Chapter 20
Social Security
Reading
• Essential reading
– Hindriks, J and G.D. Myles Intermediate Public Economics.
(Cambridge: MIT Press, 2005) Chapter 20.
• Further reading
– Banks, J. and Emmerson, C. (2000) “Public and private pension
spending: principles, practice and the need for reform”, Fiscal
Studies, 21, 1 - 63.
– Diamond, P.A. (1997) “Macroeconomic aspects of social security
reform”, Brookings Papers on Economic Activity, 1 – 87.
– Mulligan, C.B., Gil, R. and Sala-i-Martin, X. (2004) “Do
democracies have different public policies than
nondemocracies?” Journal of Economic Perspectives, 18, 51 74.
– Samuelson, P.A. (1975) “Optimum social security in a life-cycle
growth model”, International Economic Review, 16, 539 - 544.
Reading
• Challenging reading
– Bernheim, B.D. and Bagwell, K. (1988) “Is everything neutral?”,
Journal of Political Economy, 96, 308 - 338.
– Diamond, P.A. (2001) “Issues in Social Security Reform” in S.
Friedman and D. Jacobs (eds.), The Future of the Safety Net:
Social Insurance and Employee Benefits (Ithaca: Cornell
University Press).
– Galasso, V. and Profeta, P. (2004) “Lessons for an aging
society: the political sustainability of social security systems”,
Economic Policy, 38, 63 - 115.
– Miles, D. (1998) “The implications of switching from unfunded to
funded pension systems”, National Institute Economic Review,
71 - 86.
– Mulligan, C.B., Gil, R. and Sala-i-Martin,X. (2002) “Social
Security and Democracy”, NBER Working Paper no. 8958.
Introduction
• One part of social security is the provision of
pensions to the retired
• Pensions raise questions about:
– The transfer of resources between generations
– The effect on incentives to save
• The policy relevance of pensions is emphasized
by the “pension crisis”
– The crisis may force major revision in pensions
provision
Types of System
• Pensions may be paid from:
– An accumulated fund
– From current tax contributions
• Pay-as-you-go: Taxes on workers pay the
pensions of the retired
– The systems in the US, UK, and many other countries
are (approximately) pay-as-you-go
• A pay-as-you-go systems satisfies
Benefits received by retired = Contributions of workers
Types of System
• Let b be the pension, R the number of retired, t
the average social security contribution, and E
the number of workers, then
bR=tE
• With constant population growth at rate n
b = [1 + n]t
• The system effectively pays interest at rate n on
taxes
• The return is determined by population growth
Types of System
• Fully funded: Taxes are invested by the social
security system and returned, with interest, as a
pension
• The budget identity is
Pensions = Social security tax plus interest
= Investment plus return
• Denoting the interest rate by r
b = [1 + r]t
• A fully funded system forces each worker to
save an amount t
Types of System
• A pay-as-you-go system leads to an
intergenerational transfer
• A fully funded system causes an intertemporal
reallocation
• The returns (r and n) will differ except at a
Golden Rule allocation
• Systems between these extremes are non-fully
funded
– Hold some investment but may also rely on tax
financing or disinvestment
The Pensions Crisis
• There are three factors causing the
pensions crisis
– The fall in the birth rate
– The increase in longevity
– The fall in the retirement age
• These factors cause the proportion of
retired in the population to grow
• The output of each worker must support
an ever larger number of people
The Pensions Crisis
• The dependency ratio
measures the proportion
of retired relative to
workers
• Tab.20.1 reports this ratio
for several countries
• The ratio is forecast to
increase substantially
• For Japan the rise is
especially dramatic
1980 1990 2000 2010 2020 2030 2040
Australia 14.7
16.7
18.2
19.9
25.9
32.3
36.1
France
21.9
21.3
24.5
25.4
32.7
39.8
45.4
Japan
13.4
17.2
25.2
34.8
46.9
51.7
63.6
UK
23.5
24.1
24.1
25.3
31.1
40.4
47.2
US
16.9
18.9
18.6
19.0
25.0
32.9
34.6
Table 20.1: Dependency ratio (population
over 65 as a proportion of population 15 - 64)
Source: OECD
(www.oecd.org/dataoecd/40/27/2492139.xls)
The Pensions Crisis
• Define the dependency ratio D by D = R/E
• For a pay-as-you-go system
t = bD
• As D increases either
– The tax rate rises for given b
– The pension falls for given t
• Without changes in b and/or t the system goes
into deficit as D increases
• None of the options is politically attractive
The Pensions Crisis
Cost Rate
18
16
14
12
10
8
6
4
2
0
20
80
20
70
20
60
20
50
20
40
20
30
20
20
20
10
20
00
Income Rate
19
90
• Fig. 20.1 shows the
forecast deficit for the US
Old Age and Survivors
Insurance fund
• The income rate is the
ratio of income to the
taxable payroll
• The cost rate is the ratio
of cost to taxable payroll
• Holding b and t constant
the system goes into
permanent deficit from
2018 onwards
Figure 20.1: Annual Income and Cost
Forecast for OASI
(www.ssa.gov/OACT/TR/TR04)
The Pensions Crisis
• The UK government has
followed a policy of
reducing the real value of
the pension
• Tab. 20.2 reveals the
extent of this decrease
• The pension has fallen
from 40% of average
earnings to 26% in 25
years
• It is forecast to continue
to fall
Date
1975
1980
1985
1990
Rate as a % of
average earnings
39.3
39.4
35.8
29.1
1995
28.3
2000
25.7
Table 20.2: Forecasts for UK Basic State
Pension Source: UK Department of Work
and Pensions
(www.dwp.gov.uk/asd/asd1/abstract/Abstrat2003.pdf)
The Simplest Program
• Assume an overlapping generations economy:
– With no production
– With constant population
– A good that cannot be saved
• Consumers have an endowment of 1 unit of
consumption when young
• They have no endowment when old
• Consumers would prefer to smooth consumption
over the lifecycle
The Simplest Program
• The only competitive equilibrium has no trade
– Young and old wish to trade
– The old have nothing to trade
• All consumption takes place when young
• This autarkic equilibrium is not Pareto-efficient
• A social security program can engineer a
Pareto-improvement by making
intergenerational transfers
The Simplest Program
• Fig. 20.2 shows the effect
of a pay-as-you-go
system
• A tax of ½ a unit of
consumption is paid by
young
• A pension of ½ a unit is
received by old
• This is a Paretoimprovement over the notrade equilibrium
Consumption
when Old
1
1/ 2
x
1*
, x 2*

1/ 2
1 Consumption
when Young
Figure 20.2: Pareto-Improvement and
Social Security
The Simplest Program
• A correctly designed system can achieve the
Pareto-efficient allocation ( {x1*, x2*} in Fig. 20.2)
• This result shows the benefits of introducing
intergenerational transfers
• The system has to be pay-as-you-go since a
fully funded program requires a commodity that
can be saved
• These conclusions generalize to economies with
production
Social Security and Production
• Social security can affect saving and capital
accumulation
• The consequence depends on the position of
the economy relative to the Golden Rule
• Consider a program that taxes each worker t
and pays a pension b
• The program owns K ts units of capital at time t,
or kts  Kts / Lt units of capital per unit of labor
• A program is optimal if t, b, and kts are feasible
and the economy achieves the Golden Rule
Social Security and Production
• A feasible program satisfies the budget
constraint
bLt 1  tLt  rt kts Lt  kts1Lt 1  kts Lt


• In the steady state this becomes
b 1  n  t  r  nk s
• Assuming the economy is at the Golden Rule
with r = n the budget constraint becomes
b 1  n  t
• A pay-as-you-go program with b = [1 + n]t
attains the Golden Rule
Social Security and Production
• A fully-funded system does not affect equilibrium
• The budget constraint of a fully funded program
is
s
bLt 1  tLt 11  rt   k Lt 1  rt 
• At the steady state this becomes
b  t 1  r   k s 1  n1  r 
• The individual budget steady-state budget is
x1  x 2 /1  r   w t  b /1  r 
• The program variables cancel
– Individuals adjust saving to offset social security
– Social security crowds out private saving
Population Growth
• The fall in the rate of population growth is one of
the causes of the pensions crisis
• With a pay-as-you-go program a given level of
pension requires a higher rate of tax
• Assume initially that there is no pension program
• Holding k fixed the consumption possibility
frontier shows that
x1
 k
n
x 2
 k 1  f ' k 
n
• First period consumption is decreased but
second period consumption is increased
Population Growth
x2
• The effect of population
growth on consumption
possibilities is shown in
Fig. 20.3
• An increase in n shifts the
frontier upwards
• Evaluated at the Golden
Rule
x 2
n

 
x1
  1  f ' k *  1  n
n
• The Golden Rule
allocation moves along a
line with gradient – [1 + n]
Frontier after
Increase in n
Gradient
 1  n
Initial
Frontier
x1
Figure 20.3: Population Growth and
Consumption Possibilities
Population Growth
• The effect of an increase
in n on welfare depends
on the capital stock
• If k < k* welfare is reduced
as the capital stock
moves further from k*
• This is shown be the
move from e0 to e1 in Fig.
20.4
• If k > k* welfare is
increased
x2
e1
e0
x1
Figure 20.4: Population Growth and
Consumption Possibilities
Population Growth
• Assume the social
x2
New
security program is
Frontier
adjusted to maintain the
New Golden
Golden Rule
Rule Allocation
• As n increases the
Initial Golden
frontier shifts and the
Rule Allocation
tangent line becomes
steeper
• As shown in Fig. 20.5 the
Golden Rule allocation
Initial
moves to a point below
Frontier
the original tangent line
x1
• Per capital consumption
Figure 20.5: Population Growth and
is reduced
Social Security
Sustaining a Program
• In the economy without production the
introduction of social security is a Pareto
improvement
• But it is not privately rational
– The young in any generation can gain by not giving a
pension to the old provided they still expect to receive
a pension
– Giving a transfer is not a Nash equilibrium strategy
• This raises the question of how the program can
be sustained
Sustaining a Program
• One explanation is that the young are altruistic
– They care about the consumption level or utility of the
old
• Altruism alters the nature of preferences but is
not inconsistent with the aim of maximizing utility
• Altruistic preferences can be written as
or

 U x , x
U t  U xtt , xtt 1, xtt1
Ut
t
t


t 1
t , U t 1
• Both forms of utility provide a private incentive
for the young to transfer resources to the old
Sustaining a Program
• A second reason why a program can be
sustained is the threat of removal of pension
• Not making a transfer to the old is a Nash
equilibrium strategy
• This argument relies on believing a transfer will
still be received
• The social security program is repeated over
many periods so more complex strategies are
possible
• Punishment strategies can be adopted
Sustaining a Program
• Don’t contribute is the
Nash equilibrium strategy
of the game in Fig. 20.6
• If the game is repeated
an equilibrium strategy is
“Contribute until the other
player chooses Don’t
contribute, then always
play don’t contribute”
• This is a punishment
strategy
Player 1
Contribute
Contribute
Don’t contribute
5, 5
0, 10
Player 2
Don’t
contribute
10, 0
2, 2
Figure 20.6: Social Security Game
Sustaining a Program
• Assume the discount factor is d
• The payoff from always playing Contribute is 5 +
5d + 5d2 + … = 5[1/1 – d]
• If Don’t contribute is played the payoff is 10 + 2d
+2d2 + … = 10 + 2[d/1 – d]
• The payoff from Contribute is higher is d > 5/8
• The punishment strategy supports the efficient
equilibrium
• The same mechanism can work for social
security
Ricardian Equivalence
• Ricardian equivalence applies when changes in
government policy do not affect economic
equilibrium
• This occurs when changes in individual behavior
completely offset the policy change
• Changes in private saving ensure a fully-funded
social security system does not affect the
capital-labor ratio
– This was an example of Ricardian equivalence
Ricardian Equivalence
• Ricardian equivalence can also apply to
programs that are not fully funded
• A program that is not fully funded will affect a
number of generations
– The costs and benefits of the program are distributed
across time
• If generations are linked through
intergenerational concern then a dynasty of
consumers can offset a program
• This generates Ricardian equivalence for a
broader range of policies
Ricardian Equivalence
• Assume utility is given by

~
U t  U xtt , xtt 1,U t 1
• Substituting for U~t 1 gives




~
U t  U xtt , xtt 1,U xtt11, xtt12 ,U t 2
– Repeating shows that the consumer at t cares about
all future consumption levels
• If population growth is 0 the budget constraints
of the two generations alive at t are
xtt 1  st 1  rt 1   bt
xtt11  wt 1  bt  st 1
Ricardian Equivalence
• With a pension the budget constraints are
t 1
x  s 1  r   t  bˆ
t
t 1
xt 1
t
t 1
t
 wt 1  bˆt  t  st 1
• Nothing changes if the bequest changes to
b̂t  bt  t
• The same logic can be applied to any series of
transfers
• Reallocation of resources by the household
offsets the effect of the transfer
Ricardian Equivalence
• The dynasty adjusts bequests to eliminate the
effect of the policy
• This argument is limited by the need for there to
be active intergenerational altruism
• The initial bequest must also be larger than the
pension (unless transfers from children to
parents are allowed)
• Ricardian equivalence can also be applied to
government debt
Social Security Reform
• Increasing longevity and the decline in the birth
rate are increasing the dependency ratio
• Many pension programs are unsustainable with
significant tax increases
• This has lead to numerous reform proposals
• The reform most often discussed is to move to a
fully funded system
– A fully funded system can be government-run or
utilize private pensions
Social Security Reform
• The transition from pay-as-you-go to fully funded
social security will take time
• Those currently in work will bear two costs
– Financing the pensions of the retired
– Purchase capital to finance their own pensions
• The welfare of those currently working will be
reduced
– The benefits will accrue to future generations
• This leads to political resistance to reforms
Social Security Reform
• Tab. 20.3 reports a
simulation of transition for
the UK
• The pension is 20% of
average earnings for the
UK and 40% for Europe
• Pension reform is
announced in 1997,
implemented in 2020, and
completed in 2040
• The numbers are the
change in wage in base
case equivalent to the
reform
Age in 1997
UK
Europe
> 57
0
0
50 – 57
-0.09
-0.6
50 – 50
-1.1
-2.3
30 – 40
-3.0
-5.7
20 – 30
-3.8
-7.2
10 – 20
-2.3
-4.2
0 – 10
0.7
1.7
-10 – 0
3.95
9.2
-20 - -10
6.5
15.7
-40 - -30
7.4
18.7
< -40
7.2
18.9
Table 20.3: Gains and Losses in transition
Source: Miles (1998)
Social Security Reform
• Reform reduces welfare
for the young and middleaged
• These are the voters who
must support the reform if
it is to be implemented
• Tab. 20.4 illustrates the
political problem
• The age of the median
voter is forecast to rise
• This is the group that
suffer from pension
reform
Country
France
Germany
Italy
Spain
UK
US
Year
Age of median voter
2000
43
2050
53
2000
46
2050
55
1992
44
2050
57
2000
44
2050
57
2000
45
2050
53
2000
47
2050
53
Table 20.4: Age of the Median Voter
Source: Galasso and Profeta (2004)
Social Security Reform
• A fully-funded government system is equivalent
to private pensions
– Provided both invest in the same assets
• In the US the state system invests only in longterm Treasury debt
– This implies low risk and low return
– Few private investors would select this portfolio
• Reform in the US could also allow investment in
risky asset
– But this raises questions about the acceptable degree
of risk
Social Security Reform
• A further issue is the choice between defined
benefit and defined contribution systems
• A defined contribution system involves
investments in a fund which are annuitized on
retirement
– The risk falls on the worker since the value of the fund
is uncertain
• A defined benefit system involves contributions
which are a constant proportion of income and a
known fraction of income is paid as a pension
– The risk falls on the pension fund to meet
commitments