
“dynamic”, in contrast to the equilibrium rate determined
by FEER models. The reason is that in NATREX models
the equilibrium rate changes, reflecting the long term
dynamics of domestic savings and investments. It follows
that in a very long run (a stationary state equilibrium) all
agents will be satisfied with their asset positions. That
implies that both gross and net capital flows will cease,
hence domestic savings must equal to domestic invest-
ments. Current account—i.e. the external position—is
balanced. In this sense the strictly theoretical long term
FEER equilibrium real effective exchange rate is the
limit value for the NATREX equilibrium real effective
exchange rate.
Given its complexity and the simultaneous equations
structure, the estimation of the NATREX models runs
into similar difficulties as FEER approaches. To avoid
some of the problems, most of empirical research utiliz-
ing NATREX approach uses reduced form estimations.
That of course raises both the question of a stability of
estimated coefficients (given the long run dynamics of
factors determining saving—investment nexus, the Lucas
type critique is certainly possible) and value of funda-
mentals free of short term and cyclical variations. For the
more detailed discussions of NATREX type of models
and their estimations see Gandolfo and Felettigh [9],
Siregar and Rajan [7], Stein [8,10].
Both FEER and NATREX approaches define the equi-
librium real effective exchange rate as the one corre-
sponding to some definition of the general macroeco-
nomic equilibrium. In contrast, in the BEER (behavioral
equilibrium exchange rate) approach the equilibrium rate
is the one consistent with the prevailing level of economic
First specified by Clark and MacDonald [11], the
BEER approach is derived from the basically simple as-
sumption of a uncovered interest parity (the more de-
tailed discussion of the BEER approach is provided in
the next part). The result is the single equation suitable
for the estimating purposes. This makes the BEER ap-
proach especially suitable for situations where we are
faced with a relatively short time series, as is in the case
of the subject of this paper. The works utilizing the BEER
approach include Bouveret [12], Clark and MacDonald
[11,13], Dias and MacDonald [14], Giannellis and Kouk-
ouritakis [15], MacDonald [16-18], Maeso-Fernandez et
al. [19], Osbat et al. [20]. BEER, FEER and NATREX
models are compared in Siregar and Rajan [7].
3. The BEER Type of the Equilibrium Real
Effective Exchange Rate Model
Let us specify the uncovered interest parity in real terms as:
t+1tt t
Essr r
 (1)
where st is the real exchange rate (which here is defined
as a foreign currency per unit of the domestic currency
times domestic to foreign price ratios—i.e. an increase in
st is an appreciation and vice versa). Est + 1 is the expected
future value of the real exchange rate. Est + 1 – st is then
the expected rate of depreciation of the real exchange
rate s (assuming that (1) is in logs). rt – rt* is the domestic
to foreign interest rate differential, where r is the domestic
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A. RUSEK 537
real interest rate (defined generally as a nominal interest
rate minus the expected rate of inflation) and the r* is the
“world” real interest rate.
We can rewrite (1) as
s rrsE (2)
that is, the real exchange rate is the function of its own
expected value and the real interest rate differential.
The BEER approach assumes that the expected real
exchange rate is the function of economic fundamentals
only. That is:
t+1 t
ttt t
where Zt is the vector of economic fundamentals charac-
terizing an economy at the period t.
From the empirical standpoint, the actual real exchange
rate s can be influenced not only by its expected value
(i.e. the economic fundamentals) and the interest rate
differential, but by a variety of other short term variables
—some of them cyclical, some reflecting short term
shocks—as well. Let as denote the vector of such vari-
ables as At which influences the real exchange rate via
some function g(At).
By substituting (3) into (2) and adding g(At) , we get
tt ttt
SfZrrgAF  (4)
where F(···) is a general functional form.
Expresion (4) is the general BEER formulation of the
real exchange rate. From here the equilibrium real ex-
change rate can be defined as the function of the eco-
nomic fundamentals only, where the fundamentals values
t are cleared of the random short term influences and
measurement errors. i.e. tt
, where εt repre-
sents random and measurement errors and E(εt) = 0.
The equilibrium real exchange rate than can be ex-
pressed as:
where denotes the equilibrium real exchange rate.
Assuming that the variables in the expression (4) are
cointegrated (i.e. the coefficients reflect the long run
equilibrium relationships) then the relevant coefficients
in (4) and (5) may be assumed to be the same. Hence the
estimate of (4) can be used to calculate the equilibrium
and the implicitly the misalignment of the real exchange
rate from the expression (5).
To estimate (4), we need to specify the set of variables
for vectors Zt and At. In the economic literature, the
commonly used set of variables to represent the eco-
nomic fundamentals (i.e. the vector Zt) are the terms of
trade (TOT), the relative price of traded to non-traded
goods (TNT), the net foreign assets (NFA), productivity
(PROD) and the current account (CU). (For the relevant
literature see for example Clark and MacDonald [11],
MacDonald [18], Maeso-Fernandez, Osbat and Schnatz
[19], Siregar and Rajan, [7]).
It goes beyond the scope of this paper (which is pri-
marily empirical) to discuss in detail this choice of vari-
ables. Interested reader is referred to the authors men-
tioned above for the detailed and thoroughly argued ex-
But one should mention that this set of variables is
based on the stok-flow consistent model of an open econ-
omy specified by Frankel and Mussa [21]. In general,
those variables represent the fundamental characteristics
of an economy like relative productivity and growth,
international competitiveness and its changes, prefer-
ences of agents, domestic investments—savings nexus, a
general fiscal stance etc. (again, an interested reader
should consult the literature listed above for clear and
consistent arguments).
The vector At contains only one variable, namely the
ratio of the share of the domestic public debt in GDP
(DGDP). At = Dt.
This variable was originally specified by Clark and
MacDonald (and subsequently used by others) as a meas-
ure of the risk premium. However, one may argue that in
the context of the currency union where national gov-
ernments are deprived of tools of monetary and nominal
exchange rate policies, the fiscal policies are the ones
primarily used as a countercyclical and counter outside
shocks tools. And this certainly will be reflected in short
term variations of the debt to GDP ratios.
Substituting the expressions for Zt and At into (4), we
By the same logic, (5) can be replaced by:
tt tttt
where tt tt
, and t
CU are
values representing the economic fundamentals minus
their short term shock effects and measurement errors.
is some “equilibrium” value of Dt.
In the following analysis (6) will be used to estimate
the real effective exchange rate, whereas (7) (utilizing
coefficients obtained by estimating (6) will be used to
calculate the “equilibrium” real effective exchange rate.
4. Estimation
All variables were tested for unit roots and were found to
be I(1). Hence the estimation equation is defined in first
differences (denoted below by the Greek letter Δ. No
logarithmic transformation could be used because of some
negative observation of levels in CU and r – r*.) Hence,
for the purposes of the estimation, the Equation (6) is
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Copyright © 2012 SciRes. ME
6 t
expressed as follows: in RATS software. Results for all 7 countries are reported
in Table 1.
t0 t2
7t t
rr CU
 
 
To calculate the “equilibrium” values, the relevant form
of the expression (7) can be written as
where Δst is the (first difference) of the real effective
exchange rate (REER), ΔTOTt is the first difference of
terms of trade (defined here as prices of exports over
prices of imports), ΔTNTt is the first difference of the
ratio of the producer to consumer price indexes (used
here as the proxy for the tradeables to non-tradeables
price ratio), ΔNFAt is first difference of the ratio of net
foreign assets to GDP (both in Euro terms),
1t tt
t02 3
***E* E
4tt 56
 
 
is the first difference real interest rate differential, ΔDt is
the first difference of the ratio of the share of the domes-
tic public debt in GDP to the same share for the world
and ΔPRODt is the value for productivity, represented
here by the first differences of the output per capita. εt is
the error tem. The REER’s are reported by the Eurostat as
the foreign currency per unit of domestic currency (Euro)
times domestic over foreign unit labor costs indexes.
Hence an increase in st indicates a real appreciation and
vice versa.
where αi (i = 1 to 7) are the estimated coefficients (from
the estimation of Equation (8) and the superscript E in-
dicates the medium term “equilibrium” values of explana-
tory variables (excluding random effects and measurement
errors). These were obtained by applying the Hodrick-
Presscot filter.
Utilizing results from (9), the degrees of misalignment
were calculated using the formula
ss 1.0
tt . Those results are reported
and discussed below.
Explanations: All coefficients are from the estimate of
the Equation (8) by the Johansen cointegration technique,
using CATS2 program in Rats. All variables which the
exclusion test indicated should be included are reported,
even if the t-test indicates that they may not be statisti-
cally significant. In contrast, if the exclusion test indi-
cated that a variable is not a part of the cointegrated vec-
tor such a variable was excluded—hence no value is re-
All data needed for the all estimates of (8) were ob-
tained from the Eurostat for the period 1999:Q1 to 2011:Q3
i.e. 47 observations. The cointegration approach pio-
neered by Johansen was applied, using CATS2 program
Table 1. Estimates for individual countries.
Terms of Trade Tradeables to
Current Accoun
to GDP RatioInterest RateNFA to GDP
(GDP per Capita)
Public Debt to
GDP Ratio Constant
Germany 0.934 2.086 6.232 –10.134 –0.096 0.888
(2.506) (2.902) (11.623) (4.700) (2.888) (2.090)
France 0.830 –23.172 –0.239 –2.283
(2.659) (27.729) (2.687) (2.301)
Italy 0.478 4.305) –0.745 1.265 –0.303
(1.984) (5.045) (12.249) (3.512) (2.417)
Spain 0.428 1.878 –0.784 –2.238 –0.135 –0.378 –0.138
(4.242) (7.986) (5.094) (3.845) (14.698) (2.551) (2.601)
Greece –0.206 –1.142 –1.001 0.290 10.365 1.1773
(1.960) (4.852) (13.916) (19.004) (1.985) (4.280)
Portugal –1.137 –0.985 –1.641 0.155 –22.468 1.168
(6.639) (13.714) (5.104) (14.855) (3.688) (5.478)
Ireland 5.783 0.035 –41.888 –1.977 3.794
(6.371) (2.811) (13.555) (11.852) (6.549)
Numbers in parenthesis are the relevant t-statistics.
A. RUSEK 539
5. Results: What Do They Tell Us
Real equilibrium exchange rates (REERs) for the seven
Eurozone countries (Germany, Greece, Italy, Spain, France,
Portugal, Ireland) are reported in the Figure 1(a). The cor-
responding equilibrium values (calculated using Equation
(9) are then in the Figure 1(b).
The visual inspection of the Figure 1(a) indicates the
well known dynamics of the rising discrepancies between
the individual countries REERs. Interestingly enough, it
appears that the individual equilibrium REERs converged
for 5 countries (Germany, France, Italy, Spain and Por-
tugal) by the beginning of 2007—i.e. just before the on-
set of current difficulties. But those rates subsequently
diverged again. Ireland and Greece remained the outliers
throughout the analyzed period.
The comparisons of the individual national REERs
with the calculated equilibrium values are shown in the
Figure 2. Figure 3 than shows the misalignment of the
individual national REERs, calculated by the formula
stated above.
EX ch ang e
Germany France Spain Italy Greece Portugal Ireland
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011
Germany France Spain Italy Greece Portugal Ireland
20111999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010
Figure 1. Real effective exchange rates: actual and equilibrium across countries. (a) Real effective exchange rates: 1999:1-
2011:3; (b) Equilibrium real effective exchange rates: 1999:1-2011:3.
Figure 2. Real effective exchange rates: actual and equilibrium for individual countries.
Copyright © 2012 SciRes. ME
Figure 3. Overvaluation (+) and undervaluation (–) of real effective exchange rates.
These results indicate that relative to their long run
BEER equilibrium values the REER for Greece is sig-
nificantly overvalued, whereas the REER for Germany is
noticeably undervalued.
Other countries are close to their estimated BEER equi-
libria, albeit with a slight tendency for undervaluation for
France and Ireland. Italy went from overvaluation to un-
dervaluation, the dynamics which may be helpful in on-
going difficulties. The REERs for Spain and Portugal are
basically at their BEER long term equilibrium throughout.
6. Conclusions
The results represented in Table 1 and Figures 1-3 are
somewhat surprising. Whereas they do indicate an in-
creased divergence between the analyzed countries, es-
pecially between the “Southern 5” and Germany, for the
5 countries (Italy, Spain, Ireland, Portugal, France) no
significant disequilibria can be identified when the BEER
equilibrium concept is used.
Comparing the actual national REERs to national equi-
libria (Figure 3), we see clear divergence only for Ger-
many (Undervaluation) and Greece (overvaluation).
In this context a simple thought experiment can be il-
luminating. Assuming that unit labor costs change only
slowly over time and the nominal REER can be approxi-
mated by USD/EURO rate (on average $1.30 per euro at
the time of writing), then observed German 20% - 25%
undervaluation would imply the “nominal equilibrium
exchange rate about $1.60 per Euro. On the other side the
observed about 30% overvaluation for Greece (relative to
the calculated BEER equilibrium) would imply the
nominal exchange rate $1.0 per Euro.
One may see the calculations in the previous paragraph
as the “justification” for demands of the so called “Troika”
for Greece to reduce radically their unit labor costs. (Re-
portedly requiring the reduction in private sector wages
and benefits by the combined amount about 30%). The
“internal devaluation” at work!
However, one should caution that BEER estimates are
based on the assumption of the existing economic poli-
cies and dynamics, albeit smoothed out by eliminating
temporary shocks and other short term phenomena. It is
therefore not surprising that the actual and the “estimated
equilibrium” REERs often come relatively close together.
Hence, only a significant and protracted deviation from
the estimated equilibrium will be observed. In other words,
it is recognized that the methodology employed in this
analysis may be implicitly biased toward the equilibrium
and hence to underestimate the extent of the actual com-
petitiveness problem inherent in the Eurozone construc-
tion and policies.
Nevertheless the competitiveness problem within the
Eurozone clearly exists. Whether the solution is in the
Eurozone’s restructuring, “internal devaluation” in some
countries (which is the actual, even if unspoken, rationale
behind the austerity programs in the “southern tier” coun-
tries (plus Ireland)) or some combination of both remains
to be seen. But, clearly, the current situation is unsustain-
able and has to be addressed.
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