Modelling the Cash Payments in the Economy: an Application to France

Modeling the demand for cash and deposits is a primary concern for central banks. Within a wide range of academic contributions, payment choice models based on transaction sizes (TS models) have been promoted. However, TS models induce strong predictions about the use of payment instruments. In particular, all equal-sized transactions are supposed to be paid with the same payment instrument. We propose a simple alternative model based on cash holding (CH model) that allows equal-sized transactions to be paid for in cash or with other payment instruments. Using micro-level payment data from two representative samples of the French population in 2005 and 2011, we test how well each model replicates the observed shares of cash payments in the French economy for each size of transaction. We find that the CH model outperforms TS models, as it better predicts the observed shares of cash payments with notably less demanding information on individuals.