CBDC and Financial Stability: ECB Working Paper Reveals U-Shaped Bank Fragility Curve

Why Central Banks Are Rethinking CBDC Financial Stability

The global push toward central bank digital currencies has reached a critical inflection point. Over 130 countries — representing 98% of global GDP — are now exploring CBDC projects, yet the fundamental question of how digital currencies affect financial stability remains hotly debated. The European Central Bank’s Working Paper No. 2783, authored by Ahnert, Hoffmann, Leonello, and Porcellacchia, provides the most rigorous analytical framework to date for understanding the complex interplay between CBDC design choices and bank fragility.

At the heart of this debate lies a deceptively simple concern: if central banks offer citizens a risk-free digital alternative to bank deposits, will depositors flee commercial banks during periods of stress, triggering the very bank runs that financial regulation aims to prevent? The conventional wisdom among many banking executives and some regulators has been that any CBDC remuneration would inherently destabilize the financial system. This ECB research challenges that assumption fundamentally.

In the United States, commercial bank funding relies on deposits for approximately 75% of total funding, with roughly half of those deposits being uninsured. This structure makes the banking system particularly sensitive to depositor behavior during stress events. The introduction of a CBDC — even a modestly remunerated one — could reshape these dynamics in ways that are not immediately intuitive. Understanding these dynamics is essential for policymakers designing interactive analyses of financial regulation and monetary policy frameworks.

The ECB Working Paper 2783 Framework Explained

The ECB researchers employ a sophisticated global-games bank-run model — building on the foundational work of Goldstein and Pauzner (2005) — to analyze how CBDC introduction affects bank fragility. Unlike simpler models that treat CBDC adoption as binary, this framework captures the strategic interactions between depositors, banks, and central bank policy instruments with mathematical precision.

The model operates across three time periods. In the initial funding stage, depositors choose between placing their wealth in a commercial bank or holding CBDC. The bank invests in a long-term project with uncertain returns tied to a fundamental quality parameter θ. In the interim period, depositors receive private signals about the bank’s health and decide whether to withdraw early (triggering potential liquidation costs) or wait for maturity. The CBDC serves as the depositor’s outside option — the alternative they turn to when withdrawing from the bank.

What makes this model particularly powerful is its unique equilibrium selection mechanism. Through the global-games approach with vanishing noise in private signals, the researchers derive a single failure threshold θ* — the critical level of bank fundamentals below which a bank run occurs. This threshold directly corresponds to the probability of a bank run, making it the central measure of financial fragility in the analysis. The model also endogenizes bank behavior: banks anticipate the effect of their deposit contract offers on depositor withdrawal incentives and optimize accordingly.

CBDC is modeled as a perfectly safe asset with gross return ω per period, where ω ≥ 1 captures both explicit remuneration and any convenience benefits relative to physical cash. Cash, by contrast, is unremunerated (ω = 1). This elegantly simple parameterization allows the researchers to study the full spectrum from zero to substantial CBDC remuneration within a unified framework. The ECB Working Paper Series has published several related analyses, but this paper’s integrated treatment of both direct and indirect effects through bank optimization represents a significant methodological advance.

CBDC Remuneration and the U-Shaped Fragility Curve

The paper’s central finding is both elegant and counterintuitive: the relationship between CBDC remuneration and bank fragility follows a U-shaped curve. This means that starting from zero, increasing CBDC remuneration initially reduces the probability of bank runs, reaching a minimum at an optimal positive rate ω_min, before higher remuneration begins to increase fragility again.

This U-shape emerges from the interaction of two opposing channels. The direct effect operates through depositor withdrawal incentives: higher CBDC remuneration makes the outside option more attractive, encouraging depositors to withdraw during stress — which increases run risk. This is the mechanism that most commentators focus on when arguing against CBDC remuneration.

However, the indirect effect works through bank competition and deposit contract design. When CBDC remuneration rises, depositors’ outside option improves, meaning banks must offer more attractive long-term deposit rates to attract funding. These higher promised returns make depositors more willing to remain through periods of uncertainty — reducing run risk. The bank’s strategic response to CBDC competition effectively counterbalances the direct withdrawal incentive.

In their numerical illustrations, the researchers demonstrate this with parameters L = 0.9 (liquidation value) and R = 15 (gross return), yielding an optimal remuneration of ω_min ≈ 1.049 — a CBDC rate of roughly 4.9% above the cash baseline. At this rate, the failure threshold θ* reaches approximately 0.127, its minimum value. The formal condition for the indirect effect to dominate is captured in Lemma 1: fragility decreases in CBDC remuneration if and only if the elasticity of the failure threshold with respect to the bank’s long-term deposit rate exceeds unity.

This U-shaped relationship has profound implications for CBDC design. It means that blanket opposition to CBDC remuneration — often voiced by banking industry representatives — is theoretically unfounded. A well-calibrated positive interest rate on CBDC can actually strengthen financial stability by disciplining bank behavior and improving deposit contract terms for consumers.

How Holding Limits Shape Digital Euro Bank Run Risk

CBDC holding limits — caps on the amount any individual can store in digital currency — have emerged as the most discussed policy tool for managing financial stability concerns. The ECB has explored a digital euro holding limit of approximately €3,000 per individual, while the Bank of England has discussed limits between £10,000 and £20,000 for a potential digital pound. The BIS and various Eurosystem publications (Bindseil et al., 2021) have extensively debated the merits of such caps.

The ECB working paper models holding limits through a parameter γ ∈ [0,1], representing the fraction of wealth a depositor can allocate to CBDC. When γ = 1, there is no limit; when γ = 0, CBDC is effectively unavailable. The key finding in Proposition 4 is nuanced and context-dependent: holding limits reduce fragility only when CBDC remuneration is sufficiently high — specifically, when ω exceeds the fragility-minimizing ω_min.

When CBDC remuneration is low (below ω_min), imposing holding limits can increase bank fragility and reduce welfare. This is because at low remuneration levels, the beneficial indirect effect (banks offering better deposit rates) is active and valuable. Restricting CBDC access weakens the competitive pressure on banks, allowing them to offer less attractive deposit contracts, which paradoxically makes depositors more inclined to withdraw during stress.

This finding carries direct implications for the ongoing digital euro design process. If the ECB sets CBDC remuneration at a moderate level (close to or below ω_min), then the proposed €3,000 holding limit could actually be counterproductive from a financial stability perspective. Policymakers must therefore calibrate holding limits in conjunction with remuneration decisions, not independently.

Contingent CBDC Remuneration as a Crisis Management Tool

Perhaps the most operationally relevant finding of the paper concerns contingent CBDC remuneration — the ability to lower the CBDC interest rate during periods of financial stress. This concept, sometimes called “tiered remuneration” in policy discussions, adds a dynamic dimension to CBDC design that static analysis misses entirely.

The mechanism works through two dimensions: the trigger threshold (how early the rate cut activates as conditions deteriorate) and the depth (how much the rate is cut). The ECB researchers find that more restrictive triggers — those that activate earlier in a stress episode — monotonically reduce bank fragility. This is because early intervention removes the CBDC withdrawal incentive before depositor panic can cascade into a full run.

The optimal size of the rate cut, however, depends on model parameters and the prevailing CBDC remuneration level. In some configurations, larger cuts are always better; in others, there is an interior optimal cut size. This parameter dependence means that central banks would need to calibrate contingent remuneration policies based on their specific banking system structure and macroeconomic conditions.

From a practical standpoint, contingent CBDC remuneration resembles existing central bank crisis management tools — like emergency liquidity assistance or deposit insurance adjustments — but operates through a novel channel. Rather than backstopping banks directly, it works by reducing the attractiveness of the alternative that depositors flee to. This is a meaningful addition to the central banking toolkit analyzed in our library of financial policy research.

Deposit Market Competition and CBDC Stability Effects

The paper’s extensions reveal that deposit market structure fundamentally shapes how CBDC affects financial stability. In the baseline model, the bank has sufficient market power to adjust its deposit rates in response to CBDC competition — which produces the beneficial indirect effect. But what happens in more competitive banking markets?

When the model introduces Nash bargaining or perfect competition in deposit markets, the bank’s ability to raise long-term deposit rates is constrained. In the extreme case of perfect competition, the indirect stabilizing effect disappears entirely, and higher CBDC remuneration always increases bank fragility. This finding has significant implications for different jurisdictions: countries with highly concentrated banking sectors (like Canada or Australia) may experience stability benefits from CBDC remuneration, while countries with fragmented, competitive banking (like parts of the US community banking system) may face predominantly destabilizing effects.

The researchers also extend the model to include Diamond-Dybvig style liquidity insurance, where banks serve risk-averse depositors who value the option of early withdrawal. In this setting, banks adjust not only long-term rates but also interim repayment amounts, adding another margin of adjustment. The core U-shaped relationship persists, but the specific optimal remuneration level shifts depending on depositor risk preferences and bank contract flexibility.

A third extension incorporates endogenous bank risk-taking through monitoring effort. When banks can invest costly effort to improve their project success probability, CBDC remuneration creates additional incentive effects. Higher CBDC competition can motivate banks to monitor more carefully (reducing risk) or, if margins are compressed too far, lead to reduced monitoring (increasing risk). This financial stability dimension studied by the BIS underscores the importance of considering bank behavioral responses in CBDC policy design.

Policy Design Implications for the Digital Euro

The ECB working paper yields several concrete policy prescriptions that directly inform the ongoing digital euro design process and broader CBDC policy debates worldwide. First, the central bank should actively use CBDC remuneration as a financial stability tool, setting it at the fragility-minimizing level ω_min rather than defaulting to zero remuneration. This represents a shift from the prevailing assumption that CBDC remuneration should be minimized or eliminated to protect bank stability.

Second, holding limits and remuneration must be calibrated jointly. The finding that holding limits can be counterproductive at low remuneration levels means that the €3,000 digital euro cap should not be evaluated in isolation. If the ECB chooses moderate CBDC remuneration, the case for strict holding limits weakens considerably. Conversely, if political or monetary policy considerations dictate high CBDC remuneration, holding limits become an important safeguard.

Third, contingent remuneration mechanisms should be incorporated into CBDC architecture from the outset. The ability to lower CBDC rates during crises provides a powerful new tool for macroprudential policy. However, this requires robust real-time monitoring systems and clear governance frameworks for triggering rate changes — infrastructure that should be built into the digital euro’s technical design, not added as an afterthought.

Fourth, policy design must account for the domestic banking market structure. The ECB serves 20 member states with vastly different banking sector structures — from the highly concentrated Nordic markets to the fragmented Southern European systems. A one-size-fits-all CBDC design may produce stability benefits in some countries while creating risks in others. This tension supports tiered or jurisdiction-sensitive implementation approaches, though such approaches would add complexity to an already ambitious project.

The redistributive dimension also deserves attention: CBDC remuneration shifts rents from banks to depositors. For moderate remuneration levels, this redistribution can be socially desirable — not only because it improves consumer welfare but because the competitive pressure it creates leads to more stable banking configurations. This insight connects CBDC design to broader debates about financial regulation and consumer protection explored across our research library.

Comparing Global CBDC Financial Stability Approaches

The ECB’s analytical framework arrives at a pivotal moment in global CBDC development. China’s e-CNY pilot — the world’s most advanced large-economy CBDC — operates without explicit remuneration and with various transaction and holding limits. The People’s Bank of China’s approach prioritizes payment system efficiency over monetary policy transmission, effectively sidestepping the stability tradeoffs that the ECB paper analyzes by keeping remuneration at zero.

The Bank of England’s digital pound proposal has engaged more directly with stability questions, proposing holding limits of £10,000–£20,000 and suggesting that the digital pound would not be remunerated initially. The ECB research suggests this combination — zero remuneration with moderate holding limits — may not be optimal, as it forgoes the beneficial indirect effect while the holding limits provide limited stability benefit at zero remuneration.

The Federal Reserve’s approach remains more cautious, with the 2022 discussion paper noting that any US CBDC would need to protect monetary policy transmission and financial stability. The ECB model’s emphasis on market structure is particularly relevant here: the US banking system’s diversity — spanning megabanks, regional banks, and community institutions — means CBDC effects would vary significantly across market segments. James (1991) documented that losses at US bank failures average approximately 30% of assets, underscoring the real-world cost of getting stability analysis wrong.

Emerging economies face different calculations entirely. In countries with less developed banking systems or high financial exclusion, CBDC can serve primarily as a financial inclusion tool. The stability tradeoffs identified in the ECB paper — centered on sophisticated deposit markets and depositor strategic behavior — may be less binding where formal banking participation is limited. Nevertheless, as these economies develop, the paper’s insights about market structure and competitive dynamics become increasingly relevant.

What CBDC Design Means for Banking and Monetary Policy

The ECB Working Paper 2783 fundamentally reshapes the intellectual landscape for CBDC policy design. By demonstrating the U-shaped relationship between CBDC remuneration and bank fragility, the researchers challenge the simplistic narrative that CBDC poses an inherent threat to financial stability. The truth is more nuanced: CBDC design — not CBDC existence — determines stability outcomes.

For commercial banks, the paper’s implications are significant but not necessarily alarming. Banks that can compete effectively — by offering attractive deposit rates, superior services, and relationship value — will benefit from a well-designed CBDC framework that disciplines the market without undermining the banking system. Banks that rely on depositor inertia and information friction, however, face a structural challenge that CBDC introduction will accelerate regardless of specific design choices.

For monetary policy, CBDC remuneration introduces a powerful new transmission channel. The ability to adjust CBDC rates — both in normal times and contingently during crises — gives central banks a direct instrument that operates alongside traditional interest rate policy. This is particularly valuable in environments where the effective lower bound constrains conventional monetary policy tools.

The welfare analysis reveals an important alignment: the CBDC remuneration level that minimizes bank fragility also maximizes social welfare in the model. This means that central banks need not face a tradeoff between stability and efficiency when setting CBDC remuneration — a finding that substantially simplifies the policy design challenge.

Looking ahead, the paper highlights several areas where further research is critical. The interaction between CBDC remuneration and deposit insurance design remains underexplored. The dynamic effects of CBDC introduction on banking sector structure — entry, exit, and consolidation — are outside the paper’s static framework but clearly important. And the cross-border dimensions of CBDC — including potential capital flow implications and currency substitution — add layers of complexity that single-country models cannot fully capture.

What is clear from this ECB research is that CBDC design decisions carry enormous stakes. The difference between a well-calibrated and a poorly calibrated CBDC can be the difference between strengthening and weakening financial stability. Central banks have the analytical tools — now demonstrated in this paper — to get these decisions right. The challenge is translating rigorous academic insights into practical policy design under real-world political, institutional, and technical constraints.