A Unified Framework for Central Bank Digital Currency Design

In recent years, the digital payment field has grown rapidly and technology giants have entered the market, raising concerns about the security and data protection of digital currencies, and this paper investigates the macroeconomic effects of central bank digital currencies under a dynamic general equilibrium model.

In recent years, the digital payment field has grown rapidly and technology giants have entered the market, triggering concerns about the security and data protection of digital currencies. Will the widespread use of digital currencies have an impact on monetary sovereignty and the economy? In response, central banks have initiated their own work programs to assess the prospects of central bank-issued digital currencies applied to retail. This paper investigates the macroeconomic effects of central bank digital currencies under a dynamic general equilibrium model. It has been compiled by the Institute of Financial Technology of Renmin University of China (WeChat ID: ruc_fintech).

Abstract

This paper investigates the macroeconomic effects of central bank digital money in a dynamic general equilibrium model. Time and information frictions create demand for money, and these demands include both internal funds (bank deposits) and external funds (central bank digital currency) for financing production. To control the amount of central bank digital money, central banks can set interest rates on loans and deposits of digital money, set collateral or quantity limits. A lower legal reserve ratio by the central bank means that commercial banks need to accrue fewer reserves, while higher lending rates can curb financial disintermediation if commercial bank deposits and central bank digital money are close enough substitutes. When the elasticity of substitution between bank deposits and central bank digital money is small, central bank digital money with positive spreads and tighter collateral can reduce welfare.

INTRODUCTION

The digital payments space has grown rapidly over the past few years. The emergence of encrypted assets and the thinking of tech giants about issuing corporate digital currencies have raised concerns about the security and data protection of digital currencies. The widespread use of private currencies may also pose risks to monetary sovereignty and economies, raising concerns about financial stability. In response, central banks have launched their own work programs to assess the prospects for central bank-issued digital currencies with retail applications.

A recent survey by the Bank for International Settlements (BIS) suggests that about one-fifth of central banks representing the world’s total population will issue a common central bank digital currency in the next three years, suggesting that the central bank digital currency project is poised to make greater progress than previous surveys.

The motivation for central banks to issue digital currencies is that they can provide a secure, efficient and universally available means of payment. Beyond this, however, central bank digital currencies have important implications for the conduct of monetary policy, with implications for monetary policy transmission and financial stability that depend on specific design features of central bank digital currencies, such as the way interest is accrued, the choice of holding limits, and the pricing of how assets held in central bank digital currencies are priced.

These parameters can be adjusted by the central bank, which would mitigate the potential adverse consequences of central bank digital currencies on monetary transmission and financial stability. What is less well known, however, is the effectiveness of these parameters in guiding the demand for central bank digital money and the possible macroeconomic implications, in particular, their changes may affect equilibrium allocations and welfare.

To investigate these issues, we construct a general equilibrium model with search and matching frictions, as previously conceived by Lagos and Wright, conditional on the need for entrepreneurs to borrow internally and externally (internal and external funds). These two types of money (specifically, internal money in the form of bank deposits and external money in the form of central bank digital money) are used to pay for two different types of inputs required for production. The setting motive is the different preferences of the workers responsible for the production for a particular form of remuneration.

A subset of workers may hold bank accounts with access to a range of banking services, so they will prefer bank deposits, even though these deposits may not provide sufficient data protection for private payments. In contrast, other workers may prefer the security of a CBDC, even though it is a liability of the central bank and may not have access to the services that commercial banks typically provide to their customers.

Alternatively, this model setup can be driven by spatial separation: some workers produce and sell their inputs (goods or services) in places where bank deposits are limited. While other workers operate in environments that do not prefer to accept central bank digital currency.

Our model does not consider the effect of cash, and this model reflects the macroeconomic effects of different central bank policies on parameters that allow studying the management of the supply of central bank digital money, according to the assumption of a production function where the CBDC is in equilibrium.

Modeling approach of this paper

The model includes three continuously operating markets: the settlement market, the loan market and the investment market. In the settlement market, which constitutes the centralized market, banks, firms and workers produce and consume common goods and settle borrowing contracts. Entrepreneurs exist in only one time interval: they emerge in the loan market, where investment opportunities are fewer. In each time interval, the entrepreneur is subject to a particular shock that determines the optimal scale of his production. In order for the project to succeed, the entrepreneur needs capital goods produced by workers.

Workers in the investment market demand payment in the form of a generally accepted medium of exchange, which causes frictions in the demand for money since the entrepreneur cannot commit to repaying the debt.

In the loan market, entrepreneurs borrow internal and external funds from commercial banks and central banks. However, due to limited commitment frictions, they need pledged collateral. The (decentralized) investment market produces capital goods that are not storable and therefore cannot be transferred from one market to another. There are two types of workers who produce capital: C workers accept only central bank digital currency as payment, while D workers accept only commercial bank deposits.

Entrepreneurs need to borrow from both commercial banks and central banks to make productive inputs. The central bank can set the interest rate charged on the entrepreneur’s loan and the interest rate on the worker’s deposit paid with the central bank’s digital currency, as well as set limits on the size of each loan and deductions for future income used as collateral for the loan.

The modeling approach in this paper allows to analyze the impact of different central bank digital currency design parameters on credit allocation and welfare within a unified framework. Interest rates and discounts already exist in the operational framework of today’s central banks and are used to influence the demand for central bank reserves. The welfare gains from a central bank digital currency depend on the degree of substitutability of production inputs paid in internal or external currencies. As the degree of substitutability between the two currencies increases, the welfare gains of the central bank digital currency decrease, and if both currencies are perfect substitutes, the welfare gains are close to zero.

Conclusion

In this paper, we constructed a general equilibrium search model in which central and commercial banks compete for financial investments through different ways of providing funds, paid in internal funds, or in digital currencies.

Production and trade occur in different island economies, which are driven by preferences for particular forms of payment. Since entrepreneurs cannot commit to repaying their debts, workers need to be paid in the form of a generally accepted medium of exchange, and this friction causes a demand for money. Workers borrow internal and external funds from commercial banks and central banks. However, with limited commitment frictions, they need pledged collateral. We define a central bank digital currency as a public or central bank liability that bears or pays interest and may be quantitatively constrained by the central bank. The availability of internal and external funds is constrained by collateral. The central bank determines the interest rate and possible volume or exogenous collateral limits for digital money, and banks and companies negotiate the interest rate and volume of bank loans.

In this paper, we place the impact of central bank digital money on the transmission of monetary policy in the business cycle or observations about financial stability in a later study. In our setting, prices in the business cycle are flexible, currencies are relatively neutral, and assets are safe and liquid. Therefore, our modeling framework provides information on the impact of central bank digital currencies on the steady state, i.e., structural changes in the financial system.

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A Unified Framework for Central Bank Digital Currency Design
A Unified Framework for Central Bank Digital Currency Design

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