Transcript Lucas Critique and the Essence of New Classical Approach

Lucas Critique and the Essence of New Classical Approach:
Rational expectation
Consider the IS curve or the AD curve as derived by the
Keynesian economists.
The parameters a, b q, k, nu, I0 are estimated using the
structural model and time series observations on variables.
IS:
AD:
a  bT  I  qr  G
0
Y
1 b
 

1
M


a  bT  I  q  kY    G
0  
P 
Y
1 b
Policies such as G and M based on these models are already
known to individuals. It is internalised in their decisions.
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There are five essential features
in a New Classical model
1.
2.
3.
4.
5.
It has a supply side based on optimisation.
It assumes that market clears at every
instance, no glut or voluntary
unemployment.
Rational expectations.
Natural rate hypothesis.
Policy irrelevance.
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2
Aggregate Supply and Technology Shock
AD-As in the short run
Shocks to Technology and Fluctuations
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A Simple long run new classical macro economic
model with the productivity shock (very similar to
Ramsey (1927) problem)
Preference of a representative consumer:
Max 
  tU Ct 
Ct t 0
Budget constraint
Ct  It  Gt  X t  M t  zt F  K , Lt , At 
 t 1

Evolution of the capital stock:
Boundary conditions:
Kt  1  K
t 1
 It
K  0 and K  0
T
0
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Aggregate supply
Yt  Y *   Pt  Pte   ets (1)
t 1 

Where t 1Pte is the price in period t as expected in
Pte  E  Pt | I 
t 1
t 1

where It 1 is the information set which includes
past values of all endogenous variables and
parameters.
ets is the supply shock,
Y * is the target output,
Yt and Pt are the actual prices and outputs.
period t-1,
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Price Movement and Monetary Policy Rule
Price moves according to the money
supply and a demand shock
Pt M t  etd
(2)
where etd is the demand shocks
and the money supply rule is given by


M t     Y * Y   etm (3)
0 1
t 1


where etm is the policy error or
unanticipated money supply, with Eetm   0
and a constant variance.
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Expected and Actual Prices
Rational expectation implies that expected price
does not contain any policy error and will be given
by the systematic part of (2)








e
*
*


Pt      Y Y    Y Y  (4)
0 1
t 1
0
1
t 1

But the actual price will contain systematic as well
as the error parts


Pt   Y * Y  etm  etd
0
1
t 1
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(5)
7
Policy Irrelevance Proposition
The errors in the expectation of the prices are given
by the differences between the expected and actual
prices
Pte  Pt etm  etd
(6)
Substitution (6) into (1) we get



*
m
d
Yt Y  et  et   ets etm etd  ets


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(7)
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Policy Irrelevance Proposition
The errors in the expectation of the prices is given
by the differences between the expected and actual
prices
Pte  Pt etm  etd
(6)
Substitution (6) into (1) we get output in terms of
errors


Yt Y *  etm  etd   ets etm etd  ets


(7)
Policy variable does not determine the output.
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How to Test a Rational Expectation Model?
UM t  M t  M t
where UMt is unanticipated money supply,
M t is the actual money supply and M t is the
anticipated money supply, given by a trend.
Now to find whether the unanticipated money
supply will have a real impact regress the
following model.
Yt      M t  M t   et
0 1

In case of persistence take the unanticipated
money supply for several years in the past, such
as


Yt      M t  M t     M  M   et
0 1
2  t 1
t 1




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
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What do other economists think of this
conclusion?
New Keynesian consider that the conclusion of policy
irrelevance coming out of the New Classical model is
dangerous because if policy makers think that way it
may have serious welfare consequences due to lack of
economic policies to contain unemployment and
inflation in recession or in hyperinflation.
Mankiw (1989) has explicitly stated that the New
classical paradigm will be discarded as an analysis of
economy as the micro foundation to the Keynesian
models becomes more solid.
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Adaptive Expectation
People learn by mistake and adjust their expectations
accordingly


Pte  P e    P  P e 
t 1  t 1 t 1
(1)
Here Pte is the expected price and is the adjustment
parameter between zero and 1, 0   1 . There is no
observation available about the expected price,Pte . How
can it be used in a model? . The trick is to solve (1) for
Pte and eliminate it using observed variables. First (1)
can be written as
Pte  P  1   P e
t 1
t 1
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(2)
12
Adaptive Expectation
By one step backward iterations (2) can be written as
Pe  P  1   Pe
t 2
t 1
t 2
(3)
Now use (3) into (2)


Pte  P  1  P  1   Pe  =
t 1
t 2
t 2 

2
P  1  P  1   Pe (4)
t 1
t 2
t 2
Now further iterate (3) and substitute the result back in (4)
2
3
Pte  P  1  P   1   P  1   Pe
t 1
t 2
t 3
t 3
(5)
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Adaptive Expectation
If this process continues (5) can be written as
2
n e






e
Pt  P  1  P   1   P ... 1   Pt n
t 1
t 2
t 3
(6)
n e
Lim 

0



1
1   P
Since
,
 0 . Therefore (6)
t

n


n 
can be written only in terns of the observed values of the
actual price, Pt i .
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References
1. K. A.Chrystal and Simon Price (1994) Controversies in Macroeconomics, Harvester Wheatsheaf,
2.
3.
4.
5.
6.
chapter 4.
Lucas, Robert Jr. and Sargent, After Keynesian Macroeconomics, Spring 1979, Federal
Reserve Bank of Monneapolis Quarterly Review.
Mankiw N.G. (1989) Real Business cycle: A New Keynesian Perspective, Journal of Economic
Perspectives, vol. 3, no. 3 pp. 79-90.
Plosser Charles I (1989) Understanding Real Business Cycle, Journal of Economic Perspectives, vol.
3, no. 3 pp. 51-77.
Ramsey, F.P. (1928) “A Mathematical Theory of Saving,” Economic Journal 38, 543-559.
Sargent, Thomas J. and Wallace, Neil (1975) “Rational” Expectations, the Optimal Monetary
Instrument, and the Optimal Money Supply Rule, Journal of Political Economy, pp. 241254.
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