## wpiea2024223-print-pdf

## Source details

**Canonical URL:** [wpiea2024223-print-pdf](https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024223-print-pdf.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/wp/2024/english/wpiea2024223-print-pdf.pdf.md)
- [Structured JSON version](/-/media/files/publications/wp/2024/english/wpiea2024223-print-pdf.pdf.json)

---

### Introduction — demographics, pension structure, and macro implications
- Demographics and macro implications
  - Fertility and life expectancy trends:
    - Fertility dropped from almost 6 in 1950 to well below 2 by 1990, falling even further below 1 by 2020.
    - Fertility declined from 6.0 in 1960 to less than 1 in 2023.
    - Life expectancy at age 65 increased from 15 years in 1990 to more than 20 in 2020.
    - Life expectancy at age 65 rose from 11.6 years in 1960 to 21.5 years in 2020; Japan’s was 22.6 years in 2020.
  - Old-age dependency ratio (OADR):
    - OADR = population aged 65+ divided by population aged 15-64.
    - Korea’s OADR is projected to rise sharply and is expected to surpass Japan by around 2050.
  - Demographic projections (Statistics Korea, medium scenario):
    - Projected population aged 25 and above will peak in 2032.
    - Population between 25 and 64 started to decline in 2022.
    - Population older than 65 will continue to rise and is projected to exceed the 25-64 group by 2058.
  - Macro implications:
    - Shrinking labor force, lower consumption and investment growth, and lower GDP growth.
    - Upward pressure on pension spending and fiscal sustainability risks.

- Structure of Korea’s pension system (tiers and coverage)
  - Multi-tier structure:
    - First tier: Basic old-age pension (means-tested, government funded).
    - Second tier: National Pension Scheme (NPS) and occupational schemes (civil servants, teachers, military).
    - Third tier: Corporate pensions, retirement pay allowance, other private pensions (limited fiscal impact).
  - Basic Pension specifics:
    - Introduced in 2007; targets poorest 70 percent among the elderly.
    - Eligibility and amount depend on household income, contribution period to NPS, and other status (single/couple, property).
    - Accessible from age 65.
    - Benefit categories:
      - Full Basic Pension if old-age pension income < KRW 484 770.
      - Partial Basic Pension with withdrawal against (part of) own NPS benefits.
      - Half the full Basic Pension where withdrawal formula would lead to a negative value.
    - Scale of Basic Pension spending:
      - Increased from 0.3 percent of GDP in 2009 to 0.9 percent of GDP in 2022.
    - 2022 take-up:
      - 6.2 million people received a (partial) Basic Pension, among which 2.9 million also received an NPS pension.
  - National Pension Scheme (NPS) and contributory pensions:
    - NPS introduced in 1988; coverage expanded substantially.
    - Contributors and beneficiaries:
      - NPS contributors grew from 4.4 million in 1988 to 22.5 million in 2022 (from 15 percent to 64 percent of working-age population).
      - Beneficiaries grew from 1.1 million in 2003 (27 percent of elderly) to 6.4 million in 2022 (71 percent of elderly).
    - Average benefits and spending:
      - Average pension benefit in 2022: 586 thousand KRW per month (15 percent of the average wage).
      - NPS spending increased from 0.6 percent of GDP in 2009 to 1.6 percent of GDP in 2022.
      - Combined pension spending (all schemes) increased from 1.8 percent to 4.0 percent of GDP between 2009 and 2022.
    - Fiscal outlook and timing:
      - NPS is expected to go into deficit in 2041 and assets would be depleted by 2055 (NABO (2023)), despite legislated reductions of replacement rates and increases in the retirement age.
      - GEPS (civil service pension) already running deficits; GEPS spending increased from 0.6 percent of GDP in 2009 to 1.0 percent of GDP in 2022.

- NPS design, recent changes, and replacement rates
  - Benefit formula and redistribution:
    - NPS benefits link strongly to career length; A-value uses the average earnings of NPS contributors over the past three years.
    - Design makes NPS relatively redistributive: low earners receive relatively higher benefits than proportional contributions would predict; high earners receive relatively lower benefits.
  - Interaction with Basic Pension:
    - Total pension benefit = NPS pension (A + B) + Basic Pension (S) or adjusted formulas depending on old-age income thresholds (S = KRW 484 770).
    - Three cases in the Box 1 formulation preserve piecewise expressions and thresholds.
  - Historical changes:
    - Contribution rates raised from 3 percent to 9 percent in 1998.
    - Accrual rates reduced from 1.75 percent per year to 1.0625 percent in 2023, and further decreasing to 1 percent in 2028.
    - Reference wage made more redistributive (greater weight on average wage).
    - Retirement age being raised:
      - From 60 years in 2012 to 65 in 2033 (legislated path).
      - Current retirement age referenced as 62 in some passages; planned changes bring future statutory retirement to 65 by 2033.
    - Minimum years of contribution lowered from 20 years in 1992 to 10 years in 1999.
    - No contributions or accrual after age 60 (i.e., increases in statutory retirement age do not add accrual beyond age 60 under current rules).
  - Cohort dynamics and replacement-rate trajectory:
    - As scheme matures, participants retire with longer contribution histories (short-run upward pressure on replacement rates).
    - Ongoing reductions in accrual rates and no accrual after age 60 imply long-run falling replacement rates.
    - Cohort retiring in 2032 projected to be the first to have contributed during their entire working lives (assuming labor market entry at age 20) and thus to have the highest replacement rates.
    - For an average wage worker with a 50 percent contribution density since age 20:
      - Replacement rate declines from 27 percent in 2020 to 22 percent in 2070.
    - OECD comparisons:
      - Korean future theoretical gross replacement rate for a full career average wage worker: 31 percent (OECD (2023) comparison: OECD average 51 percent).
      - Replacement rates by earnings: low earners (half the average wage) 48 percent; higher earners (twice the average wage) 19 percent.
      - Contribution rates are low internationally; OECD average contribution rate is 18 percent.
      - Current retirement age of 62 is below OECD average (64); Korea reaches 65 by 2033 while OECD average future retirement age 66.

### Model, calibration, and core quantitative findings
- Model specification:
  - OGRE, a dynamic overlapping generation with retirement model (Baksa and Munkacsi (2016)), structure close to Gertler (1999).
  - Extensions: additional fiscal instruments (social security contributions, labor taxes, consumption taxes) and unemployment modeled à la Blanchard and Gali (2010).
- Calibration and focus:
  - Calibrated to Korea using demographic projections and announced policy changes.
  - Focus on consolidated fiscal position (government net debt) rather than NPS reserves alone.
- Main quantitative projections:
  - Under current policies and announced future policy changes:
    - Pension spending would increase by 4 percentage points of GDP by 2070.
    - Contribution revenue would remain largely constant.
    - If additional spending is absorbed by the government, consolidated government’s net debt is expected to increase by nearly 180 percent of GDP by 2070.
  - Decomposition of debt increase drivers:
    - Only one fifth of the increase in debt is attributed to non-demographic factors (for example, expected increase in number of NPS beneficiaries as the NPS matures).
    - About four fifths of the debt increase is explained by the sharp change in demographics.
  - Model yields lower projected economic growth rates than some prior studies under similar demographic assumptions because capital accumulation endogenously decelerates with a declining working-age population.

### Questions, scope, and limitations
- Guiding questions:
  - Projected fiscal position under current policies given demographic changes?
  - Quantitative importance of different factors (demographics vs. announced pension reforms) in influencing the projected trajectory?
  - Which policies could improve long-run fiscal sustainability of pensions in Korea?
- Scope and limitations:
  - Emphasis on fiscal position of the consolidated government rather than solely on NPS financial health.
  - Results presented as an academic exercise under a no-policy-change assumption after the announced reforms.

### Theoretical Structure (model details)
- Demographics and population law of motion:
  - Two household types: young and retired.
  - Transition probabilities: young born with probability 푛푡, young turn retired with probability 휔푌푡, retired die with probability 휔푂푡.
  - Population equations:
    - 푁푌푡 = (1−휔푌푡−1)푁푌푡−1 + 푛푡푁푌푡−1
    - 푁푂푡 = (1−휔푂푡−1)푁푂푡−1 + 휔푌푡−1푁푌푡−1
    - 푁푡 = 푁푌푡 + 푁푂푡
  - Assumption: young can work; retirees earn pension income but not labor income.

- Household optimization:
  - Retiree Bellman equation and budget constraint (symbols preserved exactly as in source).
  - Young Bellman equation and budget constraint (symbols preserved exactly as in source).
  - Definitions include VAT rate 휏퐶푡, private saving 푏, pension income 푇푅, unemployment benefit 푤푈푡, labor variables 퐿 and 푈, taxes 푇, and others as in the model text.

- Production, capital, and frictions:
  - Physical capital producers and differentiated goods producers under monopolistic competition.
  - Capital accumulation:
    - 퐾푡 = (1−훿)퐾푡−1 + 퐼푡 [1 − 푆(퐼푡/퐼푡−1)]
    - 푆(퐼푡/퐼푡−1) = 휑퐾/2 [ 퐼푡(1+푔푡)/퐼푡−1 − 1 ]^2
  - Trend factor:
    - 1+푔푡 = (1+푔퐴푡) (푁푡/푁푡−1)
  - Hiring costs and labor market frictions follow Blanchard and Gali (2010) style setup with hiring cost 퐻퐶푡 and job separation rate 푓푡.
  - Wage bargaining by Nash bargaining; outside option for unemployed is 푤푈푡.

- Pension benefits (defined benefit scheme):
  - Pension benefit: 푇푅0,푡(푖) = 휉푡 퐼퐵(푖)
  - Pre-retirement average wage stream:
    - 퐼퐵(푖) = (1/X) (푤푡 퐿푡 + 푤푡−1 퐿푡−1 + ... + 푤푡−푋+1 퐿푡−푋+1)
  - 휉푡 is the exogenous replacement rate.

- Monetary and fiscal policy:
  - Central bank follows a Taylor rule (nominal interest rate 푖푡 responds to expected inflation).
  - Government revenue sources: VAT 휏퐶푡, personal income tax 휏푃퐼푇, social security contributions, lump-sum tax.
  - Expenditures: pension spending 푇푅푡, unemployment benefits 푤푈푡 푈푡, other expenditure 퐺푡.
  - Government budget constraint:
    - 퐵푡 + 푅푒푣푡 = (1−푟푡−1)퐵푡−1 + 퐸푥푝푡

### Calibration — targets and parameter values
- Calibration approach:
  - OGRE calibrated to match long-run properties of the Korean economy.
  - Steps: match aggregate ratios, then fiscal variables.
- Key parameter values and targets (numerics preserved exactly):
  - Production:
    - Capital weight 훼 = 0.307.
    - Annual growth rate of 퐴푡 = 1.0159 (equivalent to annual TFP growth at 1.1 percent).
  - Social security contributions (SSC):
    - Combined SSC rates (employer + employee) = 12.8 percent.
  - Replacement rate:
    - Calibrated long-run replacement rate 휉 = 0.22 to match public pension spending 2019-2020 (3.3 percent of GDP).
  - Fiscal parameters:
    - Effective VAT tax rate 휏퐶 = 8.1 percent.
    - Personal income tax rate 휏푃퐼푇 = 21 percent.
    - Unemployment benefit parameter 푤푈 = 0.11 (model-implied UI payment about 0.3 percent of GDP).
    - Lump-sum tax revenue 푇푡 = 3.9 percent of GDP.
    - Non-pension or UI spending 퐺푡 = 19.3 percent of GDP.
    - These yield a 23 percent revenue-to-GDP ratio and a zero debt-to-GDP ratio at the start of projection, consistent with 2018-19.
  - Other parameters:
    - Time discount 훽 = 0.9999 (corresponds to a real interest rate at 1.5 percent).
    - Job separation rate = 7.5 percent annually.
    - Worker Nash bargaining power = 0.9 (yields labor share of 54 percent).
    - Hiring cost parameter 휅 = 0.158 (long-run unemployment close to NAIRU of around 3.5 percent).

### Baseline Scenario — assumptions and projections
- Baseline assumptions (incorporated):
  1. Replacement (NPS and basic pension) rate will decrease from the current 27 percent to 22 percent.
  2. Statutory retirement age increases by 1 year every 5 years from 62 in 2020 to 65 by 2033; average age of labor market exit assumed to remain three years above statutory retirement age.
  3. As NPS matures, share of elder population covered by NPS increases by a factor of 0.54 from 2018 to 2060.
  4. Average duration of pension contribution per retiree increases from 17.1 years in 2018 to 21.9 years by 2040 (stays constant after 2040).
  5. Old-age dependency ratio rises from 25 to 110 percent between 2021 and 2075.
  6. Non-pension and non-UI public expenditure and non-labor or VAT tax revenue kept constant relative to GDP.
- Baseline projections and mechanisms:
  - Public pension spending-to-GDP projected to increase by 4 percent of GDP by 2070 as number of pensioners increases.
  - Revenue remains stable as share of GDP because labor share remains constant while working-age population declines.
  - Net public debt-to-GDP projected to increase by around 180 percent of GDP by 2070 if pension deficits absorbed by the government.
  - Macro outcomes:
    - Severe drop in GDP, large shift from young to old consumption.
    - Declining working-age population leads to lower unemployment rates via tighter labor markets and reduced unemployment benefit spending.
    - Real GDP growth rates become negative after the 2050s.
    - Aggregate capital increases during 2020-60 due to positive exogenous TFP growth, but capital accumulation pace slows relative to pre-2020, causing faster public debt-to-GDP increases during 2050-60 than 2020-50.
    - GDP per capita growth turns negative, driven by steep fall in young’s share of aggregate consumption and pay-go transfers reducing investment.
  - Caveats:
    - Stronger productivity growth, foreign investment, and immigration could counteract these effects; model does not endogenously incorporate such policies unless explicitly modeled.

### Reform options — policy levers, quantitative impacts, and mixes
- Policy levers considered:
  - Increase contribution rate (SSC).
  - Increase retirement age.
  - Lower replacement rate.
  - Mix of policies combining the above.
- Increasing contribution rates:
  - Raising contribution rate by 13.8 percentage points would increase revenue by 7 percentage points of GDP by 2070 and offset the entire upward pressure on public debt.
  - Higher pension contribution rates produce no visible loss in growth or employment in the Korea calibration for the stated reasons (relatively less generous UI, very low projected unemployment).
- Increasing retirement age:
  - Under 2007 reform, retirement age scheduled to reach 65 by 2034 (from 62).
  - To stabilize pension spending by raising retirement age alone would require an additional increase of 6 years (to 71).
  - Even raising retirement age to 71 reduces pension spending in the short run, but spending-to-GDP would still increase by 2 percentage points by 2070.
  - Raising retirement age increases labor force relative to baseline, yielding higher GDP growth and slightly higher unemployment rates.
- Lowering replacement rate:
  - Stabilizing debt solely by cutting benefits would require lowering replacement rates by 10 percentage points (almost half of the long-run replacement rate).
  - Given high old-age poverty rates and already low replacement rates internationally, such cuts are undesirable.
- Mix of policies:
  - Large single-policy adjustments needed to stabilize debt if used in isolation; combinations of smaller adjustments across levers yield better results.
  - Example mix (to largely stabilize public debt):
    - Increase retirement age by 2 years;
    - Increase contribution rate by 4.6 percent;
    - Lower replacement rate by 3.3 percentage points.
  - Under this mix:
    - GDP per capita growth slightly higher than baseline due to increased labor supply;
    - Unemployment and young consumption largely unaffected.
    - Slightly lower replacement rate could be offset by a slightly higher basic pension financed from a VAT increase.
  - Alternative mixes:
    - To maintain NPS benefit rules, either raise retirement age further (4 years instead of 2) or increase contribution rate further (9.2 percentage points extra instead of 4.6).
  - Additional option (not modeled): mandate pension contributions above age 60 to improve revenue and benefit adequacy — in long run this has limited impact on deficits but could mitigate almost half of projected drop in theoretical replacement rates under baseline.

### Conclusion — synthesis and policy implications
- Key conclusions:
  - Aging will put substantial pressure on public pension spending and public debt accumulation under current policies (including announced changes); economic growth will slow, worsening fiscal pressure.
  - Baseline estimate: by 2070 public debt-to-GDP projected to increase by around 180 percent despite legislated reforms; accompanied by severe drop in GDP per capita.
  - Two caveats highlighted:
    1. This figure results from a no-policy assumption (only demographic change, no public/pension policy changes for >50 years).
    2. Result illustrative and subject to significant uncertainty inherent in highly stylized macro models.
- Policy implications:
  - Single-policy levers required to significantly limit debt growth are large and likely politically or socially infeasible:
    - Retirement age increase of 6 years;
    - Halving replacement rate;
    - Increasing SSC by 13.8 percentage points.
  - A combination of smaller adjustments across levers is preferable; exact mix should reflect social preferences and account for distributional consequences and political economy constraints.

*Source: wpiea2024223-print-pdf — Introduction; 3.1 Theoretical Structure; 3.2 Calibration; 4.1 Baseline Scenario; 4.2 Reform options; 5 Conclusion.*

### Introduction ...........................................................................................................

### Introduction

### Demographics and macroeconomic implications
- Korea’s population is expected to age rapidly due to lower fertility rates and longer life expectancy.
- Fertility and life expectancy trends:
  - Fertility dropped from almost 6 in 1950 to well below 2 by 1990, falling even further below 1 by 2020.
  - Fertility declined from 6.0 in 1960 to less than 1 in 2023.
  - Life expectancy at age 65 increased from 15 years in 1990 to more than 20 in 2020.
  - Life expectancy at age 65 rose from 11.6 years in 1960 to 21.5 years in 2020; Japan’s was 22.6 years in 2020.
- Old-age dependency ratio (OADR) definition and projection:
  - OADR = population aged 65+ divided by population aged 15-64.
  - Korea’s OADR is projected to rise sharply and is expected to surpass Japan by around 2050.
- Demographic projection highlights (Statistics Korea, medium scenario):
  - Projected population aged 25 and above will peak in 2032.
  - Population between 25 and 64 started to decline in 2022.
  - Population older than 65 will continue to rise and is projected to exceed the 25-64 group by 2058.
- Macro implications of aging:
  - Shrinking labor force, lower consumption and investment growth, and lower GDP growth.
  - Upward pressure on pension spending and fiscal sustainability risks.

### Structure of Korea’s pension system (tiers and coverage)
- Multi-tier structure:
  - First tier: Basic old-age pension (means-tested, government funded).
  - Second tier: National Pension Scheme (NPS) and occupational schemes (civil servants, teachers, military).
  - Third tier: Corporate pensions, retirement pay allowance, other private pensions (limited fiscal impact).
- Basic Pension specifics:
  - Introduced in 2007; targets poorest 70 percent among the elderly.
  - Eligibility and amount depend on household income, contribution period to NPS, and other status (single/couple, property).
  - Accessible from age 65.
  - Benefit categories:
    - Full Basic Pension if old-age pension income < KRW 484 770.
    - Partial Basic Pension with withdrawal against (part of) own NPS benefits.
    - Half the full Basic Pension where withdrawal formula would lead to a negative value.
  - Scale of Basic Pension spending:
    - Increased from 0.3 percent of GDP in 2009 to 0.9 percent of GDP in 2022.
  - 2022 take-up:
    - 6.2 million people received a (partial) Basic Pension, among which 2.9 million also received an NPS pension.

- National Pension Scheme (NPS) and contributory pensions:
  - NPS introduced in 1988; initially limited coverage, now majority coverage.
  - Contributors and beneficiaries:
    - NPS contributors grew from 4.4 million in 1988 to 22.5 million in 2022 (from 15 percent to 64 percent of working-age population).
    - Beneficiaries grew from 1.1 million in 2003 (27 percent of elderly) to 6.4 million in 2022 (71 percent of elderly).
  - Average benefits and spending:
    - Average pension benefit in 2022: 586 thousand KRW per month (15 percent of the average wage).
    - NPS spending increased from 0.6 percent of GDP in 2009 to 1.6 percent of GDP in 2022.
    - Combined pension spending (all schemes) increased from 1.8 percent to 4.0 percent of GDP between 2009 and 2022.
  - Fiscal outlook and timing:
    - NPS is expected to go into deficit in 2041 and assets would be depleted by 2055 (NABO (2023)), despite legislated reductions of replacement rates and increases in the retirement age.
    - GEPS (civil service pension) already running deficits; GEPS spending increased from 0.6 percent of GDP in 2009 to 1.0 percent of GDP in 2022.

### NPS design, recent changes, and replacement rates
- Benefit formula behavior and redistributive features:
  - NPS benefits link strongly to career length; A-value (part of reference wage) uses the average earnings of NPS contributors over the past three years.
  - This design makes NPS relatively redistributive: low earners receive relatively higher benefits than proportional contributions would predict; high earners receive relatively lower benefits.
- Interaction between NPS and Basic Pension (formalized piecewise in source):
  - Total pension benefit = NPS pension (A + B) + Basic Pension (S) or adjusted formulas depending on old-age income thresholds (S = KRW 484 770).
  - Three cases in the Box 1 formulation (text preserves the piecewise expressions and thresholds).
- Historical changes in contribution and accrual:
  - Contribution rates were raised from 3 percent to 9 percent in 1998.
  - Accrual rates reduced from 1.75 percent per year of contributions to 1.0625 percent in 2023, and further decreasing to 1 percent in 2028.
  - Reference wage used in benefit calculations made more redistributive (greater weight on average wage).
  - Retirement age being raised:
    - From 60 years in 2012 to 65 in 2033 (legislated path).
    - Current retirement age referenced as 62 in some passages; planned changes bring future statutory retirement to 65 by 2033.
  - Minimum years of contribution lowered from 20 years in 1992 to 10 years in 1999.
  - No contributions or accrual after age 60 (i.e., increases in statutory retirement age do not add accrual beyond age 60 under current rules).
- Cohort dynamics and replacement-rate trajectory:
  - As scheme matures, participants retire with longer contribution histories (short-run upward pressure on replacement rates).
  - Ongoing reductions in accrual rates and the lack of accrual after age 60 imply long-run falling replacement rates.
  - Cohort retiring in 2032 projected to be the first to have contributed during their entire working lives (assuming labor market entry at age 20) and thus to have the highest replacement rates.
  - For an average wage worker with a 50 percent contribution density since age 20:
    - Replacement rate declines from 27 percent in 2020 to 22 percent in 2070.
  - OECD comparisons:
    - Korean future theoretical gross replacement rate for a full career average wage worker: 31 percent (OECD (2023) comparison: OECD average 51 percent).
    - Replacement rates by earnings: low earners (half the average wage) 48 percent; higher earners (twice the average wage) 19 percent.
    - Contribution rates are low internationally (Korea among lowest except Mexico and Lithuania); OECD average contribution rate is 18 percent.
    - Current retirement age of 62 is below OECD average (64); Korea reaches 65 by 2033 while OECD average future retirement age 66.

### Model, calibration, and core quantitative findings
- Model applied:
  - OGRE, a dynamic overlapping generation with retirement model (Baksa and Munkacsi (2016)), structure close to Gertler (1999).
  - Extensions relative to Gertler (1999): additional fiscal instruments (social security contributions, labor taxes, consumption taxes) and unemployment modeled à la Blanchard and Gali (2010).
- Calibration and scenarios:
  - Calibrated to Korea using demographic projections and announced policy changes.
  - Explores baseline and reform options, focusing on consolidated fiscal position (government net debt) rather than NPS financials alone because government may ultimately cover pension liabilities after reserve depletion.
- Main quantitative projections (preserve numbers and attribution exactly as presented):
  - Under current policies and announced future policy changes:
    - Pension spending would increase by 4 percentage points of GDP by 2070.
    - Contribution revenue would remain largely constant.
    - If additional spending is absorbed by the government, consolidated government’s net debt is expected to increase by nearly 180 percent of GDP by 2070.
  - Decomposition of debt increase drivers:
    - Only one fifth of the increase in debt is attributed to non-demographic factors (for example, expected increase in number of NPS beneficiaries as the NPS matures).
    - About four fifths of the debt increase is explained by the sharp change in demographics.
  - Model produces lower projected economic growth rates than some prior studies (e.g., MHW (2018), Kim (2002)) under similar demographic assumptions because capital accumulation endogenously decelerates with a declining working-age population.

### Questions addressed and paper scope
- Three guiding questions:
  - Projected fiscal position under current policies given demographic changes?
  - Quantitative importance of different factors (demographics vs. announced pension reforms) in influencing the projected trajectory?
  - Which policies could improve long-run fiscal sustainability of pensions in Korea?
- Focus and limitations:
  - Emphasis on fiscal position of the consolidated government rather than solely on NPS financial health.
  - Results are framed as an academic exercise: fiscal implications if no further reforms occur and government eventually covers deficits after reserve exhaustion.

*Content derived from the "Introduction" section of the source PDF.*

### 3.1  Theoretical Structure

### 3.1  Theoretical Structure

### Model structure and demographics
- Dynamic general equilibrium model with demography, overlapping generations and unemployment (Baksa and Munkacsi (2016), builds on Gertler (1999)).
- Two household types: the young and the retired.
- In each period:
  - Young households are born with probability 푛푡.
  - Young turn retired with probability 휔푌푡.
  - Retired households die with probability 휔푂푡.
- Law of motion for population sizes {푁푡, 푁푌푡, 푁푂푡} governed by time-varying demographic parameters {푛푡, 휔푌푡, 휔푂푡}:
  - 푁푌푡 = (1−휔푌푡−1)푁푌푡−1 + 푛푡푁푌푡−1
  - 푁푂푡 = (1−휔푂푡−1)푁푂푡−1 + 휔푌푡−1푁푌푡−1
  - 푁푡 = 푁푌푡 + 푁푂푡
- All probabilities are non-age dependent.
- Assumption: all young households are working age and can enter the labor market; retirees earn pension income but not labor income.

### Household optimization: Retired
- Retiree i who retired a periods ago maximizes Bellman equation:
  - 푉푂푡(푏푂푡−1,푎−1(푖)) = max { u(푐푂푡,푎(푖)) + 훽(1−휔푂푡)푉푂푡+1(푏푂푡,푎(푖)) }
- Budget constraint:
  - (1+휏퐶푡)푐푂푡,푎(푖) + (1−휔푂푡)푏푂푡,푎(푖) = (1−푟푡−1)푏푂푡−1,푎−1(푖) + 푇푅푎,푡(푖) + 푃푟표푓푖푡푂푎,푡(푖) − 푇푂푎,푡(푖)
- Definitions:
  - 푉 value function, u utility, 푐 consumption, 휏퐶푡 VAT rate, 푏 private saving, 푇푅 pension income, 푃푟표푓푖푡 dividend payments, 푇 lump-sum tax.

### Household optimization: Young
- Young household i born a periods ago maximizes:
  - 푉푌푡(푏푌푡−1,푎−1(푖)) = max { u(푐푌푡,푎(푖)) + 훽{(1−휔푌푡)푉푌푡+1(푏푌푡,푎(푖)) + 휔푌푡푉푂푡+1(푏푌푂푡,푎(푖))} }
- Budget constraint:
  - (1+휏퐶푡)푐푌푡,푎(푖) + (1−휔푌푡)푏푌푡,푎(푖) = (1+푟푡−1)푏푌푡−1,푎−1(푖) + (1−휏푃퐼푇 − 휏퐿푊)푤푡퐿푡,푎(푖) + 푤푈푡 푈푡,푎(푖) + 푃푟표푓푖푡푌푡,푎(푖) − 푇푌푡,푎(푖)
- Definitions:
  - 퐿푡,푎(푖) employed members, 푈푡,푎(푖) unemployed members, 푤푡 wage rate, 푤푈푡 unemployment benefit.

### Production, capital and frictions
- Producers:
  - Infinitely many physical capital producers (identical).
  - Many goods producers each producing a differentiated good under monopolistic competition.
- Physical capital producer problem (chooses investment 퐼푡 to accumulate capital):
  - 푉(퐼푡−1,퐾푡−1) = max { 푟퐾푡 퐾푡−1 − 퐼푡 + 1/(1+푟푡) 푉(퐼푡,퐾푡) }
- Capital accumulation:
  - 퐾푡 = (1−훿)퐾푡−1 + 퐼푡 [1 − 푆(퐼푡/퐼푡−1)]
  - 푆(퐼푡/퐼푡−1) = 휑퐾/2 [ 퐼푡(1+푔푡)/퐼푡−1 − 1 ]^2
- 푟퐾푡 real capital rental rate defined as 푟퐾푡 = 푅퐾푡/푝푡 (nominal rental rate over CPI).
- Trend factor:
  - 1+푔푡 = (1+푔퐴푡) (푁푡/푁푡−1)
- Goods producers:
  - Rent labor and capital, face Rotemberg price stickiness and hiring costs (Blanchard and Gali (2010)).
  - Maximize discounted dividends with constraints:
    - 푑푡(푗) = 푝푡(푗)푦푡(푗) − 푅퐾푡 푘푡−1(푗) − (1+휏푆푆퐶퐹푡)푤푡 푙푡(푗) − 퐻퐶푡 ℎ푡(푗) − 퐴푑푗푡(푗)
    - 푦푡(푗) = 푘푡−1(푗)^훼 (퐴푡 푙푡(푗))^(1−훼)
    - 퐴푑푗푡 = 푝푡(푗)푌푡 R(푝푡(푗)/푝푡−1(푗))
- Hiring costs and labor market:
  - Total hiring cost = unit hiring cost 퐻퐶푡 times new hires ℎ푡(푗).
  - 퐻퐶푡 = 휅 휃훼 / 휃푡, where 휃푡 = 퐻푡 / (푈푡−1 + 푓푡 퐿푡−1); ℎ푡(푗) dynamics: 푙푡(푗) = (1−푓푡)푙푡−1(푗) + ℎ푡(푗).
  - 푓푡 exogenous job separation rate (identical across goods producers).
  - Unit hiring cost curvature governed by parameter 훼휃.
- Wage bargaining:
  - Nash bargaining determines wages; outside option for unemployed is unemployment benefit 푤푈푡.

### Pension benefits (defined benefit scheme)
- Pension benefit for retiree i:
  - 푇푅0,푡(푖) = 휉푡 퐼퐵(푖)
- 퐼퐵(푖) is the pre-retirement average wage income stream over the last X years:
  - 퐼퐵(푖) = (1/X) (푤푡 퐿푡 + 푤푡−1 퐿푡−1 + ... + 푤푡−푋+1 퐿푡−푋+1)
- 휉푡 is the exogenous replacement rate.

### Monetary policy
- Central bank follows a standard Taylor rule: nominal interest rate 푖푡 responds to expected inflation.
- Note: alternative specifications (e.g., adding output gap) may change short-term dynamics numerically little for long-term pension spending and fiscal sustainability projections.

### Fiscal policy and government budget
- Revenue sources: VAT tax, labor income tax, social security contributions (employees and employers), lump-sum tax.
- Expenditures: pension spending, unemployment benefit spending, other expenditure.
- Revenue and expenditure aggregates:
  - 푅푒푣푡 = 휏퐶푡 + (휏푃퐼푇푡 + 휏푆푆퐶푊푡 + 휏푆푆퐶퐹푡) 푤푡 퐿푡 + 푇푡
  - 퐸푥푝푡 = 푇푅푡 + 푤푈푡 푈푡 + 퐺푡
- Government budget constraint:
  - 퐵푡 + 푅푒푣푡 = (1−푟푡−1)퐵푡−1 + 퐸푥푝푡
- Lump-sum tax revenue 푇푡 and other expenditure 퐺푡 modeled as exogenous residuals so model-implied totals match data moments.

---

### 3.2  Calibration

### Targets and approach
- OGRE calibrated to match long-run properties of the Korean economy (Table 1).
- Calibration steps:
  1. Calibrate macroeconomic parameters to match aggregate ratios (consumption-to-GDP, investment-to-GDP).
  2. Target fiscal variables (government consumption and investment shares; VAT, income tax, employee and employer SSC shares of GDP).

### Key parameter values and targets (preserve exact numerics)
- Production:
  - Cobb-Douglas: 퐹(퐾푡, 퐴푡 퐿푡) = 퐾푡^훼 (퐴푡 퐿푡)^(1−훼)
  - Capital weight 훼 = 0.307 (set to match private consumption-to-investment ratio in steady state to 2018 national account).
  - Annual growth rate of 퐴푡 = 1.0159 (equivalent to annual TFP growth at 1.1 percent).
- Social security contributions (SSC):
  - Combined SSC rates (employer + employee) = 12.8 percent (so model SSC income-to-GDP at projection start matches 2020).
- Replacement rate:
  - Calibrated long-run replacement rate 휉 = 0.22 to match public pension spending 2019-2020 (3.3 percent of GDP).
- Fiscal parameters:
  - Effective VAT tax rate 휏퐶 = 8.1 percent.
  - Personal income tax rate 휏푃퐼푇 = 21 percent.
  - Unemployment benefit parameter 푤푈 = 0.11 (model-implied UI payment about 0.3 percent of GDP).
  - Lump-sum tax revenue 푇푡 = 3.9 percent of GDP.
  - Non-pension or UI spending 퐺푡 = 19.3 percent of GDP.
  - These assumptions yield a 23 percent revenue-to-GDP ratio and a zero debt-to-GDP ratio at the start of the projection period, consistent with actual revenue and debt during 2018-19.
- Other parameters:
  - Time discount 훽 = 0.9999 (corresponds to a real interest rate at 1.5 percent).
  - Job separation rate = 7.5 percent annually (from Schauer (2018), Table 2).
  - Worker Nash bargaining power = 0.9 (yields labor share of 54 percent).
  - Hiring cost parameter 휅 = 0.158 (long-run unemployment close to NAIRU of around 3.5 percent).

---

### 4.1  Baseline Scenario

### Assumptions incorporated
- Projected aging (following UN projections), current policies, and all announced policy changes including:
  1. Replacement (NPS and basic pension) rate will decrease from the current 27 percent to 22 percent.
  2. Statutory retirement age increases by 1 year every 5 years from 62 in 2020 to 65 by 2033; average age of labor market exit assumed to remain three years above statutory retirement age.
  3. As NPS matures, share of elder population covered by NPS increases by a factor of 0.54 from 2018 to 2060.
  4. Average duration of pension contribution per retiree increases from 17.1 years in 2018 to 21.9 years by 2040 (stays constant after 2040).
  5. Old-age dependency ratio rises from 25 to 110 percent between 2021 and 2075.
  6. Non-pension and non-UI public expenditure and non-labor or VAT tax revenue kept constant relative to GDP.

### Baseline projections and mechanisms
- Public pension spending-to-GDP ratio projected to increase by 4 percent of GDP by 2070 as number of pensioners increases.
- Revenue remains stable as share of GDP because labor share remains constant while working-age population declines.
- Net public debt-to-GDP ratio projected to increase by around 180 percent of GDP by 2070 if pension deficits absorbed by the government.
- Associated macro outcomes:
  - Severe drop in GDP, large shift from young to old consumption.
  - Declining working-age population leads to lower unemployment rates via tighter labor markets and reduced unemployment benefit spending.
  - Real GDP growth rates become negative after the 2050s.
  - Aggregate capital continues to increase during 2020-60 due to positive exogenous TFP growth, but capital accumulation pace slows relative to pre-2020, causing faster public debt-to-GDP increases during 2050-60 than 2020-50.
  - GDP per capita growth turns negative, driven by steep fall in young’s share of aggregate consumption and pay-go transfers reducing investment.
- Caveats: stronger productivity growth, foreign investment, and immigration could counteract these effects; model does not endogenously incorporate such policies unless explicitly modeled.

---

### 4.2  Reform options

### Policy levers considered
- Increase contribution rate (SSC).
- Increase retirement age.
- Lower replacement rate.
- Mix of policies combining the above.

### Increasing contribution rates
- Raising contribution rate by 13.8 percentage points would increase revenue by 7 percentage points of GDP by 2070 and offset the entire upward pressure on public debt.
- Higher pension contribution rates produce no visible loss in growth or employment in the Korea calibration, due to:
  1. Relatively less generous UI benefit in Korea (coverage and take-up), making unemployed workers more willing to accept jobs at lower take-home pay.
  2. Projected unemployment rate is very low due to declining labor force; same increase in contribution rates would have larger effects in countries with growing labor force.

### Increasing retirement age
- Under 2007 reform, retirement age scheduled to reach 65 by 2034 (from 62).
- To stabilize pension spending by raising retirement age alone would require an additional increase of 6 years (to 71).
- Even raising retirement age to 71 reduces pension spending in the short run, but spending-to-GDP would still increase by 2 percentage points by 2070.
- Raising retirement age increases labor force relative to baseline, yielding higher GDP growth and slightly higher unemployment rates.

### Lowering replacement rate
- Stabilizing debt solely by cutting benefits would require lowering replacement rates by 10 percentage points (almost half of the long-run replacement rate).
- Given high old-age poverty rates and already low replacement rates internationally, such cuts are undesirable.

### Mix of policies
- Large single-policy adjustments needed to stabilize debt if used in isolation; combinations of smaller adjustments across levers yield better results.
- Example mix (to largely stabilize public debt):
  - Increase retirement age by 2 years;
  - Increase contribution rate by 4.6 percent;
  - Lower replacement rate by 3.3 percentage points.
- Under this mix:
  - GDP per capita growth slightly higher than baseline due to increased labor supply;
  - Unemployment and young consumption largely unaffected.
  - Slightly lower replacement rate could be offset by a slightly higher basic pension financed from a VAT increase.
- Alternative mixes:
  - To maintain NPS benefit rules, either raise retirement age further (4 years instead of 2) or increase contribution rate further (9.2 percentage points extra instead of 4.6).
- Additional option (not modeled): mandate pension contributions above age 60 to improve revenue and benefit adequacy — in long run this has limited impact on deficits but could mitigate almost half of projected drop in theoretical replacement rates under baseline.

---

### 5  Conclusion

- Overlapping generations general equilibrium model used to evaluate Korea’s fiscal trajectory under demographic change.
- Under current policies (including announced changes), aging will put substantial pressure on public pension spending and public debt accumulation; economic growth will slow, worsening fiscal pressure.
- Baseline estimate: by 2070 public debt-to-GDP projected to increase by around 180 percent despite legislated reforms; accompanied by severe drop in GDP per capita.
  - Two caveats highlighted by authors:
    1. This figure results from a no-policy assumption (only demographic change, no public/pension policy changes for >50 years).
    2. Result illustrative and subject to significant uncertainty inherent in highly stylized macro models.
- Single-policy levers required to significantly limit debt growth are large and likely politically or socially infeasible:
  - Retirement age increase of 6 years;
  - Halving replacement rate;
  - Increasing SSC by 13.8 percentage points.
- A combination of smaller adjustments across levers is preferable; exact mix should reflect social preferences and account for distributional consequences and political economy constraints.

*Source: wpiea2024223-print-pdf - 3.1  Theoretical Structure*

---


_Source: https://www.imf.org/-/media/files/publications/wp/2024/english/wpiea2024223-print-pdf.pdf_