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21-1
Chapter 21
Advanced Topics
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McGraw-Hill/Irwin
Macroeconomics, 10e
© 2008 The McGraw-Hill Companies, Inc., All Rights Reserved.
21-2
Introduction
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This chapter offers advanced material presenting the
revolution in macroeconomics that has developed over
the last 30 years
We look at four theories in this chapter:
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Rational expectations
The random walk of GDP
Real business cycle theory
New Keynesian models of price stickiness
These models yield contrasting conclusions about the conduct of monetary
policy, but they are alike in their emphasis on the importance of
consistency between macroeconomic and microeconomic theory.
21-3
Rational Expectations
Equilibrium Models
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In a rational expectations equilibrium model, markets
clear and there is nothing systematic that monetary policy
can do to affect output or unemployment
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The term “rational expectations equilibrium” identifies two key
features of this approach
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It places weight on the role of expectations (rational ones)
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Economic agents do not know the future with certainty  base their
plans/decisions on their forecasts or expectations about the future
If agents are rational, they will use all available information when forming
those expectations
The rational expectations model insists on equilibrium
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Markets clear immediately
21-4
Rational Expectations
Equilibrium Models
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The full neoclassical theory of AS asserts that:
 Unemployment
is always at the natural rate
 Output is always at the full-employment level
 Any unemployment is purely frictional
 Neither monetary nor fiscal policy changes will have any
systematic effect on output
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The rational expectations equilibrium approach offers a
deviation from that model:
Some people do not know the aggregate price level but do know
the nominal wage or price at which they can buy or sell.
21-5
Rational Expectations
Equilibrium Models
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Assume a simple AD schedule:
mv  p y
(1)
Assume a simple short run AS
curve, including price
expectations:
p  pe   ( y  y* )
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(2)
The AD and AS equations can
be combined to solve for
output (3) and prices (4) in
terms of m and other variables
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Rewrite AD as p = m + v – y,
equating AD and AS, and
solving for y:
m  v  y  pe   ( y  y* )
m  v  p e  y *  y (1   )
m  v  p e  y *
y
(1   )
m
(v  p e )




y * (3)
(1   ) (1   ) (1   )
21-6
Rational Expectations
Equilibrium Models
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Assume a simple AD schedule:
mv  p y
(1)
Assume a simple short run AS
curve, including price
expectations:
p  pe   ( y  y* )
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(2)
The AD and AS equations can
be combined to solve for
output (3) and prices (4) in
terms of m and other variables
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Plugging equation (3) into the
rewritten AD schedule, and
solve for p yields:
 m v  p e   * 
p  m  v  


y 
 1    1    1    
m
v
pe
 *
m
v


y
1    1    1    1   

1 e
*


m  v  y 
p
(4)
1   
1   
21-7
Rational Expectations
Equilibrium Models
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Together, equations (3) and (4) tell us the equilibrium
output and prices in our model economy
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If money supply rises 1 percent, output rises by 1/(1+) percent
and prices rise by /(1+ ) percent
If m, v, and y* are known, given price expectations,
predictions for y and p can be calculated using equations
(3) and (4)
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Often the model generates values that are different from
expectations  the standard AS/AD model assumes that
economic agents make predictions for the economy that are
inconsistent with the predictions the model itself makes
The Lucas Critique
21-8
The Perfect-Foresight Model
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The previous model can be altered to assume that
economic agents are correct in their predictions, or p = pe
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Economic decision makers use equation (4) to predict prices and
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
compute pe: e
p  p
(m  v  y * ) 
pe
(1   )
(1   )
(5)
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Collecting terms containing pe, we can rearrange (5) to give the
perfect foresight forecast and solution for the price level and the
corresponding solution for output:
p  p mv y
e
y  y*
*
(6)
(7)
21-9
The Perfect-Foresight Model
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The perfect-foresight predictions in equations (6) and (7)
are quite different from the original AS/AD predictions
embodied in equations (3) and (4)
 The
latter assume exogenously given price expectations
 The former assume that price expectations are formed
endogenously, and that expectation formation is consistent with
the predictions of the model
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These differences have implications for the effectiveness
of monetary policy
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Under a perfect foresight model:
A 1% increase in the money supply leads to exactly a 1% increase
in the price level
 A 1% increase in the money supply leads to NO increase in output
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21-10
A Rational Expectations Model
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A rational expectations model assumes that:
Agents make the best use of whatever information is available to
them
• Expectations are formed in a manner consistent with the way the
economy actually operates
 Similar to a perfect foresight model in which some of the key
variables are uncertain
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Suppose before money supply is known, economic
decision makers expect the money supply to equal me
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If the money supply turns out to be m, the difference between
e


m

m
agents’ expectations and the actual money supply is m
21-11
A Rational Expectations Model
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The monetary policy multiplier with respect to anticipated
money, me, is zero, just as in the perfect-foresight model
The monetary policy multiplier with respect to
unanticipated money, m, is positive, just as in the AS/AD
model
The equilibrium solutions for price and output are:
1

yy 
m 
 y*
(1   )
(1   )

e
*e
p m v y 
( m   y* )
(1   )
*e
(11)
(12)
21-12
A Rational Expectations Model
y  y *e 
1

m 
 y*
(1   )
(1   )
p  m e  v  y *e 
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
( m   y )
(1   )
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The effect of an increase in the money supply under
rational expectations must be broken down into two parts:
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The effect of an anticipated increase in the money supply
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Rational expectations predicts NO effect on output
Rational expectations predicts an equal change in prices
The effect of an unanticipated increase in the money supply
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Rational expectations predicts an increase in output of 1/(1+)
Rational expectations predicts an increase in prices of /(1+ )
21-13
The Random Walk of GDP
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Fluctuations in output can be transitory or permanent
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If fluctuations are primarily permanent, changes in AD must be
of relatively little importance:
According to the AS/AD model, the effect of AD shocks wears off
with time because the long-run aggregate supply curve is vertical
 If the effect of shocks is permanent, their source must be something
other than aggregate demand
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The idea that changes in output are permanent can be
described by saying that GDP follows a random walk
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Having wandered up or down, GDP has no tendency to return to
trend  stark contrast to implicit model of text
21-14
The Random Walk of GDP
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Nelson and Plosser challenged
the predominating idea that:
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[Insert Figure 21-3 here]
GDP fluctuates about a smooth
trend line
Shocks to AD are the primary
cause of the transitory fluctuations
Suggested that the trend is not
so smooth and is subject to
large and frequent shocks that
have a permanent effect on the
level of GDP
Figure 21-3 presents a stylized
view of trend growth and
fluctuations around the trend
21-15
The Random Walk of GDP
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Need to detrend the data:
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Suppose the trend in y can be represented by a literal time trend:
y t    t
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(22)
Equation (22) states that y rises by β in every time period
Subtracting last period’s y from each side of the equation yields:
yt  yt 1  [  t ]  [   (t  1)] (23)
OR
yt  yt 1    y  
(24)
Equations (22) and (24) are equivalent to one another
21-16
The Random Walk of GDP
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Suppose we add an output
shock, ut, to equation (22):
y t    t  u t
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According to equation (25), the
effect of a shock lasts one
period
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(25)
y t    u t  u t 1
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Alternatively, the shock could
be added to equation (24):
yt  yt 1    u t
OR
(26)
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Can be made stationary by taking
out a time trend  trend
stationary
Dominated by transitory shocks
According to equation (26), the
effect of a shock on the level of
y is permanent
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yt    t  u t  u t 1  u t 2  ...  u 0
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Can be made stationary by
differencing  difference
stationary
Dominated by permanent shocks
21-17
The Random Walk of GDP
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According to the AS/AD model:
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[Insert Figure 21-4 here]
Business cycles caused by AD
fluctuations are relatively short-lived
Shocks to AS might be permanent if
the derived from permanent
productivity improvements
Nelson and Plosser showed that GDP
includes both permanent and
transitory shocks, but GDP process
dominated by permanent shocks
Figure 21-4 shows the importance of
permanent shocks
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Prior 1973 consistent with
fluctuations about trend
Post 1973 a permanent downward
shift
21-18
The Random Walk of GDP
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The idea that shocks with long-lasting impact are
important to the economy is now generally accepted
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The inference that AD is relatively unimportant remains
controversial
An alternative view is that large and relatively permanent
aggregate supply shocks occur, but only on rare occasions
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In between, AD shocks dominate (Pierre Perron)
Trend stationary with breaks
Importance of aggregate demand shocks remains
a controversial area.
21-19
Real Business Cycle Theory
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RBC theory asserts that:
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Fluctuations in output and employment are the result of a variety
of real shocks that hit the economy
Markets adjust rapidly and remain in equilibrium
RBC theory is the natural outgrowth of the theoretical
implication of:
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The rational expectations approach  anticipated monetary
policy has no real effect
The empirical implication of the random walk theory 
aggregate demand shocks are not an important source of
fluctuations
21-20
Real Business Cycle Theory
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RBC must do two things:
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2.
Explain the shocks that hit the
economy
Explain the propagation
mechanisms  mechanism
through which a disturbance is
spread through the economy
Why do shocks to the economy
seem to have long-lived
effects?
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The intertemporal substitution
of leisure is the propagation
mechanism that is most
associated with equilibrium
business cycles
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Why do people work more at some
times than at others?
• During booms employment is
high and jobs are easy to find
• During recessions employment
is lower and jobs are hard to
find
Empirical evidence does not support
the explanation that people work
more when wages are higher.
21-21
Real Business Cycle Theory
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RBC models explain large movements in output with
small movements in wages as follows:
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There is a high elasticity of labor supply in response to
temporary changes in the wage
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People are willing to substitute leisure intertemporally
People care about their total work effect but care very little about
when they work
Suppose that within a two-year period they plan to work 4,000
hours at the going wage
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If wages are equal in the two years, they would work 2,000 each
year
If wages are 2% higher in one year than the other, they might work
2,200 in the high wage year, and 1,800 in the other
21-22
Real Business Cycle Theory
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RBC models explain large movements in output with
small movements in wages as follows:
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There is a high elasticity of labor supply in response to
temporary changes in the wage
Labor is not sensitive to permanent changes in wages
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If the wage rises, and will remain high, there is nothing gained by
working more in one year over another
The intertemporal substitution of leisure is clearly capable
of generating large movements in the amount of work
done in response to small shifts in wages
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Could account for large output effects in the cycle accompanied
by small changes in wages
21-23
Real Business Cycle Theory
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The mechanisms that propagate business cycles are set in
motion by events/disturbances that change the
equilibrium levels of output and employment in
individual markets and the economy as a whole
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The most important disturbances in RBC theory are:
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Shocks to productivity or supply shocks
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Weather, new methods of production
Shocks to government spending
The evidence for the importance of money seems persuasive, making it
difficult for proponents of the RBC to be successful at converting the
profession to their views.
21-24
New Keynesian Models
of Price Stickiness
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The previous three models presented in this chapter are
all in the equilibrium-market-clearing tradition
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Inconsistent with the AS/AD behavior that many economists
believe characterizes the real world
New Keynesians accept the premise of individual rational
behavior but develop models in which:
 Markets
do not quickly reach the full classical equilibrium
 Prices do not always adjust to changes in the money supply
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Gregory Mankiw developed a model of price stickiness
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Gives an explanation for why prices to not adjust rapidly and the
economy can be in disequilibrium
21-25
New Keynesian Models
of Price Stickiness
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Suppose the money supply increases
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According to equilibrium theories, firms should all increase
prices proportionately
But suppose changing prices is expensive  menu costs are the
costs associated with changing prices
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Firms might choose to leave their prices at the old (wrong) value as
the cost of changing prices outweighs the benefits
An increase in the nominal money supply (and imperfect
competition) may leave prices unchanged  real money increases,
as does output
New Keynesian models explain how individually rational
decisions under imperfect competition lead to socially
undesirable booms and busts
21-26