Research. Michigan. Center. Retirement. Exchanging Delayed Social Security Benefits for Lump Sums: Could This Incentivize Longer Work Careers?

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1 Michigan Universiy of Reiremen Research Cener Working Paper WP Exchanging Delayed Social Securiy Benefis for Lump Sums: Could This Incenivize Longer Work Careers? Jingjing Chai, Raimond Maurer, Olivia S. Michell and Ralph Rogalla M R R C Projec #: UM12-08

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3 Exchanging Delayed Social Securiy Benefis for Lump Sums: Could This Incenivize Longer Work Careers? Jingjing Chai Goehe Universiy Raimond Maurer Goehe Universiy Olivia S. Michell The Wharon School, Universiy of Pennsylvania Ralph Rogalla Goehe Universiy Ocober 2012 Michigan Reiremen Research Cener Universiy of Michigan P.O. Box 1248 Ann Arbor, MI (734) Acknowledgemens This work was suppored by a gran from he Social Securiy Adminisraion hrough he Michigan Reiremen Research Cener (Gran # 5 RRC ). The findings and conclusions expressed are solely hose of he auhor and do no represen he views of he Social Securiy Adminisraion, any agency of he Federal governmen, or he Michigan Reiremen Research Cener. Regens of he Universiy of Michigan Julia Donovan Darrow, Ann Arbor; Laurence B. Deich, Bloomfield Hills; Denise Ilich, Bingham Farms; Olivia P. Maynard, Goodrich; Andrea Fischer Newman, Ann Arbor; Andrew C. Richner, Grosse Poine Park; S. Marin Taylor, Gross Poine Farms; Kaherine E. Whie, Ann Arbor; Mary Sue Coleman, ex officio

4 Exchanging Delayed Social Securiy Benefis for Lump Sums: Could This Incenivize Longer Work Careers? Absrac Social Securiy benefis are currenly provided as a lifelong benefi sream, hough some workers would be willing o rade a porion of heir annuiy sreams in exchange for a lump sum amoun. This paper explores wheher allowing people o receive a lump sum as a paymen for delayed reiremen raher han as an addiion o heir lifeime Social Securiy benefis migh induce hem o work longer. We model he facors ha influence how people rade off a Social Securiy sream for a lump sum, and we also examine he consequences of such radeoffs for work, reiremen, and life cycle wellbeing. Our base case indicaes ha workers given he chance o receive heir delayed reiremen credi as a lump sum paymen would boos heir average reiremen age by l.5-2 years. This will ineres policymakers seeking o reform he Social Securiy sysem wihou raising coss or cuing benefis, while enhancing he incenives o delay reiremen. Auhors Acknowledgemens The research repored herein was performed pursuan o a gran from he Social Securiy Adminisraion (SSA) o he Michigan Reiremen Research Cener (MRRC) as par of he Reiremen Research Consorium. Addiional research suppor was provided by he Deusche Forschungsgemeinschaf (DFG), he Gennan Invesmen and Asse Managemen Associaion (BYI), he Pension Research Council a The Wharon School of he Universiy of Pennsylvania, and he Mezler Exchange Professor program. Opinions and errors are solely hose of he aul10rs and no of he insiuions wih whom he auhors are affiliaed Chai, Maurer, Michell, and Rogalla. All righs reserved.

5 Exchanging Delayed Social Securiy Benefis for Lump Sums: Could This Incenivize Longer Work Careers? Jingjing Chai, Raimond Maurer, Olivia S. Michell, and Ralph Rogalla Deciding when o reire and claim Social Securiy benefis is one of he mos imporan financial decisions ha people make. Tradiionally, claiming riggers he beginning of a lifelong annuiy paymen. Ye if workers who delayed claiming were offered a lump sum insead of an acuarially-adjused deferred annuiy, i is possible ha a leas some would decide o work longer. This paper models he facors ha influence wheher individuals would be willing o rade off delayed Social Securiy benefis in exchange for a lump sum. Addiionally, we examine he consequences of providing a lump sum reward in lieu of an acuarially-adjused annuiy for work, reiremen, and life cycle well-being. Economic heory suggess ha reirees value lifelong income benefi sreams ha proec hem from running ou of money in old age (Yaari, 1965; Davidoff e al., 2005; Michell e al., 1999). An implicaion of he heory is ha mos risk-averse individuals would be expeced o hold a subsanial porion of heir porfolios in annuiized asses. Neverheless, empirical evidence suggess ha many people value lump sum payous over lifelong benefi sreams (Brown e al., 2008; Warner and Pleeer, 2001). We explore hese key oucomes by developing and implemening a realisically-calibraed life cycle model for forward looking raional agens wih endogenous labor supply, saving, invesmen, and reiremen decisions, ha allows for imevarying invesmen opporuniy ses and risky labor income. The goal of his research is o evaluae wheher his poenial approach o Social Securiy reform would induce workers o reire laer on a volunary basis. We find ha such a policy has he poenial o increase reiremen ages subsanially, wih lile or no decline in welfare. Three 1

6 facors help explain why he lump sum reward for deferred reiremen can induce more work while no decreasing lifeime uiliy. Firs, many people would prefer o have a lump sum raher han an addiion o heir lifeime Social Securiy benefi, as his affords hem flexibiliy over he iming of heir consumpion and leisure decisions. A second reason is liquidiy driven: ha is, if people desire o leave a sock of asses o heir heirs, having a lump sum enhances his possibiliy. And hird, financially sophisicaed individuals able o paricipae in he equiy marke will find aracive he opporuniy o inves some of heir lump sum amouns. Policymakers seeking ways o reform he Social Securiy sysem may be ineresed in our findings, since he acuarially fair lump sum for delayed reiremen does induce some individuals o work longer volunarily. In our base case, workers given he chance o receive heir delayed reiremen credi as a lump sum paymen would boos heir average reiremen age by years. Moreover, when he reform is implemened, his booss he probabiliy of working beyond he normal reiremen age from 29% o 86% for he young, and from 4% o 49% for 60-year olds. Resuls vary, of course, across individuals of differen ypes: he effec is even larger for less riskaverse older households, while he mos risk-averse respond leas. Financially unsophisicaed households (i.e., hose who lack access o he equiy marke) are also relaively unresponsive o he lump sum opion; even here, hough, he less risk-averse sill end o work longer and reire laer. Moreover, we show ha such a lump sum policy would generally no derac from wellbeing: in he base case, young workers ypically have virually no change in lifeime uiliy, whereas older individuals gain slighly. Among he less financially sophisicaed, boh he young and he old experience lile change. I is worh noing ha offering a lump sum equivalen in expeced presen value o he delayed reiremen credi would be cos-neural o he sysem, on average. Addiionally, if older 2

7 individuals worked longer volunarily, his could enhance sysem solvency via addiional payroll ax collecions. Prior Sudies This paper conribues o he research examining he effecs of Social Securiy policies on labor supply. 1 A number of sudies in he porfolio choice lieraure have invesigaed how individuals migh aler heir work, invesmen, annuiizaion, and reiremen decisions in response o change in Social Securiy benefis assuming a parameerizaion similar o ha in he US Social Securiy sysem. 2 Ye hese analyses have no examined opimal household life cycle behavior wih flexible work hours and reiremen, o assess wha migh happen if people were afforded he opporuniy o ake par of heir Social Securiy benefis as a lump sum insead of as a benefi flow. Experimenal research and survey evidence has suggesed ha a majoriy of workers would favor lump-sum paymens over lifeime benefis, if hese were approximaely acuarially equivalen. Furhermore, here is some modes price sensiiviy associaed wih his preference (Brown e al. 2008, 2011). Orszag (2001) discussed some imporan insiuional design aspecs of Social Securiy (e.g. compuaion of presen values, spousal/widow benefis) and offered commens on how lump sum benefis migh replace he delayed reiremen (annuiy) credi. His work provided some preliminary evidence ha claiming probabiliies could rise in response. Fehersonhaugh and Ross (1999) repored ha for 80 percen of heir survey respondens, a lump-sum paymen insead of an increase in annual benefi amouns due o delayed claiming 1 See Feldsein and Leibman (2002) for a review, and mos recenly, Lainer and Silverman (2012). 2 See Kolikoff and Viceira (2008), Chai, Horneff, Maurer, and Michell (2011), and Chai, Maurer, Michell, and Rogalla (2012). 3

8 would provide an incenive o claim laer. Neverheless, hose sudies focus specifically on he claiming decision (and how hese decisions are framed), bu hey absrac from oher imporan facors including preferences (risk aversion, leisure, impaience), he sae of he business cycle, uncerainy wih respec o labor income and capial markes, asse allocaion, household saving, and healh saus. Mos imporanly, hey assume ha he claiming decision is independen of labor force paricipaion. Therefore ha research is silen on he likely impac of such lump-sum opions on work hours, reiremen ages, saving, and household well-being. Moreover, offering such lump-sums could poenially induce workers o delay reiremen and claiming of Social Securiy benefis, which could enhance sysem susainabiliy. There has been no heoreical research on his opic o dae. Mehodology Our prior work on which we build his sudy developed, implemened, and calibraed a realisic discree ime life cycle model of endogenous work hours, reiremen behavior, consumpion, saving, and porfolio choice (c.f. Chai, Maurer, Michell, and Rogalla, 2012). Allowing for uninsurable labor income risk and capial marke risk, his model incorporaes individual risk aversion, ime preferences, and leisure preferences, as well as borrowing consrain, and uncerain lengh of life. Preferences in each period are characerized by an isoelasic and ime-separable power uiliy funcion defined over a composie good consising of consumpion C and leisure L a ime, and wealh Q bequeahed o he nex generaion. As is convenional in he heoreical lieraure, he relaive imporance of leisure and consumpion is valued using a modified Cobb-Douglas funcion, which ensures ha he elasiciy of subsiuion beween consumpion and leisure is equal o one. The value funcion is given by: 4

9 V = α 1 ( C L ) 1 ρ ρ + βe p V (1 p 1 ( Q + 1) ) b 1 ρ ρ (1) α 1 ρ 1 ρ C L Q V The parameer p T T denoes he 1 ρ 1 ρ wih erminal uiliy (a age 100) ( T T ) ( T + 1) = + βe b. subjecive probabiliy of surviving o ime + 1, given he consumer is alive a. The parameer ρ is he coefficien of relaive risk aversion, and β is he rae of ime preference. Leisure preferences are governed by he parameer α. The srengh of he beques moive is conrolled by he parameer b. In each period, he individual mus decide how much o work, consume, and inves in he capial marke. Also he worker mus decide when o reire and claim Social Securiy benefis. This problem is solved hrough backward inducion of he value funcion. The opimal policies are hen evaluaed by conducing a Mone Carlo simulaion (for furher deails see Appendix A). For he base case worker, preference parameers are se as follows: coefficien of relaive risk aversion ρ = 5, discoun facor β = 0.97, leisure preference value α = 1.3, and beques srengh b = 0. The one-period survival raes p are aken from he US 2000 populaion moraliy able for females. 3 In addiional sensiiviy analysis we vary preference parameers. The sock and labor marke processes are governed by a regime-swiching process for he business cycle. Asse reurns are characerized by eiher a normal capial marke (wih low volailiy/high expeced reurns) or a crisis scenario (wih high volailiy/low expeced reurns). The deerminisic componen of he wage rae process and he labor income shock process follows Chai, Maurer, Michell, and Rogalla (2012). Housing-relaed expendiures are esimaed using daa from he Consumer Expendiure Survey (as described in Appendix B). 3 Using a similar model framework; Chai, Horneff, Maurer, and Michell (2011) show ha hese parameer values replicae several empirical facs including he hump-shaped paern of work hours, he wo peaks in reiremen raes, and he sizeable decline in consumpion a reiremen. 5

10 We also implemen a realisic approach o deermining Social Securiy benefis, where he worker may claim a benefi beween he early reiremen age (ERA) of 62 and he lae reiremen age (LRA) of 70. If he worker claims prior o her normal reiremen age (NRA), she receives a permanenly lower benefi for life; if she claims laer, her Social Securiy benefi paymen is increased by he delayed reiremen credi. For our alernaive scenario, we examine how reiremen behavior would change if he individual could ake a par of her Social Securiy benefis as a lump sum paymen, by working beyond he NRA. This lump sum paymen would be equal, in presen value erms, o he addiional benefi sream paid o he worker claiming Social Securiy benefis afer he NRA. Several facors migh be anicipaed o lead people o favor a lump sum over an annuiy sream. For insance, people migh wish o leave a beques, have a higher or lower discoun rae, value leisure srongly, or be very risk-averse. Oher influences could include changes in he reiremen sysem such as a lower replacemen rae and a higher normal reiremen age. We also explore how financial sophisicaion migh shape peoples responses o he Social Securiy lump sum opion versus he annuiy. This akes ino accoun he finding ha many Americans lack knowledge of and easy access o sophisicaed financial insrumens such as equiies (Lusardi and Michell, 2007; Gomes and Michaelides, 2005). 4 Addiionally we provide a welfare analysis ha evaluaes he exen o which he abiliy o conver deferred Social Securiy benefis ino a lump sum can enhance worker well-being. In wha follows, we presen resuls for individuals iniially observed a age 20, and separaely a age 60. This allows us o explore he likely behavioral responses of older versus younger workers. We presen wo ses of resuls: in he base case, workers have access o he sock and he bond marke, which we deem he financially sophisicaed group. In an alernaive 4 Using a daase on Swedish invesors, Calve, Campbell, and Sodini (2009) find empirical evidence ha he share of risky asses held by households is srongly posiively correlaed wih an index for financial sophisicaion. 6

11 scenario, he analysis assumes ha individuals can hold only bonds paying a safe reurn, bu hey have no access o equiies. The model assumes ha 20-year olds hold no iniial wealh. For 60- year olds, we esimae disribuions of income and wealh-o-income raios using he Healh and Reiremen Sudy (HRS) for single female households. 5 To his end, we firs group all households iniially aged 60 ino wo caegories: sockholders and non-sockholders. Then, wihin each household caegory, we drop he lower and upper labor income quariles (o avoid daa ouliers). Hence, here are 50 labor income perceniles lef (i.e., he 25 h -74 h perceniles). 6 In order o specify disinc combinaions of wealh-o-income raios and labor income perceniles, we esimae average wealh-o-income raios for each of he 50 income perceniles. We hen simulae 10,000 life cycle pahs for every combinaion of wealh-o-income raios and income quaniles using opimal feedback conrols obained from he numerical opimizaion model. All resuls are repored as he average of 50,000 pahs (i.e., 50 10,000). Resuls Under he Social Securiy sysem s curren rules, a worker who delays claiming her benefi unil afer he Normal Reiremen Age (NRA) is eniled o a benefi increase of abou 8% per year ha reiremen is deferred. 7 In our model, under an acuarially fair lump-sum scheme, an individual who oped o work o age 66 insead of claiming benefis a age 65 would hen receive a lump sum worh of abou 1.2 imes her age-65 benefi, plus he age-65 benefi sream for life. 5 The HRS (here we use waves one o en) is a longiudinal panel sudy which surveys a represenaive sample of over 26,000 respondens age 50+ every wo years; see hp://hrsonline.isr.umich.edu/. 6 This procedure generaes wealh-o-income-raios for sockholders (non-sockholders) wih a mean value of 3.76 (1.31), and a sandard-deviaion of 1.7 (0.75). 7 The Social Securiy delayed reiremen credi of 8% per year s delay was inended o be acuarially fair a he ime he law was passed; his was consisen wih average moraliy ables a he ime, as well as a 2.9% real assumed ineres rae. In his paper we assume a real ineres rae of 2%, a rae more consisen wih he curren low ineres rae regime. As Shoven and Slavov (2012) noe, in such a case he delayed reiremen credi of 8% per annum will be beer han acuarially fair for mos people, hus embodying addiional incenives o defer reiremen. To he exen his is rue, he lump sums we compue are also beer han acuarially fair wih respec o he 2.9% assumpion. 7

12 Similarly, an individual deferring reiremen even laer, o age 70, would receive a lump sum worh abou 6 imes he saring-age annual benefi paymen, plus he age-65 benefi sream for life (see Appendix A for deails). Resuls for he Base Case To illusrae how our life cycle model works, we refer o he base case resuls in Figure 1. Average consumpion increases wih age in he op panel, since workers are no able o borrow agains fuure labor income. Consisen wih empirical evidence, 8 consumpion drops sharply around he reiremen age and coninues o decrease hereafer. The model also generaes a relaively realisic work hours profile by age, as repored in he second panel. Younger workers in heir 20 s and 30 s work more han 40 hours per week. Individuals in heir 40 s (50 s) devoe abou 40 (35) hours per week o heir jobs; afer ha, hey sharply cu back on average work hours and sar o reire from full-ime employmen. 9 The hird panel repors asse allocaion paerns by age. For hose aged 20-30, he bond fracion is 60%, somewha higher han found in empirical work. Ye from heir 30 s onward, individuals hold abou 30-40% of heir wealh in bonds, and 60-70% in socks; hese raios are in line wih empirical evidence. 10 Overall, our life cycle model is able o generae consumpion, work, and invesmen paerns ha accord reasonably well wih empirical evidence. Figure 1 here Nex we examine how he wo differen delayed reiremen schemes affec resuls in he base case for individuals iniially age 20 (lef side of Figure 1) versus age 60 (righ side). Offering a lump sum Social Securiy insead of a larger benefi paymen for deferred reiremen changes life cycle consumpion, work hours, and invesmen paerns. For he younger group, 8 See Bernheim, Skinner and Weinberg (2001), Banks, Blundell, and Tanner (1998), Baisin, Brugiavini, and Weber (2009), and he discussion in Chai, Horneff, Maurer, and Michell (2011). 9 For more on his poin see Chai, Horneff, Maurer, and Michell (2011). 10 See for example Gomes and Michaelides (2005). 8

13 consumpion and work hours do no respond much unil hey reach heir 60 s. A ha poin, hose who will receive he lump sum can consume more and enjoy less leisure. This occurs because he lump sum can be spen as well as invesed, poenially earning a marke reurn ha permis more spending. Addiionally, his higher consumpion is raded off for less leisure a older ages (more work hours). Overall, asse allocaion under he wo scenarios is also quie similar, hough afer age 60, having he lump sum leads o a slighly higher equiy exposure and hence slighly lower bond fracion. Similarly, for hose age 60 when he lump sum is inroduced, consumpion and work hours increase, while bond holdings fall slighly. Addiional deail on reiremen paerns is provided in Table 1, where young people knowing hey will receive a lump sum for deferred reiremen shif raher markedly oward laer reiremen. In fac, he lef panel indicaes ha he average reiremen age rises by 1.8 years (from 64.5 o 66.3); he probabiliy of claiming benefis afer he NRA rises from 29% o 86%. Among hose already age 60 when he lump sum scenario is implemened (righ panel), he average reiremen age again rises, hough by a bi less, 1.4 years (from 63.5 o 64.9). While mos older workers do claim benefis by age 68, heir probabiliy of working beyond he NRA rises subsanially, from 4% o 49%. 11 Table 1 here Sensiiviy Analysis Thus far, resuls for he base case provide suppor for he conclusion ha providing a lump sum insead of an increased annuiy benefi for deferred reiremen under Social Securiy would induce people o work longer. Nex, in sensiiviy analyses presened in Table 2, we explore wha 11 Table 1 shows wo spikes in reiremen frequency, a ages 63 and 66 (for he group iniially age 20). These are slighly laer han he wo reiremen peaks a age 62 and 65 repored by Gusman and Seinmeier (2005). Ye ha sudy denoes people as reired if hey leave full-ime work, while we assume ha individuals claim reiremen benefis and move o full leisure a he same age. If we define reiremen as working less han 20 hours per week, his would shif reiremen raes earlier. 9

14 happens when key preference parameers are changed. In addiion, we analyze he impac of wo oher poenial changes in he Social Securiy rules, repored in Panel A. Finally, Panel B illusraes he policy impacs on households who do no access he equiy marke. Table 2 here Several alernaive calibraions for preference parameers are provided in Table 2, o be compared wih he average reiremen age resuls for he base case as well as he esimaed probabiliy of working beyond he normal reiremen age. Ineresingly, workers wih a moderae versus a srong beques moive (b = 2 or 5 in Panel A), compared o he base case wihou bequess, behave relaively similarly when given a lump sum insead of a delayed reiremen annuiy. Thus young workers seeking o leave a beques would defer reiremen by 1.9 years, on average, versus 1.8 if hey had no ineres in bequess; he older group would boos is reiremen age by 1.3 years versus 1.4 wih no beques moive. I is also worh noing ha he probabiliies of working beyond he NRA are comparable across he board. In sum, even when workers have a beques moive, he delayed reiremen impac of he reform is similar. Accordingly, providing a lump sum does no simply resul in wealh ransfers o one s heirs, consisen wih he raionale for Social Securiy as a naional social insurance scheme inended o suppor consumpion for he elderly. The nex six rows of Panel A in Table 2 illusrae how resuls change for lower/higher subjecive discoun raes, lower/higher risk aversion, and lower/higher levels of ases for leisure versus consumpion. Less paien younger and older workers (β = 0.96) will chose o reire earlier as compared o he base case, bu he lump sum reform sill induces more o work beyond he normal reiremen age, and on average reiremen ages rise. As discoun raes fall, hose who are more paien (β = 0.99) will work longer han in he base case, wih an average increase of over one year in he reiremen age; here oo, he lump sum induces laer reiremen. Turning nex 10

15 o differences by level of risk olerance, older workers who are no paricularly risk averse (ρ = 2) will reire a he same age as in he base case. Ye offering hem he lump sum insead of he delayed annuiy credi produces a much larger impac on reiremen ages: on average, he reiremen age rises by 3.3 years compared o 1.3 in he base case. A young household wih low risk aversion reires 1.8 years earlier on average han he base case household bu delays reiremen by a comparable 1.6 years in he lump sum regime. Early reiremen is also he norm for he exraordinarily risk averse (ρ = 8), under any of he circumsances depiced. This is because such individuals end o work very hard and save a grea deal a younger ages o proec agains shocks; hen, as hey approach heir 60 s, hey favor cerain leisure and early reiremen insead of worrying abou no being able o consume due o uncerain moraliy. Addiionally, offering hem a lump sum has hardly any effec on reiremen behavior. Nex we urn o wo alernaive formulaions for leisure preferences: one individual values consumpion much more highly (α = 0.7) han in he base case, and he oher values leisure more (α = 1.9). Here, he lump sum reform has virually no impac. Tha is, leisure lovers sill qui work early, and hose who srongly prefer consumpion sill reire laer since longer worklives generae more spendable income. The final wo rows of Panel A in Table 2 examine he impac of wo variaions on Social Securiy sysem parameers. No surprisingly, if he Social Securiy benefi replacemen rae were reduced from λ = 60% o 45%, reiremen ages rise subsanially. Those who have a lifeime o adjus, who are iniially age 20, work 2.7 years longer, and he older group works 3.3 more years. In boh insances he probabiliy of working over he NRA exceeds 90%. This resul obains regardless of wheher he delayed reiremen credi is replaced by he lump sum. In our second policy varian, we raise he NRA from 65 o 67 for hose iniially age 20. This again would raise he average reiremen age in he annuiy regime, bu moving o he lump sum scenario would 11

16 have hardly any addiional impac on reiremen behavior. If he aim is o raise reiremen ages, he las wo policies work in he same direcion as replacing he delayed reiremen credi wih a lump sum as described above. Ye cuing he replacemen rae and raising he NRA will be poliically unpopular, since hese represen benefi reducions; offering he lump sum does no represen a benefi cu bu a raher a change in he iming of benefi receip. To his poin, we have assumed ha consumers have access o he equiy marke if hey wish o allocae heir porfolios across risky and risk-free asses. Panel B illusraes resuls if consumers do no access he equiy marke. This migh be he case for people who are no financially savvy due o lack of ime, informaion, or he requisie guidance on how o buy sock. We call his group he financially unsophisicaed, consisen wih van Rooij, Lusardi and Alessie (2011) who show ha hose who lack financial lieracy do no inves in he sock marke. I is well known ha some 50% of households do no paricipae in he sock marke oday (SCF, 2012; Gomes and Michaelides, 2005); hence for his group, his second se of resuls could be relevan. Once again, we evaluae how reiremen ages would change if he lump sum were offered in lieu of he Social Securiy delayed benefi. The firs row indicaes ha, in he base case, boh he young and he old would reire laer han in Panel A. Bu giving workers a lump sum for deferred reiremen insead of an increased annuiy would be less effecive in inducing prolonged work a older ages. The second row of Panel B indicaes ha people who love risk (ρ = 2) worry less abou smoohing consumpion, so for hem he lump sum induces longer work and higher consumpion. By conras, for exremely risk averse younger individuals (ρ = 8), he reform has again he opposie incenive: hey reire earlier and have a much lower probabiliy of working beyond he 12

17 Normal Reiremen Age. This can be explained by he fac ha he financially unsophisicaed place a high value on he Social Securiy annuiy as i allows hem o smooh consumpion and also proecs agains longeviy risk. These individuals canno replicae he benefi sream by invesing he lump sum in he bond marke. Evidenly, boosing Americans level of financial lieracy would help srenghen he incenive effecs of a lump sum reform. Welfare Implicaions Finally we urn o an analysis of he welfare implicaions of replacing he delayed reiremen benefi wih a lump sum. The approach evaluaes how much addiional wealh (as a percen of firs-year labor earnings) he individual would need under he curren regime, o be as well off as under he lump sum regime. Accordingly, a posiive value implies he reform is welfare enhancing, while a negaive value implies he opposie. Table 3 repors he resuls for various parameerizaions of people iniially age 20 and age 60 when he reform is implemened. In he base case, he change in welfare for he young is miniscule (10 basis poins). For hose age 60 when he reform is implemened, he change in lifeime uiliy is valued slighly posiively, a 4%. Under alernaive preference seings, here is virually no impac on he young he welfare changes in all cases do no exceed -1%. Moreover, he young financially unsophisicaed also experience almos no change in uiliy, wih he excepion of he very risk averse, where lifeime welfare declines by 10% of he iniial labor income. Table 3 here Turning o he older group (iniially age 60), welfare impacs are all posiive bu relaively small (below 5%) in mos cases. One excepion is for he risk-lover (ρ = 2) who has access o he sock marke. Here, he consumer s welfare gains amoun o a subsanial 29%, because she can 13

18 rade off higher consumpion levels early in reiremen in exchange for lower consumpion laer (when moraliy risk increases). Moreover she has access o he equiy marke and can inves par (or all) of he lump sum. The welfare gain is much lower (18%) when he worker does no inves in he equiy marke. For wo groups of older individuals, welfare rises under he lump sum regime, bu here is lile impac on reiremen (see Table 2). Those wih lile ase for leisure (α = 0.7) appreciae he lump sum bu do no change work paerns as compared o he annuiy regime; his is because hey are already willing o work a long ime (up o age 70, in some cases) o finance heir high consumpion needs. Their lenghy worklives generae high lump sum paymens for he delayed reiremen credi, which in urn can be invesed in he sock marke and used o boos consumpion. The welfare gains of a lump sum paymen compared o higher annuiy benefis disappears for 60-year old work lovers (α = 0.7) wih no access o he sock marke. 12 The reiree wih a less generous replacemen raio (λ = 0.45) profis by receiving he delayed reiremen credi as a lump sum insead of a higher lifelong pension (welfare rises by 22.3%). Again, he reform has lile impac on work effor, because in boh cases he reiree is willing o work longer o compensae he lower replacemen rae. Raher he welfare improvemen resuls again from he possibiliy o inves he lump sum in he sock marke. 13 In general, he lump sum reform offers an incenive for people o rade off more consumpion for less leisure, by working longer and deferring reiremen. Overall, his reform has lile impac on he young, relaively speaking, and i slighly enhances welfare among he older populaion. Accordingly, such a reform could be an appealing alernaive o encourage longer worklives. 12 Such preferences for very long worklife may no be relevan for he broader populaion, bu hey would apply o enured universiy professors (Ashenfeler and Card, 2002). 13 For consumers lacking access o he sock marke, he welfare gain is posiive bu small (less han 2%). 14

19 Conclusions This paper has explored wheher people migh volunarily work longer if hey were offered a lump sum insead of a delayed reiremen annuiy under Social Securiy. We adop a realisically calibraed life cycle model wih forward looking raional agens wih endogenous labor supply, saving, invesmen, and reiremen decisions, and allowing for ime-varying invesmen opporuniy ses and risky labor income. This model generaes consumpion, work, and invesmen profiles, relaively consisen wih empirical evidence. We show heoreically ha subsiuing a lump sum for he delayed Social Securiy annuiy provides an incenive for many workers o volunarily defer reiremen, wih lile reducion in lifeime welfare. In oher words, giving workers a lump sum a heir delayed reiremen dae permis hem o adjus he iming of heir consumpion and leisure ime o adap heir preferences. People who receive heir delayed reiremen credi as a lump sum paymen should opimally boos heir average reiremen age by years. Having a lump sum in lieu of a higher lifeime Social Securiy benefi allows reirees o shif consumpion o he earlier phase of reiremen when moraliy risk is low. In addiion, he lump sum paymen permis households o paricipae in he sock marke, seeking o earn he risk premium. These resuls hold wheher or no workers have a posiive beques moive, implying ha he lump sum does no simply resul in wealh ransfers o heirs. Households wihou access o he equiy marke are less responsive o he lump sum opion, bu even here, he less risk-averse also work longer and reire laer, and he lump sum policy generally does no derac from well-being. In years o come, US policymakers will be acively seeking ways o reform Social Securiy o resore he sysem o solvency. Proposing cus in benefis ends o be quie poliically difficul. By conras, offering a fair lump sum in place of he delayed reiremen annuiy credi 15

20 may be more poliically aracive. By (volunarily) delaying heir reiremen dae due o he lump sum opion, workers would coninue o pay Social Securiy payroll axes for more years, which could help reurn he sysem o solvency via addiional payroll ax collecions. Moreover, such a policy could be designed o be cos-neural, albei in he real world one would also need o consider addiional issues including spouse and survivor benefis, changes in annuiy facors, sudden demands for liquidiy due o healh shocks, and oher facors. These are all avenues of fuure research. 16