## wp1794

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### Appendix I — Addressing demographic uncertainty: key findings
- Longer life expectancy driven by rising income, medical technology, and public healthcare expansion has been GOOD for wellbeing; falling fertility introduces a BAD aspect when combined with longevity.
- Example (LAC5: Argentina, Brazil, Chile, Colombia, Mexico):
  - Average life expectancy at birth increased from 58 years in 1960 to 76 years in 2014 (Saad, 2009).
- Demographic uncertainty affects:
  - The number of estimated pensioners.
  - Cash flows under defined benefit (DB) pension systems.
  - Government spending on public healthcare.
- Policy implication:
  - Addressing demographic uncertainty requires explicit scenario analysis and sensitivity checks around mortality, fertility, and cohort-size assumptions.

### Public finance pressures, objective and contributions of the paper
- Observed pressures:
  - Public pension systems designed with a favorable worker-to-pensioner ratio; demographic shifts raise old-age dependency and public pension spending.
  - Healthcare technology costs concentrated among older cohorts increase fiscal pressures.
- Paper objective:
  - Develop an integrated methodology and a user-friendly toolkit to project long-term public pension cash flows and healthcare spending, illustrated for the LAC5.
  - Estimate pension funding and pension and healthcare expenditures under a baseline (no policy changes) scenario.
  - Enable estimation of fiscal implications of alternative reforms in DB and DC systems, including fiscal cost of a minimum guaranteed pension (MGP) and migration from DB to DC.
- Applicability:
  - Toolkit is versatile, country-specific features can be incorporated, and data requirements are relatively low.

### Key illustrative results for the LAC5 (baseline and stylized comparisons)
- Pension projections (baseline, 2015-50):
  - Argentina and Brazil’s net cash flows projected to worsen to close -4 and -22 percent of GDP, respectively, between 2015-50.
  - Other LAC5 balances projected to stay constant or improve.
- Revenue and system-type dynamics:
  - Argentina: revenues expected to grow continuously.
  - Brazil: revenues exhibit an inverted U-shape.
  - Colombia (hybrid DC/DB): constant revenue flows as share of GDP.
  - Chile (earlier DC): revenues negligible; Mexico (transition to DC completed): declining revenue trend.
- Present discounted value (PDV) of system cash flows over projection horizon is negative and substantial (discount factor assumed constant at 1 percent).
- Country stylized facts:
  - Argentina: only mandatory pillar is a PAYGO DB public scheme (1994 DC introduced, reversed in 2008); 2007 Moratoria Provisional affects budgeted beneficiaries.
  - Brazil: compulsory PAYGO DB with sub-schemes; reforms in 1999, 2003, 2012, 2015; recent reforms partially implemented in baseline.
  - Chile: shifted from PAYGO DB to fully-funded DC starting 1981; coexistence of DB and DC; 2008 “solidarity pillar” targets poorest 60 percent.
  - Mexico: 1997 reform introduced DC; first DC retirees assumed starting in 65; introduced Pension Universal to address old-age poverty.

### Pension system primer and risk allocation
- PAYGO: current workers’ contributions fund current retirees.
- Fully funded: contributions purchase assets; accumulated stock and returns pay future benefits.
- DC: benefits depend on accumulated assets and rate of return; uncertainty borne by individual.
- DB: benefits determined by formula; government bears risk of shortfalls and finances via borrowing, taxes, or reallocation.
- Other configurations: PAYGO DC, DC/DB hybrids, multiple pillars.

### Demographic trends and mitigation levers
- Trends:
  - Falling fertility and rising life expectancy yield a temporary demographic dividend then shift to older-age distribution increasing pension and health pressures.
- Mitigating factors:
  - Increases in labor force participation, savings rates, human capital, female participation incentives, better health, and increases in retirement age.

### Pension reform scenarios and quantified impacts (selected)
- Reforms analyzed: onetime increase in retirement age; indexation of retirement age; reduction in replacement rate; reduction in indexation of benefits; increase in contribution rate; transition to funded DC; MGP implications.
- Onetime increase in retirement age (increase by 5 years, phased 2016-25):
  - On average reduces pension spending in 2050 by 2.2 percent of GDP relative to baseline.
  - Country impacts in 2050:
    - Brazil: 7.5 percent of GDP reduction.
    - Argentina: 3.0 percent of GDP reduction.
    - Chile and Mexico: smaller improvements (already shifted to DC).
- Indexation of retirement age (start 2026; automatic tie to average age of retirees):
  - Average reduction of public pension expenditure: 1.1 percent of GDP.
  - Largest gain: Brazil 4.2 percent of GDP.
- Reduction of replacement rate (new pensioners’ replacement rate falls by 0.5 percentage points each year for 10 years, 2016-25; net 5 percentage points lower from 2025):
  - Average reduction of pension spending: 0.7 percent of GDP.
- Reduction in indexation of benefits (existing pensioners indexed at four-fifths of inflation from 2016 onward):
  - Average reduction in pension spending: 1.7 percent of GDP.
  - Larger gains in Argentina and Brazil; moderate in DC-dominant countries.
- Increase in contribution rate (permanent 1 percentage point increase implemented 2016):
  - Impact largest for Argentina and Brazil; small for Chile, Colombia, Mexico.
  - For DB systems, effect appears as higher revenues; for DC systems, higher contributions raise accumulated savings and reduce government MGP payouts.
- Dependency-indexed contribution rate (self-correcting):
  - Illustrative required contribution increases to achieve 2015 balance:
    - Argentina: from 21 percent to 39 percent of average wage.
    - Brazil: from 28 percent to 34 percent of average wage.
  - Required rates by 2050 as dependency rises:
    - Argentina: 45 percent of average wage.
    - Brazil: 115 percent of average wage.
  - Conclusion: reliance solely on contribution increases is infeasible.

### Cumulative reform adoption and interaction effects
- Simultaneous reforms considered: onetime retirement increase; indexation of retirement age; reduction in replacement rate; reduction in indexation of benefits; onetime contribution rate increase.
- Interaction/second-round effects reduce additive savings; examples for 2050:
  - Argentina:
    - Onetime retirement age reduces 2050 expenditure by 3.0 percent of GDP.
    - Reduction in indexation reduces 2050 expenditure by 3.3 percent of GDP.
    - Sum = 6.3 percent of GDP; simultaneous cumulative impact = 5.5 percent of GDP.
    - Reported second-round effect: 1.5.
  - Brazil:
    - Onetime retirement age reduces 2050 expenditure by 7.5 percent of GDP.
    - Reduction in indexation reduces 2050 expenditure by 5.0 percent of GDP.
    - Sum = 12.5 percent of GDP; simultaneous cumulative impact = 11.3 percent of GDP.
    - Reported second-round effect: 3.3.
- Policy implication: sequencing and combination of reforms matter because reforms interact.

### Transition from PAYGO DB to funded DC: scenarios and fiscal dynamics
- Scenarios (Argentina, Brazil):
  - Full shift: cohorts entering labor market from 2020 contribute only to funded DC.
  - Partial shift: 50 percent of new entrants post-2020 to old DB; 50 percent to new DC.
  - Projection horizon extended to 2100 (first DC cohorts retire in 2060).
  - Contribution rates in DC set equal to old DB rates; MGP access requires prior contributions.
- Fiscal dynamics:
  - Short run: pension system balances worsen due to transition costs.
  - Long run: DC transition (full or partial) improves sustainability and increases private savings; accumulated private stock eventually outpaces transitional public deficits.
- Political and distributional risks: financing transition, low retirement benefits under DC, MGP fiscal burden; careful design needed.

### Healthcare baseline projections and reform scenario
- Baseline assumptions:
  - Excess cost growth (ECG) = 1 percent constant (Clements, Coady, & Gupta, 2012).
  - Age-specific spending index = OECD average for all LAC5.
- Baseline projected increase in public sector healthcare costs in LAC5 during 2015-50:
  - Average increase: 4.1 percent of GDP.
  - Drivers roughly split: half due to excess cost growth, half due to demographics.
  - Country-specific increases (2015-50):
    - Mexico: 3.1 percent of GDP.
    - Colombia: 5.3 percent of GDP.
- Healthcare reform illustrated:
  - Reduction in ECG by 0.5 percentage points starting in 2016.
  - Projected fiscal impact (2015-50):
    - Average reduction in healthcare spending: 0.8 percentage points of GDP.
    - Point estimates range: 0.5 to 1.0 percentage points of GDP depending on country.
- Potential policy measures to curb ECG:
  - Caps on services/treatments.
  - Centralize parts of system to limit hospital autonomy over budgets.
  - Promote competition among providers.
  - Foster incentives for private insurers to expand plan offerings.

### Comparison with other projection approaches
- Compared approaches: AEW, FAD, WHD.
- Findings:
  - Pension projections show similar general trends across AEW, FAD, WHD, with notable differences driven by indexation parameters, demographic beneficiary projections, and replacement rate assumptions.
    - AEW higher for Brazil from 2030 onward; about 60 percent of difference due to indexation parameters; equalizing real GDP growth reduces difference by 2050 to 4 percent of GDP.
  - Healthcare projections are closer across methods; driven mainly by ECG evolution and beneficiary numbers, less sensitive to macroeconomic parameters.

### Policy implications and concluding remarks
- Aging and DB structures create substantial long-run fiscal pressures; PDV of cash flows negative in all cases.
- Parametric reforms (retirement age, indexation, replacement rates, contribution rates) can materially reduce long-term spending, especially in DB-dominant countries (Argentina, Brazil).
- Contribution-rate increases alone would require politically and economically challenging hikes.
- Transitioning to funded DC improves long-run sustainability and private savings but entails short-run fiscal costs and distributional/political trade-offs.
- Healthcare costs projected to outpace economic growth; reforms addressing ECG important to contain spending.

### Appendix I sensitivity: fertility variants and extended horizon
- Two alternative scenarios using UN high and low fertility variants; projection horizon extended to 2100.
- Assumptions:
  - New cohorts enter labor market at age 20 and start retiring at age 60.
  - Effects on contributors/balance observable starting 2036; effects on expenditure starting 2076.
- Key result:
  - The impact of higher (lower) fertility on pension system cash flow peters out over time for Argentina and Brazil (short- and long-run offsetting mechanisms between contributors and later pensioners).

### Appendix II — Methodology: framework and modeling components (selected)
- Toolkit: Excel-based, deterministic projections adaptable to DB and DC schemes, supports transition modeling and automatic summary outputs.
- Population input: UN medium fertility variant in five-year age groups.
- Core assumptions (unless reforms analyzed): disability and survivor rates, labor force participation, size of formal sector, contribution rates, replacement rate for new pensioners (constant at latest value), average wage evolves with nominal GDP.
- No-policy-change scenario assumptions:
  - Age and gender employment patterns constant.
  - Average age of retirement fixed at each country’s current level.
  - Existing individual pensions indexed to CPI inflation rate (relaxed under reform scenarios).
- DC assumptions:
  - Income shares by quintile constant.
  - Minimum pension evolves with wages.
  - Life expectancy after retirement and average number of contributions per year constant at latest country-specific values.
  - Return on contributions equals implied interest rate from fixed discount factor and GDP growth.

### Selected formulas and modeling notes (headlines preserved)
- DB: number of pensioners computed from population exceeding average retirement age, participation, formal sector size, disability and survivor rates, and a correction term.
- DB benefits: new-pension average = replacement rate × average wage; average wage aligned with nominal GDP growth for t ≥ 2016.
- Indexation of existing beneficiaries uses three parameters: ߙ (to inflation), ߚ (to nominal wages), ߛ (other rules); example four-fifths inflation indexation = ߙ = 0.8, ߚ = 0, ߛ = 0.
- Contributions: average monthly contribution per person = total contribution rate × average wage; decomposition into employee, employer, and government components.
- DC per-capita account balance evolves with contributions and interest; annuity computed using constant discount factor and life expectancy after retirement.
- Healthcare projections: average per capita health cost index = weighted average across 21 five-year age groups; real per capita spending grows with real per capita GDP growth and excess cost growth factor.
- Reform impact on healthcare modeled as reduction in ECG; example decrease ݎܿ݁݀ = 0.5 percent starting 2016, phased over 5 years.

### Selected key numeric assumptions and values (reported exactly)
- Discount factor d: 1 percent.
- Excess cost growth (baseline): 1.00%.
- Decrease in excess cost growth for reform: 0.5 percent (starts 2016, takes 5 years).
- Increase in contribution rate (one-time): 1%.
- Projection horizon reference years: last known value 2015; projections to 2050.
- Retirement age (listed): 60, 60, 60, 60, 65 (Argentina, Brazil, Chile, Colombia, Mexico).
- Replacement rate (last available): 71.60%, 69.50%, 32.80%, 64.10%, 25.50% (Argentina, Brazil, Chile, Colombia, Mexico).
- Contribution rate (last available): 21.17%, 28.00%, 11.49%, 16.00%, 6.50% (Argentina, Brazil, Chile, Colombia, Mexico).
- Number of beneficiaries (last known): 18,962,523; 144,988,372; 13,612,038; 44,770,148; 118,617,542 (Argentina, Brazil, Chile, Colombia, Mexico).
- Health expenditure (percent of GDP, latest available): 4.17%, 4.24%, 3.31%, 4.98%, 3.10% (Argentina, Brazil, Chile, Colombia, Mexico).
- Average per capita health expenditure cost index (latest available): 1.25, 1.17, 1.29, 1.15, 1.11 (Argentina, Brazil, Chile, Colombia, Mexico).
- Life expectancy after retirement (latest available): -, -, 25, 20, 18 (Argentina, Brazil, Chile, Colombia, Mexico).
- DC contribution rate (statutory): -, -, 11.49%, 16.00%, 8.88% (where applicable).
- Minimum pension (statutory) examples: Chile 1,685,978; Colombia 7,732,200; Mexico 25,587.
- Average months of contributions per year (latest available) for Chile: 6.

*Source: wp1794 (IMF working paper content provided).*

### Appendix I. Addressing demographic uncertainty ....................................................................... 3

### Appendix I. Addressing demographic uncertainty

### Introduction and key demographic findings
- Increases in life expectancy over the last decades have been GOOD for societies’ wellbeing, driven by rising income levels, technological advances in medicine, and increases in public healthcare systems’ coverage.
- Example for five Latin-American economies analyzed (LAC5: Argentina, Brazil, Chile, Colombia and Mexico):
  - Average life expectancy at birth increased from 58 years in 1960 to 76 years in 2014 (Saad, 2009).
- There is a BAD aspect when rising life expectancy is combined with ongoing reductions in fertility rates.
  - Fertility rates decreased from 5.6 children per woman in 1960 to [text truncated in source].

### Demographic dynamics and policy relevance
- Longer lifespans and falling fertility jointly change age distributions and raise old-age dependency, with implications for public pension and healthcare systems.
- Demographic uncertainty matters for long-run fiscal projections because small differences in mortality or fertility trends can substantially affect:
  - The number of estimated pensioners.
  - Cash flows under defined benefit (DB) pension systems.
  - Government spending on public healthcare.
- Addressing demographic uncertainty requires explicit scenario analysis and sensitivity checks around mortality, fertility, and cohort size assumptions.

### Modeling components referenced (headings preserved from source)
- The appendix outlines methodologies used (headings only; detailed formulas and steps are in the source):
  - A. Defined benefit public pension scheme
    - The Number of Estimated Pensioners
    - Cash Flows Under a DB System
    - Contributions Under a DB System
    - Net Government Cash Flow Under a DB System
  - B. Alternative Pension Reforms on Government’s Cash Flows Under a DB System
    - Reduction in the Generosity of the Pension System
    - Reduction in the Indexation of Benefits
    - An Increase in the Contribution Rate
  - C. DC Pension Scheme
    - Per Capita Account Balance Under a DC System
    - Government Spending, Revenue and Net Cash Flow Under a DC System
  - D. Total Public Expenditure of Pension Systems
  - E. Healthcare Projections
  - F. Analyzing the Impact of Reforms on Healthcare Expenditure
  - G. Calibration to Implement Toolkit

### Analytical emphasis for readers and policymakers
- Quantitative projection modules focus on:
  - Translating demographic change into pensioner counts and age-specific entitlement streams.
  - Projecting DB and DC pension cash flows and net government fiscal impacts.
  - Projecting public healthcare expenditure and analyzing reform impacts.
  - Calibrating toolkit parameters to country-specific demographic and fiscal data.

*Source: Appendix I. Addressing demographic uncertainty — wp1794*

### 2.0 in 2014 for the LAC5): public finance pressures. Public pension systems have generally been

### wp1794 - 2.0 in 2014 for the LAC5): public finance pressures. Public pension systems have generally been

### Public finance pressures: overview and motivations
- Public pension systems were designed when the ratio of working to pension age population was particularly benign—a large contributing base with a significantly smaller beneficiary population.
- Ongoing demographic changes have resulted in growing old-age dependency ratios with a concomitant increase in public pension spending.
- Costs associated with the development of new healthcare technologies, tapped intensively by older cohorts, are adding substantial pressures to public coffers.
- Public finance pressures can become unpleasant in the absence of prompt measures to correct pension and healthcare funding gaps, given the typical long lags associated with reforms to social security systems.

### Objective and contributions of the paper
- Develop an integrated methodology to project long-term public pension cash flows and healthcare spending, illustrated for the LAC5.
- Estimate pension funding (from workers’ contributions) and pension and healthcare expenditures under a baseline (no policy changes) scenario.
- Provide a user-friendly toolkit to estimate fiscal implications of alternative reforms in both defined benefits (DB) and defined contribution (DC) pension systems, including:
  - Assessment of the fiscal cost of a minimum guaranteed pension under DC.
  - Quantification of fiscal implications of a migration from DB to DC.
  - Assessment of effects on the government budget of a stylized public healthcare system reform.
- Show versatility to incorporate country-specific features and applicability to a broad set of countries with relatively low data requirements, while noting the approach does not replace more granular country-specific analysis.

### Key illustrative results for the LAC5
- Among the LAC5, the negative impact of demographic changes on the public pension system will be most pronounced in Argentina and Brazil—both have maintained their defined-benefit pay-as-you-go (PAYGO) systems.
- In the absence of significant increases in pension contributions, countries will have to rely on:
  - Increases in the retirement age, and
  - Reductions in the indexation of benefits (among the most effective cost cutting measures),
  to mitigate public pension liabilities.
- Healthcare spending is expected to grow substantially in all these countries due to aging and the associated healthcare expense growth resulting from technological innovation outpacing output per capita growth—the so-called excess growth factor.
- Reforms that can help curb the excess growth factor (e.g., enhanced competition in the healthcare sector) could aid in containing healthcare spending.

### Pension system primer: definitions and risk allocation
- PAYGO system: current workers’ contributions are used to fund benefits to current retirees.
- Fully funded system: contributions of current workers purchase assets; accumulated stock and returns pay future benefits.
- DC (defined contribution): a worker’s benefits depend on accumulated assets and rate of return.
- DB (defined benefit): benefits determined by a fixed formula (total contributions, years worked, pension base, age at retirement, etc.); benefits do not depend on accumulated asset returns.
- Under public DB systems, government bears significant risks and must finance shortfalls via borrowing, tax increases, or reallocation of budgeted expenses.
- Under funded DC, uncertainty about future benefits is borne by the individual worker.
- Other configurations: PAYGO DC, DC/DB hybrids, multiple pillars, and varying public/private management structures.

### Demographic trends in the LAC5
- Medium-term shifts: falling fertility rates and rising life expectancy.
- Transition from high to low fertility and mortality can produce a temporary “demographic dividend” (higher labor force growth relative to dependent population).
- Continued fertility decline and longevity increases shift population to older-age distribution, contributing to sovereign pension and health spending pressures.
- Factors that can limit pressures: increases in labor force participation, savings rates, human capital investment, incentives to raise female participation, better health, and increases in retirement age.
- Old-age dependency ratio is expected to increase substantially (old-age dependency ratio defined as fraction of population aged 65+ over working-age population between 20 years and the retirement age).

### Integrated methodology and toolkit: inputs and core assumptions
- Projections use the medium fertility variant of the UN total population projections on an annual basis divided by five-year age groups.
- Total pension beneficiaries and contributors under DB or DC schemes calculated using population projections, labor force participation rates, size of the formal sector, and disability and survivor rates.
- Disability and survivor rates, labor force participation rates, size of the formal sector, and contribution rates under DC and DB systems are assumed constant at the latest known value unless a reform affecting these parameters is analyzed.
- Pension benefits and contributions under DB calculated using average wage and the replacement rate; replacement rate for new pensioners assumed constant at the latest known value; average wage evolves in line with nominal GDP.
- For current pensioners, the average pension to average wage ratio (benefits ratio) could change with pension benefits’ indexation.
- Inflation rate (assumed equal to the GDP deflator) and real GDP per capita growth are assumed constant from 2020 onwards at the average of 2016-20.
- In the no-policy change scenario:
  - Age and gender patterns of employment remain the same over the projection period.
  - Average age of retirement across genders fixed at each country’s current level.
  - Existing individual pensions are indexed to the CPI inflation rate (this assumption is relaxed in a reform scenario).
- Under DC:
  - Income shares of different population quintiles assumed constant throughout the projection horizon.
  - Minimum pension assumed to evolve in line with wages.
  - Life expectancy after retirement and average number of contributions per year assumed constant at the latest country-specific value.
  - Return of paid contributions assumed equal to an implied interest rate obtained from a combination of a fixed discount factor and GDP growth.
- Healthcare spending modeled with key drivers:
  - Demographic dynamics (age-specific healthcare spending and population age distribution).
  - Excess cost growth factor: per capita real healthcare spending growth above per capita real GDP growth, after controlling for population growth; largely driven by technological innovation and institutional factors.

### Country-specific LAC5 pension features (stylized facts)
- Argentina:
  - Only mandatory pillar is a PAYGO DB public scheme.
  - 1994 introduced DC system; reversed in 2008 with return to DB.
  - 2007 Moratoria Provisional allowed workers over statutory retirement age who had not met minimum contributions to pay outstanding payments; budget implications subsumed under other beneficiaries (including non-contributory) in the toolkit.
- Brazil:
  - Compulsory PAYGO DB system with separate sub-schemes for private sector workers and civil servants (analyzed together for simplicity).
  - Reforms in 1999, 2003, 2012, and 2015 reduced generosity; in the no-policy reform scenario the most recent reforms are partially implemented (e.g., retirement age set to 60 to account for 2015 reform incentives).
  - Voluntary pension saving accounts have been gradually created as a complementary pillar.
- Chile:
  - Reform switching from PAYGO DB to fully-funded DC introduced in 1980 (implementation started in 1981).
  - Cohorts contributing to DB in the five years before reform could choose DC and received “recognition bonds”; first contributing cohort to DC assumed as 1976, retiring after 40 years in 2016.
  - Coexistence of DB and DC systems throughout projection period; 2008 “solidarity pillar” introduced targeting poorest 60 percent to finance benefits for those who never contributed or have too low contributions.
- Mexico:
  - 1997 reform introduced DC system; active workers at reform could opt for DB or DC upon retirement.
  - For simplicity, first pensioners under the new DC assumed to start retiring at age of 65 (entering labor market at 20 and after 45 years of contributions).
  - Participants who contributed to the old DB remain in that system; only new cohorts enter DC.
  - To address old-age poverty, Mexico introduced Pension Universal.

### Projections, reform scenarios, and comparisons
- The paper summarizes projections of pension cash flows under a no-policy change scenario (beyond recently implemented legislatives) as the basis for analyzing alternative reform scenarios.
- Healthcare spending projections provided under no-policy change and reform scenarios; reforms aiming at curbing excess cost growth can materially affect healthcare spending trajectories.
- Methodology compared with IMF’s Fiscal Affairs and Western Hemisphere Departments projections (IMF, 2016; IMF, 2017); found to produce adequate ballpark estimates and to compare well, while remaining simpler and requiring fewer data.
- The approach remains highly stylized to balance simplicity and applicability; more granular models may be preferable for short-run accuracy or detailed policy design.

*Source: Excerpt from wp1794 (IMF working paper) content provided.*

### 2015. Under this program, retirees 65 years of age or older could be entitled to a minimum

### wp1794 - 2015. Under this program, retirees 65 years of age or older could be entitled to a minimum guaranteed pension (MGP) (IMSS, 2016).

### A. Pensions baseline results
- Baseline projections for LAC5 public pension cash flows (methodology in Appendix):
  - Between 2015-50 Argentina and Brazil’s net cash flows are projected to worsen to close -4 and -22 percent of GDP, respectively.
  - For the other LAC5, the balance is projected to stay constant or improve.
- Revenue dynamics:
  - Revenues are expected to grow continuously in Argentina and exhibit an inverted U-shape in Brazil (driven by working-age population dynamics).
  - Colombia (hybrid DC/DB) exhibits constant revenue flows as share of GDP during the projection period.
  - In pure DC systems: revenues negligible for Chile (system introduced earlier) and declining trend for Mexico (transition to DC completed).
- Despite some countries not showing a worsening balance over time, the present discounted value (PDV) of system cash flows over the projection horizon is negative and substantial.
  - PDV calculations assume a constant discount factor of 1 percent.

### B. Pensions reform scenarios — overview
- Reforms analyzed (parametric and structural):
  - Parametric: onetime increase in retirement age; indexation of retirement age; reduction in replacement rate; reduction in indexation of benefits; increase in contribution rate.
  - Structural: transition from DB PAYGO to funded DC system; introduction of individual accounts; fiscal cost of minimum guaranteed pension (MGP) under DC.
- Methodology focuses on population distribution as given; behavioral responses and wage-distribution dynamics are not modeled in full.

### Increase in retirement age (one-time + phased)
- Reform design:
  - Onetime increase of DB retirement age by 5 years, transition spread over 10 years (2016-25).
- Impacts:
  - On average reduces pension spending in 2050 by 2.2 percent of GDP relative to baseline.
  - Biggest reductions:
    - Brazil: 7.5 percent of GDP reduction in 2050.
    - Argentina: 3.0 percent of GDP reduction in 2050.
  - Smaller improvements for Chile and Mexico attributed to prior shift to DC schemes (DB expenditure small; DC public expenditure linked to government MGP low).

### Indexation of retirement age
- Reform design:
  - Starts in 2026 (2016-26 remains at current level); automatic increases in retirement age tied to increases in average age of retirees (annual augmentation equal to the increase in average age of those retired).
- Impacts:
  - Average reduction of public pension expenditure: 1.1 percent of GDP.
  - Largest gain projected for Brazil: 4.2 percent of GDP.
  - Almost no gains for Chile and Mexico (small DB share).

### Reduction of replacement rate
- Reform design:
  - In DB schemes, replacement rate for new pensioners falls by 0.5 percentage points every year for 10 years (2016-25), so from 2025 onwards its level is 5 percentage points lower than baseline.
- Impacts:
  - On average, reduction of pension spending equals 0.7 percent of GDP.

### Reduction in the indexation of benefits
- Reform design:
  - Pensions of existing pensioners indexed at fourth-fifths of inflation (baseline: full indexation); reform in place from 2016 through projection horizon.
- Impacts:
  - Average reduction in pension spending equals 1.7 percent of GDP.
  - Larger gains in Argentina and Brazil; moderate gains in countries with DC systems.

### Increase in contribution rate
- Reform design:
  - Permanent increase of 1 percentage point in contribution rate, implemented in 2016.
- Impacts and interpretation:
  - For pure DB systems, impact is on revenue side; for pure DC systems, impact shows up through reduced government spending because higher contributions raise accumulated savings and lower the number of beneficiaries below MGP.
  - Effect most significant for Argentina and Brazil; small for Chile, Colombia, Mexico.

### Dependency-indexed contribution rate (self-correcting contribution)
- Design:
  - Contribution varies proportionally with changes in dependency ratio; interpreted as the contribution needed to close PAYGO underfunding and balance the system over time (calculated for Argentina and Brazil).
- Illustrative required increases:
  - To achieve pension system balance in 2015:
    - Argentina: contribution rate would have to increase from 21 percent to 39 percent of average wage.
    - Brazil: contribution rate would have to increase from 28 percent to 34 percent of average wage.
  - By 2050 (as old-age dependency ratio rises), contribution rates would need to reach:
    - Argentina: 45 percent of average wage.
    - Brazil: 115 percent of average wage.
- Conclusion: relying exclusively on contribution increases would require unfeasible hikes.

### Cumulative impact of introducing all reforms simultaneously
- Reforms introduced simultaneously: (i) onetime increase in retirement age; (ii) indexation of retirement age; (iii) reduction of replacement rate; (iv) reduction in indexation of benefits; (v) onetime increase in contribution rate.
- Interaction and second-round effects:
  - Policies can offset or reinforce each other; simultaneous adoption produces second-round effects (interaction terms) that change the net impact relative to the simple sum of separate impacts.
  - Examples:
    - Argentina:
      - Onetime increase in retirement age reduces 2050 expenditure by 3.0 percent of GDP.
      - Reduction in indexation of benefits reduces 2050 expenditure by 3.3 percent of GDP.
      - Sum of these separate reforms = 6.3 percent of GDP; simultaneous introduction yields cumulative impact = 5.5 percent of GDP.
      - Reported second-round effect: 1.5 (from Table 8).
    - Brazil:
      - Onetime increase in retirement age reduces 2050 expenditure by 7.5 percent of GDP.
      - Reduction in indexation of benefits reduces 2050 expenditure by 5.0 percent of GDP.
      - Sum of these separate reforms = 12.5 percent of GDP; simultaneous introduction yields cumulative impact = 11.3 percent of GDP.
      - Reported second-round effect: 3.3 (from Table 8).
- Overall message: simultaneous reforms can yield less-than-additive savings because, e.g., raising retirement age reduces the stock of pensioners to whom benefit-indexation reforms apply.

### Transition from a PAYGO DB to a funded DC system
- Motivation:
  - Pressure from demographic and fiscal trends; desire to boost savings and potential investment/growth.
- Challenges:
  - Financing benefits to cohorts already retired or close to retirement during transition.
  - Political/social risks from potentially low retirement benefits under private DC systems (example: protests in Chile).
  - Fiscal burden of a minimum guaranteed pension (MGP) under DC systems.
- Scenarios analyzed for Argentina and Brazil (PAYGO DB countries):
  - Full shift to private DC system: cohorts entering labor market from 2020 contribute only to the funded DC system.
  - Partial transition: 50 percent of new entrants post-2020 contribute to old DB; 50 percent to new DC.
  - Projection horizon extended to 2100 because first DC cohorts start retiring in 2060; contribution rates in the DC system set equal to old DB rates.
  - Assumption: to access MGP, participants must have contributed (non-contributory MGP ruled out).
- Transitional fiscal dynamics:
  - Short run: pension system balances worsen (transition costs).
  - Long run: DC transition (full or partial) has a positive and substantial impact on sustainability; private savings increase as accumulated stock in individual accounts rises, more than compensating higher public sector pension deficit during transition.

### Country-specific MGP and non-contributory rules (design considerations)
- Mexico and Chile:
  - Under their frameworks, retirees in DC whose accumulated savings do not provide enough funds to meet a monthly pension above an MGP threshold receive the MGP even if they have never contributed.
- Colombia:
  - Under private account regimes, a person who has never contributed is not entitled to a government pension (Asofondos, 2016); therefore, no additional spending need be accounted for in that respect.

### Policy implications (high-level)
- Aging and DB system structures create substantial long-run fiscal pressures; PDV of cash flows is negative in all cases.
- Parametric reforms (retirement age, indexation, replacement rates, contribution rates) can materially reduce long-term spending, especially in DB-dominant countries (Argentina, Brazil).
- Contribution-rate increases alone would be politically and economically challenging due to large required hikes (dependency-indexed examples).
- Combining reforms produces interaction effects; sequencing and combination matter for realized savings.
- Transitioning to funded DC systems improves long-run sustainability and raises private savings but entails short-run fiscal costs and distributional/political trade-offs (necessitating careful design, possible MGP arrangements, and financing of transition costs).

*Source: IMF staff calculations and analysis as presented in the supplied content.*

### Section VI).

### Section VI)

### Key stylized facts about healthcare systems in LAC5
- Healthcare services are provided by a combination of private and public subsystems in the LAC5 countries; the methodology focuses only on the public spending subcomponent.
- Public spending subcomponent shares of total healthcare spending (World Bank, 2016):
  - Brazil: 46 percent
  - Chile: 75 percent
- Majority of the population relies on the public healthcare system:
  - Argentina: 46 percent of total population
  - Mexico: close to 100 percent of total population
- Funding sources are heterogeneous across countries: contributions and payroll taxes, general taxes, copayments.
  - Chile: mandatory contributions, two forms of co-payments, and general taxes.
  - Argentina: public healthcare sector mostly financed through general taxes.
  - Mexico: multiple public institutions; IMSS financed by government, employers and employees’ contributions; other institutions rely mainly on the government and sometimes out-of-pocket payments.
  - Colombia and Brazil: funding is a mixture of contributions and resources from the public budget.
- Age-specific spending index used in projections: assumed equal to the OECD average for all LAC5.

### Healthcare baseline results
- Baseline assumption for excess cost growth (ECG): 1 percent constant (Clements, Coady, & Gupta, 2012).
- Projected increase in public sector healthcare costs in LAC5 during 2015-50:
  - Average increase: 4.1 percent of GDP
- Drivers of the increase:
  - Roughly half of the increase is estimated to be due to the excess cost growth factor.
  - Roughly half is due to pure demographics.
- Country-specific 2015-50 increases (projection range):
  - Mexico: increase of 3.1 percent of GDP
  - Colombia: increase of 5.3 percent of GDP
- Methodological inputs:
  - Projections based on total number of beneficiaries, OECD-based age-specific spending index, and the excess cost growth factor.

### Healthcare reform scenario (reductions in excess cost growth)
- Reform illustrated: reduction of the excess cost growth factor by 0.5 percentage points starting in 2016 for all countries.
- Projected fiscal impact of reform (2015-50):
  - Average reduction in healthcare spending: 0.8 percentage points of GDP
  - Point estimates range: 0.5 to 1.0 percentage points of GDP depending on the country
- Possible policy measures to curb public healthcare spending:
  - Setting caps on certain services or treatments.
  - Moving parts of the healthcare system to the central level to limit hospital autonomy over budgets.
  - Promoting competition between health service providers where public contract systems exist.
  - Fostering incentives for private insurers to offer varied medical plan insurances to increase competition (Clements, Coady, & Gupta, 2012).

### Comparison with other projections
- Projections compared: AEW (Acosta-Ormaechea, Espinosa-Vega and Wachs), FAD (Fiscal Affairs Department), WHD (Western Hemisphere Department).
- FAD projections: cross-country methodology using public spending, macroeconomic and pension indicators, and demographic identities.
- WHD projections: largely incorporate detailed country-specific information provided by authorities.
- Calibration: levels of public pensions and healthcare expenditure as a share of GDP in 2015 in AEW projections equal those of WHD for comparability.
- Observations:
  - Public pension expenditure projections show similar general trends across AEW, FAD, WHD, with notable differences:
    - AEW projections for Brazil are noticeably higher than WHD or FAD starting in 2030; about 60 percent of the difference is due to differences in pensions’ indexation parameters.
    - If real GDP growth rate is set equal to WHD’s, the difference in pension expenditure projections by 2050 drops to 4 percent of GDP for Brazil.
    - Remaining differences attributed to higher number of beneficiaries projected in AEW (demographics) and possible differences in replacement rate assumptions.
    - In Chile and Mexico discrepancies in beneficiary evolution explain divergences in outer years.
  - Public healthcare expenditure projections are much closer across approaches:
    - Healthcare projections are driven primarily by the evolution of the excess cost growth factor and the number of beneficiaries (demographics), and are less sensitive to macroeconomic parameter differences.

### Concluding remarks and policy implications
- Demographic shifts will have significant fiscal implications for LAC5 countries.
- Two sided effect:
  - Positive: longer and healthier lives.
  - Negative: increasing burden of age-related rising costs on public finances; many pension and healthcare systems are not designed for rapidly rising dependency ratios.
- Healthcare costs are projected to outpace economic growth, adding to government balance pressures.
- Project findings for LAC5:
  - Projected increases in pension spending are especially pronounced for Brazil and Argentina (the two with pure DB PAYGO systems).
  - Countries with at least partially introduced DC systems, like Colombia and Mexico, are expected to face less severe public spending pressures over the long run.
- Suggested reforms to tackle aging-related fiscal pressures:
  - Argentina and Brazil might consider an increase in the retirement age.
  - Reduction in the indexation of benefits.
  - Shift to a DC system (total or partial), following other Latin-American examples.
  - Careful evaluation of reforms to address healthcare expenditure pressures associated with aging and technological-driven cost growth (excess cost growth factor).

### Appendix I — Addressing demographic uncertainty
- Approach: two alternative scenarios of pension expenditure using the high and low fertility variants of the UN population projections; projection horizon extended to 2100.
- Assumptions:
  - New cohorts enter the labor market at age 20 and start retiring at age 60.
  - Effects on contributors and balance observable starting in 2036 (when new cohorts enter the labor market).
  - Effects on expenditure observable starting in 2076 (when new cohorts start to retire).
- Key results:
  - The impact of higher (lower) fertility on the pension system cash flow peters out over time for both Argentina and Brazil.
  - Example mechanism: increased fertility raises the number of contributors (positive effect) but is later offset by higher number of pensioners when cohorts reach retirement age.
- Figures presented: time series of pension expenditure, pension contributions, and pension system net cash flow for Argentina and Brazil under medium, high and low fertility variants (percent of GDP).

*Source: Section VI). wp1794 - Section VI).*

### APPENDIX II. METHODOLOGY FOR PUBLIC PENSION AND HEALTHCARE PROJECTIONS

### APPENDIX II. METHODOLOGY FOR PUBLIC PENSION AND HEALTHCARE PROJECTIONS

### Framework overview
- Toolkit: fairly simple yet comprehensive Excel-based toolkit producing short- to medium-term deterministic projections and flexible long-term projections adaptable to cross-country features.
- Applicability: public pension system projections apply to both DB schemes—assumed public PAYGO—and DC schemes (private or public). Reform transitions from DB to DC can be modeled with transition dynamics and coexistence.
- Outputs: automatic summary tables and charts comparing baseline and reform scenarios.

### A. Defined benefit (DB) public pension scheme — population and beneficiaries
- Pension-age population: cohorts whose age equals or exceeds the country-specific retirement age; effective retirement age is used instead of the official retirement age.
- Beneficiary groups: retirees, survivors, and permanently disabled workers in the formal sector.
- Calibration/correction: a correction term between 2010-15 can be included to better match observed initial-year figures; correction based on the latest known value of total pensions spending.

- Number of pensioners receiving government benefits (as given in source notation):
  ݌_݂݊ܤ
  ௧
  ݌݋ܲ_݊݁ܲ
  ௧
  ∗ݏ݂∗݌݈∗
  ሺ
  ݎݏ൅ݎ݀1൅
  ሻ
  ݎݎ݋ܿ_݂݊ܤ൅
  ௧
  , 
  - where ݌_݂݊ܤ
  ௧
  is total beneficiaries; ݌݋ܲ_݊݁ܲ
  ௧
  is population exceeding average retirement age; ݌݈ is labor force participation rate; ݏ݂ is formal sector size; ݎ݀ is rate of permanently disabled workers in formal sector; ݎݏ is survivor rate of pensioners; ݎݎ݋ܿ_݂݊ܤ
  ௧
  is correction term; subscript t refers to time (years).

- DB/DC coexistence rules:
  - Mandatory DC: full shift modeled considering that employees who already started contributing to DB and are not shifted remain in DB until death; new cohorts enter DC; full shift completes only after death of all DB participants; parallel coexistence modeled during transition.
  - Non-mandatory DC: population divided using constant shares; already retired or already-contributing individuals remain in DB; new cohorts split according to calibrated constant shares.

### Cash flows under a DB system — pensions
- Average monthly pension for new beneficiaries in year t (source notation preserved):
  ܾ݊_ܾ݀_݊݁ܲ_ݒܣ
  ௧
  ∗ݎݎൌ
  ஺௩_௪௔௚௘
  ೟
  ଵଶ
  , 
  - rr is the replacement rate for new retirees; ݁݃ܽݓ_ݒܣ
  ௧
  is average wage in year t.

- Average wage calculation for t ≤ 2016:
  ݁݃ܽݓ_ݒܣ
  ௧
  ೌ
  ್
  ೟
  ೌ
  ್
  ೟
  ಽ஽௉_௡
  ೟
  ∗௪௦
  ற௠௣௟
  ೟
  , 
  - where ݊_ܲܦܩ
  ௧
  is nominal GDP in local currency; ws is share of compensation of employees to GDP; ݈݌݉ܧ
  ௧
  is total employment.

- Total employment calculation:
  ݈݌݉ܧ
  ௧
  ൌ
  ሺ
  ݑ1െ
  ሻ
  ݌݋ܲ_݇ݎ݋ܹ∗݌݈∗
  ௧
  , 
  - where u is unemployment rate and ݌݋ܲ_݇ݎ݋ܹ
  ௧
  is total working-age population.

- For t ≥ 2016: average monthly wage growth aligned with nominal GDP growth rate ݊_݃
  ௧
  :
  ݁݃ܽݓ_ݒܣ
  ௧
  ݁݃ܽݓ_ݒܣ	ൌ
  ௧ିଵ
  ∗
  ሺ
  ݊_݃1൅
  ௧
  ሻ
  , 
  - nominal GDP growth ݊_݃
  ௧
  is product of real per capita GDP growth ܿ݌݃
  ௧
  , population growth ݌݋݌_݃
  ௧
  , and inflation ߨ
  ௧
  :
  ݊_݃
  ௧
  ൌ	
  ሺ
  ܿ݌݃1൅
  ௧
  ሻ
  ∗ቀ1൅݃
  ௣௢௣
  ௧
  ቁ∗
  ሺ
  ߨ1൅
  ௧
  ሻ
  ൌ1. 

- Indexation of existing beneficiaries by cohort:
  ܾ݁_ܾ݀_݊݁ܲ_ݒܣ
  ௧
  ௖
  ܾ݀_݊݁ܲ_ݒܣൌ
  ௧ିଵ
  ௖
  ∗
  ሺ
  ߨ1൅
  ௧
  ߙ∗
  ሻ
  ∗
  ሺ
  ݓ1൅
  ௧
  ߚ∗
  ሻ
  ∗ሺ1൅ߛሻ
  - where ߙ determines indexation to inflation, ݓ
  ௧
  is nominal wage growth, ߚ determines indexation to nominal wages, and ߛ accounts for other country-specific rules. Example: indexation only to current inflation implies ߙൌ1, ߚൌ0, ߛൌ0.

- Average pension for all beneficiaries (new and existent) is a weighted average using cohort beneficiary counts (source notation preserved).

- Total benefits under DB system:
  ܾ݀_݂݁݊݁ܤ_ݐ݋ܶ
  ௧
  ܾ݀_݊݁ܲ_ݒܣൌ
  ௧
  ܾ݀_݌_݂݊ܤ∗
  ௧
  ∗12, 
  - where ܾ݀_݌_݂݊ܤ
  ௧
  is total number of pensioners under DB in year t. When DB and DC coexist, ܾ݀_݂݁݊݁ܤ_ݐ݋ܶ
  ௧
  constitutes the share of total beneficiaries ݌_݂݊ܤ
  ௧
  .

### Contributions under a DB system
- Number of formal sector contributors to DB:
  ܾ݀_ݎݐ݊݋ܥ
  ௧
  ܾ݀_݌݋ܲ_݇ݎ݋ܹൌ
  ௧
  ݏ݂∗݌݈∗, 
  - where ܾ݀_ݎݐ݊݋ܥ
  ௧
  is number of pension system participants in DB and ܾ݀_݌݋ܲ_݇ݎ݋ܹ
  ௧
  is working-age population of cohorts assigned to DB.

- Average monthly contribution per person in local currency:
  ܾ݀_ݎݐ݊݋ܥ_ݒܣ
  ௧
  ∗ܾ݀_ݎܿൌ
  ஺௩_௪௔௚௘
  ೟
  ଵଶ
  , 
  - where ܾ݀_ݎܿ is total contribution rate under DB.

- Total contributions:
  ܾ݀_ݎݐ݊݋ܥ_ݐ݋ܶ
  ௧
  ܾ݀_ݎݐ݊݋ܥ_ݒܣൌ
  ௧
  ܾ݀_ݎݐ݊݋ܥ∗
  ௧
  ∗12. 

- Contribution rate decomposition (source notation):
  ݃_ܾ݀_ݎܿ൅ݎ݁_ܾ݀_ݎܿ൅݁݁_ܾ݀_ݎܿൌܾ݀_ݎܿ
  - where ݁݁_ܾ݀_ݎܿ is employee rate, ݎ݁_ܾ݀_ݎܿ is employer rate, and ݃_ܾ݀_ݎܿ is government rate.

### Net government cash flow under a DB system
- Defined as the difference between total contributions and total benefits.

### B. Alternative pension reforms and impacts on government cash flows (DB system)
- Five pension reforms analyzed (stand-alone or combined). Source details provide formulas for specific reforms; two are summarized below.

- Onetime increase in retirement age:
  - Increase by ݎܿ݊݅ years; example case uses 5 years.
  - Phased in over 10 years (between 2016-25).
  - Affects only number of old-age pensioners and working-age population by shifting timing when cohorts become beneficiaries.
  - Pension-age population under reform (source notation):
    ܾ݀_݌݋ܲ_݊݁ܲ
    ௧
    ௥
    ܾ݀_݌݋ܲ_݊݁ܲൌ
    ௧
    ್
    ሺ
    ௧ି௧଴
    ሻ
    ଵ଴
    ∗
    ್ೋ௘௙௢௥௠_஺௚௘
    ೟
    ہ
    ݎܿ݊݅∗  
  - Working-age population under reform (source notation):
    ܾ݀_݌݋ܲ_݇ݎ݋ܹ
    ௧
    ௥
    ܾ݀_݌݋ܲ_݇ݎ݋ܹൌ
    ௧
    ್
    ൅
    ሺ
    ௧ି௧଴
    ሻ
    ଵ଴
    ∗
    ್ೋ௘௙௢௥௠_஺௚௘
    ೟
    ہ
    ݎܿ݊݅∗, 
  - 0ݐ is year preceding reform (in example, 2015); ݁݃ܣ_݉ݎ݋݂ܴ݁
    ௧
    is five-year age cohort affected; if ݎܿ݊݅ exceeds five years, formulas adjusted to account for multiple five-year cohorts.

- Permanent indexation of the retirement age:
  - At every year t, the official retirement age increases by the difference between the average age of those who reached/exceeded the initial retirement age in year t and in year ݐ-1.
  - Effective retirement age is assumed equally affected and used in calculations.
  - Reform assumed to enter into effect in 2026; impact occurs after any rise in retirement age takes place.
  - Working-age and pension-age populations under this reform are given in source notation using indexed effective retirement age ܽݎ
    ௧
    ௥
    , where:
    ܽݎ
    ௧
    ௥
    ܽݎൌ
    ௧ିଵ
    ௥
    ݒܽ൅ሺ
    ௧ିଵ
    ݒܽെ
    ௧
    ሻ,  
    - meaning indexed effective retirement age in year t equals its value in year t-1 plus difference between average age of those retired (ݒܽ
    ௧
    ) between years t and t-1.

*Italic source attribution: APPENDIX II. METHODOLOGY FOR PUBLIC PENSION AND HEALTHCARE PROJECTIONS (content unit: wp1794).*

### introduction of the reform, but these also take into account the reform of the increase in the

### wp1794 - introduction of the reform, but these also take into account the reform of the increase in the

### Reduction in the Generosity of the Pension System
- Reform affects only DB systems.
- Replacement rate of new pensioners is reduced linearly by a constant value, ݀݁ݎ, every year throughout a chosen horizon equal to 10 years.
- If reform implemented, in years 2016-25 the replacement rate equals:
  - ݎݎ
    ௧
    ݎݎൌ
    ௧ିଵ
    ݀݁ݎെ
- For ݐ൐2025:
  - ݎݎ
    ௧
    ݎݎൌ
    ௧ିଵ
- After the reform the replacement rate stays at a lower level through the projection horizon.

### Reduction in the Indexation of Benefits
- Reform reduces the indexation coefficient of the average pension for existent beneficiaries according to the formula:
  - ܾ݁_ܾ݀_݊݁ܲ_ݒܣ
    ௧
    ௖
    ܾ݀_݊݁ܲ_ݒܣൌ
    ௧ିଵ
    ௖
    ∗
    ሺ
    ߨ1൅
    ௧
    ߙ∗
    ሻ
    ∗
    ሺ
    ݓ1൅
    ௧
    ߚ∗
    ሻ
    ∗ሺ1൅ߛሻ
- Parameters ߙ, ߚ and ߛ chosen so indexation is reduced relative to baseline.
- Example: baseline indexation only to current inflation (ൌ1ߙ, ൌ0ߚ, ߛൌ0); to update pensions at four-fifths of inflation set ߙൌ0.8, ൌ0ߚ and ߌൌ0ߛ.
- Assumptions:
  - Reform starts in 2016 and affects only current pensioners.
  - New pensioners receive DB benefits according to replacement rate and average wage (unaffected by this reform).

### An Increase in the Contribution Rate
- Increase takes effect in 2016; permanent, immediate, one-time increase in total contribution rate.
- Assumed increase equals 1 percentage point.
- Contribution rate for 2016 equals:
  - ܾ݀_ݎܿ
    ଶ଴ଵ଺
    ܾ݀_ݎܿൌ
    ଶ଴ଵହ
    ௅1%
- Stays at that level until end of projections.
- For ݐ ൐2016:
  - 36 
  - ܾ݀_ݎܿ
    ௧
    ܾ݀_ݎܿൌ
    ௧ିଵ

### C. DC Pension Scheme — Per Capita Account Balance Under a DC System
- Working-age population divided into quintiles q and five-year age cohorts c.
- Contribution per capita of quintile q in year t:
  - ܿ݀_ݎݐ݊݋ܥ_ݒܣ
    ௧
    ௤
    ݏ݅	ൌ
    ௤
    ݁݃ܽݓ_ݒܣ∗
    ௧
    ܿ݀_ݎܿ∗
  - ݏ݅
    ௤
    is income share of quintile q; ܿ݀_ݎܿ is contribution rate of DC system.
- Per capita private account balance of quintile q and cohort c, ݈ܾ݁ܿ݊ܽܽ_ݐ݊ݑ݋ܿܿܣ
  ௤
  ௖
  , each year:
  - ݈ܾ݁ܿ݊ܽܽ_ݐ݊ݑ݋ܿܿܣ
    ௤
    ௖
    ݈ܾ݁ܿ݊ܽܽ_ݐ݊ݑ݋ܿܿܣ	ൌ
    ௤
    ௖
    ∗
    ሺ
    ݅1൅
    ௧
    ሻ
    ܿ݀_ݎݐ݊݋ܥ_ݒܣ	൅
    ௧
    ௤
    12/ݕܿ∗
  - ݅
    ௧
    is interest rate; ݕܿ is number of contributions per year (captures unemployment and temporary interruptions).
- Account balance grows until year before retirement; annuity calculated using balance for life expectancy after retirement ܿ݀_݊݁ܲ_ݒܣ
  ௤
  ௖
- Average yearly pension per capita ܿ݀_݊݁ܲ_ݒܣ
  ௤
  ௖
  is derived assuming constant discount factor ݂݀ and country-specific expected life span after retirement n:
  - ݈ܾ݁ܿ݊ܽܽ_ݐ݊ݑ݋ܿܿܣ
    ௤
    ௖
    ൌ	
    ஺௩_௉௘௡_ௗ௖
    ੜ
    ੎
    ሺଵାௗ௙ሻ
    భ
    ൅
    ஺௩_௉௘௡_ௗ௖
    ੜ
    ੎
    ሺଵାௗ௙ሻ
    మ
    ൅⋯൅
    ஺௩_௉௘௡_ௗ௖
    ੜ
    ੎
    ሺଵାௗ௙ሻ
    ೙

### Government Spending, Revenue and Net Cash Flow Under a DC System
- Public pension expenditure under DC:
  - Either total pensions (public notional DC) or only government contribution to minimum pension (private DC).
- Government contingent liability: minimum guaranteed pension.
- Total government contribution in year t, ݎݐ݊݋ܥ_ݒ݋ܩ
  ௧
  , equals sum over quintiles q and cohorts c of average per capita government contributions times number of beneficiaries:
  - ݎݐ݊݋ܥ_ݒ݋ܩ
    ௧
    ൌ
    ∑∑
    ݊݁ܲ_݊݅ܯቀ
    ௧
    ܿ݀_݊݁ܲ_ݒܣെ
    ௧
    ௤
    ௖
    ݀ቁ∗
    ௧
    ௤
    ௖
    ܿ݀_݌_݂݊ܤ∗
    ௧
    ௤
    ௖
    ௦
    ௖ୀଵ
    ହ
    ௤ୀଵ
- Indicator ݀
  ௧
  ௤
  ௖
  = 1 when average pension ܿ݀_݊݁ܲ_ݒܣ
  ௧
  ௤
  ௖
  is lower than minimum pension ݊݁ܲ_݊݅ܯ
  ௧
  ; otherwise zero.
- ܿ݀_݌_݂݊ܤ
  ௧
  ௤
  ௖
  is number of beneficiaries under DC system (evaluated for time t, q, c).
- Public notional DC: government collects contributions and pays benefits.
  - Total benefits, ܿ݀_݂݁݊݁ܤ_ݐ݋ܶ
    ௧
    :
    - ܿ݀_݂݁݊݁ܤ_ݐ݋ܶ
      ௧
      ൌ
      ∑∑
      ܿ݀_݊݁ܲ_ݒܣ
      ௧
      ௤
      ௖
      ܿ݀_݌_݂݊ܤ∗
      ௧
      ௤
      ௖
      ௦
      ௖ୀଵ
      ݎݐ݊݋ܥ_ݒ݋ܩ	൅
      ௧
      ହ
      ௤ୀଵ
- Total contributions, ܿ݀_ݎݐ݊݋ܥ_ݐ݋ܶ
  ௧
  :
  - ܿ݀_ݎݐ݊݋ܥ_ݐ݋ܶ
    ௧
    ൌ
    ∑∑
    ܿ݀_ݎݐ݊݋ܥ_ݒܣ
    ௧
    ௤
    ௖
    ܾ݀_݌_݋ܲ_݇ݎ݋ܹ∗
    ௧
    ௤
    ௖
    ௦
    ௖ୀଵ
    ହ
    ௤ୀଵ
- Balance in year t = total contributions − total benefits.

### D. Total Public Expenditure of Pension Systems
- Public liabilities equal relevant component(s) of expenditures described.
- Transition from public DB PAYGO to private fully-funded DC:
  - Total expenditure, ݂݁݊݁ܤ_ݐ݋ܶ
    ௧
    :
    - ݂݁݊݁ܤ_ݐ݋ܶ
      ௧
      ܾ݀_݂݁݊݁ܤ_ݐ݋ܶ	ൌ
      ௧
      ݎݐ݊݋ܥ_ݒ݋ܩ	൅
      ௧
- Transition from public DB PAYGO to public notional DC:
  - Total expenditure includes payment of all regular pensions from accumulated contributions:
    - ݂݁݊݁ܤ_ݐ݋ܶ
      ௧
      ܾ݀_݂݁݊݁ܤ_ݐ݋ܶ	ൌ
      ௧
      ܿ݀_݂݁݊݁ܤ_ݐ݋ܶ	൅
      ௧

### E. Healthcare Projections — Building Blocks and Formulas
- Key inputs: number of beneficiaries and health cost index (relative to newborns).
- Number of beneficiaries grows in line with population (UN medium fertility variant).
- Average per capita health expenditure cost index relative to reference group, ܿ݌_ݒܽ_ݔ݁݀݊݅_ݐݏ݋ܿ
  ௧
  , computed as weighted average across 21 five-year age groups:
  - ܿ݌_ݒܽ_ݔ݁݀݊݅_ݐݏ݋ܿ
    ௧
    ൌ
    ∑
    ௉௢௣
    ೎
    ೟
    ∗௖௢௦௧_௜௡ௗ௘௫_௔௩
    ೎
    ∑
    ௉௢௣
    ೎
    ೟
    మభ
    ೎సభ
    ଶଵ
    ௖ୀଵ
- Real per capita spending for reference group in first year:
  - ݎ_݂݁ݎ_݌ݔܧ
    ௧
    ൌ
    உ௘௔௟௧௛_ୣ୶୮_௥
    ೟
    ஻௡௙_௛
    ೟
    ∗௖௢௦௧_௜௡ௗ௘௫_௔௩_௣௖
    ೟
- ݎ_݌ݔ݁_݄ݐ݈ܽ݁ܪ
  ௧
  is actually incurred real health expenditure.
- Nominal public health expenditure, ݊_݌ݔ݁_݄ݐ݈ܽ݁ܪ
  ௧
  , equals:
  - ݊_ܲܦܩൌ
    ௧
    ݐ݄݁∗
    ௧
    ݌݄݁∗
    ௧
  - where ݐ݄݁ is nominal GDP, ݌݄݁ is total health expenditure as percent of GDP, and ݌݄݁ is share of public spending in total health expenditure (latest known value).
- Real per capita spending grows in line with real per capita GDP growth ܿ݌݃
  ௧
  and excess cost growth factor݃ܿ݁, via:
  - ݎ_݂݁ݎ_݌ݔܧ
    ௧
    ݎ_݂݁ݎ_݌ݔܧൌ
    ௧ିଵ
    ∗
    ሺ
    ݃ܿ݁1൅
    ሻ
    ܿ݌݃∗ሺ1൅
    ௧
    ሻ
- Total real public health expenditure in year t:
  - ݎ_exp_݄ݐ݈ܽ݁ܪ
    ௧
    ݄_݂݊ܤൌ
    ௧
    ݎ_݂݁ݎ_݌ݔܧ∗
    ௧
    ܿ݌_ݒܽ_ݔ݁݀݊݅_ݐݏ݋ܿ∗
    ௧
- Nominal public health expenditure = real public health expenditure adjusted by inflation.
- Healthcare spending growth decomposition:
  - Share related to excess cost growth, ݃ܿ݁_ݏ, calculated by formulae in text.
  - Share related to population aging equals growth rate of average per capita healthcare index relative to reference group; computed via provided multiyear formulae with n = number of years between last known value (2015) and last projection year (2050). Subscript t1 refers to 2015.

### F. Analyzing the Impact of Reforms on Healthcare Expenditure
- Reforms reducing healthcare expenditure are modeled as reductions in the excess cost growth factor.
- Decrease in this factor, ݎܿ݁݀, set to 0.5 percent, starts in 2016 and takes 5 years.
- Therefore between 2016-20 excess cost growth ݃ܿ݁ equals:
  - ݃ܿ݁
    ௧
    ݃ܿ݁ൌ
    ௧ିଵ
    ્
    ௗ௘௖௥
    ହ
- Stays at that level from 2020 until end of projections.

### G. Calibration to Implement Toolkit
- Inputs:
  - United Nations Population Projections (age distribution in five-year groups until 2050, and until 2100 in some scenarios).
  - Macroeconomic variables (GDP and GDP deflator = inflation) taken from WEO projections until 2020.
  - Inflation and unemployment fixed at average WEO projections for 2016-20.
  - Real GDP per capita obtained from WEO and population projections until 2020; after 2021 kept constant at average 2016-20.
- Discount factor d assumed constant; set at 1 percent (d = 1 percent), following literature.
  - This equals average interest rate-growth differential (~1 percent).
- Effective interest rate derived by:
  - ݅
    ௧
    ൌ
    ሾ
    1൅݀∗
    ሺ
    ݃1൅
    ௧
    ሻ
    ݃൅
    ௧
    ሿ
    ∗
    ሺ
    ߨ1൅
    ௧
    ሻ
    ൌ1.
- Baseline excess cost growth factor (ecg) = 1 percent.
- Calibration of reform effect on ecg: decrease calibrated to quarter of standard deviation of emerging-economy estimates in Clements, Coady, & Gupta (2012) ≈ 0.5 percent.
- Health cost index by age group assumed equal across countries, constant over horizon, taking OECD average (de la Maisonneuve & Oliveira Martins, 2013).
- Other variables largely held constant through projection horizon; country-specific assumptions summarized in Table 11 (assumptions include labor force participation, wage share, size of formal sector, real GDP per capita growth, inflation, unemployment, income shares by quintile, demographic and pension parameters, health parameters).

### Selected Key Numeric Assumptions and Values (as reported)
- Discount factor d: 1 percent.
- Excess cost growth (baseline): 1.00% (for Argentina, Brazil, Chile, Colombia, Mexico as reported).
- Decrease in excess cost growth for reform: 0.5 percent (starts 2016, takes 5 years).
- Increase in contribution rate (one-time): 1% (point increase in 2016).
- Projection horizon reference years: last known value 2015; projections to 2050.
- Retirement age (listed): 60, 60, 60, 60, 65 (country-specific).
- Replacement rate (last available): 71.60%, 69.50%, 32.80%, 64.10%, 25.50% (Argentina, Brazil, Chile, Colombia, Mexico).
- Contribution rate (last available): 21.17%, 28.00%, 11.49%, 16.00%, 6.50% (Argentina, Brazil, Chile, Colombia, Mexico).
- Number of beneficiaries (last known): 18,962,523; 144,988,372; 13,612,038; 44,770,148; 118,617,542 (Argentina, Brazil, Chile, Colombia, Mexico).
- Health expenditure (percent of GDP, latest available): 4.17%, 4.24%, 3.31%, 4.98%, 3.10% (Argentina, Brazil, Chile, Colombia, Mexico).
- Average per capita health expenditure cost index (latest available): 1.25, 1.17, 1.29, 1.15, 1.11 (Argentina, Brazil, Chile, Colombia, Mexico).
- Life expectancy after retirement (latest available): -, -, 25, 20, 18 (Argentina, Brazil, Chile, Colombia, Mexico).
- DC contribution rate (statutory): -, -, 11.49%, 16.00%, 8.88% (where applicable).
- Minimum pension (statutory) examples listed for Chile, Colombia, Mexico: 1,685,978; 7,732,200; 25,587 (values as reported).
- Average months of contributions per year (latest available) reported as 6 for Chile.

*Source: wp1794 - introduction of the reform, but these also take into account the reform of the increase in the*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp1794.pdf_