  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.
