Phillips Curve Inflation Calculator

The Phillips curve describes the short-run inverse relationship between unemployment and inflation. When unemployment falls below its natural rate, inflation rises. When unemployment is high, inflation falls.

A bit of history. The original relationship was published by A.W. Phillips in 1958 from UK wage-and-unemployment data covering 1861-1957. He plotted the rate of money-wage change against unemployment and found a clean inverse curve. The relationship became central to 1960s macroeconomic policy until stagflation in the 1970s (simultaneous high inflation AND high unemployment) showed the original curve was incomplete. Friedman and Phelps independently fixed it by adding inflation expectations.

The expectations-augmented Phillips curve (Friedman-Phelps, 1968):

pi = pi_e - beta x (u - u*)

where pi is actual inflation, pi_e is expected inflation, beta is the sensitivity of inflation to labor market slack, u is actual unemployment, and u* is the natural rate of unemployment (NAIRU).

How to read it. If unemployment equals NAIRU, actual inflation matches expected inflation. If unemployment is 2 percentage points below NAIRU, inflation runs above expectations by 2 x beta. Typical US estimates of beta are 0.3-0.5.

The long run. Friedman and Phelps showed the original Phillips tradeoff disappears in the long run. Workers and firms adjust their expectations. If policymakers keep unemployment permanently below NAIRU, inflation accelerates without bound. This is why central banks focus on keeping unemployment near the natural rate rather than minimizing it.

NAIRU estimates vary by country and time period. The US Congressional Budget Office estimates NAIRU around 4.0-4.5%. Europe’s structural unemployment is higher. Estimating NAIRU in real time is notoriously difficult, which is part of why monetary policy is so challenging.

Supply shocks. A fuller version of the equation includes a supply-shock term ν:

pi = pi_e - beta x (u - u*) + ν

ν captures cost-push pressures unrelated to the labor market, such as oil-price spikes, food-price jumps from a bad harvest, or supply-chain disruptions. The 1970s stagflation is the canonical example: OPEC oil embargoes pushed ν positive while unemployment was also high. This calculator uses the simpler form without ν, but for any period when an external shock dominates, you should add an estimate of ν to the result.

The chart shows the short-run Phillips curve at fixed inflation expectations. Shifts in expected inflation shift the entire curve up or down.