How this calculator works
The Phillips curve describes the short-run tradeoff between inflation and economic slack. The traditional expectations-augmented version says inflation equals expected inflation minus a sensitivity times the unemployment gap, plus supply shocks: when unemployment is below its natural rate, inflation runs above expectations. The new classical version keeps the same accounting but treats expectations as rational, so only unexpected inflation can move unemployment away from its natural rate, and systematic policy cannot exploit the tradeoff. The new Keynesian version is forward looking and written in terms of the output gap: inflation today depends on expected inflation next period, the slope on the output gap and a shock. These are reduced-form descriptions, not forecasts, and the parameters must be estimated from data.
Formula
Traditional and new classical: inflation = expected inflation - beta x (unemployment - natural rate) + shock. New Keynesian: inflation = beta x expected inflation next period + kappa x output gap + shock, where beta is the household discount factor. The unemployment gap is unemployment - natural rate, and unexpected inflation is inflation - expected inflation.
Worked example
With expected inflation at 2.5%, unemployment at 6%, a natural rate of 4.5%, a sensitivity of 0.5 and no shock, inflation is 1.75%. Under the new classical reading, unexpected inflation is -0.75%. In the new Keynesian version, a 0.99 discount factor, 2.5% expected inflation, a slope of 0.1 and a 1% output gap give 2.575%.
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Frequently asked questions
Why does the new Keynesian version use a discount factor?
Firms that cannot change prices today set them based on expected future prices and costs. The discount factor beta, usually close to one, converts that future marginal cost into today's value, so expected inflation enters with a weight just below one.
Does a lower unemployment rate always raise inflation?
Only relative to the natural rate and only in this reduced form. If both unemployment and its natural rate fall together, the gap may not change. Anchored expectations also weaken the short-run tradeoff.
Where do the parameters come from?
They are estimated econometrically and differ by country and sample. The values here are illustrative defaults, so edit them to match the estimates you want to use rather than treating them as universal constants.