Phillips Curve Calculator
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The Phillips Curve Calculator computes the macroeconomic relationship between the national Inflation Rate and the Unemployment Rate based on the Expectations-Augmented Phillips Curve. Discovered by A.W. Phillips and refined by Milton Friedman and Edmund Phelps, the model illustrates how central bank monetary policy creates a short-run trade-off between inflation and job growth.
Calculating the Phillips Curve enables monetary policymakers, bond investors, and researchers to project wage-push inflation, analyze supply shocks, and evaluate central bank interest rate decisions.
Phillips Curve Formulas
The standard modern Expectations-Augmented Phillips Curve equation is:
Inflation Rate (π) = Expected Inflation (πe) - γ × (Unemployment Rate - Natural Rate) + Supply Shock
Where:
- π (Actual Inflation Rate): The total annual percentage rate of Consumer Price Index (CPI) inflation.
- πe (Expected Inflation Rate): The baseline inflation expectation held by businesses and households.
- Unemployment Rate (u): The actual percentage of the civilian labor force currently unemployed.
- Natural Rate (un / NAIRU): The Non-Accelerating Inflation Rate of Unemployment at full employment baseline.
- γ (Slope / Sensitivity Parameter): The responsiveness of inflation to shifts in the unemployment gap (γ > 0).
- Supply Shock (ν): External price shocks (such as sudden oil price spikes or supply chain disruptions).
Short-Run vs. Long-Run Phillips Curve Matrix
Macroeconomic dynamics differ fundamental between short-run monetary policy shifts and long-run economic equilibrium:
| Macroeconomic State | Unemployment vs. NAIRU | Inflation Outcome & Policy Context |
|---|---|---|
| Overheating Economy | Unemployment < Natural Rate (u < un) | Labor shortages force employers to raise wages. Actual Inflation exceeds Expected Inflation (π > πe). Central bank rate hikes required. |
| Long-Run Equilibrium | Unemployment = Natural Rate (u = un) | Full employment. Actual Inflation equals Expected Inflation (π = πe). Vertical Long-Run Phillips Curve (LRPC). |
| Recessionary Slump | Unemployment > Natural Rate (u > un) | Labor slack depresses wage growth. Actual Inflation falls below Expected Inflation (π < πe). Central bank rate cuts required. |
| Stagflation Shock | Unemployment > Natural Rate + Supply Shock | Adverse supply shock shifts SRPC upward. Simultaneous high inflation and high unemployment (e.g., 1970s oil crisis). |
Step-by-Step Phillips Curve Example
Consider a central bank evaluating monetary policy under the following parameters:
- Expected Inflation Rate (πe): 2.5%
- Actual Unemployment Rate (u): 3.5%
- Natural Rate of Unemployment (un): 4.5%
- Inflation Sensitivity (γ): 0.5
- Supply Shock (ν): 0.0%
Step 1: Calculate Unemployment Gap
u - un = 3.5% - 4.5% = -1.0% (Tight Labor Market)
Step 2: Multiply by Sensitivity Parameter (γ)
0.5 × (-1.0%) = -0.5%
Step 3: Compute Final Inflation Rate
Inflation Rate (π) = 2.5% - (-0.5%) + 0.0% = 3.0%
Result: Pushing unemployment 1.0% below the natural rate causes the actual Inflation Rate to rise to 3.0% (0.5 percentage points above expected inflation).
Frequently Asked Questions (FAQ)
Why is the Long-Run Phillips Curve vertical?
The Long-Run Phillips Curve (LRPC) is vertical at the Natural Rate of Unemployment (NAIRU) because in the long run, workers adjust their inflation expectations (πe = π). Monetary policy cannot permanently keep unemployment below NAIRU without triggering accelerating inflation.
What causes the Short-Run Phillips Curve to shift?
The Short-Run Phillips Curve shifts upward when expected inflation rises or when an adverse supply shock occurs (like a sharp spike in global oil prices or food supply disruptions).
What is “Stagflation”?
Stagflation is an economic condition where inflation and unemployment rise simultaneously. It invalidates the simple early Phillips Curve trade-off and occurs during major adverse supply shocks.
How do central bank inflation targets affect the Phillips Curve?
When a central bank establishes a credible 2.0% inflation target, household and business inflation expectations anchor at 2.0% (πe = 2.0%), stabilizing the Short-Run Phillips Curve around that baseline.