Abstract
Could the introduction of central bank digital currencies lead to the disappearance of physical cash from the payments system? This extinction would be fraught with several insidious risks, as most of the benefits of the other payments instruments hinge on the continued possibility to use cash for retail transactions. This paper investigates how the use of different payments instruments may evolve over time in a two-sided market where different types of agents can choose which instrument(s) they would use. It shows that while more instruments can continue to be used indefinitely in equilibrium, there are also cases where one instrument becomes extinct and this new equilibrium can be stable, hence, irreversible. The paper also shows that very different outcomes can be reached from very similar initial conditions, and that a minor perturbation, such as the introduction, even on a small scale, of a new instrument can lead to the eventual extinction of one instrument. These results call for caution with the introduction of digital currencies and, more generally, with the digitalization of the financial system.
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Data Availability
This study is not based on actual data. The data used for the examples and charts were generated by the authors by running simulations based on the formulas included in the text and in the Online Supplemental Appendix and on the parameters indicated in the text.
Notes
A discussion on the pros and cons of cashless societies can be found in Fabris (2019).
Depending on the values of the parameters, one or more of these lines may not intersect the set S, which may thus be divided into only two regions or may be entirely included in one. In such cases, one or two of the sets B, C, and D would be empty.
This is the standard extension to a two-sided market setting of the Nash equilibrium concept, whereby no agent can gain by changing his behavior insofar as all other agents keep their behavior unchanged.
The participation constraints for a single-currency equilibrium are somewhat looser. For the cash-only equilibrium, they require that pcH + qc < ξ and cf – βL < w and for the cards-only equilibrium that pdH + qd < ξ and cd – rd < w. If these constraints are violated, some agents leave the market, but this fact by itself does not result in the introduction of another payment instrument. It is assumed that these fairly obvious and general conditions are always satisfied.
Simulations show that this is a stable equilibrium, in the sense that the system converges back to it if the initial vector π lies in an open neighborhood of (0,0).
We abstract here from deficiencies in financial inclusion that prevent some customers from opening bank accounts or obtaining debit or credit cards. This model assumes that the entire population has full access to financial services, and their choice of instrument depends only on their preferences.
We are grateful to Professor David Humphrey for referring this source of data to us.
Here, the simple average of their estimates of the costs incurred were used for accepting different types of cards.
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Acknowledgements
We are grateful to Alexei G. Goumilevski for valuable technical support in developing the code running the simulations, to Mohamad Nassar for precious technical help and advice, and to Tanai Khiaonarong, Trevor W. Chamberlain, Alvaro Pedraza, David Humphrey, Evan Kraft, Munacinga Simatele, and other participants at the 95th International Atlantic Economic Conference in Rome, Italy, 22-25 March 2023, and at the 2023 Annual Conference of the Society of Government Economists for valuable comments and suggestions. We are solely responsible for how we used their help and advice.
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Maino, R., Pani, M. Could CBDCs Lead to Cash Extinction? Insights from a “Merchant-Customer” Model. Int Adv Econ Res 30, 21–45 (2024). https://doi.org/10.1007/s11294-024-09888-z
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DOI: https://doi.org/10.1007/s11294-024-09888-z