Monetary Policy Simulation

We will simulate the effects of monetary policy on an economy using a simplified model.

The main variables are:

  1. Interest Rate (r):
    Set by the central bank.
  2. Inflation Rate (π):
    Determined by economic conditions and influenced by monetary policy.
  3. Output Gap (Y):
    The difference between actual output and potential output, affected by interest rate changes.

This simulation will follow the logic of the Taylor Rule, a common monetary policy guideline:
r=r∗+ϕπ(π−π∗)+ϕYY

  • (r∗) is the neutral interest rate.
  • (π∗) is the target inflation rate.
  • (ϕπ)and(ϕY) are policy reaction coefficients for inflation and output gap.

Python Implementation

Below is the Python code to simulate the impact of monetary policy adjustments on inflation and the output gap over time.

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import numpy as np
import matplotlib.pyplot as plt

# Parameters for the model
r_star = 2.0  # Neutral interest rate (% per year)
pi_star = 2.0  # Target inflation rate (% per year)
phi_pi = 1.5   # Reaction to inflation deviation
phi_Y = 0.5    # Reaction to output gap

# Initial conditions
T = 20  # Number of periods
time = np.arange(1, T + 1)

# Arrays to store values
inflation = np.zeros(T)
output_gap = np.zeros(T)
interest_rate = np.zeros(T)

# Initial values
inflation[0] = 3.0  # Initial inflation rate
output_gap[0] = -1.0  # Initial output gap

# Simulation loop
for t in range(1, T):
    # Determine interest rate using the Taylor Rule
    interest_rate[t] = (
        r_star + phi_pi * (inflation[t-1] - pi_star) + phi_Y * output_gap[t-1]
    )
    
    # Update output gap and inflation based on interest rate
    output_gap[t] = output_gap[t-1] - 0.5 * (interest_rate[t] - r_star)
    inflation[t] = inflation[t-1] - 0.3 * output_gap[t]

# Plotting the results
plt.figure(figsize=(12, 8))

# Plot inflation
plt.subplot(3, 1, 1)
plt.plot(time, inflation, label='Inflation Rate', color='red')
plt.axhline(pi_star, linestyle='--', color='black', label='Target Inflation Rate')
plt.title('Monetary Policy Simulation')
plt.ylabel('Inflation Rate (%)')
plt.legend()

# Plot output gap
plt.subplot(3, 1, 2)
plt.plot(time, output_gap, label='Output Gap', color='blue')
plt.axhline(0, linestyle='--', color='black', label='Zero Output Gap')
plt.ylabel('Output Gap (%)')
plt.legend()

# Plot interest rate
plt.subplot(3, 1, 3)
plt.plot(time, interest_rate, label='Interest Rate', color='green')
plt.axhline(r_star, linestyle='--', color='black', label='Neutral Interest Rate')
plt.xlabel('Time (Periods)')
plt.ylabel('Interest Rate (%)')
plt.legend()

plt.tight_layout()
plt.show()

Explanation of the Code

  1. Model Setup:
    • The neutral interest rate (r∗), target inflation rate (π∗), and policy reaction coefficients (ϕπ, ϕY) are defined.
  2. Simulation Loop:
    • The interest rate is updated using the Taylor Rule.
    • The output gap and inflation rate are updated based on the interest rate, reflecting the dynamics of monetary policy.
  3. Visualization:
    • The results for inflation, output gap, and interest rate over time are plotted.

Expected Results

  1. Inflation Rate:
    Gradually converges toward the target rate (π∗=2％).
  2. Output Gap:
    Oscillates and eventually stabilizes around zero.
  3. Interest Rate:
    Adjusts dynamically based on the Taylor Rule to stabilize inflation and output.

The graphs will visually illustrate these dynamics, helping to understand how monetary policy impacts an economy over time.