Comparing Proposals for Social Security Reform

Studies | Social Security

No. 227
Wednesday, September 01, 1999
by Liqun Liu and Andrew J. Rettenmaier


Appendix

Table B-I

APPENDIX A

The Simulation Model

The simulation model developed at the Private Enterprise Research Center at Texas A&M University under a research grant by the National Center for Policy Analysis is a substantial adaptation of the one previously developed to analyze prefunding the Medicare program (Rettenmaier and Saving, 1999). The building blocks for this type of simulation model are population and earnings forecasts. Applying expected future tax rates to the aggregate earnings forecast, which combines the demographic and earnings forecasts, identifies the system's revenue stream. When considering privatization of the system, the contribution rate as a percent of our forecasted earnings also identifies the funds flowing into individual accounts. The age-by-sex population distribution in future years is the Census Bureau's intermediate projections for 1995 to 2050. The data are extended to 2075 by continuing the trends that exist in the later years of the forecast. To estimate future earnings we calculate growth rates within detailed age by education categories for both men and women. The historical data used to calculate the various growth rates are the 1964 to 1998 March Demographic Supplements to the Current Population Survey (CPS). Because the survey questions refer to the previous year, the data run from 1963 to 1997. The growth rates within age by education by sex categories are applied to the most recent data to produce the earnings forecast.

Once earnings are forecast, the system's future benefit payments can be estimated. A worker's Social Security benefit is calculated based on a formula that translates past earnings into a monthly payment. In light of the benefit formula, tracking and forecasting taxable earnings within detailed categories is important for several reasons. First, unlike the Medicare tax which is applied to all labor earnings, the Social Security tax is limited to earnings up to a maximum. The taxable maximum is scheduled to grow at the same rate as average earnings. However, over the last 25 years the distribution of earnings has widened, resulting in an increasing proportion of workers whose earnings will exceed the taxable maximum. Also, the benefit formula is redistributive in nature in that the replacement rate for workers with low lifetime earnings is higher than the replacement rate for workers who had high lifetime earnings. Because Sens. Gramm and Domenici's proposal guarantees that retirees will receive at least their expected Social Security payment, plus a bonus based on the size of the private account, the distribution of workers across lifetime income classes matters when estimating the proportion of benefit payments that remain the government's responsibility in future years.

Table B-II

Building the simulation model proceeds through the following steps. Earnings are forecast for each age by sex and by education category. Thus for the years from 1999 to 2075, we have an estimate of real taxable annual earnings in each category. Next, for each of the categories of workers born in a given year, we calculate the expected Social Security benefit. Given that the earnings histories go back to 1963, and that Social Security benefits are based on workers' highest 35 years of earnings, it is possible to estimate benefits at retirement for all retirees born in 1933 and later. Assuming all individuals retire at the normal retirement age, currently 65 with scheduled increases to 67 over the next 28 years, we calculate the expected Social Security benefit for all categories of individuals born between 1933 and 2008 - those retiring in 1998 to 2075. The benefits are calculated using projected values of the parameters in the benefit formula. The projected values for average earnings, maximum earnings, the inflation rate and the bend points in the formula used to convert average monthly earnings into workers' expected benefits are all based on the intermediate assumptions in the 1998 Trustees Report. For these new beneficiaries we adjust spousal benefits to account for both the survivor benefit and the dependency benefit. We further adjust aggregate benefit payments for non-spouse dependents and survivors in all future years.1 Individuals born in 1932 and earlier are given the average current benefits by age and sex. We assume these will grow at the projected growth in the cost of living. Summing across all new and existing retirees in each future year we have an estimate of the system's annual expenditures.

The Old Age and Survivors Insurance (OASI) program is the focus of our analysis. To determine how closely our estimates match the Social Security Administration's, we identify the year in which expenditures will exceed revenues and the year in which the trust fund is exhausted before we proceed with the simulation of the privatization proposal. In aggregate, our model produces simulation results quite similar to the Social Security Administration's estimates. Using our estimates of future taxable earnings and benefit payments, we identify 2014 as the first year in which OASI expenditures exceed tax revenues and 2034 the year the trust fund will be exhausted. These dates were 2015 and 2035, respectively, based on the intermediate estimates in the 1998 Trustees Report.

  1. Total non-spouse survivor and dependent benefits have been declining over time and accounted for less than 5 percent of total benefit payments under the OASI program in 1995. These benefits as a proportion of the total are expected to further decline in the future. Thus the adjustment we make to the aggregate benefit payment declines in future years.

APPENDIX B

The Simulation Tables

All of the benefits and revenues in the simulations are measured relative to taxable payroll. The first column indicates the percent of taxable payroll required to pay Social Security benefits if they were funded with contemporaneous taxes. The next column shows benefit payments coming from PRA annuities. The third column shows net benefits that continue to be paid by Social Security under the proposal being analyzed. (The 20 percent bonus in the Gramm-Domenici plan is reflected in the net benefits column, so it is more than the status quo benefits minus the PRA benefits. )

Table B-III

The next four columns identify the funding sources. Corporate taxes, presented as a percent of taxable payroll, rise continuously as the additions to the capital stock increase. The next column shows the payroll tax less the contribution rate, and the column after that shows the taxes collected on Social Security benefits as a percent of taxable payroll. The combination of the three revenue sources is presented in the column under "Total Funding." The difference between the net benefits and total funding produces the transition costs as a percent of taxable payroll. These transition costs now explicitly take into account the corporate tax revenues. The transition costs identified in Table I and the tables that follow are those costs not covered by payroll taxes and corporate taxes. These costs are met from the on-budget surpluses. The final column shows the percentage of average Social Security benefits that can be replaced by the PRA annuities for new retirees in each of the years. The smaller table below each simulation table shows the effects of using the surplus to reduce the payroll tax. Here the taxation on benefits is reduced or eliminated first, with the remainder used for payroll tax relief.

The calculation of aggregate PRA benefits as a percent of taxable earnings should be interpreted with care. Table B-I showed that a contribution rate of 4.2 percent would produce annuities for some groups that are in excess of their expected Social Security benefits and annuities for other groups that fall short of their expected Social Security benefits. Thus summing across all groups of workers would overstate the degree to which the annuities would replace aggregate Social Security benefits. For presentation in this table the aggregate PRA benefits are limited to PRA annuities up to an amount equal to Social Security benefits plus any bonus. If worker annuities exceed the amount they would expect from Social Security, they keep the full amount of excess funds. Only for the accounting in the table do we cap the PRA benefits within a group at the Social Security benefits plus the bonus.

APPENDIX C

Indexing Life Expectancy

One way to do the indexation proposed in the bipartisan proposal is to fix the number of expected retirement years at the level that exists for the age group retiring in 2011 at age 67. Men born in 1944 who reach age 67 in 2011 have a conditional life expectancy of 15.367 years and women have a conditional life expectancy of 18.962 years. Starting with the life expectancies for the age group retiring in 2011, it is then possible to find the youngest birth cohort for which the conditional life expectancy at age 68 is at least 15.367 for men and 18.962 for women. The same can be done for ages 69, 70 and 71. The life tables used in this study are from the Census Bureau and the last year in the data is 2050. From the Census data we calculate life tables for specific birth cohorts. The highest indexed retirement age based on maintaining a fixed number of retirement years is 71. The results are presented in Table C-I.

Table B-IV

As the table indicates, the indexation based on women's longevity gains lags behind men's. A conservative indexation would use the women's timing. The effect of this choice would slightly extend the phase-in period relative to an indexing based on a gender-neutral index. A possible criticism of indexing the retirement age based on a fixed number of retirement years is that it would produce a falling average retirement period relative to potential work years. For example, assuming that an individual born in 1944 enters the labor force at age 22 and works until retirement at age 67, then for the average male the retirement period is equal to 34.15 percent of the working period (15.367 retirement years / 45 work years). By 2045 the ratio drops to 31.36 percent (15.367 retirement years / (71-22) work years).

An alternative is to fix the ratio of retirement years to work years at the ratio that exists for the individuals who turn 67 in 2011. Such indexation results in a smaller reduction in scheduled benefits than does setting the retirement period at a constant number of years. Indexing the retirement age so that the ratio of retirement to work years remains constant produces the results in Table C-II.

As before, indexation based on women's longevity gains lags behind men's. The first year in which the normal retirement age is fully increased to 66 is assumed to be 2006. Adopting the female experience results in a normal retirement age, indexed so the ratio of the retirement to work period is held constant, of 67 in 2011, 68 in 2028, 69 in 2040 and 70 in 2049. We adopt this latter indexation method in our simulation.

Table B-V

Table B-VI

Table C-I


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