the future of cash: falling legal use and implications for government policy

Int. Fin. Markets, Inst. and Money 14 (2004) 221–233

The future of cash: falling legal use and implicationsfor government policy

David Humphreya,∗, Aris Kaloudisb,1, Grete Øwreb,2

a Department of Finance, School of Business, Florida State University, Tallahassee, FL 32306-1042, USAb Norges Bank, Bankplassen 2, P.O. Box 1179 Sentrum, N-0107 Oslo, Norway

Received 10 November 2002; accepted 23 July 2003

Abstract

As legal use of cash falls with the expansion of privately-issued payment cards, governments loseseigniorage benefits and revenues will be needed to redeem currency. To address this issue, one countryis considering replacing cash with government-issued smart cards. The first step in assessing the needfor such a policy lies in determining a county’s trend in cash use and its forecast for the future. As nocountry regularly collects data on cash use, this has to be estimated. We provide an econometric modelthat determines the share of cash in consumer transactions and illustrate how this information can beused to estimate illegal use as well. Applied to Norway, the share of cash in consumer transactionsfell from 81% in 1990 to around 54% in 2000 and may fall to 25% by 2010. Cash used in illegalactivities was 7.5% of GDP in 2000.© 2003 Elsevier B.V. All rights reserved.

JEL classification: E41; H26

Keywords: Cash; Money; Tax evasion

1. Introduction

Anecdotal information suggests that the use of cash for legal transactions is falling inmany developed countries as cards increasingly replace cash transactions at the point of sale.

∗ Corresponding author. Tel.:+1-850-644-7899; fax:+1-850-644-4225.E-mail addresses: [email protected] (D. Humphrey), [email protected] (A. Kaloudis),

[email protected] (G. Øwre).1 Present address: STEP, Centre for Innovation Research, SINTEF Industrial Management, Hammersborg Torg

3, NO-0179, Oslo, Norway. Tel.:+47-22-86-80-12; fax:+47-22-86-80-49.2 Tel.: +47-22-31-66-83; fax:+47-22-31-65-42.

1042-4431/$ – see front matter © 2003 Elsevier B.V. All rights reserved.doi:10.1016/j.intfin.2003.07.003

222 D. Humphrey et al. / Int. Fin. Markets, Inst. and Money 14 (2004) 221–233

As cash use falls governments are left in the uncomfortable position of losing seignioragerevenues (i.e., paying zero interest on “cash debt” outstanding) and finding revenues toredeem likely excess cash holdings in the future. From a political perspective it will alsobecome more obvious that government provision of cash (increasingly composed of largedenomination currency) is focused on providing the means of payment for illegal activities(ranging from tax evasion to drug dealing). The importance of this trend to policy makerswill be influenced by estimates of legal and illegal cash use in their country. However, thisinformation is very difficult to obtain since, unlike card use or the stock of cash outstanding,the level and trend in the use of cash (a flow) is not reported. Once information on cash useis developed and becomes known, policy makers may follow Singapore’s lead and considerthe possibility of replacing physical cash with government-issued smart cards. This wouldallow governments to retain the seigniorage benefits of cash, save tax revenues by redeemingcash with an electronic alternative, and potentially place greater control on illegal activitiesthat are facilitated by circulating anonymous cash.

Our purpose is to provide an econometric model that can be used to determine the leveland trend in legal cash use in a country. From this information, and knowledge of the stockof cash outstanding, we can also estimate the likely use of cash in illegal activities. Weillustrate our approach using data from Norway since it has experienced a substantial sub-stitution of debit card use for cash by consumers at the point-of-sale. Different approachesto inferring illegal cash use across countries were recently surveyed bySchneider and Enste(2000). Our results are compared to those developed using one of these alternativemethods.

The revenues obtained by issuing currency are substantial: it only costs about 0.08 eurosto print a 20 euro note and about US$ 0.04 to print a US$ 20 bill.3 Even when the governmentcost of currency distribution, examination for fitness, storage, and replacement are factoredin, the total expense of issuing cash is small compared to the value of obtaining an interestfree “cash-loan” from the public to the government. While the seigniorage benefit is large,the potential expense of having to redeem cash in the future is larger still. For the 12 countriesthat issue the euro, their cash-loan totals 348 billion euros and comprises 5.4% of aggregateGDP. For the US, the cash-loan is US$ 521 billion and is 5.6% of GDP. As it stands, thereis no sinking fund established to repay this loan in the future.4

In what follows,Section 2outlines a procedure that can be used to obtain a first approx-imation of the legal use of cash in a country. We also present the results of an econometricmodel that should provide a more accurate estimate. Due to the high quality of Norwegiandata, both approaches yield reasonably similar results in our illustration. However, this isunlikely to occur in other countries.

3 The cost difference is due to different anti-counterfeiting devices in the two currencies.4 To “buy” cash, users pay an equal value of bank deposits to the government. As cash can be redeemed, its

use by the public is really a zero interest loan to the government. Seigniorage revenues equal the value of theinterest payment that would otherwise have to be made for this loan minus the cost of producing and replacingcurrency over time. At an interest rate of 5%, a 20 euro note would generate revenues of 2 euros over 2 years (theapproximate lifetime of the most used note) minus its replacement cost of about 0.08 euros and perhaps 0.02 eurosfor other expenses. This yields a net revenue of 1.90 euros but neglects the fact that the 20 euro loan will have tobe paid back at some point in time if cash use falls in the future.

D. Humphrey et al. / Int. Fin. Markets, Inst. and Money 14 (2004) 221–233 223

Forecasts of future cash use by consumers, which drives cash use by stores and banks,are obtained using Logistic and Gompertz growth or “S-curves” inSection 3. S-curves havebeen applied to forecast telephone, television, and internet adoption and use, the adoptionof robots in automobile manufacturing, the spread of ATMs in banking markets, and arean accepted method to gauge the spread and adoption of innovations in industry. They areused here to gauge the adoption of card technology and spread of terminal availability thatare among the primary determinants of the growth of payment methods that substitute forcash in legal activities.

A turnover ratio transforms the estimate of legal consumer use of cash (a flow) fromSection 2into a cash stock measure which is then augmented with the value of other sourcesof legal cash use (at businesses, public authorities, and banks). Subtracting this value of thestock of total legal cash use from the total value of cash in circulation gives an estimate ofthe stock of cash used for illegal activities inSection 4. Expressed as a percent of GDP, ourestimate of illegal cash use is compared to that developed by other researchers using differ-ent methods as well as to “official” government estimates derived from one-time surveys.Section 5provides a summary of our results and potential implications for governmentpolicy.

2. Estimating cash use in legal activities

2.1. A first approximation to consumer use of cash

Depending on the quality of payment information in a country, consumer use of cash maybe approximated by first summing the values of various activities in the national accountswhere cash is thought to be a significant means of payment, both in current transactionsas well as in the recent past. In our illustration, cash has been almost entirely restrictedto consumer point-of-sale transactions since 1980 where it competes with debit and creditcards or checks as the typical payment method.

The total value of household consumption reported in the national accounts, adjustedfor some items not paid for in cash in Norway, gives the point-of-sale sales value weuse (POSsales).5 Subtracting the value of consumer check payments and all card trans-actions from POSsales gives an estimate of the value of consumer cash payments at thepoint-of-sale.6 While good time-series information usually exists for the value of cardpayments, no country has time-series information on the value of consumer check pay-ments. Fortunately, Norway has historical information on the ratio of the values of personalchecks to all checks at commercial banks over 1966–1985 and this provides an estimate ofpoint-of-sale check use up to 1986. As consumer check use was continuously falling toward

5 In Norway, automobile purchases, housing expenses, insurance, and most air transportation costs are typicallypaid by giro—not by cash—and so are excluded from our measure of POSsales. A giro payment is equivalent toan Automated Clearing House (ACH) transaction in the US except that giro payments are credit transfers (i.e., themoney has to be in the account or typically the transaction will not be made) while a ACH payment can be a debitor a credit transfer.

6 Giro transactions do not compete with cash payments and so the value of giro payments is excluded here.


Fig. 1. Consumer point-of-sale payments made by check, cards and cash: 1980–2000 in euros.

Table 1Change in the value of payment shares

Cash share Point-of-sale sales value Check payments Card payments Cash payments

Falling share 1980–1984 +6.2 billion +4.1 billion +0.1 billion +2.0 billionRising share 1985–1992 +12.5 −4.2 +2.8 +13.9falling Share 1993–2000 +17.1 −2.0 +19.9 −0.8

Note: values are in euros (current exchange rate is approximately NOK 7.6 = 1 euro).

zero over this period, the trend was estimated and used to provide values for the remainingyears to generate a full time-series over 1980–2000.7 To summarize, we have observed dataon the value of household consumption where cash is typically used (POSsales), observeddata on the value of all card payments (CARD), and estimated data on the value of con-sumer check payments (CHECK). As a first approximation, the value of cash payments isdetermined as a residual in the following equality: CASH= POSsales−CARD−CHECK.The yearly evolution of these payment values is illustrated inFig. 1. Note that cards appearfirst to have replaced checks at the point-of-sale followed by the replacement of cash, aprocess that likely will continue in the future. The substitution among types of paymentinstruments is illustrated for three time periods inTable 1.

7 The value share of personal checks, which was falling, was reported for 2 months in every year over1966–1985. This share was projected for 1986–2000 by fitting a quadratic function of time to the observedshare data (R2 = 0.96). An alternative procedure, used in our working paper (same title), determined the value ofconsumer checks by multiplying the average value of a card payment (currently around 60 euros) by the volume ofall checks written. The actual value of all checks written can not be used as it is strongly dominated by a relativelysmall number of large value business checks. Both procedures led to similar cash shares for the late 1990s but theprocedure used here yields more accurate consumer check values (and hence cash shares) for the 1980s.


In the first period identified (1980–1984), the computed share of cash in point-of saletransactions was falling while the value of point-of-sale payments rose by 6.2 billion euros.Two-thirds of this increase in sales (4.1 billion euros) was paid for by checks while theremaining one-third (2.0 billion euros) was seemingly accounted for by cash payments. Cardpayments contributed almost nothing. In the second period (1985–1992), the cash share wasrising and cash is seen to contribute 110% to the change in total sales while cards contributed22%. Of course, this is only possible because check payments had fallen by as much as theyhad risen in the earlier period. In the last period (1993–2000), the value of checks continuedto fall and by 2000 were almost eliminated as a consumer payment instrument (the valuewas only 66 million euros). As well, although point-of-sale sales value rose by 17.1 billioneuros, cash use fell absolutely so that more than the entire increase in sales value wasassociated with a dramatic rise in card use. By 2000, the value of point-of-sale transactionswas 52.5 billion euros. Card purchases made up 46% of this total while consumer cashtransactions accounted for 54%.8

2.2. An econometric model of consumer use of cash

Depending on the quality of the available payment information (especially for checks),our results above may be reasonably accurate or represent only a rough first approxima-tion. A likely more accurate procedure relies on an econometric model that takes moreinformation into account, such as the stock of currency outstanding, the changing avail-ability of card and automated teller machine (ATM) terminals, and the level of interestrates.

Traditional money demand analysis has been concerned with how the stock of currencyoutstanding (as part of the money supply) is affected by the level of economic activity andthe interest rate. Our analysis, based onSnellman et al. (2001), extends this literature intwo directions. First, we estimate the flow of cash being used by consumers using changesin the stock of currency outstanding along with traditional determinants of changes in thisstock (economic activity and the interest rate). Second, as cards and (to a lessor degree)checks can substitute for cash at the point-of-sale, the value of these payments and thediffusion of the technology that influences this substitution are incorporated directly intothe analysis. Specifically, growth in the availability of electronic funds transfer terminalsat the point-of-sale (EFTPOS) allows card payments to replace both cash and checks whilethe concurrent expansion of ATM terminals and the possibility of receiving “cash back”from a point-of-sale transaction without incurring an ATM fee have made it easier to usecash. A force in the background has been the pricing of many payment transactions and theassessment of ATM fees.

Our basic model is expressed in three equations. The first is almost an identity andstates that changes in the value of all consumer payments where cash, cards, and checkstypically occur (�POSsales) equals the sum of changes in the value of cash, card, and checkpayments:

flow to flow : �CASH+ �CARD + �CHECK = φ �POSsales (1)

8 54% is the estimated share of cash in 2000 shown below in Table 2 using this direct calculation method.


If these data are accurate, and if other influences on cash use are weak, then the parameterφ should be close to 1.0. The value of consumer use of cash (�CASH) is unknown andno country has complete time-series data on the value of checks used at the point-of-sale(�CHECK).

The second equation states that changes in the stock of coin and currency (�CURR) areassociated with changes in cash use at the point-of-sale and the interest rate (�r):

stock to flow :�CURR= α1 �CASH+ α2 �r (2)

Of course, not all changes in currency stock are associated with legal activities and we tryto ensure that the parameterα1 relating to consumer cash use for legal activities is locallywell identified. This brings us to the third equation and the final specification of the model.

Solving (1) and (2) for�CASH, setting them equal to one another, expressing the resultin terms of the use of cards (since cards substitute for both cash and checks), and adding avariable reflecting the availability of ATMs, the final equation estimated is:

�CARDt = α0 + β �CURRt−1 + β �CHECKt + φ �POSsalest

− α2β �rt + α3ATMPOPt (3)

To help identify that portion of the change in currency outstanding which is associated withlegal activities,α1 in (2) is specified as a function of year-to-year changes in the number ofEFTPOS terminals per million persons (EFTPOP) sinceβ = (β0+β1EFTPOP) = −1/α1 in(3). Changes in EFTPOS terminal availability also affect the substitution of cards for checksandβ �CHECK replaces−1.0�CHECK above. The number of ATM terminals per millionpopulation (ATMPOP) is added to (3) to allow for a similar terminal availability influence fa-voring cash use. Finally, the change in the supply of coin and currency outstanding is laggedone period (�CURRt−1) to allow for possible simultaneous equation bias in decisions tosupply and use cash. Once (3) is estimated, the change in consumer use of cash for legalactivities can be determined from�CASH = −�CARD + β �CHECK+ φ �POSsales.

The parameter estimates are shown inTable 2. The relationship between the flows ofcash, card, and consumer check use in (3) isφ = 1.18 and is not significantly different from1.0 at the 95% level of confidence (but is significantly different from zero at the 99% level).Indeed, ifφ is restricted to be 1.00, the estimated parameters inTable 2are quite similarand have the same significance levels. The value ofβ should reflect the substitution of cardsfor currency (and, indirectly, cash use) and checks at the point-of-sale after other influencesare accounted for. Sinceφ is close to 1.0, the flow-to-flow relationship specified in (1)dominates the estimated results from (3) andβ is seen to fall only slightly over 1985–2000in Table 2.

To illustrate this “tradeoff” betweenφ andβ, (3) was reestimated without lagging�CURRby one period. In this reestimation,φ is larger at 1.44 whileβ turns negative in 1990(indicating substitution of cards for cash) and falls from 0.966 in 1985 to−6.49 in 2000.The 1990–2000 period is when EFTPOS terminals expanded from 9,000 to 65,000 whilethe growth in ATM terminals had flattened out. Apparently, the rise inφ—which weakensthe flow-to-flow relationship specified in (1)—allows the stock-to-flow relationship in (2)to play a greater role in the overall results.

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Table 2Determinants of consumer use of cash: Norway, 1980–2000

Equation to be estimated:�CARDt = α0 + β �CURRt−1 + β �CHECKt + φ �POSsalest − α2β �rt + α3ATMPOPt

Parameter estimates Estimated value ofβ (= β0 + β1EFTPOP) for different years

α0 = −25659a 1985 0.605β0 = 0.60549a 1990 0.603β1 = −0.000001 1995 0.597φ = 1.1803a 2000 0.590α2 = 710.99α3 = 52.157a

Estimated and projected cash sharesEstimation period 1980 1985 1990 1995 2000

Econometric model – 0.710 0.808 0.766 0.518Direct calculation 0.680 0.673 0.809 0.786 0.543

Projection period 2000 2005 2010 adjR2

Symmetric linear logistic model 0.557 0.369 0.214 0.89Asymmetric non-linear Gompertz model 0.556 0.400 0.276 0.90

a Different from zero at 99% level of confidence;R2 = 0.76 (adjR2 = 0.66); number of observations= 19.


2.3. Data stationarity

Estimation of (3) with first differenced data from consumer consumption statistics (POS-sales) yielded Durbin–Watson statistics that were inconclusive regarding significant positiveautocorrelation. As well, unit root tests (Weighted Symmetric and Dickey-Fuller) suggestedthat some of the first-differenced variables were not stationary. If we wished to accuratelyseparate the individual effects of each of the variables specified in (3), some non-stationaritycould be a cause for concern. However, we wish to predict cash use rather than identifythe relative importance of the different variables that give us this result. It turns out thatdifferent specifications of (3), which can alter the relative importance of the independentvariables, yields similar predictions of overall cash use.9

2.4. Estimated cash shares

Cash shares from the econometric model by 5-year increments are shown in the lowerhalf ofTable 2.10 The rise in cash use over 1980–1990 is associated with the rapid expansionof ATMs and the pricing of check use. The number of ATM terminals rose from 150 in 1980to 1,735 in 1992 but flattened out after that (since only 384 additional ATMs were installedgoing forward to 2000). Importantly, banks implemented charges for low value checks in1981 and for all checks by 1985. This shifted many consumer point-of-sale check paymentsto cash.

The fall in the share of cash during the 1990s is associated with a number of changes.First, the number of EFTPOS card terminals rose from a little over 9,000 in 1990 to over65,000 by 2000. Second, per transaction pricing was also imposed on the use of debit cardsand ATM cash withdrawals (after normal banking hours and at other banks’ ATMs). Thesefees were differentiated so that an electronic payment using a debit card was the cheapest,followed by an (evening or weekend) ATM cash withdrawal, with the most expensive feereserved for check use. By 2000, each electronic card payment cost a user around 0.28euros, an ATM withdrawal 0.48 euros, while each check payment was a considerably moreexpensive 1.95 euros. Clearly, there was a price inducement to pay with a debit card atthe point of sale.11 Third, from 1992 forward it was possible to obtain “cash back” from apoint-of-sale transaction. Since this service was free, the use of a card at the point-of-saleenabled consumers to both pay for their purchases as well as obtain cash for small valuecash transactions without having to access an ATM and (possibly) pay a fee.

9 For example, changing the specification of (3) to�CARDt = α0 + β �CURRt−1 + θ �CHECKt +φ �POSsalest −α1 �rt , whereβ = (β0 +β1ATMPOP) andθ = (θ0 +θ1EFTPOP), gave a similar cash predictioneven though the importance of the variables specified changed. As well, second differencing of the data used in(3) yielded cash use estimates that were clearly at variance with anecdotal and partial survey information on cashuse in Norway and so are not reported.

10 These shares are obtained from cumulating the estimated�CASH values from the model over time, startingwith an estimate of the level of cash use in 1982 from the direct calculation method outlined in the beginningof this section. If this level estimate is under- or overstated, then the cash shares themselves–but not their fallingpattern—will be under- or overstated as well.

11 Unfortunately, pricing data did not extend far enough back in time for it to be incorporated into our modeland its effect is thus attributed to other variables in (3).


As shown inTable 2, consumer use of cash at the point-of-sale is estimated to be 52–54%of total point-of-sale payments in 2000 for Norway. Using a direct calculation approachsimilar to that outlined at the beginning of this section, similar results were obtained forFinland (54% in 2000,Paunonen and Jyrkönen, 2002) and Sweden (58% in 1999 for “reg-istered trade”,Andersson and Guibourg, 2001). Thus, there appears to be reasonably closeagreement on the share of legal cash within these three Scandinavian countries.

2.5. Total legal use of cash

The value of consumer cash use and the cash shares reported inTable 2are flows, notstocks. To be comparable to the stock data on other uses of cash in legal activities, theconsumer cash use estimate needs to be divided by a turnover ratio. On average, consumersappear to have replenished their stock of cash holdings around every 9.4 days prior to 1992,giving an average turnover ratio of 39 (= 365/9.4).12

After 1992, it was possible to receive “cash back” from a transaction at a retail store andnot incur an ATM cash withdrawal fee. This increased convenience, greater availability,and lower cost of obtaining cash meant that consumers could make more withdrawals forsmaller amounts and decrease their average cash balances. After cash-back, which wasrapidly implemented, we estimate that consumers on average replenished their stock ofcash around every 7.5 days, giving an average turnover ratio of 49 for the years 1992–2000.These two time-dependent turnover ratios are used to deflate our estimate of the flow ofconsumer cash use derived from the econometric model and gives a time-series estimate ofthe stock of cash held by consumers.

Bank statistics and the national accounts were the source of information on holdingsof cash by stores, banks, public authorities, and private firms. Other sources provided in-formation on cash held by foreign visitors who have returned home, consumer hoardingreported on tax returns (and subject to a tax), and an assumed precautionary value held byconsumers.13 The results suggest that the total stock of cash used for legal activities reachedits highest level during 1995–1997 as the number of ATMs approached market saturation.After 1997, the stock of cash held for legal activities fell as EFTPOS terminals became 25times more numerous than ATMs and cash-back was implemented at retail stores.

3. Forecasting cash use

3.1. Logistic And Gompertz forecasts of consumer use of cash

Logistic and Gompertz growth or S-curves have been used in a variety of situations to fore-cast the adoption and dispersion of technologies in industry. They are used here to forecast

12 The turnover methodology used here is discussed in more detail in our working paperHumphrey et al.(2001a). Briefly, the consumer turnover ratios are based on value and volume data on cash withdrawals fromATMs, cash back at stores, and withdrawals over the counter at bank/post branch offices, giving an averagenumber of withdrawals per adult. This changes as the number of access points expands over time, especially cashback at stores.

13 To be conservative, it was assumed that individuals on average hold about 53 euros for precautionary purposes.


changes in the share of consumer use of cash at the point-of-sale over 2000–2010 resultingfrom the dispersion of card payment technologies.14 In a detailed empirical comparison,Meade and Islam (1995)have shown that the standard logistic and Gompertz S-curves out-perform more complicated models.15 The logistic and Gompertz models used to forecastconsumer cash shares (St) as a function of time (t) are:

logistic(linear, symmetric) : ln

(St

1 − St

)= a + bt + εt (4)

logistic(non-linear, symmetric) : St = St∗

1 + c exp(−bt)+ εt (5)

Gompertz(non-linear, asymmetric) : St = St∗

exp(−c exp(−bt))+ εt (6)

whereSt∗ is the estimated saturation (or end) share value at timet, b the coefficient of

diffusion or the slope of the S-curve, andc the scaling coefficient which determines thevertical position of the curve.16

In the linear logistic model (4), the pattern of initial cash replacement is used (via sym-metry around its inflection point) to predict the remaining pattern of replacement. As well,the predicted end share should approach one (or, in our case, zero). The non-linear logisticmodel (5) is more general since it permits the data to determine the end share (St

∗) butstill uses symmetry around an inflection point to predict the remaining pattern of cash re-placement. The non-linear Gompertz model (6) is the most general of the three as it can beasymmetric about its inflection point.17

The predicted consumer cash shares from the linear, symmetric, logistic and non-linear,asymmetric, Gompertz S-curve estimations are shown inTable 2, along with their adjustedR2. The non-linear, symmetric, logistic model (not shown) had anR2 of 0.93 and a predictedcash share of 0.18 in 2010 and so is closest to the linear logistic result with an end periodshare of 0.21. The linear logistic model, since it imposes the most “structure” on the data (i.e.,symmetry and an end cash share that should approach zero), could be directly estimated.Estimation of the non-linear logistic and Gompertz models, with less imposed “structure”,required a grid search.18

14 The only important technical change on the horizon that would likely have a large impact on our projection forfuture cash use would be the widespread adoption of “cash-in-a-chip” smart cards. To date, this innovation has notbeen well-received and results from pilot programs have been disappointing (with some being discontinued—VanHove, 2000).

15 This is largely because more complicated models have more parameters to estimate and the data availabletypically can not support the increased complexity.

16 In implementation, since the end cash share is expected to fall while (4)–(6) estimate a relationship whichcan approach 1.0,St is actually measured as (1—cash share). After estimation, 1− St

∗ gives the predicted endingcash share which may be a small percentage amount.

17 The estimated results are: (4) ln(St/(1 − St)) = −3.446 + (0.1532)t; (5) St = 0.99/(1 +42.14 exp(−0.1714t)); and (6)St = 0.99(exp(−5.772 exp(−0.0940t))). All estimated parameters are differentfrom zero at the 99% confidence level.

18 The search process stipulated values forSt∗ between 0.01 and 0.99 in (5) and (6), permitted the free estimation

of parametersb andc, and the result with the highestR2 was selected. While cash shares associated with search


New data on cash shares over the next few years can improve the accuracy of theseforecasts since the inflection point should become better defined. At present, however,consumer use of cash in legal activities is projected to keep falling from its current levelof 52–54% in 2000 and may fall by half–down to 21–28%–in 10 years. These resultssuggest that cash used in legal activities may become so small in Norway that governmentseigniorage revenues may be due primarily to providing the means of payment for illegalactivities.

4. Estimating cash use in illegal activities

4.1. Total illegal use of cash (measured as a residual)

Subtracting our estimate of the total value of the stock of cash used in legal activities inSection 2from the total value of cash outstanding (CURR) gives an estimate of the stockof cash used in illegal and hoarding activities. The stock of cash associated with illegal and(some) hoarding activities was 63% of the total outstanding in 1980, fell to a low of 54%in 1990, and then rose to 67% by 2000.19 These values are so large that significant changesin our methodology in estimating the value of legal cash use would not have much effecton our conclusion that the majority of the stock of cash funds illegal activities.

4.2. Illegal activities as a percent of GDP

Estimating the value of illegal activities as a percent of GDP involves the messy as-sumption that we can approximate a turnover ratio for illegal activities. Lacking exactdata, this turnover ratio in previous work has been the ratio of GDP to M1 (Schneider andEnste, 2000). The stock of cash associated with illegal activities is multiplied by an annualGDP/M1 turnover ratio using recently revised M1 data. This suggests that the value of ille-gal activities was 7.6% of GDP in 1994, rose to 9.1% in 1998, and fell to 7.5% in 2000.20

Although the absolute value of estimated illegal cash use rose over 1994–2000, the risingshare of illegal activities in GDP experienced during 1994–1998 appears to have reversedcourse over the last 2 years.

Using survey information for 1980 and 1983,Isachsen and Strom (1985)estimated thattax evasion activities in Norway accounted for 4–6% of GDP.21 The tax authorities came toa similar conclusion as tax evasion was estimated to amount to 5–6% of GDP in the 1980swhile other illegal activities were thought to raise this value by around one-fourth (givinga figure of 6.3–7.5%). Thus, our procedure seems to generate estimates of illegal cash use

results for the Gompertz model with the highest adjustedR2 are presented inTable 2, theR2 values changed onlyslightly as the end cash shares were varied between 0.01 and 0.10, or even higher specified end period shares.

19 Including giro cash payments reduces this share to 63% in 2000.20 Due to the large size of the oil sector in Norway, little of which is associated with domestic payment media,

the GDP figure used here and elsewhere excludes the oil sector.21 The surveys also suggested that during a 1-year period around 35% of the a adult population participated in

a transaction whose purpose was to hide income or escape sales taxes.


similar to those obtained through government surveys. Other researchers, using a differentand more aggregate modeling framework, have suggested that the value of illegal activitiesto GDP could be 19% (Schneider and Enste, 2000).22

5. Summary, conclusions, and policy implications

Using an econometric model of consumer cash use at the point-of-sale, we have estimatedhow the use of cash has fallen as a share of point-of-sale cash, card, and check paymentsfor Norway over 1980–2000. The results are robust to alternative specifications and aresimilar to cash shares derived by direct calculation with available data. The share of cashin consumer point-of-sale payments for legal activities was 0.62 in 1982, reached a peakof 0.83 in 1992, and then fell to 0.52 in 2000. The decline occurred as card paymentsexpanded rapidly in response to the increased availability of EFTPOS terminals and (asshown inHumphrey et al., 2001b) from direct and differential pricing of different paymentinstruments and ATM use.

Cash share estimates over 1980–2000 are used in three logistic and Gompertz growthor S-curve models to forecast future cash shares over 2000–2010. All three models givebroadly similar results. As averages of the two projections inTable 2, cash shares at thepoint-of-sale will continue to fall, although at a slower rate, and may be 0.38 in 2005 and0.25 in 2010.23 These are tentative projections that can be improved in a few years whenthe inflection point in the cash share time-series data becomes more prominent.

We estimated the value of the stock of cash used by consumers in legal activities atthe point-of-sale as well as that for bill payments through giros. Values of cash holdingsfor banks, stores, and public authorities were obtained from bank statistics and nationalaccounts. Subtracting these values from the value of total cash outstanding provides anestimate of the stock of cash used in illegal and (some) hoarding activities. Most of theseactivities are believed to be associated with sales and income tax evasion, especially after1992 when sales and income tax rates were raised substantially in an effort to reduce taxeson capital. As a total, these activities accounted for 41% of the value of cash outstandingin 1994, rising to 63% in 2000. The value of illegal activities was 7.6% of GDP (excludingthe oil sector) in 1994, rose to 9.1% in 1998, and fell to 7.5% in 2000. These percentagesare in line with those estimated using survey procedures by the tax authorities.

Overall, it appears that cash used in illegal activities contributes over 60% of the Nor-wegian government’s seigniorage revenues, a contribution percentage that will likely risein the future. This is a dubious position for a government to be in. In the future, should allbut the smallest denomination currency be withdrawn from circulation as legal use of cashcontinues to contract? Should all currency be withdrawn and coins (a cost-effective sub-stitute for notes due to their long lifetimes) be substituted for the smallest value currency?Or should the government consider following the lead of Singapore (Kok, 2002) and study

22 This estimate relies on an older (and now revised) ratio of M1 to GDP and this contributes to some of thedifference between their and our results.

23 This process is starting. The most recent information suggests that 1999 was a peak year in cash holdingsand the total value of all currency and coin in circulation has fallen by 4.7% over 1999–2002.


the possibility of redeeming physical cash and replacing it with government-issued smartcards to retain seigniorage benefits and eliminate the need to use tax revenues to redeemexcess cash holdings in the future? Would these actions be effective in curbing somewhatillegal activities when large denomination currencies of other countries still circulate? Thesequestions will likely frame the debate in the future.

Acknowledgements

We wish to thank Thorvald Grung Moe, Henning Strand, Bent Vale, Leif Veggum, ananonymous referee, as well as participants at Norges Bank, Sveriges Riksbank, and FederalReserve Bank of Philadelphia seminars for helpful comments. Financial support for the firstauthor from the Foundation BBVA in Spain is gratefully acknowledged.

References

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the future of cash: falling legal use and implications for government policy

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