II. EQUATION SELECTION AND PARAMETER ESTIMATION
The disability incidence rate for a given year is the proportion of the exposed population at the beginning of that year who become newly entitled to disability benefits during the year. The exposed population is comprised of workers who are disability insured but not entitled to disability benefits. The historical disability incidence rates used to fit the equations are age-adjusted to the 1996 exposed population. The age-adjusted disability incidence rates (male and female) are the crude rates that would occur in the disability exposed population as of January 1, 1996, if that population were to experience the observed or assumed age-sex specific disability incidence rates in the selected year.
Data on disability incidence are obtained from SSA administrative records and the age-adjusted disability incidence rates are computed by OCACT. Over the historical period from 1970 to 2003, disability incidence rates have varied widely due to changes in legislation and program administration as well as economic and demographic factors.
The equations for disability incidence rates are selected separately for males and females. Over the historical period of 1970 through 2003, both the male and the female series fail their tests for stationarity. However, in this model it is assumed that the nonstationarity in these series is due to the various changes in the law over the historical period. Therefore, both series were modeled without correcting for nonstationarity. Using time-series analysis, both series were modeled individually as AR(2) processes. The R-squared values for the male and female disability incidence rate equations were 0.89 and 0.87, respectively. The actual and fitted values for males and females are shown in figures II.7 and II.8, respectively.
The modified male disability age-adjusted incidence rate equation is:
DIM_{t} = DIM_{t}^{TR} +1.47dim_{t}_{-1} −0.63dim_{t}_{-2} + ε_{t} . (10)
In this equation, DIM_{t} represents the male disability incidence rate in year t; DIM_{t}^{TR} represents the male disability incidence rate from the TR04II in year t; dim_{t} represents the deviation of the male disability incidence rate from the TR04II male disability incidence rate in year t; and ε_{t} is the random error in year t.
The modified female age-adjusted disability incidence rate equation is:
DIF_{t} = DIF_{t}^{TR} +1.45dif_{t}_{-1} −0.62dif_{t}_{-2} + ε_{t} . (11)
In this equation, DIF_{t} represents the female disability incidence rate in year t; DIF_{t}^{TR} represents the female disability incidence rate from the TR04II in year t; dif_{t} represents the deviation of the female disability incidence rate from the TR04II female disability incidence rate in year t; and ε_{t} is the random error in year t.