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

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


Each year the Board of Trustees of the Federal Old-Age and Survivors Insurance (OASI) and Disability Insurance (DI) Trust Funds provides three separate sets of long-range (75-year) assumptions for key demographic and economic variables that affect the future financial status of the combined OASI and DI (OASDI) programs. The intermediate (alternative II) set of assumptions represents the Trustees' best estimate for future experience, while the low cost (alternative I) and high cost (alternative III) sets of assumptions are more and less favorable, respectively, from the perspective of the trust funds' future financial outlook. The Office of the Chief Actuary (OCACT) of the Social Security Administration (SSA) uses the three sets of assumptions to project the principal factors affecting the financial status of the OASDI program. Taken together, these three projections give policy makers a sense of the range of variation in the assumptions and in the financial status of the OASDI program. However, this deterministic approach makes no attempt to assign values to the likelihood of these sets of assumptions.

This Actuarial Study documents the OCACT Stochastic Model (OSM), Version 2004.1. The OSM assigns random variation for some of the key demographic and economic assumptions. These include the total fertility rate, rates of change in mortality, levels of immigration, emigration, and net other immigration, unemployment rate, inflation rate, real interest rate, growth rate in the real average wage, and disability incidence and recovery rates. The OSM is designed such that the projected values for each variable are centered on the intermediate assumptions of the 2004 Trustees Report (TR04II).

Stochastic variation is introduced by developing equations based on standard time-series models. Generally, an equation may include the following: the variable's prior-period values, prior-period error terms, and other variables. In addition, each equation includes a random error term. The ranges of the regressions depend on the nature and quality of the historical data. Projected values for each variable in each year are computed using Monte Carlo techniques to assign the degree of stochastic variation around the Trustees' intermediate assumptions. Each simulation projects annual values for each variable over the 75-year period, in addition to summary measures of the financial status of the combined OASDI Trust Funds (e.g., the long-range actuarial balance).

It is important to note that the results presented here should be interpreted with caution and with a full understanding of the inherent limitations of the process. If certain changes are made to the model specifications, then the projections could be significantly altered. For example, if any one equation is respecified, or if the degree of interdependency among variables is modified, or if the historical period used in fitting any equation is changed, the results would be different. In addition, if variables other than those mentioned above (such as labor force participation rates, retirement rates, marriage rates, and divorce rates) were included in the stochastic modeling, the results would differ. Finally, additional variability would be expected to result from incorporating statistical approaches that would allow for potential structural shifts in the long-range central tendencies (i.e., parameter uncertainty). In conclusion, the current OSM's projected variation is likely to be narrower than the true range of uncertainty for the future.

The remaining chapters of this Actuarial Study provide detailed information from the OSM. Chapter II presents the equations used to model random variation in the assumptions. Chapter III explains the overall structure of the OSM and its modules. Chapter IV presents projection results, including the projected probability distributions for the stochastic assumptions and the summary actuarial measures used to assess the long-range financial status of the OASDI program. Chapter IV also presents a sensitivity analysis for each stochastic assumption.

Six appendices to this Actuarial Study are included. Appendix A contains background material on various financial estimates of the OASDI program. Appendices B and C contain introductions to time-series modeling and Monte Carlo simulation, respectively. Appendix D provides additional details of the time-series equations used in the OSM. Appendix E provides a glossary of terms used in this study, and appendix F is a bibliography of references cited in this study.

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