The Phillips curve, in its first iteration, described the relationship between inflation and unemployment.  This relationship held true until the 1970s, where it broke down.  It was reborn as a relationship between changes in inflation compared to unemployment.

The original Phillips curve

The original Phillips curve

Inflation and unemployment

Starting with the basic AS curve in terms of unemployment:

P = (1+μ)PeF(u, z)

The function F captures the effects on the wage on unemployment rates.  μ is the markup value (typically less than 1).  A specific form of F can be:

F(u, z) = 1 − αu + z, α > 0

The function α gives the strength of the relationship between unemployment and wages (higher unemployment leads to lower wages).  This leads to:

P = (1+μ)Pe(1 − αu + z)

Defining inflation π and expected inflation πe gives:

1 + π ≡ P/P−1, 1 + πe ≡ Pe/P−1

Therefore, after dividing both sides by P−1 leaves:

(1 + π) = (1+μ)(1 + πe)(1 − αu + z)

Expanding the right-hand-side of the equation gives:

1 + π = 1+μ + πe − αu + z + cross product terms (the cross product terms are 2nd order, e.g., if μ = 0.1 and πe = 0.05, then μπe = 0.005).

Considering just the first order terms for the moment:

π = πe − αu + (μ + z)

This predicts that:

  • an increase in expected inflation πe increases actual inflation π 1-for-1
  • an increase in unemployment u reduces inflation π (for given πe)
  • an increase in markup μ increases inflation π (for given πe)
  • other factors z that affects wage-setting also affect inflation

Less complicatedly, an increase in expected inflation πe leads to an increase in inflation π.  To see why, note that an increase in expected prices Pe leads to an increase in P.  If wage setters expect a higher price level, a higher nominal wage is set, which leads to an increase in the price level.  A higher price level leads to higher expected inflation.  So an increase in expected prices leads to an increase in actual prices, which also means that an increase in expected inflation leads to an increase in actual inflation. Additionally, with a given expected level of inflation πe, an increase in the markup μ also leads to a higher rate of inflation.  Given an expected level of inflation πe, an increase in unemployment leads to a decrease in inflation.

The Phillips curve – the early version

In a particular period t (say, one year)

πt = πet − αut + (μ + z)

This translates to saying that the inflation rate in a given time is equal to the expected rate of inflation for that time minus αut (the strength of the relationship between unemployment and wages multiplied by the actual rate of unemployment at that point in time) plus the markup level μ and z.  As a simplification, consider inflation as close to zero (which was the case in many countries, including Australia, in the 1960s).  This means that expected inflation is zero, and so the relationship is:

πt = −αut + constant

This demonstrates the relationship between inflation and unemployment that Phillips (1957) found for the UK and Australia and Samuelson and Solow (1960) found for the US.  For Phillips, this was an empirical generalisation. For Samuelson and
Solow, it was considered a policy tradeoff (meaning that a country can choose its inflation rate and accept the corresponding rate of unemployment, or vice versa).

Australian data from the 1900s to the 1960s.

Australian unemployment and inflation data from the 1900s to the 1960s.

In Australia from 1900-1960, a low unemployment rate was typically associated with a high inflation rate, and a high unemployment rate was typically associated with a low or negative inflation rate.

This relationship began to break down after then.

  1. persistent inflation incorporated into expected inflation
  2. oil price shocks

Wage/price inflation spiral

  • expansionary policy, kept unemployment rate low
  • low unemployment ⇒ higher nominal wages in tight labor market
  • prices rise as marginal costs (wages) rise
  • expected inflation begins to increase
  • wages build in higher inflation (indexation) etc
  • self-reinforcing spiral of higher wages and prices

More is required on:

NAIRU – modern Phillips curve.  Consider expected inflation, which is lagged inflation (accelerationist Phillips curve).  If unemployment is above the natural rate, the price level is rising at a diminishing rate.  (more study needed here :-) T