## _wp0690

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---

### Introduction and purpose
- Renewed international interest in monetary integration after the euro launch motivates assessment of West African monetary-area boundaries and readiness for an Optimum Currency Area (OCA).
- Methodology:
  - Cluster analysis classifies West African countries according to OCA and convergence criteria.
  - Both fuzzy clustering and traditional (crisp) hierarchical agglomerative clustering are used; countries are assigned the largest membership coefficient corresponding to the cluster with greatest similarity.

### OCA criteria and West Africa — analytical highlights
- Principal OCA criteria emphasized:
  - Nature of shocks: symmetric shocks lower union costs; asymmetric shocks raise costs.
  - Speed of adjustment: labor mobility, fiscal transfers, wage adjustments, labor force participation changes, and capital mobility mitigate asymmetric-shock costs.
- Characteristics relevant to OCA assessment:
  - Many economies are small, open, commodity-exporting and vulnerable to large, uncorrelated terms-of-trade movements; several depend on a single commodity for 50 percent or more of earnings.
  - Nigeria: large oil exporter; terms-of-trade variability larger than any other country in the region and distinct from oil-importing WAMZ members.
  - Correlations of terms-of-trade shocks are higher among WAEMU members than between WAEMU and WAMZ or among WAMZ members.
- Adjustment mechanisms and constraints:
  - Historical migration within West Africa has been high but reduced recently due to conflicts.
  - Fiscal transfers are constrained by limited financial resources and weak transfer/tax systems.
  - Intraregional trade: WAEMU countries trade considerably more among themselves; trade within non-WAEMU (WAMZ) is limited.
  - Infrastructure weaknesses and low intraregional trade limit gains from lower transaction costs.
- Potential benefits of monetary union:
  - Fixed exchange rates and a common currency can credibly lower inflation and improve price stability.
  - A common independent central bank could act as an “agent of restraint” on fiscal policies and address seigniorage-driven money creation.

### Institutional and historical context
- CFA franc (CFAF) zone: 14 countries in two monetary unions: WAEMU and CEMAC.
- ECOWAS: founded 1975, 15 members; 8 are WAEMU members.
- WAMZ formed April 2000 by five non-WAEMU ECOWAS members (Nigeria, The Gambia, Ghana, Guinea, Sierra Leone) to converge toward a common currency.
- WAMZ common-currency planned launch moved from July 2005 to December 2009 because convergence criteria were not met.
- Post-unification ECOWAS monetary arrangement not announced.

### Methodological approach (summary)
- Clustering advantages: accounts for multiple variables, less stringent time-series requirements, identifies group patterns and country-specific convergence needs.
- Crisp clustering (hierarchical agglomerative) details:
  - Euclidean distance used as proximity metric.
  - Linkage methods applied: Group Average, Single linkage, Ward linkage.
  - Dendrograms used; cophenetic correlation coefficient measures fidelity to original dissimilarities.
  - Optimal cluster number: visual dendrogram inspection and Calinski-Harabasz Index (CHI) where CHI = (S_b / S_w) * ((n − k) / (k − 1)).
- Fuzzy clustering (fuzzy c-means) details:
  - Membership coefficients μ_ik ∈ [0,1]; objective J = ∑_{i=1}^N ∑_{k=1}^c μ_{ik}^m d^2(x_i, v_k).
  - Cluster centers v_k computed by v_kj = (∑_{i=1}^N μ_{ik}^m x_{ij}) / (∑_{i=1}^N μ_{ik}^m).
  - Validation indices used: Dunn’s Partition Coefficient (DPC), Xie and Beni’s Index (XBI), silhouette plot; multiple indices compared to select optimal cluster number.

### Variable construction and sample
- Variables (normalized by deviation from mean divided by standard deviation): output synchronization (HP-filtered cyclical correlation with euro area), terms-of-trade synchronization (first differences correlated with euro area), real exchange rate variability (std. dev. of log diff), regional trade intensity ((exports to region + imports from region) / (total exports + total imports)), inflation (log diff of CPI averaged), government balance (central government balance excluding grants as % of GDP averaged), debt-servicing requirement (average ratio of debt-servicing to total exports).
- Data sources: IMF WEO April 2005, IMF Direction of Trade Statistics, World Bank World Development Indicators 2004, African Development Indicators 2004, INS database (effective real exchange rate).
- Samples: WAMZ (non-WAEMU countries except Liberia), ECOWAS (WAMZ + WAEMU). Periods analyzed: 1990-2004, 1995-2004, 2000-04 (focus on 1995-2004 and 2000-04).

### Hierarchical clustering — key empirical findings and statistics
- Cophenetic coefficients reported for dendrograms: 0.86, 0.85, 0.89, 0.90 (figures cited).
- WAMZ (Group Average linkage; CHI guidance):
  - CHI highest when number of clusters = 4 (1995-2004).
  - Cluster membership (1995-2004):
    - Group 1: The Gambia, Guinea, Cape Verde.
    - Singletons: Ghana, Nigeria, Sierra Leone.
  - Interpretation: The Gambia, Guinea, Cape Verde link at smaller distances; Ghana, Nigeria, Sierra Leone join at much higher distances (greater dissimilarity).
- ECOWAS clustering:
  - 1995-2004 (CHI suggests 6 clusters):
    - Cluster 1: Benin, Burkina Faso, Mali, Niger, Togo.
    - Cluster 2: Côte d’Ivoire, Senegal, The Gambia, Guinea.
    - Cluster 3: Ghana, Sierra Leone.
    - Singletons: Cape Verde, Nigeria, Guinea-Bissau.
  - 2000-04 (CHI suggests 5 clusters):
    - Cluster 1: Benin, Burkina Faso, Mali, Niger, Togo, Senegal.
    - Cluster 2: Cape Verde, Côte d’Ivoire, The Gambia, Guinea.
    - Cluster 3: Guinea-Bissau, Sierra Leone.
    - Ghana and Nigeria remain singletons.
- Hierarchical-summary conclusion:
  - WAEMU countries (except Guinea-Bissau) tend to group together and link at smaller distances.
  - WAMZ countries link at higher link lengths with each other and with WAEMU.
  - Ghana, Guinea-Bissau, Nigeria, Sierra Leone are most different in considered macroeconomic attributes.

### Fuzzy clustering — key empirical findings and statistics
- Validity statistics indicate:
  - Presence of three clusters for 1995-2004 and four clusters for 2000-04 in WAMZ fuzzy results.
  - ECOWAS fuzzy validity: DPC and silhouette width very small (less than 0.500).
  - ECOWAS fuzzy clustering indicates five clusters for both 1995-2004 and 2000-04.
- WAMZ membership patterns:
  - Cape Verde, The Gambia, Guinea: highest membership coefficients for same cluster in both periods.
  - Nigeria: forms its own cluster (singleton/outlier).
  - Ghana and Sierra Leone: high membership for same cluster in 1995-2004; less consistent in 2000-04.
  - Partition fuzziness decreased in 2000-04 vs. 1995-2004 (increased cluster distinctness).
- Selected membership coefficients (Table 1 examples):
  - Cape Verde: 0.883 (1995-2004) and 0.844 (2000-04) for its primary cluster.
  - Gambia, The: 0.909 (1995-2004) and 0.719 (2000-04) for its primary cluster.
  - Guinea: 0.824 (1995-2004) and 0.827 (2000-04) for its primary cluster.
  - Ghana: reported as 1.000 in one membership column for 2000-04 (strong assignment).
  - Nigeria: membership near singleton behavior (values showing 0.999 / 1.000 in singleton columns).
- WAEMU fuzzy findings (1995-2004):
  - Best-performing cluster: Burkina Faso, Mali, Niger, Togo with cluster silhouette width > 0.500 and average silhouette width of 0.614.
  - Characteristics: well-correlated business cycles, greater regional trade intensity, low inflation, low budget deficits.
- ECOWAS fuzzy statistics (selected):
  - Avg. SW cluster-level values reported for ECOWAS 1995-2004 include 0.274, -0.025, 0.502, 0.288, 0.614.
  - Normalized DPC = 0.358 (1995-2004); DPC = 0.486 (1995-2004).
  - 2000-04: normalized DPC = 0.466; DPC = 0.573.
  - XBI reported as 0.924 (1995-2004) and 1.112 (2000-04).
- West and Central Africa fuzzy clustering (1995-2004, Table 4):
  - CHI and visual inspection suggest six clusters.
  - Table 4 Avg. SW values: 0.289, -0.145, 0.410, 0.350, 0.424, 0.519; overall Avg. SW = 0.340.
  - DPC (normalized) = 0.280; DPC = 0.400; XBI = 0.871.
- Euro Area fuzzy clustering (1995-2004, Table 5):
  - Two clusters (core and periphery).
  - Avg. SW cluster-level: 0.540 and 0.224; overall Avg. SW = 0.423.
  - DPC = 0.599; XBI = 0.817.

### Principal Components Analysis (PCA) robustness checks
- PCA selection criteria:
  - (i) collectively explain at least 60 percent of variation;
  - (ii) each eigenvalue > 1;
  - (iii) each principal component explains at least 20 percent of variation.
- Findings:
  - First two principal components satisfy the properties for WAMZ and ECOWAS samples.
  - PCA scatter plots with fuzzy clustering contours largely reproduce fuzzy/hierarchical cluster results.
  - Nigeria remains a singleton in PCA visualization.
  - Most WAEMU countries cluster together; Côte d’Ivoire and Guinea-Bissau differ and sometimes cluster with WAMZ countries in 2000-04.
- Selected principal component outputs (normalized data) — WAMZ (1995-2004) principal-component row 1 and variance example:
  - Row 1: -0.51 0.03 -0.20 -0.05 0.21 -0.21 -0.78 3.66 -0.46 -0.06 0.49 0.22 -0.34 0.61 -0.08 3.19
  - Row 2: -0.18 -0.60 0.05 -0.06 0.70 -0.13 0.31 2.21 -0.08 -0.62 0.25 0.26 -0.20 -0.47 0.47 2.32
  - (Additional rows and 2000-04 entries reported in Appendix II.)

### Dissimilarity analysis (average pair-wise distances, Table 3)
- WAMZ:
  - Mean = 3.57 (1990-2004), Mean = 3.59 (1995-2004), Mean = 3.59 (2000-04)
  - Std. deviation = 1.15 (1990-2004), 1.21 (1995-2004), 1.09 (2000-04)
- WAEMU:
  - Mean = 3.14 (1990-2004), Mean = 3.23 (1995-2004), Mean = 3.28 (2000-04)
  - Std. deviation = 1.50 (1990-2004), 1.09 (1995-2004), 1.14 (2000-04)
- ECOWAS:
  - Mean = 3.26 (1990-2004), Mean = 3.31 (1995-2004), Mean = 3.33 (2000-04)
  - Std. deviation = 1.17 (1990-2004), 1.03 (1995-2004), 0.96 (2000-04)
- CEMAC:
  - Mean = 3.43 (1990-2004), Mean = 3.43 (1995-2004), Mean = 3.40 (2000-04)
  - Std. deviation = 0.46 (1990-2004), 0.52 (1995-2004), 0.70 (2000-04)
- Euro area:
  - Mean = 2.54 (1990-2004), Mean = 2.58 (1995-2004), Mean = 2.63 (2000-04)
  - Std. deviation = 1.24 (1990-2004), 1.09 (1995-2004), 1.03 (2000-04)
- Interpretations:
  - WAMZ countries have the highest pair-wise average distance among themselves.
  - WAEMU countries have the highest variation in distances.
  - Euro area countries have the lowest average distance; CEMAC has the lowest dispersion around the mean.
- Box-plot observations:
  - Median dissimilarities differ considerably across WAMZ countries.
  - Ghana, Nigeria, Sierra Leone: less dispersion but farther from other countries.
  - WAEMU: Guinea-Bissau has highest median, minimum and maximum distances; Burkina Faso, Mali, Niger, Senegal, Togo have lower medians.
  - Including WAEMU and WAMZ together increases distance ranges for almost all countries.

### Larger-sample clustering (West + Central Africa) and Euro Area comparisons
- Combined WAMZ + WAEMU + CEMAC hierarchical clustering (1995-2004) suggests six clusters by CHI and visual inspection.
  - Example groupings (hierarchical/fuzzy congruent): Burkina Faso, Côte d’Ivoire, Niger, Senegal; Benin, Chad, Mali, Togo; Cameroon and Congo; Cape Verde, Central African Republic, The Gambia, Guinea; Equatorial Guinea, Gabon, Nigeria; Ghana, Guinea-Bissau, Sierra Leone.
- Observations:
  - CEMAC and WAEMU countries do not group together despite both in the CFA franc zone.
  - Several WAMZ countries group with CEMAC countries; Nigeria shows relatively higher membership coefficients with CEMAC clusters (reflecting oil reliance).
- Euro Area clustering (1995-2004, debt-servicing excluded):
  - Two groups:
    - Group I (“core”): Austria, Belgium, France, Germany, Italy, Portugal, Spain.
    - Group II (“periphery”): Finland, Greece, Ireland, Netherlands.
  - Validity statistics corroborate two clusters; interpretation aligns with “core” and “periphery” findings in the literature.

### Calinski-Harabasz Index (selected WAMZ and ECOWAS F-index values, Table C1)
- WAMZ 1995-2004:
  - Clusters 2: F-index 2.24
  - Clusters 3: F-index 5.35
  - Clusters 4: F-index 5.89
  - Clusters 5: F-index 5.88
  - Clusters 6: F-index 6.45
- WAMZ 2000-04:
  - Clusters 2: F-index 2.25
  - Clusters 3: F-index 3.11
  - Clusters 4: F-index 6.10
  - Clusters 5: F-index 6.04
  - Clusters 6: F-index 5.28
- ECOWAS 1995-2004:
  - Clusters 2: F-index 5.50
  - Clusters 3: F-index 4.78
  - Clusters 4: F-index 5.09
  - Clusters 5: F-index 4.33
- ECOWAS 2000-04:
  - Clusters 2: F-index 3.00
  - Clusters 3: F-index 3.33
  - Clusters 4: F-index 2.87
  - Clusters 5: F-index 5.40

### Forced classification (selected entries, Table C4)
- 1995-2004 forced classification (Country | Closest | Crisp Cluster | Closest Neighbor Cluster):
  - BEN                          2                          5
  - BFA                          5                          2
  - CPV                          1                          4
  - CIV                          4                          5
  - GMB                          1                          4
  - GHA                          3                          4
  - GIN                          4                          1
  - GNB                          3                          2
  - MLI                          5                          2
  - NER                          5                          4
  - NGA                          2                          5
  - SEN                          4                          5
  - SLE                          3                          4
  - TGO                          5                          2
- 2000-04 forced classification entries reported in concatenated format in source (CountryClosest Crisp ClusterClosest Neighbor Cluster): examples include BEN34, BFA43, CPV13, CIV14, etc.

### Main conclusions and policy implications
- Main conclusions:
  - Considerable dissimilarities exist across West African countries (WAEMU + WAMZ); immediate formation of an ECOWAS-wide monetary union is questionable.
  - WAMZ countries show highest internal dissimilarity; WAEMU countries tend to cluster together.
  - Ghana and Nigeria often appear as singletons, casting doubt on inclusion in a single WAMZ monetary union.
  - Combining West and Central Africa reveals heterogeneities within the CFA franc zone; WAEMU and CEMAC do not cluster together; several WAMZ countries group with CEMAC members.
- Policy implications and considerations:
  - Heterogeneity and asymmetric shocks imply substantial costs and challenges for ECOWAS-wide monetary union.
  - Institutional prerequisites to improve feasibility:
    - Strengthen fiscal institutions and develop robust fiscal-transfer systems to absorb asymmetric shocks.
    - Enhance labor mobility and reduce migration barriers.
    - Promote intraregional trade via improved infrastructure, diversification, and policies exploiting comparative advantages to increase shock synchrony.
    - Consider staged or subset monetary unification where smaller, more synchronized groups form unions prior to broader integration.
    - For WAMZ: address country-specific heterogeneities (e.g., Nigeria’s distinct terms-of-trade profile and financing needs) and ensure convergence criteria are achievable and credible.
  - Endogeneity caveat: countries may become more similar after adopting a currency union (Frankel and Rose 1998); this effect warrants further analysis and is not fully addressed here.
  - Identification of homogeneous subgroups is a first step; further analysis needed to weigh benefits and costs and to determine sequencing of monetary vs. other integration forms.

*Italic source: _wp0690 - References (PDF).*

### References..............................................................................................................

### _wp0690 - References..............................................................................................................

### Introduction
- Following the launch of the euro as the single currency of the European Economic and Monetary Union (EMU), there has been renewed international interest in the economics of monetary integration and in emulating the EMU institutional framework and convergence processes.
- The paper assesses the comparative relevance of proposed “monetary area boundaries” in West Africa and evaluates whether candidate countries are ready to form an Optimum Currency Area (OCA).
- Methodological approach:
  - Uses cluster analysis to classify West African countries according to OCA and convergence criteria for common currency adoption.
  - Employs fuzzy clustering and traditional hard clustering to account for data noise and allow countries to have partial membership across clusters.
  - Countries are assigned the largest membership coefficient corresponding to the cluster with which they share the greatest similarities.

### OCA criteria and West Africa: key analytical points
- Two principal OCA criteria emphasized:
  - Nature of shocks: symmetric shocks across members reduce costs of monetary union; asymmetric shocks increase costs because common monetary policy or depreciation can be inappropriate for some members.
  - Speed of adjustment: mechanisms such as labor mobility, fiscal transfers, wage adjustments, labor force participation changes, and capital mobility mitigate costs of asymmetric shocks.
- Characteristics of West African economies relevant to OCA assessment:
  - Many are small, open, commodity-exporting economies with limited diversification and high susceptibility to asymmetric shocks.
  - Several countries depend on a single commodity for 50 percent or more of their earnings.
  - Terms of trade movements tend to be very large and uncorrelated across many countries due to differences in commodity export composition.
  - Nigeria is a distinctive case: a large oil exporter with terms of trade shocks that are very different from other WAMZ countries (which are oil importers); Nigeria’s terms of trade variability is large and higher than that of any other country in the region.
  - Correlations of terms of trade shocks are higher among WAEMU member countries than between WAEMU and WAMZ countries, or among WAMZ countries themselves.
- Adjustment mechanisms and constraints:
  - Migration between WAEMU and traditional migratory trade routes within West Africa seems high historically, though less high in recent years because of conflict.
  - Fiscal transfers are inhibited by limited financial resources and weak transfer and tax systems.
  - Intraregional trade within ECOWAS is relatively low: WAEMU countries trade considerably more among themselves than with non-WAEMU countries; trade within non-WAEMU countries is limited.
  - Limited intraregional trade and weak infrastructure constrain potential gains from reduced transaction costs.
- Potential benefits of monetary union:
  - Fixed exchange rates and a common currency can provide a credible commitment to lower inflation and price stability.
  - A common independent central bank could act as an “agent of restraint” on fiscal policies and help address seigniorage-driven money creation when fiscal deficits persist.

### Institutional and historical context: West African arrangements
- The CFA franc (CFAF) zone comprises 14 countries grouped into two monetary unions: WAEMU and CEMAC.
- ECOWAS (founded 1975) has 15 members; 8 are members of WAEMU.
- Since April 2000, five non-WAEMU members of ECOWAS (Nigeria, The Gambia, Ghana, Guinea, and Sierra Leone) formed the West African Monetary Zone (WAMZ) with a convergence process toward a common currency.
- The originally planned launch date of the WAMZ common currency was July 2005; this was postponed to December 2009 because WAMZ member states failed to achieve the convergence criteria.
- Monetary unification across ECOWAS is envisaged but the post-unification monetary arrangement has not been announced.

### Empirical evidence and comparative findings (as presented)
- Cluster analysis results (summary statements):
  - Considerable dissimilarities exist in economic characteristics across West African countries.
  - WAMZ countries do not form a single cluster with WAEMU countries.
  - Significant lack of homogeneity within WAMZ: Nigeria and Ghana appear as independent singletons in clustering results.
  - These results question the feasibility of a separate monetary union comprising all WAMZ countries and raise doubts about prospects for wider ECOWAS monetary integration.
  - When west and central African countries are analyzed together, significant heterogeneities arise within the CFA franc zone:
    - WAEMU and CEMAC countries do not cluster together.
    - Some similarities are observed between CEMAC and WAMZ countries, which tend to group together in parts of the analysis.

### Recent literature and methodological notes
- Prior research on African monetary arrangements has focused on the CFA franc zone and comparisons with non-CFA neighbors.
- VAR-based studies (Bayoumi and Ostry (1997); Hoffmaister, Roldos and Wickham (1998); Fielding and Shields (2001)) find little correlation of disturbances to real output per capita among SSA countries; external shocks are important and more detrimental to CFA franc countries under fixed exchange rates.
- Recent studies on ECOWAS monetary union feasibility:
  - Bénassy-Quéré and Coupet (2005): used crisp clustering for SSA.
  - Celasun and Justiniano (2005): dynamic factor analysis showing that small groups within ECOWAS have relatively synchronized output fluctuations, suggesting subset unifications may be preferable.
  - Debrun, Masson and Pattillo (2005): policy-interaction model indicating proposed monetary union desirable for most non-WAEMU countries but not for most WAEMU members unless Nigeria reduces its financing needs via institutional changes.
- Endogeneity issue: Frankel and Rose (1998) highlight that countries may become more similar after adopting a common currency; this endogeneity is not widely addressed in cost–benefit analyses.
- Despite empirical concerns about dissimilarities and asymmetric shocks, political and socio-economic motivations sustain commitment to ECOWAS monetary integration.

### Policy implications (derived from analysis)
- The heterogeneity and asymmetric shocks across West African countries imply substantial costs and challenges for forming a comprehensive ECOWAS-wide monetary union.
- Institutional prerequisites to improve feasibility:
  - Strengthen fiscal institutions and develop robust systems for fiscal transfers to help absorb asymmetric shocks.
  - Enhance labor mobility and reduce barriers to migration to aid labor-market-based adjustment.
  - Promote intraregional trade through improved infrastructure, diversification, and policies that exploit comparative advantages to increase synchrony of shocks.
  - Consider staged or subset monetary unification where smaller groups with higher synchronization form unions before broader integration.
  - For WAMZ prospects specifically, address country-specific heterogeneities (e.g., Nigeria’s distinct terms-of-trade profile and financing needs) and ensure convergence criteria are achievable and credible.

*Italic source: _wp0690 - References (PDF)._

### 2000. In doing so, we investigate the homogeneity of the candidate countries in terms of a

### _wp0690 - 2000. In doing so, we investigate the homogeneity of the candidate countries in terms of a

### Methodological overview
- Purpose: assess homogeneity of candidate countries using clustering analysis to account simultaneously for multiple variables inspired by OCA criteria and convergence criteria.
- Advantages of clustering stated:
  - accounts for symmetry of business cycles and symmetry of other relevant variables;
  - less stringent time-dimension data requirements than other methodologies (useful for countries with limited consistent time-series data, e.g., African economies);
  - identifies group patterns and areas where each country needs improvement to achieve macroeconomic convergence.
- Two broad classes of clustering methodologies discussed:
  - crisp (hard) clustering — mutually exclusive clusters;
  - fuzzy (soft) clustering — overlapping clusters with membership degrees.

### Crisp clustering (hierarchical agglomerative approach)
- Crisp clustering properties (set notation as in source):
  - partition X with N objects and p variables into c clusters defined by subsets A_i (i = 1..c) such that:
    - ⋃_{i=1}^c A_i = X,  (1)
    - A_i ∩ A_j = ∅ for i ≠ j,  (2)
    - A_i ⊂ X and A_i ≠ Φ for i = 1..c.  (3)
- Membership-coefficient conditions (μ_ik):
  - μ_ik ∈ {0,1} and c,k,N,i ranges as in source; (4)
  - ∑_{k=1}^c μ_ik = 1 for i = 1..N; (5)
  - 0 < ∑_{i=1}^N μ_ik < N for k = 1..c. (6)
- Hierarchical clustering procedure used:
  - agglomerative method (successive fusions from N singletons to one cluster);
  - proximity measure: Euclidean distance (definition referenced in footnote: for row vectors x1 and x2, d_12 = (x1 − x2)′(x1 − x2), producing n(n–1)/2 distance values for n objects).13
  - linkage (cluster-proximity) methods applied and compared:
    - Group Average linkage: dist_12 = (1/(n1 n2)) ∑_{i=1}^{n1} ∑_{j=1}^{n2} d(x_{1i}, x_{2j}). (7)
    - Single linkage: dist = {min d(x_{1i}, x_{2j}) for i=1..n1, j=1..n2}. (8)
    - Ward linkage: dist = ((n1+n2) d(x̄_1, x̄_2)^2) / (n1 n2) where x̄_c = (1/n_c) ∑_{i=1}^{n_c} x_{ci}. (9)
  - output represented as a dendrogram; link heights represent fusion distances (greater dissimilarity → taller link).
- Validation and selection of linkage and cluster number:
  - cophenetic correlation coefficient: measures linear correlation between dendrogram-derived distances and original dissimilarities; values close to 1 indicate better clustering (dendrogram preserves original structure).
  - determination of optimal number of clusters:
    - visual inspection of dendrogram (large changes in fusion levels indicate best cut) as suggested by Everitt, Landau and Leese (2001).14
    - formal rule used: Calinski-Harabasz Index (CHI) defined as CHI = (S_b / S_w) * ((n − k) / (k − 1)), where S_b = between-clusters sum of squares, S_w = within-clusters sum of squares, k = number of clusters, n = number of observations. (10)
    - higher CHI values indicate distinct partitioning and better clustering.
  - literature note: Milligan and Cooper (1985) find pseudo-F index (Calinski and Harabasz, 1974) as best performer among evaluated stopping rules.

### Fuzzy clustering (fuzzy c-means and validation)
- Conceptual difference from crisp clustering:
  - fuzzy set theory (Zadeh, 1965): elements may belong to multiple sets with membership degrees in [0,1];
  - fuzzy clustering assigns membership coefficients μ_ik ∈ [0,1] indicating partial membership.
- Fuzzy c-means (FCM) objective:
  - c-means functional to be minimized (Dunn 1974; Bezdek 1981):
    - J = ∑_{i=1}^N ∑_{k=1}^c μ_{ik}^m d^2(x_i, v_k), where d is Euclidean distance between object x_i and cluster center v_k, and m (fuzziness exponent) is as in source formulation. (11)
  - cluster center v_k computed per variable j as:
    - v_kj = (∑_{i=1}^N μ_{ik}^m x_{ij}) / (∑_{i=1}^N μ_{ik}^m). (12)
- Constraints on membership coefficients in FCM:
  - 0 ≤ μ_{ik} ≤ 1,  (13)
  - ∑_{k=1}^c μ_{ik} = 1 for i = 1..N,  (14)
  - 0 < ∑_{i=1}^N μ_{ik} < N for k = 1..c.  (15)
- Validation of fuzzy clusters:
  - multiple indices recommended because no single index is reliable;
  - measures used in this paper:
    - Dunn’s Partition Coefficient (DPC);
    - Xie and Beni’s Index (XBI);
    - silhouette plot.
  - literature guidance: Balasko, Abonyi and Feil (2004) advise choosing optimal number of clusters after comparing several indices.

### Key methodological implications for empirical application
- Use of multiple linkage methods (Group Average, Single, Ward) and comparison via cophenetic correlation ensures selection of linkage that best preserves original dissimilarities.
- CHI used as primary formal rule to identify optimal number of clusters in hierarchical analysis, complemented by dendrogram inspection.
- For fuzzy clustering, use multiple validity indices (DPC, XBI, silhouette) to determine optimal cluster number and assess partition quality.
- Fuzzy clustering preferred when overlapping cluster membership is realistic; crisp clustering suitable when mutually exclusive partitioning is desired.

*Source: IMF working paper excerpt _wp0690 - 2000. In doing so, we investigate the homogeneity of the candidate countries in terms of a*

### Appendix I.

### Appendix I

### A. Choice of variables and normalization
- Purpose: examine feasibility of a proposed West African currency union by assessing whether economic structures of candidate countries are similar enough to support a fixed exchange rate arrangement.
- Variables chosen based on OCA literature and convergence criteria: synchronization of output and terms of trade shocks, exchange rate variability, inflation, regional trade intensity, government balance, and debt-servicing requirement.
- Normalization: each variable is normalized by taking the deviation from its mean and dividing by its respective standard deviation; clustering performed on normalized variables.
- Euclidean distance used as dissimilarity metric:
  - "The Euclidean distance d is defined as ..." (formula given in source).

### B. Variable construction and interpretation

- Output volatility (business cycle synchronization)
  - Anchor for correlations: euro area (following Bénassy-Quéré and Coupet 2005).
  - Method: Hodrick-Prescott filter to detrend annual real GDP series for ECOWAS countries and aggregate real GDP series of the euro area; cross-correlations of cyclical components estimated vis-à-vis the euro area. Correlations also estimated using annual GDP growth rates (did not alter results).
  - Interpretation: similar correlation values (positive or negative) imply relatively parallel business cycles; differing magnitude or sign indicates higher costs of joining a monetary union.
  - Empirical note: During 1995-2004, average correlation of output fluctuations was higher for the WAEMU region compared with the WAMZ region and the entire ECOWAS region.

- Terms of trade synchronization
  - Anchor: euro area.
  - Method: first difference of annual terms of trade index for every country; correlation with annual change in aggregate euro area terms of trade index.
  - Interpretation: similar correlation coefficients (positive or negative) imply parallel terms of trade shocks; dissimilar coefficients imply asymmetric shocks and higher costs of monetary unification.
  - Empirical note: WAEMU countries appear to have more synchronized terms of trade changes than WAMZ countries.

- Real exchange rate variability
  - Measured as the standard deviation of the log difference of annual real exchange rates of individual countries.
  - Included only when examining grouping of WAMZ countries (WAEMU countries already have a pegged exchange rate system).
  - Rationale: countries with small exchange rate variation will face lower adjustment costs from abandoning monetary independence.

- Regional trade intensity
  - Measured as (exports to region + imports from region) / (total exports + total imports) averaged annually over sample period.
  - Computed for trade intensity with WAMZ and ECOWAS groups.
  - Interpretation: higher values indicate greater intraregional trade and larger gains from joining a currency union.
  - Empirical note: average regional trade intensity is low among WAMZ countries and between WAMZ and WAEMU countries; considerably higher among WAEMU countries.

- Inflation
  - Constructed as log difference of annual consumer price index, averaged across years.
  - WAMZ primary convergence criterion: maintain inflation at single-digit level.
  - WAEMU primary convergence criterion: inflation below 3 percent.
  - Empirical notes:
    - Among WAMZ: The Gambia and Guinea average in single digits; Ghana, Nigeria, and Sierra Leone recorded double-digit average inflation rates.
    - In WAEMU (notable exception Guinea-Bissau): Guinea-Bissau inflation 14.5 percent; other WAEMU countries average between 2.0 and 4.0 percent.

- Government balance
  - Convergence criterion for WAMZ: budget deficit to GDP ratio (excluding grants) of less than 4 percent.
  - Constructed as annual central government balance (excluding grants) as a percentage of annual GDP, averaged for each country.
  - Empirical note: WAMZ countries have generally run fiscal deficits and have had difficulty meeting the benchmark.

- Debt-servicing requirement
  - Represented as the average ratio of debt-servicing requirements to total exports of goods and services.
  - Rationale: high debt-service ratios increase willingness to peg (debt servicing denominated in hard currencies) but impose constraints.
  - Empirical note: for WAMZ countries the ratio has been steadily declining but the average in recent years still exceeds the threshold of debt sustainability of 10 percent.

### C. Data sources and sample construction
- Data sources:
  - Real and nominal GDP series, terms of trade index, consumer price index, government balance: IMF’s World Economic Outlook, April 2005.
  - Bilateral trade data for regional trade intensity: IMF’s Direction of Trade Statistics.
  - Debt-servicing ratio: World Bank’s World Development Indicators 2004 and African Development Indicators 2004.
  - Effective real exchange rate (monthly): Information Notice Systems (INS) database; monthly values averaged to annual.
- Clustering samples:
  - First sample: non-WAEMU countries except Liberia (incomplete data) — referred to as the WAMZ group (five out of six non-WAEMU countries belong to WAMZ).
  - Second sample: ECOWAS member countries (WAMZ + WAEMU) to assess broader similarities/dissimilarities.
  - Note: Cape Verde had not formalized WAMZ membership (not a signatory of the “Accra declaration”) at time of source.

### D. Empirical approach: periods and clustering methods
- Periods analyzed: 1990-2004, 1995-2004, and 2000-04.
  - Results for 1990-2004 and 1995-2004 are similar; focus presented on 1995-2004 and 2000-04.
  - 2000-04 considered particularly policy-relevant as it reflects progress after WAMZ inception.
- Clustering methods:
  - Hierarchical clustering (Group Average, Ward, Single linkage); cophenetic coefficient reported with dendrograms to assess goodness of fit.
  - Fuzzy clustering with validity statistics: Dunn’s partition coefficient (DPC), silhouette width (SW), and Xie and Beni’s index (XBI).
- Practical consideration: grouping based on a single latest data point is not recommended.

### E. Hierarchical clustering: key findings and statistics
- Cophenetic coefficients reported for dendrograms (ECOWAS/WAMZ analyses):
  - Values cited in figures: 0.86, 0.85, 0.89, 0.90.
- WAMZ countries (Group Average linkage; Calinski-Harabasz Index (CHI) guidance)
  - For WAMZ, CHI highest when number of clusters = 4.
  - Cluster membership (1995-2004 as reported):
    - Group 1: The Gambia, Guinea, Cape Verde.
    - Singletons: Ghana, Nigeria, Sierra Leone.
  - Interpretation: The Gambia, Guinea, and Cape Verde linked at relatively smaller distances; Ghana, Nigeria, Sierra Leone join at much higher distances (greater dissimilarity).
- ECOWAS clustering (WAMZ + WAEMU)
  - For 1995-2004, CHI suggests 6 clusters. Cluster composition:
    - Cluster 1: Benin, Burkina Faso, Mali, Niger, Togo (five WAEMU countries).
    - Cluster 2: Côte d’Ivoire, Senegal (WAEMU) and The Gambia, Guinea (WAMZ).
    - Cluster 3: Ghana and Sierra Leone.
    - Remaining three clusters: Cape Verde, Nigeria, Guinea-Bissau as singletons.
  - For 2000-04, CHI suggests 5 clusters with some changes:
    - Cluster 1: Benin, Burkina Faso, Mali, Niger, Togo, and Senegal.
    - Cluster 2: Cape Verde, Côte d’Ivoire, The Gambia, Guinea.
    - Cluster 3: Guinea-Bissau and Sierra Leone.
    - Ghana and Nigeria remain singletons.
- Overall hierarchical-summary conclusion:
  - All WAEMU countries except Guinea-Bissau tend to group together and link at relatively smaller distances.
  - WAMZ countries link with each other and with WAEMU at higher link lengths.
  - Ghana, Guinea-Bissau, Nigeria, and Sierra Leone appear most different in the macroeconomic attributes considered.

### F. Fuzzy clustering: key results
- Validity statistics indicate:
  - Presence of three clusters for 1995-2004 and four clusters for 2000-04 in the WAMZ fuzzy clustering results.
- Membership patterns (WAMZ):
  - Cape Verde, The Gambia, and Guinea have the highest membership coefficients for the same cluster during both time periods.
  - Nigeria forms its own cluster.
  - Ghana and Sierra Leone have highest membership coefficients for the same cluster for the longer series (1995-2004) but not during 2000-04.
- Partition fuzziness:
  - Less fuzziness observed in partitioning during 2000-04 compared with 1995-2004 (fuzzy clustering indicates increased distinctness of clusters in the more recent period).

*Source: Appendix I, _wp0690 - Appendix I.*

### 2004. Countries that form a group in both years–that is, Cape Verde, The Gambia, and

### _wp0690 - 2004. Countries that form a group in both years–that is, Cape Verde, The Gambia, and

### Fuzzy and crisp clustering results: WAMZ and WAEMU membership and characteristics
- Fuzzy clustering and crisp (hierarchical) clustering produce broadly consistent groupings, but considerable dissimilarities remain across WAMZ countries.
- Fuzzy clustering validity statistics indicate substantial fuzziness:
  - DPC and silhouette width are very small (less than 0.500) for ECOWAS estimates overall.
  - For ECOWAS, the validity statistics indicate the presence of five clusters for both time periods considered (1995-2004 and 2000-04).
- WAMZ country groupings and key characteristics:
  - Cape Verde, The Gambia, and Guinea form a group in 2000-04 with:
    - positive but not very high correlation of business cycles and terms of trade changes with each other;
    - relatively lower real exchange rate volatility;
    - low trade intensity within the WAMZ region;
    - low average inflation;
    - low debt-service requirements.
  - Ghana and Sierra Leone:
    - Have the highest membership coefficient for the same cluster in 1995-2004.
    - Have positive and relatively high correlation coefficients for output variation and terms of trade changes.
    - Low average silhouette width of their cluster suggests dissimilarities in other characteristics.
    - Sierra Leone’s most outstanding characteristic is its large debt-servicing requirements.
    - Ghana has the highest within-region trade intensity, relatively moderate exchange rate volatility (1995-2004), high average inflation during 1995-2004, and greater real exchange rate fluctuations during 2000-04.
  - Nigeria:
    - Identified as an outlier (idiosyncratic characteristics).
    - Weak correlation of business cycles and negative correlation of terms of trade changes with other countries.
    - Moderate average inflation, a low budget deficit to GDP ratio, and low regional trade intensity.
    - Notable reduction in real exchange rate volatility in the recent period.
- Specific membership coefficients (selected WAMZ entries from Table 1):
  - Cape Verde: 0.883 (1995-2004) and 0.844 (2000-04) for its primary cluster.
  - Gambia, The: 0.909 (1995-2004) and 0.719 (2000-04) for its primary cluster.
  - Guinea: 0.824 (1995-2004) and 0.827 (2000-04) for its primary cluster.
  - Ghana: membership shows strong assignment in 2000-04 (1.000 in one column).
  - Nigeria: membership indicates near singleton behavior in 1995-2004 and 2000-04 (values showing 0.999 / 1.000 in singleton columns).
- WAEMU clustering (1995-2004):
  - Best performing cluster comprises Burkina Faso, Mali, Niger, and Togo.
    - These four have silhouette width greater than 0.500 and an average silhouette width of 0.614.
    - Characteristics: well-correlated business cycle movements, relatively greater regional trade intensity, low inflation rates, and low budget deficits.
  - Another WAEMU cluster with average silhouette width > 0.500 comprises Ghana, Guinea-Bissau, and Sierra Leone (higher government deficit to GDP ratios, relatively higher inflation and debt servicing requirements).
- ECOWAS fuzzy clustering observations:
  - Côte d’Ivoire, Guinea, and Senegal have high membership coefficients for the same cluster but Guinea’s membership coefficient is less than 0.500 when forced into that cluster and has a negative silhouette width if forced in, indicating stronger similarity with Cape Verde and The Gambia.

### Cluster validity and summary statistics (selected numerical results)
- ECOWAS fuzzy clustering validity (selected values from Table 2 and related text):
  - Avg. SW (average silhouette widths for clusters when forced by membership coefficients) for ECOWAS 1995-2004: reported cluster Avg. SW values include 0.274, -0.025, 0.502, 0.288, 0.614 (table layout denotes cluster-level Avg. SW).
  - Normalized DPC and DPC for ECOWAS (examples reported): normalized DPC 0.358 (1995-2004), DPC 0.486 (1995-2004); 2000-04 normalized DPC 0.466, DPC 0.573.
  - XBI reported as 0.924 (1995-2004) and 1.112 (2000-04) for ECOWAS estimates (Table 2).
- West and Central Africa fuzzy clustering (Table 4, 1995-2004):
  - Optimal number of clusters suggested visually and by CHI: six clusters.
  - Table 4 Avg. SW values for clusters: 0.289, -0.145, 0.410, 0.350, 0.424, 0.519; overall Avg. SW = 0.340.
  - DPC (normalized) reported as 0.280; DPC = 0.400; XBI = 0.871.
- Euro Area fuzzy clustering validity (Table 5, 1995-2004):
  - Two clusters identified (core and periphery).
  - Avg. SW cluster-level reported as 0.540 and 0.224 with overall Avg. SW = 0.423.
  - DPC = 0.599; XBI = 0.817.

### Principal Components Analysis (PCA) robustness check
- PCA used as a robustness check for clustering results.
- Criteria applied for selecting principal components:
  - (i) collectively explain at least 60 percent of the variation;
  - (ii) each associated eigenvalue > 1;
  - (iii) each principal component explains at least 20 percent of the variation.
- Findings:
  - The first two principal components satisfy the above properties for the sample of WAMZ and ECOWAS countries.
  - Two-dimensional scatter plots (PC1 on x-axis, PC2 on y-axis) with fuzzy clustering contour maps:
    - WAMZ PCA plot supports earlier fuzzy/hierarchical clustering results.
    - ECOWAS PCA plot shows cluster composition almost identical to prior results.
    - Nigeria remains a singleton (does not form part of any group) in PCA-based visualization.
    - Most WAEMU countries fall together; Côte d’Ivoire and Guinea-Bissau appear different from the rest of WAEMU and cluster with WAMZ countries in 2000-04.

### Dissimilarity analysis: West Africa, Central Africa, and Euro Area comparisons
- Average pair-wise distances (Euclidean) and standard deviations (Table 3):
  - WAMZ:
    - Mean = 3.57 (1990-2004), Mean = 3.59 (1995-2004), Mean = 3.59 (2000-04)
    - Std. deviation = 1.15 (1990-2004), 1.21 (1995-2004), 1.09 (2000-04)
  - WAEMU:
    - Mean = 3.14 (1990-2004), Mean = 3.23 (1995-2004), Mean = 3.28 (2000-04)
    - Std. deviation = 1.50 (1990-2004), 1.09 (1995-2004), 1.14 (2000-04)
  - ECOWAS:
    - Mean = 3.26 (1990-2004), Mean = 3.31 (1995-2004), Mean = 3.33 (2000-04)
    - Std. deviation = 1.17 (1990-2004), 1.03 (1995-2004), 0.96 (2000-04)
  - CEMAC:
    - Mean = 3.43 (1990-2004), Mean = 3.43 (1995-2004), Mean = 3.40 (2000-04)
    - Std. deviation = 0.46 (1990-2004), 0.52 (1995-2004), 0.70 (2000-04)
  - Euro area:
    - Mean = 2.54 (1990-2004), Mean = 2.58 (1995-2004), Mean = 2.63 (2000-04)
    - Std. deviation = 1.24 (1990-2004), 1.09 (1995-2004), 1.03 (2000-04)
- Interpretations:
  - WAMZ countries have the highest pair-wise average distance among themselves.
  - WAEMU countries have the highest variation in distances.
  - Euro area countries have the lowest average distance.
  - CEMAC region has the lowest dispersion around the mean.
- Box plot observations (Figures 8–10 summarized):
  - Median dissimilarities differ considerably across WAMZ countries.
  - Ghana, Nigeria, and Sierra Leone have less dispersion in their distance values but are farther from other countries.
  - Among WAEMU, Guinea-Bissau has the highest median distance and highest minimum and maximum distances; Burkina Faso, Mali, Niger, Senegal and Togo have lower median distances.
  - Inclusion of WAEMU and WAMZ in the same sample increases distance ranges for almost all countries.

### Larger-sample clustering (West + Central Africa) and Euro Area clustering
- Combined WAMZ + WAEMU + CEMAC hierarchical clustering (1995-2004) suggests six clusters (visual inspection and CHI):
  - Example cluster compositions (hierarchical/fuzzy congruent):
    - Cluster examples: Burkina Faso, Côte d’Ivoire, Niger, Senegal; Benin, Chad, Mali, Togo; Cameroon and Congo; Cape Verde, Central African Republic, The Gambia, Guinea; Equatorial Guinea, Gabon, Nigeria; Ghana, Guinea-Bissau, Sierra Leone.
  - Observations:
    - CEMAC and WAEMU countries do not group together despite both being CFA franc zone members.
    - Many WAMZ countries group with CEMAC countries; Nigeria shows relatively higher membership coefficients for clusters consisting of CEMAC countries (reflecting oil reliance).
- Euro Area clustering (1995-2004), excluding debt-servicing:
  - Two groups present:
    - Group I (“core”): Austria, Belgium, France, Germany, Italy, Portugal, Spain.
    - Group II (“periphery”): Finland, Greece, Ireland, Netherlands.
  - Validity statistics corroborate two clusters (Table 5).
  - Interpretation consistent with literature: presence of a “core” and “periphery” in EMU.

### Conclusions and policy implications
- Main conclusions:
  - Considerable dissimilarities exist in economic characteristics across West African countries (WAEMU + WAMZ), making immediate formation of ECOWAS monetary union questionable.
  - WAMZ countries show the highest internal dissimilarity; WAEMU countries tend to cluster together.
  - Ghana and Nigeria often appear as singletons independent of other clusters, casting doubt on their inclusion in a common WAMZ monetary union.
  - When West and central Africa are combined, heterogeneities exist within the CFA franc zone; WAEMU and CEMAC do not cluster together and several WAMZ countries group with CEMAC countries.
- Policy implications and considerations:
  - Identification of homogeneous subgroups is only a first step; heterogeneity does not automatically preclude benefits from monetary integration.
  - Endogeneity of criteria suggests that candidate countries might become more similar after joining a currency union (citing Frankel and Rose 1998; Boreiko 2003).
  - Results raise questions over the geographic composition of proposed unions and highlight the need for further analysis to assess merits and de-merits of proposed unions and alternatives.
  - The analysis informs debate on whether monetary union creation should precede or follow other forms of integration.

*Source: Authors’ calculations and analysis in the provided content unit.*

### APPENDIX II

### APPENDIX II

### Hierarchical clustering results (ECOWAS)
- Figures report hierarchical clustering results using Ward and Single Linkage algorithms for periods:
  - 1995-2004
  - 2000-2004
- Reported cophenetic correlation coefficients (as shown in figures):
  - Cophenetic correlation coefficient=0.81
  - Cophenetic correlationcoefficient=0.80
  - Cophenetic correlation coefficient=0.69
  - Cophenetic correlationcoefficient=0.79
- Distance axes shown with tick marks at: 0.5, 1.0, 1.5, 2.0, 2.5, 3.0, 3.5, 4.0, 4.5, 5.0 (varies by panel)

### Calinski-Harabasz Index for the Number of Clusters (Table C1)
- WAMZ and ECOWAS indices for periods 1995-2004 and 2000-04 are reported in tabular form. Entries shown exactly as in source:
  - WAMZ 1995-2004:
    - Clusters 2: F-index 2.24
    - Clusters 3: F-index 5.35
    - Clusters 4: F-index 5.89
    - Clusters 5: F-index 5.88
    - Clusters 6: F-index 6.45
  - WAMZ 2000-04:
    - Clusters 2: F-index 2.25
    - Clusters 3: F-index 3.11
    - Clusters 4: F-index 6.10
    - Clusters 5: F-index 6.04
    - Clusters 6: F-index 5.28
  - ECOWAS 1995-2004:
    - Clusters 2: F-index 5.50
    - Clusters 3: F-index 4.78
    - Clusters 4: F-index 5.09
    - Clusters 5: F-index 4.33
  - ECOWAS 2000-04:
    - Clusters 2: F-index 3.00
    - Clusters 3: F-index 3.33
    - Clusters 4: F-index 2.87
    - Clusters 5: F-index 5.40

### Principal Component Analysis Results: WAMZ (Table C2)
- Note: The results are for normalized data.
- 1995-2004 principal component loadings and variances (entries presented exactly as in source):
  - Row 1: -0.51 0.03 -0.20 -0.05 0.21 -0.21 -0.78 3.66 -0.46 -0.06 0.49 0.22 -0.34 0.61 -0.08 3.19
  - Row 2: -0.18 -0.60 0.05 -0.06 0.70 -0.13 0.31 2.21 -0.08 -0.62 0.25 0.26 -0.20 -0.47 0.47 2.32
  - Row 3: 0.50 -0.15 -0.24 -0.05 -0.10 -0.81 -0.08 0.70 0.07 0.65 0.01 0.13 -0.28 0.02 0.71 1.21
  - Row 4: 0.22 0.55 0.14 -0.66 0.45 -0.02 0.01 0.27 0.48 0.22 0.31 0.26 -0.52 -0.30 -0.45 0.18
  - Row 5: 0.28 -0.39 0.72 -0.19 -0.13 0.10 -0.43 0.16 0.30 -0.29 -0.63 0.42 -0.29 0.40 0.06 0.09
  - Row 6: 0.45 0.20 0.02 0.65 0.49 0.16 -0.25 0 0.47 -0.25 0.20 -0.69 -0.25 0.30 0.21 0.00
  - Row 7: 0.36 -0.34 -0.60 -0.32 -0.00 0.50 -0.21 0 0.48 -0.05 0.40 0.39 0.61 0.26 0.11 0.00
- 2000-04 principal component loadings and variances (entries presented exactly as in source):
  - Row 1: -0.20 -0.05 0.21 -0.21 -0.78 3.66 -0.46 -0.06 0.49 0.22 -0.34 0.61 -0.08 3.19
  - Row 2: 0.31 2.21 -0.08 -0.62 0.25 0.26 -0.20 -0.47 0.47 2.32
  - Row 3: -0.08 0.70 0.07 0.65 0.01 0.13 -0.28 0.02 0.71 1.21
  - Row 4: 0.48 0.22 0.31 0.26 -0.52 -0.30 -0.45 0.18
  - Row 5: 0.30 -0.29 -0.63 0.42 -0.29 0.40 0.06 0.09
  - Row 6: 0.47 -0.25 0.20 -0.69 -0.25 0.30 0.21 0.00
  - Row 7: 0.48 -0.05 0.40 0.39 0.61 0.26 0.11 0.00

### Principal Component Analysis Results: ECOWAS (Table C3)
- Note: The results are for normalized data.
- 1995-2004 principal components and variances (entries presented exactly as in source):
  - Row 1: -0.03 0.74 -0.11 0.03 -0.21 0.63 2.18 0.40 -0.51 0.38 -0.17 0.58 -0.26 1.99
  - Row 2: 0.15 0.43 0.66 0.36 0.41 -0.26 1.65 0.28 -0.51 -0.01 0.72 -0.35 0.15 1.28
  - Row 3: 0.54 -0.31 -0.17 0.30 0.47 0.52 1.20 -0.53 0.03 0.40 0.35 0.45 0.49 1.07
  - Row 4: -0.53 -0.21 -0.02 0.80 -0.17 0.12 0.49 0.25 0.62 0.29 0.49 0.11 -0.46 0.87
  - Row 5: 0.52 -0.17 0.38 0.15 -0.73 0.04 0.32 0.46 0.22 -0.56 0.11 0.47 0.43 0.42
  - Row 6: -0.35 -0.31 0.62 -0.36 0.09 0.51 0.16 -0.46 -0.22 -0.54 0.27 0.32 -0.52 0.36
- 2000-04 principal components and variances (entries presented exactly as in source):
  - Row 1: 0.40 -0.51 0.38 -0.17 0.58 -0.26 1.99
  - Row 2: 0.28 -0.51 -0.01 0.72 -0.35 0.15 1.28
  - Row 3: -0.53 0.03 0.40 0.35 0.45 0.49 1.07
  - Row 4: 0.25 0.62 0.29 0.49 0.11 -0.46 0.87
  - Row 5: 0.46 0.22 -0.56 0.11 0.47 0.43 0.42
  - Row 6: -0.46 -0.22 -0.54 0.27 0.32 -0.52 0.36

### Forced Classification of ECOWAS Countries Based on Fuzzy Clustering (Table C4)
- 1995-2004 (columns displayed as in source: Country | Closest | Crisp Cluster | Closest Neighbor Cluster)
  - BEN                          2                          5
  - BFA                          5                          2
  - CPV                          1                          4
  - CIV                           4                           5
  - GMB                         1                         4
  - GHA                         3                         4
  - GIN                           4                           1
  - GNB                          3                          2
  - MLI                           5                           2
  - NER                          5                          4
  - NGA                         2                         5
  - SEN                          4                          5
  - SLE                           3                           4
  - TGO                          5                          2
- 2000-04 (columns shown in source concatenated as CountryClosest Crisp ClusterClosest Neighbor Cluster)
  - BEN34
  - BFA43
  - CPV13
  - CIV14
  - GMB14
  - GHA15
  - GIN14
  - GNB51
  - MLI34
  - NER43
  - NGA23
  - SEN43
  - SLE51
  - TGO43

*Source: APPENDIX II*

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