Short-Range Actuarial Projections of the Old-Age, Survivors, and Disability Insurance Program, 2001 Actuarial Study No. 115 Chris Motsiopoulos and Tim Zayatz, A.S.A.

# Appendix

### B. DISABLED WORKER INCIDENCE AND AWARDS

Awards are tabulated as of calendar age-the integral age attained in the year disability benefits begin. For example, individuals born in 1965 and awarded benefits in 2000 are considered to be age 35 regardless of whether or not they had a birthday. Note that the year of award may not be the same as the year of disability onset, or even the year in which the individual became entitled to benefits. Award relates specifically to the time benefits commence.

As it relates to awards, exposure is the estimated amount of time-measured in life-years-that individuals in the insured population are exposed to the incidence of disability. This quantity is estimated by observing the progression of different birth cohorts through time. For example, consider a period during which insured workers born in 1965 are observed for disability during 2000, at calendar age 35. Under the assumption that births are uniformly distributed throughout the year, the average age of the cohort is 34 on average, the cohort is exposed for 6 months before their birthday-January through June; and 6 months after their birthday-July through December. This is expressed mathematically by multiplying both the beginning-of-year and end-of-year disability insured population by one-half. An adjustment is then made for the amount of time contributed by beneficiaries already in force.

Alternatively, award exposure for a given calendar age in a particular year can be defined as the average number of people insured for disability during the year, who are not already disabled. This can be estimated by subtracting the beginning-of-year in-force population from the average number insured-which is the arithmetic average of the beginning-of-year and end-of-year insured population. As shown in the following examples, this method is equivalent to calculating exposure using the "life-years" concept.

Finally, historical incidence rates are computed as awards divided by exposure. For future years, awards are computed by multiplying projected incidence rates by projected exposure.

### Disabled Worker Incidence Rate-Male Age 35 in 2000 (1965 Birth Cohort)

• Awards (SSA administrative records): 4,146

• Disability insured on January 1 (average age $34$1/2): 1,887,249

• Disability insured on December 31 (average age $35$1/2): 1,878,874

• In force on January 1: 33,787--assume 12 months of exposure for each

• Award exposure: 1/2(1,887,249) + 1/2(1,878,874) - 33,787 = 1,849,274.5 aggregate life-years

• Incidence rate: $4,146 / 1,849,274.5 = 0.002242 or 2.24 awards per thousand exposed$

### Disabled Worker Awards-Male Age 45 in 2010 (1965 Birth Cohort)

• Projected incidence rate: 0.004379

• Projected disability insured on January 1 (average age $44$1/2): 1,866,978

• Projected disability insured on December 31 (average age $45$1/2): 1,880,550

• Projected in force on January 1: 69,797

• Projected award exposure: 1/2(1,866,978) + 1/2(1,880,550) - 69,797 = 1,803,967

• Projected awards: $0.004379 x 1,803,967 = 7,900$

List of Studies
December 26, 2001