New Classical Critique
Aggregate Demand
Write a simple version of the aggregate demand
curve based on the monetary policy rule.
– αt: Expenditure shift
– μt: Monetary policy shift
– πtFED: Central Bank Measure of inflation.
IS : yt t d rt
MP : rt t b t
FED
AD : yt t d t b tFED t d t b tFED
Supply Curve
Output differs from potential output only to the
degree that wage stickiness causes fluctuations in
labor usage or due to temporary supply shocks
(such as changes in the price of oil).
• A more realistic pricing rule, might set inflation as
an increasing function of deviations from long-
term output.
• SRAS: gW: Wage Growth, vt : Supply shift
t g yt y t
W
t
Rational Expectations
• In early 1970’s, Lucas, Sargent, and Wallace
pointed out logical flaw in story of adaptive
expectations.
• In periods following a demand shock, workers
expect that inflation equal to last years inflation,
though clearly and systematically the inflation
level will be accelerating.
• RE theory suggests that economic modeling of
expectations about the future should be consistent
with what the models say will predictably happen
in the future.
Simple Version of the RE Model.
• Driving forces of the model (expenditure shifts,
monetary policy shifts, and supply shifts) can be split
into two parts.
1. An algebraic function of the past reflecting that part of shifts
which can be estimated based on past behavior .
2. Unpredictable white noise shocks with zero average value.
t mt 1 ( yt 1..; t 1..; t 1..; t 1..; t 1...) tM
t vt 1 ( yt 1..; t 1..; t 1..; t 1..; t 1...) tV
t at 1 yt 1..; t 1..; t 1..; t 1..; t 1... tA
Rational Expectations
• A rational forecaster would use the
systematic parts of money growth and
velocity to forecast their future behavior.
REt 1 t mt 1 REt 1 t vt 1 REt 1 t t 1
• Rational Expectations Hypothesis: Workers
make rational forecasts of inflation based on
the forecasts of the shifts and the basic
structure of the model.
gtW REt 1 t
RE Business Cycles: Demand
• Abstract from supply shocks: t 0
t REt 1[ t ] yt y
• Suppose that central bank cannot adjust monetary
policy to contemporary inflation, but must predict it
based on past experience. FED
t REt 1 t
• Law of Iterated Expectations The expectation of an
expectation is the expectation.
• Forecast of planned inflation is planned inflation.
Solve for gW
Step 1: Solve for REt-1[yt]
• Expected value of inflation is expected value of
SRAS RE [ ] RE RE [ ] y y
t 1 t t 1 t
t 1 t
REt 1 REt 1[ t ] REt 1 yt y
REt 1[ t ] REt 1 yt y
REt 1 yt y
• Output is different from y only if inflation is
different than planned inflation. Since people
forecast inflation to be equal to planned inflation,
they will forecast output to be equal to y.
Solve for gW
Step 2: Solve for REt-1[πt]
• FED forecast of inflation when output is
equal to potential
y REt 1 yt REt 1 t d t b REt 1 t
REt 1 t d REt 1 t d b REt 1 REt 1 t
at 1 d mt 1 d b REt 1 t y
a d mt 1 y
REt 1 t t 1
d b
Solve for yt
• Insert the forecast of inflation into
aggregate demand curve
yt t d t b d REt 1 t
at 1 d mt 1 y
t d t b d
d b
yt y t at 1 d t mt 1
yt y tA d tM
Implications
• Fluctuations of output away from potential output
are transient, white noise shocks. No persistent
changes in output caused by fluctuations in
demand or monetary policy shocks.
• Systematic monetary policy (e.g. choice by the
central bank of mt-1 and d) have no effect on
output (since it would be predictable by workers
and factored into demand growth).
Implications
• Only unpredictable shocks will affect output. Since any
predictable aspects of monetary policy or volatility of
shocks will be priced into planned inflation, predictable
increases in demand will not increase output but only
inflation.
• Predictable stabilization policy will not stabilize
output, but unpredictable policy will destabilize it. Any
systematic attempts to affect output, including
accelerating money growth will fail as they will
automatically be priced into planned inflation.
Inflation Depends on Systematic
Monetary Policy
t REt 1[ t ] yt y
at 1 d mt 1 y
yt y
d b
at 1 d mt 1 y
d b
tA d tM
Monetary policy with extra
information
• Suppose that central bank can adjust
monetary policy to contemporary inflation.
tFED t
• No exchange in workers expectation of
inflation y RE y RE d b
t 1 t t 1 t t t
REt 1[ t ] REt 1 REt 1[ t ] yt y
REt 1 t d REt 1 t d b REt 1 t
REt 1 REt 1[ t ] REt 1 yt y
at 1 d mt 1 d b REt 1 t y
REt 1[ t ] REt 1 yt y a d mt 1 y
REt 1 t t 1
REt 1 yt y d b
Inflation Depends on Systematic
Monetary Policy
t REt 1[ t ] yt y
at 1 d mt 1 y
d b
t d t b t y
a d mt 1 y
1 d b t t 1 t d t y
d b
1 a d mt 1 y
t t 1 t d t y
1 d b d b
yt t d t d b t
d b a d mt 1 y
t d t t 1 t d t y
1 d b d b
Solve for y: Role for monetary
policy
• The more sensitive real interest rate is to
inflation, the smaller the response of output
to demand shocks.
yt
d b a d mt 1 y
at 1 d mt 1 tA d tM t 1
1 d b d b
at 1 d mt 1 tA d tM y
d b
yt y tA d tM
1 d b
tA d tM
yt y
1
1 d b
tA d tM
Supply Shocks
• Assume demand and monetary policy shifts
are constant. Normalize for simple algebra
t t 0
• Shifts in the supply curve
t
REt 1[ t ] REt 1 REt 1[ t ] yt y t
REt 1 REt 1[ t ] REt 1 yt y vt 1
REt 1[ t ] REt 1 yt y vt 1
vt 1
REt 1 yt y
Expected Inflation: Supply Shocks
Only
vt 1
y REt 1 yt REt 1 d b t d b REt 1 t
vt 1
y
REt 1 t
d b
Supply Shocks are not transitory
t REt 1[ t ] yt y t
vt 1
y
d b
d b t y t
v
y t 1
t
1
y
t
1 d b d b
d b v
yt d b t
1 d b t 1 t y
d b
Nobel Prize Ideas
• One implication of this argument is that output
fluctuations are white noise. Since actual business
cycles are fairly persistent, they must be driven by
supply shocks.
• Kydland & Prescott develop a model in which
business cycles are driven by shocks to TFP called
Real Business Cycle theory.
• Fluctuations in technology will lead to fluctuations
in output. PIH households will smooth
consumption, but investment will respond in a
more volatile manner.
Technology shocks and labor
• With log-log utility, the optimal labor-leisure
trade-off is given by wt
T Lt Ct
– A negative technology shock will reduce labor
productivity and real wages reducing the incentive
to work (substitution effect) but also reduce
consumption increasing the incentive to work
(income effect).
• Under Cobb-Douglas,
wt Yt T
Lt
T Lt Ct Ct L Ct
t 1
Yt
RBC Models
• A business cycle shock that increases the
consumption output ratio will lead to lower
levels of equilibrium employment.
– If temporary slow technology growth reduces
investment spending, capital may increase as a
share of output and optimal employment
decline.
– If long-term government spending (and lifetime
tax bills) slow, consumption as a share of
output may decline.
Nobel Ideas pt. 2
• K & P warn that not only is stabilization
unlikely to be effective, but it is likely to be
biased toward high inflation.
• Assume that the government has preferences
toward stable prices and would like to push
output to some target level of output y* > y.
• To increase output, the government has to push
up inflation beyond inflationary expectations
but this would come at some cost in terms of
inflation.
• The government tries to minimize a
weighted function of inflation volatility and
output stability. min a×(πt)2 + b×(yt –y* )2
• Faces SRAS
πt = gtW + θ∙[yt – y]
Minimization
• Minimize using Lagrangian method
min a×(πt)2 +b×(yt – y*)2+λ[gtW +θ∙[yt – y]- πt ]
1
2a b( y* y ) 2b[ y* y ( g W )]
• FOC 1
y y
P * gW
a 1
b
• The governments optimal inflation plan, πP, is
an increasing function of wage growth in order
to stimulate higher output, but because of dislike
of inflation, optimal inflation does not increase 1
for 1 with wage growth.
Government’s Monetary Policy
π
πP
1
θ
a +1
b θ
y*-y
gW
Rational Expectations
• If expectations were fixed, the government
could achieve its goals, trading off higher
inflation for higher output.
• However, if workers are rational
forecasters, they should set their
expectations about the governments
monetary policy according to the way the
government sets policy: RE[π] = πP
Equilibrium Inflation Under RE
RE[π] = πP
π
πP
y*-y
RE[π]
y>y π* y
Policy & Rational Expectations
• Whenever RE[π] = πP then output will be equal to
long-term output. When workers have rational
expectations, the government cannot push up
output.
• However, their desire to boost output gives
policy an inflationary bias. When they choose
their optimal policy they will get high inflation,
π*, and no boost in output.
• Government is better off sticking to a strict price
stability rule π = 0. If workers set RE[π] = 0, the
government could at least minimize inflation.
Credibility
• Government would benefit if they could build
credibility for a low inflation policy. But can they?
• K&P argue not. Since workers know that if they
came to expect π = 0 and demand low wage
growth, the government would like to take
advantage of the inflation-output tradeoff and run
a higher than 0 inflation.
• A government with discretionary power cannot
build credibility for a policy that would not be
what the government would want to choose if it
did build credibility.
Time Consistency & Rules vs.
Discretion
• A time consistent policy is a policy plan that
the government will want to stick to when it
actually becomes time to implement it.
– In this example, zero inflation is a time
inconsistent policy.
• K & P argue that the only way to implement a
credible time inconsistent policy is to set up an
institutional framework that will ignore the
short-term goals of the government
Other Potentially Inconsistent
Policies
• Low taxes on corporate profits/capital
income. The government may propose a
low corporate tax rate to encourage firms to
invest in capital. But once the capital has
been invested, the government may want to
take a share of the profits.
• Fixed exchange rate.
Institutional policies
• Independent Central Bank with
Conservative Central Banker. It is thought
that professionals from financial community
dislike monetary volatility. Giving one of
these individuals the power to control
money supply will move toward a low
inflation commitment.
• Central Bank with a constitutional
commitment toward low inflation. New
Zealand’s central bank is instructed to
follow an inflation-target in 1989.
Inflation in New Zealand
30.00%
25.00%
20.00%
15.00%
10.00%
5.00%
0.00%
70
72
74
76
78
80
82
84
86
88
90
92
94
96
98
00
02
19
19
19
19
19
19
19
19
19
19
19
19
19
19
19
20
20
-5.00%
Inflation Money Growth
Midterm Exam 3
• Tuesday, December 16 9-11
– 3007 | (Thu) | 08:30-11:30
• Coverage: Fiscal Policy, Money, Keynesian
Model, New Classical Critique
• Bring Calculator, Writing Instruments, 1 A4
sized paper with written notes.