Macroeconomics guide, Unit 5, step 15 of 23Previous step Next step

Step 15: The Phillips Curve and Expectations

By the EconTutorials team. 10-minute read with 6 practice questions.

SyllabusAP Macro 5.1–5.2 · Cambridge 10.2 · IB 3.3

In 30 seconds

In the short run there is a trade-off: lower unemployment comes with higher inflation. This is the short-run Phillips curve (SRPC).
The trade-off works only when inflation is higher than people expected. The expectations-augmented Phillips curve is \( \pi = \pi^e – \beta(u – u_n) + v \).
In the long run, when \( \pi = \pi^e \), unemployment returns to its natural rate whatever the inflation rate, so the long-run Phillips curve (LRPC) is vertical.
Exam point: a change in AD moves the economy along the SRPC; a change in expected inflation shifts the whole SRPC.

Video lesson coming soonA short animated lesson for this step will appear here.

The original Phillips curve

Picture the job market in a busy year. Cafés, shops and offices are all hiring, so workers can ask for bigger pay rises, and employers pass the higher costs on in prices. In a slow year, people are queuing for jobs, pay rises are small, and prices rise slowly. Low unemployment seems to go with fast-rising wages and prices; high unemployment with slow-rising ones.

In 1958 A. W. Phillips found exactly this in UK data from 1861 to 1957: a stable negative relationship between unemployment and the rate of change of money wages. In 1960 Paul Samuelson and Robert Solow restated it in terms of price inflation and described it as a menu of choices for policymakers. A government that wanted unemployment of 4% instead of 6% could, it seemed, simply accept 5% inflation instead of 2%.

You already have this relationship in the AD/AS model. Shift AD right: along an upward-sloping SRAS, prices rise and output rises. More output means more hiring, so unemployment falls. Inflation up, unemployment down. The Phillips curve is the AD/AS diagram redrawn with inflation on the vertical axis and unemployment on the horizontal.

Key termShort-run Phillips curve (SRPC): the downward-sloping trade-off between inflation and unemployment available for a given level of expected inflation.

Why the short-run trade-off exists

Nominal wages are agreed in advance, in contracts, based on the inflation people expect. Suppose workers expect 2% inflation and accept a 2% pay rise. If inflation turns out to be 5%, their real wage (the wage adjusted for prices) is lower than they planned. Labour is cheaper than firms expected, so firms hire more and produce more, and unemployment falls below its natural rate.

Notice what this needs: inflation must be higher than expected. It is the surprise that does the work. If everyone correctly expects 5% inflation, wage deals build it in, the real wage does not change, and employment does not change either. This simple point is what destroyed the policy menu.

The expectations-augmented Phillips curve

In 1967 to 1968, Milton Friedman and, independently, Edmund Phelps argued that there is no permanent trade-off. The SRPC is drawn for a given expected inflation rate, and expectations adjust. They wrote this before the data changed, and were later proved right.

\[ \pi = \pi^e – \beta(u – u_n) + v \]

\(\pi\): actual inflation. \(\pi^e\): expected inflation, which decides which SRPC the economy is on.
\(u\): actual unemployment. \(u_n\): the natural rate of unemployment.
\(\beta\): how strongly inflation responds to the unemployment gap (the slope of the SRPC).
\(v\): a supply shock term, positive for an adverse shock such as an oil price rise.

The key result: set \(\pi = \pi^e\) and \(v = 0\). Then \(0 = -\beta(u – u_n)\), so \(u = u_n\). Once expectations catch up, unemployment is at the natural rate whatever the inflation rate. The long-run Phillips curve is vertical at \(u_n\), for the same reason LRAS is vertical: in the long run, nothing real depends on a nominal variable.

Worked example

Expected inflation is 3%, the natural rate of unemployment is 5%, \(\beta = 0.5\) and there is no supply shock. The government pushes unemployment down to 3%. What is inflation? If expectations then adjust to that rate, what inflation is needed to hold unemployment at 3% next period?

Step 1\( \pi = 3 – 0.5(3 – 5) + 0 = 3 – 0.5(-2) = 3 + 1 = 4\% \)

Step 2Workers now expect 4%, so \( \pi^e = 4 \). The whole SRPC shifts up by 1 point.

Step 3\( \pi = 4 – 0.5(3 – 5) = 4 + 1 = 5\% \)

Holding unemployment 2 points below the natural rate costs 4% inflation in the first period and 5% in the next, and it keeps rising by 1 point each period. Inflation has to keep accelerating to keep the surprise going.

Exam tipThe SRPC is drawn for a given \(\pi^e\). A change in AD moves the economy along the SRPC. A rise in expected inflation shifts the whole SRPC upward. Mixing these up is the same error as mixing up a shift of AD with a movement along it, and it is penalised just as heavily.

The accelerationist hypothesis

Suppose a government insists on 4% unemployment when the natural rate is 6%. The chapter traces the path:

Point A: unemployment is at 6% with actual and expected inflation both 2%.
Point B: the government boosts demand. Unemployment falls to 4% and inflation rises to 5%. Workers expected 2%, so real wages fall and firms hire.
Point C: workers now expect 5%. The SRPC shifts up, wage demands rise, real wages are restored, and unemployment returns to 6%, now with 5% inflation. Nothing has been gained.
Points D and E: to get 4% unemployment again, inflation must beat the new expectation, rising to 8%. Expectations catch up again, and unemployment returns to 6% at 8% inflation.

The only way to keep unemployment permanently below the natural rate is to keep inflation permanently accelerating. That is why the natural rate is also called the NAIRU: the non-accelerating inflation rate of unemployment.

Key termNAIRU: the non-accelerating inflation rate of unemployment, the rate at which inflation is stable; in practice the same as the natural rate.

How expectations are formed decides how long the short run lasts.

	Adaptive expectations	Rational expectations
How people form expectations	By looking back at past inflation	Using all available information, including how policy works
Can policy surprise people?	Yes, for a while, until expectations catch up	Not if the policy is announced or systematic
Cost of bringing inflation down	Large: a recession is needed	Can be small if the announcement is believed

Robert Lucas developed rational expectations in the 1970s. Its strong form, the policy ineffectiveness proposition, says only unanticipated policy has real effects.

Common mistakeSaying that holding unemployment below the natural rate needs “high” inflation. It needs rising inflation. A constant high inflation rate soon becomes expected, and then unemployment drifts back to the natural rate.

Credibility and the cost of disinflation

The sacrifice ratio is the cumulative percentage of a year’s output given up for each percentage point of inflation removed. Under adaptive expectations it is large: expected inflation only falls after actual inflation falls, and that only happens after unemployment has stayed above the natural rate for a while. The recession is not a side effect; it is the mechanism.

Under rational expectations, if the central bank credibly announces a lower target and people believe it, \(\pi^e\) falls at once. The SRPC shifts down and inflation can fall without unemployment rising. Thomas Sargent found that four hyperinflations of the 1920s (Austria, Hungary, Poland and Germany) ended within weeks after credible reforms, without long depressions.

Using the equation: if \(\pi^e\) is 6% and the target is 2%, a believed announcement brings \(\pi^e\) to 2% and \(u\) can stay at \(u_n\). If it is not believed, the bank must create \(\pi – \pi^e = -4\), which needs unemployment \(\frac{4}{\beta}\) points above the natural rate. The recession is the price of disbelief. This is why independent central banks with public inflation targets matter.

Supply shocks and the 1970s breakdown

An adverse supply shock, such as the 1973 oil embargo or the 2022 energy crisis, raises \(v\) and shifts the SRPC up. Inflation and unemployment rise together, so the data stop tracing a downward-sloping curve.

That is what happened in the US. In the 1960s the points sat neatly on a Phillips curve: inflation drifted from 1% to 5% as unemployment fell from 6.7% to 3.5%. From 1970 they spiralled up and to the right: 9.1% inflation with 8.5% unemployment in 1975, and 13.5% with 7.1% in 1980. Rising expectations and oil shocks both pushed the curve up. After 2010 the curve looked flat, but the chapter argues this was because expectations were firmly anchored at about 2%, not because the trade-off had vanished. In 2021 inflation reached 9.1%, then fell back quickly because expectations stayed anchored.

Practise: 6 questions

Try each one on paper first, then check the worked answer.

EasyQ1. Using \( \pi = \pi^e – \beta(u – u_n) + v \): \(\pi^e = 3\%\), \(\beta = 0.5\), \(u_n = 5\%\), \(u = 3\%\), \(v = 0\). Find inflation. Show worked answer

\( \pi = 3 – 0.5(3 – 5) + 0 = 3 – 0.5(-2) = 3 + 1 = 4\% \).
Unemployment is 2 points below the natural rate, so inflation is 1 point above expectations.

EasyQ2. State whether each causes a movement along the SRPC or a shift of it: (a) a rise in government spending, (b) a rise in expected inflation, (c) a sharp rise in oil prices. Show worked answer

(a) Movement along: it is a change in AD.
(b) Shift up: the SRPC is drawn for a given \(\pi^e\).
(c) Shift up: an adverse supply shock raises \(v\), so inflation and unemployment can both rise.

MediumQ3. \( \pi = \pi^e – 0.5(u – 5) + v \). Initially \(\pi^e = 2\%\), \(u = 5\%\), \(v = 0\). (a) Find inflation. (b) Demand rises and unemployment falls to 3%. Find inflation. (c) If \(\pi^e\) adjusts to that rate, what inflation keeps \(u\) at 3%? Show worked answer

(a) \( \pi = 2 – 0.5(0) = 2\% \): actual equals expected, so \(u = u_n\).
(b) \( \pi = 2 – 0.5(3 – 5) = 2 + 1 = 3\% \).
(c) \( \pi^e = 3 \), so \( \pi = 3 – 0.5(3 – 5) = 3 + 1 = 4\% \). Inflation must keep rising by 1 point a period: the accelerationist result.

MediumQ4. \(u_n = 6\%\), \(\beta = 1\), \(v = 0\). Expected inflation is 8% and the central bank wants 2% inflation. How high must unemployment go if the announcement is not believed? What if it is believed? Show worked answer

Not believed: \(\pi^e\) stays at 8%. We need \( 2 = 8 – 1(u – 6) \), so \( u – 6 = 6 \) and \( u = 12\% \).
Believed: \(\pi^e\) falls to 2%, so \( 2 = 2 – 1(u – 6) \) gives \( u = 6\% \). Unemployment stays at the natural rate.
Credibility saves 6 percentage points of unemployment.

MediumQ5. An oil shock adds \(v = 2\). With \(\pi^e = 2\%\), \(\beta = 0.5\), \(u_n = 5\%\), what is inflation if unemployment stays at 5%? What if the shock also pushes unemployment to 7%? Show worked answer

At \(u = 5\): \( \pi = 2 – 0.5(0) + 2 = 4\% \).
At \(u = 7\): \( \pi = 2 – 0.5(7 – 5) + 2 = 2 – 1 + 2 = 3\% \).
Compared with the starting point (2% inflation, 5% unemployment), inflation and unemployment have both risen: stagflation, which the old fixed curve cannot show.

ExamQ6. Using a Phillips curve diagram, explain why there is no long-run trade-off between inflation and unemployment. [6 marks] Show worked answer

Diagram (2): inflation on the vertical axis, unemployment on the horizontal; a vertical LRPC at \(u_n\); SRPC1 for \(\pi^e = 2\%\) and a higher SRPC2 for a higher \(\pi^e\); arrows showing a move along SRPC1 then back to the LRPC on SRPC2.
Short run (2): wages are set on expected inflation (1). Higher demand raises inflation above expectations, real wages fall, firms hire and unemployment falls below \(u_n\) along SRPC1 (1).
Long run (2): workers revise \(\pi^e\) upward, so the SRPC shifts up and real wages are restored, returning unemployment to \(u_n\) at higher inflation (1). With \(\pi = \pi^e\), the equation gives \(u = u_n\) at any inflation rate, so the LRPC is vertical; keeping \(u\) below \(u_n\) needs accelerating inflation (1).

Check yourself

1. A rise in expected inflation will:

The SRPC is drawn for a given expected inflation rate, so a change in it shifts the curve.

2. The long-run Phillips curve is vertical because:

Setting \(\pi = \pi^e\) forces \(u = u_n\).

3. Under rational expectations with a fully credible central bank, an announced disinflation would:

A believed announcement shifts the SRPC down immediately.

Your score: 0 out of 3

The short version

Phillips (1958) found that low unemployment went with fast wage growth; it was later treated as a policy menu.
The short-run trade-off exists only because inflation can surprise people whose wages are set on expected inflation.
\( \pi = \pi^e – \beta(u – u_n) + v \). When \(\pi = \pi^e\), \(u = u_n\): the long-run Phillips curve is vertical.
Holding unemployment below the natural rate (the NAIRU) needs ever-accelerating inflation.
Credibility makes disinflation cheap; supply shocks shift the SRPC up and produce stagflation, as in the 1970s.

This guide covers the core of Chapter 29 of Economics Made Simple. For the full chapter, with the case study on the curve from 1958 to 2023 and 15 exam-style questions with a complete answer key, see the book.