## _wp12170

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---

### Introduction: scope and headline quantitative impacts
- Longevity risk defined: the risk that, on average, people live longer than expected.
- Empirical focus: U.S. Department of Labor Form 5500 data to estimate effect of life expectancy assumptions on pension liabilities.
- Estimated sensitivity:
  - Each year of life expectancy raises pension liabilities by 3 to 4 percent.
- Aggregate U.S. private DB pension context (as of 2007):
  - Private DB pension plans underfunded by $83 billion.
  - Total aggregate pension liabilities approximately $2.2 trillion.
  - A one-year shock to longevity could increase U.S. private DB pension liabilities by as much as $84 billion, doubling the degree of underfunding.
- Broader magnitudes:
  - Impact of an additional year of life expectancy on U.S. private and public pension liabilities corresponds to an amount equivalent to 1.5 percent of U.S. 2007 Gross Domestic Product (GDP).
  - Aggregate value of global private DB pension liabilities: $23 trillion.
  - A similar one-year longevity shock could raise global private pension liabilities by as much as $2.8 trillion.
- Novelty and methodological strengths:
  - First empirical assessment (per authors) using actual Form 5500 actuarial assumptions to estimate average longevity impact across U.S. private DB pension plans.
  - Method disentangles the effect of an additional year of life expectancy on pension liabilities without imposing exogenous improvement magnitudes.

### Related literature: forecasting, liability impact estimates, and risk transfer
- Mortality forecasting approaches:
  - Extrapolative approaches (historical trends) and process-based methods (biomedical causes of death).
  - The Lee and Carter (1992) model: time-series-based mortality index; explains 93 percent of past variation in U.S. mortality rates.
  - Limitations: difficulty detecting structural changes and cohort effects; references to Lee and Miller (2001), CMI (2004), CMI (2011), Girosi and King (2007).
- Evidence of persistent underestimation of longevity improvements:
  - U.K. Office for National Statistics: forecasts were consistently too low in each successive forecast.
  - Bongaarts and Bulatao (2000): 20-year forecasts in Australia, Canada, Japan, New Zealand and the United States underestimated longevity improvements by three years on average.
- Prior pension liability impact estimates:
  - Antolin (2007): unexpected improvement in life expectancy of one-year per decade could increase pension liabilities by 8-10 percent for a hypothetical closed fund (age-structure dependent).
  - Dushi, Friedberg, and Webb (2010): updating mortality tables (Lee-Carter implied increase of life expectancy at age 60 of about 3 years since early 1980s) would increase liabilities by 12 percent for the average male plan participant.
- Longevity risk transfer and mitigation:
  - Market solutions: pension buy-ins, buy-outs, securitization, longevity swaps, longevity bonds.
  - Bifis and Blake (2009) compare trade-offs across methods; IMF (2012) documents growing but overall small global activity in capital-market-based longevity risk transfer (with exceptions: United Kingdom and the Netherlands).
  - Sponsor-side mitigation: shift from DB to DC transfers longevity risk to employees; purchasing annuities is an employee hedge but:
    - Mitchell, Poterba, Warshawsky, and Brown (1999): annuity purchase cost is significant for average retiree.
    - Dushi and Webb (2006): few households purchase annuities; prices often not actuarially fair due to adverse selection.
    - Fong, Mitchell, and Koh (2011): mandatory public-sector annuitization (Singapore) yields cheaper annuities than private provision.

### Data: Form 5500, measurement definitions, mortality tables, and sample coverage
- Primary dataset: filings of Form 5500 pension plan data from U.S. Department of Labor, with research assistance from the Center for Retirement Research at Boston College.
- Sample period: filings between 1995 and 2007.
  - Motivation: since 1995 information on mortality tables used in actuarial computations became available; starting in 2008, Schedule B replaced by schedules MB and SB which do not explicitly identify mortality tables.
- Coverage and liability definition:
  - As of 2007, private DB pension plans covered approximately 42 million plan participants.
  - Pension liabilities correspond to the current liability measure as stated in Schedule B of Form 5500 (similar to accumulated benefit obligations; nominal value of already promised and accrued payments).
  - This definition excludes future years of service and potential wage increases (conservative).
  - Distinction between liability measures:
    - Actuarial Liability (AL): sponsor-set assumptions used for funding standard account; typically lower.
    - Current Liability (CL): state-imposed discount rates and mortality assumptions; typically higher.
- Actuarial assumptions reported: interest rate, mortality tables for men and women (pre- and post-retirement), etc.
- Mortality tables recorded (men, active workers, 1995–2007 sample) include:
  - 1951 Group Annuity Mortality Table (1951 GAM)
  - 1971 Group Annuity Mortality Table (1971 GAM)
  - 1971 Individual Annuity Mortality Table (1971 IAM)
  - Unisex Pensioner 1984 (UP 1984)
  - 1983 Individual Annuity Mortality Table (1983 IAM)
  - 1983 Group Annuity Mortality Table (1983 GAM)
  - Uninsured Pensioner Table 1994 (UP 1994)
  - 2007 Mortality Table (2007 Table)
  - Other (unspecified)
  - None (no table used)
  - Hybrid (modified standard tables)
- Observed patterns and descriptive statistics:
  - Substantial variation over time and across funds in mortality-table usage.
  - Fraction employing the 1983 GAM Table ranged between 69 percent and 16 percent over the sample period.
  - 12 percent of funds switched to the most recent mortality table in 2007.
  - The fraction of funds using unspecified tables (“Other”) increased from 7 percent in 2000 to 57 percent in 2007.
  - Plans using the most current mortality table or unspecified tables are on average larger than funds employing the 1983 GAM mortality table.
  - Steady increase in the average pension liabilities per plan over the sample period.
- Mortality-table differences and ranking:
  - For males aged 60:
    - Highest death rates: 1951 Group Annuity Mortality Table and 1984 Unisex Pension Table.
    - Most conservative longevity assumptions (lowest death rates): 1983 Individual Annuity Mortality Table and the 2007 Table.
  - Difference in implied life expectancy between the oldest and most current mortality table amounts to 4.20 years.
  - Longevity variable (implied life expectancy for males aged 63 under each mortality table) — Value (years):
    - No Table 14.32
    - 1951 Group Annuity Table 14.32
    - Unisex Pensioner 1984 Table 14.74
    - 1971 Group Annuity Mortality 15.34
    - 1983 Group Annuity Table 17.20
    - 1971 Individual Annuity Mortality 17.41
    - Uninsured Pensioner Table 1994 17.76
    - 1983 Individual Annuity Table 18.24
    - 2007 Mortality Table 19.54
  - Focusing on firms employing the 1983 Group Annuity Table, the difference with respect to the most recent table equals 2.34 years.

### Empirical approach: valuation model and regression specification
- Simple annuity-based valuation model:
  - L = p b Σ_{i=1}^T (1 − s_i) / (1 + r)^i
  - Approximation: L ≈ p b [1 − (1 + r)^{−n}] / r
- Log-linearized regression (panel regression with plan fixed effects):
  - log[L] = α + β1 log(p) + β2 log(b) + β3 log(r) + β4 n + β5 log(r)×n + ε
- Main parameter of interest: β4, the impact of one additional year of life expectancy on present value of pension liabilities.
- Note: average retirement age for sample equals 63.18 years.
- Sample selection:
  - Starting full sample: 157,320 plan-year observations.
  - After excluding observations classified as “Other”: 132,288 plan-year observations.
  - After deleting observations classified as “Hybrid”: final sample of 110,968 plan-year observations.

### Main empirical results and heterogeneity
- Retired participants subsample (baseline, Table 4):
  - Coefficients:
    - log(r) -0.945 ∗∗∗
    - log(p) 0.914 ∗∗∗
    - log(b) 0.519 ∗∗∗
    - n 0.030 ∗∗∗
  - Observations 89552
  - R2 0.742
  - Interpretation: liabilities to retired participants increase by about 3 percent for each year retirees live longer than expected.
- Subsample by liability size (Table 5): coefficient on n across quartiles (Small / Medium / Large / Very Large):
  - n 0.032 ∗∗∗ ; 0.024 ∗∗∗ ; 0.036 ∗∗∗ ; 0.036 ∗∗∗
  - Interpretation: an additional year of life expectancy increases liabilities to retired plan participants by 2.4 percent to 3.6 percent across quartiles.
  - Observations listed as a concatenation: 21410225942270922839 (as provided).
  - R2 values concatenated: 0.6100.5530.6160.730 (as provided).
- Total pension liabilities (full-sample adjustment using age-workforce distribution, Table 6):
  - Age-workforce distribution (subsample of 447 pension plans, 2005–2007):
    - Average (median) age equals 46.04 (47.25) years.
    - Half of the average workforce is older than 50 years; notable retirements at ages 50, 55, and 60.
  - Regression coefficients:
    - log(r) -1.675 ∗∗∗
    - log(p) 0.613 ∗∗∗
    - log(b) 0.054 ∗∗∗
    - n 0.037 ∗∗∗
    - X -0.007
  - Observations 11154
  - R2 0.531
  - Interpretation: using the age-workforce proxy for 2005–2007, an additional year of life expectancy raises pension liabilities by 3.7 percent.

### Robustness checks
- Treating unclassified mortality tables as RP-2000 (Table 7):
  - Full-sample coefficients:
    - log(r) -0.915 ∗∗∗
    - log(p) 0.933 ∗∗∗
    - log(b) 0.526 ∗∗∗
    - n 0.034 ∗∗∗
  - Observations concatenated: 11060726475278452802428263 (as provided).
  - R2 concatenated: 0.7640.6350.5710.6560.755 (as provided).
  - Interpretation: an additional year raises liabilities by 3.4 percent in this specification; larger funds show stronger impacts (coefficients up to 0.045 and 0.043 in some quartiles noted in text).
- Alternative assumptions for unclassified tables (most conservative 2007 Table or common 1983 GAM) — results unchanged: additional year raises liabilities between 2.4 percent to 3.4 percent.
- More recent time period (2001–2007) (Table 8):
  - Full-sample coefficients:
    - log(r) -0.655 ∗∗∗
    - log(p) 0.814 ∗∗∗
    - log(b) 0.431 ∗∗∗
    - n 0.034 ∗∗∗
  - Observations concatenated: 406639770102521026410377 (as provided).
  - R2 concatenated: 0.5500.4420.4530.5380.511 (as provided).
  - Interpretation: results qualitatively unchanged for more recent period.
- Robustness tables for unclassified mortality tables (Tables 9 and 10) report similar coefficient patterns and significance:
  - Table 9 (assume Other = 2007 Table) main n coefficients by subsample: 0.024 ∗∗∗ ; 0.024 ∗∗∗ ; 0.024 ∗∗∗ ; 0.030 ∗∗∗ ; 0.025 ∗∗∗
  - Table 10 (assume Other = 1983 GAM) main n coefficients by subsample: 0.027 ∗∗∗ ; 0.026 ∗∗∗ ; 0.023 ∗∗∗ ; 0.034 ∗∗∗ ; 0.034 ∗∗∗
  - Observations and R2 figures are reported in the paper (concatenated format in source).

### Quantitative magnitudes and economic significance
- Summary sensitivity: each additional year of life expectancy increases liabilities by 3 percent to 4 percent (baseline and robustness checks).
- Private DB pension liabilities in the United States amount to approximately $2.2 trillion.
  - Implication: a one-year shock to longevity would raise U.S. private DB pension liabilities by as much as $84 billion.
  - This would increase the amount by which private DB pension funds are underfunded by approximately 100 percent and imply that corporate pension sponsors have to make many multiples of typical annual pension contributions to match these extra liabilities.

### Policy-relevant observations and implications
- Longevity shocks create potentially large, lumpy increases in pension liabilities because mortality-table updates and legal update frequencies (Pension Protection Act of 2006 requires mortality-table updates at least every ten years) can produce discrete liability jumps.
- Pension Protection Act of 2006 constrained sponsor freedom to use outdated mortality tables but cannot fully mitigate underestimation of future life expectancy; ten-year update requirement allows room for large increases when tables are updated.
- Historical forecast underestimation implies longevity risk realization is likely; plans and sponsors face material funding and risk-management challenges.
- Risk-management options:
  - Market-based longevity risk transfer instruments exist but global activity remains limited overall.
  - Sponsor-side structural change (DB to DC) shifts risk to employees but raises issues due to annuity market frictions, adverse selection, and potentially high annuity costs.

### Conclusion
- Empirical assessment shows longevity assumptions have a statistically significant and economically meaningful impact on U.S. pension liabilities.
- Findings robust across sample definitions, assumptions about unclassified mortality tables, fund sizes, and time periods.
- Given past systematic underestimation of life-expectancy improvements and decennial minimum update frequency for mortality tables under U.S. regulation, large, lumpy increases in pension liabilities due to longevity risk are a likely scenario.

*Source: _wp12170 - References*

### References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

### _wp12170 — References (excerpt): Introduction, Related Literature, Data

### Introduction: scope and headline quantitative impacts
- Longevity risk is defined as the risk that, on average, people live longer than expected.
- Empirical focus: U.S. Department of Labor Form 5500 data to estimate the effect of life expectancy assumptions on pension liabilities.
- Estimated sensitivity:
  - Each year of life expectancy raises pension liabilities by 3 to 4 percent.
- Aggregate U.S. private DB pension context (as of 2007):
  - Private DB pension plans underfunded by $83 billion.
  - Total aggregate pension liabilities approximately $2.2 trillion.
  - A one-year shock to longevity could increase U.S. private DB pension liabilities by as much as $84 billion, doubling the degree of underfunding.
- Broader magnitudes:
  - Impact of an additional year of life expectancy on U.S. private and public pension liabilities corresponds to an amount equivalent to 1.5 percent of U.S. 2007 Gross Domestic Product (GDP).
  - Aggregate value of global private DB pension liabilities: $23 trillion.
  - A similar one-year longevity shock could raise global private pension liabilities by as much as $2.8 trillion.
- Novelty and methodological strengths:
  - First empirical assessment (per authors) using actual Form 5500 actuarial assumptions to estimate average longevity impact across U.S. private DB pension plans.
  - Method disentangles the effect of an additional year of life expectancy on pension liabilities without imposing exogenous improvement magnitudes.

### Related literature: forecasting, liability impact estimates, and risk transfer
- Mortality forecasting approaches:
  - Extrapolative approaches (historical trends) and process-based methods (biomedical causes of death).
  - The Lee and Carter (1992) model: time-series-based mortality index; explains 93 percent of past variation in U.S. mortality rates.
  - Limitations noted: difficulty detecting structural changes and cohort effects; references to Lee and Miller (2001), CMI (2004), CMI (2011), Girosi and King (2007).
- Evidence of persistent underestimation of longevity improvements:
  - U.K. Office for National Statistics: forecasts were consistently too low in each successive forecast.
  - Bongaarts and Bulatao (2000): 20-year forecasts in Australia, Canada, Japan, New Zealand and the United States underestimated longevity improvements by three years on average.
- Prior pension liability impact estimates:
  - Antolin (2007): an unexpected improvement in life expectancy of one-year per decade could increase pension liabilities by 8-10 percent for a hypothetical closed fund (age-structure dependent).
  - Dushi, Friedberg, and Webb (2010): updating mortality tables (Lee-Carter implied increase of life expectancy at age 60 of about 3 years since early 1980s) would increase liabilities by 12 percent for the average male plan participant.
- Longevity risk transfer and mitigation:
  - Market solutions: pension buy-ins, buy-outs, securitization, longevity swaps, longevity bonds.
  - Bifis and Blake (2009) compare trade-offs across methods; IMF (2012) documents growing but overall small global activity in capital-market-based longevity risk transfer (with exceptions: United Kingdom and the Netherlands).
  - Sponsor-side mitigation: shift from defined benefit (DB) to defined contribution (DC) plans transfers longevity risk to employees; purchasing annuities is an employee hedge but:
    - Mitchell, Poterba, Warshawsky, and Brown (1999): annuity purchase cost is significant for average retiree.
    - Dushi and Webb (2006): few households purchase annuities; prices often not actuarially fair due to adverse selection.
    - Fong, Mitchell, and Koh (2011): mandatory public-sector annuitization (Singapore) yields cheaper annuities than private provision.

### Data: Form 5500, measurement definitions, mortality tables, and sample coverage
- Primary dataset: filings of Form 5500 pension plan data from the U.S. Department of Labor (DOL), with research assistance from the Center for Retirement Research at Boston College.
- Sample period: filings between 1995 and 2007.
  - Motivation: since 1995 information on mortality tables used in actuarial computations became available; starting in 2008, Schedule B was replaced by schedules MB and SB which do not explicitly identify mortality tables.
- Coverage and liability definition:
  - As of 2007, private DB pension plans covered approximately 42 million plan participants.
  - Pension liabilities correspond to the current liability measure as stated in Schedule B of Form 5500 (similar to accumulated benefit obligations; nominal value of already promised and accrued payments).
  - This definition excludes future years of service and potential wage increases (conservative).
  - Distinction between liability measures:
    - Actuarial Liability (AL): sponsor-set assumptions used for funding standard account; typically lower.
    - Current Liability (CL): state-imposed discount rates and mortality assumptions; typically higher.
- Actuarial assumptions reported: interest rate, mortality tables for men and women (pre- and post-retirement), etc.
- Mortality tables recorded (men, active workers, 1995–2007 sample): categories include:
  - 1951 Group Annuity Mortality Table (1951 GAM)
  - 1971 Group Annuity Mortality Table (1971 GAM)
  - 1971 Individual Annuity Mortality Table (1971 IAM)
  - Unisex Pensioner 1984 (UP 1984)
  - 1983 Individual Annuity Mortality Table (1983 IAM)
  - 1983 Group Annuity Mortality Table (1983 GAM)
  - Uninsured Pensioner Table 1994 (UP 1994)
  - 2007 Mortality Table (2007 Table)
  - Other (unspecified)
  - None (no table used)
  - Hybrid (modified standard tables)
- Observed patterns and descriptive statistics:
  - Substantial variation over time and across funds in mortality-table usage.
  - Fraction employing the 1983 GAM Table ranged between 69 percent and 16 percent over the sample period.
  - 12 percent of funds switched to the most recent mortality table in 2007.
  - The fraction of funds using unspecified tables (“Other”) increased from 7 percent in 2000 to 57 percent in 2007.
  - Plans using the most current mortality table or unspecified tables are on average larger than funds employing the 1983 GAM mortality table.
  - There has been a steady increase in the average pension liabilities per plan over the sample period.
- Mortality-table differences and ranking:
  - Table snapshots of implied death rates show, for males aged 60:
    - Highest death rates: 1951 Group Annuity Mortality Table and 1984 Unisex Pension Table.
    - Most conservative longevity assumptions (lowest death rates): 1983 Individual Annuity Mortality Table and the 2007 Table.
  - Note: table titles do not necessarily reflect construction year but the year for which the forecast was undertaken; underlying samples differ.
  - To rank tables by implied longevity, the implied life expectancy at age 63 for working males is computed from mortality rates via survival rates and summed multi-period survival probabilities.

### Policy-relevant observations and implications (from text)
- Longevity shocks create potentially large, lumpy increases in pension liabilities because mortality-table updates and legal update frequencies (e.g., Pension Protection Act of 2006 requires mortality-table updates at least every ten years) can produce discrete liability jumps.
- Pension Protection Act of 2006 constrained sponsor freedom to use outdated mortality tables but cannot fully mitigate the problem of underestimating future life expectancy; ten-year update requirement allows room for large increases when tables are updated.
- Longevity risk realization is likely given historical forecast underestimation; therefore plans and sponsors face material funding and risk-management challenges.
- Risk-management options:
  - Market-based longevity risk transfer instruments exist but global activity remains limited overall.
  - Sponsor-side structural change (DB to DC) shifts risk to employees but raises issues due to annuity market frictions, adverse selection, and potentially high annuity costs.

_Italic: Source: Excerpt from _wp12170 (References, Appendix snippets), Form 5500 based analysis (1995–2007) — IMF working paper content provided in the source PDF._

### Section 1.412(I)(7)-1 of the income tax regulations provides an update to the 1983 GAM table.

### _wp12170 - Section 1.412(I)(7)-1 of the income tax regulations provides an update to the 1983 GAM table

### Overview and key context
- Note that the average retirement age for our sample is equal to 63.18 years.
- Starting full sample: 157,320 plan-year observations.
- After excluding observations classified as “Other”: 132,288 plan-year observations.
- After deleting observations classified as “Hybrid”: final sample of 110,968 plan-year observations.
- The Pension Protection Act of 2006 specifies that as of 2008, pension plans have to base computation of pension liabilities on mortality tables prescribed by the Secretary of the Treasury; the regulation requires that these tables shall be updated at least every ten years. Companies can apply to use their own mortality tables if certain conditions are met.

### Data, mortality tables, and the longevity variable
- Table 2 and Table 3 compare liabilities and mortality rates across mortality tables (examples include: 1951 GAM, 1971 GAM, 1971 IAM, UP 1984, 1983 IAM, 1983 GAM, UP 1994, 2007 Table).
- The difference in implied life expectancy between the oldest and most current mortality table amounts to 4.20 years.
- The most outdated table still in use is the 1971 Group Annuity Table.
- Longevity variable (implied life expectancy for males aged 63 under each mortality table) — Value (years):
  - No Table 14.32
  - 1951 Group Annuity Table 14.32
  - Unisex Pensioner 1984 Table 14.74
  - 1971 Group Annuity Mortality 15.34
  - 1983 Group Annuity Table 17.20
  - 1971 Individual Annuity Mortality 17.41
  - Uninsured Pensioner Table 1994 17.76
  - 1983 Individual Annuity Table 18.24
  - 2007 Mortality Table 19.54
- Focusing on firms employing the 1983 Group Annuity Table, the difference with respect to the most recent table equals 2.34 years.

### Simple valuation model and regression specification
- Pension liability model (annuity-based) summarized:
  - L = p b Σ_{i=1}^T (1 − s_i) / (1 + r)^i
  - Approximation used: L ≈ p b [1 − (1 + r)^{−n}] / r
  - Log-linearized regression specification used (panel regression with plan fixed effects):
    - log[L] = α + β1 log(p) + β2 log(b) + β3 log(r) + β4 n + β5 log(r)×n + ε
- Main parameter of interest: β4, the impact of one additional year of life expectancy on the present value of pension liabilities.

### Main empirical results (retired participants subsample)
- Baseline regression results (Table 4):
  - Coefficients:
    - log(r) -0.945 ∗∗∗
    - log(p) 0.914 ∗∗∗
    - log(b) 0.519 ∗∗∗
    - n 0.030 ∗∗∗
  - Observations 89552
  - R2 0.742
  - Interpretation: U.S. pension funds face longevity risk that would see liabilities to retired participants increase by about 3 percent for each year that retirees live longer than expected.
- Subsample by liability size (Table 5):
  - Coefficients across quartiles (Small / Medium / Large / Very Large):
    - log(r) -1.226 ∗∗∗ ; -0.932 ∗∗∗ ; -0.924 ∗∗∗ ; -0.820 ∗∗∗
    - log(p) 0.809 ∗∗∗ ; 0.719 ∗∗∗ ; 0.707 ∗∗∗ ; 0.832 ∗∗∗
    - log(b) 0.405 ∗∗∗ ; 0.380 ∗∗∗ ; 0.413 ∗∗∗ ; 0.559 ∗∗∗
    - n 0.032 ∗∗∗ ; 0.024 ∗∗∗ ; 0.036 ∗∗∗ ; 0.036 ∗∗∗
  - Observations   21410225942270922839
  - R2 0.6100.5530.6160.730
  - Interpretation: an additional year of life expectancy increases pension liabilities to retired plan participants by 2.4 percent to 3.6 percent across quartiles.

### Results for total pension liabilities (full-sample adjustment using age-workforce distribution)
- Age-workforce distribution (subsample of 447 pension plans, 2005–2007):
  - Average (median) age equals 46.04 (47.25) years.
  - Half of the average workforce is older than 50 years; notable retirements at ages 50, 55, and 60.
- Regression for total pension liabilities (Table 6):
  - Coefficients:
    - log(r) -1.675 ∗∗∗
    - log(p) 0.613 ∗∗∗
    - log(b) 0.054 ∗∗∗
    - n 0.037 ∗∗∗
    - X -0.007
  - Observations 11154
  - R2 0.531
  - Interpretation: using the age-workforce proxy for 2005–2007, an additional year of life expectancy raises pension liabilities by 3.7 percent.

### Robustness checks
- Treating unclassified mortality tables as RP-2000 (Table 7):
  - Coefficients for full sample:
    - log(r) -0.915 ∗∗∗
    - log(p) 0.933 ∗∗∗
    - log(b) 0.526 ∗∗∗
    - n 0.034 ∗∗∗
  - Observations   11060726475278452802428263
  - R2 0.7640.6350.5710.6560.755
  - Interpretation: an additional year of life expectancy raises pension liabilities by 3.4 percent in this specification; larger funds show stronger impacts (for example, coefficients up to 0.045 and 0.043 in some quartiles).
- Alternative assumptions for unclassified tables (most conservative 2007 Table or common 1983 GAM) — results unchanged: additional year raises liabilities between 2.4 percent to 3.4 percent.
- More recent time period (2001–2007) (Table 8):
  - Coefficients for full sample:
    - log(r) -0.655 ∗∗∗
    - log(p) 0.814 ∗∗∗
    - log(b) 0.431 ∗∗∗
    - n 0.034 ∗∗∗
  - Observations   406639770102521026410377
  - R2 0.5500.4420.4530.5380.511
  - Interpretation: results qualitatively unchanged for more recent period.

### Quantitative magnitudes and economic significance
- Each additional year of life expectancy increases liabilities by 3 percent to 4 percent (baseline and robustness checks).
- Private DB pension liabilities in the United States amount to approximately $2.2 trillion.
  - Implication: a one-year shock to longevity would raise U.S. private DB pension liabilities by as much as $84 billion.
  - This would increase the amount by which private DB pension funds are underfunded by approximately 100 percent and imply that corporate pension sponsors have to make many multiples of typical annual pension contributions to match these extra liabilities.

### Conclusion and implications
- This paper provides an empirical assessment showing that longevity assumptions have a statistically significant and economically meaningful impact on U.S. pension liabilities.
- Findings are robust across sample definitions, assumptions about unclassified mortality tables, fund sizes, and time periods.
- Given past systematic underestimation of life-expectancy improvements and the decennial minimum update frequency for mortality tables under U.S. regulation, the potential realization of large, lumpy increases in pension liabilities due to longevity risk is a likely scenario.

*Source: _wp12170 - Section 1.412(I)(7)-1 of the income tax regulations provides an update to the 1983 GAM table.*

### References

### _wp12170 - References

### References
- Aegon. Paying the price for living longerwhat is the right price for removing longevity risk? Aegon Global Pensions View,2011.
- Pablo. Antolin. Longevity risk and private pensions.OECD Working Papers on Insurance and Private Pensions,3:1–28,2007.
- Enrico Bifis and David Blake. Mortality-linked securities and derivatives. In M. Bertocchi and W.T. Schwartz, S.L. Ziemba, editors,Optimizing the Aging, Retirement and Pensions Dilemma. John Wiley Sons, 2009.
- John Bongaarts and Rodolfo A. Bulatao.Beyond Six Billion:  Forecasting the Worlds Population. Washington: National Academy Press), 2000.
- Continuous Mortality Investigation CMI. Projecting future mortality: a discussion paper. Working Paper No. 3,2004.
- Continuous Mortality Investigation CMI. The mortality projections model.Working Paper No. 55,2011.
- Johan De Witt. Value of life annuities in proportion to redeemable annuities.Assurance Magacine, 2:232–249, 1671.
- Irena Dushi and Antony Webb. Rethinking the sources of adverse selection in the annuity market. In Pierre? Andre Chiappori and Christian Gollier, editors,Competitive Failures in Insurance Markets:  Theory and Policy Implications, pages 481–503. MIT Press, 2006.
- Irena Dushi, Leora Friedberg, and Antony Webb. The impact of aggregate mortality risk on defined benefit pension plans.Journal of Pension Economics and Finance,9:481–503, 2010.
- Joelle H.Y. Fong, Olivia S. Mitchell, and Benedict S. K. Koh. Longevity risk management in singapore’s national pension system.Journal of Risk and Insurance,78:961–982,2011.
- Federico Girosi and Gary King. Understanding the lee-carter forecasting method.Working Paper,2007.
- 4 H.R. Pension protection act of 2006.GovTrack.us (database of federal legislation),2006.
- Hymans and Robertson. Ias 19 assumptions report.Note,2011.
- IMF. Global financial stability report. 2012.
- Internal Revenue Service IRS. Instructions for form 5500.Department of the Treasury,2007.
- Lane Clark Peacock LCP. Accounting for pensions uk and europe.Annual Survey,2006.
- Ronald D. Lee and Lawrence R. Carter. Modeling and forecasting u.s. mortality.Journal of the American Statistical Association,87:659–671,1992.
- Ronald D. Lee and Timothy Miller. Evaluating the performance of the lee-carter method for forecasting mortality.Demography,38:537–549,2001.
- Olivia S. Mitchell, James M. Poterba, Mark J. Warshawsky, and Jeffrey R. Brown. New evidence on the money’s worth of individual securities.American Economic Review,89:1299–1318, 1999.
- Robert Novy-Marx and Joshua Rauh. Public pension promises: How big are they and what are they worth?Journal of Finance,66:1207–1245,2011.
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### Appendix 1 — Extended regression setup and testable equation
- Present value modification: the present value of an annuity starting t years in the future equals the present value of an annuity starting one period into the future, discounted over the additional (t-1) periods.
- Sample split: sample is split into deciles based on the age distribution implied by Figure (1).
- Extended valuation expression (equation (5)):
  - L≈pb [ 1−(1 +r)−n r ] [ 0.1 (1 +r)(t r −min [t r ,t 1 ]) + 0.1 (1 +r)(t r −min [t r ,t 2 ]) + ... + 0.1 (1 +r)(t r −min [t r ,t 10 ]) ]
  - where t r and t i denote retirement (age) and current age where i∈(1,2,...,10).
  - The minimum of current age and retirement age is applied to avoid negative time-to-retirement.
- Testable log-linear equation (equation (6)):
  - log[L]=α+β1 log(p)+β2 log(b)+β3 log(r)+β4 n+β5 log(r)×n+β6 X′
  - where X=log [ 0.1 (1+r)(t r −min [t r ,t 1 ]) + 0.1 (1+r)(t r −min [t r ,t 2 ]) + ... + 0.1 (1+r) t r −min ([t r ,t 10 ]) ].

### Robustness checks — Table 9: Unclassified Mortality Tables (2007 Table)
- Description: Results when estimating the baseline regression of Table (4) for a larger sample of firms; funds classifying the underlying mortality table as Other are assumed to follow the 2007 Mortality Table.
- Coefficients by subsample (columns (1) All; (2) Small; (3) Medium; (4) Large; (5) Very Large):
  - log(r): -0.906 ∗∗∗ ; -1.164 ∗∗∗ ; -0.964 ∗∗∗ ; -0.877 ∗∗∗ ; -0.763 ∗∗∗
  - log(p): 0.931 ∗∗∗ ; 0.847 ∗∗∗ ; 0.718 ∗∗∗ ; 0.736 ∗∗∗ ; 0.850 ∗∗∗
  - log(b): 0.525 ∗∗∗ ; 0.408 ∗∗∗ ; 0.384 ∗∗∗ ; 0.435 ∗∗∗ ; 0.558 ∗∗∗
  - n: 0.024 ∗∗∗ ; 0.024 ∗∗∗ ; 0.024 ∗∗∗ ; 0.030 ∗∗∗ ; 0.025 ∗∗∗
- Observations: 11060726475278452802428263
- R2: 0.7640.6360.5710.6570.755
- Significance notation: ∗ p<0.05, ∗∗ p<0.01, ∗∗∗ p<0.001

### Robustness checks — Table 10: Unclassified Mortality Tables (1983 GAM)
- Description: Results when estimating the baseline regression of Table (4) for a larger sample of firms; funds classifying the underlying mortality table as Other are assumed to follow the 1983 GAM Table and the longevity variable n is updated accordingly.
- Coefficients by subsample (columns (1) All; (2) Small; (3) Medium; (4) Large; (5) Very Large):
  - log(r): -0.952 ∗∗∗ ; -1.193 ∗∗∗ ; -1.006 ∗∗∗ ; -0.934 ∗∗∗ ; -0.807 ∗∗∗
  - log(p): 0.937 ∗∗∗ ; 0.850 ∗∗∗ ; 0.724 ∗∗∗ ; 0.747 ∗∗∗ ; 0.863 ∗∗∗
  - log(b): 0.529 ∗∗∗ ; 0.409 ∗∗∗ ; 0.386 ∗∗∗ ; 0.442 ∗∗∗ ; 0.567 ∗∗∗
  - n: 0.027 ∗∗∗ ; 0.026 ∗∗∗ ; 0.023 ∗∗∗ ; 0.034 ∗∗∗ ; 0.034 ∗∗∗
- Observations: 11060726475278452802428263
- R2: 0.7630.6350.5690.6530.753
- Significance notation: ∗ p<0.05, ∗∗ p<0.01, ∗∗∗ p<0.001

*Source: _wp12170 - References*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12170.pdf_