Short-Range Actuarial Projections |
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ACTUARIAL STUDY NO. 119
by Chris Motsiopoulos and Richard B. Tucker | |||||
C. DISABLED WORKER INCIDENCE AND AWARDS
Awards are tabulated as of calendar agethe integral age attained in the year disability benefits begin. For example, individuals born in 1969 and awarded benefits in 2004 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 timemeasured in life-yearsthat 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 1969 are observed for disability during 2004, at calendar age 35. Under the assumption that births are uniformly distributed throughout the year, the average age of the cohort is 34½ on January 1; the average age is 35 on July 1; and the average age is 35½ on December 31. So on average, the cohort is exposed for 6 months before their birthdayJanuary through June; and 6 months after their birthdayJuly 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 insuredwhich 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 RateMale Age 35 in 2004 (1969 Birth Cohort)
Disabled Worker AwardsMale Age 45 in 2014 (1969 Birth Cohort)