Evaluating a Self-Organizing Map for Clustering and Visualizing Optimum Currency Area Criteria

Abstract

Optimum currency area (OCA) theory attempts to define the geographical region in which it would maximize economic efficiency to have a single currency. In this paper, the focus is on prospective and current members of the Economic and Monetary Union. For this task, a self-organizing neural network, the Self-organizing map (SOM), is combined with hierarchical clustering for a two-level approach to clustering and visualizing OCA criteria. The output of the SOM is a topologically preserved two-dimensional grid. The final models are evaluated based on both clustering tendencies and accuracy measures. Thereafter, the two-dimensional grid of the chosen model is used for visual assessment of the OCA criteria, while its clustering results are projected onto a geographic map.

Full text

  
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Volume 31, Issue 2

Evaluating a Self-Organizing Map for Clustering and Visualizing Optimum
Currency Area Criteria

Peter Sarlin
DepartmentofInformationTechnologies,ÅboAkademiUniversity
Abstract
Optimum currency area (OCA) theory attempts to define the geographical region in which it would maximize
economic efficiency to have a single currency. In this paper, the focus is on prospective and current members of the
Economic and Monetary Union. For this task, a self-organizing neural network, the Self-organizing map (SOM), is
combined with hierarchical clustering for a two-level approach to clustering and visualizing OCA criteria. The output
of the SOM is a topologically preserved two-dimensional grid. The final models are evaluated based on both clustering
tendencies and accuracy measures. Thereafter, the two-dimensional grid of the chosen model is used for visual
assessment of the OCA criteria, while its clustering results are projected onto a geographic map.
IacknowledgethefinancialsupportfromJubileumsfondenvidÅboAkademiandDagmarochFerdinandJacobssonsfondandTomasEklund
for comments.
Citation: Peter Sarlin, (2011) ''Evaluating a Self-Organizing Map for Clustering and Visualizing Optimum Currency Area Criteria'', Economics
Bulletin, Vol. 31 no.2 pp. 1483-1495.
Submitted:Nov242010.Published: May 22, 2011.
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Economics Bulletin, 2011, Vol. 31 no.2 pp. 1483-1495
1. Introduction
Optimum currency area (OCA) theory attempts to define the geographical region in
which it would maximize economic efficiency to have a single currency. The seminal work
on the OCA theory was done in the early 1900s by Abba Lerner (Scitovsky, 1984). However,
the concrete OCA criteria suggested in the 1960s and 70s are the following: mobility of
factors of production (Mundell, 1961), the degree of economic openness (McKinnon, 1963),
product diversification (Kenen, 1969), the degree of financial integration (Ingram, 1969),
similarity of inflation rates (Haberler, 1970 and Fleming, 1971) and the degree of policy
integration (Tower and Willet, 1970).1 For an overall review of the OCA theory, see Horvath
(2003).
Research from the turn of last century concerns, however, mainly empirical
assessments of the OCA theory. The empirical literature is divided into two groups of
methods: econometric and pattern recognition techniques. Coenen and Wieland (2000),
Smets and Wouters (2002), Banerjee et al. (2005) and Raguseo and Sebo (2008) explore
OCA criteria using econometric techniques, while Eichengreen (1991), Bayoumi and
Eichengreen (1992), Eichengreen and Bayoumi (1996), Alesina et al. (2002), Boreiko (2002),
Komárek et al. (2003) and Kozluk (2005) employ pattern recognition techniques for
assessing OCA criteria. The group of pattern recognition techniques consists also of a few
studies that utilize computational clustering techniques for assessing prospective and current
members of the Economic and Monetary Union (EMU). The clustering analyses have mainly
employed fuzzy techniques, such as fuzzy c-means (FCM) clustering, and assume that
Germany is the center country used for measuring convergence. By applying fuzzy clustering
techniques to variables suggested by OCA theory, Artis and Zhang (2001; 2002) look for
heterogeneities in the actual and prospective EMU membership. Similarly, Boreiko (2002)
apply fuzzy clustering analysis on measuring the readiness of the accession countries of
Central and Eastern Europe for the EMU. Boreiko’s set of variables includes both the
Maastricht criteria (nominal convergence) and the OCA criteria (real convergence). By a
similar application of fuzzy clustering, Kozluk (2005) judges the suitability of the accession
countries for the EMU in relation to current members using the OCA criteria, and measures
readiness – and the effort it will take to fulfill the entry requirements – using the Maastricht
criteria. Further, Ozer and Ozkan (2007, 2008a and 2008b) employed recently FCM
clustering on identifying OCA variables that distinguish prospective and current EMU
member countries. This paper is mainly based on the previous work done by Ozer and Ozkan.
Exploratory data analysis (EDA) attempts to describe different aspects of the
phenomena of interest in an easily understandable form by illustrating the structures in a data
set, but by simultaneously preserving information of the original data set. There exist two
distinguishable categories of EDA methods: projection and clustering techniques. The
clustering techniques, such as FCM clustering, attempt to reduce the amount of data by
enabling analysis of a small number of clusters, whereas the projection methods, such as
multidimensional scaling (MDS) and its many variants (Cox and Cox, 2001), attempt to
project multidimensional data onto a lower dimension, while attempting to preserve the
whole structure of the data set. When attempting analysis of multidimensional data, such as
statistical OCA indicators, methods of EDA are feasible techniques. The clustering methods
do not, however, enable visual representation of the data distribution, while the projection
techniques do not enable simultaneous clustering.
The Self-organizing map (SOM) (Kohonen, 1982, 2001) is an unsupervised general
purpose EDA tool that elegantly combines the goals of projection and clustering techniques,
1 Additional studies in the early stage of the OCA theory are, for example, Corden (1972) and Ishiyama (1975). Subsequently, the OCA
criteria have been reassessed in, for example, Bertola (1989), Giavazzi and Giovannini (1989), Artis (1991), Mélitz (1991), Krugman
(1991), Krugman (1993) Tavlas (1993) and Tavlas (1994).
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enabling utilization of the pattern recognition capabilities of our own human brains. On the
one hand, the SOM projection differs from other projection techniques, such as MDS, by
focusing on preserving the local neighborhood relations, instead of trying to preserve the
global distances between data. Rather than projecting data into a continuous space, such as
MDS methods, the SOM uses a grid of nodes onto which data are projected, and which are
subsequently clustered. The two-level clustering of the SOM, i.e., separation of data into
nodes and nodes into clusters as proposed by Vesanto and Alhoniemi (2000), differs from
other statistical clustering techniques. In this paper, the second-level clustering is done using
Ward’s (1962) hierarchical clustering. Vesanto and Alhoniemi assert that the two-level
clustering of the SOM differs from other clustering methods by being more robust on data
that are non-normally distributed, by not needing a priori specification of the number of
clusters, and by being efficient and fast especially in comparison with other clustering
techniques. Thus, the mapping of the SOM may either be thought of as a projection
maintaining the neighborhood relations in the data (Kaski, 1997) or as a spatially constrained
form of k-means clustering (Ripley, 1996).
The applications of the SOM concern mainly studies in engineering and medicine (Oja
et al., 2003), while it has been applied infrequently in macroeconomic time-series analysis.
For example, Sarlin and Marghescu (2011) and Sarlin (2011) have used the SOM for
monitoring indicators of currency and debt crises, respectively, while Länsiluoto et al. (2004)
have used the SOM for analyzing the macro environment for the pulp and paper industry. The
SOM has only been briefly introduced to analysis of economic convergence in Serrano-Cinca
(1997). Our paper, however, differs by addressing specifically OCA convergence rather than
convergence of the EU member states in general and in terms of countries, indicators, time
span and visualization of the SOM output. We attempt to identify OCA variables that
distinguish prospective and current EMU member countries. The created SOM model enables
also analysis over time and across countries of convergence or divergence to the EMU on a
two-dimensional plane. Further, we pair the SOM with a geospatial dimension by plotting the
color code of the cluster representative, enabling a projection of multidimensional
information on a geographic map. We also use an evaluation framework for choosing the
model and introduce an OCA index for analysis of overall convergence. The visual
explorations in this paper illustrate the usefulness of the SOM for clustering and visual
monitoring of the OCA criteria. Since the projection preserves the neighborhood relations,
not the absolute distances between data, the map will present convergence in a rank-ordered
manner rather than showing absolute distances between countries.
The paper is organized as follows. The first part introduces the methodology used for
assessing the OCA criteria. First, the SOM is introduced, whereafter the OCA criteria and
sample of countries are discussed. The second part explains the training criteria and the
construction of the SOM model. The third part shows visual analyses using the SOM model
and a geospatial mapping. Finally, the fourth part concludes by presenting the key findings
and recommendations for future research.
2. Methodology
2.1 Self-Organizing Maps
The SOM is a projection and vector quantization technique utilizing an unsupervised,
competitive learning method developed by Kohonen (1982, 2001). Through projection, the
SOM reduces the dimensions of the data space (as factor analysis does), while the vector
quantization enables representation of data in specific mean profiles (as clustering does).
Formally, the SOM performs a mapping from the input data space Ω onto a k-dimensional
array of output nodes. In this paper, for visualization purposes k equals to 2. The vector
quantization allows modeling from the continuous space Ω, with some probability density
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function f(x), to a finite set of nodes. However, the location of these nodes on the map
depends on the neighborhood structure of the data in the input space.
For its superior visual features, the software Viscovery SOMine 5.1 is used in this
study.2 It employs the batch training algorithm; instead of processing the data vectors
sequentially, it processes all data vectors simultaneously. The training process starts with an
initialization of the reference vectors. Instead of random initialization, the reference vectors
are set in the same direction as the two principal components using principal component
analysis (PCA). Following Kohonen (2001), this is done in three steps:
1. Determine the two eigenvectors, v1 and v2, with the largest eigenvalues from the
covariance matrix of all data vectors x.
2. Let v1 and v2 span a two-dimensional linear subspace and fit a rectangular array along
it, where the main dimensions are the eigenvectors and the center coincides with the
mean of x. Thus, the direction of the long side is parallel to the longest eigenvector v1
and its length is defined to be 80% of the length of v1. The short side is parallel to v2
and its length is 80% of the length of v2.
3. Identify the initial value of the reference vectors mi(0) with the array points, where the
corners of the rectangle are 21 4.04.0 vv  .
This has been shown to lead to rapid convergence and enables reproducible models (Forte et
al., 2002). The batch training algorithm operates according to the following two steps: (1)
pairing the input data with the most similar nodes, or best-matching units (BMUs), and (2)
adapting the BMU’s, and its neighbors, reference vectors based on the paired data. The steps
are repeated for a specified number of iterations.
In the first step, each input data vector x is compared with the network's reference
vectors mi,
i
i
cmxmx  min . (1)
such that the distance between the input data vector x and the winning reference vector mc is
less than or equal the distance between x and any other reference vector mi. During the first
step, all the input vectors are presented to the map.
In principle, the second step estimates the reference vectors i
m such that the
distribution of the map fits the distribution of the input space. Formally, each reference vector
i
m is adjusted using the equation for the batch algorithm:
,
)(
)(
)1(
1)(
1)(




 N
jjic
N
jjjic
ith
xth
tm (2)
where )(
)( th jic is a weight that represents the value of the neighborhood function defined for
the node
i
in the BMU c(j) at time t. The index j indicates the input data vectors that belong to
the node c, and N is the number of the data vectors. The function


1,0
)( 
jic
h is defined as a
Gaussian function:
,
)(2
exp 2
2
)( 









 t
rr
hic
jic

(3)
2 For a thorough discussion of the software, see Deboeck (1998).
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where c
r and i
r are two-dimensional coordinates of the reference vectors mc and mi,
respectively, and the radius of the neighborhood


2,0)(

t

is a decreasing function of time t.
Beginning from half the diagonal of the grid size ( 2/)( 222 YX 

), the radius )(t

decreases monotonically towards a specified tension value. A rule of thumb is that a high
tension results in stiff maps that stress topological ordering at the cost of quantization
accuracy (Vesanto et al., 2003). The rest of the parameters in SOMine are the following: map
size (the number of nodes), map format (the ratio of X and Y dimensions), and the training
schedule (number of training cycles). Furthermore, the second-level clustering is done using a
modified agglomerative hierarchical clustering. Starting with a clustering where each single
node forms a cluster by itself, in each step of the algorithm the two clusters k and l with the
minimal Ward (1962) distance are merged. The Ward distance is defined as follows:
,
otherwise
adjacent are and clusters if
2








lkcc
nn nn
dlk
lk
lk
kl (4)
where k and l represent two specific clusters, k
n and l
n the number of data points in the
clusters and 2
lk cc  the squared Euclidean distance between the cluster centers of clusters
k
Sand l
S. For coherent clusters, the algorithm is modified to only merge clusters with
neighboring clusters by defining the distance between non-adjacent clusters as infinitely
large.
The quality of the map is measured in terms of quantization error (QE) and the
distortion measure (DM) (Vesanto et al., 2003). The QE represents the fitting of the map to
the data measured by an average of the distances between all input vectors xi and their
corresponding best matching reference vectors mc, i.e.,


 N
jjcj mx
N
QE 1
2
)(
1. (5)
The normalized distortion measures the fit of the map with respect to both the shape of
the data distribution and the radius of the neighborhood, and is computed as follows.
Mh
mxh
N
DM N
j
M
ijic
N
j
M
iijjic


 
 


1 1 )(
1 1
2
)(
1 , (6)
where M is the number of reference vectors, mi is the ith reference vector, xj is the jth data
vector, and hic(j) is the neighborhood function.
The output of the SOM algorithm is, for the purpose of this analysis, visualized using a
mapping of the data points onto a two-dimensional plane. The dimensions of this plane are
visualized using layers, namely feature planes. For each corresponding indicator, the feature
planes represent graphically the distribution of the variable values on the two-dimensional
map. In this paper, the feature planes are produced in color, where low to high values are
represented by cold to warm scales. The color scales are shown below each corresponding
feature plane. For visual interpretation purposes, the distances between each node and its
corresponding cluster center are shown by shading the clusters; nodes close to the center take
a lighter color and nodes further away take a darker color.
2.2 Choice of Countries, Indicators and Index
The utilized data set is a replica of the data used in Ozer and Ozkan (2007). The
computation of the OCA variables and the choice of countries follows the practice in Artis
and Zhang (2001 and 2002), Boreiko (2003), Kozluk (2005). The set of countries is
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representative for current and prospective EMU member countries.3 Further, two benchmarks
(Canada and Japan) are included to also account for a control group. A representative set of
countries enables exploration of possibly divergent countries. Although enabling analysis of
EMU member countries is the main target of this paper, it is important to include the other
states of OCA criteria to enable temporal analysis between various states. The data set used in
this study includes cross-sectional data for 26 countries. Although temporal data have not
been collected for this paper, the projection of the OCA criteria over time would be a
meaningful further refinement for assessing convergence or divergence of countries over
time.
The indicators and their descriptive statistics are shown in Table 1, while sources,
frequency and time interval of the data can be found in the Appendix. Synchronization in
business cycles is represented by the cross-correlation of the cyclical components of
deseasonalized industrial production series with that in Germany. Following Artis and Zhang
(2001 and 2002) and Boreiko (2003), the detrending is done using the Hodrick-Prescott (H-P)
filter (Hodrick and Prescott, 1997) with a smoothing parameter of 50,000. Synchronisation in
the real interest rates is represented by the cross-correlation of the cyclical components of the
real interest-rate cycle of a country with that in Germany. The real interest rates have been
obtained by deflating with consumer price indices and detrended utilizing the H-P filter with
optimum smoothing parameters based on the nature of the time-series data (Dermoune et al.,
2006: 2-4) as also done in Schlicht (2005). For both cross-correlation variables, -1 represents
perfect negative correlation (perfect desynchronization) and 1 perfect positive correlation
(perfect synchronization). Volatility in the real exchange rates is represented before 1999 by
the standard deviation of the log-difference of bilateral real exchange rates with the Deutsche
Mark and after 1999 with that of the Euro. To obtain real exchange rates, nominal rates have
been deflated by relative wholesale and producer price indices, as available. For Portugal, the
consumer price index is used instead. Degree of trade integration is measured by




ii
EU
i
EU
imxmx  /
2525 where i
x and i
mrepresent total exports and imports of country i and
25EU
i
xand 25EU
i
mrepresent exports and imports of country i to and from European Union
countries EU25 as of May 2004 (Jules-Armand, 2007). Convergence of inflation is measured
by gi ee , where i
e and g
e represent the respective inflation rates in country i and Germany.
The reason for collapsing the panel data to a cross section is that for the variables measuring
inflation and trade we have only collected data for one year. In the future, the main task will
be to collect an extensive panel data set for up-to-date temporal analysis.
Table 1. Descriptive statistics of the OCA criteria.
VARIABLES OBS
MEAN STD.DEV
MIN MAX
Synchronization in Business Cycles 26
0.46
0.27
-0.11
0.90
Synchronization in the Real Interest Rates 26
0.33
0.41
-0.60
0.95
Volatility in the Real Exchange Rates 26
0.01
0.01
0.00
0.07
The Degree of Trade Integration 26
64.91
17.90
8.38
83.13
Convergence of Inflation 26
0.73
1.96
-2.23
7.04
OCA Index 26
0.71
0.14
0.38
0.93
The above criteria are used for computing an OCA index. For a consistent index, the
criteria have been transformed and normalized as follows. First, volatility in the real
exchange rate is multiplied by -1, so that an increase in the criterion indicates convergence to
the currency area. Since both positive and negative inflation differentials indicate divergence,
3 The countries are Austria, Belgium, Croatia, Cyprus, Czech Republic, Denmark, Finland, France, Greece, Hungary, Ireland, Italy,
Luxembourg, Netherlands, Norway, Poland, Portugal, Romania, Slovak Republic, Slovenia, Spain, Sweden, Turkey and United Kingdom.
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we define it as the negative deviation from zero measured by gi ee  , as above. For
standardizing the contribution of each criterion, they are normalized columnwise by range.
Finally, the index is defined as the country-specific average of the normalized criteria.
3. The SOM Model
3.1 Training Criteria
Ozer and Ozkan (2008b) show that the first three principal components explain more
than 80 % of the variability in the data. Thus, by exploring the three principal components,
the general structure of the data can be quite accurately assessed. In particular, both Canada
and Japan, and Turkey and Romania form their own clusters, while the rest of the countries
are grouped in a sparse cluster, indicating differences across these countries. Following Ozer
and Ozkan (2008b), the performance of the SOM analysis can be assessed using the
following clustering tendencies in the data:
1. Canada and Japan form their own cluster
2. Turkey and Romania form their own cluster
3. At least 12 EMU members form their own cluster
Further, for assessing states that differ from the countries that have converged to the
EMU, a further criterion is the existence of two additional clusters, each with at least two
countries, be they EMU members, accession countries or benchmarks. Thereby, since EMU
members may be mapped into the differing states, it is appropriate to only require 11 EMU
members for criterion 3. In addition to the above criteria, the maps are further assessed based
on two accuracy measures on the fit of the map to the data distribution, the QE and the DM,
and based on interpretability, measured by the visual cluster structure. For the set of
experiments, the maps with QE and DM in the 50th percentile are evaluated as accurate.
Percentiles are preferred over absolute thresholds on the measures, since the absolute values
of the QE and DM are not informative; they are dependent on the used data sample and
should be compared with models on the same sample. The topographic ordering of the maps
is evaluated using Sammon’s mapping (1969), a non-linear mapping from a high-dimensional
input space to a two-dimensional plane. We use it for assessing the topological relations of
the reference vectors on 3D planes. Topographic ordering is defined to be adequate if the map
is not twisted at any point and has only adjacent nodes as neighbors in the data space. To sum
up, most of the criteria concern the clustering tendency, while only the topological ordering
assesses the visual quality. The distribution of the criteria is motivated by mainly aiming at
proper clustering of the OCA criteria, but on the side also preferring an easily interpretable,
intuitive map.
3.2 Training the SOM Model
For equal weighting of the indicators and a computation-wise easier training process,
the OCA criteria have been standardized by variance. The constructed map is trained using
26 row vectors – one for each country – with a dimensionality of 5 – one for each variable.
The OCA index is not included in finding each BMU (Eq. 1), it is only associated to the map
using Eq. 2. During the course of the experiment, several maps were trained using different
parameter values (tension, cycles of training, number of clusters, number of nodes and map
format). In the final experimental stage, the map format is, however, kept constant. The map
format is chosen to be 75:100, since Kohonen (2001, p. 120) recommend that the map ought
to be of oblongated form, rather than square, in order to achieve a stable orientation in the
data space. The number of clusters is, according to the training criteria on the clustering
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tendencies, chosen to be five; one for Canada and Japan, one for Romania and Turkey, one
for the EMU members and two for assessing differing states. The parameters that have been
varied are tension and number of nodes.
Table 2. The SOM experiments.
Te ns io n
N eur o ns 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7
x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x x x x x x xxxxxxxx x x x x x x x
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x
7 6 -8 5
115-13 7
18 8 - 2 4 7
13 7 -18 8
9
No te: The c hos en map is sho wn in bo ld and X marks in columns 1–7 indica te q uality meas ure fulfillment . The co lumns per t ensio n value re pres ent the fo llowing quality
meas ures : 1, Cana da a nd Ja pan f orm th eir own c luste r; 2, Turke y and R omania f orm th eir own c luste r; 3, at leas t 11 EMU memb ers form t heir ow n cluste r; 4, e xis tence of
tw o ad ditio nal clus ters with a t leas t tw o co untries eac h; 5, QE is in t he 50t h pe rcent ile; 6 , DM is in th e 50t h per centile; 7, ad eq uate top og rap hic or der ing .
0 ,0 0 0 1 0 . 3 0 .5 0 .7 5 1 1. 5 2
2 2 -2 7
4 5- 52
Although Kohonen (2001, p. 111) notes that the selection of the parameters is not
crucial if the map size is less than a few hundred nodes, the experiments show that different
parameter values still result in varying outcomes. The SOM experiments are shown in Table
2 and resulted in the following conclusions. The experiments show that increasing the tension
value leads to imprecise clustering, measured both by the clustering tendencies and the
accuracies, while it leads to a better topographic ordering of the map. Increases in the number
of nodes leads, on the other hand, not only to precise clustering, but also to a decrease in the
topographic ordering. Based on the seven training criteria, the best SOM model is chosen. In
Table 2, it is shown that the accuracy and ordering of the maps meet in the middle of the
table, i.e., combining the accuracy and the ordering of the map.
After the extensive training process, a neural network with 5 nodes in the input layer
and 137 output nodes ordered on a map of the size 13 x 10 was chosen. The data were trained
with a tension of 1 (where


2,0)( t

) for 7 cycles, resulting in a QE of 0.09 and a DM of
0.79. The two-dimensional topological grid is shown on the left in Figure 1, while its feature
planes are shown on the right. Data are subsequently projected onto the map using Eq. (1).
4. The SOM for Mapping Countries Based on the OCA Criteria
The clusters, and the subsequently projected data, in Figure 1 can be assessed using the
feature planes in Figure 2. The feature plane for the OCA index (Figure 2) shows a composite
measure of convergence for each country. The map in Figure 1 shows that the most dissimilar
countries, i.e., Canada and Japan, and Romania and Turkey, are mapped into Cluster 1 and 2
in the upper corners of the map. Cluster 1 (C1) is especially characterized by high volatility
in the real exchange rate and a positively diverging inflation rate, while Cluster 2 (C2) shows
low values of the degree of trade integration and a strong negative divergence of the inflation
rate. For both clusters, the rest of the criteria show medium values. Interestingly, Japan and
Canada (C2) are shown to have higher convergence than Romania and Turkey (C1). Cluster 3
(C3) and Cluster 4 (C4) represent states that slightly differ from convergence with EMU. C3
shows a low synchronization in business cycles and real interest rates and a high degree of
trade integration, while otherwise representing neutral values. C4 is, especially, characterize
by a high synchronization in business cycles and a low in real interest rates. In C3, only the
Slovak Republic out of three countries is a member country, while in C4, only Greece and
Slovenia out of four countries are members of the EMU. Finally, Cluster 5 (C5) represents
convergence with the EMU. It is characterized by high synchronization in business cycles
and real interest rates, degree of trade integration and convergence of inflation, and low
volatility in the real exchange rate. Eleven out of the 15 countries in C5 are EMU members.
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The non-EMU countries that show convergence are Denmark, Norway, Poland and Sweden,
i.e., three Nordic countries.
Turkey
Hungary
United Kingdom
Japan
Greece
Slovak Republic
Slovenia
Croatia
Italy Finland
Czech Republic
Ireland
France
Sweden
Netherlands
Denmark
Spain
Cyprus
Norway
Luxembourg
Poland
Belgium
Austria
C1
C2
C3
C4
Romania
Canada
Portugal
C5
Figure 1. The two dimensional SOM grid.
Business Cycles
C1
C2
C3
C4
C5
-0.069 0.230 0.530 0.829
Real Interest Rates
C1
C2
C3
C4
C5
-0.525 -0.068 0.388 0.845
Real Exchange Rates
C1
C2
C3
C4
C5
0.0030 0.0221 0.0412 0.0603
Trade Integration
C1
C2
C3
C4
C5
10.7 25.0 39.2 53.5 67.7 81.9
Convergence of Inflation
C1
C2
C3
C4
C5
-1.51 0.56 2.62 4.69 6.76
OCA index
C1
C2
C3
C4
C5
2.00 2.51 3.02 3.53 4.04 4.55
Figure 2. The feature planes of the SOM grid.
4.1 A Geographic Representation of the SOM Clusters
For further visual representation, the clustering results can be projected on a geographic
map. By projecting the color code of each cluster on a geographic map, we can combine the
multidimensional data dimensions with a geospatial dimension. We restrict the geographic
area of interest to Europe, since visualizing the clustering results of the two correctly
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clustered benchmark countries does not bring any real added value. Germany is included into
the EMU cluster (C5), since it is converged by definition of the criteria. The mapping onto a
geographic map is shown in Figure 3. The geospatial dimension shows that the countries, be
they EMU or non-EMU countries, mapped into the differing states of the EMU are mainly in
Eastern Europe, while the United Kingdom is the only Western European country mapped
into any of Clusters 1–4. In Figure 3, the economic region with the highest convergence is
shown in light blue (Cluster 5).
Figure 3. A projection of the clustering results on a geographic map (excluding benchmarks).
5. Conclusions
In this study, we have identified, clustered and visualized OCA criteria that distinguish
prospective and current EMU member countries. Further, this study pairs the SOM with a
geospatial dimension by plotting the color coding of the cluster representative, enabling a
projection of multidimensional information on a geographic map. The visual explorations in
this paper illustrate the usefulness of the SOM for clustering and visual monitoring of the
OCA criteria. The novelty of this two-level clustering approach is a simultaneous
visualization of the clustering results, and the inclusion of the geospatial dimension. Future
work includes performing the framework presented in this paper on an extended panel data
set for up-to-date analysis, especially for assessing convergence over time.
Appendix 1
Table A. Sources, frequencies and time intervals of the data (as per Ozer and Ozkan, 2007).
Variables
Frequency
Data Sources Time Interval
Real exchange rates monthly IFS, TURKSTAT 1996:1-2005:6
Industrial production series monthly IFS 1991:1 - 2006:12
Real interest rates monthly IFS, EUROSTAT, Central Bank of Luxembourg 1997:2-2006:10
Trade data annual UNCTAD, Handbook of Statistics Online 2004
Inflation data annual WDI 2005
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