Simulating the Adoption of a Retail CBDC
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Carlos León
,
Jose F. Moreno
Abstract
We use agent-based modelling to build a digital twin of the retail payment system, where heterogeneous consumers and merchants interact, learn, and adapt as they meet and use different monies and payment instruments. As we introduce an rCBDC, the model simulates its adoption. We calibrate this digital twin to Spain’s retail payment ecosystem. We run hypothetical scenarios that correspond to public discussions about the digital euro. Results show that introducing an rCBDC without attractive design options and stimulus results in low and slow adoption. Results suggest that the reverse waterfall functionality, a positive remuneration spread, and the distribution of government subsidies via rCBDC are effective in fostering adoption; yet, the distribution of government subsidies via rCBDC is the only one that creates incentives to reduce the use of cash. Balance limits and top-up limits are effective in restraining adoption. Results also suggest that combining design options and stimulus with limits to holding rCBDCs could aid in achieving a sweet spot of adoption.
1 Introduction
Money and payment instruments[1] enable the efficient and safe functioning of the retail payment ecosystem, where consumers acquire goods and services from merchants, and where consumers make peer-to-peer transfers. Introducing a new form of money and/or payment instrument could affect the behaviour of consumers and merchants and, eventually, reshape the retail payment system.
When the new form of money and payment instrument is a digital liability of the central bank, available to the public, i.e. a retail central bank digital currency (rCBDC), the potential effect on the behaviour of consumers and merchants is sizable. From increasing financial inclusion and crowding out existing payment instruments (e.g. cash, debit cards) to causing a destabilising migration from deposits, the adoption of an rCBDC could change the retail payment ecosystem, impact interdependent markets (e.g. money market, credit market), and affect the macroeconomic equilibria. All in all, rCBDC’s potential effect depends on its adoption.
Simulating the adoption of an rCBDC is a challenging task. It demands modelling the retail payment ecosystem as a complex system, i.e. one composed of multiple interacting adaptive agents whose aggregate behaviour is not predictable from themselves.[2] Simulating the adoption of an rCBDC requires modelling a myriad of interacting and adaptive agents that not only display intrinsic differences related to their type (e.g. consumers and merchants are different) but also differ among those of the same type (e.g. not all consumers are equal), which corresponds to the disparate preferences to hold, use, and accept different forms of money and payment instruments.
In this article, we use agent-based modelling (ABM) to build a digital twin of the retail payment ecosystem and to simulate the adoption of an rCBDC. Heckbert, Baynes, and Reeson (2010) define ABM as the computational study of systems of interacting autonomous entities, each with dynamic behaviour and heterogeneous characteristics. According to Heckbert et al., it is the interaction among adaptive decision-makers that is the first solid criterion for choosing ABM to model a system. In this vein, as consumers and merchants are adaptive decision-makers in the retail payment ecosystem, we choose ABM to simulate the adoption of an rCBDC.
We calibrate the ABM model of the retail payment ecosystem to data from Spain. As suggested by literature related to modelling human decision-making and behaviour with ABM, we use surveys (see An et al. 2021; Bonabeau 2002; Heckbert, Baynes, and Reeson 2010). From the European Central Bank’s (ECB) Study on the Payment Attitudes of Consumers in the Euro area (henceforth, the SPACE survey), we filter out and derive the individual behaviour of consumers and merchants from Spain and generate statistical descriptions of how different cohorts of consumers use the different payment instruments available.
As highlighted by Zamora-Pérez, Coschignano, and Barreiro (2022), investigation is needed to determine the essential features for the successful adoption of rCBDCs. Therefore, we run different hypothetical scenarios that correspond to publicly available technical discussions about the digital euro. Those scenarios incorporate design options such as account balance limits, tiered anonymity, remuneration, and reverse waterfall functionality; regarding the latter, to the best of our knowledge, this is the first article that models and evaluates automatic transfers of funds from deposits to the rCBDC wallet to complete a transaction – a functionality the ECB (2022b, 2023a, 2023b) envisages for the digital euro. Also, the scenarios include policy decisions, such as making rCBDC legal tender, private sector payrolls paid in rCBDC, and the government paying subsidies in rCBDC. The potential for offline transactions has not been incorporated explicitly into the modelling as it is still a complex undertaking with many unknowns (see BIS 2023); however, as physical (proximity) low-value transactions between consumers and merchants are modelled, offline transactions are partially and implicitly incorporated.
There are several insights to highlight. First, introducing an rCBDC without including attractive design features or stimulus policies results in low and slow adoption. This overlaps with early evidence reported for Nigeria, The Bahamas, and the People’s Republic of China (see Anthony 2022; Feng 2022; Fortis 2023; Osae-Brown, Onu, and Irrera 2023; Ree 2023; Walker 2022; Zamora-Pérez, Coschignano, and Barreiro 2022). Second, results suggest that design options differ in their effectiveness. The reverse waterfall functionality, a positive remuneration spread, and the distribution of government subsidies via rCBDC are effective in fostering adoption; yet, the distribution of government subsidies via rCBDC is the only one that fosters adoption and reduces the use of cash. Conversely, balance limits and top-up limits are effective in restraining adoption. Third, combining attractive design options and stimulus policies with limits to holding rCBDCs could be the key to achieving a sweet spot of adoption – one that is high enough to foster effective use of rCBDC but low enough to neither crowd out existing payment instruments nor threaten the stability of the financial system by, say, pushing for deposit migration. However, it is worth noting that results and conclusions are restricted to the case of Spain; it is well-known that other retail payment ecosystems in the Eurozone (and elsewhere) have a higher preference for cash (e.g. Germany) or digital payments (e.g. Finland).
Our results highlight the importance and convenience of simulating the adoption of an rCBDC. By implementing an agent-based learning-by-simulation approach, the complex interdependence between the initial conditions of the retail payment ecosystem and the rCBDC design options can be modelled and studied before incurring the costs and risks of a learning-by-doing approach. Following Flyvbjerg and Gardner (2023), adopting a learning-by-simulating approach would enable central banks and other stakeholders to sufficiently and seriously iterate and test, with the simulation evolving into a reliable plan for the design, pilot, roll-out, and adoption of rCBDCs. In this vein, our quantitative approach enables central banks to test whether design choices are in line with agents’ expectations before real-world trials and controlled experiments (see Zamora-Pérez, Coschignano, and Barreiro 2022). Further, instead of working with assumed adoption scenarios, central banks and other stakeholders could study and discuss the potential impact of an rCBDC based on adoption figures that correspond to the features of the retail payment ecosystem and the most likely design options.
The next section presents a literature review that focuses on current rCBDC modelling and the need to implement ABM to better understand how an rCBDC is adopted. The third section describes the methodology. The fourth section presents the main results, in the form of the digital twin of the retail payment ecosystem. The fifth section discusses the results. The last section presents our final remarks.
2 Literature Review
This article is related to two main strands of literature: rCBDCs modelling and agent-based modelling. Regarding the first strand, most literature has focused on how rCBDC could affect the macroeconomic equilibria.[3] Dynamic Stochastic General Equilibrium (DSGE) models (see Assenmacher et al. 2021; Barrdear and Kumhof 2016; Burlon et al. 2022; Ferrari, Mehl, and Stracca 2020; George et al. 2022; Wright et al. 2022) and non-DSGE models (see Agur, Ari, and Dell’Ariccia 2022; Andolfatto 2021; Chiu et al. 2019; Garrat et al. 2022; Keister and Monnet 2021; Li 2023; Tan 2023) have been implemented to study the macroeconomic consequences of introducing an rCBDC, namely on economic activity; welfare; household asset allocation; lending; monetary policy; financial inclusion; financial stability; exchange rate stability; credit cycles; banking competition and market power; and banks’ and central bank’s balance sheets.
These models that focus on how rCBDC could affect the macroeconomic equilibria are top-down approaches,[4] which do not model the adoption of rCBDC as the result of the interactions of end-users, namely consumers and merchants – the main constituents of the retail payment system. These models neither deal with how consumers and merchants meet in the goods and services market; nor their heterogeneity; nor how they use, adopt, and abandon the different forms of money and the related payment instruments. These models do not incorporate design options, policy decisions, and how they affect adoption. Further, their calibration does not include observed consumers’ preferences for and merchants’ acceptance of payment instruments. That is, in top-down approaches, the adoption of the rCBDC occurs as agents maximize their utility functions in an abstraction of how they meet and learn in the retail market and choose from different available payment instruments to settle their transactions.
Some cases of rCBDC modelling do not focus on the macroeconomic equilibria. Ramadiah, Galbiati, and Soramäki (2021) study the macro-financial effects of introducing an rCBDC in Germany. Martens (2021) studies the crowding out of payment instruments caused by the introduction of an rCBDC in the Netherlands. Castrén, Kavonius, and Rancan (2022) introduce a rCBDC into the network of financial accounts and run scenarios to study how the banking sector would adjust and induce changes in the financial network structure. Gross and Letizia (2023) develop a simulation model that focuses on the impact on deposit rate spreads, reserve borrowing, and monetary policy pass-through; however, the adoption of the rCBDC is not modelled.
Ramadiah, Galbiati, and Soramäki (2021), Martens (2021), and Gross and Letizia (2023) are bottom-up approaches. In bottom-up approaches (see De Grauwe 2010), agents use simple rules or heuristics to guide their behaviour instead of assuming that they can find the optimum under the assumptions of a complete understanding of the system and rational expectations;[5] they are “bottom-up” as the behaviour that is observed in the model is generated by the direct interactions of the agents that form the basis of the model – from the bottom of the system (Miller and Page 2007). In the case of Ramadiah et al., consumers use heuristics to determine their choice of payment instruments and wealth whereas merchants start accepting rCBDC based on consumers’ previous demands. In Martens, rCBDC is adopted as households and firms maximize their utility while they choose to use and adopt (or remove) payment instruments, respectively. In Gross and Letizia, banks and non-banks use heuristics while seeking an equilibrium for deposit rates after an rCBDC is introduced.
These three bottom-up approaches to rCBDC modelling share a common methodological ground: Agent-based modelling (ABM). Bonabeau (2002) defines ABM as describing a system from the perspective of its constituent units. Wilensky and Rand (2015) define ABM as a form of computational modelling whereby a phenomenon is modelled in terms of agents and their interactions.
ABM has been the usual choice for modelling complex systems – those composed of multiple individual elements that interact with each other yet whose aggregate properties or behaviour is not predictable from the elements themselves, whereas through those interactions a characteristic phenomenon of emergence [6] arises (Wilensky and Rand 2015). It is the presence of dynamic feedback, evolution, autonomy, heterogeneity and interaction, and explicit adaptive decision-making that makes ABM an appropriate approach to modelling complex systems (see Heckbert, Baynes, and Reeson 2010; Novizayanti et al. 2021).[7]
One defining feature of ABM is the explicit representation of the dynamic behaviour of heterogeneous agents (Wilensky and Rand 2015), generally, human decision-makers who use heuristics rather than optimisation for making decisions and whose preferences and behaviour can change as new information becomes available (Heckbert, Baynes, and Reeson 2010; Turrell 2016). This explicit representation is encoded in the decision-making functions that agents follow when interacting among themselves or with the environment, in the form of rule-based and analytical decision-making functions. Another defining feature is the repetitive interactions between the agents, which relies on computational power to explore dynamics that are out of reach of pure mathematical methods (Bonabeau 2002).
The retail payment ecosystem is a complex system. It is the dynamic and adaptive behaviour of consumers and merchants that yields an intricate network of transactions with certain topological features that can’t be explained at the agent level. This makes ABM an appropriate approach to bottom-up modelling rCBDC. All in all, acknowledging that the retail payment ecosystem is a complex system is the reason why Turrell (2016) highlights the potential of ABM to model rCBDC, whereas Ramadiah, Galbiati, and Soramäki (2021), Martens (2021), and Gross and Letizia (2023) implemented ABM accordingly. This is the reason why we choose ABM as our methodological mainstay, aimed at simulating the adoption of an rCBDC.
Tightly related to the adoption of a new form of money and payment instrument, ABM has been applied to studying the adoption of new consumer technologies (i.e. innovation diffusion) in social systems (see Alexandrova-Kabadjova, Castellanos Pascacio, and García-Almanza 2012; Bonabeau 2002; Christensen et al. 2020; Klioutchnikov, Sigova, and Klioutchnikova 2022; Moglia, Podkalicka, and McGregor 2018; Novizayanti et al. 2021; Pakravan and MacCarty 2021; Rai and Robinson 2015).[8]
3 The Methodology
Adoption means that consumers make full use of the innovation (Christensen et al. 2020). In the retail payment ecosystem representation, rCBDC adoption occurs as consumers buy goods and services from merchants (C2M) and as consumers make transfers among themselves (C2C) with rCBDC. That is, adoption is not about consumers opening an rCBDC wallet or allocating money to it but about paying with rCBDC. Adoption also conveys that consumers and merchants learn and make decisions about which monies to hold and which payment instruments to use. It is the repeated payment interaction between consumers and merchants that determines the adoption and/or abandonment of the modelled payment instruments. Therefore, the agents, the payment mechanics, and the learning process are the three mainstays of the representation of the retail payment ecosystem and the simulation of the adoption of an rCBDC.
3.1 The Agents
Two types of agents are the mainstay of the ABM retail payment ecosystem representation: consumers and merchants. Consumers and merchants are the interacting adaptive decision-makers that determine whether and how the rCBDC is used and adopted in the retail payment ecosystem. Other agents, such as commercial banks, the central bank, and the government fulfil ancillary roles that correspond to their economic function, yet they are not adaptive decision-makers in our modelling of rCBDC adoption.
Both agents, consumers and merchants, are created based on the data available from payment surveys. In the case of consumers, they are segmented in cohorts according to sociodemographic information (e.g. age, location, income), in what we refer to as consumer personas. Each consumer persona has a number of consumers that corresponds to the size of that cohort with respect to the country’s overall population distribution. Income distribution and money holdings data allow the different forms of money to be allocated to each consumer persona and each consumer. To simulate consumer behaviour, we incorporate data on cash holdings and withdrawals, including withdrawal values, frequency, and the average number of days between withdrawals. Additionally, we consider information on the holdings and usage of the payment instruments modelled in the simulation, along with consumer preferences for each payment instrument, ensuring a comprehensive representation of their payment behaviour.
In the case of merchants, they are also segmented in cohorts according to their type (e.g. supermarkets, retail stores, utilities), in what we refer to as merchant personas; also, merchants differ in that they correspond to recurrent payments (e.g. rent, subscriptions, mortgages) or not. Each merchant persona is related to a consumer priority; this is a vector that reflects how important the different types of goods and services are to the lives of the consumers. Also, each merchant persona is related to a payment instrument acceptance vector; this vector contains information about the willingness of merchants to accept the payment instruments.
3.2 Payment Mechanics
The payment mechanics are determined by two steps. First, the initial allocation of money and payment instruments, and the assignment of initial preferences for payment instruments. Second, the simulation of payments between consumers and merchants (C2M), and among consumers (C2C).
3.2.1 Initial Allocations and Assignments
In this representation of the retail payment ecosystem, there are three forms of money available to consumers, merchants, and the government: cash, deposits, and rCBDC.[9] Different payment instruments are available to consumers, merchants, and the government to make their payments based on the transfer of money. Cash operates simultaneously as money and a payment instrument. In contrast, other payment instruments, such as debit and credit cards, direct debits, credit transfers, and mobile wallets, enable the user to initiate a transfer of value residing on deposits. Although the rCBDC function is very similar to cash, in this representation the rCBDC is managed by two distinct payment instruments, anonymous and non-anonymous rCBDC, depending on the value of the payment and a threshold that enables simulating a two-tiered rCBDC scheme by anonymity (see ECB 2019). Payments with a value below (above) the threshold are made with the anonymous (non-anonymous) rCBDC, with the option to be made offline as physical proximity allows – as suggested in ECB (2023b).[10]
Each consumer has a set of money forms assigned according to random draws from the corresponding consumer persona dataset. Therefore, not all consumers have the same set of forms of money available, e.g. some consumers have cash as their only form of money available at the start of the simulation, whereas others have the three forms of money herein available to retail transactions – depending on the consumer persona they belong to. At the start of the simulation, no consumer has rCBDC assigned.
The initial balance held by consumers corresponds to the salary they receive at the start of the first day of the simulation, determined by a random draw from the corresponding consumer persona dataset; for simplicity, the salary remains fixed for each consumer during the simulation. Afterwards, the available balance corresponds to the sum of the balance at the end of the previous day (i.e. after making payments) and the subsequent income from new salaries, subsidies, and returns on remunerated forms of money.
The initial availability of payment instruments held by consumers corresponds to the random draw from the consumer persona data set. However, for a payment instrument to be allocated to a consumer, she must have the corresponding form of money available; for instance, a debit card can’t be allocated to a consumer without a deposit account.
After allocating the forms of money and payment instruments to the consumers, each consumer will be assigned an initial preference for payment instruments. As initial preferences are extracted from the consumer persona dataset, they encode all the information consumers have gathered about the payment instruments available in the economy; that is, under the technology acceptance model of Davis (1989), initial preferences encode payment instruments’ perceived usefulness and ease of use – respectively, the degree to which users believe a payment instrument will enhance their payment experience and the degree to which users feel that using a payment instrument demands little or no effort.
These initial preferences are key for two reasons. First, they are the starting point for the simulation to randomly draw how each consumer will pay for the first time. Initial preferences work as a prior that is subsequently and continuously updated according to the payments that consumers were able and unable to make to the merchants and other consumers – a learning process, as explained in a forthcoming section.
Second, the initial preference for cash could be used as an imperfect proxy for the initial preference for rCBDCs. As rCBDCs are payment instruments that are being designed to share some of the salient features of cash (i.e. a liability of the central bank, available to everyone, enabling private and offline payments), the initial preference for cash may reveal the attitude of the public towards some forms of rCBDC, namely those that offer some degree of privacy in the form of an anonymous rCBDC. In this case, the initial preference for cash may be shared with an anonymous rCBDC by defining an affinity parameter; that is, by defining to what extent the consumer would find cash and an anonymous rCBDC similarly useful and easy to use. In a two-tiered rCBDC scheme by anonymity (see, ECB 2019), the initial preference for deposit-like (i.e. non-anonymous) payment instruments (e.g. credit cards, debit cards, transfers) may be shared with a non-anonymous rCBDC; in this case, an affinity parameter to non-anonymous payment instruments is used to determine to what extent the consumer would find a non-anonymous rCBDC useful and easy to use.
As mentioned, no consumer has rCBDC assigned as a form of money or as a payment instrument at the start of the simulation. A consumer will open a rCBDC wallet whenever she finds that there is a potential use for it. This happens in four cases during the simulation. First, when there is a sufficiently large fraction of failed transactions that could have been completed by opening an rCBDC wallet and changing her allocation of money to rCBDC; that is, when the consumer discovers that holding rCBDC could enhance her C2M and C2C payment experience. Second, by demonstration effects (i.e. imitation behaviour), when a significant fraction of her peers has an rCBDC wallet; that is, when the consumer becomes aware that her peers have enhanced their C2M and C2C payment experience by opening an rCBDC wallet. Third, when the remuneration of rCBDC surpasses that of deposits by a determined spread, a consumer may open an rCBDC wallet and demand that her monthly salary be transferred to it. Fourth, if the government decides to transfer subsidies to rCBDC wallets, an rCBDC wallet is opened automatically by the simulation. In all four cases, right after the rCBDC wallet is opened, there is a transfer of funds to it. This first top-up is determined by the consumer’s preference for anonymous and non-anonymous rCBDC – as previously depicted. If, for any reason, the top-up exceeds the rCBDC balance limit, a waterfall functionality ensures that the exceeding value is automatically transferred to a designated deposit account, as suggested in ECB (2022, 2023a); in this case, as explained in ECB (2023b), the balance limit is consistent with avoiding rCBDC use as means of investment and maintaining a healthy equilibrium between deposits and central bank money.
On the other hand, each merchant has a set of payment instruments that it is willing to accept. Akin to the allocation of payment instruments to consumers, payment instrument acceptance by each merchant is determined by a random draw from the merchant persona dataset. Yet, payment instrument acceptance has some particularities. First, unlike consumers’ preferences, merchants’ acceptance of payment instruments could be determined by law, in the form of legal tender status.[11] Second, the nature of a merchant (i.e. physical, online, both) determines the payment instruments it is willing to accept.
Akin to consumers’ preferences, merchants’ acceptance of payment instruments is dynamic. The initial acceptance will change as consumers and merchants meet in the goods and services market. However, unlike the update of consumers’ preference for payment instruments, the acceptance of payment instruments does not change continuously. In this vein, accepting a new payment instrument is a discrete process, one that depends on reaching a tipping point of impact on the merchant’s sales – again, this is a learning process, as explained in a forthcoming section.
3.2.2 Simulation of C2M Payments
After the initial allocations and assignments have been set, the model will randomly select a consumer. The consumer will either meet a merchant in the market of goods and services or a consumer in the peer-to-peer network of transfers. When going to the market of goods and services, if the consumer has disposable money, based on the consumer and merchant persona data, the model will randomly generate transactions and the merchants that will act as the counterparties of these transactions.
The number of transactions for each combination of consumer and merchant is randomly drawn from the consumer persona dataset. The random selection of the merchants follows a vector of priorities that determines the preference for purchasing different types of goods and services. Such vector reflects how important the goods and services are to the lives of the consumers; for instance, consumers will likely prioritise recurrent payments (e.g. rent, mortgage, utilities) and purchases of basic goods (e.g. day-to-day retail, medicines) over non-fundamental goods (e.g. entertainment, durable goods). Afterward, based on the selected merchants and the merchant persona they belong to, the number and value of the transactions are randomly drawn.
Then, the simulation attempts to complete each transaction. First, the simulation will verify that the value of the transaction is equal to or lower than the sum of all consumer’s monies. If the verification is negative, the transaction will be cancelled and the next one will be processed, recursively. If positive, the simulation will find the vector of payment instruments that are available to the consumer and accepted by the merchant, i.e. the intersection of the consumer’s preferences and the merchant’s acceptance. From a (non-empty) vector, based on the consumer’s preferences, the simulation will randomly draw the first payment instrument the consumer will try to use. If the money balance corresponding to that payment instrument is enough to make the payment, the transaction will occur; if not, the simulation will attempt to make the payment by making subsequent random draws from the remaining payment instruments. When the selected payment instrument is an rCBDC but the balance is not enough to complete the transaction, a reverse waterfall functionality is available: an automatic transfer of funds from deposits to the rCBDC wallet allows the consumer to complete the transaction, as suggested in ECB (2022b, 2023a, 2023b). If needed, the simulation will attempt to complete the transaction by using several monies simultaneously, i.e. by fractionating the payment. When necessary, as a last attempt to make the payment, payment instruments that are not accepted by the merchant but that are available to the consumer will be used to rebalance accepted payment instruments, e.g. the consumer withdraws cash when the merchant does not accept digital payment instruments.
This payment mechanics is repeated until all the transactions randomly drawn for the consumer are processed. Afterwards, the next consumer is selected. The payment mechanics continue recursively until all consumers and their transactions, on all days of the simulation, have been processed.
3.2.3 Simulation of C2C Payments
On the other hand, when the selected consumer meets another consumer in the peer-to-peer network of transfers, the model will look for all the transfers in which the former acts as an originator (i.e. the sender of funds) in the C2C network. The C2C network contains all possible combinations of consumers that could make part of the peer-to-peer network of transfers. It is generated for all days after the initial allocations and assignments have been set, based on the random graph model of Erdős-Rényi (see Barabási 2016; Erdős and Rényi 1959; Newman 2010).
In the Erdős-Rényi model, each pair of N nodes is connected with probability p. Literature agrees that the Erdős-Rényi model is a poor representation of real-world networks and financial networks. However, the C2C network does not correspond to most real-world and financial networks. The C2C network is a financial network with a rather specific and limited purpose: to enable end-users to send funds among themselves. Unlike the Internet, where all nodes have to be reachable to allow the exchange of data (see Newman 2010), or the interbank lending market, where the efficient exchange of liquidity depends on the intermediation role of a well-connected core that serves as a hub to those in the periphery (see Craig and von Peter 2014; Fricke and Lux 2014, Fricke and Lux 2015; León, Machado, and Sarmiento 2018; Martínez-Jaramillo 2014; Soramäki et al. 2007), the C2C network displays a sparser and simpler connective structure that diverges from those typical of real-world networks.
The literature about the topological features of peer-to-peer retail payment networks is scarce. To the best of our knowledge, León (2021) is the single reference that reports those topological features based on daily data; as the steps in the simulation correspond to a daily frequency, this is essential. León reports that the largest non-banking peer-to-peer mobile wallet in Colombia is distinctly sparse (i.e. one of the stylized facts of financial networks) but exhibits particular features such as the prevalence of unconnected nodes and two-node components, low clustering, and the absence of a large component.[12] , [13] Also, the distribution of connections is reported to be skewed – a stylized fact of real-world networks that, according to Unger et al. (2020) and León (2021), corresponds to micro businesses being well-connected nodes in peer-to-peer mobile wallet networks.
A salient feature of the Erdős-Rényi model is that changing p (i.e. the probability of each pair of N nodes being connected) achieves different network topologies. Regarding the C2C network, by choosing a particularly low p it is possible to generate a peer-to-peer payments network that is sparse, dominated by two-node components, without a large component, with low clustering, and with most nodes remaining unconnected – that is, as those reported in León (2021) for peer-to-peer payments. Therefore, the Erdős-Rényi model is a natural choice to simulate the C2C network because it is a well-documented network model that can generate the main features of a peer-to-peer network under a fair choice of p.
Consequently, the C2C payments network is simulated by generating a list of pairs of nodes. Based on the Erdős-Rényi model, for each pair, there is a random uniform draw that determines whether it is a connected pair or not. If the random uniform draw is lower than the probability of each pair of N nodes being connected (p), then the pair is connected; otherwise, they remain unconnected. The list of connected nodes is used as the initial C2C payments network. Figure A1 (in the Appendix) presents an example of a C2C network based on the Erdős-Rényi model.
Therefore, when a consumer enters the peer-to-peer network of transfers, the model will look for all the transfers in which the randomly selected consumer acts as a sender of funds in the C2C network. The simulation will attempt to make the payment from the payer to the payee. If the payer consumer has disposable money, based on the peer-to-peer payment statistics from the consumer persona data, the model will randomly generate the number and value of the transactions and find the vector of payment instruments that are available to both consumers. For the selected consumer, this procedure is repeated until all the transactions in her list (as the sender of funds) are processed. The payment mechanics continue recursively until all consumers and their transactions, on all days of the simulation, have been processed.
3.3 The Learning Process
Consumers and merchants learn and adapt while meeting in the market for goods and services and when making peer-to-peer transactions. They both learn from each other and adapt their preferences and acceptance accordingly. Learning comes in two forms. First, as consumers and merchants meet, they learn which payment instruments allow them to complete transactions during the payment mechanics phase – this is mechanical learning. Second, when failing to complete a transaction, consumers and merchants realize that they may enhance their payment experience and avoid failed transactions by changing their preferences and acceptance, respectively – this is awareness learning.
3.3.1 The Consumers
When a transaction is completed, the mechanical process required to complete the transaction is registered. Completed transactions will allow consumers to learn about their choice of preferred payment instruments. The value of completed transactions will determine the value of the consumer’s allocation (i.e. the top-up) of rCBDC, deposits, and cash in a forthcoming step of the simulation; if the outstanding balance is equal or higher than the value of completed transactions, no additional allocation is required.
Nevertheless, the consumer not only learns from the mechanics of completed transactions. Failed transactions show the consumer that by changing her allocation of money to be used with different payment instruments she could enhance her payment experience – to avoid the inconvenience of incomplete transactions. Together, the value of completed and failed transactions, corresponding to mechanical and awareness learning, will determine the value of the consumer’s allocation (i.e. the top-up) of rCBDC, deposits, and cash in a forthcoming step of the simulation.
Therefore, consumers regularly (e.g. weekly) use the sum of completed and failed transactions to update their allocation of money available to use with different payment instruments and, thus, their preferences for payment instruments; this sum corresponds to the effective and potential use of each payment instrument based on experience. By relating the money allocation to the experience in C2M and C2C transactions, subsequent adoption or abandonment of payment instruments is determined by consumers’ adaptive decision-making.
3.3.2 The Merchants
The consumer’s preference for a payment instrument is a continuous variable, i.e. a continuum of possible values that correspond to the likelihood of using it in a transaction. On the other hand, acceptance by a merchant is a boolean variable that reflects whether a payment instrument is accepted or not. This determines how merchants learn and adapt – and how merchants’ preferences for payment instruments are updated.
Regarding mechanical learning, the merchants do not update their acceptance of payment as marginal changes in the payment mechanics occur. Once a payment instrument is accepted, an increase in usage by the consumers has no further effect on acceptance. Similarly, a marginal decrease in usage by consumers should not affect acceptance because sunk costs and other non-recoverable expenses deter the merchant from abandoning a payment instrument. Nevertheless, if the decrease in usage is large enough not to cover maintenance costs, the merchant could consider abandoning the payment instrument. In the simulation, if the usage of a payment instrument is below a threshold, the merchant decides whether to continue accepting it based on a uniform random draw. That is, marginal changes in consumers’ usage of a payment instrument do not trigger the abandonment of that payment instrument by the merchant; only a drastic negative change in consumers’ usage could make a merchant choose to stop accepting a payment instrument.
From the awareness learning viewpoint, the merchant updates his acceptance of payment instruments by focussing on those transactions that failed. Failed transactions show the merchant that by changing his acceptance of payment instruments he could increase the number of transactions, i.e. he could increase sales. However, to start accepting a payment instrument, a merchant must incur technological and logistic changes and costs (e.g. a banking account, a physical or virtual terminal, and communications services) that he will be willing to afford if the potential increase in the number of transactions is materially important. Consequently, the awareness learning process of the merchant is based on the number of transactions that failed and that could have been completed if the consumer’s preferred payment instrument had been accepted – after excluding legal tender instruments. If the number of transactions that could have been completed represents a material fraction of the completed transactions, then the merchant will decide to start accepting this payment instrument as a random draw based on the fraction of failed transactions.
Therefore, unlike the consumers’ preference for payment instruments, the acceptance and abandonment by merchants are of a tipping point type, from non-accepted to accepted after some threshold is reached, and vice versa. Only when the fraction of failed transactions to total transactions reaches a threshold, the merchant decides to start accepting that payment instrument; conversely, only when the usage by consumers is particularly low, the merchant considers abandoning it.[14]
4 A Retail Payment Ecosystem Digital Twin
The mainstay of our approach to simulating the adoption of an rCBDC is a digital twin of the retail payment ecosystem; that is, an empirical representation of the retail payment ecosystem to iterate and test different rCBDC design options and scenarios. We present the data we used for calibrating the digital twin, along with the calibration and scenarios designed to simulate the adoption of the rCBDC and the main results. Consistent with the concept of adoption as full use of the innovation (Christensen et al. 2020), we focus on how payments were made.
4.1 Data
To properly calibrate an ABM representation of the retail payment ecosystem, we require various details about the agents we intend to model. For instance, to comprehend how consumers make payments, we need information about the payment amount, frequency of transactions, purchase locations, payment instruments used, and consumption preferences. In addition, we require details about consumers, such as their income, and cash and deposit balances. For merchants, the model requires information about the payment instruments they accept.
This information is available from several sources, such as transactional data and surveys, including payment diaries. Transactional data is more comprehensive, but it does not cover cash payments, and it may be hard to access because it is mostly private and dispersed. Yet, retail payment surveys and payment diaries are publicly available in some jurisdictions, and multiple central banks work with them.
We model the Spanish retail payment ecosystem using information from ECB’s 2022 SPACE survey.[15] The survey and its study aim to provide insights into euro-area consumers’ payment habits, preferences, and perceptions. The survey gathered data from 50,000 consumers, across the 19 member countries using the euro in 2022. The study provides valuable information about consumer behaviour and preferences regarding the available payment methods, including digital payments, instant payments, and crypto-assets. It also explores the perceived access to different payment instruments and the impact of the COVID-19 pandemic on payment behaviour.
We aggregated consumers in 20 personas. The personas are defined by their monthly household income (5 groups) and their age (4 groups).[16] For each group, we computed the number of people surveyed (population distribution) and statistics of their cash holdings, cash withdrawals and daily payments per merchant persona (amount and number). On the other hand, we differentiate merchants according to the survey questions related to them. In particular, we aggregate merchants based on the point-of-sale location, the type of good or service when using online payments, and the recurrent payments explored through the survey. We then define 26 merchant personas; eight merchants correspond to recurrent payments.[17]
We group different payment instruments based on the survey and the payment instrument essence. Thus, we model cash, cards (debit and credit), credit transfers, direct debits, internet, mobile, and Paypal, as payment instruments.[18] Thus, we compute the vector of consumer’s payment instrument preferences per merchant persona, i.e. the share of each payment instrument group in the total number of payments per merchant persona. This vector is the baseline consumer’s preference at the beginning of the simulation as we explained in a previous section.
4.2 Calibration and Scenarios
As some information relevant to analysing the adoption of an rCBDC is neither available nor observable, we establish a set of parameters to propose different scenarios and explore further ideas around rCBDC introduction into the retail payment ecosystem. Furthermore, we model rCBDC design options and adoption incentives discussed in the literature.[19] In particular, we explore design options like rCBDC balance and top-up limits, tiered anonymity, (reverse) waterfall functionalities and remuneration, and policy decisions such as rCBDC legal tender status, private sector rCBDC payroll integration, and government subsidy disbursement with rCBDC. Furthermore, as explained, we incorporated affinity parameters to assess the consumer’s preference for anonymous and non-anonymous rCBDC based on cash and deposit-like payment instrument preferences, respectively.
Based on the design options and policy decisions, we propose different scenarios aligned with the current discussions. The first scenario does not consider an rCBDC in the economy; this baseline scenario is relevant for calibrating the model to the current Spanish retail payment ecosystem. The second scenario corresponds to a basic rCBDC design, comprising basic features portrayed in recent documents presented by the ECB. In this case, the rCBDC is accompanied by a legal tender status, €3,000 balance limit, reverse waterfall functionality, no top-up limits, and high privacy, i.e. there is no anonymity threshold. The basic scenario will be modified by adding bespoke rCBDC design options to measure their impact on the rCBDC adoption in Spain. All scenarios assume that rCBDC will have legal tender status. Table 1 depicts the baseline, basic, and additional scenarios herein simulated.
rCBDC baseline, basic and additional scenarios. The baseline scenario corresponds to the calibrating scenario, i.e. before the rCBDC is introduced into the retail payment ecosystem. The basic scenario comprises basic design options in recent documents presented by the ECB. Scenarios 1 to 6 (Esc.1 to Esc.6) correspond to additional design features or a combination of them.
| Design options | Baseline | Basic | Sce. 1 | Sce. 2 | Sce. 3 | Sce. 4 | Sce. 5 | Sce. 6 |
|---|---|---|---|---|---|---|---|---|
| Legal tender | NA | Yes | Yes | Yes | Yes | Yes | Yes | Yes |
| Balance limit | NA | €3,000 | €3,000 | €3,000 | €3,000 | €3,000 | €3,000 | €1,000 |
| Top-up limit | NA | NA | €500 | NA | NA | NA | NA | NA |
| Anonymity threshold | NA | ∞ | ∞ | €200 | ∞ | ∞ | ∞ | ∞ |
| Reverse waterfall | NA | Yes | Yes | Yes | No | Yes | Yes | Yes |
| Government benefits | NA | NA | NA | NA | NA | Yes | NA | NA |
| Remuneration spread | NA | NA | NA | NA | NA | NA | Yes | Yes |
-
Source: authors’ design.
4.3 Results
Results herein reported correspond to a single 365-day simulation of each one of the scenarios described in Table 1.[20] We simulated 350 consumers and 130 merchants, distributed as extracted from the consumers’ and merchants’ persona data, respectively.[21]
Figure 1 presents a sample of the C2M and C2C networks built by the simulation. This sample was extracted from the 180th day of the basic scenario simulation.
C2C and C2M networks. Extracted from the 180th day of the basic scenario simulation. Green nodes correspond to consumers and blue nodes to merchants. The arrows point to the receiver of the payment; the colour of the arrow corresponds to the payment instrument. The networks are displayed with a force-directed layout; the more (less) connected a node is the more (less) central it is in the network. Source: authors’ calculations.
Panel a. shows the network of interactions between consumers (green nodes) and merchants (blue nodes) as they meet in the market for goods and services; as we discard non-C2M payments, other nodes (i.e. government, banks, the central bank) are not displayed. We use a force-directed layout; the more (less) connected a node is the more (less) central it is in the network. Arrows in the network correspond to payments for goods and services, from the consumer to the merchant. Arrows have different colours, corresponding to the payment instrument used by the consumer and accepted by the merchant.
[Corrections Statement added after online publication 18.07.2024: the color description of the consumer nodes (green) and merchant nodes (blue) was changed to consumer nodes (red) and merchant nodes (green).]
Panel b. shows the interactions among consumers as they meet in the peer-to-peer transfer network. As before, green nodes correspond to consumers; all other types of agents are not displayed. Again, we use a force-directed layout; yet, as the network is sparse, with low (no) clustering, without a large component and with most components being two-node components, there is no evident structure in the C2C network – as in León (2021). Arrows have different colours, corresponding to the payment instrument used and accepted by both sender and receiver consumers, respectively.
Figure 2 presents the rCBDC adoption curve for the selected scenarios. Table 2 presents how payments were made during the last month of the 365-day simulation period for each scenario, as per cent of the number of payments; working on monthly results avoids the intra-month seasonality in the simulation. Table A1 (in the Appendix) presents results as per cent of the value of payments. Tables 2 and A1 concur in how the different scenarios affect rCBDC adoption and the usage of existing payment instruments.
rCBDC adoption curves, as a percentage of the total number of payments. Source: authors’ calculations.
Payments made during the last month of the simulation, as per cent of the number of payments. The baseline scenario corresponds to the calibrating scenario, i.e. before the rCBDC is introduced into the retail payment ecosystem. The basic scenario comprises basic design options in recent documents presented by the ECB. Scenarios 1 to 6 (Esc.1 to Esc.6) correspond to additional design features or a combination of them.
| Scenario | Cash | rCBDC | Cards | Credit transfer | Direct debit | Internet | Mobile | Paypal | |
|---|---|---|---|---|---|---|---|---|---|
| anonymous | non-anon. | ||||||||
| Baseline | 24.77 % | 0.00 % | 0.00 % | 46.93 % | 5.34 % | 6.80 % | 0.03 % | 13.41 % | 2.71 % |
| Basic | 25.08 % | 1.29 % | 0.00 % | 45.87 % | 5.19 % | 6.41 % | 0.02 % | 13.73 % | 2.40 % |
| 1 | 23.34 % | 0.91 % | 0.00 % | 47.06 % | 5.03 % | 6.60 % | 0.01 % | 14.29 % | 2.75 % |
| 2 | 25.64 % | 1.23 % | 0.02 % | 46.46 % | 4.70 % | 6.68 % | 0.00 % | 12.76 % | 2.51 % |
| 3 | 27.20 % | 0.32 % | 0.00 % | 44.50 % | 3.91 % | 6.48 % | 0.01 % | 15.08 % | 2.50 % |
| 4 | 10.93 % | 7.84 % | 0.00 % | 49.06 % | 5.76 % | 7.59 % | 1.14 % | 13.98 % | 3.70 % |
| 5 | 29.62 % | 8.88 % | 0.00 % | 39.61 % | 4.09 % | 5.48 % | 0.00 % | 10.41 % | 1.92 % |
| 6 | 28.67 % | 6.68 % | 0.00 % | 41.00 % | 4.27 % | 5.99 % | 0.02 % | 11.41 % | 1.95 % |
-
Source: authors’ design.
The baseline scenario does not include an rCBDC – it corresponds to the calibration of the digital twin to the retail payment system of Spain; thus it is not displayed in Figure 2. The basic scenario, comprising an rCBDC with legal tender status, €3000 balance limit, reverse waterfall functionality, and no anonymity threshold, shows that after 365 days a basic rCBDC achieves low adoption: about 1.29 % of payments are made with rCBDC. Payments made with cash increased slightly with respect to the baseline scenario. Conversely, payments made with deposit-related payment instruments (i.e. cards, credit transfer, direct debit, internet, Paypal) decreased slightly. The results correspond to what has been reported for The Bahamas and Nigeria – namely, a low and slow adoption. Furthermore, results are intuitive: consumers start using the rCBDC sparingly and some likely competing digital payment instruments are slightly affected. Consequently, after 1 year, the adoption curve and the results in Table 2 suggest that an rCBDC with a basic design does not affect the retail payment ecosystem manifestly.
Scenario 1 introduces a €500 top-up limit. As expected, imposing a limit to transfer funds from other forms of money to rCBDC has a negative impact on its adoption. Although the adoption curve does not change manifestly with respect to the basic scenario, about 0.91 % of payments in the last month are made with rCBDC, compared to the 1.29 % in the basic scenario. Scenario 1 suggests that a top-up limit curtails the adoption of an rCBDC.
Scenario 2 discards the €500 top-up limit and introduces a €200 anonymity threshold. The anonymity threshold forces the consumers to split payments into two forms of rCBDC, anonymous and non-anonymous. But the sum of both (1.25 %) is somewhat lower than that of the basic scenario 1.29 %; arguably, splitting the rCBDC into two different payment instruments by anonymity entangles the usage by the consumers. Once again, as in the basic scenario, the number of payments with cash increased, whereas payments made with deposit-related payment instruments decreased. As before, the adoption curve for scenario 2 is not materially different from the basic scenario.
Scenario 3 removes the €200 anonymity threshold and deactivates the reverse waterfall functionality. As expected, the adoption of rCBDC is lower than in the basic scenario and scenarios 1 and 2; adoption in scenario 3 is about one-quarter, one-third, and one-quarter of the adoption in the basic, 1 and 2 scenarios, respectively. At the end of the period, the adoption curve stands below the previous scenarios. As deactivating the reverse waterfall functionality causes the rejection of all transactions with insufficient rCBDC balances, the usage and subsequent adoption of rCBDC are negatively affected. Also, as those rCBDC payments are rejected, other payment instruments are used; interestingly, mobile payments and cash usage increase, whereas cards and credit transfers drop. The results from scenario 3 suggest that the reverse waterfall envisaged by ECB (2022b, 2023a) for the digital euro is a useful functionality to support adoption: as intended, it makes paying with rCBDC easier for the consumer. Also, it is worth noting that removing the reverse waterfall not only reduces rCBDC adoption but also increases the use of cash, whereas the impact on digital payment instruments is heterogenous.
Scenario 4 reintroduces the reverse waterfall functionality and adds the distribution of government benefits (i.e. subsidies) via rCBDC wallets. The adoption curve shows a rather fast adoption of rCBDC in the first 2 months (from 0 to 4.6 %), followed by a protracted increase during the period. When the government distributes benefits via rCBDC, about 7.84 % of payments are made with rCBDC during the last month of the period, compared to 1.29 % in the basic scenario. Conversely, the number of payments with cash decreases manifestly (from 25.08 % to 10.93 %), whereas that of cards, credit transfers and direct debit increases. Therefore, the results suggest that using rCBDC as a vehicle to distribute subsidies supports the adoption of rCBDC and the decrease in the use of cash. As low-income consumers are the ones who use cash the most and receive more subsidies as a fraction of their income, results suggest that not only the government could support the adoption of rCBDC but also foster financial inclusion among those with lower access to digital payment instruments.
Scenario 5 removes the distribution of government benefits and adds a positive remuneration spread with respect to deposits. As expected, a positive remuneration spread fosters adoption manifestly; the adoption curve for scenario 5 dominates all scenarios after the third month. During the last month of the period, the number of payments with rCBDC corresponds to 8.88 %, instead of the 1.29 % in the basic scenario. Further, there is an evident decrease in the use of payment instruments related to deposits (e.g. cards, credit transfers, direct debit, internet, mobile, Paypal), whereas the use of cash increases greatly. This result is consistent with what is commonly known as the migration of deposits to rCBDC – an effect that is regarded as potentially troublesome because it may impact commercial banks’ balance sheets, the cost of funds in the economy and, eventually, affect the financial stability. Therefore, results suggest that allowing an rCBDC to compete with deposits for the store-of-value function of money may foster adoption and trigger a migration of deposits to rCBDC and an increase in the use of cash.
To test how a tighter balance limit could counter the effects of a remuneration spread (or other attractive features), scenario 6 decreases the balance limit from €3,000 to €1,000. The lower balance limit works as expected, resulting in an adoption curve below scenario 5’s. The number of payments with rCBDC under scenario 6 corresponds to 6.68 % instead of 8.88 % in scenario 5 and 1.29 % in the basic scenario. Again, there is an evident decrease in the use of payment instruments related to deposits (e.g. cards, credit transfers, direct debit, internet, mobile, Paypal), whereas the use of cash increases; however, as expected, those effects are weaker than in the absence of the tighter balance limit. This result suggests that balance limits could play a role in avoiding or mitigating deposit migration caused by the appeal of rCBDCs – as intended by ECB (2023b).
All in all, results suggest that rCBDC adoption is not guaranteed. Attractive design options for consumers are necessary for rCBDC adoption. This overlaps with recent calls to work on rCBDC attributes that could increase consumers’ preference for a given rCBDC (see Zamora-Pérez, Coschignano, and Barreiro 2022). Also, this overlaps with Henry et al. (2023), who highlight that the large mass of (Canadian) consumers that could drive adoption have weak incentives to adopt and consistently use a rCBDC as they already have access to a range of payment instruments; that is, attractive design options and stimulus are necessary to strengthen the incentives to adopt and use a rCBDC by most of the population.
In our case, the attractive design options (i.e. the reverse waterfall functionality and a positive remuneration spread) foster rCBDC adoption but reduce the use of other digital payment instruments and increase the use of cash. Therefore, results suggest that in the jurisdiction herein modelled, introducing an attractive rCBDC would compete with existing digital payment instruments – instead of replacing cash. The large mass of consumers would shift from the digital payment instruments they already use to rCBDC.
However, it is remarkable that distributing subsidies via rCBDC (scenario 4) not only promotes adoption but also reduces the use of cash and increases the use of other digital payment instruments. Following Henry et al. (2023), this corresponds to effectively encouraging consumers with unmet payment needs and low likelihood to adopt a new payment instrument (i.e. low-income, rural, older consumers) to adopt rCBDC while reducing the use of cash. In this vein, attractive incentives could foster adoption among the average consumer whereas targeted policies (e.g. subsidies distribution via rCBDC) could encourage cash-dependent consumers to adopt rCBDC – the financial inclusion rationale of rCBDCs.
5 Final Remarks
As the introduction of an rCBDC seems indisputable in many jurisdictions, studying and understanding the potential effects of introducing an rCBDC into the retail payment ecosystem, interdependent markets, and macroeconomic equilibria are of utmost importance. The first step towards studying and understanding such effects is to simulate the adoption of an rCBDC.
In this article, based on ECB’s Study on the Payment Attitudes of Consumers in the Euro area (the SPACE survey) and on agent-based modelling (ABM), we built a digital twin of the retail payment ecosystem to simulate the adoption of an rCBDC. We calibrate the digital twin to the case of Spain and run different hypothetical scenarios that correspond to publicly available technical discussions about the digital euro.
Results confirm that introducing an rCBDC without attractive design features for consumers and merchants or stimulus policies results in low and slow adoption; this overlaps with early evidence reported for Nigeria, The Bahamas, and the People’s Republic of China, and the rationale in Henry et al. (2023). Second, results suggest that design options differ in their effectiveness and consequences. The reverse waterfall functionality and a positive remuneration spread are effective in fostering adoption; the distribution of government incentives via rCBDC is effective in fostering adoption and decreasing the use of cash; and balance limits and top-up limits are effective in restraining adoption. Third, results suggest that combining design options and stimulus policies with limits to holding rCBDCs could be the key to achieving a sweet spot of adoption. Fourth, in most scenarios, the usage of cash as a payment instrument increases after the rCBDC is introduced into the retail payment ecosystem, whereas the usage of deposit-related payment instruments decreases; this suggests an attractive rCBDC could compete with the existing digital payment instruments. Nevertheless, it is worth emphasizing that results and conclusions are bound to the retail payment ecosystem herein modelled.
Our results also underscore the importance and convenience of simulating the adoption of an rCBDC. The rCBDC design options can be modelled and studied with respect to the main features of the corresponding jurisdiction before incurring the costs and risks of a learning-by-doing approach. In this vein, we explicitly answer the call for further investigation to determine the essential features for the successful adoption of rCBDCs (see Zamora-Pérez, Coschignano, and Barreiro 2022). For instance, under our methodological approach, we were able to test the reverse waterfall functionality (ECB 2022b; ECB 2023b) for the first time. This allows central banks and other stakeholders to sufficiently and seriously iterate and test until achieving an rCBDC design that fulfils the motivations of the central bank and the consumer and merchant use cases. Further, instead of working with assumed adoption scenarios, central banks and other stakeholders could study and discuss the potential impact of an rCBDC based on adoption figures that correspond to the features of the retail payment ecosystem and the most likely design options. That is, the retail payment system digital twin herein presented allows for testing policies and designs and their consequences, contributing to policymaking under the complex social dynamics that follow the introduction of an rCBDC.
Several paths exist to extend and improve our work further. First, for parsimony, we explored a handful of scenarios only. For instance, based on the likely legal tender status of rCBDC, we did not model scenarios in which merchants do not accept rCBDC. Also, as there is no consensus about the main rCBDC design options and stimulus policies, we did not attempt to test any specific cumulative scenario. Testing different cumulative scenarios – mixing design options and stimulus policies – to obtain different adoption levels is a valid purpose for rCBDC simulation. Likewise, looking for scenarios that achieve a certain level of adoption is a valid purpose too. Testing other design options, such as the two-tier remuneration (see Bindseil 2020) and offline payments (see ECB 2023b), is possible as well.
Second, for simplicity, we focused on a single country–Spain. Yet, based on the SPACE survey or other payment surveys, we could study the adoption of rCBDCs in different jurisdictions and make the corresponding cross-section analysis; the well-known dissimilarities across Eurozone jurisdictions regarding the preference for cash and digital payments suggest that results will vary manifestly.
Third, explicitly modelling commercial banks’ balances and making commercial banks adaptive decision-makers is the first step towards simulating the financial stability implications of the adoption of an rCBDC. This way, the migration from deposits to the rCBDC and the corresponding reaction from commercial banks could be studied. Relatedly, although the remuneration of rCBDCs has lost some appeal due to the unwillingness of central banks to compete with deposits as a store of value (see ECB 2023b), properly modelling commercial banks as adaptive decision-makers could include their ability to counter rCBDC remuneration or other alike (e.g. a cashback).
Fourth, results by consumer and merchant personas could be analysed to further address specific questions and to test for robustness. For instance, a central bank that is motivated by financial inclusion could focus on how particular consumer personas (e.g. low-income, remotely located) change their preferences for cash as the rCBDC is introduced into the retail payment ecosystem. Additionally, based on the nature of the merchant (i.e. physical, online, both), it is possible to gain insights about offline payments by studying the use of the corresponding payment instruments in low-value transactions, namely cash and an anonymous rCBDC. Also, results related to the impact of distributing subsidies via rCBDC on cash usage are promising about how the government could encourage adoption and increase financial inclusion. We leave this granular analysis for future research.
Fifth, several modelling enhancements are advisable. Due to the inherent randomness in the simulation, calculating confidence intervals is needed to better interpret results and use them in policymaking. Using data about the costs of holding forms of money and using payment instruments to better model consumers’ preferences and merchants’ acceptance could enhance the agents’ learning process. Also, testing other network-generating models for the C2C payments network could be necessary as the (scarce) evidence about peer-to-peer payment networks is appended. Further, M2M payments could be modelled to incorporate how merchants pay each other. Finally, to allow for comparability with available evidence and relevant literature, it is pertinent to be able to scale results (i.e. obtained using a fraction of consumers and merchants) at the national level.
Appendix
Simulated C2C network for a single day, based on Erdős-Rényi model. Simulated with parameters N = 1,000, p = 0.00005. As expected, it is a distinctly sparse network, with low (no) clustering, with most nodes unconnected (see left panel), without a large component and with most components being two-node components (see right panel). Source: authors’ calculations.
Payments made during the last month of the simulation, as per cent of the value of payments. The baseline scenario corresponds to the calibrating scenario, i.e. before the rCBDC is introduced into the retail payment ecosystem. The basic scenario comprises basic design options in recent documents presented by the ECB. Scenarios 1 to 6 (Esc.1 to Esc.6) correspond to additional design features or a combination of them.
| Scenario | Cash | rCBDC | Cards | Credit transfer | Direct debit | Internet | Mobile | Paypal | |
|---|---|---|---|---|---|---|---|---|---|
| anonymous | non-anon. | ||||||||
| Baseline | 9.29 % | 0.00 % | 0.00 % | 53.52 % | 5.41 % | 22.89 % | 0.00 % | 7.99 % | 0.91 % |
| Basic | 10.07 % | 0.35 % | 0.00 % | 52.35 % | 5.11 % | 23.12 % | 0.00 % | 8.17 % | 0.83 % |
| 1 | 9.20 % | 0.23 % | 0.00 % | 52.94 % | 4.75 % | 22.91 % | 0.00 % | 8.98 % | 1.00 % |
| 2 | 10.33 % | 0.31 % | 0.29 % | 51.87 % | 5.11 % | 22.71 % | 0.00 % | 8.62 % | 0.75 % |
| 3 | 12.00 % | 0.07 % | 0.00 % | 50.41 % | 4.98 % | 22.61 % | 0.00 % | 9.06 % | 0.86 % |
| 4 | 3.48 % | 2.58 % | 0.00 % | 55.08 % | 4.53 % | 23.49 % | 0.19 % | 9.57 % | 1.07 % |
| 5 | 13.31 % | 10.65 % | 0.00 % | 45.88 % | 4.03 % | 18.10 % | 0.00 % | 7.58 % | 0.46 % |
| 6 | 12.32 % | 6.69 % | 0.00 % | 48.76 % | 4.14 % | 18.96 % | 0.02 % | 8.63 % | 0.49 % |
-
Source: authors’ design.
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Articles in the same Issue
- Frontmatter
- Editorial
- Editorial – Special Issue on “Central Bank Digital Currency”
- Special Issue Articles
- Public Use and Distribution of Retail CBDC: An Evidence from Thailand’s Retail CBDC Pilot Program
- Simulating the Adoption of a Retail CBDC
- CBDC and the Banking System
- Banking Crises Under a Central Bank Digital Currency (CBDC)
- Monetary Policy Transmission, Central Bank Digital Currency, and Bank Market Power
- Data Observer
- The WBdigital Database: A Digital Repository for the Historical DIW-Wochenbericht, 1928–1968
- The IZA/Fable Swipe Consumption Index
Articles in the same Issue
- Frontmatter
- Editorial
- Editorial – Special Issue on “Central Bank Digital Currency”
- Special Issue Articles
- Public Use and Distribution of Retail CBDC: An Evidence from Thailand’s Retail CBDC Pilot Program
- Simulating the Adoption of a Retail CBDC
- CBDC and the Banking System
- Banking Crises Under a Central Bank Digital Currency (CBDC)
- Monetary Policy Transmission, Central Bank Digital Currency, and Bank Market Power
- Data Observer
- The WBdigital Database: A Digital Repository for the Historical DIW-Wochenbericht, 1928–1968
- The IZA/Fable Swipe Consumption Index
