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Intermediate Macroeconomics Unit 9: The Phillips Curve and Expectations

The Phillips curve links inflation to unemployment in the short run. This unit shows how expectations make the tradeoff temporary and why disinflation is costly unless policy is credible.

Covers: The expectations-augmented Phillips curve, Adaptive expectations and inflation inertia, Demand-pull and cost-push inflation, The long-run Phillips curve and NAIRU, Disinflation and the sacrifice ratio, Rational expectations and credibility

Study guide

The modern Phillips curve says inflation depends on three things: π = πᵉ − β(u − uⁿ) + v. Expected inflation πᵉ sets the baseline. Cyclical unemployment u − uⁿ captures demand: when unemployment is below its natural rate, demand-pull pressure pushes inflation up. The supply shock term v captures cost-push inflation, such as an oil price spike. The Phillips curve is another way of writing short-run aggregate supply: subtracting last year's price level from SRAS turns price levels into inflation, and Okun's law replaces the output gap with cyclical unemployment.

How expectations are formed matters. Under adaptive expectations, πᵉ = π₋₁, so inflation has inertia: it continues at its current rate unless unemployment departs from the natural rate or a supply shock hits. Holding unemployment below the natural rate requires ever-rising inflation, which is why the natural rate is also called NAIRU, the non-accelerating inflation rate of unemployment. Milton Friedman and Edmund Phelps argued in the late 1960s that there is no long-run tradeoff: once expectations catch up, unemployment returns to its natural rate at any inflation rate. The long-run Phillips curve is vertical, and the stagflation of the 1970s, when supply shocks and rising expectations shifted the short-run curve up, supported their view.

In the short run, though, there is a tradeoff. Lowering inflation under adaptive expectations requires a period of unemployment above the natural rate. The sacrifice ratio measures the cost: the percentage of a year's GDP lost per point of inflation reduction. Combining the Phillips curve slope β with Okun's coefficient gives the ratio directly: each point of inflation reduction needs 1/β point-years of cyclical unemployment, each costing about 2% of GDP. Estimates around 5 implied that the Volcker disinflation of the early 1980s would be very costly; the actual cost was large but smaller than predicted.

Rational expectations offer a different view. If people use all available information, including announced policies, then a credible disinflation plan lowers πᵉ directly, and inflation can fall without much unemployment. Credibility therefore lowers the sacrifice ratio, which is one reason central banks adopt inflation targets and value independence. The Lucas critique warns that estimated relationships such as the sacrifice ratio depend on past policy and may change when policy changes. Kydland and Prescott's time-inconsistency argument shows why a discretionary central bank tempted to create surprise inflation ends up with high inflation and no lower unemployment.

Two further ideas complicate the picture. Hysteresis suggests that long recessions can raise the natural rate itself, as unemployed workers lose skills, which makes disinflation more costly than the sacrifice ratio suggests. Favorable supply shocks and changes in the natural rate, as in the late 1990s, can let unemployment fall without rising inflation. In recent decades, firmly anchored expectations have made the short-run Phillips curve flatter and inflation less persistent: supply shocks raise inflation temporarily, but it returns to target without a recession if expectations stay put.

Key ideas

• Inflation depends on expected inflation, cyclical unemployment and supply shocks.
• With adaptive expectations, inflation is persistent and NAIRU is the only steady-inflation unemployment rate.
• The long-run Phillips curve is vertical at the natural rate.
• Disinflation costs output; the sacrifice ratio measures how much.
• Sacrifice ratio = Okun coefficient ÷ Phillips curve slope β.
• Credible policy can lower expected inflation directly and make disinflation cheaper.
• Hysteresis and time inconsistency affect the real costs and outcomes of policy.

Formulas and rules

Common mistakes

• Writing the Phillips curve with a plus sign on u − uⁿ.
• Assuming inflation returns to its old level after unemployment returns to normal under adaptive expectations.
• Thinking the long-run Phillips curve offers a permanent tradeoff.
• Confusing demand-pull inflation (low u) with cost-push inflation (supply shocks).
• Assuming an announced disinflation is painless even when it is not credible.

Before the test, make sure you can

• Calculate inflation from the expectations-augmented Phillips curve.
• Trace inflation paths year by year under adaptive expectations.
• Explain why the long-run Phillips curve is vertical and why NAIRU means non-accelerating inflation.
• Compute the sacrifice ratio from β and Okun's coefficient and the cost of a disinflation.
• Distinguish demand-pull and cost-push inflation and analyze supply shocks.
• Explain how rational expectations and credibility change the cost of disinflation.
• Explain the Lucas critique, time inconsistency and hysteresis.

Words to know

Phillips curve

The short-run negative relationship between inflation and unemployment.

Expectations-augmented Phillips curve

π = πᵉ − β(u − uⁿ) + v.

Adaptive expectations

Expectations based on past inflation, such as πᵉ = π₋₁.

Rational expectations

Expectations that use all available information, including policy announcements.

Inflation inertia

The tendency of inflation to persist because expectations are based on past inflation.

Demand-pull inflation

Inflation caused by high demand pushing unemployment below the natural rate.

Cost-push inflation

Inflation caused by adverse supply shocks that raise costs.

NAIRU

Non-accelerating inflation rate of unemployment; the natural rate in the Phillips curve.

Long-run Phillips curve

A vertical line at the natural rate: no long-run tradeoff.

Disinflation

A reduction in the rate of inflation.

Sacrifice ratio

Percent of a year's real GDP lost per point of inflation reduction.

Credibility

The extent to which people believe a central bank's announcements.

Painless disinflation

The rational-expectations idea that credible policy can lower inflation without a recession.

Lucas critique

Estimated relationships may change when policy changes because expectations change.

Time inconsistency

The incentive to deviate from an announced policy once expectations are set.

Hysteresis

The idea that past unemployment can raise the natural rate.

Sample practice questions

30 more questions like these, from level 1 to 5, are in the practice set.