# Cohort-Specific Measures of Lifetime Social Security Taxes and Benefits

by Dean R. Leimer
ORES Working Paper No. 110 (released December 2007)

The author is with the Division of Economic Research, Office of Research, Evaluation, and Statistics, Office of Policy, Social Security Administration.

Acknowledgments: The author thanks Henry Ezell for assistance in data preparation and Andrew Bershadker, Andrew Biggs, Benjamin Bridges Jr., Nicholas Bull, Chris Chaplain, Lee Cohen, Jeffrey L. Kunkel, Joyce Manchester, David Pattison, and David Podoff for providing data, commenting on the paper, or discussing various aspects of the analysis.

Working papers in this series are preliminary materials circulated for review and comment. The findings and conclusions expressed in them are the authors' and do not necessarily represent the views of the Social Security Administration.

## 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.

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

Chart 1.
OASI benefit award adjustment factor under the balanced budget award policy, by year
SOURCE: Author's calculations.

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.

Chart 2.
OASI combined payroll tax rate, by policy and year
SOURCE: Author's calculations.

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.

Chart 3.
OASI real internal rate of return, expressed as a percent, by policy and cohort
SOURCE: Author's calculations.

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).

Chart 4.
OASI lifetime benefit/tax ratio under the award adjustment policy, by interest rate assumption and cohort
SOURCE: Author's calculations.
Chart 5.
OASI lifetime benefit/tax ratio under the tax adjustment policy, by interest rate assumption and cohort
SOURCE: Author's calculations.

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.

Chart 6.
OASI real lifetime net transfer per initial cohort member under the award adjustment policy evaluated as of the initial cohort year, by interest rate assumption and cohort (in 2001 dollars)
SOURCE: Author's calculations.
Chart 7.
OASI real lifetime net transfer per initital cohort member under the tax adjustment policy evaluated as of the initial cohort year, by interest rate assumption and cohort (in 2001 dollars)
SOURCE: Author's calculations.

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.

Table 1. Aggregate OASI lifetime net transfers under the award adjustment policy, evaluated as of year-end 2001 using alternative interest rate assumptions, by 10-year birth cohort (in billions of dollars)
Birth cohort Interest rate assumption
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Pre–1901 1,637.203 3,912.972 4,313.035 13,676.469
1901–1910 1,701.736 2,303.540 3,900.322 6,719.672
1911–1920 2,357.449 2,250.763 3,654.831 1,964.335
1921–1930 2,352.271 1,259.806 1,123.712 -5,787.376
1931–1940 2,364.471 587.418 -493.337 -7,080.525
1941–1950 3,998.263 833.139 -1,504.711 -9,181.005
1951–1960 5,711.384 1,232.563 -1,781.017 -7,942.031
1961–1970 5,018.370 781.136 -1,305.644 -3,020.509
1971–1980 4,265.825 431.199 -1,025.572 -1,251.318
1981–1990 4,698.171 271.206 -1,087.081 -927.633
1991–2000 5,069.634 203.841 -975.594 -562.255
2001–2010 5,460.787 155.808 -847.483 -325.776
2011–2020 6,130.699 145.612 -734.038 -191.678
2021–2030 7,026.295 178.775 -613.178 -111.681
2031–2040 7,972.794 164.718 -526.148 -66.335
2041–2050 9,028.033 143.183 -452.030 -39.434
2051–2060 10,324.157 151.022 -380.821 -23.137
2061–2070 11,725.448 137.560 -325.002 -13.656
2071–2080 13,332.387 130.641 -275.819 -8.016
2081–2090 15,218.277 135.823 -232.287 -4.678
2091–2100 17,326.575 131.947 -196.804 -2.741
SOURCE: Author's calculations.
Table 2. Aggregate OASI lifetime net transfers under the tax adjustment policy, evaluated as of year-end 2001 using alternative interest rate assumptions, by 10-year birth cohort (in billions of dollars)
Birth cohort Interest rate assumption
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Pre–1901 1,637.203 3,912.972 4,313.035 13,676.469
1901–1910 1,701.736 2,303.540 3,900.322 6,719.672
1911–1920 2,357.443 2,250.758 3,654.827 1,964.332
1921–1930 2,352.263 1,259.792 1,123.695 -5,787.393
1931–1940 2,364.468 587.339 -493.455 -7,080.644
1941–1950 4,008.346 838.868 -1,501.456 -9,180.301
1951–1960 6,234.408 1,533.047 -1,603.422 -7,889.690
1961–1970 6,499.709 1,519.906 -935.459 -2,951.643
1971–1980 6,622.329 1,424.428 -627.558 -1,221.464
1981–1990 8,380.259 1,576.463 -691.412 -940.021
1991–2000 9,864.792 1,630.610 -667.030 -600.901
2001–2010 11,301.554 1,600.784 -646.621 -370.280
2011–2020 12,894.472 1,502.106 -650.623 -233.583
2021–2030 14,209.973 1,284.397 -650.675 -147.299
2031–2040 15,844.085 1,064.899 -646.060 -94.445
2041–2050 17,898.792 906.113 -612.521 -59.732
2051–2060 20,326.286 809.545 -553.586 -36.729
2061–2070 23,429.706 767.217 -490.938 -22.357
2071–2080 27,052.836 749.290 -428.593 -13.439
2081–2090 31,161.822 736.474 -371.196 -8.018
2091–2100 35,982.899 726.448 -321.944 -4.793
SOURCE: Author's calculations.

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).

Chart 8.
Aggregate OASI lifetime net transfers under the award adjustment policy evaluated as of year-end 2001, by interest rate assumption and cohort (in billions of dollars)
SOURCE: Author's calculations.
Chart 9.
Aggregate OASI lifetime net transfers under the tax adjustment policy evaluated as of year-end 2001, by interest rate assumption and cohort (in billions of dollars)
SOURCE: Author's calculations.

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.

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.

Chart 10.
Aggregate OASI lifetime net transfers as a percent of aggregate OASI lifetime taxable earnings under the award adjustment policy, by interest rate assumption and cohort
SOURCE: Author's calculations.
Chart 11.
Aggregate OASI lifetime net transfers as a percent of aggregate OASI lifetime taxable earnings under the tax adjustment policy, by interest rate assumption and cohort
SOURCE: Author's calculations.

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."

Chart 12.
OASI real internal rates of return projected under present law as established in the present analysis; Anderson, Yamagata, and Tuljapurkar [AYT] (2001); and Goss (2001), expressed as percents, by birth cohort
SOURCE: Anderson, Yamagata, and Tuljapurkar (2001), Goss (2001), and author's calculations. The legend notification is clarified in the text.

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.

Chart 13.
OASI real internal rates of return projected under present law in the present analysis and Leimer (1994), expressed as percents, by birth cohort
SOURCE: Leimer (1994) and author's calculations.

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.

Chart 14.
OASI real internal rates of return projected under the balanced budget award policy in the present analysis and Leimer (1994), expressed as percents, by birth cohort
SOURCE: Leimer (1994) and author's calculations.
Chart 15.
OASI real interanl rates of return projected under the balanced budget tax policy in the present analysis and Leimer (1994), expressed as percents, by birth cohort
SOURCE: Leimer (1994) and author's calculations.

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.

Table A–1 OASI money's worth and redistributional measures (including unfunded benefits) under present law, by birth cohort
Birth
cohort
Real
internal
rate of
return
(percent)
member evaluated as of the initial cohort
year in constant (2001) dollars
evaluated as of year-end 2001
in billions of dollars
as a percent of
Interest rate assumption Interest rate assumption Interest rate assumption Interest rate assumption
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Pre–1901 18.367 12.037 6.093 12.037 3.207 31,365 6,478 36,760 2,165 1,637.203 3,912.972 4,313.035 13,676.469 34.97 13.39 35.27 5.12
1901 10.868 8.065 3.718 7.688 2.186 63,959 8,809 70,672 2,473 130.104 207.357 323.140 608.789 28.47 8.57 26.75 3.05
1902 10.481 7.683 3.546 7.262 2.168 71,461 9,477 78,181 2,711 143.414 220.098 352.677 658.360 27.81 8.28 25.84 3.07
1903 10.329 7.518 3.517 7.037 2.244 71,974 9,286 77,732 2,757 150.715 225.014 365.871 698.657 28.30 8.50 25.91 3.36
1904 9.881 7.074 3.323 6.552 2.163 73,349 9,106 78,018 2,690 157.567 226.369 376.721 699.208 27.19 8.04 24.52 3.19
1905 9.444 6.733 3.150 6.170 2.064 76,601 9,167 80,121 2,644 167.332 231.728 393.407 698.935 26.21 7.54 23.26 2.94
1906 9.061 6.392 3.001 5.784 1.985 77,991 8,989 79,971 2,540 173.566 231.504 400.043 683.963 25.36 7.15 22.08 2.76
1907 8.950 6.296 2.997 5.610 2.030 84,950 9,594 85,292 2,750 185.763 242.778 419.234 727.784 25.90 7.41 22.05 2.97
1908 8.583 5.906 2.840 5.185 1.935 86,906 9,461 85,196 2,628 193.056 243.223 425.403 706.590 24.78 7.01 20.62 2.75
1909 8.170 5.641 2.695 4.857 1.807 85,464 8,919 81,453 2,313 196.610 237.439 421.196 643.861 23.86 6.52 19.31 2.40
1910 7.918 5.471 2.622 4.612 1.714 87,207 8,810 80,531 2,101 203.609 238.030 422.630 593.524 23.58 6.35 18.50 2.15
1911 7.827 5.396 2.626 4.436 1.718 90,647 8,974 80,737 2,077 211.908 242.761 424.247 587.565 24.23 6.65 18.31 2.25
1912 7.447 5.102 2.485 4.077 1.574 96,353 9,113 82,184 1,835 223.759 244.892 428.995 515.688 23.14 6.19 16.74 1.83
1913 7.319 5.039 2.474 3.906 1.508 99,764 9,222 81,382 1,630 233.270 249.526 427.725 461.109 23.57 6.34 16.30 1.67
1914 6.948 4.718 2.326 3.531 1.357 101,417 8,908 78,101 1,213 242.292 246.283 419.411 350.614 22.30 5.86 14.55 1.20
1915 6.820 4.660 2.309 3.365 1.288 100,249 8,595 73,098 945 246.675 244.736 404.299 281.400 22.58 5.93 13.94 1.00
1916 6.650 4.535 2.263 3.147 1.210 105,892 8,797 72,334 716 252.141 242.387 387.148 206.414 22.48 5.92 12.99 0.75
1917 6.333 4.237 2.127 2.831 1.082 96,989 7,647 61,573 267 243.594 222.256 347.606 81.261 21.10 5.43 11.34 0.30
1918 5.912 3.919 1.958 2.497 0.927 96,059 7,010 55,225 -256 242.391 204.685 313.232 -78.107 19.35 4.70 9.41 -0.27
1919 5.578 3.608 1.827 2.196 0.835 88,188 5,988 45,165 -554 223.952 175.974 257.809 -170.316 17.88 4.27 7.75 -0.66
1920 5.378 3.492 1.771 2.027 0.754 93,299 6,018 42,712 -881 237.471 177.265 244.361 -271.293 17.52 4.11 6.80 -1.02
1921 5.098 3.295 1.677 1.834 0.673 95,665 5,730 38,368 -1,245 243.133 168.538 219.185 -382.817 16.53 3.73 5.64 -1.40
1922 4.949 3.225 1.643 1.722 0.619 93,622 5,350 33,189 -1,404 237.395 156.975 189.167 -430.817 16.43 3.64 4.97 -1.68
1923 4.748 3.114 1.589 1.602 0.565 94,704 5,094 29,216 -1,626 236.927 147.486 164.291 -492.440 15.94 3.44 4.22 -2.00
1924 4.554 3.004 1.534 1.494 0.519 98,910 4,976 26,144 -1,899 241.876 140.816 143.705 -562.013 15.43 3.20 3.52 -2.28
1925 4.453 2.964 1.517 1.427 0.490 99,944 4,850 23,018 -1,982 241.940 135.861 125.249 -580.543 15.47 3.18 3.10 -2.51
1926 4.249 2.853 1.460 1.331 0.447 98,621 4,411 18,445 -2,153 235.838 122.065 99.144 -622.990 14.89 2.90 2.44 -2.82
1927 4.114 2.776 1.426 1.259 0.419 103,283 4,348 15,545 -2,342 239.855 116.858 81.143 -658.247 14.63 2.78 1.95 -3.11
1928 3.910 2.664 1.368 1.173 0.387 102,655 3,894 10,862 -2,499 231.153 101.469 54.976 -680.970 13.99 2.48 1.33 -3.42
1929 3.735 2.566 1.321 1.097 0.360 100,946 3,454 6,267 -2,570 221.021 87.513 30.841 -680.943 13.51 2.25 0.76 -3.80
1930 3.627 2.501 1.294 1.049 0.344 103,705 3,304 3,321 -2,670 223.263 82.312 16.072 -695.571 13.25 2.14 0.39 -4.12
1931 3.546 2.474 1.279 1.012 0.330 101,916 3,064 772 -2,593 219.617 76.413 3.742 -676.321 13.29 2.10 0.09 -4.43
1932 3.476 2.442 1.264 0.980 0.318 100,466 2,856 -1,310 -2,537 220.560 72.564 -6.462 -673.988 13.24 2.04 -0.16 -4.68
1933 3.259 2.332 1.205 0.914 0.296 94,529 2,201 -5,715 -2,553 208.711 56.248 -28.365 -682.229 12.42 1.62 -0.72 -5.02
1934 3.228 2.329 1.203 0.898 0.295 97,235 2,211 -6,856 -2,527 217.958 57.341 -34.544 -685.424 12.59 1.65 -0.87 -5.16
1935 3.068 2.246 1.162 0.851 0.285 95,654 1,806 -10,317 -2,568 220.733 48.238 -53.512 -717.143 11.98 1.34 -1.29 -5.40
1936 2.995 2.218 1.150 0.826 0.284 96,211 1,682 -12,201 -2,533 224.664 45.446 -64.041 -715.951 11.88 1.27 -1.52 -5.57
1937 3.127 2.314 1.205 0.850 0.295 103,510 2,242 -10,262 -2,373 251.299 62.990 -56.000 -697.310 13.07 1.78 -1.33 -5.62
1938 2.966 2.229 1.165 0.806 0.284 105,471 1,774 -14,962 -3,395 258.062 54.569 -78.136 -745.349 12.38 1.46 -1.75 -5.85
1939 2.946 2.233 1.172 0.797 0.283 108,138 2,082 -16,035 -3,323 266.743 57.262 -82.060 -735.035 12.60 1.55 -1.85 -5.97
1940 2.882 2.204 1.165 0.778 0.279 111,409 2,255 -18,384 -3,012 277.107 56.972 -93.547 -751.622 12.47 1.52 -2.05 -6.13
1941 2.837 2.190 1.163 0.765 0.274 110,124 2,535 -17,739 -2,343 291.573 58.910 -102.993 -772.605 12.46 1.53 -2.19 -6.28
1942 2.645 2.098 1.115 0.721 0.255 107,346 2,154 -20,575 -2,711 315.264 47.969 -141.609 -900.313 11.58 1.10 -2.64 -6.53
1943 2.653 2.110 1.132 0.720 0.254 111,133 2,803 -20,363 -3,240 337.248 56.436 -146.335 -911.186 11.84 1.27 -2.67 -6.62
1944 2.745 2.158 1.174 0.739 0.260 118,614 3,737 -18,808 -3,641 343.021 70.932 -128.963 -832.063 12.53 1.71 -2.52 -6.65
1945 2.717 2.144 1.178 0.732 0.256 123,276 3,745 -19,767 -4,912 346.853 72.388 -132.121 -818.324 12.49 1.78 -2.61 -6.76
1946 2.668 2.125 1.175 0.720 0.243 124,077 3,418 -17,811 -3,810 416.281 84.820 -164.438 -972.930 12.39 1.77 -2.75 -6.94
1947 2.621 2.105 1.172 0.710 0.235 124,877 3,506 -17,216 -3,657 470.790 93.940 -191.099 -1,082.200 12.26 1.76 -2.87 -7.08
1948 2.681 2.139 1.204 0.724 0.236 131,898 4,329 -16,264 -3,626 474.929 106.022 -172.228 -997.688 12.76 2.11 -2.76 -7.12
1949 2.743 2.173 1.235 0.739 0.239 139,635 4,960 -15,738 -4,232 499.661 121.892 -160.550 -956.532 13.28 2.46 -2.63 -7.16
1950 2.759 2.185 1.252 0.745 0.238 140,088 5,202 -14,257 -4,951 521.045 131.430 -156.765 -934.246 13.51 2.66 -2.59 -7.22
1951 2.711 2.163 1.245 0.737 0.235 141,470 6,659 -14,337 -5,711 541.900 132.889 -167.058 -947.420 13.32 2.61 -2.70 -7.31
1952 2.709 2.163 1.254 0.740 0.237 145,600 7,338 -14,300 -6,476 571.007 142.010 -168.329 -937.441 13.41 2.73 -2.68 -7.35
1953 2.745 2.183 1.277 0.753 0.245 149,506 8,274 -13,439 -5,947 600.837 156.315 -159.425 -896.490 13.72 3.00 -2.57 -7.34
1954 2.727 2.176 1.280 0.754 0.248 153,273 8,363 -13,738 -8,797 629.674 163.515 -162.041 -883.842 13.70 3.06 -2.57 -7.36
1955 2.686 2.151 1.275 0.752 0.254 152,518 9,588 -13,836 -10,825 636.546 162.019 -162.835 -842.972 13.45 3.02 -2.61 -7.36
1956 2.666 2.138 1.277 0.756 0.267 152,684 10,065 -13,226 -10,302 653.526 165.564 -160.348 -794.148 13.34 3.06 -2.59 -7.30
1957 2.643 2.120 1.277 0.761 0.286 152,467 10,297 -12,561 -8,084 663.144 166.888 -155.544 -731.175 13.17 3.08 -2.55 -7.17
1958 2.627 2.111 1.281 0.767 0.299 153,648 10,138 -11,986 -10,367 667.117 167.523 -147.070 -664.453 13.11 3.13 -2.50 -7.10
1959 2.580 2.086 1.273 0.768 0.312 154,490 10,953 -11,954 -10,570 667.137 163.217 -144.339 -610.827 12.83 3.06 -2.51 -7.03
1960 2.499 2.048 1.253 0.760 0.323 151,590 10,235 -12,252 -9,628 659.903 152.490 -147.509 -566.522 12.38 2.85 -2.61 -7.00
1961 2.528 2.062 1.272 0.779 0.347 155,207 10,913 -11,096 -10,636 673.974 161.220 -130.576 -495.272 12.59 3.07 -2.41 -6.82
1962 2.525 2.063 1.279 0.789 0.362 159,313 11,615 -10,553 -8,695 678.355 162.986 -119.882 -440.298 12.63 3.16 -2.31 -6.73
1963 2.549 2.074 1.296 0.808 0.383 162,508 12,305 -9,395 -9,174 680.694 167.682 -103.699 -378.297 12.79 3.37 -2.12 -6.56
1964 2.534 2.071 1.299 0.814 0.399 166,497 12,978 -9,119 -9,614 676.319 165.594 -95.829 -333.969 12.77 3.41 -2.05 -6.43
1965 2.541 2.074 1.310 0.827 0.422 170,944 13,997 -8,409 -9,424 657.964 162.619 -82.714 -281.168 12.82 3.53 -1.91 -6.22
1966 2.547 2.078 1.319 0.839 0.443 174,956 17,398 -7,689 -7,308 645.481 160.635 -72.423 -240.139 12.87 3.65 -1.79 -6.01
1967 2.550 2.075 1.327 0.849 0.461 180,569 18,461 -7,186 -7,920 647.141 161.603 -65.320 -210.127 12.84 3.73 -1.68 -5.83
1968 2.559 2.079 1.337 0.859 0.473 182,780 20,444 -6,461 -7,501 655.557 164.653 -59.228 -187.793 12.89 3.85 -1.57 -5.70
1969 2.541 2.074 1.337 0.859 0.476 184,081 20,532 -6,189 -5,989 676.797 167.933 -59.137 -178.229 12.82 3.85 -1.57 -5.68
1970 2.514 2.062 1.333 0.857 0.480 184,851 19,833 -6,109 -5,443 694.725 169.434 -59.974 -167.941 12.67 3.81 -1.59 -5.63
1971 2.527 2.071 1.345 0.864 0.481 189,533 20,328 -5,788 -5,576 687.464 168.625 -53.910 -150.141 12.78 3.94 -1.51 -5.62
1972 2.545 2.080 1.358 0.872 0.480 196,059 23,241 -5,461 -5,992 661.889 163.651 -46.492 -130.516 12.90 4.09 -1.42 -5.62
1973 2.529 2.075 1.359 0.870 0.470 200,555 25,083 -5,341 -4,536 650.829 159.162 -45.008 -121.088 12.83 4.10 -1.44 -5.72
1974 2.521 2.074 1.362 0.870 0.461 202,700 25,418 -4,962 -2,835 660.016 160.212 -44.345 -115.863 12.83 4.14 -1.44 -5.82
1975 2.513 2.072 1.365 0.869 0.451 205,094 24,891 -4,866 -3,472 669.830 161.331 -43.800 -111.012 12.80 4.17 -1.45 -5.92
1976 2.502 2.069 1.366 0.867 0.440 206,315 26,245 -4,921 -3,930 685.851 163.501 -44.277 -108.234 12.76 4.19 -1.48 -6.04
1977 2.495 2.068 1.368 0.866 0.431 207,855 27,168 -4,866 -3,264 711.182 168.038 -44.992 -106.440 12.75 4.22 -1.49 -6.13
1978 2.501 2.073 1.376 0.868 0.417 211,718 28,392 -4,623 -3,076 735.687 173.411 -44.164 -104.230 12.82 4.30 -1.47 -6.28
1979 2.501 2.075 1.380 0.867 0.401 213,732 29,267 -4,294 -3,107 772.232 180.727 -44.990 -104.732 12.85 4.35 -1.48 -6.46
1980 2.480 2.066 1.376 0.862 0.385 220,333 29,180 -4,342 -3,655 812.891 186.890 -48.113 -106.766 12.73 4.31 -1.54 -6.63
1981 2.491 2.073 1.383 0.864 0.372 222,695 29,584 -4,180 -3,055 833.015 190.946 -46.538 -103.656 12.83 4.40 -1.51 -6.77
1982 2.501 2.080 1.390 0.867 0.361 226,192 30,397 -4,284 -3,425 853.854 194.931 -45.103 -100.351 12.92 4.48 -1.48 -6.89
1983 2.519 2.090 1.400 0.871 0.357 230,199 31,703 -4,311 -3,822 862.212 196.603 -42.172 -94.148 13.05 4.59 -1.43 -6.94
1984 2.536 2.099 1.408 0.876 0.357 233,664 34,184 -4,360 -3,668 882.359 200.800 -39.984 -89.089 13.17 4.69 -1.38 -6.94
1985 2.546 2.105 1.415 0.879 0.356 236,196 35,466 -4,460 -4,385 909.691 205.925 -38.878 -85.293 13.24 4.77 -1.35 -6.95
1986 2.557 2.113 1.422 0.881 0.352 240,188 37,976 -4,712 -4,867 929.692 209.309 -37.493 -81.219 13.35 4.85 -1.33 -6.99
1987 2.567 2.120 1.428 0.883 0.350 243,040 38,869 -4,761 -4,627 953.317 213.298 -36.400 -77.632 13.45 4.93 -1.30 -7.02
1988 2.578 2.128 1.435 0.886 0.349 245,655 39,857 -4,764 -4,859 985.860 219.302 -35.440 -74.576 13.54 5.01 -1.27 -7.03
1989 2.584 2.133 1.439 0.887 0.347 247,283 40,769 -4,810 -5,745 1,028.081 226.788 -35.404 -72.691 13.61 5.06 -1.26 -7.05
1990 2.593 2.140 1.445 0.889 0.346 252,579 41,032 -4,791 -4,981 1,065.362 233.370 -34.729 -70.069 13.70 5.13 -1.24 -7.06
1991 2.602 2.147 1.451 0.891 0.344 257,024 41,326 -4,887 -5,982 1,083.693 235.694 -33.453 -66.404 13.80 5.20 -1.22 -7.09
1992 2.617 2.157 1.460 0.895 0.345 262,509 42,682 -4,893 -5,914 1,093.268 236.636 -31.312 -61.974 13.93 5.30 -1.18 -7.08
1993 2.632 2.167 1.468 0.898 0.345 268,413 43,975 -4,898 -5,998 1,100.319 236.925 -29.266 -57.799 14.06 5.40 -1.14 -7.08
1994 2.645 2.176 1.475 0.901 0.344 274,113 45,932 -4,912 -5,605 1,110.573 237.665 -27.568 -54.100 14.18 5.49 -1.10 -7.08
1995 2.652 2.182 1.481 0.903 0.345 279,197 47,429 -4,989 -7,115 1,119.283 237.583 -26.331 -50.695 14.25 5.55 -1.08 -7.08
1996 2.666 2.192 1.489 0.907 0.346 284,863 49,023 -4,920 -8,003 1,137.774 240.083 -24.826 -47.698 14.38 5.65 -1.04 -7.07
1997 2.677 2.199 1.495 0.909 0.347 289,710 52,046 -4,940 -9,894 1,160.961 243.312 -23.644 -45.115 14.48 5.73 -1.01 -7.06
1998 2.686 2.205 1.501 0.912 0.348 293,872 55,253 -4,983 -11,792 1,183.926 246.162 -22.712 -42.721 14.56 5.79 -0.99 -7.05
1999 2.698 2.213 1.508 0.915 0.349 298,644 57,756 -4,903 -13,089 1,204.470 248.743 -21.470 -40.270 14.66 5.88 -0.95 -7.04
2000 2.701 2.216 1.511 0.916 0.350 301,163 59,460 -4,899 -10,818 1,255.330 256.734 -21.446 -39.129 14.70 5.92 -0.94 -7.03
2001 2.713 2.224 1.518 0.919 0.351 306,570 62,249 -4,868 -8,858 1,274.224 258.732 -20.234 -36.818 14.80 6.00 -0.91 -7.02
2002 2.726 2.232 1.525 0.922 0.353 312,258 63,480 -4,799 -9,136 1,295.008 261.229 -18.930 -34.653 14.91 6.09 -0.87 -7.00
2003 2.738 2.240 1.532 0.925 0.354 317,768 66,170 -4,692 -9,307 1,316.223 263.581 -17.795 -32.647 15.01 6.17 -0.83 -6.99
2004 2.750 2.248 1.539 0.929 0.356 323,380 68,448 -4,557 -9,460 1,339.611 266.352 -16.668 -30.790 15.11 6.25 -0.80 -6.97
2005 2.761 2.255 1.546 0.932 0.357 328,861 70,670 -4,431 -9,597 1,364.303 269.156 -15.682 -29.070 15.21 6.33 -0.76 -6.96
2006 2.769 2.261 1.551 0.934 0.359 333,867 72,676 -4,346 -9,729 1,388.975 271.633 -14.916 -27.490 15.28 6.39 -0.74 -6.94
2007 2.781 2.269 1.558 0.938 0.360 339,617 74,890 -4,173 -9,855 1,418.446 275.335 -13.907 -26.007 15.39 6.48 -0.70 -6.93
2008 2.792 2.276 1.564 0.940 0.362 345,077 77,000 -4,036 -9,981 1,448.234 278.793 -13.073 -24.633 15.48 6.55 -0.67 -6.91
2009 2.800 2.281 1.569 0.943 0.363 350,238 78,857 -3,934 -10,103 1,477.762 281.897 -12.400 -23.348 15.56 6.61 -0.64 -6.90
2010 2.810 2.288 1.575 0.945 0.365 355,752 80,797 -3,794 -10,217 1,508.907 285.343 -11.642 -22.126 15.64 6.68 -0.61 -6.88
2011 2.818 2.294 1.580 0.948 0.366 361,277 82,677 -3,670 -10,332 1,539.684 288.515 -10.959 -20.968 15.72 6.74 -0.58 -6.87
2012 2.828 2.301 1.586 0.951 0.367 367,076 84,637 -3,519 -10,444 1,570.982 291.769 -10.226 -19.863 15.81 6.81 -0.55 -6.86
2013 2.837 2.307 1.591 0.953 0.368 372,922 86,540 -3,384 -10,555 1,601.612 294.687 -9.565 -18.809 15.90 6.88 -0.53 -6.85
2014 2.846 2.314 1.596 0.956 0.369 378,969 88,478 -3,233 -10,664 1,632.292 297.555 -8.888 -17.806 15.99 6.94 -0.50 -6.84
2015 2.855 2.320 1.601 0.958 0.370 385,052 90,364 -3,089 -10,769 1,662.351 300.149 -8.257 -16.850 16.07 7.00 -0.47 -6.83
2016 2.864 2.327 1.607 0.961 0.371 391,363 92,289 -2,927 -10,869 1,692.787 302.743 -7.609 -15.937 16.16 7.07 -0.44 -6.82
2017 2.872 2.333 1.612 0.963 0.372 397,598 94,172 -2,786 -10,970 1,722.270 304.973 -7.038 -15.073 16.24 7.13 -0.41 -6.81
2018 2.881 2.340 1.617 0.966 0.373 404,166 96,148 -2,624 -11,074 1,752.665 307.327 -6.443 -14.256 16.33 7.19 -0.39 -6.80
2019 2.889 2.346 1.622 0.968 0.373 410,709 98,111 -2,479 -11,182 1,782.360 309.382 -5.914 -13.484 16.42 7.25 -0.36 -6.79
2020 2.896 2.352 1.626 0.970 0.373 417,259 100,030 -2,352 -11,299 1,811.317 311.143 -5.450 -12.757 16.49 7.30 -0.34 -6.79
2021 2.903 2.358 1.630 0.972 0.373 423,893 101,959 -2,227 -11,418 1,839.705 312.698 -5.009 -12.065 16.57 7.35 -0.32 -6.79
2022 2.910 2.364 1.634 0.974 0.373 430,657 103,891 -2,101 -11,541 1,867.678 314.091 -4.584 -11.406 16.65 7.40 -0.30 -6.79
2023 2.916 2.370 1.638 0.975 0.373 437,524 105,848 -1,976 -11,668 1,895.138 315.301 -4.181 -10.781 16.72 7.45 -0.28 -6.79
2024 2.922 2.375 1.642 0.977 0.373 444,498 107,842 -1,849 -11,796 1,922.293 316.379 -3.792 -10.186 16.80 7.50 -0.25 -6.79
2025 2.929 2.381 1.646 0.979 0.373 451,559 109,850 -1,727 -11,930 1,949.558 317.374 -3.433 -9.627 16.87 7.55 -0.24 -6.80
2026 2.935 2.386 1.650 0.981 0.373 458,708 111,898 -1,598 -12,063 1,976.966 318.329 -3.079 -9.095 16.94 7.59 -0.22 -6.80
2027 2.941 2.391 1.654 0.983 0.373 465,597 113,886 -1,473 -12,189 2,010.823 320.213 -2.761 -8.620 17.01 7.64 -0.20 -6.79
2028 2.946 2.396 1.657 0.984 0.373 472,548 115,912 -1,344 -12,314 2,045.293 322.101 -2.451 -8.170 17.08 7.68 -0.18 -6.79
2029 2.952 2.402 1.661 0.986 0.373 479,561 117,979 -1,222 -12,445 2,080.459 323.981 -2.169 -7.746 17.15 7.72 -0.16 -6.79
2030 2.957 2.406 1.664 0.987 0.373 486,612 120,066 -1,106 -12,580 2,116.261 325.844 -1.910 -7.348 17.21 7.76 -0.14 -6.80
2031 2.962 2.411 1.667 0.989 0.373 493,738 122,192 -986 -12,715 2,152.850 327.734 -1.658 -6.970 17.28 7.80 -0.13 -6.80
2032 2.967 2.416 1.670 0.990 0.373 500,953 124,363 -860 -12,850 2,190.229 329.660 -1.408 -6.611 17.34 7.84 -0.11 -6.80
2033 2.973 2.421 1.674 0.992 0.373 508,276 126,582 -726 -12,982 2,228.389 331.623 -1.156 -6.269 17.41 7.88 -0.09 -6.80
2034 2.978 2.426 1.677 0.993 0.373 515,668 128,845 -597 -13,121 2,267.128 333.554 -0.927 -5.947 17.48 7.92 -0.07 -6.80
2035 2.983 2.431 1.680 0.995 0.373 523,150 131,133 -471 -13,263 2,306.496 335.472 -0.711 -5.643 17.54 7.96 -0.06 -6.80
2036 2.988 2.436 1.683 0.996 0.373 530,743 133,459 -338 -13,405 2,346.484 337.394 -0.497 -5.353 17.61 8.00 -0.04 -6.80
2037 2.993 2.441 1.686 0.998 0.373 538,448 135,822 -199 -13,548 2,387.019 339.305 -0.286 -5.078 17.67 8.04 -0.02 -6.80
2038 2.998 2.446 1.690 0.999 0.373 546,283 138,228 -55 -13,691 2,428.094 341.205 -0.077 -4.816 17.74 8.07 -0.01 -6.80
2039 3.003 2.451 1.693 1.001 0.373 554,241 140,673 94 -13,835 2,469.572 343.072 0.128 -4.567 17.80 8.11 0.01 -6.80
2040 3.009 2.456 1.696 1.003 0.373 562,332 143,146 247 -13,981 2,511.411 344.896 0.326 -4.330 17.87 8.15 0.03 -6.80
2041 3.013 2.461 1.699 1.004 0.373 570,521 145,624 397 -14,132 2,553.381 346.631 0.509 -4.105 17.94 8.19 0.05 -6.80
2042 3.019 2.466 1.702 1.006 0.373 578,826 148,126 554 -14,283 2,595.504 348.307 0.692 -3.891 18.00 8.23 0.06 -6.80
2043 3.024 2.470 1.706 1.007 0.373 587,231 150,642 720 -14,431 2,637.666 349.909 0.875 -3.686 18.07 8.27 0.08 -6.80
2044 3.029 2.475 1.709 1.009 0.373 595,734 153,175 885 -14,583 2,679.894 351.423 1.045 -3.492 18.14 8.31 0.10 -6.80
2045 3.034 2.480 1.712 1.010 0.373 604,364 155,728 1,061 -14,733 2,722.380 352.900 1.218 -3.307 18.20 8.35 0.12 -6.80
2046 3.039 2.485 1.715 1.012 0.373 613,110 158,294 1,233 -14,888 2,765.168 354.317 1.376 -3.132 18.27 8.38 0.13 -6.80
2047 3.045 2.490 1.718 1.013 0.373 621,980 160,884 1,408 -15,046 2,808.362 355.700 1.527 -2.966 18.33 8.42 0.15 -6.80
2048 3.049 2.495 1.721 1.015 0.373 630,961 163,494 1,581 -15,207 2,851.984 357.045 1.668 -2.809 18.40 8.46 0.17 -6.80
2049 3.054 2.500 1.724 1.017 0.373 640,082 166,143 1,765 -15,366 2,896.226 358.396 1.808 -2.659 18.46 8.50 0.19 -6.80
2050 3.059 2.505 1.727 1.018 0.373 649,214 168,781 1,944 -15,529 2,940.571 359.662 1.936 -2.518 18.53 8.53 0.20 -6.80
2051 3.064 2.509 1.730 1.020 0.373 658,526 171,459 2,131 -15,692 2,985.843 360.970 2.063 -2.384 18.59 8.57 0.22 -6.80
2052 3.069 2.514 1.733 1.021 0.374 667,985 174,180 2,326 -15,855 3,031.981 362.307 2.188 -2.258 18.66 8.61 0.24 -6.79
2053 3.074 2.519 1.736 1.023 0.373 677,566 176,928 2,515 -16,025 3,078.930 363.639 2.300 -2.138 18.72 8.65 0.25 -6.79
2054 3.079 2.524 1.739 1.024 0.374 687,304 179,725 2,718 -16,192 3,126.923 365.029 2.415 -2.025 18.79 8.68 0.27 -6.79
2055 3.084 2.528 1.742 1.026 0.374 697,174 182,562 2,926 -16,360 3,175.919 366.454 2.528 -1.917 18.85 8.72 0.29 -6.79
2056 3.089 2.533 1.746 1.027 0.374 707,183 185,432 3,138 -16,530 3,225.994 367.917 2.636 -1.816 18.92 8.76 0.31 -6.79
2057 3.094 2.538 1.749 1.029 0.374 717,340 188,341 3,351 -16,703 3,277.229 369.417 2.737 -1.720 18.98 8.80 0.32 -6.79
2058 3.099 2.543 1.752 1.030 0.374 727,684 191,301 3,563 -16,881 3,329.836 370.975 2.830 -1.630 19.04 8.83 0.34 -6.79
2059 3.103 2.547 1.754 1.032 0.374 738,191 194,299 3,770 -17,067 3,383.696 372.563 2.912 -1.545 19.11 8.87 0.36 -6.79
2060 3.107 2.552 1.757 1.033 0.374 748,834 197,329 3,977 -17,256 3,438.653 374.174 2.988 -1.465 19.17 8.90 0.37 -6.79
2061 3.112 2.556 1.760 1.034 0.374 759,611 200,390 4,185 -17,449 3,494.659 375.800 3.058 -1.389 19.23 8.94 0.39 -6.79
2062 3.116 2.561 1.763 1.036 0.374 770,557 203,507 4,406 -17,639 3,551.822 377.474 3.132 -1.317 19.29 8.97 0.40 -6.79
2063 3.121 2.565 1.766 1.037 0.374 781,664 206,661 4,633 -17,831 3,610.035 379.167 3.204 -1.249 19.35 9.01 0.42 -6.79
2064 3.125 2.570 1.769 1.039 0.374 792,931 209,859 4,869 -18,022 3,669.240 380.874 3.275 -1.183 19.41 9.04 0.44 -6.78
2065 3.130 2.574 1.772 1.040 0.375 804,384 213,100 5,109 -18,215 3,729.481 382.594 3.343 -1.122 19.47 9.08 0.45 -6.78
2066 3.134 2.579 1.774 1.042 0.375 815,965 216,373 5,361 -18,406 3,790.431 384.302 3.413 -1.063 19.53 9.11 0.47 -6.78
2067 3.139 2.583 1.777 1.043 0.375 827,650 219,677 5,620 -18,596 3,851.917 385.975 3.480 -1.007 19.60 9.15 0.49 -6.77
2068 3.144 2.588 1.780 1.045 0.376 839,410 223,001 5,887 -18,785 3,913.757 387.593 3.545 -0.954 19.66 9.19 0.51 -6.77
2069 3.149 2.592 1.783 1.046 0.376 851,274 226,349 6,161 -18,972 3,976.051 389.166 3.609 -0.904 19.72 9.22 0.52 -6.76
2070 3.154 2.597 1.786 1.048 0.377 863,307 229,735 6,442 -19,161 4,039.068 390.720 3.669 -0.856 19.78 9.26 0.54 -6.76
2071 3.159 2.601 1.789 1.050 0.377 875,520 233,170 6,729 -19,351 4,102.869 392.258 3.727 -0.810 19.84 9.30 0.56 -6.75
2072 3.164 2.606 1.792 1.051 0.378 887,898 236,643 7,021 -19,542 4,167.363 393.768 3.782 -0.767 19.91 9.33 0.58 -6.75
2073 3.169 2.610 1.795 1.053 0.379 900,454 240,160 7,317 -19,736 4,232.628 395.257 3.832 -0.726 19.97 9.37 0.59 -6.74
2074 3.174 2.615 1.798 1.054 0.379 913,196 243,721 7,618 -19,933 4,298.741 396.730 3.879 -0.688 20.03 9.40 0.61 -6.73
2075 3.179 2.619 1.801 1.056 0.380 926,074 247,313 7,923 -20,130 4,365.490 398.169 3.923 -0.651 20.09 9.44 0.63 -6.73
2076 3.183 2.624 1.804 1.057 0.380 939,141 250,953 8,234 -20,330 4,433.153 399.599 3.963 -0.616 20.15 9.47 0.65 -6.72
2077 3.188 2.628 1.807 1.059 0.381 952,533 254,680 8,552 -20,534 4,502.439 401.083 4.002 -0.583 20.21 9.51 0.67 -6.72
2078 3.193 2.633 1.809 1.061 0.382 966,284 258,530 8,877 -20,745 4,573.561 402.635 4.038 -0.552 20.27 9.55 0.68 -6.71
2079 3.198 2.637 1.812 1.062 0.382 979,333 262,203 9,207 -20,937 4,641.529 403.830 4.072 -0.522 20.33 9.58 0.70 -6.70
2080 3.203 2.642 1.815 1.064 0.383 993,320 266,129 9,548 -21,147 4,708.479 404.850 4.100 -0.494 20.40 9.62 0.72 -6.70
2081 3.207 2.646 1.818 1.065 0.383 1,007,255 270,035 9,885 -21,358 4,781.038 406.250 4.127 -0.468 20.46 9.65 0.74 -6.69
2082 3.212 2.650 1.821 1.067 0.384 1,021,363 273,990 10,226 -21,571 4,854.861 407.663 4.150 -0.443 20.52 9.69 0.75 -6.68
2083 3.217 2.655 1.824 1.068 0.385 1,035,642 277,993 10,572 -21,786 4,929.965 409.089 4.172 -0.419 20.58 9.72 0.77 -6.68
2084 3.221 2.659 1.827 1.070 0.385 1,050,094 282,044 10,922 -22,004 5,006.378 410.527 4.191 -0.397 20.64 9.76 0.79 -6.67
2085 3.226 2.663 1.829 1.071 0.386 1,064,720 286,144 11,277 -22,224 5,084.097 411.976 4.208 -0.376 20.70 9.79 0.80 -6.67
2086 3.230 2.668 1.832 1.073 0.386 1,079,521 290,292 11,636 -22,447 5,163.118 413.433 4.222 -0.356 20.75 9.83 0.82 -6.66
2087 3.235 2.672 1.835 1.074 0.387 1,094,511 294,494 12,001 -22,671 5,243.488 414.902 4.235 -0.337 20.81 9.86 0.84 -6.66
2088 3.239 2.676 1.838 1.076 0.387 1,109,694 298,750 12,372 -22,899 5,325.193 416.379 4.246 -0.319 20.87 9.89 0.85 -6.65
2089 3.243 2.680 1.840 1.077 0.388 1,125,070 303,061 12,748 -23,129 5,408.208 417.861 4.255 -0.302 20.93 9.93 0.87 -6.65
2090 3.248 2.685 1.843 1.079 0.388 1,140,645 307,429 13,131 -23,361 5,492.515 419.346 4.262 -0.286 20.99 9.96 0.89 -6.64
2091 3.252 2.689 1.846 1.080 0.389 1,156,431 311,856 13,519 -23,596 5,578.144 420.834 4.268 -0.271 21.05 10.00 0.90 -6.63
2092 3.256 2.693 1.848 1.081 0.389 1,172,412 316,338 13,913 -23,834 5,664.974 422.313 4.271 -0.257 21.11 10.03 0.92 -6.63
2093 3.261 2.697 1.851 1.083 0.390 1,188,620 320,884 14,314 -24,074 5,753.116 423.793 4.274 -0.243 21.16 10.06 0.94 -6.62
2094 3.265 2.702 1.854 1.084 0.390 1,205,040 325,491 14,721 -24,318 5,842.459 425.262 4.275 -0.230 21.22 10.10 0.95 -6.62
2095 3.269 2.706 1.856 1.086 0.391 1,221,681 330,160 15,134 -24,564 5,933.002 426.721 4.274 -0.218 21.28 10.13 0.97 -6.61
2096 3.273 2.710 1.859 1.087 0.391 1,238,546 334,891 15,554 -24,813 6,024.704 428.163 4.271 -0.207 21.34 10.16 0.98 -6.61
2097 3.278 2.714 1.862 1.089 0.392 1,255,639 339,687 15,980 -25,065 6,117.546 429.589 4.267 -0.196 21.39 10.20 1.00 -6.60
2098 3.282 2.718 1.864 1.090 0.392 1,272,964 344,549 16,414 -25,319 6,211.512 430.996 4.262 -0.185 21.45 10.23 1.02 -6.60
2099 3.286 2.722 1.867 1.091 0.393 1,290,522 349,477 16,854 -25,577 6,306.629 432.384 4.255 -0.175 21.51 10.26 1.03 -6.59
2100 3.290 2.727 1.870 1.093 0.393 1,308,324 354,473 17,301 -25,838 6,402.966 433.758 4.247 -0.166 21.57 10.30 1.05 -6.59
SOURCE: Author's calculations.

## 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.

Table B–1 OASI money's worth and redistributional measures under the award adjustment policy, by birth cohort
Birth
cohort
Real
internal
rate of
return
(percent)
member evaluated as of the initial cohort
year in constant (2001) dollars
evaluated as of year-end 2001
in billions of dollars
as a percent of
Interest rate assumption Interest rate assumption Interest rate assumption Interest rate assumption
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Pre–1901 18.367 12.037 6.093 12.037 3.207 31,365 6,478 36,760 2,165 1,637.203 3,912.972 4,313.035 13,676.469 34.97 13.39 35.27 5.12
1901 10.868 8.065 3.718 7.688 2.186 63,959 8,809 70,672 2,473 130.104 207.357 323.140 608.789 28.47 8.57 26.75 3.05
1902 10.481 7.683 3.546 7.262 2.168 71,461 9,477 78,181 2,711 143.414 220.098 352.677 658.360 27.81 8.28 25.84 3.07
1903 10.329 7.518 3.517 7.037 2.244 71,974 9,286 77,732 2,757 150.715 225.014 365.871 698.657 28.30 8.50 25.91 3.36
1904 9.881 7.074 3.323 6.552 2.163 73,349 9,106 78,018 2,690 157.567 226.369 376.721 699.208 27.19 8.04 24.52 3.19
1905 9.444 6.733 3.150 6.170 2.064 76,601 9,167 80,121 2,644 167.332 231.728 393.407 698.935 26.21 7.54 23.26 2.94
1906 9.061 6.392 3.001 5.784 1.985 77,991 8,989 79,971 2,540 173.566 231.504 400.043 683.963 25.36 7.15 22.08 2.76
1907 8.950 6.296 2.997 5.610 2.030 84,950 9,594 85,292 2,750 185.763 242.778 419.234 727.784 25.90 7.41 22.05 2.97
1908 8.583 5.906 2.840 5.185 1.935 86,906 9,461 85,196 2,628 193.056 243.223 425.403 706.590 24.78 7.01 20.62 2.75
1909 8.170 5.641 2.695 4.857 1.807 85,464 8,919 81,453 2,313 196.610 237.439 421.196 643.861 23.86 6.52 19.31 2.40
1910 7.918 5.471 2.622 4.612 1.714 87,207 8,810 80,531 2,101 203.609 238.030 422.630 593.524 23.58 6.35 18.50 2.15
1911 7.827 5.396 2.626 4.436 1.718 90,647 8,974 80,737 2,077 211.908 242.761 424.247 587.565 24.23 6.65 18.31 2.25
1912 7.447 5.102 2.485 4.077 1.574 96,353 9,113 82,184 1,835 223.759 244.892 428.995 515.688 23.14 6.19 16.74 1.83
1913 7.319 5.039 2.474 3.906 1.508 99,764 9,222 81,382 1,630 233.270 249.526 427.725 461.109 23.57 6.34 16.30 1.67
1914 6.948 4.718 2.326 3.531 1.357 101,416 8,908 78,101 1,213 242.291 246.283 419.411 350.614 22.30 5.86 14.55 1.20
1915 6.820 4.660 2.309 3.365 1.288 100,249 8,595 73,098 945 246.675 244.736 404.298 281.400 22.58 5.93 13.94 1.00
1916 6.650 4.535 2.263 3.147 1.210 105,892 8,797 72,334 716 252.141 242.387 387.148 206.414 22.48 5.92 12.99 0.75
1917 6.333 4.237 2.127 2.831 1.082 96,988 7,647 61,573 267 243.594 222.256 347.606 81.261 21.10 5.43 11.34 0.30
1918 5.912 3.919 1.958 2.497 0.927 96,058 7,009 55,225 -256 242.391 204.684 313.232 -78.107 19.35 4.70 9.41 -0.27
1919 5.578 3.608 1.827 2.196 0.835 88,188 5,988 45,165 -554 223.951 175.974 257.809 -170.316 17.88 4.27 7.75 -0.66
1920 5.378 3.492 1.771 2.027 0.754 93,299 6,018 42,712 -881 237.470 177.264 244.360 -271.293 17.52 4.11 6.80 -1.02
1921 5.098 3.295 1.677 1.834 0.673 95,664 5,730 38,368 -1,245 243.131 168.536 219.184 -382.817 16.53 3.73 5.64 -1.40
1922 4.949 3.225 1.643 1.722 0.619 93,620 5,349 33,189 -1,404 237.391 156.973 189.166 -430.817 16.43 3.64 4.97 -1.68
1923 4.748 3.114 1.589 1.602 0.565 94,702 5,094 29,215 -1,626 236.922 147.483 164.289 -492.441 15.94 3.44 4.22 -2.00
1924 4.554 3.004 1.534 1.494 0.519 98,907 4,976 26,143 -1,899 241.870 140.812 143.702 -562.014 15.43 3.20 3.52 -2.28
1925 4.453 2.964 1.517 1.427 0.490 99,941 4,850 23,018 -1,982 241.931 135.855 125.245 -580.545 15.47 3.18 3.10 -2.51
1926 4.249 2.853 1.460 1.331 0.447 98,616 4,411 18,444 -2,153 235.826 122.057 99.138 -622.992 14.89 2.90 2.44 -2.82
1927 4.114 2.776 1.426 1.259 0.419 103,276 4,348 15,543 -2,342 239.840 116.848 81.136 -658.250 14.63 2.78 1.95 -3.11
1928 3.910 2.664 1.368 1.173 0.387 102,646 3,893 10,860 -2,499 231.132 101.455 54.966 -680.974 13.99 2.47 1.33 -3.42
1929 3.734 2.565 1.321 1.097 0.360 100,935 3,453 6,264 -2,570 220.996 87.496 30.829 -680.948 13.51 2.25 0.76 -3.80
1930 3.627 2.501 1.294 1.049 0.344 103,691 3,303 3,318 -2,670 223.231 82.290 16.057 -695.577 13.25 2.14 0.39 -4.12
1931 3.546 2.474 1.279 1.011 0.330 101,898 3,063 769 -2,593 219.578 76.388 3.724 -676.328 13.29 2.10 0.09 -4.43
1932 3.476 2.442 1.264 0.980 0.318 100,445 2,855 -1,314 -2,537 220.513 72.533 -6.483 -673.996 13.24 2.04 -0.16 -4.68
1933 3.259 2.332 1.204 0.914 0.296 94,504 2,200 -5,720 -2,553 208.656 56.212 -28.389 -682.238 12.42 1.62 -0.72 -5.02
1934 3.228 2.329 1.203 0.898 0.295 97,205 2,209 -6,862 -2,527 217.890 57.297 -34.574 -685.436 12.59 1.64 -0.87 -5.16
1935 3.068 2.246 1.162 0.851 0.285 95,619 1,804 -10,323 -2,568 220.653 48.187 -53.546 -717.157 11.97 1.34 -1.29 -5.40
1936 2.995 2.217 1.149 0.826 0.284 96,170 1,680 -12,209 -2,534 224.569 45.385 -64.081 -715.966 11.87 1.27 -1.53 -5.57
1937 3.127 2.313 1.204 0.850 0.295 103,462 2,239 -10,271 -2,373 251.183 62.916 -56.049 -697.328 13.06 1.77 -1.34 -5.62
1938 2.966 2.228 1.165 0.805 0.284 105,414 1,771 -14,973 -3,395 257.923 54.481 -78.193 -745.370 12.38 1.46 -1.75 -5.85
1939 2.946 2.232 1.172 0.797 0.283 108,072 2,079 -16,048 -3,323 266.580 57.161 -82.126 -735.059 12.59 1.55 -1.85 -5.97
1940 2.881 2.203 1.164 0.778 0.279 111,336 2,251 -18,399 -3,012 276.925 56.859 -93.620 -751.647 12.46 1.51 -2.05 -6.13
1941 2.836 2.189 1.163 0.765 0.273 110,043 2,529 -17,754 -2,343 291.359 58.778 -103.076 -772.634 12.46 1.53 -2.20 -6.28
1942 2.644 2.097 1.115 0.720 0.255 107,256 2,146 -20,590 -2,711 314.998 47.807 -141.712 -900.348 11.57 1.09 -2.64 -6.54
1943 2.652 2.109 1.131 0.720 0.254 111,030 2,793 -20,379 -3,240 336.935 56.246 -146.454 -911.225 11.83 1.27 -2.67 -6.62
1944 2.744 2.157 1.174 0.739 0.260 118,496 3,726 -18,826 -3,641 342.681 70.727 -129.090 -832.105 12.52 1.71 -2.52 -6.65
1945 2.715 2.142 1.177 0.732 0.256 123,101 3,729 -19,796 -4,912 346.362 72.085 -132.314 -818.393 12.48 1.77 -2.62 -6.77
1946 2.665 2.123 1.174 0.719 0.243 123,820 3,397 -17,848 -3,811 415.419 84.284 -164.785 -973.058 12.36 1.75 -2.76 -6.95
1947 2.617 2.102 1.171 0.709 0.235 124,513 3,474 -17,266 -3,658 469.417 93.084 -191.653 -1,082.406 12.22 1.74 -2.88 -7.08
1948 2.675 2.135 1.202 0.723 0.236 131,382 4,282 -16,335 -3,627 473.073 104.869 -172.972 -997.963 12.71 2.08 -2.77 -7.13
1949 2.728 2.164 1.230 0.736 0.239 138,416 4,848 -15,918 -4,235 495.299 119.120 -162.385 -957.252 13.16 2.41 -2.66 -7.16
1950 2.731 2.167 1.242 0.739 0.237 137,850 4,993 -14,576 -4,958 512.720 126.138 -160.271 -935.621 13.29 2.55 -2.65 -7.23
1951 2.668 2.136 1.230 0.728 0.233 138,025 6,242 -14,805 -5,723 528.705 124.572 -172.515 -949.513 13.00 2.44 -2.78 -7.33
1952 2.649 2.126 1.233 0.728 0.234 140,634 6,710 -14,970 -6,496 551.532 129.858 -176.215 -940.389 12.95 2.49 -2.81 -7.38
1953 2.657 2.128 1.245 0.735 0.241 142,209 7,314 -14,423 -5,975 571.512 138.171 -171.097 -900.774 13.05 2.65 -2.76 -7.37
1954 2.612 2.105 1.239 0.730 0.244 143,490 7,105 -15,062 -8,853 589.483 138.927 -177.668 -889.422 12.82 2.60 -2.82 -7.41
1955 2.542 2.065 1.224 0.723 0.248 140,383 7,778 -15,464 -10,910 585.898 131.435 -181.998 -849.594 12.38 2.45 -2.92 -7.42
1956 2.494 2.035 1.216 0.721 0.260 138,157 7,813 -15,112 -10,401 591.348 128.525 -183.213 -801.780 12.07 2.37 -2.96 -7.37
1957 2.441 2.002 1.206 0.720 0.277 135,530 7,627 -14,686 -8,177 589.478 123.612 -181.855 -739.648 11.71 2.28 -2.99 -7.26
1958 2.396 1.978 1.199 0.720 0.290 134,146 7,170 -14,379 -10,509 582.440 118.479 -176.425 -673.568 11.44 2.21 -3.00 -7.20
1959 2.317 1.936 1.181 0.715 0.301 132,034 7,238 -14,655 -10,739 570.165 107.858 -176.953 -620.582 10.96 2.02 -3.07 -7.14
1960 2.205 1.883 1.152 0.701 0.310 126,532 6,116 -15,206 -9,802 550.821 91.126 -183.079 -576.762 10.34 1.70 -3.23 -7.12
1961 2.204 1.880 1.159 0.713 0.332 127,277 6,359 -14,359 -10,865 552.694 93.948 -168.974 -505.934 10.32 1.79 -3.12 -6.96
1962 2.170 1.865 1.156 0.717 0.345 128,133 6,440 -14,146 -8,911 545.592 90.374 -160.692 -451.227 10.16 1.75 -3.10 -6.89
1963 2.162 1.858 1.161 0.727 0.364 128,235 6,623 -13,277 -9,443 537.134 90.259 -146.546 -389.367 10.09 1.81 -3.00 -6.75
1964 2.117 1.839 1.153 0.727 0.379 128,671 6,575 -13,356 -9,933 522.670 83.892 -140.345 -345.060 9.87 1.73 -3.01 -6.64
1965 2.092 1.826 1.152 0.732 0.399 129,487 6,798 -12,969 -9,785 498.396 78.974 -127.570 -291.937 9.71 1.72 -2.95 -6.46
1966 2.067 1.813 1.150 0.737 0.418 129,904 8,093 -12,505 -7,627 479.268 74.723 -117.779 -250.640 9.56 1.70 -2.91 -6.28
1967 2.037 1.795 1.146 0.739 0.434 131,264 8,172 -12,337 -8,314 470.438 71.535 -112.131 -220.580 9.33 1.65 -2.88 -6.12
1968 2.015 1.783 1.145 0.741 0.443 130,249 8,685 -11,746 -7,918 467.151 69.950 -107.679 -198.227 9.19 1.63 -2.86 -6.02
1969 1.968 1.763 1.135 0.735 0.443 128,355 8,114 -11,541 -6,346 471.911 66.367 -110.283 -188.852 8.94 1.52 -2.92 -6.02
1970 1.912 1.737 1.122 0.728 0.446 125,885 7,154 -11,575 -5,791 473.115 61.114 -113.645 -178.683 8.63 1.37 -3.00 -5.99
1971 1.894 1.729 1.121 0.727 0.444 126,518 7,047 -11,555 -5,961 458.898 58.459 -107.615 -160.498 8.53 1.37 -3.01 -6.01
1972 1.880 1.722 1.122 0.727 0.440 128,323 7,805 -11,583 -6,437 433.215 54.957 -98.620 -140.203 8.44 1.37 -3.01 -6.04
1973 1.837 1.703 1.113 0.719 0.428 128,366 7,774 -11,491 -4,884 416.566 49.330 -96.833 -130.372 8.21 1.27 -3.10 -6.16
1974 1.802 1.689 1.106 0.712 0.417 127,004 7,331 -10,885 -3,059 413.541 46.209 -97.276 -125.008 8.04 1.19 -3.17 -6.28
1975 1.766 1.673 1.099 0.705 0.405 125,695 6,637 -10,869 -3,754 410.515 43.016 -97.836 -120.011 7.84 1.11 -3.24 -6.40
1976 1.728 1.656 1.090 0.697 0.392 123,605 6,378 -11,101 -4,254 410.897 39.734 -99.881 -117.161 7.64 1.02 -3.33 -6.54
1977 1.694 1.642 1.083 0.690 0.382 121,805 6,026 -11,115 -3,538 416.759 37.274 -102.778 -115.385 7.47 0.94 -3.41 -6.65
1978 1.674 1.633 1.080 0.686 0.366 121,709 5,951 -10,858 -3,338 422.920 36.345 -103.741 -113.121 7.37 0.90 -3.46 -6.82
1979 1.649 1.623 1.075 0.679 0.348 120,458 5,665 -10,242 -3,373 435.224 34.983 -107.300 -113.699 7.24 0.84 -3.53 -7.01
1980 1.603 1.603 1.063 0.670 0.331 121,237 4,823 -10,260 -3,966 447.289 30.891 -113.691 -115.861 7.01 0.71 -3.63 -7.20
1981 1.590 1.597 1.061 0.666 0.316 120,420 4,627 -10,160 -3,317 450.445 29.864 -113.124 -112.558 6.94 0.69 -3.67 -7.35
1982 1.576 1.591 1.059 0.663 0.304 120,276 4,491 -10,697 -3,722 454.029 28.798 -112.631 -109.055 6.87 0.66 -3.71 -7.49
1983 1.571 1.589 1.059 0.662 0.298 120,731 4,595 -11,179 -4,161 452.199 28.493 -109.350 -102.492 6.84 0.67 -3.72 -7.55
1984 1.566 1.586 1.059 0.662 0.296 120,892 4,850 -11,743 -4,001 456.509 28.487 -107.683 -97.195 6.81 0.67 -3.72 -7.57
1985 1.555 1.581 1.057 0.659 0.294 120,390 4,791 -12,353 -4,793 463.672 27.816 -107.674 -93.234 6.75 0.64 -3.75 -7.60
1986 1.546 1.578 1.056 0.657 0.288 120,690 4,905 -13,410 -5,328 467.153 27.034 -106.701 -88.916 6.71 0.63 -3.78 -7.65
1987 1.535 1.574 1.054 0.654 0.284 120,372 4,768 -13,897 -5,073 472.156 26.165 -106.246 -85.121 6.66 0.60 -3.81 -7.70
1988 1.526 1.570 1.052 0.652 0.283 120,000 4,676 -14,311 -5,338 481.580 25.729 -106.466 -81.917 6.62 0.59 -3.83 -7.72
1989 1.513 1.564 1.049 0.649 0.279 119,015 4,449 -14,709 -6,319 494.807 24.749 -108.277 -79.952 6.55 0.55 -3.86 -7.76
1990 1.502 1.560 1.047 0.646 0.277 119,874 4,232 -15,027 -5,487 505.621 24.070 -108.929 -77.194 6.50 0.53 -3.89 -7.78
1991 1.493 1.557 1.045 0.644 0.273 120,325 4,033 -15,712 -6,599 507.327 22.999 -107.559 -73.261 6.46 0.51 -3.92 -7.82
1992 1.488 1.555 1.045 0.643 0.273 121,401 4,073 -16,348 -6,538 505.596 22.583 -104.612 -68.511 6.44 0.51 -3.93 -7.82
1993 1.485 1.554 1.045 0.641 0.271 122,712 4,119 -16,993 -6,643 503.040 22.194 -101.537 -64.011 6.43 0.51 -3.94 -7.84
1994 1.479 1.552 1.044 0.640 0.270 123,832 4,178 -17,646 -6,219 501.707 21.617 -99.027 -60.020 6.40 0.50 -3.96 -7.86
1995 1.469 1.548 1.042 0.638 0.269 124,459 4,060 -18,366 -7,906 498.948 20.338 -96.938 -56.331 6.35 0.48 -3.99 -7.87
1996 1.464 1.546 1.042 0.636 0.268 125,514 4,099 -18,848 -8,910 501.319 20.076 -95.097 -53.105 6.33 0.47 -4.00 -7.87
1997 1.457 1.543 1.041 0.635 0.268 126,086 4,187 -19,613 -11,036 505.269 19.575 -93.876 -50.324 6.30 0.46 -4.02 -7.88
1998 1.448 1.540 1.039 0.633 0.268 126,300 4,214 -20,373 -13,176 508.826 18.775 -92.854 -47.735 6.26 0.44 -4.04 -7.88
1999 1.442 1.537 1.039 0.632 0.268 126,866 4,268 -20,851 -14,654 511.665 18.381 -91.307 -45.084 6.23 0.43 -4.05 -7.88
2000 1.428 1.531 1.035 0.629 0.268 126,176 4,007 -21,194 -12,130 525.937 17.303 -92.787 -43.873 6.16 0.40 -4.08 -7.88
2001 1.422 1.529 1.035 0.628 0.268 126,966 4,047 -21,911 -9,951 527.721 16.822 -91.069 -41.361 6.13 0.39 -4.09 -7.88
2002 1.418 1.527 1.034 0.627 0.268 127,940 4,047 -22,643 -10,285 530.599 16.655 -89.322 -39.010 6.11 0.39 -4.10 -7.88
2003 1.414 1.525 1.034 0.626 0.268 128,842 4,114 -23,130 -10,497 533.676 16.387 -87.720 -36.825 6.09 0.38 -4.11 -7.88
2004 1.409 1.523 1.034 0.626 0.268 129,769 4,164 -23,573 -10,693 537.573 16.203 -86.223 -34.803 6.07 0.38 -4.12 -7.88
2005 1.404 1.521 1.033 0.625 0.268 130,587 4,168 -23,988 -10,870 541.750 15.874 -84.898 -32.927 6.04 0.37 -4.13 -7.88
2006 1.396 1.518 1.032 0.623 0.268 131,072 4,052 -24,418 -11,041 545.294 15.144 -83.808 -31.199 6.00 0.36 -4.14 -7.88
2007 1.392 1.516 1.031 0.622 0.269 132,008 4,092 -24,798 -11,210 551.344 15.043 -82.634 -29.583 5.98 0.35 -4.15 -7.88
2008 1.388 1.515 1.031 0.622 0.269 132,934 4,115 -25,181 -11,377 557.903 14.899 -81.566 -28.079 5.96 0.35 -4.16 -7.88
2009 1.382 1.512 1.030 0.620 0.269 133,651 4,045 -25,580 -11,539 563.914 14.460 -80.629 -26.666 5.94 0.34 -4.17 -7.88
2010 1.378 1.511 1.030 0.620 0.269 134,626 4,055 -25,948 -11,694 571.012 14.322 -79.614 -25.324 5.92 0.34 -4.18 -7.88
2011 1.374 1.510 1.029 0.619 0.269 135,618 4,046 -26,324 -11,850 577.975 14.118 -78.610 -24.048 5.90 0.33 -4.19 -7.88
2012 1.372 1.509 1.029 0.618 0.268 136,784 4,087 -26,681 -12,003 585.398 14.089 -77.531 -22.828 5.89 0.33 -4.20 -7.88
2013 1.371 1.509 1.030 0.618 0.268 138,180 4,181 -27,022 -12,153 593.450 14.236 -76.387 -21.658 5.89 0.33 -4.20 -7.88
2014 1.371 1.509 1.030 0.618 0.268 139,853 4,357 -27,337 -12,301 602.374 14.652 -75.158 -20.541 5.90 0.34 -4.20 -7.89
2015 1.367 1.508 1.030 0.617 0.268 140,925 4,304 -27,713 -12,450 608.404 14.295 -74.084 -19.479 5.88 0.33 -4.21 -7.89
2016 1.366 1.508 1.030 0.617 0.267 142,480 4,404 -28,039 -12,590 616.279 14.446 -72.878 -18.461 5.88 0.34 -4.22 -7.90
2017 1.365 1.508 1.030 0.616 0.267 143,986 4,468 -28,378 -12,733 623.702 14.469 -71.698 -17.495 5.88 0.34 -4.22 -7.90
2018 1.366 1.509 1.031 0.616 0.266 145,858 4,641 -28,691 -12,877 632.512 14.836 -70.449 -16.577 5.89 0.35 -4.22 -7.91
2019 1.368 1.510 1.032 0.616 0.266 147,916 4,863 -28,997 -13,024 641.915 15.336 -69.177 -15.705 5.91 0.36 -4.22 -7.91
2020 1.366 1.510 1.032 0.615 0.264 149,434 4,866 -29,377 -13,184 648.690 15.137 -68.064 -14.886 5.91 0.36 -4.23 -7.93
2021 1.368 1.511 1.032 0.615 0.263 151,533 5,063 -29,709 -13,344 657.656 15.527 -66.812 -14.099 5.92 0.36 -4.23 -7.94
2022 1.371 1.514 1.034 0.615 0.262 153,891 5,335 -30,024 -13,506 667.394 16.131 -65.507 -13.348 5.95 0.38 -4.23 -7.95
2023 1.375 1.516 1.035 0.616 0.261 156,414 5,653 -30,335 -13,672 677.509 16.839 -64.178 -12.632 5.98 0.40 -4.23 -7.96
2024 1.380 1.518 1.037 0.616 0.260 158,994 5,980 -30,647 -13,840 687.590 17.542 -62.851 -11.951 6.01 0.42 -4.22 -7.97
2025 1.383 1.521 1.038 0.616 0.259 161,553 6,284 -30,975 -14,015 697.489 18.155 -61.569 -11.309 6.04 0.43 -4.22 -7.98
2026 1.387 1.523 1.040 0.616 0.258 164,093 6,577 -31,307 -14,189 707.219 18.709 -60.310 -10.698 6.06 0.45 -4.22 -7.99
2027 1.388 1.524 1.040 0.616 0.257 166,206 6,738 -31,659 -14,359 717.812 18.946 -59.336 -10.155 6.07 0.45 -4.22 -8.00
2028 1.388 1.525 1.040 0.616 0.256 168,221 6,860 -32,025 -14,529 728.097 19.064 -58.401 -9.639 6.08 0.45 -4.22 -8.01
2029 1.387 1.525 1.040 0.615 0.255 170,120 6,930 -32,414 -14,706 738.024 19.029 -57.521 -9.154 6.08 0.45 -4.23 -8.03
2030 1.385 1.525 1.040 0.614 0.253 171,881 6,939 -32,825 -14,888 747.505 18.832 -56.694 -8.696 6.08 0.45 -4.24 -8.04
2031 1.383 1.524 1.039 0.614 0.252 173,567 6,915 -33,249 -15,072 756.805 18.548 -55.899 -8.262 6.07 0.44 -4.25 -8.06
2032 1.379 1.523 1.038 0.613 0.251 175,080 6,824 -33,693 -15,258 765.470 18.088 -55.144 -7.849 6.06 0.43 -4.26 -8.07
2033 1.376 1.522 1.037 0.612 0.249 176,594 6,727 -34,140 -15,443 774.226 17.622 -54.398 -7.457 6.05 0.42 -4.27 -8.08
2034 1.372 1.521 1.036 0.610 0.248 178,099 6,614 -34,599 -15,633 783.012 17.122 -53.674 -7.086 6.04 0.41 -4.28 -8.10
2035 1.368 1.520 1.035 0.609 0.246 179,614 6,493 -35,067 -15,828 791.892 16.610 -52.964 -6.734 6.02 0.39 -4.29 -8.11
2036 1.365 1.519 1.034 0.608 0.245 181,176 6,381 -35,535 -16,023 801.005 16.131 -52.252 -6.399 6.01 0.38 -4.31 -8.13
2037 1.362 1.518 1.033 0.607 0.244 182,792 6,279 -36,003 -16,220 810.343 15.686 -51.539 -6.080 6.00 0.37 -4.32 -8.14
2038 1.359 1.517 1.032 0.606 0.242 184,481 6,194 -36,471 -16,417 819.973 15.290 -50.820 -5.775 5.99 0.36 -4.33 -8.16
2039 1.356 1.516 1.031 0.605 0.241 186,254 6,130 -36,937 -16,616 829.905 14.950 -50.094 -5.485 5.98 0.35 -4.34 -8.17
2040 1.354 1.516 1.031 0.605 0.240 188,121 6,088 -37,402 -16,817 840.162 14.669 -49.362 -5.208 5.98 0.35 -4.34 -8.18
2041 1.352 1.516 1.030 0.604 0.239 190,071 6,062 -37,871 -17,022 850.669 14.430 -48.628 -4.945 5.98 0.34 -4.35 -8.19
2042 1.351 1.516 1.030 0.603 0.238 192,121 6,066 -38,333 -17,227 861.484 14.263 -47.879 -4.693 5.98 0.34 -4.36 -8.20
2043 1.350 1.516 1.030 0.603 0.237 194,264 6,098 -38,789 -17,431 872.578 14.165 -47.117 -4.453 5.98 0.33 -4.36 -8.21
2044 1.350 1.516 1.030 0.602 0.236 196,497 6,152 -39,244 -17,638 883.938 14.115 -46.352 -4.224 5.98 0.33 -4.37 -8.22
2045 1.350 1.517 1.030 0.602 0.235 198,841 6,241 -39,692 -17,844 895.684 14.143 -45.576 -4.005 5.99 0.33 -4.37 -8.23
2046 1.351 1.518 1.030 0.602 0.234 201,260 6,344 -40,143 -18,053 907.696 14.199 -44.807 -3.797 6.00 0.34 -4.37 -8.24
2047 1.351 1.518 1.030 0.602 0.233 203,752 6,462 -40,597 -18,265 919.982 14.287 -44.043 -3.600 6.01 0.34 -4.38 -8.25
2048 1.352 1.519 1.030 0.601 0.232 206,303 6,590 -41,054 -18,481 932.503 14.391 -43.289 -3.414 6.02 0.34 -4.38 -8.26
2049 1.353 1.520 1.031 0.601 0.231 208,917 6,733 -41,511 -18,696 945.300 14.525 -42.540 -3.236 6.03 0.34 -4.38 -8.27
2050 1.354 1.521 1.031 0.601 0.231 211,549 6,882 -41,968 -18,913 958.198 14.664 -41.799 -3.067 6.04 0.35 -4.38 -8.28
2051 1.355 1.522 1.031 0.601 0.230 214,226 7,033 -42,431 -19,132 971.327 14.806 -41.072 -2.907 6.05 0.35 -4.38 -8.28
2052 1.356 1.523 1.032 0.601 0.229 216,932 7,187 -42,897 -19,351 984.654 14.949 -40.357 -2.755 6.06 0.36 -4.38 -8.29
2053 1.356 1.524 1.032 0.601 0.228 219,642 7,327 -43,378 -19,577 998.077 15.059 -39.665 -2.612 6.07 0.36 -4.39 -8.30
2054 1.357 1.524 1.032 0.601 0.228 222,366 7,467 -43,860 -19,802 1,011.664 15.165 -38.984 -2.476 6.08 0.36 -4.39 -8.31
2055 1.358 1.525 1.032 0.600 0.227 225,090 7,598 -44,349 -20,029 1,025.378 15.252 -38.320 -2.347 6.09 0.36 -4.39 -8.31
2056 1.358 1.526 1.032 0.600 0.226 227,787 7,709 -44,850 -20,258 1,039.106 15.295 -37.676 -2.225 6.09 0.36 -4.39 -8.32
2057 1.358 1.526 1.032 0.600 0.226 230,451 7,792 -45,367 -20,492 1,052.838 15.283 -37.056 -2.110 6.10 0.36 -4.39 -8.33
2058 1.357 1.526 1.032 0.600 0.225 233,090 7,846 -45,904 -20,732 1,066.605 15.215 -36.461 -2.002 6.10 0.36 -4.40 -8.33
2059 1.356 1.526 1.032 0.599 0.224 235,697 7,868 -46,462 -20,979 1,080.379 15.087 -35.891 -1.899 6.10 0.36 -4.40 -8.34
2060 1.355 1.526 1.032 0.599 0.224 238,268 7,864 -47,036 -21,230 1,094.129 14.911 -35.340 -1.802 6.10 0.35 -4.41 -8.35
2061 1.354 1.526 1.031 0.598 0.223 240,821 7,840 -47,623 -21,485 1,107.918 14.702 -34.803 -1.710 6.10 0.35 -4.42 -8.36
2062 1.352 1.526 1.031 0.597 0.222 243,372 7,807 -48,214 -21,741 1,121.805 14.481 -34.275 -1.623 6.09 0.34 -4.42 -8.37
2063 1.350 1.525 1.030 0.597 0.221 245,929 7,764 -48,815 -21,998 1,135.799 14.245 -33.757 -1.540 6.09 0.34 -4.43 -8.37
2064 1.349 1.525 1.030 0.596 0.221 248,511 7,719 -49,422 -22,257 1,149.970 14.010 -33.246 -1.462 6.08 0.33 -4.43 -8.38
2065 1.347 1.524 1.029 0.596 0.220 251,125 7,670 -50,038 -22,520 1,164.326 13.771 -32.744 -1.387 6.08 0.33 -4.44 -8.38
2066 1.346 1.524 1.029 0.595 0.220 253,796 7,639 -50,651 -22,782 1,178.966 13.567 -32.241 -1.316 6.08 0.32 -4.44 -8.39
2067 1.345 1.524 1.028 0.595 0.219 256,508 7,619 -51,262 -23,043 1,193.800 13.386 -31.739 -1.248 6.07 0.32 -4.45 -8.39
2068 1.344 1.524 1.028 0.595 0.219 259,274 7,617 -51,867 -23,303 1,208.866 13.239 -31.235 -1.184 6.07 0.31 -4.45 -8.40
2069 1.343 1.524 1.028 0.594 0.219 262,098 7,633 -52,470 -23,563 1,224.182 13.123 -30.732 -1.122 6.07 0.31 -4.46 -8.40
2070 1.342 1.524 1.027 0.594 0.218 264,997 7,664 -53,074 -23,825 1,239.816 13.035 -30.231 -1.064 6.07 0.31 -4.46 -8.40
2071 1.342 1.524 1.027 0.594 0.218 267,981 7,714 -53,681 -24,089 1,255.816 12.978 -29.734 -1.009 6.07 0.31 -4.46 -8.41
2072 1.341 1.524 1.027 0.594 0.218 271,032 7,775 -54,292 -24,356 1,272.094 12.938 -29.243 -0.956 6.08 0.31 -4.46 -8.41
2073 1.341 1.524 1.027 0.593 0.218 274,148 7,846 -54,909 -24,626 1,288.647 12.913 -28.756 -0.906 6.08 0.31 -4.46 -8.41
2074 1.341 1.525 1.027 0.593 0.217 277,380 7,943 -55,527 -24,899 1,305.724 12.929 -28.274 -0.859 6.08 0.31 -4.47 -8.41
2075 1.342 1.525 1.027 0.593 0.217 280,697 8,061 -56,145 -25,173 1,323.197 12.979 -27.795 -0.814 6.09 0.31 -4.47 -8.41
2076 1.342 1.526 1.027 0.593 0.217 284,045 8,177 -56,773 -25,450 1,340.816 13.020 -27.325 -0.771 6.09 0.31 -4.47 -8.42
2077 1.342 1.526 1.028 0.593 0.217 287,500 8,303 -57,413 -25,734 1,358.958 13.076 -26.864 -0.731 6.10 0.31 -4.47 -8.42
2078 1.343 1.527 1.028 0.593 0.217 291,043 8,431 -58,073 -26,026 1,377.546 13.130 -26.417 -0.693 6.11 0.31 -4.47 -8.42
2079 1.343 1.527 1.028 0.593 0.217 294,495 8,611 -58,665 -26,294 1,395.753 13.263 -25.944 -0.656 6.11 0.31 -4.47 -8.42
2080 1.344 1.528 1.028 0.593 0.217 298,269 8,819 -59,306 -26,585 1,413.836 13.415 -25.467 -0.621 6.12 0.32 -4.47 -8.42
2081 1.345 1.529 1.028 0.593 0.217 301,867 8,962 -59,963 -26,877 1,432.843 13.483 -25.033 -0.589 6.13 0.32 -4.47 -8.42
2082 1.345 1.529 1.029 0.593 0.217 305,498 9,104 -60,627 -27,172 1,452.130 13.546 -24.608 -0.558 6.14 0.32 -4.47 -8.42
2083 1.346 1.530 1.029 0.593 0.217 309,127 9,232 -61,303 -27,471 1,471.536 13.586 -24.193 -0.529 6.14 0.32 -4.47 -8.42
2084 1.346 1.530 1.029 0.593 0.217 312,820 9,371 -61,984 -27,773 1,491.383 13.639 -23.785 -0.501 6.15 0.32 -4.47 -8.42
2085 1.346 1.531 1.029 0.593 0.216 316,533 9,503 -62,674 -28,078 1,511.464 13.682 -23.386 -0.475 6.15 0.33 -4.47 -8.42
2086 1.346 1.531 1.029 0.592 0.216 320,166 9,592 -63,384 -28,387 1,531.287 13.660 -23.000 -0.450 6.16 0.32 -4.47 -8.42
2087 1.346 1.531 1.029 0.592 0.216 323,824 9,675 -64,103 -28,699 1,551.346 13.631 -22.620 -0.427 6.16 0.32 -4.48 -8.43
2088 1.345 1.531 1.029 0.592 0.216 327,494 9,748 -64,833 -29,015 1,571.575 13.586 -22.249 -0.404 6.16 0.32 -4.48 -8.43
2089 1.345 1.531 1.029 0.592 0.216 331,186 9,815 -65,574 -29,335 1,592.011 13.533 -21.885 -0.383 6.16 0.32 -4.48 -8.43
2090 1.345 1.531 1.028 0.592 0.216 334,914 9,880 -66,323 -29,659 1,612.701 13.476 -21.528 -0.363 6.16 0.32 -4.48 -8.43
2091 1.344 1.531 1.028 0.592 0.216 338,675 9,940 -67,083 -29,986 1,633.625 13.414 -21.176 -0.345 6.16 0.32 -4.48 -8.43
2092 1.344 1.532 1.028 0.591 0.216 342,475 10,001 -67,851 -30,317 1,654.805 13.351 -20.831 -0.327 6.17 0.32 -4.49 -8.43
2093 1.343 1.532 1.028 0.591 0.215 346,330 10,064 -68,628 -30,652 1,676.294 13.292 -20.491 -0.310 6.17 0.32 -4.49 -8.43
2094 1.343 1.532 1.028 0.591 0.215 350,238 10,131 -69,414 -30,991 1,698.078 13.236 -20.156 -0.294 6.17 0.31 -4.49 -8.44
2095 1.343 1.532 1.028 0.591 0.215 354,205 10,203 -70,208 -31,333 1,720.170 13.187 -19.826 -0.278 6.17 0.31 -4.49 -8.44
2096 1.342 1.532 1.028 0.590 0.215 358,236 10,281 -71,010 -31,680 1,742.582 13.144 -19.500 -0.264 6.17 0.31 -4.50 -8.44
2097 1.342 1.532 1.028 0.590 0.215 362,329 10,364 -71,820 -32,031 1,765.290 13.107 -19.178 -0.250 6.17 0.31 -4.50 -8.44
2098 1.342 1.533 1.028 0.590 0.215 366,505 10,461 -72,637 -32,386 1,788.384 13.085 -18.861 -0.237 6.18 0.31 -4.50 -8.44
2099 1.342 1.533 1.028 0.590 0.215 370,747 10,563 -73,463 -32,745 1,811.795 13.069 -18.547 -0.225 6.18 0.31 -4.50 -8.44
2100 1.342 1.533 1.028 0.590 0.214 375,060 10,674 -74,297 -33,108 1,835.552 13.062 -18.238 -0.213 6.18 0.31 -4.50 -8.44
SOURCE: Author's calculations.

## 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.

Table C–1 OASI money's worth and redistributional measures under the tax adjustment policy, by birth cohort
Birth
cohort
Real
internal
rate of
return
(percent)
member evaluated as of the initial cohort
year in constant (2001) dollars
evaluated as of year-end 2001
in billions of dollars
as a percent of
Interest rate assumption Interest rate assumption Interest rate assumption Interest rate assumption
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Zero
real
Tax
base
growth
Trust
fund
Large
company
stock
Pre–1901 18.367 12.037 6.093 12.037 3.207 31,365 6,478 36,760 2,165 1,637.203 3,912.972 4,313.035 13,676.469 34.97 13.39 35.27 5.12
1901 10.868 8.065 3.718 7.688 2.186 63,959 8,809 70,672 2,473 130.104 207.357 323.140 608.789 28.47 8.57 26.75 3.05
1902 10.481 7.683 3.546 7.262 2.168 71,461 9,477 78,181 2,711 143.414 220.098 352.677 658.360 27.81 8.28 25.84 3.07
1903 10.329 7.518 3.517 7.037 2.244 71,974 9,286 77,732 2,757 150.715 225.014 365.871 698.657 28.30 8.50 25.91 3.36
1904 9.881 7.074 3.323 6.552 2.163 73,349 9,106 78,018 2,690 157.567 226.369 376.721 699.208 27.19 8.04 24.52 3.19
1905 9.444 6.733 3.150 6.170 2.064 76,601 9,167 80,121 2,644 167.332 231.728 393.407 698.935 26.21 7.54 23.26 2.94
1906 9.061 6.392 3.001 5.784 1.985 77,991 8,989 79,971 2,540 173.566 231.504 400.043 683.963 25.36 7.15 22.08 2.76
1907 8.950 6.296 2.997 5.610 2.030 84,950 9,594 85,292 2,750 185.763 242.778 419.234 727.784 25.90 7.41 22.05 2.97
1908 8.583 5.906 2.840 5.185 1.935 86,906 9,461 85,196 2,628 193.056 243.223 425.403 706.590 24.78 7.01 20.62 2.75
1909 8.170 5.641 2.695 4.857 1.807 85,464 8,919 81,453 2,313 196.610 237.439 421.196 643.861 23.86 6.52 19.31 2.40
1910 7.918 5.471 2.622 4.612 1.714 87,207 8,810 80,531 2,101 203.609 238.030 422.630 593.524 23.58 6.35 18.50 2.15
1911 7.827 5.396 2.626 4.436 1.718 90,647 8,974 80,737 2,077 211.908 242.761 424.247 587.565 24.23 6.65 18.31 2.25
1912 7.447 5.102 2.485 4.077 1.574 96,353 9,113 82,184 1,835 223.758 244.892 428.995 515.688 23.14 6.19 16.74 1.83
1913 7.319 5.039 2.474 3.906 1.508 99,764 9,222 81,382 1,630 233.270 249.526 427.725 461.109 23.57 6.34 16.30 1.67
1914 6.948 4.718 2.326 3.531 1.357 101,416 8,908 78,101 1,213 242.291 246.283 419.411 350.614 22.30 5.86 14.55 1.20
1915 6.820 4.660 2.309 3.365 1.288 100,249 8,595 73,098 945 246.675 244.736 404.298 281.400 22.58 5.93 13.94 1.00
1916 6.650 4.535 2.263 3.147 1.210 105,891 8,797 72,334 716 252.140 242.386 387.148 206.414 22.48 5.92 12.99 0.75
1917 6.333 4.237 2.127 2.831 1.082 96,988 7,647 61,573 267 243.593 222.255 347.605 81.261 21.10 5.43 11.34 0.30
1918 5.912 3.919 1.958 2.497 0.927 96,058 7,009 55,225 -256 242.390 204.683 313.231 -78.108 19.35 4.70 9.41 -0.27
1919 5.578 3.608 1.827 2.196 0.835 88,187 5,988 45,165 -554 223.950 175.973 257.808 -170.316 17.88 4.27 7.75 -0.66
1920 5.378 3.492 1.771 2.027 0.754 93,298 6,018 42,712 -881 237.468 177.263 244.359 -271.294 17.52 4.11 6.80 -1.02
1921 5.098 3.295 1.677 1.834 0.673 95,663 5,730 38,367 -1,245 243.129 168.535 219.183 -382.818 16.53 3.73 5.64 -1.40
1922 4.949 3.225 1.643 1.722 0.619 93,619 5,349 33,189 -1,404 237.389 156.971 189.164 -430.819 16.43 3.64 4.97 -1.68
1923 4.748 3.114 1.589 1.602 0.565 94,701 5,094 29,215 -1,626 236.920 147.481 164.287 -492.442 15.94 3.44 4.22 -2.00
1924 4.554 3.004 1.534 1.494 0.519 98,906 4,976 26,143 -1,899 241.867 140.810 143.700 -562.016 15.43 3.20 3.52 -2.28
1925 4.453 2.964 1.517 1.427 0.490 99,940 4,850 23,017 -1,982 241.929 135.853 125.243 -580.546 15.47 3.18 3.10 -2.51
1926 4.249 2.853 1.460 1.331 0.447 98,616 4,411 18,443 -2,153 235.825 122.056 99.136 -622.994 14.89 2.90 2.44 -2.82
1927 4.114 2.775 1.426 1.259 0.419 103,276 4,348 15,543 -2,342 239.839 116.846 81.134 -658.252 14.63 2.78 1.95 -3.11
1928 3.910 2.664 1.368 1.173 0.387 102,646 3,893 10,860 -2,499 231.133 101.454 54.964 -680.976 13.99 2.47 1.33 -3.42
1929 3.734 2.565 1.321 1.097 0.360 100,935 3,453 6,264 -2,570 220.997 87.495 30.828 -680.950 13.51 2.25 0.76 -3.80
1930 3.627 2.501 1.294 1.049 0.344 103,692 3,303 3,318 -2,670 223.233 82.290 16.055 -695.580 13.25 2.14 0.39 -4.12
1931 3.546 2.474 1.279 1.011 0.330 101,899 3,063 769 -2,593 219.582 76.388 3.722 -676.331 13.29 2.10 0.09 -4.43
1932 3.476 2.441 1.264 0.980 0.318 100,447 2,855 -1,314 -2,537 220.518 72.534 -6.485 -673.999 13.24 2.04 -0.16 -4.68
1933 3.259 2.332 1.204 0.914 0.296 94,506 2,200 -5,721 -2,553 208.662 56.213 -28.392 -682.243 12.42 1.62 -0.72 -5.02
1934 3.228 2.329 1.203 0.898 0.295 97,208 2,209 -6,863 -2,527 217.896 57.297 -34.578 -685.442 12.59 1.64 -0.87 -5.16
1935 3.068 2.245 1.162 0.851 0.285 95,621 1,804 -10,324 -2,568 220.657 48.184 -53.553 -717.165 11.97 1.34 -1.29 -5.40
1936 2.994 2.217 1.149 0.826 0.284 96,172 1,679 -12,210 -2,534 224.573 45.381 -64.090 -715.976 11.87 1.27 -1.53 -5.57
1937 3.127 2.313 1.204 0.850 0.295 103,463 2,239 -10,273 -2,373 251.186 62.909 -56.061 -697.341 13.06 1.77 -1.34 -5.62
1938 2.965 2.227 1.165 0.805 0.284 105,414 1,770 -14,976 -3,395 257.922 54.469 -78.210 -745.387 12.38 1.46 -1.75 -5.85
1939 2.945 2.231 1.171 0.797 0.283 108,069 2,078 -16,053 -3,323 266.573 57.141 -82.150 -735.081 12.59 1.55 -1.85 -5.97
1940 2.881 2.202 1.164 0.778 0.279 111,325 2,250 -18,406 -3,012 276.898 56.823 -93.658 -751.679 12.46 1.51 -2.06 -6.13
1941 2.835 2.188 1.163 0.765 0.273 110,026 2,527 -17,763 -2,343 291.312 58.725 -103.131 -772.675 12.45 1.53 -2.20 -6.28
1942 2.643 2.095 1.115 0.720 0.255 107,231 2,143 -20,601 -2,711 314.923 47.728 -141.789 -900.405 11.56 1.09 -2.64 -6.54
1943 2.651 2.107 1.131 0.720 0.254 110,995 2,788 -20,394 -3,241 336.829 56.140 -146.556 -911.298 11.83 1.26 -2.67 -6.62
1944 2.743 2.154 1.173 0.738 0.260 118,447 3,719 -18,845 -3,642 342.539 70.591 -129.215 -832.191 12.51 1.71 -2.52 -6.65
1945 2.714 2.140 1.177 0.731 0.256 123,076 3,725 -19,811 -4,912 346.290 71.991 -132.414 -818.471 12.47 1.77 -2.62 -6.77
1946 2.665 2.120 1.174 0.720 0.243 123,844 3,396 -17,855 -3,811 415.501 84.271 -164.844 -973.135 12.36 1.75 -2.76 -6.95
1947 2.617 2.100 1.170 0.709 0.235 124,602 3,478 -17,265 -3,658 469.750 93.207 -191.642 -1,082.475 12.23 1.74 -2.88 -7.08
1948 2.676 2.133 1.202 0.723 0.236 131,563 4,295 -16,324 -3,627 473.723 105.172 -172.858 -998.009 12.73 2.09 -2.77 -7.13
1949 2.737 2.166 1.233 0.738 0.239 139,227 4,918 -15,813 -4,234 498.200 120.861 -161.316 -956.923 13.24 2.44 -2.65 -7.16
1950 2.752 2.176 1.249 0.744 0.238 139,613 5,153 -14,341 -4,953 519.277 130.183 -157.691 -934.719 13.46 2.63 -2.61 -7.23
1951 2.702 2.153 1.241 0.736 0.235 140,904 6,582 -14,435 -5,714 539.734 131.359 -168.194 -948.002 13.27 2.58 -2.71 -7.32
1952 2.699 2.152 1.250 0.738 0.237 144,920 7,241 -14,419 -6,481 568.341 140.127 -169.729 -938.157 13.34 2.69 -2.71 -7.36
1953 2.733 2.169 1.272 0.751 0.245 148,698 8,153 -13,582 -5,952 597.590 154.023 -161.128 -897.361 13.64 2.96 -2.60 -7.35
1954 2.712 2.160 1.274 0.752 0.248 152,313 8,220 -13,912 -8,808 625.728 160.733 -164.105 -884.893 13.61 3.01 -2.61 -7.37
1955 2.668 2.133 1.268 0.749 0.254 151,386 9,391 -14,045 -10,841 631.822 158.696 -165.294 -844.219 13.35 2.96 -2.65 -7.37
1956 2.645 2.117 1.268 0.753 0.266 151,360 9,823 -13,468 -10,321 647.859 161.588 -163.282 -795.625 13.23 2.98 -2.64 -7.32
1957 2.618 2.096 1.267 0.757 0.285 150,919 10,006 -12,841 -8,103 656.410 162.178 -159.009 -732.904 13.04 2.99 -2.61 -7.19
1958 2.598 2.084 1.269 0.763 0.299 151,852 9,809 -12,311 -10,398 659.318 162.088 -151.052 -666.422 12.95 3.03 -2.57 -7.12
1959 2.546 2.056 1.260 0.762 0.312 152,397 10,532 -12,333 -10,609 658.099 156.945 -148.912 -613.065 12.65 2.94 -2.59 -7.06
1960 2.460 2.014 1.239 0.754 0.322 149,202 9,753 -12,684 -9,671 649.508 145.311 -152.717 -569.042 12.19 2.71 -2.70 -7.03
1961 2.485 2.024 1.255 0.772 0.346 152,494 10,365 -11,593 -10,696 662.196 153.128 -136.415 -498.062 12.37 2.92 -2.52 -6.85
1962 2.476 2.021 1.260 0.781 0.360 156,212 10,972 -11,123 -8,755 665.151 153.964 -126.353 -443.349 12.38 2.99 -2.44 -6.77
1963 2.493 2.027 1.274 0.797 0.381 159,014 11,575 -10,037 -9,254 666.056 157.738 -110.787 -381.593 12.51 3.17 -2.27 -6.61
1964 2.472 2.020 1.274 0.802 0.397 162,548 12,129 -9,849 -9,715 660.279 154.765 -103.496 -337.484 12.47 3.19 -2.22 -6.50
1965 2.471 2.018 1.282 0.814 0.419 166,481 13,006 -9,232 -9,547 640.784 151.096 -90.816 -284.826 12.49 3.28 -2.10 -6.30
1966 2.470 2.016 1.288 0.823 0.439 169,967 16,070 -8,598 -7,423 627.075 148.374 -80.981 -243.943 12.51 3.37 -2.00 -6.11
1967 2.463 2.008 1.291 0.831 0.457 174,896 16,924 -8,212 -8,074 626.810 148.152 -74.640 -214.205 12.44 3.42 -1.92 -5.94
1968 2.463 2.005 1.298 0.838 0.468 176,535 18,617 -7,564 -7,675 633.160 149.943 -69.342 -192.146 12.45 3.50 -1.84 -5.84
1969 2.437 1.995 1.294 0.837 0.469 177,245 18,528 -7,358 -6,148 651.662 151.548 -70.314 -182.959 12.35 3.47 -1.86 -5.83
1970 2.400 1.977 1.287 0.833 0.473 177,350 17,698 -7,366 -5,609 666.536 151.198 -72.315 -173.077 12.15 3.40 -1.91 -5.80
1971 2.403 1.979 1.294 0.837 0.472 181,294 18,016 -7,170 -5,772 657.580 149.446 -66.782 -155.405 12.22 3.49 -1.87 -5.82
1972 2.409 1.980 1.302 0.842 0.470 186,936 20,457 -6,993 -6,233 631.091 144.047 -59.537 -135.756 12.30 3.60 -1.82 -5.85
1973 2.383 1.969 1.298 0.838 0.459 190,494 21,835 -6,955 -4,737 618.179 138.551 -58.607 -126.452 12.19 3.57 -1.88 -5.98
1974 2.364 1.961 1.297 0.835 0.449 191,827 21,902 -6,583 -2,972 624.611 138.053 -58.836 -121.476 12.14 3.57 -1.92 -6.10
1975 2.344 1.952 1.295 0.831 0.438 193,317 21,209 -6,584 -3,656 631.366 137.467 -59.268 -116.892 12.06 3.56 -1.96 -6.23
1976 2.321 1.941 1.291 0.826 0.426 193,659 22,092 -6,768 -4,155 643.778 137.629 -60.893 -114.432 11.98 3.53 -2.03 -6.39
1977 2.302 1.933 1.289 0.822 0.417 194,313 22,603 -6,809 -3,466 664.848 139.803 -62.959 -113.016 11.92 3.51 -2.09 -6.51
1978 2.295 1.930 1.290 0.820 0.402 197,134 23,382 -6,642 -3,280 685.012 142.813 -63.454 -111.156 11.93 3.54 -2.12 -6.70
1979 2.282 1.925 1.289 0.816 0.385 198,186 23,826 -6,297 -3,326 716.062 147.125 -65.974 -112.122 11.92 3.54 -2.17 -6.91
1980 2.247 1.908 1.280 0.808 0.368 203,233 23,341 -6,430 -3,928 749.803 149.494 -71.248 -114.757 11.74 3.45 -2.28 -7.13
1981 2.244 1.907 1.281 0.807 0.354 204,589 23,423 -6,367 -3,298 765.285 151.183 -70.898 -111.903 11.79 3.48 -2.30 -7.31
1982 2.240 1.905 1.282 0.806 0.343 206,951 23,812 -6,716 -3,715 781.221 152.704 -70.715 -108.848 11.82 3.51 -2.33 -7.47
1983 2.241 1.905 1.285 0.806 0.337 209,774 24,603 -7,014 -4,171 785.712 152.569 -68.609 -102.738 11.89 3.56 -2.33 -7.57
1984 2.243 1.905 1.287 0.807 0.336 212,074 26,275 -7,370 -4,029 800.829 154.343 -67.587 -97.870 11.95 3.61 -2.34 -7.62
1985 2.237 1.902 1.287 0.805 0.333 213,435 26,950 -7,795 -4,850 822.026 156.481 -67.945 -94.343 11.97 3.62 -2.36 -7.69
1986 2.233 1.901 1.287 0.804 0.328 216,140 28,551 -8,509 -5,418 836.610 157.359 -67.701 -90.414 12.01 3.65 -2.40 -7.78
1987 2.227 1.899 1.287 0.802 0.324 217,771 28,896 -8,877 -5,184 854.200 158.569 -67.865 -86.991 12.05 3.66 -2.43 -7.87
1988 2.222 1.897 1.287 0.801 0.322 219,163 29,303 -9,200 -5,484 879.541 161.235 -68.442 -84.158 12.08 3.68 -2.46 -7.93
1989 2.212 1.893 1.285 0.798 0.319 219,599 29,593 -9,553 -6,526 912.984 164.618 -70.320 -82.581 12.09 3.67 -2.51 -8.01
1990 2.205 1.890 1.284 0.795 0.316 223,297 29,434 -9,840 -5,699 941.851 167.403 -71.330 -80.174 12.11 3.68 -2.55 -8.08
1991 2.198 1.888 1.283 0.793 0.313 226,211 29,299 -10,376 -6,892 953.776 167.102 -71.034 -76.506 12.14 3.69 -2.59 -8.16
1992 2.196 1.887 1.284 0.793 0.312 230,057 29,962 -10,853 -6,865 958.118 166.116 -69.450 -71.945 12.21 3.72 -2.61 -8.22
1993 2.194 1.887 1.285 0.792 0.310 234,223 30,563 -11,352 -7,015 960.164 164.665 -67.828 -67.593 12.27 3.75 -2.63 -8.28
1994 2.190 1.885 1.285 0.791 0.308 238,127 31,579 -11,878 -6,604 964.774 163.402 -66.661 -63.738 12.31 3.77 -2.67 -8.34
1995 2.180 1.881 1.283 0.788 0.307 241,340 32,186 -12,498 -8,445 967.517 161.225 -65.968 -60.173 12.32 3.77 -2.71 -8.41
1996 2.176 1.879 1.283 0.787 0.306 245,116 32,915 -12,922 -9,573 979.021 161.194 -65.199 -57.054 12.37 3.79 -2.74 -8.46
1997 2.170 1.876 1.282 0.785 0.306 248,079 34,533 -13,568 -11,927 994.132 161.440 -64.944 -54.385 12.40 3.80 -2.78 -8.51
1998 2.160 1.871 1.280 0.783 0.305 250,339 36,175 -14,253 -14,326 1,008.545 161.167 -64.963 -51.902 12.40 3.79 -2.82 -8.57
1999 2.154 1.868 1.279 0.781 0.305 253,136 37,362 -14,727 -16,029 1,020.928 160.908 -64.491 -49.315 12.43 3.80 -2.86 -8.62
2000 2.139 1.860 1.274 0.778 0.304 253,778 37,842 -15,188 -13,351 1,057.816 163.391 -66.491 -48.291 12.39 3.77 -2.92 -8.68
2001 2.131 1.856 1.273 0.776 0.303 256,991 39,113 -15,866 -11,021 1,068.153 162.571 -65.945 -45.806 12.41 3.77 -2.96 -8.73
2002 2.125 1.853 1.272 0.775 0.303 260,414 39,405 -16,557 -11,460 1,079.998 162.158 -65.313 -43.467 12.44 3.78 -3.00 -8.78
2003 2.117 1.849 1.270 0.773 0.302 263,591 40,538 -17,105 -11,770 1,091.816 161.479 -64.871 -41.290 12.45 3.78 -3.04 -8.84
2004 2.110 1.845 1.269 0.771 0.302 266,803 41,388 -17,627 -12,066 1,105.241 161.055 -64.477 -39.270 12.47 3.78 -3.08 -8.89
2005 2.101 1.840 1.267 0.769 0.302 269,818 42,138 -18,158 -12,344 1,119.361 160.487 -64.265 -37.392 12.48 3.77 -3.12 -8.95
2006 2.089 1.834 1.263 0.767 0.301 272,291 42,648 -18,741 -12,621 1,132.803 159.400 -64.321 -35.663 12.46 3.75 -3.18 -9.01
2007 2.081 1.830 1.261 0.765 0.301 275,443 43,347 -19,257 -12,897 1,150.416 159.368 -64.169 -34.035 12.48 3.75 -3.22 -9.06
2008 2.071 1.825 1.259 0.763 0.300 278,237 43,894 -19,827 -13,178 1,167.717 158.925 -64.223 -32.522 12.48 3.73 -3.28 -9.12
2009 2.058 1.818 1.255 0.760 0.300 280,661 44,198 -20,448 -13,456 1,184.192 157.998 -64.452 -31.099 12.46 3.70 -3.33 -9.19
2010 2.047 1.813 1.252 0.757 0.299 283,359 44,553 -21,050 -13,732 1,201.856 157.343 -64.584 -29.737 12.46 3.68 -3.39 -9.25
2011 2.034 1.807 1.248 0.755 0.298 285,988 44,814 -21,687 -14,012 1,218.816 156.386 -64.763 -28.437 12.45 3.66 -3.45 -9.32
2012 2.023 1.801 1.245 0.752 0.298 288,805 45,109 -22,318 -14,294 1,236.003 155.503 -64.854 -27.184 12.44 3.63 -3.51 -9.39
2013 2.010 1.795 1.241 0.749 0.297 291,582 45,311 -22,985 -14,579 1,252.273 154.295 -64.974 -25.980 12.43 3.60 -3.57 -9.46
2014 1.998 1.790 1.238 0.747 0.296 294,471 45,509 -23,656 -14,866 1,268.342 153.047 -65.037 -24.823 12.42 3.57 -3.64 -9.53
2015 1.986 1.784 1.234 0.744 0.294 297,308 45,623 -24,354 -15,154 1,283.544 151.540 -65.105 -23.711 12.41 3.54 -3.70 -9.61
2016 1.973 1.778 1.230 0.741 0.293 300,288 45,738 -25,054 -15,440 1,298.855 150.037 -65.120 -22.641 12.40 3.50 -3.77 -9.68
2017 1.960 1.772 1.226 0.738 0.292 303,103 45,756 -25,796 -15,735 1,312.949 148.178 -65.175 -21.619 12.38 3.46 -3.84 -9.76
2018 1.947 1.766 1.222 0.735 0.291 306,170 45,819 -26,541 -16,036 1,327.705 146.455 -65.169 -20.644 12.37 3.43 -3.91 -9.85
2019 1.934 1.760 1.218 0.732 0.289 309,129 45,810 -27,326 -16,348 1,341.533 144.457 -65.191 -19.714 12.36 3.38 -3.98 -9.93
2020 1.919 1.754 1.214 0.728 0.288 312,014 45,719 -28,156 -16,676 1,354.450 142.208 -65.234 -18.829 12.33 3.34 -4.05 -10.03
2021 1.905 1.748 1.209 0.725 0.286 314,900 45,588 -29,014 -17,014 1,366.671 139.813 -65.250 -17.978 12.31 3.29 -4.13 -10.12
2022 1.890 1.742 1.204 0.722 0.284 317,834 45,424 -29,898 -17,363 1,378.385 137.329 -65.230 -17.160 12.29 3.24 -4.21 -10.22
2023 1.876 1.735 1.200 0.718 0.282 320,797 45,235 -30,808 -17,723 1,389.537 134.748 -65.179 -16.376 12.26 3.18 -4.29 -10.32
2024 1.862 1.729 1.195 0.715 0.280 323,800 45,032 -31,740 -18,092 1,400.316 132.113 -65.091 -15.623 12.24 3.13 -4.37 -10.42
2025 1.847 1.723 1.191 0.712 0.278 326,827 44,802 -32,700 -18,474 1,411.041 129.441 -64.999 -14.907 12.21 3.08 -4.46 -10.52
2026 1.833 1.718 1.186 0.708 0.276 329,888 44,566 -33,674 -18,860 1,421.771 126.783 -64.870 -14.221 12.18 3.02 -4.54 -10.62
2027 1.819 1.712 1.182 0.705 0.274 332,717 44,268 -34,651 -19,243 1,436.940 124.469 -64.944 -13.609 12.16 2.97 -4.62 -10.73
2028 1.805 1.706 1.177 0.702 0.272 335,573 43,968 -35,641 -19,630 1,452.433 122.179 -64.994 -13.023 12.13 2.91 -4.70 -10.83
2029 1.791 1.700 1.173 0.698 0.270 338,460 43,662 -36,651 -20,028 1,468.326 119.900 -65.040 -12.466 12.10 2.86 -4.78 -10.93
2030 1.777 1.695 1.168 0.695 0.268 341,358 43,341 -37,679 -20,435 1,484.554 117.623 -65.078 -11.935 12.08 2.80 -4.86 -11.04
2031 1.764 1.690 1.164 0.692 0.266 344,306 43,026 -38,716 -20,846 1,501.281 115.401 -65.091 -11.426 12.05 2.75 -4.95 -11.14
2032 1.751 1.685 1.160 0.689 0.265 347,323 42,724 -39,757 -21,260 1,518.536 113.251 -65.069 -10.937 12.03 2.69 -5.03 -11.25
2033 1.739 1.680 1.156 0.686 0.263 350,428 42,442 -40,798 -21,676 1,536.350 111.190 -65.007 -10.467 12.00 2.64 -5.10 -11.35
2034 1.727 1.675 1.152 0.683 0.261 353,585 42,164 -41,854 -22,101 1,554.534 109.155 -64.929 -10.017 11.98 2.59 -5.18 -11.45
2035 1.716 1.671 1.149 0.680 0.259 356,818 41,892 -42,919 -22,532 1,573.161 107.171 -64.823 -9.587 11.96 2.54 -5.26 -11.55
2036 1.705 1.667 1.145 0.677 0.258 360,146 41,639 -43,984 -22,966 1,592.255 105.268 -64.677 -9.172 11.95 2.50 -5.33 -11.65
2037 1.694 1.663 1.142 0.675 0.256 363,570 41,404 -45,052 -23,404 1,611.759 103.433 -64.493 -8.772 11.93 2.45 -5.40 -11.75
2038 1.684 1.659 1.138 0.672 0.254 367,105 41,191 -46,121 -23,844 1,631.692 101.676 -64.268 -8.388 11.92 2.41 -5.47 -11.85
2039 1.675 1.656 1.135 0.670 0.253 370,746 40,999 -47,192 -24,289 1,651.961 99.987 -64.003 -8.017 11.91 2.36 -5.54 -11.94
2040 1.666 1.652 1.133 0.668 0.251 374,503 40,826 -48,266 -24,738 1,672.556 98.366 -63.699 -7.661 11.90 2.33 -5.61 -12.03
2041 1.657 1.649 1.130 0.666 0.250 378,340 40,655 -49,349 -25,194 1,693.273 96.772 -63.366 -7.319 11.90 2.29 -5.67 -12.13
2042 1.649 1.646 1.127 0.664 0.249 382,283 40,506 -50,428 -25,651 1,714.188 95.248 -62.986 -6.988 11.89 2.25 -5.73 -12.22
2043 1.641 1.644 1.125 0.662 0.247 386,315 40,376 -51,503 -26,108 1,735.212 93.785 -62.561 -6.669 11.89 2.22 -5.79 -12.30
2044 1.634 1.641 1.122 0.660 0.246 390,434 40,258 -52,582 -26,571 1,756.356 92.363 -62.105 -6.363 11.89 2.18 -5.85 -12.39
2045 1.627 1.639 1.120 0.658 0.245 394,669 40,169 -53,654 -27,032 1,777.799 91.027 -61.608 -6.067 11.89 2.15 -5.91 -12.47
2046 1.620 1.636 1.118 0.656 0.244 398,998 40,089 -54,734 -27,500 1,799.508 89.733 -61.093 -5.785 11.89 2.12 -5.96 -12.56
2047 1.614 1.634 1.116 0.655 0.243 403,432 40,029 -55,816 -27,971 1,821.577 88.501 -60.554 -5.514 11.89 2.10 -6.02 -12.64
2048 1.608 1.632 1.114 0.653 0.241 407,956 39,983 -56,903 -28,447 1,843.988 87.317 -60.000 -5.254 11.90 2.07 -6.07 -12.72
2049 1.602 1.631 1.112 0.651 0.240 412,596 39,967 -57,985 -28,923 1,866.905 86.215 -59.422 -5.006 11.90 2.04 -6.12 -12.79
2050 1.597 1.629 1.111 0.650 0.239 417,268 39,960 -59,064 -29,400 1,889.987 85.152 -58.825 -4.768 11.91 2.02 -6.17 -12.87
2051 1.592 1.627 1.109 0.649 0.238 422,078 39,981 -60,143 -29,879 1,913.759 84.171 -58.216 -4.540 11.92 2.00 -6.21 -12.94
2052 1.588 1.626 1.108 0.647 0.237 427,016 40,038 -61,216 -30,357 1,938.226 83.282 -57.591 -4.323 11.93 1.98 -6.26 -13.01
2053 1.583 1.625 1.106 0.646 0.236 432,055 40,111 -62,299 -30,844 1,963.303 82.440 -56.966 -4.115 11.94 1.96 -6.30 -13.08
2054 1.579 1.624 1.105 0.645 0.236 437,227 40,226 -63,370 -31,327 1,989.184 81.700 -56.325 -3.917 11.95 1.94 -6.34 -13.14
2055 1.576 1.623 1.104 0.644 0.235 442,509 40,369 -64,438 -31,810 2,015.811 81.033 -55.678 -3.728 11.97 1.93 -6.38 -13.20
2056 1.572 1.622 1.103 0.643 0.234 447,899 40,537 -65,507 -32,295 2,043.201 80.429 -55.030 -3.548 11.98 1.91 -6.41 -13.26
2057 1.569 1.621 1.102 0.642 0.233 453,390 40,719 -66,584 -32,783 2,071.350 79.867 -54.386 -3.376 12.00 1.90 -6.45 -13.32
2058 1.566 1.620 1.101 0.641 0.233 459,009 40,920 -67,673 -33,278 2,100.399 79.352 -53.752 -3.213 12.01 1.89 -6.48 -13.38
2059 1.563 1.619 1.100 0.641 0.232 464,737 41,128 -68,778 -33,782 2,130.249 78.863 -53.130 -3.058 12.03 1.88 -6.52 -13.43
2060 1.560 1.618 1.099 0.640 0.231 470,557 41,350 -69,892 -34,291 2,160.806 78.407 -52.512 -2.911 12.04 1.87 -6.55 -13.49
2061 1.558 1.618 1.098 0.639 0.231 476,473 41,585 -71,013 -34,804 2,192.055 77.987 -51.897 -2.771 12.06 1.85 -6.58 -13.54
2062 1.555 1.617 1.098 0.638 0.230 482,506 41,851 -72,130 -35,315 2,224.074 77.627 -51.276 -2.637 12.08 1.85 -6.61 -13.59
2063 1.553 1.617 1.097 0.638 0.229 488,645 42,131 -73,254 -35,830 2,256.758 77.299 -50.657 -2.509 12.10 1.84 -6.64 -13.64
2064 1.551 1.616 1.096 0.637 0.229 494,891 42,430 -74,382 -36,346 2,290.076 77.007 -50.037 -2.387 12.12 1.83 -6.67 -13.68
2065 1.549 1.616 1.096 0.636 0.228 501,248 42,739 -75,523 -36,868 2,324.009 76.733 -49.420 -2.271 12.13 1.82 -6.70 -13.73
2066 1.547 1.615 1.095 0.636 0.228 507,702 43,073 -76,659 -37,389 2,358.448 76.503 -48.796 -2.160 12.15 1.81 -6.72 -13.77
2067 1.546 1.615 1.095 0.635 0.228 514,227 43,422 -77,796 -37,911 2,393.232 76.293 -48.168 -2.053 12.18 1.81 -6.75 -13.81
2068 1.544 1.615 1.094 0.635 0.227 520,802 43,783 -78,931 -38,431 2,428.243 76.098 -47.533 -1.952 12.20 1.80 -6.77 -13.85
2069 1.543 1.614 1.094 0.634 0.227 527,445 44,156 -80,067 -38,952 2,463.539 75.918 -46.895 -1.855 12.22 1.80 -6.80 -13.89
2070 1.541 1.614 1.093 0.634 0.227 534,192 44,541 -81,212 -39,478 2,499.271 75.752 -46.259 -1.763 12.24 1.80 -6.82 -13.93
2071 1.540 1.614 1.093 0.633 0.227 541,049 44,938 -82,370 -40,009 2,535.467 75.598 -45.625 -1.675 12.26 1.79 -6.84 -13.96
2072 1.539 1.614 1.093 0.633 0.227 547,997 45,339 -83,541 -40,547 2,572.033 75.443 -44.997 -1.592 12.29 1.79 -6.87 -14.00
2073 1.537 1.614 1.092 0.633 0.226 555,046 45,746 -84,728 -41,091 2,609.019 75.289 -44.373 -1.512 12.31 1.78 -6.89 -14.03
2074 1.536 1.613 1.092 0.632 0.226 562,197 46,157 -85,932 -41,642 2,646.463 75.134 -43.756 -1.436 12.33 1.78 -6.91 -14.07
2075 1.535 1.613 1.091 0.632 0.226 569,422 46,571 -87,147 -42,198 2,684.242 74.978 -43.143 -1.364 12.35 1.78 -6.93 -14.10
2076 1.534 1.613 1.091 0.632 0.226 576,756 46,992 -88,378 -42,760 2,722.539 74.827 -42.536 -1.296 12.38 1.77 -6.96 -14.14
2077 1.533 1.613 1.091 0.631 0.226 584,283 47,430 -89,636 -43,336 2,761.795 74.695 -41.942 -1.231 12.40 1.77 -6.98 -14.17
2078 1.531 1.613 1.090 0.631 0.226 592,024 47,889 -90,926 -43,927 2,802.133 74.583 -41.361 -1.169 12.42 1.77 -7.00 -14.21
2079 1.531 1.613 1.090 0.631 0.226 599,360 48,341 -92,130 -44,479 2,840.656 74.453 -40.743 -1.110 12.45 1.77 -7.02 -14.24
2080 1.530 1.613 1.090 0.630 0.225 607,258 48,835 -93,422 -45,073 2,878.489 74.290 -40.116 -1.053 12.47 1.77 -7.04 -14.27
2081 1.529 1.613 1.089 0.630 0.225 615,081 49,296 -94,724 -45,669 2,919.546 74.163 -39.545 -1.000 12.49 1.76 -7.06 -14.31
2082 1.528 1.612 1.089 0.630 0.225 622,998 49,762 -96,043 -46,272 2,961.308 74.040 -38.983 -0.950 12.51 1.76 -7.08 -14.34
2083 1.527 1.612 1.089 0.629 0.225 631,009 50,233 -97,377 -46,881 3,003.794 73.922 -38.429 -0.902 12.54 1.76 -7.10 -14.37
2084 1.526 1.612 1.089 0.629 0.225 639,113 50,707 -98,728 -47,498 3,047.001 73.806 -37.885 -0.857 12.56 1.75 -7.12 -14.40
2085 1.524 1.612 1.088 0.629 0.225 647,307 51,183 -100,096 -48,122 3,090.928 73.691 -37.350 -0.814 12.58 1.75 -7.14 -14.44
2086 1.523 1.612 1.088 0.628 0.225 655,595 51,663 -101,481 -48,753 3,135.571 73.578 -36.823 -0.773 12.60 1.75 -7.16 -14.47
2087 1.522 1.612 1.088 0.628 0.224 663,988 52,150 -102,881 -49,392 3,180.976 73.471 -36.304 -0.734 12.63 1.75 -7.18 -14.50
2088 1.521 1.612 1.087 0.628 0.224 672,485 52,641 -104,300 -50,038 3,227.119 73.367 -35.793 -0.697 12.65 1.74 -7.20 -14.53
2089 1.520 1.612 1.087 0.627 0.224 681,089 53,138 -105,736 -50,692 3,273.994 73.266 -35.290 -0.662 12.67 1.74 -7.22 -14.56
2090 1.519 1.612 1.087 0.627 0.224 689,802 53,641 -107,190 -51,354 3,321.584 73.168 -34.793 -0.629 12.69 1.74 -7.24 -14.60
2091 1.519 1.611 1.086 0.627 0.224 698,632 54,151 -108,663 -52,025 3,369.910 73.074 -34.302 -0.598 12.72 1.74 -7.26 -14.63
2092 1.518 1.611 1.086 0.626 0.224 707,565 54,664 -110,155 -52,703 3,418.880 72.977 -33.819 -0.568 12.74 1.73 -7.28 -14.66
2093 1.517 1.611 1.086 0.626 0.224 716,626 55,186 -111,666 -53,391 3,468.589 72.885 -33.341 -0.539 12.76 1.73 -7.30 -14.69
2094 1.516 1.611 1.086 0.626 0.223 725,803 55,714 -113,198 -54,087 3,518.947 72.791 -32.870 -0.512 12.78 1.73 -7.32 -14.72
2095 1.515 1.611 1.085 0.625 0.223 735,101 56,247 -114,749 -54,793 3,569.961 72.698 -32.403 -0.487 12.80 1.73 -7.34 -14.75
2096 1.514 1.611 1.085 0.625 0.223 744,519 56,786 -116,322 -55,508 3,621.590 72.601 -31.943 -0.462 12.83 1.72 -7.36 -14.78
2097 1.513 1.611 1.085 0.625 0.223 754,064 57,332 -117,916 -56,232 3,673.843 72.505 -31.487 -0.439 12.85 1.72 -7.38 -14.82
2098 1.512 1.611 1.084 0.625 0.223 763,737 57,885 -119,530 -56,966 3,726.705 72.408 -31.036 -0.417 12.87 1.72 -7.40 -14.85
2099 1.511 1.611 1.084 0.624 0.223 773,534 58,441 -121,168 -57,711 3,780.169 72.305 -30.591 -0.396 12.89 1.72 -7.42 -14.88
2100 1.510 1.611 1.084 0.624 0.223 783,467 59,006 -122,827 -58,464 3,834.306 72.204 -30.151 -0.376 12.92 1.71 -7.44 -14.91
SOURCE: Author's calculations.

## 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

(1)  $E s , a , t S = c t N s , a , t S p s , a , t ( 1 − u s , a , t )$ ,

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

(2)  $e s , a , t E = π s , a , t π t H t E$ ;  $e s , a , t R = π s , a , t π t H t R$ ;  $e s , a , t S E = π s , a , t π t H t S E$ ,

where  $π t$  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.,

(3)  $π t = 1 ∑ s ∑ a E s , a , t S π s , a , t$ .

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

(4)  $e s , a , t = e s , a , t E + e s , a , t S E$ .

### 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,

(5)  $T s , a , t P = τ t E e s , a , t E E s , a , t S + τ t R e s , a , t R E s , a , t S + τ t S E e s , a , t S E E s , a , t S$ ,

where  $τ t E$  and  $τ t R$  respectively represent the projected employee and employer tax rates on OASI taxable wages and  $τ t S E$  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.,

(6)  $T a , t P = ∑ s T s , a , t P$ .

The  $τ t E$  ,  $τ t R$ , and  $τ t S E$  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

(7a)  $b s , a , j , t R = β s , j b ( a , s , t , e s , 0 , t − a , ... , e s , a − 1 , t − 1 )$  for a= j, and
(7b)  $b s , a , j , t R = g t μ s , a b s , a − 1 , j , t − 1 R$  for  a > j,

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 ( $β s , j$ ). 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 ( $μ s , a$ ) 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  $μ s , a$  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

(8)  $B a , t R = ∑ s ∑ j R s , a , j , t b s , a , j , t R$ .

### 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  $R a , t S 1$  and  $R a , t S 2$ .

The corresponding average benefit by age and year ( $b a , t S 1$  ,  $b a , t S 2$ ) 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  $b s , a , t S n$  for the first two secondary beneficiary classes are first computed from the relationship  $b s , a , t S n = k s , a S n b s , a , t R$ , 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  $k s , a S n$  are determined from administrative benefit data in the last available historical year. The provisional  $b s , a , t S n$  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  $b s , a , t S n$  are then combined across gender to derive the corresponding weighted average  $b a , t S n$  by age and year. Together, then, the number of secondary beneficiaries by beneficiary class, age, and year ( $R a , t S 1$  ,  $R a , t S 2$ ) and the respective average benefit received by those secondary beneficiaries ( $b a , t S 1$ $b a , t S 2$ ) determine the aggregate benefits received by secondary beneficiaries of the first two classes in each year; i.e.,

(9)  $B a , t S 1 = b a , t S 1 R a , t S 1$  and  $B a , t S 2 = b a , t S 2 R a , t S 2$ .

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

(10)  $B a , t S 3 = b a , t S 3 R a , t S 3$ ,

where the number of secondary beneficiaries of the third class  $R a , t S 3$  and their average benefits  $b a , t S 3$  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

(11)  $B a , t S = B a , t S 1 + B a , t S 2 + B a , t S 3$ .

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

(12)  $T a , t B = τ t B ( B a , t R + B a , t S )$ ,

where the effective tax rate  $τ t B$  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,

(13)  $J a , t = B a , t R + B a , t S − T a , t P − T a , t B$ .

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

(14)  $J t = ∑ a J a , t$

### 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

(15)  $S t S = r t F F t − J t − A t − R R t$ ,

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

(16)  $F t + 1 = F t + S t S$ .

### 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.

## Notes

1 See Board of Trustees of the Federal Old-Age and Survivors Insurance and Disability Insurance Trust Funds (2002) for additional detail on these assumptions. Subsequent Trustees Reports have incorporated relatively small incremental and sometimes offsetting changes in the intermediate economic and demographic assumptions most relevant to lifetime money's worth and redistributional outcomes across cohorts. In the 2006 Trustees Report compared to the 2002 Trustees Report, for example, total fertility rate projections are generally a bit higher but age-adjusted death rate projections are also generally a bit higher, especially for the 65 and over group; projected net immigration in the 2006 Report is initially higher (primarily for other than legal immigration) but identical to the 2002 Report after 2025; the projected growth rate in total employment is very close without a uniform direction of change between the two projections; the projected growth rate of earnings relative to compensation is generally the same while the projected growth rate in average hours worked is generally slightly higher in the 2006 Trustees Report; the projected real wage differential is generally the same in both Reports, as is the ultimate real trust fund interest rate. While details of simulations based on these projections would differ between the 2002 and 2006 Trustees Report, then, the differences in assumptions between the two Reports are relatively minor and should not affect the qualitative conclusions reached in this analysis.

2 Analogous taxes and benefits for the Social Security Disability Insurance (DI) program are not included in this analysis. Under program provisions, however, DI benefits are "converted" to OASI benefits under certain circumstances, such as the disabled worker's attainment of full retirement age. Such converted benefits are included in this analysis as OASI benefits, since the converted benefits are paid out of the OASI trust fund. See the Annual Statistical Supplement to the Social Security Bulletin for further detail on the treatment of such benefits.

3 The focus in this paper, then, is on historical and projected outcomes for cohorts as a whole. As such, this analysis includes, as examples, taxes paid by cohort members who for various reasons receive no benefits and benefits received by cohort members who for various reasons paid little or no taxes prior to entitlement. The treatment of cohort-specific taxes and benefits is further clarified in the remainder of this section.

4 Benefits payable to the insured worker on whose account the benefits were earned are referred to as "primary" benefits.

5 As discussed below, the most comparable recent studies are Leimer (1994) and Anderson, Yamagata, and Tuljapurkar (2001). Except for benefits received by children, both of these studies allocate secondary benefits to the birth cohort of the secondary beneficiary. Although they use somewhat different empirically-based methods, both studies attempt to allocate child benefits to the birth cohorts of their parents. The present study allocates child benefits to the birth cohort of the child.

6 The relative merits of the two approaches depend largely, of course, on whether the policy interest of a particular analysis is on program outcomes differentiated by the characteristics of the worker on whose account the benefits are earned or by the characteristics of the beneficiaries actually receiving the benefits. For some characteristics, such as certain family income or other family or household measures, the two approaches may lead to similar conclusions. For other characteristics, including age and gender, the two approaches can lead to different conclusions.

7 While there is empirical support for this assumption, as a practical matter any general assumption other than full backward shifting would greatly complicate the identification of the specific groups bearing the tax. The payroll tax incidence assumption becomes more potentially problematic the greater the number of characteristics by which program participant outcomes are differentiated. In that sense, the incidence assumption should be less potentially problematic in the present analysis, which differentiates program participant outcomes only by birth cohort.

8 The last available version (1977) of the 0.1 percent CWHS file, which includes annual taxable earnings back to 1937 for individual records, was used to identify OASI payroll taxes prior to 1951. The 2001 version of the larger 1 percent CWHS file, which includes annual OASI taxable earnings back to 1951 for individual records, was used for later years. See Smith (1989) for a description of the CWHS.

9 The aggregate OASI payroll tax liability for each year was derived by applying historical OASI payroll tax rates to aggregate annual taxable wage and salary earnings and self-employment earnings (Tables 2.A3 and 4.B2 in the 2002 Annual Statistical Supplement). Sample payroll taxes were adjusted to aggregate controls for consistency with the benefit estimation procedure described below and because of evidence that individual wage records tend to underestimate actual taxable earnings each year based on employer reports. The adjustment adopted effectively assumes that the proportional underestimate in a given year is the same across workers of all ages.

10 These summary tables have been published annually in past issues of the Social Security Yearbook and Annual Statistical Supplement to the Social Security Bulletin based on then available administrative data. Although the format of and specific detail in these tables have varied over time, all of the summary tables except for the years 1940–1942 report monthly benefits in current payment status as of year-end. The summary tables for 1940, the first year that monthly benefits were paid, report benefits awarded during the year. The 1941 and 1942 tables report benefits in force at year-end, where benefits in force represent benefits awarded after adjustment for terminations and other factors. As examples of the tables used, see Tables 25 through 29 in the 1940 Social Security Yearbook and Tables 5.A1.1 through 5.A1.8 in the 2002 Annual Statistical Supplement. A summary table for 1981 was not published in the Annual Statistical Supplement, so the distribution of benefits by age within each beneficiary category in that year was derived by interpolating between the corresponding summary benefit table estimates for 1980 and 1982.

11 More precisely, the published tables allowed historical monthly benefits to be separated into five subcategories for greater accuracy. The largest subcategory includes monthly benefits to entitled retired workers, spouses of retired workers, widows and widowers, and dependent parents. The remaining four monthly benefit subcategories correspond to benefits to entitled children of retired workers, children of deceased workers, widowed fathers and mothers, and special age-72 beneficiaries. Leimer (2004) discusses the rationale underlying the composition of the five monthly benefit subcategories. The proportional distribution by age of aggregate year-end benefits within each of the five monthly benefit subcategories in the summary table for that year was then used to determine the age allocation of aggregate benefits paid from the OASI trust fund for that beneficiary subcategory during that year.

12 Benefit award reductions instead of benefit reductions across all beneficiaries were chosen as one of the stylized policies in this analysis because proposals to restore solvency to the program generally maintain scheduled benefits for present beneficiaries.

13 Smooth tax rate or benefit award adjustments that hit the financial balance targets precisely in every year from the end of the Trustees Report projection period and beyond were difficult to identify. A primary source of this difficulty was the effect of prior year adjustments on current year trust fund components, especially the "momentum" associated with unchanged real benefits for those already on the beneficiary rolls in the case of the benefit award adjustment policy. Various optimization techniques were applied in an effort to identify smooth tax rate and benefit award adjustment schedules with the desired financial balance characteristics.

14 Prior to 1994, all of the proceeds from the income taxation of OASI benefits were transferred to the OASI trust fund. Beginning in 1994, provisions exposing a greater proportion of Social Security benefits to income taxation went into effect, with the associated additional revenues transferred to the Hospital Insurance (HI) trust fund. The additional income tax revenues that are transferred to the HI trust fund do not contribute, of course, to the long-run financial balance of the OASI program. OASI benefit income tax liability excluding the portion transferred to the HI trust fund generally rose as a percent of total OASI benefits from about 1.5 percent in 1984 to about 3.2 percent in 2001.

15 An alternative rationale for including the income tax liabilities deriving from OASI benefits would be to provide money's worth estimates net of income taxation in general. At a minimum, this alternative rationale requires that all OASI benefit income taxation liabilities, including the portion transferred to the HI trust fund, be subtracted from OASI benefits or added to OASI payroll taxes.

16 For the lifetime net transfers and internal rate of return measures used in this analysis, it does not matter whether benefit income tax liabilities are added to payroll taxes or subtracted from gross benefits. In contrast, the interpretation of the lifetime benefit/tax ratio measure used in this analysis is affected by the inclusion of benefit income tax liabilities in the total OASI tax liabilities for each birth cohort. Specifically, contrasting gross benefits in the numerator to the sum of payroll and benefit income taxes in the denominator of the lifetime benefit/tax ratio implicitly provides a measure of the gross program benefits that are funded by all tax sources associated with the program. If, instead, benefit income tax liabilities were subtracted from gross benefits in the numerator of the ratio and compared to payroll taxes in the denominator, the lifetime benefit/tax ratio could be interpreted as a measure of the net benefits funded solely by payroll taxes under the program.

17 Historically, the effective benefit income tax rate in each year from 1984 on was identified from Department of the Treasury estimates of the aggregate OASI income tax liability in that year that was ultimately transferred back to the OASI trust fund divided by aggregate OASI benefit payments in that year. For example, U.S. Department of the Treasury (2001) reports estimates for calendar years 1994–1996 based on an analysis of tax returns in those years. Unpublished final Treasury estimates were used for calendar years 1997–1999. Unpublished preliminary Treasury estimates were used for calendar years 2000–2001. Prospectively, the effective benefit income tax rate in each year was derived from the Trustees Report projections of benefit income tax transfers to the OASI trust fund as a proportion of the corresponding projections of aggregate OASI benefit payments.

18 By way of explanation for less technical readers, the present value of a tax or benefit stream as of a selected evaluation date is equal to the sum of all the tax or benefit payments in that stream after each payment is first discounted or accumulated from the time of the payment to the selected evaluation date using a particular interest rate series. As an example, if the interest rate applicable during the period between two payments is 5 percent, the second of the two payments would be discounted by (that is, divided by) 1.05 to derive its present value evaluated at the time of the first payment, and the present value of the two-payment stream evaluated at the time of the first payment would equal the first payment plus the discounted value of the second payment.

19 The historical inflation rate series and large company stock index series correspond respectively to the Consumer Price Index for all urban consumers (not seasonally adjusted) and the S&P 500 Composite index with dividends reinvested; these series can be found in Ibbotson (2003). The estimated effective annual interest rates earned historically by the OASI trust fund were taken from Kunkel (1997) for the years 1940–1988; unpublished estimates for the years 1989–2001 with additional significant digits were provided by Jeffrey L. Kunkel of the Office of the Chief Actuary of the Social Security Administration. The OASI trust fund rate for the years 1937–1939 was assumed to be the same as the rate for 1940. The historical growth rate in aggregate OASI taxable earnings was derived from the corresponding series reported in Table 4.B1 of the 2002 Annual Statistical Supplement. The projected inflation rate series, OASI trust fund interest rate series, and OASI taxable earnings growth rate series were taken from the intermediate assumptions of the 2002 Trustees Report and extended beyond the Trustees Report projection period by assuming a continuation of patterns of change found in those series toward the end of the Trustees Report projection period. The annual rate of return for the large company stock index series was projected to maintain the same constant proportional relationship to the OASI trust fund interest rate series prospectively as was exhibited between those two series over the last five-year historical period available for this analysis (1997–2001). This assumption leads to an ultimate nominal large company stock annual rate of return of slightly over 10 percent.

20 Money's worth and redistributional analyses often fail to rationalize their choice of interest rates despite the critical dependence of analysis conclusions on that choice. See Leimer (1995) for further discussion of some of the issues involved.

21 This measure of redistribution from a program perspective abstracts from a number of complicating factors including the potential effect of large net transfers on market interest rates and therefore indirectly on the trust fund interest rate. Other complicating factors discussed more fully below include the treatment of administrative expenses and the policy basis of the trust fund interest rate determination.

22 Previous Social Security money's worth and redistributional analyses generally have not adopted this perspective. Some analysts have argued on a theoretical basis for the use of higher interest rates based on riskier market investments, as discussed below; a more common approach has been to use an interest rate based on relatively safe market investments, such as the rate of return to U.S. Treasury securities, but this approach has generally been based more on convention than on any rigorous rationale.

23 In this context, "mature" implies an existing program, past its startup period, with benefits financed by a temporally constant tax rate on the economic aggregate that serves as the program's tax base; "pure" implies that benefits are financed solely by taxes under the program, without a trust fund; "sustainable" implies that lifetime benefit adjustments of some type are automatically or episodically applied as required to maintain the solvency of a mature program over time in response to changing economic and demographic conditions. Relaxing these program characteristics can generate corresponding changes in the rate of return to affected program participants. The investment returns to a contingency or partial trust fund, for example, can affect the overall program rate of return as can the use of episodic tax adjustments to maintain program solvency. Such effects are discussed and illustrated in Leimer (2005a). Over the long-run, however, the rate of growth in the tax base necessarily represents the major component of the rate of return to a mature, sustainable program financed predominantly on a pay-as-you-go basis. Despite misstatements about program sustainability sometimes encountered in the current Social Security policy debate, pay-as-you-go programs can be designed to achieve guaranteed sustainability analogously to funded programs, with the degree of difficulty in both cases depending on program characteristics such as redistributional goals and the pooling of various types of economic and demographic risks. See Leimer (2005b) for additional discussion.

24 Leimer (2005b) provides additional discussion of this point in the context of the present Social Security policy debate. There is a growing literature concerning the potential welfare gains associated with pay-as-you-go retirement programs in the context of stochastic asset returns. As examples, see Leimer and Richardson (1992); Leimer and Pattison (1998); Dutta, Kapur, and Orszag (2000); and Matsen and Thogersen (2004). Krueger and Kubler (2006) also provide support for the potential portfolio-enhancing welfare gains of an unfunded social security system but conclude that the potential capital crowding-out effects of such a system may overturn these gains. Leimer (2005b), however, discusses ways in which the portfolio-enhancing welfare gains of a social security system can be captured without these potential capital crowding-out effects.

25 Again, see Leimer (2005b) for further elaboration of this qualification.

26 See Leimer and Richardson (1992) for a discussion of some of the associated theoretical issues, empirical estimates from the perspective of program participants, and references to other contributions in the literature. A potentially important implication of their empirical estimates is that consumers may even use a negative real interest rate when discounting expected Social Security taxes and benefits.

27 As examples, see Browning (1985) and Caldwell, Favreault, Gantman, Gokhale, Johnson, and Kotlikoff (1999). Issues central to the relative riskiness of the Social Security "investment" are discussed in greater detail in Leimer (1994, 1995, 2005b); Geanakoplos, Mitchell, and Zeldes (1999); Mariger (1999); and Diamond and Orszag (2005).

28 As such, identification of the interest rate effectively used by program participants is an empirical issue deserving additional investigation.

29 Over nearly all of the historical period, the rates of return on the special Treasury obligations held by the trust funds were based on the rates for marketable Treasury obligations sold to private investors. The mean and sample variance of the real annual rate of return to OASI trust fund assets over the 1940–2001 period both lie between the corresponding statistics for the Ibbotson (2003) intermediate-term government bond series and U.S. Treasury bill series. See Kunkel (1997, 1999) for further information on the determination and history of the rates earned on trust fund assets.

30 Under the 2002 Trustees Report projections, the geometric mean of the nominal OASI taxable earnings growth rate series over the prospective 2002–2080 period is about 1.5 percentage points larger than the geometric mean of the nominal inflation rate series, while the geometric mean of the nominal OASI trust fund interest rate series is about 1.7 percentage points larger than the geometric mean of the nominal OASI taxable earnings growth rate series over the same period.

31 Over the 1930–2001 period, for example, the mean and standard deviation were respectively about 0.087 and 0.200 for the Ibbotson (2003) real large company stock rate of return series compared to the corresponding statistics of 0.023 and 0.071 for the Ibbotson intermediate-term government bond rate series.

32 A common deficiency of redistributional and money's worth analyses is that they ignore the administrative costs of the alternative to which the Social Security program implicitly is being compared, biasing the comparison against Social Security. To the extent that they can be identified, of course, the administrative costs of specific alternatives to the Social Security program could be incorporated into such analyses. Administrative costs, operating expenses, and loading charges in private markets in part reflect marketing costs, adverse selection, and the inability to exploit the economies of scale enjoyed by a compulsory, nearly universal, public program.

33 Because administrative expenses represent a necessary cost associated with the provision of the retirement saving, annuity, and survivors insurance features of the program, net redistribution from a program perspective might be defined as the accumulated value of a group's benefits plus the accumulated value of their allocated share of administrative expenses less the accumulated value of their taxes.

34 There are, of course, a variety of other reasons why money's worth measures may not accurately reflect the value of the program to participants, including the failure of money's worth measures to adjust for market imperfections, general equilibrium effects, and individual preferences regarding risk and other program characteristics. Some of these effects are discussed more fully below. See Leimer (1995) and Geanakoplos, Mitchell, and Zeldes (1999) for additional discussion.

35 Because the program is projected to be out of long-run financial balance under present law provisions, however, the "present law" simulations imply the need for program revenue transfers that are not included in those simulations.

36 Leimer (2005a) displays and discusses projections of other annual program variables under the present law and balanced budget policies.

37 A trust fund reserve equal to annual expenditures is the contingency reserve target used in determining long-run solvency in the annual Trustees Report. See, for example, the definition of the "summarized cost rate" on page 195 of the 2002 Trustees Report.

38 See the Annual Statistical Supplement to the Social Security Bulletin for details of the determination of benefit awards under the present program. For the most part, monthly benefit awards on the account of a given worker, whether primary or secondary benefits, are derived under present law by applying proportional adjustments to the "primary insurance amount," or "PIA," calculated for that worker. The PIA is derived by applying a series of declining "replacement rates" (as given, for example, in Table 2.A11 in the 2002 Annual Statistical Supplement) to a measure of the lifetime taxable earnings for that worker denoted as "average indexed monthly earnings," or the "AIME." There are three AIME brackets in the PIA benefit formula, with successive marginal replacement rates of 90 percent, 32 percent, and 15 percent for the three brackets. The three AIME bracket thresholds or "bend points" are increased each year in the same proportion as the increase in a measure of the national average wage level, the same average wage measure used to index lifetime taxable earnings in the AIME calculation.

39 Leimer, Hoffman, and Frieden (1978) and Leimer (1979) discuss the various components of the Social Security benefit structure and the roles of these components in achieving the desired intracohort and intercohort adequacy and equity goals of the program.

40 While the focus in this study is on money's worth and redistributional effects across cohorts, policies that incorporate future reductions in average benefit awards may (depending on societal preferences) require strengthening the progressivity of the benefit formula within cohorts to preserve or enhance benefit adequacy for lower lifetime earners or address other equity concerns. This is particularly important if projected increases in longevity do not result in a narrowing of differential mortality by economic status.

41 The primary factor driving the growing divergence over time between projected expenditures and non-interest revenues under present law is the continuing declines in mortality rates underlying the Trustees Report and extended projections. See Leimer (2005a) for additional discussion of this result and its policy implications.

42 Over the entire 2015–2220 simulation period affected by the policy, the real average benefit award to new retirees declines from the preceding year in 15 years. All of these real declines occur in the 25 years from 2017 through 2041 and are under one percent in all but two of those years, with the largest real decline from the previous year being 1.78 percent in 2022. In practice, additional constraints could be placed on a balanced budget award adjustment policy to preclude, for example, any reduction in the real average benefit between successive years. Again, the stylized policies simulated in this analysis are simply intended to illustrate the general effects of policies of this type.

43 A tax increase policy can generally be effected with less lead time between the policy announcement and implementation dates than an award reduction policy-an award reduction policy must generally give workers additional time to adjust their retirement plans. The stylized policies simulated in this analysis illustrate this difference by adopting an implementation date for the award adjustment policy that is 5 years beyond the implementation date for the tax adjustment policy.

44 This definition of financial balance results, of course, in different trust fund levels and interest earnings between the two balanced budget policies corresponding to their differences in annual expenditures. Leimer (2005a) provides a more complete discussion of these trust fund differences and their policy implications.

45 See Leimer (2005a) for additional discussion of the policy implications of continuing mortality improvements over the long run.

46 The real internal rate of return is defined in this application as the constant interest rate that equates the present values of benefits and taxes for each birth cohort as a whole, where the cohort benefit and tax streams are first converted to constant dollars (that is, indexed to remove the effects of measured or projected inflation). Multiple internal rates of return are possible given the nature of the lifetime net transfer flows under the OASI program. The internal rate of return algorithm adopted in this analysis searches first for the positive root closest to zero and then similarly searches the negative domain if no positive root is found. A positive root was found, however, for all of the cohorts considered in this analysis.

47 The results displayed in Charts 3 through 11 begin with the 1901 single-year birth cohort. Results for the collective cohort group born prior to 1901 are reported in the text and in the appendix tables.

48 As indicated above, the trust fund and associated interest earnings are somewhat larger under the tax adjustment policy than under the award adjustment policy given the balanced budget criteria and fixed economic assumption set adopted in this analysis; these larger trust fund earnings contribute further to the higher internal rates of return under the balanced budget tax policy. These factors have analogous effects for the other money's worth and redistributional measures under the alternative policies, but are not discussed further in this analysis. See Leimer (2005a) for a more complete discussion.

49 As noted above, Leimer and Richardson (1992) found evidence that the appropriate interest rate from the perspective of consumers may even be negative. More generally, Leimer and Pattison (1998) found that, based on historical rates of return for broad asset classes, a pay-as-you-go retirement program with an earnings-related tax base can effectively create a retirement saving "asset" that increases expected portfolio returns over a substantial range of risk. Such results can be interpreted as suggesting that the rate of growth in the pay-as-you-go program's tax base represents an upper bound for the risk-adjusted rate of return that is appropriate for evaluating program outcomes over that range of risk subject to the constraint, of course, that the program size remains at or below a level consistent with an outward shift of the retirement asset portfolio efficiency frontier.

50 As indicated above, some analysts argue for the use of higher interest rates in Social Security analyses because of such factors as the demographic, economic growth, and political risks potentially affecting the future level of taxes and benefits. It should be kept in mind, however, that all private and public pension programs are affected by such risks, including political risks associated with possible changes in the regulatory provisions or tax treatment of such programs and associated investments.

51 See Leimer (2005a) for a more complete discussion of this issue. A "closed group" concept of unfunded liability is intended here, reflecting the expected net present value cost of the benefit and tax "promises" made under a given policy to the affected population, less the value of the trust fund assets that can be applied to meet those promises. For the affected population at a given time, this unfunded liability definition represents the amount by which the trust fund falls short of a fully funded level.

52 An alternative perspective that has been proposed (see Barro (1974, 1978, 1989)) is that (1) the intercohort transfers effected by the Social Security program may simply substitute public transfers for private transfers that would have occurred otherwise and that (2) any Social Security transfers in excess of those that would have occurred privately may be offset by increased private transfers back to younger generations to compensate them for the associated increased unfunded liability of the program. To the extent that these arguments hold, the money's worth and redistributional estimates presented in this paper become interesting accounting measures with little policy relevance-the redistribution identified by these estimates would have either occurred privately in the absence of the OASI program or been negated by offsetting private transfers. A companion implication is that the program would have no macroeconomic effects under such conditions because of these offsetting private responses.

53 The approach of using an essentially fixed economic and demographic assumption set to analyze the effects of policies with different unfunded liabilities might be justified in the context of a small open economy, but such a context is unrealistic for the U.S. economy. Alternatively, attempts to justify such an approach by effectively assuming other, offsetting, policies or behavioral responses in the public or private sector sufficient to maintain the validity of the fixed assumption set have the problem that the detailed effects of those offsetting policies or responses are not included in the analysis, leaving a partial and misleading representation of the total effects of the policies under those assumptions. Leimer (2005a) provides a more complete discussion of this issue.

54 This latter application implicitly requires that the unfunded liabilities be identical between policies at every point in time and abstracts from other macroeconomic effects arising, for example, from different microeconomic distributions of the aggregate unfunded liabilities and different public perceptions of implicit and explicit government debt. In practice, of course, these omitted macroeconomic effects may also be important.

55 In addition to the broader economic effects discussed in this paragraph, alternative policies can have other effects that are not captured by relatively narrow lifetime money's worth and redistributional measures. In addition to the market-improving and portfolio-enhancing effects discussed above, these other effects can include increased capital market access for some in a funded program; potential administrative cost reductions and freedom-of-choice tradeoffs in a mandatory program; and differences in the political feasibility of alternative financing approaches. Articles that discuss these general issues include Leimer and Pattison (1998), Geanakoplos, Mitchell, and Zeldes (1999), Mariger (1999), Diamond and Orszag (2005), and Leimer (2005b).

56 Estimates of the various money's worth and redistributional measures by birth cohort under present law are included in Appendix A for comparison purposes, but these estimates should be interpreted with the understanding that they include unfunded benefits.

57 The OASI tax base growth rate exceeded the OASI trust fund interest rate in 33 of the 43 years prior to 1981 and had a much higher average real rate (4.76 percent vs. -0.61 percent) and geometric mean real rate (4.51 percent vs. -0.67 percent) during that historical period.

58 See Leimer (2005b) for a more complete discussion of these issues, including the positive and negative characteristics that can be associated with mandatory pay-as-you-go public retirement programs and how some of the positive characteristics might be captured without incurring the negative characteristics.

59 Absolute present value measures of lifetime outcomes under the OASI program can be interpreted as "money's worth" measures when evaluated as of the initial cohort year, since this is a natural evaluation point from a participant cohort's perspective. Absolute present value measures that are evaluated as of a given point in time across all cohorts can be interpreted as "redistributional" measures, since this is a natural evaluation point from a program perspective. This is not a strong distinction, of course-the purpose of both types of measures is to illuminate the relationship between lifetime benefits and taxes under the program and both types of measures share issues regarding the choice of the appropriate interest rate series. Relative present value measures, such as the lifetime benefit/tax ratio, are independent of the evaluation date since the same evaluation date is used in both the numerator and denominator of the ratio.

60 These estimates are not equivalent to expected lifetime transfers per initial cohort member because of net immigration over the cohort's lifetime. The lifetime net transfers reflected in Charts 6 through 9 include benefits and taxes for net immigrants who are not part of the initial cohort population.

61 An interesting feature of Charts 6 through 9, which display absolute measures of lifetime outcomes, is the crossover that occurs between the plots for the OASI trust fund and the large company stock interest rate series over the cohort interval where both plots reflect negative lifetime net transfers. Such crossovers can occur when, for example, net transfer streams characterized by early predominantly negative elements and later predominantly positive elements have negative present values, as in these chart plots. For net transfer streams with uniformly negative early elements followed by uniformly positive elements, the derivative of the present value function with respect to the interest rate is negative so long as the present value itself is positive-increasing the interest rate applied to such a stream always reduces its present value, so crossovers do not occur under those conditions. When these conditions are relaxed, as in the case where the present value itself is negative, the sign of the derivative of the lifetime net transfer present value function with respect to the interest rate becomes analytically indeterminate, creating the potential for crossovers such as those observed in Charts 6 through 9 (and Tables 1 and 2).

62 This description abstracts from a number of complicating factors including the issue of the appropriate interest rate, discussed more fully below, and the treatment of administrative expenses, as discussed above. Although administrative expenses would be significantly higher under some proposed alternative policies, such expenses represent a relatively small and generally declining proportion of total trust fund expenditures for the present OASI program. Table 4.A1 of the 2002 Annual Statistical Supplement, for example, indicates that OASI administrative expenses represented 0.52 percent of total trust fund expenditures in 2001. This proportion is projected to fall even further to 0.12 percent by 2080 under the 2002 Trustees Report intermediate projections.

63 Some may take issue, however, with the specific investment terms of the marketable Treasury obligations that have been used for this purpose.

64 The aggregate lifetime net transfer tables for generally 10-year birth cohorts are included for readers interested in using these estimates for legacy debt calculations, as discussed in a subsequent subsection.

65 The signs of the corresponding estimates in Charts 6 and 8 and in Charts 7 and 9 will be identical for each single-year birth cohort, because the aggregate lifetime net transfer and the lifetime net transfer per initial cohort member for each single-year cohort under a particular policy and interest rate assumption differ only by a positive multiplicative factor that depends on the initial cohort population and the values of the interest rate index at the alternative evaluation dates. The rank order of the estimates by interest rate assumption for a particular single-year birth cohort can differ between Charts 6 and 8 and between Charts 7 and 9, however, because the relative sizes and even the rank order of the adjustments between the initial cohort evaluation date (used in Charts 6 and 7) and the fixed evaluation date of 2001 (used in Charts 8 and 9) can vary substantially over time.

66 As implemented in this analysis, the net transfers represented in the numerator and the taxable earnings in the denominator occur over only the last portions of the lifetimes of cohorts born prior to the inception of OASI taxes and benefits in 1937. For cohorts born during or after 1937, the lifetime net transfer/taxable earnings rate represents a full lifetime measure.

67 For example, see Geanakoplos, Mitchell, and Zeldes (1999) and Diamond and Orszag (2004).

68 See Geanakoplos, Mitchell, and Zeldes (1999) for one demonstration of this result. Under these abstract conditions, this is analogous to the requirement that the market interest rate exceed the economic growth rate for an economy to be "dynamically efficient." If instead the growth rate in the economy exceeds the market interest rate under these conditions, the economy can be characterized as "dynamically inefficient" with too much output allocated to capital formation and not enough to consumption. The concept of dynamic efficiency has been addressed in numerous economic growth articles; see Diamond (1965) for an early contribution to this literature.

69 In a stochastic environment, the conditions for dynamic efficiency also become much more complex. In particular, the relationships between market interest rates and the growth rates in economic aggregates cease to be reliable indicators of dynamic efficiency. See Abel, Mankiw, Summers, and Zeckhauser (1989) for further detail.

70 The legacy debt measure may also be a misleading indicator of the burden of an existing pay-as-you-go program on present and future cohorts for other reasons, such as the fiscal policy effects of the program. The Social Security program, for example, was established during a low point of the business cycle with an aged population in special need of financial assistance. Under such conditions, the establishment of a pay-as-you-go program can potentially address intergenerational equity concerns as well as lead to increased economic activity, resulting in more income and capital in subsequent periods. Such improvements in intergenerational equity and increases in private and total societal wealth would not be captured by the legacy debt accounting measure.

71 Longitudinal benefit data in files derived from administrative record samples cover only about one-half of the Social Security program's historical period. Although more historical years are available for the earnings records of sample individuals, administrative files with current earnings data only contain taxable earnings on an annual basis back to 1951. Because the life cycles of only the oldest cohorts have been completed, prospective tax and benefit streams must also be projected for most cohorts.

72 For example, Congressional Budget Office (2006) includes estimates at selected percentiles of the lifetime benefit/tax ratio for a subset of members of 10-year birth cohorts from 1940 to 2000 based on either scheduled or payable benefits under present law using a 3 percent real interest rate to discount lifetime tax and benefit flows. These estimates are not directly comparable to those presented in the present analysis for a number of reasons, including a different program and participant focus and important differences in assumptions and methods.

73 Anderson, Yamagata, and Tuljapurkar characterize these simulations as projecting results after year-end 1999 using an "autoregressive model of productivity growth, combined with stylized demographic forecasts."

74 The economic, demographic, and program variables that were constrained to the extent possible in Leimer (1994) included population, employment, beneficiary aggregates, beneficiary age distributions, inflation rates, average covered earnings, OASI taxable payroll, gross domestic output, OASI expenditures, OASI trust fund interest rates, and year-end OASI trust fund balances.

75 Figure 3 in Leimer (1992), based on an earlier but similar version of the Leimer (1994) model, illustrates the different time paths of real wage growth between the exogenous Trustees Report assumptions and the constrained general equilibrium model used in Leimer (1994).

76 More generally, if not constrained to the Trustees Report assumption set, the general equilibrium model in Leimer (1994) permitted evaluations of the broader economic effects of alternative OASI program and fiscal policies characterized by different unfunded liabilities and total government indebtedness; these evaluations included the effects on private consumption and saving, wages, prices, interest rates, and the total lifetime incomes of successive cohorts.

77 The 1991 Trustees Report projected the annual growth rate in the labor force to fall from 0.5 percent in 2010 to 0.1 percent in 2065 under the intermediate assumption set. The 2002 Trustees Report projected that rate to fall from 0.7 percent in 2010 to 0.2 percent in 2065 and remain at that level through 2080.

78 Differences in mortality rate projections are an important factor in the internal rate of return differences under the present law assumptions but not under the balanced budget policies discussed below. Under the balanced budget policies, increases in benefit costs resulting from improving survival rates are offset by either tax rate increases or benefit award decreases. Under the present law assumptions, however, the increased benefit costs resulting from improving survival rates are not offset in the simulations, resulting in higher internal rates of return for the later cohorts experiencing increased longevity. As indicated in a preceding endnote, the primary factor driving the growing divergence over time between projected expenditures and non-interest revenues under present law is the continuing declines in mortality rates underlying the Trustees Report and extended projections.

79 For example, the life expectancy for males at age 65 in 2065 under the intermediate assumption set was projected to be 18.5 years in the 1991 Trustees Report and 19.7 years in the 2002 Trustees Report. The corresponding projections for females were 22.4 and 22.6, respectively. By 2080, life expectancy at age 65 was projected to improve further under the 2002 Trustees Report intermediate assumptions to 20.4 years for males and 23.4 years for females.

80 The simulation period extends through 2150 in Leimer (1994) and through 2220 in the present analysis.

81 The Trustees Report population projections were available by single year of age except for an age 100+ group. In the present analysis, the population in each age 100+ group is allocated to single ages 100 through 120 using an approach consistent with the Trustees Report mortality rate projections, which are available by gender, year, and single year of age through age 119.

82 These average taxable earnings weights are projected over time by gender and age using estimates derived from constrained non-linear regressions on annual historical cross-sections of average taxable earnings per worker by gender and age. The cross-sections used were drawn from the 2000 1% Continuous Work History Sample (CWHS) and covered the period from 1984 through 2000. The regression data were limited to the 1984–2000 historical period because over that period there were no major changes in OASDI earnings coverage and the annual taxable maximum was automatically adjusted by the national average wage index. Separate regression equations for males and females were used to estimate the corresponding cross-section average taxable earnings profiles in each projection year. The male earnings regression allowed for both (1) age-specific effects that modify the shape of the relative cross-section profile over time and (2) proportional cohort-specific effects on the cross-section profile across successive ages as particular cohorts move through their work lives. Conditional on the projected cross-section profile of average taxable earnings for males, a second regression model was estimated and used to project age-specific changes in the relationship between the female and male average taxable earnings cross-section profiles over time.

83 The projected Trustees Report data were available by year, gender, single year of age (except for an age 95+ group) and age at entitlement (by single year of age with a separate category for disability conversions). This analysis allocates the number of retirees in each of the age 95+ groups to single years of age in the same relative proportions as found in the age distribution of the corresponding projected population in that year.

84 The OASI projections in the present analysis effectively assume that the relative distribution of benefit awards about the mean for each gender and age category remains constant over time such that the average benefit award for each gender and age category can be calculated from the average earnings history for that category. Some alternative benefit structures, such as "price-indexed" structures that index prior earnings and the "bend points" in the benefit formula by prices rather than wages, clearly violate this assumption and therefore cannot be simulated directly using the approach adopted in the present analysis.

85 Under the present benefit structure, these average benefit changes reflect such factors as the effects of additional earnings after retirement on the benefit award, changes over the retirement period in the proportion of benefits withheld due to the earnings test, and the likely positive correlation between the size of benefits and survival probabilities.

86 The Trustees Report data for each of these beneficiary classes included projections by single year of age except for an age 95+ group. The number of beneficiaries in each of these age 95+ groups is allocated in this analysis to single years of age in the same relative proportions as found in the age distribution of the corresponding population in that year.

87 The number of beneficiaries in the nondivorced category of both the total spouse and surviving spouse beneficiary groups vastly outweighs the corresponding number in the divorced category. For example, the 2002 Annual Statistical Supplement reports that the total number of nondivorced wives of retired workers with benefits in current payment status at year-end 2001 was about 2.6 million, compared to a total of about 120 thousand divorced wives of retired workers with benefits in current payment status at that point. The analogous data at year-end 2001 for aged nondivorced (nondisabled) widows was about 4.3 million compared to about 300 thousand aged divorced (nondisabled) surviving wives.

88 Since aged surviving spouse beneficiaries can be as young as age 60, average aged surviving spouse benefits at ages 60 and 61 are each provisionally assumed to remain constant over time relative to the corresponding average benefit for age-62 retirees of the same gender.

89 Based on monthly benefits in current payment status as of year-end 2001, for example, Tables 5.A1 of the 2002 Annual Statistical Supplement indicate that what are denoted here as the third class of monthly secondary benefits constituted about 23 percent of all monthly secondary benefits at that time. This proportion remains below 28 percent in all of the Trustees Report projection periods and stabilizes at less than 24 percent near the end of the Trustees Report projection period.

90 For example, Table 4.A1 of the 2002 Annual Statistical Supplement indicates that during the year 2001 the administrative expenses and transfers to the Railroad Retirement program components of the OASI trust fund respectively represented 0.5 and 0.9 percent of total OASI benefit payments in that year.

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