Econ 387L: Macro II
Spring 2008, University of Texas
Instructor: Dean Corbae
Problem Set #4 Answers  Due 2/14/08
Using matlab, you are to obtain decision rules by the method of undetermined coeﬃcients
suggested in Christiano (2002) for the economy in Hansen (1985). In particular, the problem you
are to solve is to choose
{
C
t
≥
0
,π
t
∈
[0
,
1]
,K
t
+1
≥
0
}
∞
t
=0
to solve
max
E
"
∞
X
t
=0
β
t
(
(1

α
) log(
C
t
) +
απ
t
ln(1

h
)
)
#
subject to
C
t
+
K
t
+1
=
Z
t
K
θ
t
(
π
t
h
)
1

θ
+ (1

δ
)
K
t
(1)
Z
t
= (1

ρ
) +
ρZ
t

1
+
ε
t
(2)
where
K
0
is given,
ε
t
are i.i.d.
N
(0
,σ
ε
)
,
and the steady state level of technology
Z
= 1.
You are to use the calibration that we considered in class. In particular,
θ
δ
(quar)
ρ
σ
ε
h
β
(quar)
α
0
.
36
0
.
015
0
.
95
0
.
007
0
.
53
0
.
9921
0
.
666
1. Follow the steps we did in class to get decision rules: (i) Find the steady state; (ii) Lin
earize the equations characterizing an equilibrium (i.e. ﬁrst order conditions and resource
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 Spring '07
 CORBAE
 Standard Deviation, Steady State, Impulse response, decision rules, Christiano

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