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International Journal of Public Administration
ISSN: 0190-0692 (Print) 1532-4265 (Online) Journal homepage: www.tandfonline.com/journals/lpad20
Combining the Strengths of Qualitative
Comparative Analysis with Cluster Analysis
for Comparative Public Policy Research: With
Reference to the Policy of Economic Convergence
in the Euro Currency Area
Philip Haynes
To cite this article: Philip Haynes (2014) Combining the Strengths of Qualitative Comparative
Analysis with Cluster Analysis for Comparative Public Policy Research: With Reference to the
Policy of Economic Convergence in the Euro Currency Area, International Journal of Public
Administration, 37:9, 581-590, DOI: 10.1080/01900692.2014.880849
To link to this article: https://doi.org/10.1080/01900692.2014.880849
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International Journal of Public Administration, 37: 581–590, 2014
Copyright © Taylor & Francis Group, LLC
ISSN: 0190-0692 print / 1532-4265 online
DOI: 10.1080/01900692.2014.880849
Combining the Strengths of Qualitative Comparative Analysis
with Cluster Analysis for Comparative Public Policy Research:
With Reference to the Policy of Economic Convergence
in the Euro Currency Area
Philip Haynes
School of Applied Social Science, University of Brighton, Brighton, United Kingdom
Qualitative Comparative Analysis (QCA) is a well-established method for comparing national
public policy similarities and differences. It is argued that Cluster Analysis can add additional
benefits to such research when used concurrently with QCA. Cluster Analysis provides a better
method for the initial exploration of multivariate data and examining how countries compare
because it can work with the full range of available interval data while patterns are created
and viewed. This provides the best first method for exploring patterns and likely groupings of
countries. QCA then provides a more robust method for theorizing about the construction of
such groupings and their relationship around similar variable scores. QCA makes such theorizing
transparent. The research example used to illustrate the benefits of combining Cluster
Analysis and QCA is an analysis of the evolving of macroeconomic policy for the countries
sharing the Euro, comparing 2005 (precrisis) with 2010 (postcrisis).
Keywords: case-based methods, Cluster Analysis, Qualitative Comparative Analysis
INTRODUCTION
Case-based methods in comparative public policy seek to
maintain the integrity of each country as a unique case
(Ragin, 1987). Some quantitative methods calculate multivariate
scores that represent an aggregate of variables and
therefore a summary of all cases. Examples of such methods
are linear regression and logistic regression. As an
alternative, case-based methods allow an understanding of
both similarities and differences of cases rather than a single
overall representation of the typical case. Byrne and
Ragin (2010), in their seminal text on case-based methods,
encourage the exploration of a range of case-based methods.
Cluster Analysis is a case-based method that uses a quantitative
approach, but the case-based approach also includes
some established methods that overlap both qualitative and
quantitative methods, for example, Qualitative Comparative
Correspondence should be addressed to Philip Haynes, School of
Applied Social Science, University of Brighton, School of Applied Social
Science, Mayfield House, Falmer, Brighton, BN1 9PH UK. E-mail:
p.haynes@brighton.ac.uk
Analysis (QCA) (Rihoux, 2006; Rihoux, Rezsöhazy, & Bol,
2011). Case-based methods allowed for consideration of
what Ragin (1987) described as configurational complexity
where the same policy outcomes can be linked to several
different causal patterns, rather than researchers having to
establish that one multivariate model of independent variables
determines a common dependent variable outcome.
The comparison of countries is well documented for its
methodology challenges (Rose, 1991). Countries are not historically
permanent. They are defined by their geographical
boundaries. The “fuzziness” of the country case over time
is, however, in its social and economic history and the construction
of political and economic institutions. Countries
have the levels as follows: subnational, regional, local, and
neighborhood identities. They belong to higher associations
and linkages, defined by geography, politics, and economics
(e.g., the European Union and Euro currency). There are
difficulties with the integrity of the country “case”, but nevertheless
countries can be demonstrated to be “real” by various
forms of social science evidence.
Mahoney and Larkin Terrie (2010) discuss comparative
historical analysis. The main methodological problems are a
582 HAYNES
dependence on small samples and unreliable measures. As a
result, the comparative historical approach uses a variety of
methods. Often there is a combination of quantitative and
qualitative data. Considering the reliability of variables and
their global validity is part of the task of country comparison
(Kennett, 2001).
In the last decades, QCA has been argued to be a robust
and systematic comparative case-based method that includes
aspects of both qualitative and quantitative approaches
(Rihoux et al., 2011). In this article, the argument is to
demonstrate the possibilities and benefits of combining both
Cluster Analysis (as an exploratory quantitative method)
and QCA (as a qualitative method for explanation and the
production of theory) while examining a real comparative
public policy research question. The comparative research
question used to explore the workings of the method is
the extent to which the Euro Crisis of 2010–12 can be
understood as evidence of the failure of the convergence of
macroeconomic policy because of an increasing divergence
of national macroeconomic policy trends and outcomes;
these still being evident after the setting up of the single
currency. Convergence theory has historically argued
that with the right dynamic of global market conditions,
poorer and developing countries will evolve to catch up
with the wealth of richer countries (Aghion, Howitt, &
Mayer-Foulkes, 2005). The setting up of the single European
market and soon afterwards the single European currency
for many European countries was designed not only to
increase market efficiencies via reducing transaction costs
such as currency exchange, but also to allow convergence
in wealth and income levels between member countries
with large differences in gross national income (Borsi &
Metiu, 2013). In order to answer this comparative policy
question about the nature of persisting divergence, the
17 Euro countries are examined for similarities and differences
in 2005 and in 2010. All data used are taken from
the International Monetary Fund’s (IMF’s) World Economic
Outlook Database.
CLUSTER ANALYSIS
Cluster Analysis (Aldenderfer & Blashfield, 1984) assumes
that similar and dissimilar cases exist rather than all being
heterogeneous. Cluster analytical methods do not use inferential
statistics but calculate algorithms to model similarity
(Pastor, 2010). Therefore, when a small group of countries
such as members of the European Union are used, the intention
is not to generalize results from a small sample to a
bigger population.
Patterns of cases are constructed simultaneously exploring
the interrelationship of the key variables entered into
the cluster model. The clusters of cases are defined by
their relative relationships in a matrix of scores from the
chosen variables. The analysis reduces the available data
detail and places cases into groups where similar cases
are together (Norušis, 2010; Uprichard, 2009). Hierarchical
Cluster Analysis is an appropriate form of analysis with
small data (small-n) sets.
Hierarchical Cluster Analysis can start with either all
cases separated, or all cases together. When each case is
separate at the first point of the analysis, the method is
agglomerative (Bailey, 2012). The analysis works to gather
the individual cases into logical groups. Conversely, divisive
analysis puts all the cases in one cluster and then separates
them. The advantage of the agglomerative approach
when studying countries is that it can be argued to be “critically
realistic” in the sense that countries as cases are very
complex and different (Blackman, Wistow, & Byrne, 2013;
Gerrits & Verweij, 2013). An attempt to argue countries
are similar is best worked from looking for some similarity
between individual cases rather than the opposite analytical
approach of assuming all countries are very similar and
then seeking to divide them up into groups (divisive methods).
A limitation of the hierarchical method is the selective
and overtly structured construction of cluster levels (Norušis,
2010). A hierarchy maybe imposed on the data where no real
hierarchy exists.
Agglomerative hierarchical Cluster Analysis enters all
variables at the same time, and searches first for a maximum
number of groups. It starts with the task to find the
maximum number of most likely clusters and then uses progressive
simplifications and reductions to remove the number
of clusters at each stage. Across the various stages of the
hierarchical analysis, the clusters are multidimensional or
what some refer to as “fuzzy” and not “crisp,” even though
the final computer analysis has to separate them into hierarchical
levels. The first run of the analysis produces the
largest number of clusters. These small clusters are then
reduced further and combined into larger groups at each
stage in the calculation. At any one point in the running
of the hierarchical model, clusters are artificially crisp and
separated. For example, 12 countries might be argued to
represent four different clusters, but the computer analysis
can also observe “higher” sets, such as two cluster groups
from the 12 countries. Hierarchical clusters display multiple
levels.
Hierarchical Cluster Analysis informs the researcher
about the possible similarities of cases but cannot make
the research decision and judgment about which level of
cluster groups is most valid and realistic in its portrayal
of political and economic realities. The researcher must
use their own qualitative judgment about the optimal cluster
solution, or number of clusters, from which to argue
the existence of a theoretical model. This is one of the
weaknesses of Cluster Analysis that there is an epistemological
gap between data exploration and theory development.
Nonhierarchical Cluster Analysis places less emphasis on
the qualitative judgment of the researcher because a mathematical
method calculates the final number of clusters.
COMBINING THE STRENGTHS OF QCA WITH CLUSTER ANALYSIS 583
However, the hierarchical routine of staging how countries
evolve into patterns demonstrated by hierarchical Cluster
Analysis can be argued to add to the robustness of the
exploratory modeling because analyzing the agglomerative
hierarchy of groups and cases gives depth and transparency
to the analysis. For example, all Southern European countries
might cluster together at one stage in a hierarchy, but
also two separate Southern European subclusters might be
evidenced together before the analysis reduces to individual
countries. As Norušis (2010) argues, “There is no right or
wrong answer as to how many clusters you need” (p. 364).
In this article, the clustering of cases in the research
example is derived from comparative international data provided
by the IMF. Variable scores are standardized using the
method of z scores. This reduces the chances of a wide range
in one variable having more influence on the cluster formulation
than other variables. Nevertheless, Aldenderfer and
Blashfield (1984) and Pastor (2010) caution that standardization
can have undesirable effects. It might limit the power of
a variable with a substantial range when the reality is that the
range of that variable does explain substantive country differences.
As the majority of variables used in this research
example where related to the percentage of gross domestic
product (GDP), a need to allow large variance effects was
not judged necessary. Therefore, z scores were used.
The IBM SPSS computer statistics package used in this
research is one of a number of statistical software programs
that can be used to run Cluster Analysis (Norušis, 2010, ch
16). These types of software-based Cluster Analysis measure
the distance between cases or their similarity. One frequently
used mathematical calculation for similarity and difference is
the Euclidean distance. It is “the sum of the squared differences
over all of the variables” (Norušis, 2010, p. 365). Using
the squared Euclidean distance, a proximity matrix is calculated
from the variables to show the difference between each
pair of cases. The proximity matrix produced by SPSS shows
the two countries that are most similar and those two that
are most different. The matrix output appears similar in construction
to a correlation coefficient matrix. The difference of
measurement in a proximity matrix when compared to a typical
correlation coefficient matrix is that the scores between
pairs are highly variable, and not fixed between -1 and +1.
Cluster Analysis goes beyond understanding the relationship
between pairs of cases and provides mathematical
evidence for the formation of groups as sets of cases. There
are different mathematical methods to form clusters. One
method is to average the difference between pairs of cases.
Another method is to use the smallest or largest difference.
The clustering method used in this article is the average
linkage between groups. This method is known to assist maximizing
the heterogeneity of cluster formation, does not have
a bias toward creating clusters of equal size, and is relatively
less likely to force homogeneity on the structure of
clusters. A drawback with this method is the management
of outliers and deciding when to exclude outliers. As with
the alternative single linkage method, the removal of outliers
can merely lead to further heterogeneity in the remaining
model and a new outlier is subsequently dislocated from the
weakest cluster each time the most obvious relative outlier is
fully removed. The assumption of using average linkage is
that countries—as types of cases—are fundamentally more
heterogeneous than homogenous.
The Icicle plot is a tool for seeing how cluster groups are
constructed. The bottom of the plot shows in the rows the
maximum number of hierarchical clusters. Each row above
is an agglomeration of clusters and therefore the number of
groups that has been reduced at each stage in the computer
calculation. The dendrogram is another graphics tool that
reveals the hierarchical selection of clusters according to the
mathematical method chosen. In this article, the dendrogram
is the preferred form of graphical analysis.
In summary, hierarchical Cluster Analysis is a good
method for analyzing small data sets where there is a need
to be exploratory rather than explanatory and where cases
may belong to overlapping and “fuzzy” clusters (Norušis,
2010, p. 363). Cluster modeling works by putting similar
cases together in logical ways, but is a relatively unstable
form of model creation that is dependent on the mathematical
method used. It is important that the clusters observed
be related to a theoretical model that explains why country
cases might be co-located. This is where QCA can assist and
help the researcher to move from exploration to explanation.
QUALITATIVE COMPARATIVE ANALYSIS
QCA is a contemporary method in the social sciences that
promotes the analysis of cases and is suitable for the examination
of smaller and intermediate data sets (Rihoux &
Ragin, 2009). It promotes the systematic comparison of
cases and can be used to theorize the configuration of patterns
amongst cases—in terms of explaining similarities and
differences. It can be used to model case-based outcomes
with the designation of an outcome variable and is unique
in promoting the theoretical examination of multiple routes
to the causation of outcomes. In other words, two different
clusters of cases might experience the same outcome, but
with different explanations given, or with part of the explanation
being different while there is also a shared common
component of the explanation.
QCA, in its development as a method (csQCA), focused
on dichotomous categorical variables (Rihoux & De Meur,
2009). This was the so-called Crisp set method. For example,
either a country has a particular policy or political characteristic
or it does not: an example would be classifying
a nation as having either a state-funded health service or
an insurance-funded health service. With this type of QCA,
when quantitative variables like macroeconomic variables
are used, they are either above or below a threshold set
by the researcher. Binary thresholds have to be set by the
584 HAYNES
judgment of the research and can be criticized as rather
arbitrary, but when cross-triangulated with the statistical
synthesis of Cluster Analysis, such analysis of individual
variable effects on cluster membership provide complementary
levels of understanding and detail not readily offered by
Cluster Analysis alone.
Boolean algebra is used to analyze and theorize the patterns
and overlapping clusters created from a series of ones
and zeros generated by QCA (Gullberg, 1997, pp. 252–256).
Much QCA literature prefers to call its groupings “sets”
rather than “clusters”, although for the purposes of this article
the distinction is not important or problematic, but it
should be noted that QCA “sets” require a high degree
of specification with regard to group membership. Casebased
patterns can be associated to an outcome variable
and “different constellations of factors may lead to the
same result” (Berg-Schlosser, De Meur, Rihoux, & Ragin,
2009, p. 8). Therefore, one of the advantages of QCA is
that the theoretical models it produces demonstrate multiroutes
to causation rather than a single aggregate linear score
with numerous residual effects. This is also referred to as
“Multiple Conjunctural Causation” (Berg-Schlosser et al.,
2009, p. 8). QCA has been described a useful methodological
development for comparing nation states (Berg-Schlosser
et al., 2009, p. 4). But QCA is “not an end to itself; rather
a tool to enhance our comparative knowledge about cases
in small . . . research designs” (Rihoux & De Meur, 2009,
p. 33). QCA provides a robust method for constructing theory,
with the definition of theoretical clusters (sets) and their
boundaries being demonstrated by Boolean algebra. This is
the explicit theoretical labeling of cluster groups to describe
and construct their meaning in public policy on the basis
of statements about shared variable scores. Using Boolean
algebra, threshold variable scores shared by two or more
countries can be recorded as “Primary Implicants.” These
Primary Implicants are Boolean “expressions” indicating
above or below threshold scores that are consistent for a
group of countries. An example might be; for cluster group
one, the Primary Implicant is A + b, where above threshold
scores on variable A and below threshold scores for variable
b are always present for members of that group. Uppercase
notation and lowercase notation is one convention that has
been used in QCA to illustrate above and below threshold
variable scores.
The use of QCA in addition to Cluster Analysis gives the
researcher a more robust and transparent method for theorizing
about the construction of clusters and how clusters
are defined by the influence of specific variables. There is
an opportunity for the researcher to experiment with different
threshold settings of certain variables and to observe
in a more robust and systematic manner the effect on the
fuzziness—or overlap—of clusters.
THE ADVANTAGES OF COMBINING CLUSTER
ANALYSIS AND QUALITATIVE COMPARATIVE
ANALYSIS
Table 1 shows the strengths and weaknesses of Cluster
Analysis and QCA given they are both case-based methods
designed to preserve the integrity of the case and allow
cases to be systematically compared. Both methods accept
that there is not likely to be one “ideal” solution but various
possibilities and arguments for comparing case patterns.
Cluster Analysis allows full use of the available continuous
data. A cluster method like hierarchical Agglomeration
is designed to work with continuous and interval scores, even
if standardization is often required to minimize the distortion
of one variable with a larger range. This avoids some problems
of data degrading and reduction. In contrast, QCA often
requires the variables to be degraded, for example, QCA(cs)
requires continuous variables to be transformed into dichotomous
variables based on the judgment of the researcher and
fuzzy set QCA (fsQCA) requires a limited number of ordinal
ranks to be applied to interval data. These fundamental differences
are related to the analytical strengths and weakness
of the different methods. Cluster Analysis can use an interval
data range to create logical patterns of cases, although
this means multiple versions of the same sorts of patterns
can result in repeat modeling, and the researcher still has to
make an informed decision on which final model to use in
theory and practice. QCA, however, because of its simplified
data input allows a more systematic and theoretical view
of the configuration of cases and how this is related to variables.
Higher level abstraction of theory can be explained
with a more consistent logic applied and this demonstrated
in Boolean algebra.
TABLE 1
A Comparison of Cluster Analysis and QCA
Similarities Differences Strength Weakness
Cluster analysis Allows focus on case Continuous variables Empirical use of continuous
variables to explore possible
logical patterns of cases
Instability of modeling
associated with the specific
mathematical method used
QCA Degraded variables Theorizing the configuration of
cases to explore the complexity
of case-based patterns
Empirical simplification
COMBINING THE STRENGTHS OF QCA WITH CLUSTER ANALYSIS 585
Methodological strengths can lead to paradoxical weaknesses
of method, so the problem for Cluster Analysis is
the instability of modeling that the data quality creates.
The researcher must guide against “statistical artifacts”—
sophisticated mathematical patterns that cannot be logically
attached to theoretical concepts and constructs of real social
and economic explanatory value. The weakness of QCA,
however, might lead the researcher to argue impressive logical
theorizing about the comparability of cases that is not
empirically justified by the underpinning data variables and
measurements.
When both methods are used to explore the same research
questions and data sets, they can assist coverage of the
methodological weakness that the other method displays. If a
model is at first generated by Cluster Analysis, QCA can be
used to understand the variable interactions with clusters and
to explore “fuzziness,” where some cases appear to be less
clearly linked to clusters than others. While Cluster Analysis
does have a “cluster by variable” option, this only shows
a holistic connection of the variables used, and is of limited
value when wanting to understand the dominate variable
influences on specific cases and clusters. QCA gives added
insight into the effect of variables on cluster construction.
QCA can also be used to add a dependent variable as an
outcome element to a model and this is not an option in
Cluster Analysis. For example, the researcher might wish
to see if cluster groupings can be associated in some way
with the determining the scores of one dependent variable.
An example with country comparison might be to assign
GDP as an outcome variable and to test this in the context
of the cluster patterns that already developed. QCA provides
novel ways for looking at outcomes given its ability
to express multiple paths to causation.
Like a number of complex research issues, country
comparisons will often benefit from longitudinal coverage
(Byrne & Callaghan, 2013). This option is available in both
Cluster Analysis and QCA by repeating a consistent crosssectional
model that is judged to have value and consistency
of measurement over time. For example, organizations like
the IMF and OECD (Organisation of Economic Cooperation
and Development) repeat the same data measurements each
period and have done so for many years. In longitudinal
work, the policy researcher is particularly interested in the
consistency of patterns over time and the elements of a pattern
that start to change. By using a combination of Cluster
Analysis and QCA, the researcher has an improved chance
of understanding the reasons for any movement of country
cases over time, and how this might be related to changes in
specific variable scores.
RESEARCH EXAMPLE
The example used to demonstrate the combined use of these
methods examines economic and social data before and
after the financial crisis of 2007–08. The countries used as
cases are the 17 Euro currency member nations. The data
used is taken from the IMF. A precrisis model uses country
scores from 2005. The postcrisis model uses 2010 data. The
research question is: to what extent do countries sharing the
Euro currency achieve a convergence of economic policy?
Similar models were first developed as part of an earlier
and larger research project that included all OECD countries
(Haynes, 2012) but the data in this article have been
simplified to focus only on countries sharing the Euro currency
and use IMF data. This makes the focus simpler for
the purpose of an assessment of the triangulation of the two
methods. Cluster Analysis involves the researcher undertaking
an exploratory analysis of the interrelationship of country
cases based on the variable scores available. The task is to
explore how country cases can be grouped together into clusters
and if they can be demonstrated to be similar within
those groups. The researcher is interested to observer evidence
about the relative exclusivity of groups or the extent to
which they are overlapping and appear to share some general
characteristics. The researcher can make a judgment from the
initial exploratory analysis about the status of outliers and the
most heterogeneous country characteristics. This happens
before QCA is applied.
A Cluster Analysis was formed with each of the IMF data
sets for 17 countries and using eight variables (2005; 2010).
IMF variables used (2005, 2010) are as follows:
• Gross domestic product, constant prices, percentage
change in GDP
• Gross national savings, percentage of GDP
• Inflation, average consumer prices, percentage change
• Unemployment rate, percentage of working age popu-
lation
• General government revenue, percentage of GDP
• General government total expenditure, percentage of
GDP
• General government net lending/borrowing, percentage
of GDP
• Current account balance, percentage of GDP
Hierarchical Agglomerative Cluster Analysis is used. The
calculation uses the statistical software program PASW
(v18) with the method of the squared Euclidean distance
examining average linkage between groups. All the continuous
variables are standardized as z scores. The data are
standardized using z scores to prevent variables with more
distributed scales and variance from having a more profound
effect on the final model. With z scores, all variables will
have equal impact on the clusters formed. The dendrogram
is used as the main visual method of analysis, and the number
of clusters is then checked by programming the software
to select the observed number of clusters in the dendrogram
analysis. Membership of clusters can then be validated.
586 HAYNES
FIGURE 1 Cluster analysis dendrogram: Pre-financial crisis 2005 model of Euro zone countries.
In the first model, the IMF indicators for the precrisis
period (2005) are computed into a Cluster Analysis with the
17 Euro countries each being the individual cases.
The resulting dendrogram is shown in Figure 1. Analysis
of the agglomeration schedule suggests that four clusters
are likely to be optimal with two additional outliers. This
logical separation into groups can be observed clearly in the
dendrogram and are defined as follows:
1. Belgium, France, Austria, Germany, Italy Core Europe
2. Cyprus, Malta, Portugal, Greece New Southern
3. Luxembourg, The Netherlands Northern
4. Finland
5. Slovenia, Spain, Ireland, Estonia New Growth
6. Slovak Republic
QCA is used to apply a theoretical label to each of the cluster
groups of countries present (labels in italics above). QCA
in Table 2 assists with the theoretical explanation of the relative
homogeneity of the clusters in terms of variable effect
and explaining the relationship of variable scores with cluster
definition. The most homogeneous clusters in terms of
variable effects are Clusters 2 and 5. Cluster 5 has four countries
that share six primary implicants: strong growth (GDP),
strong savings (GNS), low tax revenue (revenue) related to
below threshold government expenditure (govexp), a healthy
government current account (GOVCA), and negative trade
and capital flows (bop). This cluster is therefore named “New
Growth” as a collection of countries that seemed to demonstrate
the early benefits in 2005 of being members of the
Euro.
Cluster 2 is four countries that share five primary
implicants: low savings (gns), low tax revenue (revenue),
high government expenditure (GOVEXP), a below threshold
government current account that reflects low tax update
against high expenditure (govca), and a negative trade balance
(bop). This illustrates Euro countries with weak economic
profiles. Of course, Greece and Portugal did later
experience severe difficulties after the 2007–08 crisis (Lynn,
2011). This cluster is named “New Southern.”
Cluster 1 is five countries that include the largest Euro
economies. The defining features of this group are their large
tax take from the economy (REVENUE) and relatively high
government expenditure (GOVEXP). This cluster includes
the countries that politically drove the Euro project and
showed openness toward southern and eastern integration
with a commitment to strong fiscal intervention. This cluster
is named “Core Europe.”
Clusters 3 and 4 are strongly performing northern countries
with strong savings (GNS), government current account
COMBINING THE STRENGTHS OF QCA WITH CLUSTER ANALYSIS 587
TABLE 2
QCA Truth Table for Validation of Pre-Crisis 2005 Clusters
GDP GNS CPI Unemp Revenue GovExp GovCA BoP Cluster Id
0 1 1 1 1 1 0 1 1 Belgium
0 1 0 1 1 1 0 1 1 Germany
0 1 0 0 1 1 1 1 1 Austria
0 0 0 1 1 1 0 0 1 France
0 0 0 0 1 1 0 0 1 Italy
1 0 1 0 0 1 0 0 2 Malta
1 0 0 0 0 1 0 0 2 Cyprus
0 0 1 1 0 1 0 0 2 Greece
0 0 0 0 0 1 0 0 2 Portugal
1 1 1 0 0 0 1 1 3 Luxembourg
0 1 0 0 1 1 1 1 3 The Netherlands
0 1 0 1 1 1 1 1 4 Finland
1 1 1 1 0 0 1 0 5 Spain
1 1 1 0 0 0 1 0 5 Estonia
1 1 1 0 0 0 1 0 5 Slovenia
1 1 0 0 0 0 1 0 5 Ireland
1 0 1 1 0 0 0 0 6 Slovak Republic
Thresholds (1 = threshold or above: 0 = below threshold) Primary Implicants.
Cluster 1 gdp∗REVENUE∗GOVEXP.
Cluster 2 gns∗revenue∗GOVEXP∗govca∗bop.
Cluster 3 GNS∗unemp∗GOVCA∗BOP.
Cluster 4 (linked to 3 by GNS∗GOVCA∗BOP).
Cluster 5 GDP∗GNS∗revenue∗govexp∗GOVCA∗bop.
Cluster 6 (linked to 5 by GDP∗revenue∗govexp∗bop).
balance (GOVCA), and positive trade balances (BOP). This
cluster is called “Northern.”
In the second model, data from 2010 are used. The
same mathematical Cluster Analysis method is applied. The
following post-financial crisis clusters result (Figure 2):
1. Austria, The Netherlands, Germany, Luxembourg
Northern Plus
2. Italy, Slovenia, Belgium, France, Finland Core Europe
3. Estonia
4. Cyprus, Malta, Portugal New Southern
5. Slovak Republic, Spain Other Southern
6. Greece
7. Ireland
The QCA in Table 3 provides the theoretical explanation
of the new cluster labels added in italics above, and
movement in cluster groupings compared with 2005, and the
analysis of overall cluster homogeneity for the 2010 model.
There has been some change between the Northern and Core
European clusters. Germany has moved into the economic
stronger northern group (now cluster 1) reflected by the
primary implicants of above threshold growth (GDP) and
savings (GNS) and a positive balance of payments (BOP).
There is overlap with part of Cluster 2, as Belgium and
Finland also share these characteristics. The new larger Core
Europe cluster (Cluster 2) is rather heterogeneous with no
primary implicants and seems to be better explained using
QCA as two distinct groups. Belgium and Finland can be
identified by the variable thresholds as having overlap with
Cluster 1, leaving Italy, France and Slovenia defined by the
variable thresholds: low inflation and negative balance of
payments (cpi∗
bop). In some respects, Clusters 1 and 3 from
2005 have evolved into overlapping Clusters 1 and 2 in 2010,
but with France being more marginal in terms of its relative
strength of economic performance when compared to other
similar Eurozone countries.
The rest of the analysis tells a different story of divergence
rather than convergence. The growth (GDP) of the
2005 Cluster 5 has gone, fragmenting the economic characteristics
of these countries in 2010. The more extreme crisis
in Greece has pushed it into an outlier position, although in
reality it still has some similarities with the other nations it
was situated within 2005 (2005 Cluster 2). The other countries
that were previously similar to Greece in 2005 are still
together in 2010 in Cluster 4 with low savings (gns), low
tax revenue (revenue), and negative trade (bop). These are
consistent features for those countries in both 2005 and 2010.
Taking these QCA-based variable influences into account,
the simplest element of the dendrogram hierarchy in Figure 2
(2010) Cluster Analysis can be reduced to two higher level
cluster groups on the right-hand side of the dendrogram
figure. First, those in the top half of the dendrogram look
economically more similar, and most able to work in a shared
currency (Austria, The Netherlands, Germany, Luxembourg,
Italy, Slovenia, Belgium, France, Finland, and Estonia).
Those in the bottom half of the dendrogram have increasingly
struggled to converge and survive during the Financial
588 HAYNES
FIGURE 2 Cluster analysis dendrogram: Post-financial crisis 2010 model of Eurozone countries.
TABLE 3
QCA Truth Table for Validation of Post-Crisis 2010 Clusters
GDP GNS CPI Unemp Revenue GovExp GovCA BoP Cluster Id
1 1 1 0 0 0 1 1 1 Luxembourg
1 1 0 0 1 1 1 1 1 Austria
1 1 0 0 1 1 0 1 1 The Netherlands
1 1 0 0 1 0 1 1 1 Germany
1 1 1 0 1 1 1 1 2 Belgium
1 1 0 0 1 1 1 1 2 Finland
1 0 0 0 1 1 1 0 2 Italy
0 1 0 1 1 1 0 0 2 France
0 1 0 0 0 0 0 0 2 Slovenia
1 1 1 1 1 0 1 1 3 Estonia
1 0 1 0 0 0 1 0 4 Malta
0 0 1 0 0 0 0 0 4 Cyprus
0 0 0 1 0 1 0 0 4 Portugal
1 1 0 1 0 0 0 0 5 Slovak Republic
0 1 1 1 0 0 0 0 5 Spain
0 0 1 1 0 0 0 0 6 Greece
0 0 0 1 0 1 0 1 7 Ireland
Thresholds (1 = threshold or above: 0 = below threshold).
Primary Implicants
Cluster 1 GDP∗GNS∗unemp∗BOP.
Cluster 2 (no primary implicants) – two subsets.
2a GDP∗GNS∗unemp∗REVENUE∗GOVEXP∗GOVCA∗BOP.
2b cpi∗bop.
Cluster 3 Outlier.
Cluster 4 gns∗revenue∗bop.
Cluster 5 GNS∗UNEMP∗revenue.
COMBINING THE STRENGTHS OF QCA WITH CLUSTER ANALYSIS 589
Crisis after 2007 (Cyprus, Malta, Portugal, Slovak Republic,
Spain, Greece, and Ireland).
CONCLUSION
The research example illustrates the advantages of using
Cluster Analysis and QCA as a combined method to study
comparative similarities between countries. Cluster Analysis
is a method that can be used to search for similarities and
patterns amongst countries. It is good method for exploring
the data because it uses the full range of interval variable
scores available and data do not have to be degraded
or recoded into categories. Once exploratory patterns are
formed using Cluster Analysis, these groups can be better
understand using QCA. QCA allows for theoretical modeling
where the groups proposed in the exploratory clusters can
be validated, or alternatively rejected as artifacts that have no
logical political or economic explanation. The process of theoretical
validation during QCA necessitates linking cluster
groupings to patterns of variable scores.
Cluster groupings have hard and soft elements. The
hard elements are groupings of countries and proximities
of country characteristics that remain when modeling
is replicated with different mathematical criteria and after
using QCA for theoretical validation. When undertaking
longitudinal research, as with the example in this article,
hardness might also be argued to be present if groups of
countries remain together consistently over time. The QCA
concept of “Primary Implicants” clarifies “hardness” of linkage
in clusters. These hard links are indicated in bold in
Table 4.
TABLE 4
Comparison of Cluster Models.
Model 1 2005
Cluster 1 Core Europe gdp∗REVENUE∗GOVEXP
Cluster 2 New Southern gns∗revenue∗GOVEXP∗govca∗bop
Cluster 3 Northern GNS∗unemp∗GOVCA∗BOP
Cluster 4 (linked to 3 by GNS∗GOVCA∗BOP)
Cluster 5 New growth GDP∗GNS∗revenue∗govexp∗GOVCA∗bop
Cluster 6 (linked to 5 by GDP∗revenue∗govexp∗bop)
Model 2 2010
Cluster 1 Northern plus GDP∗GNS∗unemp∗BOP
Cluster 2 Core Europe (no primary implicants)—two subsets
2a GDP∗GNS∗unemp∗REVENUE∗GOVEXP∗
GOVCA∗BOP
2b cpi∗bop
Cluster 3 Outlier
Cluster 4 New Southern gns∗revenue∗bop
Cluster 5 Southern GNS∗UNEMP∗revenue
Notes
1. Key primary implicants that have influence over similar clusters from
2005 to 2010 are indicated in bold.
2. Computer generated cluster numbers change between 2005 and 2010.
For example, “Core Europe” moves from Cluster 1 in 2005 to Cluster
2 in 2010.
Soft elements are country outliers and countries prone
to move clusters easily when different mathematical criteria
and QCA are used. This is where replication and cross triangulation
for validation is difficult and cannot easily validate
consistent patterns. However, when examining the political
economy of countries over time, softness also illustrates
countries that are relatively unstable.
The robustness of the Northern Plus and Core Europe
cluster over time (Table 4) is linked to its enduring positive
balance of payments (BOP), higher national savings (GNS),
and above threshold government revenue (REVENUE).
Across the 17 countries, the reducing homogeneity of
clusters illustrates the lack of convergence achieved by
the Eurozone single currency countries and suggests that
economic patterns will continue to evolve and surprise commentators
as the world economy moves through a prolonged
crisis and that this will continue to change traditional patterns
of economic stability and activity. There is no indication
from this data analysis that the policy of sharing the Euro
currency will enable European Union countries to achieve a
homogeneous economic experience.
The assumption is that the clusters are a holistic representation
of the numerous variables entered and that higher
abstraction demonstrated by cluster definition is evidence
of the combination of variables into a possible synthesis of
“political economy type,” “economic policy,” or “economic
performance”. However, Cluster Analysis alone provides a
weak theoretical basis for such theoretical labeling. With
Cluster Analysis alone, it is difficult to understand the
microelement of variable effects when these clusters are
created. QCA allows the researcher to understand the interrelationship
of variable effects with cluster group definition, in
terms of which variables are assisting the definition of similarity
in particular clusters. Where the robustness of cluster
groups remain or change over time, it is also important to
remember that the cluster variable characteristics are actually
dynamic and changing. The cluster (or a proportion of
cluster members) may evolve their variable score characteristics
over time. Country cases may remain together, but not
necessarily because of the same defining features of variables.
Variables that define clusters may change dynamically
over time, but the same cluster might remain, even if defined
differently by its relationship with variables. Over time, cluster
groups of countries might remain together dynamically
because the underlying variable influences evolve and influence
the countries in a similar way. For example, it can be
hypothesized in a financial crisis that a group of countries
will experience the same combined negative effects. What
is particularly interesting is when one country breaks away
from its historical grouping based on some unexpected variable
scores. This illustrates the highly dynamic relationship
of countries with each other and their changing variable
scores over time. The political economy of countries is not
static but always evolving. These complex interactions and
relationships are best understood by case-based methods
590 HAYNES
(Byrne & Callaghan, 2013), of which Cluster Analysis and
QCA are two examples recently used in public policy and
public administration. What is innovative in this article is
the demonstration of how these methods can be used concurrently
to answer the same research question. Using a
combination of the methods of Cluster Analysis and QCA
with the added benefit of a longitudinal view better aids
the researcher in understanding the complex interaction of
country cases with each other and the dynamic movement
of underlying variables over time. The patterns between
cases and variables depend on mutual interactions rather
than the predetermined relationship of variables that always
determine the path of others.
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