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Chapter 18: Expectations and Macroeconomics
Instructor’s Manual
Chapter 18: Expectations and Macroeconomics
Problem 1
The Phillips curve is an empirical relationship between the unemployment rate and the rate of
wage inflation. The neoclassical wage equation, on the other hand, is a theoretical construct
explaining how wage inflation and unemployment may be related in the short run, given
expectations of price inflation. The Phillips curve relationship can be obtained from the
neoclassical wage equation only if expectations of price inflation are constant.
If the inflation rate were to become very high, it is unreasonable to assume that future
inflation rates will be constant. This means that once people start observing high inflation, they
will begin to expect even higher inflation rates in the future. Higher expectations of inflation will
be built into wage contracts that firms and workers enter into, and will push up the wage inflation
rate. Hence, we would start observing wage inflation without a corresponding reduction in the
unemployment rate as the Phillips curve predicts. In other words, the Phillips curve relationship
would cease to hold in a world where inflationary expectations were not constant.
Problem 2
E
 w
 P
 g 
 cU  U * . We can see that an
P
 w

The new-Keynesian wage equation is 
P E
increase in
increases the rate of nominal wage inflation for a given level of unemployment
P
holding other variables constant. In other words, an increase in expected inflation shifts the
Phillips curve to the right. During both the 1969-1979 and 1979-1989 periods we observed
increasing nominal wage inflation during periods of steady or increasing unemployment, which
could be caused by an increase in the expected inflation rate.
Problem 3
The parameter c in the neoclassical wage equation:
w
P E
g
 c(U  U * ) ,
w
P
determines how fast the nominal wage rate adjusts to restore balance whenever unemployment is
different from its natural rate.
Recall that the classical model says that wages and prices adjust instantaneously because
economic agents react very quickly to profit opportunities; therefore, unemployment is always at
its natural rate. In the neoclassical wage equation, if people react quickly whenever
unemployment is different from U*, this means that the speed of adjustment of nominal wage
inflation to the gap (U - U*) is very high. In the limiting case when c is infinite, the adjustment is
instantaneous, and the neoclassical wage equation behaves like the classical one.
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Chapter 18: Expectations and Macroeconomics
Problem 4
 w

 5%   4%  2U  6%  .
 w

a.
The Phillips curve equation is 
b.
It must be true that 4%  5%  4%  2U  6% or U = 8.5%.
c.
The short run aggregate supply curve is
d.
No. Unemployment is above its natural rate and output growth is below its natural rate
because price inflation is significantly below the expected inflation rate. Eventually,
expected inflation will fall which will decrease unemployment back to its natural rate of
6% and increase output growth to its natural rate of 5%.
P
 4%  5%   4%  5% 
P
= -2%.
Problem 5
The NAIRU, or the non-accelerating inflationary rate of unemployment, is the level of
unemployment that can be maintained by the Federal Reserve without putting upward or
downward pressure on the current inflation rate. In other words, the NAIRU is the
unemployment rate when actual price inflation equals expected price inflation. Unfortunately, the
NAIRU is not observable. There is always some uncertainty as to the unemployment rate that the
Fed should try to target if its goal is inflation stability. Because of this uncertainty, there is
always a chance the Fed is targeting the wrong unemployment rate and, as a result, in danger of
either accelerating inflation or maintaining a level of unemployment that is too high.
Problem 6
The natural rate of employment is the employment rate consistent with the natural rate of growth
of GDP. The natural rate of unemployment is the unemployment rate consistent with search costs
in the labor market (see Chapter 7). If the productivity growth rate and labor supply both increase,
but the increase in productivity growth is not enough to absorb the increased labor pool, then both
rates will increase.
Problem 7
The theory of rational expectations says that agents do not make predictable, or systematic, errors
in forming their expectations. As a result, though agents may make mistakes in the future, they
are as likely to be too high as too low. Thus, mistakes can be made, but on average expectations
are correct. If expectations are consistently too high or too low, this new information will be
adopted by agents and their expectations will change accordingly.
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Chapter 18: Expectations and Macroeconomics
Problem 8
In the short run, an increase in the money growth rate increases the dynamic aggregate demand
curve, increasing price inflation and output growth above its natural rate. This increase in price
inflation without any change in nominal wage inflation reduces unemployment below its natural
rate. See Figure 18.4 in the text. In the long run, agents increase their expected inflation rate and
wage inflation increases. As a result, the short run aggregate supply curve shifts to the left,
eventually reducing output growth back to its natural rate. The increase in the expected price
level increases the unemployment rate for a given level of price inflation, eventually returning
unemployment to its natural rate. See Figure 18.5 in the text.
Problem 9
In order to reduce unemployment, the Fed will have to increase the rate of money growth and
price inflation above its current levels. This will reduce unemployment temporarily. However,
the economy is not in a long run equilibrium when unemployment is at 5% but when it is at 6%.
Eventually, inflation expectations and wages will adjust to this increase in the inflation rate,
shifting the Phillips curve to the right and increasing the unemployment rate back toward its
natural rate. If the Fed persists in attempting to reduce unemployment below its natural rate by
undertaking a series of increases in the money growth rate, it will lead to a series of increases in
the price inflation rate. Hence, targeting an unemployment rate that is too low can lead to
accelerating inflation.
Problem 10
A policy that permanently reduces unemployment below its natural rate is one that permanently
increases GDP growth above the natural rate. Consider Figure 3 below which shows how this can
be done using a certain type of monetary policy.
P
P
LRAS
SRAS1
C
P/P)2
SRAS0
P/P)Et+2 = (P/P)1
P/P)Et+1 = P/P)Et
= (P/P)0
B
AD1
A
AD0
Y/Y)0 = g
Y/Y)1
Figure 3
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Y
Y
Instructor’s Manual
Chapter 18: Expectations and Macroeconomics
Suppose the economy is in long-run equilibrium at point A. If the current year is year t, and
the economy is at A in the year (t-1) as well, then the expected inflation rate is (P/P)Et =
(P/P)0.
Now suppose the Fed increases the rate of money creation in the year t+1 so that the
aggregate demand curve shifts from AD0 to AD1, i.e., the aggregate demand curve for the year
t+1 is AD1. Since people were expecting the rate of inflation in year t+1 to be (P/P)0, the
relevant short-run aggregate supply curve for the year is still SRAS0. Therefore, the economy will
move from A to B along SRAS0. In year t+1, GDP growth will increase above g, and
unemployment will fall below its natural rate. The actual inflation rate will be (P/P)1.
In the following year (i.e., t+2), the expected inflation rate will be (P/P)1. Since the
expected inflation rate has increased, and unemployment has fallen below its natural rate, the
nominal wage inflation rate will increase in t+2. This will shift the year t+2 short-run aggregate
supply curve to SRAS1.
If the aggregate demand curve remains at AD1 from year t+1 onwards, then expectations will
soon adjust and take the economy to the long-run equilibrium point C. Compared to the case
where expectations are rational, the only difference here will be that the adjustment towards C
will take longer. So, if the Fed is to permanently decrease the unemployment rate below the
natural rate, it will have to keep pushing the AD curve to the right, i.e., increase the rate of money
creation every period. In other words, the Fed has to increase the money supply at an increasing
rate.1
Problem 11
First, the traditional Keynesian model ignored the effects of inflation expectations and how
changes in these expectations can affect the relationship between inflation of unemployment.
Second, the traditional Keynesian model ignored the natural rate of unemployment, arguing that
the Fed can keep unemployment at any level if it chooses the proper level of inflation.
Obviously, the fact that the expected inflation rate and the natural rate of unemployment, neither
of which the Fed controls, are important factors in the tradeoff between inflation and
unemployment suggests that it is very difficult, maybe impossible, to reliably control the
unemployment rate using monetary policy.
This has the effect of “surprising” people every period, since they look backwards in forming their
expectations. Had expectations been rational, such a policy would have had no permanent effect as price
expectations would be adjusted every period in anticipation of the Fed's actions.
1
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Chapter 18: Expectations and Macroeconomics
Problem 12
This is a good question for class discussion.
a.
What Friedman is saying here is that money neutrality holds in the long run, meaning that
the Fed can control nominal variables by changing the money supply but it cannot control
real variables by changing the money supply. Thus, the tradeoff between inflation and
unemployment does exist, but it only exists in the short run, because unemployment
eventually returns to its natural rate, and the tradeoff is unstable, because changes in
expected inflation can change the tradeoff.
b.
If the Fed tries to target a nominal interest rate, it may lead to exploding inflation.
Consider the following example. Suppose that there is an increase in productivity that
increases the natural rate of output growth, reduces the natural rate of unemployment, and
increases real and nominal interest rates. What will happen if the Fed tries to target
nominal interest rates and prevent this increase in interest rates from occuring? The Fed
will be forced to increase the money supply to drive nominal interest rates down.
However, this will eventually increase inflation and expected inflation, putting more
upward pressure on nominal interest rates. This will once again force the Fed to increase
the money supply to keep interest rates from rising and the whole process will continue to
repeat itself. The end result of this policy to target nominal interest rates will be
significantly higher inflation over time. Accelerating inflation will end only when the
Fed gives up its interest rate target. Thus, the Fed cannot target nominal interest rates
over long periods of time
Problem 13
First, the Fed has imperfect information about the economy, such as the future state of the
economy or what exactly the natural rate of unemployment is. As a result, it is prone to making
mistakes because of this imperfect information. Second, the public’s expectations are not
constant but will vary with changes in monetary policy. Thus, the results of policy can be
unpredictable depending upon how agents form their expectations. Third, there are long logs in
policy. The time between when a policy is enacted and when it actually has some effect on the
economy can be so long that by the time the policy has an effect it may no longer be needed or it
might be the wrong policy. Fourth, if the Fed tries to stabilize output and unemployment after
aggregate supply shocks, the end result will be very high levels of inflation and will lead to
inflationary expectations that may be very costly to remove over time.
Problem 14
A class discussion is useful here.
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