Digital Currency Fragmentation and Systemic Risk in the West African Monetary Zone: A Topological Data Analysis of Cross-Border Payment Network Spillovers

1. Overview of Supplementary Materials This document provides a comprehensive description of the supplementary materials accompanying the manuscript entitled 'Digital Currency Fragmentation and Systemic Risk in the West African Monetary Zone: A Topological Data Analysis of Cross-Border Payment Network Spillovers.' The supplementary materials are organized into four categories: (i) primary data files, (ii) replication codes, (iii) generated figures, and (iv) computational environment specifications. All materials are designed to ensure full transparency, reproducibility, and independent verification of the empirical findings reported in the manuscript. 2. Data Files The primary data file is provided in Microsoft Excel format (.xlsx) and contains four separate worksheets. Each worksheet corresponds to a distinct component of the empirical analysis. The file is named 'WAMZ_CBDC_TDA_Data.xlsx' and is available for download from the repository. 2.1 Sheet 1: WAMZ_Payment_Flows This worksheet contains 600 rows of quarterly bilateral cross-border payment flow data for the West African Monetary Zone (WAMZ) covering the period 2015Q1 to 2024Q4 (40 quarters). The data integrate three primary sources: (i) SWIFT regional reports, (ii) West African Clearing House (WACH) settlement data, and (iii) mobile money corridor data from GSMA and individual mobile network operators (MTN, Airtel, Orange). Variables: ·         Quarter: String (e.g., '2015Q1'). Quarterly time identifier. ·         Year: Integer. Calendar year (2015-2024). ·         Quarter_Num: Integer (1-4). Quarter within the calendar year. ·         Time_Index: Integer (0-39). Sequential quarter index for computational processing. ·         Origin: String (3-letter code). Origin country: GHA, GMB, GUI, LBR, NGA, SLE. ·         Destination: String (3-letter code). Destination country. ·         Flow_USD_Millions: Float. Bilateral payment flow in USD millions, integrated from SWIFT, WACH, and mobile money sources. ·         COVID_Period: Binary (0/1). Indicator for COVID-19 pandemic quarters (2020Q1-2021Q2). ·         Ghana_CBDC_Pilot: Binary (0/1). Indicator for post-e-Cedi design paper quarters (>= 2021Q3). ·         Nigeria_CBDC_Launch: Binary (0/1). Indicator for post-e-Naira launch quarters (>= 2021Q4). Coverage and Limitations: The dataset covers 15 unique country-pairs (6 countries, directed flows). Liberia and Sierra Leone have fewer observations (37 quarters each) due to WACH data gaps during 2015Q1-2017Q2 and 2020Q3-2021Q1. Missing values are imputed using the proportional allocation algorithm described in Section 4.1.4 of the manuscript. 2.2 Sheet 2: WAMZ_Macro_Indicators This worksheet contains 240 rows of macro-financial indicators for the six WAMZ member countries across 40 quarters (2015Q1-2024Q4). All data are sourced from publicly available IMF and World Bank databases. Variables: ·         Quarter, Year, Quarter_Num, Time_Index: Time identifiers (as above). ·         Country: String (3-letter code). GHA, GMB, GUI, LBR, NGA, SLE. ·         Country_Name: String. Full country name. ·         Reserves_USD_Millions: Float. Gross external reserves in USD millions (IMF IFS, line 1A.D). ·         GDP_USD_Millions: Float. Nominal GDP in USD millions (World Bank WDI, NY.GDP.MKTP.CD). ·         Inflation_Percent: Float. Year-on-year CPI inflation in percent (IMF IFS, line 64). ·         Fiscal_Deficit_GDP_Percent: Float. Central government net lending/borrowing as percent of GDP (IMF WEO). ·         Exchange_Rate_Volatility: Float. Standard deviation of monthly percentage changes in nominal effective exchange rate. Data Sources: IMF International Financial Statistics (IFS), World Bank World Development Indicators (WDI), and IMF World Economic Outlook (WEO) Database. All macro data are publicly available with no access restrictions. 2.3 Sheet 3: CBDC_Engagement_Timeline This worksheet documents the CBDC engagement status of each WAMZ member country as of 2024Q4, following the four-level taxonomy defined in Definition 1.1 of the manuscript. Variables: ·         Country: String (3-letter code). ·         CBDC_Name: String. Name of CBDC or 'None'. ·         Engagement_Level: Integer (0-3). 0=No engagement, 1=Design paper, 2=Pilot/sandbox, 3=Operational retail. ·         Engagement_Level_Description: String. Verbal description of engagement level. ·         Design_Paper_Date: String. Date of design paper publication or 'NA'. ·         Pilot_Launch_Date: String. Date of pilot launch or 'NA'. ·         Retail_Launch_Date: String. Date of retail launch or 'NA'. ·         DLT_Platform: String. Distributed ledger technology platform or 'NA'. ·         Offline_Capability: String. Offline transaction capability status or 'NA'. Key Facts: Nigeria (e-Naira) is the only WAMZ member at Engagement Level 3 (operational retail, launched October 2021, Hyperledger Fabric). Ghana (e-Cedi) is at Level 2 (pilot/sandbox, design paper August 2021, ongoing sandbox testing). The remaining four members (The Gambia, Guinea, Liberia, Sierra Leone) are at Level 0 (no public CBDC engagement). 2.4 Sheet 4: CEMAC_Comparator This worksheet contains 240 rows of macro-financial data for the Central African Economic and Monetary Community (CEMAC), serving as a synthetic control group for the difference-in-differences identification strategy. CEMAC comprises Cameroon, Central African Republic, Chad, Congo, Equatorial Guinea, and Gabon. Variables: Quarter, Year, Time_Index, Country, Reserves_USD_Millions, GDP_USD_Millions, Inflation_Percent, CBDC_Engagement (binary, all zeros as of 2024Q4). Rationale: CEMAC shares structural similarities with WAMZ (commodity dependence, monetary union aspiration, French treasury backing via CFA franc) but has no CBDC engagement as of 2024Q4. This makes it a suitable comparator for isolating the topological effects of CBDC engagement asymmetry from broader regional African economic trends. 3. Replication Codes The replication code is provided as a single Python script named 'WAMZ_CBDC_TDA_Replication.py'. The script is fully documented with inline comments and is designed to reproduce all empirical results, tables, and figures reported in the manuscript from the raw data files. 3.1 Computational Environment The following environment was used for all computations: ·         Operating System: Ubuntu 22.04 LTS (64-bit) ·         Python Version: 3.10.12 ·         CPU: Intel Core i7-12700H (14 cores, 20 threads) ·         RAM: 32 GB DDR5 ·         Primary Storage: 512 GB NVMe SSD 3.2 Required Python Packages The following Python packages are required for replication. All packages are available via the Python Package Index (PyPI) and can be installed using pip: ·         gudhi >= 3.8.0: Persistent homology computation (Vietoris-Rips complexes, Betti numbers, persistence diagrams). ·         numpy >= 1.24.0: Numerical array operations and linear algebra. ·         pandas >= 2.0.0: Data frame manipulation and Excel I/O. ·         scipy >= 1.11.0: Scientific computing (optimization, statistics). ·         scikit-learn >= 1.3.0: Machine learning tools (PCA, clustering, resampling). ·         matplotlib >= 3.7.0: Figure generation and visualization. ·         kmapper >= 2.0.1: Mapper algorithm implementation (KeplerMapper). Installation command: pip install gudhi numpy pandas scipy scikit-learn matplotlib kmapper 3.3 Code Structure and Modules The replication script is organized into eight modular sections, each corresponding to a specific analytical task: ·         Module 1: Data Loading and Preparation. Functions load_data(), construct_payment_matrix(), and construct_distance_matrix() load the Excel data and build symmetric payment flow matrices and distance matrices. Four distance metrics are implemented: inverse-flow (primary), correlation, normalized Euclidean on log-flows, and Jaccard binary. ·         Module 2: Persistent Homology Computation. Functions compute_persistent_homology(), extract_betti_numbers(), and compute_persistence_landscape() construct Vietoris-Rips complexes using GUDHI, extract Betti numbers at specified filtration values, and compute persistence landscapes for topological feature visualization. ·         Module 3: Topological Stress Index (TSI). Functions compute_tsi() and compute_subgraph_betti() implement the normalized composite index defined in Definition 3.2 of the manuscript. The TSI bridges the first Betti number (topological fragility) with the aggregate fiscal capacity ratio (macroeconomic absorption). ·         Module 4: Bootstrap Confidence Intervals. Function bootstrap_betti_ci() performs 1000 resamples of the quarterly distance matrices with replacement, computing percentile-based 95% confidence intervals for Betti-1 at each filtration level. ·         Module 5: Placebo Test. Function placebo_test() randomizes CBDC engagement dates across the 40-quarter sample while maintaining the same number of engagement events, testing whether observed TSI changes are statistically distinguishable from random temporal variation. ·         Module 6: Mapper Algorithm. Function compute_mapper_graph() applies the Mapper algorithm (KeplerMapper) with PCA lens functions and DBSCAN clustering to detect systemic risk regimes (stable, fragile, crisis) in the payment network topology. ·         Module 7: CEMAC Comparator Analysis. Functions compute synthetic control differences between WAMZ (treated) and CEMAC (control) for the difference-in-differences identification strategy. ·         Module 8: Main Analysis Pipeline. Function main_analysis() orchestrates the full replication workflow, generating all tables, figures, and diagnostic outputs reported in the manuscript. 3.4 Execution Instructions To replicate the full analysis: 1.      Step 1: Download the data file 'WAMZ_CBDC_TDA_Data.xlsx' and the script 'WAMZ_CBDC_TDA_Replication.py' into the same directory. 2.      Step 2: Install required packages: pip install gudhi numpy pandas scipy scikit-learn matplotlib kmapper 3.      Step 3: Execute the script: python WAMZ_CBDC_TDA_Replication.py 4.      Step 4: The script will automatically load data, compute topological invariants, perform bootstrap and placebo tests, and generate all figures. 5.      Step 5: Expected runtime: approximately 8-12 minutes on a standard laptop (Intel i5, 16GB RAM) or 3-5 minutes on the specified hardware. 4. Generated Figures Four primary figures are generated by the replication code and reported in the manuscript. Each figure is saved as a high-resolution PNG file (300 DPI) suitable for publication. All figures are vector-quality and can be regenerated at arbitrary resolution by re-running the replication script. 4.1 Figure 1: Network Evolution Diagram File: Figure1_Network_Evolution.png This figure presents three panels illustrating the evolution of the WAMZ payment network topology across CBDC engagement windows. Panel (A) shows the pre-engagement star topology (2015Q1-2021Q2) with Nigeria (NGA) as the central hub and all other members connected directly. Panel (B) shows the post-e-Cedi design paper period (2021Q3-2023Q4) where Ghana (GHA) begins emerging as a secondary hub with weakened edges to Nigeria. Panel (C) shows the post-e-Naira launch period (2021Q4-2024Q4) with severe fragmentation: all edges are dashed (weakened), three disconnected subgraphs are visible, and the Betti-1 count rises to 5. Edge labels indicate mean quarterly payment flows in USD millions from the integrated dataset. Generation method: Matplotlib scatter and line plots with custom node positioning. Node colors indicate engagement status (red = operational CBDC, yellow = pilot, blue = no engagement). Edge styles indicate flow strength (solid = strong, dashed = weakened by CBDC friction).   [Figure 1: Network Evolution Diagram] 4.2 Figure 2: Persistence Diagrams File: Figure2_Persistence_Diagrams.png This figure presents two persistence diagrams comparing topological features before and after CBDC engagement. Panel (A) shows the pre-engagement period (2015Q1-2021Q2) with three short-lived features near the diagonal (birth-death pairs: 0.05-0.15, 0.10-0.25, 0.15-0.30), indicating a tree-like (acyclic) topology. Panel (B) shows the post-e-Naira launch period (2021Q4-2024Q4) with five highly persistent features far from the diagonal (birth-death pairs: 0.05-1.80, 0.15-2.10, 0.25-2.25, 0.10-1.60, 0.20-1.90), indicating five independent 1-dimensional cycles (fragility loops). The dashed diagonal line represents the locus of zero-persistence features (instantaneous birth and death). Generation method: Matplotlib scatter plots with GUDHI-computed persistence pairs. Each point represents a topological feature with coordinates (birth filtration, death filtration). Distance from the diagonal indicates persistence duration. 4.3 Figure 3: Betti-1 Curves File: Figure3_Betti_Curves.png This figure plots the first Betti number (beta_1) as a function of the filtration parameter epsilon for four CBDC engagement scenarios. The pre-engagement curve (blue, solid) remains near zero across all filtration values, confirming the star topology has no cycles. The post-e-Cedi curve (orange, dashed) shows a moderate peak at epsilon approximately 0.35, indicating two emergent cycles. The post-e-Naira curve (red, dash-dot) shows the highest and most persistent peak at epsilon approximately 0.40, with beta_1 reaching 3.8, confirming severe topological fragmentation. The harmonized counterfactual curve (green, dotted) shows a low peak at beta_1 approximately 0.9, demonstrating that interoperability would substantially reduce fragility loops. The vertical gray dashed line marks the median filtration value (epsilon = 0.5) used for Betti number reporting in Tables 3 and 4. Generation method: Matplotlib line plots with GUDHI-computed Betti curves. For each engagement window, the distance matrix is averaged across quarters, the Rips complex is constructed, and Betti-1 is computed at 200 logarithmically spaced filtration values between 0.01 and 2.0. 4.4 Figure 4: Mapper Graph File: Figure4_Mapper_Graph.png This figure visualizes the Mapper graph output for systemic risk regime detection in the WAMZ payment network. Nodes represent clusters of quarters with similar topological and macro-financial characteristics. Node colors indicate regime classification: blue for stable (TSI < 1.0), orange for fragile (1.0 <= TSI < 3.0), red for crisis (TSI >= 3.0), and green for the harmonized counterfactual. Node sizes are proportional to cluster density. Edges connect clusters that share at least one data point (quarter). The graph reveals a clear temporal progression from stable regimes (2015-2019) through fragile regimes (2020-2023) to a crisis regime (2024), with the harmonized counterfactual remaining in the stable cluster throughout. Generation method: KeplerMapper (kmapper) with PCA lens (2 components) on the feature matrix combining payment flows, reserves, inflation, and exchange rate volatility. DBSCAN clustering (eps=0.5, min_samples=2) with 4 overlapping intervals per dimension and 20% overlap. Matplotlib circle patches and line plots for visualization. 5. Data Access and Licensing The supplementary materials are made available under the following terms: Data License: The macro-financial indicators (Sheet 2) and CBDC engagement timeline (Sheet 3) are derived from publicly available sources (IMF, World Bank, Atlantic Council, Bank of Ghana, Central Bank of Nigeria) and are provided without restriction for academic and research use. The integrated payment flow data (Sheet 1) incorporate WACH settlement data obtained under a non-disclosure agreement with the West African Monetary Institute (WAMI). While the raw WACH bilateral values cannot be publicly released, the aggregated statistics, topological invariants, and derived indicators reported in this repository are not subject to the NDA. Researchers seeking access to the raw WACH component should contact WAMI directly. Code License: The Python replication script is released under the MIT License, permitting unrestricted use, modification, and distribution with appropriate attribution. Citation: If using these supplementary materials in subsequent research, please cite the original manuscript: Opue, J.A. (2026). 'Digital Currency Fragmentation and Systemic Risk in the West African Monetary Zone: A Topological Data Analysis of Cross-Border Payment Network Spillovers.' Submitted to the 2026 Jacques Polak Annual Research Conference, International Monetary Fund.