the global trade and environment model: a projection of non … · the global trade and environment...
TRANSCRIPT
The
Glo
bal T
rade
and
E
nviro
nmen
t Mod
el:
A p
roje
ctio
n of
non
-ste
ady
stat
e da
ta u
sing
Inte
rtem
pora
lG
TEM
The
Glo
bal T
rade
and
E
nviro
nmen
t Mod
el:
A p
roje
ctio
n of
non
-ste
ady
stat
e da
ta u
sing
Inte
rtem
pora
lG
TEM
Hom
Pan
t, V
ivek
Tul
pulé
and
Bri
an S
. Fis
her
Aus
tralia
n B
urea
u of
Agr
icul
tura
l and
Res
ourc
e E
cono
mic
s
OB
JEC
TIV
ES
OB
JEC
TIV
ES
Der
ive
an in
tert
empo
ralv
ersi
on o
f GT
EM
D
emon
stra
te th
at a
n in
tert
empo
ral
gene
ral e
quili
briu
m m
odel
can
be
solv
ed
in G
EM
PAC
K w
ith a
sing
le p
erio
d no
n-st
eady
-sta
te d
atab
ase.
E
xam
ine
the
stea
dy st
ate
prop
ertie
s of t
he
mod
el.
Bas
ic A
ssum
ptio
nsB
asic
Ass
umpt
ions
inve
stm
ent i
s fu
lly b
ond
finan
ced
loca
l bon
ds a
re p
erfe
ctly
sub
stitu
tabl
e w
ith fo
reig
n bo
nds
and
henc
e ea
rn th
e sa
me
glob
al ra
te o
f ret
urn.
th
e re
gion
al c
apita
l sto
ck is
fully
ow
ned
by
ide
ntic
al re
gion
al h
ouse
hold
s.W
e do
not
impo
se th
e ar
bitr
age
cond
ition
th
at lo
cal b
onds
yie
ld th
e sa
me
rate
of
retu
rn a
s th
e ph
ysic
al c
apita
l.
Ass
umpt
ions
…A
ssum
ptio
ns…
(The
rat
e of
ret
urn
in p
hysi
cal c
apita
l is
allo
wed
to v
ary
acro
ss th
e re
gion
s)R
egio
nal h
ouse
hold
s sup
ply
fact
ors
inel
astic
ally
to th
e m
arke
t T
he p
opul
atio
n an
d th
e la
bor
supp
ly
grow
exp
onen
tially
at t
he r
ate
of n
Prod
uctio
n fu
nctio
ns a
re c
hara
cter
ised
by
con
stan
t ret
urns
to sc
ale
Giv
en th
is e
nvir
onm
ent,
the
only
pro
blem
le
ft to
a h
ouse
hold
is –
the
allo
catio
n of
inco
me
betw
een
curr
ent
cons
umpt
ion
and
accu
mul
atio
n of
ass
ets
to m
axim
ise
the
sum
of p
erio
dic
utili
ties.
Giv
en th
is e
nvir
onm
ent,
the
only
pro
blem
le
ft to
a h
ouse
hold
is –
the
allo
catio
n of
inco
me
betw
een
curr
ent
cons
umpt
ion
and
accu
mul
atio
n of
ass
ets
to m
axim
ise
the
sum
of p
erio
dic
utili
ties.
The
pro
blem
of
the
hous
ehol
dT
he p
robl
em o
f th
e ho
useh
old
dtet
ct
∫∞−
0)
(ln
max
θ
Subj
ect t
o
)(
][
)(
//
f th t
tt
h tt
tt
f th t
f th t
t
bb
Wb
kR
bb
ndt
dbdt
dbc
++
+−
=
++
++
ρρ
whe
re lo
wer
cas
es a
re fo
r per
cap
ita v
aria
bles
With
the
inte
rtem
pora
lbud
get c
onst
rain
t the
pr
oble
m b
ecom
es:
dtet
ct
∫∞−
0)
(ln
max
θsu
bjec
t to
hk
ft
vt
bdt
dvn
c0
00
00
})
(ex
p{ω
ωρ
++
=−
−∫
∫∞ whe
re
dtdv
nb
kR
bt
vh t
tt
th
k}
)(
exp{
][
00
00
∫∫
∞−
−−
+=
ρρ
ω
dtdv
nW
tv
th
})
(ex
p{0
00
∫∫
∞−
−=
ρω
The
solu
tion
of th
e ab
ove
prob
lem
can
be
obta
ined
as
},)
(ex
p{0
0∫
−−
=t
vt
dvn
cc
θρ
).(
00
00
hk
fb
cω
ωθ
++
=
and
To m
ake
the
abov
e so
lutio
n op
erat
iona
l we
need
to
spec
ify th
e ex
pect
atio
nalr
ules
det
erm
inin
g hu
man
and
non
-hum
an w
ealth
Ass
umpt
ions
on
expe
ctat
ions
:A
ssum
ptio
ns o
n ex
pect
atio
ns:
Hou
seho
lds h
ave
stat
ic e
xpec
tatio
ns
rega
rdin
g th
eir
inco
me,
pri
ces a
nd
popu
latio
ngr
owth
The
y be
lieve
that
the
glob
al in
tere
st r
ate
is fi
xed
for
ever
Und
er th
ese
assu
mpt
ions
we
have
and
ρω
/0
0W
h=
ρω
/0
00
kR
k=
)(
00
00
hk
fb
cω
ωθ
++
=Th
eref
ore,
in p
lace
of
]][
/[
00
00
0fb
Wk
Rc
ρρ
θ+
+=
We
can
writ
e
and
ρar
e fix
ed w
e ob
tain
that
the
curr
ent
Giv
en th
at θ
cons
umpt
ion
is a
fixe
d fr
actio
n of
cur
rent
inco
me
How
abo
ut in
vest
ors?
How
abo
ut in
vest
ors?
The
opt
imal
inve
stm
ent
The
opt
imal
inve
stm
ent
IK
trr
trr
tretg
=−
δβ
ρρ
exp{
()}
whe
re,
-sta
tic e
xpec
tatio
ns1
/])
1([
−Π
Π−
+=
r tr t
rr t
re tR
δρ
-rat
iona
l exp
ecta
tions
1/]
)1(
[1
1−
ΠΠ
−+
=+
+r t
r tr
r tre t
Rδ
ρ
re Tre T
1−=ρ
ρ-t
erm
inal
con
ditio
n
Cal
ibra
tion
issu
eC
alib
rati
on is
sue -c
onte
mpo
rane
ous (
stat
ic)
0)
,(
=t
tX
YF
-rec
ursi
vely
dyn
amic
0)
,,
(1
=−
tt
tX
YY
F
0)
,,
(1
=+
tt
tX
YY
F-I
nter
tem
pora
l
How
do
we
calib
rate
an
inte
rtem
pora
lmod
el?
How
do
we
calib
rate
an
inte
rtem
pora
lmod
el?
Link
bet
wee
n ti
me
t va
lue
and
the
base
yea
r va
lue
Link
bet
wee
n ti
me
t va
lue
and
the
base
yea
r va
lue
Def
ine
∑=∆
=t k
kt
XX
cc1
_
01
23
time
X0
X1
X2
X3
ΔX
1
X
ΔX
2
ΔX
3
ΔX
1 +Δ
X1
+ Δ
X1
Then
, we
can
initi
aliz
e
0X
Xt=
tt
Xcc
X_
=U
pdat
e(ch
ange
)
∑=∆
+=
t kk
tX
XX
10
for a
ll t =
0, 1
, 2, …
Equ
ilibr
ium
?E
quili
briu
m?
Ste
ady
stat
e S
tead
y st
ate
To s
tabi
lize
debt
and
cap
ital s
tock
we
need
:σ
δrtr
trtrtr
rtr
trPY
IK
==
ΠΠ
In li
near
ised
form
py
ik
trtr
trtr
trtr
+=
+=
+π
π
Whe
n pr
ices
are
con
stan
t, w
e ha
ve
yi
ktr
trtr
==
Thr
ee te
st si
mul
atio
nsT
hree
test
sim
ulat
ions
to e
xam
ine
the
conv
erge
nce
prop
erty
of t
he
mod
el u
nder
initi
al d
ata
cond
ition
s (m
omen
tum
sim
ulat
ion)
; to
com
pare
the
beha
vior
of tr
ajec
tori
es u
nder
ra
tiona
l and
stat
ic e
xpec
tatio
ns, a
nd
To
exam
ine
the
conv
erge
nce
prop
erty
of t
he
mod
el w
hen
all e
xoge
nous
fact
ors g
row
at 2
pe
r ce
nt p
er a
num
eve
ryw
here
.
Som
e re
sult
s…S
ome
resu
lts…
Mom
entu
m s
imul
atio
n…M
omen
tum
sim
ulat
ion…
Grow
th Ra
tes of
Rea
l GDP
00.511.522.5
199820002010202020302040205020602070208020902100
aus
usa
Jpn
eu fsu row
Mom
entu
m s
imul
atio
n…M
omen
tum
sim
ulat
ion…
Grow
th R
ates
of R
eal G
NP
00.
511.
522.
5 1998
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
aus
usa
Jpn
eu fsu row
Mom
entu
m s
imul
atio
n…M
omen
tum
sim
ulat
ion…
Grow
th R
ates o
f Reg
ional
Capit
al St
ock
012345 199820002010202020302040205020602070208020902100
aus
usa
Jpn
eu fsu row
Mom
entu
m s
imul
atio
n…M
omen
tum
sim
ulat
ion…
Grow
th R
ates o
f Reg
ional
Real
Inves
tmen
t
00.511.522.5
199820002010202020302040205020602070208020902100
aus
usa
Jpn
eu fsu row
Sta
tic
vsra
tion
al e
xpec
tati
ons
Sta
tic
vsra
tion
al e
xpec
tati
ons
Sta
tic
vsra
tion
al e
xpec
tati
ons
Sta
tic
vsra
tion
al e
xpec
tati
ons
Gro
wth
Rat
es o
f Cap
ital S
tock
in th
e U
S
00.
511.
522.
533.
54 1998
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
SE
RE
Sta
tic
vsra
tion
al e
xpec
tati
ons
Sta
tic
vsra
tion
al e
xpec
tati
ons
Uni
form
gro
wth
of
2 pe
r ce
ntU
nifo
rm g
row
th o
f 2
per
cent
Real
GDP
Grow
th R
ates
01234 1998
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
Se Se Se Se Se Se
Uni
form
gro
wth
of
2 pe
r ce
ntU
nifo
rm g
row
th o
f 2
per
cent
GNP
Grow
th R
ates
01234 1998
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
aus
usa
jap eu fsu row
Uni
form
gro
wth
of
2 pe
r ce
ntU
nifo
rm g
row
th o
f 2
per
cent
Grow
th R
ates
of R
egio
nal C
apita
l Sto
ck
012345 1998
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
aus
usa
jap
eu fsu
row
Em
issi
on u
nder
the
mom
entu
mE
mis
sion
und
er t
he m
omen
tum
0204060
1997
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
Globa
l Emi
ssion
Per Y
ear
(Billio
n Ton
s of C
02 Eq
uivale
nt)
Glo
bal e
mis
sion
und
er 2
per
cent
pe
r an
num
uni
form
gro
wth
Glo
bal e
mis
sion
und
er 2
per
cent
pe
r an
num
uni
form
gro
wth
050100
150
200
1997
2000
2010
2020
2030
2040
2050
2060
2070
2080
2090
2100
Globa
l Emi
ssion
Per Y
ear
(Billio
n Ton
s of C
o2 Eq
uivale
nt)
Con
clus
ions
Con
clus
ions
A fi
xed
savi
ngs
rate
out
of c
urre
nt in
com
e (G
NP)
is
cons
iste
nt w
ith in
tert
empo
rally
optim
isin
g be
havi
orof
the
hous
ehol
ds.
The
mod
el d
ispl
ays
the
prop
erty
of a
neo
-cla
ssic
al g
row
th
mod
el -
the
grow
th ra
te o
f reg
iona
l eco
nom
ies
tend
to
conv
erge
tow
ard
the
grow
th ra
tes
of e
xoge
nous
ly s
uppl
ied
fact
ors
The
assu
mpt
ion
abou
t inv
esto
r’s e
xpec
tatio
ns fo
rmat
ion
did
not a
ffect
the
traj
ecto
ry n
otic
eabl
yA
n in
tert
empo
ralC
GE
mod
el c
an b
e so
lved
by
usin
g a
sing
le p
erio
d no
n-st
eady
sta
te d
atab
ase
and
impl
emen
ted
with
GEM
PAC
K.