Phillips Curve

Phillips Curve

The Phillips Curve illustrates the inverse relationship between the rate of unemployment and the rate of inflation within an economy.

Let’s create a simple example where we model this relationship using synthetic data.

We’ll use $Python$ to perform the calculations and visualize the results.

Step 1: Create Synthetic Data

First, we’ll generate some synthetic data for unemployment rates and corresponding inflation rates.

Step 2: Analyze and Plot the Data

We’ll analyze this data to see the relationship and plot the Phillips Curve.

Here is the $Python$ code for generating the data, analyzing it, and plotting the curve:

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import linregress

# Step 1: Create synthetic data
np.random.seed(42) # for reproducibility
unemployment_rate = np.random.uniform(3, 10, 50) # Unemployment rate between 3% and 10%
inflation_rate = np.random.uniform(0, 5, 50) - 0.5 * unemployment_rate # Simple inverse relationship

# Add some noise to make the data more realistic
inflation_rate += np.random.normal(0, 0.5, inflation_rate.shape)

# Step 2: Analyze and plot the data
slope, intercept, r_value, p_value, std_err = linregress(unemployment_rate, inflation_rate)

# Calculate regression line
regression_line = intercept + slope * unemployment_rate

# Plotting
plt.scatter(unemployment_rate, inflation_rate, label='Data points')
plt.plot(unemployment_rate, regression_line, color='red', label=f'Regression line: y={slope:.2f}x+{intercept:.2f}')
plt.xlabel('Unemployment Rate (%)')
plt.ylabel('Inflation Rate (%)')
plt.title('Phillips Curve')
plt.legend()
plt.grid(True)
plt.show()

Explanation

  1. Data Generation:
    We create synthetic data for the unemployment and inflation rates.
    The relationship is modeled with some random noise to simulate real-world data.
  2. Regression Analysis:
    We use linear regression to find the best-fit line that describes the relationship between unemployment and inflation rates.
  3. Plotting:
    We plot the data points and the regression line to visualize the Phillips Curve.

Graph Interpretation

  • The scatter plot shows individual data points representing different unemployment and inflation rate pairs.
  • The red line is the regression line, indicating the trend or the average relationship between unemployment and inflation rates.
    According to the Phillips Curve, as the unemployment rate decreases, the inflation rate tends to increase, and this inverse relationship is depicted by the slope of the line.