working paper SerieS
The Use of Cash and
the Size of the Shadow economy
Gabriela Guibourg and Björn Segendorf
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The Use of Cash and the Size of the Shadow Economy in
Gabriela Guibourg * and Björn Segendorf**
Sveriges Riksbank Working Paper Series
We use an “unexplained demand for cash” approach to measure the size of the shadow economy in
Sweden. The size of the shadow economy is found to have increased from 3.8 to 6.5 per cent of
GDP from 1990 to 2004. This result is also supported by our finding of an increased residual
between households’ recorded disposable income and their consumption, investments and changes
in net financial positions. Moreover, the correlation between the demand for cash that cannot be
explained by recorded transactions and this residual is strong.
Keywords: Cash use; demand for cash, shadow economy, National Accounts, Financial Accounts
JEL classifications: E41; E26; H26
We are grateful to Tor Jacobson, Mikael Carlsson, Paolo Giordani, Jonas Niemeyer, Kerstin Mitlid and Mats Bergman for valuable
suggestions and comments. We would also like to thank Statistics Sweden for help with providing and interpreting data.
The views expressed in this working paper are solely the responsibility of the authors and should not be interpreted as reflecting the
view of the Executive Board of Sveriges Riksbank.
* Research Department, Sveriges Riksbank SE-103 37 Stockholm, Sweden. E-mail: email@example.com.
**International Secretariat, Sveriges Riksbank SE-103 37 Stockholm, Sweden, E-mail:firstname.lastname@example.org.
The shadow economy comprises non-recorded economic activity of which surprisingly little is
known. 1 All of these types of economic activities are not intrinsically bad; a considerable share of
them accounts for transactions that would otherwise not have taken place in the formal economy. In
this sense, they add to the total value of goods and services produced in the economy On the other
hand, an increasing share of the shadow economy of total GDP may reflect the fact that citizens’
law and rule abiding principles, as well as their support for the welfare state, are being undermined.
For these reasons, it is important to better understand the shadow economy.2 The purpose of this
study is to estimate the size of the shadow economy in Sweden and how it has developed from
1990 to 2004.
The method we use builds on the fact that cash is a payment instrument that is difficult to trace and
that this property makes it an attractive means of payment in the shadow economy. Hence, if the
share of the currency in circulation that is used in the shadow economy could be estimated, this
could be used as a starting point to estimate the size of the shadow economy itself. The way this is
done is by reducing the total demand for cash by the demand that can be explained by recorded
transactions including the value of cash held by banks, merchants, users and public authorities. The
part of the demand for cash that cannot be explained is then assumed to derive from activities in the
shadow economy. Multiplying this unexplained demand by the assumed velocity of cash in the
shadow economy gives the shadow-economy turnover. The total currency in circulation is measured
as M0 and we find that the unexplained demand for cash has increased from 31 per cent to 58 per
cent of M0 over the period 1990 – 2004.3 Multiplying the unexplained demand for cash by the ratio
GDP/M1, which is a standard estimate of the velocity of cash in the shadow economy, we find that
the shadow economy almost doubled its share of GDP over the studied period. More precisely, it
has increased from 3.8 per cent of GDP to 6.5 per cent. Its average size was 5.7 per cent of GDP.
However, the results are sensitive to the estimated velocity of cash in the shadow economy. To
corroborate our finding of a growing shadow economy, we compare households’ annual disposable
income including loans with households’ annual consumption, investments and savings. Any residual
between the income and the expenditure sides captures part of the transactions in the shadow
economy, mostly the net flows of unrecorded savings and income in and out of the country. This
does not allow us to estimate the size of the shadow economy, however. But since the residual is
most likely a function of the turnover in the shadow economy, we can confirm the trend of a
1 The shadow economy comprises barter transactions and other non-recorded legal transactions as well as criminal activities
including tax evasion. For taxonomy of types of underground economic activities, see Schneider and Enste (2000).
2 Alm and Torgler (2006) show the importance of social norms for tax morale in country comparisons between the U.S. and 14
European countries,(see Alm and Torgler 2006). It turns out that the U.S. has the highest tax morale and the smallest shadow
economy, while Belgium and Portugal have the lowest tax morale and the largest shadow economies. Sweden and Spain both have
relatively large shadow economies but also a relatively high tax morale. For this comparison, Alm and Torgler use estimates from a
working paper by Scheider and Klinglmair.
3 M0 is calculated as the total stock of banknotes and coins in circulation each year minus the Swedish monetary financial
institutions’ cash balances in Swedish kronor. In absolute terms, M0 increased from SEK 55 billion in 1990 to SEK 94 billion in 2004.
growing shadow economy. More precisely, we find there to be a strong positive correlation between
the residual and the unexplained demand for cash.
In a recently published study (2006), the Swedish Tax Agency estimates the value of undeclared
earnings to SEK 115 – 120 billion. Our own estimates for 1998 – 2004 give an average of SEK 151
billion. The difference may be explained by the fact that our estimates include all kinds of non-
registered transactions including narcotics trade, prostitution etc. According to the Swedish Tax
Agency, undeclared earnings were more widespread in small-sized companies and among skilled
workers than in other groups in the economy. Engström and Holmlund (2006) study income and
expenditure data and estimate that Swedish households with at least one self-employed member
underreport their income by at least 30 percent. This result is consistent with other revision methods
used by the Swedish Tax Agency.
Our study is not the first to estimate the demand for cash and the size of the shadow economy.
Humphrey et al. (2000) study Norwegian data and find that the size of the shadow economy is
approximately 10 percent of GDP in 1999. Schneider and Enste (2000) review the currency demand
and other methods and present estimates in 76 developing, transition, and OECD countries. Like our
estimates, the estimates obtained by Schneider and Enste (2000) show an increase in the size of the
shadow economy in Sweden over time. Their estimates are larger, however. Schneider (1994 and
2005) gives estimates ranging from 15.8 percent of GDP in 1989/90 to 18.7 percent in 2002/2003
with a peak of 19.9 percent in 1997/1998.4 The difference in the results between our study and that
of Schneider and Enste is due to our different approaches to estimate the currency demand.
Schneider and Enste use an econometric method that estimates the demand for cash as a function of
macro-economic variables such as average tax rate, the saving-deposit interest rate, per-capita
income etc. while our more direct approach builds on point-of-sale transaction data.
The structure of this paper is as follows. First, we describe the method for estimating the demand for
cash and then we apply it to the Swedish data. This is done in Section 2. In Section 3, we estimate
the shadow economy through the use of the unexplained cash demand and evaluate the qualitative
results by use of household data and, finally, Section 4 concludes.
2. The Demand for Cash
We describe the method in Section 2.1 and apply it to Swedish data in Section 2.2. In Section 2.3,
we discuss and refine our estimate of the unexplained demand for cash.
4 With a slightly different approach for the computation of the data series Johnson, Kaufman and Zoida-Lobotón (1998a, 1998b)
obtain estimates for the Swedish shadow economy of 10.6 per cent of GDP.
The method we use follows Humphrey et al (2000). We start by estimating the use of cash in
registered transactions at the point of sale (POS), where buyers and sellers meet directly. In this type
of transactions, cash, cards, and checks can be used interchangeably. Data on POS turnover card
and check payments is of high quality while there is no reliable data on cash payments. The value of
cash payments is therefore estimated as the difference between total turnover from POS
transactions and the value of card- and check payments. The value of cash payments in POS
transactions is a flow variable, however. In order to estimate the stock of cash needed to sustain the
estimated value of cash payments in registered transactions, we must divide the value of cash
payments with an appropriate velocity for cash. This measure captures the velocity of cash in
recorded POS transactions. Here, we compute the velocity as the average number of cash
withdrawals per adult Swede and year. 5 Our data only covers an ATM withdrawal which means that
we underestimate the number of withdrawals and thus also the velocity of cash and that we
overestimate the stock of cash needed.
Cash is also used for other legal purposes than registered POS transactions. It is held by financial
institutions, merchants and the public sector to meet customers’ demand for cash, it is held by
individuals to meet liquidity needs, and it is used for non-recorded transactions between individuals,
e.g. in the second-hand market.
The estimated total cash requirement is thus the sum of the cash held by private and public sectors
and the cash required for registered sales. The difference between the actual demand for cash as
measured by M0 and the estimate is the unexplained demand for cash, most of which is likely to be
used in the shadow economy.
2.2 The Explained Demand for Cash in Sweden
Data on POS transactions was obtained from the part of the national accounts that contains
statistics on households’ annual consumption expenditure by purpose. By deducting from total
household consumption those expenditures that are most likely to be paid for with credit transfers or
direct debits, we get the annual consumption expenditures that are likely to have been paid for at
the point of sale. These expenditures cover retail purchases, hotels, restaurants, purchases of
communications and transport services etc.6 In Section 2.3, we refine the calculations by including
the estimated turnover in the second-hand market.
5 Individuals may withdraw cash through the ATM terminals, through bank and post branches and through cash back services at
certain chains of grocery stores. Adult individuals are defined as older than 14. The computation of the velocity of cash followed the
methodology of Humphrey et al. (2000).
6 The expenditure purposes chosen and their statistical codes are: 01 food and non-alcoholic beverages, 02 alcoholic beverages and
tobacco, 03 clothing and footwear, 043 materials and services for the maintenance and repair of dwellings, 0454 solid fuels, coal,
coke, briquettes, firewood, charcoal, peat and the like, 05 furnishings, household equipment and routine household maintenance,
06 health, 0713 bicycles, 072 operation costs of personal transport equipment, 073 transport services, 0811 postal services, 0812
The Riksbank collects annual data on the value and number of card- and check payments as well as
other non-cash payments.7 Data on cash holdings by financial institutions and the public sector is
published by Statistics Sweden.8 Cash holdings by non-financial firms had to be estimated. 9
The value of cash-based POS transactions is estimated by deducting the value of card- and check
payments from the POS turnover. We show that the share of cash payments of the total turnover
has decreased by 34 percentage units from 71 percent to 33 percent between 1990 and 2004 (see
Figure 1). For the level of POS cash payments, see Table 1. Most of the decrease can be explained
by the cash payments being replaced by card payments. Card payments have also replaced checks,
the use of which fell sharply during the first part of the studied period and virtually disappeared at
the end of the period. Two thirds of the fall in cash payments occurred between 1999 and 2004; a
period characterised by a very rapid growth of card payments. During these years, the share of card
payments of the total number of non-cash payments increased from 34 to 63 per cent
Figure 1. The use of cash, cards and checks at the point of sale measured each instrument’s share of
total value of point-of-sale transactions.
The value of cash payments for the years 2000 – 2004 can be found in Table 1. In order to obtain
the stock of cash needed in registered trade, we divide the value of cash payments in registered
sales with the velocity for cash in recorded POS transactions To this, we add the other cash holdings
telephone and telefax equipment, 09 recreation and culture, 10 education, 11 restaurants and hotels, 121 personal care, 123
personal effects, 127 fees for legal services, employment agencies, etc, 15-16 net tourist expenditure.
7 See Andersson and Guibourg (2001).
8 Financial Accounts, annual figures by sector, item and counter-part sector.
9 Norway has statistics on cash holdings by non-financial firms. Given the existent similarities between Sweden and Norway in the
payment market, we assumed that the ratio between cash holdings by financial and non financial firms in Norway could be applied
to Swedish data. For the years 2000-2004, we assumed that the same average ratio applied.
as described in section 2.1, i.e. cash holdings by individuals for transaction purposes, safety buffers
held by individuals, cash held by banks and the government and estimations of cash held by non-
financial companies. As seen in Table 1, the cash requirement that can be explained by POS-
transactions and cash holdings sums up to approximately SEK 30 billion. Hence, the explained
demand for cash is approximately 33 - 35 percent of the total currency in circulation in the period
2000 – 2004.
Table 1. Cash use in Sweden. Amounts are in SEK million and the share is in percentage of M0.
Value of cash payments in registered sales
/ velocity of cash (No. of ATM withdrawals per year and person)
= Cash requirements for transactions
+ Safety buffer
+ cash in banks, government and companies
= Total cash requirement
= Explained share
1 - explained share = unexplained share
unexplained share with larger velocity of cash
2.3 The Unexplained Demand for Cash
The unexplained demand for cash is the part of the currency in circulation that cannot be explained
by the purposes specified in Table 1. Between 2000 and 2004, this unexplained demand has
remained relatively constant at between 63 and 67 percent of the total currency in circulation (for
the whole period 1990-2004, see the solid line in Figure 2). These results are robust to different
estimates of the velocity of cash in POS transactions. Assuming that our figures underestimated the
true velocity by as much as 20 percent, this would result in a moderate increase in the residual of 2-
3 percentage units (see Table 1). Our estimates of both the explained and the unexplained shares of
the stock of outstanding cash are consistent with estimates from Norway. According to an update of
the study by Humphrey et al (2000), the unexplained share of cash in 2000 amounted to 67 percent
in Norway, which is in line with the 65 per cent in Sweden in the same year. 10
However, in our calculations, we have not accounted for cash used for second-hand trade and cash
that has been lost or accidentally destroyed. The former increases the explained demand for cash
and the latter reduces the currency in circulation. Below we refine our estimate of unexplained
demand by accounting for these factors.
10 Humphrey et al (2004).
We estimate the second-hand market turnover to be SEK 96 billion in 2004. This includes second-
hand trade on the Internet. 11 However, adding this estimate only decreased the unexplained
demand for cash by two percentage units, i.e. from 67 percent to 65 percent in 2004. We do not
have estimates for second-hand trade on the Internet for the previous 1-2 years, i.e. the period in
which this type of trade became popular. It turns out that differences in the estimate of the value
spent on the second hand-market do not have any significant effect on the result. Increasing
(decreasing) the estimated turnover by 50 percent only reduces (increases) the unexplained demand
with one percentage unit.
Part of the stock of cash officially in circulation is likely to have been lost or accidentally destroyed.
In the 2001 Euro cash changeover process, a number of European national currencies were replaced
by the Euro. On average 90 percent of the national currencies were redeemed, but the national
differences were large. 12 In the following, we assume this average of 10 percent not redeemed to be
a fair approximation of lost and destroyed cash in Sweden. This reduces the stock of cash in
circulation by 10 percent which, in turn, reduces the unexplained demand. However, accounting for
second-hand trade and lost cash, the unexplained demand for cash was still 58 percent of M0 in
2004 (see the dotted line in Figure 2).
Figure 2. Percentage of currency in circulation not used in recorded economic activity.
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
Refined unexplained demand
11 Andersson and Guibourg (2001) estimate the value spent on the second-hand markets to be SEK 40 billion in 1999. In 2004, we
estimate the value spent on the second-hand market over the Internet to be SEK 56 billion. This estimate is based on direct surveys
of second-hand market web sites. It is likely that second-hand trade over the Internet has crowded out some of the second-hand
trade previously conducted outside the Internet. However, to be certain that we do not underestimate the total second-hand
market, we add the estimates of Internet based and non-Internet based second-hand trade.
12 Stenkula (2003).
Between 1990 and 2004, cash has come to be used relatively less as means of payment at the POS.
In nominal terms, we estimate the use of cash at POS to be SEK 289 billion in 1990 and SEK 279
billion in 2004.13 The nominal use of cash is thus almost unchanged but the velocity of cash in
recorded POS transactions almost doubled from 24 to 45 during the same period which reduced the
explained demand for cash in nominal terms by almost one half. The increased velocity also made
the demand for cash less sensitive to changes in the use of cash, i.e. an increase in the velocity
implies that a given cash POS turnover can be sustained with less cash in circulation. Including cash
held by the government, financial institutions, firms and consumers, the nominal demand for cash
remained almost unchanged during the period – SEK 35 billion in 1990 and SEK 31 billion in 2004.
However, the amount of cash in circulation increased from SEK 55 billion to SEK 94 billion. Hence,
the unexplained demand for cash increased from 31 to 58 percent of M0. Our explanation of this
unexplained increase in the demand for cash is that it is used for non-registered economic activities,
i.e. that it is used in the shadow economy.
3 The Shadow Economy
In this section, we estimate the size of the shadow economy. The underlying assumptions are that
the shadow economy is cash based and that the stock of cash that we cannot explain from
registered transactions and cash holdings is used for transactions in the shadow economy. However,
in order to express the unexplained cash demand, which is a stock measure, as a share of GDP,
which is a flow measure, we need to transform the stock of unexplained cash into a turnover in the
shadow economy. We believe there to be a significant difference between cash use in recorded POS
transactions and cash use in non-recorded transactions in the shadow economy, e.g. cash payments
are likely to be larger in the shadow economy and there is likely to be relatively fewer transaction
opportunities. For this reason, we will not use the same ATM-withdrawal based velocity measure as
above. Instead, we will follow earlier studies, e.g. Schneider and Enste (2000), of the shadow
economy which have approximated the velocity of cash in the shadow economy with the velocity of
money (M1) in the formal economy, i.e. GDP/M1. 14 Relating the estimated turnover in the shadow
economy to GDP gives the relative size of the shadow economy:
Relative size of the
13 During the same period, the estimated POS turnover increased from SEK 409 billion to SEK 752 billion.
14 M1 is equal to the sum of M0 and demand deposits in monetary financial institutions and the Swedish National Debt Office by
the Swedish public. Demand deposits are defined as overnight loans and deposits in transaction accounts.