Bank of Canada Survival Analysis of Banknote Circulation

Survival Analysis of Bank Note Circulation: Fitness, Network Structure and Machine Learning ¹

The Bank of Canada (BOC) has a Currency Inventory Management Strategy (IMS) based on its high-speed sorters that capture the image of every banknote, including the serial number, along with the date the banknote was created, shipped from the central bank’s distribution sites and returned to them. The context for the study, even before the pandemic, was the decline of cash used at the point of sale while cash in circulation relative to GDP has been stable or even rising.

The BOC issues banknotes through its Agency Operation centres in Montreal and Toronto to ten regional distribution centres. The regional centres then distribute the notes to financial institutions. BOC carries out fitness sorting, studying 22 criteria, of returned notes. Its Note Exchange System manages the flow of notes, keeps the ledger and is used for forecasting note demand.

The study

The BOC studied 900 million unique scans collected between August 2017 and July 2018 to understand what affects the duration of banknotes in circulation, particularly the importance of network structures.

After data cleaning there were 179 million shipment and 165 million deposit records. 5% of notes were found to be unfit. Region 5 received most notes. Regions 1, 5 and 7 drew more notes than other regions. Region 1 received more banknotes than it deposited.

The study only looked at the duration of the first cycle, from first issue to first return of the notes, but did look at an accelerated failure time model for circulation duration.

Findings

The data supported some conclusions that were known already, a Canadian $5 lasts less long in circulation than a $10 but provided new insights as well as some interesting detail.

The $5 and $10 circulated for a shorter time than the $20, 50 and 100 irrespective of their fitness. As expected, notes that were withdrawn as unfit had been longer in circulation than other notes irrespective of the denomination. Fit notes spent a shorter time in the market than unfit notes.

The $5 starts to deteriorate after 100 days in circulation, while the $10 after 200 days. The deterioration of the $10 after 200 days was relatively rapid becoming unfit after 400 days. This was an unexpected result given that the $5 and $10 are substitutable denominations.

The $100’s duration was more dispersed than other denominations, and the median duration was lower than that of the $5. The authors assumed that this is because the $100 is not issued by ATMs and is used differently.

When the flow of notes around the regions was analysed, region 1 behaved very differently from the others. The study did not identify the regions. There is no logical economic reason why region 1 should be different. All denominations had a higher dispersion in duration than the other regions.

The $100 behaves differently between the regions compared with other denominations. Region 1 and 7 receive more $100 banknotes but that does not lead to reverse flows. The $100 stays in region 1 but, again, there is no economic reason to explain this.

Conclusions

As a determinant of duration in circulation, unsurprisingly the fitness measures were found to be statistically significant, but not economically. The denominational structure as found to be economically and statistically significant.

Nodes that behave as principle senders and receivers of notes persist across all denominations, underlying the importance of each geographical region.

Certain banknotes are involved in specific types of transactions that make certain denominations more or less likely to be deposited back. Understanding the denominational structure helps understand payment choice.

Final thought

The IMS approach of BOC, with its serial number capture, allowed this study. For privacy reasons the report does not go into the banknote level findings of the work. This paper demonstrates the power of data to enable insights, and to confirm or dispel assumptions, that allow central banks to manage cash efficiently and effectively.

1 - Survival Analysis of Bank Note Circulation: Fitness, Network Structure and Machine Learning. Staff working paper 2020-33. Diego Rojas, Juan Estrada, Kim P. Huynh, David T. Jacho-Chávez.