Holding Periods of Money

This repository demonstrates a new methodology for estimating the average holding period of money from transaction data recorded by real-world payment systems. This is applied to Sarafu, a small digital community currency active in Kenya from transactions recorded between 25 January 2020 and 15 June 2021. We apply a computational technique to measure the durations for which funds were held in individual accounts, compute the average holding period, and use its inverse to study the transfer velocity of Sarafu.

This serves as the replication code and supplementary material for:

Mattsson, C. E. S., Luedtke, A., & Takes, F. W. (2025). Holding Periods: Measuring the Inverse of Money Velocity from Transaction Records (arXiv:2209.01512). arXiv. https://doi.org/10.48550/arXiv.2209.01512

Repository & environment

To reproduce our analysis, please download a copy of this repository. The dependencies are listed in environment.yml; we used conda to build the environment. If you would like to do the same, first ensure that conda or miniconda is installed, then navigate into the project folder, then run the following commands in the terminal:

conda env create -f environment.yml
conda activate velocity

Downloading the data

The Sarafu CIC 2020–2021 dataset is available via the UK Data Service (UKDS) ReShare platform and has been suitably documented (Mattsson et al., 2022; https://reshare.ukdataservice.ac.uk/855142/). The dataset is “safeguarded”, meaning that access is limited to those who have registered with the UKDS and re-use is constrained by the UKDS End User License (EUL). Seeking to re-identify individuals is explicitly prohibited. - This page allows you to apply for an account: https://beta.ukdataservice.ac.uk/myaccount/credentials - Check the box with "My organisation is not listed, I need to request a UK Data Service username” - Follow the instructions

To reproduce our analysis, please download the original data and update the $DATA/sarafu_xDAI directory.

Trajectory extraction

Funds can be systematically traced through individual accounts, from transaction to transaction. Holding periods are the spaces between transactions so this gives us their weight and duration. This technique is called "trajectory extraction" and we make use of the open-source software available at https://github.com/carolinamattsson/follow-the-money. Please download this a copy of this repository ($FOLLOW).

Empirical holding times

The bash script follow.sh obtains empirical holding times from the Sarafu transaction records.

It performs this list of tasks:

1. Define the filepaths to the $DATA directory and the follow-the-money repository.
2. A basic pre-processing step, sending output to $DATA/transactions/.
3. Performing pairwise trajectory extraction, sending output to $DATA/trajectories/.
4. Produce datasets of empirical holding times, sending output to $DATA/durations/.

In addition to the transaction dataset, trajectory extraction requires an input file specifying the relevant system parameters. These are encapsulated in transactions/sarafu_config.json. Please avoid deleting this file.

These flags are used in extracting trajectories: * --no_balance is used because the Sarafu dataset is complete and accounts started off empty * --pairwise traces in-transactions to out-transactions within each account, but not between accounts * --mixed refers to the allocation heuristic, whereby all possible pairs are considered * --smallest 0.01 stops tracking for pairs involving less than 0.01 Sarafu

The final step produces two neat datasets of empirical holding times, treating the small untracked pairs in two different ways. The first uses the creation of the system to provide an upper bound on each untracked duration (--timewindow_beg "2020-01-25 00:00:00.000000"). The second uses the moment funds became untracked as a lower bound on each untracked duration. This lets us quantify the measurement uncertainty introduced by the size limit in tracking; at 0.01 Sarafu this is truly negligible.

To reproduce our analysis, please update the filepaths and make follow.sh excecutable:

chmod +x follow.sh

Then run follow.sh in the command line:

bash follow.sh

Tables and plots

To reproduce our analysis, please open velocity.ipynb as a python notebook, update the filepaths, find the environment, and run all.

References

• Mattsson, C. E. S., Luedtke, A., & Takes, F. W. (2025). Holding Periods: Measuring the Inverse of Money Velocity from Transaction Records (arXiv:2209.01512). arXiv. https://doi.org/10.48550/arXiv.2209.01512

• Mattsson, C. E. S., Criscione, T., & Ruddick, W. O. (2022). Sarafu Community Inclusion Currency 2020-2021. Scientific Data, 9(426). https://doi.org/10.1038/s41597-022-01539-4

• Mattsson, C. E. S., & Takes, F. W. (2021). Trajectories through temporal networks. Applied Network Science, 6(35), 1–31. https://doi.org/10.1007/s41109-021-00374-7.