How to measure fertility? parity progressions - demografi.dk · Socioeconomic Determinants for...
Transcript of How to measure fertility? parity progressions - demografi.dk · Socioeconomic Determinants for...
Soci
oec
onom
icD
eter
min
ants
for
Fer
tilit
y
Met
teG
erst
er
PhD
Def
ense
,Sep
tem
ber
15th
2009
How
tom
easu
refe
rtili
ty?
�Fer
tilit
y-
actu
albirth
s
�Fer
tilit
yis
apr
oce
ssth
atev
olve
sov
erse
vera
lye
ars
(in
prin
ciple
,from
men
arch
eto
men
opau
se)
�Sev
eral
aspec
tsar
epot
ential
lyof
inte
rest
-se
vera
lway
sto
mea
sure
it:
1.N
um
ber
ofch
ildre
nat
agi
ven
age→
stat
icor
2.th
epar
ity
prog
ress
ions→
dyn
amic
(mag
nifyi
ng
glas
s)
How
tom
easu
refe
rtili
ty?
�Fer
tilit
y-
actu
albirth
s
�Fer
tilit
yis
apr
oce
ssth
atev
olve
sov
erse
vera
lye
ars
(in
prin
ciple
,from
men
arch
eto
men
opau
se)
�Sev
eral
aspec
tsar
epot
ential
lyof
inte
rest
-se
vera
lway
sto
mea
sure
it:
1.N
um
ber
ofch
ildre
nat
agi
ven
age→
stat
icor
2.th
epar
ity
prog
ress
ions→
dyn
amic
(mag
nifyi
ng
glas
s)
How
tom
easu
refe
rtili
ty?
�Fer
tilit
y-
actu
albirth
s
�Fer
tilit
yis
apr
oce
ssth
atev
olve
sov
erse
vera
lye
ars
(in
prin
ciple
,from
men
arch
eto
men
opau
se)
�Sev
eral
aspec
tsar
epot
ential
lyof
inte
rest
-se
vera
lway
sto
mea
sure
it:
1.N
um
ber
ofch
ildre
nat
agi
ven
age→
stat
icor
2.th
epar
ity
prog
ress
ions→
dyn
amic
(mag
nifyi
ng
glas
s)
How
tom
easu
refe
rtili
ty?
�Fer
tilit
y-
actu
albirth
s
�Fer
tilit
yis
apr
oce
ssth
atev
olve
sov
erse
vera
lye
ars
(in
prin
ciple
,from
men
arch
eto
men
opau
se)
�Sev
eral
aspec
tsar
epot
ential
lyof
inte
rest
-se
vera
lway
sto
mea
sure
it:
1.N
um
ber
ofch
ildre
nat
agi
ven
age→
stat
icor
2.th
epar
ity
prog
ress
ions→
dyn
amic
(mag
nifyi
ng
glas
s)
How
tom
easu
refe
rtili
ty?
�Fer
tilit
y-
actu
albirth
s
�Fer
tilit
yis
apr
oce
ssth
atev
olve
sov
erse
vera
lye
ars
(in
prin
ciple
,from
men
arch
eto
men
opau
se)
�Sev
eral
aspec
tsar
epot
ential
lyof
inte
rest
-se
vera
lway
sto
mea
sure
it:
1.N
um
ber
ofch
ildre
nat
agi
ven
age→
stat
icor
2.th
epar
ity
prog
ress
ions→
dyn
amic
(mag
nifyi
ng
glas
s)
Det
erm
inan
tsfo
rfe
rtili
ty
�B
iolo
gica
lfa
ctor
s,hea
lth,fe
cundity
�Fac
tors
whic
hpot
ential
lyin
fluen
ceth
e(w
oman
’s)
choi
ce(w
hen
)to
hav
ech
ildre
n�
Iw
illgi
vetw
oex
ample
sof
the
latt
er:
the
soci
oec
onom
icfa
ctor
s
1.ed
uca
tion
and
2.la
bou
rm
arke
tat
tach
men
t
Det
erm
inan
tsfo
rfe
rtili
ty
�B
iolo
gica
lfa
ctor
s,hea
lth,fe
cundity
�Fac
tors
whic
hpot
ential
lyin
fluen
ceth
e(w
oman
’s)
choi
ce(w
hen
)to
hav
ech
ildre
n�
Iw
illgi
vetw
oex
ample
sof
the
latt
er:
the
soci
oec
onom
icfa
ctor
s
1.ed
uca
tion
and
2.la
bou
rm
arke
tat
tach
men
t
Det
erm
inan
tsfo
rfe
rtili
ty
�B
iolo
gica
lfa
ctor
s,hea
lth,fe
cundity
�Fac
tors
whic
hpot
ential
lyin
fluen
ceth
e(w
oman
’s)
choi
ce(w
hen
)to
hav
ech
ildre
n�
Iw
illgi
vetw
oex
ample
sof
the
latt
er:
the
soci
oec
onom
icfa
ctor
s
1.ed
uca
tion
and
2.la
bou
rm
arke
tat
tach
men
t
●
t
●
tt−
X(t
−)
tt++
ΔΔt
t−
X(t
−)
●
tt++
ΔΔt
t−
X(t
−)
●
●
T
X((T
))↔↔
N((T
))
Edu
cation
and
labou
rm
arke
tat
tach
men
tEffec
ton
fert
ility
?
�Subje
ctof
num
erou
sst
udie
sin
the
dem
ogra
phic
liter
ature
for
man
yye
ars
�Eco
nom
ican
dso
ciol
ogic
alth
eory
prov
ide
ath
eore
tica
lfram
ewor
kfo
rth
eunder
lyin
gm
echan
ism
s
�G
ary
Bec
ker,
Nob
elPrize
(eco
nom
ics)
1992
-A
Tre
atise
onth
eFam
ily[B
ecke
r,19
91]
Edu
cation
and
labou
rm
arke
tat
tach
men
tEffec
ton
fert
ility
?
�Subje
ctof
num
erou
sst
udie
sin
the
dem
ogra
phic
liter
ature
for
man
yye
ars
�Eco
nom
ican
dso
ciol
ogic
alth
eory
prov
ide
ath
eore
tica
lfram
ewor
kfo
rth
eunder
lyin
gm
echan
ism
s
�G
ary
Bec
ker,
Nob
elPrize
(eco
nom
ics)
1992
-A
Tre
atise
onth
eFam
ily[B
ecke
r,19
91]
Edu
cation
and
labou
rm
arke
tat
tach
men
tEffec
ton
fert
ility
?
�Subje
ctof
num
erou
sst
udie
sin
the
dem
ogra
phic
liter
ature
for
man
yye
ars
�Eco
nom
ican
dso
ciol
ogic
alth
eory
prov
ide
ath
eore
tica
lfram
ewor
kfo
rth
eunder
lyin
gm
echan
ism
s
�G
ary
Bec
ker,
Nob
elPrize
(eco
nom
ics)
1992
-A
Tre
atise
onth
eFam
ily[B
ecke
r,19
91]
Two
exam
ples
Par
ity
tran
sition
s
�Lab
our
mar
ket
atta
chm
ent
�N
orway
�Sim
ultan
euos
Equat
ions
Model
s
�A
dm
inistr
ativ
ere
gist
erdat
a:Sta
tist
isk
Sen
tral
byra
Ultim
ate
fert
ility
�Educa
tion
alat
tain
men
t
�D
enm
ark
�M
argi
nal
Str
uct
ura
lM
odel
s
�A
dm
inistr
ativ
ere
gist
erdat
a:D
anm
arks
Sta
tist
ik
Two
exam
ples
Par
ity
tran
sition
s
�Lab
our
mar
ket
atta
chm
ent
�N
orway
�Sim
ultan
euos
Equat
ions
Model
s
�A
dm
inistr
ativ
ere
gist
erdat
a:Sta
tist
isk
Sen
tral
byra
Ultim
ate
fert
ility
�Educa
tion
alat
tain
men
t
�D
enm
ark
�M
argi
nal
Str
uct
ura
lM
odel
s
�A
dm
inistr
ativ
ere
gist
erdat
a:D
anm
arks
Sta
tist
ik
Two
exam
ples
Par
ity
tran
sition
s
�Lab
our
mar
ket
atta
chm
ent
�N
orway
�Sim
ultan
euos
Equat
ions
Model
s
�A
dm
inistr
ativ
ere
gist
erdat
a:Sta
tist
isk
Sen
tral
byra
Ultim
ate
fert
ility
�Educa
tion
alat
tain
men
t
�D
enm
ark
�M
argi
nal
Str
uct
ura
lM
odel
s
�A
dm
inistr
ativ
ere
gist
erdat
a:D
anm
arks
Sta
tist
ik
Two
exam
ples
Par
ity
tran
sition
s
�Lab
our
mar
ket
atta
chm
ent
�N
orway
�Sim
ultan
euos
Equat
ions
Model
s
�A
dm
inistr
ativ
ere
gist
erdat
a:Sta
tist
isk
Sen
tral
byra
Ultim
ate
fert
ility
�Educa
tion
alat
tain
men
t
�D
enm
ark
�M
argi
nal
Str
uct
ura
lM
odel
s
�A
dm
inistr
ativ
ere
gist
erdat
a:D
anm
arks
Sta
tist
ik
Two
exam
ples
Par
ity
tran
sition
s
�Lab
our
mar
ket
atta
chm
ent
�N
orway
�Sim
ultan
euos
Equat
ions
Model
s
�A
dm
inistr
ativ
ere
gist
erdat
a:Sta
tist
isk
Sen
tral
byra
Ultim
ate
fert
ility
�Educa
tion
alat
tain
men
t
�D
enm
ark
�M
argi
nal
Str
uct
ura
lM
odel
s
�A
dm
inistr
ativ
ere
gist
erdat
a:D
anm
arks
Sta
tist
ik
Ove
rvie
w
Par
ity
tran
sition
sin
Nor
way
Ultim
ate
fert
ility
inD
enm
ark
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Bac
kgro
und
�Tra
nsition
from
bei
ng
aon
e-ch
ildm
other
toa
two-
child
mot
her
and
from
two-
child
toth
ree-
child
mot
her
�H
owdoes
itdep
end
onher
curr
ent
labou
rm
arke
tat
tach
men
t(e
mplo
yed
vsnon
-em
plo
yed)?
�Is
this
rela
tion
ship
pos
sibly
diff
eren
tac
ross
the
par
itie
s?
�D
ounob
serv
edch
arac
terist
ics
ofth
ewom
enpla
ya
role
?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Bac
kgro
und
�Tra
nsition
from
bei
ng
aon
e-ch
ildm
other
toa
two-
child
mot
her
and
from
two-
child
toth
ree-
child
mot
her
�H
owdoes
itdep
end
onher
curr
ent
labou
rm
arke
tat
tach
men
t(e
mplo
yed
vsnon
-em
plo
yed)?
�Is
this
rela
tion
ship
pos
sibly
diff
eren
tac
ross
the
par
itie
s?
�D
ounob
serv
edch
arac
terist
ics
ofth
ewom
enpla
ya
role
?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Bac
kgro
und
�Tra
nsition
from
bei
ng
aon
e-ch
ildm
other
toa
two-
child
mot
her
and
from
two-
child
toth
ree-
child
mot
her
�H
owdoes
itdep
end
onher
curr
ent
labou
rm
arke
tat
tach
men
t(e
mplo
yed
vsnon
-em
plo
yed)?
�Is
this
rela
tion
ship
pos
sibly
diff
eren
tac
ross
the
par
itie
s?
�D
ounob
serv
edch
arac
terist
ics
ofth
ewom
enpla
ya
role
?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Bac
kgro
und
�Tra
nsition
from
bei
ng
aon
e-ch
ildm
other
toa
two-
child
mot
her
and
from
two-
child
toth
ree-
child
mot
her
�H
owdoes
itdep
end
onher
curr
ent
labou
rm
arke
tat
tach
men
t(e
mplo
yed
vsnon
-em
plo
yed)?
�Is
this
rela
tion
ship
pos
sibly
diff
eren
tac
ross
the
par
itie
s?
�D
ounob
serv
edch
arac
terist
ics
ofth
ewom
enpla
ya
role
?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Stu
dypop
ulat
ion
�A
llwom
enof
NO
-origi
n
�w
hos
efirs
tch
ildre
aches
age
15m
ths
Apr
il19
94-O
ct20
02
�19
-40
year
sol
dat
firs
tbirth
�re
gist
ered
with
apar
tner
atfirs
tbirth
�no
studen
ts
�→
1266
08wom
en
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Stu
dypop
ulat
ion
�A
llwom
enof
NO
-origi
n
�w
hos
efirs
tch
ildre
aches
age
15m
ths
Apr
il19
94-O
ct20
02
�19
-40
year
sol
dat
firs
tbirth
�re
gist
ered
with
apar
tner
atfirs
tbirth
�no
studen
ts
�→
1266
08wom
en
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Stu
dypop
ulat
ion
�A
llwom
enof
NO
-origi
n
�w
hos
efirs
tch
ildre
aches
age
15m
ths
Apr
il19
94-O
ct20
02
�19
-40
year
sol
dat
firs
tbirth
�re
gist
ered
with
apar
tner
atfirs
tbirth
�no
studen
ts
�→
1266
08wom
en
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Why
effec
tof
empl
oym
ent?
�Em
plo
ymen
tst
atus
mig
ht
influen
ceth
edec
isio
nto
hav
eth
enex
tch
ildvi
ase
vera
lch
annel
s:�
Per
iods
away
from
the
labou
rm
arke
tar
epot
ential
lym
ore
cost
lyfo
rwom
enw
ho
are
curr
ently
ina
job
1.lo
ssof
skill
s(h
um
anca
pital
)2.
forg
one
inco
me
�th
erigh
tto
pai
dm
ater
nity
leav
e
�Can
bet
ter
affor
dto
hav
ea
child
?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Why
effec
tof
empl
oym
ent?
�Em
plo
ymen
tst
atus
mig
ht
influen
ceth
edec
isio
nto
hav
eth
enex
tch
ildvi
ase
vera
lch
annel
s:�
Per
iods
away
from
the
labou
rm
arke
tar
epot
ential
lym
ore
cost
lyfo
rwom
enw
ho
are
curr
ently
ina
job
1.lo
ssof
skill
s(h
um
anca
pital
)2.
forg
one
inco
me
�th
erigh
tto
pai
dm
ater
nity
leav
e
�Can
bet
ter
affor
dto
hav
ea
child
?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Why
effec
tof
empl
oym
ent?
�Em
plo
ymen
tst
atus
mig
ht
influen
ceth
edec
isio
nto
hav
eth
enex
tch
ildvi
ase
vera
lch
annel
s:�
Per
iods
away
from
the
labou
rm
arke
tar
epot
ential
lym
ore
cost
lyfo
rwom
enw
ho
are
curr
ently
ina
job
1.lo
ssof
skill
s(h
um
anca
pital
)2.
forg
one
inco
me
�th
erigh
tto
pai
dm
ater
nity
leav
e
�Can
bet
ter
affor
dto
hav
ea
child
?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Why
effec
tof
empl
oym
ent?
�Em
plo
ymen
tst
atus
mig
ht
influen
ceth
edec
isio
nto
hav
eth
enex
tch
ildvi
ase
vera
lch
annel
s:�
Per
iods
away
from
the
labou
rm
arke
tar
epot
ential
lym
ore
cost
lyfo
rwom
enw
ho
are
curr
ently
ina
job
1.lo
ssof
skill
s(h
um
anca
pital
)2.
forg
one
inco
me
�th
erigh
tto
pai
dm
ater
nity
leav
e
�Can
bet
ter
affor
dto
hav
ea
child
?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Why
effec
tof
empl
oym
ent?
�Em
plo
ymen
tst
atus
mig
ht
influen
ceth
edec
isio
nto
hav
eth
enex
tch
ildvi
ase
vera
lch
annel
s:�
Per
iods
away
from
the
labou
rm
arke
tar
epot
ential
lym
ore
cost
lyfo
rwom
enw
ho
are
curr
ently
ina
job
1.lo
ssof
skill
s(h
um
anca
pital
)2.
forg
one
inco
me
�th
erigh
tto
pai
dm
ater
nity
leav
e
�Can
bet
ter
affor
dto
hav
ea
child
?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Why
effec
tof
empl
oym
ent?
�Em
plo
ymen
tst
atus
mig
ht
influen
ceth
edec
isio
nto
hav
eth
enex
tch
ildvi
ase
vera
lch
annel
s:�
Per
iods
away
from
the
labou
rm
arke
tar
epot
ential
lym
ore
cost
lyfo
rwom
enw
ho
are
curr
ently
ina
job
1.lo
ssof
skill
s(h
um
anca
pital
)2.
forg
one
inco
me
�th
erigh
tto
pai
dm
ater
nity
leav
e
�Can
bet
ter
affor
dto
hav
ea
child
?
PhD
Def
ense
,Sep
tem
ber
2009
Uno
bser
ved
hete
roge
neity
Intu
itio
n
Why
...
�Pos
sibly
influen
cing
the
birth
inte
nsities
(e.g
.m
ore
fam
ily-o
rien
tation
)
�Pos
sibly
influen
cing
the
emplo
ymen
tpr
oce
ss(e
.g.
care
er-o
rien
tation
)
�M
ight
give
rise
toa
spuriou
sre
lation
ship
�Pot
ential
lyco
rrel
ated
�T
he
emplo
ymen
tst
atus
isen
dog
enou
s(a
sop
pos
edto
exog
enou
s)
How
...
�Set
up
model
equat
ions
for
the
birth
sw
ith
random
effec
t
�Set
up
model
equat
ions
for
the
emplo
ymen
tpr
oce
ssw
ith
random
effec
t(s)
�al
low
thes
era
ndom
effec
tsto
be
corr
elat
edby
estim
atin
gth
ese
equat
ions
sim
ultan
eously
Uno
bser
ved
hete
roge
neity
Intu
itio
n
Why
...
�Pos
sibly
influen
cing
the
birth
inte
nsities
(e.g
.m
ore
fam
ily-o
rien
tation
)
�Pos
sibly
influen
cing
the
emplo
ymen
tpr
oce
ss(e
.g.
care
er-o
rien
tation
)
�M
ight
give
rise
toa
spuriou
sre
lation
ship
�Pot
ential
lyco
rrel
ated
�T
he
emplo
ymen
tst
atus
isen
dog
enou
s(a
sop
pos
edto
exog
enou
s)
How
...
�Set
up
model
equat
ions
for
the
birth
sw
ith
random
effec
t
�Set
up
model
equat
ions
for
the
emplo
ymen
tpr
oce
ssw
ith
random
effec
t(s)
�al
low
thes
era
ndom
effec
tsto
be
corr
elat
edby
estim
atin
gth
ese
equat
ions
sim
ultan
eously
Uno
bser
ved
hete
roge
neity
Intu
itio
n
Why
...
�Pos
sibly
influen
cing
the
birth
inte
nsities
(e.g
.m
ore
fam
ily-o
rien
tation
)
�Pos
sibly
influen
cing
the
emplo
ymen
tpr
oce
ss(e
.g.
care
er-o
rien
tation
)
�M
ight
give
rise
toa
spuriou
sre
lation
ship
�Pot
ential
lyco
rrel
ated
�T
he
emplo
ymen
tst
atus
isen
dog
enou
s(a
sop
pos
edto
exog
enou
s)
How
...
�Set
up
model
equat
ions
for
the
birth
sw
ith
random
effec
t
�Set
up
model
equat
ions
for
the
emplo
ymen
tpr
oce
ssw
ith
random
effec
t(s)
�al
low
thes
era
ndom
effec
tsto
be
corr
elat
edby
estim
atin
gth
ese
equat
ions
sim
ultan
eously
Uno
bser
ved
hete
roge
neity
Intu
itio
n
Why
...
�Pos
sibly
influen
cing
the
birth
inte
nsities
(e.g
.m
ore
fam
ily-o
rien
tation
)
�Pos
sibly
influen
cing
the
emplo
ymen
tpr
oce
ss(e
.g.
care
er-o
rien
tation
)
�M
ight
give
rise
toa
spuriou
sre
lation
ship
�Pot
ential
lyco
rrel
ated
�T
he
emplo
ymen
tst
atus
isen
dog
enou
s(a
sop
pos
edto
exog
enou
s)
How
...
�Set
up
model
equat
ions
for
the
birth
sw
ith
random
effec
t
�Set
up
model
equat
ions
for
the
emplo
ymen
tpr
oce
ssw
ith
random
effec
t(s)
�al
low
thes
era
ndom
effec
tsto
be
corr
elat
edby
estim
atin
gth
ese
equat
ions
sim
ultan
eously
Uno
bser
ved
hete
roge
neity
Intu
itio
n
Why
...
�Pos
sibly
influen
cing
the
birth
inte
nsities
(e.g
.m
ore
fam
ily-o
rien
tation
)
�Pos
sibly
influen
cing
the
emplo
ymen
tpr
oce
ss(e
.g.
care
er-o
rien
tation
)
�M
ight
give
rise
toa
spuriou
sre
lation
ship
�Pot
ential
lyco
rrel
ated
�T
he
emplo
ymen
tst
atus
isen
dog
enou
s(a
sop
pos
edto
exog
enou
s)
How
...
�Set
up
model
equat
ions
for
the
birth
sw
ith
random
effec
t
�Set
up
model
equat
ions
for
the
emplo
ymen
tpr
oce
ssw
ith
random
effec
t(s)
�al
low
thes
era
ndom
effec
tsto
be
corr
elat
edby
estim
atin
gth
ese
equat
ions
sim
ultan
eously
Uno
bser
ved
hete
roge
neity
Intu
itio
n
Why
...
�Pos
sibly
influen
cing
the
birth
inte
nsities
(e.g
.m
ore
fam
ily-o
rien
tation
)
�Pos
sibly
influen
cing
the
emplo
ymen
tpr
oce
ss(e
.g.
care
er-o
rien
tation
)
�M
ight
give
rise
toa
spuriou
sre
lation
ship
�Pot
ential
lyco
rrel
ated
�T
he
emplo
ymen
tst
atus
isen
dog
enou
s(a
sop
pos
edto
exog
enou
s)
How
...
�Set
up
model
equat
ions
for
the
birth
sw
ith
random
effec
t
�Set
up
model
equat
ions
for
the
emplo
ymen
tpr
oce
ssw
ith
random
effec
t(s)
�al
low
thes
era
ndom
effec
tsto
be
corr
elat
edby
estim
atin
gth
ese
equat
ions
sim
ultan
eously
Uno
bser
ved
hete
roge
neity
Intu
itio
n
Why
...
�Pos
sibly
influen
cing
the
birth
inte
nsities
(e.g
.m
ore
fam
ily-o
rien
tation
)
�Pos
sibly
influen
cing
the
emplo
ymen
tpr
oce
ss(e
.g.
care
er-o
rien
tation
)
�M
ight
give
rise
toa
spuriou
sre
lation
ship
�Pot
ential
lyco
rrel
ated
�T
he
emplo
ymen
tst
atus
isen
dog
enou
s(a
sop
pos
edto
exog
enou
s)
How
...
�Set
up
model
equat
ions
for
the
birth
sw
ith
random
effec
t
�Set
up
model
equat
ions
for
the
emplo
ymen
tpr
oce
ssw
ith
random
effec
t(s)
�al
low
thes
era
ndom
effec
tsto
be
corr
elat
edby
estim
atin
gth
ese
equat
ions
sim
ultan
eously
Uno
bser
ved
hete
roge
neity
Intu
itio
n
Why
...
�Pos
sibly
influen
cing
the
birth
inte
nsities
(e.g
.m
ore
fam
ily-o
rien
tation
)
�Pos
sibly
influen
cing
the
emplo
ymen
tpr
oce
ss(e
.g.
care
er-o
rien
tation
)
�M
ight
give
rise
toa
spuriou
sre
lation
ship
�Pot
ential
lyco
rrel
ated
�T
he
emplo
ymen
tst
atus
isen
dog
enou
s(a
sop
pos
edto
exog
enou
s)
How
...
�Set
up
model
equat
ions
for
the
birth
sw
ith
random
effec
t
�Set
up
model
equat
ions
for
the
emplo
ymen
tpr
oce
ssw
ith
random
effec
t(s)
�al
low
thes
era
ndom
effec
tsto
be
corr
elat
edby
estim
atin
gth
ese
equat
ions
sim
ultan
eously
Uno
bser
ved
hete
roge
neity
Intu
itio
n
Why
...
�Pos
sibly
influen
cing
the
birth
inte
nsities
(e.g
.m
ore
fam
ily-o
rien
tation
)
�Pos
sibly
influen
cing
the
emplo
ymen
tpr
oce
ss(e
.g.
care
er-o
rien
tation
)
�M
ight
give
rise
toa
spuriou
sre
lation
ship
�Pot
ential
lyco
rrel
ated
�T
he
emplo
ymen
tst
atus
isen
dog
enou
s(a
sop
pos
edto
exog
enou
s)
How
...
�Set
up
model
equat
ions
for
the
birth
sw
ith
random
effec
t
�Set
up
model
equat
ions
for
the
emplo
ymen
tpr
oce
ssw
ith
random
effec
t(s)
�al
low
thes
era
ndom
effec
tsto
be
corr
elat
edby
estim
atin
gth
ese
equat
ions
sim
ultan
eously
Uno
bser
ved
hete
roge
neity
Intu
itio
n
Why
...
�Pos
sibly
influen
cing
the
birth
inte
nsities
(e.g
.m
ore
fam
ily-o
rien
tation
)
�Pos
sibly
influen
cing
the
emplo
ymen
tpr
oce
ss(e
.g.
care
er-o
rien
tation
)
�M
ight
give
rise
toa
spuriou
sre
lation
ship
�Pot
ential
lyco
rrel
ated
�T
he
emplo
ymen
tst
atus
isen
dog
enou
s(a
sop
pos
edto
exog
enou
s)
How
...
�Set
up
model
equat
ions
for
the
birth
sw
ith
random
effec
t
�Set
up
model
equat
ions
for
the
emplo
ymen
tpr
oce
ssw
ith
random
effec
t(s)
�al
low
thes
era
ndom
effec
tsto
be
corr
elat
edby
estim
atin
gth
ese
equat
ions
sim
ultan
eously
Mode
l
Birth
inte
nsitie
s
log
λ2(t
)=
log
λ(2
)0
(t)+
β′ 2·X
(2) (
t−)
log
λ3(t
)=
log
λ(3
)0
(t)+
β′ 3·X
(3) (
t−)
wher
et
den
otes
age
ofpr
evio
us
child
(-15
mon
ths)
Em
ploy
men
tan
dno
n-em
ploy
men
tin
tens
itie
s
log
λe(s
)=
log
λ(e
)0
(s)+
β′ e·X
(e) (
s)
log
λne(s
)=
log
λ(n
e)0
(s)+
β′ ne·X
(ne)
(s)
wher
es
den
otes
tim
esince
beg
innin
gof
each
spel
l
→Sim
ultaneo
us
Equations
Model
(SEM
)
Mode
l
Birth
inte
nsitie
s
log
λ2(t
)=
log
λ(2
)0
(t)+
β′ 2·X
(2) (
t−)
log
λ3(t
)=
log
λ(3
)0
(t)+
β′ 3·X
(3) (
t−)
wher
et
den
otes
age
ofpr
evio
us
child
(-15
mon
ths)
Em
ploy
men
tan
dno
n-em
ploy
men
tin
tens
itie
s
log
λe(s
)=
log
λ(e
)0
(s)+
β′ e·X
(e) (
s)
log
λne(s
)=
log
λ(n
e)0
(s)+
β′ ne·X
(ne)
(s)
wher
es
den
otes
tim
esince
beg
innin
gof
each
spel
l
→Sim
ple
Model
(SM
)
Mode
l
Birth
inte
nsitie
s
log
λ2(t
)=
log
λ(2
)0
(t)+
β′ 2·X
(2) (
t−)+
ε b
log
λ3(t
)=
log
λ(3
)0
(t)+
β′ 3·X
(3) (
t−)+
ε b
wher
et
den
otes
age
ofpr
evio
us
child
(-15
mon
ths)
Em
ploy
men
tan
dno
n-em
ploy
men
tin
tens
itie
s
log
λe(s
)=
log
λ(e
)0
(s)+
β′ e·X
(e) (
s)+
ε e
log
λne(s
)=
log
λ(n
e)0
(s)+
β′ ne·X
(ne)
(s)+
ε ne
wher
es
den
otes
tim
esince
beg
innin
gof
each
spel
l
→Sim
ultaneo
us
Equations
Model
(SEM
)
Not
quite
done
...
Ass
ume
that
�(ε
bε e
ε ne)T
∼N 3
(0,Ω
ε b,ε
e,ε
ne)
�co
nditio
nal
on(ε
bε e
ε ne)T
,th
ese
par
ate
birth
spel
lsfo
rea
chwom
anar
ein
dep
enden
t
�an
dso
are
the
emplo
ymen
tan
dnon
-em
plo
ymen
tsp
ells
Not
quite
done
...
Ass
ume
that
�(ε
bε e
ε ne)T
∼N 3
(0,Ω
ε b,ε
e,ε
ne)
�co
nditio
nal
on(ε
bε e
ε ne)T
,th
ese
par
ate
birth
spel
lsfo
rea
chwom
anar
ein
dep
enden
t
�an
dso
are
the
emplo
ymen
tan
dnon
-em
plo
ymen
tsp
ells
Not
quite
done
...
Ass
ume
that
�(ε
bε e
ε ne)T
∼N 3
(0,Ω
ε b,ε
e,ε
ne)
�co
nditio
nal
on(ε
bε e
ε ne)T
,th
ese
par
ate
birth
spel
lsfo
rea
chwom
anar
ein
dep
enden
t
�an
dso
are
the
emplo
ymen
tan
dnon
-em
plo
ymen
tsp
ells
Not
quite
done
...
Ass
ume
that
�(ε
bε e
ε ne)T
∼N 3
(0,Ω
ε b,ε
e,ε
ne)
�co
nditio
nal
on(ε
bε e
ε ne)T
,th
ese
par
ate
birth
spel
lsfo
rea
chwom
anar
ein
dep
enden
t
�an
dso
are
the
emplo
ymen
tan
dnon
-em
plo
ymen
tsp
ells
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Res
ults
2nd
child
:
Model
SEM
Model
SM
RR
pRR
p
Em
plo
yed
(ref
)1
-1
-N
on-e
mplo
yed
0.92
9<
0.01
0.95
6<
0.01
Con
trol
led
for...
mot
her
’sag
e,ca
lendar
year
,an
ded
uca
tion
.
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Res
ults
3rd
child
:
Model
SEM
Model
SM
RR
pRR
p
Em
plo
yed
(ref
)1
<0.
011
<0.
01N
on-e
mplo
yed
1.09
7<
0.01
1.13
2<
0.01
Con
trol
led
for...
mot
her
’sag
e,ca
lendar
year
,an
ded
uca
tion
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Res
ults
Unobse
rved
het
erogen
eity
sd(ε
b)
0.37
9co
rr(ε
b,ε
e)
−0.2
45sd
(εe)
1.43
6co
rr(ε
b,ε
ne)
−0.3
18sd
(εne)
0.78
2co
rr(ε
e,ε
ne)
0.55
1
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Con
clus
ion
Par
ity
tran
sitions
inN
orway
�T
he
seco
nd
birth
inte
nsity
issm
alle
rfo
rnon
-em
plo
yed
wom
en(R
R=
0.93
)
�T
he
third
birth
inte
nsity
isla
rger
for
non
-em
plo
yed
wom
en(R
R=
1.09
7)
�Child
2:w
hen
??
�Child
3:if??
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Con
clus
ion
Par
ity
tran
sitions
inN
orway
�T
he
seco
nd
birth
inte
nsity
issm
alle
rfo
rnon
-em
plo
yed
wom
en(R
R=
0.93
)
�T
he
third
birth
inte
nsity
isla
rger
for
non
-em
plo
yed
wom
en(R
R=
1.09
7)
�Child
2:w
hen
??
�Child
3:if??
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Con
clus
ion
Par
ity
tran
sitions
inN
orway
�T
he
seco
nd
birth
inte
nsity
issm
alle
rfo
rnon
-em
plo
yed
wom
en(R
R=
0.93
)
�T
he
third
birth
inte
nsity
isla
rger
for
non
-em
plo
yed
wom
en(R
R=
1.09
7)
�Child
2:w
hen
??
�Child
3:if??
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Con
clus
ion
Par
ity
tran
sitions
inN
orway
�T
he
seco
nd
birth
inte
nsity
issm
alle
rfo
rnon
-em
plo
yed
wom
en(R
R=
0.93
)
�T
he
third
birth
inte
nsity
isla
rger
for
non
-em
plo
yed
wom
en(R
R=
1.09
7)
�Child
2:w
hen
??
�Child
3:if??
PhD
Def
ense
,Sep
tem
ber
2009
Ove
rvie
w
Par
ity
tran
sition
sin
Nor
way
Ultim
ate
fert
ility
inD
enm
ark
Illus
trat
ion
tt++
ΔΔt
t−
X(t
−)
●
●
T
X((T
))↔↔
N((T
))
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ultim
ate
fert
ility
�N
um
ber
ofch
ildre
nat
age
41
�H
owdoes
itdep
end
oned
uca
tion
alat
tain
men
t?
�Is
this
rela
tion
ship
stat
ic?
�Fee
dbac
k...
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ultim
ate
fert
ility
�N
um
ber
ofch
ildre
nat
age
41
�H
owdoes
itdep
end
oned
uca
tion
alat
tain
men
t?
�Is
this
rela
tion
ship
stat
ic?
�Fee
dbac
k...
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ultim
ate
fert
ility
�N
um
ber
ofch
ildre
nat
age
41
�H
owdoes
itdep
end
oned
uca
tion
alat
tain
men
t?
�Is
this
rela
tion
ship
stat
ic?
�Fee
dbac
k...
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ultim
ate
fert
ility
�N
um
ber
ofch
ildre
nat
age
41
�H
owdoes
itdep
end
oned
uca
tion
alat
tain
men
t?
�Is
this
rela
tion
ship
stat
ic?
�Fee
dbac
k...
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Why
aneff
ect
ofed
ucat
ion
onfe
rtili
ty?
�W
omen
with
ahig
her
educa
tion
mig
ht
hav
ehig
her
oppor
tunity
cost
s-
mor
elik
ely
topurs
ue
aca
reer
�T
hei
rla
bou
rm
arke
tsitu
atio
nm
ight
be
mor
eflex
ible
-ea
sier
toco
mbin
e
�O
ther
fact
ors?
Mor
ere
sourc
es?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Why
aneff
ect
ofed
ucat
ion
onfe
rtili
ty?
�W
omen
with
ahig
her
educa
tion
mig
ht
hav
ehig
her
oppor
tunity
cost
s-
mor
elik
ely
topurs
ue
aca
reer
�T
hei
rla
bou
rm
arke
tsitu
atio
nm
ight
be
mor
eflex
ible
-ea
sier
toco
mbin
e
�O
ther
fact
ors?
Mor
ere
sourc
es?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Why
aneff
ect
ofed
ucat
ion
onfe
rtili
ty?
�W
omen
with
ahig
her
educa
tion
mig
ht
hav
ehig
her
oppor
tunity
cost
s-
mor
elik
ely
topurs
ue
aca
reer
�T
hei
rla
bou
rm
arke
tsitu
atio
nm
ight
be
mor
eflex
ible
-ea
sier
toco
mbin
e
�O
ther
fact
ors?
Mor
ere
sourc
es?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
The
stud
ypop
ulat
ion
All
wom
enw
ho...
�bor
nin
1963
�liv
ing
inD
enm
ark
Jan
1st
1981
(and
each
year
1982
-200
5)
�of
Dan
ish
orig
in
�w
ho
hav
eco
mple
ted
apr
epar
ator
yupper
seco
ndar
yed
uca
tion
(PU
SE,da:
Stu
den
tere
ksam
en)
no
late
rth
anO
ctob
er19
83
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Des
crip
tive
sEduca
tion
and
fert
ility
(2005)
Educa
tion
%ch
less
Avg
.ch
ildre
nFre
quen
cyPer
cent
PU
SE
17.8
1.71
1169
14.6
Voca
tion
al13
.21.
8413
1716
.4Shor
tte
rtia
ry14
.71.
8067
28.
4M
ediu
mte
rtia
ry11
.41.
9735
4444
.1Lon
gte
rtia
ry16
.71.
8113
3016
.6
Tot
al13
.81.
8780
3210
0.1
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Des
crip
tive
sEduca
tion
and
fert
ility
(2005)
Educa
tion
%ch
less
Avg
.ch
ildre
nFre
quen
cyPer
cent
PU
SE
17.8
1.71
1169
14.6
Voca
tion
al13
.21.
8413
1716
.4Shor
tte
rtia
ry14
.71.
8067
28.
4M
ediu
mte
rtia
ry11
.41.
9735
4444
.1Lon
gte
rtia
ry16
.71.
8113
3016
.6
Tot
al13
.81.
8780
3210
0.1
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Des
crip
tive
sEduca
tion
and
fert
ility
(2005)
Educa
tion
%ch
less
Avg
.ch
ildre
nFre
quen
cyPer
cent
PU
SE
17.8
1.71
1169
14.6
Voca
tion
al13
.21.
8413
1716
.4Shor
tte
rtia
ry14
.71.
8067
28.
4M
ediu
mte
rtia
ry11
.41.
9735
4444
.1Lon
gte
rtia
ry16
.71.
8113
3016
.6
Tot
al13
.81.
8780
3210
0.1
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Des
crip
tive
sEduca
tion
and
fert
ility
(2005)
Educa
tion
%ch
less
Avg
.ch
ildre
nFre
quen
cyPer
cent
PU
SE
17.8
1.71
1169
14.6
Voca
tion
al13
.21.
8413
1716
.4Shor
tte
rtia
ry14
.71.
8067
28.
4M
ediu
mte
rtia
ry11
.41.
9735
4444
.1Lon
gte
rtia
ry16
.71.
8113
3016
.6
Tot
al13
.81.
8780
3210
0.1
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Des
crip
tive
sEduca
tion
and
fert
ility
(2005)
Educa
tion
%ch
less
Avg
.ch
ildre
nFre
quen
cyPer
cent
PU
SE
17.8
1.71
1169
14.6
Voca
tion
al13
.21.
8413
1716
.4Shor
tte
rtia
ry14
.71.
8067
28.
4M
ediu
mte
rtia
ry11
.41.
9735
4444
.1Lon
gte
rtia
ry16
.71.
8113
3016
.6
Tot
al13
.81.
8780
3210
0.1
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Fee
dbac
kIn
tuitio
n �W
ew
ish
toas
sess
tow
hic
hex
tent
educa
tion
aldiff
eren
ces
inultim
ate
fert
ility
are
attr
ibuta
ble
tofe
edbac
kpat
tern
s�
Exa
mple
:�
Ass
um
ewom
enw
ho
bec
ome
mot
her
sw
hile
enro
lled
inuniv
ersity
are
mor
ein
clin
edto
inte
rrupt/
chan
geto
ash
orte
ron
e(d
evia
tefrom
thei
ror
igin
alst
rate
gyas
are
sult
ofth
eir
fert
ility
)�
→fe
wer
child
ren
amon
ghig
hly
educa
ted
wom
en
�T
he
birth
proce
ssitse
lfac
tsas
atim
e-dep
enden
tco
nfo
under
for
the
effec
tof
educa
tion
onfe
rtili
ty
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Fee
dbac
kIn
tuitio
n �W
ew
ish
toas
sess
tow
hic
hex
tent
educa
tion
aldiff
eren
ces
inultim
ate
fert
ility
are
attr
ibuta
ble
tofe
edbac
kpat
tern
s�
Exa
mple
:�
Ass
um
ewom
enw
ho
bec
ome
mot
her
sw
hile
enro
lled
inuniv
ersity
are
mor
ein
clin
edto
inte
rrupt/
chan
geto
ash
orte
ron
e(d
evia
tefrom
thei
ror
igin
alst
rate
gyas
are
sult
ofth
eir
fert
ility
)�
→fe
wer
child
ren
amon
ghig
hly
educa
ted
wom
en
�T
he
birth
proce
ssitse
lfac
tsas
atim
e-dep
enden
tco
nfo
under
for
the
effec
tof
educa
tion
onfe
rtili
ty
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Fee
dbac
kIn
tuitio
n �W
ew
ish
toas
sess
tow
hic
hex
tent
educa
tion
aldiff
eren
ces
inultim
ate
fert
ility
are
attr
ibuta
ble
tofe
edbac
kpat
tern
s�
Exa
mple
:�
Ass
um
ewom
enw
ho
bec
ome
mot
her
sw
hile
enro
lled
inuniv
ersity
are
mor
ein
clin
edto
inte
rrupt/
chan
geto
ash
orte
ron
e(d
evia
tefrom
thei
ror
igin
alst
rate
gyas
are
sult
ofth
eir
fert
ility
)�
→fe
wer
child
ren
amon
ghig
hly
educa
ted
wom
en
�T
he
birth
proce
ssitse
lfac
tsas
atim
e-dep
enden
tco
nfo
under
for
the
effec
tof
educa
tion
onfe
rtili
ty
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Fee
dbac
kIn
tuitio
n �W
ew
ish
toas
sess
tow
hic
hex
tent
educa
tion
aldiff
eren
ces
inultim
ate
fert
ility
are
attr
ibuta
ble
tofe
edbac
kpat
tern
s�
Exa
mple
:�
Ass
um
ewom
enw
ho
bec
ome
mot
her
sw
hile
enro
lled
inuniv
ersity
are
mor
ein
clin
edto
inte
rrupt/
chan
geto
ash
orte
ron
e(d
evia
tefrom
thei
ror
igin
alst
rate
gyas
are
sult
ofth
eir
fert
ility
)�
→fe
wer
child
ren
amon
ghig
hly
educa
ted
wom
en
�T
he
birth
proce
ssitse
lfac
tsas
atim
e-dep
enden
tco
nfo
under
for
the
effec
tof
educa
tion
onfe
rtili
ty
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Fee
dbac
kIn
tuitio
n �W
ew
ish
toas
sess
tow
hic
hex
tent
educa
tion
aldiff
eren
ces
inultim
ate
fert
ility
are
attr
ibuta
ble
tofe
edbac
kpat
tern
s�
Exa
mple
:�
Ass
um
ewom
enw
ho
bec
ome
mot
her
sw
hile
enro
lled
inuniv
ersity
are
mor
ein
clin
edto
inte
rrupt/
chan
geto
ash
orte
ron
e(d
evia
tefrom
thei
ror
igin
alst
rate
gyas
are
sult
ofth
eir
fert
ility
)�
→fe
wer
child
ren
amon
ghig
hly
educa
ted
wom
en
�T
he
birth
proce
ssitse
lfac
tsas
atim
e-dep
enden
tco
nfo
under
for
the
effec
tof
educa
tion
onfe
rtili
ty
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Fee
dbac
kIs
itin
the
dat
a?Can
we
rem
ove
it?
1.Is
feed
bac
kpr
esen
tin
the
study
pop
ula
tion
athan
d?
2.If
so,to
whic
hex
tent
are
the
educa
tion
aldiff
eren
ces
inultim
ate
fert
ility
attr
ibuta
ble
toth
efe
edbac
k?
3.Educa
tion
aldiff
eren
ces
inultim
ate
fert
ility
ifth
ere
wer
eno
feed
bac
k?
4.O
ne
par
ticu
lar
aspec
tof
ultim
ate
fert
ility
:W
hat
isth
epr
obab
ility
ofhav
ing
3ch
ildre
nat
age
41fo
rdiff
eren
ted
uca
tion
alat
tain
men
ts?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Fee
dbac
k(E
ndog
enei
ty)
Defi
nitio
n[H
ernan
etal
.,2001]
�A
ssum
est
udy
pop
ula
tion
follo
wed
thro
ugh
out
the
tim
e-per
iod
{0,1
,...
,T}
�Let
B(t
)be
the
fert
ility
proce
ssan
dE
(t)
the
educa
tion
proce
ss
�Fee
dbac
k:If
ther
eex
ists
t∈{0
,1,.
..,T
}s.t.
the
conditio
n
E(t
)∐ B
(t)|(
E(t
−1)
,Z)
isnot
met
.
�Endogen
eity
(vs.
exogen
eity
)
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Fee
dbac
k(E
ndog
enei
ty)
Defi
nitio
n[H
ernan
etal
.,2001]
�A
ssum
est
udy
pop
ula
tion
follo
wed
thro
ugh
out
the
tim
e-per
iod
{0,1
,...
,T}
�Let
B(t
)be
the
fert
ility
proce
ssan
dE
(t)
the
educa
tion
proce
ss
�Fee
dbac
k:If
ther
eex
ists
t∈{0
,1,.
..,T
}s.t.
the
conditio
n
E(t
)∐ B
(t)|(
E(t
−1)
,Z)
isnot
met
.
�Endogen
eity
(vs.
exogen
eity
)
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Fee
dbac
k(E
ndog
enei
ty)
Defi
nitio
n[H
ernan
etal
.,2001]
�A
ssum
est
udy
pop
ula
tion
follo
wed
thro
ugh
out
the
tim
e-per
iod
{0,1
,...
,T}
�Let
B(t
)be
the
fert
ility
proce
ssan
dE
(t)
the
educa
tion
proce
ss
�Fee
dbac
k:If
ther
eex
ists
t∈{0
,1,.
..,T
}s.t.
the
conditio
n
E(t
)∐ B
(t)|(
E(t
−1)
,Z)
isnot
met
.
�Endogen
eity
(vs.
exogen
eity
)
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Fee
dbac
k(E
ndog
enei
ty)
Defi
nitio
n[H
ernan
etal
.,2001]
�A
ssum
est
udy
pop
ula
tion
follo
wed
thro
ugh
out
the
tim
e-per
iod
{0,1
,...
,T}
�Let
B(t
)be
the
fert
ility
proce
ssan
dE
(t)
the
educa
tion
proce
ss
�Fee
dbac
k:If
ther
eex
ists
t∈{0
,1,.
..,T
}s.t.
the
conditio
n
E(t
)∐ B
(t)|(
E(t
−1)
,Z)
isnot
met
.
�Endogen
eity
(vs.
exogen
eity
)
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Isfe
edba
ckpr
esen
tin
the
stud
ypop
ulat
ion?
You
ngm
othe
rsan
ddr
op-o
uts
�M
other
bef
ore
1986
-ed
uca
tion
in20
05?
Table
�Lea
ving
educa
tion
afte
rbirth
-ed
uca
tion
in20
05?
Table
Mode
lpr
obab
ility
ofdr
oppi
ngou
tof
educ
atio
n
�Y
it:
indic
ator
for
wom
ani
inte
rrupting
educa
tion
alen
rolm
ent
inye
art
(con
d.
onbei
ng
enro
lled)
�lo
git
[Pr(
Yit|X
it,Z
i,en
rolle
d)]
=α
+β′ ·
Xit
+γ′ ·
Zi
�In
tera
ctio
nbet
wee
ngi
ving
birth
and
educa
tion
inw
hic
hsh
eis
enro
lled
Illu
stra
tion
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Isfe
edba
ckpr
esen
tin
the
stud
ypop
ulat
ion?
You
ngm
othe
rsan
ddr
op-o
uts
�M
other
bef
ore
1986
-ed
uca
tion
in20
05?
Table
�Lea
ving
educa
tion
afte
rbirth
-ed
uca
tion
in20
05?
Table
Mode
lpr
obab
ility
ofdr
oppi
ngou
tof
educ
atio
n
�Y
it:
indic
ator
for
wom
ani
inte
rrupting
educa
tion
alen
rolm
ent
inye
art
(con
d.
onbei
ng
enro
lled)
�lo
git
[Pr(
Yit|X
it,Z
i,en
rolle
d)]
=α
+β′ ·
Xit
+γ′ ·
Zi
�In
tera
ctio
nbet
wee
ngi
ving
birth
and
educa
tion
inw
hic
hsh
eis
enro
lled
Illu
stra
tion
PhD
Def
ense
,Sep
tem
ber
2009
Edu
cation
aldi
ffer
ence
sif
ther
ewer
eno
feed
back
?M
argin
alStr
uct
ura
lM
odel
s(M
SM
)[H
ernan
etal
.,2001]
Pot
ential
Out
com
es:
Ye:
the
indic
ator
ofbei
ng
am
other
of3
child
ren
(as
oppos
edto
less
than
3)by
age
41if
educa
tion
alst
rate
gye
wer
efo
llowed
Mar
gina
lStr
uctu
ralM
ode
l(M
SM
):
logi
t[ P
r(Y
e=
1|Z
i)] =
δ 1+
ε 1·Z
i+
φ1·f
(e)
How
toas
sess
info
rmat
ion
onpot
ential
outc
omes
?
Use
obse
rved
dat
a-
alon
gw
ith
asu
itab
lese
tof
assu
mption
s
Edu
cation
aldi
ffer
ence
sif
ther
ewer
eno
feed
back
?M
argin
alStr
uct
ura
lM
odel
s(M
SM
)[H
ernan
etal
.,2001]
Pot
ential
Out
com
es:
Ye:
the
indic
ator
ofbei
ng
am
other
of3
child
ren
(as
oppos
edto
less
than
3)by
age
41if
educa
tion
alst
rate
gye
wer
efo
llowed
Mar
gina
lStr
uctu
ralM
ode
l(M
SM
):
logi
t[ P
r(Y
e=
1|Z
i)] =
δ 1+
ε 1·Z
i+
φ1·f
(e)
How
toas
sess
info
rmat
ion
onpot
ential
outc
omes
?
Use
obse
rved
dat
a-
alon
gw
ith
asu
itab
lese
tof
assu
mption
s
Edu
cation
aldi
ffer
ence
sif
ther
ewer
eno
feed
back
?M
argin
alStr
uct
ura
lM
odel
s(M
SM
)[H
ernan
etal
.,2001]
Pot
ential
Out
com
es:
Ye:
the
indic
ator
ofbei
ng
am
other
of3
child
ren
(as
oppos
edto
less
than
3)by
age
41if
educa
tion
alst
rate
gye
wer
efo
llowed
Mar
gina
lStr
uctu
ralM
ode
l(M
SM
):
logi
t[ P
r(Y
e=
1|Z
i)] =
δ 1+
ε 1·Z
i+
φ1·f
(e)
How
toas
sess
info
rmat
ion
onpot
ential
outc
omes
?
Use
obse
rved
dat
a-
alon
gw
ith
asu
itab
lese
tof
assu
mption
s
Mar
gina
lStr
uctu
ralM
ode
ls(c
ontd
)In
vers
eP
robab
ility
ofT
reat
men
tW
eights
�Id
ea:
re-w
eigh
tth
eor
igin
alpop
ula
tion
toco
nst
ruct
ahyp
othet
ical
(pse
udo-
)pop
ula
tion
whic
his
free
offe
edbac
k
�
SW
i(T
+1)
=∏ s≤
T
Pr( E
i(s)
=e i
s|E
i(s−
1),Z
i)Pr( E
i(s)
=e i
s|E
i(s−
1),B
(s),
Zi)
�Rec
allth
edefi
nitio
nof
feed
bac
k:If
ther
eex
ists
t∈{0
,1,.
..,T
}s.t.
the
conditio
n
E(t
)∐ B
(t)|(
E(t
−1)
,Z)
isnot
met
�T
he
wei
ghts
nee
dto
be
estim
ated
-nee
dm
odel
s
Mar
gina
lStr
uctu
ralM
ode
ls(c
ontd
)In
vers
eP
robab
ility
ofT
reat
men
tW
eights
�Id
ea:
re-w
eigh
tth
eor
igin
alpop
ula
tion
toco
nst
ruct
ahyp
othet
ical
(pse
udo-
)pop
ula
tion
whic
his
free
offe
edbac
k
�
SW
i(T
+1)
=∏ s≤
T
Pr( E
i(s)
=e i
s|E
i(s−
1),Z
i)Pr( E
i(s)
=e i
s|E
i(s−
1),B
(s),
Zi)
�Rec
allth
edefi
nitio
nof
feed
bac
k:If
ther
eex
ists
t∈{0
,1,.
..,T
}s.t.
the
conditio
n
E(t
)∐ B
(t)|(
E(t
−1)
,Z)
isnot
met
�T
he
wei
ghts
nee
dto
be
estim
ated
-nee
dm
odel
s
Mar
gina
lStr
uctu
ralM
ode
ls(c
ontd
)In
vers
eP
robab
ility
ofT
reat
men
tW
eights
�Id
ea:
re-w
eigh
tth
eor
igin
alpop
ula
tion
toco
nst
ruct
ahyp
othet
ical
(pse
udo-
)pop
ula
tion
whic
his
free
offe
edbac
k
�
SW
i(T
+1)
=∏ s≤
T
Pr( E
i(s)
=e i
s|E
i(s−
1),Z
i)Pr( E
i(s)
=e i
s|E
i(s−
1),B
(s),
Zi)
�Rec
allth
edefi
nitio
nof
feed
bac
k:If
ther
eex
ists
t∈{0
,1,.
..,T
}s.t.
the
conditio
n
E(t
)∐ B
(t)|(
E(t
−1)
,Z)
isnot
met
�T
he
wei
ghts
nee
dto
be
estim
ated
-nee
dm
odel
s
Mar
gina
lStr
uctu
ralM
ode
ls(c
ontd
)In
vers
eP
robab
ility
ofT
reat
men
tW
eights
�Id
ea:
re-w
eigh
tth
eor
igin
alpop
ula
tion
toco
nst
ruct
ahyp
othet
ical
(pse
udo-
)pop
ula
tion
whic
his
free
offe
edbac
k
�
SW
i(T
+1)
=∏ s≤
T
Pr( E
i(s)
=e i
s|E
i(s−
1),Z
i)Pr( E
i(s)
=e i
s|E
i(s−
1),B
(s),
Zi)
�Rec
allth
edefi
nitio
nof
feed
bac
k:If
ther
eex
ists
t∈{0
,1,.
..,T
}s.t.
the
conditio
n
E(t
)∐ B
(t)|(
E(t
−1)
,Z)
isnot
met
�T
he
wei
ghts
nee
dto
be
estim
ated
-nee
dm
odel
s
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
The
hypot
hetica
lpop
ulat
ion
The
pse
udo-p
opula
tion
�B
yem
plo
ying
the
wei
ghting
tech
niq
ue
we
get
ahyp
othet
ical
pop
ula
tion
inw
hic
hso
me
wom
enar
e”w
eigh
ted
up”
and
som
ear
e”w
eigh
ted
dow
n”
-an
dby
const
ruct
ion
the
educa
tion
alat
tain
men
tin
2005
isnot
affec
ted
bypr
evio
us
fert
ility
�H
ence
,by
using
this
pop
ula
tion
we
can
answ
erth
eques
tion
What
wou
ldbe
the
educa
tion
aldiff
eren
ces
inth
eodds
ofbei
ng
am
other
of3
-if
ther
ewer
eno
feed
bac
kin
the
dat
a?
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
The
hypot
hetica
lpop
ulat
ion
The
pse
udo-p
opula
tion
�B
yem
plo
ying
the
wei
ghting
tech
niq
ue
we
get
ahyp
othet
ical
pop
ula
tion
inw
hic
hso
me
wom
enar
e”w
eigh
ted
up”
and
som
ear
e”w
eigh
ted
dow
n”
-an
dby
const
ruct
ion
the
educa
tion
alat
tain
men
tin
2005
isnot
affec
ted
bypr
evio
us
fert
ility
�H
ence
,by
using
this
pop
ula
tion
we
can
answ
erth
eques
tion
What
wou
ldbe
the
educa
tion
aldiff
eren
ces
inth
eodds
ofbei
ng
am
other
of3
-if
ther
ewer
eno
feed
bac
kin
the
dat
a?
PhD
Def
ense
,Sep
tem
ber
2009
Exa
mpl
e
Imag
ine
awom
anw
ho...
�Tak
esher
Stu
den
tere
ksam
enin
1983
,en
rols
inuniv
ersity
�B
ecom
esa
mot
her
1984
�Lea
ves
univ
ersity
,st
art
nurs
ing
school
1985
�G
raduat
es19
91,2
mor
ech
ildre
nat
ages
30an
d32
Wei
ghts
:
�Pr( E
i(19
85)
=nurs
e|E
i(19
84),
Zi) =
1 20
�Pr( E
i(19
85)
=nurs
e|E
i(19
84),
B(1
984)
,Zi) =
1 10
�SW
i(20
05)
=1·1
·(10
)/20
·1···1
=0.
5
Exa
mpl
e
Imag
ine
awom
anw
ho...
�Tak
esher
Stu
den
tere
ksam
enin
1983
,en
rols
inuniv
ersity
�B
ecom
esa
mot
her
1984
�Lea
ves
univ
ersity
,st
art
nurs
ing
school
1985
�G
raduat
es19
91,2
mor
ech
ildre
nat
ages
30an
d32
Wei
ghts
:
�Pr( E
i(19
85)
=nurs
e|E
i(19
84),
Zi) =
1 20
�Pr( E
i(19
85)
=nurs
e|E
i(19
84),
B(1
984)
,Zi) =
1 10
�SW
i(20
05)
=1·1
·(10
)/20
·1···1
=0.
5
Exa
mpl
e
Imag
ine
awom
anw
ho...
�Tak
esher
Stu
den
tere
ksam
enin
1983
,en
rols
inuniv
ersity
�B
ecom
esa
mot
her
1984
�Lea
ves
univ
ersity
,st
art
nurs
ing
school
1985
�G
raduat
es19
91,2
mor
ech
ildre
nat
ages
30an
d32
Wei
ghts
:
�Pr( E
i(19
85)
=nurs
e|E
i(19
84),
Zi) =
1 20
�Pr( E
i(19
85)
=nurs
e|E
i(19
84),
B(1
984)
,Zi) =
1 10
�SW
i(20
05)
=1·1
·(10
)/20
·1···1
=0.
5
Exa
mpl
e
Imag
ine
awom
anw
ho...
�Tak
esher
Stu
den
tere
ksam
enin
1983
,en
rols
inuniv
ersity
�B
ecom
esa
mot
her
1984
�Lea
ves
univ
ersity
,st
art
nurs
ing
school
1985
�G
raduat
es19
91,2
mor
ech
ildre
nat
ages
30an
d32
Wei
ghts
:
�Pr( E
i(19
85)
=nurs
e|E
i(19
84),
Zi) =
1 20
�Pr( E
i(19
85)
=nurs
e|E
i(19
84),
B(1
984)
,Zi) =
1 10
�SW
i(20
05)
=1·1
·(10
)/20
·1···1
=0.
5
Res
ults
Act
ual
vs.
hyp
oth
etic
alpopula
tion
Act
ual
:H
ypot
het
ical
:Educa
tion
(200
5)O
Rp-v
alue
OR
p-v
alue
Nev
eren
rolle
d0.
840.
150.
36<
.000
1Pre
ven
rolle
d0.
810.
120.
46<
.000
1Ter
t(s)
/voc
0.92
0.40
0.51
<.0
001
Ter
t(m
)1.
320.
001
0.65
<.0
001
Ter
t(l)
(REF)
1−
1−
Enro
lled:
T(s
)/vo
c2.
540.
021.
130.
80Enro
lled:
T(m
)1.
470.
071.
220.
24Enro
lled:
T(l)
0.97
0.91
1.52
0.01
(con
trol
led
for
bas
elin
eva
riab
les)
Res
ults
Act
ual
vs.
hyp
oth
etic
alpopula
tion
Act
ual
:H
ypot
het
ical
:Educa
tion
(200
5)O
Rp-v
alue
OR
p-v
alue
Nev
eren
rolle
d0.
840.
150.
36<
.000
1Pre
ven
rolle
d0.
810.
120.
46<
.000
1Ter
t(s)
/voc
0.92
0.40
0.51
<.0
001
Ter
t(m
)1.
320.
001
0.65
<.0
001
Ter
t(l)
(REF)
1−
1−
Enro
lled:
T(s
)/vo
c2.
540.
021.
130.
80Enro
lled:
T(m
)1.
470.
071.
220.
24Enro
lled:
T(l)
0.97
0.91
1.52
0.01
(con
trol
led
for
bas
elin
eva
riab
les)
Res
ults
Act
ual
vs.
hyp
oth
etic
alpopula
tion
Act
ual
:H
ypot
het
ical
:Educa
tion
(200
5)O
Rp-v
alue
OR
p-v
alue
Nev
eren
rolle
d0.
840.
150.
36<
.000
1Pre
ven
rolle
d0.
810.
120.
46<
.000
1Ter
t(s)
/voc
0.92
0.40
0.51
<.0
001
Ter
t(m
)1.
320.
001
0.65
<.0
001
Ter
t(l)
(REF)
1−
1−
Enro
lled:
T(s
)/vo
c2.
540.
021.
130.
80Enro
lled:
T(m
)1.
470.
071.
220.
24Enro
lled:
T(l)
0.97
0.91
1.52
0.01
(con
trol
led
for
bas
elin
eva
riab
les)
Res
ults
Act
ual
vs.
hyp
oth
etic
alpopula
tion
Act
ual
:H
ypot
het
ical
:Educa
tion
(200
5)O
Rp-v
alue
OR
p-v
alue
Nev
eren
rolle
d0.
840.
150.
36<
.000
1Pre
ven
rolle
d0.
810.
120.
46<
.000
1Ter
t(s)
/voc
0.92
0.40
0.51
<.0
001
Ter
t(m
)1.
320.
001
0.65
<.0
001
Ter
t(l)
(REF)
1−
1−
Enro
lled:
T(s
)/vo
c2.
540.
021.
130.
80Enro
lled:
T(m
)1.
470.
071.
220.
24Enro
lled:
T(l)
0.97
0.91
1.52
0.01
(con
trol
led
for
bas
elin
eva
riab
les)
Res
ults
Act
ual
vs.
hyp
oth
etic
alpopula
tion
Act
ual
:H
ypot
het
ical
:Educa
tion
(200
5)O
Rp-v
alue
OR
p-v
alue
Nev
eren
rolle
d0.
840.
150.
36<
.000
1Pre
ven
rolle
d0.
810.
120.
46<
.000
1Ter
t(s)
/voc
0.92
0.40
0.51
<.0
001
Ter
t(m
)1.
320.
001
0.65
<.0
001
Ter
t(l)
(REF)
1−
1−
Enro
lled:
T(s
)/vo
c2.
540.
021.
130.
80Enro
lled:
T(m
)1.
470.
071.
220.
24Enro
lled:
T(l)
0.97
0.91
1.52
0.01
(con
trol
led
for
bas
elin
eva
riab
les)
Res
ults
Act
ual
vs.
hyp
oth
etic
alpopula
tion
Act
ual
:H
ypot
het
ical
:Educa
tion
(200
5)O
Rp-v
alue
OR
p-v
alue
Nev
eren
rolle
d0.
840.
150.
36<
.000
1Pre
ven
rolle
d0.
810.
120.
46<
.000
1Ter
t(s)
/voc
0.92
0.40
0.51
<.0
001
Ter
t(m
)1.
320.
001
0.65
<.0
001
Ter
t(l)
(REF)
1−
1−
Enro
lled:
T(s
)/vo
c2.
540.
021.
130.
80Enro
lled:
T(m
)1.
470.
071.
220.
24Enro
lled:
T(l)
0.97
0.91
1.52
0.01
(con
trol
led
for
bas
elin
eva
riab
les)
Res
ults
Act
ual
vs.
hyp
oth
etic
alpopula
tion
Act
ual
:H
ypot
het
ical
:Educa
tion
(200
5)O
Rp-v
alue
OR
p-v
alue
Nev
eren
rolle
d0.
840.
150.
36<
.000
1Pre
ven
rolle
d0.
810.
120.
46<
.000
1Ter
t(s)
/voc
0.92
0.40
0.51
<.0
001
Ter
t(m
)1.
320.
001
0.65
<.0
001
Ter
t(l)
(REF)
1−
1−
Enro
lled:
T(s
)/vo
c2.
540.
021.
130.
80Enro
lled:
T(m
)1.
470.
071.
220.
24Enro
lled:
T(l)
0.97
0.91
1.52
0.01
(con
trol
led
for
bas
elin
eva
riab
les)
Res
ults
Act
ual
vs.
hyp
oth
etic
alpopula
tion
Act
ual
:H
ypot
het
ical
:Educa
tion
(200
5)O
Rp-v
alue
OR
p-v
alue
Nev
eren
rolle
d0.
840.
150.
36<
.000
1Pre
ven
rolle
d0.
810.
120.
46<
.000
1Ter
t(s)
/voc
0.92
0.40
0.51
<.0
001
Ter
t(m
)1.
320.
001
0.65
<.0
001
Ter
t(l)
(REF)
1−
1−
Enro
lled:
T(s
)/vo
c2.
540.
021.
130.
80Enro
lled:
T(m
)1.
470.
071.
220.
24Enro
lled:
T(l)
0.97
0.91
1.52
0.01
(con
trol
led
for
bas
elin
eva
riab
les)
Res
ults
Act
ual
vs.
hyp
oth
etic
alpopula
tion
Act
ual
:H
ypot
het
ical
:Educa
tion
(200
5)O
Rp-v
alue
OR
p-v
alue
Nev
eren
rolle
d0.
840.
150.
36<
.000
1Pre
ven
rolle
d0.
810.
120.
46<
.000
1Ter
t(s)
/voc
0.92
0.40
0.51
<.0
001
Ter
t(m
)1.
320.
001
0.65
<.0
001
Ter
t(l)
(REF)
1−
1−
Enro
lled:
T(s
)/vo
c2.
540.
021.
130.
80Enro
lled:
T(m
)1.
470.
071.
220.
24Enro
lled:
T(l)
0.97
0.91
1.52
0.01
(con
trol
led
for
bas
elin
eva
riab
les)
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ass
umpt
ions
are
they
poss
ibly
viola
ted?
�4
mai
nas
sum
ption
s:
1.Exc
han
geab
ility
(no
unm
easu
red
confo
under
s)Y
e
∐ E|Z
base
line
cov
2.N
om
is-s
pec
ifica
tion
ofth
em
odel
sfo
rth
ewei
ghts
Wei
ght
Model
3.Con
sist
ency
4.Pos
itiv
ity
�A
llof
thes
ear
eim
por
tant→
allsu
bje
ctto
pos
sible
viol
atio
ns
�N
otte
stab
le...
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ass
umpt
ions
are
they
poss
ibly
viola
ted?
�4
mai
nas
sum
ption
s:
1.Exc
han
geab
ility
(no
unm
easu
red
confo
under
s)Y
e
∐ E|Z
base
line
cov
2.N
om
is-s
pec
ifica
tion
ofth
em
odel
sfo
rth
ewei
ghts
Wei
ght
Model
3.Con
sist
ency
4.Pos
itiv
ity
�A
llof
thes
ear
eim
por
tant→
allsu
bje
ctto
pos
sible
viol
atio
ns
�N
otte
stab
le...
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ass
umpt
ions
are
they
poss
ibly
viola
ted?
�4
mai
nas
sum
ption
s:
1.Exc
han
geab
ility
(no
unm
easu
red
confo
under
s)Y
e
∐ E|Z
base
line
cov
2.N
om
is-s
pec
ifica
tion
ofth
em
odel
sfo
rth
ewei
ghts
Wei
ght
Model
3.Con
sist
ency
4.Pos
itiv
ity
�A
llof
thes
ear
eim
por
tant→
allsu
bje
ctto
pos
sible
viol
atio
ns
�N
otte
stab
le...
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ass
umpt
ions
are
they
poss
ibly
viola
ted?
�4
mai
nas
sum
ption
s:
1.Exc
han
geab
ility
(no
unm
easu
red
confo
under
s)Y
e
∐ E|Z
base
line
cov
2.N
om
is-s
pec
ifica
tion
ofth
em
odel
sfo
rth
ewei
ghts
Wei
ght
Model
3.Con
sist
ency
4.Pos
itiv
ity
�A
llof
thes
ear
eim
por
tant→
allsu
bje
ctto
pos
sible
viol
atio
ns
�N
otte
stab
le...
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ass
umpt
ions
are
they
poss
ibly
viola
ted?
�4
mai
nas
sum
ption
s:
1.Exc
han
geab
ility
(no
unm
easu
red
confo
under
s)Y
e
∐ E|Z
base
line
cov
2.N
om
is-s
pec
ifica
tion
ofth
em
odel
sfo
rth
ewei
ghts
Wei
ght
Model
3.Con
sist
ency
4.Pos
itiv
ity
�A
llof
thes
ear
eim
por
tant→
allsu
bje
ctto
pos
sible
viol
atio
ns
�N
otte
stab
le...
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ass
umpt
ions
are
they
poss
ibly
viola
ted?
�4
mai
nas
sum
ption
s:
1.Exc
han
geab
ility
(no
unm
easu
red
confo
under
s)Y
e
∐ E|Z
base
line
cov
2.N
om
is-s
pec
ifica
tion
ofth
em
odel
sfo
rth
ewei
ghts
Wei
ght
Model
3.Con
sist
ency
4.Pos
itiv
ity
�A
llof
thes
ear
eim
por
tant→
allsu
bje
ctto
pos
sible
viol
atio
ns
�N
otte
stab
le...
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ass
umpt
ions
are
they
poss
ibly
viola
ted?
�4
mai
nas
sum
ption
s:
1.Exc
han
geab
ility
(no
unm
easu
red
confo
under
s)Y
e
∐ E|Z
base
line
cov
2.N
om
is-s
pec
ifica
tion
ofth
em
odel
sfo
rth
ewei
ghts
Wei
ght
Model
3.Con
sist
ency
4.Pos
itiv
ity
�A
llof
thes
ear
eim
por
tant→
allsu
bje
ctto
pos
sible
viol
atio
ns
�N
otte
stab
le...
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Con
clus
ion
Ultim
ate
fert
ility
inD
enm
ark
�T
her
ear
eed
uca
tion
aldiff
eren
ces
inultim
ate
fert
ility
�T
her
eis
som
ete
nden
cyth
atwom
enw
ho
bec
ome
mot
her
sw
hile
enro
lled
ined
uca
tion
are
mor
elik
ely
todro
pou
tan
dwom
enw
ho
bec
ome
mot
her
sea
rly
are
less
likel
yto
hav
ea
univ
ersity
deg
ree,
mor
elik
ely
tohav
eno
furt
her
deg
ree
ora
T(m
)
�T
his
mig
ht
pla
ya
role
inth
ere
lation
ship
bet
wee
nultim
ate
fert
ility
and
educa
tion
alat
tain
men
t
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Con
clus
ion
Ultim
ate
fert
ility
inD
enm
ark
�T
her
ear
eed
uca
tion
aldiff
eren
ces
inultim
ate
fert
ility
�T
her
eis
som
ete
nden
cyth
atwom
enw
ho
bec
ome
mot
her
sw
hile
enro
lled
ined
uca
tion
are
mor
elik
ely
todro
pou
tan
dwom
enw
ho
bec
ome
mot
her
sea
rly
are
less
likel
yto
hav
ea
univ
ersity
deg
ree,
mor
elik
ely
tohav
eno
furt
her
deg
ree
ora
T(m
)
�T
his
mig
ht
pla
ya
role
inth
ere
lation
ship
bet
wee
nultim
ate
fert
ility
and
educa
tion
alat
tain
men
t
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Con
clus
ion
Ultim
ate
fert
ility
inD
enm
ark
�T
her
ear
eed
uca
tion
aldiff
eren
ces
inultim
ate
fert
ility
�T
her
eis
som
ete
nden
cyth
atwom
enw
ho
bec
ome
mot
her
sw
hile
enro
lled
ined
uca
tion
are
mor
elik
ely
todro
pou
tan
dwom
enw
ho
bec
ome
mot
her
sea
rly
are
less
likel
yto
hav
ea
univ
ersity
deg
ree,
mor
elik
ely
tohav
eno
furt
her
deg
ree
ora
T(m
)
�T
his
mig
ht
pla
ya
role
inth
ere
lation
ship
bet
wee
nultim
ate
fert
ility
and
educa
tion
alat
tain
men
t
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Tha
nkyo
uve
rym
uch!
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ref
eren
ces
Bec
ker,
G.S.(1
991)
.A
Tre
atise
onth
eFam
ily.
Har
vard
Univ
ersity
Pre
ss,Cam
brid
ge,M
assa
chuss
etts
.
Her
nan
,M
.A
.,B
rum
bac
k,B
.,an
dRob
ins,
J.M
.(2
001)
.M
argi
nal
Str
uct
ura
lM
odel
sto
Est
imat
eth
eJo
int
Cau
sal
Effec
tof
Non
random
ized
Tre
atm
ent.
Journ
alof
the
Am
eric
anSta
tist
ical
Ass
oci
atio
n,96
:440
–448
.
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ass
umpt
ions
for
MSM
sExc
han
gea
bili
ty
Nee
dto
incl
ude
enou
ghbas
elin
eco
variat
es,Z
,s.t.
within
each
subgr
oup
defi
ned
byth
ese,
the
wom
enar
eex
chan
geab
le:
Inth
isst
udy,
Zin
cludes
:
1.m
ark
atta
ined
atth
ePU
SE
2.num
ber
ofm
other
-sib
lings
3.gr
andm
other
’sag
eat
firs
tbirth
4.gr
andm
other
’san
dgr
andfa
ther
’sed
uca
tion
alat
tain
men
t
What
’sm
issing?
Hea
lth,m
en,ot
her
s?
exch
ange
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ass
umpt
ions
for
MSM
sExc
han
gea
bili
ty
Nee
dto
incl
ude
enou
ghbas
elin
eco
variat
es,Z
,s.t.
within
each
subgr
oup
defi
ned
byth
ese,
the
wom
enar
eex
chan
geab
le:
Inth
isst
udy,
Zin
cludes
:
1.m
ark
atta
ined
atth
ePU
SE
2.num
ber
ofm
other
-sib
lings
3.gr
andm
other
’sag
eat
firs
tbirth
4.gr
andm
other
’san
dgr
andfa
ther
’sed
uca
tion
alat
tain
men
t
What
’sm
issing?
Hea
lth,m
en,ot
her
s?
exch
ange
PhD
Def
ense
,Sep
tem
ber
2009
Par
ity
transitions
inN
orway
Ultim
ate
fert
ility
inD
enm
ark
Ass
umpt
ions
for
MSM
sExc
han
gea
bili
ty
Nee
dto
incl
ude
enou
ghbas
elin
eco
variat
es,Z
,s.t.
within
each
subgr
oup
defi
ned
byth
ese,
the
wom
enar
eex
chan
geab
le:
Inth
isst
udy,
Zin
cludes
:
1.m
ark
atta
ined
atth
ePU
SE
2.num
ber
ofm
other
-sib
lings
3.gr
andm
other
’sag
eat
firs
tbirth
4.gr
andm
other
’san
dgr
andfa
ther
’sed
uca
tion
alat
tain
men
t
What
’sm
issing?
Hea
lth,m
en,ot
her
s?
exch
ange
PhD
Def
ense
,Sep
tem
ber
2009
Mode
lfo
rth
ewei
ghts
Mode
ls
log
[ πik
t
πi1
t
] =α
k+
βk·A
it+
γk·Z
i,k
=2,
...,
8
log
[ πik
t
πi1
t
] =α
k+
βk·A
it+
γk·Z
i+
δ k1·B
i,t−
1+
δ k2·B
i,t−
2
wher
eπ
ikt=
Pr(
Ei(
t)=
k)
Cat
egor
ies
(k):
1.not
enro
lled,se
vera
lsu
bca
tego
ries
2.en
rolle
d,se
vera
lsu
bca
tego
ries
exch
ange
Fin
aled
ucat
iona
lat
tain
men
ts
Eve
ren
rolle
din
univ
ersity
Edu(2
005)
PU
SE
Voc/
T(s
)T
(m)
T(l)
Tot
al
Eve
ryon
e14
.6%
24.8
%44
.1%
16.6
%80
32In
t/Chan
ge17
.6%
10.1
%44
.1%
28.2
%10
07
Eve
ren
rolle
din
univ
ersity→
child
(yes
/no)
Edu(2
005)
PU
SE
Voc/
T(s
)T
(m)
T(l)
Tot
al
Child
24.8
%5.
7%51
.4%
18.1
%10
5N
och
ild16
.7%
10.6
%43
.2%
29.4
%90
2
Int/
Chan
ge17
.6%
10.1
%44
.1%
28.2
%10
07
Go
Back
!
Fin
aled
ucat
iona
lat
tain
men
ts
Eve
ren
rolle
din
univ
ersity
Edu(2
005)
PU
SE
Voc/
T(s
)T
(m)
T(l)
Tot
al
Eve
ryon
e14
.6%
24.8
%44
.1%
16.6
%80
32In
t/Chan
ge17
.6%
10.1
%44
.1%
28.2
%10
07
Eve
ren
rolle
din
univ
ersity→
child
(yes
/no)
Edu(2
005)
PU
SE
Voc/
T(s
)T
(m)
T(l)
Tot
al
Child
24.8
%5.
7%51
.4%
18.1
%10
5N
och
ild16
.7%
10.6
%43
.2%
29.4
%90
2
Int/
Chan
ge17
.6%
10.1
%44
.1%
28.2
%10
07
Go
Back
!
Fin
aled
ucat
iona
lat
tain
men
ts
Eve
ren
rolle
din
univ
ersity
Edu(2
005)
PU
SE
Voc/
T(s
)T
(m)
T(l)
Tot
al
Eve
ryon
e14
.6%
24.8
%44
.1%
16.6
%80
32In
t/Chan
ge17
.6%
10.1
%44
.1%
28.2
%10
07
Eve
ren
rolle
din
univ
ersity→
child
(yes
/no)
Edu(2
005)
PU
SE
Voc/
T(s
)T
(m)
T(l)
Tot
al
Child
24.8
%5.
7%51
.4%
18.1
%10
5N
och
ild16
.7%
10.6
%43
.2%
29.4
%90
2
Int/
Chan
ge17
.6%
10.1
%44
.1%
28.2
%10
07
Go
Back
!
Fin
aled
ucat
iona
lat
tain
men
ts
Eve
ren
rolle
din
univ
ersity
Edu(2
005)
PU
SE
Voc/
T(s
)T
(m)
T(l)
Tot
al
Eve
ryon
e14
.6%
24.8
%44
.1%
16.6
%80
32In
t/Chan
ge17
.6%
10.1
%44
.1%
28.2
%10
07
Eve
ren
rolle
din
univ
ersity→
child
(yes
/no)
Edu(2
005)
PU
SE
Voc/
T(s
)T
(m)
T(l)
Tot
al
Child
24.8
%5.
7%51
.4%
18.1
%10
5N
och
ild16
.7%
10.6
%43
.2%
29.4
%90
2
Int/
Chan
ge17
.6%
10.1
%44
.1%
28.2
%10
07
Go
Back
!
Fin
aled
ucat
iona
lat
tain
men
ts
Eve
ren
rolle
din
univ
ersity
Edu(2
005)
PU
SE
Voc/
T(s
)T
(m)
T(l)
Tot
al
Eve
ryon
e14
.6%
24.8
%44
.1%
16.6
%80
32In
t/Chan
ge17
.6%
10.1
%44
.1%
28.2
%10
07
Eve
ren
rolle
din
univ
ersity→
child
(yes
/no)
Edu(2
005)
PU
SE
Voc/
T(s
)T
(m)
T(l)
Tot
al
Child
24.8
%5.
7%51
.4%
18.1
%10
5N
och
ild16
.7%
10.6
%43
.2%
29.4
%90
2
Int/
Chan
ge17
.6%
10.1
%44
.1%
28.2
%10
07
Go
Back
!
Mot
hers
byJa
n1s
t19
86by
educ
atio
n(2
005)
Mot
her
PU
SE
Voc
T(s
)T
(m)
T(l)
Tot
al
No
14.4
%16
.2%
8.5%
44.0
%17
.0%
7677
Yes
18.0
%21
.4%
6.5%
47.6
%6.
5%35
5
Tot
al14
.6%
16.4
%8.
4%44
.1%
16.6
%80
32
Go
Back
!
Mot
hers
byJa
n1s
t19
86by
educ
atio
n(2
005)
Mot
her
PU
SE
Voc
T(s
)T
(m)
T(l)
Tot
al
No
14.4
%16
.2%
8.5%
44.0
%17
.0%
7677
Yes
18.0
%21
.4%
6.5%
47.6
%6.
5%35
5
Tot
al14
.6%
16.4
%8.
4%44
.1%
16.6
%80
32
Go
Back
!
Mot
hers
byJa
n1s
t19
86by
educ
atio
n(2
005)
Mot
her
PU
SE
Voc
T(s
)T
(m)
T(l)
Tot
al
No
14.4
%16
.2%
8.5%
44.0
%17
.0%
7677
Yes
18.0
%21
.4%
6.5%
47.6
%6.
5%35
5
Tot
al14
.6%
16.4
%8.
4%44
.1%
16.6
%80
32
Go
Back
!
Isfe
edba
ckpr
esen
tin
the
stud
ypop
ulat
ion?
Go
Back
!
Bir
th t
his
year
log odds
Up
2 (
voc)
Te
rt(s
)T
ert
(m)
Te
rt(l)
Intercept −4−3−2
Birth
No
birth
β1
=1
.27
β2
=0
.34
β3
=0
.39
β4
=0
.3