Dynamic Impact of Population Aging on Regional Economies in Korea Using a Recursive-Dynamic Interregional CGE-Population Model

Abstract

This chapter estimates dynamic effects of population aging on regional economies using a recursive-dynamic interregional CGE-Population model of Korea. The model accounts for the economic behavior of producers and consumers on the real side economies of two regions: the Seoul Metropolitan Area and the rest of Korea. Population demographics in each region are disaggregated into eight age cohorts that have different labor productivities and participation rates on the supply side and consumption behaviors on the demand side. The aging trend could have negative effects on the economy, reducing the GDP by 2.37 % on a 15-year average. The economic recovery from this decline could require an annual increase in educational investments on age cohort 20–29 by at least 12 % for 15 years. It implies a net increase rate of 4.60 % because the educational investments have increased annually by 7.40 % since 2007.

The earlier version of this chapter has been presented at the third Asian Seminar in Regional Science, Hualien, Taiwan August 7–8, 2013.

Appendices

Appendix 1: Major Equations of ICGEP Model

1.1 Equations

• (1) Production and Faction inputs

Output	${X}_i^r(t)={VA}_i^r(t)+\sum_r\sum_j{\mathrm{io}}_{ji}^{rs}{X}_j^r(t)$
Value added	$\ln \left({VA}_i^r(t)\right)={\beta}_{0i}^{\kern0.5em r}+{\beta}_{1i}^{\kern0.5em r} \ln \left({K}_i^r(t)\right)+\left(1-{\beta}_{1i}^{\kern0.5em r}\right)\sum_{h=2}^7{\beta}_{2hi}^{\kern1.25em r} \ln \left({H}_{hi}^{\kern0.5em r}(t)\right)$
	s.t. $\sum_{h=2}^7{\beta}_{2hi}^{\kern1.25em r}=1$
Human capital	${H}_{hi}^{\kern0.75em r}(t)={\mathrm{hO}}_{hi}^{\kern0.75em r}{L}_{hi}^{\kern0.75em r}(t)\ {HQ}_h^r(t)$
Labor demand	${WA}^r(t)\ {\mathrm{wdist}}_{hi}^{\kern0.5em r}\ {H}_{hi}^{\kern0.5em r}(t)={VA}_i^r(t)\ {PVA}_i^r(t)\ {\left(1-{\beta}_1\right)}_i^r\ {\beta}_{2hi}^{\kern1.25em r}$
Average wage rate	${WA}^r(t)=\sum_{h=2}^7\sum_{i=1}^3{W}_h^r(t){H}_{hi}^{\kern0.5em r}(t)/\sum_{h=2}^7\sum_{i=1}^3{H}_{hi}^{\kern0.5em r}(t)$
Capital demand	${R}^r(t)\ {\mathrm{kdist}}_i^r\ {K}_i^r(t)={VA}_i^r(t)\ {PVA}_i^r(t)\ {\beta}_{1i}^{\kern0.5em r}$
Quality of labor input	$\ln \left({W}_h^r(t)\right)={\eta}_{0h}^{\kern0.75em r}+{\eta}_{1h}^{\kern0.75em r} \ln \left({\mathrm{EXPE}}_h^r(t)\right)+{\eta}_{2h}^{\kern0.75em r} \ln \left({\mathrm{TEDU}}_h^r(t)\right)+{\eta}_{3h}^{\kern0.75em r}{\mathrm{GEN}D}^r(t)+{\eta}_{4h}^{\kern0.75em r}{\mathrm{MANU}}^r(t)$

• (2) Trade

Output	${X}_i^r(t)={AT}_i^r{\left[\ {\gamma}_i^r\ {\mathrm{EX}}_i^{r{\rho}_i^r}(t)+\left(1-{\gamma}_i^r\right)\ {XD}_i^{r{\rho}_i^r}(t)\right]}^{\frac{1}{\rho_i^r}}$
Production price	${PX}_i^r(t){X}_i^r(t)={PE}_i^r(t){\mathrm{EX}}_i^r(t)+{PD}_i^r(t){XD}_i^r(t)$
Export	$\frac{{\mathrm{EX}}_i^r(t)}{XD_i^r(t)}={\left[\frac{PE_i^r(t)}{PD_i^r(t)}\ \frac{\left(1-{\gamma}_i^r\right)}{\gamma_i^r}\right]}^{\frac{1}{\rho_i^r-1}}$
Total demand	${Q}_i^r(t)={A}_i^r{\left[{\delta}_i^r\ {IM}_i^{r-{a}_i^r}(t)+\left(1-{\delta}_i^r\right)\ {XD}_i^{ra_i^r}(t)\right]}^{-\frac{1}{a_i^r}}$
Composite goods price	${PC}_i^r(t){Q}_i^r(t)={\mathrm{PM}}_i^r(t){IM}_i^r(t)+{PD}_i^r(t){XD}_i^r(t)$
Import	$\frac{IM_i^r(t)}{XD_i^r(t)}={\left[\frac{PD_i^r(t)}{{\mathrm{PM}}_i^r(t)}\ \frac{\delta_i^r}{\left(1-{\delta}_i^r\right)}\right]}^{\frac{1}{a_i^r+1}}$

• (3) Household

Household income	${Y}^r(t)=\sum_i\sum_h{WA}^r(t){\mathrm{wdist}}_{hi}^{\kern0.5em r}{H}_{hi}^{\kern0.5em r}(t)+\sum_i{R}^r(t){\mathrm{kdist}}_i^r{K}_i^r(t)+{\mathrm{YSUB}}^r(t)$
Household consumption	$\ln \left({CD}_i^{rs}(t)\right)={\alpha}_{0i}^{\kern0.5em rs}+\sum_{h=0}^7{\alpha}_{1h}^{\kern0.75em rs}{D}_h^s(t)+{\alpha}_2^{\kern0.5em rs}{\mathrm{GEND}}^s(t)+\sum_{h=2}^7{\alpha}_{3h}^{\kern0.75em rs} \ln \left({W}_h^r(t)\right)$
Household saving	$\ln \left({\mathrm{HSAV}}^r(t)\right)={\beta}_0^{\kern0.5em r}+{\beta}_1^{\kern0.5em r}{\mathrm{GEND}}^r(t)+{\beta}_2^{\kern0.5em r}{\mathrm{NUMH}}^r(t)+{\beta}_3^{\kern0.5em r} \ln \left({\mathrm{DEBT}}^r(t)\right)+\sum_{h=0}^7{\beta}_{4h}^{\kern0.5em r} \ln \left({W}_h^r(t)\right)$

• (4) Government

Government revenues	$\mathrm{GR}(t)=\sum_r\sum_i{\mathrm{IM}}_i^r(t)\mathrm{ER}(t)\left(1+{\mathrm{tm}}_i^r\right)+\sum_i{\mathrm{itax}}_i^r{\mathrm{PVA}}_i^r(t){\mathrm{VA}}_i^r(t)+\sum_r{\mathrm{htax}}^r{Y}^r(t)$
Government use of funds	$GE(t)=\mathrm{GSAVE}(t)+SUB(t)+\sum_r\sum_i{\sum}_s{GC}_i^{sr}(t)$

• (5) Market equilibrium

Balance of payment	$\sum_r\sum_i{pwm}_i^r{IM}_i^r(t)+\mathrm{FSAV}(t)=\sum_r\sum_i{pwe}_i^r{\mathrm{EX}}_i^r(t)$
Labor supply	${LS}_h^r(t)={P}_h^r(t){lpr}_h^r$
Capital market	$\sum_r{\mathrm{HSAV}}^r(t)+\sum_r\sum_i{\mathrm{depr}}_i^r{\mathrm{PK}}_i^r(t){K}_i^r(t)+\mathrm{FSAV}(t)\mathrm{ER}(t)+\mathrm{GSAVE}(t)=\sum_r\sum_i{\mathrm{IND}}_i^r(t)$
Sectoral investment	${IND}_i^r(t)={\mathrm{INDE}}_i^r(t)+\left({IND}_i^r(t)-{\mathrm{INDE}}_i^r(t)\right)$
Commodity market	${Q}_i^r(t)=\sum_j\sum_s{\mathrm{io}}_{ij}^{rs}{X}_j^s(t)+\sum_s{CD}_i^{rs}(t)+{INV}_i^r(t)+\sum_s{GC}_i^{rs}(t)$

• (6) Capital accumulation

Capital accumulation

${K}_i^r(t)=\left(1-{\mathrm{depr}}_i^r\right){K}_i^r\left(t-1\right)+{IND}_i^r(t)$

1.2 Variables

${CD}_i^{rs}(t)$	Private consumption expenditure of sector i of region r by region s
${D}_h^r(t)$	Average number of family members by age cohort (h) by region r
d rs(t)	Physical distance between region r and region s
DEBT r(t)	Household financial asset of region r
ER(t)	Nominal foreign exchange rate (Korean won per dollar)
${\mathrm{EX}}_i^r(t)$	Foreign export of sector i of region r
${\mathrm{EXPE}}_h^r(t)$	Worker’s total years of working experience by age cohort (h) of region r
FSAV(t)	Foreign saving
${GC}_i^{sr}(t)$	Consumption expenditure of sector i of region s by region r
GE(t)	Government expenditures
GENDr(t)	Gender of household (GEND = 1 for male) of region r
GR(t)	Government revenues
GSAVE(t)	Government savings
${H}_{hi}^r(t)$	Human capital stock by age cohort (h) of sector i of region r
${HQ}_h^r(t)$	Quality of labor input by age cohort (h) of region r
HSAVr(t)	Private savings in region r
${IM}_i^r(t)$	Foreign import of sector i of region r
${IND}_i^r(t)$	Investment by destination of sector i of region r
${INV}_i^r(t)$	Investment by origin of sector i of region r
${\mathrm{INDE}}_i^r(t)$	Education investment by destination of sector i of region r
${K}_i^r(t)$	Physical capital stock of sector i of region r
L r(t)	The number of workers in region r
${L}_{hi}^r(t)$	Quantity of labor input of sector i of region r by age cohort (h)
${LS}_h^r(t)$	Labor supply of region r by age cohort (h)
MANUr(t)	Industrial dummy (MANU = 1 for manufacturing sector) of region r
${MIG}_h^{rs}(t)$	The number of gross migrants from region r to region s by age cohort (h)
NUMHr(t)	The number of family members of region r
P r(t)	Population size of region r
${P}_h^r(t)$	Population size of region r by age cohort (h)
${PC}_i^r(t)$	Price of composite goods of sector i of region r
${PD}_i^r(t)$	Domestic goods price of sector i of region r
${PE}_i^r(t)$	Domestic price of foreign exports of sector i of region r
${PK}_i^r(t)$	Price of capital of sector i of region r
${\mathrm{PM}}_i^r(t)$	Domestic price of foreign imports of sector i of region r
${PVA}_i^r(t)$	Value-added price of sector i of region r
${PX}_i^r(t)$	Production price of sector i of region r
${Q}_i^r(t)$	Composite goods of demand of sector i of region r
R r(t)	Average rate capital return of region r
SUB(t)	Total subsidies to both producers and households
${\mathrm{TEDU}}_h^r(t)$	Worker’s total schooling years of region r by age cohort (h)
TOTSAV(t)	Total saving
V r(t)	Gross regional product of region r
${VA}_i^r(t)$	Value added of sector i of region r
${W}_h^r(t)$	Each worker’s wage of region r by age cohort (h)
WAr(t)	Average wage rate of region r
${X}_i^r(t)$	Gross output of sector i of region r
${XD}_i^r(t)$	Consumption of domestically produced goods of sector i of region r
Y r(t)	Total income of household of region r
YSUBr(t)	Subsidies to household of region r

1.3 Parameters

${\mathrm{depr}}_i^r$	Depreciation rate of sector i of region r
${\mathrm{hO}}_{hi}^r$	Shift parameter of human capital
htaxr	Direct tax rate
${\mathrm{io}}_{ij}^{rs}$	Leontief technical input-output coefficient
${\mathrm{itax}}_i^r$	Indirect tax rate
${\mathrm{kdist}}_i^r$	Capital return adjustment parameter of sector i of region r
${lpr}_h^r$	Labor force participation rate of region r by age cohort (h)
${pwe}_i^r$	Export price in world market
${pwm}_i^r$	Import price in world market
${svr}_h^r$	Survival rate of region r by age cohort (h)
${tm}_i^r$	Tariff rate
${\mathrm{wdist}}_{hi}^r$	Wage adjustment parameter of sector i of region r by age cohort(h)
h	Age cohort (h = 0 for 0–9 years old; h = 1 for 10–19 years old; h = 2 for 20–29 years old; h = 3 for 30–39 years old; h = 4 for 40–49 years old; h = 5 for 50–59 years old; h = 6 for 60–69 years old; h = 7 for over 70 years old)
i(j)	Industrial sector (agriculture, manufacturing, construction, and services)
r(s)	Region (SMA and ROK )

Appendix 2: Model Specification and Parameter Estimates

1.1 Consumption and Saving Functions

The functional types for consumption and saving of regional households are derived from Mankiw and Weil (1989), who attempted to identify how housing demand was affected by changes in the size of different age cohorts. The private consumptions for three industrial goods by region are modeled with gender of household, and the number of family members and income by age cohort serve as an additive function of the demand of its members. The private savings amount by region is also estimated with these consumption determinants and the household asset. The primary data set for estimating these equations is the Korean Labor and Income Panel Study (KLIPS) of the Korea Labor Institute. KLIPS is a longitudinal survey of the labor market and the income activities of households and individuals, including schooling, unemployment experiences, job training and education , working conditions and welfare, income and consumption. The basic structure is similar to NLS, NLSy and PSID of the USA, SLID of Canada, and BHPS of the UK. It has been used for the microeconomic analysis of labor market activities and transitions to assess labor market policies in Korea since the late 1990s.

1.1.1 Private Consumption by Age Cohort

$$ \ln \left({CD}_i^{rs}(t)\right)={\alpha}_{0i}^{rs}+\sum_{h=0}^7{\alpha}_{1h}^{rs}{D}_h^s(t)+{\alpha}_2^{rs}{\mathrm{GEND}}^s(t)+\sum_{h=2}^7{\alpha}_{3h}^{rs} \ln \left({W}_h^r(t)\right) $$

${CD}_i^{rs}(t)$	Private consumption expenditure of sector i of region r by region s
${D}_h^r(t)$	Average number of family members by age cohort (h) by region r
GENDr(t)	Gender of household (GEND = 1 for male) of region r
${W}_h^r(t)$	Worker’s wage of region r by age cohort (h)
h	Age cohort (h = 0 for 0–9 years old; h = 1 for 10–19 years old; h = 2 for 20–29 years old; h = 3 for 30–39 years old; h = 4 for 40–49 years old; h = 5 for 50–59 years old; h = 6 for 60–69 years old; h = 7 for over 70 years old)

• (1) SMA region

	Commodity produced in SMA			Commodity produced in ROK (regional imports)
	Primary sector	Manufacturing sector	Service sector	Primary sector	Manufacturing sector	Service sector
Constant	4.167***	4.726***	5.476***	4.166***	4.728***	5.480***
D 0	0.132***	0.039	0.011	0.132***	0.040	0.013
D 1	0.155***	0.108***	0.174***	0.154***	0.108***	0.174***
D 2	0.185***	0.233***	0.294***	0.186***	0.232***	0.291***
D 3	0.234***	0.222***	0.208***	0.234***	0.219***	0.200***
D 4	0.208***	0.107**	0.174***	0.211***	0.110**	0.181***
D 5	0.218***	0.248***	0.226***	0.222***	0.247***	0.224***
D 6	–	–	–	0.245***	0.181***	0.098*
D 6 + D 7	0.215***	0.179***	0.089**	–	–	–
D 7	–	–	–	0.194***	0.180***	0.086*
GEND	0.114***	0.194***	0.256***	0.111***	0.192***	0.252***
ln(W 2)	0.022***	0.090***	0.094***	0.022***	0.090***	0.094***
ln(W 3)	0.030***	0.092***	0.110***	0.031***	0.093***	0.111***
ln(W 4)	0.038***	0.102***	0.110***	0.038***	0.102***	0.109***
ln(W 5)	0.034***	0.091***	0.109***	0.034***	0.091***	0.110***
ln(W 6)	–	–	–	0.031***	0.071***	0.084***
ln(W 6+W 7)	0.035***	0.069***	0.079***	–	–	–
ln(W 7)	v	–	–	0.038***	0.059***	0.057***
R 2	0.37	0.23	0.32	0.37	0.23	0.32

1. *p < 0.10; **p < 0.05; ***p < 0.01

• (2) ROK region

	Commodity produced in SMA (regional imports)			Commodity produced in ROK
	Primary sector	Manufacturing sector	Service sector	Primary sector	Manufacturing sector	Service sector
Constant	4.139***	4.612***	5.197***	4.139***	4.612***	5.196***
D 0	0.053**	0.008	−0.005	0.055**	0.014	0.002
D 1	0.128***	0.040	0.087	0.129***	0.042	0.089
D 2	0.150***	0.229***	0.322***	0.149***	0.226***	0.319***
D 3	0.215***	0.275***	0.301***	0.211***	0.265***	0.288***
D 4	0.166***	0.084	0.169*	0.175***	0.109	0.198**
D 5	0.187***	0.054	0.062	0.188***	0.057	0.062
D 6	–	–	–	0.189***	0.309***	0.304***
D 6 + D 7	0.126***	0.139*	0.102	–	–	–
D 7	–	–	–	0.088***	0.038	−0.014
GEND	0.246***	0.332***	0.358***	0.234***	0.299***	0.320***
ln(W 2)	0.040***	0.092***	0.105***	0.041***	0.095***	0.109***
ln(W 3)	0.038***	0.109***	0.136***	0.039***	0.114***	0.142***
ln(W 4)	0.048***	0.136***	0.155***	0.048***	0.135***	0.154***
ln(W 5)	0.047***	0.186***	0.210***	0.048***	0.190***	0.215***
ln(W 6)	–	–	–	0.028***	0.077***	0.093***
ln(W 6+W 7)	0.033***	0.090***	0.106***	–	–	–
ln(W 7)	–	–	–	0.022**	0.060**	0.066**
R 2	0.33	0.15	0.22	0.37	0.16	0.22

1. *p < 0.10; **p < 0.05; ***p < 0.01

1.1.2 Private Savings by Region

$$ \ln \left({\mathrm{HSAV}}^r(t)\right)={\beta}_0^r+{\beta}_1^r{\mathrm{GEND}}^r(t)+{\beta}_2^r{\mathrm{NUMH}}^r(t)+{\beta}_3^r \ln \left({\mathrm{DEBT}}^r(t)\right)+\sum_{h=0}^7{\beta}_{4h}^r \ln \left({W}_h^r(t)\right) $$

HSAVr(t)	Private savings in region r
GENDr(t)	Gender of household (GEND = 1 for male) of region r
NUMHr(t)	The number of family members of region r
DEBTr(t)	Household financial asset of region r
${W}_h^r(t)$	Worker’s wage of region r by age cohort (h)
h	Age cohort (h = 0 for 0–9 years old; h = 1 for 10–19 years old; h = 2 for 20–29 years old; h = 3 for 30–39 years old; h = 4 for 40–49 years old; h = 5 for 50–59 years old; h = 6 for 60–69 years old; h = 7 for over 70 years old)

	SMA	ROK
Constant	0.560***	0.084
GEND	−0.074	0.356***
NUMH	0.143***	0.139***
DEBT	−0.014	−0.055***
ln(W 2)	0.577***	0.599***
ln(W 3)	0.544***	0.594***
ln(W 4)	0.450***	0.522***
ln(W 5)	0.510***	0.515***
ln(W 6)	0.434***	0.404***
ln(W 6+W 7)	0.194***	0.273***
R 2	0.29	0.39

1. *p < 0.10; **p < 0.05; ***p < 0.01

The value added is determined by two types of physical capital stock (K) and human capital by age cohort (H _h ). The latter is defined as the number of workers (L _h ) multiplied by the quality of human capital possessed by workers (HQ _h ).

$$ \ln \left({VA}_i^r(t)\right)={\beta}_{0i}^r+{\beta}_{1i}^r \ln \left({K}_i^r(t)\right)+\left(1-{\beta}_{1i}^r\right)\sum_{h=2}^7{\beta}_{2hi}^r \ln \left({H}_{hi}^r(t)\right) $$

$$ \mathrm{s}.\mathrm{t}\ \sum_{h=2}^7{\beta}_{2 hi}^r=1 $$

$$ {H}_{hi}^r(t)={\mathrm{hO}}_{hi}^r\ {L}_{hi}^r(t)\ {\mathrm{HQ}}_h^r(t) $$

${VA}_i^r(t)$	Value added of sector i of region r
${K}_i^r(t)$	Physical capital stock of sector i of region r
${H}_{hi}^r(t)$	Human capital stock by age cohort (h) of sector i of region r
${HQ}_h^r(t)$	Quality of labor input by age cohort (h) of region r
${L}_{hi}^r(t)$	Quantity of labor input of sector i of region r by age cohort (h)
${hO}_{hi}^r$	Shift parameter of human capital

1.1.3 Wage Function

$$ \ln \left({W}_h^r(t)\right)={\eta}_{0h}^r+{\eta}_{1h}^r \ln \left({\mathrm{EXPE}}_h^r(t)\right)+{\eta}_{2h}^r \ln \left({\mathrm{TEDU}}_h^r(t)\right)+{\eta}_{3h}^r{\mathrm{GEND}}^r(t)+{\eta}_{4h}^r{\mathrm{MANU}}^r(t) $$

${W}_h^r(t)$	Worker’s wage of region r by age cohort (h)
${\mathrm{EXPE}}_h^r(t)$	Worker’s total years of working experience by age cohort (h) of region r
${\mathrm{TEDU}}_h^r(t)$	Worker’s total schooling years of region r by age cohort (h)
GENDr(t)	Gender of household (GEND = 1 for male) of region r
MANUr(t)	Industrial dummy (MANU = 1 for manufacturing sector) of region r

• (1) SMA

Age cohort	20–29	30–39	40–49	50–59	60–69
Constant	1.986***	2.256***	3.019***	3.016***	3.580***
ln(EXPE)	1.062***	1.007***	0.639***	0.630***	0.194***
ln(TEDU)	0.174***	0.158***	0.184***	0.187***	0.145***
GEND	0.204***	0.323***	0.519***	0.434***	0.487***
MANU	0.010	0.022	0.011	0.157**	0.179
R 2	0.17	0.35	0.49	0.51	0.36

1. *p < 0.10; **p < 0.05; ***p < 0.01

• (2) ROK

Age cohort	20–29	30–39	40–49	50–59	60–69
Constant	2.515***	3.025***	2.734***	2.717***	3.727***
ln(EXPE)	0.819***	0.641***	0.733***	0.781***	0.265***
ln(TEDU)	0.188***	0.221***	0.223***	0.203***	0.132***
GEND	0.199***	0.334***	0.462***	0.333***	0.193
MANU	0.170***	0.091***	0.042	0.067	0.158
R 2	0.22	0.42	0.54	0.55	0.23

1. *p < 0.10; **p < 0.05; ***p < 0.01