Transcript Social Security Rosen 5th Edition, pp. 183

Social Security
Rosen 5th Ed pp. 183-199
Rosen 6th Ed, pp. 179-195
Rosen 7th Ed, pp. 190-210
• Government Accounting
• Generational Accounting
• Social Security Accounting
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The Government Budget Constraint
Gt
Tt
Bt
r
R
P DEFt
DEFt
-
Governm ent spending on everyt hing except interest on it s bonds
Net taxes and other revenues (taxes m inus t ransfers)
Governm ent bonds (debt) at the beginning of period t
Int erest rat e on government bonds, paid in period t
(1+r)
Governm ent primary deficitG=t -( Tt)
Governm ent t ot al deficitG=t +
( rBt - Tt)
T he government budget deficit is financed by selling government bonds. T he governm ent
must sell enough bonds so t hat t he proceeds will pay for any current spending it cannot pay
for with t ax revenue (this fact is called t he ‘governm ent budget const raint ,’ which just says
t hat the government must obt ain the money it spends either by taxat ion or by borrowing).
T hus t he st ock of government bonds accumulates according t o:
Bt+1 - Bt
= DEFt
= (Gt + rBt) - Tt
Bt+1
= Gt + RBt - Tt
Bt+1 +(Tt-Gt)
= RBt
Bt
= Bt+1 /R + (Tt - Gt)/R
but
Bt+1
= Bt+2 /R + (Tt+1 - Gt+1 )/R
so
Bt
= [Bt+2 /R + (Tt+1 - Gt+1 )/R]/R + (Tt - Gt)/R
= (Tt - Gt)/R + [(Tt+1 - Gt+1 )/R]/R + ...
= P DEFt/R + [P DEFt+1 /R]/R + ...
so
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RBt
= P DVt(T ) -P DVt(G)
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Generational Accounting in a TwoPeriod Lifetime
• ty,t- Taxes minus transfers of young
• to,t- Taxes minus transfers of old
The Generational Account:
GAt = ty,t + to,t+1/R
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Generational Accounts and
Budget Balance
Tt = ty,t + to,t
The present discounted value is:
PDV(Tt) = Tt + Tt+1/R + Tt+2/RR + ...
=ty,t +ty,t+1/R +ty,t+2/RR + ...
+to,t +to,t+1/R +to,t+2/RR
=to,t + [ty,t+to,t+1/R]+[ty,t+1+to,t+2/R]/R + ...
=to,t + GA t + GA t+1/R + GAt+2/RR + ...
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“Pay As You Go”
Social Security
• Revenues from SS taxes in each period are
paid in the same period as benefits to the old:
ty,t = -to,t
• Constant size:
t* = ty,t = - to,t = ty,t+1 …
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GA’s for PAYG Social Security
Introduced at time t
• Generation young at time t-1:
GAt-1 = ty,t-1 + to,t / R
= -t*/R
Ida Mae
Fuller:
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GA’s for PAYG Social Security
Introduced at time t
• Generation young at time t:
GAt = ty,t + to,t+1/R
= t* (R/R - 1/R)
= t*(r/R)
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GA’s and “Funded” Social Security
• “Fully Funded” means gov takes SS taxes
paid by workers and actually saves it
• Old people get benefits based on what they
paid in while working, plus interest
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GA’s and Funded Social Security
• Net transfers when old equal taxes plus interest:
to,t+1=-Rty,t
• Generation that was old when system was
introduced gets no benefits => GAt-1 = 0
• Future generations are identical
GAt = ty,t+to,t+1/R
= ty,t-ty,t
=0
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Rate of Return on Social Security
• Depends on whether there is productivity
growth and/or population growth
• Intuition: If economy is growing, taxes paid
by young will exceed taxes that were paid
by current old when they were young
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No-Growth Economy
• Suppose government tried to pay interest on SS
to,t+1 = -Rty,t
ty,t+1 = Rty,t
ty,t+2 = Rty,t+1 = RRty,t= R2ty,t
ty,t+3 = R3ty,t
…
No matter how small the SS system is to start with,
eventually it grows larger than entire economy
It’s a “Ponzi scheme”
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“Ponzi Scheme”
• Approach a small group of gullible people, promise
them fantastic returns in a short period
• Approach larger group, get new contributions, use
their money to fulfill promise to first group
• Wait for the money to roll in
• Escape before it collapses
• Examples:
– Ponzi (1929)
– Russia (early 90s)
– Albania (mid 90s)
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Productivity Growth
• Suppose wages are growing:
wy,t+1 = (1+g)wy,t
wy,t+2 = (1+g)wy,t+1
• Suppose the tax rate is constant:
Taxes = ty,twy,t
• Tax revenues grow with wages, and size of SS can
grow over time if it grows at rate g or slower
• Rate of return on contributions is g
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Population Growth
Define t.,t as per-capita taxes paid; assume population
growing: Pt = (1+n)Pt-1
PAYG implies:
-Pt-1to,t = ty,t Pt
-to,t
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= ty,t (Pt/Pt-1)
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Population Growth: Option One
Keep ty,t = ty,t-1
-to,t = ty,t-1 (Pt/Pt-1)
= ty,t-1 (1+n)
=> rate of return equals population growth
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Population Growth (cont)
Option two: keep to,t = to,t-1= to
-Pt+1ty,t+1 = Ptto
ty,t+1
ty,t
to
-to,t+1
= -(Pt/Pt+1)to
= -(Pt-1/Pt)to
= -(Pt/Pt-1) ty,t
= ty,t (1+n)
=> Rate of return equals population growth
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A Baby Boom
Suppose population is constant at P, except that
generation t is 20 percent larger, Pt = 1.2 P.
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BB Option 1: Keep Taxes Fixed
ty,t = t
Earlier we showed that
-to,t = ty,t(Pt/Pt-1)
Pre-Boomer Generation’s benefits:
to,t = t (1.2)
Boomers’ benefits:
= t(1/1.2)
≈ .83 t ≈ .70 to,t
Boomers get SS benefits that are 83 percent of generations before t, and 70
percent of the benefits received by their parents.
Not likely!
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BB Option 2: Maintain Benefits
ty,t
= -(Pt-1/Pt)to
= -(1/1.2)to
≈ .83 t
ty,t+1
= -(Pt/Pt+1)to
= -(1.2/1)to
= 1.2 t
= 1.2*1.2 ty,t
=> You are screwed!
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BB Option 3: Partial Funding
1) with constant taxes on the young, the t-1 generation
benefited because taxes on the BB’s were large
2) with constant benefits for old, the t generation benefited,
because taxes when they were young were low
Idea: Let’s keep constant taxes on the young, but don’t give the
proceeds to the old - save them instead!
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‘Partial Funding’
Keep benefits for the old constant at t
Keep taxes on the young constant at t
Generates a surplus in period t:
1.2 tP - tP
= 0.2 tP
Invest this ‘trust fund’ at rate R, generating
0.2 tP R in period t+1
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Partial Funding (cont)
Total paid to boomers in period t+1:
0.2 tP R + tP = 0.2 tP (1+r) + tP
= 0.2 tP r + 1.2 tP
Per capita benefits for boomers when old:
t + (0.2/1.2)t r
Conclusion: Nobody loses, BB’s win!
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Conclusion
• SS wins from an unexpected baby boom
• Problem comes if there is a baby bust
• Conclusion: You guys are screwed!
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Why Do We Have Social Security?
•
•
•
•
Efficiency?
Equity?
Stupidity?
Paternalism?
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Efficiency Justification 1:
Longevity Insurance
• If you don’t know how long you will live
after retirement, how can you know how
much to save?
• Social Security benefits are an ‘annuity’
– You keep getting the same payment no matter
how long you live
• Ida Mae Fuller lived to 100
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Why can’t private market solve the
‘outliving your assets’ problem?
• Private annuities do exist
– Purchase annuity for $x
– Annual payment of $ax until death
• Suppose company knows average life expectancy at age 65 is
16 years, so it offers an annuity with value a = (1/16)
– If you know you’re likely to die soon, won’t buy
– If you know you will probably live longer than 16 years (you’re
healthy, mom is 102), buy
– People who buy live > 16 years, company goes bankrupt
• ‘Adverse Selection’ problem is severe
– Mortality rate of annuity buyers is half the rate for general population
– People have a pretty good idea of life expectancy
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Efficiency Argument 2:
Lifetime Income Insurance
• Highly progressive structure of SS benefits
means system implicitly provides insurance
• If you lose your job and your pretax wage
falls by half, your prospects for retirement
income do not fall by nearly as much
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Efficiency Argument 3:
Insurance Against Financial Risk
• If you save for your own retirement, suppose the
economy and stock market go through a bad spell
right when you are about to retire
– From 1929 peak to 1933 trough, Dow fell by 90%
– From 1969 peak to 1975 trough, Dow fell by over 60%
– 1970s wiped out a lot of bond wealth
• Social Security is much safer
– Wage and population growth don’t fluctuate as much
– In bad times, SS can borrow from future generations
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Equity Argument
• Redistribution
– Standard utilitarian arguments
– Clear that original purpose of the program was
mainly to alleviate poverty among the elderly
– Particularly acute problem for those who had
saved for retirement but had savings wiped out
by the Great Depression
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Equity/Efficiency Interactions
• The “Samaritan’s Dilemma”
– Suppose we are just too “nice” to tolerate poverty
among the elderly
– Some smart young people may spend everything
today and rely on generosity of society to care for
them when old
• Mandatory system makes everyone
contribute; nobody can exploit the rest of us
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Stupidity Argument:
Hard to figure out how much to save
for retirement
• To do it right, need to make good forecasts of:
–
–
–
–
–
Future interest rates
Future stock returns
Future rates of wage growth
Future changes in life expectancy
Degree of uncertainty about all these
• May make sense to let experts do it
• Analogy to building codes
– We don’t ask each individual or builder decide exact characteristics
of home (wall thickness, foundation depth, etc)
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“Ulysses Paternalism”
• Idea is that many people would not save for
their own retirement if SS did not exist,
because they don’t have the self control
– Considerable evidence for this:
• Poverty rates of elderly were quite high before SS
• SS accounts for 70 percent of income of the lowincome elderly
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Criticisms of Social Security
• Inefficiencies
– Reduces saving
– Induces earlier retirement
– Causes labor market distortions
• High SS taxes may convince one member of a
household to stay home rather than working
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Criticisms of Social Security
(cont)
• Inequities
– Across generations
• Generational accounts show this
– Across similar individuals
• Horizontal equity: similar people should be treated similarly
• Single versus married with nonworking spouse
– Married gets benefits 50 percent higher
– Across different individuals
• Everyone should get a ‘fair deal’
– Reality: Low income people get a much better deal than high
income
– Violates freedom of choice
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History and the
Current Problems
• Original Social Security law was for a ‘fully
funded system’
• In 1939, switched over to a PAYG system
• Ida Mae Fuller
–
–
–
–
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Paid SS taxes on one paycheck
Retired the next week
Lived to the age of 100
Net benefit from SS: $20-30 K
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1970s Disasters
• Large increases in benefits passed in early 70s
– Recall 3 options for responding to Baby Boom
– Congress chose to increase benefits of elderly
• Slowdown in productivity growth after 1973
• Size of baby bust became clear
• Remember: Return on PAYG SS equals pty
growth plus pop growth
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Greenspan Commission (1980s)
• In 1981 payments > benefits
• Greenspan commission
– Raise taxes, reduce benefits, build up a Social
Security ‘Trust Fund’
• Trust fund would contain excess of SS taxes
over benefits while BB’s were working, be
drawn down when they retire
– Supposedly ‘partial funding’
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More Government Accounting
‘On-Budget’ surplus:
(N-S)=(iNcome minus Spending)
‘Off-Budget’ surplus:
(Ptty,t+Pt-1to,t)
‘Unified’ surplus:
(N-S)+(Ptty,t+Pt-1to,t) = T-G
Greenspan commission plan:
•
•
•
•
Boost Ptty,t and cut Ptto,t+1
Put SS surplus in a ‘trust fund’
Should boost ‘unified surplus,’ increase national saving
Nation richer when BBs retire, can more easily afford it
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The problem
• Big Reagan tax cuts not matched by spending cuts, so in
80s gov started running huge ‘on-budget’ deficits
• From early 80s into 90s Greenspan SS tax increases
generated larger and larger SS surpluses
• Both parties want to look good to voters, so focus on
‘unified’ budget
• Soc Sec Surplus=Ptty,t+Pt-1to,t was not saved
– Spent on government programs
– Also claimed to be putting the same money in ‘Trust Fund’
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Example
• Suppose year t Social Security surplus is $100 billion
• Suppose year t ‘on-budget’ deficit is $100 billion
• Treasury says to SS “here’s $100 billion of ‘special’ gov
bonds. Now give us your $100 billion”
• Gov then spends the $100 billion it gets from SocSec
• SocSec ‘trust fund’ grows $100 billion by addition of
‘special’ bonds
• ‘Unified budget’ balance
– $100 billion + $100 billion = 0
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Analogy
• Suppose you are saving for retirement in Individual Retirement
Account (IRA)
• Suppose you can borrow against the money in your IRA
• Every year you put $10,000 in IRA
• Every year, you also ‘borrow back’ that same $10,000 and spend it,
replacing it with a ‘bond’ that says “I owe my IRA $10,000”
• Then ‘trust fund’ of your IRA has ‘bonds’ in it that are worth, say,
$200,000 when you retire - but they are promises to repay yourself
• Difference is that gov bonds are promises to tax future young
generations (you!)
• It’s as if you could redeem the ‘bonds’ in your IRA by forcing your
kids to pay them off
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Conclusion
• ‘Trust fund’ is a bipartisan fraud
• Made it look like gov was responsibly
saving up for the retirement of the Boomers,
when actually it was spending the money
and putting IOU’s in the ‘trust fund’
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Now the Facts
• Demographics
• Social Security projections
• Budget projections
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Demographics
of
Social
Security
Demographics of Social Security
Workers and Beneficiaries
Workers and Beneficiaries
Recall formula for tax rate of the young: ty,t+1 =-(Pt/Pt+1)to
3.4 is almost twice 1.8, so taxes must double from current levels to
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boomers promised benefits
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Social
Security
Finances
2075
Social
Security
Finances Through
through 2075
Social Security Bulletin • Vol. 63 • No. 1 • 2000 from http://www.ssa.gov/OACT/TR/TR03/index.html
Observe puny size of the “Social Security surplus” thru 2015 compared
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to the
huge deficit thereafter
Important Dates
• When do projected benefit payments start to
exceed projected tax revenues? That is,
when does (Ptty,t+Pt-1to,t) become negative?
– 2015, or when you are entering your prime
taxpaying years
• When is the ‘trust fund’ completely
exhausted?
– Who cares? Trust fund is meaningless
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Bottom Line
• You’re doomed!
• Nothing can be done to escape your doom
– Ida Mae Fuller is dead
– Boomers already approaching retirement age
• But doom isn’t quite as bad as you sometimes hear
– More believe in space aliens than believe they’ll get any
SS benefits
– Truth: Benefits will be enough to afford decent and
nutritious food:
• Purina
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