The Transition Model is a mathematical model which calculates retirement benefits, traces cash flows, and reports the yearly status of the system for selected values of the model parameters (rates of return on stock funds, percent of benefits "bought down", etc.) The model is a simplified version of the actual Social Security system, so it differs from the actual system in many details. One of these differences is that the basic unit in the model is a year-group of retirees rather than an individual, as it is in the actual Social Security system. All the workers who retire during a particular year constitute a basic unit and the retirement benefits for that year-group is the sum of the benefits for all retirees in that group. (This is similar to the designation of groups of college students as freshmen or seniors.) It is presumed that the benefits would be distributed to individuals in the group according to their own covered earnings records. For example, all the workers who retire in 2004 receive an aggregate first-year benefit of $30 billion which would be divided among the individual retirees. Similarly, workers are grouped according to their years in the work force, and their OASI contributions are aggregated to represent the total contributions for the entire group.

The model also matches the actual Social Security system in a number of important ways. First, it is based on the Intermediate Cost Assumptions from the 2002 Trustees Report shown in Table 10, which provide basic input to the model including: Income, Outgo (the model treats Outgo as promised benefits), interest rates on the Trust Fund, and CPI adjustments. And, most important, the model produces programmed benefits equal to or greater than the promised benefits for transition retirees (those retirees who retire during the transition) and those already retired.

The model divides Social Security covered workers and retirees into three sets: those retirees who retired before the transition begins in 2004; those workers in the work force in 2003, the first of which will retire in 2004 (referred to as the transition retirees); and those new workers who begin to enter the workforce in 2004. Those retirees who had retired before 2004 are paid full promised benefits over their twenty years of retirement. Transition Retirees begin to receive 50% (a parameter) of their benefits via a variable annuity when the first-year group retires in 2004. Their variable annuity benefits will be determined by the performance of the stock fund. The variable annuity benefits will be supplemented by Social Security benefits to bring their total benefits up to the promised level. Also, in 2004, the other thirty-nine year-groups of Transition Retirees will begin making annual investments equal to 25% of their OASI contributions in the Social Security Stock Fund. The new workers who begin entering the workforce in 2004 will be covered by the new Investment/Insurance Social Security system. They will invest 25% of their OASI contributions in the Social Security Stock Fund and their accounts in the Bond/Insurance fund will be credited with 35% (25% investment in the bond fund and 10% income level insurance premium) of their OASI contributions. When they begin to retire some 40 years later, their benefits will be determined by their investments in the stock and bond funds.

The transition begins in 2004 with all workers making investments equal to 25% of their OASI contributions in the stock fund. Also, beginning in 2004, all Transition Retirees receive an annuity equal to at least 50% of their first-year benefits in the form of a twenty-year variable annuity as a part of their retirement benefits. These annuities are funded by the accumulated funds in their individual stock fund accounts supplemented by funds from the Social Security Trust Fund. Any excess funds from the surplus and the tax cut are deposited in the Trust Fund.

In order to keep the model manageable, it is designed with a number of simplifying design characteristics. Some of the more important of these are:

1. The basic units in the model are groups of retirees and workers who will retire in the same year.

2. The investment period (working years) is 40 years, and the retirement period is twenty years.

3. All dollar figures are in the same units as those used in the 2002 Trustees' Report, Table VI.E9, current billions of dollars, unadjusted for inflation.

4. The model deals with aggregate benefits for each year group. It is presumed that the benefits will be distributed to retirees on the basis of their promised benefits or contributions and to survivors on the basis of their entitlements.

5. The total contributions to OASI in any one year are made up of equal contributions from each year-group. This permits the model to calculate the contribution from any year group as 1/40th of the total amount contributed.

The Transition Model is described by Tables 7, 8, 9, and 17. Table 17 shows the basic data from the Social Security Trustees Report, Ref 2, upon which the model is based. Table 7 shows the retirement benefits paid to the transition Retirees, i.e., those workers who were in the covered workforce at the time the transition to the new system is initiated and who will retire during the first forty years of the transition. Table 8 shows the sources of funds for the annuities and stock fund accounts for all workers during the transition and the Year End Balances in the Social Security Trust Fund. It also shows the total promised benefits and the expected benefits produced by the model for comparison. Table 9 shows the year-by-year status of the new Investment/Insurance Social Security system. All workers who enter the covered workforce after the transition has begun will be covered by the new system. The operation of the model is best described by a column-by-column explanation of how the numbers in Tables 7, 8, and 9 were calculated.

Column K: This column shows the estimated revenues (income) for the OASI fund. It is calculated as 85.5% (10.6/12.4) of the OASDI projections from Column A, Table 17.

Column L: This column shows the estimated benefits promised to future retirees. It is calculated as 85.5% of the OASDI projections from Column E.

Column M: This Column shows the portion of the benefits shown in Column L which is paid to those already retired when the transition began. It is simply the amount shown in Column L less the portion of the benefits assumed to be paid to transition retirees. It is calculated by subtracting Column N from Column L.

Column N: This column shows the portion of the benefits shown in Column L assumed to be promised to transition retirees. It is based on the first year of retirement benefits shown in Column O. In 2004, it is the amount paid as first-year benefits to the transition retires who retire in the first year of transition, $30. In 2005, it is the sum of the benefits paid in the second year of retirement, ($31 increased by the cost of living adjustment shown in Column J) and the first year benefits paid to those retired in 2005. This is repeated for twenty years when the 2004 retirees are assumed to reach their life expectancy, and their benefits are no longer counted. In subsequent years, one group of workers retires and one group of retirees is dropped from the retirement rolls. When the last group of Transition Retirees retires in 2043, a new group is no longer added to the entries in Column N which drops to zero when the last transition retirees reach their life expectancy in 2063. (The calculations for this column are made in a diagonal matrix in which twenty-year benefits are calculated for each group and added to determine annual benefits to all retirees in each year.)

Column O: This column shows the first-year benefits assumed to be promised to transition retirees year by year. The benefits are calculated as 7% of the total promised benefits shown in Column L. These percentages were chosen to assure that all programmed benefits equal or exceed promised benefits shown in Column L.

Column P: This column shows the minimum annuity required to replace at the selected replacement rate, 50% in this case, of the benefits promised in Column O. The replacement rate is a parameter of the model and can be varied to test the effects of different replacement rates. Column P is simply 50% of Column O.

Column Q: This column shows the actual annuity paid. Since the annuity is based on the accumulated value of the workers' investments in the stock fund, augmented by funds from the Social Security Trust Fund, it can exceed the minimum required annuity when the stock fund accumulation exceeds that which is necessary to pay the minimum. This occurs in year 2038 where the actual annuity, shown in blue, exceeds the minimum required annuity. From this point on, Stock Fund annuities are based entirely on the accumulated value of the investments just as in the new Investment/Insurance system.

Column R: This column shows the first year benefits which will be paid to the transition retirees from Social Security funds. It is the difference between the programmed benefits shown in Column O and the actual stock fund annuity shown in Column Q. annually by the cost-of-living factor shown in Column J.

Column S: This column shows the total first year benefits for the group of transition retirees retiring this year. It is the sum of the annuity benefits shown in Column Q and the benefits paid from Social Security funds in Column R.

Column T: This column shows the total annual expected benefits from stock fund annuities to all transition retirees in each year if the yearly rate of return were equal to the assumed annual rate of return. The first row, $15, is the amount expected to be paid to the first group of transition retirees in 2004. The second row shows the amount paid to the 2005 transition retirees in their first year, also $15, plus the amount paid to the 2004 retirees in 2005, first-year benefits increased by the assumed stock fund interest rate. (As with Column N, the calculations for this column are made in a diagonal matrix in which 20-year benefits are calculated for each group and added to determine annual benefits to all transition retirees.)

Column U: This column shows the total benefits from Social Security funds paid all transition retirees in any one year. It is the difference between Column N, programmed benefits for all transition retirees, and Column T, benefits paid from the Social Security stock fund.

Column V: This column shows the total expected benefits paid to all Transition Retirees in any one year. It is simply the sum of Columns T and U.

Table 8 -- Funding of Annuities and Stock Fund Accounts

Column AA: This column is a copy of Column K, Table 7. It is the OASI projected income.

Column AB: This column shows the total annual benefits paid from Social Security funds to all those who were already retired when the transition began plus the benefits paid to transition retirees and, after 2043, the benefits paid to retirees under the new system. It is the sum of Columns M and U, Table 7 and Column BA, Table 9.

Column AC: This column shows the Social Security surplus available to fund the various accounts. It is the difference between the total OASI income, Column AA, and total benefits paid from Social Security funds, Column AB, for each year.

Column AD: This column shows the cost of the minimum annuity required to replace part of the benefits to be paid to transition retirees each year. It is the cost of the annuity which would produce the income specified in Column P, Table 7, for twenty years at an interest rate of 6.5%. Since the annuity must be purchased the year before retirement begins, the annuity for the transition retirees retiring in 2004 must be purchased in year 2003 and is shown in the parameter line of Column AD. It is funded from the Trust Fund. Subsequent entries in this column are the funds required for those retiring in the following year. (The 6.5% interest rate is a parameter of the model.)

Column AE: This column shows the amount invested in the stock fund this year for each of the forty working groups of transition retirees. It is simply 1/40th of 25% of OASI income, Column AA. This calculation is based on the assumption that each of the forty groups of workers contribute equal amounts to OASI.

Column AF: This column shows the cumulative value of the stock fund in the last year of work for workers who will retire the next year. Transition workers who will retire in 2005 will have invested in the Stock Fund only one year, 2004. Hence, the value of their stock fund is shown as $3 (the rounded value of $2.84), the amount invested in 2004. Those retiring in 2006 will have invested two years and the cumulative value of their investment will be $7. As the value of the investments in the bond fund grow, the smaller the requirement for outside funding for the annuities. By the year 2039, no outside funding is required, as shown in Column AG, where the funding for annuities from the Social Security Trust Fund drops to zero.

Column AG: This column shows the amount of funding for annuities coming from the Trust Fund. It is the difference between Column AD, cost of the minimum annuity, and Column AF, value of the stock fund for those retiring next year.

Column AH: This column shows the annual investment in stock fund accounts made by all workers, both those who will retire as transition retirees and new workers who will retire under the new Investment/Insurance Social Security system. It is simply 25% of the total OASI income shown in Column AA.

Column AI: This column shows the annual amounts of the supplement required to keep the Trust Fund positive. The supplement is determined by the parameter shown in the heading of the column, in this case, 6.5% of OASI. The sum of the first ten years cost of the supplement are shown in the heading to the column.

Column AJ: This column shows the short falls which would occur if the transition were to be made without the supplement. They are calculated by the model as being the outside funds needed each year to complete the transition and still maintain a minimum balance in the Trust Fund of $100 billion. The NPV of the short falls and the NPV of the supplement are shown in the heading of the column.

Column AK: This column shows the OASI Trust Fund year-end balance. It is calculated by adding to last years balance the interest earned on the previous years balance (based on the interest rates in Column D of Table 17), the Social Security Surplus, Column AC, and the proceeds from the tax cut, Column AJ, and deducting the funds used to purchase annuities, Column AG, and the funds invested in the stock accounts, Column AH.

Column AL: This column is a copy of Column L of Table 7, Promised Benefits. It is shown here for comparison with Column AM.

Column AM: This column shows the total expected benefits paid to all beneficiaries through 2087. It is the sum Columns M and V in Table 7 and column BB in Table 9.

Table 9 -- Investment/Insurance Social Security System: This table shows the development of the new system which will cover all new workers entering the work force after 2000. Entries shown in Blue indicate that for these particular columns are as they would be in the new system. For these columns the transition is completed.

Column AP: This column shows the percent of total contributions to OASI made by new workers, 1/40th the first year, 2/40ths the second, etc. It is used to make the calculations in Column AS and AX.

Column AQ: This column is a copy of Column K, Table 7. After 2063 the numbers are shown in blue to indicate that all retirees under the old system have been completely phased out.

Column AR: This column shows the annual investment of each year-group in the stock fund. It is 1/40th of 25% of Column AQ. It is used to calculate first-year stock fund benefits in Column AU.

Column AS: This column shows the annual investments in the stock fund made by all new workers. In 2004, the only new workers are those who began working in 2004. They contribute 1/40th, or 2.5% of the OASI total income. Twenty-five percent of this, $3 (rounded), is invested in their stock fund accounts. In 2005, a second group of workers enter the workforce, so these two groups of workers contribute 2/40ths of the total OASI income and 25% of this, $7, is invested in the stock fund. This column is used to calculate the values in Column AT. After the last transition retiree retires, this column is simply 25% of OASI income.

Column AT: This column shows the cumulative value of the stock fund as it grows over the years. Entries in this column are calculated by adding the contributions each year to the previous year's balance plus earnings at the selected stock fund rate of return. After 2043, when new workers begin to retire, the cumulative value of the stock fund is reduced by the annual retirement payments made on the variable annuities shown in Column AV.

Column AU: This column shows the first-year benefits paid from the stock fund to each year-group as it retires. It is calculated by determining the cumulative value of the stock fund account for a particular group in their last year of work and calculating the-twenty year annuity this cumulative value would purchase at 5%.

Column AV: This column shows the total annual benefits paid to all retirees from the stock fund. (The calculations for this column are made in a diagonal matrix where twenty-year benefits are determined for each year-group of retirees and added year by year to determine annual benefits paid to all retirees.)

Column AW: This column shows the annual investment credited to the accounts in the bond/insurance fund for each year-group of new workers. It is 1/40th of 35% of Column AQ. The 35% is the 25% investment in the bond fund and the 10% income level insurance premium. Entries in this column are used to calculate first-year benefits in Column AZ.

Column AX: This column shows the annual investments in the bond/insurance fund by all new workers. In 2004, the only new workers are those who began working in 2004. They contribute 1/40th, or 2.5%, of the OASI total income for that year. Thirty-five percent of this contribution, $5, is credited to their accounts in the bond/insurance fund. In 2005, a second group of workers enters the workforce. These two groups of workers contribute 2/40ths, or 5%, of the total OASI income. Thirty-five percent of this share is shown in the 2005 row of Column AX, $10, as the amount invested by the two groups in 2005 in the bond/insurance fund. It is calculated as .35 x Column AP x Column AQ. After the last transition retiree leaves the work force, this column becomes 35% of OASI income.

Column AY: This column shows the cumulative value of the bond/insurance fund as it would grow over the years if investments were actually made. No funds are involved. This column actually formally reflects the government's liability for future bond fund annuities. Calculations are the same for the bond/insurance fund as those made in Column AT for the stock fund.

Column AZ: This column shows the first-year benefits paid from the bond/insurance fund to workers retiring under the new system. It is calculated by determining the cumulative value of the bond/insurance fund account at 5% for a particular group in their last year of work and calculating the annuity this cumulative value would buy at 2% for twenty years for a graded annuity.

Column BA: This column shows the annual benefits paid from the bond/insurance fund to all retirees. The actual calculations for this column are made in a diagonal matrix in which twenty-year benefits are calculated for each group of retirees and added to determine total benefits paid each year.

Column BB: This column shows the total annual expected benefits paid by the new program. Entries are the sums of Columns AV and BA.

Links: Home     Appendix A     Appendix B     Appendix C     Appendix D     Appendix E     Appendix F    

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