Social Security and Retirement

131 Undergraduate Public Economics

Emmanuel Saez
UC Berkeley

1
 RETIREMENT PROBLEM

Life-Cycle: Individuals ability to work declines with aging and

continue to live after they are unwilling/unable to work

Standard Life-Cycle Model Prediction: Absent any govern-

ment program, rational individual would save while working to
consume savings while retired [Modigliani life cycle graph]

Optimal saving problem is extremely complex: uncertainty in

returns to saving, in life-span, in future ability/opportunities
to work, in future tastes/health

In practice: When govt was small ⇒ Many people worked till

unable to (often till death) and then were taken care of by
family members

Today: Govt is taxing workers to provide for retirees through

social security retirement systems
2
 Life Cycle Model

Wealth
Earnings

Consumption
savings

dissaving

time
0: work starts R: retirement T: death
Figure 2.6: Employment rate of men aged 65+ in the UK and the US

Source: Blundell, French, and Tetlow (2017)

 Figure 2.7: Life expectancy of men at age 65 in the UK and the US

Source: UK data from the Office for National Statistics. US data from the Human Mortality Database.
Source: Blundell, French, and Tetlow (2017)
 Panel B. Employment rates of men aged 60-64, 1970-2019
80%
US lowers early retirement age from
65 to 62 in 1961

60%

Germany lowers retirement age from

65 to 60 in 1973,
40%
increases it to 65 in 2000s

US

20%
France

Germany
0%
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Source: Saez '21 using OECD database

 GOVT INTERVENTION IN RETIREMENT POLICY

Actual Retirement Programs: All OECD countries imple-

ment substantial government funded retirement programs (sub-
stantial share of GDP around 6-10%, US smaller around 5%),
started in first part of 20th century and have been growing.

Common structure:

Individuals pay social security contributions (payroll taxes) while

working and receive retirement benefits when they stop work-
ing till the end of their life (annuity)

Extension of the earlier family model: it’s no longer your own

working kids who take care of you in old age but all workers
in the country

In the United States, the public retirement program is called

Social Security
6
 Figure 10.15. The rise of the social State in Europe, 1870-2015
60%
Other social spending
Uses of fiscal revenues as % national income

50% Social transfers (family, unemployment, etc.) 47%

Health (health insurance, hospitals, etc.)
Retirement and disability pensions 6%
40% Education (primary, secondary, tertiary) 5%
Army, police, justice, administration, etc.
9%
30%

11%
20%

6%
10%
2%
1%
8% 10%
6%
0%
1870 1880 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010
Interpretation. In 2015, fiscal revenues represented 47% of national income on average in Western Europe et were used as follows: 10%
of national income for regalian expenditure (army, police, justice, general administration, basic infrastructure: roads, etc.); 6% for education;
11% for pensions; 9% for health; 5% for social transfers (other than pensions); 6% for other social spending (housing, etc.). Before 1914,
regalian expenditure absorbed almost all fiscal revenues. Note. The evolution depicted here is the average of Germany, France, Britain and
Sweden (see figure 10.14). Sources and séries: see piketty.pse.ens.fr/ideology.
 SOCIAL SECURITY: PROGRAM DETAILS

How Is Social Security Financed?

Almost all workers in the United States pay the Federal Insur-
ance Contributions Act (FICA) tax on their earnings.

Tax is 12.4% of earnings (6.2% paid by employer, 6.2% paid

by employees) up to a cap of $176,000 in 2025

Who Is Eligible to Receive Social Security?

A person must have worked and paid this payroll tax for 40
quarters (10 years) over their lifetime, and must be of age 62
or older.

8
 SOCIAL SECURITY: PROGRAM DETAILS

How Are Social Security Benefits Calculated?

Annuity: A payment that lasts until the recipient’s death.

Annuity amount is a progressive function of the recipient’s

average (taxable) earnings over the person’s 35 highest earning
years where each month’s earnings are expressed in today’s
dollars using average wage growth
AIME = average indexed monthly earnings

Once benefits start for a given person, they are indexed to

price inflation once every year (“real” annuity)

Higher earners live longer. Progressivity of benefits formula

roughly offsets this (but life expectancy gap between rich and
poor is increasing)
9
232 American Economic Journal: economic policy AUGUST 2017

Source: Gelber et al. AEJ:EP 2017

$2,500

$2,000
Primary insurance amount

15%
32%
$1,500

$1,000

$500
90%

$0
$0 $1,000 $2,000 $3,000 $4,000 $5,000 $6,000 $7,000 $8,000

Average indexed monthly earnings

Figure 1. Primary Insurance Amount as a Function of Average Indexed Monthly Earnings

Notes: The figure shows the primary insurance amount (PIA) as a function of average indexed monthly earnings
(AIME) in 2013. The percentages are marginal replacement rates.
Source: SSA (2013)
Source: Bosworth et al. 2016
 How Are Social Security Benefits Paid Out?

Full Benefits Age (FBA): The age at which a Social Security

recipient receives full retirement benefits (Primary Insurance
Amount): currently 67 if born 1960+ (used to be 65)

Early Entitlement Age (EEA): The earliest age at which a

Social Security recipient can receive reduced benefits is 62

If you claim benefits 1 year before FBA, you get 6% less in an-
nual benefits (permanently), if you claim 2 years before FBA,
you get 12% less in annual benefits (permanently), etc.

You get 8% more in benefits if you claim 1 year after FBA,

etc. Benefits automatically paid at 70.

12
Adjustments to Social Security Benefits based on claiming age

Table 1: Initial Benefits Based on Initiation Age

Age Benefits
62 $700
63 $750
64 $800
65 $867
66 $933
67 $1,000
68 $1,080
69 $1,160
70 $1,240
Note: $1,000 is the monthly base at a full retirement age of 67.
 SOCIAL SECURITY: PROGRAM DETAILS

Are There Benefits for Family Members?

-Spouses of claimants (get own benefits or 50% of primary
earner benefits, whichever is biggest)
-Children of deceased workers.
-Spouses who survive a Social Security recipient get 100% of
primary earners’ benefits

Can You Work and Receive Social Security?

The earnings test reduces benefits of the 62 to 66-year old by
$0.50 for each dollar of earnings they have above about $20K

Not really a tax because later benefits are increased (as if

you had retired later) but most people don’t understand the
system and perceive the earnings test as a pure tax

⇒ Bunching at earnings test kink at ages 62-64 (Gelber-Jones-

Sacks ’19) when normal retirement age was 65
14
 Earning test for Social Security Benefit
Benefit

Slope -0.5
full benefit

phasing cut
of benefit no benefit

O
$20k earnings
 Source: Gelber, Jones, Sacks (2013)

Figure E.6: Adjustment Across Ages: Histograms of Earnings and Normalized Excess Mass,
59-73-year-olds Claiming OASI by Age 65, 2000-2006
Panel A: Earnings histograms, by age

Panel B: Normalized excess mass, by age

 Quiz on the Earnings Test for Social Security

Which one of these about the Earnings Test is FALSE?

A. The earnings test reduces benefits by $.5 per dollar earned

above the $20K earnings disregard

B. Some social security beneficiaries respond to the test by

limiting their earnings to $20K to avoid losing benefits

C. The earnings test is like a tax on earnings and hence it

is rational for beneficiaries to reduce their earnings to avoid
losing benefits

D. If a beneficiary loses some benefits because of the earnings

test, she will recoup these lost benefits in the form of slightly
higher benefits for the rest of her life.

E. Actually A, B, C, D are all true

17
 SOURCES OF RETIREMENT INCOME IN THE US

1) Govt provided retirement benefits (US Social Security): For

2/3 of retirees, SS is more than 50% of income. 1/3 of elderly
households depend almost entirely on SS.

2) Home Ownership: 75% of US elderly are homeowners

(home purchase with 30-year traditional mortgage is a key
form of life cycle savings)

3) Employer pensions (tax favored): 40-45% of elderly US

households have employer pensions. Two types:

a) Traditional: Defined Benefit (DB) and mandatory: em-

ployer carries full risk [in sharp decline, many in default]

b) New: Defined Contribution (DC) and elective: 401(k)s,

employee carries full risk
18
4) Extra additional savings: significant only for wealthy mi-
nority [=10% of retirees]

Key lesson: Bottom 90% wealth is (a) housing (net of mort-

gage debt), (b) pensions, (c) minus other debts (consumer
credit, student loans)

All 3 components are heavily affected by government policy

(education finance), institutions (such as employers), financial
regulations (mortgage refinance, credit card and loans)

Note: student loans make you start negative (instead of zero)

in life-cycle model
 FUNDED VS. UNFUNDED PROGRAMS

Two forms of retirement programs:

1) Unfunded (pay-as-you-go): benefits of current retirees

are paid out of contributions from current workers [genera-
tional link]

current benefits = current contributions

2) Funded: workers contributions are invested in financial as-

sets and will pay for benefits when they retire [no generational
link]

current benefits = past contributions + market returns on

past contributions

Social security (as most public retirement systems) is unfunded

Most private pension plans (such as 401(k)s) are funded

19
 FUNDED VS UNFUNDED SYSTEMS

1) Funded system: each generation gets a market return r

on contributions:
benefits=tax you paid ·(1 + r)

2) Unfunded system: 1st generation of retirees gets free

benefits when the system starts

For later generations: pay tax (for older generation) and you
get benefits from younger generation

Generation t is size Nt, earns wt, pays taxes Tt = τ Ntwt in

period t and receives benefits Bt = τ Nt+1wt+1 from gen. t + 1

Bt/Tt = (Nt+1/Nt) · (wt+1/wt) = (1 + n) · (1 + g)

Implicit return on taxes is the sum of population growth n and

real wage growth (per worker) g
20
 FUNDED VS UNFUNDED SYSTEMS

Unfunded system is always desirable when n + g > r (Diamond

1965): an economy with n + g > r is called dynamically inef-
ficient and introducing an unfunded system makes a Pareto
improvement

US economy: Annual n = 1% and g = 1% [n + g was higher

in 1940-1970]. r ' 5%. In general r > n + g in practice.

Note that r is much more risky than n+g: risk adjusted market
rate of return should be lower than average market rate r but
still higher than n + g

Funded system delivers higher returns because it does not

deliver a free lunch to 1st generation

Choice between funded vs. unfunded system is an inter-

generational redistribution trade-off
21
 MODEL: RATIONAL VS. MYOPIC SAVERS

Most important reason for social security: many people

are unable to save rationally for retirement (due to myopia,
self-control problems, lack of information, etc.)

Life-cycle model: work and save in period 1, retire in period 2

1) Rational individuals: [draw graph]

maxc1,c2 u(c1) + δu(c2) st c1 + s = w and c2 = s · (1 + r)

⇒ c1 + c2/(1 + r) = w

FOC: u0(c2)/u0(c1) = 1/[(1 + r)δ], let s∗ be optimal saving

Example: If δ = 1 and r = 0 then c1 = c2 = w/2 and s∗ = w/2

2) Myopic individuals:

maxc1,c2 u(c1) st c1 + s = w and c2 = s · (1 + r)

⇒ c1 = w and s = c2 = 0
22
 c2 Rational vs. Myopic Individual
Rational individual
W(1+r) (c1=c1*, c2=c2*)
Myopic individual
(c1=W, c2=0)

c2*

0 c1* W c1
s*
 MODEL: RATIONAL VS. MYOPIC SAVERS

Social welfare is always u(c1) + δu(c2)

Govt imposes forced saving tax τ such that τ = s∗ and benefits

b = τ · (1 + r). Cannot borrow against b [as in current Social
Security]

1) Rational individual unaffected: adjusts s one-to-one so that

outcome unchanged [rational unaffected as long as τ ≤ s∗]:
100% crowding out of private savings by forced savings
c1 = w − (s∗ + s0 ) and and c2 = (s∗ + s0 ) · (1 + r) ⇒ choosing s0 is equivalent
to choosing s = s∗ + s0 , rational person chooses s0 = 0

2) Myopic individual affected (0% crowding out): new out-

come maximizes Social Welfare

Forced savings is a good solution: does not affect those re-

sponsible, affects the myopic individuals in socially desired way
24
 Adding forced savings τ=s*
c2
Rational individual
stays at (c1=c1*, c2=c2*)

c2* Myopic individual

moves to (c1=c1*, c2=c2*)

0 c1* W c1
Forced savings τ=s*
 Quiz on the Model with Myopic and Rational Savers

Which of A, B, C, D is FALSE?

A. Social security forces myopic individuals to save

B. Social security does not affect rational individuals

C. Social security increases consumption in old age for the

myopic but not the rational

D. Social security transfers resources from rational savers to-

ward myopic savers

E. Actually A, B, C, D are ALL true

26
 MODEL: COMMENTS

1) Universal vs. Means-Tested Program: Universal forced

savings is better than means-tested program financed by tax
on everybody. With means-test program, two drawbacks:

a) Responsible individuals subsidize myopic individuals

b) Incentives to under-save to get means-tested pension

2) Heterogeneity in w: Forced saving should be proportional

to w (as long as govt does not care about redistribution)

27
 Crowd-Out Effect of Social Security on Savings

The effect of Social Security on private savings has been the

subject of a large number of studies over the past 30 years

To measure the impact of Social Security on savings, there

must be a way to compare people with different levels of Social
Security benefits who are otherwise identical
In the United States, Social Security is a national program that applies to
almost all workers; very similar people usually have very similar benefits.
Recent studies have provided evidence on the impact of Social Security-like
programs on private savings in Italy.

Italian Reforms in 1992 substantially reduced the benefits, and thus future
SSW, for younger workers in the public sector, while reducing much less
the benefits of older workers and those in the private sector.

Studies estimate that only about 1/3 of the reduction in SSW was offset
by higher private savings.

28
 Evidence for Myopia and adequate savings

1) Diamond JpubE 1977: old age poverty has fallen as Social

Security expanded. Poverty for other groups has not fallen
nearly as much

2) Fall in consumption at retirement: Bernheim, Skinner,

Weinberg (2001) show that drop in consumption is significant
for all groups except the wealthiest [consistent with myopia]

29
 CHAPTER 13 ■ SOCIAL SECURITY
13.2
Living Standards of the Elderly, 1959−2009

Public Finance and Public Policy Jonathan Gruber Fourth Edition Copyright © 2012 Worth Publishers 20 of 41
Source: Bernheim et al. (2001), p. 847
SOCIAL SECURITY AND RETIREMENT: THEORY

If a 62-year-old worker works until 63, instead of retiring at 62

and claiming her Social Security benefits, three things happen
through the Social Security system:

1) She pays an extra year of payroll taxes on her earnings.

2) She receives one year less of Social Security benefits.

3) She gets a higher Social Security benefit level through the

actuarial adjustment (' 6-8% extra permanently per year of
delay)

Adjustment is called actuarially fair if those 3 effects can-

cel out in Present Discounted Value (US system has been
reformed decades ago to be close to fair on average)
32
 SOCIAL SECURITY AND RETIREMENT: THEORY

Three key elements of a social security system may affect

retirement behavior:

1) Availability of benefits at Early Retirement Age (EEA):

(62 in US)
Those effects arise because of myopia or lack of information [a rational
individual is not affected by EEA because he/she can use own savings while
retired till he/she reaches age 62]

2) Non-actuarially fair adjustments of benefits for those retir-

ing after the EEA:
If benefits are not adjusted in a fair way, they can create a huge implicit
tax on work (US used to have very little adjustment)

3) Social norm created by retirement benefits: govt calling

some age the “Normal Retirement Age” (NRA) can affect
decisions in spite of no underlying economic incentives (see
Seibold ’21 for such effects in Germany)
33
 CHAPTER 13 ■ SOCIAL SECURITY
13.3
Spike in Retirement Hazard at EEA

• Retirement hazard rate: The percentage of workers

retiring at a certain age.

Public Finance and Public Policy Jonathan Gruber Fourth Edition Copyright © 2012 Worth Publishers 24 of 41
 CHAPTER 13 ■ SOCIAL SECURITY
13.3
Spike in Retirement Hazard at EEA

Public Finance and Public Policy Jonathan Gruber Fourth Edition Copyright © 2012 Worth Publishers 25 of 41
 CHAPTER 13 ■ SOCIAL SECURITY
13.3
Evidence: Retirement Age in Germany, 1968−1992

• Retirement age lowed from 65 to 60 in 1973.

Public Finance and Public Policy Jonathan Gruber Fourth Edition Copyright © 2012 Worth Publishers 27 of 41
 Social Security and Retirement: Implications

Evidence suggests that it is potentially very costly to design

Social Security systems that allow very early retirement and/or
penalize additional work beyond the retirement age.

Adjusting systems to more fairly reward work at old ages can

increase labor supply of elderly

It seems better to have an early retirement age that is not too

low and provide disability benefits to those who truly cannot
work and haven’t yet reached the early retirement age

“Normal retirement age” labelling can also have an impact

through social norms and focal points (as in Germany as shown
in Seibold ’21)

35
 Panel B. Employment rates of men aged 60-64, 1970-2019
80%
US lowers early retirement age from
65 to 62 in 1961

60%

Germany lowers retirement age from

65 to 60 in 1973,
40%
increases it to 65 in 2000s

US

20%
France

Germany
0%
1970 1975 1980 1985 1990 1995 2000 2005 2010 2015

Source: Saez '21 using OECD database

Social Security Reform: Problems with Current System

Rate of return n + g has declined from over 3% to about 2%

due to:

1) n: Retirement of baby boom large cohorts born 1945-1965:

2) Increase in life expectancy at retirement age

Note: top half of individuals (in terms of lifetime earnings) has seen large
life expectancy gains while bottom half life expectancy has stagnated in
recent decades

1)+2) imply number of elderly per working age person in-

creases from .15 in 1960 to .35 in 2030

3) g: Slower productivity growth since 1975 (from 2% to 1%)

Requires adjusting taxes or benefits to remain in balance

37
 CHAPTER 13 ■ SOCIAL SECURITY
13.4
Social Security Reform

Public Finance and Public Policy Jonathan Gruber Fourth Edition Copyright © 2012 Worth Publishers 32 of 41
 1983 GREENSPAN COMMISSION

Demographic changes are predictable, so 1st reform was im-

plemented in 1983 (designed to solve budget problems over
next 75 years)

1) Increased payroll taxes to build a trust-fund

2) Increased retirement age in the future (from age 65 to 67)

Trust fund invested in Treasury Bills (Fed gov debt):

T Ft+1 = T Ft · (1 + i) + SST axt − SSBent

Trust fund peaked at $2.8T in 2013 and will be exhausted by

2033, taxes will then cover about 75% of promised benefits

Requires additional adjustment: increasing payroll tax rate by

3.5 pp (from 12.4% to 15.9%, not huge)
39
 CHAPTER 13 ■ SOCIAL SECURITY
13.4
APPLICATION: The Social Security Trust Fund and
National Savings

• In theory, one benefit of the partial funding of Social

Security through the build-up of the trust fund is an
increase in national savings.
• The trust fund is “off budget,” not supposed to be part
of budget discussion.
• But typically the government reports the
deficit/surplus from the “unified budget,” which
incorporates off-budget categories.
• Makes it easy to treat trust fund as an asset, avoid
fixing the deficit.

Public Finance and Public Policy Jonathan Gruber Fourth Edition Copyright © 2012 Worth Publishers 34 of 41
 Social Security Small Reform Options

1) Increase contributions: increase tax rate or earnings cap

2) Reduce benefits: straight cut not politically feasible: a)

Index retirement age to life expectancy, b) Index benefits to
chained-Consumer Price Index instead of regular CPI after re-
tirement, c) Make benefits fully taxable for income tax

3) Means-tested benefits: bad for savings incentives and could

make program politically unstable [a program for the poor is
a poor program]. Explains conservatives support.

Key issue is distributional: low income earners have seen in-

come and life expectancy stagnate but they have increased for
high income earners
41
 SOCIAL SECURITY PRIVATIZATION

This is the more radical reform option. Two components:

1) Funding the system

2) Replace DB by DC:

benefits = past contributions + market return

Main arguments in favor:

(a) Micro: get higher return on contributions r > n + g for

individuals

(b) Macro: higher savings and hence will increase the capital
stock and wages

Some countries such as Chile, Mexico, Uruguay, UK have pri-

vatized (partly) their systems
42
SOCIAL SECURITY PRIVATIZATION ACCOUNTING

Exactly the reverse of pay-as-you-go calculations:

1) First generation loses as they need to fund current retirees

and own contributions. All future generations gain [genera-
tional redistribution]

2) If govt increases debt to pay for current retirees: future

generations get higher return on contributions but need to
re-pay higher govt debt ⇒ Complete wash for all generations

⇒ Only way funding generates real changes is by hurting some

transitional generations which have to double pay

43
 ADDITIONAL PRIVATIZATION ISSUES

1) Risk: individuals bear investment risk (stock market fluc-

tuates too much relative to economy) and cannot count on
defined level of benefits [Privatization needs to include mini-
mum pension provision]

2) Annuitization: hard to impose in privatized system because

of political constraints [hard to force sick person to annuitize
her wealth] ⇒ Some people will exhaust benefits before death
and be poor in very old age [looming problem with 401(k)s]

3) Lack of financial literacy: Individuals do not know how to

invest. Complicated choice, govt can do it for people more
efficiently

4) Administrative costs: privatized systems (Chile, UK) admin

costs very high (1% of assets = 10 times more than Social Se-
curity) due to wasteful advertisement by mutual funds because
of lack of financial literacy
44
 Evidence on Lack of Financial Literacy

401(k) private pensions in the US offer strong evidence of lack

of financial literacy

1) 1/N investment choices of 401(k) contributions: many peo-

ple invest contributions by dividing them equally into invest-
ment options (regardless of the options)

2) Default effects: opt-in vs. opt-out have enormous effects

on 401(k) enrollment [Madrian and Shea QJE’01]

3) People often invest 401(k) in company stock which is ex-

tremely risky (Enron). Strong evidence of default effects in
investment choices as well

⇒ Much better to force people to save via mandatory social

security system than rely on individual rationality
45
Automatic enrollment effect
Automatic enrollment dramatically increases participation.

401(k) participation by tenure at firm: Company B

100%

80%
Fraction of employees ever
participated

60%

40%

20%

0%
0 6 12 18 24 30 36 42 48
Tenure at company (months)
Hired before automatic enrollment Hired during automatic enrollment
Hired after automatic enrollment ended

6
Source: Madrian and Shea (2001)
Automatic enrollment effect
Employees enrolled under automatic enrollment cluster at
the default contribution rate.
Distribution of contribution rates: Company B
80%

70% 67
Default contribution
rate under automatic
Fraction of participants

60%
enrollment
50%

40% 37
31
30% 26
20
20% 17 18
14 14
9 9 10
6 7
10% 6 4
3 1
0%
1% 2% 3-5% 6% 7-10% 11-16%
Contribution rate
Hired before automatic enrollment Hired during automatic enrollment (2% default)
Hired after automatic enrollment ended

7
Source: Madrian and Shea (2001)
 The Flypaper Effect in Individual Investor
Asset Allocation (Choi,
(Choi Laibson
Laibson, Madrian 2007)

Studied a firm that used several different match systems in

their 401(k) plan.
I’ll discuss two of those regimes today:

Match allocated to employer stock and workers can reallocate

 Call this “default”
default case (default is employer stock)

Match allocated to an asset actively chosen by workers;

workers
orkers required
req ired to make an active
acti e designation.
designation
 Call this “no default” case (workers must choose)

Economically,
E i ll ththese ttwo systems
t are id
identical.
ti l
They both allow workers to do whatever the worker wants.

Source: courtesy of David Laibson

 Consequences of the two regimes
Balances in employer stock
Default No
ES Default
Own Balance in Employer Stock 24% 20%
Matching
g Balance in Employer
p y Stock 94% 27%
Total Balance in Employer Stock 56% 22%

14

Source: courtesy of David Laibson

 CONCLUSION

Social Security is the largest social insurance program in the

United States, and the largest single expenditure item of the
federal government

Key reason for existence of social security programs is the

inability of individuals to save adequately for retirement on
their own

Social Security faces a long-run financing problem requiring to

increase taxes or cut benefits in the long-run

This will be a big policy debate in the coming decade (as some
adjustment needed after 2033 when trust fund runs out)

Most other rich countries face even bigger challenges (more

generous programs, lower fertility than the US)
47
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