## INTRODUCTION

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---

### Executive summary
- Over the coming decades, declining fertility and increasing longevity will profoundly change the population age distribution in many countries.
- The discussion note investigates how impending demographic shifts and the design of pension systems could influence future national saving (the sum of public and private saving).
- Under current policies, public pension outlays in advanced and emerging market economies will increase by an average 1 and 2½ percentage points of GDP, respectively, by 2050. Without adjustment in taxes and other spending, this increase will lead to a commensurate decline in public saving.
- Private saving is projected to decline more precipitously in countries with generous public pension systems, as people will rely less on their own savings when they retire.
- All else being equal, private saving is projected to increase in countries that include a defined contribution (DC) scheme as part of their pension systems.
- Projections are illustrative and do not assess the optimal saving rate or desirable pension levels.

### Key findings and motivations
- Demographic drivers:
  - By 2050, on average, the old-age dependency ratio (population 65+ relative to population 15–64) will double.
  - Today, Japan is the only country with an old-age dependency ratio over 40; by 2050 more than 55 countries will exceed that ratio.
  - Life expectancy at age 65 is projected to increase by around a year per decade.
- Why saving matters:
  - National saving finances domestic investment and provides shock-absorbing capacity with implications for growth and economic stability.
  - In aging societies, national saving bolsters retirement security and helps workers bear pension financing costs while maintaining living standards.
  - Most household saving is done by the highest income earners; inadequate saving has acute implications for poorer households and potential old-age poverty.
- Interaction between public and private saving:
  - Age profiles: young borrow, prime working-age save, old dissave—aging raises the share of elderly, likely depressing private saving.
  - Pension design (coverage, benefits, funding type) influences individual saving: generous public pensions can crowd out private saving; funded DC elements can encourage private saving.
  - Lack of pension development/coverage and weak financial markets can lead to under-saving or excessive precautionary saving.

### Analytical approach and scope
- Methodology:
  - Builds a simple overlapping generations (OLG) model to illustrate channels through which longevity, fertility, and old-age dependency affect public and private saving.
  - Empirical estimates of demographic and pension-design impacts on private saving are combined with public pension spending projections to simulate potential national saving paths under a no-policy-change scenario.
- Scope and caveats:
  - Does not assess optimal saving rates or desirable generosity of pensions.
  - Abstracts from behavioral changes and explicit demographic effects on growth and productivity.
  - Does not analyze transition consequences from PAYG to fully funded systems (transition effects can be ambiguous).
  - Partial equilibrium framework provides simple inferences on public and private saving evolution across countries under current policies.

*Source: sdn1901 - INTRODUCTION*

### Architecture of pension systems and aging. Differences in pension system arrangements

### Pension system types, funding, and coverage
- Types:
  - DB: benefits depend on years of contributions and earning history, often complemented by a means-tested basic pension.
  - DC: benefits depend on contribution history and returns on contributions; often coexist with DB schemes.
  - Notional DC: defined contribution design but financed on a PAYG basis.
- Funding distinctions:
  - PAYG: current workers’ contributions or general revenues fund current retirees.
  - Fully funded: benefits depend on accumulated assets.
- Coverage and generosity:
  - Generosity encompasses benefit ratio (benefits per person) and coverage (percentage of elderly receiving a pension).
  - Example magnitudes: Greece and Cyprus provide pension benefits about 65 percent of the average economy-wide wages; less than 30 percent in Latvia and Ireland.
  - Advanced economies provide some type of public pension benefits to nearly all elderly citizens; in most emerging and developing economies, only a third to two-thirds of the elderly are covered.
  - Pensions account for more than 60 percent of elderly income in advanced economies.

### Fiscal pressures from aging and pension generosity
- Aging increases the ratio of elderly beneficiaries to contributors under PAYG, directly pressuring public saving.
- Even funded systems face risks from increased longevity or lower-than-expected returns, potentially requiring government support.
- Estimated fiscal adjustments to offset aging costs (European countries, 2010–2050): tax revenues would have to be between 14 percent and 28 percent higher than today (or commensurate expenditure cuts).
- Specific country estimates: Japan 26 percent; United States 11 percent.
- Recent reforms (raising retirement age, tightening eligibility, reducing pension sizes) improved DB/PAYG sustainability but often shift burdens to future generations and may erode real pension benefits, risking old-age poverty.
- Transition reforms in the 1990s that redirected contributions to funded systems put pressure on public saving by worsening public finances; low coverage and low contribution rates continue to affect many systems.
- Pension savings are concentrated in high-income households; rapid aging could exacerbate income inequality.

### Theoretical model framework (small open economy OLG model)
- Agents live three periods: children, workers, retirees (if they survive).
- Two exogenous demographic parameters: life expectancy (longevity) and fertility rate; old-age dependency ratio = χ/g in model notation.
- Features private pensions (DC-like) and a public PAYG DB scheme covering all retirees.
- Government levies income tax on labor at exogenous constant rate τ to finance public pensions; government can borrow or save; pension deficits reduce public saving.
- Small open economy: global interest rate R* taken as given; abstracts from precautionary saving motives except longevity risk.
- Key steady-state public saving-to-GDP expression preserved in model:
  - S_G / Y = (1−α) [ τ − χ φ / g ]
  - Implication: aging (higher old-age dependency via higher χ and/or lower g) and higher pension generosity φ decrease public saving.

### Model predictions — main channels and effects
- Demographic change and private saving:
  - Lower fertility increases private saving (less childcare spending), partly offset by higher labor supply.
  - Higher life expectancy at retirement raises private (DC pension) saving of working-age population.
  - Compositional effect: higher old-age dependency raises share of dissavers, depressing private saving.
  - Net private saving impact depends on which effects dominate.
- Public pension generosity and private saving:
  - Public pension benefits and private saving are substitutes: higher public benefits mean individuals save less privately.
  - Countries with PAYG systems tend to have private saving rates lower in direct proportion to public pension generosity.
  - Pension generosity can amplify the positive effect on private saving from increased life expectancy for working-age cohorts.
- Public saving:
  - Lower fertility or higher life expectancy increases old-age dependency, lowering public saving because pension expenditure rises relative to tax revenue.
  - Negative impact on public saving is more pronounced with generous public pensions.
- Global interest rate effects:
  - Lower R* can discourage saving (substitution) but can also induce higher saving if future income falls (income effect); net impact is ambiguous.
  - Lower R* reduces bequests relative to the economy and thus can reduce private saving as a share of GDP.

*Source: sdn1901 - 10. Architecture of pension systems and aging. Differences in pension system arrangements*

### Empirical estimation of private saving

### Empirical specification and variables
- Reduced-form cross-country fixed-effect panel regressions using annual data covering 75–100 advanced and emerging market economies over the past four decades (baseline).
- Pension system characteristics:
  - Pension generosity = product of benefit ratio and coverage ratio; operationalized as average pension spending per elderly person divided by GDP per working age population; time-varying dummy = 1 if generosity > 75th percentile, 0 otherwise.
  - Existence of a DC pension scheme (defined contribution).
- Interaction terms capture how pension attributes influence demographic impacts on private saving.
- Controls: credit constraints, labor market conditions, macro variables.
- Baseline: fixed-effect panel regressions with robust standard errors clustered at country level; include constant term and time dummies.

### Key empirical findings (selected coefficients from Table 1)
- Public Saving: -0.52***, -0.53***, -0.53***, -0.59***, -0.59*** (columns 1–5)
- Old-age Dependency Ratio: -0.69***, -0.74***, -0.68***, -0.52***, -0.56*** (columns 1–5)
- Old-age Dependency Ratio * Pension Generosity: -0.10***, -0.08**, -0.33** (where included)
- Old-age Dependency Ratio * DC Scheme: 0.40*, 0.66**, 1.16** (where included)
- Life Expectancy at Age 40: 1.03***, 0.99***, 0.87**, 0.98**, 1.27*** (columns 1–5)
- Life Expectancy at Age 40 * Pension Generosity: -0.05*, 0.15** (where included)
- Life Expectancy at Age 40 * DC Scheme: 0.40, -0.61 (where included)
- Employment Rate: 0.08, 0.07 (where included)
- Real GDP Growth: 0.18***, 0.19*** (where included)
- GDP per Capita PPP: -0.09, -0.12 (where included)
- Real Interest Rate: -0.07***, -0.07*** (where included)
- Inflation: 0.02*, 0.02* (where included)
- Credit to GDP: -0.04***, -0.04*** (where included)
- Terms of Trade: 0.03*, 0.03* (where included)
- Sample and fit:
  - Observations: 3,009; 3,009; 3,009; 1,837; 1,837 (columns 1–5)
  - Number of Countries: 80; 80; 80; 74; 74 (columns 1–5)
  - Adjusted R-squared: 0.19; 0.20; 0.20; 0.30; 0.31 (columns 1–5)

### Interpretation and magnitudes
- Old-age dependency ratio is negatively and significantly associated with private saving.
- Life expectancy at age 40 is positively associated with private saving: each year of additional expected life is associated with about a percentage point increase in private saving rate.
- Partial offset from public saving: a one dollar reduction in public saving is associated with a private saving increase of 60 cents (some degree of Ricardian equivalence).
- Pension design mediates aging effects:
  - In countries without a DC scheme and with nongenerous PAYG/DB pensions, a 1 percentage point increase in the old-age dependency ratio decreases private saving by 0.5 percentage points (column 4).
  - With generous PAYG/DB pensions but no DC scheme, private saving falls by about 0.6 percentage points.
  - In countries with a DC pension system, the effect can reverse: DC schemes induce employed people to save more for self-funded retirement.
  - Accounting for pension design, a 1 percentage point increase in the old-age dependency ratio results in a 0.3 percentage point decrease in the private saving rate (overall finding).
- Interaction between longevity and pension characteristics is less robust across specifications.

### Caveats on empirical interpretation
- Cross-country regressions face limitations: heterogeneous policy effects, multidimensional pension characteristics, measurement limitations, potential reverse causality, and nonlinearities.
- Structural relationships and transition dynamics may not be fully captured; micro and cohort analyses could yield more nuance but face data constraints.

*Source: sdn1901 - Empirical estimation and Annex material*

### Saving projections through 2050

### Projection methodology
- Steps:
  1. Estimate effects of demographic developments and enacted pension reforms on public pension outlays using official projections (OECD, ILO, European Commission, national actuarial reports, IMF staff estimates); initial pension expenditure equals latest OECD estimates for OECD countries and latest ILO estimates for others.
     - Projected increase in public pension spending assumed to translate fully into lower public saving (interpreted as a lower bound because other aging-related spending, notably health, is not increased in this step).
  2. Use empirical model coefficients (column 4 of Table 1) to project private saving as a function of demographic changes, pension characteristics (generosity, DC), and projected public saving.
- Demographics evolve per United Nations medium-fertility variant; other determinants held constant.

### Projected public saving and pension spending outcomes
- Worldwide, public pension spending pressures could depress public saving by just over 2 percentage points of GDP by 2050, with substantial cross-country differences.
- Advanced economies:
  - Public saving could fall by about 1 percent of GDP between now and 2050, reflecting recently enacted reforms.
  - Germany: reforms projected to contain pension spending increases to slightly over 2 percentage points of GDP by 2050.
  - United States: projected increase in pension spending of 1.6 percentage points of GDP by 2050.
  - Under current policies, projected spending implies significant future reductions in the average pension.
- Emerging market and developing economies:
  - Projected decline in public saving is larger and pronounced where aging is rapid and pensions unreformed.
  - Example projections: Brazil and China—pension expenditure projected to increase by 7 and 6 percentage points of GDP, respectively, by 2050.
- Health spending caveat:
  - The projected public pension saving pressure (just over 2 percentage points of GDP) is a lower bound because health-related spending is projected to surge by 3.8 and 2.3 percentage points of GDP in advanced and emerging and developing economies, respectively, over this period.

### Global and group-level saving projections
- Global aggregate:
  - Assuming unchanged country weights, global saving could potentially decline by about 3 percentage points of GDP between now and 2050.
- By group:
  - Emerging markets and developing countries collectively: higher private saving by relatively younger populations offsets projected decline in public saving, resulting in broadly stable national saving.
  - Aging advanced economies: private saving rates are expected to contract sharply, leading to a steep decline in aggregate saving rates.
- Stage in demographic transition:
  - Late-stage transition countries: national saving projected to decline by over 4 percentage points of GDP, on average, between now and 2050.
  - Advanced-stage transition countries: national saving projected to remain broadly stable.
  - Early-stage transition countries: demographic bonus fades; private and aggregate saving increases moderate.
  - Pretransition countries: both public and private saving projected to increase significantly given young, rapidly growing populations.
- World GDP sample shares (2016): Late-stage Transition 63.3%; Advanced-stage Transition 20.6%; Early-stage Transition 8.4%; Pre-Transition 0.3%.

### Role of pension system characteristics in projections
- DC schemes versus PAYG:
  - Private saving is projected to increase in countries with DC schemes, on average by about 8 percentage points of GDP by 2050.
  - Private saving is projected to decrease by about 6 percentage points of GDP in countries with PAYG pension schemes.
- Pension generosity:
  - Generous public pensions push up pension spending and reduce public saving; private saving falls somewhat as retirees rely less on own saving, leading to sharp projected declines in aggregate saving in generous-system countries.
  - Countries with least generous public pensions see slight projected private saving increases by 2050.
- World GDP sample shares for pension groupings (2016):
  - With DC Scheme: 32.39% of world GDP.
  - Without DC Scheme: 59.81% of world GDP.
  - Generous Public Pensions grouping: 41.36% of world GDP (29 countries).
  - Ungenerous Public Pensions grouping: 50.84% of world GDP (45 countries).

### Illustrative country examples
- Tajikistan (with a DC scheme): aggregate saving projected to increase by 2 percentage points of GDP between now and 2050.
- Pakistan (without a DC scheme): aggregate saving projected to decline by about 2½ percentage points of GDP between now and 2050.
- Russia vs Australia: both have DC systems but Russia’s pensions are more generous; aggregate saving in Australia expected to increase faster than in Russia.
- China:
  - National saving rate exceeded 40 percent of GDP since 2000, peaking at 52 percent of GDP in 2008.
  - Old-age dependency ratio expected to more than triple between 2015 and 2050 from current level of 13 percent.
  - Assuming unchanged policies, low pension generosity, and presence of a DC system, national saving broadly holds steady rather than decrease over the projection horizon.
  - Policy efforts and behavioral changes could reduce saving further: strengthening social safety nets and changing younger generations’ consumption could decrease national saving by about 4 percentage points by 2022 (Zhang 2017).

### Limits, caveats, and uncertainty
- Projections are partial equilibrium, hold many determinants constant, and assume projected public pension spending fully lowers public saving (lower-bound estimate).
- Historical regression relationships may not predict the future; cohort effects, behavioral change, productivity evolution, and asset-return responses could alter outcomes.
- Demographic projections are uncertain; fertility, mortality, and migration may diverge from UN medium-fertility variant assumptions.
- Projections are illustrative, not forecasts.

*Source: sdn1901 - Saving projections and related analysis*

### Evolution of private and aggregate saving; policy implications

### Global projection overview and heterogeneity
- Global saving could decline by about 3 percentage points of GDP by 2050 (assuming unchanged country weights).
- Heterogeneity driven by demographics and pension design:
  - Advanced economies: sharp contraction in private saving leads to steep aggregate saving declines.
  - Emerging markets: younger populations may offset public dissaving, keeping national saving broadly stable.

### Policy implications and recommended actions
- Pension reform:
  - Further public pension reforms needed in many emerging market and advanced economies to encourage higher private saving and reduce long-term fiscal vulnerabilities, but reforms must avoid undercutting welfare or increasing old-age poverty.
  - In countries with relatively high saving rates and inadequate social security, improving pension generosity may reduce excessive private saving.
  - Countries with enabling macro and legal environments and developed financial systems could complement public pensions with funded DC schemes to encourage private saving; transition from PAYG to funded systems requires careful weighing of transition budget costs.
- Complementary policies:
  - Financial sector policies to expand retirement-relevant financial products and deepen financial inclusion.
  - Labor market policies to encourage older-worker participation, reduce gender gaps, and tackle informality.
  - Measures to increase private saving: tax-preferred retirement vehicles, automatic enrollment, financial literacy, and development of annuities and long-term care insurance markets.
- Specific quantified policy options (advanced economies example):
  - For those born between 1990 and 2009 in advanced economies with largely reformed pensions:
    - Increasing the retirement age by five years (from average 63 to 68 in 2050) would close half the projected gap in benefit ratios relative to today’s retirees.
    - If members of same cohort put aside an additional 6 percent of their earnings each year, they would close the other half of the gap in the benefit ratio.
- Balancing sustainability and equity:
  - Reforms need careful calibration to avoid fueling elderly poverty.
  - Options include linking retirement-age increases to longevity gains with provisions for the poor, and well-targeted antipoverty programs to minimize negative aggregate-saving consequences.
- Reducing precautionary saving via pension adequacy:
  - Countries like China and Korea with weak coverage and low replacement rates can reduce household precautionary saving by expanding coverage, raising social pensions, and enhancing targeted transfers.
- Preconditions for successful DC/funded expansion:
  - Macro stability, sound financial sector and infrastructure, supervisory capacity, proper collateralization and bankruptcy procedures, creditor and property rights, accounting regulation, and adequate payment systems.
  - Caveats: low coverage, insufficient contributions, and underfunded private pension funds; average ratio of underfunded pension liabilities to annual revenues remained about 6 percent from 2011 through 2016 (Grunfeld 2017, using 5,100 global public companies).
  - Transition from PAYG to funded schemes can generate large persistent fiscal costs that reduce national saving.

*Source: sdn1901 - Evolution of saving and policy conclusions*

### Counteracting the effect of aging on labor supply and annex highlights

### Labor supply policies to counteract aging
- Key challenge: declining labor force will drive down saving.
- Policy focus: close gender gaps, lengthen productive work lives, and encourage labor force participation.
- Specific actions listed:
  - Ensure equal remuneration for equal work.
  - Provide childcare services.
  - Reconsider taxes and benefits that favor early retirement to make it easier for older people to remain in the workforce.
  - Consider migration to boost labor force (politically contentious).
  - In emerging markets, reduce share of youths neither working nor studying.
  - Reduce informality so more workers pay taxes and contribute to social security.
  - Modify education and training to align skills with technological change.
- Saving’s role: private (and to some extent public) saving helps individuals cope with demographic and technological changes.

### Annexes (descriptive findings and model details)
- Annex 1: demographic trends—mortality declining everywhere; global fertility fell from nearly five births per woman in 1950s to about half that in 2015; four country groups identified by demographic stage.
- Annex 2: OLG model details—three-period agents, public PAYG pension with flow budget constraint and solvency condition, expressions for labor supply and private saving preserved in source; comparative statics highlight ambiguous effects of longevity on private saving and clear negative effects of pension generosity on private saving.
- Annex 3: empirical specification and robustness—sample over 4,500 observations (1960–2015), 70–80 countries; robustness checks include alternative aggregations, separate samples, alternative controls, system GMM, dynamic specifications; in-sample and out-of-sample fit reported (standard deviation of prediction errors: World 0.76; Germany 1.12; Japan 1.84).

*Source: sdn1901 - Counteracting aging, annexes, and empirical robustness*

### INTRODUCTION ____________________________________________________________________________________ 6

### INTRODUCTION

### Executive summary
- Over the coming decades, declining fertility and increasing longevity will profoundly change the population age distribution in many countries.  
- This discussion note investigates how impending demographic shifts and the design of pension systems could influence future national saving (the sum of public and private saving).  
- Under current policies, public pension outlays in advanced and emerging market economies will increase by an average 1 and 2½ percentage points of GDP, respectively, by 2050. Without adjustment in taxes and other spending, this increase will lead to a commensurate decline in public saving.  
- Private saving is projected to decline more precipitously in countries with generous public pension systems, as people will rely less on their own savings when they retire.  
- All else being equal, private saving is projected to increase in countries that include a defined contribution (DC) scheme as part of their pension systems.  
- Projections in this note are illustrative and do not include an opinion on the optimal saving rate or the desirable level of pensions.

### Key findings and motivations
- Demographic drivers:
  - Declining fertility and rising life expectancy will result in older populations; by 2050, on average, the old-age dependency ratio (elderly population 65 years and older relative to working age population 15–64 years) will double.
  - Today, Japan is the only country with an old-age dependency ratio over 40; by 2050 more than 55 countries will exceed that ratio.
  - Life expectancy at age 65 is projected to increase by around a year per decade.
- Why private and national saving matter:
  - National saving finances domestic investment and provides shock-absorbing capacity with implications for growth and economic stability.
  - In aging societies, national saving is important to bolster retirement security and allow workers to bear pension financing costs while maintaining living standards.
  - Most household saving is done by the highest income earners; inadequate saving has acute implications for poorer households and potential old-age poverty.
- Interaction between public and private saving:
  - Age profiles: young borrow, prime working-age save, old dissave—aging raises the share of elderly, likely depressing private saving.
  - Pension system design (coverage, benefits, funding type) influences individual saving decisions; generous public pensions can crowd out private saving, while funded DC elements can encourage private saving.
  - Lack of pension development/coverage and weak financial markets can lead to under-saving or excessive precautionary saving.

### Analytical approach and scope
- Methodology:
  - The note builds a simple overlapping generations (OLG) model to illustrate channels through which longevity, fertility, and old-age dependency affect public and private saving.
  - Empirical estimates of demographic and pension-design impacts on private saving are combined with public pension spending projections to simulate potential national saving paths under a no-policy-change scenario.
- Scope and caveats:
  - The analysis does not assess the optimal saving rate or the desirable generosity of pensions.
  - It abstracts from behavioral changes and an explicit examination of demographic effects on growth and productivity.
  - It does not analyze the consequences for saving of transitions from pay-as-you-go (PAYG) to fully funded systems (transition effects can be ambiguous).
  - The partial equilibrium framework provides simple inferences on public and private saving evolution across countries under current policies.

### Policy implications highlighted
- Pension reform:
  - Encouraging higher private saving for retirement and reducing long-term fiscal vulnerabilities will require further public pension reforms in many emerging market and advanced economies, but reforms must be carefully calibrated to avoid undercutting welfare or increasing old-age poverty.
  - In countries with relatively high saving rates and inadequate social security systems, improving pension generosity may be warranted to reduce excessive private saving.
  - Countries with enabling macroeconomic and legal environments and sufficiently developed financial systems could consider complementing public pensions with funded DC schemes to encourage private saving; shifting from PAYG to funded systems requires careful weighing of transition budget costs.
- Complementary policies:
  - Financial sector policies are needed to expand availability of retirement-relevant financial products to allow households to save and diversify retirement risks.
  - Labor market policies should encourage participation by older workers, attenuate gender gaps, and tackle informality to support pension and saving dynamics.

*Source: sdn1901 - INTRODUCTION*

### 10.      Architecture of pension systems and aging. Differences in pension system arrangements

### 10.      Architecture of pension systems and aging. Differences in pension system arrangements

### Pension system types, funding, and coverage
- Most countries rely on defined benefit (DB) pension schemes, under which benefits depend on the number of years of contributions and the individual’s earning history, typically complemented by a means-tested basic pension.
- Some countries have defined contribution (DC) contribution pension systems based on individual accounts, which often coexist with the DB scheme.
- Funding distinctions:
  - PAYG (pay as you go): general revenues or specific contributions from current workers and employers fund benefits of current retirees.
  - Fully funded (typical of private pensions): benefits depend on the value of accumulated assets over the individual’s working life.
  - Notional defined contribution systems are defined contribution but financed on a PAYG basis (examples noted in source).
- Coverage and generosity:
  - Pension system generosity encompasses both the size of benefits per person (the benefit ratio) and the coverage (the percentage of elderly people who receive a pension).
  - Example magnitudes reported: Greece and Cyprus provide pension benefits about 65 percent of the average economy-wide wages; less than 30 percent in Latvia and Ireland.
  - Advanced economies provide some type of public pension benefits to nearly all elderly citizens. In most emerging and developing economies, only a third to two-thirds of the elderly are covered.
- Role of pensions in elderly income:
  - Pensions account for more than 60 percent of elderly income in advanced economies.

### Fiscal pressures from aging and pension generosity
- Aging can directly impact public saving under PAYG schemes by increasing the ratio of elderly beneficiaries to younger workers who fund benefits.
- Even in funded systems, increases in longevity or lower-than-expected investment returns can cause funding shortfalls and require government fiscal support.
- Estimated fiscal adjustments needed to offset increased costs of aging (European countries, 2010–2050): tax revenues would have to be between 14 percent and 28 percent higher than today (or expenditures commensurately lower, or some combination).
- Specific country estimates: Japan 26 percent; United States 11 percent.
- Many recent pension reforms (raising retirement age, tightening eligibility, reducing pension sizes) have improved long-term sustainability of DB/PAYG systems but often shift adjustment burdens to future generations and may erode real pension benefits over time, potentially contributing to old-age poverty.
- Transition from PAYG to funded DC systems in the 1990s (redirecting contributions) put pressure on public saving by worsening finances of public schemes. Lack of advance funding, low coverage, and low contribution rates continue to affect many DB and DC systems, with implications for future pension adequacy.
- Pension savings tend to be concentrated in high-income households; rapid aging could exacerbate income inequality.

### Box 1: Taxonomy of pension systems (arrangements, funding, compliance) — key points
- Arrangements:
  - DB: benefits depend on years of contributions and ultimate (or average) covered earnings.
  - DC: benefits depend on contribution history and returns on contributions.
  - Some countries offer a flat-rate component that does not depend on previous earnings and may be means-tested.
- Funding:
  - PAYG systems use current employer and employee contributions to pay current retirees; sustainability depends on ratio of contributors to pensioners.
  - Funded systems invest contributions to finance future retirement benefits.
  - Most public systems are PAYG; a few have some degree of private funding. Private pensions are typically fully funded.
  - Mixed arrangements exist (e.g., notional DC financed on PAYG basis; some DB systems are funded).
- Compliance:
  - Most governments mandate participation in some pension scheme; some schemes are voluntary, typically to complement mandatory schemes.

### Theoretical model framework (small open economy OLG model) — setup and assumptions
- Agents live for three periods: (1) children, (2) workers, (3) retirees (if they survive into old age).
- Assets of those who do not survive into old age are redistributed to workers as bequests (within-family intergenerational transfers).
- Working-age agents decide labor supply, consumption, and saving; they give birth at an exogenous fertility rate and bear childrearing costs proportional to number of offspring.
- Two exogenous demographic parameters: life expectancy (longevity) and fertility rate; these jointly determine the old-age dependency ratio.
- Model features both private pensions (workers save to fully fund private pension benefits, viewed as DC) and a public PAYG defined benefit scheme that covers all retirees.
- Government levies an income tax on labor at an exogenous constant rate to finance the public pension; government can borrow or save; pension deficits reduce public saving, surpluses increase it.
- Small open economy takes global interest rate as given; model abstracts from precautionary saving motives except longevity risk.

### Model predictions — main channels and effects
- Demographic change and private saving:
  - Lower fertility rate increases private saving (less childcare spending), partially mitigated by labor supply responses (individuals may work more, increasing consumption).
  - Higher life expectancy at retirement raises private (DC pension) saving of the working-age population to finance old-age consumption.
  - Both lower fertility and higher life expectancy increase the old-age dependency ratio, raising the share of dissavers relative to savers and depressing private saving (compositional effect).
  - Overall impact on private saving depends on which effects dominate.
- Public pension system generosity and private saving:
  - Public pension benefits and private saving are substitutes: higher pension benefits mean individuals save less for retirement.
  - Empirical and theoretical findings indicate countries with PAYG systems tend to have private saving rates lower in direct proportion to the generosity of public pension benefits.
  - Indirect effect: pension generosity amplifies the positive effect on private saving by the working-age population as life expectancy rises; economies with similar demographics can show different private saving behavior owing to pension characteristics.
- Public saving:
  - Reduction in fertility or higher life expectancy increases the old-age dependency ratio, lowering public saving because pension expenditure rises relative to tax revenue.
  - Negative impact on public saving is more pronounced in countries with relatively generous public pension systems.
  - Higher pension generosity reduces both public and private saving.
- Changes in the global interest rate:
  - A lower return on assets discourages saving (substitution effect), but lower future income from savings can induce workers to reduce current consumption, increasing saving (income effect).
  - Overall impact depends on which effect dominates.
  - A lower global interest rate reduces the size of bequests relative to the economy; because bequests are a source of saving, a lower global interest rate reduces private saving as a share of GDP.

### Transition dynamics and reform trade-offs
- Transition from unfunded to funded systems typically involves transitional generations bearing costs (potentially paying for two retirements), which can raise national saving by reducing consumption of transitional generations but worsen welfare of those generations.
- Empirical evidence on the impact of transitions to funded systems on saving rates is mixed:
  - Some studies (Boersch-Supan and others 2006) suggest saving rates increase during transition to partially funded systems.
  - Other studies (Aguila 2011; Samwick 2000; Villagomez and Hernandez 2010; World Bank 2006) find the impact on saving rates to be inconclusive.
- Recent parametric reforms (increase retirement age, tighten eligibility, reduce benefit formulas) have often protected current pensioners and shifted most adjustment burdens to future retirees; some indexation changes may erode real benefits and risk increasing old-age poverty.

*Source: sdn1901 - 10.      Architecture of pension systems and aging. Differences in pension system arrangements (chapter content provided).*

### 18.      Additional considerations not captured in this framework. The small open economy

### 18.      Additional considerations not captured in this framework. The small open economy

### Limitations and additional channels not captured
- Small open economy assumption simplifies analysis but precludes assessment of how demographic changes affect the global interest rate and international capital flows.
- Two-country model with unrestricted international capital flows: impact of aging on private saving is dampened by the decrease in the global interest rate, lowering incentives to save.
- Financial and labor market imperfections are not incorporated; these could affect saving decisions:
  - Availability of financial instruments that satisfy diverse portfolio preferences or raise the net return on savings could increase private saving.
  - Financial sector development could alleviate credit constraints and drive down precautionary saving.
  - Labor market conditions (for example, risk of unemployment) increase precautionary saving when unemployment risk is higher.
- Risk of government default on pension obligations is not explicitly modeled; model implies working-age population will save more if this risk becomes more prominent and effective pension generosity declines.
- Aging may influence asset returns and risk aversion; for instance, if risk aversion increases with age, relative demand for safe assets could rise.
- Population aging could interact with labor market imperfections and early retirement incentives, affecting labor force participation by the elderly.
- Despite limitations, the model provides insights into how demographics and pension system attributes, and their interaction, affect saving rates and cross-country differences.

*Empirical Estimation of Private Saving*

### Empirical specification and variables
- Reduced-form cross-country fixed-effect panel regressions using annual data covering 75–100 advanced and emerging market economies over the past four decades (baseline).
- Pension system characteristics represented by two variables:
  - Pension generosity = product of the benefit ratio and the coverage ratio; operationalized as average pension spending per elderly person divided by GDP per working age population. Regressions include a time-varying dummy equal to 1 if generosity > 75th percentile in sample, 0 otherwise.
  - Existence of a DC pension scheme (defined contribution).
- Interaction terms capture how pension attributes influence the impact of demographics on private saving.
- Controls include credit constraints, labor market conditions, and macroeconomic variables informed by prior literature.
- Baseline empirical approach: fixed-effect panel regressions with robust standard errors clustered at the country level; all regressions include a constant term and time dummies.

### Key empirical findings (Table 1, private saving panel regressions)
- Coefficients reported (statistical significance: ***, **, * at 1 percent, 5 percent, 10 percent):
  - Public Saving: -0.52***, -0.53***, -0.53***, -0.59***, -0.59*** (columns 1–5)
  - Old-age Dependency Ratio: -0.69***, -0.74***, -0.68***, -0.52***, -0.56*** (columns 1–5)
  - Old-age Dependency Ratio * Pension Generosity: -0.10***, -0.08**, -0.33** (columns where included)
  - Old-age Dependency Ratio * DC Scheme: 0.40*, 0.66**, 1.16** (columns where included)
  - Life Expectancy at Age 40: 1.03***, 0.99***, 0.87**, 0.98**, 1.27*** (columns 1–5)
  - Life Expectancy at Age 40 * Pension Generosity: -0.05*, 0.15** (columns where included)
  - Life Expectancy at Age 40 * DC Scheme: 0.40, -0.61 (columns where included)
  - Employment Rate: 0.08, 0.07 (columns where included)
  - Real GDP Growth: 0.18***, 0.19*** (columns where included)
  - GDP per Capita PPP: -0.09, -0.12 (columns where included)
  - Real Interest Rate: -0.07***, -0.07*** (columns where included)
  - Inflation: 0.02*, 0.02* (columns where included)
  - Credit to GDP: -0.04***, -0.04*** (columns where included)
  - Terms of Trade: 0.03*, 0.03* (columns where included)
- Sample and fit statistics:
  - Observations: 3,009; 3,009; 3,009; 1,837; 1,837 (columns 1–5)
  - Number of Countries: 80; 80; 80; 74; 74 (columns 1–5)
  - Adjusted R-squared: 0.19; 0.20; 0.20; 0.30; 0.31 (columns 1–5)

### Interpretation of empirical results and magnitudes
- Negative and statistically significant relationship between old-age dependency ratio and private saving (columns 1–5).
- Life expectancy at age 40 (longevity) associated with higher private saving: each year of expected additional life adds about a percentage point to the private saving rate.
- Partial offset from public saving: a one dollar reduction in public saving is associated with a private saving increase of 60 cents, indicating some degree of Ricardian equivalence through intergenerational links.
- Pension system design mediates aging effects:
  - In countries without a DC scheme and with nongenerous PAYG/DB public pensions, a 1 percentage point increase in the old-age dependency ratio decreases private saving by 0.5 percentage points (column 4).
  - In countries with generous PAYG/DB public pension schemes but no DC scheme, private saving falls by about 0.6 percentage points.
  - In countries with a DC pension system, the effect is reversed: DC schemes induce employed people to save more for self-funded retirement.
  - Accounting for pension system design, a 1 percentage point increase in the old-age dependency ratio results in a 0.3 percentage point decrease in the private saving rate (overall finding).
- Interaction between longevity and pension system characteristics is less robust (loses significance for presence of DC scheme in some specifications).

### Caveats on empirical interpretation
- Cross-country regression analysis has limitations: pension policies likely have heterogeneous effects across countries and over time.
- Pension system characteristics are multidimensional and subject to measurement limitations (coverage, retirement incentives, replacement rates).
- Reverse causality and nonlinear relationships between covariates and private saving components are possible.
- Structural relationships and transition dynamics may not be fully captured; microeconomic and cohort analysis could yield more nuanced insights but face data limitations.

*Saving Projections*

### Projection methodology
- Aim: project effects of demographic changes and pension characteristics on public and private saving through 2050.
- Steps:
  1. Estimate effect of expected demographic developments and enacted pension reforms on public pension system outlays, relying on authorities’ projections for future pension spending that incorporate enacted reforms (including those that will take effect in the future).
     - Initial pension expenditure set equal to latest OECD estimates for OECD countries and latest International Labour Organization estimates for other countries.
     - Projections for pension spending as a share of GDP reflect available official estimates through 2050 (European Commission 2015 Aging Report for European countries; national actuarial reports for some advanced and emerging economies; IMF staff estimates for other emerging market economies accounting for enacted reforms).
     - Projected increase in public pension spending is assumed to translate fully into lower public saving (interpreted as a lower bound because other aging-related spending, notably health, is assumed not to increase in this step).
  2. Use model coefficients from empirical analysis (column 4 of Table 1) to project private saving as a function of demographic factors (changes in old-age dependency ratios and life expectancy), pension system characteristics (pension generosity and existence of a DC system), and projected public saving (owing to changes in public pension spending).
- Demographic variables evolve in line with the United Nations medium-fertility variant scenario; all other determinants are held constant.

### Projected public saving and pension spending outcomes
- Demographic developments will drive up pension costs and put public saving on a long-term downward trend globally.
- Worldwide, public pension spending pressures could depress public saving by just over 2 percentage points of GDP by 2050, with significant cross-country differences.
- Advanced economies:
  - Public saving could fall modestly by about 1 percent of GDP between now and 2050, reflecting recently enacted reforms.
  - Example: Germany—past reforms to curtail generosity and increase retirement age projected to contain pension spending increases to slightly over 2 percentage points of GDP by 2050.
  - Example: United States—less significant reforms but a relatively younger population and higher population growth; projected increase in pension spending of 1.6 percentage points of GDP by 2050.
  - Under current policies, projected spending on public pensions implies significant future reductions in the average pension.
- Emerging markets and developing economies:
  - Projected decline in public saving is larger and particularly pronounced for countries experiencing rapid aging and those where pensions have yet to be reformed.
  - Example projections: Brazil and China—pension expenditure projected to increase by 7 and 6 percentage points of GDP, respectively, by 2050.
- Health spending caveat:
  - The projection that public pension spending pressures depress public saving by just over 2 percentage points of GDP by 2050 should be viewed as a lower bound because health-related spending is projected to surge by 3.8 and 2.3 percentage points of GDP in advanced and emerging and developing economies, respectively, over this period (Clements and others 2015).
  - Rising incomes in many emerging and developing economies could increase demands for higher benefits and broader coverage, potentially understating future public expenditure burdens.

*Box 2. Health Care and Saving — summary points relevant to projections*
- Health care costs follow a life-cycle pattern and are expected to rise with an increasing share of elderly people.
- Aging-related pressures on saving grow with higher longevity due to precautionary saving for medical expenditure and long-term care.
- Health care costs are also affected by nondemographic factors (new technologies, lower productivity increases in services), making projections of health care spending more uncertain than pension projections.

*Empirical and projection limitations reiterated*
- Projections assume projected public pension spending translates fully into lower public saving and hold other determinants constant; this provides a lower-bound estimate of aging’s impact on public saving.
- Annex 3 contains in-sample predictions and the full list of countries used for projections.

*Source: IMF staff calculations.*

### 25.      Evolution of private and aggregate saving. The evolution of private and national saving

### 25.      Evolution of private and aggregate saving. The evolution of private and national saving

### Global projection overview
- Assuming unchanged country weights, global saving could potentially decline by about 3 percentage points of GDP between now and 2050.
- In emerging markets and developing countries collectively, higher private saving by relatively younger populations offsets the projected decline in public saving, resulting in broadly stable national saving.
- In contrast, private saving rates in aging advanced economies are expected to contract sharply, leading to a steep overall decline in aggregate saving rates.
- These aggregates mask substantial heterogeneity across countries, driven by differences in demographics and pension system design.

### Saving rate heterogeneity: stage in demographic transition
- Late-stage transition countries:
  - Private saving is projected to fall significantly as older age groups (which have high dissaving) make up an increasing share of the total population.
  - Together with lower public saving, this translates into a sharp projected decline in national saving by over 4 percentage points of GDP, on average, between now and 2050.
- Advanced-stage transition countries:
  - National saving is projected to remain broadly stable, as higher private saving offsets public dissaving.
  - Large disparities underlie this average. Saving in many countries in Latin America and the Caribbean has hovered below 20 percent of GDP in recent decades. China is notable for its high saving rate over the past 35 years (see Box 3).
- Early-stage transition countries:
  - The bonus from a growing working age population and declining family sizes will fade, moderating the increase in private and aggregate saving observed in the recent past.
- Pretransition countries:
  - Both public and private saving are projected to increase significantly given their relatively young and rapidly growing populations.
- World GDP sample note:
  - Projections in 2016 and later years include data for 74 countries that accounted for over 80 percent of world GDP in 2016.
  - Demographic grouping shares of world GDP as of 2016: Late-stage Transition (63.3%); Advanced-stage Transition (20.6%); Early-stage Transition (8.4%); Pre-Transition (0.3%).

### Saving rate heterogeneity: role of pension system characteristics
- Presence of DC schemes versus PAYG:
  - Private saving is projected to increase in countries with DC schemes, on average by about 8 percentage points of GDP by 2050. This effect more than offsets the projected decline in public saving, owing to the simultaneous presence of PAYG public pensions in some countries.
  - Private saving is expected to decrease by about 6 percentage points of GDP in countries with PAYG pension schemes, as the system itself does not encourage higher wealth-holding by individuals. This, combined with higher age-related public pension spending, will lead to a substantial decline in national saving.
- Pension generosity effects:
  - Benefit generosity pushes up pension spending while weighing down public saving. Private saving falls somewhat as retirees need to rely less on their own saving; thus, aggregate saving in countries with generous public pension systems is projected to decline sharply.
  - In countries with the least generous public pension systems, private saving is projected to increase slightly by 2050, especially where precautionary motives against longevity or earnings risk are important.
- World GDP sample shares for pension system groupings (as of 2016):
  - With DC Scheme: 32.39% of world GDP.
  - Without DC Scheme: 59.81% of world GDP.
  - Generous Public Pensions grouping: 41.36% of world GDP (29 countries).
  - Ungenerous Public Pensions grouping: 50.84% of world GDP (45 countries).
  - Note: The generosity grouping is taken for the year 2015.

### Individual country trends and illustrative examples
- Early-stage transition comparison — Tajikistan vs Pakistan:
  - Tajikistan (with a DC scheme): aggregate saving rates are projected to increase by 2 percentage points of GDP between now and 2050.
  - Pakistan (without a DC scheme): aggregate saving rates are projected to decline by about 2½ percentage points of GDP between now and 2050.
- Late-stage transition comparison — Russia vs Australia:
  - Both have a DC system, but pensions in Russia are more generous relative to national income than those in Australia.
  - As a consequence, aggregate saving in Australia is expected to increase at a much faster pace than in Russia.
- China (Box 3 highlights):
  - China has one of the highest national saving rates in the world, exceeding 40 percent of GDP since 2000 and peaking at 52 percent of GDP in 2008, with a gradual decline thereafter.
  - The old-age dependency ratio is expected to more than triple between 2015 and 2050 from the current level of 13 percent, exerting downward pressure on both public and private saving.
  - Assuming unchanged policies, low pension generosity, and the presence of a defined contribution system, the model suggests that national saving will broadly hold steady rather than decrease over the projection horizon.
  - Policy efforts and behavioral changes could lead to a further reduction in saving: strengthening the social safety net and changing consumption behavior of younger generations will likely decrease the national saving rate by about 4 percentage points by 2022 (as detailed in Zhang 2017).

### Limits and caveats of the illustrative projections
- Framework limitations:
  - Based on partial equilibrium analysis and abstracts from behavioral and policy changes and price effects.
  - Evolution of government saving could depend on tax and labor market reform and changes in non-age-related spending.
  - Relationships observed in the past between aging and private saving (estimated regression coefficients) may not be good predictors of the future.
  - Cohort effects may shift saving profiles at different ages (for example, future middle-aged people might increase saving in response to longer lifespans).
  - Analysis could be refined with more granular data on replacement rates or accounting for pension system assets.
  - Changes in saving rates would be driven by long-term productivity growth; demographic changes could depress productivity and growth prospects, lowering the rate of return on savings.
- Uncertainty:
  - Given considerations and the substantial uncertainty surrounding demographic projections, the projections should be viewed as illustrative and are not intended as forecasts.
  - Past demographic projections have been subject to significant errors and future realizations of fertility, mortality, and migration might differ substantially from projected levels.

### Conclusions and policy options
- Aging challenge and saving:
  - Under current policies, public pension outlays in advanced and emerging market economies will increase by an average of 1 to 2½ percentage points of GDP, respectively, by 2050, depressing public saving.
  - The impact on private and aggregate saving depends on the interaction of asynchronous demographic transitions and the design of retirement systems: funding, coverage, benefits promised to the elderly, and timing of transfers.
  - Appropriate responses will vary across countries and must account for country-specific policy and institutional settings.
  - In countries with relatively high saving rates and inadequate social security systems, increasing generosity may be warranted.
  - In rapidly aging countries with relatively low saving rates and rising pension liabilities, the challenge will be to increase saving ratios in a sustainable way.
  - For today’s younger generations, saving more for the future will become increasingly important to ensure retirement income security.
- Public pension system reforms:
  - Overly generous pension benefits (owing to high benefit ratios or a low statutory retirement age) can interact with projected demographic trends to lower aggregate saving.
  - Reducing public pension generosity (for example, curtailing early retirement benefits or reducing benefit ratios) could attenuate long-term fiscal vulnerabilities and moderate the fall in aggregate saving.
  - For those born between 1990 and 2009 in advanced economies where pensions have been largely reformed:
    - Increasing the retirement age by five years (from today’s average of 63 to 68 in 2050) would close half the projected gap in benefit ratios relative to today’s retirees.
    - If members of the same cohort were to put aside an additional 6 percent of their earnings each year, they would close the other half of the gap in the benefit ratio.
  - Financial sector and labor market policies could support such behavioral changes.
- Balancing sustainability and equity:
  - Distributional consequences of pension system reform can be significant.
  - Ongoing and planned reforms will improve pension system sustainability, but average benefit ratios are projected to decline sharply in many countries.
  - Additional reforms need careful calibration to avoid undercutting the welfare of future retirees and fueling poverty among the elderly.
  - One option: link additional increases in retirement age to longevity gains, with adequate provisions for the poor (whose life expectancy tends to be shorter than average).
  - Antipoverty programs should be carefully designed and targeted to minimize unintended negative consequences on aggregate saving (either through excessive fiscal costs or indirectly by crowding out private saving).
- Improving pension system adequacy to reduce precautionary saving:
  - Examples: China and Korea have weak pension coverage and low replacement rates, inducing high household saving rates (China: low pension generosity; Korea: public pension covers only about a third of the elderly and replacement rates are low).
  - These countries have room for fiscal maneuver to redirect resources to reduce old-age poverty by expanding coverage of social security systems, raising social pensions, and enhancing targeted social transfers.
  - Such actions would reduce households’ need for precautionary saving while ameliorating inequality and old-age poverty.
- Boosting private saving by improving pension system architecture:
  - The presence of a DC scheme can support higher private saving rates, attenuating the negative effect of aging on national saving.
  - Countries with an enabling environment might consider complementing the public pension scheme with a funded DC scheme.
  - Preconditions for an enabling environment include: macroeconomic stability, a sound financial sector and infrastructure (legal and regulatory), adequate supervisory capacity, proper collateralization and bankruptcy procedures, creditor and property rights, accounting regulations, and adequate payment systems.
  - Caveats: too few people may be covered or contribute; contributions may fall short of providing adequate benefits; many private pension funds are underfunded. The average ratio of underfunded pension liabilities to annual revenues remained at about 6 percent from 2011 through 2016 (Grunfeld 2017, using 5,100 global public companies).
  - Pension transitions from PAYG to funded schemes can generate large and persistent fiscal costs that reduce national saving.
- Development of financial sector instruments to encourage voluntary saving:
  - Households’ ability to diversify retirement-related risks depends on the availability of age-specific financial products (for example, annuities and long-term care insurance).
  - Countries with underdeveloped financial sectors would benefit from boosting financial inclusion (for example, efforts to reduce the costs of bank accounts for individuals) and creating sound and resilient banking sectors that offer long-term saving instruments.
  - Financial literacy could foster a culture of saving and help people better plan for retirement.
  - Government policies could increase voluntary private saving by providing tax-preferred saving vehicles related to pensions (for example, 401(K) plans in the United States), or tax-preferred general or education saving accounts, but participation of middle-income households would be essential for these schemes to generate additional saving rather than displacing existing saving elsewhere.
  - Nudges such as automatic enrollment in pension schemes can help (for example, the United Kingdom).

*Source: THE FUTURE OF SAVING: THE ROLE OF PENSION SYSTEM DESIGN IN AN AGING WORLD (International Monetary Fund, selected chapter).*

### 36.      Counteracting the effect of aging on labor supply. On current demographic trends, many

### 36.      Counteracting the effect of aging on labor supply. On current demographic trends, many

### Counteracting aging’s effects on labor supply — findings and policy recommendations
- Key challenge: Declining labor force on current demographic trends will drive down saving.
- Policy focus: Reforms that close gender gaps in labor force participation and encourage lengthening of productive work lives given increased longevity.
- Specific policy actions listed in the source:
  - Ensuring equal remuneration for equal work.
  - Providing childcare services.
  - Reconsidering taxes and benefits that favor early retirement to make it easier for older people to remain in the workforce.
  - Migration as a potential means to boost labor force in many advanced economies (noting political contentiousness).
  - In many emerging market economies, decreasing the large share of young people who are neither participating in the labor market nor studying.
  - Reducing the large share of the labor force that does not work in the formal sector (thus does not pay taxes or contribute to social security) to boost saving.
  - Modifying education and training policies to better align skills with rapid technological change (which will replace labor in some sectors but may be labor-augmenting in others).
- Role of saving: Private (and to some extent public) saving will play a key role in helping individuals cope with demographic trends and technological change.

### Annex 1. Current state of demographic transition — descriptive findings
- Mortality: Declining in all countries; drivers differ across regions (long-term low child mortality in advanced economies versus more recent drops in less-developed regions).
- Fertility: Average worldwide fertility rates declined from nearly five births per woman in the 1950s to half that in 2015.
- Result: Narrowing of the gap between highest and lowest fertility regions.
- Country grouping method: k-means clustering using variables:
  - (1) average annual population growth (excluding migration) between 2010 and 2016;
  - (2) child and old-age dependency ratios between 2010 and 2016;
  - (3) number of years before or after the minimum total dependency ratio is reached.
- Four groups identified:
  - Late-stage transition or posttransition: decelerating or declining population, rising old-age dependency ratios; includes most advanced economies and a few emerging market countries.
  - Advanced-stage transition: rapid transition from high child dependence to high old-age dependence after peaking in early 2000s; includes many emerging market economies in Asia and Latin America (example countries listed in source).
  - Early-stage transition: fertility declining but still relatively high; working-age share expected to peak in first half of 21st century — still benefiting from demographic dividend; includes several low-income developing and emerging market economies in Asia, Latin America, and MENA.
  - Pretransition: high fertility while mortality declines, yielding rapid population growth and large youth cohorts; many low-income developing countries, mostly in sub-Saharan Africa.

### Annex 2. Small open economy overlapping generations model — structure and theoretical results
- Model purpose: Study effects of demographic change on private and public saving, highlighting role of public pension system design; small open economy setting with extension possibilities to two-country framework.
- Pension system: Public pay-as-you-go (PAYG) scheme with possible financial imbalance; government can borrow and lend so public saving reacts to demographic and pension parameters.
- Labor: Endogenous labor supply; agents live for at most three periods (children, young working age y, old o). Young give birth at fixed rate g, survive to old age with probability χ. Life expectancy at birth = 1 + χ. Old-age dependency ratio = χ/g. Population growth rate = fertility rate g.
- Young agents’ problem (notation preserved from source):
  - Young supplies labor lt at wage wt, pays labor income tax at rate τ and childcare costs η as share of income per child, saves at gross return R* in private pension fund, receives bequests vt if others do not survive.
  - Public pension payment per retiree: bt+1 = φ wt lt (φ is fraction of old people’s labor income when young).
  - Bequest: vt = (1−χ) R* at g.
  - Utility function used: u(c,l) = log(c − θ/(1+ε) l^(1+ε)).
  - Labor supply first order condition solution shown in source:
    - lt = [ (φ/R* + 1 − τ − gη) wt / θ ]^(1/ε)
  - Key comparative statics from the model:
    - Labor supply increases with wage rate and pension generosity (substitution effect).
    - No wealth effect on labor supply given utility specification; substitution effect dominates.
    - Higher life expectancy does not induce more labor supply by the young because offsetting effects (suppression of consumption to save more raises marginal utility of leisure).
    - Lower fertility reduces effective tax rate on labor income, encouraging more labor supply.
    - Young’s saving at t+1 (as given in source):
      - at+1 = [ (1−τ−gη) − ( (1+ε)/(1+βχ) ) (1−τ−gη+φ/R*) ] wl_t + (βχ/(1+βχ)) v_t  (expression preserved as in source context)
    - Interpretation:
      - Savings decompose into savings out of present value of after-tax wage income and expected pension benefits, plus saved portion of received bequests.
      - Higher life expectancy increases both components (makes young more patient); effect amplified with more generous pension.
      - Lower fertility frees up income to be saved but partly offset by greater labor supply and consumption.
      - More generous pension reduces incentive to save.
- Public PAYG pension system (formulas preserved):
  - Total pension payout Bt = bt Nt.
  - Government flow budget constraint: τ w_t L_t + D_t+1 − B_t − R* D_t = 0.
  - Government solvency constraint (as in source): Σ (R*)^(−t) (τ w_t L_t − B_t) ≥ R* D_0 with D_0 = 0 assumed.
  - Public savings S_t^G = −D_t+1.
  - Tax revenue and pension expenditure constant as share of GDP in equilibrium:
    - T_t / Y_t = τ(1−α)
    - B_t / Y_t = (1−α) χ φ / g
  - Restriction imposed: τ ≥ χ φ / g to ensure solvency and that g > R* so asset-to-GDP ratio converges.
  - Public saving-to-GDP ratio:
    - S_G / Y = (1−α) [ τ − χ φ / g ]
  - Implication: Aging (higher old-age dependency via higher life expectancy and/or lower fertility) and higher pension generosity decrease public saving.
- Bequests and private saving:
  - Steady-state bequest: v = (1−χ) R* a / g (increasing in interest rate).
  - Young worker steady-state saving (preserved expression in source):
    - a = [ (1−τ−gη) − (1−τ−gη+φ/R*)/(1+ε) ] (1 + ε)/(1 + βχ) [ 1 − (1−χ) R* / g ] (βχ/(1+βχ)) wl.  (expression preserved in descriptive form)
  - Aggregate private saving S^P_t = a N_t / Y_t (retirees consume all income).
  - Private saving-to-GDP ratio (as in source):
    - S_P / Y = [ (1−τ−gη) − (1−τ−gη+φ/R*)/(1+ε) ] (1 + ε)/(1 + βχ) [ 1 − (1−χ) R* / g ] (βχ/(1+βχ)) (1−α)
  - Comparative statics:
    - Private saving decreases with pension generosity.
    - Lower fertility increases private saving rate and increases size of bequests relative to output.
    - Effect of higher life expectancy on private saving ambiguous (it decreases size of bequests).

### Annex 3. Empirical specification, data, and robustness — private saving regressions
- Empirical specification estimated (as in source):
  - S_{i,t}^P = α + β × X_{i,t} + γ × Y_{i,t} × X_{i,t} + δ × S_{i,t}^G + θ × Z_{i,t} + μ_i + μ_t + ε_{i,t}
  - X: vector of demographic variables (main demographics: old-age dependency ratio and life expectancy at age 40).
  - S^G: government saving as share of GDP.
  - Y: pension system characteristics represented by time-variant dummies indicating (1) whether public pensions are relatively generous and (2) existence of a defined contribution (funded) pension scheme.
  - Pension generosity measure: product of average pension as share of GDP per worker (benefit ratio) and number of pensioners divided by population over 65 (coverage ratio). Binary generosity variable set to 1 for top 25 percent of countries (threshold at the 75 percent quartile).
- Sample: more than 4,500 observations spanning the period from 1960 to 2015, covering 70–80 countries; panel is unbalanced.
- Control variables included (guided by theory and prior literature): employment rate (share of employed in total population), financial depth (private sector credit to GDP), real interest rate, real GDP growth, inflation, terms of trade, and other macro variables (see source).
- Robustness checks summarized in the source:
  - Alternative data aggregations: annual baseline with country and time fixed effects; also averaging over three- and five-year periods.
  - Separate samples: (1) advanced economies and (2) emerging market and low-income countries.
  - Alternative specifications including projection using a different table specification.
  - Additional controls tested: share of public health expenditure, expected life expectancy of a current 60-year-old, share of prime savers (ages 45–64) as proportion of working-age population, overall quality of institutions, fertility and mortality rates, young-age dependency ratio.
  - Replacement rates used instead of generosity variable for smaller OECD subsample.
  - Adding government debt level as control indicates high government debt depresses private saving.
  - Using future/projected values for old-age dependency ratio or projected generosity leaves baseline results largely unchanged.
  - Endogeneity and unobserved heterogeneity addressed using system generalized method of moments (Arellano and Bond 1991; Arellano and Bover 1995); demographic and interaction effects robust to this specification.
  - Dynamics: dynamic specification with lagged dependent variable and mean group estimator (Pesaran and Smith 1995) confirm baseline results for short- and long-term effects.
- In-sample performance: Model fit gauged by comparing in-sample and out-of-sample projections to actual private saving globally and for country cases (Japan and Germany); in-sample fitted values examined for period 1980– (source continues beyond provided extract).

*International Monetary Fund — THE FUTURE OF SAVING: THE ROLE OF PENSION SYSTEM DESIGN IN AN AGING WORLD (content unit excerpt provided)*

### 2000. We also gauge the out-of  -sample performance, estimating the model on the data up to the

### Annex 3 — Private Saving Regression, Fit, and Projections (model estimated up to year 2000; out-of-sample projections for 2001–15)

### Model fit and out-of-sample performance
- Estimation approach: model estimated on the data up to the year 2000 and used to project developments for the years 2001–15. Both in-sample and out-of-sample lines, as well as actual values, are shown in Annex Figure 3.1.
- In-sample performance:
  - "The in-sample predictions for global private saving are close to observed levels."
  - The empirical model captures two main trends in the actual data:
    1. "the steady trend in private saving as a share of GDP since the 1980s," and
    2. "the sharp increase in global private saving as a share of GDP in the second half of the 2000s."
- Country-level performance and heterogeneity:
  - "For individual countries, the model’s fit reflects idiosyncratic developments. This is due to large heterogeneity in the development of saving rates across countries."
  - Germany: "the model’s in-sample prediction for private saving in Germany matches actual values, but the out-of-sample performance misses the trend increase in the German private saving rate in the 2000s."
  - Japan: "the out-of-sample performance is reasonable but misses the uptick in saving toward the end of the sample period."
- Fit statistics (Annex Figure 3.1 note):
  - "Standard deviation of the difference between predicted and real values in the World panel is 0.76; in Germany panel, 1.12; and in the Japan panel, 1.84."
- Weighting used for world estimates:
  - "World private saving estimates are obtained by weighing private saving of individual countries by their GDP in nominal US dollars."

### Regression variables (Annex Table 3.1)
- Public saving: "Public saving as a percent of GDP" — Source: IMF, WEO
- Old-age dependency ratio: "Ratio of population 65 years and older to population aged 15–64" — Source: United Nations
- Life expectancy at age 40: "Life expectancy at age 40 years is the average number of years that a person at that age can be expected to live, assuming that age-specific mortality levels remain constant." — Source: United Nations
- Pension generosity: "A dummy indicating whether a country’s pension expenditure is above the 75th percentile (as a percent of GDP per capita) in the overall sample or for the country-specific sample" — Source: IMF
- Defined contribution pension scheme: "A dummy indicating that the country has a defined contribution scheme. It includes mandatory individual account schemes, which are normally financed through social security contributions, accumulate in personified accounts, and are managed by the private sector and occasionally by the public sector (also known as provident funds)." — Source: US Social Security Administration (various years)
- Employment rate: "Ratio of employed population to total population or labor force participation rate" — Source: WDI
- GDP per capita: "PPP-based per capita GDP" — Source: IMF, WEO
- GDP growth: "Annual real GDP growth rate" — Source: IMF, WEO
- Real interest rate: "Real interest rate" — Source: WDI
- Inflation: "Annual percentage change in consumer price index" — Source: IMF, WEO
- Credit to GDP: "Banking-sector private credit as a percent of GDP" — Source: WDI
- Terms of trade: "Ratio of the deflator of exports of goods and services to the deflator of imports of goods and services." — Source: WEO
- Source line: "Source: IMF Staff."

### Determinants of private saving — literature evidence (Annex Table 3.2)
- Table purpose: "Private Saving Determinants: Review of Empirical Literature"
- General pattern reported (signs and significance as used in the table; (*) denotes statistical significance at 1, 5, or 10 percent level):
  - Demographics:
    - Young-age Dependency: Young-age Dependency[-]*
    - Old-age Dependency: Old-age Dependency[-]*[-]*[-]*[-]*[-]*[-]*[+]
    - Total (young and old) Dependency: Total (young and old) Dependency[-]*[-]*[-][-]*[-]*[-][-]*[-]*
  - Employment rate: Employment Rate 3 [-]
  - Income and wealth:
    - Real per Capita Income: Real per Capita Income[+]*[+]*[+]*[+][+]*[+][+]*[+]*[+]*[+]
    - Growth of Real Income: Growth of Real Income[+]*[+]*[+]*[+]*[+]*[-][-][+]*(+)[-][+]*
    - Private Wealth: Private Wealth 4 [-][+]*[-]*[+]
  - Government sector:
    - Public Saving: Public Saving[-]*[-]*[-]*[-]*[-]*[-]*
    - Budget Balance: Budget Balance[-]*[-]*[-]*[-]*[-]*[-]*[-]*
  - Interest rate: Real Interest Rate[+][-][-][+]*[-]*[-]*[+]*[+]*[+]*[-]
  - Relative prices: Terms of Trade[+]*[+][+]*[+]*[+]*[+]*[+]*[+]*[+]*[+]*
  - Macroeconomic uncertainty: Inflation[+]*[-][+][+]*[-][-][+]*[+]*[+]*[-]*
  - Financial sector depth:
    - Money [+]*[-][+]*[-]*[-]*[-]*[+]
    - Private Sector Credit[+]*[-]*[-][-]*
    - Flow of Private Sector Credit[-]*[-]*
  - Pension system:
    - Generosity of Pension System 5 [-]*[-]*[-]*
    - Funded Pension Scheme 6 [+]*[+]*[+]*
  - Other variables found significant (selected): Urbanization[-]*[-][-]*; Government Current Expenditure[-]*[-]*[-]*; Government Capital Expenditure[-]*[-]*[-]*; Income Distribution[+]*; Life Expectancy at Birth[+]*; Current Account Balance[+]*[+]*; Business Saving; Health Care Expenditure; Government Financial Liabilities[+]*.
- Notes on measurement and studies (footnotes reproduced from table):
  - 1 For the majority of studies, the dependent variable is private saving. In the others, the dependent variable is aggregate saving (Li and others 2006) and household saving (Hufner and Koske 2010).
  - 2 Studies are based on panel data models but use different estimation techniques.
  - 3 Li and others (2006) use labor force participation.
  - 4 Masson and others (1995) use the sum of beginning of period capital stock, government debt, and net foreign assets; Haque and others (1999) use the cumulative sum of past nominal private saving in percent of GDP; De Mello and others (2004) use house and equity price indexes as proxies; Roehn (2010) uses house prices and stock prices, which have opposite but insignificant effects on private saving.
  - 5 Edwards (1996) uses the ratio of public expenditure on social security and welfare to total public expenditure as a proxy for generosity; Bailliu and Reisen (1998) use government spending on public pay-as-you-go pensions divided by population older than 65; and Dayal-Ghulati and Thimann (1997) use expenditure on social security in percent of GDP.
  - 6 Bailliu and Reisen (1998) use pension funds' and life insurance assets scaled by the population between 19-65; Dayal-Gulati and Thimann (1997) use pension funds' savings; Rezk and others (2009) use pension funds' assets in percent of GDP.
  - Note: "(*) denotes statistical significance at 1, 5, or 10 percent level; if multiple specifications are used, signs and significance reflect at least one of the specifications."

### Countries with saving projections (Annex Table 3.3)
- "80 Countries in the Sample" (table lists the 80 countries included in the projections).
- Note on data exclusions: "* Country not included in the projections owing to data unavailability."

### Annex Figure 3.1 (description)
- Figure title: "Fitted versus Actual Private Saving (Percent of GDP)"
- Panels shown: World, Germany, Japan.
- Weighting and fit statistics as noted above (World estimates weighted by GDP in nominal US dollars; standard deviations of prediction errors: World 0.76; Germany 1.12; Japan 1.84).
- Source: "IMF staff calculations."

*Source: IMF staff (Annexes and tables reproduced from "THE FUTURE OF SAVING: THE ROLE OF PENSION SYSTEM DESIGN IN AN AGING WORLD").*

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_Source: https://www.imf.org/-/media/files/publications/sdn/2019/sdn1901.pdf_