SBP Working Paper Series STATE BANK OF PAKISTAN

Appendix E
Table E1: Common Equations
Levels Form
Log-linearized Form
y
t
~ ~ ~
~
A
t 1
= exp ht
kt
yt
= At
1
ht
kt
kt
h
t
w
=
1
r
t
k
t
~ ~
k h = w~
~ r
t
t
t
k
t
mc
P ( m)
=
t
P
A
t
t
1
A
k
1
1
k
= 1
w r
t
t t t
t
t
t
mc ~ ~
= 1
w~
~
r A
i
E P y ( m)
mc
p t
i=0
p ti
ti
t ~ ~ 1
p
1
p
t
t
1
=
i
p
1
Et
p
yti
( m)
p
i=0
1
1
p
1
p 1
=
p
pPt
1
1
p
Pˆ
~ ~
~
= 1
P
Rt
rt
=
E
t t1
t
1
= invt
(1
k ) k
t
= exp AAt
1
1
t
A
A
t
A
t
P t
p P t1
~ ~
r = R ~
t
p
t
Et
t1
k
~ t
= inv
~
1
t (1
)
~ ~
A = A
t
A
t1
A
t
t
~
k
t
m c ~
t
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