## A Stochastic Model

of the Long-Range Financial Status

of the OASDI Program—September 2004

II. EQUATION SELECTION AND PARAMETER ESTIMATION

###
G. DISABILITY RECOVERY RATE

The *disability recovery rate* for a given year is the proportion of disabled-worker beneficiaries whose disability benefits terminate as a result of the individual's recovery from disability. The age-adjusted disability recovery rates (male and female) are the crude rates that would occur in the in-current-payment population as of January 1, 1996, if the population were to experience the observed or assumed age-sex specific disability recovery rates in the selected year.

Data on disability recovery are obtained from SSA administrative records and the age-adjusted disability recovery rates are computed by OCACT. Over the historical period from 1970 to 2003, there has been substantial variation in the age-adjusted disability recovery rates. This variation is believed to be mostly due to changes in the law. For example, the age-adjusted disability recovery rate for males jumped from 10.3 per thousand in 1996 to 24.4 per thousand in 1997, largely as a result of the effects of a provision in Public Law 104-121. This provision prohibited benefit payments to individuals where drug addiction and/or alcoholism was material to the determination of disability.

The equations for disability recovery rates were modeled separately for males and females. The historical disability recovery rates used to fit the equations were age-adjusted to the 1996 in-current-payment population. Due to the frequent changes in the law, the time period considered was narrowed to 1985 through 2003. The value for 1997 was excluded in the development of the equation due to the change in the law described above. The AR(1) model provided the best fit of the models that were tested. The R-squared values for the male and female disability recovery rate equations were 0.83 and 0.50, respectively.

The modified male age-adjusted disability recovery rate equation is:

*DRM*_{t} = *DRM*_{t}^{TR}
+0.58*drm*_{t}_{-1} + *ε*_{t} . (12)

In this equation, *DRM*_{t} represents the male disability recovery rate in year *t*; *DRM*_{t}^{TR}
represents the male disability recovery rate from the TR04II in year *t*; *drm*_{t} represents the deviation of the male disability recovery rate from the TR04II male disability recovery rate in year *t*; and *ε*_{t} is the random error in year *t*.

The modified female age-adjusted disability recovery rate equation is:

*DRF*_{t} = *DRF*_{t}^{TR}
+0.57*drf*_{t}_{-1} + *ε*_{t} . (13)

In this equation, *DRF*_{t} represents the female disability recovery rate; *DRF*_{t}^{TR}
represents the female disability rate from the TR04II in year *t*; *drf*_{t} represents the deviation of the female disability recovery rate from the TR04II female disability recovery rate in year *t*; and *ε*_{t} is the random error in year *t*.