Analyzing defined contribution pension reform in Korea using a general equilibrium model

Shin, Seung-Ryong
A icle
Analyzing de ined con ibu ion pension e o m in Ko ea
using a gene al equilib ium model
KDI Jou nal o Economic Policy
P o ided in Coope a ion wi h:
Ko ea De elopmen Ins i u e (KDI), Sejong
Sugges ed Ci a ion: Shin, Seung-Ryong (2024) : Analyzing de ined con ibu ion pension e o m in
Ko ea using a gene al equilib ium model, KDI Jou nal o Economic Policy, ISSN 2586-4130, Ko ea
De elopmen Ins i u e (KDI), Sejong, Vol. 46, Iss. 4, pp. 1-48,
h ps://doi.o g/10.23895/kdijep.2024.46.4.1
This Ve sion is a ailable a :
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KDI Jou nal o Economic Policy 2024, 46(4):1-48
h ps://dx.doi.o g/10.23895/kdijep.2024.46.4.1
1
Analyzing De ined Con ibu ion Pension Re o m in Ko ea
Using a Gene al Equilib ium Model†
By SEUNG-RYONG SHIN
*
Ko ea’s Na ional Pension Fund (NPF) is p ojec ed o be in de ici
by he 2040s and exhaus ed by he 2050s. Inc easing con ibu ion
a es may be una o dable, p omp ing conside a ion o s uc u al
e o ms, pa icula ly shi ing om a de ined bene i (DB) o a
de ined con ibu ion (DC) sys em. The DC sys em links bene i s o
con ibu ions and in es men e u ns, ensu ing inancial s abili y bu
aising conce ns abou income adequacy and edis ibu ion. This
s udy uses an o e lapping gene a ions model wi h he e ogeneous
agen s o assess hese e o ms. By 2070, demog aphic changes will
make he DB sys em unsus ainable wi hou subs an ial go e nmen
subsidies, ad e sely a ec ing axes, income, and sa ings. Con e sely,
he DC sys em would emain balanced wi hou subsidies, esul ing in
lowe in e es a es, highe wages, and be e economic ou pu . The
model shows ha he DB sys em would equi e an annual subsidy o
11.3% o GDP a a 9% con ibu ion a e by 2070, while he DC sys em
would be sel -su icien . E en wi h lowe e u ns, he DC sys em could
be mo e e icien and equi able wi h pa ial subsidies, imp o ing
economic ou comes and educing inequali y.
Key Wo d: De ined Bene i , De ined Con ibu ion, Pay-as-you-go,
Public Pension, Gene al Equilib ium, OLG, Aging
JEL Code: H55, J11, E60
* Associa e Fellow, Ko ea De elopmen Ins i u e (E-mail: seushi@kdi. e.k )
* Recei ed: 2024. 6. 26
* Re e ee P ocess S a ed: 2024. 6. 26
* Re e ee Repo s Comple ed: 2024. 8. 9
† This pape is an ex ension o Shin, 2023, Analyzing De ined Con ibu ion Pension Re o m in Ko ea using a
Gene al Equilib ium Model, Policy S udy 2023-12, KDI (in Ko ean). I hank wo anonymous e e ees and he Edi o
o hei use ul sugges ions. Hee Won Noh p o ided excellen esea ch assis ance. All emaining e o s a e mine.
2 KDI Jou nal o Economic Policy NOVEMBER 2024
I. In oduc ion
he inances o he Na ional Pension Fund (NPF) a e de e io a ing, wi h
p ojec ions indica ing a de ici by he 2040s and comple e exhaus ion by
he 2050s. The media and expe s equen ly ad oca e o aising he con ibu ion
a e as a solu ion. Howe e , he equi ed inc ease o s abilize he und’s inances
may exceed wha indi iduals can a o d, ende ing his app oach insu icien .
Consequen ly, he e is a g owing call o s uc u al e o ms a he han me e
pa ame ic adjus men s. Among he a ious p oposals o s uc u al e o m, he shi
o a de ined con ibu ion (DC) pension sys em has gained ac ion. Unlike he
cu en de ined bene i (DB) sys em, whe e bene i s a e la gely decoupled om
con ibu ions, he DC sys em ensu es inancial s abili y by aligning bene i s wi h
con ibu ions and in es men e u ns.
Despi e he po en ial ad an ages o he DC sys em, public skep icism pe sis s.
Conce ns include he possibili y ha , i implemen ed a he cu en con ibu ion a e,
he DC sys em may esul in a lowe income eplacemen a e, he eby jeopa dizing
he adequacy o e i emen income. Addi ionally, he DC sys em could lack he
edis ibu i e unc ion inhe en in he DB sys em. Un o una ely, he e is a pauci y
o esea ch on he economic impac s o possible DC pension e o ms in Ko ea. The
p e alen iscal p ojec ion model used by he Ko ean go e nmen is inadequa e
o add essing hese conce ns, as i does no ack indi idual beha io s and is
homogeneous in i s ca ego iza ion o indi iduals by gende , age, and con ibu ion
pe iod. This model also ails o conside endogenous changes in mac oeconomic
a iables such as in e es a es and wages. To o e come hese limi a ions, his s udy
employs a s a iona y gene al equilib ium analysis using an o e lapping gene a ions
model wi h he e ogeneous agen s o examine he endogenous economic esponses o
a ious age and income g oups o changes in he pension sys em and he economic
en i onmen .
Acco ding o Fu u e Popula ion P ojec ions (2021), he wo king-age o e i emen -age
a io is expec ed o decline om 79.2:20.8 in 2022 o 48.7:51.3 by 2070. Main aining
he DB pension sys em unde hese demog aphic condi ions is heo e ically
unsus ainable wi hou signi ican inancial suppo om he go e nmen . Po en ial
consequences include highe ax bu dens, educed a e - ax income, lowe sa ings,
inc eased in e es a es, lowe wage a es, and diminished GDP. Addi ionally, a
educed labo o ce pe capi a may lowe i ms’ capi al demand, causing in e es a es
o all, wage a es o ise, and agg ega e ou pu o decline. The co ela ion be ween
he popula ion s uc u e and sa ings li ecycle may weaken, educing he agg ega e
supply o capi al. E en i households main ain hei sa ings beha io , he agg ega e
supply o capi al may decline due o an inc eased popula ion in lowe -sa ing age
g oups. Con e sely, declining mo ali y may lead households o inc ease sa ings,
esul ing in lowe in e es a es, highe wage a es, and highe agg ega e ou pu .
The DC sys em, in con as , main ains a inancial balance wi hou go e nmen
in e en ion. This ensu es ha some unds a e in es ed domes ically, po en ially
lowe ing in e es a es, aising wage a es, and inc easing g oss p oduc ela i e o
he DB sys em. While he aging popula ion and declining mo ali y a es a ec bo h
T
VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 3
sys ems somewha simila ly, he DC sys em ampli ies he ini ial in e es a e changes.
Fo ins ance, a capi al demand shock in he DC sys em leads o declining in e es
a es and und e u ns, educing pension bene i s and p omp ing households o sa e
mo e. Simila ly, supply shocks o capi al may cause households o educe sa ings in
esponse o ising in e es a es and inc easing pension bene i s, e en ually
ampli ying he e ec . Declining mo ali y can u he inc ease household sa ings
unde he DC sys em as pension bene i s dec ease due o he DC bene i o mula.
Howe e , excessi ely low in e es a es and high wage a es could wo sen inequali y,
bene i ing wo king-age indi iduals mo e han e i ees.
The mac oeconomic impac s on he DB and DC pension sys ems by 2070 di e
signi ican ly in di ec ion and magni ude. Gi en he unp eceden ed a e o aging in
Ko ea, an empi ical analysis would be limi ed. Thus, his s udy employs a s uc u al
gene al equilib ium model, calib a ed o he Ko ean economy, o assess he po en ial
ou comes o changes o he Na ional Pension sys em.
The model, adap ed om Lee e al. (2019), analyzes households in a li ecycle
amewo k, dis inguishing be ween wo king and e i emen ages. Wo king-age
indi iduals supply inelas ic labo and make consump ion and sa ings decisions
subjec o p oduc i i y shocks, while e i ees base hei decisions on Na ional
Pension and Basic Pension bene i s. Fi ms ope a e using a Cobb-Douglas p oduc ion
unc ion, combining capi al and labo . The go e nmen balances i s budge h ough
a ious axes and inances pension de ici s, wi h he consump ion ax se ing as he
baseline due o i s age neu ali y and minimal labo ma ke dis o ions. Fo he DC
sys em analysis, he model includes a minimum o eign in es men sha e, wi h
o eign in e es a es se ing he lowe bound o domes ic a es.
Re lec ing ealis ic mac oeconomic condi ions is challenging. The o al amoun o
pension con ibu ions is “ma u e,” bu he dis ibu ion o con ibu ion pe iods is
ma u e only up o age 40 as o 2022, as he expansion o he Na ional Pension Scheme
o co e he en i e popula ion was only ecen ly implemen ed in 1998. Full ma u i y
o o al bene i s will no be achie ed un il all 41-yea -olds in 2022 ha e died, di e ging
om a s a iona y equilib ium. To add ess his, he s udy es ima es an exogenous
labo supply and pension con ibu ion unc ion, i ing con ibu ion pe iod dis ibu ion
da a o indi iduals up o age 40 and employmen a e da a o hose a olde ages.
The con ibu ion a e is adjus ed o ma ch he 2022 a io o o al con ibu ions o
GDP, and he income eplacemen a e coe icien is adjus ed acco dingly.
The model p edic s ha in 2070, main aining he DB sys em would equi e an
annual go e nmen subsidy amoun equi alen o 11.3% o GDP a a 9% con ibu ion
a e, o 8.8% o GDP e en i he a e is inc eased o 18%. In con as , he DC sys em
would achie e iscal balance wi hou go e nmen suppo .
The compa a i e analysis shows ha a he same con ibu ion a e, he DC sys em
wi hou o eign e u ns (0% o eign e u n) may lowe e i emen li ing s anda ds
compa ed o he DB sys em due o lowe in e es a es and highe wage a es.
Howe e , i only a po ion o he DB subsidy is edi ec ed o supplemen he
uni e sal pension as pa o he Basic Pension unde he DC sys em, i can p o ide
g ea e economic bene i s and a be e income edis ibu ion in e i emen .
E en unde conse a i e assump ions ega ding he und a e o e u n, a de ined
con ibu ion (DC) sys em wi h iscal subsidies can achie e g ea e e iciency. This
e iciency is e iden in he highe g oss p oduc and o al a e - ax income associa ed
4 KDI Jou nal o Economic Policy NOVEMBER 2024
wi h he DC sys em. When a ce ain amoun o he DC unds is in es ed domes ically,
bo h g oss ou pu and o al a e - ax income su pass hose o he de ined bene i
(DB) sys em e en wi hou iscal suppo , al hough add essing inequali y emains a
challenge. A modes inc ease in he uni e sal pension bene i can signi ican ly
na ow he income gap be ween wo king-age and e i emen -age indi iduals. This
adjus men p omp s households o educe hei sa ings, subsequen ly lowe ing wage
a es and aising in e es a es, which in u n ele a es pension le els. Fu he mo e,
inc easing he con ibu ion a e om 9% o 18% enhances he a e age pension bene i
le el unde he DC sys em, he eby educing he need o addi ional inancial suppo .
Addi ionally, o a gi en con ibu ion a e, he DC sys em can o e highe long-
e m pension bene i s compa ed o he un unded pay-as-you-go (PAYGO) sys em,
p o ided he und a e o e u n exceeds he nominal g ow h a e, known as he
“Aa on (1966) condi ion.” This ela ionship holds ue e en in ealis ically quan i ied
models. As he popula ion con inues o age, he dispa i y be ween he DC and
PAYGO sys ems will widen due o a smalle wo king-age popula ion suppo ing a
la ge numbe o e i ees. This unde sco es he long- e m ad an ages o ansi ioning
o a DC sys em in e ms o sus ainabili y and economic ou comes.
This s udy ela es o p e ious Ko ean esea ch on he income edis ibu ion e ec s
o he Na ional Pension. Kim (2002) examines he impac o he Na ional Pension’s
in oduc ion o he Gini coe icien using Daewoo panel da a. Kang e al. (2008) ind
ha he 2007 e o m o he Na ional Pension educed pension bene i s, leading o a
highe Gini coe icien . Yuh and Yang (2011) demons a e a signi ican income
edis ibu ion e ec o he Na ional Pension h ough analyses o expec ed e u n
a ios ha accoun o su i al a es by income decile. Lee e al. (2016), Choi (2016),
Choi and Han (2017), and Choi (2021b) also in es iga e he income edis ibu ion
e ec o he e u n a io.
This s udy is also ela ed o mac oeconomic analyses o he Na ional Pension,
such as hose by Jeon (1997), Kim (2003), Jeon and Yoo (2004), Nam (2008), and
Kim (2018). No ably, Shin e al. (2010), Kim (2011), Oh (2012), Moon and Lee
(2013), Choi e al. (2015), Kwon (2016), Hong e al. (2016), Hong (2018), Lee e al.
(2019), Kim and Lee (2019), Lim and Kim (2021), Choi (2021a), Woo (2021), and
Yoon e al. (2022) ha e analyzed he ela ionship be ween he Na ional Pension
sys em and u u e demog aphic ends using a a ie y o di e en mac oeconomic
models. This s udy closely e e ences Lee e al. (2019), which o e s de ailed insigh s
in o old-age income and edis ibu ion e ec s h ough model cons uc ion and
quan i ica ion. O cou se, Kwon (2016) and Woo (2021) include he endogenous
labo supply, unlike Lee e al. (2019), and o e use ul ools o analyzing he
ansi ion pa h o a pension e o m. Howe e , hey do no add ess he dis ibu ion o
con ibu ion pe iods, esul ing in lowe speci ici y ega ding he dis ibu ion o
e i emen income. The e o e, he model by Lee e al. (2019) was chosen.
Addi ionally, while he e a e discussions o DC pension sys ems wi hin a
mac oeconomic con ex in Heo (2007), Pa k and Heo (2008), Pa k (2009), and Heo
(2016), esea ch on social inequali y ela ed o DC public pensions is sca ce. To
he bes o my knowledge, his is he i s s udy in Ko ea o analyze he long- e m
mac oeconomic and dis ibu ional impac s o e o ming om a DB o a DC
pension sys em using a he e ogeneous agen gene al equilib ium model in a u u e
demog aphic con ex .

VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 5
Sec ion 2 ou lines he o e lapping gene a ions gene al equilib ium model, Sec ion
3 de ails he calib a ion me hodology, Sec ion 4 explains he heo e ical amewo k,
Sec ion 5 p esen s he expe imen al esul s, and Sec ion 6 concludes he pape .
II. Model
The o e lapping gene a ions model used in his s udy is p ima ily based on he
wo k o Lee, Han, and Hong (2019). Fo mo e de ails, please e e o hei pape .
Conside a gene al equilib ium model consis ing o o e lapping gene a ions
o households, ep esen a i e i ms, and he go e nmen . Households a e u ili y
maximize s, i ms a e p o i maximize s, and he public sec o (including he gene al
go e nmen and he Na ional Pension Se ice) adjus s ax a es o sa is y budge
cons ain s. We analyze his h ough a s a iona y equilib ium model whe e indi idual
household s a es (and hus decisions) can change o e ime, bu he mac o dis ibu ion
emains in a ian . Fo simplici y, we assume he labo supply o be inelas ic.
A. Household P oblem
The household u ili y maximiza ion p oblem in he o e lapping gene a ions model
assumes a li ecycle amewo k. A con inuum o he e ogeneous households is
economically ac i e a each age
{1, , } .
iI
∈
Households a e gi en wi h exogenous
and independen mo ali y p obabili ies
i
γ
a age
1i+
be o e eaching he inal
age o
iI+
, whe e
1
I
γ
=
is gi en o he inal age.
A household en e s he labo ma ke a age
1i=
o ea n labo income
l
i
y
and
can wo k un il age
1
R
ii= −
Ages
{1, , 1}
R
ii∈−
a e called he "wo king age."
Labo income
l
ii
y w xl
ε
=
is composed o labo p oduc i i y shock
x
, labo hou s
l
(in e p e ed as he numbe o mon hs in a yea ) gi en by an exogenous ansi ion
unc ion, age-speci ic labo p oduc i i y
i
ε
, and wage
w
de e mined by he
gene al equilib ium. A household pays capi al income ax
k
a
τ
gi en asse a and
capi al income
a
, and pays income ax
()
i
Ty
gi en g oss income
i
y=
(1 ) l
ki
a y
τ
−+
.1 Those whose wo king hou s
l
exceed he lowe limi
l
a e ecognized as en olled in he Na ional Pension and pay con ibu ions o
min( , )
ss i
w xl
τ κε
o he Na ional Pension Se ice; i.e., he lowe alue be ween he
mon hly labo income
i
wx
ε
and he uppe limi o ecognized income
κ
is
applied along wi h wo king hou s and he con ibu ion a e
ss
τ
. The uppe limi
κ
is de ined as he p oduc o a cons an
k
and g oss domes ic p oduc
:Y
kY
κ
= ×
.
Gi en disposable income
[]
(1 ) 1 min( , ) ( )
l
k i l l ss i i
a y w x l T y
τ τ κε
>
− +− −

, a household
1This is in e p e ed as a co po a e ax, allowing o double axa ion.
6 KDI Jou nal o Economic Policy NOVEMBER 2024
decides upon sa ing
aa
′−
and consump ion
c
and pays consump ion ax
c
c
τ
,
whe e sa ing is subjec o he incomple e inancial ma ke cons ain
0 .a′≥
Each
age is associa ed wi h a pe iod u ili y unc ion
()uc =
1
( 1) / (1 )
u
u
c
σσ
−−−
, which is
discoun ed o e ime by
β
. The p og essi e income ax is modeled using he
o mula ion in Hea hco e e al. (2017):
1
( ) max[ ,0]
i ii
Ty y y
τ
λ
−
= −
.
The dis ibu ion o u u e labo hou s
l′
is de e mined by he cu en labo hou s
ia he ansi ion unc ion
( ) .
i
ll
′= Λ
Independen and he e ogeneous labo
p oduc i i y shocks ollow an AR(1) p ocess:
2
ln( ) ln( ) , (0, )
x xx x
x x N
ρσ
′
′= + 
.
Age
{ , ,}
R
ii I∈
is e e ed o as he " e i emen age." Du ing his pe iod, a
household does no gene a e any labo income bu ecei es in e es income
a
,
Na ional Pension income
ξ
,2 and he Basic Pension income
ˆ
ϕ
. Simila o he
wo king age, he household pays bo h income ax and capi al gains ax. Addi ionally,
consump ion axes a e incu ed as he household makes sa ing and consump ion
decisions based on disposable income.
The household u ili y maximiza ion p oblem a e i emen age is ep esen ed by
he Bellman equa ion:
11
,
( ; , ) max { ( ) (1 )(1 ) ( ; , )}
u
ii
R ca i z R
V aBn uc g V a Bn
σ
βγ
−+
′
′
= +− +
..s
ˆ
(1 ) (1 ) (1 ) ( , ; , ) ( , , ; , ) ( ),
cz k i
c a g a a BnA aBnA T y
τ τ ξ αϕ α
′
+ + + =+− + + −
(1 )
ik
y a
τ
= −
,
1
( ) max[ ,0]
i ii
Ty y y
τ
λ
−
= −
,
0a≥
,
0c≥
,
< R
ni
.
He e,
z
g
is he adjus men ac o o g ow h ia o al ac o p oduc i i y
z
.
Na ional Pension income
(,; , )
BnA
ξα
is de e mined by he a e age mon hly labo
income du ing he mon hs he household was en olled
()B
, he con ibu ion pe iod
()n
, a e age mon hly labo income o all en olled membe s
()A
, and he income
eplacemen a e3 coe icien
()
α
. The income o mula o he cu en DB pension
sys em, which will be used as a baseline sys em, is as ollows:
2In he eal wo ld, na ional pensions a e also subjec o income ax, bu he ax c edi is la ge compa ed o ha
o labo income and is hus igno ed he e.
3The income eplacemen a e (%) is de ined as
100 / (12 )B
ξ
××
.
VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 7
[ 10]
( ) (1 0.05 1 ( 20)) i 10
(,; , ) ( ) 0.5 o.w.
n
AB n n
BnA AB
α
ξα α
≥
+ ⋅+ × + ≥

=+⋅

.4
A
and
B
a e combined a a a io o 1:1, implying an income edis ibu ion
unc ion. The o mula o he
A
alue is
1
[]
1
1
[]
1
1 (, )
12 1 ( )
R
R
ii
i i ll
i
ii
i ll
i
w xl l x
All
µε ψ
µψ
−
〉
=
−
〉
=
×
≡×
∑∫
∑∫
.
The Basic Pension
ˆ(, ,; , )aBnA
ϕα
is also a ec ed by he same ou inpu s as he
Na ional Pension income because i is a ec ed by he amoun o Na ional Pension
income. Addi ionally, i is in luenced by asse
a
, as he Basic Pension can only be
ecei ed when he combined income om in e es and he Na ional Pension is less
han
y
, which ep esen s he lowe 70% income le el o e i emen age. The
ollowing o mulas hold o he Basic Pension:
ˆ( , , ; , ) min{ ,max{ ( ( , ; , )),0}}
i
aBnA y y BnA
ϕ αϕ ξα
= −+
,
1, 2
i ( , ; , ) 1.5
(,; , ) max{ } i 1.5 ( , ; , )
BnA
BnA BnA
ϕ ξ αϕ
ϕα ϕϕ ϕ ξ α
≤

=<

,
1
max[ (2 / 3) ( ; , ),0] 0.5
A
INC n A
ϕϕ α ϕ
=−+
,
2
max{2.5 ( , ; , ),0}
BnA
ϕ ϕξ α
= −
,
(;,) (,;,)
A
INC nA AnA
αξ α
=
.
When Na ional Pension income
ξ
is less han o equal o 1.5 imes base pension
ϕ
, he po en ial Basic Pension
ϕ
is
ϕϕ
=
. I
ξ
inc eases o mo e han 1.5 imes
ϕ
,
ϕ
dec eases as much as
ξ
inc eases
( 2.5 )
ξϕ ϕ
+=
un il i eaches
(2 / 3) A
INC
ϕ
+
, whe e
A
INC
is he Na ional Pension income when
BA=
.
ϕ
is
ixed a
1
ϕϕ
=
i
ξ
inc eases u he and
ϕ
dec eases o each lowe bound
1
ϕ
.5 Fo
ξ
alues ha a e e en g ea e ,
ϕ
is adjus ed so he o al e i emen
income
i
y
ξϕ
++
does no exceed
y
.
The wo king-age u ili y maximiza ion p oblem can be exp essed as a Bellman
equa ion:
4The o iginal Na ional Pension Regula ion e e s o he i s 20 yea s o con ibu ions as “ ull old-age pension”
and he second 10 yea s o mo e bu less han 20 yea s as “ educed old-age pension,” bu because he bene i amoun
is linea , he same o mula can be used.
5h ps://basicpension.mohw.go.k /menu.es?mid=a10103010000.
8 KDI Jou nal o Economic Policy NOVEMBER 2024
11
, ( , )|( , )
( , , , , ) max { ( ) (1 )(1 ) ( , , , , )}
u
ii
ca i z x l xl
V laxBn uc g E V l a x B n
σ
βγ
−+
′ ′′ ′′′′
= +− +
..s
[]
(1 ) (1 ) (1 ) 1 min( , ) ( )
l
c z k i l l ss i i
c a g a a y w x l T y
τ τ τ κε
>
′
+ + + =+− + − −
,
(1 )
l
i ki
y a y
τ
=−+
,
l
ii
y w xl
ε
=
,
+1 i
i
n ll
nn ll
>

′==

,
12 min( , ) i
12
B i
i
B n w xl ll
Bn
ll
κε
×+
>

′=′

=

,
2
log log , (0, )
x xx x
x x N
ρσ
′= + 
,
0a≥
,
0c≥
,
ni
≤
.
Fo each age
i
, i
ll>
,
l
is ecognized as a con ibu ion pe iod, included in he
calcula ion o
n′
, and, oge he wi h he lowe limi o
i
wx
ε
and he uppe limi
κ
, e lec ed in he calcula ion o he a e age mon hly labo income
B′
. Age
1i=
akes
0anB
= = =
as he ini ial condi ion.
The model does no include all speci ic p o isions o he Na ional Pension and he
Basic Pension. Fo example, he model does no accoun o pension educ ions due
o ea ly eceip o inc eases due o de e ed pensions, no does i speci ically add ess
income axes o ax c edi s on pensions. Howe e , we belie e ha we ha e cap u ed
he essen ial elemen s o ou esea ch opic.
B. Fi m P oblem
Homogeneous i ms use capi al inpu s
K
, labo inpu s
N
, o al ac o p oduc i i y
z
, and he capi al income sha e
θ
o gene a e g oss domes ic p oduc
Y
h ough
Cobb-Douglas p oduc ion echnology:6
1
Y zK N
θθ
−
=
.
Fi ms ace dep ecia ion a e
δ
, in e es a e
, and wage a e
w
when sol ing he
ollowing p oblem:
6To al ac o p oduc i i y
z
g ows by
1
(1 )g
θ
−
+
e e y yea .
VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 15
i
γ
di ec ly om Fu u e Popula ion P ojec ions (2021). Fo con enience, we
adjus ed he popula ion in 2022 such ha i sums o 1. Labo P oduc i i y by age
i
ε
was ex ac ed om he Ko ean Labo Panel (2019)10 by di iding he a e age income
by he a e age wo king s a us o each age.
i
ε
is la e adjus ed so ha
1N=
using
he explici de i a ion o he labo hou s dis ibu ion om
Λ
. In an icipa ion o
a ge ing
/3
KN
=
, we adjus
z
in ad ance so ha
1Y=
.11 Based on a 2022
co po a e ax e enue- o-GDP a io o 4.79%, we se
0.3992
k
τ
=
.12
Fo he exogenous labo -hou ans e unc ion
Λ
, simila o Lee e al. (2019),
he s a es a e
1 {1 / 3, 2 / 3, 1}∈
wi h
1/3l=
. The wo king age is di ided in o
h ee bins (20-34, 35-49, and 50-64) and he e o e we es ima e h ee
33×
ma ices
and he ini ial labo dis ibu ion. Gi en ha he na ional pension is only ma u e un il
he age o 40, we i he dis ibu ion da a o he age 32 and age 40 con ibu ion
pe iods o 2022 p o ided by he Minis y o Heal h and Wel a e. To iden i y he labo
supply a e age 40, we es ima e he ans e unc ion
Λ
by i ing i s dis ibu ion o
wo king hou s o a combina ion o he employmen a e da a by age g oup om he
Economic Ac i i ies Census and he a e age wo king s a us by age om he Ko ean
Labo Panel (2019). Figu es 1, 2, and 3 show ha hese a ge s a e well me , indica ing
high explana o y powe . In he model, e i ees ha e an a e age con ibu ion pe iod
o 23.5 yea s, which is mo e ma u e han he a e age con ibu ion pe iod o 59-yea -
olds in 2022, which is 13.9 yea s. I we assume ha all employed people o e he
age o 20 con ibu e, he a e age con ibu ion pe iod om he Economic Ac i i y
Su ey (2019) is 31.7 yea s, indica ing ha he model’s con ibu ion pe iod is much
lowe han he ideal con ibu ion pe iod. The con ibu ion pe iod dis ibu ion ac oss
all ages in he model and da a is p esen ed in he Appendix.
(Uni : Densi y)
FIGURE 1. MODEL TO DATA COMPARISON OF THE AGE 32 (LEFT)
AND AGE 40 (RIGHT) CONTRIBUTION PERIOD DENSITY LEVELS
Sou ce: Au ho ’s igu e based on 2022 popula ion da a by age×con ibu ion pe iod om he Minis y o Heal h and Wel a e.
10We chose 2019 because i is he las yea wi hou he impac o COVID-19 and i is possible ha he labo
en i onmen a e 2019 has no eco e ed om he impac o COVID-19.
11
1
1/z KN
θθ
−
=
12
4.79(%) / ( / )
k
KY
τ θδ
= −
0 2 4 6 8 10 12
Yea s
0
0.05
0.1
0.15
Da a
Model
0 5 10 15 20
Yea s
0
0.02
0.04
0.06
0.08
0.1
Da a
Model

16 KDI Jou nal o Economic Policy NOVEMBER 2024
FIGURE 2. EMPLOYMENT RATE DATA VS MODEL
Sou ce: Au ho ’s igu e based on labo hou s da a om he Ko ea Labo Panel (2019).
FIGURE 3. MODEL TO DATA COMPARISON OF LABOR HOURS
Sou ce: Au ho ’s igu e based on 2022 popula ion da a by age×con ibu ion pe iod o he Minis y o Heal h and Wel a e.
20 25 30 35 40 45 50 55 60
Age
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Da a
Model
20 25 30 35 40 45 50 55 60 65
Age
0
5
10
15
20
25
Con ibu ion Yea s
Da a
Model
VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 17
The ollowing pa ame e s we e es ima ed by sol ing he model.
β
, ollowing
Lee e al. (2019), is calib a ed so ha
/3KY=
.
l
λ
is se o ma ch he 2022 income
ax e enue o GDP a io 5.96%.
c
τ
is adjus ed so ha he consump ion ax e enue
a io is 3.78%, and
ϕ
is se o achie e he Basic Pension expendi u e a io o
0.75%. The uppe limi o mon hly con ibu ion
κ
is based on an a e age o 13.5%
o membe s alling wi hin he uppe limi . The con ibu ion a e was 9% in 2022, bu
because he size o he Na ional Pension sys em as a sha e o GDP is c i ical o he
esul s o his s udy, we es ima ed

ss
τ
o ma ch he 2022 con ibu ion o GDP a io
o 2.59%. To simula e a u u e con ibu ion a e o 18%, we double he con ibu ion
a e o
2
ss
τ
= ∗

ss
τ
. The income eplacemen a e coe icien was adjus ed o
1.2
α
= ∗

ss
τ
/0.09
.
In ha he Na ional Pension Fund had no ye been exhaus ed in 2022, we assume
ha he und
M
was as la ge as 42% o GDP solely o he pu pose o quan i ying
he model o ma ch he 2022 economic en i onmen . Consequen ly, we modi y he
capi al ma ke clea ing condi ion as ollows:
1
min[ , ]
Ii
i
i
K ad M K
µ ψω
∗
=
= +
∑∫
.
He e,
1 0.506
ω
−=
ep esen s he cu en p opo ion o o eign in es men s, which
is also used in he expe imen s o he DC sys em. The de i a ion o his igu e is
de ailed in he Appendix.
Because he Na ional Pension Fund emains in su plus un il 2022, we assume ha
he Na ional Pension Se ice’s inances do no a ec he go e nmen budge
cons ain o e lec his accu a ely. Thus, he go e nmen budge cons ain is
modi ied only in he es ima ion phase, as ollows:
TG= +Φ
.
Fo he baseline und a e o e u n, he o eign in e es a e is se o
0
∗=
o
compa e DB and DC unde simila ci cums ances. La e , we adjus
∗
o analyze
he impac o o eign in e es a es on DC.
IV. Theo y
The main ocus o his s udy is he e ec o each pension sys em on he economy
unde he 2070 demog aphic en i onmen (popula ion s uc u e and mo ali y).
Be o e e iewing he esul s o he analysis, we p o ide a heo e ical discussion o
he mac oeconomic consequences o changes in he demog aphic en i onmen and
co esponding inc eases in con ibu ion a es o bo h he DB and DC sys ems wi hin
he o e lapping gene a ions model.
As men ioned ea lie , in ou model, popula ion s uc u e
i
µ
is no de e mined by
mo ali y a e
i
γ
; ins ead, each is exogenously inpu ed using da a om he
18 KDI Jou nal o Economic Policy NOVEMBER 2024
P ospec i e Popula ion P ojec ions da ase (2021). The e o e, i is necessa y o
clea ly dis inguish he oles o he popula ion s uc u e and mo ali y in he model.
In he model, households a e unawa e o he popula ion s uc u e bu assume ha
hei mo ali y a e is
i
γ
. Thus, u ili y-maximizing households a e in o med wi h
ega d o p ices, mac o a iables, and mo ali y, bu no
i
µ
. Mo eo e , mo ali y
a ec s bene i le els and he dea h ax e enue in DC sys ems, as shown in he
model’s equa ions. The popula ion s uc u e
i
µ
is used as a weigh o agg ega e
indi idual a iables o o m agg ega e a iables, mainly a ec ing ma ke clea ing
and go e nmen budge cons ain s.
We begin by summa izing he heo e ical discussion o he mac oeconomic e ec s
changes in he popula ion s uc u e, declines in mo ali y a es, and inc eases in
con ibu ion a es in each pension sys em.
FIGURE 4. CHANGES IN POPULATION STRUCTURE (LEFT) AND MORTALITY (RIGHT)
No e: The e ical dashed line indica es he age o e i emen .
Sou ce: Au ho ’s illus a ion based on Fu u e Popula ion P ojec ions (2021).
TABLE 1. 2022 VS 2070: POPULATION, POPULATION STRUCTURE, LABOR, AND MORTALITY RATES
All ages Ages 20-64 Ages 65-98
2022
Model Popula ion 1.000 0.792 0.208
Popula ion Densi y 1.000 0.792 0.208
/
i
N
µ
1.000 1.262 0.000
Mo ali y 0.031 0.002 0.072
2070
Model Popula ion 0.770 0.375 0.395
Popula ion Densi y 1.000 0.487 0.513
/
i
N
µ
0.597 1.227 0.000
Mo ali y 0.021 0.000 0.049
No e: Mo ali y a es weigh each age equally;
/
i
N
µ
is labo pe capi a, which is o al labo di ided by he
popula ion o each age g oup.
20 40 60 80 100
Age
0
2
4
6
8
10
Popula ion
10
5
2022
2070
20 40 60 80
Age
0
5
10
15
20
25
30
%
2022
2070
VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 19
A. Impac o he Aging Popula ion S uc u e
The mos signi ican di e ence be ween he popula ion s uc u es o 2070 and
2022 is he much highe dependency a io o he elde ly. As shown in Table 1, he
sha e o e i emen -age adul s is p ojec ed o inc ease om 20.8% in 2022 o 51.3%
in 2070, ep esen ing a 146.6% inc ease. Con e sely, he sha e o wo king-age
people eligible o pensions will dec ease, esul ing in less con ibu ion e enue o
he pension unds. The sha e o wo king-age people is expec ed o d op om 79.2%
in 2022 o 48.7% in 2070, a dec ease o 38.5%.
The mac oeconomic e ec s o he demog aphic ansi ion o 2070 include a dec ease
in he labo supply pe capi a. As he labo supply pe capi a alls, i ms wi h Cobb-
Douglas unc ion p oduc ion echnology will educe hei demand o complemen a y
capi al in p oduc ion. Consequen ly, in equilib ium, capi al pe capi a alls, he in e es
a e alls, he wage a e ises, and agg ega e ou pu ises. The p ima y economic
phenomenon ha occu s when he wage a e ises is ha he consump ion and income
gap be ween he wo king-age and e i emen -age g oups widens. Al hough he le el
o pension bene i s a e i emen age also inc eases as he wage a e ises, inequali y
wo sens because he wo king-age popula ion gains mo e om wages.
A second mac oeconomic e ec o he 2070 popula ion s uc u e is a po en ial
decline in he co ela ion be ween li ecycle sa ings and he weigh ing o he
popula ion s uc u e. While sa ings ypically peak in he li e cycle jus be o e
e i emen , Figu e 4 shows ha in 2022, he popula ion has a ela i ely high
p opo ion o people nea ing e i emen . In con as , by 2070, he highes p opo ion
will be in hei mid-70s, a pe iod when sa ings ha e signi ican ly declined. This
sugges s ha e en i people main ain he same sa ings pa e ns h oughou hei
li es, he demog aphic shi alone can educe o al sa ings pe capi a. In esponse o
his capi al supply shock, agg ega e capi al dec eases, in e es a es inc ease, wage
a es dec ease, and agg ega e ou pu dec eases. I a demand shock o capi al occu s
simul aneously wi h he decline in he pe capi a labo supply, he decline in
agg ega e ou pu is heo e ically ce ain, bu he inal di ec ions o changes in in e es
a es and wage a es a e unce ain.
While he i s wo shocks can occu in bo h he DB and DC cases, i is only in he
DB case ha he aging popula ion s uc u e leads o a de ici in he pension und and
a highe ax bu den. This occu s because he pension bene i o he cu en ex eme
DB sys em in Ko ea esponds o he o e all income le el o he popula ion, as shown
in he bene i o mula, and does no espond o demog aphic changes. Because he
con ibu ion a e and he le el o bene i s applied o membe s a e sepa a e, a highe
dependency a io o he elde ly may simply inc ease he p opo ion o people
ecei ing bene i s, wo sening he inances. In such a si ua ion, i he con ibu ion
a e is no high enough, he o al con ibu ions will be insu icien o co e he o al
bene i s each yea . Consequen ly, in he long un, he economy will need con inuous
injec ions o gene al go e nmen unds o achie e equilib ium wi h he same
popula ion s uc u e as in 2070. Highe axes would educe households’ a e - ax
income, po en ially leading o lowe sa ings, which in u n could lead o highe
in e es a es, lowe wage a es, and dec eased ou pu .
Assuming ha he go e nmen ’s p oposal o inc ease ax a es o close he unding
20 KDI Jou nal o Economic Policy NOVEMBER 2024
de ici in he DB sys em passes, he iscal balance would ha e o be achie ed h ough
h ee main sou ces: income axes, co po a e axes, and consump ion axes. Inc easing
income axes o inance pension de ici s ends o educe inequali y wi hin he
wo king-age g oup due o he p og essi e na u e o income axes. Howe e , because
he la ges po ion o income axes is le ied on wo king-age incomes, his app oach
educes he dispa i y in disposable income be ween wo king-age and e i emen -age
indi iduals, po en ially imp o ing inequali y measu es such as he Gini coe icien .
Ano he ea u e o highe income axes is ha in e es income can also be subjec
o income ax, which can educe o e all sa ings and hus in es men . This can cause
in e es a es o ise and he economy o con ac . Wage a es will also decline along
wi h g oss domes ic p oduc , educing pensions bu educing o e all inequali y as well.
On he o he hand, co po a e axes can dep ess he economy by lowe ing a e - ax
in e es income, which discou ages sa ing and in es men . Gi en ha co po a e
axes a e pu ely a ge ed a capi al income, hei dep essi e e ec may be s onge
han ha o income axes i he same e enue is a ge ed. As a esul , capi al may
dec ease, aising he ma ginal p oduc o capi al. This, in u n, lowe s wages, which
gene ally lowe s consump ion o e all.
Compa ed o he ea u es o income and co po a e axes, consump ion axes a e
neu al o he popula ion as a whole, as e e yone is axed a a single a e, and i
labo supply is inelas ic, ax dis o ions a e minimized. Unlike income axes,
consump ion axes do no di ec ly shi he bu den o he wo king-age popula ion,
and he ax bu den is ela i ely high o he e i ed popula ion. To emain neu al on
he age concen a ion o he e ec s and labo dis o ions, we use consump ion axes
as he main sou ce o e enue in his s udy.13 Rega dless o he chosen e enue
sou ce, households’ a e - ax income alls, leading o educed sa ings, which has a
con ac iona y e ec on he economy, al hough he in ensi y o his e ec may a y
depending on he ype o ax selec ed.
Whe eas DB aces a se ious p oblem o ising ax a es, DC emains inancially
s able e en i he elde ly dependency a io ises, as shown in Figu e 4. This a ises
because indi iduals only ecei e bene i s equi alen o con ibu ions and in es men
e u ns. As a esul , some o he unds a e in es ed domes ically, which is why
in e es a es can be lowe in he DC case e en unde condi ions iden ical o hose o
he DB case. The e o e, DC can ha e highe o al capi al, lowe in e es a es, highe
wage a es, and highe g oss p oduc han DB.
B. Impac o Lowe Mo ali y
Declining mo ali y gi es households an incen i e o inc ease sa ings a mos
ages as li e expec ancy inc eases. As shown in Table 1, he decline in mo ali y is mo e
p onounced in he e i emen -age g oup han in he wo king-age g oup. Consequen ly,
he e i emen -age g oup may sa e mo e o sel -insu e agains longe li espans. As
o e all sa ings ise, he in e es a es all, and he wage a e ises, inc easing wages
13O cou se, e ec i e ax a es a y by age, which should be in e p e ed wi h some cau ion. Fo example, Kim
(2020) shows ha he p opo ion o ax-exemp consump ion is highe among he olde and he elde ly, so an inc ease
in consump ion axes could na ow he gap be ween he wo king and e i emen age g oups.

VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 21
o wo king-age indi iduals. This can exace ba e inequali y measu es by u he
widening he income gap be ween wo king-age and e i emen -age indi iduals.
C. E ec o Reduced Sa ings as DC Bene i s Decline
In gene al, households end o inc ease hei sa ings in esponse o an expec ed
dec ease in u u e pension bene i s. Howe e , while DB does no adjus bene i le els
in esponse o ac o s o he han income le els, he bene i le els o DC can change
elas ically wi h in e es a es, making he equilib ium ou come esponsi e o a ious
ex e nal shocks. When in e es a es ise, he pension und g ows, leading o highe
bene i le els, which subsequen ly educes sa ings and u he inc eases in e es
a es. Con e sely, a dec ease in in e es a es has an ampli ying e ec in he opposi e
di ec ion, causing in e es a es o all u he .
I we exp ess his in a pa ial equilib ium o he capi al ma ke , he slope o he
capi al supply cu e o DC is s eepe han ha o DB. The o al supply cu e o DC
is di ided in o he capi al supply o households and he supply o unds h ough he
DC und. The o al amoun o he DC und in his case slopes upwa d ela i e o he
in e es a e because he und also g ows as he a e o e u n
ˆ
(p opo ional o he
in e es a e) ises. Wi h ega d o he supply o household capi al, some incen i es
may be upwa dly sloping, as in DB, bu he e is also an incen i e o households o
sa e less as pension bene i s inc ease when in e es a es ise. As a esul , he capi al
supply cu e o DC is likely o be coun e clockwise s eepe han he DB capi al
supply cu e. F om he pe spec i e o a gene al equilib ium analysis, bo h he DB
and DC capi al supply cu es may be s eepe han he slopes in pa ial equilib ium
because when in e es a es all, wages necessa ily ise, inc easing he income le el
o households. Howe e , he capi al supply cu e is s ill s eepe in he DC case han
in he DB case because households ha e an incen i e o educe hei capi al supply
u he as in e es a es ise.
In such a si ua ion, a demog aphic demand shock ha educes labo pe capi a
will cause in e es a es o all mo e in DC han in DB. Howe e , equilib ium pe
capi a capi al will all less in he DC case, esul ing in a smalle decline in agg ega e
ou pu , as shown in Figu e 5. This ou come is p ima ily due o households inc easing
FIGURE 5. DB VS DC RESULTS FOR DEMAND SHOCKS (LEFT) AND SUPPLY SHOCKS (RIGHT) OF CAPITAL
22 KDI Jou nal o Economic Policy NOVEMBER 2024
hei sa ings in esponse o lowe in e es a es as pension bene i s a e educed.
Con e sely, i he e is a supply shock due o a decline in he co ela ion be ween
capi al and he popula ion s uc u e, he same shock may cause in e es a es o ise
mo e and agg ega e ou pu o all mo e in DC han in DB. This is due o he sa ings
esponse e ec , as shown in Figu e 5.
Mo ali y is also a ac o ha a ec s bene i le els in DC, meaning ha a decline
in mo ali y may ha e di e en impac s on DC and DB. Like DB, DC bene i s om
he sa ings boos ha comes om longe li e expec ancy. Howe e , lowe mo ali y
di ec ly educes he le el o bene i s unde he DC bene i o mula. Because he
con ac ual e ms o DC dic a e ha he unds o iginally belonging o deceased
indi iduals a e passed on o he su i o s, he la e he popula ion in he coho dies,
he lowe he bene i le el. The esul ing ise in sa ings can boos he economy, lowe
in e es a es, and inc ease wage a es, po en ially leading o a ise in inequali y indices.
D. E ec o Con ibu ion Ra e Inc eases
I is possible o DB o emain in place and o he con ibu ion a e o ise as he
sys em’s inances de e io a e owa d 2070. Ano he possibili y is ha he DC e o m
would occu only a e an 18% inc ease in he con ibu ion a e as DB emains in
place. Al e na i ely, he DC e o m may occu when he con ibu ion a e is 9%, bu
he a e would need o be aised due o an insu icien income eplacemen a e.
The e o e, le ’s b ie ly discuss he implica ions o ha ing a con ibu ion a e highe
han 9% in each pension sys em.
A simple in e p e a ion o inc easing con ibu ion a es in he DB case wi hin his
model is ha , ins ead o inancing he pension de ici wi h consump ion axes, i is
inanced wi h a single- a e labo income ax. An inc ease in he con ibu ion a e
would educe sa ing among he wo king-age popula ion, which is he main sa ing
age g oup, leading o educ ions in g oss domes ic p oduc and wage a es. This
edis ibu i e e ec inc eases he a e - ax income o he e i emen -age g oup while
dec easing he a e - ax income o he wo king-age g oup, hus imp o ing he
inequali y index. Howe e , i he inc ease in he con ibu ion a e eplaces co po a e
o income axes a he han consump ion axes, i may ac ually inc ease sa ings. The
inal equilib ium capi al gains o losses may depend on he choice o ax adjus ed o
achie e a iscal balance.
On he o he hand, he DC case does no ha e he same subs i u ion e ec on ax
e enues compa ed o DB. An inc ease in he con ibu ion a e in he DC case
inc eases he amoun o unds di ec ly in es ed in Ko ea bu also inc eases pension
bene i s, which c ea es an incen i e o households o sa e less. Addi ionally,
wo king-age indi iduals who make highe con ibu ions due o he inc eased
con ibu ion a e will ha e lowe a e - ax incomes, simila o he DB case, and hus
ha e an incen i e o sa e less. Essen ially, he ela i e magni udes o hese h ee
e ec s de e mine whe he capi al is ul ima ely inc eased o dec eased. I he inc ease
in pension unds in es ed domes ically is no subs an ial, he wo king-age g oup is
likely o be he wo se o due o lowe wage a es, which could lead o an imp o emen
in inequali y measu es.
VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 23
TABLE 2. DB GENERAL EQUILIBRIUM EFFECT DIAGRAM
Shock Channel Resul
Pension De ici ↑ → Taxes↑→ [A e - ax Income↓ Sa ings↓ In e es Ra e↑]
Capi al↓
In e es Ra e↑
Wage Ra e↓
G oss P oduc ↓
Labo ↓ → Capi al Demand↓→ In e es Ra e↓
Capi al↓
In e es Ra e↓
Wage Ra e↑
G oss P oduc ↓
Sa ings ×
Popula ion S uc u e↓ → Capi al Supply↓→ In e es Ra e↑
Capi al↓
In e es Ra e↑
Wage Ra e↓
G oss P oduc ↓
Mo ali y↓ → Sa ings↑→ In e es Ra e↓
Capi al↑
In e es Ra e↓
Wage Ra e↑
G oss P oduc ↑
Con ibu ion Ra e↑ → [A e - ax Income↓ Sa ings↓ In e es Ra e↑]
De ici ↓ → Taxes↓→ [A e -Tax Income↑ Sa ings↑ In e es Ra e↓]
Capi al (↓)
In e es Ra e (↑)
Wage Ra e (↓)
G oss P oduc (↓)
No e: Pa en heses indica e ambi alen esul s. Single a ows indica e an e ec . Double a ows indica e a s ong e ec .
TABLE 3. DC GENERAL EQUILIBRIUM EFFECT DIAGRAM
Shock Channel Resul
Funds In es men ↑ → Capi al Supply↑ → In e es Ra e↓→ [Bene i ↓ Sa ings↑ In e es Ra e↓]
Capi al↑↑
In e es Ra e↓↓
Wage Ra e↑↑
G oss P oduc ↑↑
Labo ↓ → Capi al Demand↓ → In e es Ra e↓→ [Bene i ↓ Sa ings↑ In e es Ra e↓]
Capi al (↓)
In e es Ra e↓↓
Wage Ra e↑↑
G oss P oduc ↓
Sa ings ×
Popula ion S uc u e↓ → Capi al Supply↓ → In e es Ra e↑→ [Bene i ↑ Sa ings↓ In e es Ra e↑]
Capi al↓↓
In e es Ra e↑↑
Wage Ra e↓↓
G oss P oduc ↓↓
Mo ali y↓ →
Sa ings↑ → In e es Ra e↓→ [Bene i ↓ Sa ings↑ In e es Ra e↓]
[Bene i ↓ Sa ings↑ In e es Ra e↓]
Capi al↑↑
In e es Ra e↓↓
Wage Ra e↑↑
G oss P oduc ↑↑
Con ibu ion Ra e↑ →
[A e - ax Income↓ Sa ings↓ In e es Ra e↑]
→ [Bene i ↑ Sa ings↓ In e es Ra e↑]
[Bene i ↑ Sa ings↓ In e es Ra e↑]
Funds↑ → In e es Ra e↓→ [Bene i ↓ Sa ings↑ In e es Ra e↓]
Capi al (↓)
In e es Ra e (↑)
Wage Ra e (↓)
G oss P oduc (↓)
No e: Pa en heses indica e ambi alen esul s. Single a ows indica e an e ec . Double a ows indica e a s ong e ec .
24 KDI Jou nal o Economic Policy NOVEMBER 2024
Howe e , a he han ocusing on he e ec o inc easing he con ibu ion a e, his
s udy examines on he impac o changing he pension sys em a a gi en con ibu ion
a e. Rega ding he e ec o an inc ease in he con ibu ion a e in he DB case, see
Lee e al. (2019).
E. Summa y
Tables 2 and 3 summa ize his discussion. The main di e ence be ween he wo
pension sys ems is ha he capi al supply cu e is mo e coun e clockwise in he DC
han in he DB case. This is due o he e ec o he sa ing esponse o changes in
pension bene i s, making he in e es a e mo e elas ic o any shock. Addi ionally, i
is e iden ha he di ec ions o pension bene i s and wage a es a e always opposi e
in he DC case. This occu s because he in e es a e and wage a e a e nega i ely
co ela ed acco ding o he i m’s op imiza ion o mula, while pension bene i s and
in e es a es a e posi i ely co ela ed h ough he pension o mula and he
household’s sa ings esponse. The e o e, o any shock, he gains o wo king-age
and e i emen -age indi iduals mo e in opposi e di ec ions, leading o co esponding
changes in he Gini coe icien s.
V. Coun e ac ual Expe imen Resul s
This sec ion highligh s he challenges in main aining he DB pension sys em o e
he long e m in he 2070 demog aphic en i onmen and sugges s ha a DC e o m
could be a iable solu ion. We also p opose a supplemen a y e o m o he Basic
Pension sys em as a way o add ess he issues associa ed wi h he DC e o m. In his
sec ion, we assume ha he go e nmen p ima ily adjus s he consump ion ax a e
o achie e a iscal balance. This sec ion assumes ha
0
z
g=
.
A. Resul s o he Demog aphic En i onmen Change
1. DB Pension Sys em
a) Pension und de ici esul s
Table 4 shows he p ojec ed de ici o DB in 2070. I he cu en demog aphic
en i onmen (popula ion s uc u e and mo ali y) con inues as i is oday (2022) wi h
a 9% con ibu ion a e, he unde lying iscal de ici o he Na ional Pension Fund is
only 0.8% o GDP each yea . Doubling he con ibu ion a e o add ess his would
esul in a iscal su plus o 1.8% o GDP annually. Cu en ly, p oposals o inc ease
he con ibu ion a e o 13% o 15% a e equen ly discussed in he media, sugges ing
ha such an inc ease would be su icien o balance he und. Howe e , i he
demog aphic en i onmen p ojec ed o 2070 pe sis s, a 9% con ibu ion a e will
VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 31
disposable income Gini coe icien is lowe in DB as he con ibu ion a e inc eases,
he imp o emen is mo e signi ican in DC. On he o he hand, he gap in
consump ion Gini coe icien s be ween he wo pension sys ems widens. While an
inc ease in he con ibu ion a e also educes he consump ion o wo king-age people
in he DC case, o DB, he economic con ac ion a ec s wo king-age people mo e,
leading o a g ea e imp o emen in consump ion inequali y in DB.
One o he weaknesses o en ci ed in ela ion o DC sys ems is he inabili y o
hese sys ems o edis ibu e income in li e in la e , hough his is only pa ially ue.
Admi edly, he DC case, in con as o he Ko ean DB sys em ha equally weighs
he
A
and
B
alues in he bene i , a e based on he concep ha indi iduals
con ibu e and ecei e only as much as hey in es . This sugges s ha DC would
ha e highe income inequali y in e i emen . Howe e , he Gini coe icien o
e i emen disposable income is ac ually lowe o he DC han he DB case.
Al hough he Gini coe icien o e i emen disposable income o DC inc eases
when he con ibu ion a e ises o 18%, i is s ill lowe han ha o DB.
The eason o his lowe inequali y in e i emen disposable income in he DC case
is ha e e yone’s bene i le el is e y low in he DC sys em, as shown in Figu e 8.18
O cou se, aising he con ibu ion a e un il he le el o e i emen disposable
income in DC is simila o ha in DB could make he Gini coe icien o e i emen
disposable income in he DC case highe , bu he easibili y o his app oach is
doub ul gi en he common no ion ha an 18% con ibu ion a e is al eady oo
bu densome o households in Ko ea. Thus, while i is plausible ha DC e o ms
could widen he social gap be ween he wo king- and e i emen -age g oups, leading
o g ea e o e all inequali y han in he DB case, i is impo an o examine u he
whe he inequali y wi hin he e i emen -age g oup i sel will wo sen.
C. Analyzing he Uni e sal Pension Policy unde DC
As we ha e seen, one o he main p oblems wi h he DC sys em is no he
edis ibu ion o income in e i emen bu a he he gene ally low le el o e i emen
income. We ind ha DC could be wo se han DB in e ms o he income eplacemen
a e, e u n a io, disposable income a e i emen age, and a e - ax income a
e i emen age. We also ind ha he Gini coe icien o consump ion in e i emen
age is highe in DC, p ima ily because pension bene i s a e oo low in DC, causing
households o ely mo e on sa ings o consump ion. As a solu ion o hese p oblems,
we p opose expanding go e nmen iscal suppo o e i emen -age indi iduals. Fo
simplici y, we assume a uni e sal pension ha p o ides he same amoun o ans e
paymen s o all e i emen -age g oups. 19 The Basic Pension is assumed o be
educed based on he sum o he Na ional Pension and he uni e sal pension. We also
conside his uni e sal pension when calcula ing he income eplacemen a es.
Unlike he DB case, he DC case is no inancially p oblema ic; howe e , he
18The highe Gini coe icien o e i emen consump ion o he DC sys em is also due o he ac ha e i emen
age income is so low ha hey ely p ima ily on sa ings o consump ion, while sa ings inequali y is highe han
ha o he pension bene i .
19How o implemen hese subsidies in he eal wo ld h ough he Basic Pension sys em is le o u u e esea ch.

32 KDI Jou nal o Economic Policy NOVEMBER 2024
DC sys em’s pension bene i s a e highly sensi i e o dec eases in in e es a es.
Addi ionally, he inc ease in sa ings in p epa a ion o such si ua ions can u he
dec ease pension bene i s h ough addi ional dec eases in in e es a es. Al hough i
is ine i able ha in e es a es and pension bene i le els will all due o he ini ial
decline in he labo o ce pe capi a, we sugges expanding he uni e sal pension o
mi iga e he phenomenon o households inc easing hei sa ings e en mo e o
p epa e o hei own e i emen , which in u n lowe s he le el o bene i s. The
eason his s udy p oposes his solu ion ins ead o inc easing he con ibu ion a e
u he o 18% is o emphasize he need o s uc u al e o m by making a di ec
compa ison wi h he cu en DB pension sys em in an equalized en i onmen . We
ha e al eady shown ha a go e nmen ans e o 9-11% o GDP o he pension each
yea would be necessa y o main ain he DB in he 2070 demog aphic en i onmen .
I such policy is easible, i may be ealis ic as well o p o ide a smalle ac ion o
his ans e as a uni e sal pension unde he DC sys em. Model expe imen s can be
used o de e mine he amoun o he addi ional uni e sal pension bene i needed o
achie e he wel a e e ec s o he DB sys em.
To de e mine whe he DC is be e han DB, we will use he ollowing c i e ia,
e e ed o as he “key indica o s:” (1) he a e age s anda d o li ing a wo king age
(consump ion and a e - ax income), (2) he a e age s anda d o li ing a e i emen age
(consump ion, a e - ax income, income eplacemen a e, and g oss e u n a io), and
(3) inequali y wi hin he e i emen -age g oup (consump ion and disposable income
Gini coe icien s). Because his analysis elies on consump ion ax as he main sou ce
o go e nmen e enue, a e age disposable income ha does no conside consump ion
ax is no a good measu e o wel a e. Mo eo e , gi en ha a e - ax income can be
nega i e in eali y, we will conside disposable income ins ead o a e - ax income
o he Gini coe icien . We also exclude he inequali y index wi hin he wo king-age
g oup o ocus on he pension and wel a e o he e i emen -age g oup. Howe e ,
eade s a e ee o use hei own c i e ia o compa e pension sys ems.
Fo he 2070 demog aphic en i onmen and he gi en con ibu ion a e, we
expe imen ed on he DC sys em by a adding uni e sal pension amoun ing o only a
ac ion o he 100% o he go e nmen ans e needed o main ain he DB sys em.20
The esul s o he key indica o s in Table 8, Table 9, Figu e 10, and Figu e 11 show
ha a a con ibu ion a e o 9% in 2070, DC needs less han 90% o he go e nmen
ans e equi ed o main ain DB o imp o e he key indica o s compa ed o DB. A
an 18% con ibu ion a e, a subsidy o less han 60% is su icien o imp o e he key
indica o s.21
The p ima y eason why DC is mo e e icien o e all han DB a e accoun ing
o go e nmen subsidies is ha he o al ou pu and a e - ax income a e inhe en ly
highe in he DC case. E en wi hou he supplemen al uni e sal pension, o al ou pu
and a e - ax income a e highe in DC han in DB, meaning ha he main issue wi h
DC emains edis ibu ion. As we ha e seen, he e is an ampli ying e ec be ween
in e es a es, pension bene i s, and household sa ings in he DC case, which can
lead o a la ge income gap be ween wo king and e i emen ages han in he DB
20The e o e, o he same weigh (%), he subsidy is la ge a a 9% con ibu ion a e han a an 18% con ibu ion a e.
21Consump ion and disposable income Gini coe icien s, wo king-age consump ion and disposable income Gini
coe icien s wo sen.
VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 33
FIGURE 10. DB VS DC (90% SUPPLEMENTAL) AFTER-TAX INCOME-CONSUMPTION (LEFT)
AND SAVINGS (RIGHT): 9% CONTRIBUTION RATE
No e: The e ical dashed line indica es he age o e i emen .
FIGURE 11. DB VS DC (60% SUPPLEMENTAL) AFTER-TAX INCOME - CONSUMPTION (LEFT)
AND SAVINGS (RIGHT): 18% CONTRIBUTION RATE
No e: The e ical dashed line indica es he age o e i emen
case. Howe e , his ampli ying e ec also means ha e en a small go e nmen
subsidy can signi ican ly educe he gap. Geome ically speaking, he capi al supply
cu e o DC is s eepe han ha o DB, which means ha i is possible o educe he
gap in li ing s anda ds be ween he wo king-age and e i emen -age g oups by
aising in e es a es and lowe ing wage a es wi h less go e nmen ans e . I he
con ibu ion a e inc eases, al hough he a e - ax income o he wo king-age g oup
will dec ease, he e i emen -age g oup will need e en less inancial suppo h ough
he uni e sal pension due o he highe DC pension bene i .
The second eason is ha when he und a e o e u n is highe han he nominal
g ow h a e (in e p e ed as nominal wage g ow h plus popula ion g ow h a es) and
he popula ion s uc u e is aging, he pay-as-you-go (PAYGO) sys em becomes e y
ine icien in he long un.22 Fo example, i we assume ha he same amoun o
22The ac ha unded sys em is be e han he PAYGO sys em i he und a e o e u n is highe han he sum
o popula ion g ow h and wage g ow h a es is called he Aa on (1966) condi ion.
20 40 60 80
Age
0
1
2
3
4
5
6
7
DB
DC
20 40 60 80
Age
0
0.2
0.4
0.6
0.8
1
DB Cons
DB A e axinc
DC Cons
DC A e inc
20 40 60 80
Age
0
1
2
3
4
5
6
DB
DC
20 40 60 80
Age
0
0.2
0.4
0.6
0.8
1
DB Cons
DB A e axinc
DC Cons
DC A e inc
34 KDI Jou nal o Economic Policy NOVEMBER 2024
go e nmen ans e goes o he DC economy as o he DB economy, he ela i e
e iciency o each sys em o a gi en con ibu ion a e is heo e ically de e mined
by he di e ence be ween he und a e o e u n and he nominal g ow h a e. In his
analysis, we assume ha wage g ow h is
0
z
g=
and assume as well a nega i e
popula ion g ow h a e
( 0)g
µ
<
consis en wi h a la ge popula ion o se e al age
g oups han younge g oups, wi h und a es o e u n be ween 0% and 0.5%
(depending on he size o he uni e sal pension). Al hough he und a e o e u n is
a ec ed by he assump ion o 0% o eign in e es a es, his analysis assumes a
smalle gap be ween he und a e o e u n and wage g ow h han in gene al pension
p ojec ions, which is less a o able o he DC case.23 In such a si ua ion whe e he
und a e o e u n is g ea e han he nominal g ow h a e, he PAYGO sys em
FIGURE 12. DB VS DC (90% SUPPLEMENTAL) GROSS RETURN RATIO (LEFT)
AND INCOME REPLACEMENT RATE (RIGHT): 9% CONTRIBUTION RATE
FIGURE 13. DB VS DC (60% SUPPLEMENTAL) RETURN RATIO (LEFT)
AND INCOME REPLACEMENT RATE (RIGHT): 18% CONTRIBUTION RATE
23The Fi h Go e nmen Pension P ojec ion assumes a long- e m nominal wage g ow h a e o 3.7% and a und
a e o e u n o 4.5%.
12345
Quin ile
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
DB quin iles
DC quin iles
DB mean
DC mean
12345
Quin ile
0.08
0.1
0.12
0.14
0.16
0.18
DB quin iles
DC quin iles
DB mean
DC mean
12345
Quin ile
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
DB quin iles
DC quin iles
DB mean
DC mean
1 2 3 4 5
Quin ile
0.09
0.1
0.11
0.12
0.13
0.14
0.15
0.16
DB quin iles
DC quin iles
DB mean
DC mean
VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 35
becomes inc easingly ine icien as he demog aphic s uc u e ages. This ine iciency
a ises because a smalle numbe o wo king-age indi iduals mus suppo a la ge
numbe o e i emen -age indi iduals wi hou bene i ing om o high und a e o
e u n. A ma hema ical explana ion o his phenomenon is p o ided in he Appendix.
Rega ding inequali y wi hin he e i emen -age g oup, we ini ially obse e ha he
Gini coe icien o disposable income is al eady lowe in he DC case wi hou a
go e nmen subsidy compa ed o he DB case. This occu s simply because DC has
lowe bene i le els. Con e sely, he Gini coe icien o consump ion a e i emen
age is highe in DC, which is in e p e ed as a esul o he highe dependence o
consump ion on sa ings. The e o e, inc easing he le el o disposable income
h ough he uni e sal pension while lowe ing he Gini coe icien o disposable
income can lowe he Gini coe icien o consump ion. An inc ease in he uni e sal
pension lowe s he Gini coe icien o disposable income because i aises he li ing
s anda d o e e yone wi hin he e i emen age g oup by he same amoun . I is likely
ha he Gini coe icien o consump ion will also be educed, unless an in e es a e
inc ease due o lowe household sa ing leads o a e y s ong inc ease in he a iance
o pension bene i s.
Fu he mo e, we analyzed he g oss e u n a io and income eplacemen a e o
he combined uni e sal and DC Na ional Pension by li ecycle income quin iles,
whose p esen alues a e calcula ed wi h he discoun ac o
1/ 1
β
−
. The esul s
show ha he inequali y in he g oss e u n a io imp o es, as indica ed by he lowe
slope o he quin ile igu es o DC compa ed o DB, as shown in Figu e 12.
Simila ly, he inequali y in he income eplacemen a e imp o es, as he slope o he
quin ile igu es o DC is also lowe han ha o DB, as shown in Figu e 13.
36 KDI Jou nal o Economic Policy NOVEMBER 2024
TABLE 8. 2070 DC+UNIVERSAL PENSION, 9% CONTRIBUTION RATE
DB DC
DC
Uni .
60%
DC
Uni .
70%
DC
Uni .
80%
DC
Uni .
90%
DC
Uni .
100%
G oss P oduc
0.683
0.750
0.739
0.728
0.718
0.708
0.698
Capi al (demand)
2.598
3.376
3.239
3.107
2.984
2.868
2.765
Capi al (household)
2.598
3.648
2.781
2.650
2.528
2.412
2.310
Consump ion
0.369
0.411
0.395
0.392
0.389
0.386
0.382
Disposable Income
0.515
0.466
0.509
0.514
0.520
0.525
0.531
A e - ax Income
0.331
0.360
0.353
0.352
0.351
0.349
0.347
Labo
0.597
0.597
0.597
0.597
0.597
0.597
0.597
K/N
4.348
5.651
5.422
5.200
4.994
4.800
4.628
In e es Ra e
0.015
0.000
0.002
0.004
0.007
0.009
0.011
Wage Ra e
0.731
0.804
0.792
0.780
0.769
0.758
0.748
Income Tax
0.040
0.043
0.043
0.042
0.041
0.041
0.040
Consump ion Tax
0.183
0.106
0.156
0.162
0.169
0.176
0.184
Capi al Tax
0.015
0.000
0.003
0.005
0.008
0.010
0.012
Dea h Tax
0.009
0.016
0.009
0.009
0.008
0.007
0.007
Go e nmen Spending
0.117
0.117
0.117
0.117
0.117
0.117
0.117
Pension Spending
0.095
0.035
0.035
0.036
0.036
0.036
0.037
Pension Con ibu ion
0.018
0.019
0.019
0.019
0.018
0.018
0.018
Pension Fund
0.000
0.930
0.928
0.926
0.924
0.922
0.921
Basic Pension
0.017
0.014
0.012
0.012
0.013
0.013
0.013
Uni e sal Pension
0.000
0.000
0.046
0.054
0.062
0.070
0.077
Income Replacemen Ra e
0.142
0.048
0.113
0.126
0.139
0.153
0.166
Pension Re u n Ra io (be a)
0.988
0.332
0.339
0.347
0.355
0.363
0.371
G oss Re u n Ra io (be a)
0.108
0.063
0.098
0.105
0.111
0.117
0.123
Pension Re u n Ra io
2.197
1.000
0.978
0.955
0.933
0.911
0.892
G oss Re u n Ra io
0.222
0.177
0.258
0.263
0.266
0.268
0.270
Gini Consump ion
0.264
0.288
0.276
0.271
0.265
0.260
0.255
Gini Disposable
0.408
0.544
0.451
0.431
0.413
0.396
0.380
Gini Asse
0.577
0.546
0.593
0.601
0.609
0.617
0.624
Consump ion (wo k)
0.444
0.529
0.501
0.492
0.483
0.474
0.466
Disposable (wo k)
0.806
0.858
0.849
0.840
0.832
0.823
0.816
A e - ax (wo k)
0.585
0.721
0.652
0.637
0.622
0.607
0.592
Asse (wo k)
2.866
3.759
3.050
2.934
2.827
2.725
2.633
Income Tax (wo k)
0.081
0.089
0.088
0.086
0.085
0.084
0.083
Consump ion Tax (wo k)
0.221
0.137
0.197
0.204
0.210
0.217
0.223
Gini Consump ion (wo k)
0.227
0.223
0.223
0.222
0.221
0.220
0.220
Gini Disposable (wo k)
0.303
0.305
0.305
0.304
0.304
0.304
0.304
Gini Capi al (wo k)
0.595
0.593
0.612
0.614
0.617
0.619
0.622
Consump ion ( e )
0.298
0.299
0.296
0.298
0.300
0.302
0.304
Disposable ( e )
0.239
0.095
0.186
0.205
0.224
0.243
0.261
A e - ax ( e )
0.091
0.018
0.070
0.082
0.094
0.105
0.115
Asse ( e )
2.343
3.541
2.526
2.381
2.244
2.116
2.004
Income Tax ( e )
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Consump ion Tax ( e )
0.148
0.077
0.116
0.123
0.131
0.138
0.146
Gini Consump ion ( e )
0.252
0.266
0.248
0.242
0.236
0.231
0.226
Gini Disposable ( e )
0.152
0.044
0.045
0.047
0.048
0.050
0.051
Gini Asse ( e )
0.543
0.486
0.561
0.574
0.588
0.601
0.614
Popula ion
0.770
0.770
0.770
0.770
0.770
0.770
0.770
Popula ion (wo k)
0.375
0.375
0.375
0.375
0.375
0.375
0.375
Popula ion ( e )
0.395
0.395
0.395
0.395
0.395
0.395
0.395
No e: “Re u n Ra io” is he p esen alue a io o bene i s o con ibu ions using he domes ic in e es a e as he
discoun a e. “Pension” only conside s he Na ional Pension, “G oss” conside s go e nmen he iscal sec o as well,
and “(be a)” akes uses he discoun a e
1/ 1
β
−
o calcula e he p esen alue; No malized o pe capi a igu es.
He e, “(wo k)” deno es wo king age and “( e )” deno es e i emen age. Excep o he Gini coe icien s and
popula ion, a iables in (wo k) and ( e ) a e no malized using hei espec i e popula ions; “Uni . 30%,” o example,
means ha 30% o he DB sys em’s de ici amoun o go e nmen ans e is used in he uni e sal pension case.

VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 37
TABLE 9. 2070 DC+UNIVERSAL PENSION, 18% CONTRIBUTION RATE
DB DC
DC
Uni .
20%
DC
Uni .
30%
DC
Uni .
40%
DC
Uni .
50%
DC
Uni .
60%
G oss P oduc
0.658
0.750
0.742
0.735
0.728
0.721
0.714
Capi al (demand)
2.342
3.376
3.270
3.188
3.105
3.022
2.943
Capi al (household)
2.342
2.513
2.353
2.273
2.191
2.110
2.032
Consump ion
0.352
0.402
0.399
0.397
0.394
0.392
0.390
Disposable Income
0.488
0.488
0.496
0.499
0.503
0.506
0.510
A e - ax Income
0.326
0.368
0.367
0.366
0.365
0.364
0.363
Labo
0.597
0.597
0.597
0.597
0.597
0.597
0.597
K/N
3.921
5.651
5.473
5.336
5.197
5.059
4.927
In e es Ra e
0.021
0.000
0.002
0.003
0.004
0.006
0.007
Wage Ra e
0.705
0.804
0.795
0.787
0.780
0.772
0.765
Income Tax
0.038
0.043
0.043
0.042
0.042
0.042
0.041
Consump ion Tax
0.161
0.120
0.129
0.133
0.137
0.142
0.147
Capi al Tax
0.020
0.000
0.002
0.004
0.005
0.007
0.009
Dea h Tax
0.008
0.008
0.007
0.007
0.006
0.006
0.006
Go e nmen Spending
0.117
0.117
0.117
0.117
0.117
0.117
0.117
Pension Spending
0.092
0.070
0.071
0.071
0.071
0.072
0.072
Pension Con ibu ion
0.034
0.039
0.038
0.038
0.037
0.037
0.037
Pension Fund
0.000
1.860
1.857
1.854
1.851
1.849
1.846
Basic Pension
0.017
0.020
0.017
0.017
0.016
0.016
0.015
Uni e sal Pension
0.000
0.000
0.012
0.017
0.023
0.029
0.035
Income Replacemen Ra e
0.142
0.095
0.113
0.122
0.132
0.142
0.152
Pension Re u n Ra io (be a)
0.494
0.332
0.337
0.342
0.347
0.352
0.358
G oss Re u n Ra io (be a)
0.105
0.097
0.104
0.108
0.113
0.117
0.122
Pension Re u n Ra io
0.960
1.000
0.983
0.969
0.955
0.940
0.926
G oss Re u n Ra io
0.192
0.272
0.281
0.284
0.287
0.289
0.291
Gini Consump ion
0.248
0.280
0.276
0.273
0.270
0.266
0.262
Gini Disposable
0.390
0.456
0.437
0.426
0.414
0.403
0.391
Gini Asse
0.570
0.585
0.591
0.594
0.598
0.602
0.607
Consump ion (wo k)
0.415
0.514
0.506
0.500
0.494
0.487
0.481
Disposable (wo k)
0.750
0.818
0.812
0.806
0.801
0.795
0.789
A e - ax (wo k)
0.559
0.665
0.648
0.639
0.629
0.619
0.608
Asse (wo k)
2.542
2.755
2.617
2.546
2.472
2.400
2.328
Income Tax (wo k)
0.078
0.089
0.088
0.087
0.086
0.085
0.084
Consump ion Tax (wo k)
0.191
0.154
0.163
0.168
0.172
0.177
0.181
Gini Consump ion (wo k)
0.215
0.220
0.221
0.221
0.221
0.221
0.220
Gini Disposable (wo k)
0.293
0.295
0.295
0.294
0.294
0.294
0.294
Gini Capi al (wo k)
0.594
0.607
0.607
0.608
0.608
0.609
0.611
Consump ion ( e )
0.292
0.296
0.298
0.299
0.300
0.302
0.303
Disposable ( e )
0.239
0.175
0.196
0.208
0.220
0.233
0.245
A e - ax ( e )
0.106
0.086
0.100
0.107
0.115
0.123
0.131
Asse ( e )
2.153
2.283
2.103
2.014
1.925
1.835
1.751
Income Tax ( e )
0.000
0.000
0.000
0.000
0.000
0.000
0.000
Consump ion Tax ( e )
0.134
0.088
0.096
0.100
0.105
0.109
0.114
Gini Consump ion ( e )
0.240
0.253
0.250
0.247
0.244
0.241
0.237
Gini Disposable ( e )
0.153
0.104
0.115
0.118
0.120
0.119
0.117
Gini Asse ( e )
0.532
0.547
0.557
0.563
0.570
0.579
0.587
Popula ion
0.770
0.770
0.770
0.770
0.770
0.770
0.770
Popula ion (wo k)
0.375
0.375
0.375
0.375
0.375
0.375
0.375
Popula ion ( e )
0.395
0.395
0.395
0.395
0.395
0.395
0.395
No e: “Re u n Ra io” is he p esen alue a io o bene i s o con ibu ions using he domes ic in e es a e as he
discoun a e. “Pension” only conside s he Na ional Pension, “G oss” conside s go e nmen iscal sec o as well,
and “(be a)” akes uses discoun a e
1/ 1
β
−
o calcula e he p esen alue; No malized o pe capi a igu es. He e,
“(wo k)” deno es wo king age and “( e )” deno es e i emen age. Excep o he Gini coe icien s and popula ion,
a iables in (wo k) and ( e ) a e no malized using hei espec i e popula ions; “Uni . 30%,” o example, means
ha 30% o he DB sys em’s de ici amoun o go e nmen ans e is used in he uni e sal pension case.
38 KDI Jou nal o Economic Policy NOVEMBER 2024
VI. Conclusion
This s udy examines he challenges o con inuing he DB pension sys em in he
2070 demog aphic en i onmen and he e ec s o e o ming o a DC pension sys em
using a s a iona y gene al equilib ium model wi h o e lapping gene a ions. In so
doing, we con ine ou analysis o long- e m e ec s, abs ac ing om he ansi ion
pa h analysis o he DC e o m.
Fi s , i he DB sys em con inues wi h he aging demog aphics p ojec ed o 2070,
i will equi e 11.3% o GDP in go e nmen iscal suppo each yea a a 9%
con ibu ion a e and 8.8% o GDP i he con ibu ion a e ises o 18%. Unde he
same demog aphic condi ions in 2070, eplacing he DB sys em wi h a DC sys em
and assuming no ne o eign income, would imp o e he g oss p oduc and he
a e age li ing s anda d o he wo king-age g oup. Howe e , i would also de e io a e
he li ing s anda d o he elde ly, leading o a widening gap be ween age g oups
compa ed o he DB sys em. I he DC sys em is supplemen ed by a uni e sal
pension, he a e age li ing s anda ds o bo h wo king- and e i emen -age g oups,
as well as inequali y indica o s wi hin he e i emen -age g oup, can be imp o ed by
using only a ac ion o he inancial suppo equi ed o he DB pension sys em.
Addi ionally, he DC pension could po en ially imp o e u he i he e is posi i e
ne o eign income.
This s udy does no aim o iden i y he op imal pension sys em. Ins ead, we ocus
on demons a ing ha pa ame ic e o ms ha me ely main ain he cu en DB
pension sys em and double he con ibu ion a e a e iscally ine icien in he long
un. We p opose a policy combining a DC sys em wi h a uni e sal pension as a
compa ison. We do no discuss wha con ibu ion a es a e op imal o he DC
sys em, which could be an in e es ing opic o u u e esea ch.
The e may also be policies ha a e supe io o he combina ion o DC and a
uni e sal pension wi hin he s a iona y equilib ium amewo k. Fo example,
explo ing he e ec s o educing he cu en DB pension sys em and eplacing i wi h
a uni e sal pension could be an in e es ing esea ch opic. Adding au oma ic
s abilize s o he cu en DB pension sys em o inco po a ing a PAYGO la o in o
he DC pension sys em h ough a no ional de ined con ibu ion (NDC) sys em a e
also wo hy o u he s udy.
Howe e , eali y de ia es signi ican ly om s a iona y equilib ium, and a s a iona y
equilib ium analysis alone does no cap u e he dynamic esponses o popula ion
shocks. Fo example, along a ansi ion pa h o s a iona y equilib ium, unexpec ed
e ili y declines o longe i y shocks may de e io a e he e u n a io o a PAYGO
pension bene i , lea ing some gene a ions disp opo iona ely wo se o han o he s.
The op imal pension sys em canno be ully discussed wi hou conside ing his
dynamic pe spec i e.
E en om his dynamic poin o iew, ex eme DB sys ems like ha o Ko ea
ha e se ious p oblems: hey a e no inancially esilien o a ious shocks, and
PAYGO pension sys ems wi hou adequa e unding canno a oid lowe pension
e u n a ios. Con e sely, e en in a coun y wi h one o he lowes e ili y a es in
he wo ld, DC pension sys ems ensu e inancial s abili y and a s able pension e u n
VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 39
a io because ese es always exis . While he isk o old-age income in DC sys ems
mainly comes om he und a e o e u n, in eali y, unlike in ou model, he
p opo ion o o eign in es men is de e mined endogenously, which makes i
possible o hedge agains domes ic shocks. The e o e, he analysis wi hin his s udy’s
equilib ium amewo k may unde es ima e he bene i s o he DC pension sys em.
40 KDI Jou nal o Economic Policy NOVEMBER 2024
APPENDIX
Assuming a ixed mo ali y a e, he budge cons ain o he DC pension und
wi h g ow h adjus ed o popula ion and wage g ow h looks like
1
(1 )(1 ) (1 ) Re
z z
Ex g g S S
α
+
++ + =+ +
.
: yea
z
g
: wage g ow h a e
g
µ
: popula ion g ow h a e
: und a e o e u n
Ex
: DC yea ly expendi u e pe capi a (when he e u n a io is 1)
Re
: DC yea ly con ibu ion pe capi a
S
: DC und pe capi a
α
: e u n a io ac o (in DC, by de ini ion,
1
α
=
)
In his con ex , adjus ing he g ow h a e means ha he ollowing equa ions hold
in long- un equilib ium:
0
[(1 )(1 )]
z
Ex Ex g g
µ
= ×+ +
,
0
Re Re [(1 )(1 )]
z
gg
µ
= ×+ +
,
0
[(1 )(1 )]
z
SS g g
µ
=×+ +
.
The long- un equilib ium equa ion wi hou
is
Re [(1 ) (1 )(1 )] ( )
zz
Ex S g g S g g
µµ
α
− = +−+ + ≈ − −
.
The pension iscal de ici (le ) is equal o he “ eal” in e es a e ( igh ) exp essed
as he di e ence be ween he und a e o e u n (
) and he nominal g ow h a e
()
z
gg
µ
+
. Assuming ha he con ibu ion a e Is ixed and ha
Re
is ixed as
well, he equa ion leads o he ollowing conclusions.
P oposi ion 1. I
z
g g
µ
>+
, he DC bene i is highe han in a ully un unded
PAYGO sys em; i.e., in DC plan
0S>
,
Re 0Ex
α
−>
, and
1
α
=
, whe eas in an
un unded sys em,
ˆ0S=
and
Re
ˆ1
Ex
α
= <
.
P oposi ion 2. I
z
g g
µ
>+
, a la ge
z
g g
µ
−−
means a la ge he gap in
pension bene i s be ween he DC and he PAYGO sys em. We e e o his as he
“ eal in e es a e e ec .”
VOL. 46 NO. 4 Analyzing De ined Con ibu ion Pension Re o m in Ko ea Using a Gene al Equilib ium Model 47
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