VoxEU Column Financial Regulation and Banking Frontiers of economic research

Designing central bank digital currencies

Various central banks are currently weighing up the introduction of central bank digital currency. This column proposes a framework that captures the key features and studies the implications of such a payment system. Central bank digital currency can be designed with attributes similar to cash or deposits. Currency that closely competes with deposits would likely depress bank credit, while cash-like currency could lead to the disappearance of cash. The optimal central bank digital currency design hence trades off bank intermediation against the social value of maintaining diverse payment instruments. The currency could be interest-bearing, which may help alleviate this trade-off.

Evolving payment systems

Payment systems and, more fundamentally, money are evolving rapidly. Developments in digital networks, information technology and the increasing share of internet-based retailing have created the demand and technological space for peer-to-peer digital transactions that have the potential to radically change payment and financial intermediation systems.

Central banks have been pondering whether and how to adapt. Many are exploring the idea of issuing a central bank digital currency (CBDC) - a new type of fiat money that expands digital access to central bank reserves to the public at large, instead of restricting it to commercial banks (BIS 2018, Mancini-Griffoli et al. 2018).1 A CBDC would combine the digital nature of deposits with the peer-to-peer transaction use of cash. But would it also resemble deposits by coming in the form of an account at the central bank, or would it come closer to cash, materializing as a digital token? Would it pay interest rates like a bank deposit, or would its nominal return be fixed at naught, like cash?2

An analytical approach

In Agur et al. (2019), we build a theoretical framework geared at analysing the relationship between CBDC design, the demand for money types, financial intermediation, and network effects.3 The starting point is a model economy where banks collect deposits, extend credit to firms, and create social value in doing so: firms' projects are worth less if they cannot receive bank loans. Households have heterogeneous preferences over anonymity and security in payments, represented by an interval with cash and deposits at opposite ends: cash provides anonymity in transactions, while bank deposits are more secure.

A CBDC can take any point on this interval, depending on its design. For instance, a central bank could provide partial anonymity (e.g. towards third-parties but not the authorities), set transaction limits below which anonymity is retained, or make anonymity conditional, only to be lifted under court order. All of those possibilities are under consideration in central banks' CBDC studies (Mancini-Griffoli et al. 2018). As emphasized by Lagarde (2018), there is potential demand for partially anonymous means of payment that can, for example, protect consumers from the use of personal transactions data for credit assessments. This possibility is increasingly enabled by technological developments, as for instance discussed by Yao (2018) in the Chinese context.

Taking into account the design of the CBDC, households sort into different types of money according to three considerations: their (heterogeneous) preferences, network effects which make it inconvenient to use payment instruments with few users, and the interest rates offered on deposits and possibly on CBDC.

Figure 1 Money shares and CBDC design characteristics

Figure 1 depicts how money shares evolve in relation to CBDC design, where θ represents how cash-like the CBDC is made (0 is fully deposit-like and 1 is fully cash-like) and rcbdc is the interest rate offered on the CBDC.4 Panel A shows that cash holdings decline, and bank deposits rise as the CBDC becomes more cash-like. Panel B shows that a higher CBDC rate reduces the shares of both cash and deposits, while raising that of CBDC. Notably, when CBDC becomes sufficiently cash-like or rcbdc is sufficiently high, network externalities drive cash out of use. Deposits prove more resilient to competition from CBDC, as banks raise deposit rates in response.

Designing a non-interest-bearing CBDC

Variety in payment instruments increases welfare because of heterogeneity in household preferences. CBDC then has social value due to its ability to blend features of cash and deposits. At the same time, introducing a CBDC has welfare costs to the extent that it crowds out demand for cash and deposits. Specifically, a cash-like CBDC design can reduce cash demand to the point where network effects cause the disappearance of cash, while a deposit-like design causes an increase in deposit and loan rates, and a contraction in bank lending to firms. Because of relationship lending frictions, this decline in bank intermediation also curtails investment and output.5

The best way to design a CBDC hinges on whether the CBDC is interest-bearing and the strength of network effects.  When the CBDC is not interest-bearing, its similarity to cash becomes the sole design instrument and a non-linear optimal design pattern emerges as shown in Figure 2.

Figure 2 Optimal non-interest-bearing CBDC design

On the one hand, locating the CBDC ‘centrally’ relative to deposits and cash serves the payment needs of households with diverse preferences. On the other hand, when bank intermediation has more value, the CBDC is optimally made more cash-like to limit its adverse impact on bank credit. As the value of bank intermediation rises, a threshold is eventually reached, beyond which optimal design ‘freezes’. This is because optimal policy prevents the disappearance of cash in order to protect payment instrument variety.

As long as the welfare gains from variety outweigh the welfare costs from lost bank intermediation, optimal policy maintains all three payment instruments. However, when preserving bank intermediation becomes the dominant concern (at the right end of the figure), optimal policy foregoes on variety, allowing for the disappearance of cash, in exchange for a larger deposit base for banks. Moreover, once cash vanishes, the CBDC bears the brunt of servicing former cash users, and therefore optimally moves further towards cash than it would have if all three forms of money were still in existence.

Bringing in the CBDC interest rate

When network effects do not constrain policy, the CBDC interest rate is best kept at zero, because it creates price distortions in households' choice of payment instruments. However, an adjustable CBDC rate may be desirable as a second design instrument when network effects are strong. With a non-interest-bearing CBDC, the only means to safeguard deposits is to make the CBDC eat into cash demand. But with a variable CBDC rate, the central bank may combine a (more) cash-like CBDC with a negative CBDC interest rate, thereby avoiding adverse network effects on cash use and preserving payment instrument variety, while simultaneously limiting the CBDC's impact on financial intermediation, as shown in Figure 3.

Figure 3 Optimal interest-bearing CBDC design

This is a policy-relevant finding that provides an economic counterweight to political economy considerations that may otherwise drive central banks to opt for non-interest-bearing CBDCs. Notably, all ongoing central bank CBDC initiatives currently centre on non-interest-bearing CBDCs.

Who gains from CBDC and who loses?

Introducing an optimally designed CBDC always raises aggregate welfare in this framework, but this is far from a Pareto improvement: some households gain while others lose. Figure 4 shows the welfare impact of introducing a CBDC across the distribution of household preferences (represented by i). The blue line depicts the impact of a non-interest-bearing CBDC.6

Figure 4 Distributional effects of CBDC

To begin with, households with payment preferences closest to deposits remain as deposit users after the introduction of a CBDC. On the one hand, the decline in financial intermediation reduces the profit transfers that these households receive from firms. On the other hand, CBDC competition with bank deposits drives up deposit rates. Overall, the latter effect dominates and the introduction of a CBDC raises the welfare of all deposit users.

At the other end of the spectrum, households with a strong preference for anonymity remain  cash users. These households also suffer from the decline in financial intermediation, but do not benefit from higher deposit rates, leading to a welfare loss. Moreover, their welfare losses are aggravated if CBDC leads to the disappearance of cash, forcing them to switch to a less preferred payment instrument. Finally, for households that switch to CBDC, the interplay between the gains from using the new payments instrument and the losses brought about by reduced financial intermediation is complex, and some emerge with a net gain and others with a net loss.

The fact that depositors emerge as winners and cash holders as losers, hints at a potentially regressive impact of a CBDC. In our analysis, all households have identical endowments. In practice, however, households that primarily conduct their payments with cash tend to have lower income, while higher income households more often rely on deposit-based payments.

Beyond network effects

Are network effects the only reason that CBDC rates optimally diverge from zero? Extending the analysis shows that also considerations other than network effects can lead to situations where the optimal CBDC rate is non-zero. Imperfect competition in the banking sector is one example. When banks have market power, it may be socially optimal for CBDC to compete harder with bank deposits, leading CBDC rates to diverge from zero, regardless of network effects. The same is true when there are negative externalities associated with anonymity in payments, possibly because this may spur illicit activities. When policymakers have an additional ball to juggle – such as countering a negative externality – an interest-bearing CBDC may provide a valuable design instrument.

Disclaimer: The views expressed are those of the authors only and do not represent the views of the IMF, its Executive Board or IMF management.


Agur, I, A Ari and G Dell'Ariccia (2019), “Designing Central Bank Digital Currencies”, IMF Working Papers 19/252.

Bank for International Settlements (2018), “Central Bank Digital Currencies. Technical report”, Basel Committee on Payments and Market Infrastructures.

Diamond, D W and R G Rajan (2001), “Liquidity Risk, Liquidity Creation, and Financial Fragility: A Theory of Banking”, Journal of Political Economy 109(2): 287-327.

Donaldson, J R, G Piacentino and A Thakor (2018), “Warehouse Banking”, Journal of Financial Economics 129(2): 250-267.

Lagarde, C (2018), “Winds of Change: The Case for a New Digital Currency”, Remarks at the Singapore Fintech Festival.

Mancini-Griffoli, T, M S Martinez Peria, I Agur, A Ari, J Kiff, A Popescu and C Rochon (2018), “Casting Light on Central Bank Digital Currencies”, IMF Staff Discussion Notes 18/08.

Yao, Q (2018), “A Systematic Framework to Understand Central Bank Digital Currency”, Science China Information Sciences, 61(3): 033101.


1 Notably, the central banks of China, Norway, Sweden, and Uruguay are actively investigating the possibility of introducing a CBDC for domestic retail payments.

2 See Mancini-Griffoli et al. (2018) for other design aspects of CBDCs, which are mostly of an operational nature, such as the means to disseminate, secure and clear CBDCs.

3 Swings in the usage of payment instruments become particularly disruptive in the presence of network effects. For example, with declining cash use, banks may cut back on ATMs or shops may refuse to accept cash. Because of such network effects, payment instruments may disappear when their use falls below a critical threshold.

4 The striped areas at the left ends of Panel A and B represent domains where CBDC design is not attractive enough for households, and CBDC falls out of use.

5 A central bank could attempt to mitigate the decline in bank lending by providing banks with cheap liquidity to replace lost deposits. However, this may not be feasible for two reasons. First, banks' ability to intermediate funds may depend on their reliance on deposits (see e.g. Diamond and Rajan 2001, Donaldson et al. 2018). Second, this policy would permanently expose the central bank to credit risk.

6 The distributional impact of an interest-bearing CBDC is more intricate, and we refer to Agur et al. (2019) for details.

3,675 Reads