A3: Will CBDCs Kill Commercial Banks?

L03 CBDCs
Assignment Brief

Introduction

A CBDC (Central Bank Digital Currency — digital money issued directly by a country's central bank, like a digital version of cash) could cause bank disintermediation (when people move their money from commercial banks to the central bank's digital currency). This model simulates how bank deposits D change over time using a differential equation (a formula describing how something changes from one moment to the next):

dD/dt = -α(r_CBDC - r_D)D + β·confidence(t)

Where:

Variations to Explore

Variation 1: Increase Rate Sensitivity

Task: Change α from 0.8 to 2.0

Question: How much faster do deposits flee when people are more sensitive to interest rate differences?

Variation 2: Zero CBDC Interest Rate

Task: Set CBDC rate to 0% in all scenarios (instead of 0%, 1%, 2%)

Question: Do banks still lose deposits even if CBDC pays nothing? Why or why not?

Variation 3: Early Crisis

Task: Move crisis start from quarter 8 to quarter 2

Question: How does an early crisis change the outcomes? Why does timing matter?

Open Extension

Task: Add a "tiered CBDC" scenario where:

Question: How does this tiered structure protect banks compared to a flat 2% CBDC rate? Who benefits most from this policy design?

How to Run

  1. Google Colab (recommended): Upload the chart.py file to Google Colab
  2. Install dependencies: Run !pip install scipy in a Colab cell (needed for solving the differential equation)
  3. Run the code: Execute the chart.py file
  4. Create variations: Modify parameters and observe changes

Time Allocation

Deliverables

  1. Presentation slides (5-7 slides) showing:
    • The baseline model and what it means
    • Results from all three variations with charts
    • Your interpretation of what changes
    • (Optional) Extension results for tiered CBDC
  2. Key insight: What is the most important policy lever for protecting banks from CBDC competition?

References

Model Answer
Show Model Answer Presentation

Slide 1

CBDC and Bank Disintermediation

Will Central Bank Digital Currencies Kill Commercial Banks?

Reference: Brunnermeier & Niepelt (2019) - On the Equivalence of Private and Public Money

Slide 2

The Model: How Deposits Change Over Time

Differential Equation:
dD/dt = -α(r_CBDC - r_D)D + β·confidence(t)

In Plain Language:
The rate of deposit outflow from banks depends on two forces:

  1. Interest Rate Gap (-α term): If CBDC pays more than bank deposits, people move money to CBDC. The bigger the gap, the faster the outflow. Parameter α (rate sensitivity) = 0.8 means deposits are moderately responsive to rate differences.
  2. Confidence Shocks (β term): During a crisis, people lose confidence and withdraw deposits even if rates are equal. Parameter β (confidence sensitivity) = 1.2 amplifies panic effects.

Slide 3

Baseline Results: Four Scenarios

Key Findings:

  • 0% CBDC rate (green): Deposits barely change (<5% loss over 5 years)
  • 1% CBDC rate (blue): Deposits fall to ~85% after 5 years
  • 2% CBDC rate (orange): Deposits crash to ~65% (35% loss)
  • Crisis + 1% CBDC (red): Combined shock drives deposits to ~70%, nearing tipping point

Slide 4

Variation 1: High Rate Sensitivity (α = 2.0)

Panel 2 (top-right): When α = 2.0 instead of 0.8, deposit outflow accelerates dramatically.

Result: With 2% CBDC rate, deposits collapse to ~40% (60% loss) — bank failure territory.

Interpretation: If people are highly sensitive to interest rates, even small CBDC rate advantages trigger massive disintermediation.

Slide 5

Variation 2: Zero CBDC Rate Always

Panel 3 (bottom-left): All scenarios have CBDC rate set to 0%.

Result: Deposits fall by less than 5% in all cases. Even the crisis scenario (red dashed) shows minimal outflow.

Key Insight: CBDC interest rate is the critical policy variable. Without an interest rate advantage, CBDC adoption remains low regardless of other factors.

Policy Implication: Central banks can protect commercial banks by keeping CBDC rates at or below deposit rates.

Slide 6

Variation 3: Early Crisis (Quarter 2 Instead of 8)

Panel 4 (bottom-right): Crisis starts at quarter 2 instead of quarter 8.

Result: Deposits fall further (to ~60% instead of ~70%) because the confidence shock has more time to compound with interest rate effects.

Interpretation: Timing matters. An early crisis combined with CBDC competition gives less time for stabilization policies to work.

Real-world parallel: If CBDC launches during economic turbulence, disintermediation risks multiply.

Slide 7

Key Insight: CBDC Interest Rate is the Policy Lever

What We Learned:

  1. 0% CBDC rate = Safe: Banks keep deposits even during crises
  2. Rate above deposit rate = Dangerous: Disintermediation accelerates, especially if people are rate-sensitive (high α)
  3. Crisis timing matters: Early shocks compound over more quarters

Policy Tools:

  • Rate ceiling: Cap CBDC interest at 1% → deposits stabilize at 75-80%
  • Quantity limits: Restrict CBDC holdings → reduces α (rate sensitivity) by limiting arbitrage
  • Tiered rates: Pay 2% on first EUR 3,000 only → protects small savers while limiting bank run risk

Bottom line: Central banks face a trade-off. Higher CBDC rates attract users but destabilize banks. The baseline chart shows intervention at quarter 12 can stabilize deposits if policy acts quickly.

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