Cohort-Specific Measures of Lifetime Social Security Taxes and Benefits

Introduction

This paper develops estimates of lifetime money's worth and redistributional outcomes under the Old Age and Survivors Insurance (OASI) program for all past, present, and future birth cohorts affected by the program through the cohort born in 2100. The estimates presented in this study incorporate a comprehensive accounting of all OASI taxes and benefits and blend historical administrative data with tax and benefit projections. Projected taxes and benefits are consistent with the detailed intermediate economic and demographic assumptions underlying the 2002 Trustees Report and extended beyond the Trustees Report projection period using an approach consistent with the Trustees Report assumptions. The qualitative conclusions reached in this analysis should be unaffected by the relatively minor changes in key economic and demographic assumptions that characterize subsequent Trustees Reports.

Because the present OASI program is projected to be in long-run deficit, estimates are also developed in this paper under two stylized alternative policies that bring the program into long-run financial balance over the Trustees Report projection period and beyond. The first alternative policy achieves long-run financial balance through a series of proportional benefit award adjustments and the second alternative policy through a series of payroll tax rate adjustments.

Lifetime outcomes for each birth cohort are examined both from the perspective of cohort members, indicating the extent to which each cohort has received or can expect to receive their "money's worth" from the program, and from the perspective of the program, indicating the extent of redistribution across the cohorts. These estimates update similar estimates presented in Leimer (1994) and, under certain assumptions, can be used to calculate the "legacy debt" associated with program transfers to early cohorts.

This paper

• describes the methods used in this analysis to develop program and cohort outcomes under the alternative policies,
• describes and analyzes these program and cohort outcomes,
• compares these outcomes with analogous outcomes in the most comparable previous analyses and identifies key differences in assumptions and approaches underlying the different outcomes, and
• presents some concluding observations.

Method

As indicated, this analysis combines Social Security administrative data for historical years with projections of OASI outcomes under alternative tax and benefit policies conditional on the intermediate economic and demographic assumptions of the 2002 Trustees Report.¹ The historical and projected data include OASI benefits of all types, OASI payroll taxes of all types (including those on employees, employers, and the self-employed), and OASI benefit income tax liabilities.² These variables are identified historically and simulated prospectively through the year 2220 both as annual program aggregates and as program participant disaggregates by single year of age (from age 0 through 120, the maximum age assumed for any cohort member). This level of detail permits comprehensive estimates of the balance between lifetime taxes and benefits under the program for all past, present, and future birth cohorts affected by the program through the cohort born in 2100.³ The rest of this section discusses specifics of the method adopted in this analysis.

Allocation of Secondary Benefits

Under the OASI program, monthly benefit payments to dependents of a retired worker or survivors of a deceased worker are referred to as "secondary" benefits.⁴ In this analysis, secondary benefits are allocated to the birth cohort of the secondary beneficiary. This allocation has been referred to as "individual-specific" and follows the general approach used in the most comparable previous studies.⁵ An alternative allocation used in many previous studies has been referred to as the "worker-account" approach and allocates secondary benefits to the birth cohort of the worker on whose account the benefits were earned. These two secondary benefit allocation approaches provide different perspectives on the redistributional and money's worth effects of the program, with each having advantages and disadvantages depending on the specific questions being addressed.⁶ Because the benefit and tax data used in the present analysis are not linked on an individual-record basis, however, they permit the use of the individual-specific approach but not the worker-account approach.

Payroll Tax Incidence

The allocation of payroll taxes in this analysis assumes full backward shifting of the employer portion of the payroll tax to workers in the form of lower wages. Although there is disagreement among economists about the incidence of the payroll tax, full backward shifting is the standard incidence assumption in analyses of the redistributional and money's worth effects of the Social Security program.⁷

Historical Taxes and Benefits

The approach used in this analysis to identify historical OASI benefits of all types (all lump-sum and monthly benefit payments), OASI payroll taxes of all types, and OASI benefit income tax liabilities by year and age from Social Security administrative data is identical to the approach used and explained in detail in Leimer (2004). The only difference is that two additional years of historical data were available for the present analysis. A brief summary of the approach is provided here, but interested readers can consult Leimer (2004) for additional detail.

The aggregate OASI payroll taxes paid by workers of each age in each year from 1937 through 2001 were derived from a combination of two Continuous Work History Sample (CWHS) administrative data files.⁸ These files contain information on annual Social Security taxable earnings for a random sample of all Social Security numbers and were used to identify OASI taxable wages and self-employment income for each valid record in each year. The associated OASI payroll tax liabilities for each of these observations were then computed using the OASI payroll tax rates and rules for that year, adjusting for complications such as multiple employers and the mix between taxable wages and self-employment income. Aggregate OASI payroll tax liabilities for workers of each age in each year were then calculated from the sample and adjusted proportionally across all ages to sum to the actual aggregate OASI payroll tax liability for that year.⁹ In effect, the sample data were used to identify the proportional distribution of aggregate OASI payroll tax liability by age in each year.

A similar approach was used to identify historical OASI benefits by age, except that published summary tables drawn from administrative records on year-end OASI monthly benefit payments by beneficiary type and age ¹⁰ were used in place of electronic beneficiary sample data files. The electronic beneficiary sample data files that are available now do not contain complete historical benefit records, necessitating the use of the published summary tables. Accordingly, the proportional distribution by age of aggregate year-end OASI benefit payments from each summary benefit table was used to identify the age-allocation of aggregate benefits paid from the OASI trust fund during the corresponding year.¹¹

Projected Taxes and Benefits

In this analysis, projected future OASI benefits of all types, OASI payroll taxes of all types, and OASI benefit income tax liabilities by year and age are based on and constrained by the 2002 Trustees Report detailed projections of economic, demographic, and program variables under the intermediate assumption set. These economic, demographic, and program variable projections are extended beyond the Trustees Report projection period, which ends in 2080, by assuming a continuation of patterns of change found in those projections toward the end of the Trustees Report projection period. OASI benefits and taxes by year and age are then projected through 2220 conditional on these extended economic, demographic, and program variable projections. Appendix D provides additional detail on the method used.

As indicated, this analysis simulates program outcomes under present program provisions and under two stylized alternative policies that bring the program into long-run financial balance. When projecting the effects of alternative policies, of course, aspects of the Trustees Report projections that are specific to present program provisions are modified as appropriate.

The alternative policies considered in this analysis involve across-the-board proportional adjustments in either payroll tax rates or benefit awards. Many other specific tax, benefit, or benefit award adjustment policies could have been used, of course, to bring the OASI program into financial balance over the Trustees Report projection period and beyond. Payroll tax rate adjustments and proportional adjustments in benefit awards were adopted in this analysis because these policies achieve solvency while maintaining key elements of tax and benefit determination under the present program.¹²

The main criteria used to select the particular tax rate and benefit award adjustment schedules used in this analysis were (1) early implementation, (2) precise attainment of the financial balance targets by the end of the Trustees Report projection period and in each subsequent year, and (3) annual tax rate or benefit award adjustment schedules, depending on the policy, that were as smooth as possible consistent with the first two criteria.¹³ The particular tax rate and benefit award adjustment schedules identified by this process and used in this analysis, then, are reasonable, but obviously not unique, solutions. While not unique, these schedules serve to illustrate the general nature of the intercohort redistributional and money's worth effects of program changes required to achieve financial balance consistent with the Trustees Report economic and demographic assumptions. Many of the qualitative insights produced by such an exercise, of course, are not dependent on the specific schedule of tax or benefit adjustments.

Income Taxation of Benefits

This analysis incorporates estimates by year and age of a portion of the historical and projected income taxation of OASI benefits that began in 1984. A large portion of the proceeds from the income taxation of OASI benefits is returned to the OASI trust fund as a transfer from general revenues. Over part of the historical and all of the projection period, this portion of benefit income tax liabilities represents a significant source of the income used to finance OASI benefits.¹⁴ As such, the "financial balance" principle of comparing benefits and taxes in the context of a self-financed system requires that redistributional or money's worth estimates even gross of income taxation in general include an adjustment for the portion of benefit income tax revenues returned to the trust fund.¹⁵ In the present analysis, this is accomplished by defining the total OASI tax liability for each birth cohort as the sum of their OASI payroll taxes and that portion of their OASI benefit income tax liability that is ultimately returned to the OASI trust fund.¹⁶

Accurately identifying the incidence of benefit income taxation across birth cohorts in each year would require much more information than was available in the source data used for this analysis. Consequently, the effective rate of benefit income taxation (benefit income tax liability as a proportion of benefits) was assumed to be identical across birth cohorts in any given year.¹⁷ This assumption introduces potential bias into the analysis. The actual effective benefit income tax rate will tend to be higher, ceteris paribus, for groups with higher earnings and taxable income. This might suggest that younger retirement age groups, for example, may generally experience higher effective benefit income tax rates than older retirement age groups in any given year. Such effects will tend to balance out to some extent over the lifetimes of most birth cohorts. Differences across beneficiary income groups in the effective benefit income tax rate will also tend to diminish over time because the income thresholds beyond which benefit income taxation applies are fixed in nominal terms.

Interest Rate Series

The money's worth and redistributional present value estimates ¹⁸ in this analysis are calculated for four alternative interest rate series. These four series correspond to (1) a nominal interest rate equal to the rate of inflation (a zero real interest rate); (2) the rate of return earned on OASI trust fund assets; (3) the total rate of return to an index of large company stocks; and (4) an interest rate equal to the growth rate in aggregate OASI taxable earnings.¹⁹ The appropriate interest rate series to use in analyzing Social Security program outcomes depends on the particular questions being addressed and on how the analysis takes into account risk differentials among retirement asset types. The particular questions being addressed are defined by such issues as the nature of the alternative to which the Social Security program is explicitly or implicitly compared and the perspective of the evaluation, whether from a program, program participant, or societal standpoint.²⁰

Using the interest rates at which the OASI program was or is projected to be able to actually transform funds over time through trust fund saving and dissaving, for example, can be interpreted as identifying redistribution from the perspective of the program. The present value of lifetime benefits less taxes for each birth cohort, calculated using the interest rates earned by the trust fund, is a measure of the cost to the fund of those net transfers. That is, this present value reflects the amount by which the trust fund would have been different as of a selected valuation date had those specific net transfers not occurred.²¹

Alternatively, the interest rate series used in this analysis can be interpreted from a money's worth perspective. A complicating factor from this perspective is that the "investment" and "return" stream corresponding to lifetime Social Security taxes and benefits does not have a direct market equivalent, since the program is financed primarily on a pay-as-you-go rather than a funded basis. An individual or collective evaluation of that stream, then, requires the identification of an interest rate series that most closely reflects the perceived characteristics, including relative risk, of the Social Security "investment." As such, the appropriate interest rate series depends in large part on the perceptions of the evaluator(s).

Standard portfolio analysis offers a clarifying perspective on this issue, with the Social Security "investment" viewed as another available portfolio asset.²² The interest rate series associated with a fungible market asset effectively equates the present values of the investment and return streams expected by the market for that asset. The analogous interest rate for a mature, pure pay-as-you-go social insurance program is the rate of growth in the tax base used to finance the program. That is, the rate of growth in the underlying tax base represents the major component of the rate of return to program participants generated on average in a mature, sustainable pay-as-you-go social insurance retirement program.²³ Society can collectively gain access to this pay-as-you-go retirement "asset" with historically attractive risk and return characteristics ²⁴ by establishing a mandatory public retirement program financed on a pay-as-you-go basis. Assuming that the size of a pay-as-you-go program is consistent with the share of the program in the optimal retirement portfolio, ²⁵ then, the growth rate in the program's tax base represents a logical choice for the interest rate series used to evaluate lifetime taxes and benefits under the program. Consequently, the growth rate in aggregate OASI taxable earnings is included as one of the interest rate series in this analysis.

Various other characteristics of the program, however, can require adjustments to the appropriate interest rate series for evaluating program outcomes. Some features of the Social Security program can reduce overall portfolio risk for program participants; other features of the program are "market-improving" in the sense of addressing various deficiencies of private insurance and annuity markets. Some examples include the automatic inflation adjustment of benefits after entitlement without default risk, the effective provision of actuarially fair annuities without the inefficiencies of adverse selection, insurance against various types of human capital and earnings risk, and advantageous retirement portfolio intercorrelations.²⁶ These potential market-improving and portfolio-enhancing features of the program suggest the use of an interest rate lower than the tax base growth rate to evaluate program outcomes, since such features lower the overall risk of the Social Security "investment" below that represented by the program's financing basis. Alternatively, some analysts argue on a theoretical basis that the program is subject to demographic, economic growth, and political risks that justify the use of a higher interest rate in money's worth analyses.²⁷ In short, different evaluators have different perceptions of the appropriate interest rate to use in analyzing lifetime outcomes under the Social Security program.²⁸

In this context, the zero real interest rate series can be interpreted as incorporating a downward adjustment from the OASI taxable earnings growth rate series to adjust at least in part for various portfolio-enhancing and market-improving characteristics of the Social Security program. Alternatively, the OASI trust fund interest rate series can be interpreted as a proxy for a government bond rate series ²⁹ that prospectively incorporates an increment to the OASI taxable earnings growth rate series that is slightly larger than the decrement represented by the zero real interest rate series.³⁰ Since a few studies have used even higher interest rates to evaluate the Social Security program, estimates using the large company stock series are also included in this analysis, providing a comparison with a private investment alternative that has exhibited both higher risk and higher return, on average, than a government bond series over the historical period.³¹

The various interest rate series and redistributional and money's worth measures included in this analysis, then, are intended to facilitate comparison with previous analyses and to increase the range of questions to which the results can be applied. Two fundamental implications of this analysis are that (1) the evaluation of program outcomes, whether from a program, participant, or societal perspective, depends critically on the interest rates used in the analysis and (2  in a stochastic world where retirement saving alternatives have different risk and return characteristics including crucial intercorrelations, the choice of an appropriate risk-adjusted interest rate to evaluate program outcomes is difficult and controversial.

Administrative Expenses

The redistributional and money's worth measures presented in this paper do not adjust for the costs of administering the program. Some of the taxes collected under the program are used to cover the expenses of administering the program, which necessarily creates an imbalance between taxes and benefits. Analogous and potentially higher expenses would be associated with private alternatives to the retirement saving, annuity, and survivors insurance features of the OASI program.³² Estimated negative values for lifetime benefits less lifetime taxes, then, do not by themselves suggest that the corresponding groups of program participants are net redistributional losers from a program perspective ³³ or fail to receive their money's worth under the program from a participant perspective.³⁴

Analysis

This section presents and analyses OASI program outcomes simulated under present law provisions and under the two stylized alternative policies that bring the program into long-run financial balance consistent with the underlying Trustees Report projections. Program outcomes that are simulated by applying the OASI benefit and tax provisions now scheduled under present law are denoted in the discussion as "present law" outcomes.³⁵ The two alternative policies adopted in this analysis to restore solvency consistent with the Trustees Report projections are referred to in the discussion as the "balanced budget" award and tax adjustment policies. The discussion first identifies the benefit award and tax rate adjustments adopted to achieve solvency ³⁶ and then examines the associated lifetime money's worth and redistributional outcomes for past, present, and future birth cohorts under the alternative policies.

Benefits and Taxes under the Policy Alternatives

Balanced Budget Award Adjustment Policy. The balanced budget award adjustment policy adopted in this analysis employs a series of annual proportional adjustments in benefit awards, beginning in 2015, that bring the OASI program into financial balance over the Trustees Report projection period through 2080 as well as in all subsequent years. These award adjustments effectively extend the drawdown of the OASI trust fund so that the trust fund/expenditure ratio gradually declines until equaling 1.0 in 2080. Beyond 2080, the benefit award adjustments are derived endogenously as those required to maintain an annual trust fund/expenditure ratio of 1.0 in each year. Financial balance is defined in this instance, then, as the attainment and maintenance of a trust fund equal to annual expenditures by 2080 and beyond.³⁷ This balanced budget award adjustment policy can be conceptualized as a series of annual proportional adjustments to all of the marginal "replacement rates" in the present law benefit formula, with the effect that initial benefit awards in a given year across all beneficiary types and ages experience the same proportional adjustment.³⁸

A wide variety of benefit adjustments, including the type of proportional award adjustments simulated in the present analysis, are available to meet specific cost objectives. The choice among these alternatives depends, of course, on the desired adequacy, equity, and efficiency goals of the program.³⁹ The particular award adjustment policy adopted for this analysis is not intended to convey any special merit relative to those goals and was identified primarily on the basis of the technical criteria described above.⁴⁰

The adjustment factor applied in each simulation year to present law OASI benefit awards under the balanced budget award policy is displayed in Chart 1. This chart illustrates rather dramatically the extent of the award adjustments required to maintain solvency at present tax rates under the extended Trustees Report assumptions. The award adjustment factor in Chart 1 represents aggregate benefit awards in each year under the balanced budget award policy as a proportion of the aggregate benefits that would have been awarded in that year under present law. Benefit awards under the balanced budget award policy equal those under present law through 2014, then decline to about 62 percent of present law benefit awards by 2080, and then generally decline further at a more gradual pace to about 48 percent of present law benefit awards by the end of the extended projection period in 2220. This continuing decline in benefit awards under the balanced budget award policy relative to present law is attributable to the projected continuing improvements in mortality under the Trustees Report and extended projections.⁴¹

The data displayed in Chart 1 reflect benefit award reductions relative to those scheduled under present law, not relative to benefit awards in preceding years. The average nominal benefit award to new retirees under the balanced budget award policy increases in every year despite the reductions relative to present law. The average real benefit award to new retirees does decline in some years under the balanced budget award adjustment policy during the period of steepest declines relative to present law toward the start of the policy.⁴² Benefits after entitlement are automatically adjusted for inflation in each subsequent year under the balanced budget award policy (and under the balanced budget tax policy), just as under present law.

Balanced Budget Tax Adjustment Policy. The combined employer and employee payroll tax rate under each of the three policies simulated in this analysis is displayed in Chart 2. The combined tax rate under the balanced budget award policy remains at 10.6 percent, the same rate scheduled under present law.

Under the balanced budget tax policy, the combined payroll tax rate increases linearly each year beginning in 2010 ⁴³ until reaching about 12.9 percent in 2049 and then increases annually at a faster linear rate until reaching about 16.3 percent in 2080. This tax rate schedule has the effect of extending the drawdown of the OASI trust fund so that the trust fund/expenditure ratio gradually declines until equaling 1.0 in 2080, analogous to the corresponding pattern under the balanced budget award policy.

Financial balance is defined for both of the balanced budget policies as the attainment and maintenance of a trust fund equal to annual expenditures by 2080 and in all subsequent years.⁴⁴ The tax rates displayed in Chart 2 beyond 2080 for the balanced budget tax policy, then, are derived endogenously as the tax rates required to maintain an annual trust fund/expenditure ratio of 1.0 in each of those years. As such, this policy illustrates the extent of the tax rate increases required to maintain solvency with present law benefit provisions under the extended Trustees Report assumptions.

Primarily because of the projected continuing improvements in mortality, the payroll tax rates required to maintain an annual trust fund equal to annual expenditures continue to increase over the full simulation period, reaching a combined rate of nearly 21.6 percent by 2220, the last simulation year. Continuing increases in contributions to maintain financial balance in response to continuing mortality improvements are equivalent to a continuing succession of small program expansions. As a consequence, such a policy is not sustainable over the very long-run. At some point, further increases in contributions would cause the program to grow beyond its optimal size. This general increasing contribution or benefit reduction consequence of continuing mortality improvements applies to any retirement program, regardless of its ownership or funding basis (whether publicly or privately owned, whether fully funded, partially funded, or funded on a pure pay-as-you-go basis).⁴⁵

Money's Worth and Redistributional Measures by Birth Cohort

The remaining charts and tables in this section present various money's worth and redistributional measures of lifetime outcomes by birth cohort under present law and under the two stylized balanced budget policies. Appendices A through C present corresponding estimates in table form by single-year birth cohort under each of the policies.

Real Internal Rate of Return. One measure of the relative balance between taxes and benefits for each birth cohort is the internal rate of return. The real internal rate of return ⁴⁶ for each annual birth cohort considered in this analysis is displayed in Chart 3 under the three alternative policies. One striking feature of Chart 3 is the steep decline in internal rates of return across the early birth cohorts, following the expected general pattern for a maturing pay-as-you-go social insurance program that grants generous benefits to early cohorts that have not contributed to the program over full working lives. The real internal rate falls from 18.37 percent for the collective cohort group born through 1900 to about 2.71 percent for the 1945 single-year birth cohort under each of the policies considered.⁴⁷ Lifetime outcomes for these early cohorts are largely unaffected by the prospective policy changes considered in this analysis, but the rates of return begin to diverge more noticeably across policies for cohorts born after about 1950.

Because award reductions affect earlier cohorts than tax increases when instituted at about the same time, the internal rates of return in Chart 3 are lower for earlier affected cohorts under the balanced budget award policy than under the balanced budget tax policy. For later cohorts, internal rates remain higher in Chart 3 under the balanced budget tax policy than the under the balanced budget award policy in large part because the balanced budget tax policy effectively incorporates a succession of small program expansions in response to declining mortality rates.⁴⁸ For the most distant cohorts, the projected internal rates of return in Chart 3 are about 1.34 percent under the balanced budget award policy and about 1.51 percent under the balanced budget tax policy.

Clearly, the earliest cohorts have gotten much more than their money's worth from the OASI program as indicated by their very high internal rates of return. Whether all present and future cohorts will continue to receive their money's worth from the program is a much more difficult question to answer because of disagreement over the appropriate rate of interest to use for comparison. If a risk-adjusted real interest rate less than about 1.35 percent is deemed appropriate, as suggested by some research,⁴⁹ then the estimates displayed in Chart 3 indicate that even the most distant birth cohorts are projected to receive their money's worth from the OASI program under either of the balanced budget policies considered. If instead a risk-adjusted real interest rate of 2 percent or above is considered appropriate,⁵⁰ then the estimates displayed in Chart 3 indicate that no cohort born after about 2015 is projected to receive their money's worth from the program under either of the balanced budget policies considered.

While internal rates of return under all three policies are included in Chart 3 for expositional convenience, it should be noted that it is inappropriate to compare money's worth and redistributional outcomes across policies that have different unfunded liabilities.⁵¹ In the context of the present analysis, policies with different unfunded liabilities likely also have different macroeconomic effects and related behavioral responses ⁵² that are inconsistent with the fixed economic and demographic assumption set upon which the analysis is based.⁵³ As such, analyses based on an essentially fixed set of economic and demographic assumptions are best suited to examining the redistributional effects of a given policy or of alternative policies with equal unfunded liabilities where it might reasonably be assumed that the policies are consistent with the fixed assumption set.⁵⁴ The present analysis consequently focuses on the intercohort money's worth and redistributional effects of a given policy conditional on the extended Trustees Report demographic and economic assumption set, although differences in estimated outcomes across the policies are explained in the context of this fixed assumption set.⁵⁵

In addition, outcomes under present law are not discussed for the remaining money's worth and redistributional measures considered in this analysis because the present program is projected to be out of long-run financial balance. For money's worth and redistributional measures to be meaningful, the analysis must include all of the funding sources that are required to finance the benefits included in the analysis, a requirement that the present program fails to satisfy without further assumptions about how the long-run deficit in the program will be resolved.⁵⁶

Lifetime Benefit/Tax Ratio. Another relative money's worth measure is the lifetime benefit/tax ratio, defined here as the ratio of the present values of lifetime benefits and taxes for each birth cohort as a whole using a particular interest rate series. A lifetime benefit/tax ratio of one, then, indicates that the estimated present values of lifetime benefits and taxes are equal for the cohort as a whole. Ratios greater (less) than one indicate that lifetime benefits are estimated to be greater (less) than lifetime taxes for that cohort.

The estimated OASI lifetime benefit/tax ratio across birth cohorts for each of the four interest rate series considered in this analysis under the two balanced budget policies are displayed in Charts 4 and 5. Both charts exhibit a relatively rapid decline in the lifetime benefit/tax ratio across the early cohorts, analogous to the decline in internal rates of return across those cohorts. Under each of the balanced budget policies, the lifetime benefit/tax ratio for the collective cohort group born through 1900 ranges from 12.04 under the OASI trust fund interest rate assumption to 3.21 under the large company stock total rate of return series. By the 1945 single-year birth cohort, these ratios are lower under all of the interest rate assumptions, ranging from 2.14 for the zero real interest rate series to 0.26 for the large company stock series. As with the real internal rate of return measure, the lifetime benefit/tax ratios begin to diverge more noticeably between the two balanced budget policies for cohorts born after about 1950, as projected benefits and taxes begin to play a more important role and historical outcomes a less important or nonexistent role. For the most distant cohort (born in 2100) simulated in this analysis, the lifetime benefit/tax ratio ranges from 1.53 for the zero real interest rate series to 0.21 for the large company stock series under the award adjustment policy (Chart 4) and ranges from 1.61 for the zero real interest rate series to 0.22 for the large company stock series under the tax adjustment policy (Chart 5).

The general levels of and relationships among the lifetime benefit/tax ratio plots for each interest rate series in both Charts 4 and 5 reflect the general levels of and relationships among the interest rate series themselves-generally, the higher the interest rate assumption, the lower the lifetime benefit/tax ratio, given the predominant life cycle pattern of early tax payments and later benefit receipts under the OASI program. Over the entire projection period and much of the historical period, the general order of the interest rate series, from lowest to highest, is the zero real, OASI tax base growth rate, OASI trust fund, and large company stock series. The early-cohort cross-over in the lifetime benefit/tax ratio measures between the tax base growth rate and trust fund interest rate assumptions in both Charts 4 and 5 is linked to a corresponding cross-over in the historical levels of those interest rate series.⁵⁷

A result of special interest in Charts 4 and 5 is the level of the benefit/tax ratios under each policy and interest rate assumption relative to a value of one. Under all of the interest rate assumptions, the benefit/tax ratios for the earliest cohorts exceed one by substantial margins, indicating lifetime benefits well in excess of lifetime taxes. As was evident with the internal rate of return measure, however, the question of whether present and future cohorts will continue to experience lifetime benefits in excess of lifetime taxes depends critically on the risk-adjusted interest rate deemed appropriate for the lifetime benefit/tax ratio calculation.

The lifetime benefit/tax ratios displayed in Charts 4 and 5 exceed one for all past, present, and future birth cohorts for both the zero real and tax base growth rate interest rate assumptions under either balanced budget policy. This result is consistent with the interpretation that factors such as the market-improving and portfolio-enhancing features of the OASI program justify the use of a relatively low interest rate in the lifetime benefit/tax calculation and imply that all cohorts can benefit from the establishment and continuation of such a program.

In contrast, the lifetime benefit/tax ratios fall below one for many present and all future birth cohorts for both the trust fund and large company stock interest rate assumptions under either balanced budget policy. This result is consistent with the interpretation that factors such as the market-improving and portfolio-enhancing features of the OASI program are insufficient to justify the use of a relatively low interest rate or are dominated by offsetting program characteristics such as perceived political risk differentials, making a higher interest rate assumption more appropriate.⁵⁸ Because a mature public retirement program financed on an essentially pay-as-you-go basis tends to generate a rate of return for program participants largely determined by the growth rate in the program's tax base, lifetime benefit/tax ratios will tend to be greater (less) than one if a risk-adjusted interest rate series generally smaller (larger) than the growth rate in the program tax base is used to calculate lifetime taxes and benefits.

Lifetime Net Transfer per Initial Cohort Member. In contrast to the relative measures of lifetime outcomes presented thus far, measures of the absolute difference between lifetime benefits and taxes under the OASI program across birth cohorts are displayed in Charts 6 through 9. These charts again illustrate the dependence of OASI lifetime money's worth and redistributional estimates on the particular interest rate assumption used to evaluate program outcomes but also illustrate that the relationships across the alternative interest rate series can differ between the relative and absolute measures.

The estimates displayed in Charts 6 and 7 can be interpreted as evaluating money's worth outcomes from the perspective of program participants. These charts display the present value of lifetime net transfers (benefits less taxes) under the program for each birth cohort as a whole divided by the initial population of the cohort. The lifetime net transfer for each cohort is evaluated as of the end of the "initial cohort year," defined as the birth year of the cohort or as 1937, the first year of OASI benefit and tax payments, for cohorts born prior to 1937.⁵⁹ These present values are then converted to constant dollars reflecting the 2001 price level. The aggregate real lifetime net transfer estimated for each cohort as a whole is divided by the number of initial members of that cohort to provide a feel for the level of estimated net lifetime transfers per person in each birth cohort.⁶⁰ For cohorts born in 1937 or later, the initial cohort population is defined as the population of the cohort as of the end of their birth year. For cohorts born prior to 1937, the initial cohort population is defined as the population of the cohort at the end of 1937. To summarize, then, the estimates displayed in Charts 6 and 7 represent the real present value of the lifetime net transfer under each interest rate assumption per initial member of each birth cohort as of the year of their birth or, if later, the beginning of the OASI program.

The estimated lifetime net transfer per initial cohort member is displayed in Chart 6 for the balanced budget award policy and in Chart 7 for the balanced budget tax policy. Under either policy, the lifetime net transfer per initial cohort member for the collective cohort group born through 1900, evaluated as of 1937, ranges from $36,760 under the OASI trust fund interest rate assumption to $2,165 under the large company stock total rate of return series. By the 1945 single-year birth cohort, this differential increases substantially, with a range from about $123,100 for the zero real interest rate series to about -$19,800 for the trust fund interest rate series. As with the other measures, the estimated lifetime net transfer per initial cohort member under a given interest rate assumption begins to diverge more noticeably between the two balanced budget policies for cohorts born after about 1950, as projected benefits and taxes begin to play a more important role. For the cohort born in 2100, the most distant cohort simulated in this analysis, the projected lifetime net transfer per initial cohort member, evaluated as of 2100, ranges from about $375,100 for the zero real interest rate series to about -$74,300 for the OASI trust fund interest rate series under the award adjustment policy (Chart 6) and ranges from about $783,500 for the zero real interest rate series to about -$122,800 for the OASI trust fund interest rate series under the tax adjustment policy (Chart 7).⁶¹

A key comparison in Charts 6 and 7 is the level of the lifetime net transfer under each policy and interest rate assumption relative to a value of zero. Under both of the balanced budget policies and all of the interest rate assumptions, the lifetime net transfer per initial cohort member for the earliest cohorts is positive, indicating lifetime benefits in excess of lifetime taxes. As with the prior measures considered, however, the question of whether present and future cohorts will continue to experience lifetime benefits in excess of lifetime taxes depends critically on the risk-adjusted interest rate deemed appropriate for the lifetime net transfer calculation.

Aggregate Lifetime Net Transfers. As noted above, the accumulated or discounted present value of lifetime benefits less taxes for each birth cohort as a whole, evaluated at a specific point in time using OASI trust fund interest rates, is a measure of the cost of those net transfers to the trust fund as of that evaluation date and can be interpreted as identifying the extent of redistribution across cohorts from the perspective of the program.⁶² The interest earned by the OASI trust fund reflects an internal government transaction, however, and can be viewed as a policy or managerial choice open to debate. The rates of return earned by the special Treasury obligations held by the trust fund have historically been based primarily on then current rates for marketable Treasury obligations, a conceptually appropriate basis for such interest payments.⁶³ These rates are not necessarily appropriate, however, for the evaluation of redistributional outcomes under the program from the perspective of program participants or from the broader perspective of society in general. In a pure pay-as-you-go program, of course, there is no trust fund and consequently no trust fund interest rate. The return to contributions under the present program has primarily been generated by the growth in the payroll tax base, with a much smaller proportion of expenditures funded by the return to trust fund assets.

More generally, the issues involved in the choice of an appropriate interest rate to use in developing redistributional estimates as of a particular evaluation date mirror the issues discussed above in conjunction with the money's worth estimates presented in the previous charts. To illustrate the importance of this effect, measures of lifetime redistribution under the OASI program are developed in this analysis using the same alternative interest rate series applied to develop the money's worth estimates presented above.

The present values of aggregate lifetime net transfers (benefits less taxes) for each single-year birth cohort, evaluated as of the end of 2001 using each of the four interest rate series, are displayed in Charts 8 and 9 under the two balanced budget policies. Analogous tabular estimates are presented in Tables 1 and 2 for generally 10-year birth cohorts.⁶⁴ These aggregate lifetime net transfer estimates reflect the size of each cohort group as well as the average outcome for members of that group.

Under either balanced budget policy, the aggregate lifetime net transfer for the collective cohort group born through 1900, evaluated as of 2001, ranges from $13,676 billion under the large company stock interest rate assumption to $1,637 billion under the zero real interest rate assumption. The aggregate lifetime net transfer under either balanced budget policy for the 1945 single-year birth cohort, evaluated as of 2001, ranges from about $346 billion for the zero real interest rate series to about -$818 billion for the large company stock series. As with the other measures, the estimated aggregate lifetime net transfer begins to diverge more noticeably across policies under a given interest rate assumption for cohorts born after about 1950. The projected aggregate lifetime net transfer for the single-year cohort born in 2100, discounted to 2001, ranges from about $1,836 billion for the zero real interest rate series to about -$18 billion for the OASI trust fund interest rate series under the award adjustment policy (Chart 8) and ranges from about $3,834 billion for the zero real interest rate series to about -$30 billion for the OASI trust fund interest rate series under the tax adjustment policy (Chart 9).

A key comparison in Charts 8 and 9 and Tables 1 and 2 is the level of the lifetime net transfer under each policy and interest rate assumption relative to zero. Under either of the balanced budget policies, aggregate lifetime net transfers for the earliest cohorts are positive for all of the interest rate assumptions; the question of whether present and future cohorts will continue to experience positive lifetime net transfers again depends critically on the risk-adjusted interest rate used in the calculation.⁶⁵

Lifetime Net Transfer/Taxable Earnings Rate. Another money's worth measure of interest is the present value of lifetime net transfers (benefits less taxes) relative to the present value of lifetime taxable earnings under the program.⁶⁶ If negative (positive) for a particular cohort, this measure can be interpreted as the implicit lifetime tax (subsidy) rate experienced by that cohort under the program.

Estimates for the lifetime net transfer/taxable earnings rate under the two balanced budget policies are displayed in Charts 10 and 11. The general intercohort pattern and implications of this measure are analogous to those for the lifetime benefit/tax ratio, which is also a relative measure. Under either balanced budget policy, the lifetime net transfer/taxable earnings rate for the collective cohort group born through 1900 ranges from 35.3 percent under the OASI trust fund interest rate assumption to 5.1 percent under the large company stock interest rate assumption, a significant subsidy under all of the interest rate assumptions. The net transfer/taxable earnings rate generally declines across subsequent cohorts so that by the 1945 single-year birth cohort the rate ranges from about 12.5 percent for the zero real interest rate series, representing a net subsidy, to about -6.8 percent for the large company stock series, representing a net tax. The net transfer/taxable earnings rate begins to diverge more noticeably across policies for subsequent cohorts under each interest rate assumption. For the most distant projected single-year birth cohort, born in 2100, the projected lifetime net transfer/taxable earnings rate ranges from about 6.2 percent for the zero real interest rate series to about -8.4 percent for the large company stock interest rate series under the award adjustment policy (Chart 10) and ranges from about 12.9 percent for the zero real interest rate series to about -14.9 percent for the large company stock series under the tax adjustment policy (Chart 11).

As in Charts 6 through 9, a key comparison in Charts 10 and 11 is the level of the lifetime net transfer/taxable earnings rate relative to zero. Again, the lifetime net transfer/taxable earnings rate is positive for the earliest cohorts under either of the balanced budget policies for all of the interest rate assumptions, but the question of whether present and future cohorts will continue to experience positive lifetime subsidies depends critically on the risk-adjusted interest rate used in the calculation.

Legacy Debt Calculations. Some studies have used estimates of aggregate net transfers by cohort based on the OASI trust fund interest rate, analogous to the estimates presented in the third data column of Tables 1 and 2, to identify the accumulated sum of aggregate net transfers under the program to past and present cohorts.⁶⁷ This accumulated sum has been referred to as the "legacy debt" associated with the OASI program, with the implication that lifetime net transfers for future cohorts under the program must necessarily be negative because of the positive net transfers experienced by past and present cohorts. Some analysts have suggested that a portion of this legacy debt be repaid as part of OASI reform.

The relevance of such legacy debt measures would be clear in an abstract world where interest rates and economic growth rates were known with certainty. Under these abstract conditions, the present value of aggregate net transfers across all past, present, and future cohorts in a pure pay-as-you-go program with a constant tax rate approaches zero if the market interest rate generally exceeds the growth rate in the tax base of the pay-as-you-go retirement program.⁶⁸ Under such abstract conditions, then, the positive net transfers received by early cohorts under a pay-as-you-go program are offset by negative net transfers from later cohorts, and the accumulation of net transfers across early cohorts under the program can be interpreted as a "legacy debt" that is borne by later cohorts.

Under real world conditions, however, such legacy debt measures may lose quantitative and even qualitative relevance, reflecting the much more complex relationships among uncertain, stochastic market interest rates and the growth rates in economic aggregates.⁶⁹ As discussed above, the risk-adjusted interest rate appropriate to the evaluation of program outcomes from the perspective of program participants or society in general may be lower than the trust fund or other market interest rate or even the growth rate in the program's tax base as a result of the program's potential market-improving and portfolio-enhancing characteristics. Legacy debt calculations based on inappropriate risk-adjusted interest rates will misstate the burden, if any, imposed by the program on present and future cohorts.⁷⁰ In short, the legacy debt concept and measure are critically sensitive to the choice of the interest rate series deemed appropriate for the evaluation of program outcomes, just as in the case of the money's worth and lifetime redistributional measures presented in this analysis.

Comparison with Previous Research

This section provides a brief general literature context for the present analysis but focuses on a review and comparison of results with the most similar previous analyses. Special attention is paid to the differences in method and results between the present analysis and Leimer (1994), which this analysis updates.

A number of studies have included intercohort analyses based on longitudinal data for individual sample cases drawn from Social Security Administration files; these studies include Frieden, Leimer, and Hoffman (1976), Burkhauser and Warlick (1981), Meyer and Wolff (1987), and Duggan, Gillingham, and Greenlees (1993). Social Security administrative data files with samples drawn from individual records contain taxes, benefits, or both over only partial lifetimes for most cohorts, however, limiting the range of cohorts that can be analyzed or necessitating the simulation of missing tax or benefit data, even for historical periods.⁷¹ Other studies have focused on results for cohorts as a whole. Leimer and Petri (1981) used a long-run general equilibrium model that included a detailed OASI sector to project future taxes and benefits by cohort but employed a less accurate accounting of historical taxes and benefits by cohort than the present study. Moffitt (1984) used historical administrative data on benefits by cohort, but estimated the historical taxes of each included cohort using median earnings by age and gender; the Moffitt analysis was also limited to a relatively narrow range of cohorts born between 1875 and 1910.

More recently, as part of the current policy debate related to restoring solvency to the OASI program, there have been numerous studies projecting various types of outcomes for varying sets of cohorts under alternative program provisions.⁷² The most comparable of these more recent analyses include Leimer (1994), Anderson, Yamagata, and Tuljapurkar (2001), and Goss (2001), the latter being a comment on the Anderson, Yamagata, and Tuljapurkar analysis. These analyses are sufficiently similar to the present analysis to merit an examination of differences in results.

These prior studies use less accurate or less recent estimates of the historical taxes and benefits experienced by each birth cohort, employ prospective simulation methods that differ in a number of important respects from those in the present analysis, and are limited to a narrower range of cohorts. Leimer (1994), for example, had access to 13 fewer years of historical administrative data on OASI taxes and benefits by age and year than the present analysis, projects results for cohorts born through 2050 compared to 2100 in the present analysis, is based on projections from a much earlier (1991) Trustees Report, and, as discussed more fully below, uses projection methods that do not conform as closely to the Trustees Report projections. The stochastic simulations in Anderson, Yamagata, and Tuljapurkar (2001) use historical estimates patterned on those in Leimer (1994) but use projections that differ in important respects from the Trustees Report projections;⁷³ results are limited to selected cohorts born between 1941 and 1999. While fully consistent with the 2001 Trustees Report projections, the Goss (2001) comment only presents results for the combined 1982–1986 birth cohort.

Some results from the Anderson, Yamagata, and Tuljapurkar (2001) and the Goss (2001) analyses are contrasted with those from the present analysis in Chart 12. This chart shows projected real internal rates of return under present law for the birth cohorts that are included in the Anderson, Yamagata, and Tuljapurkar and in the Goss analyses. The legend in Chart 12 reflects some aspects of the different measures and treatment of benefit income taxation used in the analyses. As indicated above, the present analysis projects internal rates of return for each birth cohort as a whole net of the portion of OASI benefit income taxation returned to the OASI trust fund. The Chart 12 legend reflects this OASI benefit income tax treatment as "After OASI portion of tax." The Anderson, Yamagata, and Tuljapurkar (AYT) estimates in Chart 12 represent the median rate of return from the distribution of rates of return generated for the cohort as a whole from their set of stochastic simulations. Although not characterized in detail in their paper, their estimates appear to be net of all OASI benefit income taxes, including the benefit income tax revenues returned to the HI trust fund. The Chart 12 legend reflects this measure and OASI benefit income tax treatment as "Median, after tax." The Goss comment presents both "pre tax" and "after tax" estimates of the real internal rate of return for the combined 1982–86 birth cohort as a whole based on the 2001 Trustees Report assumptions. Again, while not characterized in detail in the comment, these estimates appear to be gross and net, respectively, of all OASI benefit income taxes, including those returned to the HI trust fund. The Chart 12 legend reflects this OASI benefit income tax treatment for the two estimates as "Pre tax" and "After tax."

The two Goss estimates are displayed in Chart 12 as single data points located at the middle (1984) birth cohort in the 1982–86 cohort group. Not surprisingly, given the similarity of method and assumptions, the estimate for the 1984 birth cohort in the present analysis lies between the "pre tax" and "after tax" estimates for the 1982–1986 birth cohort group from the Goss (2001) comment. The differences between the median estimates from the Anderson, Yamagata, and Tuljapurkar (2001) analysis and the cohort estimates from the present analysis are not surprising given the differences in measure, method, and assumptions, although it is not clear why their median estimates for the 1949 and 1959 birth cohorts dip so far below those for the surrounding cohorts.

One of the primary purposes of the present analysis is to update the Leimer (1994) estimates. Despite many similarities, the projection method used in Leimer (1994) differs substantially from the method used in the present analysis. A major difference is that the present analysis enforces exact consistency with the detailed economic and demographic assumptions underlying the Trustees Report. The economic and demographic projections in Leimer (1994) were simulated using a long-run general equilibrium model of the U.S. economy and its interrelationships with the OASI program, with various parameters of the model calibrated to achieve as high a degree of correspondence as possible between the simulated geometric mean growth rates of key economic, demographic, and program variables and the corresponding geometric mean growth rates of those variables as projected by the 1991 Trustees Report.⁷⁴ Despite a close correspondence in the cumulative growth in these variables over the full Trustees Report projection period, the annual time paths of some of the economic variables nevertheless differed in important ways between the two projection methods within and beyond that projection period. These differences had associated significant effects on estimated outcomes across birth cohorts.

The simulated time path of real wage growth under the two projection methods is an important example. In contrast to the exogenous and generally flat real wage growth rate assumptions in the Trustees Report, annual real wages in the Leimer (1994) general equilibrium model responded endogenously to simulated changes in labor productivity arising from such factors as the assumed rate and nature of technological progress, the changing demographic structure of the work force, and the ratio of capital to effective (productivity-weighted) labor. The effects of the demographic structure and capital/labor ratio factors varied significantly over the Trustees Report projection period as, for example, the baby-boom cohorts moved through various life cycle stages characterized by different productivity, labor supply, and saving behavior. As a consequence, the simulated real wage growth rate in the Leimer (1994) projections was significantly above the Trustees Report real wage growth rate assumptions during the first part of the projection period but significantly below the Trustees Report assumptions during the last part of the projection period.⁷⁵ This different time path in simulated real wage growth in turn affected the simulated pattern of lifetime outcomes under the program across affected birth cohorts. In particular, since real wage growth under these constraints was lower during the last part of the projection period in the Leimer (1994) projections than in the Trustees Report, relative lifetime outcomes under the program for the most distant birth cohorts were also projected to be less favorable than if higher real wage growth had been projected over that period.

Whether the constrained general equilibrium approach adopted in Leimer (1994) or the approach of exact adherence to the Trustees Report assumptions adopted in the present analysis is preferable depends on the interpretation and use of the analysis results. The approach in the present analysis has the advantage of precise and continuous consistency with the economic and demographic assumptions underlying the Trustees Report, which represents the official projection of the financial status of the program. In contrast, the simulation approach in Leimer (1994) has the advantage of generating projections that are internally consistent across all of the economic and demographic variables within the context of a general equilibrium model of the U.S. economy and its interrelations with the OASI program.⁷⁶

Some of the effects of the alternative simulation methods are reflected in Chart 13, which contrasts projections of OASI real internal rates of return for single-year birth cohorts under present law in the Leimer (1994) analysis and the present analysis. The different projected time path of real wage growth accounts for much of the difference between the two sets of results. Another contributing factor is the somewhat lower labor force growth projected towards the end of the projection period in the 1991 Trustees Report underlying the Leimer (1994) estimates than in the 2002 Trustees Report underlying the present analysis.⁷⁷ Another important difference in the internal rate of return estimates under present law assumptions arises from differences in the mortality rate projections underlying the two analyses;⁷⁸ mortality rates were projected to be generally higher and life expectancies corresponding lower for distant cohorts in the 1991 Trustees Report than in the 2002 Trustees Report.⁷⁹ For a number of reasons, then, the real internal rates of return projected under present law for the most distant cohorts differ substantially between the two analyses. For example, the real internal rate projected for the 2050 cohort under the present law policy was 1.71 percent in the Leimer (1994) analysis in contrast to 3.06 percent in the present analysis.

Analogous comparisons between the simulations of balanced budget award and balanced budget tax policies in the Leimer (1994) and present analyses are presented in Charts 14 and 15. In addition to the differences discussed above in the economic and demographic assumptions and simulation approaches underlying the two analyses, details of the balanced budget award and balanced budget tax policies differ between the two analyses. Nevertheless, the balanced budget award and balanced budget tax policies in both analyses are designed to bring the OASI program into financial balance over a simulation period extending far beyond the respective Trustees Report projection periods.⁸⁰ The higher internal rates of return that are projected for the most distant cohorts under each balanced budget policy in the present analysis compared to the Leimer (1994) analysis are illustrated in Charts 14 and 15. The real internal rate of return for the 2050 cohort, for example, is projected as 0.80 percent under the Leimer (1994) balanced budget award policy and as 1.35 percent for the balanced budget award policy in the present analysis. The real internal rate of return for the 2050 cohort is projected as 0.94 percent under the Leimer (1994) balanced budget tax policy compared to 1.60 percent under the balanced budget tax policy in the present analysis. Again, much of the difference in the internal rates of return projected for the most distant cohorts in the present analysis compared to those projected in the Leimer (1994) analysis can be attributed to differences between the projected time paths of real wage growth and the labor force in the two analyses.

Concluding Comments

This study presents various measures of the balance between lifetime taxes and benefits for past, present, and future birth cohorts under OASI present law and under stylized solvent tax rate and benefit award adjustment policies conditional on the intermediate assumptions in the 2002 Trustees Report. These estimates update corresponding estimates presented in Leimer (1994) and reflect an accounting of OASI taxes and benefits that is more comprehensive, more accurate historically and extensive prospectively, and/or conforms more closely to the official Trustees Report projections than analogous estimates in previous analyses. The various interest rate series and redistributional and money's worth measures included in this analysis are intended to facilitate comparison with previous analyses and to increase the range of questions to which the results can be applied.

While lifetime benefits exceed lifetime taxes for early cohorts under all of the interest rate assumptions, net program outcomes for many present and future cohorts depend critically on the interest rates used to calculate the various measures. In a stochastic world where retirement saving alternatives have different risk and return characteristics, the choice of an appropriate risk-adjusted interest rate to evaluate program outcomes is difficult and controversial.

Based on the internal rate of return estimates in this analysis, even the most distant birth cohorts will receive their money's worth from the OASI program under any of the policies considered if a risk-adjusted real interest rate below 1.35 percent is deemed appropriate for evaluating program outcomes. If instead, a risk-adjusted real interest rate of 2 percent or above is deemed appropriate, then no cohort born after about 2015 is projected to receive its money's worth by this measure under either of the balanced budget policies considered.

Based on the other money's worth and lifetime redistributional measures in this analysis, estimated lifetime benefits exceed lifetime taxes for all past, present, and future birth cohorts for both the zero real and tax base growth rate interest rate assumptions under either balanced budget policy. This result is consistent with the interpretation that the market-improving and portfolio-enhancing features of the OASI program justify the use of a relatively low interest rate in the calculation of the money's worth and lifetime redistributional measures. In contrast, estimated lifetime taxes exceed lifetime benefits for many present and all future birth cohorts for both the trust fund and large company stock interest rate assumptions under either balanced budget policy. This result is consistent with the interpretation that the market-improving and portfolio-enhancing features of the OASI program are insufficient to justify the use of a relatively low interest rate or are dominated by offsetting characteristics of the program, such as perceived political risk differentials. Because a mature public retirement program financed on an essentially pay-as-you-go basis tends to generate a rate of return for program participants roughly equal to the growth rate in the program's tax base, lifetime benefits will tend to be greater (less) than lifetime taxes if the risk-adjusted interest rate series used in the calculations is generally less (greater) than the growth rate in the program tax base.

Under certain assumptions, the aggregate lifetime net transfer estimates developed in this analysis can be used to calculate the legacy debt associated with net transfers to early cohorts under the OASI program. The legacy debt concept and measure are critically sensitive to the choice of the interest rate series deemed appropriate for the evaluation of program outcomes, however, just as for the money's worth and lifetime redistributional measures. As such, the typical practice of using the trust fund or other market interest rate unadjusted for risk in the legacy debt calculation may produce a quantitatively misleading or even qualitatively invalid indication of any "debt" or "burden" imposed by the program on present and future cohorts.

Appendix A.

This appendix presents OASI money's worth and redistributional measures of lifetime outcomes by birth cohort as simulated under the present law policy consistent with the underlying Trustees Report projections. Because the program is projected to be out of long-run financial balance under present law provisions, these present law outcomes include unfunded benefits.

Appendix B.

This appendix presents OASI money's worth and redistributional measures of lifetime outcomes by birth cohort as simulated under the balanced budget award adjustment policy. As discussed in the text, this stylized policy brings the program into long-run financial balance consistent with the underlying Trustees Report projections.

Appendix C.

This appendix presents OASI money's worth and redistributional measures of lifetime outcomes by birth cohort as simulated under the balanced budget tax rate adjustment policy. As discussed in the text, this stylized policy brings the program into long-run financial balance consistent with the underlying Trustees Report projections.

Appendix D: OASI Benefit and Tax Projections

This analysis simulates Old Age and Survivors Insurance (OASI) program outcomes in future years under present program provisions and under certain alternative policies. These projections identify the effects of the program on OASI taxpayers and beneficiaries by age and track the associated implications for the OASI trust fund and the long-run financial balance of the program. In conjunction with comprehensive administrative data on historical taxes and benefits by age, these projections enable estimates of the lifetime money's worth and redistributional effects of specific policies on past, present, and future birth cohorts. The projections in this analysis are derived from and consistent with the data and relationships underlying the intermediate projections of the annual Trustees Report. When projecting the effects of alternative policies, of course, aspects of the Trustees Report projections that are specific to the present program are modified as appropriate. This appendix provides a general description of the determination of OASI program variables in the present analysis at the aggregate and required disaggregate level within and beyond the Trustees Report projection period. Some implementation details are omitted for the sake of brevity and expositional clarity.

Social Security Area Population

The Social Security area population by gender, age, and year in the present analysis is based on the corresponding detailed projections underlying the annual Trustees Report.⁸¹ These population data are denoted here as  $N_{s,a,t}^S$ , where the s, a, and t subscripts respectively represent gender, age, and the projection period.

Covered Employment

Employment is derived from the Social Security area population by applying gender-, age-, and year-specific labor force participation rates and unemployment rates as projected in the annual Trustees Report. In each projection year, a proportional adjustment is applied across all gender and age groups to derive OASI covered employment from total employment. Specifically, OASI covered employment by gender, age, and year is derived as

where  $c_t$  denotes the projected ratio between OASI covered employment and total employment in each projection year,  $p_{s,a,t}$  denotes the projected gender-, age-, and year-specific labor force participation rate, and  $u_{s,a,t}$  denotes the corresponding unemployment rate.

Taxable Earnings

The OASI projections in the present analysis use Trustees Report projections of annual aggregate employee taxable wages ( $H_t^E$ ), employer taxable wages ( $H_t^R$ ), and self-employment taxable income ( $H_t^{SE}$ ). In each of these taxable earnings categories, the corresponding average taxable earnings for each gender and age group in each projection year are simulated by applying relative average taxable earnings weights differentiated by gender and age in each year ( ${\pi }_{s,a,t}$ ).⁸² Given these relative average taxable earnings weights, the average taxable earnings subject to each type of OASI tax by gender, age, and year are given by

where  ${\pi }_t$  is a period-specific effective taxable earnings factor that depends on the gender and age composition of covered employment and ensures that aggregating average taxable earnings in each category across covered employment by gender and age yields the Trustees Report projections of annual aggregate taxable earnings for that taxable earnings category in that year; i.e.,

For use in the subsequent computation of primary retirement benefits, the average OASI taxable earnings by gender, age, and year that are creditable for use in the benefit formula are then assumed equal to

OASI Taxes on Earnings

The total OASI payroll taxes paid in each projection year by gender and age are denoted as  $T_{s,a,t}^P$  and are given by the sum of the OASI employee, employer, and self-employment income taxes. Specifically,

where  ${\tau }_t^E$  and  ${\tau }_t^R$  respectively represent the projected employee and employer tax rates on OASI taxable wages and  ${\tau }_t^{SE}$  represents the projected OASI self-employment income tax rate in each projection year. The total OASI payroll taxes paid in each year by age are derived by summing across both genders; i.e.,

The  ${\tau }_t^E$  ,  ${\tau }_t^R$ , and  ${\tau }_t^{SE}$  OASI tax rates scheduled under present law can be modified exogenously or endogenously in the OASI projections, depending on the alternative policy under consideration.

Retirement Benefits

The number of retirees in current payment status in each projection year by gender, age, and age at entitlement is based on corresponding projections underlying the annual Trustees Report.⁸³ The corresponding variable is denoted here as  $R_{s,a,j,t}$ , where the s, a, j, and t subscripts respectively represent gender, age, age at entitlement (including a separate category for disability conversions), and the projection period.

Average OASI benefit payments to retirees are derived as

where the first line represents the determination of average retirement benefit awards for new retirees under present Social Security law and the second line represents average benefits for previously retired workers. The present law benefit award computation function, b(…), in equation (7a) depends on age at retirement, gender, year of retirement, and the lifetime OASI taxable earnings of the retiree to that point. To calibrate the present law benefit award computation function b, administrative data on actual average benefits for new retirees of each gender and age in the last available historical year, along with average benefits for disability conversions in that year, were used to determine a proportional adjustment factor for each gender at each age of retirement or disability conversion ( ${\beta }_{s,j}$ ). This proportional adjustment factor is assumed to apply to the determination of benefit awards in all projection years. Alternative benefit award computation functions could be substituted to simulate certain other benefit structures in place of the present law benefit structure.⁸⁴

Equation (7b) determines average benefits for previously retired workers. The average benefit in the previous period for a given gender, age, and age at retirement group is adjusted by a general retirement benefit adjustment factor ( $g_t$ ) applicable to all previous retirees and by a gender- and age-specific adjustment factor ( ${\mu }_{s,a}$ ) that reflects the effect of average retirement benefit changes over the retirement period.⁸⁵ Under the present benefit structure, the general retirement benefit adjustment factor  $g_t$  represents the effect of the annual automatic inflation adjustment. The gender- and age-specific benefit adjustment factor  ${\mu }_{s,a}$  is assumed constant over time and is derived by gender and age from administrative data on average benefits for retirees in recent retirement cohorts who had benefits in current payment status at successive year-ends. Aggregate benefits to retirees by age in each projection year can then be derived as

Secondary Benefits

OASI secondary benefits to dependents and survivors of primary beneficiaries are split into three main classes to take advantage of the corresponding level of detail available in the data underlying the annual Trustees Report projections. The three classes of OASI secondary benefits are (1) benefits to aged spouses, (2) benefits to aged surviving spouses (widows and widowers), and (3) all other OASI secondary benefits.

For the first two classes, the available data underlying the Trustees Report respectively included gender-, age-, and year-specific projections of the number of aged nondivorced spouse beneficiaries in current payment status and the number of aged nondivorced surviving spouse beneficiaries in current payment status.⁸⁶ These relative age distributions are assumed to apply respectively to the corresponding total number of aged spouse beneficiaries (including the divorced spouse category) and the total number of aged surviving spouse beneficiaries (including the divorced surviving spouse category) in current payment status in each year as projected in the data underlying the annual Trustees Report.⁸⁷ For the first two secondary benefit classes, then, this approach is used to identify the number of secondary beneficiaries by beneficiary class, age, and year, denoted as  $R_{a,t}^{S1}$  and  $R_{a,t}^{S2}$ .

The corresponding average benefit by age and year ( $b_{a,t}^{S1}$  ,  $b_{a,t}^{S2}$ ) received by secondary beneficiaries in each of these first two secondary beneficiary classes is provisionally derived under the assumption that the average secondary benefit by age and gender within each of these beneficiary classes remains constant over time relative to the corresponding average benefit for retirees of the same age and gender.⁸⁸ These provisional average benefits are then adjusted proportionally across all applicable age and gender groups in each projection year to ensure that simulated aggregate secondary benefits of each class equal the aggregate projected for that class in the Trustees Report (or other policy projection) for that year. In effect, provisional  $b_{s,a,t}^{Sn}$  for the first two secondary beneficiary classes are first computed from the relationship  $b_{s,a,t}^{Sn}=k_{s,a}^{Sn}{b}_{s,a,t}^R$ , where n refers to secondary beneficiary class 1 or 2, the  $b_{s,a,t}^R$  refer to the average retirement benefit across all retirees of that age and gender in that year, and the  $k_{s,a}^{Sn}$  are determined from administrative benefit data in the last available historical year. The provisional  $b_{s,a,t}^{Sn}$  are then adjusted proportionally across all age and gender groups for consistency with the Trustees Report (or alternative policy) projection of aggregate secondary benefits of that class in that year. For use in subsequent simulation calculations, these adjusted  $b_{s,a,t}^{Sn}$  are then combined across gender to derive the corresponding weighted average  $b_{a,t}^{Sn}$  by age and year. Together, then, the number of secondary beneficiaries by beneficiary class, age, and year ( $R_{a,t}^{S1}$  ,  $R_{a,t}^{S2}$ ) and the respective average benefit received by those secondary beneficiaries ( $b_{a,t}^{S1}$ $b_{a,t}^{S2}$ ) determine the aggregate benefits received by secondary beneficiaries of the first two classes in each year; i.e.,

Less information is available in the Trustees Report projections for the age allocation of the third class of all other OASI secondary benefits.⁸⁹ Consequently, OASI secondary benefits of the third class by age and year are simulated in the present analysis as

where the number of secondary beneficiaries of the third class  $R_{a,t}^{S3}$  and their average benefits  $b_{a,t}^{S3}$  are derived under the assumptions that (1) the proportion of persons of each age and gender receiving secondary benefits of the third class remains constant over time subject to any additional proportional adjustment across all age and gender groups in each projection year required to achieve the Trustees Report (or other policy) projection of total secondary beneficiaries of the third class in that year and (2) average secondary benefits of the third class at each age and gender remain constant over time relative to average secondary benefits of the third class at each other age and gender, with average secondary benefits of the third class proportionally adjusted across all age and gender groups in each projection year to achieve the ratio of aggregate secondary benefits of the third class to aggregate retiree benefits as projected by the Trustees Report (or other policy).

Given the determination of aggregate secondary benefits for each of the three secondary benefit classes, aggregate secondary benefits of all types are simply given by their sum

Unless simulating the effects of an alternative policy that dictates otherwise, the OASI projections convert the Trustees Report nominal aggregate benefits projected for each secondary class in each simulation year to the corresponding proportion of the aggregate retirement benefits projected in that year. This approach has the effect that a simulated adjustment in retirement benefits or awards in a given projection year under an alternative policy leads to a corresponding proportional adjustment in the secondary benefits projected for that year. Of course, other aggregate constraints on each class of secondary benefits could also be imposed, depending on the policy being simulated.

Income Taxation of Benefits

Revenues returned to the OASI trust fund from the income taxation of OASI benefits are determined by age in each year as

where the effective tax rate  ${\tau }_t^B$  is determined by the Trustees Report projection of benefit income taxation proceeds that are returned to the OASI trust fund as a proportion of total OASI benefits. This approach assumes that the effective benefit taxation rate is identical across age groups in any given projection year.

Net Transfers

OASI program net transfers by age in each year can then calculated as retirement and secondary benefits less OASI payroll taxes and OASI benefit income taxes that are returned to the OASI trust fund. Specifically,

Aggregating across all ages gives aggregate OASI program net transfers in each simulation period; i.e.,

Other Trust Fund Components and Net Surplus

The data underlying the Trustees Report also contain projections of administrative expenses, denoted here as  $A_t$ , and net financial interchange transfers with the Railroad Retirement program, denoted here as  $R{R}_t$ , both of which are relatively small trust fund components.⁹⁰ To complete the simulation of OASI trust fund components, the OASI projections in the present analysis convert the Trustees Report nominal projections of these trust fund components to the corresponding proportions of aggregate OASI benefits projected in that year. This has the effect that a simulated adjustment in OASI benefits under an alternative policy leads to a corresponding proportional adjustment in the administrative expenses and Railroad Retirement program net financial interchange transfers. Again, other relationships involving these trust fund components could also be imposed depending on the policy being simulated.

Given the determination of the major OASI trust fund components, the net surplus for the OASI trust fund in each projection period can be identified as

where  $F_t$  denotes OASI trust fund assets as of the beginning of the period and  $r_t^F$  denotes the rate of return to OASI trust fund assets applicable to period t as projected in the annual Trustees Report. Trust fund assets as of the beginning of the succeeding period are then given by

Data Extensions beyond the Trustees Report Projection Horizon

Because the present analysis projects lifetime OASI taxes and benefits for past, present, and future birth cohorts with assumed potential life spans of up to 120 years each, the projection period required in the present analysis is considerably longer than that used in the annual Trustees Report. The present analysis must extend the projections of program outcomes well beyond the Trustees Report projection horizon, then, in a way that maintains consistency with the relationships underlying the Trustees Report projections.

Consistent extensions are facilitated by the nature of the Trustees Report projections over the last part of the Trustees Report projection period. After an initial transition period, the Trustees Report projections generally converge to a constant level or growth pattern, depending on the projected variable. As examples, under the intermediate assumptions of the 2002 Trustees Report, the total fertility rate is projected to reach its ultimate level by 2026; after adjustment for changes in the age-sex distribution of the population, annual percentage reductions in total death rates are also projected to reach their ultimate average levels by 2026; the labor force is projected to attain a constant annual growth rate over the final 25 years of the 75 year projection period, reflecting the combined effect of a number of underlying variables; and other key economic and demographic variables used in this analysis are projected to attain constant values or growth rates relatively early in the Trustees Report projection period.

The projections of each Trustees Report variable of interest are analyzed at the required aggregate or age and gender disaggregate level in the present analysis, then, to identify the systematic pattern of change in the variable toward the end of the Trustees Report projection period. This pattern of change is then applied to extend the variable beyond the Trustees Report projection horizon. These extended projections are consistent with the Trustees Report projections, then, in the sense that they maintain the same systematic pattern of change found in each variable toward the end of the Trustees Report projection period throughout all subsequent projection periods.