| ACTUARIAL NOTE                                                                |                                           |
|-------------------------------------------------------------------------------|------------------------------------------------|
|                                                                          | SOCIAL SECURITY ADMINISTRATION                 |
| Number 144June 2001                                                           | Office of the Chief ActuaryBaltimore, Maryland |
| INTERNAL REAL RATES OF RETURN UNDER THE OASDI PROGRAMFOR HYPOTHETICAL WORKERS |
| by Orlo R. Nichols, Michael D. Clingman, and Milton P. Glanz                  |

Introduction

 This note presents analysis of internal real rates ofreturn for hypothetical workers with various earnings patterns and levelsunder the Old-Age, Survivors and Disability Insurance (OASDI) program. Theinternal real rate of return (hereinafter referred to as the internal rateof return) is the real interest rate (effective real annual yield) forwhich the present value of expected payroll taxes is equal to the presentvalue of expected benefits. Therefore, internal rates of return representan attempt to answer the question: If the contributions of a group ofworkers with selected characteristics were invested to fund the futurebenefits of the workers and their dependents, at what real annual yieldwould the contributions need to be invested1?Because contributions are not expected to besufficient to fully finance scheduled benefits after 2037, analysis isincluded for the OASDI program both as in present law, and with assumedfuture increases in contribution rates that would fully finance thebenefits of present law.

 Because the Social Security program has operated on alargely pay-as-you-go (PAYGO) basis, the level of contributions of eachgeneration of workers is not directly related to the benefits they willreceive. Under a PAYGO plan, benefits are not based on the accumulation ofindividual contributions, as in a defined contribution plan, nor areannual contributions determined based on scheduled future benefits ofcurrent workers and beneficiaries, as in an advance-funded defined benefitplan. Rather, the combined amount of contributions from workers needed tofund the system at any time has been largely determined by the combinedamount of benefits paid at that time. The internal rates of return dependon the contribution tax rates and Social Security benefit levels set byCongress. They do not in any significant way reflect the rate of intereston assets invested in the OASI and DI Trust Funds.

 Internal rate of return does not reflect the full valueof insurance in reducing the risk for extreme outcomes, like death ordisability at very young ages or survival to very old ages. In addition,calculations of the internal rate of return from Social Security benefitsare not fully adequate for making comparisons with private-sector plans,since many features of Social Security benefits are not typicallyavailable in private-sector plans. Examples include guaranteedcost-of-living adjustments based on the Consumer Price Index, and benefitsfor life in the event of disability. However internal rates of return areof value for exploring the relative value of benefits provided acrossgenerations and types of workers.

 Hypothetical workers are presented in this note with twotypes of earnings patterns. These are designated as *steady* and *scaled* . A worker with a *steady* pattern has earnings that are a constantpercentage of the average wage2 for each year of work. A worker with a*scaled* earnings pattern has earnings that varywith age as a percentage of the average wage. Steady workers are assumedto enter covered employment at age 22 and remain employed untildisability, death, or retirement at age 65. Scaled workers are assumed toenter the labor force at age 21, and reflect varying rates of employmentuntil disability, death, or retirement at age 65. 

 The Office of the Chief Actuary has for years beenproducing internal rates of return. An example can be found in Appendix IIof Volume I of the 1994-96 Advisory Council Report on Social Security. Theoffice has only recently developed an approach for representing non-steadyhypothetical workers, referred to in this note as scaled workers.Alternative approaches to considering non-steady earnings histories havebeen addressed by other authors, and it is recognized that a broader setof earnings patterns might be desirable to more fully explore thedistributions of benefits payable and internal rates of return under theOASDI program. However, for the sake of practicality, the number of casesconsidered in this note is limited. 

 Internal rates of return are presented in tables 3, 4, 5,and 6 for hypothetical workers who differ by year of birth, earningslevel, family grouping, and earnings pattern (steady and scaled).

Methodology and Assumptions

 Computation of internal rates of return requires acomplete simulation of the experience of each hypothetical group ofworkers for all years after first entering the labor force (assumed at age21 or 22 for this note). The possibility of dying or becoming disabled ineach year after entering the labor force must be taken into account.Actual experience is used for historical years. Projections of futureexperience are based on the intermediate assumptions of the 2001 TrusteesReport. While it is recognized that mortality and disability both tend tobe higher for lower paid workers, this fact is not reflected in the casespresented in this note. Further analysis will be necessary to properlyaddress this issue. We have chosen hypothetical cases with 11 differentyears of birth from 1920 through 2004 to demonstrate the variation ininternal rates of return across generations. Our analysis includes thepayment of all OASDI benefits for death, disability, and retirement,reflecting historical and projected probabilities of death, disability,and recovery from disability. Retirement is assumed to be at age 65 fornon-disabled workers. 

 As mentioned above, two types of hypothetical earningspatterns are presented, *steady* and *scaled*.  The *steady* earnings pattern assumes that the worker is a steady full-time employeewith no interruptions in employment. The *steady*worker begins working in covered employment at age 22 and the worker'searnings increase each year at the same rate as the average wage. The*steady* worker is assumed to stay employed,except for periods of disability, until death, or until retirement at age 65.For the *steady* earnings pattern, the followingfour levels of earnings are presented in tables 3, 4, 5, and 6. 

- **Low:**  Annual earnings are equal to 45 percent of the average wage.
- **Average:**  Annual earnings are equal to the average wage. 
- **High:**  Annual earnings are equal to 160 percent of the average wage  3.
- **Maximum:**  Annual earnings are equal to the OASDI Contribution and Benefit Base  4.

 The OASDI benefit levels associated with these fourearnings levels "best represent"5 different proportions of the male, ascompared with the female, worker populations. The table below summarizes therepresentation of actual male and female retirees in 1999 by these fourcases. Additional discussion of the distributions illustrated in thistable is included in the section "Discussion of Worker Earnings andBenefit Levels".

| Hypothetical case | Percent with PIA 1 less than PIA for hypothetical case |   | Percent with PIA closest to PIAfor hypothetical case 2 |
|-------------------|--------------------------------------------------------|--------|--------------------------------------------------------|
||