## _wp0715

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---

### Introduction
- The U. S. Social Security system calculates initial benefits without adjusting for systematic differences in mortality risk; individuals with identical lifetime earnings and contribution histories receive identical initial benefits irrespective of expected length of life.
- Unintended redistribution can occur because higher income people have higher life expectancy and thus receive benefits for longer periods (Friedman, 1972).
- Existing reform proposals, including individual accounts with annuitization provisions, generally ignore mortality risk and could cause transfers from groups with higher mortality risk to those with lower risk (Brown, 2002).
- The paper analyzes the relationship between mortality and individual-specific socioeconomic status using administrative SSA records (CWHS and MBR) that contain actual covered earnings from 1937 to 2002 and month and year of death information.

### Data and variable definitions
- Primary data:
  - Social Security Administration’s 2002 one-percent Continuous Work History Sample (CWHS) and Master Beneficiary Record (MBR).
  - Historical Social Security earnings for over three million current or former workers spanning 1937 to 2002; matched to benefit and death records in the MBR.
- Sample selection:
  - All retired-worker beneficiary records with birth years 1900 to 1942 who claimed benefits at age 62 or later.
  - After edits, sample size: nearly 550,000 observations (sample=548,681).
  - Death coverage: benefit/death information extends through 2004; oldest observed age is 104.
- Lifetime earnings measure:
  - Sum of real earnings (2005 dollars) over ages 35 through 60 (ages 37–60 and 36–60 for birth years 1900 and 1901, respectively).
- Adjustments to earnings data:
  - 1937–1950 lump-sum prorated assuming earnings grew at 1.0 percent per year of age beyond economy-wide wage growth for males and 0.5 percent for females (Myers (1993) averages).
  - For years 1937–1980 when earnings at taxable maximum, imputed earnings above the maximum using a Tobit model under lognormal assumption.
  - Earnings indexed to 2005 using the Consumer Price Index.
- Race classification:
  - Administrative records permit a three-way classification (blacks, whites, other) for the vast majority of records used.
- Earnings trend classification:
  - AE1 = average real earnings ages 37–44, AE2 = ages 45–52, AE3 = ages 53–60.
  - Trend = (AE3 – AE1)/(AE1 + AE3).
  - Declining if Trend < -1/9.
  - Flat if -1/9 ≤ Trend ≤ 1/9.
  - Rising if Trend > 1/9.

### Sample characteristics and descriptive findings
- Sample composition and basic statistics (Authors' calculations based on CWHS and MBR (sample=548,681)):
  - Sample (%) — Females: 100.0 with breakdowns White 38.5, Black 3.7, Other 1.1; Males: 100.0 with breakdowns White 50.6, Black 4.4, Other 1.7.
  - Dead (%) — Females: 49.0 overall; White 43.6; Black 45.4; Other 24.4. Males: 54.2 overall; White 59.0; Black 37.5.
  - Median Age of Death — Females: 77.0 overall; White 80.0; Black 78.0; Other 79.0. Males: 76.0 overall; White 75.0; Black 77.0.
  - Median Lifetime Earnings* — Females overall: 517,158; White 269,574; Black 236,917; Other 233,227. Males overall: 921,999; White 476,051; Black 413,088.
  - *Sum over ages 35 through 60 in 2005 dollars.
- Mortality and earnings patterns:
  - Nearly half of retired-worker beneficiaries in the sample have died; percentages higher for males than females and higher for blacks than whites.
  - For deceased retired-worker beneficiaries:
    - Median female lived about four years longer than median male.
    - Median white lived about one to two years longer than median black.
  - Lifetime earnings patterns:
    - Males earned more than females; whites earned more than blacks.
  - Cohort and trend observations (described figures):
    - Difference in age of death between highest and lowest earnings deciles: about twenty months for 1910–14 cohorts, about fifteen months for 1920–24 cohorts, about eight months for most recent cohorts.
    - Steady decline in percentage of male retired workers with a rising Trend and steady rise in percentage with a declining Trend across birth cohorts (1910–34); similar but more modest changes for females.
    - Cumulative age-of-death distribution: those with declining earnings Trend have a distribution lying above those with rising or flat trends; difference in median age of death between rising and declining trends is about four years.

### Empirical mortality models (logit hazard models)
- Model setup:
  - Unit of observation: individual year of life; dependent variable: binary indicator of death in that year given survival to prior year.
  - Model estimated using logit so positive coefficients imply higher death rates and shorter expected lifetimes.
- Explanatory variables:
  - Log of real lifetime earnings (specified as a cubic polynomial: LE, LE^2, LE^3).
  - Age.
  - Year of birth (cohort).
  - Indicators for Rising and Flat earnings Trend (Declining omitted).
- Interpretation highlights:
  - Probability of death rises with age and falls with cohort birth year (mortality improvements for more recent cohorts).
  - An additional year of age increases the odds of death by nine to ten percent for retired male workers (example based on coefficient .0952).
  - For white and black males born in 1930 vs. 1920, odds of death are 16 percent and 5 percent lower, respectively, ceteris paribus.
  - Earnings Trend effects for retired males:
    - Rising Trend reduces odds of mortality by about 20 percent relative to Declining.
    - Flat Trend reduces odds by about 10 to 13 percent relative to Declining.
  - Mortality is significantly negatively related to the log of lifetime earnings for male retired workers.
- Retired male workers sample sizes:
  - Basic sample: 277,571 white males and 24,160 black males.
  - In person-year format: over 3.8 million white-male observations and over 317 thousand black-male observations.
- Selected parameter values from Table 2 (Estimated Mortality Hazard Models for Male Retired Workers 62+):
  - Intercept:
    - White males -9.991 (0.000)
    - Black males -9.400 (-0.142)
  - Age:
    - White males 0.095 ( -1.092)
    - Black males 0.088 (-0.001)
  - Birth Year:
    - White males -0.017 (-0.994)
    - Black males -0.006 (-0.001)
  - LE:
    - White males -0.341 (-0.667)
    - Black males -0.406 (-0.064)
  - LE^2:
    - White males 0.067 (-1.083)
    - Black males 0.079 (-0.010)
  - LE^3:
    - White males -0.003 (-0.996)
    - Black males 0.004 (-0.000)
  - Rising (Trend):
    - White males 0.214 (-0.823)
    - Black males 0.195 (-0.022)
  - Flat (Trend):
    - White males 0.101 (-0.879)
    - Black males 0.129 (-0.029)
  - *Estimated standard errors appear in parentheses.

### Female retired-worker models and dual vs. nondual distinctions
- Definitions:
  - Female dual beneficiaries: retired-worker beneficiaries who also received a spousal or widow’s benefit based on a current or former spouse.
  - Female nonduals: retired-worker beneficiaries with no auxiliary benefit.
- Sample sizes:
  - Nonduals: 123,979
  - Duals: 94,945
  - Note: omitted about 10 percent of duals who were mainly divorced wives and widows who were not the primary claimants on a dual account.
- Income reference points used in cross-group comparisons:
  - Low income: $77,642
  - High income: $1,163,370
  - Percentile correspondences (from footnote):
    - White males—5th and 65th
    - Black males—12th and 88th
    - White females—9th and 95th
    - Black females—17th and 95th
- Duals vs nonduals (Table 3 highlights):
  - Duals (N=94,945) / Nonduals (N=123,979).
  - Median lifetime income* (own / spouse):
    - White duals own 150,749 spouse 1,013,750
    - White nonduals own 420,491
    - Black duals own 130,029 spouse 501,740
    - Black nonduals own 310,227
  - Years with positive income: Duals 20; Nonduals 23 (White) and 28 (Black).
  - *Lifetime income is the sum of real earnings (2005 dollars) over ages 35–60.
  - Duals have considerably lower own lifetime earnings and fewer years with positive earnings than nonduals; spouses of duals often have substantially higher earnings.
- Female mortality model findings (Table 4 summary):
  - Lifetime earnings (LE) coefficients (preserved signs and reported values):
    - LE: -0.180 (White Duals), -0.205 (White Nonduals), -0.451 (Black Duals), -0.179 (Black Nonduals)
    - LE^2: 0.039 (White Duals), 0.046 (White Nonduals), 0.086 (Black Duals), 0.048 (Black Nonduals)
    - LE^3: -0.002 (reported uniformly)
  - Trend in earnings:
    - Rising trend coefficients: -0.263, -0.273, -0.188, -0.289 (for White Duals, White Nonduals, Black Duals, Black Nonduals respectively)
    - Flat trend coefficients: -0.125, -0.116, -0.163, -0.170
  - Lifetime earnings of current/former spouse (LESP) in dual equations:
    - LESP coefficients: 0.342 (White Duals), 0.000 (White Nonduals), -0.086 (Black Duals), 0.000 (Black Nonduals)
    - LESP^2 and LESP^3 values reported in table (including zeros for nonduals)
  - Notes:
    - Trend in earnings variables have a significantly negative effect on mortality for all four female groups.
    - In the dual equations, birth year has a positive coefficient, in contrast to birth-year effect in the other mortality equations.
    - For female duals: higher own lifetime earnings has a significantly negative effect on mortality; higher spousal lifetime earnings has a significantly negative effect for white female duals but an insignificant effect for black duals.

### Survivor rates and life expectancy (selected quantitative findings)
- White male retired workers born in 1920 (flat real earnings profile):
  - Median age of death:
    - 10th percentile: 78.8
    - Median (50th): 80.3
    - 90th percentile: 81.6
  - Difference between 90th and 10th: 33 months
  - Rising earnings trend raises median ages by about 1 year at each percentile (e.g., median becomes 81.3)
- Black male retired workers born in 1920 (flat real earnings profile):
  - Median age of death:
    - 10th percentile: 76.8
    - Median (50th): 77.8
    - 90th percentile: 80.3
  - Difference between 90th and 10th: 42 months
  - Positive earnings trend results in about a half year greater life expectancy
- Female nonduals born in 1920 (flat trend):
  - White nonduals:
    - 10th percentile: 82.1
    - Median: 83.1
    - 90th percentile: 84.3
    - 90th - 10th: 26 months
  - Black nonduals:
    - 10th percentile: 81.1
    - Median: 82.5
    - 90th percentile: 84.8
    - 90th - 10th: 45 months
  - For both white and black nonduals, a positive earnings trend adds over a year to life expectancy.
- Female duals (flat trend) — own earnings vs husband’s earnings scenarios:
  - White duals (own earnings):
    - 10th: 84.1; Median: 85.0; 90th: 86.4; 90th - 10th: 28 months
  - White duals (husband’s earnings):
    - 10th: 84.6; Median: 85.0; 90th: 85.4; 90th - 10th: 10 months
  - Black duals (own earnings):
    - 10th: 82.1; Median: 83.3; 90th: 85.9; 90th - 10th: 46 months
  - Black duals (husband’s earnings):
    - 10th: 83.2; Median: 83.3; 90th: 83.5; 90th - 10th: 4 months
  - For both white and black duals, a positive earnings profile adds about another year of life.
- Cross-group age-of-death differences at constant lifetime incomes (Table 6 excerpts):
  - At low income ($77,642):
    - White males: 78.9
    - Black males: 76.8 (white males 26 months more)
    - White female (nondual): 82.1 (white males -38 months relative)
    - Black females (nondual): 81.3 (black males -54 months relative)
  - At high income ($1,163,370):
    - White males: 80.8
    - Black males: 79.5 (white males 15 months more)
    - White female (nondual): 84.7 (white males -47 months relative)
    - Black females (nondual): 85.6 (black males -73 months relative)
  - Observations:
    - The white-black male age-of-death gap is about 26 months at the low-income level and narrows to 15 months at the high-income level.
    - Gender gaps (male vs female) are large and persistent across income levels.
- Mortality rates for 65-year-old men by earnings level (figure highlights):
  - Rates decline as earnings increase.
  - The mortality rate difference between blacks and whites begins at about 0.5 percentage points at the lowest income level and falls by a third at about $1.4 million in lifetime earnings (95th percentile of the black male earnings distribution).

### Interpretation, conclusions, and implications for Social Security
- Main empirical conclusions:
  - Mortality is negatively related to lifetime income across black and white males and females.
  - The difference in age of death between low and high lifetime income is on the order of two to three years for the groups studied.
  - Workers with positively-trended earnings over their work life may live an additional six to eighteen months.
  - Income-related mortality differences between blacks and whites are largest at low-income levels, particularly for males, and narrow substantially at higher income levels.
  - Gender differences in mortality are large and persistent across income levels.
- Implications for Social Security design and reform:
  - Income-related differences in life expectancy materially affect the distributional assessment of Social Security reforms and the existing program.
  - Income-related differences curtail, but do not reverse, the progressivity of the basic Social Security benefit structure.
  - Accounting for income-related mortality differences is important when evaluating proposals such as raising the normal retirement age or increasing the early-retirement age.
  - The feedback of life expectancy on retirement decisions complicates attempts to adjust benefits by age of retirement; an “actuarially fair” adjustment will vary across income groups and may induce selection behavior (low-income workers retiring earlier than high-income workers), so a single adjustment factor can cause workers to select “against” the system.

*Source: _wp0715 (Authors' calculations based on CWHS and MBR, sample=548,681).*

### References..............................................................................................................

### _wp0715 - References..............................................................................................................

### Tables
- 1. Characteristics of Retired Worker Beneficiaries ................................................................6
- 2. Estimated Mortality  Hazard Models for Male Retired Workers 62+ ..............................10
- 3. Income and Work Years of Median Dual and Nondual Beneficiaries .............................11
- 4. Estimated Mortality Hazard Models for Female Retired Workers 62+ ...........................12
- 5. Median Ages of Death for Retired Workers Born in 1920...............................................13
- 6. Age-of-Death Differences at Constant Lifetime Incomes* ..............................................16

### Figures
- 7. Deviations from Average Age of Death for Male Retired Workers...................................7
- 8. Distribution of Male Retirees by Trend in Earnings ..........................................................7
- 9. Cumulative Distribution of Age of Death of Male Retirees by Trend in Earnings ............9
- 10. Cumulative Distribution of Lifetime Earnings for Retired Workers Born 1900–1942......9
- 11. Survivor Rates for White Male Retired Workers Born in 1920, Flat Earnings Profile....14
- 12. Survivor Rates for Black Male Retired Workers Born in 1920, Flat Earnings Profile ....14
- 13. Mortality Rates for 65-Year Old Men, by Earnings Levels .............................................15
- 14. Survivor Rates for White Female Non-Duals Born in 1920, Flat Earnings Profile .........17

*Source: _wp0715 - References..............................................................................................................*

### 15. Survivor Rates for Black Female Non-Duals Born in 1920, Flat Earnings Profile..........17

### 15. Survivor Rates for Black Female Non-Duals Born in 1920, Flat Earnings Profile..........17

### Introduction
- The U. S. Social Security system calculates initial benefits without adjusting for systematic differences in mortality risk; individuals with identical lifetime earnings and contribution histories receive identical initial benefits irrespective of expected length of life.
- Unintended redistribution can occur because higher income people have higher life expectancy and thus receive benefits for longer periods (Friedman, 1972).
- Existing reform proposals, including individual accounts with annuitization provisions, generally ignore mortality risk and could cause transfers from groups with higher mortality risk to those with lower risk (Brown, 2002).
- The paper analyzes the relationship between mortality and individual-specific socioeconomic status using administrative SSA records (CWHS and MBR) that contain actual covered earnings from 1937 to 2002 and month and year of death information.

### Data and variable definitions
- Primary data: Social Security Administration’s 2002 one-percent Continuous Work History Sample (CWHS) and Master Beneficiary Record (MBR).
- Coverage: historical Social Security earnings for over three million current or former workers spanning 1937 to 2002; matched to benefit and death records in the MBR.
- Sample selection: all retired-worker beneficiary records with birth years 1900 to 1942 who claimed benefits at age 62 or later. After edits, sample size: nearly 550,000 observations (sample=548,681).
- Death coverage: benefit/death information extends through 2004; oldest observed age is 104.
- Lifetime earnings measure: sum of real earnings (2005 dollars) over ages 35 through 60 (ages 37–60 and 36–60 for birth years 1900 and 1901, respectively).
- Adjustments to earnings data:
  - 1937–1950 lump-sum prorated assuming earnings grew at 1.0 percent per year of age beyond economy-wide wage growth for males and 0.5 percent for females (Myers (1993) averages).
  - For years 1937–1980 when earnings at taxable maximum, imputed earnings above the maximum using a Tobit model under lognormal assumption.
  - Earnings indexed to 2005 using the Consumer Price Index.
- Race classification: administrative records permit a three-way classification (blacks, whites, other) for the vast majority of records used.
- Earnings trend classification:
  - AE1 = average real earnings ages 37–44, AE2 = ages 45–52, AE3 = ages 53–60.
  - Trend = (AE3 – AE1)/(AE1 + AE3).
  - Declining if Trend < -1/9.
  - Flat if -1/9 ≤ Trend ≤ 1/9.
  - Rising if Trend > 1/9.

### Sample characteristics and descriptive findings
- Table 1 summary (Retired Worker Beneficiaries; Source: Authors' calculations based on CWHS and MBR (sample=548,681)):
  - Sample (%) — Females: 100.0 with breakdowns White 38.5, Black 3.7, Other 1.1; Males: 100.0 with breakdowns White 50.6, Black 4.4, Other 1.7.
  - Dead (%) — Females: 49.0 overall; White 43.6; Black 45.4; Other 24.4. Males: 54.2 overall; White 59.0; Black 37.5.
  - Median Age of Death — Females: 77.0 overall; White 80.0; Black 78.0; Other 79.0. Males: 76.0 overall; White 75.0; Black 77.0.
  - Median Lifetime Earnings* — Females overall: 517,158; White 269,574; Black 236,917; Other 233,227. Males overall: 921,999; White 476,051; Black 413,088.
  - *Sum over ages 35 through 60 in 2005 dollars.
- Nearly half of retired-worker beneficiaries in the sample have died; percentages higher for males than females and higher for blacks than whites.
- For deceased retired-worker beneficiaries:
  - Median female lived about four years longer than median male.
  - Median white lived about one to two years longer than median black.
- Lifetime earnings patterns:
  - Males earned more than females; whites earned more than blacks.
  - Figure 1 (described): For male retired workers, difference in age of death between highest and lowest earnings deciles: about twenty months for 1910–14 cohorts, about fifteen months for 1920–24 cohorts, about eight months for most recent cohorts — indicating a positive relationship between lifetime earnings and length of life.
- Earnings trend over cohorts (Figure 2 described):
  - Steady decline in percentage of male retired workers with a rising Trend and steady rise in percentage with a declining Trend across birth cohorts (1910–34); similar but more modest changes for females.
  - Figure 3 described: Cumulative age-of-death distribution for male workers shows those with declining earnings Trend have a distribution lying above those with rising or flat trends; difference in median age of death between rising and declining trends is about four years.
- Figure 4 described: Cumulative distribution of lifetime earnings for retired workers born 1900–1942 by race/sex groups (thousands of 2005 dollars).

### Empirical mortality models (logit hazard models)
- Unit of observation: individual year of life; dependent variable: binary indicator of death in that year given survival to prior year.
- Model estimated using logit so positive coefficients imply higher death rates and shorter expected lifetimes.
- Explanatory variables:
  - Log of real lifetime earnings (specified as a cubic polynomial: LE, LE^2, LE^3).
  - Age.
  - Year of birth (cohort).
  - Indicators for Rising and Flat earnings Trend (Declining omitted).
- Interpretation highlights:
  - Probability of death rises with age and falls with cohort birth year (mortality improvements for more recent cohorts).
  - An additional year of age increases the odds of death by nine to ten percent for retired male workers (interpretation example provided: effect for white male workers derived from coefficient .0952).
  - For white and black males born in 1930 vs. 1920, odds of death are 16 percent and 5 percent lower, respectively, ceteris paribus.
  - Earnings Trend effects for retired males:
    - Rising Trend reduces odds of mortality by about 20 percent relative to Declining.
    - Flat Trend reduces odds by about 10 to 13 percent relative to Declining.
  - Mortality is significantly negatively related to the log of lifetime earnings for male retired workers.
- Retired male workers sample sizes:
  - Basic sample: 277,571 white males and 24,160 black males.
  - In person-year format: over 3.8 million white-male observations and over 317 thousand black-male observations.
- Table 2 (Estimated Mortality Hazard Models for Male Retired Workers 62+):
  - Variables and reported parameter values (standard errors in parentheses):
    - Intercept: White males -9.991 (0.000); Black males -9.400 (-0.142).
    - Age: White males 0.095 ( -1.092); Black males 0.088 (-0.001).
    - Birth Year: White males -0.017 (-0.994); Black males -0.006 (-0.001).
    - LE: White males -0.341 (-0.667); Black males -0.406 (-0.064).
    - LE^2: White males 0.067 (-1.083); Black males 0.079 (-0.010).
    - LE^3: White males -0.003 (-0.996); Black males 0.004 (-0.000).
    - Rising (Trend): White males 0.214 (-0.823); Black males 0.195 (-0.022).
    - Flat (Trend): White males 0.101 (-0.879); Black males 0.129 (-0.029).
  - *Estimated standard errors appear in parentheses.

### Female retired-worker models and dual vs. nondual distinctions
- Female models consider that many female workers’ primary source of earned income may include spousal earnings; SSA records identify auxiliary benefits allowing matching of spouse earnings for dual beneficiaries.
- Definition:
  - Female dual beneficiaries: retired-worker beneficiaries who also received a spousal or widow’s benefit based on a current or former spouse.
  - Female nonduals: retired-worker beneficiaries with no auxiliary benefit.
- Dual prevalence and characteristics:
  - About half of female retired workers are dual beneficiaries; for black females about five percent are duals.
  - Table 3 (Income and Work Years of Median Dual and Nondual Beneficiaries):
    - Duals (N=94,945) / Nonduals (N=123,979).
    - Median lifetime income* (own / spouse): White duals own 150,749 spouse 1,013,750; White nonduals own 420,491 (no spouse column); Black duals own 130,029 spouse 501,740; Black nonduals own 310,227.
    - Years with positive income: Duals 20; Nonduals 23 (White) and 28 (Black) — table formatting in source indicates differences in work years.
    - *Lifetime income is the sum of real earnings (2005 dollars) over ages 35–60.
  - Duals have considerably lower own lifetime earnings and fewer years with positive earnings than nonduals; spouses of duals often have substantially higher earnings (median spouse earnings for white duals nearly seven times own; for black duals nearly four times own).
- Female mortality model findings:
  - Own lifetime earnings has a significantly negative effect on mortality for both dual and nondual females.
  - For white female duals, spouse lifetime earnings also enters models (spouse earnings were computed similarly to primary worker earnings).

### Key substantive findings emphasized
- Strong empirical support for a negative relationship between individual lifetime income and mortality across race and gender groups.
- Differences in age of death between low and high lifetime income are on the order of two to three years for black and white males and females.
- Workers with positively-trended earnings over their work life may live an additional six to eighteen months relative to those with declining earnings (earnings-trend effect described in Section III).
- Income-related mortality differences between blacks and whites are largest at low-income levels, particularly for males, and narrow substantially at higher income levels.
- Gender differences in mortality are large and persistent across income levels.

*Source: Authors' calculations based on CWHS and MBR (sample=548,681).*

### section III.  That is, we first impute above-cap earnings for those earning the maximum and then sum their real

### _wp0715 - section III.  That is, we first impute above-cap earnings for those earning the maximum and then sum their real

### Sample and data
- Empirical sample sizes:
  - 123,979 nonduals
  - 94,945 dual beneficiaries
  - Note: omitted about 10 percent of duals who were mainly divorced wives and widows who were not the primary claimants on a dual account.
- Lifetime income reference points used in cross-group comparisons:
  - Low income: $77,642
  - High income: $1,163,370
  - Percentile correspondences (from footnote):
    - White males—5th and 65th
    - Black males—12th and 88th
    - White females—9th and 95th
    - Black females—17th and 95th

### Estimated mortality models (summary points drawn from Table 4 and text)
- Lifetime earnings (LE) effects on mortality for female retired workers 62+:
  - LE coefficients (signs and higher-order terms preserved as presented):
    - LE: -0.180 (White Duals), -0.205 (White Nonduals), -0.451 (Black Duals), -0.179 (Black Nonduals)
    - LE^2: 0.039 (White Duals), 0.046 (White Nonduals), 0.086 (Black Duals), 0.048 (Black Nonduals)
    - LE^3: -0.002 (all groups reported with same sign)
  - Trend in earnings:
    - Rising trend coefficients: -0.263, -0.273, -0.188, -0.289 (for the four female groups respectively)
    - Flat trend coefficients: -0.125, -0.116, -0.163, -0.170
  - Lifetime earnings of current/former spouse (LESP) (duals):
    - LESP coefficients: 0.342 (White Duals), 0.000 (White Nonduals), -0.086 (Black Duals), 0.000 (Black Nonduals)
    - LESP^2 and LESP^3 values as presented in table (including zeros for nonduals)
- Additional model notes from text:
  - Trend in earnings variables have a significantly negative effect on mortality for all four groups in Table 4.
  - In the dual equations, birth year has a positive coefficient, in contrast to birth-year effect in the other mortality equations; this may reflect intertemporal changes in the relationship between dual-beneficiary status and health status.
  - For female duals: higher own lifetime earnings has a significantly negative effect on mortality; higher spousal lifetime earnings has a significantly negative effect for white female duals but an insignificant effect for black duals.

### Survivor rates and life expectancy (key quantitative findings)
- White male retired workers born in 1920 (flat real earnings profile):
  - Median age of death:
    - 10th percentile: 78.8
    - Median (50th): 80.3
    - 90th percentile: 81.6
  - Difference between 90th and 10th: 33 months
  - Rising earnings trend raises median ages by about 1 year at each percentile (e.g., median becomes 81.3)
- Black male retired workers born in 1920 (flat real earnings profile):
  - Median age of death:
    - 10th percentile: 76.8
    - Median (50th): 77.8
    - 90th percentile: 80.3
  - Difference between 90th and 10th: 42 months
  - Positive earnings trend results in about a half year greater life expectancy
- Female nonduals (born in 1920):
  - White nonduals median ages of death (flat trend):
    - 10th percentile: 82.1
    - Median: 83.1
    - 90th percentile: 84.3
    - 90th - 10th: 26 months
  - Black nonduals median ages of death (flat trend):
    - 10th percentile: 81.1
    - Median: 82.5
    - 90th percentile: 84.8
    - 90th - 10th: 45 months
  - For both white and black nonduals, a positive earnings trend adds over a year to life expectancy.
- Female duals (own earnings vs husband’s earnings scenarios; flat trend):
  - White duals (own earnings):
    - 10th: 84.1; Median: 85.0; 90th: 86.4; 90th - 10th: 28 months
  - White duals (husband’s earnings):
    - 10th: 84.6; Median: 85.0; 90th: 85.4; 90th - 10th: 10 months
  - Black duals (own earnings):
    - 10th: 82.1; Median: 83.3; 90th: 85.9; 90th - 10th: 46 months
  - Black duals (husband’s earnings):
    - 10th: 83.2; Median: 83.3; 90th: 83.5; 90th - 10th: 4 months
  - For both white and black duals, a positive earnings profile adds about another year of life.
- Cross-group age-of-death differences at constant lifetime incomes (Table 6 excerpts):
  - At low income ($77,642):
    - White males: 78.9
    - Black males: 76.8 (white males 26 months more)
    - White female (nondual): 82.1 (white males -38 months relative)
    - Black females (nondual): 81.3 (black males -54 months relative)
  - At high income ($1,163,370):
    - White males: 80.8
    - Black males: 79.5 (white males 15 months more)
    - White female (nondual): 84.7 (white males -47 months relative)
    - Black females (nondual): 85.6 (black males -73 months relative)
  - Observations:
    - The white-black male age-of-death gap is about 26 months at the low-income level and narrows to 15 months at the high-income level.
    - Gender gaps (male vs female) are large and persistent across income levels.
- Mortality rates for 65-year-old men by earnings level (Figure 7 highlights):
  - Rates decline as earnings increase.
  - The mortality rate difference between blacks and whites begins at about 0.5 percentage points at the lowest income level and falls by a third at about $1.4 million in lifetime earnings (95th percentile of the black male earnings distribution).

### Interpretation and main conclusions
- Mortality is negatively related to lifetime income across black and white males and females.
- The difference in age of death between low and high lifetime income is on the order of two to three years for the groups studied.
- Workers with positively-trended earnings over their work life may live an additional six to eighteen months.
- Income-related mortality differences between blacks and whites are largest at low-income levels, particularly for males, and narrow substantially at higher income levels.
- Gender differences in mortality are large and persistent across income levels.
- The income-related differences in life expectancy materially affect the distributional assessment of Social Security reforms and the existing program:
  - Income-related differences curtail, but do not reverse, the progressivity of the basic Social Security benefit structure.
  - Accounting for income-related mortality differences is important when evaluating proposals such as raising the normal retirement age or increasing the early-retirement age.
  - The feedback of life expectancy on retirement decisions complicates attempts to adjust benefits by age of retirement; an “actuarially fair” adjustment will vary across income groups and may induce selection behavior (low-income workers retiring earlier than high-income workers), so a single adjustment factor can cause workers to select “against” the system.

*Source: _wp0715 - section III.  That is, we first impute above-cap earnings for those earning the maximum and then sum their real*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2007/_wp0715.pdf_