Page 85 - Special Topic Session (STS) - Volume 4

STS566 Richard Finlay
Australia’s approach to these two issues, and also briefly summarises recent
work on estimating the contribution to overall banknote demand from various
sections of the economy and society.

2. Forecasting banknote demand
The RBA currently uses an ARMA time-series model to forecast seasonally
adjusted banknote demand. The general model takes the form:

= + + ∑ + ϵ + ∑
t

−
−
=1 =1
where yt is the logarithm of seasonally adjusted banknote demand for a given
denomination, t is the time period, and ϵt is an error term. This model is simple
and robust and has performed relatively well over time. Its main drawback,
however, is the lack of any economic factors driving the model, meaning that
structural changes to banknote demand will only be picked-up with a lag. The
RBA has also investigated using models with more economic and financial
market content, such as error correction (ECM) or vector error correction
(VECM) models. These models are based on cointegrating relationships
between banknote demand and various macroeconomic variables. The
general form of the ECM investigated is

Δ = + Δ −1 + Δ + ( −1 − −1 ) +

0

1

= [ℎ ; ; ; ; ; ]

where yt is seasonally adjusted banknote demand for a specific denomination
in period t, Xt is a vector of variables including the cash rate, number of ATMs,
number of EFTPOS terminals, the trade weighted index (TWI) of the Australian
dollar exchange rate, nominal GDP, and population, and α is a vector of long-
run parameters. A global financial crisis dummy variable is also included for
2
the higher denominations. All variables except the cash rate are in logarithms.
The speed of adjustment term is λ. The main drawback of the ECM model is
that it relies on various macroeconomic series, and these need to be
forecasted in order to produce banknote demand forecasts. To do this we use:
vintages of the RBA’s real GDP and CPI forecasts (to construct a nominal GDP
forecast); historical overnight forward rates as implied by financial markets (for
the cash rate); long run average growth rates to project forward data on ATMs,
EFTPOS terminals and population, as no forecasts are available; and we
assume that the exchange rate (TWI) remains constant.

2 Nominal GDP and population capture the effect of rising household income, and more people,
on banknote demand. The cash rate accounts for the opportunity cost of holding cash. I include
the number of ATMs and EFTPOS machines to control for the ease of withdrawing currency. The
exchange rate captures foreign demand for Australian banknotes.
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