Phillips Curve Calculator
Estimate inflation from the Phillips curve: inflation = expected inflation − coefficient × (actual unemployment − natural unemployment), showing the short-run trade-off.
Input Data
Results
At a glance:The Phillips curve links inflation and unemployment in the short run. Estimated inflation = expected inflation − β × (actual unemployment − natural unemployment). A lower actual unemployment than the natural rate pushes inflation up; a higher one pushes it down. β is the slope.
Formula
Inflation = expected inflation − β × (actual unemployment − natural unemployment).
$$\pi = \pi^{e} - \beta \,(u - u_{n})$$How to Use
- Enter the expected inflation and the coefficient β.
- Enter the actual and natural unemployment rates.
- Read the estimated inflation.
FAQ
What is the Phillips curve and what relationship does it describe?
The Phillips curve describes the relationship between unemployment and inflation. In the short run there is a trade-off: when unemployment is low, inflation tends to be high, and when unemployment is high, inflation tends to be low. The modern version adds inflation expectations — estimated inflation = expected inflation − β × (actual unemployment − natural unemployment). When actual unemployment falls below the natural rate, inflation is pushed above expectations; when it is above, inflation is below.
Why does the formula include expected inflation and the natural rate?
Early versions ignored inflation expectations, which broke down during 1970s stagflation. Friedman and Phelps showed that people form expectations and build them into wages and pricing. Expected inflation (π^e) is the inertia of inflation; the natural rate (u_n) is the neutral benchmark — only when actual unemployment deviates from it does inflation face pressure. That is why the long-run Phillips curve is vertical: expectations adjust and unemployment returns to its natural level.
What does the Phillips curve imply for monetary policy, and is it reliable?
It shows why short-run easing can lower unemployment at the cost of higher inflation, and why anchoring inflation expectations (via credible targets and forward guidance) lets a central bank stabilise the economy at lower cost. But the relationship is not stable — it flattened in some periods and broke down in stagflation — and its key inputs (natural rate, expectations, coefficient) are estimates. Treat it as a thinking framework and trend reference, not a precise forecast; combine it with other indicators.
Why add the expected-inflation term at all?
Because people are not blind to inflation. If they expect 3%, that expectation is built into wage and price setting, becoming the baseline. The corrected formula, inflation = expected − β × (unemployment gap), means actual inflation only diverges from expectations when unemployment deviates from the natural rate. So a permanent inflation push only works until expectations catch up — then you are left with higher inflation and unemployment back at its natural level, which is exactly the 'vertical long-run curve' result.
What is the natural rate of unemployment (NAIRU) and why can't unemployment be zero?
The natural rate (NAIRU) is the unemployment consistent with stable inflation — the labour market's equilibrium. It can never be zero because of frictional unemployment (people between jobs) and structural unemployment (skills or location mismatches), neither of which demand stimulus can remove. Pushing unemployment below the natural rate overheats the market and accelerates inflation. The natural rate itself shifts with demographics, institutions and structure, and like potential GDP is only estimated, not observed.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.