04/25/23 1

Social Security Rosen 5th Ed pp. 183-199Rosen 6th Ed, pp. 179-195Rosen 7th Ed, pp. 190-210

• Government Accounting• Generational Accounting• Social Security Accounting

04/25/23 2

Gt - Government spending on everything except interest on its bondsTt - Net taxes and other revenues (taxes minus transfers)Bt - Government bonds (debt) at the beginning of period tr - Interest rate on government bonds, paid in period tR - (1+r)PDEFt - Government primary deficit = (Gt - Tt)DEFt - Government total deficit = (Gt + rBt - Tt)

The government budget deficit is financed by selling government bonds. The governmentmust sell enough bonds so that the proceeds will pay for any current spending it cannot payfor with tax revenue (this fact is called the ‘government budget constraint,’ which just saysthat the government must obtain the money it spends either by taxation or by borrowing).Thus the stock of government bonds accumulates according to:

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 + (T t+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 + ...

= PDEFt/R + [PDEF t+1/R]/R + ...

so RBt = PDVt(T) - PDVt(G)

The Government Budget Constraint

04/25/23 3

Generational Accounting in a Two-Period Lifetime

• y,t- Taxes minus transfers of young• o,t- Taxes minus transfers of old

The Generational Account:

GAt = y,t + o,t+1/R

04/25/23 4

Generational Accounts and Budget Balance

Tt = y, + o,

The presen discouned value is:

PDV (T) = T + T+1/R + T+2/RR + ...

=y, +y,+1/R +y,+2/RR + ...+o, +o,+1/R +o,+2/RR

=o, + [y,+o,+1/R]+[y,+1+o,+2/R]/R + ...

=o, + GA + GA+1/R + GA+2/RR + ...

04/25/23 5

“Pay As You Go”Social Security

• Revenues from SS taxes in each period are paid in the same period as benefits to the old:y,t = -o,t

• Constant size:* = y,t = - o,t = y,t+1 …

04/25/23 6

GA’s for PAYG Social SecurityIntroduced at time t

• Generation young at time t-1:GAt-1 = y,t-1 + o,t / R

= -*/RIda MaeFuller:

04/25/23 7

GA’s for PAYG Social SecurityIntroduced at time t

• Generation young at time t:GAt = y,t + o,t+1/R

= * (R/R - 1/R) = *(r/R)

04/25/23 8

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

04/25/23 9

GA’s and Funded Social Security

• Net transfers when old equal taxes plus interest:o,t+1=-Ry,t

• Generation that was old when system was introduced gets no benefits => GAt-1 = 0

• Future generations are identicalGAt = y,t+o,t+1/R

= y,t-y,t

= 0

04/25/23 10

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

04/25/23 11

No-Growth Economy

• Suppose government tried to pay interest on SSo,t+1 = -Ry,t

y,t+1 = Ry,t

y,t+2 = Ry,t+1 = RRy,t= R2y,t

y,t+3 = R3y,t

…No matter how small the SS system is to start with,

eventually it grows larger than entire economyIt’s a “Ponzi scheme”

04/25/23 12

“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)

04/25/23 13

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 = y,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

04/25/23 14

Population GrowthDefine .,t as per-capita taxes paid; assume population growing: Pt = (1+n)Pt-1

PAYG implies:

-Pt-1o,t = y,t Pt

-o,t = y,t (Pt/Pt-1)

04/25/23 15

Population Growth: Option One

Keep y,t = y,t-1

-o,t = y,t-1 (Pt/Pt-1)

= y,t-1 (1+n)

=> rate of return equals population growth

04/25/23 16

Population Growth (cont)

Option two: keep o,t = o,t-1= o

-Pt+1y,t+1 = Pto

y,t+1 = -(Pt/Pt+1)o y,t = -(Pt-1/Pt)o o = -(Pt/Pt-1) y,t

-o,t+1 = y,t (1+n)

=> Rate of return equals population growth

04/25/23 17

A Baby BoomSuppose population is constant at P, except that generation t is 20 percent larger, Pt = 1.2 P.

04/25/23 18

BB Option 1: Keep Taxes Fixedy,t =

Earlier we showed that-o,t = y,t(Pt/Pt-1)

Pre-Boomer Generation’s benefits: o,t = (1.2)

Boomers’ benefits:= (1/1.2)≈ .83 ≈ .70 o,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!

04/25/23 19

BB Option 2: Maintain Benefitsy,t = -(Pt-1/Pt)o

= -(1/1.2)o

≈ .83

y,t+1 = -(Pt/Pt+1)o

= -(1.2/1)o

= 1.2 = 1.2*1.2 y,t

=> You are screwed!

04/25/23 20

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!

04/25/23 21

‘Partial Funding’Keep benefits for the old constant at

Keep taxes on the young constant at

Generates a surplus in period t:

1.2 P P= .2 P

Invest this ‘trust fund’ at rate R, generating

0.2 P R in period t+1

04/25/23 22

Partial Funding (cont)

Total paid to boomers in period t+1:

0.2 P R + P = 0.2 P (1+r) + P

= 0.2 P r + 1.2 P

Per capita benefits for boomers when old:

+ (0.2/1.2) r

Conclusion: Nobody loses, BB’s win!

04/25/23 23

Conclusion

• SS wins from an unexpected baby boom• Problem comes if there is a baby bust• Conclusion: You guys are screwed!

04/25/23 24

Why Do We Have Social Security?

• Efficiency?• Equity?• Stupidity?• Paternalism?

04/25/23 25

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

04/25/23 26

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

04/25/23 27

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

04/25/23 28

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

04/25/23 29

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

04/25/23 30

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

04/25/23 31

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)

04/25/23 32

“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 low-

income elderly

04/25/23 33

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

04/25/23 34

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

04/25/23 35

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

– Paid SS taxes on one paycheck– Retired the next week– Lived to the age of 100– Net benefit from SS: $20-30 K

04/25/23 36

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

04/25/23 37

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’

04/25/23 38

More Government Accounting‘On-Budget’ surplus: (N-S)=(iNcome minus Spending)

‘Off-Budget’ surplus: (Pty,t+Pt-1o,t)

‘Unified’ surplus: (N-S)+(Pty,t+Pt-1o,t) = T-G

Greenspan commission plan:• Boost Pty,t and cut Pto,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

04/25/23 39

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=Pty,t+Pt-1o,t was not saved

– Spent on government programs– Also claimed to be putting the same money in ‘Trust Fund’

04/25/23 40

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

04/25/23 41

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

04/25/23 42

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’

04/25/23 43

Now the Facts

• Demographics• Social Security projections• Budget projections

04/25/23 44

Demographics of Social SecurityWorkers and Beneficiaries

Demographics of Social Security

Workers and Beneficiaries

Recall formula for tax rate of the young: y,t+1 =-(Pt/Pt+1)o

3.4 is almost twice 1.8, so taxes must double from current levels to pay boomers promised benefits

04/25/23 45

Social Security Finances Through 2075Social Security Finances 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 to the huge deficit thereafter

04/25/23 46

Important Dates

• When do projected benefit payments start to exceed projected tax revenues? That is, when does (Pty,t+Pt-1o,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

04/25/23 47

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