Social Security and Education

Studies | Education | Social Security

No. 240
Wednesday, January 31, 2001
by Dr. Liqun Liu and Dr. Andrew J. Rettenmaier


Appendix

Appendix Table I - Mortality Ratios for Education Groups

Earnings. Our forecast of future taxable earnings follows a methodology described in Rettenmaier and Saving (2000).20 In short, the real growth rates of the component parts of annual earnings are calculated for each group of workers, where group defines age, education, sex and race. The component parts of annual earnings for a group are the percentage working, their annual hours of work and their hourly wage. Growth rates for each earnings component are estimated using inflation-adjusted data from the Current Population Surveys. Past earnings are deflated using the Personal Consumption Expenditures implicit price deflator.

The calculated real growth rates then become the basis for projecting earnings into the future. In previous work we forecast the earnings subject to the Medicare payroll tax, and since the Medicare tax applies to all labor earnings, historical earnings were not capped at some maximum prior to calculating the growth rates. In the present study, the current Social Security taxable maximum was inflation-adjusted and retrospectively imposed on earnings in earlier years.

Longevity. An excellent source of birth year specific life tables is found in Bell et al. (1992).21 They provide separate life tables for every fifth birth cohort between 1900 and 1990. We initially used their life tables, but for consistency with our analysis of racial groups we use the Census Bureau estimates. The base U.S. Census Bureau life tables are from the 1995, 2005 and 2050 middle series life tables. The tables are organized by single years of age, by sex, by race and by Hispanic origin. They provide expected mortality at each age in the three cross-sections. However, we are interested in the mortality experienced by individuals born in a given year, not mortality in a given year at various ages. To create life cycle mortality tables, we use linear interpolation to fill in the cross-section life tables for intervening years. From the entire set of cross-sectional life tables, we identify the experience of the individuals born in the years under study.

Appendix Figure I - Survivorship within Education Groups for Men Born in 1960

Individuals born in 1935 through 1980 are the focus of our study; therefore, the interpolated Census data results in mortality estimates for those born in 1935 from the age of 60 to the age of 100. For the youngest birth year, 1980, the Census data covers mortality rates between 15 and 70 years of age. Extrapolated data are used for the years 2051 to 2080, which allows for tracking mortality out to the age of 100 for the youngest birth year.

The void for years prior to 1995 is filled using death registration data from Anderson (1998). The death registration data indicate the number of survivors for every fifth year of age at 10-year intervals between the turn of the century and 1996. The data are further partitioned by race and sex. Mortality rates between ages and the years 1940 to 1980 are interpolated to fill in the pre-1995 data, allowing us to complete the set of cross-sectional life tables from which the birth year life tables are constructed.

Transforming the life tables derived from the Census Bureau and death registration data for men and women into education category-specific life tables is accomplished by using the relative mortality estimates of Sorlie and Backlund (1995). They estimated mortality ratios for various classifications of the population according to race, employment status, income, education, marital status and household size. Appendix Table I shows their estimates of the education-specific relative mortality rates. Their findings suggest that less-educated men and women are more likely to die than those with high school educations. At higher ages the education differentials decline, indicating a convergence in mortality among those who survive.

Two things need to be done to obtain applicable mortality ratios. First, the ratios in each age-sex group above are stated relative to high school graduates. This reference group does not correspond to the "average" person in that category, but the mortality rates in general sex-specific life tables do. Therefore, we must first restate the relative mortality rates with reference to the average person in a particular age-sex group. Second, the mortality ratios are estimated for discrete age groups rather than for single years of age. In essence, the ratios above represent an "average" relative mortality rate in age-sex-education category, but for the same reason that the relative mortality differs between the 24-44 age group and the 45-64 age group, the relative mortality should also differ at each age between 25 and 44. See Liu and Rettenmaier (2000) for a detailed discussion of how we arrived at differing mortalities based on education.

By using the constant mortality adjustment by education categories, we implicitly assume that the differences are constant and persistent. In other words, there is no divergence over time in the longevity of high school and college graduates, for example, even though our estimates of life cycle earnings show greater disparity in their wages. The increased disparity in life cycle earnings suggests that there may be greater disparity in longevity estimates based on education. Because the Sorlie and Backlund relative risk ratios reflect a point-in-time difference in mortality, future compositional changes will affect the relative differences, but in these estimates the differences are constant over time. Some of the disparity in outcomes that we report would be dampened by mortality differences that grow over time.

Appendix Figure I presents the survival curves for men born in 1960. Based on the aforementioned education adjustments, we estimate that 70.8 percent of men with less than a high school education, 75.9 percent of high school graduates, 77.5 percent of those with 13 to 15 years of schooling, 82.7 percent of college graduates and 85.2 percent of those with some graduate school are expected to live to age 67.


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