Monetary Union Membership in West Africa: A Cluster Analysis

World Development Vol. 36, No. 7, pp. 1261–1279, 2008 Ó 2008 Elsevier Ltd. All rights reserved 0305-750X/$ - see front matter www.elsevier.com/locate/worlddev

doi:10.1016/j.worlddev.2007.06.019

Monetary Union Membership in West Africa: A Cluster Analysis CHARALAMBOS G. TSANGARIDES International Monetary Fund, Washington, USA

and MAHVASH SAEED QURESHI University of Cambridge, UK

*

Summary. — Applying hard and soft clustering algorithms to a set of variables suggested by the convergence criteria and the theory of optimal currency areas, this paper examines the suitability of countries in the west African region to form the proposed monetary unions, the West African Monetary Zone (WAMZ) and the Economic Community of West African States (ECOWAS). Our analysis reveals considerable dissimilarities in the economic characteristics of member countries, particularly WAMZ countries. 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 central African and WAMZ countries. Ó 2008 Elsevier Ltd. All rights reserved. Key words — monetary integration, cluster analysis, West Africa, CFA franc zone

1. 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 Mundell (1961). In this spirit, this paper attempts to assess the comparative relevance of the proposed ‘‘mone-

tary area boundaries’’ in West Africa and seeks to determine if the candidate countries 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 toward achieving the OCA and convergence criteria for common currency adoption. Considering the noisy nature of the data, we employ the more realistic technique of fuzzy clustering, along with the traditional hard clustering methods. Fuzzy clustering takes into account the possibility that a country may be * We are grateful to the editor, the anonymous referees, Anne-Marie Gulde, Michael Hadjimichael, Cathy Pattillo, and seminar participants at the International Monetary Fund’s African Department and the 2007 CSAE Conference at the University of Oxford for their helpful comments and suggestions. The views expressed and all errors or omissions are the sole responsibility of the authors and should not be attributed to the International Monetary Fund, its Executive Board, or its management. Final revision accepted: June 11, 2007.

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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. It therefore provides more information about the data than conventional clustering methods. Our findings reveal considerable dissimilarities in the economic characteristics of West African countries. In particular, the West African Monetary Zone (WAMZ) countries do not group with the West Africa Economic and Monetary Union (WAEMU) member 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 (CFAF) zone, with 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 remainder of the paper is structured as follows. Section 2 presents some background on the existing and proposed monetary arrangements in West Africa and the relevant literature. Section 3 describes the methodology used in this paper. Section 4 discusses the data and variables used in the empirical analysis. Section 5 presents the results. Section 6 concludes and discusses the relevant policy implications of our findings. 2. BACKGROUND 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 independence, while after World War II, former French colonies and France set up a monetary arrangement in the form of CFAF zone. The CFAF zone comprises 14 countries grouped into two monetary unions, WAEMU and CEMAC. 1 Another proposed monetary union project in the region is ECOWAS. Founded in 1975, ECOWAS is an organization of 15 members (eight of which are members of 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, WAMZ, and established a convergence process toward launching a common currency. 2 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 possibility of a wider monetary unification in ECOWAS poses several important institutional and economic issues, as discussed in detail by Masson and Pattillo (2005). First, the choice of a central bank for WAMZ remains a consideration. None of the WAMZ countries has a central bank with a track record of currency stability and low inflation, and as a result, there is no natural candidate to provide the nucleus of a regional central bank. Second, in the context of ECOWAS, it is unlikely that the French Treasury’s guarantee of convertibility of the CFA franc to the euro at a fixed parity would continue for a monetary union of that size, especially given issues relating to monetary and fiscal disciplines of the larger zone. 3 This implies that within a possible full monetary union ECOWAS countries would have to decide about the exchange rate regime of their currency, that is, would it be pegged to the euro as is presently the case for the CFA franc, pegged to some other currency (or basket of currencies), or float with or without intervention by the central bank. Several observers have questioned the feasibility of the proposed monetary unions and the ability of member countries to adjust to external shocks in the absence of exchange rate as a policy instrument. 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 elaborations by Kenen (1969) and Krugman (1990). The OCA theory compares the benefits and costs to countries of participating in a currency union. Benefits include lower transaction costs, price stabilization, improved efficiency of resource allocation, and increased access to product, factor, and financial markets. The main cost, however, is the country’s loss of sovereignty to maintain national monetary and exchange rate policies. Both costs and benefits depend on the nature of exogenous shocks affecting potential mone-

MONETARY UNION MEMBERSHIP IN WEST AFRICA

tary union member countries and the speed with which they adjust to them. The costs tend to be lower (higher) if shocks are symmetric (asymmetric) and market mechanisms are quick (slow) to restore equilibrium after the shock. 4 Much of the earlier research on monetary arrangements in Africa focused on the CFAF zone and examined whether CFAF zone member economies have fared better than their nonmember neighboring countries (e.g., Devarajan & Rodrik, 1991; Elbadawi & Majd, 1996; Ghura & Hadjimichael, 1996). The asymmetry of shocks accruing to the sub-Saharan African (SSA) economies is examined by Bayoumi and Ostry (1997), and Fielding and Shields (2001) who find little correlation in real output per capita volatility among SSA countries. Hoffmaister, Roldos, and Wickham (1998) show that external shocks are an important source of macroeconomic fluctuations in SSA and that they are more detrimental to CFAF countries than to non-CFAF countries. A few studies have analyzed the costs and benefits of adopting a common currency in South and East Africa. For example, Huizinga and Khamfula (2004) focus on the Southern African Development Community (SADC) and investigate the desirability of forming a Southern African Monetary Union by examining the variation in real exchange rates across countries. They find a low degree of symmetry in real exchange rate shocks across most SADC economies and conclude that adopting common currency would imply larger costs than benefits. Buigut and Valev (2005) assess the suitability of a regional monetary union among the East African countries. Their results indicate that the structural shocks accruing to the economies are highly asymmetric, hence these countries are unsuitable to form an OCA. Recently, the focus has shifted to analyzing the feasibility of forming a monetary union in the ECOWAS region. Celasun and Justiniano (2005) use a dynamic factor analysis to study the synchronization of output fluctuations among member countries. Their results indicate that small groups of countries within ECOWAS experience relatively more synchronized output fluctuations. They therefore suggest monetary unification among subsets of countries as preferable over wider monetary integration in West Africa. Debrun, Masson, and Pattillo (2005) assess the potential for monetary integration in ECOWAS using a model of monetary and fiscal policy interactions. Their findings show that the proposed monetary union is desirable for most

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non-WAEMU countries but not for the existing WAEMU member states. Be´nassy-Que´re´ and Coupet (2005), hereafter referred to as BQC, use crisp cluster analysis to examine the monetary arrangements in SSA on the basis of different macroeconomic characteristics stemming from the OCA theory. Using data for the period 1986–99, they find that CEMAC and WAEMU countries do not share similarities hence the existing CFAF zone cannot be viewed as an OCA. Their results also suggest that Nigeria should not form part of WAMZ, while the creation of a regional monetary arrangement in the limited sense of connecting the Gambia, Ghana, and Sierra Leone to the WAEMU appears to be more economically viable. In this paper, we update the work of BQC by using recent macroeconomic data sets of SSA countries. We adopt a different approach and methodology to assess how well prepared the West African states are to form a monetary union and 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. We use both crisp and fuzzy clustering analyses to examine the similarity between countries within and across the proposed monetary regions, and test the robustness of our results using principal component analysis. Cluster analysis is a modern statistical tool which offers a number of advantages. First, by allowing 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 data than other methodologies and works well for countries with limited time-series data, 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 to achieve macroeconomic convergence, which is necessary for forming the union, and provides useful information for making informed policy choices. We apply both crisp and fuzzy clustering techniques to allow the two possibilities that (i) each country fully belongs to one group (as in crisp clustering); and (ii) the (more) realistic possibility that some countries may have common characteristics with more than one group of countries (fuzzy clustering). This enables us

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to investigate the common characteristics between countries in detail. 3. 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. 5 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. In general, clustering methodologies are classified into two groups according to the types of clusters obtained: crisp (or hard) clustering approaches and soft (or fuzzy) clustering techniques. These approaches are discussed in detail below. (a) Crisp clustering Crisp clustering algorithms divide the data into mutually exclusive clusters such that each object in the data set belongs to only one cluster. Expressed mathematically, crisp clusters must satisfy the following properties: lik 2 0; 1 and 1 6 i 6 N ; 1 6 k 6 c; c X lik ¼ 1; 1 6 i 6 N ; and

ð1Þ ð2Þ

k¼1

0<

N X

lik < N ;

1 6 k 6 c;

ð3Þ

i¼1

where lik indicates the membership coefficient or degree of belongingness of an object i to a cluster k, c is the number of possible clusters/ groups, and N is the number of objects in the data set. Properties (1)–(3) state that a membership coefficient is either zero or one (in our context it means that a country belongs to either one cluster or the other), the sum of the membership coefficients of an object across clusters is equal to one (i.e., every country must belong to a cluster), and the sum of membership coefficients in a cluster lies between zero and the total number of objects in the data set (i.e., each cluster must contain at least one but less than all countries in the data set), respectively. Different methods have been developed to partition data according to the above proper-

ties. In this paper, we perform crisp clustering using agglomerative hierarchical clustering, a procedure consisting of successive fusions of objects into groups. At each stage, countries that share the greatest similarities are joined together to form a cluster until the last group consisting of all countries is reached. Various approaches have been proposed for joining the objects such as Group Average, Ward, and Single Linkage methods. These approaches differ in their definition of distance or dissimilarity between objects (see Appendix for a description of these methods). Here we apply these three methods and opt for the one that best represents our data based on the cophenetic correlation coefficient. The cophenetic correlation coefficient is a measure which determines how well the generated clusters represent dissimilarities between objects, with values closer to one representing better clustering. 6 The outcome of hierarchical clustering is presented in the form of a tree known as dendrogram. The heights of the links of the dendrogram represent the distance at which each fusion is made such that greater dissimilarity between objects is reflected by larger distances and taller links. Although the dendrogram is a natural guide to cluster divisions, where large changes in fusion levels indicate the best cut for forming clusters, various ‘‘formal’’ rules have also been proposed to determine the best number of clusters (Everitt, Landau, & Leese, 2001). Milligan and Cooper (1985) evaluate the performance of thirty cluster-stopping rules and find that the pseudo-F index developed by Calinski and Harabasz (CH) (1974) performs the best. Therefore, to determine the optimal number of clusters, we compute the CH index defined as CHI ¼

S b =ðk  1Þ ; S w ðn  kÞ

ð4Þ

where Sb is the between clusters sum of squares, Sw is the within clusters sum of squares, k is the number of clusters, and n is the number of observations. Higher values of the index indicate distinct partitioning and better clustering. (b) Fuzzy clustering Fuzzy clustering does not force objects to belong to one cluster only; rather each object belongs to different clusters to some degree. Objects are assigned a membership coefficient between zero and one for each cluster, which

MONETARY UNION MEMBERSHIP IN WEST AFRICA

indicates their partial membership or degree of belongingness to that cluster. 7 Fuzzy clustering is, therefore, different from crisp clustering primarily because it takes into account the realistic possibility that an object may share some similarities with objects in other clusters and permits overlapping clusters. Hence it conveys more information about the data than crisp partitioning and is preferable. Fuzzy clustering is performed using the fuzzy c-means algorithm (FCM) developed by Dunn (1974) and further extended by Bezdek (1981), which is based on the minimization of an objective function: N X c X ðlik Þ2 d 2 ðxi ; vk Þ; ð5Þ J ðl; vÞ ¼ i¼1

k¼1

where lik is the degree of membership that xi belongs to cluster k. d is the Euclidean distance between xi and the center of the cluster k, vk, where , N N X X 2 lik xi l2ik : vk ¼ i¼1

i¼1

The minimization of (5) is subject to the following constraints: 0 6 lik 6 1; ð6Þ c X lik ¼ 1; 1 6 i 6 N ; and ð7Þ

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are entirely fuzzy. However, when every object has l = 1 in one cluster and 0 in all others, DPC is equal to one and fuzzy clustering is similar to crisp clustering. Xie and Beni’s index, XBI, compares total variation within and between clusters, and is defined as PN Pc ðl Þ2 d 2 ðxi  vk Þ : ð10Þ XBI ¼ i¼1 k¼1 ik2 nmini;k d ðxi  vk Þ Unlike DPC, the aim is to minimize XBI since low XBI indicates less (greater) variation within (between) clusters and better clustering. The silhouette width is another useful tool for assessing how well classification is performed. It is defined as sðiÞ ¼

bðiÞ  aðiÞ ; max½aðiÞ; bðiÞ

1 6 sðiÞ 6 1;

ð11Þ

where a(i) denotes average dissimilarity within a cluster, and b(i) denotes the smallest dissimilarity between xi and other clusters. Values of s(i) close to 1 indicates that the object is well classified; s(i) close to 0 implies that a(i) and b(i) are almost equal, and it is unclear which cluster the object belongs to; and s(i) close to 1 indicates that dissimilarity within the cluster is greater than dissimilarity with other clusters, hence the object is misclassified. 8

k¼1

0<

N X

lik < N ;

1 6 k 6 c;

ð8Þ

i¼1

where (6) implies that membership coefficients may take any value in the closed interval zero and one (that is, a country can share similarities with various countries and belong to different clusters simultaneously), and (8) and (9) are similar to the constraints (2) and (3), respectively. To ensure that the chosen number of clusters gives an optimal representation of data, and to assess the effectiveness of our analysis, we compute three measures: Dunn’s (1974) partition coefficient, Xie and Beni’s (1991) index, and the silhouette width. The Dunn’s partition coefficient (DPC) is defined as the sum of squares of all membership coefficients divided by the number of objects in data, as DPC ¼

N X c X l2ik : N i¼1 k¼1

ð9Þ

When each object has the same l in all clusters, DPC is equal to 1/c and the obtained clusters

4. DATA AND VARIABLES (a) Choice of variables We explore the feasibility of the proposed currency union in West Africa by examining whether the economic structures of candidate countries are similar enough to support a fixed exchange rate arrangement. Therefore, our choice of variables is based on the OCA literature as well as the convergence criteria set for establishing a monetary zone in the region. 9 In particular, we use variables that measure the synchronization of output and terms of trade shocks, exchange rate variability, inflation, regional trade intensity of individual countries, government balance, and debt-servicing requirements. 10 The variables used are described in detail below. (i) Output volatility Measuring the synchronization of business cycles between countries requires choosing an anchor country (or a group of countries) for

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computing correlations. Research on the EMU has focused on Germany and assessed the performance of individual countries with respect to Germany. 11 Since the choice of an anchor country in West Africa is unclear, alternatively, one can use an area outside of West Africa as a benchmark. 12 Therefore, we calculate the correlation of business cycles of the West African countries with respect to the euro area as in BQC. 13 Estimating the synchronization of output shocks between ECOWAS countries requires de-trending the annual real GDP series of all countries using the Hodrick–Prescott filter. Next, cross-correlations of the cyclical components of individual GDP series are estimated vis-a`-vis the euro area. Countries with similar correlation values (positive or negative) are considered to have relatively parallel business cycles, while correlation coefficients different in magnitude or in sign indicate no correlation of output shocks (and higher costs of joining the monetary union). (ii) Terms of trade synchronization The costs of monetary unification are higher if terms of trade shocks are not well correlated across countries, because the exchange rate is no longer available as an instrument to cushion against these shocks. To measure the cross-correlation of terms of trade movements, we compute first differences of the annual terms of trade index for ECOWAS countries and the euro area, and measure the correlation between them. As before, similar (dissimilar) values of the correlation coefficient imply parallel (asymmetric) terms of trade shocks. (iii) Real exchange rate variability The OCA theory emphasizes that one of the primary costs of monetary unification is the loss of exchange rate flexibility. We measure the variability in exchange rates as the standard deviation of the log difference of annual real exchange rates of individual countries. This variable is included only when we examine the WAMZ grouping, because the ECOWAS arrangement includes both non-CFAF (WAMZ) countries and CFAF (WAEMU) countries, with the latter already under a pegged exchange rate system. (iv) Regional trade intensity According to the OCA theory, countries with strong trade links benefit more from forming a monetary union as transaction costs are re-

duced. The measure used commonly in earlier literature to assess this criterion is bilateral or regional trade intensity, that is, the share of trade of country i with other country/countries in the total trade of country i (see, e.g., Artis & Zhang, 2001; Boreiko, 2003). Hence, for any country i, trade links with other WAMZ and ECOWAS member countries are given by (Xi,WAMZ + Mi,WAMZ)/(Xi + Mi) and (Xi,ECOWAS + Mi,ECOWAS)/(Xi + Mi), respectively, where X represents exports and M denotes imports. We compute the annual regional trade intensity for each country and average it over the sample period, where a higher value of trade intensity indicates greater intra-regional trade and larger potential gains from joining the currency union. 14 (v) Inflation The primary criteria set by WAMZ for achieving macroeconomic convergence includes maintaining the inflation rate at a single-digit level. We construct the inflation rate variable for each country by taking the log difference of the annual consumer price index and averaging across the years. (vi) Government balance Another primary convergence criterion for WAMZ is a budget deficit to GDP ratio (excluding grants) of less than 4%. This ratio is calculated by taking the annual central government balance (excluding grants) as a percentage of annual GDP and then averaging observations for every country. (vii) Debt-servicing requirement The convergence criteria require member countries to build up surpluses to attain sustainable debt levels so as to ensure that they service their debt stock without creating inflation. 15 We represent debt servicing for every country as the average of the ratio of its debtservicing requirements to its total exports of goods and services. (b) Data sources Data for the above variables are compiled on an annual basis from various sources. The real and nominal GDP series, terms of trade index, consumer price index, and government balance statistics are obtained from the IMF’s World Economic Outlook, April 2005. The regional trade intensity variable is computed using bilateral data from the IMF’s Direction of Trade

MONETARY UNION MEMBERSHIP IN WEST AFRICA

Statistics. The debt-servicing ratio is compiled from the World Bank’s World Development Indicators 2004 and the African Development Indicators 2004. Information on the effective real exchange rate is taken from the Information Notice Systems (INS) database. Clustering is applied to two different samples of countries. The first sample consists of the non-WAEMU countries except Liberia, for which complete data series are unavailable. Since five out of the six non-WAEMU countries belong to WAMZ, henceforth, we refer to non-WAEMU countries as WAMZ. 16 Clustering of WAMZ countries allows us to examine their performance in terms of the OCA and the established primary macroeconomic convergence criteria. The second sample comprises the ECOWAS member countries, that is, the WAMZ and WAEMU countries taken together, and allows an assessment of the similarities among the economic characteristics of countries to be included in the proposed larger West African monetary union. All countries used in the analysis with their respective monetary zones are listed in Table A.1. 5. EMPIRICAL RESULTS Clustering of the West African states is performed for three overlapping periods (1990– 2004, 1995–2004, and 2000–04), making it possible to analyze the extent to which the changing national and international policy environments have influenced homogeneity across countries over time. The results for both hierarchical and fuzzy clustering reveal a high degree of similarity between groupings for the time periods 1990– (a) 1995-2004

Distance

2004 and 1995–2004. Therefore, we present and discuss our findings for 1995–2004 and 2000–04 only. For policy purposes, the results obtained for 2000–04 may be more relevant because they indicate the progress countries have made toward monetary unification after the inception of WAMZ. (a) Hierarchical analysis We begin with the hierarchical analysis and organize countries into discrete groups based on the seven variables discussed above. Figures 1 and 2 present the results of hierarchical clustering for WAMZ and ECOWAS countries, respectively. In each figure, the horizontal axis represents countries included in the sample, and the vertical axis indicates distances (or dissimilarities) between them. The cophenetic coefficient (reported with the dendrograms) has a reasonably high value in all cases indicating that the cluster information generated by the dendrograms is a good representation of dissimilarities in the data. In addition, the results obtained from the hierarchical clustering of WAMZ and ECOWAS show that the groupings do not depend on the type of agglomerative method used and remain similar across the Group Average, Ward, and Single linkage aggregation algorithms. The cophenetic correlation coefficient corresponding to the Group Average linkage function is the highest for all samples, so we discuss those results here. 17 For WAMZ, the CHI attains the highest value when the number of clusters is equal to four. Based on this, The Gambia, Guinea, and Cape Verde form one group, whereas (b) 2000-2004

Distance 4.5 Cophenetic coefficient=0.89

4.5 Cophenetic coefficient=0.90

4.0

4.0

3.5

3.5

3.0

3.0

2.5

2.5

2.0

2.0

GMB

GIN

CPV

GHA

1267

SLE

NGA

GMB

GIN

CPV

SLE

NGA

GHA

Figure 1. Hierarchical clustering analysis: WAMZ countries. Source: Author’s calculations. See Appendix for the list of abbreviations and the corresponding country names.

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Distance

(b) 2000-2004 Distance

Cophenetic coefficient=0.86

4.0

4.0

Cophenetic coefficient=0.85

3.5

3.5 3.0

3.0 2.5

2.5 2.0

2.0 1.5

1.5 1.0

1.0 BFA

NER BEN

MLI TGO CIV

SEN GMB GIN CPV NGA GHA SLE GNB

BEN

MLI BFA

NER

SEN

TGO CPV

GMB

GIN CIV GHA

NGA GNB

SLE

Figure 2. Hierarchical clustering analysis: ECOWAS countries. Source: Author’s calculations. See Appendix for the list of abbreviations and the corresponding country names.

Ghana, Nigeria, and Sierra Leone are singletons. This finding is supported by an inspection of the two panels of Figure 1, which illustrate that, among WAMZ, The Gambia, Guinea, and Cape Verde are linked to each other at relatively smaller distances in both time periods and that the remaining three countries join the group at much higher distances (indicating larger dissimilarities). The reason why The Gambia, Guinea, and Cape Verde group together is because of similar business cycles and terms of trade changes with each other, relatively lower real exchange rate volatility, low intra-regional trade intensity, low average inflation, and low debt-service requirements. Ghana, Nigeria, and Sierra Leone are dissimilar in terms of most variables and hence do not group with any other WAMZ country. In Figure 2, both WAEMU and WAMZ countries are considered together. For the period 1995–2004, the CHI suggests that six is the optimal number of clusters. 18 The first group consists of five WAEMU countries—Benin, Burkina Faso, Mali, Niger, and Togo—that have similar business cycle movements, regional trade intensity, inflation rates, and budget deficits. The second group comprises two WAEMU countries (Coˆte d’Ivoire and Senegal) and two WAMZ countries (The Gambia and Guinea), which have positive correlations for output variations, inflation rates, and budget deficit ratios. The third group consists of Ghana and Sierra Leone that have high government deficit to GDP ratios, high inflation rates, and debt-servicing requirements. Finally, Cape Verde, Nigeria, and Guinea-Bissau appear as singletons. For 2000–04, the CHI suggests grouping the data into five clusters but the composition of

clusters is not too different from 1995–2004. The first group now includes Senegal in addition to Benin, Burkina Faso, Mali, Niger, and Togo. Cape Verde, Coˆte d’Ivoire, The Gambia, and Guinea form the second group. GuineaBissau and Sierra Leone make up the third group. Once again, Ghana and Nigeria do not seem to be part of any group. Overall, we notice that all WAEMU countries except Guinea-Bissau group together and link with each other at relatively smaller distances, whereas the WAMZ countries link with each other as well as with the WAEMU countries at higher link lengths. Ghana, Guinea-Bissau, Nigeria, and Sierra Leone appear to be the most different in terms of the macroeconomic attributes considered here. Next, we extend our analysis to include the central African countries that are members of the CFAF zone. We do this because given the geographical proximity of the West and central African regions and the existing monetary arrangements in place in the CFAF zone, it is interesting to examine similarities among countries in a larger setting and explore the feasibility of alternative monetary groupings in SSA using the clustering tools. We perform clustering for all countries in the WAMZ, WAEMU, and CEMAC regions and use data for 1995–2004. Visual inspection of the dendrogram obtained from the Group Average method and CHI suggest the presence of six clusters (Figure 3). Burkina Faso, Coˆte d’Ivoire, Niger, and Senegal form one group; Benin, Chad, Mali, and Togo form the second group; Cameroon and Congo group together in one cluster; Cape Verde, the Central African Republic, The Gambia, and Guinea form the

MONETARY UNION MEMBERSHIP IN WEST AFRICA

1269

Distance 4.5 Cophenetic correlation coefficient = 0.80 4.0

3.5

3.0

2.5

2.0

1.5

1.0 BFA

NER

CIV SEN BEN

MLI TCD TGO CMR COG CPV CAF GIN GMB GNQ GAB NGA GHA GNB SLE

Figure 3. Hierarchical clustering analysis: West and Central Africa. Source: Author’s calculations.

fourth group; Equatorial Guinea, Gabon, and Nigeria make up the fifth group; and Ghana, Guinea-Bissau, and Sierra Leone make up the final group. (b) Fuzzy clustering The results obtained from fuzzy clustering of WAMZ countries are reported in Table 1. The validity statistics—namely, DPC, SW, and

XBI—indicate the presence of three clusters in 1995–2004 and of four clusters in 2000–04. We observe greater clarity in the partitioning of clusters for 2000–04 than 1995–2004 as indicated by higher values of average SW and DPC for the former period. Cape Verde, The Gambia, and Guinea have the highest membership coefficients for the same cluster during both time periods and therefore form a group together. As mentioned above, these countries

Table 1. Membership coefficients for WAMZ countriesa 1995–2004 Cluster I Cluster II Cluster III

2000–04 SW

Cluster I Cluster II Cluster III Cluster IV

SW

Cape Verde Gambia, The Ghana Guinea Nigeria Sierra Leone

0.883 0.909 0.064 0.824 0.001 0.197

0.068 0.057 0.869 0.094 0.001 0.691

0.049 0.034 0.067 0.082 0.999 0.112

0.805 0.758 0.524 0.736 1.000 0.325

0.844 0.719 0.000 0.827 0.000 0.001

0.069 0.125 0.000 0.065 0.000 0.999

0.037 0.080 1.000 0.039 0.000 0.000

0.050 0.077 0.000 0.069 1.000 0.000

0.750 0.594 1.000 0.713 1.000 1.000

Avg. SWb DPC (normalized)c DPC XBId

0.766 0.650

0.425

1.000

0.691

0.686 0.768

1.000

1.000

1.000

0.843

0.767 1.135

0.826 1.378

Source: Authors’ calculations. a The values in italics indicate the highest membership coefficient for a country across all clusters. b Avg. SW = average Silhouette width. c DPC = Dunn’s partition coefficient. d XBI = Xie and Beni’s index.

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experience similar business cycles and terms of trade movements, relatively lower real exchange rate volatility, low trade intensity within the WAMZ region, low average inflation, and low debt-service requirements. However, their statistics for government balance to GDP ratio and real exchange rate volatility are less uniform (Figure 4). Ghana and Sierra Leone have the highest membership coefficients for the same cluster if the longer data series is considered but not during the most recent time period. They have positive and relatively high correlation coefficients for output variation and terms of trade changes in 1995–2004. However, as is evident from the low average silhouette width of their cluster, they are not very similar in terms of other characteristics. The most outstanding characteristic of Sierra Leone is its large debt-servicing requirements. Ghana is the country with the highest within-region trade intensity. It experienced relatively moderate exchange rate volatility and high average inflation during 1995–2004 but greater real exchange rate fluctuations during 2000–04. Nigeria has idiosyncratic characteristics and therefore forms a cluster on its own in both sets of results. Although it has a low budget deficit to GDP ratio, moderate average inflation, and experienced low real exchange rate volatility in recent years, it has a low regional trade intensity, and no correlation of business cycles and terms of trade changes with other countries. Broadly speaking, the results reported in Tables 1 and 2 appear to be consistent with

1995-2004 TI

the grouping suggested by crisp clustering in Figure 1. Based on these results, we may conclude that considerable dissimilarities remain in the economic characteristics of WAMZ countries. Countries differ in not only the output and terms of trade shocks they experience, but also in terms of the progress they have made toward meeting the primary convergence criteria, which are a prerequisite for establishing the monetary union. Countries that share the greatest similarities in the WAMZ group are Cape Verde, The Gambia, and Guinea. Table 2 presents the results for ECOWAS countries. The validity statistics indicate the presence of five clusters for both time periods. The DPC and silhouette width are very small (less than 0.500) in both cases and reveal lack of clarity in the data, which means that countries do not share clear similarities. However, the average SW and DPC for 2000–04 are slightly higher than those of 1995–2004 and indicate improved within-cluster similarity. For 1995–2004, the best performing cluster comprises four WAEMU countries: Burkina Faso, Mali, Niger, and Togo. These four countries have a silhouette width of greater than 0.500 and an average silhouette width of 0.614. They have well-correlated business cycle movements, relatively greater regional trade intensity, low inflation rates, and low budget deficits. The other cluster with an average silhouette width of greater than 0.500 comprises Ghana, Guinea-Bissau, and Sierra Leone. These countries have higher government deficit to GDP ratios and relatively higher inflation rates and debt-servicing requirements. The

GDP

GDP

2

3

1.5

2

2000-2004

1

1

TI

TOT

0.5

TOT

0

0 -0.

-1

5 -1

-2 \

-1.5

-3

-2

REER REER

GB

CPI

DEBT DEBT

Cape Verde Guinea

CPI

GB

Gambia, The Nigeria

Ghana Sierra Leone

Figure 4. Characteristics of the WAMZ countries. Source: Author’s calculations. GDP is the correlation of business cycles with the euro area; TOT denotes the correlation of changes in terms of trade with the euro area; CPI is the average annual inflation rate; GB is the average government balance to GDP ration; TI is the average trade intensity; DEBT is the average of debt servicing to exports ratio; and REER is real exchange rate variability.

Table 2. Membership coefficients for ECOWAS countriesa 1995–2004

2000–04

Cluster II

Cluster III

Cluster IV

Cluster V

SW

Cluster I

Cluster II

Cluster III

Cluster IV

Cluster V

SW

0.029 0.008 0.942 0.039 0.373 0.070 0.256 0.108 0.036 0.038 0.110 0.032 0.059 0.051

0.813 0.031 0.017 0.068 0.118 0.090 0.233 0.132 0.365 0.112 0.395 0.082 0.058 0.228

0.017 0.008 0.012 0.055 0.098 0.635 0.087 0.520 0.036 0.050 0.166 0.023 0.726 0.060

0.061 0.030 0.018 0.732 0.298 0.111 0.314 0.118 0.100 0.165 0.156 0.777 0.096 0.150

0.080 0.923 0.012 0.107 0.113 0.095 0.109 0.123 0.464 0.635 0.173 0.087 0.061 0.510

0.468 0.731 0.613 0.436 0.066 0.498 0.065 0.519 0.588 0.507 0.418 0.494 0.488 0.630

0.030 0.036 0.502 0.380 0.878 0.261 0.882 0.238 0.012 0.072 0.006 0.147 0.018 0.073

0.050 0.021 0.093 0.100 0.022 0.204 0.029 0.114 0.013 0.051 0.977 0.058 0.010 0.051

0.839 0.101 0.144 0.148 0.032 0.145 0.030 0.184 0.936 0.198 0.009 0.155 0.011 0.144

0.065 0.819 0.138 0.234 0.040 0.172 0.031 0.149 0.031 0.623 0.005 0.578 0.013 0.693

0.016 0.023 0.123 0.139 0.029 0.219 0.209 0.316 0.008 0.057 0.004 0.062 0.949 0.040

0.880 0.512 0.269 0.091 0.395 0.071 0.535 0.301 0.851 0.379 1.000 0.480 0.328 0.587

Avg. SWb DPC (norm.)c DPC XBId

0.274 0.358 0.486 0.924

0.025

0.502

0.288

0.614

0.380

0.207 0.466 0.573 1.112

1.000

0.866

0.490

0.315

0.454

Source: Authors’ calculations. a The values in italics indicate the highest membership coefficient for a country across all clusters. b Avg. SW = average Silhouette width. c DPC = Dunn’s partition coefficient. d XBI = Xie and Beni’s index.

MONETARY UNION MEMBERSHIP IN WEST AFRICA

Cluster I Benin Burkina Faso Cape Verde Coˆte d’Ivoire The Gambia Ghana Guinea Guinea-Bissau Mali Niger Nigeria Senegal Sierra Leone Togo

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output fluctuations of Ghana and Sierra Leone are relatively synchronized, but the same does not hold for Guinea-Bissau. The three countries, however, experience dissimilar terms of trade shocks. Coˆte d’Ivoire, Guinea, and Senegal have the highest membership coefficients for the same cluster. The comparative statistics in Figure 5 show that the three countries have low average inflation, higher budget deficits ratio, and positive but low business cycle correlations although they differed in terms of other statistics. Guinea, however, has a lower membership coefficient (less than 0.500) than the other two countries and a negative silhouette width if forced to be included in this cluster. This is probably because of its high membership coefficient for the first cluster, which indicates that it also shares some similar characteristics with Cape Verde and The Gambia. Cape Verde and The Gambia form another cluster based on the membership coefficients although as shown in Table 2, The Gambia does not have a very low membership coefficient for cluster IV, which indicates some similarity of characteristics with countries in that group. Surprisingly, Benin and Nigeria have the highest membership coefficients for the same group, although the silhouette width for Benin indicates that it does not belong to the same cluster as Nigeria. Nigeria experienced output and terms of trade shocks that are very different from those experienced by other countries in the region; it therefore seems best to identify Nigeria as a separate group.

Analysis of the period 2000–04 does not reveal much difference in countries’ economic performance. The clustering algorithm identifies five groups where most of WAEMU countries cluster together. Benin and Mali, which experience symmetrical terms of trade and output shocks, form one group. Guinea-Bissau and Sierra Leone continue to group together, and Nigeria is identified as a singleton. Cape Verde, Coˆte d’Ivoire, The Gambia, Ghana, and Guinea have the highest membership coefficients for the same cluster, but the silhouette widths and the magnitudes of their membership coefficients indicate that only Cape Verde, The Gambia, and Guinea are well specified in the cluster. Strict classification of Cote d’Ivoire and Ghana is not clear. Coˆte d’Ivoire differs from other countries mainly in terms of its output fluctuations, whereas Ghana has a high average inflation rate. Overall, results from fuzzy clustering are very similar to the groupings obtained from hierarchical clustering. With the exception of Guinea-Bissau, the remaining WAEMU countries group together. Of the WAMZ countries, Cape Verde, The Gambia, and Guinea are relatively similar to each other in terms of meeting the OCA and convergence criteria but are different from the rest of the ECOWAS group. Ghana does not have much in common, and therefore cannot be identified, with one particular group or country. The same is true for Nigeria, whose behavior pertaining to terms of trade shocks, inflation and exchange rate variability is highly idiosyncratic. GDP

GDP

2 1.5 1

2

1995-2004

1.5

2000-2004

1 0.5

TI

0

TOT

TI

0.5 0 -0.5

TOT

-1 -1.5 -2 -2.5

-0.5 -1 -1.5 -2

DEBT

DEBT

GB

CPI

CPI

GB

Benin Guinea-Bissau

Burkina Faso Mali

Côte d'Ivoire Niger

Figure 5. Characteristics of the WAEMU countries. Source: Author’s calculations. GDP is the correlation of business cycles with the euro area; TOT denotes the correlation of changes in terms of trade with the euro area; CPI is the average annual inflation rate; GB is the average government balance to GDP ration; TI is the average trade intensity; DEBT is the average of debt servicing to exports ratio; and REER is real exchange rate variability.

MONETARY UNION MEMBERSHIP IN WEST AFRICA

We also perform fuzzy clustering for ECOWAS and CEMAC countries together. The optimal number of clusters, as well as the composition of clusters according to the highest membership coefficients is identical to that obtained from hierarchical clustering presented in Figure 3. Two interesting observations emerge from this analysis. First, CEMAC and WAEMU countries, despite being members of the CFAF zone, do not group together. WAEMU countries form their own clusters and seem to share greater similarities, as identified by the distances at which fusions are made. Second, a majority of WAMZ countries group with CEMAC countries. Nigeria has relatively higher membership coefficients for clusters consisting of CEMAC countries, which indicates that greater similarities exist among them. This is not surprising considering the heavy reliance of Nigeria and the CEMAC countries on oil for revenue. (c) Empirical evaluation: principal component analysis A robustness check recommended for groupings generated from clustering analysis is the principal component analysis (PCA). PCA is a procedure for multivariate analysis which reduces the number of possibly correlated variables into a smaller number of uncorrelated variables known as the principal components. Each principal component, PC, is a linear combination of the original variables and may be expressed as PCi ¼ ai1 X 1 þ ai2 X 2 þ    þ aip X p ; where i = 1, 2, . . . , p, and X is a data matrix with n observations and p variables. The first principal component is supposed to account for much of the variability in data, whereas the following principal components explain the remaining variation. We generate PCs and cluster ECOWAS countries based on the PCs that satisfy the following properties: (i) collectively explain at least 60% of the variation in data; (ii) have an eigenvalue of greater than 1; and (iii) explain at least 20% of the variation individually. The results show that the first twoPCs satisfy the above properties for WAMZ and ECOWAS countries. Hence, we generate two-dimensional scatter plots of countries, measuring the first principal component on the x-axis and the second principal component on the y-axis

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(Figure 6). Further, we superimpose contour maps generated by fuzzy clustering on the scatter plots to visualize the results. 19 The plot for WAMZ supports the results obtained earlier. Similarly, for ECOWAS, the composition of clusters is almost identical to that obtained earlier. Nigeria does not form part of any group in either case, whereas most WAEMU countries fall together. Coˆte d’Ivoire and Guinea-Bissau appear to be different from the rest of the WAEMU group and cluster with WAMZ countries in 2000–04 (Table 3). To numerically assess the dissimilarities between WAEMU, WAMZ, ECOWAS, and CEMAC regions, we compute a dissimilarity matrix for each region. 20 We do so by calculating the average distance between all pairs of countries in every region using the Euclidean distance as the dissimilarity measure. Table 4 shows that WAMZ has the highest average pair-wise distance between countries whereas WAEMU and CEMAC have the highest and lowest variation in distances, respectively. For comparison purposes, we also examine how countries are grouped within the euro area. 21 In contrast to the results obtained for WAMZ and the ECOWAS, analysis of the euro area results in a much smaller optimal number of clusters (two versus five) and greater similarities among member countries. 22 Specifically, the dendrogram obtained from the hierarchical analysis clearly indicates the presence of two groups: the first group consists of Austria, Belgium, France, Germany, Italy, Portugal, and Spain, and the second group comprises Finland, Greece, Ireland, and the Netherlands. The validity statistics for fuzzy clustering also indicate the presence of two groups, in line with the results of Artis and Zhang (2001, 2002). 23 Overall, our findings are broadly similar to those of BQC, despite the different time period and clustering criteria used here. BQC find that the CFAF zone cannot be viewed as an OCA in the sense that the CEMAC and WAEMU countries do not belong to the same cluster. In addition, their analysis does not support the inclusion of Nigeria in WAMZ, and—based on the fact that they find similarities between the Gambia, Ghana, Sierra Leone, and the WAEMU—they support the creation of a limited regional monetary arrangement with these countries as members. In contrast, our analysis, which employs a more recent data set and considers both OCA and the convergence criteria to identify clusters, finds that these three

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Figure 6. Clustering based on principal components analysis. Source: Author’s calculations.

WAMZ countries do not group with WAEMU countries. In fact fuzzy clustering provides additional policy information and shows that WAMZ countries form first best clusters (where they have the highest membership coefficients) and second best clusters (where they have the second highest membership coefficients) with CEMAC countries. This suggests that WAMZ countries share greater similarities with CEMAC as compared to WAEMU. 6. CONCLUSION Using hard and soft clustering methods, this paper examines the preparedness and status of candidate countries for the proposed WAMZ and ECOWAS monetary unions. It provides in-

sights into the similarities of countries’ economic structures based on the convergence and OCA criteria, and identifies the existing homogeneous subgroups within the region. In addition, by studying the West and central African regions together, this analysis helps in evaluating the feasibility of new monetary arrangements and the desirability of changing the existing ones to alternative configurations. Our findings reveal considerable dissimilarities in the economic characteristics of the countries in West Africa (that is, WAEMU and WAMZ viewed as one group), suggesting that the formation of ECOWAS may not be advisable at this stage. Of all the groups examined, WAMZ countries exhibit the highest degree of dissimilarity and have little in common with the WAEMU countries, which, in principle,

MONETARY UNION MEMBERSHIP IN WEST AFRICA

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Table 3. Fuzzy clustering for West and Central Africaa 1995–2004 Cluster I

Cluster II

Cluster III

Cluster IV

Cluster V

Cluster VI

SW

Benin Burkina Faso Cameroon Cape Verde Central African Rep. Chad Congo, Rep. of Coˆte d’Ivoire Equatorial Guinea Gabon Gambia, The Ghana Guinea Guinea-Bissau Mali Niger Nigeria Senegal Sierra Leone Togo

0.161 0.032 0.257 0.245 0.187 0.142 0.883 0.097 0.035 0.187 0.114 0.098 0.040 0.159 0.061 0.038 0.221 0.097 0.043 0.076

0.200 0.028 0.248 0.089 0.118 0.068 0.023 0.070 0.871 0.289 0.053 0.070 0.014 0.072 0.047 0.032 0.278 0.077 0.024 0.078

0.146 0.040 0.158 0.375 0.465 0.090 0.038 0.196 0.026 0.127 0.547 0.113 0.898 0.118 0.044 0.050 0.121 0.244 0.049 0.069

0.137 0.725 0.122 0.095 0.086 0.115 0.015 0.368 0.022 0.111 0.113 0.109 0.018 0.110 0.145 0.749 0.100 0.332 0.041 0.229

0.327 0.159 0.158 0.120 0.106 0.547 0.031 0.157 0.036 0.221 0.101 0.106 0.021 0.119 0.686 0.101 0.164 0.203 0.038 0.509

0.029 0.017 0.057 0.077 0.038 0.038 0.011 0.112 0.010 0.066 0.074 0.505 0.010 0.422 0.017 0.030 0.113 0.048 0.805 0.039

0.176 0.081 0.382 0.562 0.273 0.622 0.195 0.601 0.097 0.112 0.462 0.563 0.340 0.398 0.523 0.505 0.130 0.376 0.597 0.447

Avg. SWb DPC (norm.)c DPC XBI d

0.289 0.280 0.400 0.871

0.145

0.410

0.350

0.424

0.519

0.340

Source: Authors’ calculations. a The values in italics indicate the highest membership coefficient for a country across all clusters. b Avg. SW = average Silhouette width. c DPC = Dunn’s partition coefficient. d XBI = Xie and Beni’s index. Table 4. Dissimilarities between Member Countriesa 1990–2004

WAMZ WAEMU ECOWAS CEMAC Euro area

1995–2004

2000–04

Mean

Std. deviation

Mean

Std. deviation

Mean

Std. deviation

3.57 3.14 3.26 3.43 2.54

1.15 1.50 1.17 0.46 1.24

3.59 3.23 3.31 3.43 2.58

1.21 1.09 1.03 0.52 1.09

3.59 3.28 3.33 3.40 2.63

1.09 1.14 0.96 0.70 1.03

Source: Authors’ calculations. a Dissimilarities measure differences in economic characteristics (output volatility, terms of trade synchronization, real exchange rate variability, and regional trade intensity. Government balance, and debt-servicing requirement) and are computed using the Euclidean distance formula.

tend to cluster together. Furthermore, although Ghana and, especially, Nigeria usually appear as singletons and are independent of any other cluster, the remaining WAMZ countries tend to group together. This outcome raises questions about the inclusion of Nigeria and Ghana in the proposed zone, and the feasibility of a sep-

arate monetary union that includes all WAMZ countries and highlights the need for concerted efforts to achieve convergence. Finally, when West and central Africa are examined as one group, we find heterogeneities within the CFAF zone and some interesting similarities between CEMAC and WAMZ: WAEMU and CEMAC

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countries do not cluster together, and WAMZ countries tend to group with CEMAC countries. Based on our analysis, a few points are worth emphasizing. First, the project to create the ECOWAS has implications for the WAEMU and the CFAF zone itself. Although the terms of the eventual merger between WAMZ and WAEMU have not been agreed, the issues of the exchange rate regime and the institutional framework of the CFA Franc will necessarily come up for reexamination. Second, our analysis, which is primarily a test of the feasibility of the existing and proposed monetary unions, has identified some hypothetical clustering arrangements. These arrangements need not be considered as viable separate monetary unions per se since other factors—including political and institutional—need to be considered when gauging the viability of the suggested/implied monetary unions. Identifying groups of countries that have achieved a high degree of macroeconomic convergence is only the first step and may raise more questions than it answers. The existence of differences or heterogeneities across coun-

tries does not necessarily imply that benefits cannot be achieved through monetary integration. This follows from the endogeneity argument of the OCA criteria—originally flagged by Frankel and Rose (1998)—which suggests that countries become similar when they share a common currency. At the same time, homogeneities do not ensure that gains will be achieved by forming a monetary union as economies may become more specialized, less diversified, and more sensitive to exogenous shocks due to increased integration as pointed out by Krugman (1993). Nonetheless, the analysis in this paper raises questions about the geographical boundaries of the existing and proposed unions, and highlights the need of undertaking further analysis to assess the merits and de-merits of the proposed unions as well as of the possible alternatives. Viewed in this light, the conclusions of our analysis are a valuable contribution to the scholarly and policy debate over whether creation of a monetary union should precede or follow other forms of integration.

NOTES 1. Members of the WAEMU are Benin, Burkina Faso, Coˆte 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. See Hadjimichael and Galy (1997) for an analysis of the CFAF zone and its institutions. 2. The launch date of the common currency, initially set for July 2005, has been postponed to December 2009 because the WAMZ member states did not achieve the convergence criteria. 3. In addition, in accordance with the European Council decision of November 23, 1998, France is required to inform European institutions of the operation of the CFAF zone and, any changes in its scope or membership have to be approved by the European Council, on recommendation of the EU Commission and after consultation with the European Central Bank. 4. Two mechanisms that ensure rapid adjustment are labor mobility and fiscal transfers. Adjustments in relative wages, changes in labor force participation

induced by wage changes, and capital mobility are other mechanisms for responding to shocks (see Blanchard & Katz, 1992). 5. The term ‘‘similarity’’ however should be understood as mathematical similarity measured in a welldefined sense. In metric spaces, for example, similarity is defined by means of a distance function such as Euclidean distance. 6. Cophenetic correlation coefficient measures the correlation between distances generated by the linkage method and the simple Euclidean distances between objects. The Euclidean distance between two objects x1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

and x2 is given by d 12 ¼

ðx1  x2 Þ2 .

7. A membership coefficient close to or equal to zero (one) suggests that the object is dissimilar (similar) to other objects in that cluster. 8. The silhouette width of a cluster is obtained by averaging the silhouette widths of all objects within a cluster. This is an indicator of how well a cluster is classified.

MONETARY UNION MEMBERSHIP IN WEST AFRICA

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9. Clustering was also performed considering the OCA and convergence criteria separately. However, this did not have any significant effect on the groupings.

16. Cape Verde was not a signatory of the ‘‘Accra declaration’’ on the creation of WAMZ and is yet to formalize its membership of WAMZ.

10. To attach equal weights to all variables, we perform clustering on normalized variables, achieved by taking the deviation of each variable from its mean and dividing by its standard deviation.

17. Results for the Ward and Single linkage algorithms are available from the authors.

11. See Artis and Zhang (2001, 2002), Boreiko (2003), and Kozluk (2004). 12. Nigeria could be a potential candidate however it lacks the financial development and disciplined fiscal policies of Germany, and has an export structure that differs greatly from its neighbors. 13. BQC point out that the euro area is preferable as an anchor because of the current CFA arrangement, as well as because of the large trade flows between the two regions. 14. To take into account the sizes of respective economies, we compute the ratio of regional trade intensity to the share of country i’s trade in world trade as an alternate measure of trade intensity. However, the groupings remain the same if this measure is used. 15. Adequate reserve coverage is important for ensuring foreign debt repayments. It also lowers the risk associated with a country, improves its credit ratings and strengthens the confidence of foreign investors, thereby increasing capital inflow. However, reserve accumulation may lead to a rapid expansion of lending by domestic banks and cause monetary expansion resulting in inflation. Central banks can mop up excess liquidity and limit this inflation to some extent using banks’ reserve requirement ratio and sterilization. Sterilization entails costs and becomes difficult to manage as reserves grow.

18. In general, an effective representation of data requires that the number of clusters be neither too small nor too large. As our sample contains 14 elements, considering a solution with more than seven groups does not seem feasible. We therefore examine CHI for 2–6 cluster solutions only. 19. Fuzzy clustering is performed using the first two PCs. Each big circle represents a cluster and the innermost circle represents the center of the cluster. The placement of the clusters gives an idea about the distances/dissimilarities between them and the placement of the countries indicates the similarities within a cluster. See Balasko, Abonyi, and Feil (2004) for a detailed explanation of the generation of contour maps. 20. A dissimilarity matrix presents the distance between every pair of objects in the data set. For a data set with n observations, the total number of pairs of distances is n (n  1)/2. 21. We use the criteria described in Section 4 to calculate distances within the euro area. 22. Results of this analysis are available from the authors. 23. Following earlier literature on the EMU, this result can be interpreted as reflecting a ‘‘core’’ (Austria, Belgium, France, Germany, Italy, Portugal, and Spain) and a ‘‘periphery’’ (Finland, Greece, Ireland, and the Netherlands), where the core consists of countries that are more homogeneous than those in the periphery (Artis & Zhang, 2001, 2002; Bayoumi & Eichengreen, 1993).

REFERENCES Artis, M. J., & Zhang, W. (2001). Core and periphery in EMU: A cluster analysis. Economic Issues, 6(2), 39–58. Artis, M. J., & Zhang, W. (2002). Membership of EMU: A fuzzy clustering analysis of alternative criteria. Journal of Economic Integration, 17(1), 54–79. Balasko, B., Abonyi, J., & Feil, B. (2004). Fuzzy clustering and data analysis toolbox: For use with Matlab. Hungary: University of Veszprem. Bayoumi, T., & Eichengreen, B. (1993). Shocking aspects of European monetary integration. In F.

Giavazzi, & F. Torres (Eds.), Adjustment and growth in the European Monetary Union. Cambridge and New York: Cambridge University Press. Bayoumi, T., & Ostry, J. D. (1997). Macroeconomic shocks and trade flows within sub-Saharan Africa: Implications for optimum currency arrangements. Journal of African Economies, 6(3), 412–444. Be´nassy-Que´re´, A., & Coupet, M. (2005). On the adequacy of monetary arrangements in sub-Saharan Africa. World Economy, 28(3), 349–373.

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Bezdek, J. C. (1981). Pattern recognition with fuzzy objective function algorithms. New York: Plenum Press. Blanchard, O., & Katz, L. (1992). Regional evolutions. Brookings Papers on Economic Activity, 2, 1–61. Boreiko, D. (2003). EMU and accession countries: Fuzzy cluster analysis of membership. International Journal of Finance and Economics, 8, 309–325. Buigut, S. K., & Valev, N. T. (2005). Is the proposed East African Monetary Union an optimal currency area? A structural vector autoregression analysis. World Development, 33(12), 2119–2133. Calinski, T., & Harabasz, J. (1974). A dendrite method for cluster analysis. Communications in Statistics, 3, 1–27. Celasun, O., & Justiniano, A. (2005). Synchronization of output fluctuations in West Africa: Implications for monetary unification. Unpublished manuscript, International Monetary Fund, Washington DC. Debrun, X., Masson, P., & Pattillo, C. (2005). Monetary union in West Africa: Who might gain, who might lose, and why? Canadian Journal of Economics, 38(2), 454–481. Devarajan, S., & Rodrik, D. (1991). Do the benefits of fixed exchange rates outweigh their costs? The Franc zone in Africa. NBER Working Paper No. 3727. Cambridge, MA: National Bureau of Economic Research. Dunn, C. J. (1974). Well-separated clusters and optimal fuzzy partitions. Journal of Cybernetics, 4, 95–104. Elbadawi, I., & Majd, N. (1996). Adjustment and economic performance under a fixed exchange rate: A comparative analysis of the CFA zone. Word Development, 24, 939–951. Everitt, B. S., Landau, S., & Leese, M. (2001). Cluster analysis. London: Arnold. Fielding, D., & Shields, K. (2001). Modeling macroeconomic shocks in the CFA Franc zone. Journal of Development Economics, 66, 199–223. Frankel, J. A., & Rose, A. K. (1998). The endogeneity of the optimum currency area criteria. Economic Journal, 108, 1009–1025. Ghura, D., & Hadjimichael, M. T. (1996). Growth in sub-Saharan Africa. IMF Staff Papers, 43, 605–634. Hadjimichael, M. T., & Galy, M. (1997). The CFA Franc zone and the EMU. IMF Working Paper No. 97/156. Washington DC: International Monetary Fund. Hoffmaister, A. W., Roldos, J., & Wickham, P. (1998). Macroeconomic fluctuations in sub-Saharan Africa. IMF Staff Papers, 45, 132–160. Huizinga, H., & Khamfula, Y. (2004). The Southern African Development Community: Suitable for a monetary union?. Journal of Development Economics, 73(2), 699–714. Kenen, P. B. (1969). The theory of optimum currency areas: An eclectic view. In A. K. Swoboda, & R. A. Mundell (Eds.), Monetary problems of the international economy. Chicago: University of Chicago Press. Kozluk, T. (2004). CEEC accession countries and the EMU: An assessment of relative suitability and readiness for Euro-area membership. Paper pre-

sented at European University Institute conference ‘‘Economic, Econometric and Cross-Disciplinary Aspects of European Union Enlargement,’’ in Italy, May 13–15. Krugman, P. (1990). Policy problems of a Monetary Union. In P. De Grauwe, & L. Papademos (Eds.), The European monetary system in the 1990s. London and New York: Longman. Krugman, P. (1993). Lessons of Massachusetts for EMU. In F. Giavazzi, & F. Torres (Eds.), The transition to economic and monetary union in Europe. New York: Cambridge University Press. Masson, P., & Pattillo, C. (2005). The monetary geography of Africa. Washington, DC: Brookings Institution Press. McKinnon, R. I. (1963). Optimum currency area. American Economic Review, 53, 717–724. Milligan, G. W., & Cooper, M. C. (1985). An examination of procedures for determining the number of clusters in a data set. Psychometrika, 50, 159– 179. Mundell, R. A. (1961). A theory of optimum currency areas. American Economic Review, 53, 657–664. Xie, X., & Beni, G. A. (1991). Validity measure for fuzzy clustering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 13, 841–847.

APPENDIX A. METHODOLOGY A.1. Group average method This method uses the average distance between all pairs of individuals in each group to calculate the distance between clusters. Hence, for two clusters (1 and 2) with n1 and n2 observations, respectively, this method measures proximity, DistGA, as DistGA12 ¼

n X n 1 X dðx1i ; x2j Þ: n1 n2 i¼1 j¼1

A.2. Single linkage method The single linkage method uses the nearestneighbor distance or the smallest distance between objects in two groups. In other words, it looks for an object in a cluster that is most closely placed to another object in a different cluster and uses the distance between them to measure the closeness of clusters. It is expressed as DistW12 ¼ minfdðx1i ; x2j Þg; i 2 ð1; 2; . . . ; n1 Þ; j 2 ð1; 2; . . . ; n2 Þ:

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Table A.1. Countries and regions Country Austria Belgium Benin Burkina Faso Cameroon Cape Verde Central African Rep. Chad Congo Cote d’lvoire Equatorial Guinea Finland France Gabon Gambia, The Germany

Abbreviation

Region

Country

Abbreviation

Region

AUT BEL BEN BFA CMR CPV CFA TCD COG CIV GNQ FIN FRA GAB GMB DEU

Euro Area Euro Area WAEMU WAEMU CEMAC WAMZ CEMAC CEMAC CEMAC WAEMU CEMAC Euro Area Euro Area CEMAC WAMZ Euro Area

Ghana Greece Guinea Guinea-Bissau Ireland Italy Mali Niger Nigeria Netherlands Portugal Senegal Sierra Leone Spain Togo

GHA GRC GIN GNB IRL ITA MLI NER NGA NLD PRT SEN SLE ESP TGO

WAMZ Euro Area WAMZ WAEMU Euro Area Euro Area WAEMU WAEMU WAMZ Euro Area Euro Area WAEMU WAMZ Euro Area WAEMU

A.3. Ward linkage method This method uses the change in the total within-cluster sum of squares when two clusters are joined to determine the groupings of objects. It is expressed as DistS12 ¼

P1 where xc ¼ n11 ni¼1 xci is the center of each cluster and d 2 ðx1 ; x2 Þ is the distance between the centers of two clusters.

n1 n2 d 2 ðx1 ; x2 Þ ; ðn1 þ n2 Þ Available online at www.sciencedirect.com