## A Stochastic Model of the Long-Range Financial Status of the OASDI Program—September 2004

II. EQUATION SELECTION AND PARAMETER ESTIMATION

### B. MORTALITY

The annual rate of decrease in the central death rate1 (which is sometimes referred to as the annual rate of improvement in mortality) is calculated as the negative of the percent change in the central death rate for a given year. Thus, a positive value represents a decrease in the central death rate from one year to the next.

Central death rates were calculated for 42 age-sex groups (under 1, 1-4, 5-9, 10-14, ..., 85-89, 90-94, and 95+; male and female) for the period 1900 through 2000.2 Data for the annual numbers of deaths and the U.S. resident population are from the National Center for Health Statistics and the U.S. Census Bureau, respectively. For the population aged 65 or older, annual deaths and enrollments are from the Centers for Medicare & Medicaid Services.

Using the approach of other researchers (Congressional Budget Office, 2001), an AR(1) equation was selected for the annual rate of decrease in the central death rate for each age-sex group. The general form of the modified equation is:

MRk,t = MRk,tTR + φkmrk,t-1+ εk,t .               (2)

In this equation, MRk,t represents the annual rate of decrease in the central death rate for group k in year tMRk,tTR represents the projected annual rate of decrease from the TR04II for group k in year t; mrk,t represents the deviation of the annual rate of decrease from the TR04II value for group k in year t; and εk,t represents the random error for group k in year t. Appendix D contains the estimates of the parameters, fk, in Equation (2).

A Cholesky decomposition was performed using the residuals from the 42 fitted equations. Appendix B discusses this technique. The Cholesky matrix used was 42 x 42 with the age groups in ascending order with alternating male and female groups.

### Footnotes—

1 The central death rate is defined as the annual number of deaths for a particular group divided by the estimated population of that group at midyear.

2 A detailed description of the methodology used in calculating death rates by age and sex can be found in Actuarial Study No. 116. www.socialsecurity.gov/OACT/NOTES/as116/as116_Foreword.html