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

E. DURATION ANALYSIS

For any particular select age¹ of a disabled worker beneficiary, the highest probability of death occurs within the first 2 years of entitlement. Afterward, the probability of death decreases significantly so that the chances of survival beyond the first 2 years are greatly improved. In general, disabled workers of a particular attained age² exhibit mortality rates that are inversely related to the amount of time spent on the rolls-up until roughly the tenth duration. After 10 years on the rolls, the short-range model assumes mortality rates are no longer a function of select age, but a function of attained age only.

Death

The following table shows the composition of disabled workers, attained age 50 in current-payment status, sorted by select age and duration. As shown, mortality rates at different durations can vary greatly. New 50-year-old entitlements experience mortality at a rate of 82.14 deaths per thousand beneficiaries. Deaths fall to 52.20 per thousand for select 49-year-olds who have been on the rolls for 1 year; 38.68 per thousand for select 48-year-olds who have been on the rolls for 2 years, etc.; after 10 or more years on the rolls, mortality experience is not expected to differ significantly with regard to select age³.


Select age at entitlement	Complete years since entitlement (duration)	Attained age	Death rates per thousand beneficiaries¹	Recovery rates per thousand beneficiaries	DI male disabled workers with benefits in current-payment status as of December 31
					2000		1995
					Number	Percent	Number	Percent
50	0	50	82.14	3.60	4,244	4.84	3,571	5.52
49	1	50	52.20	7.53	5,914	6.74	4,814	7.44
48	2	50	38.68	4.02	6,329	7.22	5,744	8.87
47	3	50	33.47	3.57	6,065	6.91	6,244	9.65
46	4	50	30.38	6.48	5,703	6.50	6,096	9.42
45	5	50	28.98	5.76	5,599	6.38	4,931	7.62
44	6	50	28.29	5.03	5,316	6.06	3,846	5.94
43	7	50	27.59	4.61	5,320	6.07	3,189	4.93
42	8	50	26.85	4.24	5,267	6.00	2,794	4.32
41	9	50	24.80	3.16	4,884	5.57	2,597	4.01
40	10	50	22.15	1.82	4,182	4.77	2,385	3.68
39	11	50	22.15	1.82	3,212	3.66	2,136	3.30
38	12	50	22.15	1.82	2,749	3.13	1,762	2.72
37	13	50	22.15	1.82	2,421	2.76	1,440	2.22
36	14	50	22.15	1.82	2,265	2.58	1,221	1.89
35	15	50	22.15	1.82	2,138	2.44	1,342	2.07
34	16	50	22.15	1.82	1,901	2.17	1,148	1.77
33	17	50	22.15	1.82	1,685	1.92	1,079	1.67
32	18	50	22.15	1.82	1,310	1.49	1,125	1.74
31	19	50	22.15	1.82	1,134	1.29	1,210	1.87
30	20	50	22.15	1.82	1,179	1.34	1,148	1.77
29	21	50	22.15	1.82	1,100	1.25	1,015	1.57
28	22	50	22.15	1.82	1,053	1.20	921	1.42
27	23	50	22.15	1.82	1,061	1.21	655	1.01
26	24	50	22.15	1.82	1,156	1.32	603	.93
25	25	50	22.15	1.82	1,031	1.18	495	.76
24	26	50	22.15	1.82	1,003	1.14	477	.74
23	27	50	22.15	1.82	864	.99	696	1.08
22	28	50	22.15	1.82	634	.72	38	.06
21	29	50	22.15	1.82	499	.57	8	.01
20	30	50	22.15	1.82	337�	.38	1	.00
19	31	50	22.15	1.82	132	.15	1	.00
18	32	50	22.15	1.82	26	.03	0	.00
Total					87,713	100.00	64,732	100.00

¹ Based on DI disabled worker experience over the 5-year period 1991-95.

Since the rate of death decreases dramatically after the first several durations, a higher average duration indicates lower mortality for that particular age. For example, the average duration among 50-year-olds increased from 8.0 years in 1995 to 9.1 years in 2000 as the "mix" of beneficiaries became more heavily weighted toward those having 6 or more years on the rolls, and less weighted toward relatively newer beneficiaries having 5 or fewer years on the rolls.

Recovery

For a particular select age, the recovery rate exhibits a noticeable bimodal distribution. Recoveries tend to peak after 1 year of entitlement, decline for several years then peak again after 4 or 5 years of entitlement, finally declining thereafter. The fact that CDR schedules are based on the likelihood of medical improvement helps to explain this pattern. When improvement is expected, reviews are scheduled between 6 and 24 months following initial entitlement-this accounts for the initial peak in recoveries. For cases in which medical improvement is possible but less likely to occur within the first 2 years, reviews are scheduled every 36 months-this accounts for a second peak. If medical improvement is not expected, reviews are scheduled every 5 to 7 years. Note that recovery rates in the above table are based on data collected over 1991-95. During this period, the DI program experienced a significant growth in claims, which delayed or even limited the number of reviews performed.

¹ Age at which the beneficiary is initially entitled to DI benefits.

² Calculated as the select age plus the number of complete years (duration) spent on the DI rolls since selection.

³ A complete DI termination analysis by select age and duration can be found in Actuarial Study #114: Social Security Disability Insurance Program Worker Experience (Tim Zayatz, June 1999).

List of Studies
December 26, 2001