The Estimation of Banknote Lifespan in Iran Using Survival Model Estimation Method

Understanding the lifespan of banknotes is critical for the efficient management of their production, distribution, and storage by issuing authorities. Calculating the lifespan of banknotes through the recording of their serial numbers at issuance and destruction involves significant operational costs. Utilizing macroeconomic data and statistical inference enables the estimation of the lifespan of various banknote denominations. This study investigates this subject in Iran using the inverse destruction rate method, the Feige method (1989), and survival model estimation. Due to data limitations, the survival model estimation was implemented for the 10,000 Toman banknote. The results show that the average lifespan of 10,000 Toman banknotes, using the inverse destruction rate method, Feige's method, and the survival model, is 22.6, 21, and 23.4 years, respectively. Furthermore, using the Weibull distribution, we provide evidence for the hypothesis that the probability of banknotes being destroyed increases over time at an increasing rate. Nevertheless, the estimated values are relatively high compared to reported statistics from other economies, such as the United States or Japan. Although the lifespan estimates for other denominations vary, the calculated values remain relatively high. These results may provide evidence supporting the hypothesis that different durability thresholds are chosen by the central bank in a developed country and a developing country.