How this instrument works
The Phillips curve used here is the expectations-augmented version economists actually work with, not the raw wage-inflation scatterplot A.W. Phillips published from British data in 1958. It states that inflation departs from what people expect in direct proportion to how far unemployment sits from its natural rate — the rate consistent with stable prices, sometimes called NAIRU. Unemployment above that natural rate signals slack in the labor market and pulls inflation down; unemployment below it signals a tight market and pushes inflation up.
Central bank staff economists and bank macro research desks lean on this relationship to translate a labor-market forecast into an inflation forecast, feeding short-run projections that inform interest-rate decisions. A regional Fed research team watching unemployment drift two points above its estimated natural rate would read that gap as disinflationary pressure working through the economy, independent of any supply-side story.
The sensitivity coefficient β is the model's weakest link — not a physical constant but an estimate that has drifted across decades and flattened noticeably since the 1990s in developed economies, meaning the same unemployment gap now moves inflation less than it once did. The natural rate itself is never observed directly; it is inferred, revised, and disputed, so treat any single run of this instrument as one scenario built on someone's estimate, not a law of nature.
- Enter Expected inflation, % — the anchor the curve pulls actual inflation toward when the labor market is balanced.
- Set Actual unemployment rate, % and Natural rate of unemployment, % — the gap between them is the slack term.
- Adjust Sensitivity coefficient, β to match how strongly inflation has responded to slack in the period you're modeling.
- Read Implied inflation rate, % — the curve's estimate of where inflation lands given that slack and your expected-inflation anchor.
Worked example — two points of labor-market slack
Set Expected inflation, % to 2, Sensitivity coefficient, β to 0.5, Actual unemployment rate, % to 6, and Natural rate of unemployment, % to 4. The gap (u − u*) is 6 − 4 = 2 points of slack. Multiply by β: 0.5 × 2 = 1. Subtract that from expected inflation: π = 2 − 1 = 1.0 percent — the figure the instrument returns as Implied inflation rate, %.
That 1.0 percent sits a full point below the 2 percent people expected, purely because unemployment is running above its natural rate — the slack mechanism the original 1958 Phillips curve was built to describe. Close the gap by dropping unemployment to 4 percent and the slack term vanishes, so implied inflation rises back to exactly the 2 percent anchor; no slack means no pull away from expectations.
Questions
What does the natural rate of unemployment actually represent?
It's the unemployment rate consistent with stable, non-accelerating inflation — often called NAIRU. It isn't zero unemployment; frictional and structural job search always leaves some people between jobs. Statistical agencies and central banks estimate it from historical inflation and labor data, revise it periodically, and disagree on its exact level, which is why this instrument leaves it as an input you set rather than a fixed constant.
Why does inflation drop below expectations when unemployment rises?
Higher unemployment means workers have less bargaining power to demand raises and firms face weaker demand for their output, so wage and price growth both slow relative to what was expected. The curve captures that as a direct subtraction: every point unemployment sits above the natural rate removes β points from expected inflation, which is why the sign on the slack term is negative.
How is this different from Okun's law?
Okun's law links the unemployment gap to lost output — how far GDP sits below potential. The Phillips curve used here links that same kind of gap to inflation instead. They're companion relationships built on the same idea of labor-market slack, but one predicts growth shortfall and the other predicts price behavior; conflating the two is a common misreading.
Why did the original Phillips curve break down in the 1970s?
The 1958 version had no expectations term, so it implied a stable, exploitable trade-off between inflation and unemployment. Once workers and firms started anticipating inflation and building it into contracts, that trade-off collapsed — the U.S. saw high inflation and high unemployment together during the 1970s oil shocks. Friedman and Phelps added the expected-inflation term used here specifically to explain that failure.
What's a realistic value for the sensitivity coefficient β?
Empirical estimates for developed economies since the 1990s often fall between 0.1 and 0.3, well below the steeper values fitted to 1960s data — economists call this the flattening of the Phillips curve. There's no single correct β; it depends on the country, time period, and how the underlying study defined slack, so treat it as a scenario input rather than a known parameter.
Can this calculator forecast next year's actual inflation rate?
No. It shows what one simplified, widely taught relationship implies given the inputs you choose — it excludes supply shocks, commodity-price swings, exchange-rate effects, and the harder-to-model process by which people actually form expectations. Professional forecasts blend this relationship with several others; treat the output here as one piece of that picture, not a prediction.
References
- Federal Reserve — Monetary policy and the dual mandate
- U.S. Bureau of Labor Statistics — Labor force statistics definitions
- Congressional Budget Office — Employment and labor markets
Read this first: This instrument shows arithmetic, not advice. Real offers add fees, taxes and terms that vary by lender and place — verify the figures against your actual paperwork before deciding anything.