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---

### Cross-border payment shares (Section 3.1)
- Overview
  - In 2024, financial institution payments accounted for 80 percent of total Swift customer and financial-institution related payments.

- Payment shares by message type
  - Financial institution (MT 202) and customer (MT 103) payment values are aggregated annually for share calculations.
  - Financial institution payments remain the dominant message type in value terms.

- Income-group and regional breakdowns
  - Transactions within AEs account for 80.3 percent of financial institution payments on average over 2021-24.
  - Payments between AEs and EMDEs comprised 18 percent of financial institution payments.
  - Within-EMDE transactions accounted for 1.7 percent of financial institution payments.
  - Customer payments show a similar pattern with a slightly higher share of within-AE flows.
  - Regional highlights:
    - Europe has the largest share of within-region payments for both customer and financial institution transactions.
    - Payments within Asia and the Americas are also sizable.
    - Cross-regional payments are concentrated between Europe and other regions—particularly Asia and the Americas.

- Currency shares and dynamics (IMF SDR currencies focus)
  - USD shares in 2024:
    - Financial institution flows: 53.4 percent
    - Customer flows: 55.1 percent
  - EUR shares in 2024:
    - Financial institution flows: 18.0 percent
    - Customer flows: 26.2 percent
  - JPY shares in 2024:
    - Financial institution flows: 5.9 percent
    - Customer flows: 1.7 percent
  - GBP shares in 2024:
    - Financial institution flows: 4.3 percent
    - Customer flows: 4.8 percent
  - CNY shares in 2024:
    - Financial institution flows: 3.7 percent
    - Customer flows: 1.4 percent
  - Changes between 2021 and 2024 (percentage points):
    - USD: Financial institutions change 2.5; Customers change -0.0
    - EUR: Financial institutions change -6.6; Customers change 0.8
    - JPY: Financial institutions change 0.7; Customers change -0.3
    - GBP: Financial institutions change 0.2; Customers change -0.1
    - CNY: Financial institutions change 1.5; Customers change 0.2
  - Aggregate observations:
    - USD and EUR together represent over 70 percent of financial institution payments and more than 80 percent of customer payments.
    - The JPY has a higher share in financial institution payments (5.9 percent) than customer payments (1.7 percent).
    - The CNY experienced the second largest increase in financial institution payments between 2021 and 2024 (about 1.5 percentage points).
    - EUR-denominated financial institution payments declined by 6.6 percentage points between 2021 and 2024.
  - Counterparty involvement by currency:
    - A large share of USD-denominated financial institution payments occurs between third-economy originators and beneficiaries (the U.S. is neither originator nor beneficiary).
    - For USD customer payments, a large share involves the U.S. as either originator or beneficiary.
    - Similar third-economy patterns are observed for JPY and GBP payments.
    - EUR usage is relatively limited in transactions between third-economy originators and beneficiaries across both message types.
    - The CNY is more frequently used in payments that do not involve the Chinese mainland as either originator or beneficiary for both financial institutions and customer payments.
    - The rise in the CNY’s global share is predominantly driven by payments occurring within corridors that exclude the Chinese mainland.
    - Most payments in CNY are made via the Hong Kong SAR clearing center, which could contribute to this pattern.

- Transaction size distribution and currency by size
  - Eleven transaction-size categories are analyzed.
  - Payment value concentration (2024):
    - Payments above US$50 million account for:
      - Financial institution payments: 82.5 percent of total payment value
      - Customer payments: 60.5 percent of total payment value
    - Payments in US$10-50 million and US$1-10 million are the next largest shares in value for both categories.
    - Collectively, payments above US$1 million comprise:
      - Financial institution cross-border payment value: 99 percent
      - Customer cross-border payment value: 93 percent
  - Number-of-payments concentration:
    - Payments up to US$10K account for:
      - Customer payments: 62.6 percent of the total number of transactions
      - Financial institution payments: 35.3 percent of the total number of transactions
    - For financial institutions, mid-sized payments between US$500K-10M account for 36.4 percent of the number of total payments.
  - Currency share dynamics by transaction size:
    - USD dominance remains across all categories except small payments (US$0–500), where EUR plays an equally significant role.
    - The rise of the CNY is most pronounced in:
      - Customer payments up to US$500,000
      - Financial institution payments exceeding US$50 million
    - Other major SDR currency shares remain relatively stable across transaction sizes.

- Cross-border payment intermediation
  - Overall intermediation by third economies (2024):
    - Financial institution payments: 72.2 percent of the transaction value was intermediated through a third economy.
    - Customer payments: 21.3 percent of the transaction value was intermediated through a third economy.
  - Currency heterogeneity in intermediation shares:
    - The share of intermediated payment value exceeded the average for USD transactions.
    - The share was below average for EUR, GBP, JPY, and CNY transactions.
    - For GBP and EUR transactions in 2024:
      - GBP: 48.9 percent of payment value intermediated through third economies
      - EUR: 42.3 percent of payment value intermediated through third economies
  - Intermediation by transaction size:
    - The degree of intermediation is relatively stable across different transaction sizes.
    - Intermediation tends to be highest for mid-sized payments for both financial institution and customer payments.
  - Ten most frequent intermediary economies and share of intermediated transactions (2024):
    - Financial institutions (share of intermediated transactions %):
      - U.S.: 42.9
      - Germany: 10.9
      - Canada: 6.5
      - U.K.: 6.1
      - France: 3.8
      - Austria: 3.4
      - Hong Kong SAR: 3.5
      - Belgium: 3.3
      - Japan: 3.0
      - Australia: 2.0
      - Spain: 1.2
      - Switzerland: 1.8
    - Customers (share of intermediated transactions %):
      - U.S.: 48.2
      - Germany: 18.0
      - U.K.: 7.5
      - France: 5.5
      - Belgium: 2.7
      - Italy: 2.0
      - Ireland: 1.3
      - Hong Kong SAR: 1.0
  - Both for financial institution and customer payments, the U.S. intermediates the highest share of payments followed by Germany.
  - Financial centers such as Hong Kong SAR and Switzerland play a more important role in the intermediation of financial institution payments than in customer payments.

- Cross-border payment networks and centrality
  - Swift cross-border payment networks are highly interconnected with a core-periphery structure.
  - Node sizes represent each economy’s Katz-Bonacich centrality.
  - Financial institution payment network centrality (largest):
    - U.K. and U.S. exhibit the largest centrality.
    - France, Germany, and Hong Kong SAR occupy central positions.
  - Customer payment network centrality (largest):
    - U.S. ranks highest in centrality followed by U.K., Germany, Canada, and France.
  - Currency-specific network characteristics:
    - USD and EUR networks appear denser than CNY, GBP, and JPY networks.
    - Economies’ centrality depends on currency usage:
      - U.S., Euro Area economies, U.K., and Japan have highest centrality for USD, EUR, GBP, and JPY payments respectively.
    - The CNY financial institution payment network is distinct: Hong Kong SAR and the U.K.—rather than the Chinese mainland—occupy the most central positions.
    - The U.K. consistently appears highly central across currency networks, reflecting its global financial hub status beyond its third-economy intermediary role.

- Gravity analysis (aggregate bilateral cross-border payments, 2021-24)
  - Model: Dependent variable bilateral cross-border payments Yijt in US$; bilateral economic ties captured by ln(Econij) (log bilateral imports, log total portfolio investment, log outward FDI); gravity controls include geographical distance (log), common language (0/1), colonial relationship post-1945 (0/1); fixed effects: originator (θi), beneficiary (τj), year (φt); estimator: PPML with robust standard errors double clustered.
  - Main elasticity estimates (Table 3):
    - Imports:
      - Total payments (column 1): 0.167*** (0.064)
      - Financial institutions (column 2): 0.153** (0.065)
      - Customers (column 3): 0.196* (0.100)
    - Portfolio investment:
      - Total payments: 0.241*** (0.091)
      - Financial institutions: 0.245** (0.103)
      - Customers: 0.223*** (0.066)
    - FDI:
      - Total payments: 0.161*** (0.052)
      - Financial institutions: 0.162*** (0.056)
      - Customers: 0.146*** (0.034)
    - Distance (log):
      - Total payments: -0.104 (0.087)
      - Financial institutions: -0.083 (0.093)
      - Customers: -0.248** (0.098)
    - Language indicator:
      - Total payments: 0.040 (0.153)
      - Financial institutions: 0.005 (0.168)
      - Customers: 0.202 (0.138)
    - Colony indicator:
      - Total payments: 0.001 (0.196)
      - Financial institutions: 0.009 (0.216)
      - Customers: -0.174 (0.200)
  - Model fit and sample:
    - Pseudo R2:
      - Total payments: 0.934
      - Financial institutions: 0.905
      - Customers: 0.967
    - Observations:
      - Total payments: 22018
      - Financial institutions: 14934
      - Customers: 22018
    - Originator economies: 63
    - Beneficiary economies:
      - Total payments: 187
      - Financial institutions: 184
      - Customers: 187
  - Interpretation and robustness:
    - Economic ties (imports, portfolio investment, FDI) are positively and significantly associated with bilateral cross-border payments.
    - Quantitatively:
      - A 1 percent increase in imports is associated with a 0.167 percent increase in cross-border payments (total).
      - The elasticity is higher for portfolio investment at 0.241 and slightly lower for FDI at 0.161.
    - Distance is not significantly associated with financial institution payments but is significant and negative for customer payments (−0.248**).
    - Results are robust to alternative specifications that include corridor fixed effects and to using total trade (imports plus exports) or excluding intra-EU economies.
    - Intra-EU cross-border flows account for:
      - Financial institution–related: 16.1 percent of total Swift cross-border flows
      - Customer-related: 21.6 percent of total Swift cross-border flows

*Source: IMF staff analysis excerpt, “3.1  Cross-border payment shares.”*

---

### Heterogeneity across currencies and transaction sizes (Section 4.2)
- Overview
  - Objective: identify which currencies and/or transaction sizes drive the relationships between economic and gravity-related variables and cross-border payments for financial institution and customer payments.
  - Estimation method: Equation (1) estimated separately by currency and by transaction-size buckets using PPML. Dependent variable: level of bilateral cross-border payments in US$.

- Findings by currency (Table 4 summary)
  - Financial institutions (Panel A)
    - Imports:
      - USD: 0.148** 
      - GBP: 0.403***
      - CNY: 0.188***
      - EUR: 0.013 (insignificant)
      - JPY: -0.083 (insignificant)
    - Portfolio investment (Investment):
      - USD: 0.180**
      - EUR: 0.324**
      - JPY: 0.267***
      - GBP: 0.095 (insignificant)
      - CNY: 0.027 (insignificant)
    - FDI:
      - USD: 0.160***
      - EUR: 0.235*
      - GBP: 0.342***
      - JPY: 0.079 (insignificant)
      - CNY: 0.076**
    - Distance: generally insignificant for financial institution payments across currencies (USD -0.127; EUR -0.118; GBP 0.121; JPY 0.035; CNY 0.120).
    - Shared language: positive and significant only for CNY-denominated payments (0.220**).
    - Colonial ties: negatively and significantly correlated with GBP (-0.840***) and CNY (-0.356**); other currencies mixed.
  - Customers (Panel B)
    - Imports:
      - JPY: 0.153* (significant)
      - USD: 0.161 (insignificant)
      - EUR: 0.051 (insignificant)
      - GBP: -0.034 (insignificant)
      - CNY: 0.077 (insignificant)
    - Portfolio investment (Investment):
      - EUR: 0.188***
      - GBP: 0.278***
      - CNY: -0.265*** (negative)
      - USD: 0.086 (insignificant)
      - JPY: -0.067 (insignificant)
    - FDI:
      - USD: 0.214***
      - EUR: 0.121**
      - CNY: 0.176***
      - GBP: 0.123 (insignificant)
      - JPY: -0.050 (insignificant)
    - Distance: negative and significant across all currencies for customer payments:
      - USD: -0.322**
      - EUR: -0.286***
      - GBP: -0.230**
      - JPY: -0.172**
      - CNY: -0.266**
    - Colonial ties and shared language: not significant for customer-related payments at the aggregate level.

- Findings by transaction size (Table 5 summary)
  - Financial institutions (Panel A)
    - Imports: association strengthens with payment size; coefficients by size (examples):
      - 0-500: 0.054 (insignificant)
      - 500-2500: 0.126**
      - 2500-10K: 0.156***
      - 10K-25K: 0.205***
      - 25K-50K: 0.225***
      - 50K-100K: 0.216***
      - 100K-500K: 0.206***
      - 500K-1M: 0.211***
      - 1M-10M: 0.220***
      - 10M-50M: 0.193***
      - 50M-Above: 0.113*
    - Portfolio investment (Investment): significant across most sizes; generally stronger for larger transactions (e.g., 1M-10M: 0.235***; 10M-50M: 0.197***; 50M-Above: 0.215**).
    - FDI: significant across all sizes with coefficients:
      - 0-500: 0.232***
      - 500-2500: 0.200**
      - 2500-10K: 0.206***
      - 10K-25K: 0.202***
      - 25K-50K: 0.182***
      - 50K-100K: 0.196***
      - 100K-500K: 0.229***
      - 500K-1M: 0.204***
      - 1M-10M: 0.162***
      - 10M-50M: 0.124***
      - 50M-Above: 0.156**
    - Distance: significant and negative for smaller payments (0-500: -0.245**; 500-2500: -0.192*; 2500-10K: -0.169**), but often insignificant for larger sizes (e.g., 100K-500K: -0.028; 500K-1M: 0.124).
    - Colonial ties: significant primarily for smaller sizes (0-500: 0.739**; 500-2500: 0.501*; 2500-10K: 0.497**; 10K-25K: 0.296*), small or insignificant for larger sizes.
  - Customers (Panel B)
    - Imports: strong and significant across almost all sizes except the largest bucket; coefficients:
      - 0-500: 0.174***
      - 500-2500: 0.186***
      - 2500-10K: 0.193***
      - 10K-25K: 0.243***
      - 25K-50K: 0.276***
      - 50K-100K: 0.235***
      - 100K-500K: 0.212***
      - 500K-1M: 0.194***
      - 1M-10M: 0.166***
      - 10M-50M: 0.141**
      - 50M-Above: 0.179 (noted as exception)
    - Portfolio investment (Investment): positive and significant across all sizes and notably stronger for large transactions:
      - 0-500: 0.038***
      - 500-2500: 0.040***
      - 2500-10K: 0.036***
      - 10K-25K: 0.032***
      - 25K-50K: 0.033**
      - 50K-100K: 0.029***
      - 100K-500K: 0.039***
      - 500K-1M: 0.062***
      - 1M-10M: 0.145***
      - 10M-50M: 0.261***
      - 50M-Above: 0.397***
    - FDI: positive and significant across all sizes; coefficients:
      - 0-500: 0.093***
      - 500-2500: 0.071***
      - 2500-10K: 0.055***
      - 10K-25K: 0.049***
      - 25K-50K: 0.052***
      - 50K-100K: 0.057***
      - 100K-500K: 0.088***
      - 500K-1M: 0.131***
      - 1M-10M: 0.160***
      - 10M-50M: 0.153***
      - 50M-Above: 0.107**
    - Distance: negative and significant across most sizes, especially smaller ones:
      - 0-500: -0.354***
      - 500-2500: -0.303***
      - 2500-10K: -0.285***
      - 50M-Above: -0.191 (not significant)
    - Colonial ties: significant mainly for smaller sizes (0-500: 0.377**; 500-2500: 0.323**; 2500-10K: 0.233*), becoming insignificant or negative for larger sizes.

- Additional transaction-size patterns
  - Imports–financial institution payments: insignificant for payments below US$10,000.
  - Portfolio investment–financial institution payments: stronger for larger transactions (US$500K–50M-above) than for those below US$500K.
  - FDI–financial institution payments: association stronger for smaller transactions (reverse pattern relative to portfolio investment).
  - Distance and informational asymmetries: distance has a significant negative association with smaller cross-border payments but is often insignificant for larger transactions, suggesting informational asymmetries play less of a role for larger payments.
  - Colonial ties: significant primarily for smaller transaction sizes; geographic corridor patterns noted (Asian corridors with UK colonial history for financial institutions; African corridors with France colonial history for customers).

- Key takeaways
  - Cross-border payments are strongly correlated with economic ties: imports, portfolio investment, and FDI matter for both financial institution and customer payments.
  - Aggregate flows mask considerable heterogeneity across message types, currencies, and transaction sizes.
  - The elasticity of cross-border payments differs between smaller-value and higher-value payments: smaller cross-border payments, especially customer-related ones, appear to suffer more from informational asymmetries.

- Network dynamics (monthly measures, 2021–2024 medians)
  - Degree out (number of economies connected): increased over 2021–24 for both message types.
  - Strength out (value of outgoing payments): rose for both message types.
  - HHI out (outward network concentration): declined for financial institution payments, suggesting reduced concentration.
  - Regionalization proxy: no indication of increasing regionalization in cross-border payment flows over 2021–24.
  - Currency-level dynamics:
    - Customer payments: increasing interlinkages (degree out and strength out) across most currencies, exception GBP.
    - Decline in network concentration particularly evident for USD and CNY payments.
    - Financial institution payments: mixed picture, with stable or increasing interlinkages.

*Source: 4.2 Heterogeneity across currencies and transaction sizes (wpiea2025120-print-pdf).*

---

### Fragmentation and risk trends (Section 5.2)
- Empirical specification and data
  - Estimation period: 2021Q1–2024Q4.
  - Estimated equation (bilateral corridor ij, time t): Yijt = β1 s t−1 + β2 s t−1 × InterBlocij + θij + τit + φjt + εijt
    - Yijt: bilateral cross-border payments (US$) from originator economy i to beneficiary economy j at time t.
    - s t−1 ∈ {Common Fragmentation, Financial Fragmentation, Trade Fragmentation, Geopolitical Risk} — standardized within the sample period (2021Q1–2024Q4).
    - InterBlocij = 1 if i and j belong to opposite hypothetical blocs (U.S.-aligned vs Chinese mainland-aligned) based on UNGA ideal point distance; 0 otherwise.
  - Fixed effects: corridor-level time-invariant (θij), originator×year (τit), beneficiary×year (φjt).
  - Estimation method: PPML.

- Index definitions and bloc classification
  - Fragmentation indexes: common fragmentation, financial fragmentation, trade fragmentation (standardized).
  - Geopolitical risk index: standardized.
  - Blocs classification: U.S.-aligned, Chinese mainland-aligned, non-aligned; economy assigned if its UNGA ideal point distance (IPD) is within the top 25th percentile in proximity to the U.S. (or Chinese mainland).

- Main findings — aggregate corridor results (Table 6)
  - Fragmentation and aggregate payments:
    - A 1 standard deviation increase in the common fragmentation index is associated with:
      - a 5.5 percent decline in financial institution cross-border payments (column 1).
      - a 2.2 percent decline in customer cross-border payments (column 5).
    - Similar negative associations hold for financial fragmentation and trade fragmentation for both payment types (columns 1–3 and 5–7).
  - Inter-bloc differential (interaction β2):
    - Interaction terms between fragmentation measures and InterBloc are generally not statistically significant for aggregate financial institution and customer payments.
  - Geopolitical risk:
    - No significant effect of an increase in geopolitical risks on customer payments (column 8; Geopolitical Risk coefficient 0.000 with standard error (0.004)).
    - Higher geopolitical risks are associated with an increase in financial institution inter-bloc payments (column 4; Geopolitical Risk×InterBloc = 0.027***, standard error (0.002)), potentially reflecting safe-haven dynamics.
  - Exact selected coefficients (Table 6):
    - Common Fragmentation (Financial Institutions): -0.055*** (0.016).
    - Common Fragmentation (Customers): -0.022*** (0.007).
    - Geopolitical Risk (Financial Institutions): -0.005 (0.004).
    - Geopolitical Risk×InterBloc (Financial Institutions): 0.027*** (0.002).
    - Geopolitical Risk (Customers): 0.000 (0.004).
    - Geopolitical Risk×InterBloc (Customers): 0.006 (0.009).

- Currency-level heterogeneity (Table 7)
  - Analysis focuses on common fragmentation index for five currencies: USD, EUR, GBP, JPY, CNY.
  - USD-denominated financial institution payments:
    - Common Fragmentation = -0.041*** (0.015).
    - Common Fragmentation×InterBloc = -0.032** (0.016).
    - Geopolitical Risk×InterBloc = 0.030*** (0.008).
    - Interpretation: 1 standard-deviation increase in common fragmentation associated with a 4.1 percent decline in USD-denominated financial institution payments; decline is 3.2 percentage points larger for inter-bloc payments.
  - CNY-denominated financial institution payments:
    - Common Fragmentation = 0.138** (0.060).
    - Common Fragmentation×InterBloc = 0.676*** (0.229).
    - Geopolitical Risk×InterBloc = -0.515*** (0.159).
    - Interpretation: fragmentation associated with increased CNY-denominated financial institution payments, with a substantially larger positive effect for inter-bloc payments.
  - EUR and GBP financial institution inter-bloc payments:
    - Common Fragmentation×InterBloc positive and significant for EUR and GBP, indicating increases in inter-bloc EUR- and GBP-denominated payments offset negative within-bloc effects.
  - JPY:
    - Financial-institution inter-bloc payments negatively correlated with fragmentation.
    - For customer payments, JPY shows some positive association between fragmentation and inter-bloc payments.
  - Geopolitical risk patterns by currency:
    - USD: increase in geopolitical risks associated with higher USD-denominated inter-bloc financial institution payments.
    - CNY: geopolitical risks associated with a decline in CNY-denominated inter-bloc financial institution payments.
    - GBP and JPY: increases in geopolitical risk offset lower within-bloc payments via increases in inter-bloc financial institution payments.
    - Customer payments: USD-denominated customer payments within the same bloc (or between U.S./Chinese mainland-aligned and non-aligned economies) are positively associated with an increase in geopolitical risks; GBP-denominated customer payments within the same bloc are negatively correlated with geopolitical risk.

- Transaction-size heterogeneity (Tables B.8 and B.9)
  - Negative association between fragmentation and payments primarily driven by large-value transactions (US$50 million and above):
    - US$50 million and above is the only transaction size with a negative and significant association between fragmentation and both financial institution and customer payments.
    - For this size there is no differential inter-bloc effect, explaining an insignificant interaction term in aggregate Table 6.
  - Smaller and mid-sized transactions:
    - For smaller financial institution transactions (up to US$50K) and mid-sized transactions (US$25K–1M), increases in fragmentation are associated with disproportionately larger declines in payments between economies in different blocs.
  - Currency-bucket drivers:
    - Divergent effects of fragmentation on USD-denominated and CNY-denominated payments are primarily driven by transactions in the US$50 million and above category.

- Network- and system-level context (stylized facts)
  - Large-value transactions (US$50 million and above) account for:
    - over 60 percent of customer payments.
    - over 80 percent of financial institution cross-border payments.
  - Aggregate trend over 2020–2024: greater connectivity and reduced concentration on average, but rising geoeconomic fragmentation associated with declines in cross-border payment values, particularly for large-value financial institution transactions.
  - Series standardization and controls: fragmentation and geopolitical risk series standardized within the estimation sample; corridor and year fixed effects included.

- Interpretations and implications
  - Rising geoeconomic fragmentation is associated with lower bilateral cross-border payment values, especially for large-value financial institution transactions.
  - Fragmentation effects vary substantially across currencies and transaction sizes:
    - USD- and CNY-denominated payments display distinct and sometimes opposite patterns.
    - Fragmentation may be supporting the growing role of the CNY in cross-border payments in some corridors.
  - Geopolitical risk can asymmetrically influence payment activity; increases in geopolitical uncertainty are associated with higher USD-denominated transactions in certain corridors, consistent with safe-haven motives.

- Suggested directions noted by authors
  - Further research on how evolving financial innovation—particularly crypto assets and stablecoins—may impact the international monetary system (IMS), including network dynamics and corridor-level drivers.
  - Policymakers have a role in ensuring a stable and well-functioning cross-border payment network given its importance for trade and investment.

*Source: wpiea2025120-print-pdf (https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025120-print-pdf.pdf).*

### 3.1  Cross-border payment shares

### 3.1  Cross-border payment shares

### Overview
- In 2024, financial institution payments accounted for 80 percent of total Swift customer and financial-institution related payments.

### Payment shares by message type
- Financial institution (MT 202) and customer (MT 103) payment values are aggregated annually for share calculations.
- Financial institution payments remain the dominant message type in value terms.

### Income-group and regional breakdowns
- Transactions within AEs account for 80.3 percent of financial institution payments on average over 2021-24.
- Payments between AEs and EMDEs comprised 18 percent of financial institution payments.
- Within-EMDE transactions accounted for 1.7 percent of financial institution payments.
- Customer payments show a similar pattern with a slightly higher share of within-AE flows.
- Regional highlights:
  - Europe has the largest share of within-region payments for both customer and financial institution transactions.
  - Payments within Asia and the Americas are also sizable.
  - Cross-regional payments are concentrated between Europe and other regions—particularly Asia and the Americas.

### Currency shares and dynamics (focus on IMF SDR currencies)
- USD shares in 2024:
  - Financial institution flows: 53.4 percent
  - Customer flows: 55.1 percent
- EUR shares in 2024:
  - Financial institution flows: 18.0 percent
  - Customer flows: 26.2 percent
- JPY shares in 2024:
  - Financial institution flows: 5.9 percent
  - Customer flows: 1.7 percent
- GBP shares in 2024:
  - Financial institution flows: 4.3 percent
  - Customer flows: 4.8 percent
- CNY shares in 2024:
  - Financial institution flows: 3.7 percent
  - Customer flows: 1.4 percent
- Changes between 2021 and 2024 (percentage points):
  - USD: Financial institutions change 2.5; Customers change -0.0
  - EUR: Financial institutions change -6.6; Customers change 0.8
  - JPY: Financial institutions change 0.7; Customers change -0.3
  - GBP: Financial institutions change 0.2; Customers change -0.1
  - CNY: Financial institutions change 1.5; Customers change 0.2
- Aggregate currency observations:
  - USD and EUR together represent over 70 percent of financial institution payments and more than 80 percent of customer payments.
  - The JPY has a higher share in financial institution payments (5.9 percent) than customer payments (1.7 percent).
  - The CNY experienced the second largest increase in financial institution payments between 2021 and 2024 (about 1.5 percentage points).
  - EUR-denominated financial institution payments declined by 6.6 percentage points between 2021 and 2024.
- Counterparty involvement by currency:
  - A large share of USD-denominated financial institution payments occurs between third-economy originators and beneficiaries (the U.S. is neither originator nor beneficiary).
  - For USD customer payments, a large share involves the U.S. as either originator or beneficiary.
  - Similar third-economy patterns are observed for JPY and GBP payments.
  - EUR usage is relatively limited in transactions between third-economy originators and beneficiaries across both message types.
  - The CNY is more frequently used in payments that do not involve the Chinese mainland as either originator or beneficiary for both financial institutions and customer payments.
  - The rise in the CNY’s global share is predominantly driven by payments occurring within corridors that exclude the Chinese mainland.
  - Most payments in CNY are made via the Hong Kong SAR clearing center, which could contribute to this pattern.

### Transaction size distribution and currency by size
- Eleven transaction-size categories are analyzed.
- Payment value concentration (2024):
  - Payments above US$50 million account for:
    - Financial institution payments: 82.5 percent of total payment value
    - Customer payments: 60.5 percent of total payment value
  - Payments in US$10-50 million and US$1-10 million are the next largest shares in value for both categories.
  - Collectively, payments above US$1 million comprise:
    - Financial institution cross-border payment value: 99 percent
    - Customer cross-border payment value: 93 percent
- Number-of-payments concentration:
  - Payments up to US$10K account for:
    - Customer payments: 62.6 percent of the total number of transactions
    - Financial institution payments: 35.3 percent of the total number of transactions
  - For financial institutions, mid-sized payments between US$500K-10M account for 36.4 percent of the number of total payments.
- Currency share dynamics by transaction size:
  - USD dominance remains across all categories except small payments (US$0–500), where EUR plays an equally significant role.
  - The rise of the CNY is most pronounced in:
    - Customer payments up to US$500,000
    - Financial institution payments exceeding US$50 million
  - Other major SDR currency shares remain relatively stable across transaction sizes.

### Cross-border payment intermediation
- Overall intermediation by third economies:
  - Financial institution payments: 72.2 percent of the transaction value was intermediated through a third economy in 2024.
  - Customer payments: 21.3 percent of the transaction value was intermediated through a third economy in 2024.
- Currency heterogeneity in intermediation shares:
  - The share of intermediated payment value exceeded the average for USD transactions.
  - The share was below average for EUR, GBP, JPY, and CNY transactions.
  - For GBP and EUR transactions in 2024:
    - GBP: 48.9 percent of payment value intermediated through third economies
    - EUR: 42.3 percent of payment value intermediated through third economies
- Intermediation by transaction size:
  - The degree of intermediation is relatively stable across different transaction sizes.
  - Intermediation tends to be highest for mid-sized payments for both financial institution and customer payments.
- Ten most frequent intermediary economies and share of intermediated transactions (2024):
  - Financial institutions (share of intermediated transactions %):
    - U.S.: 42.9
    - Germany: 10.9
    - Canada: 6.5
    - U.K.: 6.1
    - France: 3.8
    - Austria: 3.4
    - Hong Kong SAR: 3.5
    - Belgium: 3.3
    - Japan: 3.0
    - Australia: 2.0
    - Spain: 1.2
    - Switzerland: 1.8
  - Customers (share of intermediated transactions %):
    - U.S.: 48.2
    - Germany: 18.0
    - U.K.: 7.5
    - France: 5.5
    - Belgium: 2.7
    - Italy: 2.0
    - Ireland: 1.3
    - Hong Kong SAR: 1.0
- Both for financial institution and customer payments, the U.S. intermediates the highest share of payments followed by Germany.
- Financial centers such as Hong Kong SAR and Switzerland play a more important role in the intermediation of financial institution payments than in customer payments.

### Cross-border payment networks and centrality
- Swift cross-border payment networks are highly interconnected with a core-periphery structure.
- Node sizes represent each economy’s Katz-Bonacich centrality.
- Financial institution payment network centrality (largest):
  - U.K. and U.S. exhibit the largest centrality.
  - France, Germany, and Hong Kong SAR occupy central positions.
- Customer payment network centrality (largest):
  - U.S. ranks highest in centrality followed by U.K., Germany, Canada, and France.
- Currency-specific network characteristics:
  - USD and EUR networks appear denser than CNY, GBP, and JPY networks.
  - Economies’ centrality depends on currency usage:
    - U.S., Euro Area economies, U.K., and Japan have highest centrality for USD, EUR, GBP, and JPY payments respectively.
  - The CNY financial institution payment network is distinct: Hong Kong SAR and the U.K.—rather than the Chinese mainland—occupy the most central positions.
  - The U.K. consistently appears highly central across currency networks, reflecting its global financial hub status beyond its third-economy intermediary role.

### Key empirical findings from gravity analysis (aggregate bilateral cross-border payments, 2021-24)
- Model specification:
  - Dependent variable: bilateral cross-border payments Yijt in US$ from originator economy i to beneficiary economy j in year t.
  - Bilateral economic ties captured by ln(Econij): log bilateral imports, log total portfolio investment (sum of debt and equity portfolio asset holdings), and log outward FDI positions.
  - Gravity controls: geographical distance (log), common language (0/1), colonial relationship post-1945 (0/1).
  - Fixed effects: originator (θi), beneficiary (τj), and year (φt).
  - Estimator: Poisson pseudo-maximum likelihood (PPML) with robust standard errors double clustered at originator and beneficiary economy level.
- Main elasticity estimates (Table 3):
  - Imports:
    - Total payments (column 1): 0.167***
    - Financial institutions (column 2): 0.153**
    - Customers (column 3): 0.196*
    - Standard errors: (0.064), (0.065), (0.100) respectively
  - Portfolio investment:
    - Total payments: 0.241***
    - Financial institutions: 0.245**
    - Customers: 0.223***
    - Standard errors: (0.091), (0.103), (0.066) respectively
  - FDI:
    - Total payments: 0.161***
    - Financial institutions: 0.162***
    - Customers: 0.146***
    - Standard errors: (0.052), (0.056), (0.034) respectively
  - Distance (log):
    - Total payments: -0.104 (0.087)
    - Financial institutions: -0.083 (0.093)
    - Customers: -0.248** (0.098)
  - Language indicator:
    - Total payments: 0.040 (0.153)
    - Financial institutions: 0.005 (0.168)
    - Customers: 0.202 (0.138)
  - Colony indicator:
    - Total payments: 0.001 (0.196)
    - Financial institutions: 0.009 (0.216)
    - Customers: -0.174 (0.200)
- Model fit and sample:
  - Pseudo R2:
    - Total payments: 0.934
    - Financial institutions: 0.905
    - Customers: 0.967
  - Observations:
    - Total payments: 22018
    - Financial institutions: 14934
    - Customers: 22018
  - Originator economies: 63
  - Beneficiary economies:
    - Total payments: 187
    - Financial institutions: 184
    - Customers: 187
- Interpretation and robustness:
  - Economic ties (imports, portfolio investment, FDI) are positively and significantly associated with bilateral cross-border payments.
  - Quantitatively:
    - A 1 percent increase in imports is associated with a 0.167 percent increase in cross-border payments (total).
    - The elasticity is higher for portfolio investment at 0.241 and slightly lower for FDI at 0.161.
  - Distance is not significantly associated with financial institution payments but is significant and negative for customer payments (−0.248**).
  - Results are robust to alternative specifications that include corridor fixed effects and to using total trade (imports plus exports) or excluding intra-EU economies.
  - Intra-EU cross-border flows account for:
    - Financial institution–related: 16.1 percent of total Swift cross-border flows
    - Customer-related: 21.6 percent of total Swift cross-border flows

*Source: IMF staff analysis excerpt, “3.1  Cross-border payment shares.”*

### 4.2  Heterogeneity across currencies and transaction sizes

### 4.2 Heterogeneity across currencies and transaction sizes

### Overview
- Objective: identify which currencies and/or transaction sizes drive the relationships between economic and gravity-related variables and cross-border payments for financial institution and customer payments.
- Estimation method: Equation (1) estimated separately by currency and by transaction-size buckets using Poisson pseudo-maximum likelihood (PPML). Dependent variable: level of bilateral cross-border payments in US$.

### Findings by currency (summary of Table 4)
- Financial institutions (Panel A)
  - Imports: strongly associated with payments denominated in USD (0.148**), GBP (0.403***), and CNY (0.188***); insignificant for EUR (0.013) and JPY (-0.083).
  - Portfolio investment (Investment): positive and significant for USD (0.180**), EUR (0.324**), and JPY (0.267***); smaller and insignificant for GBP (0.095) and CNY (0.027).
  - FDI: significantly correlated with all currency denominations except JPY; coefficients USD (0.160***), EUR (0.235*), GBP (0.342***), JPY (0.079), CNY (0.076**).
  - Distance: earlier insignificance for financial institution payments persists across USD (-0.127), EUR (-0.118), GBP (0.121), JPY (0.035), CNY (0.120).
  - Shared language: positive and significant only for CNY-denominated payments (0.220**).
  - Colonial ties: negatively and significantly correlated with GBP (-0.840***) and CNY (-0.356**); other currencies show mixed insignificance or positive coefficients (USD 0.180, EUR 0.219, JPY -0.725).

- Customers (Panel B)
  - Imports: significant determinant for JPY-denominated payments (0.153*); imports insignificant for USD (0.161), EUR (0.051), GBP (-0.034), CNY (0.077).
  - Portfolio investment (Investment): positive and significant for EUR (0.188***), GBP (0.278***); negative and significant for CNY (-0.265***); USD (0.086) and JPY (-0.067) not significant.
  - FDI: positively and significantly correlated with USD (0.214***), EUR (0.121**), and CNY (0.176***); GBP (0.123) and JPY (-0.050) not significant.
  - Distance: greater geographic distance associated with lower customer cross-border payments across all currencies; coefficients USD (-0.322**), EUR (-0.286***), GBP (-0.230**), JPY (-0.172**), CNY (-0.266**). Strongest negative effect observed for USD; weakest for JPY.
  - Colonial ties and shared language: do not appear to significantly affect customer-related payments for any currency at the aggregate level.

### Findings by transaction size (summary of Table 5)
- Financial institutions (Panel A)
  - Imports: association with financial institution payments strengthens with payment size; insignificant for payments below US$10,000 (coefficient for 0-500: 0.054; 500-2500: 0.126**; 2500-10K: 0.156***; 10K-25K: 0.205***; 25K-50K: 0.225***; 50K-100K: 0.216***; 100K-500K: 0.206***; 500K-1M: 0.211***; 1M-10M: 0.220***; 10M-50M: 0.193***; 50M-Above: 0.113*).
  - Portfolio investment (Investment): significant across most transaction sizes; generally stronger for larger transactions (e.g., 1M-10M: 0.235***; 10M-50M: 0.197***; 50M-Above: 0.215**), though some mid-size variation exists.
  - FDI: significant across all transaction sizes with coefficients: 0-500 (0.232***), 500-2500 (0.200**), 2500-10K (0.206***), 10K-25K (0.202***), 25K-50K (0.182***), 50K-100K (0.196***), 100K-500K (0.229***), 500K-1M (0.204***), 1M-10M (0.162***), 10M-50M (0.124***), 50M-Above (0.156**).
  - Distance: significant and negative for smaller payments (0-500: -0.245**; 500-2500: -0.192*; 2500-10K: -0.169**), but insignificant for many larger transaction sizes (e.g., 100K-500K: -0.028; 500K-1M: 0.124).
  - Colonial ties: significant primarily for smaller transaction sizes (0-500: 0.739**; 500-2500: 0.501*; 2500-10K: 0.497**; 10K-25K: 0.296*), insignificant or small for larger sizes.

- Customers (Panel B)
  - Imports: strong and significant association across almost all transaction sizes except the largest bucket; coefficients by size: 0-500 (0.174***), 500-2500 (0.186***), 2500-10K (0.193***), 10K-25K (0.243***), 25K-50K (0.276***), 50K-100K (0.235***), 100K-500K (0.212***), 500K-1M (0.194***), 1M-10M (0.166***), 10M-50M (0.141**), 50M-Above (0.179).
  - Portfolio investment (Investment): positive and significant across all transaction sizes and notably stronger for large transactions:
    - Below US$500K: 1 percent increase in bilateral portfolio investment holdings associated with a 0.038 percent increase in customer payments (coefficient 0.038*** for 0-500).
    - For US$1M–10M: 0.145 percent (coefficient 0.145***).
    - For US$10M–50M: 0.261 percent (coefficient 0.261***).
    - For US$50M and above: 0.397 percent (coefficient 0.397***).
    - Full coefficient series: 0-500 (0.038***), 500-2500 (0.040***), 2500-10K (0.036***), 10K-25K (0.032***), 25K-50K (0.033**), 50K-100K (0.029***), 100K-500K (0.039***), 500K-1M (0.062***), 1M-10M (0.145***), 10M-50M (0.261***), 50M-Above (0.397***).
  - FDI: positively and significantly associated across all transaction sizes; coefficients increase with size but differences less pronounced than for portfolio investment: 0-500 (0.093***), 500-2500 (0.071***), 2500-10K (0.055***), 10K-25K (0.049***), 25K-50K (0.052***), 50K-100K (0.057***), 100K-500K (0.088***), 500K-1M (0.131***), 1M-10M (0.160***), 10M-50M (0.153***), 50M-Above (0.107**).
  - Distance: negative and significant across most transaction sizes, especially smaller ones (e.g., 0-500: -0.354***; 500-2500: -0.303***; 2500-10K: -0.285***), but insignificant only for the very largest size (50M-Above: -0.191, not significant).
  - Colonial ties: significant mainly for smaller transaction sizes (0-500: 0.377**; 500-2500: 0.323**; 2500-10K: 0.233*), becoming insignificant or negative for larger sizes.

- Additional transaction-size patterns highlighted
  - Imports–financial institution payments: insignificant for payments below US$10,000.
  - Portfolio investment–financial institution payments: stronger for larger transactions (US$500K–50M-above) than for those below US$500K.
  - FDI–financial institution payments: association stronger for smaller transactions (reverse pattern compared to portfolio investment).
  - Distance and informational asymmetries: distance has a significant negative association with smaller cross-border payments but is often insignificant for larger transactions, suggesting informational asymmetries play less of a role for larger payments.
  - Colonial ties: significant primarily for smaller transaction sizes; geographic corridor patterns noted (Asian corridors with UK colonial history for financial institutions; African corridors with France colonial history for customers).

### Key takeaways (from gravity regressions)
- Cross-border payments are strongly correlated with economic ties: imports, portfolio investment, and FDI matter for both financial institution and customer payments.
- Aggregate flows mask considerable heterogeneity across message types, currencies, and transaction sizes.
- The elasticity of cross-border payments differs between smaller-value and higher-value payments: smaller cross-border payments, especially customer-related ones, appear to suffer more from informational asymmetries.

### Network dynamics (brief)
- Monthly network measures 2021–2024 (median across economies) indicate:
  - Degree out (number of economies each economy is connected to): increased over 2021–24 for both financial institution and customer payments, indicating greater connectivity.
  - Strength out (value of outgoing payments): rose for both message types.
  - HHI out (outward network concentration): declined for financial institution payments, suggesting reduced concentration.
  - Regionalization proxy: no indication of increasing regionalization in cross-border payment flows over 2021–24.
- Currency-level dynamics (Figures C.3 and C.4, summarized):
  - Customer payments: increasing interlinkages (degree out and strength out) across most currencies, exception GBP.
  - Decline in network concentration particularly evident for USD and CNY payments.
  - Financial institution payments: mixed picture, with stable or increasing interlinkages.

*Source: 4.2 Heterogeneity across currencies and transaction sizes (wpiea2025120-print-pdf).*

### 5.2  Fragmentation and risk trends

### 5.2  Fragmentation and risk trends

### Empirical specification and data
- Estimation period: 2021Q1–2024Q4.
- Estimated equation (bilateral corridor ij, time t):
  - Yijt = β1 s t−1 + β2 s t−1 × InterBlocij + θij + τit + φjt + εijt
  - Yijt: bilateral cross-border payments (US$) from originator economy i to beneficiary economy j at time t.
  - s t−1 ∈ {Common Fragmentation, Financial Fragmentation, Trade Fragmentation, Geopolitical Risk} — standardized within the sample period (2021Q1–2024Q4).
  - InterBlocij = 1 if i and j belong to opposite hypothetical blocs (U.S.-aligned vs Chinese mainland-aligned) based on UNGA ideal point distance; 0 otherwise.
- Fixed effects: corridor-level time-invariant (θij), originator×year (τit), beneficiary×year (φjt).
- Estimation method: Poisson pseudo-maximum likelihood (PPML).

### Definitions and indexes used
- Fragmentation indexes: common fragmentation, financial fragmentation, trade fragmentation (Fernández‑Villaverde et al. (2024)); standardized.
- Geopolitical risk index: Caldara & Iacoviello (2022); standardized.
- Blocs classification: U.S.-aligned, Chinese mainland-aligned, non-aligned — economy assigned to U.S. (or Chinese mainland) bloc if its UNGA ideal point distance (IPD) is within the top 25th percentile in proximity to the U.S. (or Chinese mainland).

### Main findings — aggregate corridor results (Table 6)
- Fragmentation and aggregate payments:
  - A 1 standard deviation increase in the common fragmentation index is associated with:
    - a 5.5 percent decline in financial institution cross-border payments (column 1). 
    - a 2.2 percent decline in customer cross-border payments (column 5).
  - Similar negative associations hold for financial fragmentation and trade fragmentation for both payment types (columns 1–3 and 5–7).
- Inter-bloc differential (interaction term β2):
  - The interaction terms between fragmentation measures and InterBloc are generally not statistically significant for aggregate financial institution and customer payments, implying no consistent differential effect of fragmentation on inter-bloc vs within-bloc aggregate flows (Table 6).
- Geopolitical risk:
  - No significant effect of an increase in geopolitical risks on customer payments (column 8; Geopolitical Risk coefficient 0.000 with standard error (0.004)).
  - Higher geopolitical risks are associated with an increase in financial institution inter-bloc payments (column 4; Geopolitical Risk×InterBloc = 0.027***, standard error (0.002)), potentially reflecting safe-haven dynamics.
- Exact coefficients and standard errors from Table 6 (selected):
  - Common Fragmentation (Financial Institutions): -0.055*** (0.016).
  - Common Fragmentation (Customers): -0.022*** (0.007).
  - Geopolitical Risk (Financial Institutions): -0.005 (0.004).
  - Geopolitical Risk×InterBloc (Financial Institutions): 0.027*** (0.002).
  - Geopolitical Risk (Customers): 0.000 (0.004).
  - Geopolitical Risk×InterBloc (Customers): 0.006 (0.009).

### Currency-level heterogeneity (Table 7)
- Analysis focuses on the common fragmentation index (due to high correlation among fragmentation measures). Results reported for five currencies: USD, EUR, GBP, JPY, CNY.
- USD-denominated financial institution payments:
  - Common Fragmentation = -0.041*** (0.015).
  - Common Fragmentation×InterBloc = -0.032** (0.016).
  - Geopolitical Risk×InterBloc = 0.030*** (0.008).
  - Interpretation: a 1 standard-deviation increase in common fragmentation associated with a 4.1 percent decline in USD-denominated financial institution payments; the decline is 3.2 percentage points larger for inter-bloc payments (column 1, Panel A).
- CNY-denominated financial institution payments:
  - Common Fragmentation = 0.138** (0.060).
  - Common Fragmentation×InterBloc = 0.676*** (0.229).
  - Geopolitical Risk×InterBloc = -0.515*** (0.159).
  - Interpretation: fragmentation is associated with increased CNY-denominated financial institution payments, with a substantially larger positive effect for inter-bloc payments — suggesting geoeconomic fragmentation may support a growing role for the CNY in cross-border payments (column 5, Panel A).
- EUR and GBP financial institution inter-bloc payments:
  - Common Fragmentation×InterBloc positive and significant for EUR and GBP (columns 2 and 3, Panel A), indicating increases in inter-bloc EUR- and GBP-denominated payments offset negative within-bloc (or non-aligned) effects.
- JPY:
  - Financial-institution inter-bloc payments negatively correlated with fragmentation (column 4, Panel A).
  - For customer payments, JPY shows some positive association between fragmentation and inter-bloc payments (column 4, Panel B).
- Geopolitical risk patterns by currency:
  - USD: increase in geopolitical risks associated with higher USD-denominated inter-bloc financial institution payments.
  - CNY: geopolitical risks associated with a decline in CNY-denominated inter-bloc financial institution payments.
  - GBP and JPY: increases in geopolitical risk offset lower within-bloc payments via increases in inter-bloc financial institution payments.
  - Customer payments: USD-denominated customer payments within the same bloc (or between U.S./Chinese mainland-aligned and non-aligned economies) are positively associated with an increase in geopolitical risks; GBP-denominated customer payments within the same bloc are negatively correlated with geopolitical risk.

### Transaction-size heterogeneity (Tables B.8 and B.9)
- The negative association between fragmentation and payments is primarily driven by large-value transactions (US$50 million and above):
  - US$50 million and above is the only transaction size with a negative and significant association between fragmentation and both financial institution and customer payments.
  - For this transaction size there is no differential inter-bloc effect, explaining an insignificant interaction term in the aggregate Table 6.
- Smaller and mid-sized transactions:
  - For smaller financial institution transactions (up to US$50K) and mid-sized transactions (US$25K–1M), increases in fragmentation are associated with disproportionately larger declines in payments between economies in different blocs.
- Currency-bucket drivers:
  - Divergent effects of fragmentation on USD-denominated and CNY-denominated payments are primarily driven by transactions in the US$50 million and above category (Table B.9).

### Network- and system-level context (selected stylized facts cited)
- Large-value transactions (US$50 million and above) account for:
  - over 60 percent of customer payments.
  - over 80 percent of financial institution cross-border payments.
- Aggregate trend over 2020–2024: greater connectivity and reduced concentration on average, but rising geoeconomic fragmentation associated with declines in cross-border payment values, particularly for large-value financial institution transactions.
- Sample-level standardization and controls: fragmentation and geopolitical risk series standardized within estimation sample; corridor and year fixed effects included as specified.

### Interpretations and implications highlighted in the chapter
- Rising geoeconomic fragmentation is associated with lower bilateral cross-border payment values, especially for large-value financial institution transactions.
- Fragmentation effects vary substantially across currencies and transaction sizes:
  - USD- and CNY-denominated payments display distinct and, at times, opposite patterns.
  - Fragmentation may be supporting the growing role of the CNY in cross-border payments in some corridors.
- Geopolitical risk can asymmetrically influence payment activity; increases in geopolitical uncertainty are associated with higher USD-denominated transactions in certain corridors, consistent with safe-haven motives.

### Suggested directions noted by authors
- Further research is needed on how evolving financial innovation—particularly crypto assets and stablecoins—may impact the international monetary system (IMS), including network dynamics and corridor-level drivers.
- Policymakers have a role in ensuring a stable and well-functioning cross-border payment network given its importance for trade and investment.

*Source: wpiea2025120-print-pdf (https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025120-print-pdf.pdf).*

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*Global Cross-Border Payments: A $1 Quadrillion Evolving Market? Working Paper No. WP/2025/120*

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_Source: https://www.imf.org/-/media/files/publications/wp/2025/english/wpiea2025120-print-pdf.pdf_