The Phillips curve is the short run link between unemployment and inflation: tighter labour markets tend to come with faster inflation, and higher unemployment with slower inflation. It is not a permanent menu a central bank can pick from, because expected inflation shifts the relationship. The short run link can still show up, especially when labour markets are very tight, and it does not survive as a fixed trade off once expectations and supply shocks move. This page is educational only. It is not investment advice.

Five readings, one name

People use one label for several different claims. The table separates them. The early rows restate published papers. The 1975 figure is from a Bank of England speech. The last two rows restate Federal Reserve staff research. That research is not a decision of the Federal Open Market Committee, and it is not an official forecast.

EraWhat was comparedWhat that record supports
1958, A. W. Phillips UK wage change against unemployment, using data from 1861 to 1957. The curve itself was fitted to averages for 1861 to 1913. A downward sloping, nonlinear curve. Assuming productivity rose 2 percent a year, and setting aside years of very fast import price rises, stable product prices lined up with unemployment a little under 2.5 percent. Stable wage rates lined up with unemployment of about 5.5 percent.
1960, Samuelson and Solow US unemployment against price inflation, drawn from the previous 25 years of American data. A short run menu, not a law. Price stability looked like something like 5 to 6 percent unemployment, about 5.5 percent on their figure. Unemployment of 3 percent looked like prices rising by as much as 4 to 5 percent a year, about 4.5 percent on the figure. They warned the menu could shift.
1967 and 1968, Phelps and Friedman Inflation against unemployment, with expected inflation allowed to move. A separate short run curve for each expected inflation rate. There is a temporary trade off. There is no permanent one. Unemployment returns to a natural rate unless inflation keeps surprising people.
The 1970s High inflation together with high unemployment, often called stagflation. A fixed curve from a calmer sample cannot put those two outcomes on one point. In the United Kingdom, CPI inflation and nominal wage growth rose to over 25 percent in 1975, despite higher unemployment.
After 2000, ordinary labour markets US city consumer prices and unemployment, in a September 2024 FEDS Note. The slope in ordinary labour markets flattened after a break in 2000, from minus 0.26 to minus 0.18. Below five percent unemployment the curve stayed steep. The extra slope in that tight region was minus 0.28 after 2000.
2021 to 2023 The inflation surge in the United States, and the debate about a steeper or nonlinear curve. Twelve month US PCE inflation reached 7.3 percent in the summer of 2022. UK CPI inflation was 10.4 percent in February 2023. Most Phillips curve estimates, even ones that allow a bend, say labour market tightness explains only part of the US rise in 2021 and 2022. Studies disagree on how large the bend is.

What Phillips actually measured

In November 1958, A. W. Phillips published a paper in Economica on UK money wage rates from 1861 to 1957. He was at the London School of Economics. The question was narrow. When employers are bidding for scarce labour, wage rates rise quickly. When unemployment is high, workers resist cuts, so wage rates fall only slowly. He expected a highly nonlinear curve, not a straight line.

For 1861 to 1913 he plotted the rate of change of money wage rates against percentage unemployment. Wage changes came from an index built by Phelps Brown and Hopkins. Unemployment came from trade union returns compiled by the Board of Trade and the Ministry of Labour. He then averaged the years inside unemployment bins, so years of rising unemployment and years of falling unemployment sat together. That averaging was meant to show the wage change that would go with a given unemployment rate if unemployment were held steady. He fitted a curve to those averages.

The form he chose was y + a = b times x raised to c. Here y is the rate of change of wage rates and x is percentage unemployment. The fitted curve he reports is y + 0.900 = 9.638 times x raised to the power of minus 1.394. In log form, the log of (y + 0.900) equals 0.984 minus 1.394 times the log of x. He estimated the slope terms on the averages between 0 and 5 percent unemployment, and chose the 0.900 shift so the curve would pass near the two averages between 5 and 11 percent.

His closing argument is the part people still quote, and it is more careful than a policy menu. Ignore years when import prices rise fast enough to start a spiral of wages and prices, which he thought were rare outside war. Assume productivity rises 2 percent a year. Then the fitted relation says that demand held at a level which kept product prices stable would come with unemployment a little under 2.5 percent. Demand held so that wage rates themselves were stable would come with unemployment of about 5.5 percent. Because the curve bends sharply at low unemployment, steady unemployment at a given rate produces a smaller average wage increase than unemployment that swings around that same rate. He called the conclusions tentative.

He also checked later decades against that 1861 to 1913 curve. For 1948 to 1957, lagging unemployment by seven months pulled the points for 1950 and for 1953 to 1957 onto a smooth curve that coincided almost exactly with the old fit. The famous diagram was a wage curve for one country, with a timing adjustment, not a claim that any central bank could buy a permanent unemployment rate with a chosen inflation rate.

The US price version, and the menu that was not a promise

In 1960, Paul A. Samuelson and Robert M. Solow redrew the idea for the United States in the American Economic Review, as a link between unemployment and the price level rather than wages alone. Their figure is captioned as a menu of choice between different degrees of unemployment and price stability, roughly estimated from the previous 25 years of American data.

The guesses they printed are specific. To keep wages rising no faster than the 2.5 percent a year they treated as productivity growth, the economy would, on that experience, have to have something like 5 to 6 percent of the civilian labour force unemployed. That, they said, would appear to be the cost of price stability in the years immediately ahead. Their figure marks price stability at about 5.5 percent unemployment. To get unemployment down to 3 percent, they guessed the price index might have to rise by as much as 4 to 5 percent a year. The figure marks that point at about 4.5 percent a year.

The same pages refuse a permanent menu. They said the discussion was about the next few years. It would be wrong to think the figure would keep its shape in the longer run. What policy did next could shift it. A period of weak demand might later move the curve down, through expectations, or it might build up structural unemployment and move the curve the other way. They did not claim to know which. The menu was a short run sketch with a warning label. Later arguments that treated it as a stable policy dial left that warning out.

The expectations augmented equation, in plain language

The version taught since the late 1960s adds one object Phillips had held fixed: what people expect inflation to be. Edmund Phelps, in Economica in 1967, set out a price version of the curve that shifts when expected inflation changes, with expected inflation adjusting gradually toward actual inflation. Milton Friedman made the policy point in The Role of Monetary Policy, the 1968 American Economic Review article from the presidential address he gave in December 1967.

Friedman argued that Phillips had not separated nominal wages from real wages. The original curve, he said, belonged to a world in which people expected stable prices and did not change that expectation when prices actually moved. Once people expect rising prices, wages have to rise with that expectation just to keep real wages unchanged. A curve fitted in a period of stable expected inflation will sit in the wrong place for a period of different expected inflation.

The classroom equation used on this site, and in the Phillips curve calculator, writes that idea as one line.

Inflation is about expected inflation, minus a slope times the gap between the unemployment rate and the natural rate.
inflation = expected inflation, minus slope times (unemployment minus natural rate)

The unemployment gap is the unemployment rate minus the natural rate, in percentage points. A positive slope means higher unemployment, relative to that benchmark, lines up with lower inflation. The calculator asks you to type the slope as a positive number, because the formula already subtracts it. A slope of 0.5 is the calculator's classroom default. It is not a law, and it is not the slope in the FEDS Note discussed below. Say which slope you used.

Friedman put the policy claim in one distinction. There is always a temporary trade off between inflation and unemployment. There is no permanent trade off. The temporary trade off comes from unanticipated inflation, which generally means a rising rate of inflation. A rising rate of inflation may reduce unemployment. A high rate will not.

His illustration is numerical and hypothetical. Suppose the authorities try to hold unemployment at 3 percent when the natural rate is higher than 3 percent, starting from a time of stable prices and higher unemployment. Faster money growth can raise spending. At first, much of that shows up as output and jobs, because prices and wages were set on the expectation of stable prices. Unemployment falls. Then employees notice that real wages are not what they expected, ask for higher nominal wages, and unemployment moves back. To hold unemployment at 3 percent, money growth would have to keep rising. The result is accelerating inflation, not a lasting drop in unemployment.

Where the natural rate and NAIRU enter

In the equation above, set the unemployment gap to zero. Inflation then equals expected inflation. That unemployment rate is the natural rate inside this sketch. Friedman described it as the level ground out by the structure of labour and product markets: frictions, imperfect information about vacancies, and the costs of moving. He was explicit that natural does not mean immutable. Minimum wages and unions could raise it. Better information about jobs could lower it. He also said there was, at that time, no accurate ready way to estimate it, and that it would change.

NAIRU, the unemployment rate consistent with stable inflation, is the close classroom cousin. If expected inflation is simply recent inflation, then inflation stays constant only when unemployment is at the benchmark. Hold unemployment below it and inflation comes in above expectations, expectations rise, and inflation accelerates. That is why the two labels travel together. They are not a published official statistic in the way the monthly unemployment rate is. Estimates differ by method and they get revised. The natural rate of unemployment page is where those estimates, and the myths around them, are set out.

Two other slack ideas are easy to mix up with this gap. The output gap is the percent difference between actual GDP and an estimate of potential output. An unemployment rate below the natural rate and a positive output gap are related stories about an economy running hot. They are not the same number. Okun's law is a rule of thumb from a GDP growth gap to a change in unemployment. It can move the unemployment rate that then enters the Phillips curve. It does not replace the curve. The output gap calculator and the Okun's law calculator are the arithmetic versions of those two steps. Each one tells you which assumption you typed.

A worked example

Example (not advice)

Classroom numbers only. They match the defaults on the Phillips curve calculator for the first case. They are not a BLS print, an ONS print, or an official natural rate. Expected inflation is 2 percent. The natural rate is 4.5 percent. The slope is 0.5. Unemployment is 5.5 percent. The gap is 5.5 minus 4.5, which is 1 percentage point. Inflation is 2 minus 0.5 times 1, which is 1.5 percent. Change unemployment to 3.5 percent. The gap is 3.5 minus 4.5, which is minus 1. Inflation is 2 minus 0.5 times minus 1, which is 2.5 percent. Now let expectations catch up. Expected inflation becomes 2.5 percent, and unemployment returns to 4.5 percent. The gap is zero, so inflation is 2.5 percent. The labour market is back at the same benchmark, and inflation is higher, because expectations moved. That third step is the shift Friedman described. It is not a forecast.

Type your own expected inflation, natural rate, slope, and either unemployment or inflation in the Phillips curve calculator. The arithmetic stays in the browser. It does not download a live series.

Does the curve still work?

The short run link still organises how economists talk about slack and inflation. It does not work as a fixed dial taken from the 1960 chart. Three public records show why.

A flatter slope in ordinary times, and a bend when unemployment is very low. A FEDS Note of 4 September 2024 by Simon C. Smith, Allan Timmermann, and Jonathan H. Wright estimates US price Phillips curves on consumer prices and unemployment for 22 metropolitan areas. The note is staff research. It does not speak for the Board of Governors. They allow a break in the slope, and a kink at five percent unemployment. That threshold is the one that fit their grid search, and it is also a threshold used in earlier Fed research they cite. In ordinary labour markets the slope flattens after a break in 2000, from a significant minus 0.26 in 1980 to 2000 to a still significant minus 0.18 in 2001 to 2022. The extra slope when unemployment is below five percent is larger after 2000 (minus 0.28) than over the full sample (minus 0.19). Their reading is that the curve flattened in normal labour markets and remained steep in a tight one. On state wage data through 2019, the slope after 2000 is minus 0.32 when unemployment is above five percent and minus 0.8 when it is below, which they describe as nearly three times steeper. A price slope of minus 0.18 means that, in their city regression for 2001 to 2022, unemployment one percentage point higher came with inflation about 0.18 percentage points lower in ordinary labour markets, holding lagged inflation and the fixed effects constant. The classroom slope of 0.5 is a steeper teaching number, and the sign is written the other way. The two figures are not substitutes.

The note opens from a question Governor Christopher Waller posed in a March 2023 speech: what happened to the Phillips curve, that it was acting so differently than before the pandemic. The estimate above is one answer on offer. It is not the only one. A slope near zero in a national scatter plot can also appear because a central bank that stabilises inflation removes the very variation a simple regression needs. The note makes that identification point and uses city data partly to get around it.

The 2021 to 2023 surge was only partly a labour market story. A 2025 Finance and Economics Discussion Series paper by Ina Hajdini, Adam Shapiro, A. Lee Smith, and Daniel Villar, Inflation since the Pandemic: Lessons and Challenges, is also staff research, written as background for the Federal Reserve's 2025 strategy review. It says the twelve month change in the PCE price index reached 7.3 percent in the summer of 2022. It says most Phillips curve estimates, even those that allow nonlinearities, suggest labour market tightness can explain only part of the rise in inflation in 2021 and 2022. In the United Kingdom, Huw Pill's April 2023 speech noted that annual CPI inflation was 10.4 percent in February 2023. That speech is a personal view, not a Monetary Policy Committee forecast. The UK figure is the price level, not a claim that the UK slope equals the US slope. The evidence on a nonlinear curve is mixed. Some studies find that tight labour markets explain much of the surge once a bend is allowed. Others find smaller effects, or no bend. It is hard to tell a steeper slope from a curve that shifted. The paper's own summary is that longer term inflation expectations stayed generally well anchored, and that inflation then fell from its peak in the middle of 2022 without a large increase in unemployment. Supply shocks, demand shifts, and a tight labour market were happening together. A single unemployment gap does not pick them apart.

The 1970s already showed the fixed menu failing. In an August 2014 speech, Ben Broadbent, speaking as Deputy Governor for Monetary Policy at the Bank of England, said that in the United Kingdom, despite higher unemployment, CPI inflation and nominal wage growth rose to over 25 percent in 1975. He also said that, at least until the early 1990s, it was hard to make out a Phillips curve even after adjusting wages for inflation expectations. On annual data from 1993 to 2012, unemployment against expectations adjusted wage growth had an R squared of 0.8. The relationship can vanish in one sample and look tidy in another. That is a reason to ask which sample a chart uses.

A curve that bends, and that jumps when expectations jump, can look flat for a decade and steep in a single tight year. Flat in one picture is not the same claim as dead.

What central banks actually use

Neither the Federal Reserve nor the Bank of England sets the policy rate by reading one Phillips curve chart. Both use the underlying question. How much slack is there, what are wages and prices doing, and are inflation expectations still near the goal.

The same April 2023 speech says the Bank of England uses a suite of wage and price models inside the forecast. Those models capture variants of the Phillips curve. Spot wages or prices depend on inflation, inflation expectations, import prices, and measures of economic slack. Import prices sit in the model as their own term. That is the modern echo of Phillips setting aside years when import prices jumped. It is not the same thing as a core inflation statistic, which drops food and energy, or sometimes other volatile items, from the price index after the fact. Core can still move because of rents, wages, or a tax change. Headline can move because of petrol. Know which one a speech means. The Bank's inflation target is 2 percent on CPI. The Federal Reserve's longer run goal is 2 percent on PCE. Those are different indexes, covered in CPI versus PCE.

A different classroom object, the Taylor rule, maps an inflation gap and an output gap into a suggested policy rate. It is not a Phillips curve. The Phillips curve is one way to think about where inflation comes from. The Taylor rule is one way to think about how a policy rate might respond. The Taylor rule calculator shows that second piece of arithmetic with numbers you type. Nothing on this page recommends a policy setting, a trade, or a portfolio.

UK and US data habits

Do not paste a US slope onto UK unemployment and call the result a fact. Institutions, price indexes, and the meaning of slack differ. Samuelson and Solow already treated the UK wage curve and the US price curve as related but not identical.

For a UK reading, start with the ONS unemployment release and the ONS inflation and price indices release. The usual companions are the Labour Force Survey unemployment rate, average weekly earnings, CPI, and CPIH. For a US reading, start with the BLS Current Population Survey for the unemployment rate and the BLS Consumer Price Index. PCE is the index in the Federal Reserve goal. FRED series UNRATE is the usual civilian unemployment rate chart. This page does not reprint a live level. Open the release dated for the month you care about. The data guides on this site are about how to read those releases, not a substitute for them.

Country context sits on the United Kingdom and United States pages. The topic pages for unemployment, inflation, and monetary and fiscal policy are the wider map. Short definitions are in the glossary under Phillips curve, natural rate, and inflation.

Misreadings that still circulate

  • Higher inflation permanently buys lower unemployment. In the expectations augmented equation, that bargain lasts only while inflation is surprising people. Once expectations catch up, unemployment is back at the natural rate and inflation is higher.
  • A scatter plot is a menu. Supply shocks can raise inflation and unemployment together. The 1975 UK outcome Broadbent cited is that pattern. A demand only curve slopes the other way, so the cloud of points is not a set of choices. On the aggregate demand and aggregate supply graph, that supply shock is a left shift of short run aggregate supply. A demand shock moves along short run aggregate supply instead.
  • One inflation measure, one slack measure, one sample. Wages, headline prices, and core prices can disagree in the same month. Unemployment, vacancies, and an output gap can disagree too. A slope from 1861 to 1913, a slope from 1993 to 2012, and a slope from a tight year after 2021 are answers to different questions.
  • Flat means finished. The 2024 FEDS Note finds a flatter slope in ordinary US labour markets after 2000 and a much steeper wage slope below five percent unemployment. Flat on a national chart of calm years does not tell you the slope in a very tight labour market.

When someone waves a Phillips curve chart, ask four things. Which inflation measure. Which slack measure. Which sample. Whether expectations are assumed to be anchored. Those four questions separate a classroom cartoon from a claim you can check against ONS, BLS, the Bank of England, or the Federal Reserve.

Common questions

What is the Phillips curve?

The Phillips curve is the short run pattern linking unemployment and inflation. Tighter labour markets tend to come with faster wage and price inflation. Higher unemployment tends to come with slower inflation. A. W. Phillips documented a wage version of that pattern for the United Kingdom from 1861 to 1957. Later US work redrew it as a link between unemployment and price inflation. It is a teaching and policy idea, not a law, and it is not investment advice.

Does the Phillips curve still work?

It still organises the short run, and it does not offer a fixed menu of inflation and unemployment pairs. A September 2024 Federal Reserve FEDS Note, which is staff research and not an official Board conclusion, finds that in US city price data the curve flattened after 2000 in ordinary labour markets but stayed steep when unemployment was below five percent. A 2025 Federal Reserve staff paper finds that US PCE inflation reached 7.3 percent in the summer of 2022, and that labour market tightness explains only part of the 2021 and 2022 rise even when estimates allow a nonlinear curve. The Bank of England still uses Phillips curve variants in its forecasting models, alongside expectations, import prices, and slack. Read any slope as something that can change with the sample, the inflation measure, and how tight the labour market already is.

What is the expectations augmented Phillips curve?

It is the version that adds expected inflation. In the classroom form used on this site, inflation is about expected inflation minus a slope times the gap between the unemployment rate and the natural rate. When unemployment equals the natural rate, inflation equals expected inflation. If unemployment is lower than the natural rate, inflation comes in above what people expected, and expectations can rise, so the short run curve shifts up. Milton Friedman set out that logic in his 1968 American Economic Review article, from the presidential address he gave in December 1967. Edmund Phelps set out a related price curve that shifts with expected inflation in Economica in 1967. The Phillips curve calculator on this site uses the same classroom form. The numbers you type are assumptions, not a forecast.

How does the Phillips curve relate to the natural rate and to NAIRU?

The natural rate is the unemployment benchmark in the expectations augmented equation. At that rate the unemployment gap is zero, so inflation matches expectations. If expectations follow recent inflation, inflation is stable only at that benchmark. That is the usual classroom meaning of NAIRU, the unemployment rate consistent with stable inflation. Friedman argued there is a temporary trade off between inflation and unemployment and no permanent one. Holding unemployment below the natural rate, in that account, takes inflation that keeps rising. The natural rate is an estimate, not a statistic a statistical agency publishes like the monthly unemployment rate, and it can move. A separate page on this site explains how to read those estimates.

Why did high inflation and high unemployment happen together in the 1970s?

A single downward sloping curve fitted in quieter times cannot put high inflation and high unemployment on the same point. The expectations augmented version can. If expected inflation rises, the whole short run curve shifts up, so a given unemployment rate comes with faster inflation than before. In an August 2014 Bank of England speech, Ben Broadbent noted that in the United Kingdom, despite higher unemployment, CPI inflation and nominal wage growth rose to over 25 percent in 1975. That episode is why a scatter plot from one era is not a policy menu for the next.

Are the UK and US Phillips curves the same?

No. Phillips fitted UK wage changes and UK unemployment. Samuelson and Solow drew a US price version and treated it as a short run menu, while warning that the menu could shift. Today the Bank of England targets 2 percent CPI. The Federal Reserve states a longer run goal of 2 percent PCE inflation. UK readers usually pair ONS unemployment and average weekly earnings with CPI or CPIH. US readers usually pair the BLS unemployment rate with CPI or with PCE, including core PCE. A slope estimated on one country's data is not a fact about the other. Open the current ONS or BLS release before treating any chart as the latest print.

Sources