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#=0Åbold Åital Åcaps SURVEY OF CONSUMER FINANCES: ! EMPLOYER SPONSORED PENSION BENEFIT PLANSÌÌÌ
#=0Richard T. Curtin
#<-Åital Åbold IntroductionÌÌ
0     The role of personal savings in shaping the course of the
 aggregate economy in the near and longer terms has received much
 attention in recent years.  Personal savings is important as well to
 the future financial viability of each American family.  American
 families have traditionally reported three major savings motives:  to
 provide reserve funds in case of emergency, illness, or income loss;
 to finance children's education; and, to provide for retirement.  How
 much is saved by households is also dependent on their entitlements to
 employer provided benefits and pensions, unemployment compensation,
 education assistance, social security benefits, health care, and other
 entitlements.  The 1983 Survey of Consumer Finances collected detailed
 information on household saving and wealth, including the amount and
 types of financial and nonfinancial investments and liabilities, as
 well as entitlements to private and public pension benefits.  The
 unique analytic potential of this data set lies in its ability to
 integrate the several sources of household wealth with private and
 public entitlements, so as to provide a systematic framework for the
 assessment of each specific component, and how they interact.
0      This paper details the overall research design and empirical
 methodology used to estimate entitlements to employer sponsored
 pension benefit plans.  The following sections describe the sample,
 research design, measurement model, benefit formulas, plan provisions,
 and the assumptions required for the estimation of entitlements.
#=-Åcaps Åital Åbold Sample DesignÌÌÌ
#<-Åital Åbold Derived SampleÌÌ
0     The sample for the study of Employer Sponsored Pension Benefit
 Plans was derived in three interdependent stages.  The overall
 research design was based on the use of the 1983 Survey of Consumer
 Finances to identify, in turn:  which households were covered by
 employer sponsored pensions; which pension providers and plans covered
 these employees; and which benefit formulas and requirements governed
 these pension entitlements.
0     Åital Åbold Stage 1:  Survey of Consumer Finances.ÌÌ  The Survey
 of Consumer Finances (SCF) was a personal interview survey based on a
 representative national sample of U.S. households. Detailed
 information on employment was obtained for the household head and
 spouse.  All respondents or spouses with work experience were
 questioned about pension coverage on their current job, as well as
 vested pension entitlements from prior employers.  Households that
 reported pension coverage were asked to identify the provider of the
 pension--in most cases, their employer.  Sections R and S of the SCF
 questionnaire, which contained the employment and pension information,
 as well as the questions used to identify and initially verify the
 name and address of the pension provider are shown in Exhibit A.
0     As shown in Table 1, there were 1886 households with 2261 people
 that reported being covered by one or more pension plans.  Of these,
 1735 households covering 2061 people gave permission and the necessary
 information to contact their pension provider.  Consequently, 91% of
 all covered employees in the original Survey of Consumers sample were
 included in the pension study sample base.  These 2061 people were
 covered by a total of 1158 different pension providers, and 1350
 different pension plans.  Thus, on average, each pension provider
 covered 1.8 sample members, and the average pension plan included 1.5
 sample members.
#0(<+>+>+>+>)
#=0Åbold Åital TABLE 1!!RESPONSE RATES ON THE SURVEY OF CONSUMER FINANCES PENSION STUDYÌÌ
#:1=^
#:2-5=Sample Base
#:2=Households
#:3=People
#:4=Providers
#:5=Plans
0Eligible for sample; 1886; 2261; ^; ^
0Permission and name given; 1735; 2061; 1158; 1350
9^; (92]%); (91]%); ^; ^
0Successful Provider Contact; 1609; 1882; 995; 1184
9^; (93]%); (91]%); (86]%); (88]%)
0Successful Plan Coding; 1421; 1641; 845; 1012
9^; (88]%); (87]%); (85]%); (85]%)
0Overall coverage rate; 75]%; 73]%; 73]%; 75]%
#:1-5
#.
0     Åital Åbold Stage 2:  Survey of Pension Providers.ÌÌ  All the
 pension providers that were identified in Stage 1 were pooled, and a
 sample listing was generated from the computerized records.  Duplicate
 references to the same provider were combined, and extensive checks
 were made on the accuracy of the name and address of the pension
 provider, and the name and telephone number of the appropriate contact
 person.  The sample base of providers was continually revised as new
 information was obtained--when it confirmed duplicate references to
 the same provider as well as when previously combined references
 proved to be different providers.
0     A telephone interview was conducted with each of the pension
 providers.  The computer generated questionnaire, shown in Exhibit B,
 automatically had inserted into it all the necessary information on
 both the pension provider and the households covered.  Each pension
 provider was asked to identify the pension plans that covered workers
 in a specific occupational classification and work location.  Each
 pension provider was asked for information on one or more members of
 the original Survey of Consumer Finances sample.  Following the
 initial telephone requests that official plan documentation be mailed
 to SRC, recontacts by telephone and mail were made as necessary to
 insure a high response rate.
0     Åital Åbold Stage 3:  Survey of Pension Plans.ÌÌ  Each pension
 plan that was identified in the provider survey was eligible for the
 Survey of Pension Plans.  Two kinds of coversheets were used to
 coordinate the coding of the various plan combinations sponsored by
 the same pension provider.  The first coversheet, generated for each
 pension provider, details all household IDs covered by each plan or
 plan combination offered by that pension provider.  The second
 coversheet, generated for each pension plan, gives detailed
 information on that single plan and the households it covered.  These
 documents are included in Exhibit C.  All information requested in the
 pension plan questionnaires was compiled from official plan documents
 by a trained staff of specialists.  General information on each plan
 was recorded in Part I of the questionnaire, defined benefit
 provisions in Part II, and defined contribution provisions in Part
 III.  These questionnaires are included in Exhibit C.  Coding
 guidelines and notation conventions are documented in Exhibit D.
0     Among all eligible pension providers, 86% were successfully
 contacted.  These providers covered 91% of all eligible sample
 members, indicating a higher success rate among the providers which
 covered multiple sample members.  In terms of individual pension
 plans, 88% were successfully contacted, again indicating that larger
 providers which offered several different plans were more likely to
 agree to participate in the study.  Once contacted, 85% of the
 providers provided sufficient information to insure accurate coding.
 When each of these stages are taken into account, the overall coverage
 rate was 73% for all eligible sample members, and 73% for all eligible
 pension providers.  The overall coverage rate for household was
 somewhat higher (75%), as was the coverage rate for all eligible
 pension plans (75%).
0     To estimate the dollar amount of pension entitlements held by
 U.S. households, data on the specific plan provisions and benefit
 formulas which cover each household member must be combined with that
 household member's employment and pension information.  Such estimates
 retain the underlying national representativeness of the original
 Survey of Consumer Finances household sample.  Analysts may also shift
 the primary focus of analysis from the household base to a base
 defined by the total number of distinct pension providers, or the
 total number of separate pension plans.
0     Depending on the objectives of analysis, weights can be devised
 to insure that each individual provider or plan has an equal
 probability of selection; or their probability of selection can be
 made proportional to the total number of persons or households covered
 by pensions; or proportional to the accumulated size of all vested
 entitlements.  Such weights would use the number of persons or
 households in each plan, the number of separate plans sponsored by
 each provider, or a measure of the financial size of the entitlements.
 The weights would take the form of the inverse of the number of
 workers covered by each plan, the inverse of the number of plans
 sponsored by each provider, and so forth.  Regardless of which weights
 or analysis focus is chosen, the underlying representativeness of the
 derived samples remains anchored at the household level.
#=-Åcaps Åital Åbold Research DesignÌÌÌ
#<-Åital Åbold Measurement StrategyÌÌ
0        Based on considerations of reporting burden, data quality, and
 analytic flexibility, a two-step procedure was selected to estimate
 vested entitlements to employer sponsored pensions.  The two steps
 separate the characteristics of pension plans from the characteristics
 and employment histories of participants.  In the first step, benefit
 formulas are identified for each pension plan in which respondents
 held vested entitlements.  In the second step, the specific
 characteristics and employment histories of respondents are combined
 with benefit formulas to produce dollar estimates of vested
 entitlements.
0        The two-step procedure insures that clearly identified and
 consistent methods are used to estimate entitlements across all the
 various types of pension plans.  The two-step procedure also expands
 the range of research designs that can be accommodated, since it
 allows the use of derived representative samples of all pension
 providers or plans, as well as all participants.  Potential changes in
 benefit amounts can be investigated by using the observed set of
 benefit formulas with simulated changes in the characteristics and
 employment histories of the participants.  Or, the observed
 characteristics and employment histories could be used along with
 simulated changes in benefit provisions, or both types of changes
 could be simulated to investigate potential developments.
#<-Åital Åbold Entitlements as WealthÌÌ
0        An important measurement objective of the 1983 Survey of
 Consumer Finances was to develop an estimate of wealth held by
 American households.  The SCF used a "balance-sheet" approach to
 systematically assess the various types of assets and liabilities held
 by households, with each component monetized at its current market
 value.  Unlike most assets held by households, vested pension benefits
 do not represent ownership of an asset "stock," but rather an
 entitlement to a "flow" of future benefits.  This issue is not limited
 to defined benefit plans, since the difference between defined benefit
 and defined contribution plans refers to how benefit amounts are
 determined, not when and how benefits are paid.  Both types of plans
 often make benefits payable only after a certain age, and may exclude
 the option of "lump-sum" withdrawals at any time.
0        Entitlements to benefit flows can be converted into stocks of
 wealth by discounting the expected stream of future benefits to their
 present value.  The present discounted value of the pension
 entitlement is the amount of money needed today to purchase an annuity
 contract which would provide for periodic payments of a certain amount
 over some given time period beginning at a specified future date.
0        Åital Åbold Economic assumptionsÌÌ.  The present discounted
 value calculations require assumptions regarding real rates-of-return
 on investments.  In addition, because of how some benefit formulas are
 structured, separate assumptions concerning nominal interest rates,
 inflation, and income growth over the relevant time horizons are often
 required.  Rather than fixing all present value calculations with a
 single set of assumptions, benefit formulas have been constructed
 using these assumptions as "exogenous" variables.  This enables the
 manipulation and control of these crucial economic assumptions, and
 thus supports a wider range of analysis designs.
0        Åital Åbold Behavioral assumptionsÌÌ.  A second set of
 assumptions involves the personal and employment characteristics
 required to calculate vested entitlements for individual respondents.
 These assumptions are required because pension entitlements are
 defined only in reference to the actual date the individual retires or
 terminates active participation in the pension plan.  Consequently,
 the exact dollar value of vested benefits depends on future decisions
 about job change and retirement.  Some analysts may prefer the "quit
 tomorrow" assumption for wealth analysis--generally, this would yield
 the minimum estimate of expected pension wealth.  Other analysts may
 want to compare this amount to that calculated under the assumption
 that the participant remained with the same employer until retirement
 --an indicator of the opportunity cost of changing employers.  More
 generally, analysts can vary these assumptions depending on the
 characteristics of the participant, for example, with the likelihood
 of remaining with the same employer increasing as the participant
 nears retirement age.
0        Differences in these behavioral assumptions can be organized
 under the following retirement circumstances:
8        1.  Normal retirement.
7        2.  Late retirement.
7        3.  Early retirement.
7        4.  Employment termination prior to retirement.
7        5.  Disability retirement.
7        6.  Death and survivor benefits.
0        The underlying reason to isolate the above retirement
 circumstances is that the dollar value of the vested entitlement often
 depends on these differences in retirement circumstances.  In general,
 different entitlement formulas apply to each of the six circumstances
 outlined above.  In many cases, pension plans specify actuarial
 adjustments to the normal retirement formula for earlier or later
 retirement, but some plans add penalties or supplements, and some
 specify minimum and maximum benefit amounts.
0        This focus on retirement circumstances is reflected in the
 overall organization of the questionnaire for the Survey of Pension
 Plans.  The major sections of Part II of the questionnaire determine
 the plan definitions, formulas, and other provisions, in turn, for
 each retirement circumstance listed above (see Exhibit C).  Using a
 standardized format, the same type of questions were asked across all
 retirement circumstances.  Each section begins with the identification
 of the variables the plan uses, and how these variables are defined in
 terms of the employment characteristics of the respondents.  In the
 middle of each section, the component formulas used to calculate
 benefits are recorded, grouped by common requirements and provisions.
 The third part of each section identifies the requirements and
 circumstances under which these benefits would be paid.  The last
 question in each section integrates the various component formulas
 along with their requirements and provisions into one final "decision"
 formula.
0        The circumstance under which participants eventually claim
 vested benefits can be viewed as a probabilistic outcome.  The
 expected pension entitlement would then be equal to a weighted sum of
 the probabilities and associated benefits that would accrue if: the
 employee terminates prior to retirement, the employee works until
 normal retirement, becomes disabled, chooses early retirement, and so
 forth.  The "quit tomorrow" assumption means the probability of
 immediate employment termination is assumed to be 1.0, and all other
 probabilities are assumed to equal 0.0.  More generally, any set of
 probabilities can be chosen, based on theoretical considerations,
 historical evidence, or respondent characteristics and preferences.
0        Åital Åbold Institutional assumptionsÌÌ.  The third set of
 assumptions involves the current and future financial viability of the
 pension plan itself, as well as how overall public policy and
 government regulation will affect these plans in the future.  Vested
 participants face a risk that the pension plan will be unable to meet
 its financial commitments when their entitlements are due.
 Developments in government policies, such as funding standards or
 benefit guarantees, also influence the type and extent of risk faced
 by participants.  Moreover, since benefits from employer sponsored
 pensions are often integrated with Social Security payments, future
 changes in Social Security benefit provisions would have an important
 impact on benefit amounts from private pensions.
#=-Åcaps Åital Åbold Measurement ModelÌÌÌ
#<-Åital Åbold Benefit FormulasÌÌ
0        A major objective of the Survey of Pension Plans was to
 identify and quantify plan provisions and benefit formulas using a
 standard format.  The standardization involves the transformation of
 benefit formulas into equations that used a limited number of
 respondent characteristics.  Although the specific form and content of
 the resulting formulas may differ widely, all the formulas share the
 same set of exogenous variables.  These formulas can then be combined
 with respondent information to estimate the specific benefit amounts
 under the various types of retirement circumstances.  In general, each
 formula was constructed as a function of a base amount plus benefits
 depending on the participants length of credited service, earnings,
 age, and so forth.  The actual future payment of the entitlements may
 also be viewed as dependent on the financial viability of the plan
 itself, and other associated factors.
0        The general form of the pension entitlement formulas can be
 written as a function of the pension plan variables, and the exogenous
 household variables as follows:
8(1)  PE@(Åital ijktÌ) = F@(Åital jkÌ) ( PPVARS@(Åital ijktÌ))
8(2)  PPVARS@(Åital ijktÌ) = H@(Åital jkÌ) ( HHVARS@(Åital ijktÌ))
0where the subscripts indicate:
8     i=1,...,n, the total number of respondents
7     j=1,...,m, the total number of pension plans
7     k=1,...,6, the six retirement circumstances
7     t=time index, with t=0 defined as the date of interview
0and the variables are defined as:
8PE@(Åital ijtkÌ) = Value of entitlements for the i$(Åital thÌ) respondent
             under the jÅital thÌ pension plan, with benefits
             calculated as of time Åital tÌ under the kÅital thÌ
             retirement circumstance.
8F@(Åital jkÌ) = Benefit formula for the jÅital thÌ pension plan under the
             kÅital thÌ retirement circumstance.
8PPVARS@(Åital ijktÌ) = Pension plan variables which determine benefit
             amounts.
8H@(Åital jkÌ) = Variable definition for the jÅital thÌ pension plan under
             the kÅital thÌ retirement circumstance.
8HHVARS@(Åital ijktÌ) = Participant's income and employment
             characteristics available from the Survey of Consumer
             Finances household survey.
0Because respondents often had entitlements to benefits from more than
 one pension plan, the total benefit amount represents the sum of the
 separate plan benefits under each of the retirement circumstances.
8(3)  TPE@(Åital iktÌ) = Åsum ^; j=1; mÌ PE@(Åital ijktÌ)
0where
8TPE@(Åital iktÌ) = Value of the sum of entitlements due to the iÅital thÌ
             respondent from all pension plans under the k$(Åital thÌ)
             retirement circumstance.
0Finally, the overall summary measure of pension entitlements
 represents the present value of the weighted sum of expected benefits
 under each of the retirement circumstances.
8(4)  WTPE@(Åital itÌ) = VÅsub Åital tÌÌÅqty Åsum ^; k=1; 6Ì (
                  PROB@(Åital ikÌ) * TPE@(Åital iktÌ)), BENDÅsub Åital ijkÌÌ,
                  DEATHDÅsub Åital ikÌÌ, RATEÅsub Åital tÌÌ, PRICEÅsub
                  Åital tÌÌ, RISKÅsub Åital jtÌÌÌ
0where
8WTPE@(Åital itÌ) = Weighted present discounted value of all pension
             entitlements for the i$(Åital thÌ) respondent.
8VÅsub Åital tÌÌ = Formula to calculate present discounted value of all
             entitlements as of time Åital tÌ.
8PROB@(Åital ikÌ) = Probability that the iÅital thÌ respondent retires
             under the kÅital thÌ circumstance.
8            Note that:  Åsum ^; k=1; 6Ì PROB@(Åital ikÌ) = 1.0
8RATE@(Åital tÌ) = Nominal interest rate over the relevant time period for
             benefit calculations made at time Åital tÌ.
8PRICE@(Åital tÌ) = Inflation rate over relevant time period for benefit
             calculations made at time Åital tÌ.
8RISK@(Åital jtÌ) = Risk factors associated with the j$(Åital thÌ) pension
             plan at time Åital tÌ.
8BENDÅsub Åital ikÌÌ = Participant's age at the time benefit payments
             begin under the k$(Åital thÌ) retirement circumstance.
8DEATHDÅsub Åital ikÌÌ = Participant's age at the time of death, given
             retirement occurred under the k$(Åital thÌ) retirement
             circumstance.
0     Åital Åbold Questionnaire Notation.ÌÌ  Instead of using the index
 Åital kÌ to identify the retirement circumstance, the questionnaire
 used separate notation for each retirement circumstance.  The term NR
 was used for the normal retirement formulas, LR for late retirement,
 ER for early retirement, VD for vested deferred retirement, DR for
 disability retirement, and DS for death and survivor benefits.  The
 two sets of notation are related as follows:
8         PE@(Åital ijktÌ) = NRT@(Åital ijtÌ) ^, for k=1
7              = LRT@(Åital ijtÌ) ^, for k=2
7              = ERT@(Åital ijtÌ) ^, for k=3
7              = VDT@(Åital ijtÌ) ^, for k=4
7              = DRT@(Åital ijtÌ) ^, for k=5
7              = DST@(Åital ijtÌ) ^, for k=6
0     Up to eight component formulas were coded for each of the
 retirement circumstances.  In order to calculate the final benefit
 amount across the separate formulas, a "decision" rule, which
 specifies how the component formulas are combined, determines the
 functional form f@(Åital jkÌ) in the equations below:
8   NRT@(Åital ijtÌ) = f@(Åital jÌ) (NR#1@(Åital ijtÌ), ......, NR#8@(Åital ijtÌ))
8   LRT@(Åital ijtÌ) = f@(Åital jÌ) (LR#1@(Åital ijtÌ), LR#2@(Åital ijtÌ))
8   ERT@(Åital ijtÌ) = f@(Åital jÌ) (ER#1@(Åital ijtÌ), ..., ER#5@(Åital ijtÌ))
8   VDT@(Åital ijtÌ) = f@(Åital jÌ) (VD#1@(Åital ijtÌ), ..., VD#5@(Åital ijtÌ))
8   DRT@(Åital ijtÌ) = f@(Åital jÌ) (DR#1@(Åital ijtÌ), ..., DR#5@(Åital ijtÌ))
8   DST@(Åital ijtÌ) = f@(Åital jÌ) (DS#1@(Åital ijtÌ), ..., DS#5@(Åital ijtÌ))
#<-Åital Åbold Plan ProvisionsÌÌ
0     In general, the variables included in benefit formulas were
 related to the employment tenure and income history of the
 participant.  Some plans also included variables which determined a
 Social Security offset or some other type of reduction to basic
 benefit amounts.  Defined contribution plans also required variables
 that defined the sources and amounts of annual contributions.  For
 each of the pension plan variables, pension plan formulas frequently
 specified several different definitions.  Most often, separate
 definitions were required by the different retirement circumstances,
 although many plans used several definitions in one or more formulas
 for the same retirement circumstance.  The questionnaire allowed from
 3 to 18 separate definitions of the plan variables.  Although the
 questionnaire allowed space for three definitions within each of the
 questionnaire sections, once defined, the plan variables could be used
 in any of the formulas.  Volume 2 of the accompaning documentation
 contains the dictionary and codebook for the pension plan survey
 instrument.
0     The plan variables specified were as follows:
8     ASY#:  Actual Service Years
7     PSY#:  Potential Service Years
7     FAP#:  Final Average Pay
7      SS#:  Social Security Offset
7     RED#:  Reduction factor
7     MAN#:  Mandatory contributions by participants
7    MMAN#:  Employer matching of mandatory contributions
7     VOL#:  Potential voluntary contributions by participants
7    MVOL#:  Employer matching of voluntary contributions
7     CTE#:  Employer contributions to plan
7     COE#:  Employer contributions to participants
7     CLS#:  Lump sum contributions at retirement
0     Åital Åbold Actual Service Years (ASY).ÌÌ  The vast majority of
 plans used the length of credited service to determine benefits.  Just
 7 percent of all plans did not include any ASY term, primarily defined
 contribution plans.  Nearly half of all plans used two or more ASY
 terms in benefit formulas.  Due to a wide variety of plan provisions,
 the use of four separate questions was required to define each ASY
 term.  The major variations involved eligibility requirements, the
 unit of accumulation, maximums, and date restrictions.  Each of these
 components of ASY were defined in terms of the participant's age, date
 of hire, work hours, and the date when employment terminates.
0     Åital Accumulation rule.Ì  Plans differed on the number of work
 hours required per year to accumulate each unit of service credit.
 Approximately one-third of all plans did not include any minimum work-
 hour requirements.  Another third required a minimum number of work
 hours per year to qualify for each unit of service credit, with no
 provisions for partial credit for part time employment.  A prorated
 credit for less than full time employment was given in about one-
 quarter of the cases.  Although the vast majority of plans limited the
 accumulation of service credit to one unit per year, a few plans
 allowed the accumulation of more than one unit per year.
0     Åital Accumulation eligibility.Ì  Most plans defined ASY to
 include all years of employment.  One-third of the plans, however,
 required that before accumulation of service credit could begin, the
 participant must have reached a certain age, or have completed a
 minimum number of years of employment, or both.
0     Åital Maximum accumulation.Ì  Over half of all plans limited the
 total number of service years that could be accumulated for benefit
 credit.  These limitations usually set a maximum age after which the
 participant could no longer accumulate service credit.  Less frequent
 were direct limitations on the total ASY that could be accumulated,
 and limitations that depended on a combination of age and ASY.
0     Åital Date restrictions.Ì  About 40 percent of the ASY terms
 covered only a specific calendar time period.  Service credit
 accumulated under a prior version of the plan often followed different
 rules than at present.  In addition, ASY terms used to determine
 supplemental benefits were also often subject to date restrictions.
0     Åital Åbold Potential Service Years (PSY).ÌÌ  Rather than
 accumulate a certain benefit amount for each year of employment, about
 one plan in six prorates benefits depending on the potential length of
 employment, given the participants date of hire.  When used in benefit
 formulas in conjunction with ASY, the ratio of actual to potential
 service years can range from 0.0 to 1.0, and was used to prorate
 benefits.  Three separate questions were used to define each PSY term,
 specifying the accumulation of the potential total service years,
 maximums, and date restrictions.  Each of the components of PSY were
 defined in terms of the participants date of hire, date of birth, and
 date of termination of employment.
0     Åital Potential accumulation rule.Ì  The definitions of PSY
 differ from ASY in that they count "backwards" from some specified age
 when the accumulation process must end.  In addition, about one-
 quarter of the plans specified a minimum number of years of employment
 before which the accumulation of service credit could not begin.
0     Åital Maximum limitations.Ì  Approximately one-fifth of the PSY
 definitions included a specific limitation on the maximum level of PSY
 that could be used in benefit formulas, regardless of the age and work
 history of the participant.
0     Åital Date restrictions.Ì  Approximately 7]% of the PSY terms
 applied to a specific calendar time period, usually to account for
 transitions in plan provisions and formulas.
0     Åital Åbold Final Average Pay (FAP).ÌÌ  Two-thirds of all benefit
 formulas depended on the income of the participants.  Plans differed
 widely on how income was defined.  In general, the various definitions
 of FAP required information on the participant's income history.
 Given an age-income profile for each participant, these definitions
 specified which age-income observations were used to define FAP.
0     Åital Averaging rule.Ì  Most plans specified a certain time
 period over which wages and salaries had to be averaged for use in
 benefit formulas.  Although the time periods ranged from one month to
 the participant's entire income history, plans usually focused on the
 last one to ten years of employment.  Some plans required averaging
 over consecutive years, while others allowed the highest average of
 any combination of years during the specified time interval.  Rather
 than using some fixed period of employment, in one-fourth of the cases
 the time period was defined by when the highest income level was
 achieved.
0     Åital Date restrictions.Ì  Plans sometimes specified specific
 calendar time periods that wages and salaries could be earned for the
 calculation of FAP variables--in about one-fifth of the cases.  These
 restrictions applied mainly to prior plan provisions and supplemental
 benefits.
0     Åital Maximum limitations.Ì  Half of all plans placed limitations
 on FAP when it was used in benefit formulas.  Two types maximums were
 specified.  The most common type of involved a maximum age after which
 any wages or salaries that were earned could not be used in the
 calculation of FAP.  The least common type was a direct limitation on
 the maximum level of wages and salaries that could be used in the
 calculation of FAP.
0     Åital Åbold Social Security Offset (SS).ÌÌ  One-third of the
 plans included an offset for social security benefits.  The offset
 provisions differed depending on the retirement circumstances under
 which benefits were paid, and on the age of the participant at the
 time of retirement, and on how future Social Security entitlements
 were estimated.
0     Åital Social security offset definition.Ì  Most plans that used
 offsets defined the offset in terms of the Social Security benefit
 amount.  Only about one-fourth of the SS terms were defined by the
 Social Security wage base.  For plans that used the SS benefit amount,
 formulas differed in whether this amount was the unreduced benefit
 payable at 65 or the reduced benefit payable at 62; and whether the
 benefit amount was based on the participant's own work history or
 whether it included spouse earnings and any additional amounts paid
 for dependents.
0     Åital Date restrictions.Ì  Only 5 percent of the SS terms had
 date restrictions, most commonly when the offset was defined by the
 annual wage base.
0     Åital Maximum limitations.Ì  One-third of the plans had maximums
 on the total amount of the SS offset that could be used in benefit
 formulas.  These offset maximums took two forms:  a maximum percentage
 of the Social Security benefit amount, and maximums on the
 participant's age or credited service years that could be used to
 calculate the SS offset.
0     Åital SS estimation methods.Ì  For participants that terminate
 employment before they are eligible to receive Social Security
 benefits, plans differed in how the offsets were estimated.  Major
 differences involved assumptions about the age at which the
 participant would begin receiving benefits, and whether the
 participant would work in the future.
0     Åital Åbold Reduction Factor (RED).ÌÌ Almost all defined benefit
 pension plans included a "reduction factor" that was used to lower
 normal retirement benefit amounts to account for other retirement
 circumstances, usually for early retirement, but also for disability
 and deferred vested retirement.  Two types of reduction factors were
 commonly used.  The first type was defined as an actuarial reduction,
 meant to leave benefits equivalent in economic value to those which
 would have been received at some later date.  The second type involved
 a fixed dollar or percentage reduction depending on the participant's
 age or credited service years at the time of retirement.
0     Åital Åbold Mandatory contributions (MAN).ÌÌ For plans that
 required contributions from participants, the provisions that governed
 these contributions were measured, including the amount of the annual
 mandatory contribution, withdrawal rights, and the time period and
 rate of interest accrual.
0     Åital Amount of contribution.Ì The most common type of mandatory
 contributions took the form of a fixed percentage of wages or
 salaries.  In a few plans, the percentage varied by income level, age,
 and service years.
0     Åital Withdrawal rights.Ì This variable specifies the conditions
 under which a participant that terminates employment can withdraw
 mandatory contributions prior to the time the participant would have
 been eligible to receive regular pension benefit payments.  Some plans
 had minimum age and service year requirements for withdrawals.
0     Åital Rate and period of Accrual.Ì Some plans included specific
 guidelines on how the rate of accrual on past contributions was
 determined, and some plans set restrictions on the length of the
 accrual time period.  Age and service year requirements were sometimes
 used to determine whether any accrued interest would be paid, and when
 the accrual period would begin.
0     Åital Åbold Matching of Mandatory contributions (MMAN).ÌÌ This
 variable specifies whether and how employers match participant's
 mandatory contributions.  Plan provisions varied in how matching
 amounts were determined, maximums on matching amounts, and whether
 matching was limited to participants that met some special
 requirement.
0     Åital Matching rule.Ì Although the most common practice was to
 match the exact amount of the participant's mandatory contribution,
 some plans provided less in matching funds for each dollar contributed
 by participants, while other plans provided more.  In a few plans, the
 rate of matching varied by the age or service years of the
 participant.
0     Åital Vesting of Matching Contributions.Ì Although all of the
 participant's contributions are immediately 100% vested, the matching
 contributions of the employers are subject to plan defined vesting
 schedules.
0     Åital Åbold Voluntary contributions (VOL).ÌÌ The measures of plan
 provisions which govern voluntary contributions are similar to those
 for mandatory contributions.  The major difference is that voluntary
 contributions can vary at the discretion of the participant, and thus
 the plan provisions are usually defined in terms of allowable ranges
 for contributions.
0     Åital Åbold Matching of Voluntary contributions (MVOL).ÌÌ These
 measures are comparable to those for matching mandatory contributions.
 The major difference is the more frequent use of maximum limits on the
 amount of the employer's matching voluntary contribution.
0     Åital Åbold Employer contributions to plan (CTE).ÌÌ Two distinct
 types of procedures were used to determine the dollar amount of the
 employer's contribution.  Under one procedure, the total amount of the
 employer's contribution to all plan members was determined first, and
 then this fixed total was allocated among plan participants.  The
 other procedure was to first determine the amount due each
 participant, and then the sum of these individual contributions
 determined the total employer contribution.  The variable CTE
 represents employer contributions that were determined using the first
 procedure, while the variable COE represents employer contributions
 determined using the second procedure.
0     Plans that first determined the total amount of the employer's
 contribution (CTE) specified both a rule for determining the total
 contribution, as well as a rule to allocate this fixed total among
 plan participants.
0     Åital Total contribution amount.Ì For plans that first determined
 the total size of the employer's contribution, the contribution amount
 often depended on the economic performance of the company, as measured
 by profits, or change in net worth.  These rules often included a
 minimum and maximum annual contribution amount.
0     Åital Allocation of total.Ì Once the total contribution is
 determined, rules for the allocation of these contributions among
 participants are needed.  Some plans divided the total employer
 contribution among participants in proportion to wages or hours
 worked; other plans varied the contribution depending on the
 participant's age or number of service years.  In addition to minimums
 and maximums on the total employer contribution, plans also frequently
 specified limits on contributions to individual participants.
0     Åital Åbold Employer contributions to participants (COE).ÌÌ Under
 this procedure, the rule for determining the annual contribution to
 each participant was measured by the variable COE.  The contribution
 rule frequently depended on the participant's wages or workhours, and
 the amount often varied by the number of service years or age of the
 participant.
0     Åital Åbold Lump sum contributions at retirement (CLS).ÌÌ In
 addition to regular annual contributions, some pension plans provided
 for lump sum contributions to the participant's account at the time of
 retirement.  Plans varied in how the amount of this additional
 contribution was determined, and whether the participant had to meet
 any special requirements.
#<-Åital Åbold Eligibility RequirementsÌÌ
0     Aside from the requirements imposed by the plan variables,
 pension plans also set specific conditions under which participants
 become eligible for particular benefit payments.  For each type of
 eligibility condition, up to 15 separate definitions were coded.  The
 requirements and conditions of payment were defined as follows:
8     RAS#:  Required age and service
7     ROT#:  Other requirements
7     DAT#:  Date restrictions
7     BEG#:  When payments begin
7     LEN#:  Length of payment period
0     Åital Åbold Required Age and Service (RAS).ÌÌ The vast majority
 of pension plans had age and service requirements which the
 participant had to satisfy to be eligible for benefits.  These
 requirements differed depending on the retirement circumstance, with
 the most restrictive requirements being for normal retirement
 benefits.  Typically, there was a set of alternative combinations of
 age and service years, and if the participant satisfied any one of the
 combinations, then they were eligible for the benefit payments.
0     Åital Åbold Other Benefit Requirements (ROT).ÌÌ Besides age and
 service year requirements, pension plans often had other requirements
 which the participant had to satisfy to receive benefits, especially
 when the benefit was a supplement or an alternative to the basic
 benefit.
0     Åital Åbold Date Restrictions on Benefit Payments
 (DAT).ÌÌ Formula date restrictions apply to the time period when the
 benefit payments begin.  These specific calendar time periods often
 applied to special supplements, or to changes in basic benefit levels
 over time.
0     Åital Åbold Date Payments Begin (BEG).ÌÌ  Although most benefits
 begin at the time of retirement and continue for the life of the
 participant, some benefit formulas determined amounts that start at
 some time after retirement.  In addition to vested deferred benefits,
 disability and survivor benefits were often timed to begin at some
 later date depending on the availability of other company provided
 disability income or the age of the beneficiary.  To account for these
 differences, the earliest time that payments could begin under each
 benefit formula was coded.
0     Åital Åbold Length of Payments (LEN).ÌÌ Each benefit formula was
 also coded as to the length of time the payments would continue.  Most
 often payments are made for life, however some benefit formulas
 determined amounts that would be paid for a fixed number of years or
 until a certain age.  In some cases, early retirement supplements were
 only paid until the participant became eligible for Social Security
 benefits.  Lump sum payments at the time of retirement were coded here
 as one time only payments.
#<-Åital Åbold Complete Entitlement FormulasÌÌ
0     The overall system of entitlement formulas, written in terms of
 the exogenous household information and the required behavioral,
 economic, and institutional assumptions, is as follows:
8WTPE@(Åital itÌ) = VÅsub Åital tÌÌÅqty Åsum ^; k=1; 6Ì ( PROB@(Åital ikÌ) *
             TPE@(Åital iktÌ)), BENDÅsub Åital ijkÌÌ, DEATHDÅsub Åital
             ikÌÌ, RATEÅsub Åital tÌÌ, PRICEÅsub Åital tÌÌ, RISKÅsub
             Åital jtÌÌÌ
8TPE@(Åital iktÌ) = Åsum ^; j=1; mÌ PE@(Åital ijktÌ)
8PEÅsub Åital ijktÌÌ = FÅsub Åital jkÌÌ(ASY#Åsub Åital ijktÌÌ, PSY#Åsub
             Åital ijktÌÌ, FAP#Åsub Åital ijktÌÌ, SS#Åsub Åital ijktÌÌ,
             RED#Åsub Åital ijktÌÌ, MAN#Åsub Åital ijktÌÌ, MMAN#Åsub
             Åital ijktÌÌ, VOL#Åsub Åital ijktÌÌ, MVOL#Åsub Åital
             ijktÌÌ, CTE#Åsub Åital ijktÌÌ, COE#Åsub Åital ijktÌÌ,
             CLS#Åsub Åital ijktÌÌ, RAS#Åsub Åital ijktÌÌ, ROT#Åsub
             Åital ijktÌÌ, DAT#Åsub Åital ijktÌÌ, BEG#Åsub Åital
             ijktÌÌ, LEN#Åsub Åital ijktÌÌ)
#Åeqn ASY#Åsub Åital ijktÌÌ = ÅalphaÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, WKHRSÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn PSY#Åsub Åital ijktÌÌ = ÅbetaÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, WKHRSÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn FAP#Åsub Åital ijktÌÌ = ÅgammaÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, WAGEÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn SS#Åsub Åital ijktÌÌ = ÅdeltaÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, WAGEÅsub Åital ijtÌÌ, BENDÅsub Åital ijÌÌ, SSWBÅsub Åital tÌÌ, SSBAÅsub Åital tÌÌ) ; ; Ì
#Åeqn RED#Åsub Åital ijktÌÌ = ÅepsilonÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ, WAGEÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn MAN#Åsub Åital ijktÌÌ = ÅetaÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ, WAGEÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn MMAN#Åsub Åital ijktÌÌ = ÅpsiÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ, WAGEÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn VOL#Åsub Åital ijktÌÌ = ÅthetaÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ, HHVOLÅsub Åital ijtÌÌ, WAGEÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn MVOL#Åsub Åital ijktÌÌ = ÅiotaÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ, HHVOLÅsub Åital ijtÌÌ, WAGEÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn CTE#Åsub Åital ijktÌÌ = ÅkappaÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ, HHVOLÅsub Åital ijtÌÌ, WAGEÅsub Åital ijtÌÌ, WKHRSÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn COE#Åsub Åital ijktÌÌ = ÅlambdaÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ, HHVOLÅsub Åital ijtÌÌ, WAGEÅsub Åital ijtÌÌ, WKHRSÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn CLS#Åsub Åital ijktÌÌ = ÅmuÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ, HHVOLÅsub Åital ijtÌÌ, WAGEÅsub Åital ijtÌÌ, WKHRSÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn RAS#Åsub Åital ijktÌÌ = ÅnuÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, WKHRSÅsub Åital ijtÌÌ) ; ; Ì
#Åeqn ROT#Åsub Åital ijktÌÌ = ÅxiÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ, QUALÅsub Åital ijÌÌ) ; ; Ì
#Åeqn DAT#Åsub Åital ijktÌÌ = ÅomicronÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ) ; ; Ì
#Åeqn BEG#Åsub Åital ijktÌÌ = ÅpiÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ) ; ; Ì
#Åeqn LEN#Åsub Åital ijktÌÌ = ÅrhoÌÅsub Åital jkÌÌ(BIRTHDÅsub Åital iÌÌ, HIREDÅsub Åital ijÌÌ, QUITDÅsub Åital ijÌÌ, BENDÅsub Åital ijÌÌ) ; ; Ì
#=-Åcaps Åital Åbold Estimation AssumptionsÌÌÌ
#<-Åital Åbold Household DataÌÌ
0     Based on information from the Survey of Consumer Finances and
 other sources, the following household variables are required for the
 estimation of pension entitlements.
8   BIRTHD@(Åital iÌ):  Date of birth.
7   HIRED@(Åital ijÌ):  Date/age hired.
7   QUITD@(Åital ijkÌ):  Date/age terminate employment.
7   BEND@(Åital ijkÌ):  Date/age retirement benefits begin.
7   DEATHD@(Åital ikÌ):  Date/age at death.
7   PROB@(Åital ikÌ):  Probability of retirement circumstance.
7   QUAL@(Åital ijÌ):  Participant's special qualifications.
7   WKHRS@(Åital ijtÌ):  Hours worked per year.
7   WAGE@(Åital ijtÌ):  Rate of pay per year.
7   HHVOL@(Åital ijtÌ):  Participant's voluntary contributions.
0     Åital Åbold Birth Date (BIRTHD).ÌÌ  The month and year of birth
 for each plan participant is available from the Survey of Consumer
 Finances.
0     Åital Åbold Hire Date (HIRED).ÌÌ  This variable defines the date
 the individual was hired by the employer for which the pension plan
 applies.  The date of hire is obtained from the SCF.  This date is in
 general different from the date of initial participation in the
 pension plan, as some plans allow participation only after a certain
 age or years of service.  However, even when plan participation did
 not commence on the date of hire, plans often included all years of
 service in the benefit formulas.  These differences in plan provisions
 are incorporated in the formulas and variable definitions specified
 above, for each of the Åital jÌ pension plans and Åital kÌ retirement
 circumstances.
0     Åital Åbold Date Terminate Employment (QUITD).ÌÌ Unlike the birth
 and hire dates, for the vast majority, the date of employment
 termination had not yet occurred at the time of the household
 interview.  For most all respondents, this date must be estimated.
 Information from the SCF includes the age at which the respondent
 expects to stop working: at their current job, at any full time job,
 and at any part time job.
0     Since pension entitlements from both current and past employers
 were included in the study, some respondent had already terminated
 employment, but had not yet begun to receive benefit payments.  For
 these cases, the date of employment termination is available from the
 SCF.  In the case of disability and death benefits, this date refers
 to the date of death or onset of the disability.
0     How this date is estimated for those who were working at the time
 of the interview is a matter of analytic objectives.  For some
 research objectives the quit date could be set to the date of the
 interview; or or it could be assumed that all participants work until
 some certain age, like 62 or 65; or the stated intentions and
 preferences of respondents about retirement could be used; or a more
 general model of decisions to retire could be employed, estimating
 differential retirement dates depending on the occupational, economic,
 demographic, and preference data available in the SCF.
0     Åital Åbold Benefit Payment Date (BEND).ÌÌ This variable defines
 the age at which actual benefit payments begin.  Although for normal
 and early retirement, the date of employment termination is often the
 same as the date when benefits begin, for other retirement
 circumstances these dates often differ.  Since all cases included in
 the sample represented future entitlements, this variable must be
 estimated for all respondents.  In most cases, the age at which
 benefit payments begin under each type of retirement circumstance is
 stipulated in the pension plan.  In some cases, however, the
 participant can choose among alternative starting dates, especially in
 the case of vested deferred retirement.  The SCF contains information
 on when the respondents expects to begin receiving benefits.
0     Åital Åbold Probability of Retirement Circumstance (PROB).ÌÌ For
 each respondent, a zero or some positive probability of occurrence can
 be assigned to each of the six retirement circumstances outlined
 above.  This variable is not independent from the other information on
 termination and benefit dates; rather, it is designed to be used in
 combination with this information so as to allow greater analytic
 flexibility.  When the age at which employment terminates is defined
 separately for each of the retirement circumstances (e.g. 65 for
 normal, 62 for early, 55 for disability, current age for vested
 deferred, etc.), a weighted sum can be estimated using the
 probabilities assigned to each circumstance.  In addition to the
 available SCF data on the respondent's future work plans, and expected
 retirement and benefit dates, the SCF included a self-assessed overall
 health status measure, and occupational and demographic information
 that could be used to estimate differential risks of disability and
 death.
0     Åital Åbold Special Qualifications (QUAL).ÌÌ Special
 qualifications are often required for special or supplemental benefit
 payments.  The most common type of special requirements involve the
 type of work (e.g. special benefit provisions for police), eligibility
 to receive other benefits (e.g. other benefits provided by the
 employer for disability, eligibility for Social Security), whether the
 respondent was employed during specific calendar time periods, and
 presence or absence of spouse.  Most of this information can be
 obtained from the SCF.  Some information, however, must be assumed,
 such as whether any potential disability qualifies for Social
 Security, whether the injury occurred at the work place, and so forth.
0     Åital Åbold Work Hours (WKHRS).ÌÌ  Unlike the above household
 variables which require an estimate of a single date or qualification,
 information on the number of annual work hours is sometimes needed for
 all years employed.  Information in the SCF documents the "average"
 number of hours worked per week, and the number of weeks worked in a
 "normal" year.  Depending on the objectives of analysis, the reported
 "average" could be used for all years, or only for years prior to the
 interview, with estimates of the years following based on expressed
 preferences about full and part time employment to take account of
 child rearing and pre-retirement years.
0     Åital Åbold Wage Rate (WAGE).ÌÌ Although most benefit formulas
 require information on the income history of the participants,
 information in the SCF gives only wage and salary data for the current
 year.  Estimates of annual wages both prior to and following the date
 of the interview are required.  For estimates of past trends in wages,
 historical data on aggregate wage trends within industry or occupation
 groups can be used in conjunction with the SCF data.  Estimates of the
 future annual growth rate in nominal wages can be divided into three
 major components:  a factor which represents cost-of-living
 adjustments; factors which represent productivity increases in the
 general economy, and for specific industries or occupational groups;
 and, factors related to the growth in wages due to the accumulation of
 skills and experience by individual workers.  Using the participant's
 birth date, date of hire, and current wage and salary data, the
 required income history can be described by the the average annual
 rate of growth, and whether the growth rate is rising or falling
 within specific age-tenure ranges.  Assumptions regarding wage
 inflation and productivity gains could then be combined with age-
 tenure related gains.  This procedure would help insure the consistent
 use and clear identification of the underlying assumptions about
 nominal wage growth.
0     Åital Åbold Voluntary Contributions (HHVOL).ÌÌ For defined
 contribution plans, the voluntary contributions made in each year that
 respondents participated in these plans is needed for entitlement
 estimates.  The information in the SCF documents the current annual
 rate of voluntary contributions made by the respondent, as well as the
 respondents estimate of the current accumulated account total.
#<-Åital Åbold Economic AssumptionsÌÌ
0     The major economic assumptions involve the real discount rate
 used in present value calculations, as measured by the difference
 between estimated nominal rates of return on investments and the
 corresponding estimated inflation rates.  The composition of pension
 portfolios can be used as a guide for the selection of the appropriate
 rate of return.  The variables used in the above equations are:
8RATE@(Åital tÌ) = Nominal rate of return over the relevant time period
             for benefit calculations made at time Åital tÌ.
8PRICE@(Åital tÌ) = Inflation rate over relevant time period for benefit
             calculations made at time Åital tÌ.
8GWAGE@(Åital tÌ) = Average overall growth in wages over relevant time
             period for benefit calculations made at time Åital tÌ.
#<-Åital Åbold Institutional AssumptionsÌÌ
0     The major institutional assumptions involve the future financial
 viability of the individual pension plans, and prospective changes in
 Social Security and other federal programs and regulations.  The risk
 associated with the eventual payment of entitlements can be
 conceptualized in the form of a probability of non-payment ranging
 from zero to one.  Estimated benefit amounts could then be adjusted by
 this risk factor.  Information on the funding status of the individual
 pension plans included in this study is available from the 5500 forms
 required to be filed under ERISA regulations.  Since Social Security
 offsets are frequently used when calculating private pension benefits,
 estimates of future changes in the wage base as well as benefit
 amounts are needed.  And since Social Security benefits reflect
 earnings levels, differential estimates are needed which are
 consistent with the participants' assumed tenure and wage history.
 The notation for the variables used in the above equations is as
 follows:
8RISK@(Åital jtÌ) = Risk factors associated with the j$(Åital thÌ) pension
             plan at time Åital tÌ.
8SSWBÅsub Åital tÌÌ = Social Security wage base at time Åital tÌ.
8SSBAÅsub Åital tÌÌ = Social Security benefit amount at time Åital tÌ.
#=-Åital Åbold Åcaps Data Analysis SystemÌÌÌ
-     The overall measurement strategy requires that the benefit
 formulas be combined with respondent data, along with behavioral,
 economic, and institutional assumptions, to estimate pension
 entitlements under each of the six retirement circumstances.  This
 strategy is depicted in Chart 1.  At opposite ends, the two raw data
 bases--the Survey of Consumer Finances and the Survey of Pension
 Providers--represent the starting points.  Each of these raw data
 bases need to be transformed to a standard format and notation, as
 indicated by the two "generator" programs; one to transform the
 participant data, and the other to transform the pension plan data.
 These two standardized data bases are then used by the "calculator"
 program to estimate pension entitlements.  The calculator program,
 shown in the center of the Chart, then produces estimates of pension
 entitlements, under the specified assumptions.  Three major computer
 programs are necessary: one to transform the participant data, one to
 transform the pension plan data, and one to estimate pension
 entitlements using information from both data bases.
#0( < )  lines=off placement=broadside
#=-!Chart 1!!Data Analysis System
#:1=^
0Åbox !SCF!HH!DATA!Ì-->Åbox Participant!Data!GeneratorÌ-->Åbox
 Input!Data!BaseÌ-->Åbox Benefit!CalculatorÌ<--Åbox
 Input!Formula!Data!BaseÌ<--Åbox Benefit!Formula!GeneratorÌ<--Åbox
 Pension!Plan!DataÌ
#:close
#.
0     Decisions regarding the type and structure of these programs were
 guided by their flexibility and ease of use.  A major purpose of this
 data analysis system is to facilitate the comparison of benefit
 entitlements under a variety of simulated or assumed circumstances.
 Thus the participant data, as well as the behavioral, economic, and
 institutional assumptions, need to be under the control of each
 individual analyst.  This meant that the programs that generate the
 participant data, and the program that controls the assumptions
 underlying the calculations, must be flexible to accommodate a wide
 array of analytic interests, and yet be easily accessible to users
 without the need to learn a completely new software system.  In
 contrast, the program that generates the pension formula data base,
 and the program that calculates the estimated entitlements, are not
 subject to change depending on the analytic objectives, as they
 represent a fixed system of equations defined by the pension plans.
 Thus the pension formula generator and calculator programs, while
 "user friendly", were designed as self contained units, using an
 highly structured and efficient computational approach.
-     Åbold Åital Participant Data Generator.ÌÌ  This program is
 necessary to prepare the participant's employment and demographic
 characteristics in a standard format.  The output from this program is
 the participants' input data base.  The requirements for this data
 base are few:  each line in the data file includes the employment and
 demographic characteristics for one participant; the values for the
 specified variables must be entered in a fixed order, separated by
 blanks.  Most standard analysis software programs are capable of
 listing the data in this manner.  Thus, OSIRIS, SPSS, SAS, or any
 other analysis package usually used by the analyst, is suitable to
 transform the raw survey data on participants' characteristics.  As
 such, users will not have to learn a new system, and the data
 transformation commands already available in these packages can be
 used to simulate any desired combination of behavioral assumptions.
0     It should also be noted that some analysts may prefer completely
 synthetic characteristics so as to compare the benefits various
 pension plans provide for a standard set of characteristics.  For
 example, the calculation of normal retirement benefits under all
 pension plan for a fixed set of employment and demographic
 characteristics.  In such a design, pension benefits could be compared
 among plans, holding constant participant characteristics.
0     Users do not necessarily need to generate new data on participant
 characteristics, as a default data base will be made available.  It is
 expected, however, that most users would generate new data bases in
 accordance with the hypotheses of interest.  Indeed, this is the
 strength of this analytic system, as it allows an unlimited number of
 variations in participant characteristics.  All that is required is
 that for each participant--whether actual or simulated--all the data
 values be entered in a fixed order on one line.
-     Åbold Åital Pension Formula Generator.ÌÌ  The purpose of this
 program is to transform the raw survey data into a integrated set of
 standardized equations.  The output from this program is an equation
 data base, with a separate set of equations for each pension plan.
 The set of equations defines the benefit entitlements under the six
 retirement circumstances for each pension plan.  Three types of
 equations were generated for each plan:  equations which defined the
 employment characteristics used to determine benefits; equations that
 defined how the benefit amounts were determined; and equations that
 defined the requirements participants needed to satisfy to receive
 these benefits.
0     The pension formula generator program was written in Pascal, a
 widely used and efficient programing language.  The source code for
 this program is included in Volume 4, which accompanies this report.
 The input formula data base, which this program produces, is shown in
 Volume 3.  The set of equations generated for each pension plan is
 identified by its ID variables which identify each of the Åital jÌ
 pensions plans.  The number of equations generated for each plan
 depended on the complexity of the provisions.  Some plans required a
 dozen or less equations, while others required up to eight dozen
 separate equations; the average plan included 28 equations.  The order
 in which the equations are listed is of importance, as the set of
 equations for each pension plan represent a recursive system.  Each
 equation must be estimated in the sequence shown, from top to bottom,
 since the variables defined in the initial equations are used in
 subsequent equations in the sequence.
0     The following example can be used to clarify the structure of the
 equations.  Suppose a pension plan had the following provisions for
 normal retirement:  the annual pension would equal 1 1/2 percent of
 final salary for each year worked, and would be paid when the
 participant reached age 65 with 10 or more years of service.  The
 formulas that determine normal retirement benefits for the Åital jÌ
 pension plan at time Åital tÌ can be expressed as follows:
0             FAP1 = WAGE(QUITD)
9             ASY1 = QUITD - HIRED
9             NR1  = 1.5% * FAP1 * ASY1
9             RAS1 = AGE>=65 ]& ASY1>=10
9             NRQ  = RAS1 -> NR1
0The first equation defines FAP as the participants final wage,
 expressed as the annual wage at the time of employment termination.
 The second equation expresses the plan provision that all years of
 employment are counted in the determination of pension benefits.  The
 third equation gives the plan formula that determines normal
 retirement benefits.  The fourth equation states the age and service
 requirements necessary to be eligible for normal retirement benefits,
 which in this example is the dual requirement that the participant be
 65 or older and have 10 years service credit.  Finally, the last
 equation in the sequence is a conditional statement that tests whether
 the participant meet the qualifications necessary for normal
 retirement benefits.  This equation is read as follows:  if the
 participant meets the requirements as defined by RAS1, then the NRQ
 variable will equal the normal retirement benefit (NR1), otherwise it
 will be set equal to zero.  It is thus the NRQ variable that is used
 as the final estimate, since it gives the benefit amounts only for
 participants that qualified for these entitlements.
0     When the data on WAGE, BIRTHD, HIRED, QUITD for the Åital iÌ th
 participant are inserted into these equations, the benefit amount can
 be estimated.  For example, if the participant's final wage was
 $$20,000, was born in 1920, hired in 1955, and retired in 1985, the
 above equations would indicate the participant qualified for an
 estimated benefit of $$9,000, since the participant meet the age and
 service requirements.
0     Of course, most plan provisions were much more complex than the
 simple example given above.  For example, the RAS variable often
 included multiple sets of qualifications, such as age 65 and at least
 10 years service, or age 60 and 25 years service, or any age with 30
 years of service.  These multiple requirements were expressed in
 formulas as follows:
0          RAS1 = AGE>=65 ]& ASY1>=10 ! AGE>=60 ]& ASY1>=25 ! ASY1>=30
0The vertical bars in this formula indicate that if participants meet
 any one of the three conditions, they would qualify for benefits.
0     Pension plans typically included several alternative benefit
 formulas depending on the participants age and service record.  For
 example, one formula may be used for participants with 30 or more
 years of service, and another formula for those with less than 30
 years.  Two different sets of requirements were expressed as follows:
0          RAS1 = ASY1>=30
9          RAS2 = AGE>=65 ]& ASY1>=10 ! AGE>=60 ]& ASY1>=25
0Suppose the two different normal retirement formulas were:
0          NR1  = 1.5% * FAP1 * ASY1
9          NR2  =   1% * FAP1 * ASY1
0Then equations that determine the final normal retirement pension for
 which the participant was qualified would be expressed as follows:
0          NR1Q = RAS1 -> NR1
9          NR2Q = RAS2 -> NR2
9          NRT  = MAX(NR1,NR2)
9          NRQ  = MAX(NR1Q, NR2Q)
0The third equation listed above gives the rule for combining the two
 different formulas, and the last equation restates this rule including
 the necessary qualifications.  If the participant did not meet the 30
 year requirement (RAS1), but did meet the other set of requirements
 (RAS2), NR1Q would be set to zero, NR2Q would be set to the value of
 NR1, and the maximum of these two amounts would always be NR2Q.  If
 the participant meet both sets of qualifications (RAS1 and RAS2), then
 the maximum of NR1Q and NR2Q would be assigned as the final benefit
 amount, which in this case would be the NR1 formula.
0     Pension plans also had more complex provisions governing the
 determination of the service years (ASY) and income (FAP) used in
 benefit formulas.  Plans often defined service years to include only
 those years worked after the participant attained age 25, excluding
 the first year of employment.  For situation such as this, the ASY
 variables were defined as:
0          ASY1 = QUITD - MAX(HIRED+1, BIRTHD+25)
0If in addition, there was a maximum on the amount of service years
 that could be used in the formulas, say 30 years, the term would be
 expressed as:
0          ASY1 = MIN(30, (QUITD - MAX(HIRED+1, BIRTHD+25))
0Needless to say, there were many variants in how the ASY term was
 defined, as shown in the actual formulas included in Volume 3.
0     Variations in the plan definitions of the income term used in the
 formulas were handled in a similar fashion.  Because the calculations
 were often defined over a specific time period, two addition terms
 were added to the program:  the start and ending dates of the period
 over which FAP is calculated.  For example, if the FAP term was
 defined as the average annual wage over the final five years of
 employment, the following equations were generated by the program:
0          SDFAP1 = QUITD - 5
9          FDFAP1 = QUITD
9          FAP1   = AVG(WAGE, SDFAP1, FDFAP1)
0The first two equations determine the start and ending dates,
 respectively.  The last equation calculates FAP1 and the average
 annual wage over the period determined by the start (SDFAP) and finish
 dates (FDFAP).  Alternatively, if the plan called for using the
 highest year during the last five years of employment, the final
 equation would be:
0          FAP1   = PEEK(WAGE,SDFAP1,FDFAP1)
0     Another common complication of the benefit formulas was how
 benefit amounts varied depending on the actual values of ASY or FAP.
 For example, a normal retirement benefit formula may differ depending
 on whether FAP was below or over a certain amount, or the benefit
 accrual rate varied with the length of service.  In such cases, the
 formulas were expressed with the restrictions within brackets, as
 follows:
0     NR1 = 1% * ASY1 * FAP1ÕFAP1<=15000å + 1.5% * ASY1 *
 FAP1ÕFAP1>15000å
0Or:
0     NR1 = 1% * ASY1ÕASY1<=15å * FAP + 1.5% * ASY1ÕASY1>15å * FAP1
0If, for example, FAP1 equaled $$25,000 and ASY1 equaled 35, the first
 equation would yield a value of 1%*35*15000 + 1.5%*35*10000, or
 $$10500.  The second equation would be evaluated as 1%*15*25000 +
 1.5%*20*25000, or $$11250.  This format was also used for plans that
 used maximums on ASY or FAP which were built directly into their
 benefit formulas.  For example:
0     NR1 = 1% * ASY1ÕASY1<=15å * FAP1 + 1.5% * ASY1Õ15<ASY1<=30å *
 FAP1
0In this example, only up to 30 years of service credit is used in the
 formula to determine benefits.  Using the same participant
 characteristics as above, the formula would be evaluated as
 1%*15*25000 + 1.5%*15*25000, or $$9375.
0     Variations in benefit amounts depending on the level of the
 participant's income were often designed to reflect the Social
 Security wage base, and thus incorporate an implicit offset for the
 employer's contributions to Social Security.  Other pension plans made
 this an explicit part of the benefit formulas.  For example:
0     NR1 = 1%*ASY1*FAP1ÕFAP1<=SS1å + 1.5%*ASY1*FAP1ÕFAP1>SS1å
0In other pension plans, the Social Security benefit amount, rather
 than the wage base entered into the formulas. A typical example of
 this was the deduction of half of the Social Security benefit amount,
 as shown below:
0     NR1 = 2%*ASY1*FAP1 - 50%*SS2
0The terms SS1 and SS2 were defined according to the plan provisions
 which governed each benefit formula.  The general form of the notation
 used to define the Social Security term is as follows:
0     SS# = (TYPE, DATE)
0The first parameter indicates the type of Social Security--whether it
 is the Social Security wage base, or the normal, early, disability, or
 survivors benefit amounts.  The second parameter defines date the
 benefit starts.  For example, the formula:
0     SS1 = (1, BIRTHD+65)
0This formula defines the Social Security term as the primary benefit
 amount the participant would receive at age 65.  A special form of the
 equation was needed for the Social Security wage base to take into
 account both beginning and ending date of the calculations.  For
 example, when formulas were based on the accumulated sum of wages than
 exceeded the sum of the wage base across all years employed, then the
 following notation was used:
0     SS1 = SUM(SSBASE, HIRED, QUITD)
-     Åital Åbold Pension Benefit Calculator.ÌÌ  This program uses
 three sources of inputs to calculate pension entitlements:  the data
 on participants' employment and demographic characteristics; the
 pension formula data base; and assumptions regarding future growth in
 wages and prices, and the assumed discount rate for present value
 calculations.  The participant and pension formula data is produced by
 the generator program described above, while the calculator program
 before estimating entitlements, first prompts for user input regarding
 the selected assumptions.  In addition, the calculator program allows
 for two different analytic strategies.  The first matches each
 participants' data with the relevant set of plan formulas;  the second
 uses a fixed set of participants' characteristics to determine
 entitlements under all pension plans.
0     The calculator program is written in Pascal, and is shown in
 Volume 4.  The executable program includes the pension formula data
 base as part of the object code, and thus this input data does not
 need to be read into the program each time it is used.  This results
 in a time saving, highly efficient computational routine, as well as
 simplicity, as the typical user will never need to run the pension
 formula generator program.  The program prompts include:  the option
 to reset the default assumptions concerning wages, inflation, and
 interest rates; the choice of whether to use actual participant or
 simulated data; the specification of the file containing the input
 data; the specification of the file to which the benefit entitlements
 will be written, and the required format; and the option to select one
 of several different standard reports detailing the results.
0     If the program is directed to estimate benefits using actual
 participant data, benefits will be estimated by matching each
 participant's data line in the input file with the corresponding plan
 formulas.  The input file may contain one line for a single
 participant, or as many lines as there are participants in the full
 sample, or any subsample desired.
0     If the program is directed to use simulated data, from one to
 five simulated data cases can be estimated.  Of course, the program
 can be rerun as many times as necessary if more than five simulated
 circumstances are desired.  For each simulated case, the program will
 estimate pension benefits from every plan included in the data base.
 Since no matching of participants and plans occur with this option,
 the ID variables for participants and plans are not needed in the
 input data base.  The output data base includes for each simulated
 case, the pension plan ID variable, and the estimated benefit amounts.
0     In addition to the choice of actual or simulated data, the
 program allows the analyst to specify the use of a single estimate of
 each participant's quit date, or the use of all potential quit dates
 for each participant.  The program calculates the pension entitlements
 due from each type of retirement circumstance--normal, early, vested
 deferred, disability, and death--for each year from the time of the
 interview to when the participant reaches age 80.  If the participant
 was eligible for more than one type of retirement benefit at any given
 age, the program automatically selects the one which yields the
 highest benefits.  Using this data base would allow more detailed
 models which specify the probability of each retirement circumstance,
 and allow those probabilities to vary over the life of the
 participant.
