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

### D. DISABLED WORKER TERMINATIONS

Terminations are tabulated as of calendar age-the integral age attained in the year disability benefits are terminated. For example, beneficiaries born in 1965 and terminated in 2000 are considered to be age 35 regardless of whether or not they had a birthday. As discussed in section III.A, benefit termination can occur for a number of reasons. The four major categories include: automatic conversion to old-age benefits upon attainment of normal retirement age; death of the beneficiary; medical recovery or return-to-work; and all other reasons.

As it relates to termination, exposure is the estimated amount of time-measured in life-years-that individuals on the disability rolls are exposed to the possibility of benefit termination. This quantity is estimated by observing the activity of the rolls for a particular birth cohort. For example, consider a period during which disabled workers born in 1965 are observed for termination during 2000, at calendar age 35. The model assumes that each beneficiary already on the rolls as of the beginning of the year will be exposed for 12 months. An adjustment is then made for the amount of time contributed by new awards. Under the assumption that awards are uniformly distributed throughout the year, each new beneficiary will be exposed for an average of 6 months.

Alternatively, termination exposure for a given calendar age in a particular year can be defined as the average number of beneficiaries on the rolls during the year. This can be estimated by adding one-half of the awards to those already in force at the beginning of the year. As shown in the following examples, this method is equivalent to calculating exposure using the "life-years" concept.

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

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

• Death terminations (SSA administrative records): 702

• Recovery terminations (SSA administrative records): 1,263

• "All other" terminations (SSA administrative records): 67

• Awards (SSA administrative records): 4,146

• In force on January 1: 33,787

• Termination exposure: $33,787 +$1/2(4,146) = 35,860 aggregate life-years

• Death rate: $702 / 35,860 = 0.01958$

• Recovery rate: $1,263 / 35,860 = 0.03522$

• "All other" rate: $67 / 35,860 = 0.00187$

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

• Projected death rate: 0.02708

• Projected recovery rate: 0.01135

• Projected "all other" rate: 0.00117

• Projected awards: 7,900

• Projected in force on January 1: 69,797

• Projected termination exposure: $69,797 +$1/2(7,900) = 73,747

• Projected death terminations: $0.02708 x 73,747 = 1,997$

• Projected recovery terminations: $0.01135 x 73,747 = 837$

• Projected "all other" terminations: $0.00117 x 73,747 = 86$

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