## Short-Range Actuarial Projectionsof the Old-Age, Survivors, and Disability Insurance Program, 2005

ACTUARIAL STUDY NO. 119
by Chris Motsiopoulos
and Richard B. Tucker

G. DISABLED WORKER PROJECTION BY SINGLE-YEAR-OF-AGE

The following is a detailed example of the projection of the number of disabled worker beneficiaries by single-year-of-age. Similar projections are made for the short-range period for each gender and age 15-NRA. The illustration is based on the 2005 Trustees Report intermediate set of assumptions.

Disabled Worker Single-Year-of-Age Projection—Male Age 36 in 2005 (1969 Birth Cohort)

Disability Insured

• Fully insured on January 1: 2,083,400
• Disability insured as a percent of fully insured on January 1: 0.922700
• Disability insured on January 1 (average age 35½): 0.922700 x 2,083,400 = 1,922,354
• Projected fully insured on December 31: 2,085,300
• Projected disability insured as a percent of fully insured on December 31: 0.921056
• Projected disability insured on December 31 (average age 36½): 0.921056 x 2,085,300 = 1,920,678
• In force on January 1: 33,661

Awards

• Projected award exposure: ½(1,922,354) + ½(1,920,678) - 33,661 = 1,887,855
• Baseline incidence rate (male age 36 in 2004): 0.002760
• Projected incidence factor 1: 1.015580
• Projected incidence rate (male age 36 in 2005): 0.002760 x 1.015580 = 0.002803
• Projected awards: 0.002803 x 1,887,855 = 5,292

Terminations

• Projected termination exposure: 33,661 + ½(5,292) = 36,307
• Baseline death rate (male age 36 in 2004): 0.017237
• Projected death termination factor 1: 0.969948
• Projected death rate (male age 36 in 2005): 0.017237 x 0.969948 = 0.016719
• Projected death terminations: 0.016719 x 36,307 = 607
• Baseline recovery rate (male age 36 in 2004): 0.027208
• Projected recovery termination factor 1: 1.005219
• Projected recovery rate (male age 36 in 2005): 0.027208 x 1.005219 = 0.027350
• Projected recovery terminations: 0.027350 x 36,307 = 993
• Baseline "all other" rate (male age 36 in 2004): 0.001380
• Projected "all other" termination factor 1: 1.276812
• Projected "all other" rate (male age 36 in 2005): 0.001380 x 1.276812 = 0.001762
• Projected "all other" terminations: 0.001762 x 36,307 = 64

End-of-year In Force, Suspensions, and Current-Payment Status

• Projected total terminations: 607 + 993 + 64 = 1,664
• Projected in force on December 31: 33,661 + 5,292 - 1,664 = 37,289
• Baseline withheld rate (male age 36 in 2004): 0.050501
• Projected withheld factor: 0.997648
• Projected withheld rate (male age 36 in 2005): (1.050501 x 0.997648) - 1 = 0.04803
• Projected suspensions: 0.04803 x 37,289 = 1,791
• Projected current-payment status on December 31: 37,289 - 1,791 = 35,498

### Section footnotes--

1 Projected incidence and termination factors by single-year-of-age are based on discussion found in section III.A.