Social Security Disability Insurance Program Worker Experience
ACTUARIAL STUDY NO. 118 by Tim Zayatz, A.S.A.

Appendix

V. STUDY POPULATION AND METHODS

A. Overview

For this study, we analyzed over 9.9 million records of Social Security Disability Insurance (DI) worker beneficiaries from the 5-year period January 1, 1996 through December 31, 2000. Data are based on a 100 percent sample from the Social Security Administration Master Beneficiary Record (MBR). The primary variables of interest include: the reason for decrement from the disability rolls, and duration since entitlement. However, factors other than time since selection affect survival. These include the standard concomitant variables of select age and sex of the beneficiary. The analysis reflects a total of roughly 21.9 million life-years of exposure for males and 15.6 million life-years of exposure for females. A 10-year select period was chosen for this study, implying that decrement for participants 10 or more years beyond selection is no longer a function of select age, but a function of attained age only.

Termination of DI benefits can occur for the following reasons:

Terminations due to "all other reasons" are treated as withdrawal from the study, and directly affect exposure. However, separate decrement tables are not developed for categories other than death and recovery. The table below provides a count of the number of deaths and recoveries collected from the MBR. Note that there exist differences in classifying various disability actions among the various data sources consulted for this study. Further note that to a certain extent, this study also covers the activity of the OASI rolls, but only as it relates to tracking disabled beneficiaries who have voluntarily switched to OASI benefits prior to normal retirement age, or have automatically been converted to the OASI rolls upon attaining normal retirement age. As a result, termination counts stated here will differ from those stated elsewhere—the number of deaths will be dramatically different as they include substantial counts from the OASI rolls.

Source: MBR database as of March 2004. Results do not include old-age conversions or terminations due to other reasons.

B. Data Considerations

The mortality experience is affected by several unique circumstances. It is recognized that a claimant may die during the 5-month waiting period required under the DI program—and therefore never becomes entitled; or the claimant may die before final disposition of the disability claim—in which case only retroactive disability benefits may be payable. With regard to the DI program, participation in this study is contingent upon entitlement to benefits. Therefore, death prior to entitlement is not a "countable" death. As a result, the probability of death during the first year of entitlement may be artificially lower than expected.

As it relates to this study, observation ends with the termination of benefits. Under the DI program, disabled workers may convert to old-age benefits at anytime beginning with age 62, with mandatory conversion taking place at normal retirement age. Such conversion is considered a termination of disability benefits as old-age benefits become payable from the OASI Trust Fund. However, disabled beneficiaries continue under observation in this study beyond the time of the switch. Consequently, deaths for attained ages 62 and older may come from the OASI rolls. Note that this is a material change from methods used in the previous DI Worker Experience study (Actuarial Study No. 114), which terminated observation with the last month in which DI benefits are payable. This enhancement allows tracking disabled lives into retirement, and further eliminates much of the "guesswork" involved in applying the cumbersome blending techniques used in that study for older attained ages. Hopefully the result is more robust estimates of mortality.

Mention was made earlier of a special disability workload of SSI recipients who are potentially eligible for DI benefits due to previously unrecognized disability-insured status. This workload has caused a supplemental increase in awards beginning in 2001. In most instances, entitlement is retroactive to well before the date of final review. However, due to the guidelines established for processing the workload, the cases involved at the time of completion of this study represent a biased sample of records. Consequently, these cases have been eliminated from the overall sample.

C. Data Collection

The model for this study utilizes a customized database that is constructed from 100 percent MBR data as of March 2004. The general record selection criteria are outlined below. The final data was subjected to numerous screenings and categorizations. Included in the study are:

Excluded from the study are:

D. Methods

The availability of complete data on each participant in the study (including date of birth, date of entitlement, and cause of decrement) allows for direct estimation of the multiple-decrement probabilities q⁽ⁱ⁾ represents the cause of decrement. The ordered pair (r,s) is determined for each age interval (x,x+1] for which a participant is under observation. The concept is that each participant enters the interval at age x+r(0 ≤ r < 1), and is scheduled to exit the interval at age x+s(0 < s ≤ 1). Numerically, s-r is the amount of time (measured in life-years) that the participant is exposed to the risk of decrement. Summing over all participants, we can calculate the scheduled exposure contributed to an interval.¹

A participant may survive to the end of an interval, or may exit the study prior to the end of the interval in the event of:

Based on these criteria, a scheduled ending age, x+s, is established for an age interval in which the participant is expected to either survive to the end (s=1), or become an observed ender (s < 1).² Scheduled exposure is then credited to the appropriate interval (or duration since selection) using the following conditions: if the participant survives to the end of the interval, then exposure is credited from x+r to x+1; if the participant dies or is an observed ender within the interval, then exposure is credited from x+r to x+s; if the participant withdraws from the study during the interval (for example, recovers), then exposure is credited from age x+r to x+s. Note that since recovery from disability is no longer considered after converting to old-age benefits, a slight modification to this method is needed in crediting exposure for use in calculating recovery probabilities. As before, scheduled exposure is credited to durations entirely within a period of DI entitlement, however, exact exposure is credited only up until time of the switch to old-age benefits; no exposure is credited for durations entirely within a period of OASI entitlement.

Multiple-decrement probabilities are found by dividing the observed number of deaths or recoveries in an interval by the aggregate scheduled exposure for that interval. As discussed later, single-decrement (absolute) rates are derived from the probabilities using a constant force assumption for the distribution of decrement within a given interval.³

E. Select Age and Exposure

Entitlement to disability benefits usually occurs at some fractional age of the beneficiary. To facilitate exposure calculations, the insuring age of the participant and corresponding insuring date of birth are substituted for the actual age at entitlement and actual date of birth. In this study, the insuring age is calculated to be the beneficiary's age last birthday as of entitlement. For example, consider the following beneficiary data:

Date of entitlement: 1-February-2000

Date of birth: 10-July-1960

Actual age at entitlement: 39 years, 206 days

Insuring age: 39 years

Insuring date of birth: 1-February-1961

Use of insuring age results in an integral select age at entitlement ensuring that subsequent durations begin on the entitlement anniversary. This is true whether the participant enters the study during the observation period, or is already part of the entitlement group when the observation period opens.

For selection during the observation period, the entry age (YI) into the study is the beneficiary's age as of the date of entitlement. For selection prior to the beginning of the observation period, the entry age is the beneficiary's age as of January 1, 1996. In either case, the beneficiary's age is measured from the insuring date of birth.

The scheduled exit age (ZI) is the age at which the participant is scheduled to exit the study as an observed ender on December 31, 2000. The actual exit age at death (THI) or withdrawal (PSI) is the exact age at which the participant exits the study under those particular decrements.

The fractional-time variables used to determine scheduled exposure contributions for an observation interval are defined below:

The amount of exposure contributed at each duration is summarized as follows:

As previously mentioned, exact exposure is used in calculating recovery probabilities. This type of exposure is only credited to the interval during which conversion to old-age benefits takes place. Using a fractional-time variable, exact exposure is defined as k-r, where k is determined as follows:

Note that in this context PSI represents the exact age at the time of switch to old-age benefits.

F. Duration and Graduation

The intervals for which a participant is under observation—measured in years since selection—are called durations. For each select age [x] and duration n, the ordered pair (r,s) represents the amount of exposure contributed to the observation interval ([x]+n,[x]+n+1]. For durations extending beyond the 10-year select period, exposure is credited to the appropriate attained age interval.

The select-and-ultimate multiple-decrement probabilities are graduated using the two-dimensional Whittaker-Henderson Type B method ⁴. The horizontal and vertical smoothing coefficients were chosen to obtain some degree of smoothness within individual durations (columns) as well as within select ages (rows), while deviating as little as possible from the original estimates.

G. Survival Tables

Survival tables 8A-8C are constructed from select-and-ultimate death probabilities. The functions l_[x],l_{[x],+1, ...,}l₁₁₀ are first calculated for select age [x] = 16, using a radix of 100,000. This step determines values for the ultimate period of the table and older attained ages. Functions for select ages [x] > 16 are then derived retrospectively from the ultimate values. For example, l_[x] is determined from l_{x + 10} using the survival probabilities of the select period for the given select age. The number l_{[x] + t} represents the number alive at the beginning of duration t from those originally entitled at select age [x]. Note that the number alive at various select ages are not actual counts of disability beneficiaries. Rather, the number living at the beginning of any duration are for illustrative purposes, chosen to represent the probability of survival based on values shown in tables 7A-7C.

Survival tables 15A-15B are similarly constructed from select-and-ultimate recovery probabilities shown in tables 14A-14B. Since recovery is no longer considered after attaining normal retirement age, these tables are truncated after attained age 64. Note that in this case, "survival" refers to beneficiaries who remain on the DI rolls by not recovering.

The survival tables are read across the row, or select period, for 0-10 years since selection, then down the last column, or ultimate period for 10 or more years since selection. Numbers for the following example can be found in table 8A. Of the male beneficiaries disabled at select age 30, the following table shows the number surviving (that is, still on the disability rolls) after the stated number of years:

H. Expected Future Lifetime

Future lifetime tables are produced from the survival functions described above using basic actuarial principles found in any standard actuarial text on life contingencies. Also presented in this study are the results of aggregating over duration, by select age (see tables 11, 18, and 25) or attained age (see tables 12, 19, and 26).

Aggregate lifetime for a specific select age is an exposure-weighted average of the expected future lifetime at each duration of that age. This differs from aggregate lifetime for a specific attained age, which is an exposure-weighted average of the expected future lifetime of those durations representing a particular attained age.

For example, aggregate lifetime for select age 40 is a weighted average of the expected lifetimes shown for each duration 0 through 34—where each duration represents a different attained age. In contrast, aggregate lifetime for attained age 40 is the average of the expected lifetimes for a select 40-year-old at duration 0, select 39-year-old at duration 1,... select 20-year-old at duration 20—all of whom are attained age 40.

I. Probabilities and Absolute Rates

The data for this study were collected in a multiple-decrement environment, however, we present results for only two major decrements—death and recovery. The symbol q^(d) represents the probability of death in the presence of the other decrements. Mathematically, this is represented by:

where p^(τ) is the probability of surviving under all decrements; and µ^(d) is the force of mortality.

For each of the causes of decrement in a multiple-decrement model, it is possible to define a single-decrement model that depends only on a particular cause of decrement. The symbol q´^(d) represents the single-decrement (absolute) rate of death. Mathematically, this is represented by:

where p´^(d) is the probability of not dying. In this representation, observation stops at the point of non-death decrement, and scheduled exposure is replaced by the smaller quantity of exact exposure. The result is lower exposure totals relative to those used in formulating death probabilities.

For each combination of select age and duration, the multiple-decrement probabilities q^(d) and q^(r) are calculated by dividing the observed number of deaths or recoveries by the exposure for that cell. These probabilities are used to derive the absolute rates of decrement q´^(d) and q´^(r) as shown below (note that d, r, and τ superscripts refer to death, recovery, and total decrement, respectively):

Derive the total decrement probability:

Under the assumption of constant force for each decrement over the age interval (x,x + 1), absolute rates may be derived using the following:

In this study, absolute rates are presented on a "per thousand" basis.

---

Section footnotes--

---

¹For a complete discussion, refer to chapter 6 of Survival Models and Their Estimation (London 1988, second edition).

²A participant who dies during the interval does so at age x+t ≤ x+s; a participant observed to withdraw from the study during the interval also does so at age less than x+s.

³For a complete discussion on multiple-decrement probabilities, the associated single-decrement rates, and construction of the select-and-ultimate multiple-decrement tables found in this study, the reader is referred to chapter 10 of Actuarial Mathematics (Bowers et al. 1997).

⁴For details, refer to chapter 8 of Graduation: The Revision of Estimates (London 1985).

List of Studies