Modelling euro banknote quality in circulation

The quality of banknotes in the cash cycles of countries in the Eurosystem varies, despite all of these countries using identical euro banknotes. While it is known that this is dependent on national characteristics, such as public use and the involvement of the central bank in cash processing operations, the influence of all relevant parameters has not yet been established. This paper presents two computer-based models for the simulation of banknote cash cycles. The first model simulates a cash cycle using a theoretical approach based on key figures and models banknote fitness as a one-dimensional profile of fitness levels. The model identifies: (i) the frequency with which banknotes are returned to the central bank; (ii) the fitness threshold used in automated note processing at the central bank; and (iii) the note lifetime as the main drivers of banknote quality in circulation as well as central bank cash cycle costs. Production variations in new banknotes, the fitness threshold applied by commercial cash handlers and the accuracy of the fitness sensors used in the sorting process have been found to have a lower but non-trivial impact. The second model simulates banknotes in circulation as single entities and is oriented towards modelling country-specific cash cycles using available single-note data. The model is constructed using data collected by monitoring banknotes in circulation over the duration of a “circulation trial” carried out in three euro area countries. We compare the predicted quality results of the second data-based model against actual cash cycle data collected outside the circulation trial, discuss the reasons for the deviations found and conclude with considerations for an optimal theoretical national cash cycle.