The Phillips curve
The trade-off between inflation and unemployment is real, temporary, and dissolves the moment you try to live on it.
1 — The puzzle
A country fears two diseases: rising prices and people without work. For about thirty years after 1958, it seemed there was a medicine cabinet with one shelf — treat one disease and the other worsens, so simply choose your poison.
Then the 1970s arrived and both struck at once. The cure had stopped working.
Why should the two be linked at all? A jobless carpenter and the price of rice seem to belong to different worlds.
2 — The story
Think of a small town with one factory. In a bad year fifty people queue for every opening. The owner offers a low wage and still fills the post — where else would anyone go?
Now a good year. Three new workshops open. The same owner advertises and nobody comes; his best welder has already been poached. To keep him, he raises the wage. That higher wage is a higher cost, and the factory’s prices creep up.
Tight labour market → higher wages → higher prices. Slack labour market → the reverse. The link between the two diseases runs through the wage.
3 — The intuition
Unemployment is a measure of bargaining power. When jobs are scarce, workers accept what they are given. When workers are scarce, they ask — and get.
So unemployment is a thermometer for how hot the economy runs, wages are what the thermometer is attached to, and inflation is the reading.
But here is the turn in the story, and it is the whole thing: what workers ask for depends on what they expect prices to do. A 10% raise is a victory if prices are flat and a defeat if prices rise 12%. Once people learn to expect inflation they build it into their demand before they sit down to bargain — and the old relationship dissolves.
4 — The theory
A. W. Phillips (1958) plotted the rate of change of British money wages against unemployment, fitting his curve to the years 1861–1913 and then showing that the decades after it lay close to the same line. Note what he measured: wage inflation, not price inflation. The move to prices came later, and it is not innocent — it quietly assumes a stable mark-up of prices over wages.
Samuelson and Solow (1960) drew the American version and described it as a menu of choices. They are often blamed for selling a permanent trade-off, and that charge is unfair: in the same paper they warned that the menu would not keep its shape, and that policy itself could move it. The myth is more famous than the caveat.
Phelps (1967) and Friedman (1968), working independently, said why. The trade-off exists only while inflation is unexpected. Push unemployment below its natural rate and you buy a temporary boom at the price of permanently higher inflation — and once expectations catch up you are back at the same unemployment, worse off. This is the natural rate hypothesis. They made the argument before the stagflation that confirmed it, which is as close to a prediction as macroeconomics usually gets.
Lucas (1976) sharpened the knife. The historical curve was never a structural law; it was a pattern produced by one particular policy regime. Exploit it and you change the behaviour that generated it. This is the Lucas critique, and it is far larger than the Phillips curve.
5 — The mathematics
The expectations-augmented form:
\[\pi_t \;=\; \pi_t^e \;-\; \alpha\,(u_t - u^{*}) \;+\; \varepsilon_t\]where $\pi_t$ is inflation, $\pi_t^e$ is the inflation people expect, $(u_t - u^{*})$ is the unemployment gap, $\alpha > 0$ measures how hard slack presses on prices, and $\varepsilon_t$ collects supply shocks — oil, food, war, freight.
Read the line slowly and the whole debate is inside it.
Set $u_t = u^{*}$ and you get $\pi_t = \pi_t^e$. At the natural rate, inflation simply equals whatever people expect. The natural rate is where inflation stops accelerating, not where it stops.
Now suppose expectations are adaptive, $\pi_t^e = \pi_{t-1}$:
\[\pi_t - \pi_{t-1} \;=\; -\alpha\,(u_t - u^{*})\]The trade-off is no longer between inflation and unemployment. It is between the change in inflation and unemployment. To hold unemployment below $u^{*}$ forever, inflation must rise forever. This is the accelerationist result, and it is why there is no standing menu.
6 — The picture
7 — The confusion
“The Phillips curve is dead.” The stable long-run menu is dead. The short-run relationship is alive and sits at the centre of every central bank’s working model.
“The natural rate is natural.” It moves — with demographics, labour law, union density, the technology of matching workers to jobs. It is also estimated with uncertainty often near a full percentage point, which in a large economy is millions of people. Policy is being set against a number nobody can see.
Natural rate and NAIRU are not quite the same thing. Friedman’s natural rate is a theoretical construct: the unemployment that would prevail once all expectations were correct. The NAIRU is a statistical object: the rate at which inflation happens not to be accelerating. They are used interchangeably and they are not interchangeable.
“A flat curve means no trade-off.” The curve has flattened since the 1990s, and that cuts both ways. Booms generate little inflation — but recessions also generate little disinflation. Cheap to run hot, expensive to cool down.
Mistaking the direction of causation. The equation does not say unemployment causes inflation. Both are responses to the same underlying pressure of demand against capacity.
Forgetting $\varepsilon$. In 1973 and 1979, oil moved inflation with no change in labour-market slack to explain it. A supply shock shifts prices without touching the gap at all.
Reading 2021–22 as a pure supply shock. It was not. Supply disruption was large, but American labour markets were also exceptionally tight — roughly two vacancies per unemployed worker, the highest on record. That episode revived an older idea: that the curve is non-linear, nearly flat while there is slack and steep once the economy is pressed against its limit. If that is right, the flat decade was not a new law. It was the shape of the curve at low pressure.
8 — Why it matters
This single equation is why central banks became independent. If the trade-off is temporary but the inflation is permanent, a politician facing an election has every reason to exploit it and leave the bill to a successor. The institutional answer was to take the lever out of the politician’s hand — the time-inconsistency argument of Kydland and Prescott (1977), and of Barro and Gordon (1983).
It is also why central banks are preoccupied with expectations. In the equation $\pi^e$ is not a forecast. It is a cause. Anchoring it is not communications strategy; it is monetary policy.
And it explains Volcker. To break American inflation after 1979 he had to make $(u - u^{})$ large and hold it there until expectations gave way. Unemployment reached 10.8% in late 1982, the worst since the Depression. The equation says that pain was not a failure of the policy. It *was the policy.
The Nobel committee has recognised this line of argument four times: Friedman (1976), Lucas (1995), Kydland and Prescott (2004), Phelps (2006).
9 — The challenge
Take $\pi_t^e = \pi_{t-1}$, $\alpha = 0.5$, $u^{*} = 5\%$, and inflation last year of 4%.
(a) A government holds unemployment at 3% for four years. Trace inflation year by year. What does the cheap boom of year one cost by year four?
(b) Now you must return inflation to 4%. You can push unemployment to 9%. How many years does it take? Multiply the gap by the years and divide by the fall in inflation: economists call that the sacrifice ratio. Compare what the boom bought with what the cure costs.
(c) Now the hard one. Replace adaptive expectations with rational ones, so that $\pi_t^e$ equals the inflation your announced policy will actually deliver — and suppose people believe you. What is the sacrifice ratio now?
Then ask the question that is the real examination: if (c) is right, why did Volcker’s disinflation cost so much? Your answer to that is your answer to whether credibility is something a central bank can announce, or something it can only earn.
Don’t just learn the concept. Learn to think with it.