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Handout on BlanchardQuah
(AER, 1989)
.
1
Deriving a VMA representation:
•
Aggregate supply (production function where
θ
t
is labor produc
tivity and
N
t
is employment):
Y
s
t
=
θ
t
+
N
t
(1)
•
Aggregate demand curve (consumption depends on real money
holdings and investment depends on productivity):
Y
d
t
=
M
t
−
P
t
+
αθ
t
(2)
•
Goods Price Setting (real wages equated to labor productivity):
P
t
=
W
t
−
θ
t
(3)
•
Wage Setting (nominal wages are set one period in advance so as
to achieve expected full employment):
W
t
=
W
¯
¯
{
E
t
−
1
N
t
=
N
}
(4)
•
Exogenous productivity process (productivity variations depend
on unobservable mean zero, iid technology shocks):
θ
t
=
θ
t
−
1
+
ε
s
t
(5)
•
Exogenous money supply process (variations in money supply de
pend on unobservable mean zero, iid money shocks):
M
t
=
M
t
−
1
+
ε
d
t
(6)
•
Assumptions on the fundamental shocks:
ε
s
t
⊥
ε
d
t
(i.e. independent)
and
σ
2
(
ε
s
t
)=1=
σ
2
(
ε
s
t
). That is, varcovar matrix is
I.
•
De
f
nitions:
Y
t
=
Y
s
t
=
Y
d
t
,U
t
=
N
−
N
t
•
Endogenous variables:
Y
t
,N
t
,U
t
,P
t
,W
t
. Exogenous variables
ε
s
t
and
ε
d
t
.
1
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View Full Document •
Let’s start with (4). That is, wages are set so that
E
t
−
1
N
t
=
N.
From (1) then
E
t
−
1
N
t
=
E
t
−
1
[
Y
t
−
θ
t
]=
N
(7a)
•
Plugging (3) into (2) we have an expression for
Y
t
=
M
t
−
W
t
+(1+
α
)
θ
t
(8)
•
Thus(8)into(7a)y
ie
lds
E
t
−
1
N
t
=
E
t
−
1
M
t
−
E
t
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This note was uploaded on 08/06/2008 for the course ECON 387 taught by Professor Corbae during the Spring '07 term at University of Texas at Austin.
 Spring '07
 CORBAE

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