Solving RBC models by
Christiano’s
method of undetermined
coe
ﬃ
cients
This handout is meant to provide a simple introduction to Christiano (2002),
“Solving Dynamic Equilibrium Models by a Method of Undetermined Coe
ﬃ

cients",
Computational Economics
, Vol. 20, p. 2155. Note that I have made
some notational changes from Christiano’s paper.
•
Recall that the Euler equation for the savings decision generates the fol
lowing second order di
f
erence equation in
b
k
t
:
E
t
∙
Y
C
b
z
t
+1
+
K
C
μ
θ
Y
K
+(1
−
δ
)
¶
b
k
t
+1
−
(1 +
γ
)
K
C
b
k
t
+2
¸
(1)
−
∙
Y
C
b
z
t
+
K
C
μ
θ
Y
K
+(1
−
δ
)
¶
b
k
t
−
(1 +
γ
)
K
C
b
k
t
+1
¸
=
(1 +
γ
−
β
(1
−
δ
))
(1 +
γ
)
E
t
h
b
z
t
+1
−
(1
−
θ
)
b
k
t
+1
i
•
Letting
ζ
t
(the greek character for
z
) denote the endogenous state variable
(in this case
ζ
t
=
b
k
t
+1
, notice the dating re
f
ects when information is
known) and letting
s
t
denote the exogenous state variable (in this case
s
t
=
b
z
t
), then we can write (1) as
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 Spring '07
 CORBAE
 Economics, Algebra, Characteristic polynomial, Recurrence relation, Method of undetermined coefficients

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