Reforming Social Security With
Progressive Personal Accounts
John Geanakoplos
Yale University
Stephen P. Zeldes
Graduate School of Business,
Columbia University
and NBER
NBER Retirement Research Conference
October 20, 2006
Woodstock, VT
President Bush has strongly advocated
replacing part of Social Security with
personal accounts
 Massive effort in 2005, including 60-day, 60city Presidential tour of US to promote this
reform
 Died in Congress due to strong Democratic
opposition and some Republican hesitation
 Funding for individual accounts nevertheless
included in President’s 2007 budget request
2
Democrats versus Republicans
 Democrats committed to keeping DB structure
 Republicans committed to shifting to DC
 Why? Which features of these structures are
important to each side?
3
Core Goals
 Democrats
• Redistribution based on lifetime earnings
• Risk-sharing across generations
• Security via inflation indexed life-annuity
 Republicans
•
•
•
•
•
Property rights via private ownership
Transparency regarding accrual of benefits
Market prices (facilitating financial planning)
Equity-like returns
Portfolio choice
 Are these reconcilable?
 If so, does that help balance the system?
4
Yes! Maybe?
 Progressive Personal Accounts
• Progressive via variable matching of contributions
• Accounts hold new financial securities (PAAWs)
that provide DB-like benefits but are priced.
 Pricing PAAWs allows us to value incremental
benefits and charge accordingly.
5
Outline (including work in progress)
 Create individual account (DC) system with same payouts
as current (DB) system
 Create marketable pools of PAAWs
 Calculate price of pooled PAAWs
 Compute match / tax
 Describe transition to progressive personal accounts
 Use PAAW prices to design rules for self-balancing system
6
Related Literature
 Implicit marginal tax rate / matching in current system
• Feldstein and Samwick (1992)
• Cushing (2005)
• Feldstein and Liebman (2002)
 Accrual of Social Security Benefits
• Geanakoplos, Mitchell, and Zeldes (1999)
• Jackson (2004)
 Self-balancing / Notional DC systems
• Valdes-Prieto (2000)
• Borsch-Supan (2005)
• Auerbach and Lee (2006)
 New financial securities
•
•
•
•
Shiller (1993) (GDP bonds)
Bohn (2002) and Goetzmann (2005) (wage bonds)
Blake and Burrows (longevity bonds)
Valdes-Prieto (2005) pay as you go securities
7
Mechanics of Current OASDI System
Contributions / Taxes
Contributions = tax rate x covered earnings
Covered earnings = min (earnings, cap)
(2006 cap $94,200)
8
Mechanics of Current OASDI System
Calculation of Benefits
1) Calculate relative earnings (ratio of individual covered
earnings to average economy-wide earnings)
2) Average worker’s relative earnings across highest 35
years
3) Compute PIA (in average wage units) as concave
function of average relative earnings
4) Benefit in first year = PIA (in average wage units) x
average wage index
Benefit in future years (each remaining year of life)
indexed to CPI
9
Mechanics of Current OASDI System
Calculation of Primary Insurance Amount (PIA)
0.70
Initial relative benefits (PIA/Average Wage Index)
0.60
0.50
slope=.15
Maximum:
AIE: 1.99
PIA: 0.64
0.40
0.30
slope =.32
Concavity generates redistribution
and individual risk sharing
Tying benefits to average wages
generates aggregate risk sharing
0.20
0.10
slope=.9
0.00
0.00
0.25
0.50
0.75
1.00
1.25
1.50
1.75
2.00
Average relative earnings (AIE/ Average Wage Index)
10
Current System Provides Insurance Against
 low lifetime earnings (35 year average)
 longevity (annuity: inflation indexed payment
for life)
 falling behind wages of next generation
 low wages of all current workers (because
still get same retirement benefits)
11
Creating Individual Accounts that Mimic the
Current System
 Define new securities (PAAWs)
 Compute accrual of balances
 Trade PAAWs in financial markets
12
Personal accounts hold PAAWs:
Personal Annuitized Average Wage Security
 Each PAAW pays
• Economy-wide average wage index in the
year of retirement (conditional on living that
long)
• Same number of inflation-adjusted dollars for
as long as the individual lives
13
PAAW is a composite of two securities
 Average Wage Security
• Pays average economy-wide earnings in a given
year (like a futures contract)
 Personal Annuity Unit (PANT)
• Pays $1 (real) for as long as the individual lives
 PAAW: composite security that pays off an
uncertain number (security 1 above) of a one
inflation-adjusted dollar life annuity (security 2
above)
14
PAAWs enhance property rights on accrued
benefits
 Current law
• No legal property rights to benefits
• No clear distinction between
•
•
benefits already accrued
benefits to be accrued in the future
• So benefit cuts often applied across the board
 PAAWs
• Give owners legal right to collect accrued benefits
• Clearly distinguish between accrued and other benefits
• B/c PAAWs provide market value, if accrued benefits
are cut, people would know how much is being “stolen”
15
How can individual accounts (with irrevocable
annual accrual) mimic redistribution based on
lifetime income?
 Current system: redistribution based on
lifetime rather than current income
 Typical individual account plans exclude
redistribution or base it on current income
 We replicate redistribution based on lifetime
income by using a variable government match
 Match formula is relatively simple: declines
with PAAW balance (PBAL)
16
How are PAAWs accrued?
 PBALit
= number of units of PAAWs accrued by worker i as of year t
= benefits a worker would be entitled to under the current
system if all future earnings = 0
 PBAL can rise, but can never fall
 Other definitions of accrual exist , but our definition
accumulates balances most rapidly
 PAAW accrual is a function of
• New contributions
• Accumulated balances (PBAL)
17
Additional PAAWs Per Additional Contribution
(measured in average wage units)
High when PBAL is low
0.30
Using this schedule for every
contribution mimics the lifetime
redistribution of the current system
0.25
0.20
0.15
And low when PBAL is high
0.10
0.05
0.00
0.01
0.06
0.11
0.16
0.21
0.26
0.31
0.36
0.41
0.46
0.51
0.56
0.61
0.66
0.71
PAAW Balance
18
Variable Match Proposal
 A historically high wage worker will be getting
worse allocation of PAAWs per contribution
than a historically low wage worker of same
age.
 Could be added to other, more traditional,
individual account proposals (e.g.
MacGuineas, Liebman, and Samwick, 2005)
as a way of enhancing progressivity
19
Notes about Variable Government Matching
 Formula slightly different for late-in-life
contributions
• only excess of contribution over 35th highest
relative contribution to date counts toward PAAW
accrual
 Match so far defined in units of PAAWs
• Match “rate” (i.e. dollar of match per dollar of
contribution) requires market valuation of PAAWs
(later)
20
Simple Numerical Examples
 Worker 1: Relative earnings = 1
(earnings = average economy-wide earnings in every
year)
 Worker 2: Relative earnings = average relative
earnings for cohort born in 1938
 Worker 3: Earnings = ½ earnings of Worker 2
 Worker 4: Earnings = 1.5 earnings of Worker 2
 Future work: examine realizations of stochastic
earnings process
21
Additional PAAWs Per Additional Contribution
(measured in average wage units)
Worker 2: Cohort Average
Worker 1: Economy Average
1.2
0.30
1.0
0.25
1.8
0.30
1.6
0.25
1.4
Relative Wage
0.8
0.20
0.6
0.15
1.2
0.20
1.0
0.15
0.8
Additional PAAWs per Additional Contribution
0.4
0.10
0.6
0.10
0.4
0.2
0.05
0.05
0.2
0.0
0.00
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64
0.0
Age
Age
Worker 3: 0.5 Cohort Average
0.9
0.00
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62
Worker 4: 1.5 Cohort Average
0.30
3.0
0.30
0.25
2.5
0.25
0.20
2.0
0.20
0.15
1.5
0.15
1.0
0.10
0.5
0.05
0.8
0.7
0.6
0.5
0.4
0.3
0.10
0.2
0.05
0.1
0.0
0.00
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62
Age
0.0
0.00
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62
Age
22
PAAW Balances (PBAL)
Worker 1: Economy Average
1.2
1.0
0.8
Relative Wage
Worker 2: Cohort Average
0.50
1.8
0.45
1.6
0.40
1.4
0.35
1.2
0.30
0.6
0.6
0.5
0.4
1.0
0.3
0.25
0.20
0.4
0.15
PAAW Balance
0.2
0.0
0.8
0.6
0.10
0.4
0.05
0.2
0.00
0.0
0.1
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64
0
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62
Age
Age
Worker 3: 0.5 Cohort Average
Worker 4: 1.5 Cohort Average
0.9
0.40
0.8
0.35
0.7
0.2
3.0
0.8
0.7
2.5
0.30
0.6
0.25
0.6
2.0
0.5
0.5
0.20
0.4
1.5
0.4
0.15
0.3
0.3
1.0
0.10
0.2
0.1
0.05
0.0
0.00
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62
Age
0.2
0.5
0.1
0.0
0
23
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62
Age
Extensions (future work)
 Spousal benefits
• Separate spousal account, with vesting after 10
years of marriage
 Survivors benefits (children/spouses)
• Can be handled as well
24
Turning PAAWs into Marketable Securities
 Require individuals to sell small percentage of their
PAAWs (e.g. 10%) to the market
 All individuals in same cohort receive same price
 SSA (or private firms) package together pools of
PAAWs and sell them
 Similar to pools of mortgages
 Over time, pools of PAAWs turn into pools of PANTS,
which are identical to longevity or survivor bonds
25
Pricing PAAWs
 Allows individuals to observe
• value of account
• value of contribution – value of additional PAAWs
 Useful later for
•
•
•
•
valuing aggregate S. Sec. assets and liabilities
making system self-balancing
allowing for the possibility of trade within accounts
providing market signal about aggregate survival
probabilities
26
PAAWs (especially PANTS) market useful for
private sector
 Would help private insurance companies
price annuities.
 Same for reverse mortgages.
 Could be held by these companies as hedge
or collateral for their promises.
27
Approaches to pricing PAAWs
 Assume risk neutrality
 Allow for risk aversion
28
Pricing PAAWs under risk neutrality
Required Input
Our assumption
Expected growth of average real
wages
Future path of real interest rate
1.1 %
Mortality probabilities
3%
SSA cohort life tables
Based on assumptions in 2005 SSA Trustees Report
29
Projected market price of one PAAW
(under risk neutrality, measured in average wage units)
14
12
10
8
6
4
2
0
20
30
40
50
60
Age
Price rises with age because:
• r > growth of average wages
• probability of survival to retirement rises with age
30
Projected Market Value of Accrued PAAWs
(measured in average wage units)
Worker 1: Economy Average
Worker 2: Cohort Average
1.2
6
1.0
5
Relative Wage
1.8
8
1.6
7
1.4
0.8
6
4
1.2
0.6
3
5
1.0
4
0.8
0.4
2
3
0.6
Market Value of Accrued PAAWs
0.2
1
0.0
0
2
0.4
1
0.2
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64
0.0
0
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62
Age
Age
Worker 3: 0.5 Cohort Average
Worker 4: 1.5 Cohort Average
0.9
4.50
0.8
4.00
3.0
9
8
2.5
0.7
3.50
0.6
3.00
0.5
2.50
0.4
2.00
0.3
1.50
0.2
1.00
7
2.0
6
5
1.5
0.1
0.50
0.0
0.00
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62
Age
4
1.0
3
2
0.5
1
0.0
0
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62
Age
31
Defining the match
 Match (tax/subsidy) = value of extra
PAAWs - value of contribution
 Average match rate
• [P PAAW * (Δ PBAL) / Annual contribution] -1
 Marginal match rate
• [P PAAW * (increment to PBAL per additional
dollar of contribution)] -1
32
Properties of the Match
 Match rate can be + or –
 Match rate cannot be < -100%
• balances cannot be taken away
• all redistribution occurs on the way in, none
on the way out
 Unlike simple DC plans, match rate not
constant across people or time
• Depends on PBAL, price of PAAWs, and fraction of
contribution that “counts”
33
Marginal Match Rate
Worker 1: Economy Average
Worker 2: Cohort Average
1.2
0.3
1.8
0.2
1.6
0.1
1.4
0.0
1.2
-0.1
1.0
-0.2
0.8
-0.3
0.6
-0.4
0.4
-0.5
0.2
-0.6
0.0
0.4
1.0
0.2
Relative Wage
0.8
0.0
0.6
-0.2
0.4
-0.4
Marginal Match Rate
0.2
-0.6
0.0
20 22
24 26
28 30
32 34
36 38
40 42 44
46 48
50 52
54 56
58 60
62 64
-0.8
20
22
24
26
28
30 32
34
36
38
40
42
44
46
48
50
52 54
56
58
60
62
Age
Age
Worker 4: 1.5 Cohort Average
Worker 3: 0.5 Cohort Average
0.9
0.60
3.0
0.4
0.40
2.5
0.2
0.20
2.0
0.0
0.00
1.5
-0.2
1.0
-0.4
0.5
-0.6
0.8
0.7
0.6
0.5
0.4
0.3
-0.20
0.2
-0.40
0.1
0.0
-0.60
20
22
24
26
28
30
32
34
36
38
40
42
44
46
48
50
52
54
56
58
60
62
0.0
-0.8
20
Age
22
24
26
28
30
32
34
36
38
40
42
Age
44
46
48
50
52
54
56
58
60
34
62
On net, match rate is positive for young and
negative for old
 Match lower for old because
• Progressivity means that a given relative wage contribution
generates more PAAWs when young (when PBAL is low )
• 35-year averaging formula means that earnings in 36th
year and beyond only increase PBAL by the amount they
exceed the 35th highest relative wage to date
 Although this is partially offset by
• Price of PAAW rises with age [and holding PBAL constant,
increment to PBAL due to additional contribution (measured
in average wage units) is constant with age]
 Match rate concept differs from incentive to work (i.e.
implicit marginal tax rate computed by
Feldstein/Samwick and others), because working
today also affects future match rates
35
Pricing PAAWs under Risk Aversion
(work in progress)
 Recall that PAAW is a composite security,
based on
• Average Wage Security
• PANT
 First, price each separately, then price
composite (QUANTOS analogy)
 Difficulty: these securities are not currently
traded, nor are they spanned by currently
traded securities
36
Pricing Average Wage Securities
 Payout
• Average economy-wide earnings in specified year (e.g. 2030)
 Models (at least two possibilities)
• Find portfolio of traded securities that best matches payout, and
assume that residual risk has price = 0 OR
• Assume model such as consumption CAPM
 Complications
• Return on average wage security ≠ growth of wages
• Correlation of wage growth and stock returns low over short
horizons (qtrly/annual), but likely to be higher over longer horizons
(cointegration)
 Implications
• Social Security liabilities may be less than typical estimates
37
Pricing PANTs
 Similar methodology can be used to price
pools of PANTS
 Equivalent to survivor or longevity bonds
38
The current system is not balanced
 Accrued Liabilities.
 Social Security taxes have no connection to benefits,
either as a flow or in present value. Issuing PAAWS
according to old rules does not automatically balance,
even if steps taken to make it balance now.
 Benefits cannot be market-valued
 Pricing PAAWS gives us a way to address balance.
39
Transition from the current system
 Geanakoplos, Mitchell, Zeldes (1999) describe
• how to compute accrued benefits
• how to implement “cold-turkey” conversion to individual account
system, by issuing “transition bonds” or “legacy bonds” = PV of
accrued benefits
 Possible choices for bonds
• Treasury Bonds (nominal or TIPS)
• Claims on % of future payroll tax (Valdes-Prieto, 2005)
• PAAWs
 Issuing PAAWs as transition bonds leaves accrued
future benefits unchanged (in all states of the world)
40
Balancing Social Security
 Give PAAWs in lieu of accrued benefits
 Legacy Tax to pay for accrued benefits
 Buy PAAWS at market value, but with
redistribution.
 Government hedges.
41
Creating Initial Balance
 Impose a “legacy tax”
• On all payroll (including above the cap), or on all income
• GMZ estimate: 3% of taxable payroll
• Lower if tax above cap. Would be 1-2%.
 Legacy debt created by giving retirees in 1940s – 1970s
more benefits greater in PV than contributions
 So why impose this just on lower earner workers?
 Might also want to reduce legacy PAAWs awarded in
transition (i.e. cut benefits before locking in property
rights)
42
Buying at Market Value
 After legacy tax takes care of accrued
benefits, social security tax could be used to
buy PAAWS at market value. The system is
then by definition balanced on the way in.
(So for example, system balance is protected
against predictable increases in longevity.)
 However, this abandons many of the
insurance virtues of the current system.
43
Self-Balancing = Allocating Aggregate Risk
 Need theory of who can best bear the risks.
44
Adding back some insurance within cohort
 In each year, scale all new PAAW accruals of
each cohort (according to current SS rules)
by an aggregate factor λ
 λ = aggregate contributions collected / market
value of new PAAWs without adjustment
 Implies that annual increment is fully funded
45
Adding insurance across all people
contributing at the same time
 Same as before, but now involves all people
contributing in a year, not just the cohort
contributing that year.
46
Hedging is Difficult
 If live expectancy increases faster than
expected, new PAAW prices reflect that, and
government is protected.
 But old PAAWS now become more valuable,
exposing government.
 If earnings temporarily higher than expected,
then PAAWS pay more, exposing
government. (Under old system, that would
be partly offset by higher price for new
PAAWS. That could be built in.)
47
If can’t hedge, mutual fund paygo
 Change units for PAAWs payout to claims on
taxable payroll in a given year
• Claims for a given year will be issued to many
different generations in varying amounts
• In a given year, each claim pays 1/N of total
revenue (N=total claims issued)
 Alternative: create different tranches
• Total payout in each year = revenue
• Very old get less risky tranche
• Younger old get more risky tranche
48
Conclusions
 Translate DB into the language of DC, to facilitate
debate over individual accounts
 Preserves redistribution and risk sharing of the
current system
 Clarifies the link between contributions and benefits
 Enhances property rights of the system
 Might lead to a political compromise between
Democrats and Republicans
49
Conclusions
 It should be possible to create and trade
pools of PAAWs
• providing an estimate of the market value of each
individual’s account
• providing an estimate of market value of system
liabilities
• opening up the possibility of allowing (limited)
trade in these accounts
50
Conclusions
 We conjecture that we could use these and
other new securities to create a selfbalancing DC system
 Still very preliminary – much more to be
done!
51
END
52
Talking Points (1)
 Economy average worker
• Starts at .9 tier, then to .32 tier
 .5*Average cohort worker
• Same, but takes longer to get to .32 tier
 Average cohort worker and 1.5 average
• Drops to .15 tier (1.5 worker faster)
 No drop after 35 years b/c earnings late in life
always ≥ 35th highest
53
Talking Points (2)
 Similar to previous slides, but take into
account varying contributions due to age
profile of relative earnings
 After year 35, a large fraction of each
contribution does not count toward accrual
54
Talking Points (3)
 Product of PAAW balances and price of
PAAW
 Value at retirement:
• .5 worker: 4.3
• avg worker: 6.7
• 1.5 avg worker: 8.0
 Illustrates redistribution
55
Changes/Things to do empirical
 Numbers to check
• How is it that maximum AIE ratio = 1.99, yet cap is currently ~
3*average wage index? Was ratio of cap to average index lower in
the past?
• In PAAW balances slide, 1.5 worker gets up to about .7 PAAWs by
retirement, yet in early slide we say that someone always at the cap
only earns .64 PAAW. Since 1.5 worker is sometimes below the
cap, how can this be?
 Get new data for age earnings profile (SSA profiles) relative to
average earnings, and use instead?
 How variable would the price of a PAAW be? Once price it,
could run it through with shocks to generate a sample path.
Could transparency of market prices scare people (even though
benefits are not changing)?
 Add more description of how average wage index computed
(Allison). Based on all wages or just covered wages?
Compensation vs wages?
56
Changes/Things to do theory
 How distinct should the PAAW pools be?
• More distinct:
•
•
better possible signal about true value (e.g. women,
wealth, other) but
If let people sell, do you want to give women more for a
PAAW than man? Or rich more for a PAAW than a
woman? Of course, once let sell, we’re outside of the
experiment of replicating current system
 Add much more description of Notional DC,
and why we’re better. See / cite Disney
paper, + VP 1999 and Palmer.
57
Possible Models re Self Balancing
(Discussion w Alvarez 4/12/06)
 Labor income uncertainty only
•
•
•
•
4 pd OG; 2 work, 2 retire
Shocks to labor income
Opportunity for trades (not present in 2 pd OG model)
What would arrow-debreu economy with all assets traded
(only among live agents) look like?
• What would a-d economy allowing all generations to get
together at time 0 and trade.
 Length of life uncertainty only
• 4 pd OG, 2 work, 1-2 retire (aggregate uncertainty about
whether die in pd 3 or 4)
• What would optimal risk sharing look like
• Long lived generations would receive payments from all
those alive except those in pd 1 of life?
 Other risks, separately
 Ex-ante vs interim efficiency (vs others)
58
Financial innovation slides
67
Reforming Social Security:
“Progressive Personal Accounts”
 Individuals given property rights over benefits as they
accrue via a new financial security: PAAWS
 PAAWS (personal annuitized average wage security)
pays
• economy-wide average wage index in retirement year
• constant inflation-adjusted benefit from retirement until
death
 Redistribution (based on lifetime income) achieved by
using a variable government match (match declines with
PAAW balance)
 Fixed small percentage of claims would be pooled (like
mortgages) and sold and traded in the marketplace
68
PAAW balance for average worker
Worker 2: Cohort Average
1.8
0.6
1.6
Cohort earnings
1.4
(in average wage units)
0.5
1.2
0.4
1.0
PAAW balance
0.8
(in average wage units)
0.6
0.3
0.2
0.4
0.1
0.2
0.0
0
20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62
Age
69
Additional PAAWs Per Additional Contribution
(measured in average wage units)
High when PAAW balance is low
0.30
Using this schedule for every
contribution mimics the lifetime
redistribution of the current system
0.25
0.20
And low when PAAW
balance is high
0.15
0.10
0.05
0.00
0.01
0.06
0.11
0.16
0.21
0.26
0.31
0.36
0.41
0.46
0.51
0.56
0.61
0.66
0.71
PAAW Balance
70
Benefits of our approach
 Clarifies the link between contributions and benefits,
thus increasing transparency
 Enhances property rights of the system
 Yields financial market price of pools of PAAWS
• providing an estimate of the market value of each
individual’s account
• providing an estimate of market value of system liabilities
• opening up the possibility of allowing (limited) trade in these
accounts
 Preserves risk-sharing and redistribution
71
Progressive Personal Accounts:
Work in progress
 Working on market mechanisms to make the system
self-balancing
 Would entail creation and trading of additional
financial securities tied to other demographic /
economic variables (e.g. fertility, mortality)
72
Making the system self-balancing
 Current system is not self-balancing: it requires
political intervention in response to economic or
demographic shocks
 Even if current imbalance were fixed, taxes and
benefits not state-contingent in a way that makes
system self-balancing moving forward
 Nothing built into the program rules to ensure that
future revenue will be enough to support future
accrued benefits, either on a cash-flow basis or on a
present value basis
74
Time-NPV-balancing: Complications
 The government has to hedge this position
 Reduces some of intergenerational risk
sharing
• If generation puts more in, gets more out
• Demographic / economic shocks cause match to
vary across generations, yielding different benefits
per unit of contributions
75
Alternative self-balancing
 Legacy tax + buying paaws at market prices
 Leaves off
• B
76
Work in progress: Self-balancing market-based
system
 Consider possible balancing rules
•
•
•
•
year-by-year balancing
cohort-NPV- balancing
time-NPV-balancing
infinite-future-NPV balancing
 Create marketable securities that could
implement a self-balancing system
• E.g. promised benefits/payouts that vary with
aggregate life expectancy, fertility, earnings, etc.
77
The current system is not “self-balancing”
 No aggregate adjustment mechanism to tie promised
benefits to revenues
• Total revenues / total expenses:
1.3 currently (i.e. surplus)
.75 projected for 2042 (i.e. deficit)
• Actuarial balance (75 years)
= PV future revenues - PV future benefits
= - $ 3.7 trillion
 To rewrite the current system as an individual account
system, need to take a stand on how future balancing
would occur
• We start by assuming all balancing occurs via changes in
future taxes or future benefit accrual rules
78
Translating DB into DC
Current “Defined
Benefit” System
Benefits depend on individual
earnings
Translated “Defined
Contribution” System
Balances accumulate yearly
based on individual contributions
and variable government match
Progressive redistribution based Variable government match rate
on lifetime earnings
based on accrued balances
Benefits depend on growth rate
of average wages
Accounts hold assets with
payoffs that depend on average
wage index …
Benefits received as an annuity
and individual longevity
Annual statement lists earnings
history and projected future
benefits
Annual statement lists
contribution history and
accumulated account balances79
Change in PAAW Balances
Worker 2: Cohort Average
Worker 1: Economy Average
1.2
0.030
1.8
1
0.8
0.025
Relative Wage
0.6
1.6
0.030
1.4
0.020
0.015
0.4
0.035
0.010
0.025
1.2
1
0.020
0.8
0.015
0.6
0.010
0.4
0.2
PAAW Balance
0
0.005
0.000
0.005
0.2
0
0.000
21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
Age
Age
Worker 3: 0.5 Cohort Average
Worker 4: 1.5 Cohort Average
0.9
0.018
0.8
0.016
0.7
0.014
0.6
0.012
0.5
0.010
0.4
0.008
0.3
0.006
0.2
0.004
0.1
0.002
0
0.000
3
0.040
0.035
2.5
0.030
2
0.025
1.5
0.020
0.015
1
0.010
0.5
0.005
0
0.000
21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
Age
Age
80
Average Match Rate
Worker 2: Cohort Average
Worker 1: Economy Average
1.2
1.0
Relative Wage
1.8
0.2
1.6
0.0
1.4
-0.2
1.2
0.4
0.2
0.0
0.8
0.6
0.4
0.4
-0.4
Average Match Rate
-0.6
1
-0.2
0.8
-0.4
0.6
-0.6
-0.8
0.4
0.2
-1.0
-0.8
0.2
0.0
-1.2
21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
0
Age
Age
Worker 4: 1.5 Cohort Average
Worker 3: 0.5 Cohort Average
0.9
0.6
0.8
0.4
0.7
-1.0
21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
3.0
0.4
2.5
0.2
0.2
0.6
0.0
2.0
-0.2
1.5
0.0
-0.2
0.5
0.4
-0.4
-0.4
0.3
1.0
-0.6
-0.6
0.2
-0.8
0.1
0
-1.0
0.5
-0.8
0.0
-1.0
21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63
Age
Age
81
The current system is not balanced
 Current PV imbalance
• 75 year: $4 trillion
• Infinite horizon: $11 trillion
82