I. Introduction

Central bank digital currency (CBDC) is a digital form of fiat money issued by a central bank. It is designed to operate on the blockchain, although it may also be traded off-chain in certain cases. CBDC is a crypto-currency backed by a central bank and is legal tender, making it usable for nearly all transactions. Individuals can deposit cash into an electronic wallet or account provided by a central bank and exchange it on a one-to-one basis for CBDC. In this paper, I focus on retail CBDC, which can be used by anyone, as opposed to wholesale CBDC, which is restricted to financial institutions.

CBDCs offer multiple potential benefits. Recent research by IMF and BIS scholars highlights several advantages of retail CBDCs, including reductions in the cost of producing and managing cash, the promotion of financial inclusion, enhancements to payment infrastructure, the preservation of monetary sovereignty, and the mitigation of financial stability risks posed by private stablecoins (Bouis et al., 2024). Moreover, Nikitin et al. (2025) emphasize that CBDCs can be made programmable and integrated with smart contracts, enabling governments to issue restricted forms of CBDC that can be used only for specific, pre-authorized goods and services.

However, the introduction of CBDC raises significant concerns, particularly regarding the potential impact of doing so on the deposit-taking and lending activities of commercial banks. If retail CBDC is introduced, some people may choose to deposit their money with the central bank, as opposed to a commercial bank, as the central bank is generally perceived as more trustworthy. Related to this, Keister and Sanches (2022) show that CBDC may crowd out bank deposits and thereby reduce investment.1 International organizations and central banks around the world are also concerned about the potential for CBDC to reduce bank lending.2

This concern is based on the widespread belief that banks lend money primarily from deposits. Existing studies such as those by Keister and Sanches (2022), Kim and Kwon (2022), and Jun and Yeo (2021) that find contractionary effects of CBDC commonly assume that lending is constrained by net deposits (i.e., deposits minus central bank reserves). Given this assumption, it follows naturally that bank lending would contract as CBDC substitutes for bank deposits. However, in the U.S. and many other advanced countries, the central bank’s reserve requirement is no longer binding, which means it does not effectively constrain bank lending (see Bennett and Peristiani, 2002). This suggests that there are factors beyond net deposits that determine the level of bank lending.

In practice, banks do not lend out of deposits; they lend “out of nothing.” For instance, when a bank makes a loan of $100, it does not hand $100 in cash to the borrower. Instead, it simply credits the borrower’s deposit account with $100. This process is referred to as “fountain pen money creation” (Tobin, 1963), because bankers can create deposits by adjusting balances in accounts. Research from the Bank of England provides further details pertaining to how banks create money through lending (see McLeay et al., 2014). This means that in some cases, bank lending can exceed funds held in deposits. In such cases, one may expect that even if retail CBDC causes some deposits to shift from commercial banks to the central bank, banks may not reduce lending because they can create more money. If this is the case, the connection between CBDC and bank lending becomes unclear: bank lending may not decrease when CBDC is introduced, and even if it does, the reduction may not be as significant as the shift of deposits from commercial banks to the central bank. The extant literature does not consider money creation by banks and therefore does not address interactions among CBDC, deposit demand, and credit supply via money creation (see Keister and Sanches, 2022; Kim and Kwon, 2022; and Jun and Yeo, 2021).

This paper extends a recently developed model of fountain pen money creation (see Parlour et al., 2022) and addresses the following key questions regarding the impact of CBDC on financial intermediation by banks. First, what factors determine the maximum amount of loans a bank can create through lending, i.e., the loanable amount? Second, does CBDC reduce the loanable amounts available to banks? Third, does CBDC lead to a reduction in the actual amounts of bank lending? Fourth, does CBDC decrease social welfare by limiting bank lending?

The first main result is that the loanable amount equals cash deposits multiplied by an augmentation factor. This augmentation factor can be greater than, less than, or equal to 1, depending on specific characteristics of the banking sector. While banks can create money by lending “out of nothing” initially, borrowers may withdraw some or all of the newly created funds subsequently. As a result, banks must maintain sufficient cash or liquid assets to meet these withdrawal demands. In other words, when a bank issues a new loan, its money creation constraint becomes tighter. The augmentation factor will be greater than 1 if the proportion of depositors who face unexpected liquidity needs or who transfer their funds from commercial banks to the central bank is sufficiently small.

The second main result is that CBDC reduces loanable amounts as some deposits move from commercial banks to the central bank. However, the magnitude of this reduction may be greater than, less than, or equal to the decrease in deposits. If the augmentation factor is small, the reduction in loanable amounts will be smaller than the decrease in deposits. Conversely, if the augmentation factor is large, the reduction in loanable amounts will exceed the decrease in deposits.

The third main result is that CBDC may or may not reduce actual loan amounts. If the misconception that banks lend solely from cash deposits were true, the impact of CBDC on bank lending would be straightforward: if banks are constrained by deposit funding and lend up to the amount of deposits, the decrease in bank lending equals to the decrease in deposits minus central bank reserves. However, if banks are not constrained by deposits and therefore lend less than the total amount of deposits, CBDC would have no effect on lending.

However, this analogy is based on a flawed premise. In the context of fountain pen money creation, the effects of CBDC on bank lending differ from the scenario described above. If banks lend up to their deposits before the introduction of CBDC, they will continue to lend the same amount even after CBDC is introduced, provided that the transfer of money to the central bank is marginal. This will occur because when banks lend up to deposits, their loanable amounts exceed the actual deposits, assuming that we ignore the knife-edge case in which the loanable amounts are identical to the actual deposits. As a result, even if the loanable amounts decrease slightly due to a small transfer of deposits to the central bank, the loanable amounts still exceed actual deposits and commercial banks can maintain the same level of lending. For instance, in South Korea, commercial banks lend amounts nearly equal to their deposits (see Section 2). Therefore, the theoretical analysis in this paper suggests that bank lending will not significantly decrease after the introduction of CBDC, especially if there are some limits on individual CBDC holdings or other safeguards to prevent large-scale deposit outflows from commercial banks to the central bank.

The fourth main result is that social welfare may increase, decrease, or remain unchanged after the introduction of CBDC. If the money creation constraint is non-binding in the absence of CBDC, bank lending remains unchanged and social welfare stays the same, provided that the transfer of deposits to the central bank is marginal. The money creation constraint is non-binding if the productivity of projects financed by banks is high enough or if the fraction of depositors who face unanticipated liquidity needs is small.

If the money creation constraint is binding, banks will reduce lending following the introduction of CBDC. The welfare implication, however, depends on the extent to which the money creation constraint is binding. Generally, the socially efficient amount of bank lending is lower than the optimal amount that banks would lend from their perspective, as banks are protected by limited liability: they capture the full gains from successful loans while only bearing a fraction of the costs from failures. However, the social planner takes into account the full costs and benefits of both success and failure. This discrepancy gives rise to a moral hazard problem, inducing banks to take excessive risks. In other words, banks have an incentive to extend more loans than is socially optimal.

Therefore, there are two scenarios to examine. First, suppose the money creation constraint is weakly binding in the absence of CBDC in the sense that the loanable amount is smaller than banks’ optimal loan amount but still larger than the socially efficient loan amount. In this case, the introduction of CBDC will reduce bank lending and social welfare will increase as a result, as the problem of excessive risk-taking is alleviated. Keister and Sanches (2022) also find the same result that this disintermediation effect of CBDC can enhance welfare. However, in their model, welfare can increase not because the disintermediation alleviates the moral hazard problem but because it leads to an increase in the stock of liquid assets in the economy, which in turn facilitates exchange and production activities.

Alternatively, suppose the money creation constraint is strongly binding in the sense that the loanable amount is smaller than both the banks’ optimal loan amount and the socially efficient loan amount. In this case, the introduction of CBDC will decrease social welfare if the transfer of funds to the central bank is marginal, as the reduction in bank lending exacerbates the problem of insufficient lending.

In extensions, this paper also examines the effects of CBDC on bank lending in the presence of alternative sources of funding. Firstly, as banks lose deposits to the central bank, they are likely to expand wholesale funding in order to recover the funding gap and to augment their lending. Jun and Yeo (2021) and Whited et al. (2023) consider models in which banks can react to a reduction in demand deposits by increasing wholesale funding. Other studies find however that bank lending decreases because the cost of capital of wholesale funding rises as banks demand more wholesale funds and therefore can only partially recover the funding gap. However, if the wholesale funding cost is fixed, banks can recover more lending. Unlike these studies, the present study explicitly considers money creation by banks and shows that the loanable amount will decrease even if the wholesale funding cost is fixed because the introduction of CBDC ultimately reduces the ability of banks to create money and thereby their bank lending amounts.

Secondly, the literature shows that bank lending remains unchanged following the introduction of CBDC if the central bank fully passes the deposits it receives from CBDC issuance through to commercial banks. Using models in which banks do not create money but simply lend out existing cash, Brunnermeier and Niepelt (2019) and Fernández-Villaverde et al. (2021) demonstrate that a CBDC system with full pass-through lending by the central bank yields an equivalence result in economic outcomes. Building on a framework in which banks endogenously create money, this paper theoretically confirms this equivalence result. However, the result holds only when the central bank passes through the entire amount of deposits to commercial banks. Put differently, this paper shows that the equivalence breaks down even if the central bank withholds a very small share of these deposits.

This paper is structured as follows. Section 2 presents a model of fountain pen money creation and examines the effects of CBDC on bank lending. Section 3 explores the implications of these theoretical findings for the Korean economy. Section 4 extends the analysis by considering the possibility of banks raising funds in the wholesale borrowing market. Section 5 offers another extension, in which the central bank can pass deposits to commercial banks in order to recover their loanable amounts.

II. Theoretic Analysis

The model economy consists of a continuum of households, with a total mass of one, a representative entrepreneur, and a monopolist commercial bank. There is a single consumption good in the economy, and the price of this good is denominated in units of the consumption of the good itself. The economy operates over three dates: 0, 1, and 2. For simplicity, there is no time-discounting.

At date 0, each household is endowed with e units of real cash. This cash can be exchanged one-for-one with the consumption good, and it is also directly consumable. There is a central bank that offers demand deposit accounts to households, accepts cash deposits, and issues retail CBDC. For instance, if a household deposits one unit of cash into their central bank deposit account, the central bank issues one unit of CBDC to the household. Cash, CBDC, and the consumption good can be exchanged on a one-to-one basis. It is assumed here that the CBDC is non-interest bearing and hence that the net interest rate on CBDC is zero. The commercial bank also provides demand deposit accounts for households. For simplicity, I assume that the central bank or commercial banks do not provide savings deposit accounts.

There are two types of households in the economy: the CBDC type and the bank type. CBDC-type households deposit their cash into central bank deposit accounts, while bank-type households deposit their cash into commercial bank accounts. Storing cash at home is costly and inconvenient such that households prefer to deposit their cash either with the central bank or with the commercial bank rather than holding it themselves. Let ϕ represent the fraction of CBDC-type households and (1 − ϕ) represent the fraction of bank-type households. The net interest rates on demand deposits are zero for both central bank accounts and commercial bank accounts because both accounts provide convenience yields to depositors: households require rapid and convenient payment services in order to transact products and/or services, and they can access to these payment services only if they have demand deposit accounts offered by the central bank or the commercial bank. For simplicity, I assume that there is no central bank reserve requirement.3

After receiving cash deposits from households, the commercial bank makes a loan l to the representative entrepreneur (In this baseline model, the central bank does not make loans). Let R denote the gross loan interest rate. The entrepreneur uses the loan to hire labor from households and invests in a project described by the function αf(l) where α > 0, f'(l) > 0, f''(l) < 0, f(0) = 0, and . If this project is successful, it yields output αf(l), but if it fails, the output is zero. The probability of project failure is p > 0. The entrepreneur is protected by limited liability, meaning that its expected profit is given by (1 − p)[αf(l) − Rl]. Because the monopolist commercial bank has significant bargaining power over the representative entrepreneur, the entrepreneur must satisfy a zero-profit condition. This implies that the bank charges the maximum possible loan interest rate, R = αf(l), which ensures that the entrepreneur’s expected profit is zero. I use this assumption of the bank’s bargaining power only for simplicity, and the main result is not altered even if the entrepreneur has bargaining power.

A. Money Creation and Loanable Amounts

When the commercial bank decides to give a loan l to the entrepreneur, it does not physically transfer cash but instead adjusts the entrepreneur’s deposit account balance held with the bank. In other words, the bank creates deposit money by making the loan, as observed by Tobin (1963). As a result, the entrepreneur sees an increase in his deposit balance equal to the loan amount l. The entrepreneur then uses this deposit money to purchase labor from households, paying wages by transferring l to the households’ deposit accounts. A fraction ϕ of these households are of the CBDC type, meaning they hold central bank deposit accounts. Therefore, the entrepreneur must transfer amount ϕl in cash to the CBDC-type households’ central bank accounts. The remaining households are of the bank type and hold commercial bank accounts, meaning that the entrepreneur must transfer (1 - ϕ)l in cash to these households’ commercial bank accounts. As a result, the total liquidity outflow from the commercial bank to the central bank is ϕl. It is important to note that the total amount of deposits held by households at the commercial bank is (1 - ϕ)(e + l), where (1 - ϕ)e represents the initial cash deposits that bank-type households placed in the bank, and (1 - ϕ)l represents the new deposits created when the entrepreneur pays wages to these households.

At date 1, households are classified into one of two types based on whether they face unexpected cash needs. Some households, known as “impatient-type” households, have no choice but to withdraw cash immediately from their deposit accounts to cover unforeseen expenses. For example, some may need to pay medical bills, while others may have caused car accidents and need to settle cash payments with the victims. Let λ represent the fraction of impatient-type households. Because each household has (1 - ϕ)(e + l) in their bank account, the total cash withdrawn by impatient-type households is λ(1 - ϕ)(e + l). This amount represents the total cash outflow that the commercial bank faces at date 1.

The remaining ‘patient-type’ households do not face unanticipated cash needs and, as a result, choose to wait until date 2 to withdraw their deposits. Consequently, the commercial bank faces the following money creation constraint:

By rewriting the money creation constraint above, we can derive the loanable amount l^L, which is the maximum loan amount that the commercial bank can extend without violating the money creation constraint:

For expositional simplicity, let’s assume that the central bank does not introduce CBDC; i.e., ϕ = 0. Under the incorrect conventional wisdom, it is often assumed that banks make loans out of their cash deposits and that the loanable amount therefore would simply equal the initial cash deposits e. However, in actuality, banks create loans “out of nothing” in the first place (i.e., they create deposit money when they issue loans), but subsequently must be able to meet the liquidity outflows associated with those loans. In such cases, the loanable amount is given by . This amount can be either larger or smaller than the initial cash deposits e depending on the fraction λ of impatient-type households. For example, if λ → 0, the loanable amount l^L becomes unlimited because almost no households will withdraw cash early, allowing the bank to lend almost infinitely without violating the money creation constraint. Conversely, if λ = 1, the loanable amount l^L becomes zero, as the bank will have to maintain all cash to meet withdrawal demands without leaving a penny for lending. The numerator (1 − λ) of the augmentation factor represents the fraction of patient-type households who leave their deposits in the bank until date 2, while the denominator λ represents the impatient-type households who withdraw their deposits early on date 1. As λ increases, the amount of deposits available for lending decreases, thus reducing the loanable amount.

B. The Effects of CBDC on Loanable Amounts

In this section, I will discuss the effect of CBDC on banks’ lending capacity. When the central bank introduces CBDC, the commercial bank loses cash deposits to an amount of ϕe because CBDC-type households choose to deposit their endowments into the central bank instead of the commercial bank. The conventional, but incorrect, view assumes that the commercial bank’s loanable amount equals cash deposits, meaning that the size of the decrease in the lending capacity is equal to the loss of deposits.

However, a more realistic theory of fountain pen money creation suggests that while the loanable amount does decrease, the magnitude of the decrease, i.e., Δl^L, may be either smaller or larger than the reduction in cash deposits (see Figure 1). One may expect that the commercial bank could increase deposit creation to preserve liquidity if it loses cash deposits to the central bank. However, money creation does not effectively preserve the bank’s liquidity; rather, it enhances the liquidity of the borrowers who receive loans, not the bank itself. To understand this, note that the commercial bank can create money only by making loans. When a new loan is provided, the entrepreneur receives liquidity, whereas the bank loses liquidity, as the entrepreneur uses the newly created money to make payments to households, some of whom then withdraw cash from the bank. Therefore, the commercial bank is unlikely to increase its lending in response to a decrease in cash deposits due to the introduction of CBDC.

FIGURE 1.

CONTRACTIONARY EFFECTS OF CBDC

Although the introduction of CBDC ends up reducing the commercial bank’s lending capacity, the magnitude of this reduction can vary. If the augmentation factor (i.e., ) is sufficiently small, the decrease in the bank’s loanable amount will be smaller than the decrease in cash deposits. This factor is small when there is a large proportion of impatient-type or CBDC-type households. In this case, for each unit of loan the bank makes, more liquidity flows out of the bank. (Recall that when the bank makes a loan l, CBDC-type households withdraw ϕl at date 0, and impatient-type households withdraw (1 - ϕ)λl at date 1.) Consequently, the bank can make only small loan amounts for a given level of cash deposits. Therefore, even if the central bank takes some cash deposits away from the commercial bank by introducing CBDC, the reduction in the bank’s lending capacity is relatively small.

On the other hand, if there are fewer impatient-type or CBDC-type households, the augmentation factor is large, meaning the bank can extend a large amount of loans with a small amount of cash deposits. In this scenario, a small reduction in cash deposits leads to a significant cut in lending capacity, making the contractionary effect of CBDC more pronounced. The following proposition summarizes this discussion:

Proposition 1. Suppose the central bank introduces CBDC. Then:

(i) The loanable amount l^L decreases.

(ii) The reduction in the loanable amount (Δl^L) is smaller than the reduction in cash deposits (ϕe) if and only if the augmentation factor is sufficiently small; i.e., < λ. For example, Δl^L < ϕe for any ϕ when λ > 0.618, but Δl^L > ϕe for any ϕ when λ < 0.50.

Proof. The benchmark case is where there is no CBDC (i.e., ϕ = 0) and the case of interest is where the central bank introduces CBDC (i.e., ϕ > 0).

(i) The loanable amount l^L is the product of cash deposits ((1 - ϕ)e) and the augmentation factor . Both the cash deposits and augmentation factor decrease as ϕ increases from zero to a positive number. Therefore, the loanable amount decreases.

(ii) The reduction in the loanable amount is smaller than the reduction in the cash deposits if and only if

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C. Banks’ Optimal Lending

At date 2, the entrepreneur’s outcome is determined: the entrepreneur either succeeds or fails. If successful, the entrepreneur generates an output of αf(l) and repays Rl = αf(l) to the commercial bank. The bank then repays the patient-type households an amount of (1 - λ)(1 - ϕ)(e + l). Conversely, if the entrepreneur fails, no output is produced, and the bank receives nothing from the loan. Nevertheless, the bank is still obligated to repay the patient-type households as much as possible, using all of their remaining cash. The remaining cash is given by (1 - ϕ)e - ϕl - λ (1 - ϕ)(e + l), where (1 - ϕ)e represents the initial cash deposits and ϕl and λ(1 - ϕ)(e + l) represent the liquidity outflows at dates 0 and 1, respectively.

Looking ahead to dates 1 and 2, the commercial bank chooses the loan amount at date 0 in order to maximize its expected profit. This expected profit is given by the following lemma.

Lemma 1. The commercial bank’s expected profit π at date 0 is given by

Proof. At date 0, the net cash flow of the commercial bank is (1 - ϕ)e - ϕl) because the bank-type households deposit (1 - ϕ)e with the bank, while the CBDC-type households withdraw ϕl from the bank. At date 1, the bank’s net cash flow is −λ(1 - ϕ)(e + l) as impatient-type households withdraw λ(1 - ϕ)(e + l). At date 2, if the entrepreneur succeeds, the bank receives αf(l) and repays (1 - λ)(1 - ϕ)(e + l) to patient-type households. If the entrepreneur fails, the bank receives nothing but repays the remaining cash (1 - ϕ)e - ϕl-λ(1 - ϕ)(e + l) to the depositors. Thus, the bank’s expected profit equals

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The commercial bank chooses an optimal amount of loan at date 0 by solving the following profit maximization problem:

subject to the money creation constraint (2). Let l^B denote the unconstrained optimal solution to the profit maximization problem. That is,

If the unconstrained optimum l^B is no more than the loanable amount l^L , it is feasible and hence is the optimal solution to the profit maximization problem in (4). However, if l^B exceeds l^L, the unconstrained optimum violates the money creation constraint and the commercial bank therefore must choose the loanable amount. Let l^* denote the optimal solution to the profit maximization problem. This is given by

At the end of date 2, the commercial bank closes and distributes its profit to the households. The bank is owned by the households; however, management and ownership are separate, meaning that the households do not have direct influence over the bank’s management.

In Proposition 1, I show that the introduction of CBDC reduces the bank’s loanable amount. Does this mean that the bank will actually reduce lending? Because the loanable amount is the maximum loan the bank can make, the answer to this question depends on whether the optimal loan amount is constrained by the loanable amount.

This is where the fountain pen money creation theory becomes important. If we consider the mistaken belief that the bank lends money out of cash deposits, the following scenario arises. In the case where the bank is constrained by its cash deposits (i.e., it lends as much as the deposits before the introduction of CBDC), one can expect that the introduction of CBDC reduces bank lending, as cash deposits move from the bank to the central bank.

However, this expectation is incorrect when considering the reality of fountain pen money creation. If the bank lends as much as its cash deposits under the absence of CBDC, the optimal loan amount l^*(ϕ = 0) equals e, and according to the money creation constraint (2), it is smaller than the loanable amount l^L(ϕ = 0).4 If the impact of CBDC in relocating deposits from the bank to the central bank is marginal, i.e., if ϕ is small, CBDC only marginally reduces l^L(ϕ) (see Proposition 1) and e therefore remains smaller than l^L(ϕ > 0). Given that the money creation constraint (2) does not bind, the bank will not adjust its loan amount. That is, CBDC does not affect bank lending, which stands in stark contrast to the common belief that the bank’s lending is constrained by cash deposits. This arises because, in actuality, the constraint on bank lending is not cash deposits but rather the loanable amount as determined by the money creation constraint (2).

Next, we consider the nonbinding case in which the bank lends less than its cash deposits. If one adheres to the false assumption that banks lend out of cash deposits, they will expect CBDC to have no effect on lending, as the bank is not constrained by its deposits. However, under the fountain pen money creation framework, the current model implies that bank lending will decrease after the introduction of CBDC. This discussion is summarized in the following proposition:

Proposition 2. For a small amount of ϕ,

Case 1. Suppose l^* = e in the absence of CBDC. Then, after the introduction of CBDC, l^* does not change if λ ≠ 1 / 2; but if λ = 1 / 2, l^* decreases.

Case 2. Suppose l^* ≠ e in the absence of CBDC. Then, after the introduction of CBDC, l^* decreases if the money creation constraint (2) is binding at ϕ = 0 ; but if the money creation constraint (2) is not binding at ϕ = 0, l^* does not change.

Proof. In the following, I shall use the notation l^* = l^*(ϕ) for convenience.

Consider case 1. Then, l^*(0) = e ≤ l^L(0) according to the money creation constraint (2). If λ ≠ 1 / 2, then . Therefore, e ≤ l^L(0). In this case, a small increase in ϕ leads to a marginal reduction in l^L(0) and, therefore, e remains smaller than l^L(ϕ > 0). As the money creation constraint (2) is still non-binding, the bank does not change the loan amount. If λ = 1 / 2, then e = l^L(0). In this case, if ϕ increases marginally, l^L(ϕ) decreases marginally and, hence, e > l^L(ϕ > 0). That is, l^*(0) = e > l^L(ϕ > 0). Because the initial optimum l^*(0) violates the money creation constraint (2), the bank must reduce lending.

Consider case 2. If the money creation constraint is binding when ϕ = 0, the optimal loan amount is equal to the loanable amount. If ϕ increases marginally, the loanable amount decreases marginally and, therefore, the money creation constraint becomes more binding. The bank must then reduce its lending. If the money creation constraint is non-binding when ϕ = 0, the optimal loan amount is smaller than the loanable amount l^L(0). If ϕ increases marginally, the loanable amount decreases marginally and, hence, the money creation constraint is still non-binding. The bank thus does not change its lending amount.

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In South Korea, commercial banks lend nearly as much as their customer deposits. According to the Financial Supervision Service, the average loan-to-deposit ratio for general commercial banks between 2020 and 2023 was 95%.5 Specifically, the annual loan-to-deposit ratios were 96% in 2021, 93% in 2022, and 94% in 2023. During this period, the average loan-to-deposit ratio of the four largest banks (i.e., Kookmin Bank, Shinhan Bank, Woori Bank and Hana Bank) was 97%. This suggests that the Korean banking sector aligns closely with Case 1 of Proposition 2. Consequently, the proposition indicates that even if the central bank introduces CBDC, Korean banks are unlikely to reduce lending significantly provided there are safeguards in place, such as caps on individual CBDC holdings or zero interest rates on CBDC,6 preventing large-scale deposit outflows from commercial banks to the central bank.

D. Socially Efficient Lending

The society consists of the households, the entrepreneur, the commercial bank, the government, and the central bank. The payoffs for all agents, except for the government, can easily be derived.

First, we derive the government’s payoff. If the entrepreneur fails with its investment at date 2, the bank goes bankrupt. As a result, patient-type households cannot be fully repaid their deposits. In this case, I assume the government steps in to rescue the depositors for several reasons. First, there is a deposit insurance scheme in place that will effectively cover most depositors.7 Second, the government wants to prevent a systemic crisis that could arise if a large number of depositors fail to receive their money back. Third, the depositors are a large group of taxpayers who can exert pressure on the government to protect them. Although a new bail-in regime was introduced in many advanced countries after the global financial crisis, under which bank creditors were expected to absorb losses, this generally applies only to non-deposit creditors.

The shortfall in deposits that the government must repay on behalf of the failed bank is expressed as shown below.

This occurs because the patient-type households’ total claims equal (1 - λ)(1 - ϕ)(e + l), and the failed bank’s available cash for distribution at date 2 equals (1 - ϕ)e - ϕl - λ(1 - ϕ)(e + l). Therefore, the government’s expected payoff is T − pl, where T is the lump-sum tax levied on the households.

The households’ payoff equals e + π − T for the following reasons. First, the households are endowed with e. Second, they deposit their endowments and receive full repayment, regardless of whether the commercial bank fails or not, as the government steps in to rescue the households if the bank fails. Third, the households are owners of the bank and thus receive the bank’s full profit, π, as a dividend. Fourth, the households must pay a lump-sum tax T.

Note that both the entrepreneur and the central bank have zero payoffs. First, the entrepreneur repays the entire output to the bank if success ensues. Second, the central bank receives deposits from CBDC-type households and repays these deposits in full. I implicitly assume that the central bank also sets a zero net interest rate, similar to the commercial bank.

Finally, the social welfare function net of the endowment is given by

The efficient loan amount, l^W, that maximizes the net social welfare function above is given by

Note that the society wants to induce a smaller loan amount than the commercial bank wants to choose. By comparing equations (5) and (9), it becomes clear that the efficient loan amount l^W is smaller than the unconstrained optimal loan amount l^B. This arises because the full benefit of risk-taking (i.e., lending) accrues to the bank, while the cost of risk-taking is shared between the bank and society. If the bank fails at date 2, the government repays the deposit shortfall, as the bank is protected by limited liability. Thus, the bank has an incentive to make an inefficiently large loan. However, this does not necessarily mean that the bank will always lend more than society desires. If the money creation constraint (2) is binding and tight enough, the bank can make only a small amount of loans. In this case, the optimal loan amount l^* can be smaller than the efficient loan amount l^W.

Lemma 2. (i) The unconstrained optimal loan amount l^B is larger than the efficient loan amount l^W. (ii) The optimal loan amount l^* may or may not be larger than the efficient loan amount l^W.

Proof. Omitted.

E. Effects of CBDC on the Efficiency of Bank Lending

If the central bank introduces CBDC, the commercial bank will lose some deposits, which will reduce its ability to make loans. However, this does not necessarily imply that social welfare will decrease as a result. The impact of CBDC on efficiency through bank lending depends on the productivity α of the economy and the intensity of the money creation constraint (2). For now, suppose that the amount of the deposit transfer from the commercial bank to the central bank is marginal (i.e., ϕ is small). In this case, there are three scenarios to consider.

First, suppose that the money creation constraint is non-binding, as shown in Figure 2(a). This case arises when the total factor productivity α is high, financial resources e are abundant, or the liquidity outflow λ is small (as indicated by equations (2) and (5)). In this case, the unconstrained optimal loan amount is smaller than the loanable amount and, hence, the unconstrained optimal loan amount is indeed the optimum, i.e., l^* = l^B. Let l^L(ϕ) denote the loanable amount, which is determined by the money creation constraint (2). If the central bank marginally takes deposits from the commercial bank, the loanable amount decreases marginally. However, the new loanable amount remains larger than the unconstrained optimal loan amount. Therefore, the commercial bank does not adjust its lending amount, as it still has sufficient resources to lend.

Second, suppose the money creation constraint is binding and, thus, the optimal loan amount equals the loanable amount, i.e., l^* = l^L(ϕ). This situation occurs when the total factor productivity α is low, financial resources e are scarce, or the liquidity outflow λ is large. Suppose additionally that the money creation constraint is weakly binding in the sense that the loanable amount is higher than the efficient amount of loans, i.e., l^L(ϕ) > l^W, as shown in Figure 2(b). In this case, the bank makes an excessively large amount of loans. In such a “too-much-finance” scenario, the introduction of CBDC into the banking system constrains bank lending, which in turn improves social welfare. In other words, the introduction of CBDC leads to an efficient contraction.

Third, suppose the money creation constraint is strongly binding in the sense that the loanable amount is not only smaller than the unconstrained optimal loan amount but also smaller than the efficient loan amount, i.e., l^* = l^L(ϕ) < l^W, as shown in Figure 2(c). In this case, the bank undertakes an inefficiently small amount of lending due to the very tight money creation constraint. The introduction of CBDC further tightens the money creation constraint, worsening the economic outcome. This is an inefficient contraction.

Thus far, I have considered the cases where the magnitude of the money transfer from the commercial bank to the central bank due to the introduction of CBDC is relatively small. However, if the magnitude of the money transfer is very large and therefore the reduction in bank lending is drastic, social welfare will decrease in all three cases shown in Figure 2. In the extreme case, if all households deposit endowments solely with the central bank (i.e., ϕ = 1), the loanable amount becomes zero. As a result, the economic outcome is always inefficient.

FIGURE 2.

EFFECTS OF CBDC ON THE EFFICIENCY OF BANK LENDING

Proposition 3. For a small amount of ϕ,

Case 1 (Non-binding MC → Invariance)

Suppose . Then, l^* = l^B does not change after the introduction of CBDC.

Case 2 (Weakly binding MC → Efficient contraction)

Suppose . Then, l^* = l^L(ϕ) decreases, but social welfare increases after the introduction of CBDC.

Case 3 (Strongly binding MC → Inefficient contraction)

Suppose . Then, l^* = l^L(ϕ) decreases and social welfare decreases after the introduction of CBDC.

III. Discussion

Proposition 1, 2 and 3 are the main results of this paper. They show that the introduction of CBDC constrains the bank’s financial intermediation but does not necessarily lead to an efficiency loss for the economy. The welfare implications depend on the strength of the money creation constraint (2). If the money creation constraint is non-binding, CBDC does not affect social welfare (i.e., Case 1 of Proposition 3). If the money creation constraint is weakly binding in the sense that the loanable amount is smaller than the unconstrained optimal loan amount but still larger than the efficient loan amount, CBDC improves social welfare by curbing excessive lending (i.e., Case 2 of Proposition 3). If the money creation constraint is strongly binding in that the loanable amount is smaller than the efficient loan amount, CBDC is detrimental to social welfare as it exacerbates the shortage of financial intermediation (i.e., Case 3 of Proposition 3).

Then, which case best describes the Korean economy? In a sense, Case 2 may be a good fit for several reasons. Firstly, the liquidity coverage ratio (LCR) requirement is nearly binding. Under the Basel III capital accord, banks are required to hold high-quality liquid assets, such as cash or sovereign bonds, at least as much as 100% of the net liquidity outflow over a one-month period. This requirement is conceptually similar to the money creation constraint (2) in this model, which mandates that the bank to maintain cash at least equal to the deposit outflow. Since 2020, this LCR requirement has been nearly binding for most commercial banks in South Korea. According to the Financial Supervision Service, the average LCR for commercial banks between 2020 and 2023 has been 102%.

Secondly, South Korea is known for its high level of private credit. According to the Bank of International Settlements, the ratio of private credit to GDP in Korea stands at 206%, making it the ninth highest among 30 OECD countries and significantly above the OECD average of 152%.8 Many papers in the literature on the growth-finance nexus observe an inverse U-shaped relationship between economic growth and financial resources. Specifically, additional financial resources, often measured by the ratio of private credit to GDP, tend to have a negative impact on economic growth once they exceed a certain threshold. While the exact threshold level varies slightly in empirical studies, it is generally estimated to be around 80-150%, which is substantially smaller than South Korea’s current ratio of private credit to GDP. This empirical observation suggests that the equilibrium amount of bank loans could be higher than the socially efficient loan amount.

Of course, the real world is much more complex, and it is difficult definitively to determine whether the Korean economy suffers from excessive lending in general. For example, many politicians and commentators criticize the banking sector for not providing enough lending to individuals with medium or low credit ratings. On the other hand, there is also a widespread concern that lending to households and the real estate sector has become excessive. Therefore, these sectors are more or less consistent with Case 2 of Proposition 3, where excessive lending is curbed by the introduction of CBDC, while other sectors may still require more lending, which aligns with Case 3 of Proposition 3.

IV. Wholesale Funding

In the previous section, I show that the commercial bank’s loanable amount is reduced if the central bank introduces a retail form of CBDC. One may then suggest that the bank could recover the decrease in deposit funding by increasing its wholesale funding. For instance, Jun and Yeo (2021) consider a setting in which banks can react to a reduction in demand deposits by increasing wholesale funding. Also, Whited et al. (2023) find that a one-dollar increase in CBDC reduces bank deposits by 80 cents but that bank lending decreases only by 20 cents as banks increase their wholesale funding. However, existing studies do not consider the phenomenon of bank money creation. Below I shall examine whether banks substitute deposits by wholesale funding when CBDC is introduced and whether and how this substitutability depends on bank money creation.

Let b denote the amount of borrowing from non-deposit investors and r denote the net interest rate on this wholesale borrowing. In this case, the commercial bank’s money creation constraint (1) changes to

By rewriting the money creation constraint above, one can derive a new loanable amount l^L(ϕ, b) as follows:

If the entrepreneur succeeds and repays the loan, the bank is able to repay the principal and interest of the wholesale borrowing, which is (1 + r)b. However, if the entrepreneur fails and does not repay the loan, the bank goes bankrupt and can only repay the wholesale lenders the remaining amount of cash (1 + ϕ)e - ϕl + b − λ (1 − ϕ)(e + l). The bank’s profit function is then given by (1 − p)[αf(l) − l − rb], as shown in the following lemma:

Lemma 3. The commercial bank’s expected profit π at date 0 with wholesale borrowing b is given by

Proof.

■

As a benchmark, consider the case where there is no CBDC; i.e., ϕ = 0. In this case, the loanable amount without any wholesale borrowing is , according to equation (11). For the following analysis, suppose that this loanable amount is smaller than the unconstrained optimal loan amount, i.e., . In this case, the commercial bank may consider borrowing from wholesale lenders (see Figure 3). Given that wholesale borrowing is costly, the bank will borrow only as much as necessary to meet the required loan amount. That is, the money creation constraint (10) becomes binding, and the bank borrows b = λ(e + l) − e. In this case, Lemma 2 implies that the bank’s profit function is given by

FIGURE 3.

OPTIMAL WHOLESALE BORROWING BEFORE THE INTRODUCTION OF CBDC

Note that the first derivative of the terms in bracket represents the difference between the rate of return on lending and the cost of capital for wholesale borrowing. The bank will choose an optimal amount of wholesale borrowing by comparing the rate of return with the cost of capital. The rate of return on lending at the loanable amount with zero wholesale borrowing equals [αf'(l^L(0, 0)) − 1], and the effective cost of capital of wholesale borrowing is rλ. If the rate of return is smaller than the effective cost of capital, the bank will not borrow at all in the wholesale borrowing market. Conversely, if the rate of return exceeds the cost of capital, the bank will borrow an optimal amount b^*, at which the rate of return on lending equals the effective cost of capital. This optimal amount of borrowing is characterized by the equation below (14). Note that the optimal loan amount equals l^L(0, b^*), which is the loanable amount with the optimal amount of borrowing.

It is important to note that the effective cost of capital, rλ, is smaller than the actual cost of capital, r. This difference arises because the commercial bank creates money by making loans. If the bank did not create money, its loanable amount would simply be the sum of the unwithdrawn cash deposits and the wholesale borrowing amount, (1 − λ)e + b. In this case, for each unit of wholesale borrowing, the bank could make exactly one unit of loans. Therefore, the marginal cost of lending equals the actual cost of capital for wholesale borrowing r.

However, when the bank creates money, it can make more than one unit of loans for each unit of wholesale borrowing. For instance, suppose the bank increases borrowing by $1. If the bank subsequently increases lending by $1, this act will increase the deposit balance of the entrepreneur by $1. The entrepreneur then transfers this new money to households to buy labor. Households withdraw only $λ of this newly created deposit, as patient-type households do not withdraw. Consequently, the bank can use the remaining portion,$(1 − λ), to increase its loans further. This is why the effective cost of capital of wholesale borrowing is rλ, which is smaller than the actual cost of capital r.

This is one of the reasons why commercial banks are special as opposed to non-bank financial institutions or nonfinancial companies. Non-bank entities must bear the full cost of capital because they do not create money. Only commercial banks benefit from the reduced effective cost of capital due to their unique power of money creation. Moreover, this effective cost of capital is smaller when bank deposits are stickier, i.e., when λ is smaller.

Suppose the central bank introduces a retail type of CBDC and that as a result, some bank deposits are transferred to the central bank; i.e., ϕ > 0. For expositional simplicity, assume that the magnitude of money transfer is small, i.e., ϕ is small. Then, according to Proposition 1, the loanable amount l^L(ϕ, b^*) or the given amount of wholesale borrowing b^* decreases (see Figure 4). Some readers may suggest that the commercial bank will recover this decrease in deposit funding by increasing wholesale borrowing. The bank will do so if the effective cost of capital does not change after the introduction of CBDC. If the cost of capital were still rλ even with CBDC, the bank would indeed increase the amount of wholesale borrowing until the rate of return on lending [αf'(l^L(ϕ, b)) − 1], equals the cost of capital rλ. At this point, the optimal loan amount would be identical to the optimal loan amount without CBDC, l^L(0, b^*).

FIGURE 4.

OPTIMAL WHOLESALE BORROWING AFTER THE INTRODUCTION OF CBDC

However, the effective cost of capital is no longer rλ. Instead, it becomes r[ϕ + (1 − ϕ)λ]. Without CBDC, for each additional unit of lending and corresponding unit of created deposits, households withdraw only λ units of deposits. As a result, the bank can make an additional loan of (1 − λ). In contrast, with CBDC, for each additional unit of lending and the corresponding new deposits, CBDC-type households will withdraw ϕ units, while bank-type-impatient households withdraw (1 − ϕ)λ. Hence, the additional lending that the bank can undertake is reduced to (1 − ϕ − (1 − ϕ)λ). In other words, the bank’s power to make loans by raising wholesale borrowing is reduced. The new optimal loan amount is characterized by the following equation:

Equations (14) and (15) imply that the new optimal loan amount with CBDC, l^L(ϕ, b^**), is smaller than the existing optimal loan amount without CBDC, l^L(0, b^*), as the introduction of CBDC increases the effective cost of capital while leaving the rate of return on lending unchanged.

This result is related to, but distinct from, those in earlier studies. Whited et al. (2023) assume that the wholesale cost of capital increases with the volume of wholesale funding. Under this assumption, when banks replace lost deposit funding with additional wholesale funding, the wholesale cost of capital rises, preventing banks from fully offsetting the deposit shortfall and thereby reducing lending. If the wholesale funding cost is instead fixed, their framework implies that banks can largely compensate for the loss of deposits.

In contrast, this paper finds that even when the wholesale funding cost is fixed, the volume of loans declines because the introduction of CBDC directly weakens banks’ money-creation capacity. Recall that although the wholesale interest rate r is fixed in this model, the effective cost of capital rises as CBDC adoption expands.

Jun and Yeo (2021) conclude that the introduction of CBDC does not significantly affect bank lending. In their setting, banks benefit from reduced liquidity-handling costs due to CBDC—an effect that pushes lending up—yet simultaneously face higher wholesale funding rates, which push lending down. However, this paper shows that even when liquidity-handling costs fall, bank lending will decline as long as CBDC reduces the banks’ inherent ability to create money.

Thus far, I have considered the case in which the effective cost of capital is not prohibitively high such that the commercial bank borrows a non-zero amount from wholesale lenders. In other words, I implicitly assume that the rate of return on lending at the loanable amount without wholesale borrowing is higher than the effective cost of capital, regardless of whether the central bank introduces CBDC. Specifically, I assume the following two conditions:

Even if these assumptions are not realized, it can easily be shown that the loanable amount decreases due to the introduction of CBDC. I will omit the proof, but the intuition behind this result is as follows: if one (or both) of these assumptions are not satisfied, wholesale borrowing is then prohibitively costly. In this case, the commercial bank would not find it optimal to recover the decrease in deposit funding through such an expensive alternative source of funding. Consequently, the bank would not increase wholesale borrowing, and the loanable amount would decrease as a result of the introduction of CBDC.

V. Pass-Through Lending

Under the existence of a retail form of CBDC, the central bank directly takes deposits from households. The central bank may choose to hold the cash deposits in its vaults as reserves. However, alternatively, the central bank may opt to give loans to commercial banks based on the cash deposits, a process known as pass-through lending. By doing so, the central bank provides additional funds to commercial banks, which may then use these funds to extend loans to nonbank borrowers. Brunnermeier and Niepelt (2019) and Fernández-Villaverde et al. (2021) demonstrate that, under the assumption that banks do not create money, economic outcomes remain unchanged after the introduction of CBDC if the central bank provides pass-through lending. However, this equivalence result may change when considering the reality of fountain pen money creation. Below we examine the effect of CBDC with pass-through lending on bank lending, specifically in the context where banks create money.

The central bank receives ϕ(e + 1) as cash deposits from CBDC-type households at date 0, and CBDC-type impatient households withdraw cash as much as λϕ(e + 1) at date 1. Thus, the central bank can provide pass-through loans up to the amount of (1− λ)ϕ(e + 1) at date 0. Here, I implicitly assume that the central bank satisfies a money creation constraint, with its capacity to make pass-through loans limited to the cash deposits. In the real world, central banks have the ability to print money, meaning that there is no limit on the capacity of liquidity provision. However, central banks rarely provide loans by printing money, as their primary mission is to maintain price stability. Only in exceptional cases, such as during financial crises, do central banks provide an unlimited amount of loans to stabilize the financial system. In this paper, I do not consider such rare instances where the central bank’s role as the lender of last resort is required.

The central bank’s lending capacity is constrained further by its concerns about credit risks. If the central bank makes a loan to the commercial bank and the commercial bank is unable to repay, the central bank incurs a loss. Such a loss not only imposes a financial burden but also creates a political burden, as both price stability and financial stability could be negatively impacted. In this case, the government may need to provide bailout funds to the central bank, which could lead to political controversies. Consequently, it is reasonable to assume that the central bank would be reluctant to provide pass-through loans to the commercial bank.

Let ρ ∈ [0, 1] be a measure of the central bank’s willingness to make a loan to the commercial bank. Therefore, the central bank can offer pass-through loans up to ρ(1 − λ)ϕ(e + 1). Additionally, suppose that the interest rate on these pass-through loans is identical to the interest rate on the commercial bank’s deposits. In this case, the central bank would merely act as an intermediary, passing funds from households to the commercial bank without earning an interest margin.

Given the possibility of receiving pass-through loans, the commercial bank’s money creation constraint changes to

By rewriting the new money creation constraint above, the new loanable amount l^LP is as expressed as

By comparing equations (2) and (17), it is clear that the commercial bank’s loanable amount increases due to the central bank’s pass-through loans. However, the magnitude of this increase in loanable amount depends on ρ, which represents the central bank’s willingness to make pass-through loans. If ρ = 0, the central bank does not provide any pass-through loans and the loanable amount therefore does not increase at all. If ρ = 1, the central bank fully passes through the deposits from households to the commercial bank, meaning that the loanable amount becomes , which is the loanable amount in the absence of CBDC.

This paper generalizes Brunnermeier and Niepelt (2019) and Fernández-Villaverde et al. (2021), as their equivalence results hold even under the realistic framework where banks create money by making loans. However, this paper is different from these studies as it shows that the equivalence result holds only if central banks fully pass through lending. If central banks withhold a tiny little part of central bank deposits, allocation can change. In addition, this paper shows that with less pass-through lending, the loanable amount becomes smaller. Earlier studies do not find such a continuous relationship between the amount of pass-through lending and the loanable amount. Because central banks in real life cannot fully transfer deposits to commercial banks (ρ < 1), the equivalence result does not hold in general.

VI. Concluding Remarks

Central bank digital currency (CBDC) is a type of crypto-currency issued by a central bank. A key concern on CBDC is the potential negative impact on banks’ deposit-taking activities. If a retail type of CBDC is introduced, some individuals may choose to deposit their money with the central bank as opposed to commercial banks, as the central bank is generally perceived as more trustworthy. This raises the concern than commercial banks may be forced to reduce their lending due to the loss of some deposits.

This concern stems from the common belief that banks lend out of deposits. However, in reality, banks lend “out of nothing” by creating deposit money. Tobin (1963) refers to this as ‘fountain pen money.’ In some cases, banks may even lend more than the amount they receive in deposits. Therefore, even if the introduction of retail CBDC leads to a decrease in bank deposits, banks may respond by increasing their money creation and lending activities. If this is the case, the relationship between CBDC and bank lending becomes unclear: bank lending may not necessarily decrease with the introduction of CBDC, or if it does, the reduction may not be as large as the amount of money that moves from banks to the central bank.

By examining a model of fountain pen money creation in the context of CBDC, I derive the following main results. First, the loanable amount is determined by both cash deposits and an augmentation factor. This factor can be greater than or less than 1, depending on relevant underlying parameters. The augmentation factor will be greater than 1 if the proportion of depositors who withdraw early, or those who transfer their deposits from commercial banks to the central bank, is sufficiently small.

Second, the introduction of CBDC leads to a reduction in loanable amounts as some deposits shift to the central bank. However, the extent of this reduction can be greater than, smaller than, or equal to the decrease in deposits. If the augmentation factor is small, the decrease in loanable amounts is smaller than the decrease in deposits. Conversely, if the augmentation factor is large, loanable amounts will be larger than the decrease in deposits.

Third, CBDC may or may not reduce actual loan amounts, not the loanable amount. According to the mistaken belief that banks lend out of cash deposits, if banks are constrained by deposit funding and lend up to the level of deposits, CBDC would reduce bank lending as deposits decrease. However, in the actual scenario of fountain pen money creation, banks will continue to lend the same amount even after the introduction of CBDC, provided that bank lending without CBDC is more or less identical to deposits. In South Korea, for example, commercial banks lend nearly as much as they receive in deposits. Therefore, this paper suggests that bank lending will not decrease significantly with the introduction of CBDC.

Fourth, social welfare may increase, decrease, or remain unchanged after the introduction of CBDC. If the money creation constraint is non-binding in the absence of CBDC, bank lending remains unchanged, and social welfare remains invariant, provided that the transfer of funds is marginal. If the money creation constraint is weakly binding in the sense that the loanable amount is smaller than banks’ optimal loan amounts but greater than the socially efficient loan amount, then the introduction of CBDC reduces bank lending, while social welfare increases as the problem of excessive lending is alleviated. Conversely, if the money creation constraint is strongly binding in the sense that the loanable amount is smaller than both the banks’ optimal loan amount and the socially efficient loan amount, CBDC reduces social welfare.

In this paper, I assume that CBDC is a non-interest-bearing currency and that there is no limit on the amount of CBDC that an individual can hold. I believe this assumption is fair enough, as CBDC is a type of cash which does not typically pay interest. However, the central bank may consider the interest rate and a limit on CBDC as policy tools. If the money creation constraint is non-binding or weakly binding and, hence, the economy suffers from an overinvestment problem, the central bank may choose a positive interest rate and impose no limit on CBDC holdings in order to magnify the contractionary effect of CBDC. In contrast, if the money creation constraint is strongly binding and thus the economy faces an underinvestment problem, the central bank may lower the interest rate to a negative level or impose a tight limit on CBDC holdings in order to discourage depositors from choosing CBDC.