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Macroeconomics 1 Lecture Notes Spring Term 20/21
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Macroeconomics 1 Lecture Notes Spring Term 20/21
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Macro Spring Term10. The Phillips Curve, the natural rate of unemployment and in ation
Between 1900 and 1960 in the USA, a low unemployment rate was typically associated with a
high in ation rate, and a high unemployment rate was typically associated with a low or negative
in ation rate. The Phillips Curve, based on the data below, shows a negative relation between
in ation and unemployment.
Figure 1
10.1 In ation, expected in ation and unemployment
P = Pe (1 + ) F(u, z) is the aggregate supply relation derived in lecture 8. This relation can be
rewritten to establish a relation between in ation, expected in ation and the unemployment rate.
First the function F, assumes the form, F(u, z) = 1 - u + z. Then replace this function in the one
above, P = Pe (1 + ) (1 - u + z). This can then be converted to = e + ( + z) - u (this process
is shown in the appendix of the lecture slides), where = in ation, e = expected in ation, and u =
unemployment rate.
According to this equation ( = e + ( + z) - u), an increase in the expected in ation, e, leads to
an increase in in ation, . Also, given the expected in ation, e, an increase in the mark-up, , or
an increase in the factors that a ect wage determination, an increase in z, lead to an increase in
in ation, . Finally, given expected in ation, e, an increase in the unemployment rate, u, leads to
a decrease in in ation, .
When referring to in ation, expected in ation or unemployment in a speci c year, the equation
above needs to include the time indexes as follows: t = et + ( + z) - ut. The variables t, et and
ut now refer to in ation, expected in ation and unemployment in year t ( and z are assumed
constant and do not have time indexes).
10.2 The Phillips Curve
1
𝛼 fl flfl 𝜋 𝜇 flfl fl𝜇fl 𝜋𝜋 𝛼 fl
𝜋 𝜋ff 𝜇
fl fl fl 𝜋𝛼 𝛼 𝜋fl𝜋 𝜋 fl 𝜋fl𝜇𝜋 𝜋fl𝜋 𝛼 𝜇fi fl 𝛼 fl 𝜋 𝜋 𝜋𝜇
, If we set et = 0, then = ( + z) - u. This is the negative relation between unemployment and
in ation that Phillips found for the UK, and Solow and Samuelson found for the US (or the original
Phillips curve).
The wage-price spiral, given by Pet = Pet-1: ↓ ut ↑ Wt ↑ Pt ↑ (Pt - Pt-1)/Pt-1 ↑ t , is the
process by which low unemployment leads to a higher nominal wage. In response to the higher
nominal wage, rms increase their prices and the price level increases which leads to workers
asking for a higher wage. A higher nominal wage leads rms to further increase prices and, as a
result, the price level increases further. This further increases wages asked for by workers. And so
the race between prices and wages results in steady wage and price in ation.
Figure 2: in ation versus unemployment in the US, 1948-1969
The steady decline in the US unemployment rate throughout the 1960s was associated with a
steady increase in the in ation rate. Beginning in 1970, the relation between the unemployment
rate and the in ation rate disappeared in the US. This negative relation vanished due to an
increase in the price of oil, and due to the change in the way wage setters formed expectations
due to a change in the behaviour of the rate of in ation. The in ation rate became consistently
positive and in ation became more persistent.
2
fl 𝜋 fl flfi 𝜋 fl 𝜇 𝛼 fl fi fl fl 𝜋
, Figure 3: US in ation since 1900
Since the 1960s, the US in ation rate has been consistently positive. In ation has also become
more persistent: a high in ation rate this year is more likely to be followed by a high in ation rate
next year.
Suppose expectations of in ation are formed according to et = t-1. The parameter captures
the e ect of last year’s in ation rate, t-1, on this year’s expected in ation rate, et. The value of
steadily increased in the 1970s, from 0 to 1.
We can think of what happened in the 1970s as an increase in the value of over time. As long as
in ation was low and not very persistent, it was reasonable for workers and rms to ignore past
in ation and to assume that the price level this year would be roughly the same as the price level
last year. But, as in ation became more persistent, workers and rms started changing the ways
they formed expectations.
When = 0, we get the original Phillips curve, a relation between the in ation rate and the
unemployment rate: t = ( + z) - ut. When > 0, the in ation rate depends on both the
unemployment rate and last year’s in ation rate: t = t-1 + ( + z) - ut where t-1 = et. When =
1, the relation becomes (moving last year’s in ation rate to the left side of the equation): t - t-1 =
( + z) - ut. When = 1, the unemployment rate a ects not the in ation rate, but the change in
the in ation rate. Since 1970, a clear negative relation emerged between the unemployment rate
and the change in the in ation rate.
3
𝜇fl fffl𝜃 𝛼 fl 𝜃fl 𝜋 flflfl𝜇flfl 𝛼 𝜋fl 𝜃 fl 𝜋ff 𝜃𝜋fl 𝜋 𝜇 𝜃𝜋
fi flfl 𝛼 flfl 𝜃fi 𝜃𝜋
𝜋 𝜃𝜋fl 𝜋 𝜋 𝜃
, Figure 4: change in in ation versus unemployment in the US, since 1970
Since 1970, there has been a negative relation between the unemployment rate and the change in
the in ation rate in the US. The line that best ts the scatter plot for the period 1970-2006 is t -
t-1 = 4.4% - 0.73ut.
The original Phillips curve is: t = ( + z) - ut. The modi ed/expectations-augmented/
accelerationist Phillips curve is: t - t-1 = ( + z) - ut.
Friedman and Phelps questioned the trade-o between unemployment and in ation. They argue
that the unemployment rate couldn’t be sustained below a certain level known as the natural rate
of unemployment. The natural rate of unemployment is the unemployment rate such that the
actual in ation rate is equal to the expected in ation rate: 0 = ( + z) - un then un = ( + z)/ .
t - et =- [ut - ( + z)/ ] t - et =- [ut - un] t - t-1 = - (ut - un) (assuming et ≈ t-1)
This is an important relation because it gives another way of thinking about the Phillips curve in
terms of the actual and the natural unemployment rates and the change in the in ation rate.
The equation above [ t - t-1 = - (ut - un)] is an important relation for two reasons:
• It gives us another way of thinking about the Phillips curve: as a relation between the actual
unemployment rate, ut, the natural rate of unemployment, un, and the change in the in ation
rate, t - t-1.
• It also gives us another way of thinking about the natural rate of unemployment. The non-
accelerating in ation rate of unemployment (NAIRU) is the rate of unemployment required to
keep in ation rate constant.
Summary so far
• The aggregate supply relation is well captured in the US today by a relation between the change
in the in ation rate and the deviation of the unemployment rate from the natural rate of
unemployment.
• When the unemployment rate exceeds the natural rate of unemployment, the in ation rate
decreases. When the unemployment rate is below the natural rate of unemployment, the
in ation rate increases.
In the late 1960s, just as the original Phillips curve relation was working well, Milton Friedman and
Edmund Phelps, argued that the appearance of a trade-o between in ation and unemployment
4
𝜋 fl 𝜋𝜋fl flflfl𝜋 𝛼
fl 𝜇 𝜋fl 𝛼 𝜋 𝜋𝜋 𝛼𝜋𝜋 𝜇 𝜋 𝛼 𝛼𝜇 ffifl 𝛼 𝜋 fi𝜋 ff 𝛼𝜇 𝛼fl fl flfl 𝜋 𝜇fl 𝜋 𝛼 𝜋
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