Central Bank Digital Currency: Demand Shocks and Optimal Monetary Policy

We study the implications of a central bank digital currency (CBDC) for the transmission of household preference shocks and for welfare in a New Keynesian framework where the CBDC competes with bank deposits for household resources and banks have market power. We show that an increase in the perceived benefit of CBDC has a mildly expansionary effect, weakening bank market power and significantly reducing the deposit spread. As households economize on liquid asset holdings, they reduce both CBDC and deposit balances. However, the degree of bank disintermediation is low, as deposit outflows remain modest. We then examine the welfare implications of CBDC rate setting and find that, compared to a non-interest-bearing CBDC, the gains with standard coefficients for a CBDC interest rate Taylor rule are modest, but they become considerable when the coefficients are optimized. Welfare gains increase with the CBDC benefit, and the optimal policy responses vary with the banking market structure.

💡 Research Summary

The paper investigates how a central‑bank digital currency (CBDC) influences the transmission of household preference shocks and welfare within a New‑Keynesian framework that incorporates both CBDC and bank deposits as competing liquid assets, while allowing banks to exercise market power in the deposit market. The authors first extend a standard NK DSGE model by introducing a CES aggregator for liquidity services that combines real holdings of CBDC (m) and deposits (n). The relative preference for CBDC, denoted by λ, captures a broad set of factors—convenience, privacy, security, perceived safety—that affect the demand for digital central‑bank money. The elasticity of substitution between CBDC and deposits is ε. Households derive utility from consumption, labor, and the liquidity services provided by the composite asset, with a weight v on liquidity.

Banks are modeled as regional monopolists that set deposit rates above the policy rate, earning a markup that reflects their market power. Deposits finance physical capital investment and reserve holdings; a higher reserve‑to‑deposit ratio reduces banks’ cost of issuing debt, linking the CBDC supply decision to the banking balance sheet. Firms face Calvo‑type price rigidity and use capital and labor to produce intermediate goods, which are then differentiated and sold to final‑good producers. The government sets the nominal policy rate on government bonds and a separate rate on CBDC, both following a Taylor‑type rule.

The first analytical exercise subjects the economy to a positive shock to λ—a 25 % increase in the perceived benefit of CBDC. The simulation shows that aggregate liquidity services rise, yet households economize on total liquid holdings: both CBDC and deposit balances fall. The deposit spread (the effective markup on deposits) contracts sharply because the higher λ weakens banks’ pricing power. Output, consumption, and inflation all increase modestly, while investment falls only slightly. Crucially, deposit outflows are modest relative to total deposits, indicating that the degree of bank disintermediation remains low; the CBDC does not trigger a systemic run on banks.

The second part evaluates welfare implications of CBDC interest‑rate policy. The authors first apply a standard Taylor rule to the CBDC rate using baseline coefficients (similar to the rule governing the policy rate). Under this non‑optimized rule, welfare gains relative to a non‑interest‑bearing CBDC are minimal. They then solve for the Taylor‑rule coefficients that maximize expected household welfare, following the methodology of Smets‑Wouters and related optimal‑policy literature. Optimized coefficients generate substantial welfare improvements, especially when λ is high. The optimal response to inflation depends on the banking structure: with monopolistic banks, the inflation coefficient varies with λ, while the output coefficient remains stable across specifications. With competitive banks, the optimal rule places virtually all weight on output and none on inflation. Moreover, the analysis finds that smoothing the CBDC rate over time (gradual adjustments) reduces welfare, suggesting that more aggressive rate moves may be preferable in this context.

The paper contributes to three strands of literature. First, it explicitly incorporates bank market power, allowing the authors to quantify how CBDC competition erodes deposit mark‑ups. Second, it treats household preference shocks to CBDC as an exogenous driver of macro‑economic dynamics, clarifying the transmission channel from digital‑currency desirability to real variables. Third, it provides a systematic optimal‑policy design for CBDC interest‑rate rules, showing how welfare‑maximizing coefficients differ from the conventional rule and depend on the underlying banking structure.

Overall, the findings suggest that a retail CBDC does not inevitably cause large‑scale bank disintermediation; modest shifts in household liquidity preferences lead to small deposit outflows and a reduction in deposit spreads. When the central bank can set an interest rate on CBDC, carefully calibrated Taylor‑rule parameters can enhance welfare, particularly when the CBDC is perceived as highly beneficial. Policymakers should therefore consider both the perceived benefits of CBDC and the competitive landscape of the banking sector when designing CBDC interest‑rate policies, as the optimal rule may emphasize output stabilization over inflation control in competitive banking environments.