The Optimal Quantity of CBDC in a Bank-Based Economy

We provide evidence on the estimated e¤ects of digital euro news on bank valuations and lending and nd that they depend on deposit reliance and design features aimed at calibrating the quantity of CBDC. Then, we develop a quantitative DSGE model that replicates such evidence and incorporates key selected mechanisms through which CBDC issuance could a¤ect bank intermediation and the economy. Under empirically-relevant assumptions (i.e., central bank collateral requirements and imperfect substitutability across CBDC, cash and deposits), the issuance of CBDC yields non-trivial trade-o¤s and e¤ects through an expansion of the central bank balance sheet and pro ts. The issuance of CBDC exerts a smoothing e¤ect on lending and real GDP by stabilizing deposit holdings. Such "stabilization e¤ect" improves the well-known liquidity services/disintermediation trade-o¤ induced by CBDC and permits to rank di¤erent types of CBDC rules according to individual and social preferences. Welfaremaximizing CBDC policy rules are e¤ective in mitigating the risk of bank disintermediation and induce signi cant welfare gains. Keywords: central bank digital currency, bank intermediation, DSGE models, welfare. JEL classi cation: E42, E58, G21. ECB Working Paper Series No 2689 / July 2022 1 Non-technical Summary In recent years, the use of cash for transactions has signi cantly declined while the demand for digital means of payment for retail purposes has steadily increased. In response, central banks have started to investigate the implications of issuing central bank digital currencies (CBDCs). Among the potential bene ts of CBDCs, satisfying the demand for a safe, digital means of payment stands out. One of the most discussed challenges of issuing a CBDC is the risk of bank disintermediation through deposit substitution. Much of the current policy debate focuses on how to calibrate the amount of CBDC in circulation so as to ensure that potential bene ts of CBDCmaterialize without harming monetary and nancial stability through bank disintermediation. One challenge in this regard is that advanced economies have no experience with CBDCs and, hence, there is no available data on which empirical analysis can be performed. For this reason, the literature has focused on studying the implications of CBDCs based on theoretical models. This paper provides novel empirical evidence on the impact of digital euro news on bank stock prices and bank lending behavior. The study nds that such impacts depend on the CBDC design features aimed at calibrating the amount of central bank digital currency in circulation. Due to the perceived substitutatbility between CBDC and deposits, the magnitude of these e¤ects is sensitive to the reliance of banks on deposit funding. Then, the paper develops a quantitative macro-banking DSGE model for CBDC analysis that: (i) is calibrated to quarterly data of the euro area for the period 2000:I 2021:II so as to match a number of rst and second moments from banking and macroeconomic aggregates; (ii) replicates the empirical evidence provided in the paper; (iii) incorporates the main trade-o¤s and key selected transmission channels through which CBDC could a¤ect the banking sector and the macroeconomy; and (iv) allows for a careful quantitative analysis of the macroeconomic and welfare implications of issuing CBDC for both, hypothetical winners (i.e., CBDC holders) and potential losers (i.e., households who do not hold CBDC and rely on bank lending). The analysis concludes the following. First, as the empirical evidence suggests, adequately calibrating the amount of CBDC in circulation is important to mitigate the impact on the banking sector. Such impact depends on banksreliance on deposit funding and the substitutability between CBDC and deposits. Second, the issuance of CBDC exerts a scal expansion e¤ect and a bank disintermediation e¤ect through an expansion of the central bank balance sheet and pro ts. The sign and magnitude of the net impact on bank lending and real GDP depends on the relative size of these two e¤ects. Third, welfare-maximizing CBDC rules are e¤ective in mitigating the risk of bank disintermediation and induce signi cant welfare gains. They induce a stabilization e¤ect which improves the liquidity services/disintermediation trade-o¤ faced by the economy under the introduction of a CBDC and permits to rank CBDC rules in terms of attainable welfare gains. ECB Working Paper Series No 2689 / July 2022 2