RDP 2015-10: The Life of Australian Banknotes 5. Limitations of the Steady-state Methods

The traditional and Feige steady-state methods are subject to several limitations. Both methods assume that the probability of a banknote becoming unfit is the same for all banknotes on issue regardless of their age, or in other words, they assume a constant hazard function. However, since the discussion in Section 2.4 indicated that the aggregate hazard rate is likely to vary with the time since issuance, this assumption is not likely to provide the best fit to the data.

Also, neither method is able to readily accommodate exogenous shocks to the number of banknotes on issue or changes in supply-side policies on the part of the currency issuer. Feige (1989) also identifies that an underlying assumption of his equation is that the total number of transactions in the average banknote's lifetime does not change over time. Over the past twenty or so years, however, there have been a number of exogenous shocks, as follows.

5.1 Demand Shocks

Events which result in temporary fluctuations in the public's demand for banknotes can adversely affect the steady-state measures of banknote quality. Two examples include Y2K and the GFC where the public's demand for banknotes increased substantially. Even though shocks of this nature are often temporary, the impact on the number of banknotes in circulation can persist and distort banknote life estimates for several years. For example, in late 2008, the demand for $50 banknotes increased sharply in response to the GFC. Although GFC concerns quickly abated, the number of $50 banknotes in circulation took more than two years to unwind. Reflecting this sharp increase in circulating $50 banknotes, banknote life (as estimated by Equations (5) and (7)) increased and remained at that higher level for several years (Figure 3).

5.2 Banknote Quality Programs

Implicit in the steady-state methods is an assumption that the currency issuer's banknote quality programs are unchanged. This is somewhat unrealistic, however, as currency issuers are continually looking for opportunities to enhance the quality of banknotes in circulation. These improvements may take the form of new arrangements with banks and cash-in-transit companies (such as the Note Quality Reward Scheme introduced in Australia in 2006) or targeted ‘cleansing’ programs, which involve the accelerated replacement (and destruction) of specific denominations in circulation.^[9] Irrespective of the nature of the change, the outcome is the same; initially banknote life would appear to be low as destructions would be high relative to the stock of banknotes on issue, but banknote life would be higher in subsequent periods due to the higher quality of the remaining stock of banknotes on issue. Examples of the effect of cleansing programs can be clearly seen in the data for the $20 banknotes in 2006 and 2007, for the $10 banknotes in 2009 and 2010, and for the $5 in 2011 (Figure 3).

5.3 New Banknote Series

When a new series of banknotes is introduced into circulation, old series banknotes are withdrawn and destroyed. With a sharp increase in banknote issuances and destructions, the steady-state methods suggest a sharp decline in banknote life. This decline will be quickly offset, however, as the relatively higher-quality banknotes from the new series will circulate for a considerable period before being withdrawn. This profile is especially dramatic for banknotes that tend to have an average life in excess of the 12-month periods examined in the turnover formulas, which helps to explain the change in the banknote life profile of the $50 banknotes after the introduction of polymer banknotes in the mid 1990s (Figure 3).

5.4 Cash Management

Underlying the steady-state methods is an assumption that the cash management arrangements between the currency issuer and the wholesale cash industry are unchanged. To a large extent this assumption is realistic, as changes to these arrangements tend to be incremental and have a negligible impact on banknote life estimates. In the case of Australia, however, the changes to the cash management arrangements in 2001 were sufficiently large that they did affect the steady-state estimates. In addition to changing the manner in which unfit banknotes were withdrawn from circulation and destroyed, some precautionary banknote holdings were transferred from the RBA to the commercial banks. Privatising these banknote holdings to the commercial banks resulted in a permanent increase in the number of banknotes measured as ‘on issue’, thereby leading to an increase in the average banknote life estimated by the steady-state formulas.

Footnote

For more information on the Note Quality Reward Scheme, see Cowling and Howlett (2012). [9]