RDP 2015-10: The Life of Australian Banknotes 1. Introduction

Knowledge of the life of a banknote is important to managing an issuer's banknote production, processing, distribution and storage requirements. To make these policy decisions, currency issuers need an understanding of how long banknotes can remain in circulation before they are no longer fit for purpose and need to be replaced with new banknotes. It is also useful to know whether banknotes tend to return for destruction gradually over time, or whether a large proportion of banknotes become unfit around a particular age. Despite the importance of studying the life of banknotes, there is little published research in this area. This paper aims to fill that gap.

Ideally, the life of every banknote could be directly observed by recording its serial number when first issued and when returned for final destruction. While this capability is becoming increasingly available to currency issuers, it cannot retrospectively be applied to banknotes already in circulation. Instead, banknote life is typically estimated using aggregate data and samples of circulating or unfit banknotes. Using these data to produce reliable estimates of the life of banknotes presents challenges, particularly because not all banknotes are necessarily treated in the same way by the public – some may spend most of their lives being used for transactional purposes, while others may spend considerable time being used as a store of value.

I examine three methods that estimate the life of a banknote based on aggregate data. The first two are the traditional steady-state and the Feige steady-state methods that are commonly used by currency issuers due to their ease of calculation and undemanding data requirements. These two methods are typically used to calculate the average life of banknotes, but their estimates can be improved upon by instead constructing a median, which tends to be less affected by the fact that some banknotes last a very long time when they are used as a store of value.

While simple to construct, a key limitation to these measures is that they are very sensitive to demand shocks, such as the global financial crisis (GFC), and cannot control for changes to currency issuer policies that affect the quality and distribution of banknotes. Another limitation is that these methods can only be used to study measures of central tendency, including the mean or median banknote life. It is also useful, however, to gain an understanding of whether banknotes will be returned for destruction gradually over time or if a large proportion of banknotes become unfit for purpose around a certain age.

A better alternative is to develop survival models that can provide both measures of central tendency and estimates of banknotes' probability of survival over time. A key contribution of this paper is that these survival models do not require data on individual banknotes, but can be formulated using aggregate data commonly gathered by currency issuers. More importantly, the survival models can control for changes in banknote demand and changes in currency issuer policies, making the results less volatile over time, and thus providing a more useful basis for policy decisions that should look through short-run fluctuations. Another interesting innovation is that the survival models can be used to estimate the number of banknotes being held as a store of value.

To validate the predictions of the models, the estimates can be compared with samples of unfit banknotes ready for destruction and also samples from the population of banknotes in circulation. Overall, the survival models give a good fit to the sample data.