CBDC: A central bank for everyone? | National Bureau of Economic Research Working Paper

Original: NBER Author: Jesús Fernández-Villaverde, Daniel Sanches , Linda Schilling, Harald Uhlig

Source: People's Congress Institute of Financial Technology (WeChat ID: ruc_fintech)

Compilation: Li Jinxuan

In addition to reducing the use of cash, the central bank's digital currency also allows the central bank to compete with private financial intermediaries for deposits and become a “open to everyone” central bank. What impact will the introduction of CBDC and open central bank facilities have on the financial system? Recently, the National Bureau of Economic Research (NBER) released related working papers, and the Institute of Financial Technology of Renmin University of China (WeChat ID: ruc_fintech) compiled the core content of the article.

Recent advances in encryption and distributed bookkeeping have opened the door to the widespread use of digital currencies. Although these currencies were first introduced by private schemes such as Bitcoin, Ethereum, and Libra, researchers and policy makers have explored the possibility that central banks can also issue their own digital currencies.

The emergence of the Central Bank Digital Currency (CBDC) can represent an important innovation in the history of the currency and banking industry. CBDC has the potential to eliminate physical cash. In addition, it allows central banks to compete with private financial intermediaries for deposits for large-scale intermediary activities, and may borrow these deposits in some form. The CBDC offers consumers the possibility to open a bank account directly with a central bank.

At this time, the technological change introduced by digital currency may prove that the fundamental change in the financial system architecture is reasonable, and the central bank is "open to everyone". As Friedman & Schwartz (1986) demonstrated in a classic paper, external forces such as technological innovation may influence our perceptions of the role of government in establishing monetary and financial institutions and make us choose other arrangements.

What impact will the introduction of CBDC and open central bank facilities have on financial intermediaries? Will CBDC weaken the role of the financial system in allocating funds for productive investment? Can we restructure the financial system through the CBDC by allowing funds to flow reasonably between depositors and investors? Can CBDC make bank runs disappear and stabilize the financial system?

Historical review

Historically, many central banks have allowed companies and citizens to make deposits and provide loans to them. The positive impact of commercial activities such as the provision of demand deposits, credit creation, and integration of payment systems on economic growth by the central bank has also been seen as the establishment of such institutions Motivation.

Even today, one can trade the stocks of many central banks on the stock exchange, including the Swiss National Bank and the Bank of Japan. Although these stocks have strict voting rights restrictions, their active trading proves that the activities of the central bank are very different from simply implementing conventional monetary policy.

The advent of digital currencies has reignited the debate over the role of central banks. First, CBDC has become possible. Second, the Internet allows central banks to face the public directly or work with existing commercial banks without the need to build an extensive network of branches. Both factors suggest that we can and are likely to re-examine the strict wall between the central bank and the general public. For this, we need a formal economic model.

Model assumptions

The model in this paper is based on the bank run model of Diamond & Dybvig (1983), which puts the bank as the valuable term conversion service provider at the center of the model. At the same time, this model differs from the classic model in two points. First, this model will distinguish between commercial and investment banks. Second, this model will add a central bank controlled by the government. This model is still a three-phase model, and in each period, there is a commodity available for consumption or investment. There are three sectors of the economy: consumers, commercial and investment banks, and central banks.

Commercial and investment banks

Banks can use two types of investment technologies: short-term technology and long-term technology. Short-term technology, or short-term assets, is a fixed-scale return technology that acquires a unit of goods in a certain period and converts it into a unit of goods in the next period. Long-term technology, or long-term assets, is a risk-free fixed-scale return technology that uses one unit of commodity at t = 0 and converts it to R> 1 unit of commodity at t = 2. If the long-term technology is liquidated in advance at t = 1, for every unit invested, k units of goods will be paid.

Commercial banks provide consumers with demand deposit contracts and invest in short-term and long-term assets. If the consumer accepts the bank's contract, he is required to deposit a commodity in the bank at t = 0. The bank invests a proportion of the commodities in y in short-term technology and the remaining 1-y in long-term technology.

Although investment banks can also use storage technology and long-term assets, they only provide contracts that guarantee non-negative profits at t = 2. In other words, investment banks cannot provide liquidity by providing demand deposits to consumers.

All future cash flows from the investment bank to the contracting party (such as the central bank) have been determined at t = 0, and the contracting party cannot request payment at t = 1 like a demand deposit in a commercial bank. Because the return on long-term assets is greater than the return on short-term assets, investment banks only choose to operate long-term technology and maximize profits at t = 2.

The investment banks in this article include not only the financial institutions that call themselves by this name, but also industrial banks (common in continental Europe, Japan, and South Korea), as well as any other investment vehicle, such as retirement funds. Return is the goal.

Compared with individual consumers, banks have the advantage that they can share the risks of early and late consumers, while individual consumers cannot sign insurance contracts for their own special liquidity risks.

In solving the equilibrium, the author assumes that all investment banks and all commercial banks use the same contract.

Central bank

In this model, the central bank is a government-controlled institution that can use short-term investment technology instead of long-term assets. However, the central bank can use long-term assets by contracting with investment banks. Moreover, central banks cannot rely on taxes.

Among them, the fourth hypothesis is the key to analysis and the most vulnerable. If the central bank has financial support, it will have an advantage over commercial banks. At the same time, political and economic factors are likely to be the primary consideration in the actual operation of a central bank that is open to all. Many political groups will lobby banks to change their credit policies to achieve their goals, even if the operation requires financial support.

The central bank can provide consumers with deposit contracts (d1, d2), that is, it competes with commercial banks for deposits. Specifically, in order to exchange a commodity at t = 0, the central bank allows depositors to withdraw d1 units at t = 1 or d2 units at t = 2.

The central bank is at a disadvantage to compete with commercial banks. Due to the lack of long-term investment opportunities, the central bank does not appear to be able to switch liquidity. However, despite this disadvantage, the central bank can still compete in the retail deposit market by contracting with investment banks to use long-term technology called wholesale deposits. The implicit assumption is that the central bank will not encounter difficulties in the wholesale deposit market due to lack of information or expertise. Given that the central bank has participated in this market through repo operations and other means, this assumption is empirically reasonable.

At t = 0, all consumers will make a deposit decision after observing the contract issued by the commercial bank and the central bank. The central bank then deposits a 1-x portion of each deposit unit into an investment bank and invests the remaining x in short-term technology.

Consumer choice

Let f be the proportion of consumers who have deposited in the central bank at t = 0. Consumers must decide whether to deposit at the central bank and withdraw at t = 1 and consume c1 = d1 or at t = 2 with c2 = d2; = 2 consumption c2 = chat2. Consumers choose the contract that provides the greatest anticipated utility. If two contracts provide the same utility, consumers with a proportion of f will choose the central bank, and the remaining consumers will choose commercial banks, and f is uncertain.

The consumer's withdrawal strategy is the variable σ, which represents the date of the consumer's withdrawal. The impatient consumer always withdraws at probability 1 in the middle stage. A patient consumer may choose to withdraw early, depending on his perception of other patient consumer behaviors. At t = 1, consumers respond optimally based on their expectations of other consumer strategies.

in conclusion

In an equilibrium state, a socially optimal contract is provided by a commercial bank or central bank or both. If both the central bank and the commercial bank have customers 0 <f <1, then both banks will provide optimal contracts. Competition for deposits between the commercial banking sector and the central bank limits the profits that the investment banking sector receives from the central bank. It is worth noting that in the absence of competition, political and economic mechanisms may cause the central bank to obtain significantly non-optimal results.

Withdrawal games for depositors in commercial banks have two pure equilibriums. There is a good equilibrium in which all the patience of depositors continue to deposit and reach the socially optimal contract. However, there is also a bank run equilibrium. All patient depositors are panicked and withdraw. At this time, the socially optimal contract cannot be achieved. This conclusion is consistent with the conclusion of Diamond & Dybvig (1983).

If the central bank punishes depositors who cause runs, then the central bank depositors' withdrawal game has a unique equilibrium. All patient depositors continue to deposit, and only depositors lacking patience withdraw funds. The central bank will not run and always reach the socially optimal contract. The rigidity of the contract allows the depositor who continues to deposit to be rewarded when the withdrawal amount is high, because he shares the total revenue with fewer depositors. The effect of contract rigidity is reminiscent of regulatory interventions, such as the mandatory requirement for depositors to deposit and thereby discontinuing services. Diamond & Dybvig (1983) has shown that a combination of punishment and regulatory intervention (here contract rigidity) can prevent runs.

Assume that the central bank will not punish depositors who cause runs, but treats them as continuing deposits. The withdrawal game of central bank depositors has a unique equilibrium. All patient depositors continue to deposit, and only depositors lacking patience withdraw funds. Runs do not happen and socially optimal contracts are always reached.

If the central bank provides a socially optimal contract, it will attract all deposits on the market, not commercial banks, whether or not it penalizes depositors who cause runs. This is because even if the commercial banking department provides a socially optimal contract to compete with the central bank, commercial banks cannot prevent bank runs. Depositors internally believe that central bank contracts can run smoothly, so the central bank has some market power. If the central bank decides to take advantage of this market power, it can offer deposit contracts that are different from socially optimal contracts and still monopolize all deposits. When the central bank acts in this way, the economy will not be able to achieve optimal term transitions. The central bank's resilience to runs is a double-edged sword: it avoids financial panic, and it also undermines the competition that regulates the central bank's "open to everyone" behavior.

If the central bank provides a socially optimal deposit contract, then under the conditions of asset risk and equal treatment to depositors who cause runs, the run of the central bank occurs in the condition of [0, θ], and in the condition of , 1] does not occur, where θ is the threshold given by the condition. Prior to that, there were fewer runs on the central bank than on commercial banks, so the central bank absorbed all deposits.

If the central bank provides a socially optimal deposit contract under asset risk, a central bank that penalizes runs is at least as stable as a central bank that does not penalize. Therefore, under the risk of assets, the central bank is always more stable than the commercial banking sector and sucks all deposits away from the commercial banks.

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