A Stochastic Model of the Long-Range Financial Status of the OASDI Program—September 2004

IV. RESULTS

C. SENSITIVITY ANALYSIS

Two types of sensitivity analyses have been performed. A stochastic sensitivity analysis consists of performing a set of simulations in which a single equation (or group of related equations) is modeled stochastically while all other equations are modeled as the TR04II. A deterministic sensitivity analysis consists of a single simulation in which the mean of an equation (or group of related equations) is replaced with the TR04I or TR04III value, while the remaining equations are left with their means equal to the TR04II values.

1. Stochastic Analysis

A stochastic sensitivity analysis is the process in which one, or some, of the demographic, economic, and disability variables are varied independently, while the other variables are set to their values under the TR04II. This allows a measurement of how much of the variance of the final distributions can be attributed to each variable or set of variables.

Table IV.19 presents the expected long-range actuarial balance, along with the standard deviation, for each of the stochastic sensitivity runs. Each of these sensitivity runs is based on 5,000 simulations of the stochastic model. The first sensitivity run presented in table IV.19 allows only the total fertility rate to vary. The next sensitivity run varies only the 42 mortality improvement rates (21 age groups for males and females). The third run, listed as immigration, allows only the three immigration assumptions (legal immigration, emigration, net other immigration) to vary. Grouping the four economic assumptions (unemployment, inflation, real interest, and real average wage growth rates) and allowing only these variables to vary produces the economic sensitivity run. The last sensitivity run varies only the disability incidence rates (male and female together). Varying the disability recovery rates resulted in a negligible change.

Table IV.19—Sensitivity to Varying Selected Assumptions, Calendar Years 2004-78
Effect of Changing Individual Assumption:
Actuarial Balance
Median
Average
Standard
Deviation

Fertility
-1.92
-1.93
0.49

Mortality Improvement
-1.96
-1.97
0.56

Immigration
-1.89
-1.89
0.10

Economic
-1.90
-1.90
0.51

Disability Incidence
-1.89
-1.88
0.08

Effect of Changing All Assumptions Together
-1.98
-2.03
0.95

The long-range actuarial balance under the TR04II is -1.89 percent of taxable payroll.

2. Deterministic Analysis

A deterministic sensitivity analysis is the process in which the mean of one, or some, of the demographic, economic, and disability equations are set to equal the TR04I or the TR04III value, while the remaining variables are set to equal the TR04II value. In this case, the variance of all key input variables is set to zero and only one simulation is performed, since the zero variance ensures that all simulations produce the same results. This type of sensitivity analysis is similar to that done in the Trustees Report, and can therefore be used to compare the underlying nature of the OSM and the Trustees' model.

Table IV.20 compares the long-range actuarial balance results from the deterministic sensitivity run of the OSM to the results in the Trustees Report. The first row of each sensitivity grouping is from the OSM. The second row contains the actual sensitivity result from the Trustees Report. Technically speaking, the first sensitivity is not really a sensitivity analysis at all, but is included as a point of reference. The next three results (fertility, mortality, and immigration) are the demographic deterministic sensitivity runs. This is followed by three economic deterministic sensitivity runs (inflation, real interest, and real average wage). The final deterministic sensitivity run is disability incidence. Note that unemployment and disability recovery sensitivity runs are not included since no comparable sensitivity analysis is performed for the Trustees Report.

Table IV.20—Comparison of Stochastic and Deterministic Models,
Calendar Years 2004-78
Sensitivity:
Actuarial Balance
Low Cost
Intermediate 1
High Cost
None

OSM
0.40
-1.89
-4.99

TR
0.41
-1.89
-4.96
Fertility

OSM
-1.57
-1.89
-2.21

TR
-1.61
-1.89
-2.18
Mortality

OSM
-1.17
-1.89
-2.76

TR
-1.29
-1.89
-2.59
Immigration

OSM
-1.68
-1.89
-2.03

TR
-1.63
-1.89
-2.08
Inflation

OSM
-2.10
-1.89
-1.63

TR
-2.11
-1.89
-1.67
Real Interest

OSM
-1.39
-1.89
-2.47

TR
-1.38
-1.89
-2.48
Real Average Wage

OSM
-1.32
-1.89
-2.50

TR
-1.35
-1.89
-2.42
Disability Incidence

OSM
-1.57
-1.89
-2.22

TR
-1.61
-1.89
-2.17
 1This column does not show a sensitivity analysis, but is shown for comparison purposes.