Inverse estimation of the transfer velocity of money

Monitoring the money supply is an important prerequisite for conducting sound monetary policy, yet monetary indicators are conventionally estimated in aggregate. This paper proposes a new methodology that is able to leverage micro-level transaction data from real-world payment systems. We apply a novel computational technique to measure the durations for which money is held in individual accounts, and compute the transfer velocity of money from its inverse. Our new definition reduces to existing definitions under conventional assumptions. However, inverse estimation remains suitable for payment systems where the total balance fluctuates and spending patterns change in time. Our method is applied to study Sarafu, a small digital community currency in Kenya, where transaction data is available from 25 January 2020 to 15 June 2021. We find that the transfer velocity of Sarafu was higher than it would seem, in aggregate, because not all units of Sarafu remained in active circulation. Moreover, inverse estimation reveals strong heterogineities and enables comparisons across subgroups of spenders. Some units of Sarafu were held for minutes, others for months, and spending patterns differed across communities using Sarafu. The rate of circulation and the effective balance of Sarafu changed substantially over time, as these communities experienced economic disruptions related to the COVID-19 pandemic and seasonal food insecurity. These findings contribute to a growing body of literature documenting the heterogeneous patterns underlying headline macroeconomic indicators and their relevance for policy. Inverse estimation may be especially useful in studying the response of spenders to targeted monetary operations.