Research Paper No. 2001-02

Actuarial Nonequivalence in Early and Delayed

Social Security Benefit Claims

(Public Finance Review, May 2002, pp. 188-207)

by

James E. Duggan*

Christopher J. Soares*

November 2001

Office of Economic Policy, U. S. Department of the Treasury, Washington, DC. The authors

would like to thank John Hambor and David Wilcox for helpful comments. The views expressed

in this paper are the authors alone and do not necessarily reflect those of the Department of

Treasury.
Abstract

Actuarial Nonequivalence in Early and Delayed

Social Security Benefit Claims

Age-related adjustments to Social Security benefits are intended to be actuarially

equivalent, on average, rendering lifetime benefits invariant to the timing of first receipt. 

This paper analyzes actuarial equivalence with respect to early and delayed Social Security

benefit claims using a large sample of current and former retired-worker beneficiaries. We

find substantial deviations from actuarial equivalence that have resulted in “actuarial

premiums” for males, particularly low-income males, and “actuarial losses” for females who

accept benefits early. Gender-neutral actuarial adjustments partially offset the female life

expectancy advantage in Social Security. For delayed claims, the eight percent credit

scheduled in current law is too low for actuarial equivalence. The patterns of actuarial

nonequivalence should be considered in analyses of claiming behavior or in simulations of

Social Security reform proposals that may affect claiming behavior.
I. Introduction

Since 1956 women have had the option of claiming Social Security retired-worker

benefits as early as age 62. The same option was offered to men in 1961. For individuals

who postpone receipt, initial benefits are increased for each month of delay, creating a

schedule of benefits that potential recipients can choose from. This schedule is intended to

be actuarially equivalent, on average, which means that lifetime benefits should be invariant

to the timing of first receipt.

Benefit adjustments that are actuarially equivalent on average will nevertheless vary

among demographic and socioeconomic groups that exhibit systematic differences in life

expectancy. Actuarially nonequivalent benefit adjustments may have unintended

consequences. They alter claiming incentives and thereby may distort benefit acceptance

decisions. If adjustments are not actuarially equivalent then policy decisions that affect

claiming behavior will affect long-run program costs. Nonequivalent actuarial adjustments

may also affect retirement decisions and studies that ignore this effect will misstate the

incentives to continued work. Finally, benefit adjustments that deviate systematically from

actuarial equivalence create some (perhaps unintended) redistribution of benefits.

There is little empirical evidence that bears directly on the accuracy of statutory

benefit adjustments (i. e., those prescribed in Social Security law). Blinder, et al (1980),

Myers and Schobel (1990), and Mirer (1998) are exceptions but those studies are limited to

one or two birth or retirement cohorts and are based on life tables that are not specific to the

relevant population (retired workers) and that do not vary by earnings. New and more

extensive evidence on this important topic is needed, a need that is underscored by the fact

that the same statutory adjustments for early benefit claims have been in place since 1956,

notwithstanding improvements in life expectancy.

This paper analyzes actuarial equivalence with respect to early and delayed Social

Security benefit claims using a large sample of current and former retired-worker

beneficiaries. Our primary purpose is to investigate differences by gender and lifetime
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earnings in statutory and actuarial benefit adjustments that could give rise to the incentive

and distributional consequences described above. The differences are captured in relative

lifetime benefit profiles, the ratios of lifetime Social Security benefits based on statutory

benefit adjustments to those based on actuarially-equivalent adjustments. Our empirical

results reveal substantial deviations from actuarial equivalence and relative benefit profiles

that differ systematically by earnings and gender. Generally, with an age-65 normal

retirement age, the profiles imply an actuarial premium for males, particularly low-earnings

males, who accept benefits early and an actuarial loss for most females who accept benefits

early. One consequence is that gender-neutral statutory adjustments tend to offset a portion

of the female life expectancy advantage in Social Security. We also find that an eight percent

per year delayed retirement credit (scheduled in current law but not yet effective) is far from

actuarially equivalent for most beneficiaries, particularly those with lower earnings. As the

normal retirement age rises, as scheduled under current law, statutory adjustments move

further off an actuarial equivalence target for some groups, though this could change with

future improvements in life expectancy.

We begin by estimating mortality profiles, allowing the profiles to vary by age,

gender, race, birth year, and lifetime earnings. We then compute actuarially equivalent and

statutory lifetime Social Security benefits for each month that a benefit claim might be taken

after exact age 62. Because the mortality profiles estimated here are endogenous to the

population of beneficiaries that have actually confronted Social Security’s benefit schedule

they provide the relevant basis for evaluating actuarial equivalence with respect to an age-65

normal retirement age. In contrast, most available life tables are based on populations that

include disabled persons. Disabled persons, whose benefits are not subject to age-related

statutory benefit adjustments, have far higher mortality than the general population and

should be excluded when evaluating actuarial equivalence for retired workers.

The next section provides a brief description of the history of actuarial adjustment

factors, summarizes the relevant empirical evidence, and describes the calculation of
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actuarially equivalent benefit adjustments. The third section describes our data and methods,

the fourth section presents our basic results on actuarial equivalence, and the fifth section has

implications and conclusions.

II. Actuarial Adjustments

History. The original Social Security Act established age 65 as the minimum age for

males and females to qualify for retirement benefits.1

 In 1956, the minimum age was

reduced to 62 for women in order to be coincident with the same reduction for wives’

benefits made in that year.2 This provision was to be structured in a manner that would make

benefits at age 62 actuarially equivalent to benefits at age 65, the “normal retirement age.”3

 Early analysis of this issue was based on available life tables for females and a range of

discount rates, though a three-percent rate was considered to be the most reasonable at the

time. The analysis led to the conclusion that the appropriate age-62 benefit adjustment factor

was 0.80, that is, a benefit claim at exact age 62 would be 80 percent of the age-65 benefit.

 For administrative convenience, monthly adjustments between ages 62 and 65 would be

strictly proportional C that is, 5/9 of one percent of the age-65 benefit for each month above

age 62. When males became eligible for early benefits in 1961 the same adjustment factors

were applied, despite differences in life expectancy between the sexes. The early benefit

adjustment factors that were adopted in 1956 remain in effect today.

In the 1983 Social Security Amendments, Congress provided for a gradual increase

in the normal retirement age (NRA) to 67, leaving at 62 the earliest age at which benefits can

be claimed. When the higher NRA is fully phased in (2022) an age-62 benefit claim will be

 

1

A thorough treatment of the development of early and delayed adjustment factors is contained in Myers

(1980) which forms the basis for much of the discussion in this subsection.

2

Wives’ benefits were reduced because wives were, on average, three years younger than their husbands,

and couples might otherwise have to wait to retire together.

3

Actuarial equivalence was developed in the context of retired workers -- that is, without consideration to
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seventy-percent of the age-67 benefit and a new set of monthly adjustment factors will be in

place. For the first twenty-four months after age 62, the statutory benefit adjustment will be

5/12 of one percent and, for the subsequent thirty-six months, the adjustment will be 5/9 of

one percent.

For benefit claims made prior to the NRA, Congress originally intended that benefit

adjustments would be actuarially equivalent on average. For claims made above the NRA,

the actuarial equivalence objective was adopted later and implemented more gradually. The

first delayed retirement credit (DRC) was introduced in 1972 at 1 percent per year (.083

percent per month above age 65) up to age 72 (later reduced to age 70). The DRC was

increased to 3 percent by the 1977 Amendments and scheduled by the 1983 Amendments to

increase gradually to 8 percent per year.

Actuarial Equivalence. An actuarially equivalent benefit adjustment equates the

present value of benefits that begin at a certain age with the present value of benefits that

begin at the normal retirement age. The benefit streams can be compared using standard

annuity calculations. To illustrate, let a62 represent the present value of a one-dollar annuity

at age 62:

(1) a62 = ∑

∞

t=0

ts62ρt

where ts62 = ∏=

t

x 0

s62+x are survival probabilities and ρt the inverse of the real discount rate

at time t. The value of an annuity issued at age 62 but deferred for three years until age 65

(the NRA annuity) can be expressed as

(2) 3a62 = 3s62ρ3a65.

 

the lifetime of auxiliary beneficiaries (spouses/widows, for example). That is also the context of this paper.
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The present value of the age-62 annuity (1) is clearly larger than that of the age-65 annuity

(2) though the exact relationship depends upon mortality and discount rates. The multiplier

that reduces theage-62 annuity to exactly equal the deferred age-65 annuity is referred to as

the age-62 actuarial adjustment factor, AAF62:3 (AAF62:5 if the NRA is 67).4 That is, the

product of the actuarial adjustment factor and the immediate annuity is actuarially-equivalent

to the age-65 annuity:

 (3) AAF62:3*a62= 3a62.

The actuarial adjustment factor is simply the ratio of equation (2) to equation (1):

(4) AAF62:3 = 3a62/a62.

If the AAF62:3 were 0.83, for example, then beneficiaries who claim benefits at age 62 would

receive, on average, lifetime benefits that are nearly 3 percentage points lower than the

normal retirement age benefit.

For any path of survivor and discount rates, a different AAF applies to each period

away from the normal retirement age. Higher survivor rates (or lower discount rates) result

in larger AAFs and therefore larger actuarially equivalent benefits.5 Thus, for groups that

 

4

 The term adjustment factor is adopted here to be consistent with the terminology used in prior studies on

this topic (Myers, 1980-81; Myers and Schobel, 1990). The key distinction is between statutory and

actuarial adjustment factors. The former are prescribed in law; the latter are based on actual or assumed

mortality and discount rates.

5

The basic relationship between length-of-life and AAFs can be captured with a very simple example. 

Suppose person 1 and person 2 are eligible for the same real benefit X at age 65 and they differ only in that

person 1 will live until age 67 and person 2 until age 70. Person 1's lifetime benefit is 2*X and person 2's

lifetime benefit is 5*X. If they are permitted to take benefits at age 62 then person 1's benefit life is five

years and person 2's benefit life is eight years. If lifetime benefits are to be the same whether they begin at

age 62 or age 65 then person 1's annual benefit will have to be reduced proportionately more (3*X/5) than
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are expected to live longer, such as females and high-income persons, the actuarially

equivalent benefit at age 62 will be higher (i.e., their AAF is larger) than for those with lower

life expectancies, such as males and low-income persons. The differences in survivor

profiles among these groups account for the differences reported below in statutory and

actuarial adjustments.

The literature is split on the topic of the appropriate rate for discounting. Many

researchers believe the government-guaranteed, tax-preferred, inflation-indexed nature of the

Social Security benefit warrants a low discount rate. Inasmuch as the program also provides

protection against longevity, earnings, disability and intergenerational risks, a low discount

rate seems further justified. On the other hand, some authors argue that the political risk

inherent in the program outweighs the insurance considerations, and thus a premium above

the risk-free rate is proper. In addition, because Social Security benefits cannot be used as

collateral, liquidity-constraints at retirement age would rationalize a higher rate. In view of

the lack of consensus in the literature on the correct discount rate, we present results for a

range of rates that span those most commonly used.6

III. Data and Survivor Profiles

Data. Our primary data sources are the Social Security Administration’s (SSA) 1996

one-percent Continuous Work History Sample (CWHS) and Master Beneficiary Record

(MBR). The “active” portion of the CWHS is an historical record of Social Security earnings

for about 2.9 million current or former workers in covered employment spanning the period

1937 to 1996. Each record also has date of birth, and race and sex indicators. If a worker

attains beneficiary status and subsequently dies, the date of death is recorded in the MBR,

 

person 2's benefit (3*X/8).

6

See Leimer (1995) for a discussion of issues related to choice of discount rate.
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the principal official record of historical benefit payments. Death information in the MBR

is considered to be of very high quality (Aziz and Buckler, 1992).

For empirical analysis we selected from the one-percent sample current or former

retired-worker beneficiaries born during the years 1900 to 1933. All individuals in our

sample survived until at least age 62 and first became eligible for benefits between 1962 and

1995. Because our benefit/death information extends through 1998, the oldest observed age

in our working sample is 98. Accounting for edits described in the next paragraph and

deletions for anomalous cases, our working sample has over 400,000 observations.

Earned income in the CWHS consists of lump-sum taxable earnings for 1937 to

1950, annual taxable earnings from 1951 to 1977, and total (uncapped) earnings from 1978

to 1996. We use these earnings data to develop a summary measure of real lifetime earnings

following three adjustments to the data: (1) we prorated the 1937 to 1950 lump-sum under

the assumption that, between the reported first and last years of employment prior to 1951,

earnings grew at one percent per year of age beyond the economy-wide growth in wages for

males and at one-half percent for females;7 (2) for individuals who earned the taxable

maximum during years 1937-1980, we imputed earnings above the maximum using a Tobit

model of earnings under the assumption that earnings are lognormally distributed; (3)

earnings (actual or imputed) in each year were indexed to 1999 using the Consumer Price

Index. The summary measure of earnings is the average of the log of indexed earnings over

ages 35 to 60 where the average is taken only over years of nonzero earnings.8 We restricted

our sample to include only beneficiaries with some earnings between the ages of 35 and 60.

Table 1 has summary statistics for our working sample.

Survival Profiles. We first estimate mortality probability models separately for males

and females in which the unit of observation is a person-year and the dependent variable is

 

7

 The 1937-1950 average earnings series is from Myers (1993).

8

 For birth years 1900 and 1901, the average is over ages 37 to 60 and 36 to 60, respectively.
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the discrete mortality hazard, indicating whether or not death took place in that year, given

that the individual was alive at the end of the previous year. The hazard was estimated

directly using the logit probability model so that variables with positive coefficients are

associated with higher death rates and shorter expected remaining lifetimes. Explanatory

variables include real lifetime earnings (measured as described above), age, birth year, race,

and dual beneficiary status. Dual status indicates benefit receipt from another beneficiary’s

account (in addition to a benefit from their own account) and relates primarily to females

entitled to spousal or widow benefits. The dual variable accounts for the fact that dual

beneficiaries generally live longer than nonduals. The earnings variable was specified as a

cubic polynomial in each equation in order to allow flexibility in the way earnings affects

mortality. The estimated parameters, shown in Table 2, are generally highly significant and

generally have the expected effect on mortality.9 In both equations, the earnings variables

as a group are highly significant as indicated by the chi-square statistic in the last line of the

table.

Hazard rate profiles for each individual were computed by evaluating the empirical

functions in Table 2 at each age beginning with age 62. Survival profiles are derived directly

from the hazard rates. Thus, if ĥ62 is the estimated probability of dying at age 62, given

survival to age 61, ĥ63 is the estimated probability of dying at age 63, given survival to age

62, and so on, then the probability that a 62-year old beneficiary survives until age 62+x is

(5) xŝ62 = (1- ĥ62)*(1- ĥ63)* ... *(1- ĥ62+x).

 

9

 The estimated mortality models result in a marginal effect of earnings on mortality that changes sign at the

very low end of the lifetime earnings distribution. For males, this occurs below the sixth percentile of the

male earnings distribution and, for females, below the second percentile of the female earnings distribution.

 For individuals in the lowest portion of the distribution, lifetime earnings may be a relatively unimportant

determinant of life expectancy.
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We set the maximum value of x to 53 (beneficiaries do not live past age 115). With

ρ=(1/(1+r)), r the real discount rate and an NRA of 65, the estimated AAF for an age-62

benefit claim is

(6) AÂF62:3 = ∑=

53

x 3

xŝ62ρx

 / ∑=

53

x 0

ŝ62ρx.

Similarly, with an NRA of 67 the summation in the numerator of equation (6) would have

x=5. Note that, for a given age, the AAF falls as the NRA rises, that is, AAF62:5 <

AAF62:3. For a given NRA (constant numerator), a later age when the initial benefit is

claimed results in a higher AAF.

IV. Empirical Results

Normal Retirement Age=65

Table 3 displays average AAFs at exact retirement ages 62 through 70 corresponding

to three different discount rates that generally bracket rates used in previous related literature.

 The top panel displays AAFs with respect to an NRA of 65; the bottom panel is discussed

in the next subsection.10 Statutory adjustment factors are displayed in column 2.11 An AAF

that is higher than the statutory factor means the latter results in a benefit that is smaller than

the actuarially-equivalent benefit, and conversely. For example, at a discount rate of one

percent, males who claim benefits at age 62 would receive a benefit that is two and a half

percentage points less than the actuarially equivalent benefit; males who wait until age 70

 

10For beneficiaries born prior to 1938 the NRA is 65 and therefore applies to all birth cohorts under study

here.

11The statutory factors above the NRA are based on an annual DRC of 8 percent that will affect only

beneficiaries born after January 1, 1943. We use the higher credit in order to evaluate its relationship to

actuarial equivalence.
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to claim benefits would receive a benefit that is almost six percentage points less than the

actuarially equivalent amount.

The table illustrates the quantitative importance of the discount rate: a two percentage

point higher rate results in more than a three percentage point lower AAF at age 62 and about

a ten percentage point higher AAF for an age-70 benefit claim. Thus, choice of discount rate

matters and no single rate will equate statutory and actuarial adjustment factors for all

demographic groups.

Consider further the results at a three percent discount rate that nearly equilibrates

AAFs and statutory factors for females at age 62 and in this sense corresponds to the original

basis for establishing statutory factors (see section II). Particularly for males, the eight

percent annual credit for benefit claims past the NRA appears to be woefully inadequate,

falling short of the age-70 AAF by almost seventeen percentage points.12 Because the actual

DRCs facing the cohorts in this study were lower than eight percent (5.0 percent for the 1933

birth cohort and lower for prior cohorts), the post-age-65 AAF-statutory gaps in Table 3

understate actual differences. Historically, retired-worker beneficiaries faced a large

actuarial disincentive to delay claims past age 65.

Relative Benefit Profiles

The means in Table 3 make clear that the ratio of statutory to actuarially equivalent

lifetime benefits is not generally equal to one. The underlying monthly patterns provide

additional insight. We expect those patterns to vary directly with lifetime earnings, given the

link between earnings and life expectancy; that is, higher AAFs for higher earning

beneficiaries. To illustrate this, we computed relative monthly benefit profiles for each

beneficiary: the ratio of statutory to actuarially equivalent benefits at each month between

ages 62 and 70. We then sorted our sample into lifetime earnings quintiles. Figure 1 shows

 

12According to Myers (1993, p. 99) “The eventual value of the DRC (8 per year) is not much less than the
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these relative benefit profiles for males and females in quintiles one and five using a three

percent discount rate. For males in the highest earnings class the ratio is less than one in the

first month of delay, rises steadily for the first twenty-two months, and then declines slightly

before reaching one at the end of month thirty-six. Beyond age 65, the eight percent statutory

credit results in a slightly increasing ratio for the first six months, remains above one for

another six months while continuing a steady decline. For males in the lowest earnings

quintile, however, the ratios decline for every subsequent month beyond age 62 and four

months. For high-earning females the relative benefit profile begins below one and rises

fairly steadily for fifty-six months. Note that the eight percent annual DRC is below the AAF

for most beneficiaries for most months between ages 65 and 70. The credit is close to

actuarial equivalence during age 65 for high-earning beneficiaries, particularly females, but

falls below the AAF for most beneficiaries and the difference grows past the NRA.

The results displayed in Figure 1 suggest that current-law statutory benefit

adjustments can produce financial incentives relative to actuarial equivalent outcomes that

may affect claiming (and retirement) behavior.13 Particularly for high-earning females and,

to a lesser extent, high-earning males, rising relative benefit profiles mean higher lifetime

Social Security benefits when the initial claim is delayed. On the other hand, falling relative

benefit profiles means that low-earning males have an incentive to accept benefits at the

earliest possible date.

Table 4 provides additional detail by gender and earnings on the nature of those

incentives using a three-percent discount rate. The table focuses on months between ages 62

and 65. The first lines of the female and male panels show for each earnings quintile the

month (beyond age 62) of the peak statutory/actuarial equivalence ratio and second lines

 

true actuarial equivalent (about 9 percent)...”

13 A full analysis of the claiming decision is beyond the scope of the current study. Coile, et al (1999)

provide some empirical evidence on claiming for males who claimed benefits in 1980-81.
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show the potential gain in lifetime benefits if the initial claim were delayed until then.14 The

gain is greatest for high-earning females who, by delaying until almost age 65, can increase

lifetime benefits by almost $5,000, on average. Though there are relatively few high-earning

females, as shown in the last line of the panels, nontrivial gains are also available to females

in the lower quintiles. Males, on the other hand, particularly low-earning males, have very

little incentive to delay their initial benefit acceptance.

Finally, the last panel in Table 4 reveals how a single-sex statutory adjustment factor

affects the gender differential in lifetime benefits. Note that because the data are sorted by

lifetime earnings the differences between males and females in the first lines of the panels

reflect primarily differences in life expectancies. Thus, females in the first earnings quintile

could receive over $7,600 more in lifetime benefits than males due largely to a longer life

expectancy. But after the same statutory age-62 benefit adjustment is applied to both genders

the differential narrows to just over $5,700, a twenty-five percent reduction. Across the five

earnings quintiles, the age-62 gender differential in lifetime benefits is reduced by about

twenty percent due to a single-sex statutory reduction. This result suggests a somewhat

modified view of the role of life expectancy in Social Security. In any pension program with

a defined benefit structure that is designed to be gender- and income-neutral, a longer life

means, ceteris paribus, larger lifetime benefits. Yet, as the data in Table 4 show, for early

female claimers, statutory benefit adjustments offset some of the pure life expectancy

advantage.

Actual Actuarial Premiums and Losses

Realized actuarial gains and losses are the consequence of the timing and size of the

initial benefit claim. Timing depends on a number of factors including the financial

 

14 For each individual we computed an initial Social Security retirement benefit using individual earnings

histories and relevant benefit formulas that differ primarily by whether year of birth occurs by or after 1916.

 The initial benefit was then converted to 1999 dollars using the CPI.
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incentives in actuarial benefit adjustments. The median and mean actual months of delay for

our cohorts are shown in Table 5 by earnings quintile.15 Non-dually entitled females, which

comprise about half of the female sample, are shown separately since their claiming delays

are more comparable to those of males who are predominantly non-dually entitled

beneficiaries.16 Generally, delays rise with lifetime earnings consistent with the results in

Table 4, but not monotonically – they decline between the fourth and fifth quintiles as many

high-earning beneficiaries claim benefits early.17 From Figure 1, we saw that high-earning

males who claim early will have a relative benefit ratio that is below one, on average,

implying an actuarial loss whereas most males in the first quintile will experience an

actuarial premium until age 65. Figure 1 also indicates that most females will experience an

actuarial loss regardless of when they claim, though the loss can be minimized if the delay

decision is made optimally.

Figure 2 shows for our beneficiary sample the distribution of total lifetime actuarial

premiums by gender and earnings quintile and Figure 3 shows the distribution of total

lifetime actuarial losses (using a three-percent discount rate). Males experience ninety-five

percent of actuarial premiums (over seventy-percent in the middle three quintiles) and less

than thirty-percent of actuarial losses, the latter primarily from high-earning males. Females

experience over seventy-percent of actuarial losses, most of which occurs in the first four

earnings quintiles, but only five percent of actuarial gains. Clearly, males gain the most from

actuarial nonequivalence.

 

15 Months of delay are measured between exact age 62 and the date of initial benefit claim. Some workers

with relatively high earnings may delay their initial claim in order to avoid having benefits withheld due to

the earnings test.

16 Social security benefit rules make it more likely that dual beneficiaries will claim benefits as early as

possible.

17In cross a sectional analysis, Coile, et al (1999) find some evidence of an inverted u-shaped relationship

between wealth and delays in claiming.
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Normal Retirement Age=67

At a given age, AAFs vary inversely with the NRA, as seen section III and in the

lower panel of Table 3, and a higher NRA means larger discount rate differences for early

benefit claims and smaller differences for claims made past the NRA.18 Raising the NRA

has a larger effect on male AAFs due to men’s shorter life expectancy. For example, with

a three-percent discount rate, age-62 AAFs fall 15.5 and 13.6 percent for males and females,

respectively, between the age-65 and age-67 NRAs. The analogous statutory adjustment

factor (column 2 of Table 3) declines from 80 percent to 70 percent, a 12.5 percent change.

Relative Benefit Profiles

When the age-67 NRA becomes effective, monthly statutory benefit reductions will

be five-ninths of one percent for each month of claim delay between ages 64 and 67 and fivetwelfths of one percent for ages 62 and 63. Thus, effective monthly reduction rates will be

smaller than the rates used with the age-65 NRA. For our male beneficiary sample, the effect

on their relative benefit profiles is predictable. From Figure 1 we saw that the age-65 NRA

monthly statutory adjustment factors are smaller than AAFs for low-earning males.19 The

smaller statutory reductions for claims from age 62 to age 64 under the higher NRA means

relative benefit profiles will lie above the profiles under the age-65 NRA, moving them

further from an actuarial-equivalence target. Figure 4 illustrates for high- and low-earning

males the difference in relative benefit profiles between the two NRAs (using a three percent

discount rate). Compared to the age-65 NRA, male benefit profiles are steeper.20

 

18The NRA begins to increase for the 1938 birth cohort and will eventually reach age 67 for all cohorts born

after 1959. The first beneficiaries affected were those newly-eligible in January, 2000.

1973 percent of males have an exact age-62 AAF less than .80.

20 For our female sample the effects on relative benefit profiles of the higher NRA are much smaller with

profile lines that are only slightly different from those in Figure 1.
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An important caveat to these observations is that the higher NRA will apply to future

beneficiaries with longer life expectancies than the cohorts in our sample. Advances in life

expectancy cause benefit profiles, ceteris paribus, to rotate counterclockwise around the

NRA. We can therefore expect future male benefit profiles to be flatter than the profiles for

NRA=67 shown in Figure 4 and future female profiles to be steeper or somewhat further

from actuarial equivalence for early claimers.

V. Implications and Conclusion

The actuarial nonequivalence of benefit adjustments results in systematic differences

in lifetime benefit patterns between males and females and between low- and high-earning

beneficiaries. The differences are due to differences in their survivor rates. Under our midrange discount rate assumption, most male beneficiaries face actuarial premiums that decline

with benefit acceptance after age 62 and most females face actuarial losses that also decline

with delayed acceptance. Thus, males have little actuarial incentive to delay their initial

benefit claim and the disincentive is strongest for low-earning males. In contrast, most

female beneficiaries have little actuarial incentive to accept benefits early. These gender

differences in relative benefit profiles can translate into substantial lifetime actuarial

premiums for males who claim early, and actuarial losses for early-claiming females. One

consequence is that the pure life expectancy advantage of females is partially offset by

actuarially nonequivalence. More generally, the trend toward early (below NRA) claims

combined with continuing improvements in life expectancy that cause counterclockwise

rotations of relative benefit profiles imply that statutory actuarial adjustments have operated

to partially offset the inherent lifetime benefit advantage of those with relatively long life

expectancies.

The patterns of actuarial nonequivalence found here should be considered when

analyzing the claiming or retirement behavior of Social Security beneficiaries or when

simulating the cost of Social Security reform proposals that may affect claiming behavior.
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 A good example of the latter arises in the context of proposals for complete elimination of

the retirement earnings test (now relevant only for beneficiaries below the NRA). Policy

simulations often assume that enactment of such a proposal would lead beneficiaries to

advance their initial claim to the earliest eligibility date. In that case, our results show that

such a response would likely mean higher lifetime benefits for males, particularly lowearning males, and lower lifetime benefits for females, particularly high-earning females.

 But the underlying assumption implies that those beneficiaries who had initially delayed

their claim date did so because of the earnings test. An alternative hypothesis is that

claiming delays are a response to actuarial nonequivalence, a topic to be pursued in future

research.
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References

Aziz, F. and W. Buckler, "The Status of Death Information in Social Security Administration

Files," presented at the 1992 American Statistical Association meeting in Boston.

Blinder, A, R. Gordon, and D. Wise, @Reconsidering the Work Disincentive Effects of Social

Security,@ National Tax Journal, December 1980, pp. 431-442.

Coile, C., P. Diamond, J. Gruber, and A. Jousten, “Delays in Claiming Social Security

Benefits,” NBER Working Paper No. 7318, August 1999, forthcoming in Journal of

Public Economics.

Leimer, D., AA Guide to Social Security Money=s Worth Issues,@ Social Security Bulletin,

Vol. 58, No. 2, Summer 1995, pp. 3-20.

Myers, R. J., AAppraisal of Early-Retirement and Deferred-Retirement Adjustment Factors

under Social Security,@ Proceedings, Conference of Actuaries in Public Practice,

1980-1981.

Myers, R. J., Social Security. Philadelphia: University of Pennsylvania Press, 1993.

Myers, R. J. and B. Schobel, AEarly-Retirement Reduction and Delayed-Retirement Increase

Factors Under U. S. Social Security Law,@ Transactions, Society of Actuaries, Vol.

XLII, 1990, pp. 295-320.

Mirer, T., AThe Optimal Time to File for Social Security Benefits,@ Public Finance Review,

November 1998, pp. 611-636.
-18-

Table 1

Sample Characteristics

(n=401,448)

Group Sample Proportion/Means

Males

Percent of Sample

Average Lifetime Earnings

Age of Death

57.6%

 $27,151

78.5

Females

Percent of Sample

Average Lifetime Earnings

Age of Death

42.4%

$12,333

81.9
-19-

Table 2

Estimated Mortality Hazard Models

Variables Males Females

Intercept -4.8157

(.6230)

-11.1857

(.7411)

Age .0872

(.0004)

.1075

(.0006)

Birth Year -.0127

(.0004)

-.0042

(.0006)

Race (white=1) -.0913

(.0109)

-.0569

(.0139)

Dual -.5228

(.0247)

-.3955

(.0086)

Earnings -2.0126

(.2249)

-.1828

(.2789)

Earnings2 .2972

(.0269)

.0543

(.0349)

Earnings3 -.0140

(.0011)

-.0039

(.0014)

-∆2logλ with and without earnings

variables

1,537 712

Estimated standard errors are shown in parentheses.
-20-

Table 3

Actuarial Adjustment Factors for Ages 62 to 70 Benefit Claims

By Gender and Discount Rates

discount rate=1.0 discount rate=3.0 discount rate=5.0

Age Statutory Males Females Males Females Males Females

NRA=65

62 0.800 0.825 0.848 0.791 0.815 0.757 0.782

63 0.867 0.877 0.894 0.853 0.871 0.829 0.847

64 0.933 0.935 0.945 0.923 0.932 0.909 0.919

65 1.000 1.000 1.000 1.000 1.000 1.000 1.000

66 1.080 1.072 1.061 1.087 1.075 1.103 1.090

67 1.160 1.152 1.128 1.185 1.158 1.220 1.192

68 1.240 1.242 1.203 1.296 1.252 1.354 1.306

69 1.320 1.344 1.286 1.421 1.356 1.507 1.435

70 1.400 1.459 1.379 1.565 1.474 1.684 1.581

NRA=67

62 0.700 0.716 0.752 0.668 0.704 0.621 0.656

63 0.750 0.762 0.793 0.721 0.752 0.680 0.711

64 0.800 0.812 0.837 0.779 0.805 0.746 0.772

65 0.867 0.868 0.886 0.844 0.863 0.822 0.839

66 0.933 0.930 0.940 0.917 0.928 0.904 0.915

67 1.000 1.000 1.000 1.000 1.000 1.000 1.000

68 1.080 1.078 1.066 1.093 1.080 1.109 1.096

69 1.160 1.166 1.140 1.199 1.170 1.235 1.204

70 1.240 1.264 1.222 1.320 1.273 1.379 1.327

Myers and Schobel (1990) results for a 3 percent real discount rate:

NRA=65. Age-62 retirement: males=.786, females=.818; Age-70 retirement: males=1.600, females=1.464.

NRA=67. Age-62 retirement: males=.680, females=.722; Age-70 retirement: males=1.307, females=1.245.
-21-

Table 4

Actuarial Differences in Lifetime Benefits by Gender and Earnings

(Discount Rate=3%)

Quinti1e 1 Quinti1e 2 Quinti1e 3 Quinti1e 4 Quinti1e 5

Female

Months to Peak 25 27 28 30 34

Lifetime Benefit Gain

by Delaying to Peak 764 1,414 2,126 3,167 4,844

Actuarial Equivalent

Lifetime Benefits 43,564 73,846 102,430 134,298 172,050

Percent of Quintile 71 65 48 22 6

Male

Months to Peak 4 4 7 12 22

Lifetime Benefit Gain

by Delaying to Peak 47 30 186 534 2,149

Actuarial Equivalent

Lifetime Benefits 35,899 58,525 82,090 107,810 155,739

Percent of Quintile 29 35 52 78 94

Female-Male

Female-Male

Actuarial Equivalent

Benefit Difference 7,665 15,321 20,340 26,488 16,313

Female-Male Age-62

Statutory Benefit

Difference 5,748 12,162 16,502 22,220 12,735
-22-

Table 5

Actual Median and Mean Number of Months of Delay

Group Quintile 1 Quintile 2 Quintile 3 Quintile 4 Quintile 5

Males

Median

Mean

1

11.4

8

14.7

16

17.3

21

18.7

12

16.6

Females

Median

Mean

1

8.3

1

11.9

8

15.1

9

15.6

7

15.5

Nondual Females

Median

Mean

1

11.0

6

14.8

13

16.9

12

16.6

8

15.8
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