Reforming Social Security With Progressive Personal Accounts
description
Transcript of Reforming Social Security With Progressive Personal Accounts
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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
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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
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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?
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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?
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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.
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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
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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
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Mechanics of Current OASDI System Contributions / TaxesContributions = tax rate x covered earnings
Covered earnings = min (earnings, cap)(2006 cap $94,200)
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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
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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
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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)
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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
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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)
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6771.6
18875.28
22561.68
slope =.32
slope=.15
slope=.9
Maximum:AIE: 69,924PIA: 22,562
AIME (Annualized)
PIA (annual)
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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)
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Creating Individual Accounts that Mimic the Current SystemDefine new securities (PAAWs)
Compute accrual of balances
Trade PAAWs in financial markets
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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
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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)
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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
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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)
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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)
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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
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Additional PAAWs per Additional Contribution
PAAW Balance
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0.01PAAWs BalanceAdditional PAAWs per Additional Contribution
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Additional PAAWs per Additional Contribution
PAAW Balance
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Sheet3
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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
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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)
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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
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Additional PAAWs Per Additional Contribution (measured in average wage units)
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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
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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%
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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
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
0
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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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PAAW Balances
Age
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Relative Wage
Change in PAAWs
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Relative Wage
Additional PAAWs per Additional Contribution
Age
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Relative Wage
Market Value of Accrued PAAWs
Age
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Relative Wage
Average Match Rate
Age
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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
340.58