SBP Working Paper Series STATE BANK OF PAKISTAN

Table E2: Model specific equations
MIU CIA Taylor Rule
1 A
=
c t w t
1 A
=
c t w t
1 A
=
c t w t
c
t1
k
w
E t = E t (1 r t 1
)
t1
k
c
E = E t (1 r )
c t 1
1
k
t
E
t t = E t (1 r )
t
w t 1
t
c t
t
1 1 D
=
c t c
t1
t1
m t
ct
1
Rt
=
c
t
t1
m =
t t m
t1
t
c inv = y
A
1
=
w t
t1
c
t1
w
t1
R
= t
w t
t1
c m
t t
= t1
m =
t t m
t1
t
c inv = y
t t t
t t t
M
M
= exp
= exp
t1
t
t
t1
t
R
c
t1
R
= t
c t
t1
c inv = y
t
R
t
t
=
t
y
y
t
R
t1 R
y
t
1
R
R
t
Table E3: Model specific equations (log-linearized)
MIU CIA Taylor Rule
m
c t = w~
t
c t = w~
t
c ~
t = w~
t
k k
E t c~
c~
t t r E ~
1
= t r
t1
k k
E t w~
w~
t t r E ~
1
= t r
t1
k k
E t c~
c~
t t r E ~
1
= t r
t1
m
Dc
E ~
~
t c t 1 t1 Dc
m~
t
= c~
mDc
t
E ~
t
t
c~
t
= w~
1
1
t
~ ~ = ~
t c t m
t1
E
tc
~ t
c~
~
1 t
= rt
E
tw
~ t
w~
~
1 t
= rt
E
tc
~ t
c~
~
1 t
= rt
m~
= ~ ~ ~
t t t
m
t1
m~
= ~ ~ ~
t t t
m
t1
c inv
c ~
t invt
~
c inv
= y t
c ~
invt
~
c inv ~
y
y y
t =
y y
t
c~ t invt = ~ y
y y
t
M
M
~ ~
R
t
=
M
t1
t
t
=
M
t1
t
=
R
R
t
R
~
1
1
t
t
1
~ y
R
R y t t
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