The CBDC trilemma
In this paper Schilling et al. seek to evaluate the advantages and drawbacks from the introduction of a central bank digital currency (CBDC) which implies the reorganization of the banking system and also affects monetary policy, allocation and welfare. In particular, they try to answer the following questions: Can maturity transformation still occur at the socially optimal level with a CBDC? Can a central bank do better and, for instance, avoid runs? Do new trade-offs arise?
They build on the Diamond and Dybvig (1983) – “Bank Runs, Deposit Insurance, and Liquidity” – model and introduce a CBDC. In this adjusted model there is intermediation with central banks and not with private banks. This difference is important because central banks control the price level. In addition, they impose the condition that all contracts are nominal. Finally, a central bank has three goals: efficiency, financial stability (i.e., absence of runs), and price stability. They demonstrate an impossibility result that they call the CBDC trilemma: of its three goals, the central bank can achieve at most two.

As our main result, we have demonstrated that the central bank can always implement the socially optimal allocation in dominant strategies and deter central bank runs at the price of threatening inflation off-equilibrium. If price-stability objectives for the central bank imply that the central bank would not follow through with that threat, then allocations either have to be suboptimal or prone to runs.
Central Bank Digital Currency: When Price and Bank Stability Collide
Authors: Linda Schilling, Jesús Fernández-Villaverde, Harald Uhlig
From: École Polytechnique, University of Pennsylvania, University of Chicago
The CBDC triggered policy tradeoff
When a digital currency competes with bank deposits as a medium of exchange, it does tend to raise banks’ funding cost and decrease bank-funded investment. On the other hand, the availability of this new type of money increases production of those goods that can be purchased with it and can potentially increase total output. In addition, the central bank gains a new policy tool: it can choose the interest rate it pays on the digital currency.
In this paper Keister and Sanches use a model in which some form of money is essential for exchange, as in Lagos and Wright (2005) – “A unified framework for monetary theory and policy analysis” – and introduce an investment friction that creates borrowing constraints, ie bankers have access to productive projects but face credit constraints due to limited pledgeability of their returns. These credit constraints can lead to a level of aggregate investment that is inefficiently low. Finally, their model includes a central bank that issues both a physical currency and a digital one. They highlight the policy tradeoff that arises from the introduction of a CBDC:
- By designing its digital currency so that it can be used in a wider range of transactions and/or offers a more attractive interest rate, the central bank can increase the quantity of publicly-provided liquidity held by agents. A larger supply of public liquidity, in turn, tends to promote more efficient levels of exchange;
- However, this outside liquidity may also crowd out inside liquidity in the form of bank deposits and thereby lead to a decrease in bank-financed investment.
The optimal design of a digital currency may require striking a balance between these two competing effects.
Should Central Banks Issue Digital Currency?
Authors: Todd Keister, Daniel Sanches
From: Rutgers University, Federal Reserve Bank of Philadelphia