Phillips Curve Calculator
The Phillips Curve describes the short-run trade-off between unemployment and inflation. This calculator supports three model variants used in macroeconomics courses and policy work: the Traditional (Lipsey) wage-Phillips curve, the Expectations-Augmented curve (Friedman-Phelps), and the New Keynesian Phillips Curve (NKPC). Enter your variables and the result updates instantly, with a step-by-step breakdown and a short-run curve chart.
What is the Phillips Curve?
The Phillips Curve is one of the most studied relationships in macroeconomics. New Zealand economist A.W. Phillips published the original empirical finding in 1958, showing an inverse relationship between wage growth and unemployment in British data from 1861 to 1957: when unemployment was low, wages rose quickly, and when unemployment was high, wages were stagnant or fell. The idea was quickly extended to price inflation: high demand for labour tightens the labour market, pushing up wages, which firms pass on as higher prices. This gave policymakers a simple tool: accept higher inflation to reduce unemployment, or accept higher unemployment to lower inflation.
The Expectations-Augmented Phillips Curve (Friedman-Phelps)
In 1968, Milton Friedman and Edmund Phelps independently argued that the original Phillips Curve was misleading because it ignored inflation expectations. Workers care about real wages, not nominal wages, so they demand higher nominal wages when they expect inflation to be high. This means the short-run curve shifts upward whenever expectations rise: you can only get lower unemployment than the NAIRU by generating more inflation than the public expects. In the long run, people fully adjust their expectations, so the curve is vertical at the NAIRU (the Non-Accelerating Inflation Rate of Unemployment). The Friedman-Phelps model became the standard framework after the stagflation of the 1970s, which the original curve could not explain. The formula is: pi = pi_e - b * (U - NAIRU) + v, where v is a supply shock.
The New Keynesian Phillips Curve (NKPC)
The New Keynesian Phillips Curve, developed by Jordi Gali and Mark Gertler in 1999, replaces the backward-looking expectations term with a fully forward-looking version derived from a structural model of firm price-setting (Calvo pricing). The formula is: pi_t = beta * E_t{pi_{t+1}} + kappa * output_gap + u. Here beta is a firm discount factor close to 1, kappa is the slope with respect to the output gap, and u is a cost-push shock. Because expectations are forward-looking, credible central-bank policy can anchor inflation without the costly expectation spirals that plagued the 1970s. The NKPC is now the core equation in dynamic stochastic general equilibrium (DSGE) models used by central banks worldwide.
Interpreting your results
All three models predict that inflation rises when the economy is tight (unemployment below NAIRU, or output above potential) and falls when it is slack. In the Expectations-Augmented model, a positive unemployment gap (unemployment above NAIRU) reduces inflation below expectations. A negative supply shock (a fall in oil prices, for example) shifts the curve down, delivering lower inflation at any unemployment rate. In the NKPC, a negative output gap (recession) pulls inflation below the discounted expected rate. Use the reference table above to choose the right model: if you are teaching introductory macro, the Expectations-Augmented model is usually the right starting point. For central bank research or quantitative policy analysis, the NKPC is the industry standard.
Phillips Curve model comparison
| Model | Key drivers | Long-run implication | Era |
|---|---|---|---|
| Traditional (Lipsey) | Wage growth, unemployment level | Stable trade-off (now rejected) | 1958-1960s |
| Expectations-Augmented | Expected inflation, unemployment gap, NAIRU | No long-run trade-off; vertical at NAIRU | 1968-present |
| New Keynesian (NKPC) | Forward-looking expectations, output gap | Vertical long-run; policy credibility matters | 1999-present |
Key characteristics of the three main Phillips Curve frameworks used in modern macroeconomics.
Frequently asked questions
Does the Phillips Curve still work today?
The short-run trade-off is still visible in the data, but it has become flatter and harder to detect since the 1990s. Well-anchored inflation expectations, globalisation, and structural changes in labour markets mean that large swings in unemployment now produce smaller changes in inflation than the original curve suggested. After the COVID-19 pandemic, the curve appeared to steepen again, especially in goods markets, which sparked renewed academic debate.
What is the NAIRU, and how is it estimated?
The NAIRU (Non-Accelerating Inflation Rate of Unemployment) is the unemployment rate at which inflation is stable, not because unemployment is zero but because labour-market frictions, search costs, and structural mismatches always keep some workers between jobs. It is not directly observable: central banks and research institutions estimate it using statistical filters (Hodrick-Prescott, Kalman) and structural models. The U.S. Congressional Budget Office estimated the NAIRU at roughly 4.4% in 2024. It changes over time as demographics, technology, and labor market institutions evolve.
Why did the Phillips Curve break down in the 1970s?
The original trade-off broke down because inflation expectations were not anchored. After years of expansionary policy, workers and firms expected high inflation and demanded higher wages and prices pre-emptively, shifting the short-run curve upward. The OPEC oil embargo of 1973 then delivered an adverse supply shock (positive v in the model), pushing inflation higher at every unemployment rate simultaneously. This combination of high inflation and high unemployment (stagflation) was impossible in the original model but is fully consistent with the Expectations-Augmented version.
What is the difference between the output gap and the unemployment gap?
The unemployment gap is the difference between actual unemployment and the NAIRU. The output gap is the difference between actual GDP and potential GDP as a percentage of potential GDP. The two are related by Okun's Law: roughly, a 1 percentage-point fall in unemployment above the NAIRU is associated with a 2 percentage-point rise in the output gap, though this ratio varies across countries and time periods. The NKPC uses the output gap directly because it is derived from a model of firm production, whereas the Friedman-Phelps model uses the unemployment gap directly.
Can this calculator be used in reverse to find the NAIRU?
Yes, with some rearrangement. In the Expectations-Augmented model, if you know current inflation, expected inflation, the slope b, and the supply shock v, you can solve for the NAIRU as: NAIRU = U - (pi_e - pi + v) / b. Plug your values into the inputs, then adjust the NAIRU slider until the implied inflation matches your observed rate. A future dedicated NAIRU calculator will automate this reverse-solve.