What is Fuzzy About Clustering in West Africa?: Charalambos Tsangarides and Mahvash Saeed

45 Pages·2006·0.72 MB·English

WP/06/90

What is Fuzzy About Clustering in
West Africa?

Charalambos Tsangarides and
Mahvash Saeed Qureshi

© 2006 International Monetary Fund WP/06/90

IMF Working Paper

African Department

What is Fuzzy About Clustering in West Africa?

Prepared by Charalambos Tsangarides and Mahvash Saeed Qureshi1

Authorized for distribution by Reza Vaez-Zadeh

March 2006

Abstract

This Working Paper should not be reported as representing the views of the IMF.
The views expressed in this Working Paper are those of the author(s) and do not necessarily represent
those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are
published to elicit comments and to further debate.

Applying techniques of clustering analysis to a set of variables suggested by the convergence
criteria and the theory of optimal currency areas, this paper looks for country homogeneities
to assess membership in the existing and proposed monetary unions of the broader west
African region. Our analysis reveals considerable dissimilarities in the economic
characteristics of the countries in west and central Africa. In particular, the West African
Monetary Zone (WAMZ) countries do not form a cluster with the West Africa Economic and
Monetary Union (WAEMU) countries; and, within the WAMZ, there is a significant lack of
homogeneity. Furthermore, when west and central African countries are considered together,
we find significant heterogeneities within the CFA franc zone, and some interesting
similarities between the Economic and Monetary Community of Central Africa (CEMAC)
and WAMZ countries. Overall, our findings raise some questions about the geographical
boundaries of several existing and proposed monetary unions.

JEL Classification Numbers: F15, F33, C14, E61

Keywords: Monetary integration, west Africa, cluster analysis

Author(s) E-Mail Address: [email protected]; [email protected]

1 Mahvash Saeed Qureshi is currently a doctoral candidate at Trinity College, University of
Cambridge, United Kingdom, and was an IMF summer intern at the time the research was
conducted. We thank, without implicating, Anne-Marie Gulde-Wolf, Michael Hadjimichael,
Cathy Pattillo, Ruby Randall, Ajit Singh, and Reza Vaez-Zadeh, for helpful comments and
suggestions. All errors are our responsibility.
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Contents Page

I. Introduction.................................................................................................................. ..3
II. Background.....................................................................................................................4
A. Optimum Currency Area and West Africa................................................................4
B. Recent Literature ...................................................................................................... 6
III. Methodology.................................................................................................................. 7
A. Crisp Clustering........................................................................................................ 8
B. Fuzzy Clustering .................................................................................................... 11
IV. Data and Variables....................................................................................................... 13
A. Choice of Variables................................................................................................. 13
B. Data Sources............................................................................................................ 16
V. Empirical Results......................................................................................................... 17
A. Hierarchical Analysis.............................................................................................. 17
B. Fuzzy Clustering..................................................................................................... 20
C. Empirical Evaluation: Principal Component Analysis............................................ 24
D. Group Similarities: West Africa, Central Africa, and the Euro Area..................... 26
VI. Conclusion and Policy Implications.................................................................................. 31

References................................................................................................................................ 40

Appendices
Appendix I............................................................................................................................... 32
Appendix II.............................................................................................................................. 34
Appendix III............................................................................................................................. 39

Tables
1. Membership coefficients for WAMZ countries................................................................... 22
2. Membership coefficients for ECOWAS countries.............................................................. 22
3. Dissimilarities between member countries.......................................................................... 26
4. Membership coefficients for West and Central Africa........................................................ 30
5. Membership coefficients for the Euro Area......................................................................... 30

Figures
1. Hierarchical Clustering Analysis: WAMZ Countries.......................................................... 19
2. Hierarchical Clustering Analysis: ECOWAS Countries...................................................... 19
3. Characteristics of the WAMZ Countries............................................................................. 23
4. Characteristics of the WAEMU Countries.......................................................................... 23
5. Characteristics of the ECOWAS Countries......................................................................... 23
6. Clustering Based on Membership Coefficients................................................................... 24
7. Clustering Based on Principal Component Analysis .......................................................... 25
8. Box plot of the Distances: WAMZ Countries...................................................................... 27
9. Box plot of the Distances: WAEMU Countries................................................................... 27
10. Box plot of the Distances: ECOWAS Countries............................................................... 27
11. Hierarchical Clustering Analysis: West and Central Africa.............................................. 29
12. Hierarchical Clustering Analysis: the Euro Area............................................................... 29
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I. INTRODUCTION
Following the successful launch of the euro as the single currency of the European Economic
and Monetary Union (EMU), there has been a renewed interest internationally in the
economics of monetary integration. Other regions are seeking to emulate the success of the
EMU, usually by setting up similar institutional frameworks and establishing processes of
convergence as prerequisites for wider monetary integration.

The objective of wider regional integration based on a reinforcement of regional surveillance
and peer pressure for sound macroeconomic policy management is a welcome effort. In some
cases, however, the drive for regional cooperation and integration has overshadowed
concerns about the dissimilarities of the shocks accruing to the economies and of the
economies’ adjustment after they respond to the shocks—the key criteria of the optimum
currency areas (OCA) theory as pioneered by Robert Mundell (1961). In this spirit, this paper
tries to assess the comparative relevance of the proposed “monetary area boundaries” in West
Africa and seeks to determine if the candidate countries are ready to form an OCA.

We use cluster analysis to provide an assessment of the readiness and sustainability of
monetary unions by classifying West African countries into groups according to their
performance towards achieving the OCA and convergence criteria for common currency
adoption. Considering the noisy nature of the data, we employ the more realistic and
powerful technique of fuzzy clustering along with the traditional hard clustering method.
Fuzzy clustering techniques uncover useful relationships between countries in a group and
the homogeneities among group members, by taking into account the possibility that a
country may be similar to one country or group of countries in some respects and, at the same
time, share certain other characteristics with another country or group of countries. In the
end, a country is assigned the largest membership coefficient for the cluster with which it
shares the greatest similarities.

The findings of our analysis reveal considerable dissimilarities in the economic
characteristics of the countries in West Africa. In particular, the West African Monetary
Zone (WAMZ) countries do not form a cluster with the West Africa Economic and Monetary
Union (WAEMU) countries; and, within WAMZ, there is a significant lack of homogeneity,
with Nigeria and Ghana appearing as independent singletons. These results cast doubt on the
feasibility of a separate monetary union that comprises all WAMZ countries and more
important, on the prospects of the wider monetary integration in the Economic Community of
West African States (ECOWAS). Furthermore, when west and central African countries are
considered together, we find significant heterogeneities within the CFA franc zone, with the
WAEMU and Economic and Monetary Community of Central Africa (CEMAC) countries
not clustering together, and some interesting similarities between the CEMAC and WAMZ
countries, which tend to group together.

The rest of the paper is organized as follows. Section II presents a brief overview of the
literature on currency unions in the context of the West African region. Section III describes
in detail the methodology used in this paper. Section IV discusses the data and variables
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used in the empirical analysis. Section V presents the results and offers comparisons with
other monetary unions. Section VI concludes and discusses the policy implications of our
findings.

II. BACKGROUND
A. Optimum Currency Areas and West Africa
Several of the existing monetary arrangements in sub-Saharan Africa result from choices
countries made during or after the colonial era: former British colonies moved from currency
boards to flexible exchange rates after achieving independence, while after World War II,
former French colonies and France set up a monetary arrangement in the form of the CFA
franc (CFAF) zone. The CFAF zone comprises 14 countries grouped into two monetary
unions, the WAEMU and CEMAC.2 A special case is the monetary union project in the
ECOWAS. Founded in 1975, the ECOWAS is an organization of 15 members (8 of which
are the members of the WAEMU), with the mandate to promote regional economic
integration. Since April 2000, the five non-WAEMU members of ECOWAS (Nigeria, The
Gambia, Ghana, Guinea, and Sierra Leone) have formed a second monetary area, the
WAMZ, and established a convergence process toward launching a common currency.3
Wider monetary unification between member states of the ECOWAS is envisaged, although,
to date, no announcement has been made of the type of monetary arrangement that would be
adopted following the unification.

The standard tool used in economic literature to evaluate the adequacy of a currency union is
the OCA theory, pioneered by Mundell (1961) and McKinnon (1963), with important
elaborations by, among others, Kenen (1969) and Krugman (1990). The OCA theory
compares the benefits and costs to countries of participating in a currency union. On the one
hand, benefits include lower transaction costs, price stabilization, improved efficiency of
resource allocation, and increased access to product, factor and financial markets (thereby
facilitating investment and promoting economic growth). The main cost, on the other hand, is
the country’s loss of sovereignty to maintain national monetary and exchange rate policies.

Two criteria are identified in evaluating the feasibility of a monetary union—the nature of
shocks affecting the potential monetary union member countries and the speed with which
they adjust to them. First, when a country joins a common currency area, it relinquishes its
own currency and abandons monetary policy and exchange rate autonomy. If all countries in

2 Members of the WAEMU are Benin, Burkina Faso, Côte d’Ivoire, Guinea Bissau, Mali, Niger,
Senegal and Togo. The CEMAC members are Cameroon, Chad, Republic of Congo, Central African
Republic, Equatorial Guinea and Gabon. Equatorial Guinea and Guinea-Bissau, which are not former
French colonies, joined the CFA zone in 1985 and 1997, respectively. Mali joined in 1984. See
Hadjimichael and Galy (1997) for an analysis of the CFA zone and its institutions.
3 The launch date of the common currency, initially set for July 2005, has been postponed to
December 2009 because the WAMZ member states failed to achieve the convergence criteria.
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a currency area are hit with symmetric negative shocks, the adverse affects could be
mitigated by depreciating the common currency or by adopting a common expansionary
monetary policy. However, if countries are hit with asymmetric shocks, a depreciation or
monetary expansion are not feasible instruments because they might boost production in
countries with negative shocks but run the risk of triggering overheating and inflation in
countries with positive shocks. Thus, the costs of forming a common currency area are lower
if the shocks are symmetric, and higher if they are asymmetric.

Second, the speed with which economies adjust after shocks also has important implications
for the formation of a currency union. If, after the shocks, market mechanisms are quick to
restore equilibrium, then asymmetric shocks need not imply large costs even if they are large.
Two such mechanisms that ensure rapid adjustment are labor mobility and fiscal transfers.
For example, if labor can move freely throughout the currency area, unemployed workers in
a country hit by an adverse shock could move to, and find jobs in, other parts of the currency
area that experienced positive shocks, which would help mitigate the impact of a recession.
Similarly, if the region has a good system of fiscal transfers, resources could be transferred
from the country with positive shocks to countries affected by negative shocks. Adjustments
in relative wages, changes in labor force participation induced by wage changes, and capital
mobility are various other mechanisms for responding to shocks as discussed in Blanchard
and Katz (1992).

The OCA criteria are a useful benchmark for evaluating the feasibility of monetary
arrangements and may be used to analyze the establishment of the ECOWAS. First, the West
African states are small, open economies that export primary commodities; they are not well
diversified, and are highly susceptible to asymmetric shocks. Although some primary
commodities, such as coffee, cocoa, cotton, fish, timber, and groundnuts are common to a
number of countries, others are found in only one or two countries. Several countries depend
on a single commodity for 50 percent or more of their earnings.4 In addition, terms of trade
movements tend to be very large for most of these countries, with uncorrelated shocks to
terms of trade mainly because of differences in commodity exports whose prices in world
markets do not necessarily move together. For example, Nigeria, a large oil exporter, has
terms of trade shocks that are very different from other WAMZ countries, which are all oil
importers. Not only are the correlations with other members low (or negative), the variability
in Nigeria’s terms of trade changes is also large and higher than that of any other country in
the region.5 In general, correlations of terms of trade shocks are higher among the WAEMU
member countries than between WAEMU and WAMZ countries, or among the WAMZ
countries themselves.6

4 See Cashin and Pattillo (2000) and Masson and Pattillo (2005).
5 See Masson and Pattillo (2001). Ogunkola (2002) studies bilateral real exchange rate volatility in
the sub-Saharan African countries and finds the conditional volatility for Nigeria to be the highest in
the region.
6 See Table B3 in Appendix B.
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The asymmetry of shocks may be less of a problem if countries are sufficiently flexible, or if
they have sufficient shock absorbers, in particular, factor mobility or a system of fiscal
transfers. Although reliable migration data are hard to find, migration between the WAEMU
and traditional migratory trade routes within West Africa seem high, albeit less high in recent
years because of conflict.7 In contrast, fiscal transfers are inhibited by a lack of financial
resources and the poor systems of transfers and taxes. In addition, trade within the ECOWAS
region is relatively low. The WAEMU countries trade considerably more among themselves
than with the non-WAEMU countries, whereas trade within the non-WAEMU countries is
limited, which raises doubts about the magnitude of potential savings from a reduction in
transactions costs.8

In principle, however, the West African countries stand to reap significant gains by giving up
the pursuit of an independent monetary policy. Fixed exchange rates provide a way for
countries to make a credible commitment to lower inflation and can help bring about price
stability.9 In fact, in the absence of central bank independence and debt markets in which
governments can finance themselves, monetary policy is generally dictated by the need to
finance fiscal policy–persistent deficits lead to excessive money creation as governments
resort to seigniorage. In this context, a monetary union could encourage fiscal discipline, and
the common independent central bank could act as an “agent of restraint” for fiscal policies.10

B. Recent Literature
Much of the earlier research on monetary arrangements in Africa was carried out in the
context of the CFA franc zone and examines whether economies in the CFA franc zone have
fared better or worse than their neighbors that are not part of the zone.11 The asymmetry of
shocks accruing to the sub-Saharan African (SSA) economies has been studied by Bayoumi
and Ostry (1997), Hoffmaister, Roldos and Wickham (1998), and Fielding and Shields
(2001) using the vector autoregressive (VAR) approach. They find little correlation of the
disturbances to real output per capita among the SSA countries. Also, Hoffmaister, Roldos,

7 See Masson and Pattillo (2001) and van den Boogaerde and Tsangarides (2005).
8 This should be viewed in conjunction with the fact that the scope for intraregional trade is limited by
low market potential, weak transportation infrastructure, and similarities in factor endowments.
Further, benefits from reduced transaction costs do not seem to have translated into increased
intraregional trade even in the CFA zone despite years of monetary unification. Trade within the CFA
zone remains modest, especially within CEMAC, and practically nonexistent between WAEMU and
CEMAC.
9 However, Masson and Pattillo (2001) note that, so far, African countries with a common currency
have not been successful in achieving price stability and have not made optimal monetary policy
changes in response to various asymmetric shocks.
10 In examining the CFA monetary union, Masson and Pattillo (2001) conclude, “a monetary union in
West Africa can be an effective agency of restraint on fiscal policies if the hands of the fiscal
authorities are also tied by a strong set of fiscal restraint criteria.”
11 See, for example, Devarajan and Rodrik (1991), Elbadawi and Majd (1996), and Ghura and
Hadjimichael (1996).
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and Wickham (1998) show that external shocks are an important source of macroeconomic
fluctuations in SSA and are more detrimental to CFA franc countries than to the non-CFA
franc countries probably because of the fixed exchange rate regime in the former.

Recently, however, focus has shifted to analyzing the feasibility of forming a monetary union
in the ECOWAS region perhaps because of the enthusiastic drive of the West African
countries towards establishing a monetary union. Bénassy-Quéré and Coupet (2005) use
cluster analysis to examine the monetary arrangements in the entire SSA region using the
crisp clustering methodology only. Celasun and Justiniano (2005) use a dynamic factor
analysis to study the synchronization of output fluctuations among the member countries.
Their results indicate that small groups of countries within ECOWAS experience relatively
more synchronized output fluctuations. They therefore suggest that monetary unification
among subsets of countries is preferable to wider monetary integration in West Africa.
Debrun, Masson and Pattillo (2005) develop a model of monetary and fiscal policy
interactions and use it to assess the potential for monetary integration in ECOWAS. Their
findings show that the proposed monetary union is desirable for most non-WAEMU
countries but not for most of the existing WAEMU member states unless Nigeria implements
institutional changes that lower its financing needs.

In general, it is difficult to assess the overall costs and benefits associated with a potential
monetary union because of concerns about political commitment, credibility and
endogeneity. The endogeneity concern of the OCA criteria, flagged by Frankel and Rose
(1998), which implies that countries become similar when they share a common currency, is
a particularly important issue but is not addressed in most cost-benefit analyses. Furthermore,
despite a consensus about the dissimilarities in economic structures and asymmetries of
shocks, the ECOWAS countries stand by their commitment to monetary integration for
different socio-economic reasons. Against this background, in this paper we adopt a different
approach and assess how well prepared and suitable West African states are to form a
monetary union in light of their increased efforts toward macroeconomic convergence since
2000. In doing so, we investigate the homogeneity of the candidate countries in terms of a
number of economic characteristics that are inspired from the OCA criteria as well as the
convergence criteria set by these countries.

Our study differs from previous work in its approach as well in its methodology. We use
clustering analysis to assess the similarity between countries within a region and across the
regions. Cluster analysis offers a number of advantages. First, by allowing us to account for a
number of variables simultaneously, it enables us to investigate synchronization in terms of
the symmetry of business cycles as well as the symmetry of various other relevant variables.
Second, cluster analysis has less stringent data requirements in terms of the time dimension
of the data series than other methodologies and works well for countries for which consistent
time-series data are limited, such as the African economies. Third, by exploring the group
pattern in the data, this methodology identifies the areas in which each country needs to
improve if it is to achieve macroeconomic convergence, which is necessary for forming the
union, and provides useful information for making informed policy choices.
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III. METHODOLOGY
Cluster analysis refers to methods used to organize multivariate data into groups (clusters)
according to homogeneities among the objects such that items in the same group are as
similar as possible and items in different groups are as dissimilar as possible.12 The resulting
data partition improves our understanding of the data by revealing its internal structure.
Clustering is a useful exploratory tool that has been applied to a wide variety of research
problems aiming to examine the underlying relationships in the data for classification, pattern
recognition, model reduction, and optimization purposes. Broadly, clustering methodologies
may be classified into two groups according to the types of clusters obtained: crisp (or hard)
clustering approaches and soft (or fuzzy) clustering techniques.

A. Crisp Clustering
Crisp clustering algorithms divide the data into mutually exclusive clusters such that each
object belongs to only one cluster. Mathematically, crisp partitioning of a dataset X, with N
objects and p variables, into c clusters is defined as a family of subsets
{A |1≤i ≤c ⊂ X}having the following properties:
i
c A = X , (1)
U
i=1 i
A A , 1≤i ≠ j ≤c, and (2)
I
i j
Φ ⊂ A ⊂ X, 1≤i≤c, (3)
i
where condition (1) states that the subsets A contain all data in X; condition (2) states that
i
the subsets must be disjoint so that each object belongs to one cluster only; and condition (3)
states that none of the subsets is an empty set (Φ) or contains all the data in X.

In terms of membership coefficients, µ, which indicate the degree of belongingness of an
ik
object i to a cluster k, the above conditions may be expressed as
µ ∈0,1 and 1≤i ≤ N;1≤ k ≤c, (4)
ik
c
∑µ =1, 1≤i≤ N, and (5)
ik
k=1
N
0< ∑µ < N , 1≤ k ≤c, (6)
ik
i=1

12 The term “similarity” however should be understood as mathematical similarity measured in a well-
defined sense. In metric spaces, for example, similarity is defined by means of a distance function.