## wpiea2019046

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### I. Introduction and study objective
- Central banks issue and maintain a country’s currency; cash use is falling in many developed countries (Sweden: cash payments in retail transactions fell from 40 percent to 15 percent between 2010 and 2016; two-thirds of Swedish consumers say they can get by without cash).
- Cards, e-money, and mobile systems (e.g., Swish) have replaced many cash transactions.
- Study objective:
  - Estimate use of physical currency in 11 countries over 2006–2016 and forecast changes over the next 5 to 10 years.
  - Estimate current cash use via indirect and direct calculations fitted with a cubic spline; forecast cash shares using logistic curves.
  - Emphasis on demand for digital cash (CBDC) rather than only supply-side considerations.

### II. Scope, data, and measures
- Countries analyzed: Australia, China, Denmark, Germany, India, Japan, Netherlands, Norway, Singapore, United Kingdom (U.K.), United States (U.S.).
- Time period: 2006–2016 for historical estimates; forecasts to 2026 (5–10 years out).
- Key estimation approaches:
  - Simple indirect and direct calculations fitted with a cubic spline for historical series.
  - Logistic curves (reverse S-curve) for cash share forecasts.
  - Key model specification for linear trend: S_t = α + β t, where t = 2006, 2007, …, 2016.
- Four cash-use measures described:
  1. Currency in Circulation (CIC) to GDP ratio (CIC/GDP).
  2. RESIDUALHC = (HC – CARD – E-MONEY)/HC.
  3. CASHHC = (ATM + OTC cash)/HC.
  4. CASHSHARE (preferred market-for-cash measure) = (ATM + OTC cash)/(ATM + OTC cash + CARD + E-MONEY) — proper calculation would include X1 (checks, ACH/giro, instant payments) in denominator though X1 believed very small.

### III. Measurement caveats and data limitations
- CIC/GDP can be misleading because denominator should be the market for cash (consumption goods commonly bought with cash).
- RESIDUALHC overstates cash use because checks, ACH/giro, and instant payments (X1, X2) are not subtracted; X1 and X2 are unknown and differ across countries.
- CASHHC corrects numerator mismeasurement in RESIDUALHC but omits cash-back at POS.
- No data on value of cash withdrawn that is hoarded/held idle rather than spent.
- Payment diary “blown up” results may understate some national totals (example: U.S. debit card transactions: 37 billion from diary vs. 61 billion from national survey).

### IV. Historical trends (2006–2016) — main findings
- Average cash share declines across measures:
  - Remaining measures suggest average cash share falls by 1.3 to 2.2 percentage points (pp) per year.
- Estimated average annual reductions (slopes) 2006–2016:
  - RESIDUAL/HC: 1.3 pp per year.
  - CASH/HC: 1.4 pp per year.
  - CASHSHARE: 2.2 pp per year.
- Demographics:
  - Younger adults favor non-cash methods (cards, mobile); older adults favor cash.
  - Natural demographic replacement contributes to declining cash use.
- Policy implication:
  - Without significantly lower cost or improved convenience relative to existing substitutes, CBDC may at best replace current levels of cash use and likely less.

### V. Country-level reductions and levels (Table 1 preserved entries)
- Columns: RESIDUAL/HC Annual Change pp; CASH/HC Annual Change pp; CASHSHARE Annual Change pp; CASHSHARE Level in (2006) and in 2016; CASHSHARE Annual Change %
- Country-level figures (preserved exactly):
  - Australia: 1.2; 1.1; 1.6; (37)   21; 6
  - China: 17.1; -1.6; 3.6; (54)   18; 10
  - Denmark: 1.0; 2.2; 2.5; (47)   22; 7
  - Germany: 0.4; 1.5; 1.4; (84)   70; 2
  - India: 2.0; -1.7; 0.0; (45)   45; 0
  - Japan: 0.6; 1.5; 4.1; (64)   23; 9
  - Netherlands: 1.3; 0.9; 1.8; (49)   31; 5
  - Norway: 0.6; 0.9; 1.2; (22)   10; 8
  - Singapore: 1.5; 4.0; 3.1; (61)   30; 7
  - U.K.: 3.3; 0.5; 1.5; (39)   24; 5
  - U.S.: 1.4; 0.3; 1.1; (40)   29; 3
  - Average: 1.3; 1.4; 2.2; (49)   29; 6
- Additional table notes preserved:
  - For the preferred measure (CASHSHARE), the second to last column shows level for 2006 (in parenthesis) and 2016.
  - Highest level of cash use in 2016 was 70% for Germany (45% for India) while the lowest was 10% for Norway (23% for Japan).
  - Example interpretation: Australia cash use reduction of 1.6 pp over 2006–2016; average base for Australia of 29% yields an average percent reduction of 6% each year.
  - Countries where percent reductions fell faster than Australia: China, Denmark, Japan, Norway, and Singapore.
  - Countries where percent reductions fell slower than Australia: Germany, Netherlands, U.K., and U.S.; India showed no fall.

### VI. Cash withdrawals and CASHHC results
- CASHHC = (ATM + OTC cash)/HC; ATM + OTC cash assumed largely spent on household consumption.
- Empirical summary:
  - China and India show a rise in cash use by this measure; other nine countries show reductions.
  - Highest CASHHC in 2016: 36 percent for Germany (24 percent for Singapore).
  - Lowest CASHHC in 2016: 6 percent for Japan (7 percent for Norway).
  - Average reduction (excluding China and India): 1.4 pp per year.

### VII. Forecasting cash use to 2026 (CASHSHARE; logistic model)
- Forecast method:
  - Reverse logistic (symmetric logistic) model: ln((1 - S_t)/S_t) = a + b t; S’_t = 1/(exp(a’ + b’ t) + 1).
  - Historical series 2006–2016 fitted with cubic spline; logistic curve imposed for 2016–2026 forecasts.
  - Practical constraints: short series and absence of observed inflection points mean symmetric logistic used rather than Gompertz.
- Forecasted CASHSHARE values (2016 and 2026) and yearly percentage-point reductions (preserved exactly):
  - Australia: 2016 21, 2026 10, Yearly pp Reduction 1.1
  - China: 2016 18, 2026 3, Yearly pp Reduction 1.5
  - Denmark: 2016 24, 2026 9, Yearly pp Reduction 1.5
  - Germany: 2016 69, 2026 49, Yearly pp Reduction 2.0
  - India: 2016 46, 2026 46, Yearly pp Reduction 0
  - Japan: 2016 22, 2026 5, Yearly pp Reduction 1.7
  - Netherlands: 2016 29, 2026 14, Yearly pp Reduction 1.5
  - Norway: 2016 10, 2026 4, Yearly pp Reduction 0.6
  - Singapore: 2016 26, 2026 9, Yearly pp Reduction 1.7
  - U.K.: 2016 24, 2026 14, Yearly pp Reduction 1.0
  - U.S.: 2016 29, 2026 20, Yearly pp Reduction 0.9
  - Average: 2016 29, 2026 17, Yearly pp Reduction 1.4
- Forecast interpretation:
  - Two largest total reductions: Germany (20 pp) and tie between Japan and Singapore (17 pp).
  - Two smallest total reductions: India (0) and Norway (6 pp).
  - The average annual reduction over forecast period: 1.4 pp per year (total average reduction over 10 years is 13.5 pp).
  - Forecasted yearly reduction (1.4 pp) is almost two-thirds of observed yearly rate of CASHSHARE reduction over 2006–2016 (2.2 pp), consistent with S-curve deceleration toward minimal use.

### VIII. Drivers of cash decline and historical substitutions
- Major drivers: increased convenience, lower user cost, lower supplier cost, demographic change (younger cohorts favor non-cash).
- Historical substitutions illustrated:
  - Cash and checks → credit cards; paper to electronic card payments; paper giro to electronic giro; mobile phone-initiated payments; coins replacing bills; Internet-initiated 24/7 payments (e.g., Faster Payments in the U.K.).
- Regression evidence:
  - Simple linear regressions S_t = a + b t show high R^2 values (e.g., .89 for India and Singapore, .94 for the U.S., .97–1.00 for nine countries), indicating a strong fit of a linear time trend over 2006–2016.
- Demographic accounting:
  - Average (live) birth rate across the 11 countries: 1.2 percent a year; average death rate: 0.8 percent a year.
  - Population composition change modeled as C = 2 percent each year, producing a linear series similar to time (1, 2, 3, …, 11) and consistent with observed declines.

### IX. Benefits and costs of central bank digital currency (CBDC)
- Benefits of CBDC:
  - Reduction in cost of supplying cash (printing, fitness, vaults, distribution).
  - Possibility of greater user convenience depending on access method (cards, mobile, Internet).
  - If digital cash substitutes for currency, seigniorage revenues could be retained by central bank.
  - CBDC could provide a risk-free alternative during private payment system failures and check market power of card providers.
  - Digital cash accessible without travel to ATMs/branches would be more convenient than withdrawing physical cash.
- Costs, risks, and trade-offs:
  - Costs depend on implementation: debiting a user’s bank deposit account is lower cost; new central bank deposit accounts paying interest would raise central bank expense.
  - Shifting bank deposits to central bank could reduce banks’ low-cost funding, raise funding costs, lower bank credit creation; banks may respond by increasing risk exposure.
  - Non-bank credit creation could expand, potentially with less supervision and higher systemic risk.
  - Adoption incentives: convenience alone may be insufficient; interchange fees matter. If interchange fee for digital cash is zero, retailers would have incentive to encourage use.
  - Political issues if central bank supplies digital cash to retailers/billers financed by tax revenues, potentially competing with private banks.
- Policy implication on timing:
  - Introducing CBDC earlier could reduce budgetary effects from lost seigniorage as cash use declines; issuing digital cash before private substitutes dominate may preserve policy options.

### X. Policy recommendations and implications
- Measurement and monitoring:
  - Use market-for-cash denominators (CASHSHARE) where possible; be cautious with CIC/GDP and RESIDUALHC due to denominator and missing-instruments biases.
- CBDC design and adoption:
  - To attract users, CBDC must offer convenience at least comparable to bank debit cards and ideally lower acceptance costs for retailers (zero interchange).
  - Consider limiting central bank balance-sheet disruption by linking digital cash to debit of bank deposit accounts rather than creating large central-bank retail deposit balances.
  - Evaluate socio-economic cost-benefit and potential banking sector effects before issuance (country practices: Denmark concluded risks outweigh benefits; Norway conditions issuance on avoiding impairment of bank credit provision).
- Contingency and resilience:
  - CBDC could serve as backup payment network in disasters/operational failures, but alternatives include strengthening survivability of private payment networks (duplicate processing centers) and antitrust enforcement.
- Political economy:
  - Providing CBDC services to retailers/billers without charge (financed by tax revenues) may be politically contentious due to competition with private banks.

### XI. Summary and conclusions — key numerical takeaways
- Across measures, cash use declining with estimated average annual reductions around:
  - 1.3 pp per year (RESIDUALHC),
  - 1.4 pp per year (CASHHC, excluding China and India),
  - 1.3 to 2.2 pp per year across remaining measures.
- Forecast to 2026 (CASHSHARE): average 2016 value 29, 2026 value 17, average Yearly pp Reduction 1.4.
- Demographic change is a major driver: younger cohorts’ preference for non-cash explains a large share of the 1.3–2.2 pp yearly average reduction.
- For CBDC to succeed on demand grounds, it must offer incentives beyond parity with current bank debit card functionality.

*Source: wpiea2019046 (IMF working paper content unit).*

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

### References

### I. Introduction
- Central banks issue and maintain a country’s currency.
- In many developed countries, currency use is falling; Sweden example:
  - Share of cash payments in retail transactions fell from 40 percent to only 15 percent between 2010 and 2016.
  - Two-thirds of Swedish consumers say they can get by without cash (Sveriges Riksbank, 2017).
- Cards, e-money, and mobile systems (e.g., Swish) have replaced many cash transactions.
- Some central banks are investigating central bank digital currency (CBDC) as a possible replacement for physical cash.
- Study objective:
  - Estimate use of physical currency in 11 countries over 2006–16 and forecast changes over the next 5 to 10 years.
  - Estimate current cash use via indirect and direct calculations fitted with a cubic spline; forecast cash shares using logistic curves.
- Emphasis: focus on demand for digital cash (CBDC) rather than only supply-side considerations.

### II. Scope and data
- Countries analyzed: Australia, China, Denmark, Germany, India, Japan, Netherlands, Norway, Singapore, United Kingdom (U.K.), United States (U.S.).
- Time period: 2006–2016 for current estimates; forecasts for next 5 to 10 years.
- Estimation approaches:
  - Simple indirect and direct calculations fitted with a cubic spline for historical series.
  - Logistic curves for cash share forecasts.
- Key model specification: St = α + βt, where St is the share of cash payments, α is intercept, β is slope, and t is time (2006, 2007, ..., 2016).

### III. Main findings on trends (historical 2006–2016)
- Average cash share declines across measures:
  - Remaining measures suggest average cash share falls by 1.3 to 2.2 percentage points (pp) per year.
- Forecasts (Section III summary):
  - Average cash forecasted to fall by 1.4 percentage points a year over 2016–2016.
- Demographics:
  - Younger adults favor non-cash methods (cards, mobile) over cash; older adults favor cash.
  - Natural demographic replacement contributes to declining cash use.
- Policy implication:
  - Without significantly lower cost or improved convenience relative to existing substitutes, CBDC may at best replace current levels of cash use and likely less.

### IV. Measuring cash use — four approaches and comments
- Four measures described:
  1. Currency in Circulation (CIC) to GDP ratio.
  2. ResidualHC = (HC – CARD – E-MONEY)/HC, where:
     - HC = household consumption,
     - CARD = value of all debit and credit card payments,
     - E-MONEY = value of private stored value cards or mobile phones with value stored on a chip.
  3. CASHHC = (ATM + OTC cash)/HC, where ATM + OTC cash is cash withdrawn from ATMs and over the counter.
  4. Preferred measure: value of all cash withdrawals as a ratio to cash plus the value of payment instruments that substitute for cash (cards plus e-money) — reflects the market for cash.
- Payment diary point estimates are also presented where available.
- Notes on deficiencies:
  - CIC/GDP is widely used but can be misleading because denominator should be the market for cash (consumption goods commonly bought with cash).
  - ResidualHC overstates cash use because checks, ACH/giro, and instant payments are not subtracted (unknown X1 and X2 components).
  - CASHHC corrects numerator mismeasurement in ResidualHC but omits cash-back at POS.
  - Time-series of cash withdrawals approximates a national-level payment diary.

### V. Currency in Circulation to GDP (CIC/GDP)
- Presentation:
  - CIC/GDP shown for 11 countries using billions of purchasing power parity adjusted U.S. dollars.
  - Annual observations fitted with a cubic spline.
- Empirical summary:
  - Only 3 of the 11 countries show falling CIC/GDP over 2006–16: India, China, and Norway.
  - Other eight countries show increasing CIC/GDP (Japan, Singapore, Germany, Netherlands, U.S., U.K.) or approximately no change (Australia, Denmark).
- Critique:
  - CIC/GDP is rejected as the primary measure because the denominator should reflect the value of consumption goods commonly purchased with cash.

### VI. ResidualHC measure (Household Consumption Minus Card and E-money)
- Definition: RESIDUALHC = (HC – CARD – E-MONEY)/HC.
- Limitations:
  - Overestimates cash use because it excludes checks, ACH/giro, and instant payments (components X1 and X2).
  - X1 and X2 unknown and likely differ across countries.
- Empirical results (2016, excluding China due to data issues):
  - Highest cash share in household consumption: 84 percent for Germany (82 percent for Japan).
  - Lowest: 31 percent for the U.K. (39 percent for Norway).
  - Average reduction for 10 countries: 13.3 pp over 10 years, or 1.3 pp per year.
- Comment:
  - Residual approach overstates intercept but year-to-year slope variation is small; cross-country average slope of 1.3 pp per year may mix actual reduction and mismeasurement.

### VII. Cash withdrawals as share of household consumption (CASHHC)
- Definition: CASHHC = (ATM + OTC cash)/HC.
- Rationale: ATM + OTC cash assumed largely spent on household consumption and approximates national payment diary cash use.
- Empirical summary:
  - China and India show a rise in cash use by this measure; other nine countries show reductions.
  - Highest share in 2016: 36 percent for Germany (24 percent for Singapore).
  - Lowest share in 2016: 6 percent for Japan (7 percent for Norway).
- Average reduction (excluding China and India): 1.4 pp per year.

### VIII. Forecasting cash use and implications for CBDC
- Forecasting approach: logistic curves; historical series often too short to show full S-curve dynamic; trends are slightly curvilinear downward.
- General forecast: modest annual declines in cash shares (examples: average declines reported above).
- Policy considerations:
  - CBDC access may be more convenient than physical cash but equates to bank debit card functionality unless additional incentives exist.
  - If cash substitutes become ubiquitous, demand for CBDC could be weak.
  - If cash is important for monetary policy or as a risk-free alternative during operational failures of private payment methods, introducing CBDC earlier may be preferable before substitutes dominate.

### IX. Summary points
- Across measures, cash use has been declining in many countries, with estimated average annual reductions around:
  - 1.3 pp per year (residual measure),
  - 1.4 pp per year (CASHHC, excluding China and India),
  - 1.3 to 2.2 pp per year across remaining measures.
- Measurement choice matters because levels differ substantially:
  - RESIDUALHC produces higher levels (intercept overstatement) than CASHHC.
- Demographic change (younger cohorts favoring non-cash payments) is a major driver of declining cash use.
- CBDC adoption faces demand-side constraints unless it offers significantly lower cost or greater convenience than existing substitutes.

*Source: wpiea2019046 - References (IMF).*

### 1.3 percentage point reduction found for the residual method. This suggests that the intercept

### wpiea2019046 - 1.3 percentage point reduction found for the residual method. This suggests that the intercept

### Measurement approach and definitions
- Residual method: a 1.3 percentage point reduction found for the residual method. This suggests that the intercept measurement bias of the residual method has little effect on the slope.
- Preferred market-for-cash denominator: restrict denominator to consumption goods purchased with cash and current direct substitutes for cash (cards, e-money) plus the value of check, ACH, giro, and instant payments that substitute for cash in consumption (X1). Alternative formulation noted: (ATM + OTC cash)/HC – X2.
- CASHSHARE (market focus) defined exactly as: CASHSHARE = (ATM + OTC cash)/(ATM + OTC cash + CARD + E-MONEY).
  - Proper calculation would be: (ATM + OTC cash)/(ATM + OTC cash + CARD + E-MONEY + X1), although X1 is believed to be very small.
- Data limitations:
  - No information on the value of cash withdrawn that is held idle for hoarding or precautionary purposes rather than spent on consumption.
  - Lack of information on the value of check, ACH/Giro, and instant payments used to purchase consumption goods (X1).
  - Payment diary “blown up” results may understate some national totals (example: U.S. debit card transactions).

### Main findings on trend and levels of cash use (2006–2016)
- Estimated average annual reductions in cash use (slopes) for 2006–2016:
  - 1.3 pp per year for the first measure (RESIDUAL/HC).
  - 1.4 pp per year for the second measure (CASH/HC).
  - 2.2 pp per year for the third measure (CASHSHARE).
- Conclusion: the average reduction in cash use is quite similar, between 1.3 and 2.2 pp a year.
- Note on cross-country interpretation: similar driving forces may be behind reductions (possibly demographic change), but percentage changes differ because bases (levels) differ across countries.

### Table 1: Reductions in Cash Use Over 2006–16 (selected entries preserved exactly)
- Columns in table: RESIDUAL/HC Annual Change pp; CASH/HC Annual Change pp; CASHSHARE Annual Change pp; CASHSHARE Level in (2006) and in 2016; CASHSHARE Annual Change %
- Country-level figures (rows preserved exactly as in source):
  - Australia: 1.2; 1.1; 1.6; (37)   21; 6
  - China: 17.1; -1.6; 3.6; (54)   18; 10
  - Denmark: 1.0; 2.2; 2.5; (47)   22; 7
  - Germany: 0.4; 1.5; 1.4; (84)   70; 2
  - India: 2.0; -1.7; 0.0; (45)   45; 0
  - Japan: 0.6; 1.5; 4.1; (64)   23; 9
  - Netherlands: 1.3; 0.9; 1.8; (49)   31; 5
  - Norway: 0.6; 0.9; 1.2; (22)   10; 8
  - Singapore: 1.5; 4.0; 3.1; (61)   30; 7
  - U.K.: 3.3; 0.5; 1.5; (39)   24; 5
  - U.S.: 1.4; 0.3; 1.1; (40)   29; 3
  - Average: 1.3; 1.4; 2.2; (49)   29; 6
- Additional table notes preserved:
  - For the preferred measure (CASHSHARE), the second to last column shows the level of cash use for 2006 (in parenthesis) and 2016.
  - Highest level of cash use in 2016 was 70% for Germany (45% for India) while the lowest was 10% for Norway (with 23% for Japan).
  - Average percentage point changes for the CASHSHARE measure are shown in the third to last column.
  - Example: Australia cash use reduction of 1.6 pp over 2006-2016; average base for Australia of 29% yields an average percent reduction of 6% each year.
  - Countries where percent reductions in cash use fell faster than Australia: China, Denmark, Japan, Norway, and Singapore.
  - Countries where percent reductions fell slower than Australia: Germany, Netherlands, U.K., and U.S.; India showed no fall.

### Interpretation, anomalies, and data cautions
- Intercept (level) mismeasurement occurs to differing degrees due to missing data; smallest mismeasurement occurs for preferred measure.
- Mis-measured intercepts have little effect on estimated trend (slope).
- Exclusions and anomalies in averaging:
  - “Impossible results (greater than a 100% reduction in cash use for China), negative values (rising cash use for China and India), and no net change in cash use (India) reflected in Table 1 for, respectively, each of the three measures shown, were excluded when the average changes in cash use were computed.”
  - Cash use results for China and India seem to have unresolved problems.
- Payment diaries:
  - Payment diaries can provide point estimates when “blown up” to reflect adult population but may undercount compared to national surveys (example: U.S. debit card transactions: 37 billion from diary vs. 61 billion from national survey).
  - Greene and Schuh (2017) payment diary finding (U.S. example) preserved exactly: average of 14 cash payments per month with an average value of US$22; approximate national totals computed as 42.3 billion cash transactions a year and US$930.6 billion total value (calculation steps shown).

### Forecasting cash use and policy implications
- Forecast shape: annual observations of cash use over time would resemble a reverse Gompertz S-curve—initial fall, acceleration, inflection point, then deceleration toward very small cash use.
- Consequences as cash use declines:
  - Currency withdrawn from circulation (usually highest values first).
  - Average fixed costs to maintain currency fitness per 1,000 currency units would rise.
  - As currency use declines and is returned to the central bank, it no longer generates seigniorage revenues.
  - Explicit government borrowing equal to the face value of currency withdrawn would occur.
- Policy implication: central banks could minimize budgetary effects of losing seigniorage by issuing digital cash earlier rather than later, when cash may fall to minimum levels.

*Source: Author’s calculations and text from the provided PDF content.*

### Box 1. Payment Diary Studies

### Box 1. Payment Diary Studies

### Payment diary studies — representative cash-use findings
- Payment diary studies are relatively new and typically available for one or just a few years; several have been completed or commissioned by central banks.
- Representative results for cash use (both volume and value shares) from diary studies:
  - Australia 2016: Volume 37, Value 18
  - Canada 2013: Volume 44, Value 23
  - Denmark 2017: Volume 23, Value 16
  - Germany 2017: Volume 74, Value 48
  - Netherlands 2016: Volume 45, Value 27
  - Norway 2017-18: Volume 11, Value 5
  - Sweden 2018: Volume 13, Value n.a
  - U.S. 2017 (2015): Volume 27, Value (9)
- Diary measures reflect POS use of cash relative to card and e-money (CASHSHARE), but also include values of ACH/GIRO transactions for bill payments and checks in some countries; not all included payments would commonly be substituted by cash and are excluded from the cash share computations shown here.
- Note: For U.S., share of cash values for 2017 is not available so survey results from 2015 are used. Share of cash value is not available for Sweden.

*Sources cited in the original table.*

### Forecast model (methodology)
- Purpose: Forecast what cash use might look like in 11 countries 5 or 10 years out.
- Model choice and justification:
  - Logistic and Gompertz S-curves are appropriate for adoption/dispersion of new technologies; Meade and Islam (1995) found standard logistic and Gompertz S-curves outperform more complicated models.
  - A standard Gompertz S-curve: ln(S_t/(1 – S_t)) = a + b t + e_t, where S_t is share of electronic payments and b is diffusion slope.
  - For forecasting a falling cash share, the dependent variable is reversed and the estimated logistic curve used is:
    - (1) ln((1 - S_t)/S_t) = a + b t + e_t
  - Predicted cash shares S’_t are found from exp(a’ + b’ t) = (1 - S’_t)/S’_t, leading to:
    - S’_t = 1/(exp(a’ + b’ t) + 1)
- Practical considerations and limitations:
  - Degrees of freedom are low; fitting a linear trend would give a similar forecast.
  - The non-linear, symmetric logistic and asymmetric Gompertz curves require more data (observed inflection points) than available; consequently, only the linear, symmetric logistic model in (1) is estimated.
  - The pattern of initial cash use is used via symmetry around its inflection point to predict the remaining replacement pattern.

### Forecast results (CASHSHARE measure)
- Only the CASHSHARE measure (preferred measure) is forecasted.
  - CASHSHARE = S_t or S’_t = (value of ATM + OTC cash withdrawals)/(value of ATM + OTC cash withdrawals + the values of card and e-money transactions).
- General pattern:
  - Observed cash shares over 2006–16 were fitted using a cubic spline; the forecasting procedure imposes a reverse S-curve functional form estimated over 2006–2016 and applied to 2016–2026. This can create a break in slope in 2016 where observed series and assumed functional form differ.
  - All cash shares, except for India, are forecast to fall over 2016 to 2026.
  - Norway and Singapore had cash shares in the market for cash of 10 percent or less in 2016. Forecast for 2026 adds Australia, China, Denmark, and Japan to this group (resulting in six out of eleven countries at 10 percent or less in 2026).
- Table of predicted CASHSHARE values for 2016 and 2026 and yearly percentage-point reductions:
  - Australia: 2016 21, 2026 10, Yearly pp Reduction 1.1
  - China: 2016 18, 2026 3, Yearly pp Reduction 1.5
  - Denmark: 2016 24, 2026 9, Yearly pp Reduction 1.5
  - Germany: 2016 69, 2026 49, Yearly pp Reduction 2.0
  - India: 2016 46, 2026 46, Yearly pp Reduction 0
  - Japan: 2016 22, 2026 5, Yearly pp Reduction 1.7
  - Netherlands: 2016 29, 2026 14, Yearly pp Reduction 1.5
  - Norway: 2016 10, 2026 4, Yearly pp Reduction 0.6
  - Singapore: 2016 26, 2026 9, Yearly pp Reduction 1.7
  - U.K.: 2016 24, 2026 14, Yearly pp Reduction 1.0
  - U.S.: 2016 29, 2026 20, Yearly pp Reduction 0.9
  - Average: 2016 29, 2026 17, Yearly pp Reduction 1.4
- Specific quantitative outcomes and interpretation:
  - Two largest reductions: Germany (20 pp) and a tie between Japan and Singapore (17 pp).
  - Two smallest reductions: India (0) and Norway (6 pp).
  - The average annual reduction over the forecast period is 13.5 pp (total average reduction over 10 years). Except for Germany and India, most countries are near the average cash share reduction of 1.4 pp a year.
  - The forecasted yearly reduction (1.4 pp) is almost two-thirds of the observed yearly rate of CASHSHARE reduction over 2006-2016 (2.2 pp); the slower forecasted decline is consistent with the reverse S-curve assumption approaching saturation (zero or minimal use).
- Notes on model behavior:
  - If a linear projection were used cash use could become negative; the logistic curve avoids this.
  - The curves would look connected and smooth over 2006–26 if (1) were re-estimated using observed S_t plus forecasted S’_t, but that would hide how closely observed data align with assumed functional form.

### Past changes in payment use (historical substitutions)
- Major historical shifts and drivers (convenience, user cost, supplier cost):
  - (i) Cash and Checks to Credit Cards:
    - Checks and giro transactions replaced cash for payroll and bill payments historically.
    - Traveler’s checks and Diner’s Club led to credit cards; traveler’s check cost about 1 percent of value (e.g., US$1 per US$100).
    - Cards spread to Europe and elsewhere, reducing cash and check use; interchange fees became significant retailer costs.
  - (ii) Paper Credit Card Slips to Electronic Payments:
    - Paper slips required deposit at banks; electronic card payments at terminals increased convenience and lowered issuer processing costs, leading to debit cards as electronic analogs of checks.
  - (iii) Paper Giro Payment Orders to Electronic Giro Payments:
    - Europe shifted paper giro orders to electronic payments, speeding payments, reducing float, and lowering costs.
  - (iv) Mobile Phone-Initiated Payments:
    - Many card payments are now initiated by mobile phones; in some countries stored-value mobile payments substitute for cash (notably in regions with limited banking/ATM access, especially Africa). In China, mobile phone payments are tied to the two largest suppliers of products purchased over the Internet and extended to retail stores.
  - (v) Coins to Replace Currency:
    - Canada and the U.S. had different experiences replacing C$1 and US$1 bills with coins. Canada removed the C$1 bill, encouraging acceptance of the C$1 coin; the U.S. did not remove the US$1 bill and now has over US$1 billion of unused US$1 coins in Federal Reserve vaults.
    - Manufacturing cost cited as US$.30 while face value is $1.
  - (vi) Internet-Initiated 24/7 Payments:
    - The U.K. adopted Faster Payments (immediate or instant payments) to improve check system efficiency and speed; Faster Payments enable Internet-initiated credit transfers 24/7 with immediate crediting to receiver and slightly delayed back-office settlement. For person-to-person payments, it has already replaced many cash payments.

- Common attribute across innovations:
  - Significant increase in user or retailer/business convenience, often with no apparent long-term increase in user or supplier cost; in many cases the primary goal was reduced supplier and business cost.
  - For cards versus cash, increased convenience is key (no need to go to an ATM or bank). Retailers and billers typically cover direct card supply and processing costs; card costs are often large for retailers (example: cost to U.S. merchants for accepting Visa and MasterCard credit cards in 2017 was US$ 43 billion).

### Why cash is falling (drivers and explanatory power)
- Time as an explanatory factor:
  - Many plotted cash shares for CASHSHARE over 2006–16 are almost straight lines; passage of time (t) over 2006–16 is represented as a straight series (1, 2, 3, ..., 11).
  - Simple regression S_t = a + b t yields high R^2 values: .89 for India and Singapore, .94 for the U.S., and between .97 and 1.00 for the remaining nine countries — indicating a strong fit, albeit with small sample sizes.
- Demographics and cohort effects:
  - Surveys show younger adults use cards and mobile phones more and thus use less cash.
  - Average (live) birth rate across the 11 countries is 1.2 percent a year while average death rate is 0.8 percent a year.
  - As younger adults enter and older adults leave the population, the average composition changes by 2 percent a year.
    - Demographic change modeled as C = 2 percent each year: for 2006 it is C x 1, for 2007 it is C x 2, … over 11 years it is C x (1, 2, 3, ..., 11), forming a linear series like time 1, 2, 3, ..., 11.
  - For individual countries the sum of birth rate and death rate ranged from 1.3 percent in 2006 (Singapore) to [text truncated in source].

*Source: Excerpted content from the provided IMF working paper unit.*

### 2.6 percent (India). For both Denmark and Norway it was 2 percent in 2006. The cross-

### VI. BENEFITS AND COSTS OF CENTRAL BANK DIGITAL CURRENCY

### Demographic change and trends in cash use
- Cross-country average cash use for 2006 was 1.98 percent (rounds to 2 percent).  
- Demographic change over all 11 countries, and for each country individually, is a linear series; regressing S_t = a + b (birth rate + death rate) yields high R2 values comparable to regressing on time (t).  
- Two supporting facts for the demographic explanation:
  - Surveys show young adults use more cash substitutes and less cash than older adults.
  - Population composition change (new entrants plus exits) works to decrease cash use, though the rate varies across countries.
- Card and mobile phone payments have become so popular in some countries that some retailers actively discourage cash payments; accepting cash requires employees to account for receipts (and poses robbery temptation).  
- Instant payments via Internet and mobile phones tied to deposit accounts, and a CBDC with lower cost of acceptance than cards, could attract retailers and billers.

### A. Benefits of digital cash (CBDC)
- Two important benefits:
  - Reduction in the cost of supplying cash to the public (printing, maintaining fitness, vaults, distribution).
  - Possibility of greater user convenience depending on access method.
- If digital cash substitutes for currency, seigniorage revenues (difference between costs and face value) would be retained if digital cash replaces currency.
- Convenience considerations:
  - Little improvement if users must travel to ATMs/branches to reload digital cash.
  - Central bank–issued digital cash cards could be accepted at POS like debit cards; transactions could debit a user’s bank deposit account or allow cash storage on the card (up to a level) similar to cash back.
  - Accessing digital cash would be less costly for banks, supporting the argument that no bank fees should be assessed for processing these transactions.
- Digital cash supplied through central bank deposits (accessible via card, mobile, or Internet) would:
  - Be more convenient than withdrawing cash today.
  - Provide presumed safety of deposits (central banks cannot fail), though effective deposit insurance for banks would remove this advantage.
  - Allow processing independently from privately-operated centers, enabling an independent substitute payment network in events of national disasters or private-sector operational disruptions.
- Potential for greater monetary control:
  - Central bank could set interest paid on its deposits and possibly reduce it below the zero lower bound.
  - To induce banks to pay negative rates on customer deposits, moral suasion or temporary regulation might be required.
  - If significant cash remained, fees on currency withdrawal might be needed; withdrawal of digital cash would also have to be limited or charged for.
- CBDC may check market power of card providers and serve as backup payment network; however, alternatives like duplicate processing centers (Target, Fedwire) and disaster recovery already exist for large-value transfers.

### B. Costs of digital cash (CBDC)
- Costs depend on structure and implementation:
  - Lower overall expense if digital cash debits a user’s bank deposit account (preserves bank interest, lowers central bank operating cost).
  - Markedly higher expense if processing occurs through new central bank deposit accounts; paying interest on central bank deposits would increase expense (offsettable by investing funds in government securities).
  - Paying interest is likely necessary to attract deposits away from banks.
- Risks and systemic effects:
  - Significant shift of bank deposits to the central bank would reduce banks’ low-cost funding, raise funding costs, and lower bank credit creation.
  - Banks may respond by marginally increasing risk exposure to preserve spreads.
  - Reduced bank credit creation could be offset by expanded non-bank financial firm credit creation; non-bank firms may be less supervised and take riskier positions.
- Adoption incentives and pricing:
  - Increased convenience alone may be insufficient to induce users to switch from bank debit cards to CBDC.
  - Interchange fees matter: no interchange fee for cash; if interchange fee for accepting digital cash is zero, retailers would have incentives to encourage use.
  - Retailer expense of accepting digital cash would be less than current cost to accept physical cash.
  - Providing digital cash without charge to retailers/billers (financed by tax revenues) could raise political issues if central banks compete with private banks.
- Historical note:
  - Prior efforts (reloadable cash card experiment in Europe) failed due to lack of perceived need when cash was already available.

### Box 2 — Central Bank Digital Currency studies in selected countries (summary)
- Canada: Bank of Canada analytical work on digital depository receipt and Project Jasper; cross-border interbank payments cooperation with Bank of England and MAS.  
- China: People’s Bank of China established the Institute of Digital Money in 2017; investigating new payment features reportedly superior to private digital cash (specifics not disclosed).  
- Denmark: Danmarks Nationalbank concludes risks of issuing CBDC outweigh potential societal benefits; no plans to issue digital cash.  
- Norway: Any decision would follow socio-economic cost-benefit analysis; will continue issuing cash if demanded; digital cash structured to avoid impairing banks’ ability to provide credit if issued.  
- Singapore: Project Ubin experiments with digital representations of Singapore dollar for domestic interbank payments, delivery versus payment against tokenized assets, and cross-border payments.  
- Sweden: No decision to issue CBDC; pilot (e-krona) planned to assess technical, legal, balance-sheet, monetary policy impacts; e-krona targeted for smaller payments, would not pay interest initially, and offer off-line payment features for some groups.  
- United Kingdom: Bank of England explored macroeconomic impact, design principles, and balance sheet implications of central bank–issued digital currencies.

### VII. Summary and conclusions — key findings and projections
- Four estimates of physical cash use in 11 countries over 2006–16 are presented; one is rejected as misleading, one used to forecast to 2026.
- Three direct measures of cash use (each missing certain unavailable data) are fitted with cubic splines; they suggest average cash use across 11 countries is falling by an average of 1.3 percent to 2.2 percent a year.
- Logistic curves forecast cash share out to 2026 with the average reduction slowing to 1.4 percent a year (slower reduction due to the functional form used).
- Without a digital cash alternative, private-bank–tied substitute instruments could almost wholly replace cash over time.
- For CBDC to succeed there must be incentives to adopt it:
  - For users: greater convenience (avoiding ATMs/branches). But such convenience makes CBDC only as convenient as a bank debit card.
  - Absent additional incentives, the upper limit to demand for CBDC is likely below current physical cash levels.
- Demographics as a driver:
  - Younger adults prefer non-cash payments; as younger adults enter and older adults exit the population, this changes average population composition by 2 percent annually and reduces overall cash use.
  - Demographic change and younger cohorts’ non-cash preference can explain the 1.3 percent to 2.2 percent yearly average reduction in cash use across the eleven countries.
  - The younger cohort shows the strongest preference for non-cash payments, implying long-run viability of CBDC would require changing their preferences.
- Possible policy instruments to encourage CBDC adoption:
  - Central banks could provide CBDC at no cost to users or to retailers/billers (zero interchange fee), potentially encouraging retailer-driven adoption.
  - Financing central bank competition with private banks via tax revenues could be politically contentious.
- Implications for related policy goals:
  - CBDC could provide (i) an alternative substitute payment network for disasters/operational failures and (ii) a check on market power of private payment suppliers—but these goals depend on long-term viability of CBDC.
  - Alternatives include ensuring survivability of private payment networks (e.g., duplicate processing centers like Target and Fedwire) and stronger antitrust enforcement comparing costs with prices for payment services.

*Source: Excerpt from VI. Benefits and Costs of Central Bank Digital Currency and VII. Summary and Conclusions (wpiea2019046).*

### REFERENCES

### wpiea2019046 - REFERENCES

### Major literature and thematic coverage
- References focus on digital currencies, central bank digital currencies (CBDC), cash usage, payment systems, and payment statistics.
- Key thematic areas apparent from the references:
  - Central bank digital currencies and design/implications (e.g., Barrdear and Kumhof (2016); Barontini and Holden (2019); Bech and Garratt (2017); Mancini-Griffoli et al. (2018); Engert and Fung (2017); Fung and Halaburda (2016); Kumhof and Noone (2018)).
  - Payment system infrastructure, speed, and distributed ledger projects (e.g., Bech, Shimizu, and Wong (2017); Committee on Payments and Market Infrastructures publications; Project Jasper; Project Ubin; Deloitte and Monetary Authority of Singapore).
  - Empirical studies of consumer cash usage and payment choice across countries (e.g., Bagnall et al. (2014); Esselink and Hernández (2017); Greene et al.; Gerdes et al. (2016); Reserve Bank of Australia studies; country central bank studies).
  - Policy-oriented analyses on phasing out cash, negative interest rates, shadow economy, and implications for government policy (e.g., Rogoff (2015); Buiter (2009); Humphrey (2015); Schneider et al. (2015)).

### Data sources and methodology (Appendix I)
- Primary data sources used:
  - BIS, ECB, national central banks, and national statistical offices (CPMI, 2017a; ECB, 2017; Danmarks Nationalbank; Norges Bank; and Statistics Denmark).
  - Global Cash Index (Payments.com, various issues) for ATM/OTC cash withdrawal information for Australia, Germany, India, U.K., U.S.
  - Danmarks Nationalbank for Denmark ATM/OTC cash withdrawal estimated values.
  - IMF International Financial Statistics for gross domestic product and currency in circulation (with exceptions noted: for Singapore currency in circulation from Monetary Authority of Singapore; for India and the United Kingdom notes and coins in circulation outside banks from the BIS).
  - World Bank national accounts data and OECD national accounts data files for household final consumption expenditure (including the expenditures of nonprofit institutions serving households).
- Sample coverage and temporal scope:
  - Eleven countries: China, Denmark, Germany, India, Japan, Korea, Norway, Singapore, Sweden, United Kingdom, and United States.
  - Annual data obtained for the period 2006 to 2016.
  - National currencies converted to US dollars using the PPP conversion factor from the 2011 International Comparison Program Database of the World Bank.
- Methodological standards followed:
  - BIS methodology for defining payment instruments (cards, credit transfers, checks, direct debits, electronic money) and ATM cash withdrawal was followed.
  - Note: The CPMI has revised the methodology for compiling statistics on payments and FMIs (CPMI, 2017b). The revised methodology will include more information on the role of non-banks, on online and contactless payments and on fast payments; clarifies how to count debit and credit cards; and clarifies which retail cashless payments count as domestic and which as cross-border.

### Data adjustments, imputations, and limitations
- Adjustments made to allow cross-country comparisons and account for missing data:
  - For Japan:
    - Missing value for electronic money for 2006 was estimated using logarithmic growth rates.
    - Missing values for cards for 2010–11 were calculated with linear interpolation.
- Proxy choices and approximations:
  - Card payments and electronic money were used to approximate the major cash substitutes used in household final consumption expenditures due to data availability and differences in payment instrument usage across countries.
  - Cards include domestically-issued cards for local and overseas purchases, and excludes local purchases from foreign-issued cards.
  - A card which has several functions (cash, debit, delayed debit, credit, and electronic money) should not be added to avoid the risk of double counting. In cases where certain functions are not indicated separately but grouped together, this should be noted (CPMI, 2017a).
- Cautions on adding other instruments without adjustments:
  - Adding checks, credit transfers, and direct debits to card and e-money values would likely exceed the value of household final consumption unless adjusted, because:
    - Checks, credit transfers, and direct debits are widely used for business and government transactions and for large-value items not commonly paid in cash.
    - These instruments often include big-ticket items (e.g., financial market transactions, purchase of land and housing) and large-value interbank or government/business payments.
  - Specific recommended adjustments (not implemented in this report) to better approximate household-use values:
    - Checks: multiply the average value per bank card by the number of check transactions for a given year to approximate personal checks and exclude relatively large-value business or corporate checks.
    - Credit transfers: exclude large-value interbank payments.
    - Direct debits: exclude large-value payments that originate from government, businesses, or enterprise collections.
  - Note: CPMI figures related to credit transfers have not been calculated due to the relatively large value of these transactions and cross-country comparability concerns (CPMI, 2017a).
- Treatment of mobile payments:
  - Most mobile phones are not considered a payment instrument but a payment solution associated with a card.
  - Mobile payment offerings could connect a user's phone number to their bank account, making account-to-account settlements possible.
  - Differentiation of mobile payments as a card or credit transfer transaction is important to avoid double counting in statistical reporting.

### Appendix II — Cash use indicators (2006–2016)
- Appendix II presents eleven figures illustrating how cash use varied in 11 countries using three different measures.
- Countries covered in Appendix II figures: Australia, China, Denmark, Germany, India, Japan, Netherlands, Norway, Singapore, the U.K., and the U.S.
- For each country and measure, the figures show:
  - The beginning (2006) and ending (2016) cash shares.
  - The percentage point change between 2006 and 2016.
- The CASHSHARE measure is also shown in Figures 2A and 2B to facilitate cross-country comparison.

*Sources: References list; Appendix I and Appendix II (data sources and notes) as provided in the content unit.*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wpiea2019046.pdf_