In order to fulfil its obligations regarding the supply of notes
and coins, Norges Bank needs to hold cash inventories. The level of
inventories must be considered with regard to ordinary and extraordinary
circumstances. In order to predict demand and reduce the uncertainty
concerning inventory requirements, sound models that can enhance the
understanding of changes in cash circulation are required. The
explanatory variables for cash demand can be divided into three
different groups: general macro-economic variables, variables that
express the competition between cash and deposits, and variables that
may provide insight into the illegal economy. A newly developed model
for cash demand shows that demand for actual cash is dependent on real
consumption at the point of sale, bank interest rates and a negative
linear trend that captures developments in the payment system, in
addition to the historical value of real cash. The model-based forecasts
show that demand for cash will increase in the next quarters before
decreasing towards the end of 2006 and further through 2007.
According to the Norges Bank Act, Norges Bank is required to issue
notes and coins (statutory responsibility for issuing notes and coins).
Under the Norges Bank Act, Norges Bank is also responsible for ensuring
that cash is available (statutory responsibility for supplying cash).
Responsibility for issuing notes and coins and the banknote monopoly
entails issuing notes and coins in the amounts implied by demand and
ensuring that notes and coins are available to society (see Eklund,
Solberg and Veggum, 2005). Norges Bank's goal is to fulfil these
obligations in an economical, efficient and secure manner.
In 2001, Norges Bank outsourced most of the services associated
with cash storage and the handling of deposits and withdrawals from the
central bank depots. Norges Bank is still responsible for procurement of
banknotes and coins, as well as storage and transport associated with
the central bank depots. For this reason, analysing future cash needs is
an important task.
Section 2 of the article gives a brief introduction to the
organisation of cash holdings in Norway. Section 3 explains the
necessity of holding inventories of banknotes and coins. Section 4
discusses factors that affect the circulation of cash and section 5
explains the structure of a model for cash demand. The use of the model
is then demonstrated in section 6. Section 7 discusses the model's
importance in logistical planning.
2 Organisation of cash supply
The physical flow of cash may be divided into three steps:
production, storage and circulation (see Chart 1). Production of coins
takes place at the Mint of Norway, while Norges Bank is responsible for
the production of banknotes. During the course of 2007, the printing
works in Norges Bank will be closed, and thereafter production will take
place externally. Storage is organised with a central cash distribution
vault and five depots located around the country. The cash distribution
vault is operated by Norges Bank, while Norsk Kontantservice AS (NOKAS)
operates the depots on behalf of Norges Bank. The quantity of notes and
coins in use in the community at any given time is often called the
circulation of notes and coins, or cash circulation. (2) The cash
circulation level changes when banks need cash and make withdrawals from
Norges Bank, or when they have a surplus of cash and make deposits in
Norges Bank. In this context banks operate to all intents and purposes
as an intermediary between the public and Norges Bank. In practice, this
means that it is the public's demand for notes and coins that
determines the level of cash circulation.
3 The need to hold cash inventories
One of Norges Bank's goals is to fulfil its statutory
responsibility for supplying cash in as secure and cost-efficient a
manner as possible. This means that Norges Bank must be able to meet
banks' demand for cash, both under normal circumstances and under
more extraordinary circumstances. Total inventories required must be
assessed in the light of both of these circumstances.
Uncertainty regarding future demand for cash affects estimates of
holding levels. It is therefore important to have a sound understanding
of which factors affect demand for cash and how these may affect demand
in the future.
3.1 Supply capability under normal circumstances
There are various reasons for the need to hold cash inventories.
Demand is seasonal, and the purpose of the stock is to help meet these
demand fluctuations. The inventories are also held to deal with various
types of uncertainty, such as other variations in demand and transport
delays or supply delays.
When determining the appropriate level of operating inventories
under normal circumstances, two needs are assessed: transaction stock
and buffer stock.
* Transaction stocks serve to cover normal requirements during the
period between one delivery and the next from the producer. On the basis
of estimated demand for cash and expected destruction, the transaction
stock is determined by minimising the sum of order, transport and
storage costs. A large proportion of the production costs for notes and
coins are fixed, which means that unit costs are reduced when the volume
increases. On the other hand, larger volumes increase the capital tied
up in the storage of cash. Transport is often costly due to security
requirements and long distances. It will therefore be cost-efficient to
exploit certain capacities during transport. By minimising total costs,
one can determine the optimal order volume and the resulting size of the
* Buffer stocks serve as a buffer against uncertainty, primarily
uncertainty regarding demand for cash. Not all uncertainty can be
eliminated. This is why it is necessary to decide how much uncertainty
the Bank should attempt to cover. We refer to this as choice of supply
capability, i.e. the probability of being able to meet demand for a
denomination when the transaction stock approaches the level where it
needs to be replenished and until a new order arrives. The size of the
buffer stock required grows exponentially in step with the supply
capability required. The higher the supply capability, the higher the
buffer stock. This in turn will affect stock holding costs. The optimal
supply capability may be difficult to determine, but is a balance
between increased costs and the consequences of stock depletion. The
negative consequences of cash stock depletion are regarded as
significant by Norges Bank. Consequently, the Bank aims to have a
relatively high supply capability.
Inventory policy during normal circumstances can thus be expressed
as the aim of minimising overall order, transport and storage costs in
addition to setting targets for supply capability.
3.2 Emergency preparedness
The need to maintain emergency stocks in case of extraordinary
circumstances is related to the public's cash requirements in such
circumstances. Extraordinary circumstances are said to occur in the case
of various forms of failure or disturbances in key public
infrastructure, e.g. electronic payment systems. The size of the stocks
that Norges Bank needs to hold in order to handle such situations is
determined by what the Bank chooses to be prepared for and the degree of
preparedness that is chosen.
3.3 Total cash inventories
Norges Bank's operating and emergency inventories may
essentially be treated as two separate stocks. Norges Bank has
nevertheless chosen to consider them as one due to the small probability
of extraordinary circumstances occurring simultaneously with the
depletion of the entire stock for ordinary circumstances. This reduces
the overall stock requirements. The overall stocks are thus set as cash
needs in ordinary circumstances plus a minimum stock that is intended to
cover certain extraordinary circumstances.
By obtaining a sound understanding of the factors that influence
the circulation of cash, the central bank will be able to reduce the
uncertainty and thereby the levels of the overall stock.
There are several methods for estimating demand for cash. Norges
Bank has chosen to view future cash demand from both a micro and
macro-perspective. From a micro-perspective, the demand for each
denomination at each depot is considered. Short-term demand (one to
twelve months) is estimated with the aid of historical seasonal
variations and trends.
Estimates based on the macro-perspective cover the overall cash
demand in the longer term (1-3 years). These estimates are used in the
planning of order volumes from producers. In addition, the forecasting
process provides an understanding of the mechanisms that affect cash
demand. A model based on these assumptions is presented in sections 5
4 What affects cash circulation?
When assessing demand for cash, it is appropriate to make use of
economic theories concerning demand for money. These theories employ
different definitions of the money supply, and various forms of deposits
are included. (3) Cash in circulation is a small portion of what is
usually referred to as money. Cash competes with various forms of
deposits (4) in electronic transactions. The greater the liquidity of
such deposits, the lower the demand for cash. (5) Because cash may be
used for anonymous payments on the spot, it is better suited than
deposits in the illegal economy. The growth and size of the illegal
economy may therefore affect demand for cash.
The explanatory variables for cash demand may therefore be divided
into three different groups: general macroeconomic variables in money
demand theory, variables that express the competition between cash and
deposits and variables that may provide insight into the illegal
economy. Each of these groups is discussed below.
4.1 Macroeconomic variables
Money and its function
Macroeconomic explanatory variables include variables from
theoretical money demand models. The empirical literature has primarily
focused on the demand for broad monetary aggregates. (6) Broad monetary
aggregates have proven to be relatively stable functions over time. In
addition, there has proven to be a certain relationship between price
trend and growth in broad monetary aggregates. Money demand measured by
narrower concepts has a tendency to be more unstable over time and the
relationship with price trend is weaker. (7)
Money is often assigned three functions: a medium of exchange in
financial transactions, a unit of measurement for value and a store of
value (e.g. McCallum (1989)). As we take a closer look at factors that
determine demand for cash, we shall concentrate on money's function
as a medium of exchange in financial transactions and as a store of
value. The latter point is discussed in connection with the illegal
The transaction motive
Cash, as opposed to other financial assets, provides no interest or
return. The public does however hold cash, partly because it simplifies
transactions. It may be presented as a problem of optimisation to
balance the expected gain in the transaction from holding an extra unit
of cash against the cost in the form of lost interest. A model for
calculating demand for cash should therefore include both a variable
that expresses the transaction gain and one that expresses the loss of
interest due to holding cash.
The more payment transactions one wants to carry out, the more cash
one wants to hold. There is a close correlation between the number of
transactions and disposable income. However, in a modem, highly
developed economy such as the Norwegian economy, there will be a number
of types of transactions where cash is no longer a feasible means of
payment. Cash will typically only be used as a means of payment in
transactions that are carried out at the actual point of sale. Using
disposable income as an indicator of the amount of the transaction will
therefore express a broader range of transactions than is desirable. The
transaction motive for holding cash is probably best expressed by using
a narrow definition of consumption. We have therefore chosen to express
the transaction motive with a variable that includes consumption at the
point of sale (cf. Aastveit 2005).
When the public hold cash, they pay an alternative cost in the form
of lost interest income. By placing money in interest-beating financial
instruments, one may earn interest income on them. This means that the
higher the interest rate is, the higher the cost of holding cash will
be. Since cash is mainly used for transactions with settlement at the
point of sale, only money in transaction accounts may be viewed as a
realistic alternative to the use of cash. Therefore, the alternative
cost of holding cash is probably best expressed by a weighted average of
the rate of interest offered by banks for deposits in transaction
4.2 Cash or card?
Developments in the payment system
In the past 10 to 20 years we have seen significant developments in
the payment system. In particular, there has been a rapid increase in
the use of electronic payment instruments, which has reduced the use of
In empirical economic literature there have been attempts to use
different explanatory variables to express this development. However,
this has proved difficult due to short and somewhat inadequate data
series. Another issue is that developments have taken place so quickly
that it may be difficult to identify the effect of each of the new
instruments. An example of this is that cheques were a common medium of
exchange for much of the 1970s and 1980s, while their use has declined
significantly since about 1990. This has led some writers, e.g. Fischer
et al. (2004), to argue that technological developments in the payment
system are best captured by including a (negative) linear trend. By
introducing such a trend, one can capture the effect of the payment
system evolving in a direction where more technology-based transactions,
and hence less cash, are used. It can therefore be said that a negative
trend represents the effect of a gradual substitution away from cash.
It is still relevant to discuss some specific variables that may
capture the effect of technological developments on cash demand.
The availability of cash and liquidity of cash deposits
An increase in the number of ATMs will initially lead to lower
costs (in the form of time used) for making withdrawals and easier
access to cash. According to Baumol (1952) and Tobin (1956), this should
reduce the transaction-motivated demand for cash (i.e. cash holdings for
transaction purposes). Theoretically, however, it is also conceivable
that an increase in the number of ATMs may increase demand for cash
because the availability of cash increases. Cash will thereby be easier
to use and be a better alternative than other means of payment (see
Drehmann and Goodhart (2000)). Theoretically, an increase in the number
of ATMs will therefore have an indeterminate effect on cash demand.
The trend in the number of point-of-sale terminals is another
variable that may express the effect of developments in the payment
system. The more point-of-sale terminals, the easier it is to use
payment cards for transactions at points of sale, which viewed in
isolation has a negative effect on demand for cash. However, in 1992 the
option to withdraw cash ("cashback") when making purchases was
introduced. Theoretically, cashback could have four effects on cash
demand. Two of the effects are the same as the effects of an increase in
the number of ATMs, i.e. an indeterminate effect. In addition, the
introduction of cashback could lead to faster recirculation of cash
among the public; in other words, the velocity of cash circulation
increases. In isolation, this will have a negative effect on demand for
cash from Norges Bank. Second, cashback is free for the account holder.
It is therefore cheaper to use cash than other payment instruments. In
isolation, this will have a positive effect on demand for cash. Thus, in
isolation the introduction of cashback will have an indeterminate effect
on demand for cash. The aggregate effect of an increased number of
point-of-sale terminals on cash demand would therefore be purely
negative until the introduction of cashback in 1992, while in the period
following 1992 the effect would be uncertain.
The cost of transactions
When making a payment at a retail outlet (e.g. a grocery), there
are in practice two means of payment: cash or payment card. If we choose
the latter, a small fee will normally have to be paid to use the payment
card. (9) The size of this fee depends on the terms of the individual
bank. According to ordinary market theory, it is reasonable to assume
that a fee for the use of alternative payment instruments promotes the
use of cash. As an example of this, a high price on the use of cheques
is probably the reason why cheques are currently very rarely used for
point-of-sale transactions at present. We have therefore constructed a
variable that indicates the fee for using various payment instruments
(cf. Aastveit (2005).
4.3 The illegal economy
Cash is unique in the sense that it may be used for anonymous
point-of-sale transactions. Whereas the use of deposits in transaction
accounts is registered, the use of cash cannot be traced. Neither the
payer nor the receiver can be identified by information in the
settlement. The properties of cash therefore make it difficult to gain
an overview of how often and in what type of transactions it is used.
This makes cash a suitable means of payment in the illegal economy. It
has gradually become recognised that the illegal economy has a
considerable effect on cash demand (cf. e.g. Dotsey (1988)).
There are mainly two different types of motives behind the use of
cash in the illegal economy. It may therefore be appropriate to
distinguish between them and their effect on demand for cash. First, it
is well known that cash is the primary means of payment in criminal
circles. We have very little information regarding the amount and
prevalence of crime. It is also difficult to find suitable variables
that detect the effect of this type of illegal economy on cash demand.
A second motive for using cash is the need to conceal income and
thereby evade paying taxes and duties to the authorities. Here too,
there is very little information on how widespread this type of illegal
economy is. In an attempt to capture the effect of tax evasion on demand
for cash, we have looked at various tax variables. Tax variables that
have been tested are: the average tax rate for the household sector, the
average tax rate for wage-earners, and tax (and pension contribution) as
a percentage of gross domestic product (GDP). Tanzi (1982) and later
Rogoff (1998) argue that these variables should have a positive effect
on cash demand. (10) They maintain that the higher marginal tax is, or
the higher the percentage of tax (and pension contributions) as a share
of gross domestic product, the greater the incentive will be for
participants in the economy to attempt to evade tax by transferring part
of their financial activity to the illegal economy. Since cash is the
most common payment instrument in the illegal economy, this will
probably lead to an increased demand for cash.
A theoretical motive for tax evasion that no one has attempted to
model concerns the effect of inflation and tax on net worth. Low
inflation and low bank interest rates combined with wealth tax may lead
to a loss after taxes on bank deposits, while the profit on cash that is
not declared for wealth taxation will be close to nil. An increase in
real wealth taxation as a result of lower inflation could thereby lead
to an increase in tax evasion and increased demand for cash.
5 A cash demand model
We model cash demand deflated by prices (real cash). (11) One
reason for this is that it is primarily real consumption of goods and
services that is relevant to the public. A behavioural context for the
public's adaptation should therefore relate the demand for real
cash holdings to planned real transactions. (12)
We started modelling with a flexible, dynamic model that took into
consideration the effects of households' consumption at retail
outlets, banks' deposit rates, the number of ATMs, the number of
point-of-sale terminals, the price of using alternative means of
payment, various tax variables and lagged values of the cash itself. See
Charts 2 to 7 for an illustration of the data series. In addition, we
included a linear trend. This was included in an attempt to capture the
aggregate effect on demand for cash of developments in the payment
system. A large number of explanatory variables and combinations of
variables have been tested, where quarterly data from the first quarter
of 1980 up to and including the second quarter of 2004 have been used.
The series for numbers of ATMs and numbers of point-of-sale
terminals proved to be strongly correlated. (14) In order to avoid
multicolinearity problems, we chose to include only one of these
variables at a time as an explanatory variable in the estimated
equation. However, it turned out that none of them had a significant
effect on demand for real cash.
Nor did the price of using alternative payment instruments have a
significant effect on cash demand. One reason for this may be
measurement errors associated with the variable, mainly due to a lack of
data (cf. Aastveit (2005)).
A general problem with regard to the analysis and modelling of
demand for cash has been the way in which the illegal economy should be
treated. As mentioned, we have tried to include various tax variables in
an attempt to detect the part of the illegal economy that is associated
with tax evasion and its effect on demand for cash. However, it turns
out that none of the variables are significant.
The preferred model that we are left with is specified in the
appendix. The model is a so-called error-correction model for the
logarithm of the demand for real cash. (15) The model shows that demand
for real cash depends on real consumption at retail outlets, banks'
deposit rates and a negative linear trend that is intended to capture
developments in the payment system, in addition to lagged values of the
cash itself. (16) The expression in brackets measures the deviation from
an estimated long-term relationship between real cash, real consumption
at retail outlets and banks' deposit rates. The coefficient of
-0.41 indicates that demand for real cash increases (decreases) by 0.41
per cent in quarter t if the demand for real cash is one per cent below
(above) the estimated long-term relationship in quarter t-1 (all else
According to the model, demand for real cash will increase by 0.53
in the long-term if real consumption at retail outlets increases by one
per cent and the other explanatory factors remain constant. The
long-term effect on real cash of a change in interest rates is slightly
weaker. According to the model, the demand for real cash will be reduced
by 0.02 per cent in the long term if banks' deposit rate increases
by one percentage point and the other explanatory factors remain
6 Forecasts and use of the model
As mentioned, the purpose of a cash demand model is to underpin
management of the purchase and storage of notes and coins. In order for
Norges Bank to order cash in as efficient a way as possible in the
future, we are dependent on accurate forecasts.
The model is based on quarterly data and will be periodically
re-estimated when information from new quarters becomes available. New
forecasts will then be made.
The model presented in the appendix is a single-equation model.
This means that attempts to make forecasts with the aid of this model
must be based on assumptions as to how the explanatory variables will
develop. Ordinarily, Norges Bank will base its assumptions regarding
private consumption at retail outlets and banks' deposit rates on
the projections for private consumption and interest rates published in
the Inflation Report.
Chart 9 shows the model-based forecasts for cash demand up to and
including 2007. (17) The projections were prepared using data up to and
including the second quarter of 2004. The chart also shows actual
developments in demand for cash in the period after the forecasts were
The chart shows that the model-based forecasts were accurate during
the period from the third quarter of 2004 up to and including the third
quarter of 2005. The only exception is the fourth quarter of 2004, where
the forecasts overshot actual demand for cash by 4 per cent.
With regard to developments over the next two years, the model
forecasts that demand for cash will increase during the next quarters
before decreasing towards the end of 2006 and further through 2007.
Increased focus on improving cash supply efficiency has resulted in
the modernisation of inventory policies and the development of a cash
demand model. The model only provides information concerning aggregate
developments in cash circulation. Further work on the model will
therefore include testing of how well it works with different
denominations or groups of denominations, such as ATM notes or coins.
So far, we have little experience with the new policy and use of
the model. However, we have gained greater knowledge about the logistics
processes and an improved understanding of the factors that affect cash
In the future, the model will play a key role in long-term planning
with regard to the procurement of notes and coins from external
suppliers. In the case of actual orders, however, the model must be
combined with micro-models, where the distribution among different
regions and denominations is included.
Appendix A: model of cash demand
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
Estimation period: 1980 Q1--2004 Q2.
Estimation method: Least square method
Absolute t-values are provided in brackets below the estimates. In
the long-term context, long-term t-values are provided. (1) The equation
fulfils requirements (diagnostic tests) that are relevant for a well
specified model. It also passes (recursive) Chow tests for structural
breaks at one per cent significance level during the last ten years. The
explanatory variables (consumption at retail outlets and interest rate)
have weak exogeneity with regard to all of the parameters in the
structural equation for real cash. (2)
[DELTA] is a differential operator: [DELTA] Xt = (Xt - Xt - 1).
cu = The logarithm for real cash. Source: Norges Bank, Statistics
c = The logarithm for real consumption at retail outlets. Source:
i = Weighted average of the banks' deposit rate for
transaction accounts. Source: Norges Bank.
[D.sub.1991.2] = Dummy variable for 1991 Q1. Introduction of a new
500 krone note at the same time as Series V of the 1000-krone note is
with drawn from circulation. We assume that when the public turn in
their old 1000-krone notes, many choose to deposit them in an account
instead of exchanging them for new notes.
[D.sub.1993.4] = Dummy variable for 1993 Q4. 1993 and the first
half of 1994 are an unstable period in the Norwegian economy. The model
has problems with reproducing the trend in demand for cash during this
period. We have therefore chosen to introduce this dummy variable.
[D.sub.1997.4] = Dummy variable for 1997 Q4, due to exceptionally
large outstanding holdings of cash among the public at the year end.
[D.sub.1999.4] = Dummy variable for 1999 Q4 due to an exceptional
demand for cash at the turn of the millennium.
[epsilon] = Regression residuals (unexplained variation in the
[R.sup.2] = The percentage of variation in the left-hand variable
that is explained by the model
[sigma] = Standard deviation of regression residuals.
[AR.sub.1-5] = A test of 5th order autocorrelation in the
[ARCH.sub.1-4] = A test for 4th order ARCH residuals.
NORM = A test for whether the residuals have a normal distribution.
HET = A test for heteroscedasticity.
RESET = A test of the model's functional form.
The expression in brackets measures deviation from an estimated
long-term relationship between demand for real cash and real consumption
at retail outlets and the banks' deposit rates.
Aastveit, Knut Are (2005): "The demand for cash in
Norway". Master's Thesis, Department of Economics, University
Baumol, William J. (1952): "The Transaction Demand for Cash:
An Inventory Theoretic Approach", Quarterly Journal of Economics
66, pp. 545-556
Boswijk, H. Peter and Jean-Pierre Urbain: "Lagrange-Multiplier
Tests for Weak Exogeneity: A synthesis", Econometric Reviews 16,
Clements, Michael P. and David F. Hendry (1998): Forecasting
Economic Time Series. Cambridge: Cambridge University Press
Dotsey, Michael (1988): "The Demand for Currency in the United
States", Journal of Money, Credit and Banking 20, 22-44
Drehmann, Matthias and Charles Goodhart (2000): "Is Cash
Becoming Technologically Outmoded? Or Does It Remain Necessary To
Facilitate Bad Behaviour? An Empirical Investigation into the
Determinants of Cash Holdings", LSE Financial Markets Group
Discussion Paper 358, September 2000.
Eklund, Trond, Solberg, Ragnhild and Veggum, Leif (2005):
"Norges Bank's role in cash distribution". Economic
Bulletin 4/05 pp. 184-190.
Fisher, Bjorn, Petra Kohler and Franz Seitz (2004): "The
Demand For Euro Area Currencies: Past, Present And Future",
European Central Bank Working Paper Series, no. 330, April 2004
Hendry, David F. and Hans-Martin Krolzig (2001): Automatic
Econometric Model Selection Using PcGets 1.0. London: Timberlake
Hendry, David F. and Jurgen A. Doornik (2001): Empirical
econometric modelling using PcGive 10. London: Timberlake Consultants
Kmenta, Jan (1997): Elements of Econometrics 2nd edition. Ann
Arbor: The University of Michigan Press
McCallum, Bennett T. (1989): Monetary Economics, New York:
Rogoff, Kenneth (1998): "Blessing or curse? Foreign and
underground demand for Euro notes", Economic Policy 26, pp. 263-303
Tanzi, Vito (1982): The Underground Economy in the United States
and Abroad. Lexington, US: Lexington Books
Tobin, James (1956): "The Interest Elasticity of Transactions
Demand for Cash", Review of Economics and Statistics 38, pp.
(1) Thanks to Gunnvald Gronvik and Karsten Gerdrup for useful
comments and suggestions. The analysis is based on Aastveit (2005).
Especial thanks to Terje Skjerpen (Statistics Norway) for sound
guidance. The analysis was performed using PcGive 10.1 (Hendry and
(2) The amount of notes and coins in circulation is defined as the
sum of Norwegian notes and coins that is held by banks and money holding
sectors (the public and financial enterprises other than banks and state
(3) In the money supply statistics published by Norges Bank, the
public's liquidity (M2) is defined as the sum of cash, bank demand
deposits, deposits and unused bank overdrafts and building loans. Cash
comprises only slightly more than 4 per cent of this definition of
(4) Deposits are defined as bank deposits in transaction accounts.
Bank deposits in transaction accounts include deposits (in kroner or
foreign currency) that may be immediately converted to notes and coins
or used as a method of payment without incurring costs other than
ordinary transaction and arrangement fees.
(5) Liquid assets are defined as assets that can be either used
directly or may easily be converted in order to make immediate
(6) In theoretical models money is defined as a non
interest-bearing means of payment. It is often appropriate to interpret
the money supply in these models as the monetary aggregate M1. The
reason for this is that in many countries the deposit rate on
transaction accounts is very low (also historically) and thus nearly
interest free. Alternatively, "interest rate" in most
theoretical models can also be interpreted as the yield on bonds minus
the interest rate on transaction accounts.
(7) In Norway, narrow monetary aggregates have been more unstable
in the short and medium term.
(8) Money's function as a store of value will also be
emphasised by including interest that represents the alternative cost of
holding cash. From the perspective of increasing one's return, cash
is poorly suited to be a store of value. However, cash may be well
suited as a store of value for concealing income/wealth from the
authorities. Unfortunately, there is little information about this.
(9) It is worth noting that the user only pays such fees if debit
cards are used. If credit cards are used, the shop pays the fee.
(10) In Rogoff (1998) a theoretical model of demand for cash is
also presented. Among other things, he argues here that a variable for
marginal tax may capture the effect of this type of illegal economy.
(11) The price variable that is used to deflate demand for cash is
related to the variable consumption at retail outlets. The price
variable is calculated as the ratio of consumption at retail outlets in
current prices to consumption at retail outlets in fixed prices. This
means that the individual price indices for each sub-component in the
consumption term 'consumption at retail outlets' will be
weighted by the percentage the respective sub-component constitutes of
the total value of consumption at retail outlets.
(12) Another reason that it is more appropriate to model demand for
real cash is that the series for real cash is integrated of order 1.
This means that the series for percentage changes in real cash is
stationary. The series for nominal cash is neither integrated of order 0
nor integrated of order 1.
(13) We have used a so-called "general-to-specific"
approach as a basis for choice of model. See, for example, Hendry and
Krolzig (2001) for a more detailed description of this method.
(14) The variables had a correlation coefficient of 0.94.
(15) This type of model makes it very easy to interpret both
short-term and long-term effects on demand for real cash of a change in
one of the explanatory variables. For a more detailed discussion and
interpretation of such a cash demand model, see Aastveit (2005).
(16) Lagged values of cash itself are included in order to correct
the model for autocorrelation. At the same time, such lags will to a
certain degree capture any seasonal effects.
(17) In order to make the forecasts more robust, a so-called
constant adjustment has been added so that the model hits the mark
exactly in the final observation. For a thorough explanation of constant
adjustment, see Clements and Hendry (1998).
Knut Are Aastveit, economist in the Financial Markets Department,
and Thomas Kjorstad, economist in the Chief Cashier's Department