Is Loss Aversion An Explanation for Early Claiming of Social Security?
Wei Sun
Hanqing Institute and School of Finance
Renmin University of China
September 15, 2011
Incomplete draft
Abstract
Social Security provides longevity insurance for older households. According to standard
expected utility models, most rational households who are not currently liquidity-constrained
should delay claiming in order to insure their consumption in late life. However, most
individuals claim Social Security soon after they become eligible. This paper provides an
explanation for this early claiming behavior using the loss aversion feature of prospect theory.
That is, when making Social Security claiming decisions, older households do not evaluate the
final state of benefits they receive. Instead, they consider benefit gains and losses relative to
claiming immediately. In the event of early death, a household that delays claiming receive a
substantially smaller lifetime benefit than claiming at 62. Thus, households claim immediately in
order to avoid this type of loss. This paper examines the above hypothesis both theoretically and
empirically. In the first part, we calculate Social Security Equivalent Income, the factor by which
the Social Security benefits of a typical household claiming at other ages should be multiplied so
that it is as well off in prospect theory terms as it would be at the reference combination of
claiming ages. We find that if both spouses of a typical one earner couple delay claiming to their
full retirement age, they would require a 4.1 percent increase in their Social Security income to
achieve the same level of value as both claiming immediately. In the second part, using Health
and Retirement Study data matched to Social Security earnings records and Social Security
benefit claiming record, we find households who subject to higher value loss are more likely to
claim immediately.
1
I. Introduction
Social Security is a dominant component in the balance sheet of older households. It provides
majority of income for workers and their spouses after retirement. Munnell and Soto (2008)
reported that the present value of Social Security benefit accounts for 42 percent of total wealth
for a typical household at retirement. The importance of the Social Security program therefore
attracts many attentions from researchers. Many studies examined the relationship between the
Social Security program and labor supply decision.1 However, the Social Security claiming
decision itself is rarely studied.
Although usually mixed up by previous literature, Coile, et al. (2002) stated that the Social
Security claiming decision is a separate decision from retirement decision. Older workers do not
need to claim Social Security benefit as soon as they stop working if they are not liquidityconstrained. They can claim Social Security anytime between 62 and 70. The timing of claiming
determines their monthly Social Security income for the remainder of their lives. Individuals
who delay claiming receive less periods of Social Security checks. In return, they receive a larger
amount each period. For current retiring cohorts, Social Security benefit is approximately
actuarially fair using 3 percent interest rate. In other words, people receive more or less the same
expected present value of Social Security benefit no matter when they claim. However, previous
literature, i.e. Mitchell, et al. (1999), show that annuity products provide values that largely
exceed their money’s worth as the additional longevity insurance acquired can be substantial.
Sun and Webb (2010) showed that delayed claiming Social Security benefits is analogous to an
actuarially fair annuity purchase - the household can be thought of as returning checks to the
Social Security Administration (SSA), in return for an increase in its lifetime income. Using the
standard expected utility model which assumes all individuals are rational and forward looking,
the authors calculated that the optimal claiming ages for typical non-budget constrained
households are between 67 and 70. Those who claim early will suffer substantial losses in
expected utility terms and run the risk of low consumption in the event that they live unexpected
long. However, contradicting the predictions of the above models, most households claim Social
Security very early. Coile et, al. (2002) reported that over 80 percent of retired workers who
retire before age 62 claim Social Security benefit immediately after becoming eligible.
1
See Diamond and Gruber (1999) for detail.
2
This paper provides an explanation why older households claim Social Security so early. Using
the loss aversion feature of prospect theory, we calculate Social Security Equivalent Income
(SSEI), the factor by which the Social Security benefits of a typical household claiming at other
ages should be multiplied so that it is as well off in prospect theory terms as it would be at the
reference claiming age. We find that people who delay claiming Social Security benefit subject
to significant value losses in prospect theory terms comparing with claiming immediately after
eligible. For example, for a one earner couple both born in 1949, if both spouses delay claiming
to their FRA, their Social Security income must be 4.1 percent higher than they actually receives
to be as well off in prospect theory terms as both claiming at 62.
In addition, using Health and Retirement Study data matched to Social Security earnings’ record
and claiming record, this paper further investigates how much variation in claiming behavior
could be explained by loss aversion. We find that individuals with larger value loss if delayed
claiming to their FRA are more likely to claim Social Security immediately.
The remainder of the paper is organized as follows. Section 2 introduces background and
summarizes previous literature. Section 3 presents the theoretical model. Section 4 specifies the
econometric model and Section 5 concludes.
II. Background and previous literature
2.1 The Social Security program
For a typical couple household in retirement, they can claim three categories of Social Security:
retired worker benefit, spousal benefit and survivor benefit. To claim retired worker benefit, an
individual must have worked at least forty quarters in a FICA sector. In addition, his income has
to pass an earning’s test to receive full benefit at the time of claiming. Otherwise, his benefit will
be reduced one to one dollar for the difference between his actual income and the benchmark of
earning’s test. He can claim retired worker benefit any time between age 62 and 70. The amount
of benefit he receives depends on his primacy insurance amount (PIA) which is calculated based
on his highest 35 years of earnings. As shown in Table 1, people born at different year have
different full retirement age (FRA). If an individual claims Social Security at his FRA, his
3
monthly benefit income is 100 percent of his PIA. If he claims earlier than his FRA, his monthly
benefit income is reduced 5/9 of one percent for each month before his FRA until 36 months.
The percent switches to 5/12 of one percent each month after 36 months. Taking a worker who
was born in 1949 as an example, his FRA is 66. For each month he claims before his FRA, his
monthly benefit is reduced 5/9 of one percent until age 63. Therefore, his total benefit is reduced
by 20 percent and he receives 80 percent of his PIA if claimed at 63. If he claims Social Security
earlier than 63, his benefit is further reduced 5/12 of one percent each month until age 62, the
earliest claiming date. Therefore, his monthly benefit income is only 75 percent of his PIA after
reduction if claimed at 62. For those who claim after their FRA, they receive delayed retirement
credit (DRC). As shown in Table 2, the DRC is also depended on their birth cohort. Again,
taking an individual born in 1949 as an example, his DRC is 8 percent per year. It means that for
each month he delays claiming Social Security benefit, his monthly benefit income for the
reminder of his life increases 2/3 of one percent of his PIA until age 70 at which time the
increases stop. Therefore, at most he could receive 32 percent increase of his PIA by claiming at
age 70, which is 76 percent higher monthly benefit income than claiming immediately after
eligible.
Figure 1 plots the expected present value of Social Security retired worker benefit at different
claiming ages for selected birth cohorts. We use $1,000 PIA, population average mortality
reported in SSA cohort mortality table and 3 percent discount rate used in previous literature. As
shown by the figure, the increases and reductions are approximately actually fair for current
retiring cohorts. But earlier birth cohorts receive less actuarially fair DRC. In addition, the
expected present value of benefit is higher for females, reflecting their longer life expectancy.
Thus, earlier birth cohorts may have incentive to claim no later than their FRA. For current
retiring workers, especially female workers, they should delay claiming Social Security to ensure
their consumption in later life.
The spouse of the old worker is entitled to receive Social Security benefit based on earning’s
record of her husband if the spousal benefit exceeds her own retired worker benefit. The spousal
benefit can be claimed at any time after she turns 62 and given the worker has claimed. If she
claims at her FRA, she is entitled to a monthly benefit of 50 percent of her husband’s PIA. If she
claims before her FRA, her monthly benefit is reduced 25/36 of one percent each month for the
4
first 36 months. Her spousal benefit is further reduced by another 5/12 of one percent for each
month after the first 36 months. However, there is no increase for her spousal benefit if she
claims after her FRA.
A third type of benefit is for the surviving spouse. After death of one spouse, the surviving
spouse could claim survivor benefit if it exceeds her own retired worker benefit. The amount of
the benefit depends on her husband’s monthly benefit income, not his PIA. Therefore, when a
husband delays claiming Social Security, not only it increases his retired worker benefit for the
remainder of his life, but it also increases his surviving wife’s monthly income of her remaining
life. Similarly, if she claims at or after her FRA, she receives 100 percent of her husband’s
monthly benefit. If she claims earlier than her FRA, there’s a reduction, as much as 28.5 percent
if she claims at 60.
To make Social Security claiming decisions, the husband and the wife should consider all three
types of benefits. Besides retired worker benefit which is actuarially fairly priced, they need to
consider the trade-off between spousal benefit and survivor benefit. Delaying claiming Social
Security results the wife receive less periods of spousal benefit as it can be claimed only after the
husband claim, but it increases the survivor benefit for the wife after death of the husband. As
presented in Sass, Sun and Webb (2007), the loss of claiming at suboptimal age combinations is
small in money’s worth terms.
2.2 Previous Literature
There are limited studies on this topic. Gustman and Steinmeier (2005) built a dynamic lifecycle
model with heterogeneous time preference to explain why people do not delay. They concluded
that people with fewer financial assets, which may be correlated with impatience, claim Social
Security early. Benitez-Silva, Dwyer and Sanderson (2008) introduced uncertainty to single
households that Social Security benefits might be cut in the future into a dynamic lifecycle
model. They concluded that some people claim Social Security early because they would like to
lock in benefits before any prospective reduction. Although the above factors explain why some
individuals claim Social Security soon after becoming eligible, a more general explanation is
missing from the literature.
5
Brown, et, al. (2008) is the paper most related to this study. The authors illustrated that
consumers generally ignore the longevity insurance provided by annuity products, but instead
focus on their return and risk. For a variety of reasons, including moral hazard and
administration costs, annuity products are usually less than actuarially fair. Therefore, annuity
products perform poorly evaluated in terms of risk and return.
III. The Prospect Theory Model
Taken as given the conclusion of Brown, et, al. (2008) that people generally ignore the longevity
insurance provided by annuity products, this paper investigates an alternative explanation for
early claiming behavior, drawing on a psychologically rich model - prospect theory2 (Kahneman
and Tversky, 1979, 1992, KT thereafter). Through a number of experiments, KT found that when
making decisions under uncertainty, individuals tend to evaluate gains and losses relative to a
reference point. In addition, individuals behave in a risk-averse manner when evaluating positive
outcomes, but are risk seeking when making decisions over losses and exhibit diminishing
marginal sensitivity. And finally, losses loom greater than gains. As shown in Figure 2, the value
function of prospect theory model shows that when individuals receive the same magnitude of
gains and losses, the sadness from losses are greater than the happiness from gains (the loss
aversion feature).
This paper makes use of the loss aversion feature of prospect theory to explain early claiming
behavior. Because of the social norm of claiming Social Security at 62, it is natural to set the
reference point to the benefit if claimed at 62. In this case, if they receive higher Social Security
benefit than the reference point over a certain period, there is a gain. If they receive less Social
Security benefit over a certain period, there is a loss. For instance, if a single male born in 1949
with PIA $1,000 claimed Social Security at 62, he receives $750 each month immediately
starting from 62. If delayed claiming Social Security to age 63, he receives $0 benefit at age 62
and $800 each month from 63. At 62, he applies narrow framing and opens a mental account for
his Social Security benefits (Thaler, 1985). He considers the benefit of $750 a month foregone at
62 as a loss of $750 because he receives less benefit than the reference case. After claiming
2
Details of Prospect Theory can be found in Appendix.
6
Social Security at 63, he considers the $50 by which her benefit of $800 a month exceeds the
reference of $750 a month as a gain.
We calculate in a monthly basis. Single individuals can claim Social Security anytime between
62 and 70, 97 alternative claiming months3. Each alternative could be viewed as a lottery, betting
on how long he survives. The individual enters the model alive at 62. The terminal age T is set at
100. He could die any month between 62 and 100, 457 possibilities. The outcome associated
with each possibility is the discounted present value of Social Security gains and losses for each
death age, conditional on claiming age. Therefore, the 97 lotteries can be formally framed as:
(PV62.0|62.0 , d62.0 ; PV62.1|62.0 , d62.1 ; … … ; PV100.0|62.0 , d100.0 )
(PV62.0|62.1 , d62.0 ; PV62.1|62.1 , d62.1 ; … … ; PV100.0|62.1 , d100.0 )
……
(PV62.0|63.0 , d62.0 ; PV62.1|63.0 , d62.1 ; … … ; PV100.0|63.0 , d100.0 )
……
(PV62.0|70.0 , d62.0 ; PV62.1|70.0 , d62.1 ; … … ; PV100.0|70.0 , d100.0 )
where di.j is the probability of dying at age i and month j. PVi.j|k.l is the present value of benefit
gain or loss if the individual dies at age i and month j and claim Social Security benefit at age k
and month l. It can be calculated as follows:
(1)
i.j
PVi.j|k.h = ∑t=62.0 βt−62 (Bt|k.h − Bt|62.0 )
where Bt|k.h is the monthly Social Security benefit received at time t conditional on claiming at
age k and month h. β is the time preference parameter. Figure 3 shows the discounted present
value of Social Security at each age until 100 for a single male born 1949. PVi.j|k.h is the
difference between the dashed curve which indicates they claimed at k.h and solid reference
curve, claimed immediately, at each age i.j.
3
For simplicity, this paper assumes households only claim Social Security at the 2nd of each month.
7
We adopt the standard prospect theory model in KT. Consider a lottery
(𝑥−𝑚 , 𝑝−𝑚 ; … ; 𝑥−1 , 𝑝−1 ; 0, 𝑝0 ; 𝑥1 , 𝑝1 ; … ; 𝑥𝑛 , 𝑝𝑛 ) which has m negative outcomes (𝑥−𝑚 ; … ; 𝑥−1 )
and n positive outcomes (𝑥1 ; … ; 𝑥𝑛 ). The probability of getting outcome x is corresponding p.
The overall value of this lottery can be calculated using the following equation:
(1)
𝑉 = ∑𝑛𝑖=−𝑚 𝑣(𝑥𝑖 )𝜋(𝑝𝑖 )
where 𝑣 is a value function measured by gains and losses relative to a reference point; 𝜋 is a
nonlinear function of probabilities, representing decision weights associated with the outcomes.
The value function takes the following form:
(2)
𝑥𝛼
𝑣(𝑥) = {
−𝜆(−𝑥)𝛽
𝑖𝑓 𝑥 ≥ 0
𝑖𝑓 𝑥 < 0
where 𝑥 is the lottery outcome, 𝛼, 𝛽, 𝜆 capture curve of gains, curve of losses and degree of loss
aversion respectively. In the baseline model, 𝛼, 𝛽, 𝜆 are set at 0.88, 0.88 and 2.25 respectively, as
estimated in KT.
In prospect theory, individuals overweight small probabilities and underweight medium to large
probabilities. Therefore, the decision weighting function is more complex than linear. It takes the
following form:
πn+ = 𝑊 + (𝑝𝑛 )
+
+
π+
i = 𝑊 (𝑝𝑖 + 𝑝𝑖+1 + ⋯ + 𝑝𝑛 ) − 𝑊 (𝑝𝑖+1 + ⋯ + 𝑝𝑛 ) 𝑖𝑓 0 ≤ 𝑖 ≤ 𝑛
πi− = 𝑊 − (𝑝−𝑚 + 𝑝−𝑚+1 + ⋯ + 𝑝𝑖 ) − 𝑊 − (𝑝−𝑚 + ⋯ + 𝑝𝑖−1 ) 𝑖𝑓 − 𝑚 ≤ 𝑖 ≤ 0
−
πm
= 𝑊 − (𝑝−𝑚 )
The capacity W is defined as:
𝑊
+ (𝑝)
𝑊
− (𝑝)
=
=
𝑝𝛾
(𝑝𝛾 + (1 − 𝑝)𝛾 )
1⁄
𝛾
𝑝𝛿
(𝑝𝛿 + (1 − 𝑝)𝛿 )
8
1⁄
𝛿
Where 𝛾 and δ were estimated to be 0.61 and 0.69 respectively.
Table 3 reports SSEI calculated using the above prospect theory (PT) model for single male and
female households born in 1949 respectively, with expected present value (EPV) and expected
utility theory (EUT) based calculations for comparison. Because the reference scenario is
claiming at 62, SSEI of age 62 in all three kinds of models are 1. A SSEI higher than 1 indicates
the household requires higher Social Security income each period to reach the same level of
welfare in the reference case. Not surprisingly, in EPV terms, SSEI is very close to 1 no matter
when households claim because Social Security is an actuarially fair system for current retiring
cohort. Based on EUT models, households should delay claiming. Single females delaying to
their FRA would require only 90 percent of Social Security income to achieve the same expected
lifetime utility as that obtained by claiming at 62. They only require 83.9 percent of their Social
Security income if they delay to 70. However, it is not optimal for PT households to delay
claiming Social Security. Single male and female households who delay claiming Social Security
to their FRA would require 9.9 percent and 5.2 percent increase in their benefit, respectively, to
be as well off as at the reference claim age of 62. For those who delay to age 70, they would
require a 26.2 percent and 15.1 percent increase in benefit, respectively, to be as well off. Thus,
although an actuarially fair Social Security system is attractive for rational households who want
to insure their consumption in later life, it would not attract PT households who ignore the
longevity insurance provided by Socials Security. Fear of receiving a smaller amount of total
benefit induces PT households to claim immediately.
Because this paper has a calibration model, the calibrated parameters may alter people’s
decisions. We therefore try to illustrate the robustness of the proposed hypothesis by calibrating
alternative plausible preference parameters. For singles, we investigate the effect of high/low
mortality rates, and high/low rate of time preference. In addition, we examine the effect of earlier
birth cohorts who have less than fair DRC and the effect of linear decision weights, that is,
instead of overweighting small probabilities and overweight medium large probabilities, we
apply death probabilities directly as decision weights as used in expected present value
calculation. This feature makes the conclusion weaker as the possibility of dying early is
generally small, which are overweighed by prospect theory households. The results are shown in
Table 4. The upper panel reports the SSEI for a male born in 1949 except otherwise noted. The
9
lower panel reports the result for a representative female household. The results are robust across
all specifications. For prospect theory households, it is always optimal for them to claim Social
Security as soon as possible.
For couples, the calculation is more complex but the idea is the same. In the baseline case, I
examine one-earner couples that both spouses were born in the same years. Again, assume the
husband has a PIA of $1,000. The reference combination of claiming ages is both of spouses
claim immediately after becoming eligible. There are 9,409 different combinations of claiming
ages, 9,409 gambles in other words. And there are 208,849 combinations of death possibilities.
In addition, we need to take account for spousal and survivor which are also designed as
actuarially fair. Other factors, such as the age difference and the relative PIA of the couple, affect
the optimal combination of claiming ages of prospect theory households as well. As with single
households, we calculate the SSEI attached to each gamble, using the discounted present value of
flow of gains and losses for each age conditional on claiming combinations of claiming ages and
survival probabilities. The results are presented in Table 5. Again, the results are robust across all
scenarios.
IV. Empirical tests
4.1 Data
Using Health and Retirement Study data, this section examines the empirical evidence on loss
aversion. It investigates how much variation in claiming behavior can be explained by variations
of value losses calculated by prospect theory, controlling for other demographic and socioeconomic variables. The HRS originally comprised a nationally representative panel of over
7,000 individuals born between 1931 and 1941, and their spouses of any age. The original
sample has been interviewed every two years from 1992 to 2008. Older households from
Assets and Health Dynamics of the Oldest-Old (AHEAD) survey are merged to the main dataset
in 1994. Other birth cohorts have been added in 1998 and 2004. The dataset contains
considerable detail on households’ demographic and socio-economic characteristics. In 2004,
7793 respondents gave consent to use their Social Security earnings records and Social Security
benefits information. Their earnings information from January 1951 to December 2003, in
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addition to their Social Security claiming records, are available to researchers on a restricted
basis. We make use these official records in our tests. They are helpful in a couple of dimensions.
First, they are more accurate than self-reported information. Second, this dataset allows me to
distinguish the households’ specific value gains and losses which could be used to identify their
Social Security claiming behaviors.
4.2 Model
We estimate a probit model to capture individuals’ claiming decisions at age 62 as follow:
(3)
𝐷𝑖 = 𝛽0 + 𝛽1 𝐹𝑖 + 𝛽𝑥 𝑋𝑖 + 𝜀𝑖
The dependent variable, 𝐷𝑖 , is a dummy variable which captures individuals’ claiming behaviors.
It takes the value 1 if the individual delays claiming Social Security for at least one year, 0
otherwise. 𝐹𝑖 measures their loss aversion incentives. It is defined as the prospect theory value
difference between claiming immediately and delaying claiming to FRA. I would expect
individuals who incur higher value loss if they delaying claiming to FRA have lower probability
to delay claiming. 𝑋𝑖 is a vector of household demographic and socio-economic variables,
capturing the potential heterogeneous preferences. Following Coile, et, al. (2002), we include
subjective mortality (self-reported probability of living to age 75), gender, marital status, race,
education, a pension dummy capturing whether the individual is receiving any pension and years
have retired before age 62.
Four potential problems arise with the above model. The first is that older workers usually make
Social Security claiming decision and retirement decision simultaneously. They claim Social
Security immediately after they stop their primary job to maintain income flow. Therefore, the
estimating effect could be easily biased by the potential effect of financial incentives to labor
supply decision. To separate the Social Security claiming decision and retirement decision, we
estimate the above model using a sample consists of only individuals who have retired before
age 62. We use two methods to decide if they are retired. First, if an individual has 0 income at
62 and later, we consider the individual is retired before age 62. Second, if an individual passes
11
the Social Security earning’s test at 62 and later, we consider the individual is retired before age
62.
The second potential problem is that some individuals claim Social Security Disabled Benefit
before age 62 and switch to retired worker benefit immediately after they are eligible to retired
worker benefit. This group of people is generally poor and is liquidity-constrained. They would
need income for general consumption and cannot afford to delay claiming. To avoid bias from
this group of households, we keep only individuals who claim retired worker benefit as their
initial entitlement.
Third, since latest data to be December 2003, there are some individuals who are eligible for
Social Security but have not claimed Social Security yet. If they are older than 63 (or 62.2) by
the time of December 2003, I treat these individuals as claimed in January 2004. Since we
estimate s probit model, the dummy which captures their claiming decision is not affected by this
imputation.
Fourth, in the dataset, we have individuals who were born before 1930. They have passed 62
when they participate the first survey in 1992. To accurately measure their situation at age 62, we
only keep households who participated HRS when they turn 62, born after 1930 in other words.
In summary, this paper examines the claiming behaviors using clean sample which separates
claiming decision and retirement decision and focuses on retired worker benefit claiming
decision which is made at 62. The summary statistics of the sample used for the study is shown
in Table 6. The first column shows the sample which defines retirement using zero income rule
and the second column shows the sample which defines retirement using earning’s test. The
portions of individuals who delay claiming for at least one year in both samples are 16 percent
and 15 percent respectively, higher than the sample estimated by Coile, et, al. (2002). It probably
showing the higher incentive to delay claiming as a result of DRC increase.
4.3 Results
The probit regression result is presented in Table 7. The first column presents the result for the
sample using zero income as criterion to define retirement and the second column presents the
12
result for the sample using earning’s test as criterion to define retirement. The results show
similar patterns. The estimate coefficients on the variable which measures prospect theory value
losses for the two samples are -0.001 and -0.001 respectively. Both are statistically significantly
different from 0. They indicate that people with larger value loss to delay claiming are more
likely to claim immediately. The estimated coefficient indicates for each 1000 unit of additional
value loss, older workers have an additional 0.001 percent chance of claiming Social Security
immediately.
The coefficients on other variables fit tuitions as well. Shown as in the earning’s test column,
people have lower subjective mortality, who report higher probability of living to age 75, are
more likely to delay claiming because they would receive higher lifetime benefit if they could
live longer. People who retired longer have higher probability of delaying claiming. This could
because those who retire early are richer individuals. Comparing with single males, single
females are more likely to delay because women usually outlive men. Married men show no
pattern different than single men. However, Married women are more likely to claim
immediately because they are more likely to have lower PIA than their husband. Therefore they
have chances to switch to spousal benefit or survivors benefit at a later time.
V. Conclusion
The above estimates provide important policy implications. As losses loom greater than gains,
delaying claiming Social Security which is approximately the same in expected present value
terms should be unattractive to prospect theory households. Reductions in Social Security
benefits and the shift from defined benefit to defined contribution pension plans have increased
households’ exposure to longevity risk. Thus, if older households claim Social Security early
because of psychological biases, the Social Security Administration may need to consider ways
in which these biases can be countered. In addition, due to the actuarially fair design of the
Social Security program, delaying claiming of Social Security has no cost for the government
budgeting.
13
As Brown, et al. (2008) addressed, framing the claiming decision in a “consumption” way, which
focuses on how much an individual could consume if she delays claiming, rather than on how
much they could receive in monetary terms, may encourage delayed claiming.
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Tables and Figures
Table 1: Full Retirement Age by Birth Year
Birth year
Full Retirement Age
1937 and earlier
65
1938
65 and 2 months
1939
65 and 4 months
1940
65 and 6 months
1941
65 and 8 months
1942
65 and 10 months
1943-1954
66
1955
65 and 2 months
1956
65 and 4 months
1957
65 and 6 months
1958
65 and 8 months
1959
65 and 10 months
1960 and later
67
Data Source: Social Security Administration: www.ssa.gov
15
Table 2: Delayed Retirement Credit by Birth Year
Birth year
Delayed Retirement Credit
1917-1924
3.00%
1925-1926
3.50%
1927-1928
4.00%
1929-1930
4.50%
1931-1932
5.00%
1933-1934
5.50%
1935-1936
6.00%
1937-1938
6.50%
1939-1940
7.00%
1941-1942
7.50%
1943 and later
8.00%
Data Source: Social Security Administration: www.ssa.gov
Claim Time
62.0
63.0
64.0
65.0
66.0
67.0
68.0
69.0
70.0
Table 3: Social Security Equivelent Income
EPV
EUT - CRRA 2
PT
Male
Female Male
Female Male
Female
1.000
1.000
1.000
1.000
1.000
1.000
1.007
0.999
0.984
0.981
1.028
1.018
1.000
0.984
0.953
0.947
1.043
1.020
1.001
0.976
0.930
0.920
1.066
1.032
1.010
0.976
0.914
0.900
1.099
1.052
1.013
0.970
0.893
0.873
1.124
1.063
1.024
0.970
0.880
0.855
1.162
1.086
1.044
0.978
0.875
0.843
1.209
1.118
1.071
0.992
0.881
0.839
1.262
1.151
Notes: Population mortality for 1949 birth cohort. Rate of interest and time preference
both equal three percent. Coefficient of risk aversion equals two.
16
Claim Time
62.0
63.0
64.0
65.0
66.0
67.0
68.0
69.0
70.0
Table 4: Robustness Check: Social Security Equivelent Income
Male
High mortality Low mortality High discount Low discount Linear weight 1931 Male
1.000
1.000
1.000
1.000
1.000
1.000
1.045
1.021
1.047
1.011
1.019
1.018
1.077
1.028
1.081
1.007
1.024
1.045
1.118
1.045
1.125
1.013
1.040
1.080
1.170
1.070
1.180
1.026
1.064
1.142
1.215
1.088
1.229
1.033
1.084
1.212
1.273
1.117
1.292
1.049
1.114
1.292
1.338
1.156
1.363
1.073
1.155
1.382
1.419
1.200
1.452
1.102
1.207
1.486
Female
Claim Time High Mortality Low Mortality High Discount Low Discount Linear weight 1931 Female
62.0
1.000
1.000
1.000
1.000
1.000
1.000
63.0
1.031
1.013
1.035
1.001
1.007
1.005
64.0
1.048
1.012
1.057
0.988
1.001
1.018
65.0
1.075
1.019
1.086
0.984
1.004
1.038
66.0
1.107
1.035
1.126
0.987
1.014
1.082
67.0
1.136
1.041
1.156
0.981
1.018
1.134
68.0
1.169
1.059
1.202
0.986
1.032
1.194
69.0
1.217
1.086
1.258
0.999
1.053
1.259
70.0
1.266
1.120
1.317
1.013
1.082
1.338
Notes: Population mortality for 1949 birth cohort.
17
Table 5: Social Security Equivalent Income: Couples
62
63
64
65
66
67
Female claim age
Male claim age
62
63
64
65
66
67
68
69
70
Base: One earner couple. Both spouses are the same age.
1.000
1.011
1.020
1.033
1.052
1.086
1.026
1.033
1.046
1.063
1.097
1.026
1.036
1.052
1.086
1.028
1.042
1.075
1.041
1.075
1.069
62
63
64
65
66
67
68
69
70
1.000
1.016
1.013
1.011
62
63
64
65
66
67
68
69
70
1.000
1.015
1.009
1.003
1.004
1.001
1.005
1.014
1.028
1.015
1.030
1.024
1.021
1.025
The wife is three years younger
1.031
1.050
1.073
1.045
1.063
1.085
1.035
1.052
1.073
1.029
1.041
1.060
1.032
1.043
1.057
1.025
1.035
1.048
1.034
1.047
1.052
1.107
1.120
1.108
1.095
1.092
1.084
1.083
1.087
1.097
The wife's PIA is 50% of the husband's PIA
1.013
1.026
1.043
1.065
1.088
1.027
1.039
1.056
1.076
1.100
1.021
1.032
1.046
1.065
1.088
1.015
1.025
1.039
1.055
1.078
1.016
1.026
1.039
1.055
1.076
1.013
1.023
1.036
1.051
1.071
1.016
1.026
1.039
1.054
1.074
1.026
1.035
1.048
1.063
1.082
1.039
1.049
1.061
1.076
1.096
Notes: See previous tables.
18
68
69
70
1.121
1.133
1.121
1.111
1.110
1.104
1.106
1.157
1.170
1.158
1.148
1.147
1.142
1.143
1.150
1.194
1.208
1.197
1.187
1.187
1.181
1.182
1.190
1.204
1.142
1.156
1.145
1.133
1.130
1.122
1.120
1.125
1.135
1.178
1.194
1.182
1.171
1.170
1.161
1.160
1.165
1.175
1.215
1.232
1.222
1.212
1.211
1.203
1.202
1.208
1.219
1.115
1.126
1.114
1.104
1.102
1.096
1.097
1.105
1.119
1.144
1.156
1.144
1.134
1.132
1.126
1.127
1.133
1.147
1.176
1.189
1.178
1.167
1.166
1.160
1.161
1.168
1.180
Table 6: Sample Statistics
Zero Income
N Mean
S.D.
491
0.16
0.37
491 -105864.50 44246.48
455
68.09
28.22
280
3.00
1.24
490
3.69
3.83
484
0.39
0.49
491 263142.40 747227.80
Earning's Test
N Mean
S.D.
950
0.15
0.36
950 -110307.10 46034.70
875
68.11
27.29
552
3.04
1.23
950
4.39
4.49
942
0.38
0.49
950 223536.30 589949.50
Delayed claiming for at least one year
Value loss if delayed claiming to FRA
Self reported probability of living to 75
Financial planning horizon
Years of retirement
Whether have pension income
Networth
Demographics:
Birth year
491
1935.69
2.92 950
1935.76
2.93
Single male
491
0.10
0.30 950
0.09
0.29
Single female
491
0.11
0.32 950
0.12
0.33
Married male
491
0.32
0.47 950
0.39
0.49
Married female
491
0.46
0.50 950
0.40
0.49
Less than high school degree
491
0.18
0.38 949
0.19
0.39
High school degree
491
0.44
0.50 949
0.41
0.49
Some college education
491
0.38
0.49 949
0.40
0.49
White
491
0.87
0.33 950
0.87
0.33
Black
491
0.11
0.32 950
0.11
0.32
Hispanic
491
0.06
0.24 950
0.07
0.25
Note: This table reports summary statistics for the samples used in regressions. The numbers are adjusted to
2008 dollars using Consumer Price Index from Federak Reserve Economic Data (FRED) database.
19
Table 7: Probit Regression Results
Dependent Variable: Delay claiming for at least 1 year
Zero Income
Coef
Value loss if delayed claiming to FRA (in 000s)
Earning's Test
S.E.
Coef
S.E.
-0.001 ** 0.000 -0.001 *** 0.000
0.001 ** 0.001 0.001 ** 0.000
Self-reported probability of living to 75
Financial planning horizon
0.009 **
-0.048
0.022
-0.036
-0.094 **
-0.169 ***
0.093
-0.013
0.076 **
-0.017
Years retired
Pension
Networth (in 000,000s)
Networth square (in 000,000,000,000s)
Married male
Married female
Single female
Less than high school degree
Some college education
White
0.004
0.034
0.113
0.064
0.044
0.055
0.082
0.044
0.041
0.050
0.010 ***
-0.023
0.028
-0.003
-0.020
-0.113 ***
0.133 **
-0.002
0.039
-0.006
0.003
0.025
0.038
0.004
0.040
0.038
0.065
0.034
0.027
0.036
N
451
871
Note: *, **, *** indiates the coefficient is statistically significant at 10%, 5% and 1% level
respectively.
Figure 1: Expected Present Value of Social Security at differnt
claiming time for selected Cohorts
Expected Present Value (in 000s)
160
150
140
130
1931 Male
120
1931 Female
110
1949 Male
1949 Female
100
90
80
1
6
11
16
21
26
31
36
41
46
51
56
Delayed Months
20
61
66
71
76
81
86
91
96
Figure 2: Value Function of Prospect Theory
Loss Domain
Gain Domain
Reference Point
Figure 3: Discounted Present Value of Social Security at
Different Claiming Time
300000
250000
200000
62.0
150000
66.0
70.0
100000
50000
0
62
65
68
71
74
77
80
83
21
86
89
92
95
98
Appendix A
Prospect Theory
When making decisions under conditions of risk, people’s behaviors are not always consistent
with the predictions of expected utility models. Kahneman and Tversky (1979) developed a
descriptive model to frame people’s behaviors under risk through a number of lab experim
ents. The prospect theory concluded that when valuing alternative prospects, individuals’
behaviors have the following patterns, as shown in Figure 1:
1.
2.
3.
4.
They evaluate gains and losses of alternative choices relative to a reference point.
They behave as risk averse when facing gains and risk seeking when facing losses.
As usual, the curve has the feature of diminishing marginal sensitivity.
For the same magnitude of gains and losses, the sadness from losses will dominate the
happiness from gains.
Prospect theory has been widely applied to every area of economics and been used to explain the
facts which have difficulties to be explained by expected utility theory. In the following part, I
will report selected experiments from Kahneman and Tversky (1979) in order to make the above
statements easier to understand.
1. Reflection effect.
Consider the following two groups of lotteries:
1)
A: (4000, 0.8; 0, 0.2)
and
B: (3000, 1)*
2):
A: (-4000, 0.0.8; 0, 0.2)*
and
B: (3000, 1)
The experiments found that most individuals chose the latter lottery in the first group and
the former lottery in the second group, indicating people are risk averse when facing
positive prospects but risk seeking when facing negative prospects.
2. Isolation effect.
Consider a two-step experiment which also involves two groups of lotteries:
1)
A: (1000, 0.5; 0, 0.5)
and
B: (500, 1)*
2):
A: (-1000, 0.5; 0, 0.5)*
and
B: (-500, 1)
In the first step of the experiment, participants in the first group were given $1000 and
participants in the second group were given $2000. In the second step, they were
immediately asked to choose from the two groups of lotteries respectively. Kahneman
and Tversky found that people chose exactly the same answers as reflection experiments.
However, if we take a look at the second step experiment as a whole, people are actually
facing:
1)
A: (2000, 0.5; 1000, 0.5)
and
B: (1500, 1)
2):
A: (1000, 0.5; 2000, 0.5)
and
B: (1500, 1)
Therefore, the individuals should make the same choice. In other words, if people choose
lottery B in the first group, they should also choose lottery B in the second group. This
contradiction shows that individuals don’t evaluate final outcome of an event, but instead
taking a look at the gains and losses of alternatives relative to a reference point.
3. Diminishing marginal sensitivity.
This effect is very obvious. So I will pass the example here.
4. Loss aversion.
22
Consider two lotteries:
A: (500, 0.5; -500, 0.5)
and
B: (0, 1)*
Most individuals will choose lottery B, because the value loss of losing $500 dominates
the value gain of winning $500. Emotionally, the feeling of being taken away some thing
is much stronger than getting the same thing unexpected.
Theoretically, the above theory can only be applied to small number of prospects. Later, Tversky
and Kahneman (1992) introduced cumulative prospect theory. The cumulative version of
prospect theory has very similar features and can be generalized to any number of outcomes.
23