Hong Life CalculatorsUnderstanding the Phillips curve calculator — concept and principle
The Phillips curve links inflation with unemployment. This calculator uses the expectations-augmented version: inflation equals expected inflation, pushed up when unemployment is below its natural rate and down when it is above. It also finds the unemployment rate consistent with a target inflation rate and the sacrifice ratio.
How it is calculated
π = πe − b × (u − u*)
- π: predicted inflation; πe: expected inflation.
- u: unemployment rate; u*: natural rate (NAIRU).
- b: slope, the change in inflation per point of unemployment gap.
- Unemployment rate that moves inflation to a target = u* + (πe − target) ÷ b.
- Sacrifice ratio = 1 ÷ b, point-years of extra unemployment needed to lower inflation by one point.
The principle
When unemployment is low, employers compete for workers, wages rise faster and firms pass costs on in prices. When unemployment is high, the opposite happens. Milton Friedman and Edmund Phelps argued in the late 1960s that this trade-off holds only relative to what people expect: if inflation stays high, expectations adjust, and unemployment returns to its natural rate. In the accelerationist form often used in central-bank studies, expected inflation equals last period's inflation, so keeping unemployment below u* makes inflation keep rising.
Worked example
Default inputs: expected inflation 3%, unemployment 4%, NAIRU 4.5%, slope 0.3, target 2%.
- Unemployment gap = 4 − 4.5 = −0.5 points.
- Change from expected inflation = −0.3 × (−0.5) = +0.15 points.
- Predicted inflation = 3 + 0.15 = 3.15%.
- Unemployment rate for 2% inflation = 4.5 + (3 − 2) ÷ 0.3 ≈ 7.83% (for one period).
- Sacrifice ratio = 1 ÷ 0.3 ≈ 3.33 point-years per point.
| Expected inflation (%) | Predicted inflation |
|---|---|
| 0.75 | 0.9% |
| 1.5 | 1.65% |
| 2.25 | 2.4% |
| 3 | 3.15% |
| 3.75 | 3.9% |
| 4.5 | 4.65% |
| 6 | 6.15% |
How to read the result
A negative unemployment gap pushes inflation above expectations; a positive gap pulls it below. The high unemployment needed for the target in one period shows why disinflation is usually spread over several years, and why central banks care about anchoring expectations: if expectations fall by themselves, less unemployment is needed. Estimated slopes have become much flatter since the 1990s, so results are illustrations.
Common mistakes
- Treating the original Phillips curve as a stable menu of choices.
- Ignoring supply shocks such as energy prices, which shift the curve.
- Using a slope estimated for another country or era.
- Assuming the NAIRU is known precisely.
Frequently asked questions
What does the Phillips curve show?
A short-run trade-off: lower unemployment tends to go with higher inflation relative to expectations.
Why did the Phillips curve flatten?
Possible reasons include better-anchored inflation expectations, globalization and changes in wage setting; economists still debate it.
What is the sacrifice ratio?
The cumulative extra unemployment, in point-years, needed to reduce inflation by one percentage point.
Sources: Phillips, A. W. (1958). The Relation between Unemployment and the Rate of Change of Money Wage Rates in the United Kingdom, 1861–1957. Economica, 25(100). · Friedman, M. (1968). The Role of Monetary Policy. American Economic Review, 58(1).