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
ff
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
−
K
C
b
k
t
+2
¸
(1)
−
·
Y
C
b
z
t
+
K
C
μ
θ
Y
K
+ (1
−
δ
)
¶
b
k
t
−
K
C
b
k
t
+1
¸
≈
(1
−
β
(1
−
δ
))
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
fl
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
E
t
£
α
0
ζ
t
+1
+
α
1
ζ
t
+
α
2
ζ
t
−
1
+
β
0
s
t
+1
+
β
1
s
t
¤
= 0
(2)
This is Christiano’s (2.2) with
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 CORBAE
 Economics, Algebra, Recurrence relation, Method of undetermined coefficients, order difference equation

Click to edit the document details