Dynamic Macroeconomics

15.5.1 The Path of Inflation and Unemployment under Adaptive Expectations
For many years, the dominant approach to the formation of expectations in
macroeconomics was the adaptive expectations hypothesis. This was the
hypothesis adopted by Phelps [1967] and Friedman [1968]. According to this
hypothesis, expectations in each period are adjusted by a percentage of the
deviation of the actual from the expected value of a variable in the previous
period.
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Consequently, the adjustment of inflationary expectations according to this
hypothesis would take the form

---

where 0 ≤ λ < 1. According to 
(15.41)
, in each period, inflationary
expectations are adjusted by a percentage 1 − λ of the divergence between
actual and expected inflation in the previous period.
It is assumed that λ is less than one, because if it is equal to one, then there
is no adjustment in expectations, and we have the assumption of nonadaptive
or static expectations.
What are the properties of this specific hypothesis for the adjustment of
expectations? From 
(15.41)
, we have
Inflationary expectations under the adaptive expectations hypothesis are a
geometric distributed lag of past inflation rates. Thus, adaptive expectations
are backward looking.
Given that λ < 1, from the difference equation 
(15.42)
, if inflation were to
be held constant at an equilibrium rate π
A
, inflationary expectations would
gradually converge to that equilibrium inflation rate π
A
. The speed of
adjustment is equal to 1 − λ. The smaller is λ, the speedier will be the
adjustment of inflationary expectations to actual equilibrium inflation. In the
extreme case where λ = 0, expectations converge after one period. At the
other extreme (in the case where λ = 1), expectations never converge, and we
essentially have nonadaptive or static expectations.
Substituting 
(15.42)
in the Phillips curve 
(15.39)
and solving for
unemployment, one gets
If inflation were held constant at any inflation rate (say, π
A
), unemployment
would gradually converge to its natural rate u
0
with a speed of adjustment
equal to 1 − λ (that is, the speed of adjustment of inflationary expectations).
What would happen in the case where the government did not have a fixed
target for inflation, but a socially desirable fixed target for unemployment u
A
,
which happened to be lower than the natural rate of unemployment u
0
? In this
case, the government and the monetary authorities would presumably use

---

discretionary aggregate demand policies to maintain unemployment below its
natural rate u
0
at u
A
, where u
A
< u
0
.
From the unemployment equation 
(15.43)
, if the government aimed to keep
unemployment constant at u
A
< u
0
, inflation would evolve according to
The difference equation 
(15.44)
has a unit root, and thus inflation does not
converge. In fact, it increases from period to period by a percentage that
depends on the difference between the natural rate of unemployment rate u
0
and the government’s target unemployment rate u
A
. As the government uses
discretionary aggregate demand policies to keep unemployment below its
natural rate, it will be causing a constant increase in inflation, so that
inflation is always higher than the rising adaptive inflationary expectations.
Otherwise, unemployment cannot be maintained below its natural rate.
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This case is depicted in 
figure 15.10
. When the government and the
monetary authorities seek to maintain unemployment below its natural rate u
0
at the lower rate u
A
, inflation and inflationary expectations start increasing.
To keep unemployment below its natural rate, actual inflation must be higher
than expected inflation. Under adaptive expectations, this can only happen if
inflation increases continuously. If the government and the monetary
authorities allow the unemployment rate to return to its natural rate, then
inflation will stop increasing.
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