## PREFACE

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---

### Mission context and purpose
- At the request of the Minister of Finance of Luxembourg, Mr. Gilles Roth, an IMF capacity development mission was conducted in Luxembourg from July 2 to July 4, 2025, followed by online meetings in August 2025.
- Mission objectives:
  - Evaluate short- and medium-term deviations between projected and actual pension balances, including analysis of contributing factors.
  - Evaluate fluctuations in long-term pension projections.

### Mission team and interlocutors
- Mission team: Mr. Christoph Freudenberg (mission chief, FAD), Ms. Céline Thévenot (Senior Economist, FAD), Dr. Timm Bönke (FAD expert).
- Meetings held with: Ministry of Finance (Mr. Bob Kieffer, Mr. Nicolas Jost, Mr. Jérôme Merker, Mr. Yves Clarens); General Inspectorate of Social Security (IGSS) (Mr. Thomas Dominique, Mr. Thierry Mazoyer, Mr. Kevin Everard); STATEC (Mr. Bastien Larue, Mr. Gabriel Gomes, Mr. Michel Geller, Ms. Lena Rota).
- Acknowledgements: Mr. Tom Englaro for mission organization; Mr. Kevin Everard and Mr. Thierry Mazoyer for cooperation.

### Executive summary — key findings
- Purpose: review Luxembourg’s pension projections to help ensure continued reliability for fiscal planning, including projected Maastricht Deficit reporting to the European Commission.
- Short-term accuracy:
  - The pension balance was underestimated modestly over the past decade, averaging 0.04 percent of GDP for one-year horizon projections.
  - Larger deviation during COVID: 0.17 percent of GDP in 2021.
  - Short-term projections perform well overall, deviations predominantly from the revenue side.
  - Underestimation of average real contributions per employee identified as key driver of short-term deviations.
  - Similar deviations observed in peer countries (Germany, Belgium, France).
  - Linkage to inflation increases vulnerability of projections to inflation shocks.
- Long-term projections:
  - Robust across past vintages; volatility driven mainly by changes in employment and demographic assumptions, model changes, and macroeconomic shocks (e.g., COVID).
  - Timing of critical events broadly stable between 2016 and 2025:
    - Key Event 3 (reserves exhausted) shifted from 2043 to 2045 (2 years).
    - Key Event 2 (reserves below legal minimum of 1.5 times annual pension expenditure) shifted from 2035 to 2039 (4 years).
  - Even under more optimistic return assumptions, Key Events 2 and 3 likely postponed by no more than three years.
  - A lower employment growth path could shift critical years forward by around two years.
- Model quality and transparency:
  - Long-term pension projection meets high international standards; scope for improvement.
  - Recommend reassessment of rate-of-return assumptions for the Compensation Fund and presenting impacts of alternative rates.
  - Emphasize distributional aspects using micro-simulation models.
  - Improve communication on why estimates changed with model updates and provide a detailed model description.
- Policy implication:
  - Model refinements unlikely to change conclusion that reform is needed to ensure long-term sustainability.
  - Because pension reforms are typically phased, adopting reforms early is strongly advised.

### Recommendations (summary)
- Short-term Projections (for budget law preparation in 2026):
  - 1.1 Publish established systematic and regular reporting on projection deviations—highlighting the contribution of key macroeconomic variables.
  - 1.2 Refine the input variables—specifically, employment and wage forecasts.
  - 1.3 Further develop multi-model approaches to mitigate the risks of a single model forecast projections.
- Long-term Projections (for the next long-term projection / For 2027+ projections):
  - 2.1 Review rate of return assumptions of the Compensation Fund.
  - 2.2 Examine employment growth assumptions, amid low recent growth.
  - 2.3 Continue considering model improvements, including analyses backed by micro-simulation model.
  - 2.4 Strengthen communication of model updates and calculations, through greater use of executive summaries.

*Source: IMF staff, PREFACE and Executive Summary sections of the report.*

---

### Short- and medium-term projections — empirical performance and drivers

### Aggregate forecast performance (2016–2023)
- Mean Error (Bias) by horizon (Financial Balance / Revenues / Expenditures):
  - Financial Balance: Same year -0.008; 1 year -0.030; 2 years -0.035; 3 years -0.034; 4 years -0.051
  - Revenues: Same year -0.005; 1 year -0.013; 2 years -0.024; 3 years -0.038; 4 years -0.048
  - Expenditures: Same year -0.005; 1 year -0.010; 2 years -0.022; 3 years -0.039; 4 years -0.048
- Root Mean Square Error (RMSE) by horizon (Financial Balance / Revenues / Expenditures):
  - Financial Balance: Same year 0.427; 1 year 0.706; 2 years 1.225; 3 years 2.550; 4 years 3.359
  - Revenues: Same year 0.040; 1 year 0.158; 2 years 0.354; 3 years 0.479; 4 years 0.428
  - Expenditures: Same year 0.045; 1 year 0.110; 2 years 0.305; 3 years 0.419; 4 years 0.409

### Key quantitative findings and drivers
- Since 2016, projections deviated by an average of 0.04 percent of GDP for 1-year horizon projections.
- High-uncertainty periods amplified deviations: COVID (2020–21) and inflation peak after the invasion of Ukraine (2022–23).
- Revenue and expenditure forecasts exhibit a negative bias that grows with horizon; revenue projections have larger RMSE than expenditure projections.
- During COVID, revenues were overestimated; during the inflation shock following the war in Ukraine, both revenue and expenditure were underestimated (notably in 2022).
- Main driver of short-term projection deviations: underestimation of average real contributions per employee.
- Other contributors: employment and wage forecast inaccuracies; sensitivity to inflation given indexation rules.
- Recommendation emphasis: refine employment and wage inputs, develop multi-model forecasting, publish systematic reporting on projection deviations showing contributions of key macroeconomic variables.

### Revenue decomposition and statistics (2016–23)
- Revenue identity: Revenue = Number of contributors * Average contribution *COLA/100 + Other revenues
- Table 3 selected figures (Mean Error / RMSE by horizon):
  - Revenues Mean Error: Same year -0.005; 1 year -0.013; 2 years -0.024; 3 years -0.038; 4 years -0.048
  - Revenues RMSE: Same year 0.040; 1 year 0.158; 2 years 0.354; 3 years 0.479; 4 years 0.428
  - Average contribution (real terms) RMSE: Same year 0.271; 1 year 0.502; 2 years 0.804; 3 years 1.248; 4 years 1.625
  - Cost of living index RMSE: Same year 0.025; 1 year 0.216; 2 years 0.528; 3 years 0.638; 4 years 0.556
  - Other revenues RMSE: Same year 0.329; 1 year 0.596; 2 years 0.655; 3 years 0.536; 4 years 0.547
- Principal revenue findings:
  - Largest 1-year horizon revenue deviations stem from average contribution (especially 2022-2023), number of contributors (especially during COVID years), and inflation (COLA factor) in 2022 and 2023.
  - Other revenues (mostly property income; almost 90 percent of ‘other revenues’) were overestimated before COVID and underestimated during the inflation peak.

### Expenditure decomposition and statistics (2016–23)
- Expenditure identity: Expenditure = Number of pensioners * Average pension *COLA/100 * Readjustment + Other Expenditure
- Table 4 selected figures (Mean Error / RMSE by horizon):
  - Expenditures Mean Error: Same year -0.005; 1 year -0.010; 2 years -0.022; 3 years -0.039; 4 years -0.048
  - Expenditures RMSE: Same year 0.045; 1 year 0.110; 2 years 0.305; 3 years 0.419; 4 years 0.409
  - Average pension in real terms Mean Error: -0.009; -0.012; -0.013; -0.013; -0.014 (same year to 4 years)
  - Average pension in real terms RMSE: Same year 3.393; 1 year 4.649; 2 years 5.707; 3 years 5.748; 4 years 5.771
  - Number of pensioners Mean Error: 0.009; 0.012; 0.013; 0.012; 0.011
  - Number of pensioners RMSE: Same year 0.128; 1 year 0.198; 2 years 0.273; 3 years 0.365; 4 years 0.483
  - Other expenditures Mean Error: -0.096; -0.170; -0.224; -0.256; -0.248
  - Other expenditures RMSE: Same year 0.641; 1 year 1.008; 2 years 1.892; 3 years 2.432; 4 years 2.945
- Principal expenditure findings:
  - Since 2017, overall expenditures were underestimated due to underestimation in average pension in real terms, COLA, and other expenditures.
  - Number of pensioners was slightly overestimated, mitigating overall deviation.
  - Other expenditures (capital transfers, capital formation, intermediate consumption) were underestimated, possibly due to indirect inflation effects.

### Accuracy of current-year estimates (Box 1)
- Projections start in August using partial mid-year data; mid-year estimates must be partially projected.
- Mid-year estimates for cash benefits closely align with actual outcomes ex-post.
- “Other expenditure” and revenue estimates are less precise, particularly during COVID years 2020 and 2021.
- Improving current-year subcomponent estimates would likely have only a modest effect on total revenue and expenditure forecasts for the current year.

---

### Comparison with peers and institutional framework

### Comparison with peer countries (Belgium, France, Germany)
- Financial balance projections: Luxembourg less biased than France or Germany (Table 2).
- Revenues are underestimated in France and Germany as in Luxembourg.
- Expenditure bias: Luxembourg negative; Germany and Belgium show some positive bias.
- Accuracy summaries:
  - Financial balance accuracy: same magnitude as France; much better than Germany.
  - Revenue projection accuracy: slightly better than France; slightly worse than Germany.
  - Expenditure forecast accuracy: similar to Belgium; below France and Germany.
- Table 2 key statistics (1-year horizon, 2016-23):
  - Financial Balance Mean Error (Bias): Germany -4.504Na, Belgium 1.350, France -0.03, Luxembourg 2.069
  - Financial Balance RMSE: Germany Na, Belgium 0.659, France 0.706, Luxembourg 0.706
  - Revenue Mean Error: Germany -0.009Na, Belgium -0.010-0.013, France 0.132, Luxembourg Na
  - Revenue RMSE: Germany Na, Belgium 0.189, France 0.158, Luxembourg 0.158
  - Expenditure Mean Error: Germany 0.0030.151, Belgium 0.000-0.010, France 0.048, Luxembourg 0.137
  - Expenditure RMSE: Germany 0.049, Belgium 0.110, France 0.049, Luxembourg 0.110
- Institutional design note: stronger automatic indexation (minimum wage and pensions) in Luxembourg increases projection sensitivity to inflation shocks relative to France and Germany.

### Institutional framework — roles, processes, and cadence
- Projection cadence:
  - Two annual medium-term projection exercises (year y–y+4): February (intermediate update) and August (State budget and multiannual financial programming act).
  - Long-term projections (50-year horizon) every five years to ensure compliance with Article 238 of the Social Security Code.
  - AWG projections every three years for the EU Ageing Report using harmonized methodology and assumptions.
- Key institutions and responsibilities:
  - IGSS: oversees medium- and long-term forecasts and overall consistency.
  - National Pension Insurance Office: prepares annual pension expenditure and revenue forecast; reviewed by IGSS and endorsed by the Minister of Health and Social Security.
  - STATEC: provides macroeconomic assumptions and long-term demographic projections and alternate macroeconomic scenarios.
  - European Commission: provides harmonized macroeconomic assumptions for AWG and Eurostat demographic assumptions.
  - Ministry of Finance: uses medium-term projection results for pluriannual financial programming and budget process.
  - CNFP and CEFN: fora to discuss projections; gap identified: no formal communication on sources of projection deviations.

---

### Long-term projections — methodology, volatility, sensitivity, and recommendations

### A. Overview of projection methodology
- Deterministic cohort model from the ILO, customized to Luxembourg’s pension system.
- Two components: demographic (projects contributors and pensioners) and financial (estimates income and expenditure).
- Statuses modeled: active, inactive, pensioner; financial variables (salaries/revenues, pensions) projected annually until 2070.
- Key features:
  - Age- and career-length-specific earning profiles; general real wage growth and inflation adjustments.
  - Labor productivity assumptions simulate real wage growth.
  - Actuarially determined transition probabilities (mortality, disability, retirement).
  - Benefits and contributions calculated by one year age groups, gender and residency.
  - Macrosimulation implemented in LIAM2 environment.
  - Macro-economic and demographic assumptions provided by AWG, Eurostat and STATEC.

### B. Volatility of past projections and key events
- Defined events:
  - Event 1: year pension expenditures exceed contribution revenues (PAYG rate surpasses statutory contribution rate of 24 percent of wages).
  - Event 2: year pension reserve falls below statutory threshold of 1.5 times annual expenditure (triggers legislative action under Art. 238 Social Security Code).
  - Event 3: year pension reserve is fully depleted.
- Recent vintage movements:
  - Event 3: projected 2043 in 2016; delayed to 2045 in 2025 projection.
  - Event 2: consistently around 2040 across vintages.
  - In 2025 projections, all three critical events occur two years earlier compared to previous projections.
- International context:
  - Between 2021 and 2024 AWG projections, 16 out of 27 EU Member States revised 2050 pension expenditure projections downwards by an average of 1.3 percentage points of GDP.
  - Luxembourg revision between 2021 and 2024 was a reduction of 2.3 percentage points of GDP.
  - Deviations larger for smaller EU countries (less than 3 million inhabitants): standard deviation 1.0 percent of GDP, compared to 0.85 percent for larger EU countries.
- Horizon sensitivity: longer horizons amplify parameter change impacts; shorter horizons (15–20 years) more stable.

### C. Main drivers of recent shifts
- Advancement of Event 1 to 2026 driven mainly by employment growth revisions:
  - Change in employment assumptions accounts for approximately 81 percent of the increase in the projected PAYG rate by 2026 from 23.4 percent (projection 2023) to 24.3 percent (projection 2024).
  - STATEC 2024 inputs suggest employee growth and contributors growth will be significantly lower than assumed in 2023, with a downward adjustment of about one percentage point for the period 2024-2026.
  - Other contributors: slight increase in number of pensioners and real pension indexation.
- Long-term expenditure revisions (2021 vs 2024 AWG):
  - Actual pension spending in 2022 was 0.8 percentage points of GDP below 2021 AWG projections—about one-third of the deviation between 2021 and 2024 projections for 2050.
  - Revisions to employment growth, productivity, and Eurostat demographic projections are main explanations for downward revision in pension expenditures between 2021 and 2024 AWG.
- Model and methodological updates (2024 AWG) included:
  - Inclusion of non-active insured individuals, endogenous modeling of foreign insurance periods, new estimation of non-contributory periods, three-year delay assumption for automatic adjustment mechanism, revised disability and survivor pension assumptions, upward revision of number of old-age pensioners, adjusted entry ages, and updated accrual rate calculation.
  - Net effect: methodological changes improved accuracy, lowered projected expenditures by 2050, but increased them by 2070.

### D. Rates-of-return and sensitivity
- Current Luxembourg assumption: 2.2 percent nominal at the start (based on historic cash income only), rising to 4 percent by 2050.24
- Translates to 0.2–2 percent in real terms assuming 2 percent inflation.
- Fund historical average nominal return since SICAV launch in 2007 is 5.0 percent.
- Sensitivity examples:
  - If 4 percent rate of return assumed over 2024-2070: Event 2 shifts from 2039 to 2041; Event 3 shifts from 2045 to 2046.
  - If 5 percent assumed: Event 2 shifts to 2042; Event 3 shifts to 2048.
- Conclusion: alternative (higher) return assumptions have only modest impact on timing of key funding events.
- Recommendation: reassess rate of return assumption — low-resource, high-impact priority.

### Employment growth assumptions and fiscal timing sensitivity
- Over 2023–2024 employment growth was significantly overestimated.
- Most recent projections assume employment growth of over 2 percent per year for 2026–2030.
- Scenario: If employment growth assumption is revised to 1 percent:
  - Event 2 shifts from 2039 to 2037.
  - Event 3 moves from 2045 to 2043.
- STATEC is analyzing trends and considering revising medium- and long-term employment growth downward.
- Recommendation: thoroughly examine drivers behind recent weak employment growth and reflect potential downward revisions; account for potential AI impacts.

### Model refinements, micro-simulation, and documentation
- Priorities (Table 8 highlights):
  - High priority, low resource intensity: reassess rate of return assumption; reassess employment growth assumptions; improve documentation.
  - Medium/High resource intensity: implement dynamic micro-simulation (Priority: Medium; Resource Intensity: High) to capture distributional impacts.
- Micro-simulation gaps:
  - Current model lacks distributional micro-simulation; individuals assumed to follow average contribution density by age, gender, and insurance year group.
  - Consequence: potential underestimation of tails of distribution and impaired modeling of non-linear benefit features (minimum and maximum pension).
- Recommended phased approach:
  - Intermediate: assume individuals remain in observed contribution density and earnings percentile by age and gender.
  - Long-term: dynamic micro-simulation with transitions across earnings and contribution density states.
  - Consider applying updated ILO Pension Model (with micro-simulation) and collaboration with LISER.
- Survivor pensions:
  - 2024 AWG improvements link inflows to current eligibility probabilities; projected expenditures in 2070 are 0.7 percentage points of GDP lower than 2021 projections.
  - Risks suggesting further declines: falling marriage/cohabitation rates and increasing share of women with substantial own pension entitlements.
  - Income-testing rule: threshold €3,918 per month; pension reduced by 30 percent of amount exceeding threshold.
  - Recommendation: reflect trends in marriage/cohabitation and income-testing in upcoming model updates.

### Revenue and expenditure projection refinements
- Revenue side: current projections account for differences by gender, sector, and residence status but not sufficiently by age; recommendation to introduce age-specific employment rates.
- Expenditure side: non-contributory periods estimated from base-year stocks without projecting cohort evolution; recommendation to project cohort evolution for improved evaluation of reforms.
- While such refinements may not materially change baseline projections, they strengthen accuracy for reform evaluation.

### Transparency, communication, and reporting practices
- Quantify how much of projection changes stem from data revisions, methodological adjustments, or updated assumptions.
- Include sensitivity analysis with confidence intervals and present margins of error around central projections.
- Systematically categorize changes between projection rounds into: (1) updates to assumptions, (2) data revisions, and (3) methodological adjustments.
- Twice-yearly systematic analysis of deviations between subsequent projections within the CEFN framework is recommended.
- Produce concise executive summaries explaining drivers of long-term pension finances and deviations between vintages.
- Develop detailed model documentation to improve transparency, reproducibility, internal knowledge transfer, and continuity.

---

### Short-term forecast refinements and ensemble methods (Annex 3 highlights)

### Ensemble weighted-average forecasting approach
- Test a wide range of model specifications (classical, penalized, ML, mixed frequency) and compute weighted average of model forecasts.
- Weighting mechanics:
  - For model m, accuracy δ_m and inverse φ_m = 1/δ_m.
  - Initial weight ξ_m = φ_m / [∑_{m∈M} φ_m].
  - Apply exponent S: ξ_m^p = φ_m^p / [∑ φ_m^p] where p (S) determined based on lasso method.
- Input treatment: outlier treatment, seasonal adjustment, nowcasting, frequency decomposition; VARX Lasso used to test influence.
- Mixed-frequency models combine quarterly and monthly data.

### Contribution forecast models — performance and selected models
- 48 models estimated; final estimate is weighted average; mixed-frequency used.
- Two best performing models: GRU and VARX Own/Other Sparse Group Penalty.
- Selected performance metrics examples (In Sample MAPE | In Sample RMSE | Out Sample MAPE | Out Sample RMSE):
  - VAR Smoothly Clipped Absolute Deviation org: 0.92% | 4,950,000 | 2.59% | 11,600,000
  - VECM org: 0.60% | 3,210,000 | 1.35% | 8,100,000
  - Minnesota BVAR log: 0.59% | 3,150,000 | 0.74% | 3,920,000
  - GRU diff: 0.77% | 4,630,000 | 0.79% | 4,680,000
  - VARX Own/Other Sparse Group Penalty diff: 0.77% | 4,660,000 | 0.80% | 4,520,000
  - Naive org: 6.25% | 47,300,000 | 6.25% | 47,300,000
- Comparison with LPFP projections:
  - Weighted average forecast suggests a lower level of total contributions for 2025 by 1.2 percent compared to LPFP 2024/2029 projections.
  - Slightly higher contributions by 0.6 percent projected for 2026 compared to LPFP 2024/2029 projections.

### Employment and wage model ensembles
- Employment forecast models: 27 models; selected performance examples:
  - ARDL org: In-sample MAPE 0.06% | In-sample RMSE 329 | Out-of-sample MAPE 0.34% | Out-of-sample RMSE 1,753
  - VARX Lasso diff: 0.09% | 495 | 0.09% | 533
  - Naive org: 0.57% | 3,502 | 0.57% | 3,502
- Wages selected models:
  - VARX Lag Group Lasso: Number of Endogenous Variables 15; Maximum Modelled Lags 12; Penalty Parameter 7.9718
  - HVAR Own/Other Lasso: Number of Endogenous Variables 15; Maximum Modelled Lags 12; Penalty Parameter 2.7827
  - VAR Weighted Lag Lasso: Number of Endogenous Variables 15; Maximum Modelled Lags 12; Penalty Parameter 0.0004

### Two best performing contribution models — technical details
- GRU (Model 1):
  - Main Variable: Pensions contributions (differenced); Unit: Euros
  - Explanatory Variables: Y2: Contribution ceiling (differenced); Y3: Compensation of Employees, Current Prices (differenced); Y4: Number of contributors (differenced)
  - 1 layer with hidden state size 80; 8 epochs; early stopping after 5 consecutive increases in validation loss.
- VARX Own/Other Sparse Group Penalty (Model 2):
  - Main Variable: Pensions contributions (differenced); Unit: Euros
  - Explanatory Variables: Y2: Contribution ceiling EUR; Y3: Compensation of Employees, Current Prices; Y4: Number of contributors
  - Maximum of 12 modelled lag(s); Penalty parameter 0.0031 selected using time series cross-validation.

---

### Pension system rules (Annex 4 overview)

### Contributions and ceilings
- Contribution rates:
  - 24% total: 8% employer, 8% employee, 8% government; up to 5× minimum wage ceiling.
- Contribution ceilings:
  - Pensionable earnings capped at 5× social minimum wage.

### Retirement ages and insurance requirements
- Normal retirement age:
  - 65 years with at least 10 years of insurance.
- Early retirement:
  - 57 years with 40 years of contributions; or 60 years with 40 years of insurance (including credited).
- Insurance years needed (old age):
  - 40 years for maximum accrual; minimum 10 years for lifelong payment.

### Old-age benefit formula, minimum pension, and indexation
- Old-age benefit formula:
  - Mixed: flat-rate benefit + earnings-related benefit with accrual rate of 1.782% of adjusted lifetime total earnings (gradually decreasing until reaching 1.6% by 2052) plus 0.015% (gradually rising to 0.025% by 2052) of adjusted lifetime total earnings for each year the insured's age and years of coverage exceeds 94 years (gradually rising until reaching 100 by 2052).
- Minimum Pension:
  - €2,293.55 a month is paid in 2025 with at least 40 years of coverage.
  - If the insured contributed for at least 20 years but less than 40 years, the guaranteed minimum pension is reduced by 1/40 for each year of coverage less than 40 years.
- Pension indexation:
  - Fully indexed to prices and, under a semi-automatic readjustment mechanism, also to real wage growth.
  - Real wage growth adjustment applied in full when contributions exceed expenditures but reduced via a moderator coefficient between 0 and 0.5 if the system’s balance deteriorates.

### Credited periods and penalties/bonuses
- Credited periods:
  - Include sickness, maternity, work injury benefits (since 2011), unemployment support, minimum income allowance, study/apprenticeship years between ages 18 and 27, time caring for a child under age 6 (or under age 18 if the child is disabled), and periods receiving long-term care or invalidity benefits.
- Early/late retirement adjustments:
  - Pension penalty/bonus for early/late retirement: not applied.

---

*Source: IMF | Technical Report (excerpts from PREFACE, Executive Summary, Annexes 1–4).*

### PREFACE  _________________________________________________________________________________________ 6

### PREFACE

### Mission context and purpose
- At the request of the Minister of Finance of Luxembourg, Mr. Gilles Roth, an IMF capacity development mission was conducted in Luxembourg from July 2 to July 4, 2025, followed by online meetings in August 2025.
- The mission aimed to support the Government in enhancing the efficiency and sustainability of the pension system by:
  - Evaluating short- and medium-term deviations between projected and actual pension balances, including analysis of contributing factors.
  - Evaluating fluctuations in long-term pension projections.

### Mission team and interlocutors
- Mission team: Mr. Christoph Freudenberg (mission chief, FAD), Ms. Céline Thévenot (Senior Economist, FAD), Dr. Timm Bönke (FAD expert).
- Meetings held with: Ministry of Finance (Mr. Bob Kieffer, Mr. Nicolas Jost, Mr. Jérôme Merker, Mr. Yves Clarens); General Inspectorate of Social Security (IGSS) (Mr. Thomas Dominique, Mr. Thierry Mazoyer, Mr. Kevin Everard); STATEC (Mr. Bastien Larue, Mr. Gabriel Gomes, Mr. Michel Geller, Ms. Lena Rota).
- Acknowledgements: Mr. Tom Englaro for mission organization; Mr. Kevin Everard and Mr. Thierry Mazoyer for cooperation.

### Executive Summary — Key findings
- Purpose: review Luxembourg’s pension projections to help ensure continued reliability for fiscal planning, including projected Maastricht Deficit reporting to the European Commission.
- Short-term accuracy:
  - The pension balance was underestimated modestly over the past decade, averaging 0.04 percent of GDP for one-year horizon projections.
  - Larger deviation during COVID: 0.17 percent of GDP in 2021.
  - Short-term projections perform well overall, with deviations predominantly stemming from the revenue side.
  - Underestimation of average real contributions per employee identified as key driver of short-term deviations.
  - Similar deviations observed in peer countries (Germany, Belgium, France).
  - Luxembourg’s system linkage to inflation increases vulnerability of projections to inflation shocks.
- Long-term projections:
  - Long-term projections have been robust across past vintages.
  - Volatility driven mainly by changes in employment and demographic assumptions, model changes, and macroeconomic shocks (e.g., COVID).
  - Timing of critical events has been broadly stable between 2016 and 2025:
    - Estimates of when reserves would be exhausted (Key Event 3) shifted from 2043 to 2045 (2 years).
    - Estimates of when reserves drop below legal minimum of 1.5 times annual pension expenditure (Key Event 2) shifted from 2035 to 2039 (4 years).
  - Even under more optimistic return assumptions, Key Events 2 and 3 likely postponed by no more than three years.
  - A lower employment growth path could shift critical years forward by around two years.
- Model quality and transparency:
  - Luxembourg’s long-term pension projection meets high international standards but scope exists for further improvement.
  - Recommended continuing reassessment of rate-of-return assumptions for the Compensation Fund and presenting impacts of alternative rates.
  - Suggested emphasis on distributional aspects using micro-simulation models.
  - Improved communication on why estimates changed with model updates and a detailed model description to enhance transparency and trust.
- Policy implication:
  - Proposed model refinements are not expected to change the overarching conclusion that reform is needed to ensure long-term sustainability.
  - Because pension reforms are typically phased, adopting reforms early is strongly advised.

### Recommendations (summary)
Short-term Projections (for budget law preparation in 2026 / For budget law preparation)
- 1.1 Publish established systematic and regular reporting on projection deviations—highlighting the contribution of key macroeconomic variables.
- 1.2 Refine the input variables—specifically, employment and wage forecasts.
- 1.3 Further develop multi-model approaches to mitigate the risks of a single model forecast projections.

Long-term Projections (for the next long-term projection / For 2027+ projections)
- 2.1 Review rate of return assumptions of the Compensation Fund.
- 2.2 Examine employment growth assumptions, amid low recent growth.
- 2.3 Continue considering model improvements, including analyses backed by micro-simulation model.
- 2.4 Strengthen communication of model updates and calculations, through greater use of executive summaries.

### Institutional framework — roles and processes
- Projection cadence and horizons:
  - Two annual medium-term projection exercises (year y–y+4): February (intermediate update of the multiannual trajectory of the social security balance) and August (State budget and multiannual financial programming act).
  - Long-term projections (50-year horizon) every five years to ensure compliance with Article 238 of the Social Security Code.
  - AWG projections every three years for the EU Ageing Report using harmonized methodology and assumptions.
- Key institutions and responsibilities:
  - IGSS: oversees medium- and long-term forecasts and overall consistency.
  - National Pension Insurance Office: prepares annual pension expenditure and revenue forecast; reviewed by IGSS and endorsed by the Minister of Health and Social Security.
  - STATEC: provides macroeconomic assumptions for medium-term projections (employment, wages, inflation) and long-term demographic projections and alternate macroeconomic scenarios.
  - European Commission: provides harmonized macroeconomic assumptions for AWG and Eurostat demographic assumptions.
  - Ministry of Finance: uses medium-term projection results for pluriannual financial programming and budget process.
  - CNFP and CEFN: fora to discuss projections; CNFP is independent body for budgetary projections; CEFN assembles IGSS, STATEC, Ministry of Finance. Current gap: no formal communication on the sources of projection deviations.

### Short- and medium-term projections — empirical performance
- Scope: short-term defined as 1 to 4 years; analysis compares projections published in Finance laws (2016–2024) to actual outcomes.
- Aggregate performance (2016–2023), Table 1 highlights:
  - Mean Error (Bias) and Root Mean Square Error (RMSE) by horizon for Financial Balance, Revenues, Expenditures (exact table values preserved below).
  - Mean Error (Bias)
    - Financial Balance: Same year -0.008; 1 year -0.030; 2 years -0.035; 3 years -0.034; 4 years -0.051
    - Revenues: Same year -0.005; 1 year -0.013; 2 years -0.024; 3 years -0.038; 4 years -0.048
    - Expenditures: Same year -0.005; 1 year -0.010; 2 years -0.022; 3 years -0.039; 4 years -0.048
  - Root Mean Square Error (Inaccuracy)
    - Financial Balance: Same year 0.427; 1 year 0.706; 2 years 1.225; 3 years 2.550; 4 years 3.359
    - Revenues: Same year 0.040; 1 year 0.158; 2 years 0.354; 3 years 0.479; 4 years 0.428
    - Expenditures: Same year 0.045; 1 year 0.110; 2 years 0.305; 3 years 0.419; 4 years 0.409
- Key quantitative findings:
  - Since 2016, projections deviated from observed values by an average of 0.04 percent of GDP for 1-year horizon projections.
  - Larger deviations during high-uncertainty periods: COVID (2020–21) and inflation peak after the invasion of Ukraine (2022–23).
  - Revenues and expenditures were overall underestimated, indicating a negative bias that grows with projection horizon.
  - Revenue projections exhibit larger RMSE than expenditure projections, indicating revenues are less accurately forecasted.
  - During COVID, revenues were overestimated; during the inflation shock following the war in Ukraine, both revenue and expenditure were underestimated (notably in 2022).
  - 2024 observed value considered provisional at time of writing.

### Drivers of short-term projection deviations (high level)
- Main driver: underestimation of average real contributions per employee.
- Deviations concentrated on the revenue side due to:
  - Sensitivity to inflation given system indexing to inflation.
  - Employment and wage forecast inaccuracies.
- Peer country experience: comparable deviations in Germany, Belgium, France.
- Recommendation emphasis: refine employment and wage inputs, develop multi-model forecasting, publish systematic reporting on projection deviations showing contributions of key macroeconomic variables.

*Source: IMF staff, PREFACE and Executive Summary sections of the report.*

### 12. The relatively modest projection deviations in Luxembourg are similar to deviations

### 12. The relatively modest projection deviations in Luxembourg are similar to deviations observed in other countries

### Comparison with peer countries (Belgium, France, Germany, Luxembourg)
- Projections of the financial balance for Luxembourg are less biased than in France or Germany (Table 2).
- Revenues are underestimated in France and Germany as in Luxembourg.
- The bias for expenditures in Luxembourg is negative, compared to some positive bias in Germany and Belgium.
- The accuracy of the financial balance is:
  - of the same magnitude as in France,
  - much better than in Germany.
- The accuracy of revenue projection is:
  - slightly better than in France,
  - slightly worse than in Germany.
- The accuracy of expenditure forecast is:
  - similar to Belgium,
  - below the accuracy of forecasts in France and Germany.
- Projections in Luxembourg and Belgium (for expenditures) are slightly more sensitive to macroeconomic circumstances (Figure 4).
- Projections for France appeared closer to observed values than in Luxembourg, including during periods of high uncertainty (COVID 2020-2021 and the inflation-peak 2022-2023). This is likely explained by pension system and labor market designs being more strongly tied to inflation in Luxembourg.
- Institutional design notes:
  - In Luxembourg, minimum wage is adjusted automatically to prices, as is the level of pensions.
  - In Germany, minimum wage is not automatically indexed to inflation; average wages are not adjusted to inflation in France or Germany.
  - Pensions are indexed to economic indicators (wages and prices) with a longer time lag of one and more years in France and Germany, making projections less sensitive to projection errors on inflation.

### Key statistics from Table 2 (Mean Error and RMSE, 1-year horizon, 2016-23)
- Financial Balance Mean Error (Bias): Germany -4.504Na, Belgium 1.350, France -0.03, Luxembourg 2.069
- Financial Balance Root Mean Square Error (Inaccuracy): Germany Na, Belgium 0.659, France 0.706, Luxembourg 0.706
- Revenue Mean Error: Germany -0.009Na, Belgium -0.010-0.013, France 0.132, Luxembourg Na
- Revenue RMSE: Germany Na, Belgium 0.189, France 0.158, Luxembourg 0.158
- Expenditure Mean Error: Germany 0.0030.151, Belgium 0.000-0.010, France 0.048, Luxembourg 0.137
- Expenditure RMSE: Germany 0.049, Belgium 0.110, France 0.049, Luxembourg 0.110
- Note: Table 2 source: Authorities and IMF Staff estimates (Luxembourg), Rentenversicherungsbericht der Bundesregierung (Germany), Conseil d’Orientation des Retraites (France), Comité d’études sur le vieillissement (Belgium).

### Revenue projections — structure and main drivers
- Revenue construction (as presented):
  - Revenue = Number of contributors * Average contribution *COLA/100 + Other revenues
- Main components:
  - Number of contributors
  - Average contribution (real terms)
  - Cost-of-living index (COLA)
  - Other revenues (mostly property income; almost 90 percent of ‘other revenues’)
- Table 3 (Mean Error and RMSE by horizon, 2016-23) selected figures:
  - Revenues Mean Error: Same year -0.005, 1 year -0.013, 2 years -0.024, 3 years -0.038, 4 years -0.048
  - Revenues RMSE: Same year 0.040, 1 year 0.158, 2 years 0.354, 3 years 0.479, 4 years 0.428
  - Average contribution (real terms) RMSE: Same year 0.271, 1 year 0.502, 2 years 0.804, 3 years 1.248, 4 years 1.625
  - Cost of living index RMSE: Same year 0.025, 1 year 0.216, 2 years 0.528, 3 years 0.638, 4 years 0.556
  - Other revenues RMSE: Same year 0.329, 1 year 0.596, 2 years 0.655, 3 years 0.536, 4 years 0.547
- Principal findings:
  - The main driver of revenue projection deviation is systematic underestimation of average real contribution per employee.
  - Largest 1-year horizon revenue deviations stem from:
    1. Average contribution, especially in 2022-2023
    2. Number of contributors, especially during COVID years
    3. Inflation (COLA factor), especially in 2022 and 2023
  - Other revenues (property incomes, e.g., interest on reserve fund) were overestimated before COVID and underestimated during the inflation peak, reflecting challenges in anticipating interest rate changes or conservative assumptions.

### Expenditure projections — structure and main drivers
- Expenditure construction (as presented):
  - Expenditure = Number of pensioners * Average pension *COLA/100 * Readjustment + Other Expenditure
- Cash benefits are the product of:
  - Number of pensioners
  - Average real pension
  - Cost-of-living adjustment coefficient
  - Real wage adjustment factor (readjustment)
- Other expenditure components include operational and capital expenditures: intermediate consumption, gross capital formation, and employee compensation.
- Table 4 (Mean Error and RMSE by horizon, 2016-23) selected figures:
  - Expenditures Mean Error: Same year -0.005, 1 year -0.010, 2 years -0.022, 3 years -0.039, 4 years -0.048
  - Expenditures RMSE: Same year 0.045, 1 year 0.110, 2 years 0.305, 3 years 0.419, 4 years 0.409
  - Average pension in real terms Mean Error: -0.009, -0.012, -0.013, -0.013, -0.014 (same year to 4 years)
  - Average pension in real terms RMSE: Same year 3.393, 1 year 4.649, 2 years 5.707, 3 years 5.748, 4 years 5.771
  - Number of pensioners Mean Error: 0.009, 0.012, 0.013, 0.012, 0.011
  - Number of pensioners RMSE: Same year 0.128, 1 year 0.198, 2 years 0.273, 3 years 0.365, 4 years 0.483
  - Other expenditures Mean Error: -0.096, -0.170, -0.224, -0.256, -0.248
  - Other expenditures RMSE: Same year 0.641, 1 year 1.008, 2 years 1.892, 3 years 2.432, 4 years 2.945
- Principal findings:
  - Since 2017, overall expenditures were underestimated due to underestimation in:
    - Average pension in real terms
    - Cost-of-living adjustment
    - Other expenditures
  - Number of pensioners was slightly overestimated, mitigating overall deviation.
  - Other expenditures (capital transfers, capital formation, intermediate consumption) were underestimated, possibly due to indirect inflation effects on nominal values.

### Financial balance projections and drivers
- Average contribution in real terms is an important driver of financial balance projection deviations.
- Some drivers net out between revenue and expenditure sides, notably inflation via COLA affecting both wages and pensions (a specific feature of Luxembourg).
- Pension law change noted: article 225 requests a lower index once expenditures exceed contributions, expected by 2026; thereafter, real wage growth will only partially be reflected in pension indexation.
- Number of pensioners and average pension projections tend to balance each other and are not major drivers of deviations.
- The average contribution and number of contributors drive bias more significantly; the ‘other’ category is another significant driver when deviations add up.

### Accuracy of current-year estimates (Box 1)
- Projections start in August using partial mid-year data; mid-year estimates must themselves be partially projected.
- Analysis found:
  - Mid-year estimates for cash benefits closely align with actual outcomes (ex-post).
  - “Other expenditure” and revenue estimates are less precise, particularly during COVID years 2020 and 2021.
  - For some components (number of pensioners, average pension) deviations can be significant, but component deviations often cancel out at the aggregate cash benefits level.
  - Overall, improving current-year subcomponent estimates would likely have only a modest effect on total revenue and expenditure forecasts for the current year.

### Recommendations (improvements to forecasting)
- General focus: improve forecasting methodology, refine input sources, and enhance communication of model results.
- Methodology and tools:
  - Further adopt multivariate and ensemble models:
    - Combine multiple models (traditional and advanced), assign appropriate weights (Annex 3), to reduce individual model biases.
    - Multi-model strategy has proven effective at IGSS for estimating average real contributions.
  - Continue using flexible models:
    - Expand beyond ARMA and error correction frameworks to models such as GRU neural networks and SCAR VAR to capture non-linear, time-varying relationships, useful during atypical periods (e.g., 2022-2023).
  - Leverage AI-powered frameworks:
    - Use automated or low-code infrastructures to automate model selection, testing, and recommendations for small teams.
  - Apply multi-model and AI principles to other revenue streams to build a consistent, robust forecasting system across pension report components.
- Improve macroeconomic input forecasting:
  - Strengthen forecasts for employment and wages (key sources of uncertainty).
  - Develop complementary projections for important macroeconomic inputs to test sensitivity of pension finance forecasts, not to substitute STATEC inputs but to offer options.
  - Explore multivariate models and draw on a broader set of variables for wage and employment forecasts, including labor-market data from the wider Luxembourg region.
- Table 5 summary of gaps and suggestions (selected items):
  - Number of contributors: Projection gap Small; current method Based on STATEC employment forecast; suggestion Refine employment projection (input from STATEC) and consider alternative model on employed workers’ compensation.
  - Number of pensioners: Projection gap Small but persistent; current method Linear regression; suggestion None, continue past forecast improvements.
  - Average real contribution: Projection gap Most significant and persistent; current methods Error Correction Model, Transfer Function Model, ARMA; suggestion Refine wage projection (input from STATEC), extend use of flexible, multi-models.
  - Cost of living adjustment: Projection gap Negligible; current method Inflation forecast (input from STATEC); suggestion None.
  - Other revenues and Other expenditure: Projection gap Heterogenous; current method Linear based on past observations; suggestion Fine tune projection with additional co-variates.

*Source: Authorities and IMF Staff estimates (Luxembourg), Rentenversicherungsbericht der Bundesregierung (Germany), Conseil d’Orientation des Retraites (France), Comité d’études sur le vieillissement (Belgium).*

### 23.        To further strengthen the transparency of pension projections, communication could be

### IV. Long-term Projections

### Strengthening transparency and communication of pension projections
- Executive summary: quantify how much of projection changes stem from data revisions, methodological adjustments, or updated assumptions.16
- Sensitivity analysis: include a margin of error around the central projection using confidence intervals.16
- Twice-yearly systematic analysis of deviations between subsequent projections within the CEFN framework is recommended.16
- More frequent reporting to line Ministries during large economic shocks and high uncertainty to enable early detection of deviations; aim for shorter intervals of data collection in crises (good practice example: Belgium during COVID).17

*16 For this purpose, the authorities can benefit from the systematic analysis of deviations between subsequent projections twice a year within the framework of the CEFN.*
*17 Under the framework of the Economic Risk Management Group real time data was compiled to evaluate the state of the Belgian Economy in short intervals using different datasets and special ad-hoc surveys distributed to businesses by various employer associations.*

### A. Overview of projection methodology
- Model basis:
  - Deterministic cohort model from the ILO, customized to Luxembourg’s pension system.
  - Two components: demographic (projects contributors and pensioners) and financial (estimates income and expenditure).
  - Statuses modeled: active, inactive, pensioner; financial variables (salaries/revenues, pensions) projected annually until 2070.
- Key modeling features:
  - Age- and career-length-specific earning profiles; general real wage growth and inflation adjustments.
  - Labor productivity assumptions simulate real wage growth.
  - Actuarially determined transition probabilities (mortality, disability, retirement).
  - Benefits and contributions calculated by one year age groups, gender and residency to reflect high share of non-resident scheme members.
  - Macrosimulation implemented in LIAM2 environment (provided by Belgian Federal Planning Bureau LIAM2).
  - Macro-economic and demographic assumptions provided by the AWG, Eurostat and STATEC.

### B. Volatility of past projections — observed changes and implications
- Key milestones defined:
  - Event 1: year when pension expenditures exceed contribution revenues (pay-as-you-go rate surpasses statutory contribution rate of 24 percent of wages). Under current law Event 1 requires adopting lower pension indexation (limited to inflation and not more than 50 percent of real wage growth).
  - Event 2: year when pension reserve falls below statutory threshold of 1.5 times the annual expenditure; if within current or forthcoming 10-year coverage a higher contribution rate must be legislated (Art. 238 Social Security Code).
  - Event 3: year when the pension reserve is fully depleted.
- Recent vintage comparisons and movement:
  - Event 3: projected in 2043 in 2016 national projections and delayed to 2045 in the 2025 projection.
  - Event 2: consistently projected around 2040 across vintages, with some variation due to assumed rates of return.
  - In the latest 2025 projections, all three critical events occur two years earlier compared to previous projections.
- International context:
  - Between 2021 and 2024 AWG projections, 16 out of 27 EU Member States revised 2050 pension expenditure projections downwards by an average of 1.3 percentage points of GDP.
  - Luxembourg revision between 2021 and 2024 was a reduction of 2.3 percentage points of GDP.
  - Deviations are larger for smaller EU countries (less than 3 million inhabitants): standard deviation 1.0 percent of GDP, compared to 0.85 percent of GDP for larger EU countries.
- Horizon sensitivity:
  - Longer projection horizons amplify impact of parameter changes; shorter horizons (e.g., 15–20 years) are more stable across vintages.

### C. Main drivers of past volatility and recent shifts
- Drivers for the advancement of Event 1 to 2026:
  - Latest IGSS projections estimate total expenditures will surpass contributions by 2026 rather than 2028 (2024 AWG estimates).
  - Earlier Event 1 requires earlier adoption of lower pension indexation, with implementation expected from 2029.
  - Employment growth revisions are primary driver: change in employment assumptions accounts for approximately 81 percent of the increase in the projected PAYG rate by 2026 from 23.4 percent (projection 2023) to 24.3 percent (projection 2024).
  - Other contributors: slight increase in number of pensioners and real pension indexation play smaller roles.
- Employment assumptions specifics:
  - STATEC 2024 inputs suggest employee growth and contributors growth will be significantly lower than assumed in 2023, with a downward adjustment of about one percentage point for the period 2024-2026.
  - Uncertainty remains whether 2024 low growth becomes a new norm.
- Drivers of long-term pension expenditure revisions (2021 vs 2024 AWG):
  - Actual pension spending in 2022 was 0.8 percentage points of GDP below 2021 AWG projections—about one-third of the deviation between 2021 and 2024 projections for 2050 is due to 2022 updated data.
  - Revisions to economic and demographic assumptions (employment growth, productivity, Eurostat demographic projections including net migration) are the main explanations for downward revision in pension expenditures between 2021 and 2024 AWG projections.
  - Employment growth revisions increase projected GDP (denominator), reducing expenditure/GDP ratios. Lower productivity assumptions had a smaller effect.
- Model and methodological updates (implemented with 2024 AWG) that changed projections:
  - Inclusion of non-active insured individuals to improve estimates of new retirees’ pensions.
  - Endogenous modeling of foreign insurance periods replicating base-year retirement records — resulting in more retirees with incomplete Luxembourg careers, most retiring at 65 and increasing share of non-resident new retirees.
  - New estimation of non-contributory insurance periods using current retiree data.
  - Three-year delay assumed for automatic adjustment mechanism under constant policy (instead of immediate implementation).
  - Revised assumptions for disability and survivor pensions (reducing overestimation and lowering expenditures until the 2050s).
  - Number of old-age pensioners revised upward, increasing expenditures in later decades.
  - Entry ages into the labor market adjusted upward, shortening insurance careers and contributing to rise in old-age pensioners.
  - Accrual rate calculation updated to include full pension relative to total contributory income (not only earnings-related part).
  - Net effect: methodological changes improved accuracy, lowered projected expenditures by 2050, but increased them by 2070.

### D. Recommendations and sensitivity of outcomes to key assumptions
- Rate-of-return assumptions:
  - Current Luxembourg assumption: 2.2 percent nominal at the start (based on historic cash income only), rising to 4 percent by 2050.24
  - Translates to 0.2–2 percent in real terms assuming 2 percent inflation.
  - Fund historical average nominal return since SICAV launch in 2007 is 5.0 percent.
  - Sensitivity examples:
    - If 4 percent rate of return assumed over 2024-2070: Event 2 shifts from 2039 to 2041; Event 3 shifts from 2045 to 2046.
    - If 5 percent assumed: Event 2 shifts to 2042; Event 3 shifts to 2048.
  - Conclusion: alternative (higher) return assumptions have only modest impact on timing of key funding events.
- Model improvement options (Table 8 highlights priorities and resource intensity):
  - Reassess rate of return assumption — Priority: High; Fiscal Impact: Medium; Distributional Impact: Low; Resource Intensity: Low.
  - Reassess employment growth assumptions — Priority: High; Fiscal Impact: Medium; Distributional Impact: Medium; Resource Intensity: Low.
  - Implement dynamic micro-simulation — Priority: Medium; Fiscal Impact: Medium/Low; Distributional Impact: High; Resource Intensity: High.
  - Improve survivor pension projections — Priority: Medium; Fiscal Impact: Low (mainly after 2040); Distributional Impact: Medium; Resource Intensity: Medium.
  - Model documentation — Priority: Medium; Fiscal Impact: None; Distributional Impact: None; Resource Intensity: Medium.
  - Further improve revenue and expenditure projection — Priority: Medium; Fiscal Impact: Medium/Low; Distributional Impact: Medium; Resource Intensity: Medium.

*Source: IMF | Technical Report (excerpt).*

### 37.        Sensitivity analysis should be systematically included in projections to show the limited

### tarea2025105-source-pdf - 37.        Sensitivity analysis should be systematically included in projections to show the limited

### Sensitivity analysis and reporting practices
- Sensitivity analysis should be systematically included in projections to show the limited impact of alternative return assumptions, and this point should also be highlighted in executive summaries.
- For EU reporting, retaining the AWG-aligned assumption ensures comparability and fiscal prudence; for national analyses, complementary scenarios could be considered.
- Maintain a prudent central scenario to avoid overestimating fund growth, and present alternative scenarios to provide context, support policymaking, and show robustness.
- Major IGSS pension projection publications (e.g., 5-year actuarial reports and Cahier 18) already present sensitivity analysis; authorities are encouraged to add executive summaries outlining sensitivity and robustness.
- Changes between projection rounds should be systematically categorized into: (1) updates to assumptions, (2) data revisions, and (3) methodological adjustments.

### Rates of return — international comparators and Luxembourg AWG alignment
- Luxembourg (AWG): Linked to market expectations of bond interest rates in mid-term, prudent choice for long-term — real: 0.2% in 2024 → 2% by 2050 (assuming 2% inflation).
- Norway: 3% real.
- Sweden: Base: 3.25% real; Optimistic: 5.5% real.
- Finland: 2.5% real (to 2031) → 3.5% real (from 2032).
- Canada (CPP): 3.69% real.
- ILO: Country-specific.
- OECD: 2.5% real (net of fees).
- Figure 17 source: Fonds de Compensation (2025) and IMF Staff estimates.
- Recommendation: update assumed rate of return as a low-resource, high-impact priority.

### Employment growth assumptions and fiscal timing sensitivity
- Over the period 2023–2024, employment growth was significantly overestimated.
- Most recent projections assume employment growth of over 2 percent per year for the period 2026–2030.
- Scenario: If employment growth assumption is revised to 1 percent:
  - Projected year of Event 2 (when reserves fall below 1.5 times annual expenditure) shifts from 2039 to 2037.
  - Expected year of Event 3 (reserve depletion) moves from 2045 to 2043.
- STATEC is analyzing trends and considering revising medium- and long-term employment growth downward.
- Recommendation: thoroughly examine drivers behind recent weak employment growth and reflect potential downward revisions in projections; account for potential AI impacts on employment and productivity.

### Pension model refinements and prioritization
- Recent model improvements noted, but further refinements recommended—particularly after AWG 2027 long-term projections.
- Key improvement areas:
  - Introduce greater distributional granularity based on micro-simulation.
  - Enhance survivor pension projections.
  - Improve model documentation to support transparency and continuity.
- Prioritization guidance given limited administrative capacity:
  - Low-resource, high-impact: updating assumed rate of return; revisiting mid- and long-term employment growth assumptions; improving documentation.
  - Resource-intensive, deferrable: dynamic and granular micro-simulation (defer after AWG projections in 2026).
- Given current modeling relies on only two individuals, documentation and reproducibility are critical.

### Micro-simulation and distributional accuracy
- Current model lacks distributional micro-simulation; no micro-simulation used to project future contribution careers.
- Individuals assumed to follow average contribution density by age, gender, and insurance year group; episodes of high or low contribution density are generally not captured.
- Consequence: potential underestimation of tails of distribution of accrued insurance years and impaired modeling of non-linear benefit features (minimum and maximum pension).
- Recommended phased approach:
  - Intermediate: assume individuals remain in observed contribution density and earnings percentile (by age and gender) based on recent historical data.
  - Long-term: dynamic micro-simulation where individuals transition across earnings and contribution density states over time based on socio-economic characteristics and lagged labor market performance.
- Consider applying updated ILO Pension Model (with micro-simulation) and collaboration with LISER.

### Survivor pensions — assumptions and needed adjustments
- 2024 AWG projections improved survivor pension modeling by linking inflows to current eligibility probabilities; projected expenditures in 2070 are 0.7 percentage points of GDP lower than in the 2021 projections.
- Risk factors suggesting further declines in survivor pension inflows:
  - Falling marriage and cohabitation rates among younger cohorts since 2011 (STATEC, 2024).
  - Increasing share of women with substantial own pension entitlements—raising the share affected by income testing.
- Income-testing rule to reflect: survivor pensions are reduced when total income (survivor pension plus personal income) exceeds 1.5 times the reference amount—€3,918 per month per month. The pension is then reduced by 30 percent of the amount exceeding this threshold.
- Recommendation: IGSS should reflect trends in marriage/cohabitation and the likely increasing share of survivors affected by income testing in upcoming model updates.

### Revenue and expenditure projection refinements
- Revenue side: projections account for differences in labor force participation and employment rates by gender, sector, and residence status, but employment rates are not sufficiently modeled by age—most ages use a constant rate.
- Recommendation: introduce age-specific employment rates for greater precision.
- Expenditure side: simulation of contribution careers currently determines future pension entitlements; estimation of non-contributory periods relies on stock measures from base year without projecting cohort evolution (parental leave, unemployment, education, other non-contributory periods).
- While such refinements may not materially change baseline projections, they would strengthen accuracy for reform evaluation.

### Transparency, communication, and institutional capacity
- Strengthen communication by producing concise executive summaries that present main drivers of long-term pension finances and explain deviations between projection vintages.
- Develop a detailed model description documenting main calculation steps, assumptions, and data sources to improve transparency, reproducibility, internal knowledge transfer, and continuity.

### Artificial Intelligence (AI) — monitoring, scenarios, and stress testing
- Recommendation: monitor AI impacts on Luxembourg’s labor market and conduct a stress test of the pension system under “Future of Work” scenarios.
- IMF (2025) simulations for Europe: medium-term productivity gains (over a five-year horizon) could reach around 0.8 percent cumulatively; U.S. approx 0.7 percent (Acemoglu, 2024).
- Luxembourg estimates: cumulative productivity gains near 1 percent under the baseline scenario, and as much as 3 percent under more optimistic assumptions about AI exposure and adoption.
- Sectoral exposure estimates for Luxembourg:
  - Approximately 33 percent of jobs fall into sectors with high exposure to AI (e.g., IT Services, Financial Activities, Specialized Scientific Services).
  - About 50 percent lie in sectors with medium risk of AI impact (e.g., Public Administration, Health, Hospitality).
  - Remaining 16 percent are in sectors with lower or variable AI risk (e.g., Construction and miscellaneous sectors).
- Implement Consulting Group (2024) estimates: 72 percent of jobs likely to be augmented due to generative AI, 6 percent of jobs may be partially or fully displaced, and 22 percent of jobs may experience no automation at all due to AI.
- Potential labor-market consequences of AI adoption:
  - Augmented productivity that can boost pension system revenues via higher productivity and possibly longer working lives.
  - Reshaped employment patterns with uneven sectoral impacts, more frequent job transitions, career interruptions, growth in non-standard work, more fragmented careers, weaker contribution histories, and greater reliance on minimum or partial pensions.
- Recommended policy responses:
  - Integrate forward-looking labor market scenarios including AI adoption pathways into pension modelling.
  - Implement comprehensive workforce development and social protection strategies (upskilling/reskilling, smooth job transitions, reduce rigidities in hiring/termination).
  - Promote basic AI literacy across the workforce.
  - Use targeted instruments (e.g., tax incentives for training, public-private partnerships).
  - Carry out stress test simulations to assess AI adoption effects on public finances and pension distribution (via micro-simulation).

*Source: https://www.imf.org/-/media/files/publications/tar/2025/english/tarea2025105-source-pdf.pdf*

### Bibliography

### Bibliography

### Key references cited
- Accenture. 2024. Can Switzerland Lead the Way in Gen AI? Report.
- Bonfiglioli, A., R. Crinò, G. Gancia, and K. Papadakis. 2025. “Robots, AI, and the Labor Market: Evidence from US Commuting Zones.” Economic Policy 40 (121): 145–194.
- Chambre des Députés. 2024. Question Parlementaire. Grand-Duché de Luxembourg.
- CNFP. 2021. Evaluation de la soutenabilité à long terme des finances publiques, Report.
- Dekkers, G., et al. 2024. Long-Term Projections of Pension Adequacy in a Selection of Countries. Luxembourg: Publications Office of the European Union.
- Eurostat. 2025. “EU Received 4.3 Million Immigrants in 2023.”
- Finnish Centre for Pensions. 2017. Scenario Calculations of the Impact of the Change in Work on the Pension System and Public Finances. Reports No. 03/2017.
- Forbes. 2025. “Intense Debates Over Pension System Reform.” Forbes Luxembourg.
- IGSS. 2024. 2024 Aeging Report – Pension Projections, Country Fiche for Luxembourg.
- IGSS. 2025a. Contribution de l’IGSS dans la Consultation sur la Viabilité du Système des Retraites.
- IGSS. 2025b. Prolongation de la carrière professionnelle dans le contexte du régime général d’assurance pension.
- Implement Consulting Group. 2024. The Economic Opportunity of AI in Luxembourg.
- Irish Department of Finance. 2024. Artificial Intelligence: Friend or Foe.
- OECD. 2023a. Evaluation of Belgium’s COVID-19 Responses: Fostering Trust for a More Resilient Society.
- OECD. 2023b. The Impact of AI on the Workplace: Main Findings from the OECD AI Surveys of Employers and Workers.
- Question Parlementaire n°1327. Chambre des Députés du Grand-Duché de Luxembourg.
- Yejati, A. 2025. “Hybrid Jobs: How AI Is Rewriting Work in Finance.” Brookings Institution.

---

### Annex 1 — Comparison of Indexation to Inflation in France, Germany, Belgium, and Luxembourg

### Summary of indexation rules (Table A1.1)
- Germany
  - Minimum Wage (Mindestlohn): Yes indexed to inflation; Automatic Indexation: No. Adjusted every two years by an independent commission. No automatic link to inflation.
  - Average Wages: No indexed to inflation; Automatic Indexation: No. Depends on collective agreements. Adjustments often delayed.
  - Pensions: Yes indexed to inflation; Automatic Indexation: Partially. Adjusted using a formula based on wages and inflation, with a lag.
- Belgium
  - Minimum Wage (Mindestlohn): Yes; Automatic Indexation: Yes. Indexed to the “health index” (past CPI excluding alcohol and tobacco and petrol but including heating fuel, gas, and electricity) — triggered every time the index increases by 2% or more since last increase.
  - Average Wages: Yes; Automatic Indexation: Yes. Wages in most sectors automatically indexed to inflation based on the health index.
  - Pensions: Yes; Automatic Indexation: Yes. Social benefits, including pensions, automatically increased by 2% each time the index exceeds the “threshold index.”
- France
  - Minimum Wage (SMIC): Yes; Automatic Indexation: Yes. If CPI increases by at least 2% Minimum wage increases automatically in the same proportions; the minimum wage is increased every year to measured inflation for 20% households with the lowest incomes and half of the gain in purchasing power of the average hourly wage of workers and employees.
  - Average Wages: No; Automatic Indexation: No. Depends on collective bargaining.
  - Pensions: Yes; Automatic Indexation: Partially. Adjusted annually based on forecast inflation, with correction the following year.
- Luxembourg
  - Minimum Wage: Yes; Automatic Indexation: Yes. Automatically adjusted via wage indexation system when CPI increases by 2.5%.
  - Average Wages: Yes; Automatic Indexation: Yes. All wages are subject to automatic indexation via the wage scale.
  - Pensions: Yes; Automatic Indexation: Yes. Automatically adjusted with the wage indexation system, like wages.

- Source noted: OECD Employment Outlook 2023, Missoc (European Commission) and European Central Bank (2008), Wage indexation mechanisms in euro area countries, ECB Monthly Bulletin, May 2008, Box 5.

---

### Annex 2 — Decomposition of Projection Deviations

### Conceptual decomposition framework
- Fundamental decomposition: deviations of revenue, spending, and balance can be decomposed into deviations of their main components, weighted by component shares.
- Notation: “Δx” equals the difference between forecast and observed value of x.

### Decomposition of the Revenue Projection Gap
- Revenue identity:
  - Revenue = Number of contributors * Average contribution * COLA/100 + Other revenue
- Decomposition formula structure (as presented):
  - ΔRevenue / Revenue = (share of contributors) * Δ(Number of contributors / Number of contributors) + (share of average contribution) * Δ(Average contribution / Average contribution) + Δ(COLA share) + (share of Other revenue) * Δ(Other revenue / Other revenue)

### Decomposition of the Expenditure Projection Gap
- Expenditure identity:
  - Expenditure = Number of pensioners * Average pension * COLA/100 * Readjustment + Other Expenditure
- Decomposition formula structure (as presented):
  - ΔExpenditure / Expenditure = (share of pensioners-related term) * Δ(Number of pensioners) + (share of average pension) * Δ(Average pension) + Δ(COLA share) + Δ(readjustment term) + (share of Other Expenditure) * Δ(Other Expenditure / Other Expenditure)

### Decomposition of the Financial Balance Projection Gap
- Balance identity:
  - Balance = Revenue - Expenditure
- Decomposition formula structure (as presented):
  - ΔBalance / Balance = (share of Revenue) * ΔRevenue / Revenue − (share of Expenditure) * ΔExpenditure / Expenditure
- Detailed expanded form provided:
  - Balance = Number of contributors * Average contribution * COLA/100 + Other revenue − Number of pensioners * Average pension * COLA/100 * Readjustment − Other Expenditure
  - The document provides fully expanded ΔBalance expressions with component-wise Δ terms and indicates the terms can be rearranged into concise forms showing contributions of ΔNumber of contributors, ΔAverage contribution, ΔCOLA, ΔOther revenue, ΔNumber of pensioners, ΔAverage pension, ΔReadjustment, ΔOther Expenditure, and Δeconomic/other terms.

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### Annex 3 — Options for Short-term Forecast Refinements

### Ensemble weighted-average forecasting approach
- Approach: test a wide range of model specifications (classical, penalized, machine learning (ML), mixed frequency (MF)) and compute a weighted average of model forecasts.
- Model inclusion: if a model passes tests and yields a result, it is included in set M.
- Weighting mechanics:
  - For model m, accuracy is δ_m and its inverse φ_m = 1/δ_m.
  - Initial weight ξ_m = φ_m / [∑_{m∈M} φ_m].
  - To bias weights toward better models, an exponent S is applied:
    - ξ_m^p = φ_m^p / [∑ φ_m^p] where p (denoted S) is determined based on lasso method.
- Input treatment: all input variables tested and treated for outliers, seasonally adjusted, nowcasted and decomposed if frequencies differ. VARX Lasso used to test influence of variables.
- Mixed-frequency models used to combine quarterly and monthly data.

### Contribution forecast models (total contributions)
- 48 models estimated; final estimate is weighted average. Mixed-frequency models used.
- Two best performing models (in-sample and out-of-sample error indicators): Gated Recurrent Unit (GRU) and VARX Own/Other Sparse Group Penalty.
- Table A3.1: Selected performance metrics (Model, In Sample MAPE, In Sample RMSE, Out Sample MAPE, Out Sample RMSE) — examples preserved exactly:
  - VAR Smoothly Clipped Absolute Deviation org: 0.92% | 4,950,000 | 2.59% | 11,600,000
  - VAR Smoothly Clipped Absolute Deviation log: 1.10% | 5,770,000 | 0.98% | 5,260,000
  - VAR Smoothly Clipped Absolute Deviation diff: 0.78% | 4,670,000 | 0.98% | 5,520,000
  - ... (table includes many models; best performing examples highlighted below)
  - VECM org: 0.60% | 3,210,000 | 1.35% | 8,100,000
  - HVAR Componentwise Lasso diff: 0.64% | 3,400,000 | 0.98% | 5,110,000
  - VAR org: 0.61% | 3,220,000 | 1.16% | 6,630,000
  - VARMA log: 0.57% | 3,390,000 | 1.09% | 5,650,000
  - ARDL log: 0.63% | 3,680,000 | 0.83% | 4,350,000
  - LSTM diff: 0.82% | 4,610,000 | 0.82% | 4,490,000
  - GRU diff: 0.77% | 4,630,000 | 0.79% | 4,680,000
  - VARX Own/Other Sparse Group Penalty diff: 0.77% | 4,660,000 | 0.80% | 4,520,000
  - Minnesota BVAR log: 0.59% | 3,150,000 | 0.74% | 3,920,000
  - TVP BVAR with SV org: 0.55% | 2,890,000 | 1.40% | 6,560,000
  - Naive org: 6.25% | 47,300,000 | 6.25% | 47,300,000
- Source: Authorities, mission calculations.
- Note: Performance selection based on MAPE and RMSE. Naïve estimates correspond to simple ARMA model with no explanatory variable.

### Details of the two best performing contribution models (Table A3.2)
- Model 1 (GRU)
  - Main Variable: Pensions contributions (differenced)
  - Unit: Euros
  - Explanatory Variables: Y2: Contribution ceiling (differenced); Y3: Compensation of Employees, Current Prices (differenced); Y4: Number of contributors (differenced)
  - Model Type: GRU model with 4 endogenous variables
  - Technical details:
    - 1 layer with a hidden state size of 80
    - 8 epochs
    - Training stopped after 5 consecutive increases in validation loss
- Model 2 (VARX Own/Other Sparse Group Penalty)
  - Main Variable: Pensions contributions (differenced)
  - Unit: Euros
  - Explanatory Variables: Y2: Contribution ceiling EUR; Y3: Compensation of Employees, Current Prices; Y4: Number of contributors
  - Model Type: VARX Own/Other Sparse Group Penalty model with 4 endogenous variables
  - Technical details:
    - Maximum of 12 modelled lag(s).
    - Penalty parameter: 0.0031 selected using time series cross-validation
- Source: Mission’s findings.

### Employment forecast models
- Approach: similar ensemble approach; 27 models used; labor market inputs include total employment, employed, migrants, low-skilled, and labor market variables from greater Luxembourg area.
- Table A3.3: Selected model performance examples:
  - ARDL org: In-sample MAPE 0.06% | In-sample RMSE 329 | Out-of-sample MAPE 0.34% | Out-of-sample RMSE 1,753
  - ARDL log: 0.06% | 376 | 0.32% | 1,744
  - VARX Lasso diff: 0.09% | 495 | 0.09% | 533
  - VAR Elastic Net diff: 0.09% | 512 | 0.10% | 556
  - HVAR Componentwise Lasso diff: 0.07% | 429 | 0.08% | 469
  - VARX Lag Group Lasso diff: 0.06% | 368 | 0.07% | 425
  - Naive org: 0.57% | 3,502 | 0.57% | 3,502
- Source: Authorities, mission’s calculations.

### Selected models for wages (Table A3.4)
- Comparison features for three models:
  - VARX Lag Group Lasso
    - Number of Endogenous Variables: 15
    - Maximum Modelled Lags: 12
    - Penalty Parameter: 7.9718
  - HVAR Own/Other Lasso
    - Number of Endogenous Variables: 15
    - Maximum Modelled Lags: 12
    - Penalty Parameter: 2.7827
  - VAR Weighted Lag Lasso
    - Number of Endogenous Variables: 15
    - Maximum Modelled Lags: 12
    - Penalty Parameter: 0.0004
- Source: Authorities, mission’s calculations.

### Comparison with LPFP projections
- Result: The weighted average forecast method suggests:
  - A lower level of total contributions for 2025 by 1.2 percent compared to LPFP 2024/2029 projections.
  - Slightly higher contributions by 0.6 percent projected for 2026 compared to LPFP 2024/2029 projections.
- Note: The alternative contribution projection indicates that the forecasts of IGSS are relatively robust. The document suggests carrying out similar robust checks for other model components and for longer time series.

### Figure (described)
- Figure A3.1: Total Contributions in Euro: Model Fit and Forecast
  - Note: Pension Contributions only (D61).
  - Data series shown: Historic (rhs), Forecast (rhs), Fitted Values (rhs), Annual Estimate (lhs), LPFP 2024/2029 (lhs).
  - Axis scales evident: vertical axes include values up to 6,000,000,000 on one axis and up to 700,000,000 on the other; time span plotted from 2022-02 through 2026-11 (monthly points).

### Glossary of projection models (Table A3.5) — key model types and descriptions
- Classical Models: VAR; VECM; VARMA; ARDL; Bayesian VAR (BVAR) with Steady State Prior; Minnesota BVAR; Time-varying Bayesian VAR.
- Penalized Models (Regularization Methods): Ridge Regression; Lasso; Elastic Net; VECM Lasso; Group Lasso; Lag Group Lasso; Lagweighted Lasso; Endogenous-First VARX; VARX Own/Other Group Penalty; VARX Own/Other Sparse Group Penalty; HVAR models (Componentwise Lasso; Own/Other Lasso; Elementwise Lasso).
- Machine Learning Models: Artificial Neural Network (ANN); Long Short-Term Memory (LSTM); Gated Recurrent Unit (GRU).
- Mixed Frequency Models: MIDAS; Unrestricted MIDAS; MIDAS with Penalties; MIDAS Sparse Group Penalty; MIDAS Lasso.

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*Source: tarea2025105-source-pdf - Bibliography; Annex 1, Annex 2, Annex 3 (excerpts) from the provided PDF content.*

### Annex 4. Overview of Pension System Rules

### Annex 4. Overview of Pension System Rules

### Pension System Parameters
- Source: IMF Staff based on ISSA Country Profile.
- Table summarizes statutory parameters covering contributions, ceilings, retirement ages, benefit formula, minimum pension, indexation, credited periods, and penalties/bonuses.

### Contributions and Ceilings
- Contribution rates:
  - 24% total: 8% employer, 8% employee, 8% government; up to 5× minimum wage ceiling.
- Contribution ceilings:
  - Pensionable earnings capped at 5× social minimum wage.

### Retirement Ages and Insurance Requirements
- Normal retirement age:
  - 65 years with at least 10 years of insurance.
- Early retirement:
  - 57 years with 40 years of contributions; or 60 years with 40 years of insurance (including credited).
- Insurance years needed (old age):
  - 40 years for maximum accrual; minimum 10 years for lifelong payment.

### Old-Age Benefit Formula and Minimum Pension
- Old age benefit formula:
  - Mixed: flat-rate benefit + earnings-related benefit with accrual rate of 1.782% of adjusted lifetime total earnings (gradually decreasing until reaching 1.6% by 2052) plus 0.015% (gradually rising to 0.025% by 2052) of adjusted lifetime total earnings for each year the insured's age and years of coverage exceeds 94 years (gradually rising until reaching 100 by 2052).
- Minimum Pension:
  - €2,293.55 a month is paid in 2025 with at least 40 years of coverage.
  - If the insured contributed for at least 20 years but less than 40 years, the guaranteed minimum pension is reduced by 1/40 for each year of coverage less than 40 years.

### Pension Indexation and Credited Periods
- Pension indexation:
  - Fully indexed to prices and, under a semi-automatic readjustment mechanism, also to real wage growth.
  - Real wage growth adjustment applied in full when contributions exceed expenditures but reduced (via a moderator coefficient between 0 and 0.5) if the system’s balance deteriorates.
- Credited periods:
  - Periods during which the insured was covered by sickness, maternity, or work injury benefits (since 2011), unemployment support, or the minimum income allowance are treated as credited contribution periods.
  - Same applies to years spent in study or apprenticeship between ages 18 and 27, time spent caring for a child under age 6 (or under age 18 if the child is disabled), and periods of receiving long-term care or invalidity benefits.

### Early/Late Retirement Adjustments
- Pension penalty/bonus for early/late retirement:
  - not applied

*Source: IMF Staff based on ISSA Country Profile.*

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_Source: https://www.imf.org/-/media/files/publications/tar/2025/english/tarea2025105-source-pdf.pdf_