Agarwal, R. and Kimball, M. (2015). Breaking Through the Zero Lower Bound. IMF Working Papers 15/224, International Monetary Fund.
Agarwal, R. and Kimball, M. (2019). Enabling Deep Negative Rates to Fight Recessions: A Guide. IMF Working Papers 19/84, International Monetary Fund.
Andolfatto, D. (2018). Assessing the Impact of Central Bank Digital Currency on Private Banks. Working Papers 2018-25, Federal Reserve Bank of St. Louis.
Assenmacher, K. and Krogstrup, S. (2018). Monetary Policy with Negative Interest Rates: Decoupling Cash from Electronic Money. IMF Working Papers 18/191, International Monetary Fund.
Athey, S., Catalini, C., and Tucker, C. (2017). The Digital Privacy Paradox: Small Money, Small Costs, Small Talk. NBER Working Papers 23488, National Bureau of Economic Research.
Bank for International Settlements (2018). Central Bank Digital Currencies. Technical report, Basel Committee on Payments and Market Infrastructures.
Barontini, C. and Holden, H. (2019). Proceeding with Caution - a Survey on Central Bank Digital Currency. BIS Papers 101, Bank for International Settlements.
Barrdear, J. and Kumhof, M. (2016). The Macroeconomics of Central Bank Issued Digital Currencies. Bank of England working papers 605, Bank of England.
Bergara, M. and Ponce, J. (2018). Central Bank Digital Currencies: the Uruguayan e-Peso Case. In Masciandaro, D. and Gnan, E., editors, Do We Need Central Bank Digital Currency? Economics, Technology and Institutions. SUERF Conference Volume.
Biais, B., Bisière, C., Bouvard, M., and Casamatta, C. (2019). The Blockchain Folk Theorem. Review of Financial Studies, 32(5):1662–1715.
Biais, B., Bisière, C., Bouvard, M., Casamatta, C., and Menkveld, A. J. (2018). Equilibrium Bit-coin Pricing. TSE Working Papers 18-973, Toulouse School of Economics (TSE).
Bordo, M. D. and Levin, A. T. (2017). Central Bank Digital Currency and the Future of Monetary Policy. NBER Working Papers 23711, National Bureau of Economic Research.
Borgonovo, E., Caselli, S., Cillo, A., and Masciandaro, D. (2018). Between Cash, Deposit And Bitcoin: Would We Like A Central Bank Digital Currency? Money Demand And Experimental Economics. BAFFI CAREFIN Working Papers 1875.
Bounie, D., François, A., and Van Hove, L. (2017). Consumer Payment Preferences, Network Externalities, and Merchant Card Acceptance: An Empirical Investigation. Review of Industrial Organization, 51(3):257–290.
Brunnermeier, M. K. and Niepelt, D. (2019). On the Equivalence of Private and Public Money. NBER Working Papers 25877, National Bureau of Economic Research.
Chiu, J., Davoodalhosseini, M., Jiang, J. H., and Zhu, Y. (2019). Central Bank Digital Currency and Banking. Staff Working Papers 19-20, Bank of Canada.
Chodorow-Reich, G., Gopinath, G., Mishra, P., and Narayanan, A. (2018). Cash and the Economy: Evidence from India’s Demonetization. NBER Working Papers 25370, National Bureau of Economic Research.
Diamond, D. W. and Rajan, R. G. (2001). Liquidity Risk, Liquidity Creation, and Financial Fragility: A Theory of Banking. Journal of Political Economy, 109(2):287–327.
Engert, W. and Fung, B. (2017). Central Bank Digital Currency: Motivations and Implications. Discussion Papers 17-16, Bank of Canada.
Fung, B. and Halaburda, H. (2016). Central Bank Digital Currencies: A Framework for Assessing Why and How. Discussion Papers 16-22, Bank of Canada.
Garratt, R. and van Oordt, M. (2019). Privacy as a Public Good: A Case for Electronic Cash. Staff Working Papers 19-24, Bank of Canada.
Goodfriend, M. (2016). The Case for Unencumbering Interest Rate Policy at the Zero Lower Bound. Paper presented at the August 2016, Jackson Hole Conference.
Gopinath, G. and Stein, J. C. (2018). Banking, Trade, and the Making of a Dominant Currency. Working Paper 24485, National Bureau of Economic Research.
He, D., Leckow, R. B., Haksar, V., Mancini-Griffoli, T., Jenkinson, N., Kashima, M., Khiaonarong, T., Rochon, C., and Tourpe, H. (2017). Fintech and Financial Services; Initial Considerations. IMF Staff Discussion Notes 17/05, International Monetary Fund.
Kahn, C. M., Rivadeneyra, F., and Wong, T.-N. (2019). Should the Central Bank Issue E-Money? Working Papers 2019-3, Federal Reserve Bank of St. Louis.
Katz, M. L. and Shapiro, C. (1985). Network Externalities, Competition, and Compatibility. The American Economic Review, 75(3):424–440.
Keister, T. and Sanches, D. R. (2019). Should Central Banks Issue Digital Currency? Working Papers 19-26, Federal Reserve Bank of Philadelphia.
Kim, Y. S. and Kwon, O. (2019). Central Bank Digital Currency and Financial Stability. Working Papers 2019-6, Economic Research Institute, Bank of Korea.
Krugman, P. (1979). Increasing Returns, Monopolistic Competition, and International Trade. Journal of International Economics, 9(4):469–479.
Mancini-Griffoli, T., Martinez Peria, M. S., Agur, I., Ari, A., Kiff, J., Popescu, A., and Rochon, C. (2018). Casting Light on Central Bank Digital Currencies. IMF Staff Discussion Notes 18/08, International Monetary Fund.
Masciandaro, D. (2018). The Demand for a Central Bank Digital Currency: Liquidity, Return and Anonymity. In Masciandaro, D. and Gnan, E., editors, Do We Need Central Bank Digital Currency? Economics, Technology and Institutions. SUERF Conference Volume.
Meaning, J., Dyson, B., Barker, J., and Clayton, E. (2018). Broadening Narrow Money: Monetary Policy with a Central Bank Digital Currency. Bank of England working papers 724, Bank of England.
Merrouche, O. and Nier, E. (2012). Payment Systems, Inside Money and Financial Intermediation. Journal of Financial Intermediation, 21(3):359–382.
Niepelt, D. (2019). Reserves for All? Central Bank Digital Currency, Deposits, and their (Non)-Equivalence. International Journal of Central Banking, forthcoming.
Prasad, E. (2018). Central Banking in the Digital Age: Stock-Taking and Preliminary Thoughts. Discussion paper, Hutchins Center on Fiscal and Monetary Policy at Brookings.
Rochet, J.-C. and Tirole, J. (2006). Externalities and Regulation in Card Payment Systems. Review of Network Economics, 5(1):1–14.
Wakamori, N. and Welte, A. (2017). Why Do Shoppers Use Cash? Evidence from Shopping Diary Data. Journal of Money, Credit and Banking, 49(1):115–169.
Wright, R., Tekin, E., Topalli, V., McClellan, C., Dickinson, T., and Rosenfeld, R. (2017). Less Cash, Less Crime: Evidence from the Electronic Benefit Transfer Program. Journal of Law and Economics, 60(2):361–383.
Yao, Q. (2018). A Systematic Framework to Understand Central Bank Digital Currency. Science China Information Sciences, 61(3):033101.
For an overview of ongoing CBDC initiatives, see Mancini-Griffoli et al. (2018), Bank for International Settlements (2018) and Prasad (2018). In a survey of 63 central banks, a third of central banks perceived CBDC as a possibility in the medium term (Barontini and Holden, 2019). Notably, the central banks of China, Norway, Sweden, and Uruguay are actively investigating the possibility of introducing a CBDC. The Sveriges Riksbank is expected to decide on the introduction of an eKrona in 2019, while Uruguay’s central bank has run a successful pilot (Bergara and Ponce, 2018; Norges Bank, 2018; Sveriges Riksbank, 2018a).
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.
We parameterize and vary the degree to which bank financing of firms provides efficiency gains. On the special role of depository institutions in intermediation, see Diamond and Rajan (2001) and Donaldson et al. (2018), as well as Merrouche and Nier (2012) for supporting empirical evidence.
Empirical research on payment instruments choice attributes a central role to heterogeneous preferences (Wakamori and Welte, 2017). For empirical work measuring preferences for anonymity and the potential demand for CBDC, see Athey et al. (2017), Borgonovo et al. (2018) and Masciandaro (2018).
This possibility is increasingly enabled by technological developments, as for instance discussed by Yao (2018) in the Chinese context, and forms the basis for the microfoundations that we develop in Appendix D.
Nevertheless, a CBDC is certain to raise aggregate welfare in our framework, but only if it is optimally designed. Moreover, even when aggregate welfare rises, there are distributional effects, and some households are worse off due to CBDC availability. We analyze these distributional effects in Section 3.3.
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.
Beyond satisfying household preferences, the disappearance of cash may reduce economic activity when a portion of the population is unable or unwilling to transact with digital payment methods because of digital illiteracy or informality. See Chodorow-Reich et al. (2018) for an empirical assessment of such costs.
In our framework, CBDC interest rates embody any type of subsidy or cost associated with holding CBDC. For example, the pilot conducted by the central bank of Uruguay offered subsidies to CBDC holders (Bergara and Ponce, 2018). Moreover, we focus on the steady state effects of CBDC rates on financial intermediation and cash use, rather than their implications for monetary policy over the business cycle. On the relationship between CBDC and monetary transmission, see Agarwal and Kimball (2015, 2019), Assenmacher and Krogstrup (2018), Barrdear and Kumhof (2016), Bordo and Levin (2017), Bjerg (2017), Davoodalhosseini (2018), Goodfriend (2016), Meaning et al. (2018), and Niepelt (2019).
We abstract from default risk on bank deposits, which is negligible in normal times due to deposit insurance and implicit bailout guarantees.
While some legal jurisdictions allow for deposit accounts that offer a degree of anonymity, these accounts are typically incompatible with payments services. Moreover, providing anonymity in deposits may undermine their complementarity with relationship lending (see e.g., Donaldson et al., 2018).
We adopt a uniform distribution for the sake of tractability. Our qualitative results generalize to any single peaked distribution with continuous support and sufficient weight in the tails to ensure that, absent a CBDC, both deposits and cash are sustained as payment instruments.
We assume that all forms of money are traded on par.
This notion is further explored in Appendix D, which provides an example of how a Hotelling linear-city setup of payments preferences can be microfounded.
This can be interpreted as a zero-capital central bank: any revenue that the central bank makes is immediately paid out to households, and any capital shortfall arising from CBDC costs directly leads to a recapitalization through a lump-sum tax.
The manner in which we combine consumption with payment preferences bears similarity to the utility function adopted in Gopinath and Stein (2018).
We impose the restriction k0 > 1 to ensure that lending frictions always bind such that k < k0.
We adopt a quadratic functional form in the interest of tractability. Appendix C.1 considers a constant returns to scale technology as an alternative. In a derivation available upon request, we also generalize the quadratic technology to the form
The liquidation value is also in terms of consumption goods. The liquidation of projects can be microfounded in a framework similar to Stein (2012) where projects are sold to outside buyers with a lower marginal valuation. While we do not explicitly incorporate outside buyers into our model, doing so would have no impact on welfare provided these buyers are non-resident and/or projects are priced at their opportunity cost to outside buyers. In the interest of tractability, we also assume that funds from liquidated projects cannot be used towards financing other projects. This could be due to a combination of information asymmetries and timing. For example, the time required for outside buyers to verify and pay for a project may exhaust the time for implementation by firms.
An implicit assumption in our model is that the central bank does not allow any agent to take a short position in CBDC (i.e., the central bank does not grant CBDC credit to other parties). This precludes arbitrage opportunities by entities without payment preferences, such as banks, which might prefer funding themselves with CBDC rather than deposits. Based on CBDC studies currently underway at central banks, we consider this a realistic assumption.
The design constraint subsumes two conditions, rcbdc ≥ – (1 – θ) ρ−1 and θ > ρ(rd – rcbdc), which respectively rule out the strict dominance of CBDC by cash and deposits (i.e., ensure that neither cash nor deposits offer all households a strictly better utility than CBDC) as per (5) and (7). For example, a completely cash-like CBDC (θ = 1) that pays negative rates (rcbdc < 0) would violate the first condition, such that all households have a strict preference for cash over CBDC. Because of network externalities, these conditions are necessary, but not sufficient, for positive CBDC take-up.
While our model is not quantitative in nature, empirical evidence suggests that network effects only begin to play a significant role when the use of a payments instrument becomes very small, as respresented by
The restriction (A – ϕ) > 1 ensures that aggregate output (and hence consumption) increases in financial intermediation in equilibrium. This follows directly from the derivative
The three equilibria referred to as never occurring under optimal policy are further discussed in Appendix C.4, which considers outcomes under suboptimal CBDC design. The equilibria referred to as “impossible under any policy” are ruled out by the parameter restrictions which imply that, when there is no CBDC, the lowest possible shares of deposits and cash, respectively, are
Resolving multiplicity in favor of the cashless equilibrium shifts the boundary condition to θ + ρrcbdc > 1 – 2s – g (0) without any qualitative impact on our analysis.
In addition to optimal policy derived in the Proof of Proposition 1, the exact shape of Figure 2 relies on two more properties from (36) and (37): first, θnce > θce; second,
Appendix C investigates the robustness of this key result. We find that the optimality of zero CBDC rates (absent network effects) is robust to the specification of the production function. However, when banks have market power (Appendix C.3), or when anonymous payments instruments create negative social externalities (Appendix C.2), the optimal CBDC rate can deviate from zero.
This also remains valid in nce where
Formally, we can verify that
Decreasing and constant returns to scale production functions do lead to a different bank response to CBDC competition. Under decreasing returns to scale, banks push back against the competition through higher deposit rates (and also lending rates in Appendix C.3). Instead, in the constant returns to scale setup, rd = A – ϕ – 1 and therefore the deposit rate is irresponsive to θ and rcbdc
Given that each individual agent is atomistic, the space of all agents excluding one agent remains defined on [0, 1].
The same holds for the nce solutions. These are not shown here in the interest of brevity, but are available on request.
See also Garratt and van Oordt (2019), who develop a payments model with privacy as a public good, where each consumer fails to internalize that her payments data is used to price discriminate among future consumers, and privacy in government issued electronic cash can create social value.
More generally, the underlying assumption can be seen as a requirement on deposit-opening households to reveal their income to the fintech provider.