INFLATION AND

UNEMPLOYMENT: THE

PHILLIPS CURVE

Dongpeng Liu

Department of Economics

Nanjing University

ROADMAP

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INCOME

EXPENDITURE

LIQUIDITY

PREFERENCE

IS

CURVE

LM

CURVE

AGGREGATE

DEMAND

SHORT-RUN

LABOR

MARKET

AGGREGATE

SUPPLY

AS-AD

MODEL

IS-LM

MODEL

PHILLIPS

CURVE

INTERMEDIATE-RUN

SOLOW

MODEL

LONG-RUN w/

CAPITAL

ACCUMULATION

LONG-RUN

AS-AD

MODEL

LONG-RUN w/o

CAPITAL

ACCUMULATION

THE AS-AD MODEL

William Phillips published a paper in 1958 describing the

inverse relationship between unemployment rate and growth rate

of nominal wage in Great Britain from 1861 to 1957.

Similar patterns were found in the US. In 1960, Paul Samuelson

and Robert Solow took Phillips’ work and made explicit the link

between inflation and unemployment: when inflation was high,

unemployment was low, and vice versa.

The inverse relationship between rates of unemployment and

corresponding rates of inflation is called the Phillips curve.

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INFLATION AND UNEMPLOYMENT

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DEDUCTION OF THE PHILLIPS CURVE

𝑃𝑡 = 𝑃𝑡𝑒 1 + 𝜇 𝐹 𝑢𝑡, 𝑧 = 𝑃𝑡

𝑒 1 + 𝜇 1 − 𝛼𝑢𝑡 + 𝑧

𝑃𝑡

𝑃𝑡−1=

𝑃𝑡𝑒

𝑃𝑡−11 + 𝜇 1 − 𝛼𝑢𝑡 + 𝑧

1 + 𝜋𝑡 = (1 + 𝜋𝑡𝑒) 1 + 𝜇 1 − 𝛼𝑢𝑡 + 𝑧

1+𝜋𝑡

(1+𝜋𝑡𝑒) 1+𝜇

= 1 − 𝛼𝑢𝑡 + 𝑧 ≈ 1 + 𝜋𝑡 − 𝜋𝑡𝑒 − 𝜇

𝜋𝑡 = 𝜋𝑡𝑒 + 𝜇 + 𝑧 − 𝛼𝑢𝑡

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THE PHILLIPS CURVE

Phillips curve: 𝜋𝑡 = 𝜋𝑡𝑒 + 𝜇 + 𝑧 − 𝛼𝑢𝑡

Expected inflation can cause actual inflation

Given the expected inflation rate, higher unemployment rate

implies lower inflation rate

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PHILLIPS CURVE

Since 1970s,

economists found

that the

relationship between

unemployment and

inflation seemingly

disappeared

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THE PHILLIPS CURVE

Phillips curve: 𝜋𝑡 = 𝜋𝑡𝑒 + 𝜇 + 𝑧 − 𝛼𝑢𝑡

An increase in expected inflation rate will shift the Phillips

curve upwards

Before 1960s, inflation rate in the US maintained in a very low

level. The expected inflation rate was close to 0.

As a result, the position of the Phillips curve itself was

stable over time.

Due to stagflation and the expansionary monetary policies in

response of the stagflation after 1960s, inflation rate became

consistently positive and expected inflation continuously grew

The Phillips curve continuously shifts. What we saw in the last

figure is a set of short-run Phillips curves.

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THE PHILLIPS CURVE AND NATURAL RATE OF

UNEMPLOYMENT

Phillips curve: 𝜋𝑡 = 𝜋𝑡𝑒 + 𝜇 + 𝑧 − 𝛼𝑢𝑡

When expected inflation rate equals actual inflation rate,

expected price level must equal actual price level

Note: The Phillips curve is derived from the wage setting

relation and the price setting relation

According to the definition of natural unemployment rate, at

that time

𝑢𝑡 = 𝑢𝑛 =𝜇 + 𝑧

𝛼

𝜋𝑡 − 𝜋𝑡𝑒 = 𝜇 + 𝑧 − 𝛼𝑢𝑡 = −𝛼(𝑢𝑡 − 𝑢𝑛)

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MODIFIED PHILLIPS CURVE

Assume that the expected inflation rate equals the inflation

rate in the last period

𝜋𝑡𝑒 = 𝜋𝑡−1

Modified Phillips curve

𝜋𝑡 − 𝜋𝑡−1 = 𝜇 + 𝑧 − 𝛼𝑢𝑡 = −𝛼(𝑢𝑡 − 𝑢𝑛)

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MODIFIED PHILLIPS CURVE

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NAIRU

According to the modified Phillips curve, when 𝑢𝑡 = 𝑢𝑛 =𝜇+𝑧

𝛼，

𝜋𝑡 = 𝜋𝑡−1

When unemployment rate is lower than the natural rate, there is

accelerating inflation (inflation rate rises). When

unemployment rate is higher than the natural rate, there is

decelerating inflation (inflation rate drops).

Hence, the natural rate of inflation is also called Non-

accelerating inflation rate of unemployment (NAIRU)

Central banks cannot keep inflation at a low rate while

simultaneously maintain unemployment below its natural rate

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DISINFLATION AND THE CREDITABILITY OF CENTRAL

BANKS

Central banks’ efforts to reduce inflation rate is called disinflation.

Given the modified Phillips curve, disinflation can be painful. Unemployment needs to be kept above its natural rate for a period of time.

However, if promises of the central bank is credible (people believe the what the central bank says), disinflation can be painless.

The central bank can announce its target inflation rate and guarantees the target shall be achieved regardless of the cost

𝜋𝑡 − 𝜋𝑡𝑒 = 𝜇 + 𝑧 − 𝛼𝑢𝑡 = −𝛼(𝑢𝑡 − 𝑢𝑛)

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Summary

The Phillips curve

Modified Phillips curve

Non-accelerating inflation rate of unemployment

Disinflation

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