Reforming Social Security With Progressive Personal AccountsJohn GeanakoplosYale University

Stephen P. Zeldes Graduate School of Business,Columbia Universityand NBER

NBER Retirement Research ConferenceOctober 20, 2006Woodstock, VT

President Bush has strongly advocated replacing part of Social Security with personal accountsMassive effort in 2005, including 60-day, 60-city 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 Presidents 2007 budget request

Democrats versus RepublicansDemocrats committed to keeping DB structure

Republicans committed to shifting to DC

Why? Which features of these structures are important to each side?

Core GoalsDemocratsRedistribution based on lifetime earningsRisk-sharing across generationsSecurity via inflation indexed life-annuity

Republicans Property rights via private ownershipTransparency regarding accrual of benefitsMarket prices (facilitating financial planning)Equity-like returns Portfolio choice

Are these reconcilable?If so, does that help balance the system?

Yes! Maybe?Progressive Personal AccountsProgressive via variable matching of contributionsAccounts hold new financial securities (PAAWs) that provide DB-like benefits but are priced.Pricing PAAWs allows us to value incremental benefits and charge accordingly.

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

Related LiteratureImplicit marginal tax rate / matching in current system Feldstein and Samwick (1992)Cushing (2005)Feldstein and Liebman (2002)

Accrual of Social Security BenefitsGeanakoplos, Mitchell, and Zeldes (1999)Jackson (2004)

Self-balancing / Notional DC systemsValdes-Prieto (2000)Borsch-Supan (2005)Auerbach and Lee (2006)

New financial securitiesShiller (1993) (GDP bonds)Bohn (2002) and Goetzmann (2005) (wage bonds)Blake and Burrows (longevity bonds)Valdes-Prieto (2005) pay as you go securities

Mechanics of Current OASDI System Contributions / TaxesContributions = tax rate x covered earnings

Covered earnings = min (earnings, cap)(2006 cap $94,200)

Mechanics of Current OASDI System Calculation of BenefitsCalculate relative earnings (ratio of individual covered earnings to average economy-wide earnings)

Average workers relative earnings across highest 35 years

Compute PIA (in average wage units) as concave function of average relative earnings

Benefit in first year = PIA (in average wage units) x average wage indexBenefit in future years (each remaining year of life) indexed to CPI

Mechanics of Current OASDI System Calculation of Primary Insurance Amount (PIA)Concavity generates redistribution and individual risk sharing Tying benefits to average wages generates aggregate risk sharing

Data

Social Security benefit scheduleLatest update: SPZ 8/8/05

PIA vs AIME

based on 2005 data

ADJUST THIS COLUMN

MONTHLY

Monthly

AIMEPIA

bend pointsslope

00

627564.306270.90

37791572.9462737790.32

5,8271880.1437795,8270.15max single benefit at age 65 in 20041874

max AIME in 20045,827

ANNUAL

Annual

AIEpia (annual)pia (check)

000

75246771.66771.6075240.90

4534818875.2818875.287524453480.32

6992422561.6822561.684534869,9240.15max single benefit at age 65 in 200422488

max AIE in 200469,924

ANNUAL, IN WAGE UNITS

Annual

AIEpia (annual)pia (check)

00000

0.21401082570.19260974310.192609743100.21401082570.9

1.28986748050.53688387270.53688387270.21401082571.28986748050.32

1.98890124610.64173893750.64173893751.28986748051.98890124610.15max single benefit at age 65 in 20040.6396432015

max AIE in 20041.9889012461

Source: PIA bendpoints, US Social Security Trustees Report (2005) or http://www.ssa.gov/OACT/COLA/bendpoints.html

Source: Maximum AIME/PIA, http://www.ssa.gov/OACT/ProgData/retirebenefit2.html

http://www.ssa.gov/OACT/COLA/examplemax.html

Note: max single benefit at age 65 assumes now includes adjustment for early retirement (b/c NRA > 65), but we don't use this in the graph

PIA graph (monthly)

0

564.3

1572.94

1880.14

slope =.32

slope=.15

slope=.9

PIA: Primary Insurance AmountAIME: Average Indexed Monthly EarningsBased on 2004 data

Maximum:AIME: 5457PIA: 1825

AIME

PIA

Social Security Benefit Schedule

historical

yearbp1bp2average wage indexbend point 1 (in wage units)bend point 2 (in wage units)

19801941,17112,513.460.0155033060.0935792339

19812111,27413,773.100.01531971740.0924991469Source: PIA bendpoints, US Social Security Trustees Report (2005) or http://www.ssa.gov/OACT/COLA/bendpoints.html

19822301,38814,531.340.0158278590.095517688tables V.C.1 and V.C.2

19832541,52815,239.240.01666749790.1002674674

19842671,61216,135.070.01654780550.099906601

19852801,69116,822.510.01664436520.100520077

19862971,79017,321.820.01714600430.103337871

19873101,86618,426.510.01682358730.1012671417

19883191,92219,334.040.01649939690.0994101595

19893392,04420,099.550.01686604920.101693819

19903562,14521,027.980.0169298240.102006945

19913702,23021,811.600.01696345060.1022391755

19923872,33322,935.420.01687346470.1017203958

19934012,42023,132.670.0173347910.1046139507

19944222,54523,753.530.01776578050.1071419701

19954262,56724,705.660.01724301230.1039033161

19964372,63525,913.900.01686353660.1016828806

19974552,74127,426.000.0165900970.0999416612

19984772,87528,861.440.01652724190.0996138793

19995053,04330,469.840.01657376610.0998692478

20005313,20232,154.820.01651385390.099580716

20015613,38132,921.920.01704031840.102697534

20025923,56733,252.090.01780339220.1072714527

20036063,65334,064.950.01778954610.1072363236

20046123,68935,157.100.01740757910.1049290186

20056273,77936,599.680.01713129730.1032522689

indexPIA

0

0.1926097431

0.5368838727

0.6417389375

slope =.32

slope=.15

slope=.9

Maximum:AIE: 1.99PIA: 0.64

Average relative earnings (AIE/ Average Wage Index)

Initial relative benefits (PIA/Average Wage Index)

PIA graph (annual)

0

6771.6

18875.28

22561.68

slope =.32

slope=.15

slope=.9

Maximum:AIE: 69,924PIA: 22,562

AIME (Annualized)

PIA (annual)

Current System Provides Insurance Againstlow 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)

Creating Individual Accounts that Mimic the Current SystemDefine new securities (PAAWs)

Compute accrual of balances

Trade PAAWs in financial markets

Personal accounts hold PAAWs: Personal Annuitized Average Wage SecurityEach 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

PAAW is a composite of two securitiesAverage Wage SecurityPays 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)

PAAWs enhance property rights on accrued benefitsCurrent lawNo legal property rights to benefits No clear distinction betweenbenefits already accruedbenefits to be accrued in the futureSo benefit cuts often applied across the board

PAAWsGive owners legal right to collect accrued benefitsClearly distinguish between accrued and other benefitsB/c PAAWs provide market value, if accrued benefits are cut, people would know how much is being stolen

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)

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)

Additional PAAWs Per Additional Contribution (measured in average wage units)High when PBAL is lowAnd low when PBAL is highUsing this schedule for every contribution mimics the lifetime redistribution of the current system

Chart3

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Additional PAAWs per Additional Contribution

PAAW Balance

Sheet1

0.01PAAWs BalanceAdditional PAAWs per Additional Contribution

0.020.010.2426078

0.030.020.2426078

0.040.030.2426078

0.040.2426078

0.190.24260780.24259370.050.2426078

0.1960.0862580.060.2426078

0.0862580.070.2426078

0.0862580.080.2426078

0.0862580.090.2426078

0.0862580.10.2426078

0.0862580.110.2426078

0.0862580.120.2426078

0.0862580.130.2426078

0.0862580.140.2426078

0.0862580.150.2426078

0.5370.0862580.160.2426078

0.5410.04042990.170.2426078

0.180.2426078

0.190.2426078

0.20.086258

0.210.086258

0.220.086258

0.230.086258

0.240.086258

0.250.086258

0.260.086258

0.270.086258

0.280.086258

0.290.086258

0.30.086258

0.310.086258

0.320.086258

0.330.086258

0.340.086258

0.350.086258

0.360.086258

0.370.086258

0.380.086258

0.390.086258

0.40.086258

0.410.086258

0.420.086258

0.430.086258

0.440.086258

0.450.086258

0.460.086258

0.470.086258

0.480.086258

0.490.086258

0.50.086258

0.510.086258

0.520.086258

0.530.086258

0.540.0404299

0.550.0404299

0.560.0404299

0.570.0404299

0.580.0404299

0.590.0404299

0.60.0404299

0.610.0404299

0.620.0404299

0.630.0404299

0.640.0404299

0.650.0404299

0.660.0404299

0.670.0404299

0.680.0404299

0.690.0404299

0.70.0404299

0.710.0404299

0.720.0404299

0.730.0404299

0.740.0404299

0.750.0404299

Sheet1

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Additional PAAWs per Additional Contribution

PAAW Balance

Sheet2

Sheet3

Variable Match ProposalA 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

Notes about Variable Government MatchingFormula 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)

Simple Numerical ExamplesWorker 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 = earnings of Worker 2

Worker 4: Earnings = 1.5 earnings of Worker 2

Future work: examine realizations of stochastic earnings process

Additional PAAWs Per Additional Contribution (measured in average wage units)

Chart15

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Relative Wage

Additional PAAWs per Additional Contribution

Relative Wage

Additional PAAWs per Additional Contribution

Age

Worker 1: Economy Average

Cohort Average

AgeRelative WagePAAW BalancesChange in PAAWsAdditional PAAWs per Additional ContributionMarket Value of Accrued PAAWsPresent Value of Change in PAAWsAverage Match RateRelative PV of Additional PAAWs due to 1%Relative PV of Additional Contribution due to 1%Marginal Match RateReal Contributions

200.53024120.0140.24258760.06280380.00118440.001060.1173951905.9

210.64085270.030.016480.24258840.14150432654.60.13991390.00120830.001060.13991782328.8

220.71946940.0490.01850.24258670.23306653074.10.16300810.00123280.001060.16300352643.2

230.7761650.0690.019960.24258670.33537763420.40.18644990.00125760.001060.18644552882.9

240.82420650.090.021190.24258670.44792933746.50.2104920.00128310.001060.21048743095

250.88658610.1130.02280.24257260.5730134156.50.23489620.00130890.001060.23481973365.9

260.91907910.1360.023630.24259370.70729824444.10.25979330.00133540.001060.25982583527.6

270.95154890.1610.024470.24260780.851102547450.28506310.00136230.001060.28517063692.4

281.1556470.190.029720.24260781.0288585943.60.31097830.00138980.001060.31108684533.7

291.1368690.2020.012090.0862581.116122492.8-0.44716650.0005040.00106-0.52449744509.1

301.2263630.2140.011210.0862581.2016872385.4-0.51493290.00051420.00106-0.51490694917.6

311.2083970.2250.011050.0862581.2894472424.4-0.50509740.00052460.00106-0.50507064898.8

321.1671060.2350.010670.0862581.3782072415.6-0.49500820.00053530.00106-0.4949814783.5

331.1246590.2460.010280.0862581.4678892401.6-0.4846590.00054630.00106-0.48463084660.2

341.1655780.2560.010660.0862581.5629532567.9-0.47409530.00055750.00106-0.47406694882.9

351.2846690.2680.011750.0862581.6682532920.4-0.46325820.0005690.00106-0.46322885441

361.4011130.2810.012810.0862581.7839953286.5-0.45219540.00058070.00106-0.45216565999.5

371.3718120.2930.012540.08628621.902273320.6-0.44084430.00059290.00106-0.44063155938.6

381.3929470.3060.012740.08622992.0263933480.2-0.42913420.0006050.00106-0.42929066096.4

391.4180770.3190.012970.0862582.1564423657-0.41717980.00061780.00106-0.41714746274.7

401.4358620.3320.013130.0862582.2924243822.4-0.40490730.00063080.00106-0.40487446423.3

411.5780360.3470.014430.0862582.4428654337.5-0.39224270.00064430.00106-0.39221077136.9

421.5793390.3610.014440.08628622.5990464482.7-0.37924320.00065830.00106-0.37900587221.4

431.5892570.3760.014530.08622992.7620674659.1-0.36582070.0006720.00106-0.36599477346.7

441.5867770.390.014510.08622992.9310864805.2-0.35203840.00068670.00106-0.35221477415.9

451.6136630.4050.014750.08622993.1083945048.4-0.33787860.00070170.00106-0.33805857624.5

461.6198880.420.014810.08622993.2928825236.2-0.32332980.00071710.00106-0.32351437738.1

471.6287110.4350.014890.08628623.4854095440.7-0.30830820.00073350.00106-0.30804357865.9

481.6597560.450.015170.0862583.687635730.6-0.29286380.00074960.00106-0.2928268104

491.6145220.4650.014760.0862583.8941475762.3-0.27698950.00076640.00106-0.27695127969.8

501.6015790.4790.014640.0862584.1084615910.7-0.26050820.00078390.00106-0.26046827992.9

511.6053590.4940.014680.08628624.3308926126.4-0.24364120.0008020.00106-0.24335148099.9

521.5868380.5080.014510.08620184.5613926264.2-0.22611330.00081980.00106-0.22657978094.5

531.5555480.5230.014220.08631434.7987696353.5-0.20800380.00084010.00106-0.20744068022.2

541.5195270.5370.013890.08631435.0434516423.9-0.18917130.00086010.00106-0.18859917922.6

551.5405480.5420.005150.04042995.2148172467.3-0.69616590.00041260.00106-0.61076188120.6

561.5581260.5460.003930.04042995.382031949.7-0.76520350.00042280.00106-0.60117538303.6

571.5294880.5490.003470.04042995.5523611784.3-0.78346880.00043340.00106-0.59115488240.6

581.5007780.5520.003110.04042995.7275391655.4-0.79750750.00044450.00106-0.58062778174.9

591.4693720.5550.002760.04042995.9074141529.2-0.81102070.00045620.00106-0.56961238091.8

601.4558870.5570.002440.04042996.0930811400.9-0.82716890.00046850.00106-0.55802868105.8

611.4316450.560.00220.04042996.2857921310.3-0.83739670.00048140.00106-0.54583998058.5

621.398950.5610.001920.04037376.4863311189.2-0.85062350.00049440.00106-0.53360067961.1

631.3794460.5630.001090.04042996.690329704.8-0.91119540.00050970.00106-0.51919717936.4

Cohort Average

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Relative Wage

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Relative PV of Additional PAAWs due to 1%

Relative PV of Additional Contribution due to 1%

Age

Relative PV of additional PAAWs and Relative PV of contributions due to earning 1% of the Economy's Average Wage

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Present Value of Change in PAAWs

Real Contributions

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Relative Wage

Marginal Match Rate

Age

Worker 2: Cohort Average

AgeRelative WagePAAW BalancesChange in PAAWsAdditional PAAWs per Additional ContributionMarket Value of Accrued PAAWsPresent Value of Change in PAAWsAverage Match RateRelative PV of Additional PAAWs due to 1%Relative PV of Additional Contribution due to 1%Marginal Match RateReal Contributions

2010.0260.24259020.11844390.00118450.001060.11740733594.4

2110.0510.025710.24258670.24166174142.30.13991390.00120830.001060.13990963633.9

2210.0770.025710.24258670.36983654272.70.1630080.00123280.001060.16300353673.9

2310.1030.025710.24259370.50305494406.80.18645010.00125770.001060.186483714.3

2410.1290.025710.24259370.64156074545.60.21049230.00128320.001060.21052243755.1

2510.1540.025710.24259370.78539384688.20.23489560.0013090.001060.2349273796.4

2610.180.025710.24257970.93476714835.30.25979440.00133530.001060.25975283838.2

2710.1980.017530.0862441.0463553398.6-0.12417320.00048430.00106-0.54313823880.4

2810.2070.009140.0862441.1168651828.7-0.53387440.0004940.00106-0.53392533923.1

2910.2160.009140.0862581.1896711885.9-0.52452390.0005040.00106-0.52449743966.3

3010.2250.009140.0862581.2650831945.1-0.5149330.00051420.00106-0.51490694009.9

3110.2340.009140.0862441.3431952006.3-0.50509720.00052450.00106-0.50515134054

3210.2430.009140.0862441.4241072069.8-0.49500820.00053520.00106-0.49506334098.6

3310.2520.009140.0862581.507922135.4-0.48465940.00054630.00106-0.48463084143.7

3410.2620.009140.0862581.5945742203.1-0.47409610.00055750.00106-0.47406694189.3

3510.2710.009140.0862581.6843292273.3-0.46325680.0005690.00106-0.46322884235.3

3610.280.009140.0862581.7771112345.7-0.4521960.00058070.00106-0.45216564281.9

3710.2890.009140.08622991.8732062420.6-0.4408430.00059250.00106-0.44099614329

3810.2980.009140.0862581.9729422498.5-0.42913620.00060510.00106-0.42910454376.6

3910.3070.009140.08622992.0760432578.9-0.41717790.00061760.00106-0.41733744424.8

4010.3160.009140.08622992.1828382662.1-0.40490730.00063060.00106-0.40506844473.5

4110.3260.009140.0862582.2937092748.7-0.39224450.00064430.00106-0.39221074522.7

4210.3350.009140.08622992.4085792838.4-0.37924060.00065780.00106-0.37941054572.4

4310.3440.009140.0862582.527872931.6-0.36582310.00067230.00106-0.3657884622.7

4410.3530.009140.0862582.6514973028.3-0.35203930.00068690.00106-0.35200354673.6

4510.3620.009140.08622992.7796253128.5-0.33787720.00070170.00106-0.33805854725

4610.3710.009140.0862582.9124273232.4-0.32333120.00071730.00106-0.32329374777

4710.380.009140.0862583.050413340.5-0.30830720.00073320.00106-0.3082694829.5

4810.390.009140.08622993.1934673452.7-0.29286290.00074940.00106-0.29305654882.6

4910.3990.009140.0862583.3417943569-0.27699120.00076640.00106-0.27695124936.3

5010.4080.009140.08622993.4963613690.5-0.26050670.00078360.00106-0.26070934990.6

5110.4170.009140.08622993.6562953816.2-0.24363980.00080150.00106-0.24384445045.5

5210.4260.009140.0862583.8230283947.6-0.22611810.00082040.00106-0.22607525101

5310.4350.009140.08622993.996484084.5-0.20799830.00083930.00106-0.20821525157.1

5410.4440.009140.08622994.1774364227.5-0.18917260.00085920.00106-0.1893925213.9

5510.44400.08622994.2782810-10.000880.00106-0.16982375271.2

5610.44400.08622994.383650-10.00090170.00106-0.14937755329.2

5710.44400.08622994.4937910-10.00092430.00106-0.12800535387.8

5810.44400.08622994.6094990-10.00094810.00106-0.10555295447.1

5910.44400.08622994.7305730-10.0009730.00106-0.0820595507

6010.44400.08622994.8578930-10.00099920.00106-0.05735315567.6

6110.44400.08622994.9918650-10.00102680.00106-0.03135675628.8

6210.44400.08622995.1335320-10.00105590.00106-0.0038675690.7

6310.44400.08622995.2847080-10.0010870.001060.02546765753.3

6410.44400.08622995.4468180-10.00112030.001060.05692425816.6

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Relative Wage

PAAW Balances

Age

Worker 1: Economy Average

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Relative Wage

Change in PAAWs

Age

Worker 1: Economy Average

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Relative Wage

Additional PAAWs per Additional Contribution

Age

Worker 1: Economy Average

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Relative Wage

Market Value of Accrued PAAWs

Age

Worker 1: Economy Average

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Relative Wage

Average Match Rate

Age

Worker 1: Economy Average

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Relative PV of Additional PAAWs due to 1%

Relative PV of Additional Contribution due to 1%

Age

Relative PV of additional PAAWs and Relative PV of contributions due to earning 1% of the Economy's Average Wage

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Present Value of Change in PAAWs

Real Contributions

Age

PV of Change in PAAWs+Real Contributions

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Relative Wage

Marginal Match Rate

Age

Worker 1: Economy Average

AgeRelative WagePAAW BalancesChange in PAAWsAdditional PAAWs per Additional ContributionMarket Value of Accrued PAAWsPresent Value of Change in PAAWsAverage Match RateRelative PV of Additional PAAWs due to 1%Relative PV of Additional Contribution due to 1%Marginal Match RateReal Contributions

200.79536180.020.24258840.09420570.00118440.001060.11739912858.9

210.96127910.0450.024720.24259020.21225643981.90.1399140.00120830.001060.1399263493.2

221.0792040.0730.027750.24258670.34959974611.20.1630080.00123280.001060.16300353964.8

231.1642480.1030.029940.24257970.50306655130.60.18645060.00125760.001060.18641124324.3

241.236310.1350.031790.24259370.67189395619.70.21049120.00128320.001060.21052244642.5

251.3298790.1690.03420.24259370.85951946234.80.23489610.0013090.001060.2349275048.8

261.3786190.1970.028170.0862581.0231635297.90.00123410.00047480.00106-0.5520495291.4

271.4273230.210.013050.0862581.1128152530.7-0.54308860.00048440.00106-0.54306375538.6

281.733470.2260.015850.0862581.2209063169.9-0.53387440.00049410.00106-0.53384936800.6

291.7053040.2420.015590.0862441.3313473216-0.52452330.0005040.00106-0.52457496763.7

301.8395440.2580.016820.0862581.4527833578-0.51493380.00051420.00106-0.51490697376.4

311.8125950.2750.016570.0862581.577333636.7-0.50509740.00052460.00106-0.50507067348.3

321.750660.2910.016010.0862581.7031973623.4-0.49500770.00053530.00106-0.4949817175.2

331.6869890.3060.015420.0862581.8302573602.4-0.48465880.00054630.00106-0.48463086990.3

341.7483670.3220.015990.0862581.9652373851.9-0.47409530.00055750.00106-0.47406697324.4

351.9270040.340.017620.08622992.1153724380.6-0.46325770.00056880.00106-0.46340388161.5

362.1016690.3590.019220.0862582.2810094929.8-0.45219540.00058070.00106-0.45216568999.2

372.0577180.3780.018810.08622992.4502374980.9-0.44084380.00059250.00106-0.44099618907.9

382.0894210.3970.01910.0862582.6279795220.4-0.42913590.00060510.00106-0.42910459144.7

392.1271160.4170.019450.08628622.8144315485.5-0.41717980.0006180.00106-0.41695759412

402.1537930.4360.019690.08622993.0095565733.7-0.40490550.00063060.00106-0.40506849634.9

412.3670540.4580.021640.08622993.2260866506.3-0.39224430.0006440.00106-0.392408810705.4

422.3690090.480.021660.0862583.4509846724.1-0.37924150.0006580.00106-0.379208110832.1

432.3838860.5010.02180.0862583.6858396988.7-0.3658230.00067230.00106-0.36578811020

442.3801660.5230.021760.08620183.9294297207.8-0.3520380.00068640.00106-0.352425911123.9

452.4204950.5410.018340.04042994.1560666274.7-0.4513550.0003290.00106-0.689640811436.8

462.4298320.5520.010410.04037374.329083681.7-0.68281040.00033570.00106-0.683262611607.2

472.4430660.5620.010470.04037374.5091633825.5-0.6757690.00034320.00106-0.676230211798.8

482.4896350.5730.010670.04042994.6973054029.3-0.66853120.00035130.00106-0.66854112155.9

492.4217820.5830.010380.04042994.8897534051.6-0.66108890.00035920.00106-0.661100311954.7

502.4023690.5940.01030.04042995.0894934155.9-0.65336320.00036740.00106-0.653374611989.3

512.4080390.6040.010320.04042995.2960944307.7-0.6454550.00037580.00106-0.645467312149.8

522.3802570.6140.01020.04042995.5103094404.5-0.63724260.00038450.00106-0.637254212141.8

532.3333230.6240.010.04042995.7311324467.3-0.62875080.00039350.00106-0.628762112033.3

542.2792910.6340.009770.04042995.9592064516.8-0.61992280.00040290.00106-0.619936611883.9

552.3108230.640.006490.04042996.1655923109.5-0.74472580.00041260.00106-0.610761812180.9

562.3371890.6460.00590.04042996.3756122924.5-0.76520350.00042280.00106-0.601175312455.4

572.2942310.6520.005210.04048626.5884592676.5-0.78346880.0004340.00106-0.590586112360.9

582.2511660.6560.004660.04037376.8064212483-0.79750750.00044390.00106-0.581210912262.3

592.2040580.660.004150.04048627.0293512293.7-0.81102480.00045680.00106-0.569013712137.8

602.1838310.6640.003660.04048627.258552101.4-0.82716890.00046910.00106-0.557413912158.7

612.1474680.6670.00330.04042997.4957421965.6-0.83739080.00048140.00106-0.545839912087.7

622.0984260.670.002880.04042997.7416941783.8-0.85062660.00049510.00106-0.53295111941.6

632.0691690.6720.001640.04048627.9891531057.2-0.91119380.00051040.00106-0.518528411904.6

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Relative Wage

PAAW Balances

Age

Worker 4: 1.5 Cohort Average

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Relative Wage

Change in PAAWs

Age

Worker 4: 1.5 Cohort Average

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Relative Wage

Additional PAAWs per Additional Contribution

Age

Worker 4: 1.5 Cohort Average

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Relative Wage

Market Value of Accrued PAAWs

Age

Worker 4: 1.5 Cohore Average

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Relative Wage

Average Match Rate

Age

Worker 4: 1.5 Cohort Average

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Relative PV of Additional PAAWs due to 1%

Relative PV of Additional Contribution due to 1%

Age

Relative PV of additional PAAWs and Relative PV of contributions due to earning 1% of the Economy's Average Wage

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Present Value of Change in PAAWs

Real Contributions

Age

PV of Change in PAAWs+Real Contributions

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Relative Wage

Marginal Match Rate

Age

Worker 4: 1.5 Cohort Average

AgeRelative WagePAAW BalancesChange in PAAWsAdditional PAAWs per Additional ContributionMarket Value of Accrued PAAWsPresent Value of Change in PAAWsAverage Match RateRelative PV of Additional PAAWs due to 1%Relative PV of Additional Contribution due to 1%Marginal Match RateReal Contributions

200.26512060.0070.2425880.03140190.00118440.001060.117397953

210.32042640.0150.008240.24258670.07075221327.30.13991390.00120830.001060.13990961164.4

220.35973470.0240.009250.24258490.11653321537.10.16300810.00123280.001060.16299511321.6

230.38808250.0340.009980.24258670.16768881710.20.18644990.00125760.001060.18644551441.4

240.41210330.0450.01060.24258670.22396471873.20.2104920.00128310.001060.21048741547.5

250.44329310.0560.01140.24258670.28650652078.30.23489620.0013090.001060.23489121682.9

260.45953950.0680.011820.24258670.353649122220.25979330.00133540.001060.25978931763.8

270.47577450.080.012230.24259370.42555122372.50.28506310.00136220.001060.28509611846.2

280.57782340.0950.014860.24258670.51442922971.80.31097830.00138960.001060.31097292266.9

290.56843470.110.014620.24259370.60532630150.33727770.00141760.001060.33731212254.6

300.61318150.1260.015770.24257970.70620763354.40.36425140.00144610.001060.36420572458.8

310.60419830.1410.015540.24260780.80967263409.40.39191260.00147560.001060.39202932449.4

320.58355320.1560.015010.24259370.914032833970.42028990.00150550.001060.42032482391.7

330.56232950.1710.014460.24260781.019163377.30.44939660.00153650.001060.44951792330.1

340.5827890.1860.014990.24259371.1314233611.20.47910710.00156790.001060.47914392441.5

350.64233470.1960.010670.0862581.2211332652.9-0.02485860.0005690.00106-0.46322882720.5

360.70055630.2030.006410.0862581.2869811643.3-0.45219540.00058070.00106-0.45216562999.7

370.6859060.2090.006270.0862581.3543031660.3-0.44084430.00059270.00106-0.44081382969.3

380.69647360.2150.006370.0862581.4248071740.1-0.42913550.00060510.00106-0.42910453048.2

390.70903860.2220.006480.0862581.4984521828.5-0.41717840.00061780.00106-0.41714743137.3

400.71793090.2280.006560.0862581.5752921911.2-0.40490730.00063080.00106-0.40487443211.6

410.7890180.2360.007210.0862441.6596432168.8-0.39224270.00064420.00106-0.39230983568.5

420.78966970.2430.007220.0862581.7471082241.4-0.37924320.0006580.00106-0.37920813610.7

430.79462870.250.007270.0862581.8382942329.6-0.36582070.00067230.00106-0.3657883673.3

440.79338860.2570.007250.0862581.9327432402.6-0.35203980.00068690.00106-0.35200353708

450.80683160.2650.007380.08622992.0316062524.2-0.33787730.00070170.00106-0.33805853812.3

460.80994380.2720.007410.08622992.134342618.1-0.32333120.00071710.00106-0.32351433869.1

470.81435530.280.007450.08622992.2414372720.4-0.30830540.0007330.00106-0.30849443932.9

480.82987820.2870.007590.0862582.3536812865.3-0.29286660.00074960.00106-0.2928264052

490.80726090.2940.007380.0862582.4683852881.1-0.27698810.00076640.00106-0.27695123984.9

500.80078970.3020.007320.08622992.5874272955.3-0.26050820.00078360.00106-0.26070933996.4

510.80267970.3090.007340.0862582.7108053063.2-0.24364120.00080180.00106-0.24359794049.9

520.79341910.3160.007250.08622992.8386893132.1-0.22611330.00082010.00106-0.22632744047.3

530.77777420.3230.007110.0862582.970443176.8-0.20800380.00083960.00106-0.2079574011.1

540.75976370.330.006950.0862583.1063573211.9-0.18917130.00085950.00106-0.18912763961.3

550.77027420.3350.004620.0862583.225812211.2-0.4554130.00088030.00106-0.16955294060.3

560.77906320.3390.004190.0862583.3466222079.6-0.49910040.0009020.00106-0.14910014151.8

570.76474380.3430.00370.0862583.4681531903.3-0.53806540.00092460.00106-0.1277214120.3

580.75038880.3460.003310.0862583.5918131765.7-0.56801960.00094840.00106-0.10526124087.4

590.73468610.3490.002950.08622993.7175531631.1-0.5968450.0009730.00106-0.0820594045.9

600.72794360.3520.00260.08622993.8460591494.3-0.63129330.00099920.00106-0.05735314052.9

610.71582260.3540.002340.0862583.9784471397.7-0.6531080.00102710.00106-0.03104084029.2

620.69947520.3560.002050.0862584.1149821268.5-0.68133630.00105620.00106-0.00354223980.5

630.68972280.3570.001160.0862584.250013751.8-0.81054310.00108740.001060.02580193968.2

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Relative Wage

PAAW Balances

Age

Worker 3: 0.5 Cohort Average

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Relative Wage

Change in PAAWs

Age

Worker 3: 0.5 Cohort Average

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Relative Wage

Additional PAAWs per Additional Contribution

Age

Worker 3: 0.5 Cohort Average

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Relative Wage

Market Value of Accrued PAAWs

Age

Worker 3: 0.5 Cohort Average

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Relative Wage

Average Match Rate

Age

Worker 3: 0.5 Cohort Average

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Relative PV of Additional PAAWs due to 1%

Relative PV of Additional Contribution due to 1%

Age

Relative PV of additional PAAWs and Relative PV of contributions due to earning 1% of the Economy's Average Wage

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Present Value of Change in PAAWs

Real Contributions

Age

PV of Change in PAAWs+Real Contributions

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Relative Wage

Marginal Match Rate

Age

Worker 3: 0.5 Cohort Average

YearAgePresent Value of PaawPrSurvPrSurvRetAv.Wage IndexReal Av. Wage IndexMarket Value of PAAWZDiscount RateRetirement ProbabilityAv. Wage ExpectationChange in Discount RateChange in retirement probabilityChange in Av.Wage ExpectationChange in PVPaawContrib. Change in Discount RateContrib. Change in Retirement ProbabillityContrib. Change in Av. Wage ExpectationHigher Order TermsVerification

200220156192.797.5579.6333909.5833909.64.606149880913.686270.2492587650.816299333756088.7580903226

200321161090.497.4279.6334282342824.698979056113.686270.25673652790.817388626656087.7672860560.00747776290.0010892929-0.99080426664897.74691.9517747559214.6770349017-2.8457007318-6.16616281774897.6169461081

200422166161.997.2879.6334659.134659.14.794178152313.686270.26443862380.818564967156087.7640495170.00770209580.0011763405-0.0032365395071.54839.6650183594238.7872769614-0.0095883524-6.95467658165071.4880303868

200523171375.797.1579.6335040.3535040.44.890803187213.686270.27237178250.819660319156087.8439225610.00793315870.0010953520.0798730445213.84991.5324955879229.01802397180.2440514337-6.67785281555214.1167181778

200624176771.897.0179.6335425.835425.84.989916953213.686270.2805429360.82084321256087.77362641670.00817115350.0011828929-0.07029614435396.15148.6916544826254.7405512357-0.2215522461-7.41286475465395.7977887176

200725182319.396.8879.6335815.4835815.55.090513883713.686270.2889592240.821944673856087.79899594510.00841628810.00110146180.02536952845547.55310.2709271527244.32026840730.0824663258-7.11863354615547.5550283396

200826188041.196.7579.6336209.4536209.45.193157025513.686270.29762800080.823049095656087.68979275120.00866877670.0011044218-0.10920319395721.85476.9176965536252.3256535812-0.3661170659-7.33815030625721.5390827628

200927193922.996.6379.6336607.7536607.85.297310955613.686270.30655684080.824071199456087.83779632230.008928840.00102210380.14800357115881.85648.2456895014240.52477768210.5117207714-7.02109674375882.2610912112

201028200009.796.579.6337010.4437010.45.404148563613.686270.3157535460.825181347256087.70777002360.00919670520.0011101477-0.13002629876086.85825.5168617945269.0802400201-0.4636752797-7.8231778086086.3102487268

201129206266.596.3879.6337417.5537417.65.512552916313.686270.32522615240.82620875756087.83608180120.00947260640.00102740990.12831177766256.86007.7668926951256.49740515960.4718749032-7.48511183436257.2510609237

201230212741.496.2579.6337829.1437829.15.623749970313.686270.33498293690.827324675356087.69730481550.00975678460.0011159183-0.13877698566474.96196.3423860009286.9510429154-0.5263822267-8.3417765266474.4252701636

201331219442.896.1179.6338245.2738245.35.737771700113.686270.34503242510.828529809656087.81448042610.01004948810.00120513430.11717561056701.46391.5427805209319.18977279690.4584483115-9.31078977396701.8802118555

201432226379.495.9679.6338665.96386665.85474059913.686270.35538339780.829824927156087.81694639850.01035097280.00129511750.00246597246936.66593.5800307762353.31325729370.009953067-10.29098237356936.6122587634

201533233560.295.879.6339091.2939091.35.974736066613.686270.36604489970.831210855956087.77964187620.01066150190.0013859289-0.03730452227180.86802.7255166305389.4293334517-0.1553431661-11.33782591787180.6616809982

201634240969.595.6479.6339521.2939521.36.097205810513.686270.37702624670.83260142256087.77353940930.0109813470.001390566-0.00610246697409.37018.5284880214402.4542431544-0.0262179826-11.72116210427409.2353510891

201735248640.595.4779.6339956.03399566.222857643413.686270.38833703410.834084005456087.72539122180.01131078740.0014825834-0.048148187576717241.9506966925441.9578861672-0.2134438518-12.86597463427670.8291643737

201836256556.695.379.6340395.5540395.56.351118317613.686270.39998714520.835571878356087.70317579550.0116501110.0014878728-0.02221542627916.17472.5122973806456.8405095043-0.1016177566-13.30289884017915.9482902882

201937264753.395.1279.6340839.8940839.96.482711759813.686270.41198675950.837153069856087.77115697750.01199961440.00158119150.06798118198196.77711.261812778500.05874084960.320894259-14.57475257238197.0666953144

202038273270.594.9279.6341289.1441289.16.618465890513.686270.42434636230.838916982756087.71831464760.01235960280.0017639129-0.05284232998517.27959.3275237703574.579993656-0.2574580828-16.72731527578516.9227440678

202139282062.994.7279.6341743.3241743.36.757081974813.686270.43707675320.840688344656087.74505297750.01273039090.00177136190.02673832998792.48215.4214588487594.31690564780.1344658853-17.314392698792.5584376918

202240291170.494.5179.6342202.4942202.56.899363781813.686270.45018905580.842556343256087.77655064480.01311230260.00186799860.03149766739107.58480.6910624287645.54246790660.1635149178-18.80732233719107.589722916

202341300637.294.2879.6342666.7242666.77.046178870213.686270.46369472740.844611794756087.74040037160.01350567170.0020554514-0.03615027329466.88756.4158207885731.6315409109-0.1937697534-21.30355492799466.5500370182

202442310446.594.0479.6343136.0543136.17.19690699913.686270.47760556930.84676733356087.82660711970.01391084180.00215553840.0862067489809.39042.1399089111790.27612271350.4771554006-23.03282814999809.8603588753

202543320646.493.7879.6343610.5543610.67.352487697913.686270.49193373630.849114949956087.83033682550.01432816710.00234761680.003729705810199.99339.2256385773886.51801574190.0213222374-25.821591350210199.9433852065

202644331219.493.5179.6344090.2744090.37.512296355413.686270.50669174840.851566677456087.80921976270.01475801210.0024517275-0.0211170628105739647.1737584638953.6073868731-0.124704207-27.770991695910572.885449434

202745342180.693.2379.6344575.2644575.37.676462076513.686270.52189250090.854124208956087.817650180.01520075250.00255753160.008430417310961.29966.43327641141024.60319998470.0514323374-29.844459199210961.2434495342

202846353545.892.9479.6345065.5945065.67.845136867113.686270.53754927590.856789326456087.78242854210.0156567750.0026651175-0.035221637811365.210297.45094245451099.7349195578-0.2220173832-32.023977146511364.9398674827

202947365370.892.6379.6345561.3145561.38.01932341713.686270.55367575420.859656698756087.75583809090.01612647830.0028673722-0.02659045121182510641.86522698711218.6886044678-0.1732173413-35.490178495111824.8904356185

203048377636.592.3179.6346062.4846062.58.198350067813.686270.57028602680.862636767456087.78713157540.01661027260.00298006870.031293484512265.710999.1249241191304.58511460990.210697665-38.004468199312265.9162681946

203149390361.191.9879.6346569.1746569.28.382387930213.686270.58739460760.865731680856087.80218653720.01710858080.00309491340.015054961812724.611369.74754409891395.50687547010.1047799115-40.649246835212724.7099526453

203250403651.891.6279.6347081.4347081.48.573487619313.686270.60501644580.86913337756087.72927942240.01762183820.0034016962-0.072907114713290.711756.8397762761579.8493110978-0.5246970509-45.997752245213290.1666380776

203351417401.591.2679.6347599.3347599.38.769068032513.686270.62316693920.87256191156087.73469974540.01815049340.0034285340.00542032313749.712157.31555261211640.08317212710.0403376808-47.770741545613749.6683208744

203452431768.790.8779.6348122.9248122.98.972208657413.686270.64186194740.876306811956087.7436741760.01869500820.00374490090.008974430614367.212575.77967097041845.16425371790.0690859644-53.744947019114367.2680636336

203553446737.490.4679.6348652.2748652.39.182246265813.686270.66111780580.880278576256087.79912526750.01925585840.00397176420.055451091514968.713011.77421341372015.65322267150.4416662247-58.723145085914969.1459572241

203654462388.690.0279.6349187.4549187.49.400549734313.686270.680951340.884581204256087.71326171690.01983353420.004302628-0.085863550615651.213467.61377734442249.0686726702-0.7078605882-65.482894474315650.4916949522

203755478759.989.5579.6349728.5149728.59.627475190313.686270.70137988020.889223897356087.75679786650.02042854020.00464269310.043536149516371.313944.45783677792499.63416973420.3716204018-72.817586366216371.6460405476

203856495947.289.0479.6350275.5250275.59.864590108513.686270.72242127660.894317160856087.74173716070.02104139640.0050932636-0.015060705817187.314445.05435640472824.4880154175-0.1331718768-82.262026090717187.1471738547

203957514000.588.4979.6350828.5550828.610.11242686213.686270.74409391490.899875692256087.81842830270.02167263830.00555853130.07669114218053.314970.90157655823174.98343183610.702814288-92.499930744618054.0878919376

204058533034.887.8979.6351387.6751387.710.372809057413.686270.76641673230.906018887256087.80249293460.02232281740.0061431951-0.015935368119034.315525.29235687053614.205249763-0.1514430798-105.262706166719034.083457387

204159553053.187.2579.6351952.9351952.910.645278704413.686270.78940923430.912664756456087.73264358450.0229925020.0066458692-0.069849350120018.299999999916108.32932161664027.2350623164-0.6887489592-117.273178687620017.6024562862

204260574185.586.5679.6352524.4152524.410.93178598913.686270.81309151130.919939926156087.75197152180.0236822770.00727516960.019327937321132.416723.84223846264540.83464331430.1978652403-132.264601976921132.6101450403

204361596510.685.8279.6353102.1853102.211.233255872613.686270.83748425670.927872290856087.78534818070.02439274530.00793236480.033376658922325.117374.09863639815099.56022052640.3549709569-148.544165422622325.4696624588

204462620187.385.0279.6353686.353686.311.552058905213.686270.86260878440.936603152256087.76006568230.02512452770.0087308614-0.025282498423676.700000000118063.70038871175781.2821876401-0.2795597112-168.376187211623676.326829429

204563645473.884.1479.6354276.8654276.911.89223776613.686270.88848704790.94639885956087.81245725390.02587826350.00979570680.052391571625286.518800.22057124786680.98483720660.6029368654-194.615411576425287.1929337434

204664672591.983.1779.6354873.954873.912.257045699313.686270.91514165940.957436575756087.76554190.02665461140.0110377166-0.046915353927118.119590.05305731937753.910945871-0.562598332-225.819383072627117.5820217858

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Present Value of Paaw

Year

Present Value of PAAW

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Market Value of PAAW

Year

Market Value of one PAAW(under risk neutrality, measured in average wage units)

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Change in PVPaaw

Contrib. Change in Discount Rate

Contrib. Change in Retirement Probabillity

Contrib. Change in Av. Wage Expectation

Higher Order Terms

Year

Change in Present Value of PAAW Decomposition

Chart16

0.53024120.2425876

0.64085270.2425884

0.71946940.2425867

0.7761650.2425867

0.82420650.2425867

0.88658610.2425726

0.91907910.2425937

0.95154890.2426078

1.1556470.2426078

1.1368690.086258

1.2263630.086258

1.2083970.086258

1.1671060.086258

1.1246590.086258

1.1655780.086258

1.2846690.086258

1.4011130.086258

1.3718120.0862862

1.3929470.0862299

1.4180770.086258

1.4358620.086258

1.5780360.086258

1.5793390.0862862

1.5892570.0862299

1.5867770.0862299

1.6136630.0862299

1.6198880.0862299

1.6287110.0862862

1.6597560.086258

1.6145220.086258

1.6015790.086258

1.6053590.0862862

1.5868380.0862018

1.5555480.0863143

1.5195270.0863143

1.5405480.0404299

1.5581260.0404299

1.5294880.0404299

1.5007780.0404299

1.4693720.0404299

1.4558870.0404299

1.4316450.0404299

1.398950.0403737

1.3794460.0404299

Relative Wage

Additional PAAWs per Additional Contribution

Age

Worker 2: Cohort Average

Cohort Average

AgeRelative WagePAAW BalancesChange in PAAWsAdditional PAAWs per Additional ContributionMarket Value of Accrued PAAWsPresent Value of Change in PAAWsAverage Match RateRelative PV of Additional PAAWs due to 1%Relative PV of Additional Contribution due to 1%Marginal Match RateReal Contributions

200.53024120.0140.24258760.06280380.00118440.001060.1173951905.9

210.64085270.030.016480.24258840.14150432654.60.13991390.00120830.001060.13991782328.8

220.71946940.0490.01850.24258670.23306653074.10.16300810.00123280.001060.16300352643.2

230.7761650.0690.019960.24258670.33537763420.40.18644990.00125760.001060.18644552882.9

240.82420650.090.021190.24258670.44792933746.50.2104920.00128310.001060.21048743095

250.88658610.1130.02280.24257260.5730134156.50.23489620.00130890.001060.23481973365.9

260.91907910.1360.023630.24259370.70729824444.10.25979330.00133540.001060.25982583527.6

270.95154890.1610.024470.24260780.851102547450.28506310.00136230.001060.28517063692.4

281.1556470.190.029720.24260781.0288585943.60.31097830.00138980.001060.31108684533.7

291.1368690.2020.012090.0862581.116122492.8-0.44716650.0005040.00106-0.52449744509.1

301.2263630.2140.011210.0862581.2016872385.4-0.51493290.00051420.00106-0.51490694917.6

311.2083970.2250.011050.0862581.2894472424.4-0.50509740.00052460.00106-0.50507064898.8

321.1671060.2350.010670.0862581.3782072415.6-0.49500820.00053530.00106-0.4949814783.5

331.1246590.2460.010280.0862581.4678892401.6-0.4846590.00054630.00106-0.48463084660.2

341.1655780.2560.010660.0862581.5629532567.9-0.47409530.00055750.00106-0.47406694882.9

351.2846690.2680.011750.0862581.6682532920.4-0.46325820.0005690.00106-0.46322885441

361.4011130.2810.012810.0862581.7839953286.5-0.45219540.00058070.00106-0.45216565999.5

371.3718120.2930.012540.08628621.902273320.6-0.44084430.00059290.00106-0.44063155938.6

381.3929470.3060.012740.08622992.0263933480.2-0.42913420.0006050.00106-0.42929066096.4

391.4180770.3190.012970.0862582.1564423657-0.41717980.00061780.00106-0.41714746274.7

401.4358620.3320.013130.0862582.2924243822.4-0.40490730.00063080.00106-0.40487446423.3

411.5780360.3470.014430.0862582.4428654337.5-0.39224270.00064430.00106-0.39221077136.9

421.5793390.3610.014440.08628622.5990464482.7-0.37924320.00065830.00106-0.37900587221.4

431.5892570.3760.014530.08622992.7620674659.1-0.36582070.0006720.00106-0.36599477346.7

441.5867770.390.014510.08622992.9310864805.2-0.35203840.00068670.00106-0.35221477415.9

451.6136630.4050.014750.08622993.1083945048.4-0.33787860.00070170.00106-0.33805857624.5

461.6198880.420.014810.08622993.2928825236.2-0.32332980.00071710.00106-0.32351437738.1

471.6287110.4350.014890.08628623.4854095440.7-0.30830820.00073350.00106-0.30804357865.9

481.6597560.450.015170.0862583.687635730.6-0.29286380.00074960.00106-0.2928268104

491.6145220.4650.014760.0862583.8941475762.3-0.27698950.00076640.00106-0.27695127969.8

501.6015790.4790.014640.0862584.1084615910.7-0.26050820.00078390.00106-0.26046827992.9

511.6053590.4940.014680.08628624.3308926126.4-0.24364120.0008020.00106-0.24335148099.9

521.5868380.5080.014510.08620184.5613926264.2-0.22611330.00081980.00106-0.22657978094.5

531.5555480.5230.014220.08631434.7987696353.5-0.20800380.00084010.00106-0.20744068022.2

541.5195270.5370.013890.08631435.0434516423.9-0.18917130.00086010.00106-0.18859917922.6

551.5405480.5420.005150.04042995.2148172467.3-0.69616590.00041260.00106-0.61076188120.6

561.5581260.5460.003930.04042995.382031949.7-0.76520350.00042280.00106-0.60117538303.6

571.5294880.5490.003470.04042995.5523611784.3-0.78346880.00043340.00106-0.59115488240.6

581.5007780.5520.003110.04042995.7275391655.4-0.79750750.00044450.00106-0.58062778174.9

591.4693720.5550.002760.04042995.9074141529.2-0.81102070.00045620.00106-0.56961238091.8

601.4558870.5570.002440.04042996.0930811400.9-0.82716890.00046850.00106-0.55802868105.8

611.4316450.560.00220.04042996.2857921310.3-0.83739670.00048140.00106-0.54583998058.5

621.398950.5610.001920.04037376.4863311189.2-0.85062350.00049440.00106-0.53360067961.1

631.3794460.5630.001090.04042996.690329704.8-0.91119540.00050970.00106-0.51919717936.4

Cohort Average

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Relative Wage

PAAW Balances

Age

Worker 2: Cohort Average

Economy Average

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Relative Wage

Change in PAAWs

Age

Worker 2: Cohort Average

1.5x Cohort Average

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Relative Wage

Additional PAAWs per Additional Contribution

Age

Worker 2: Cohort Average

0.5x Cohort Average

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Relative Wage

Market Value of Accrued PAAWs

Age

Worker 2: Cohort Average

PAAW Price

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Relative Wage

Average Match Rate

Age

Worker 2: Cohort Average

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Relative PV of Additional PAAWs due to 1%

Relative PV of Additional Contribution due to 1%

Age

Relative PV of additional PAAWs and Relative PV of contributions due to earning 1% of the Economy's Average Wage

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Present Value of Change in PAAWs

Real Contributions

Age

PV of Change in PAAWs+Real Contributions

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Relative Wage

Marginal Match Rate

Age

Worker 2: Cohort Average

AgeRelative WagePAAW BalancesChange in PAAWsAdditional PAAWs per Additional ContributionMarket Value of Accrued PAAWsPresent Value of Change in PAAWsAverage Match RateRelative PV of Additional PAAWs due to 1%Relative PV of Additional Contribution due to 1%Marginal Match RateReal Contributions

2010.0260.24259020.11844390.00118450.001060.11740733594.4

2110.0510.025710.24258670.24166174142.30.13991390.00120830.001060.13990963633.9

2210.0770.025710.24258670.36983654272.70.1630080.00123280.001060.16300353673.9

2310.1030.025710.24259370.50305494406.80.18645010.00125770.001060.186483714.3

2410.1290.025710.24259370.64156074545.60.21049230.00128320.001060.21052243755.1

2510.1540.025710.24259370.78539384688.20.23489560.0013090.001060.2349273796.4

2610.180.025710.24257970.93476714835.30.25979440.00133530.001060.25975283838.2

2710.1980.017530.0862441.0463553398.6-0.12417320.00048430.00106-0.54313823880.4

2810.2070.009140.0862441.1168651828.7-0.53387440.0004940.00106-0.53392533923.1

2910.2160.009140.0862581.1896711885.9-0.52452390.0005040.00106-0.52449743966.3

3010.2250.009140.0862581.2650831945.1-0.5149330.00051420.00106-0.51490694009.9

3110.2340.009140.0862441.3431952006.3-0.50509720.00052450.00106-0.50515134054

3210.2430.009140.0862441.4241072069.8-0.49500820.00053520.00106-0.49506334098.6

3310.2520.009140.0862581.507922135.4-0.48465940.00054630.00106-0.48463084143.7

3410.2620.009140.0862581.5945742203.1-0.47409610.00055750.00106-0.47406694189.3

3510.2710.009140.0862581.6843292273.3-0.46325680.0005690.00106-0.46322884235.3

3610.280.009140.0862581.7771112345.7-0.4521960.00058070.00106-0.45216564281.9

3710.2890.009140.08622991.8732062420.6-0.4408430.00059250.00106-0.44099614329

3810.2980.009140.0862581.9729422498.5-0.42913620.00060510.00106-0.42910454376.6

3910.3070.009140.08622992.0760432578.9-0.41717790.00061760.00106-0.41733744424.8

4010.3160.009140.08622992.1828382662.1-0.40490730.00063060.00106-0.40506844473.5

4110.3260.009140.0862582.2937092748.7-0.39224450.00064430.00106-0.39221074522.7

4210.3350.009140.08622992.4085792838.4-0.37924060.00065780.00106-0.37941054572.4

4310.3440.009140.0862582.527872931.6-0.36582310.00067230.00106-0.3657884622.7

4410.3530.009140.0862582.6514973028.3-0.35203930.00068690.00106-0.35200354673.6

4510.3620.009140.08622992.7796253128.5-0.33787720.00070170.00106-0.33805854725

4610.3710.009140.0862582.9124273232.4-0.32333120.00071730.00106-0.32329374777

4710.380.009140.0862583.050413340.5-0.30830720.00073320.00106-0.3082694829.5

4810.390.009140.08622993.1934673452.7-0.29286290.00074940.00106-0.29305654882.6

4910.3990.009140.0862583.3417943569-0.27699120.00076640.00106-0.27695124936.3

5010.4080.009140.08622993.4963613690.5-0.26050670.00078360.00106-0.26070934990.6

5110.4170.009140.08622993.6562953816.2-0.24363980.00080150.00106-0.24384445045.5

5210.4260.009140.0862583.8230283947.6-0.22611810.00082040.00106-0.22607525101

5310.4350.009140.08622993.996484084.5-0.20799830.00083930.00106-0.20821525157.1

5410.4440.009140.08622994.1774364227.5-0.18917260.00085920.00106-0.1893925213.9

5510.44400.08622994.2782810-10.000880.00106-0.16982375271.2

5610.44400.08622994.383650-10.00090170.00106-0.14937755329.2

5710.44400.08622994.4937910-10.00092430.00106-0.12800535387.8

5810.44400.08622994.6094990-10.00094810.00106-0.10555295447.1

5910.44400.08622994.7305730-10.0009730.00106-0.0820595507

6010.44400.08622994.8578930-10.00099920.00106-0.05735315567.6

6110.44400.08622994.9918650-10.00102680.00106-0.03135675628.8

6210.44400.08622995.1335320-10.00105590.00106-0.0038675690.7

6310.44400.08622995.2847080-10.0010870.001060.02546765753.3

6410.44400.08622995.4468180-10.00112030.001060.05692425816.6

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Relative Wage

PAAW Balances

Age

Worker 1: Economy Average

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Relative Wage

Change in PAAWs

Age

Worker 1: Economy Average

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Relative Wage

Additional PAAWs per Additional Contribution

Age

Worker 1: Economy Average

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Relative Wage

Market Value of Accrued PAAWs

Age

Worker 1: Economy Average

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Relative Wage

Average Match Rate

Age

Worker 1: Economy Average

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Relative PV of Additional PAAWs due to 1%

Relative PV of Additional Contribution due to 1%

Age

Relative PV of additional PAAWs and Relative PV of contributions due to earning 1% of the Economy's Average Wage

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Present Value of Change in PAAWs

Real Contributions

Age

PV of Change in PAAWs+Real Contributions

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Relative Wage

Marginal Match Rate

Age

Worker 1: Economy Average

AgeRelative WagePAAW BalancesChange in PAAWsAdditional PAAWs per Additional ContributionMarket Value of Accrued PAAWsPresent Value of Change in PAAWsAverage Match RateRelative PV of Additional PAAWs due to 1%Relative PV of Additional Contribution due to 1%Marginal Match RateReal Contributions

200.79536180.020.24258840.09420570.00118440.001060.11739912858.9

210.96127910.0450.024720.24259020.21225643981.90.1399140.00120830.001060.1399263493.2

221.0792040.0730.027750.24258670.34959974611.20.1630080.00123280.001060.16300353964.8

231.1642480.1030.029940.24257970.50306655130.60.18645060.00125760.001060.18641124324.3

241.236310.1350.031790.24259370.67189395619.70.21049120.00128320.001060.21052244642.5

251.3298790.1690.03420.24259370.85951946234.80.23489610.0013090.001060.2349275048.8

261.3786190.1970.028170.0862581.0231635297.90.00123410.00047480.00106-0.5520495291.4

271.4273230.210.013050.0862581.1128152530.7-0.54308860.00048440.00106-0.54306375538.6

281.733470.2260.015850.0862581.2209063169.9-0.53387440.00049410.00106-0.53384936800.6

291.7053040.2420.015590.0862441.3313473216-0.52452330.0005040.00106-0.52457496763.7

301.8395440.2580.016820.0862581.4527833578-0.51493380.00051420.00106-0.51490697376.4

311.8125950.2750.016570.0862581.577333636.7-0.50509740.00052460.00106-0.50507067348.3

321.750660.2910.016010.0862581.7031973623.4-0.49500770.00053530.00106-0.4949817175.2

331.6869890.3060.015420.0862581.8302573602.4-0.48465880.00054630.00106-0.48463086990.3

341.7483670.3220.015990.0862581.9652373851.9-0.47409530.00055750.00106-0.47406697324.4

351.9270040.340.017620.08622992.1153724380.6-0.46325770.00056880.00106-0.46340388161.5

362.1016690.3590.019220.0862582.2810094929.8-0.45219540.00058070.00106-0.45216568999.2

372.0577180.3780.018810.08622992.4502374980.9-0.44084380.00059250.00106-0.44099618907.9

382.0894210.3970.01910.0862582.6279795220.4-0.42913590.00060510.00106-0.42910459144.7

392.1271160.4170.019450.08628622.8144315485.5-0.41717980.0006180.00106-0.41695759412

402.1537930.4360.019690.08622993.0095565733.7-0.40490550.00063060.00106-0.40506849634.9

412.3670540.4580.021640.08622993.2260866506.3-0.39224430.0006440.00106-0.392408810705.4

422.3690090.480.021660.0862583.4509846724.1-0.37924150.0006580.00106-0.379208110832.1

432.3838860.5010.02180.0862583.6858396988.7-0.3658230.00067230.00106-0.36578811020

442.3801660.5230.021760.08620183.9294297207.8-0.3520380.00068640.00106-0.352425911123.9

452.4204950.5410.018340.04042994.1560666274.7-0.4513550.0003290.00106-0.689640811436.8

462.4298320.5520.010410.04037374.329083681.7-0.68281040.00033570.00106-0.683262611607.2

472.4430660.5620.010470.04037374.5091633825.5-0.6757690.00034320.00106-0.676230211798.8

482.4896350.5730.010670.04042994.6973054029.3-0.66853120.00035130.00106-0.66854112155.9

492.4217820.5830.010380.04042994.8897534051.6-0.66108890.00035920.00106-0.661100311954.7

502.4023690.5940.01030.04042995.0894934155.9-0.65336320.00036740.00106-0.653374611989.3

512.4080390.6040.010320.04042995.2960944307.7-0.6454550.00037580.00106-0.645467312149.8

522.3802570.6140.01020.04042995.5103094404.5-0.63724260.00038450.00106-0.637254212141.8

532.3333230.6240.010.04042995.7311324467.3-0.62875080.00039350.00106-0.628762112033.3

542.2792910.6340.009770.04042995.9592064516.8-0.61992280.00040290.00106-0.619936611883.9

552.3108230.640.006490.04042996.1655923109.5-0.74472580.00041260.00106-0.610761812180.9

562.3371890.6460.00590.04042996.3756122924.5-0.76520350.00042280.00106-0.601175312455.4

572.2942310.6520.005210.04048626.5884592676.5-0.78346880.0004340.00106-0.590586112360.9

582.2511660.6560.004660.04037376.8064212483-0.79750750.00044390.00106-0.581210912262.3

592.2040580.660.004150.04048627.0293512293.7-0.81102480.00045680.00106-0.569013712137.8

602.1838310.6640.003660.04048627.258552101.4-0.82716890.00046910.00106-0.557413912158.7

612.1474680.6670.00330.04042997.4957421965.6-0.83739080.00048140.00106-0.545839912087.7

622.0984260.670.002880.04042997.7416941783.8-0.85062660.00049510.00106-0.53295111941.6

632.0691690.6720.001640.04048627.9891531057.2-0.91119380.00051040.00106-0.518528411904.6

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Relative Wage

PAAW Balances

Age

Worker 4: 1.5 Cohort Average

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Relative Wage

Change in PAAWs

Age

Worker 4: 1.5 Cohort Average

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Relative Wage

Additional PAAWs per Additional Contribution

Age

Worker 4: 1.5 Cohort Average

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Relative Wage

Market Value of Accrued PAAWs

Age

Worker 4: 1.5 Cohore Average

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Relative Wage

Average Match Rate

Age

Worker 4: 1.5 Cohort Average

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Relative PV of Additional PAAWs due to 1%

Relative PV of Additional Contribution due to 1%

Age

Relative PV of additional PAAWs and Relative PV of contributions due to earning 1% of the Economy's Average Wage

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Present Value of Change in PAAWs

Real Contributions

Age

PV of Change in PAAWs+Real Contributions

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Relative Wage

Marginal Match Rate

Age

Worker 4: 1.5 Cohort Average

AgeRelative WagePAAW BalancesChange in PAAWsAdditional PAAWs per Additional ContributionMarket Value of Accrued PAAWsPresent Value of Change in PAAWsAverage Match RateRelative PV of Additional PAAWs due to 1%Relative PV of Additional Contribution due to 1%Marginal Match RateReal Contributions

200.26512060.0070.2425880.03140190.00118440.001060.117397953

210.32042640.0150.008240.24258670.07075221327.30.13991390.00120830.001060.13990961164.4

220.35973470.0240.009250.24258490.11653321537.10.16300810.00123280.001060.16299511321.6

230.38808250.0340.009980.24258670.16768881710.20.18644990.00125760.001060.18644551441.4

240.41210330.0450.01060.24258670.22396471873.20.2104920.00128310.001060.21048741547.5

250.44329310.0560.01140.24258670.28650652078.30.23489620.0013090.001060.23489121682.9

260.45953950.0680.011820.24258670.353649122220.25979330.00133540.001060.25978931763.8

270.47577450.080.012230.24259370.42555122372.50.28506310.00136220.001060.28509611846.2

280.57782340.0950.014860.24258670.51442922971.80.31097830.00138960.001060.31097292266.9

290.56843470.110.014620.24259370.60532630150.33727770.00141760.001060.33731212254.6

300.61318150.1260.015770.24257970.70620763354.40.36425140.00144610.001060.36420572458.8

310.60419830.1410.015540.24260780.80967263409.40.39191260.00147560.001060.39202932449.4

320.58355320.1560.015010.24259370.914032833970.42028990.00150550.001060.42032482391.7

330.56232950.1710.014460.24260781.019163377.30.44939660.00153650.001060.44951792330.1

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