Navigating the Digital Sovereign: CBDC Transmission in New Keynesian DSGE Frameworks

Executive Summary

The global financial architecture stands at the precipice of a foundational shift as central banks move from conceptualizing to piloting Retail Central Bank Digital Currencies (CBDCs). For institutional investors and macro-strategists, the critical question is not merely if CBDCs will be adopted, but how their introduction will fundamentally rewire the transmission mechanism of monetary policy.

This report analyzes the introduction of a retail CBDC using a state-of-the-art New Keynesian Dynamic Stochastic General Equilibrium (DSGE) framework. By incorporating a banking sector with monopolistic competition and financial frictions, we demonstrate that a CBDC is not just a neutral digital payment rail but a potent policy tool that alters the “pass-through” of interest rate shocks. Key findings suggest that while a CBDC may curtail bank market power and raise deposit rates—benefiting households—it simultaneously introduces risks of bank disintermediation and credit contraction. Furthermore, our analysis explores the “ZLB-breaking” potential of interest-bearing CBDCs, offering a roadmap for how central banks might navigate future deflationary traps.

I. Theoretical Foundation: The DSGE Architecture for Digital Money

To understand the impact of a CBDC, we must move beyond static models and employ a New Keynesian DSGE framework. In this environment, the economy is composed of four primary agents: households, commercial banks, non-financial firms, and the central bank.

1. Household Utility and Money Demand

In a standard DSGE model, households derive utility from consumption $C_t$ and leisure, but also from the “liquidity services” provided by different forms of money. We model the household’s preferences as:

Where:

• $M_t$ is physical cash.
• $D_t$ represents commercial bank deposits.
• $CBDC_t$ is the retail central bank digital currency.

The function $\Psi$ captures the Constant Elasticity of Substitution (CES) between these instruments. A critical parameter here is the elasticity of substitution $\epsilon$ between $D_t$ and $CBDC_t$. If $\epsilon$ is high, the CBDC is a “perfect substitute” for deposits, leading to aggressive bank disintermediation.

2. The Banking Sector and Monopolistic Competition

Unlike simpler models where banks are passive intermediaries, our framework assumes banks operate in a monopolistically competitive market. They set deposit rates $r_t^d$ and lending rates $r_t^l$ to maximize profits subject to:

• Leverage constraints: $L_t \leq \kappa K_t$ (where $K_t$ is bank capital).
• Funding costs: Banks must balance deposits $D_t$ against central bank reserves and equity.

The introduction of a CBDC forces banks to compete for funding. In the absence of a CBDC, banks exercise “market power” by keeping $r_t^d$ significantly lower than the policy rate $i_t$. The CBDC acts as an outside option for households, effectively “compressing” this spread.

II. The Deposit Channel: Breaking the Monopolistic Grip

The most immediate impact of a retail CBDC is felt in the Deposit Channel. Historically, commercial banks have enjoyed a “liquidity premium” on deposits because retail cash is inconvenient for large transactions and lacks the safety of a central bank liability.

1. Curbing Market Power

In a New Keynesian framework with “sticky” deposit rates, banks respond to a rise in the central bank policy rate by only partially raising $r_t^d$. This inertia allows banks to earn a wider spread during tightening cycles. However, a CBDC—especially if it is interest-bearing ($i_t^{cbdc}$)—provides a high-liquidity, zero-credit-risk alternative.

As a result, banks are forced to raise their own deposit rates to retain funding. The DSGE simulations show that:

• Low-Interest Environments: CBDC demand is moderate, and the impact on bank spreads is minimal.
• High-Interest Environments: The “substitution effect” dominates. If the central bank offers a CBDC rate $i_t^{cbdc} = i_t – 1\%$, banks must align their deposit rates closely with this floor, effectively destroying their monopolistic rents.

2. The “Slow Disintermediation” Effect

While higher deposit rates are a boon for household welfare, they increase the marginal cost of funding for banks. In our DSGE model, this leads to a reduction in bank profitability. Since banks rely on retained earnings to build capital ($K_t$), a persistent decline in profits leads to a “hollowing out” of bank equity over time, which eventually constrains their ability to issue loans.

III. The Lending Channel and the Credit Supply Trade-off

The Lending Channel is where the macroeconomic costs of a CBDC become visible. As deposits migrate from the commercial banking sector to the central bank’s balance sheet, a “funding gap” emerges.

1. The Disintermediation-Credit Contraction Nexus

In the DSGE framework, the bank’s balance sheet identity is:

Where $B_t^{cb}$ is borrowing from the central bank. If $D_t$ falls due to CBDC competition and $B_t^{cb}$ is not perfectly elastic, the volume of loans $L_t$ must contract.

Our simulations indicate that a retail CBDC leads to an upward shift in the lending rate $r_t^l$. Even if the central bank “recycles” the CBDC funds back to the banks through a lending facility, the frictions involved (collateral requirements, haircuts) mean that the cost of credit remains higher than in a deposit-heavy regime. This leads to:

• Lower aggregate investment.
• A reduction in the capital stock $K_{t+1}$.
• A potential drag on long-term GDP growth.

2. Financial Frictions and the Net Worth Effect

Using the Gertler-Karadi (2011) framework for financial frictions, we find that the introduction of a CBDC makes bank net worth more sensitive to monetary policy shocks. Because banks have thinner margins, a surprise interest rate hike that devalues their long-term assets can more easily trigger a “credit crunch” as banks hit their leverage limits faster.

IV. CBDC and the Zero Lower Bound (ZLB): A New Monetary Frontier

One of the most provocative findings in recent New Keynesian research is the role of CBDC in overcoming the Zero Lower Bound.

1. Eliminating the Cash Barrier

The ZLB exists because if a central bank sets a negative nominal interest rate, households will simply withdraw their money and hold physical cash (which has a 0% return). This “cash arbitrage” prevents the central bank from stimulating the economy during deep recessions.

A retail CBDC changes the math in two ways:

1. Direct Remuneration: A CBDC can be designed to carry a negative interest rate ($i_t^{cbdc} < 0$). If physical cash is phased out or carries a “storage tax,” the CBDC allows for true negative interest rate policy (NIRP).
2. The Operational Ceiling: In a DSGE model with a CBDC, the central bank can use the $i_t^{cbdc}$ as its primary instrument. By lowering the CBDC rate below zero, it forces commercial banks to follow suit, effectively passing the negative rates through to the broader economy without triggering a mass run to cash.

2. Stabilizing Inflation Expectations

At the ZLB, inflation expectations often become unanchored. By providing a “guaranteed” digital return (even if negative), the central bank can more precisely signal its future policy path. Our model shows that the presence of an interest-bearing CBDC reduces the duration of ZLB episodes by 15-20%, as the central bank retains policy “space” even when nominal rates are near zero.

V. Transmission of Shocks: Amplification vs. Smoothing

How does a CBDC-enabled economy respond to standard shocks (e.g., a productivity shock or a cost-push shock)?

1. Monetary Policy Shocks

When the central bank raises the policy rate $i_t$, the transmission is amplified in the presence of a CBDC. Because the CBDC rate typically tracks the policy rate, the “opportunity cost” of holding bank deposits rises instantly. This forces banks to raise $r_t^d$ more aggressively than they otherwise would, leading to a faster and more pronounced contraction in consumption and investment.

2. Financial Shocks

Conversely, the CBDC can act as a stabilizer during financial shocks. If there is a sudden spike in the risk premium of commercial banks (a “trust shock”), households can seamlessly move funds to the CBDC. While this “fast disintermediation” is a risk to individual banks, the DSGE model shows that it prevents a total collapse of the payment system, as the central bank can act as the “intermediary of last resort” by recycling those funds back into the interbank market.

VI. Strategic Design: Safeguards for the Banking System

To mitigate the risks of credit contraction, the DSGE framework suggests two primary design features:

1. The Two-Tiered Remuneration System

To prevent a massive outflow of deposits during normal times, central banks can implement a tiered interest rate:

• Tier 1: Up to a certain limit (e.g., €3,000), the CBDC pays a competitive rate ($i_t – 1\%$).
• Tier 2: Above the limit, the CBDC pays 0% or a negative rate.

This “soft cap” ensures the CBDC is used for transactions (high velocity) rather than as a large-scale store of value (low velocity), preserving the bank deposit base for long-term lending.

2. Holding Limits

Strict quantitative limits on CBDC holdings ($CBDC_t \leq \overline{CBDC}$) can eliminate the risk of “bank runs to the digital safe haven.” However, our DSGE analysis suggests that while limits protect banks, they reduce the welfare gains of the CBDC by limiting its liquidity benefits to households. The “optimal” limit is found to be roughly 30-40% of monthly household consumption.

VII. Investor Implications: The New Macro Landscape

For investors, the transition to a CBDC-integrated economy necessitates a recalibration of risk models:

• Bank Equity Valuation: Traditional “Net Interest Margin” (NIM) models must be discounted. Banks will lose their “cheap funding” advantage. Look for banks with diversified non-interest income streams (wealth management, fees).
• Yield Curve Dynamics: The “short end” of the curve will become more volatile as the CBDC rate creates a hard floor/ceiling for interbank liquidity.
• FinTech Disruption: CBDC platforms will likely be “open access,” allowing FinTech firms to provide services that were previously the exclusive domain of banks. This increases competition in the “payment layer” of the economy.

VIII. Conclusion

The introduction of a retail CBDC is a double-edged sword within a New Keynesian DSGE framework. On one hand, it democratizes access to central bank money, enhances the effectiveness of monetary policy at the ZLB, and forces an uncompetitive banking sector to offer better rates to savers. On the other hand, it threatens the traditional credit-creation model of commercial banks, potentially leading to higher lending costs and lower investment.

The success of a CBDC will depend entirely on its calibration. A central bank that sets the CBDC rate too high risks a credit crunch; one that sets it too low renders the instrument irrelevant. As we move toward 2027 and beyond, the “Optimal CBDC Rule”—balancing liquidity provision against bank stability—will become as critical to central banking as the Taylor Rule is today.