Behavioral Effects of Social Security Policies on Benefit Claiming, Retirement and Saving

Transcription

1 Behavioral Effecs of Social Securiy Policies on Benefi Claiming, Reiremen and Saving Alan L. Gusman Darmouh College and Thomas L. Seinmeier Texas Tech Universiy Presened a he 14 h Annual Join Conference of he Reiremen Research Consorium Augus 2-3, 2012 Washingon, D.C. This research was suppored by gran Number UM12-04 from he U.S. Social Securiy Adminisraion (SSA) hrough he Michigan Reiremen Research Cener (MRRC) o he NBER. The findings and conclusions are solely hose of he auhors and do no represen he views of SSA, any agency of he Federal Governmen, MRRC, he NBER Reiremen Research Cener, or Boson College RRC.

2 Inroducion Social Securiy coninues o be under subsanial financial pressure (Social Securiy Adminisraion Trusees Repor, 2012). A number of policy changes have been suggesed o enhance solvency, bring liabiliies more in line wih revenue, and in he process, encourage a populaion ha is becoming increasingly long lived o delay reiremen. 1 In his paper we examine he likely effecs of hree such policy changes, increasing Social Securiy s early enilemen age, raising he full (normal) reiremen age, and eliminaing he payroll ax for hose over he full reiremen age. We also consider he sensiiviy of findings as o he effecs of hese policies o he feaures of he economeric model used o analyze heir impac. To undersand he effecs of hese policy changes, one mus have a model ha is capable of joinly explaining reiremen, saving and claiming behavior, and he disribuion of hese oucomes hroughou he populaion. Accordingly, we specify and esimae an enhanced version of a dynamic, sochasic, srucural model, where each of hese oucomes in endogenously deermined. Our esimaes, based on a sample of married households from he Healh and Reiremen Sudy, generae he key behavioral parameers required o simulae he full effecs of he proposed policy changes. Policy analyss have had rouble in explaining claiming behavior. In paricular, mos models, including an earlier version of our model, does no explain why, given oher aspecs of heir behavior, people claim heir Social Securiy benefis as early as hey do. The benefi adjusmens offered by he Social Securiy sysem o hose who delay claiming are sufficien for mos analyses o sugges ha claiming should be occurring a older ages han is found in he daa. Here we ake wo approaches o dealing wih his problem. Firs, we enhance he range of behavior analyzed by he model, including sochasic reurns o asses and reverse flows from saes of greaer o lesser reiremen in our specificaion. Second, we examine he sensiiviy of he model s predicions, and he policy simulaions, o oher dimensions of behavior ha migh explain early claiming. 1 For hese and oher policy suggesions, see Senae Commiee on Aging (2010) and Congressional Budge Office,

3 Our findings provide esimaes of he increase in age of reiremen in response o an increase in he early enilemen age, o an increase in he full reiremen age, and o eliminaion of he employee s share of he payroll ax for hose over he full reiremen age. We find ha hese policies do generae subsanial responses in reiremen. Mos imporanly, he prediced responses of reiremen o hese policy changes are no very sensiive o underlying differences in claiming behavior. More specifically, raising he early enilemen age o 64 will increase full ime work a age 62 and 63 by 11 o 13 percenage poins. Increasing he full reiremen age from 65 o 67 (for hose in he original HRS cohor) would increase full-ime work a age 64 by 1.5 o 2.5 percenage poins. Eliminaing he payroll ax for work afer full reiremen age would increase fullime work by 1.0 o 1.7 percenage poins beween he ages of 65 and 67. The prediced effecs of raising he early enilemen age and abolishing he employee s share of he payroll ax afer full reiremen age, he policy changes wih greaes effec on reiremen, are no affeced significanly by adjusmens inroduced ino he model o explain early claiming. The esimaed effec on reiremen of increasing he full reiremen age is more sensiive o which explanaion is aken o accoun for early claiming. Secion II provides some background informaion and discusses he relevan lieraure. Secion III considers he acuarial valuaion of he Social Securiy annuiy and how i affecs claiming behavior. A srucural model of reiremen, saving and claiming is developed in Secion IV. I is esimaed and is properies are examined hrough simulaion in Secion V. Secion VI explores modificaions of he model ha would explain he excessive claiming a younger ages. The effecs of he hree key policies, increasing he early enilemen and full reiremen ages, and abolishing he payroll ax for hose over he full reiremen age, are examined in Secion VII, while Secion VIII concludes. II. Background The Social Securiy sysem affecs a number of decisions made by older Americans owards he end of heir working careers. These include choices as o how long and how much o work, how much o save o finance consumpion afer reiremen, 2

4 and when o begin receiving Social Securiy benefis. Each of hese choices has characerisics ha are well documened in he daa. Unil he las couple of decades, he bes known feaure of he reiremen hazard was he spike a full reiremen age. In boh naional and inernaional daa, his spike was aribued o he failure of Social Securiy and pension plans o provide an acuarially fair adjusmen o delayed reiremen. In he U.S., changes in legislaion increased he delayed reiremen credi, abolished he earnings es afer full reiremen age, and raised incenives in pensions. These changes grealy reduced he spike in reiremens around he full reiremen age (Anderson, Gusman and Seinmeier, 1999; Gusman and Seinmeier, 2009). The key feaure of he reiremen hazard became he spike a age 62, a feaure ha is almos cerainly relaed o he Social Securiy early enilemen age. This spike has maerialized in spie of he fac ha delaying aking Social Securiy benefis beyond 62 is a leas acuarially fair for mos individuals and frequenly much beer han acuarially fair. Savings, and he wealh generaed by savings, are disribued quie heerogeneously in he populaion. Moreover, here is a wide variaion in wealh holdings even among individuals a similar poins in heir life cycles and wih similar earnings hisories. Available evidence suggess here is considerable dispersion of wealh even among hose wih he same level of lifeime income (Gusman and Seinmeier, 1999; Veni and Wise, 2001). Evidence from he HRS also shows ha here is a disressing number of age 50+ households wih essenially no reiremen savings. Among hose wih no saving ouside of Social Securiy, many have had subsanial earnings in he pas. Models have no rouble generaing a wide dispersion of wealh, bu much of he ime ha dispersion arises because of he wide dispersion in income. Generaing he dispersion of wealh for individuals wih similar earnings hisories is a difficul proposiion. Regarding Social Securiy claiming, i has been difficul o explain why so many individuals seem o wan o claim benefis as soon as possible even hough i appears ha i would be acuarially advanageous for hem o wai. To be sure, many individuals delay claiming because hey are sill working and would no be able o collec benefis much if 3

5 a all due o he earnings es. Among hose who are no working, however, many appear o claim benefis as soon as hey can, alhough a minoriy delays claiming even hough hey could receive benefis. I has been even more challenging o consruc models ha capure he spike in claiming a age 62 while also accouning for he oher relaed oucomes observable in he daa. For he reiremen spike a early enilemen age, models ha rely on he incremenal increase in he presen value of benefis, he so-called delas, fail because Social Securiy does no impose acuarial penalies a age 62 and he delas are zero. Srucural life cycle models wih low esimaes of ime preference have he same problem; hey canno accoun for he spike in reiremens a he early enilemen age. Bu wih high esimaes of ime preference, he model underesimaes wealh. A number of sudies explore he effecs of acuarial incenives on benefi claiming and/or reiremen. Some sudies simply documen he budge consrain. These sudies find ha he reward srucure is likely o encourage delayed claiming of Social Securiy benefis, especially in he year or wo following eligibiliy for early enilemen. 2 Oher sudies have analyzed he relaion of reiremen oucomes o he acuarial penalies in he law, and simulaed he effecs of Social Securiy reforms ha increased acuarial fairness afer he full reiremen age. (See Lumsdaine and Michell, 1999, for a survey of early conribuions.) Models of benefi claiming, however, have had he greaes difficuly in rying o explain he heavy early claiming of benefis despie acuarial incenives encouraging posponemen of benefi receip beyond he early enilemen age. The greaes underpredicion is for hose who reire before age 62 (Coile e al, 2002). 3 Sudies have also ried o relae changes in claiming oucomes o changes in policy. Typically 2 For example, i has been known for some ime ha a a 3 percen real ineres rae, posponing benefi receip resuls in increases in fuure benefis ha are, for many individuals, beer han acuarially fair (Gordon and Blinder, 1980; Feldsein and Samwick, 1992). Shoven and Slavov (2012a) explore he acuarial advanages o posponing benefi claiming in he curren economic environmen, characerized by low inflaion and low ineres raes. 3 In Shoven and Slavov (2012b), claiming is a dependen variable, while reiremen and wealh, joinly deermined oucomes, are reaed as explanaory variables. 4

6 hese sudies rely on difference-in-difference analysis, comparing oucomes beween members of differen cohors. 4 In he pas several years we have developed a series of models whose main purpose is o joinly explain wo of he hree key oucomes, he age 62 reiremen spike and he dispersion of wealh among households wih similar earnings hisories (E.g., see Gusman and Seinmeier, 2005.) These models esimae he exen of unobserved heerogeneiy in ime preference raes, which manifes hemselves in he dispersion of wealh households have relaive o heir previous earnings hisory. Households wih high ime preference raes also end o value fuure Social Securiy benefis less han acuarial calculaions would sugges. For hem, he earnings es sars o look more like a ax on earnings afer he early enilemen age, and his may induce hem o reire a ha poin. 5 We previously used one of hese models (Gusman and Seinmeier, 2004) o examine he issue of Social Securiy claiming. A ha ime, he model assumed a fixed, relaively low ineres rae, and reiremen was an irreversible decision. In ha model, he prediced claiming behavior seemed o be less han he observed behavior, wih he predicion error being greaes a ages prior o he normal reiremen age. Since ha ime we have inroduced sochasic reurns o asses and he possibiliy of reenering he labor force ino he model, bu in he conex of an assumpion ha individuals always claim benefis as soon as possible. I seems worhwhile now o reinroduce endogenous claiming ino he model and o deermine wheher hese modificaions improve he resuls regarding claiming behavior. Sochasic reurns o asses can cu wo ways in his exercise. The mean rae of reurn is aken o be deermined by a porfolio wih half socks and half bonds. This reurn is higher han he reurn on fixed asses we used in our previous work, which was 4 For example, Song and Mancheser (2007) provide shor run esimaes of he response of benefi claiming o he combined effecs of increasing he full reiremen age and abolishing he earnings es. 5 A relaed lieraure explores he effecs of he earnings es on reiremen (e.g., Burless and Moffi, 1984; Disney and Smih, 2002; Friedberg, 2000; Gusman and Seinmeier, 1985 and 2004; and Song, 2002). 5

7 aken as being equal o he rae used in he Social Securiy acuary s calculaions. A higher reurn should raise he value of claiming early relaive o waiing. On he oher hand, he variance of he reurn makes he higher mean reurn somewha less aracive, working in he oher direcion. This las effec would be somewha miigaed by he possibiliy of reurning o work, since he income loss from bad draws from he disribuion of reurns on asses could be offse o some degree by reurning o work. In sum, our goal is o isolae he effecs of Social Securiy incenives on claiming behavior, especially a and around he early enilemen age. We hope o make progress in he conex of a model in which reiremen and saving are reaed as joinly deermined oucomes. III. Annuiies. The cenral feaure in he claiming decision is he radeoff beween a presen lump sum and a fuure annuiy. In his ligh, i will be helpful o spend a few paragraphs looking a how individuals value annuiies such as Social Securiy. 6 The value of an annuiy o an individual can be broken down ino wo pars. Firs, here is he quesion as o he acuarial fairness of he annuiy. Tha is, how does he presen financial value of he sream of annuiy paymens, discouned a an appropriae ineres rae, compare o he cos of he annuiy? Second, here is he quesion as o how he individual values he sream of annuiy paymens relaive o is presen financial value. In oher words, how much would he individual be willing o pay currenly o receive he annuiy, and how does his compare o he cos of an acuarially fair annuiy? For purposes of analyzing claiming behavior, we are ineresed in he characerisics of a marginal annuiy. Social Securiy and possible defined benefi pensions already provide a base level annuiy, and he resul of a delay in claiming adds a marginal amoun o his annuiy. The acuarial value of he Social Securiy annuiy has been exensively documened, so he discussion here will be brief. The general conclusion is ha while he 6 For discussions of he demand for he Social Securiy annuiy, see Brown, Casey and Michell (2007). 6

8 benefis of delaying claiming are roughly acuarially neural for single individuals, a leas unil hey reach heir mid-60 s, here is a srong acuarial advanage for he higher earner of a wo earner couple o delay claiming benefis. When he individuals are 62, hey are eligible for 80 percen of heir full benefis, assuming a normal reiremen age of 65 (which is appropriae for much of he HRS sample). If hey wai unil age 63, hey are eligible for 86.7 percen of heir full benefis, which is an 8.3 percen increase. This increase will apply over heir own lifeimes, and a subsanial par will also apply over he lifeime of heir surviving spouses. Table 1 gives he acuarial raes for delaying claiming for several circumsances. 7 The firs column perains o he higher earner of a couple, where he spouse is wo years younger, wih a real ineres rae of 2%. The firs enry indicaes ha a age 62, for every dollar of benefis los because he individual delays claiming, he presen value of he increased laer benefis will be $1.67. Tha is, by claiming a age 62, he individual gives up fuure benefis ha would have an acuarial value ha is 67% higher. This acuarial advanage declines as he individual delays furher, bu even a age 69 he radeoff of presen benefis for fuure benefis is approximaely acuarially fair. As shown in he second column, he advanage declines for a real ineres rae of 4%, bu is sill more han acuarially fair for ages prior o he full reiremen age. The las column looks a a single individual, and i would also apply o he perceived acuarial calculaions for a married individual who gave no weigh o he uiliy of a surviving spouse. These figures indicae ha he fuure increases are roughly acuarially fair unil he normal reiremen age and decline sharply during he lae 60 s. The oher par of he annuiy quesion is how much individuals would be willing o pay for an acuarially fair annuiy. This can be invesigaed wih he aid of a very simple consumpion model. Le oal uiliy be given by U = 1 ( ) s 1+ ρ u(c ) 7 For a recen relaed analysis of he acuarial advanage o delayed claiming and references o he previous lieraure, see Shoven and Slavov (2012b). 7

9 Where s is he survival rae unil ime and ρ is he discoun rae. Non-annuiized asses sar a some level a 0 and evolve according o he sandard formula a + 1 = (1+ r)a + b c, a +1 0 where r is he real ineres rae and b is he level of annuiies from Social Securiy and possibly defined benefi pensions. As long as non-annuiized asses are posiive, he firs order condiions yield 1+ ρ ( ) u (c ) 1 u (c ) = c 0 c s 1+ r Evenually a advanced ages, s sars o fall rapidly, causing u c (c ) o rise and consumpion o fall. The fall in consumpion while non-annuiized asses are posiive indicaes a wopar soluion. In he firs par, consumpion sars a some level c 0 and evolves according o he firs order condiion as long as non-annuiized asses are posiive. A some poin he level of consumpion implied by he firs order condiion falls below he level of he annuiy b. A ha poin, asses reach zero and consumpion hen follows b. Two exreme cases are ha he individual sars ou wih almos no asses and ha he individual sars ou wih so many asses ha hey never reach zero. In he firs case, he value of an s addiional $1 of annuiy is (1 + ρ) he cos of an acuarially fair annuiy is s (1 + r), and he raio of value o cos is s (1 + ρ) s (1 + r). In he second case, 1 he value is (1 + r), he cos is he same, and he raio of value o cos is 1 (1 + r) s (1 + r). In he inermediae case, where asses are depleed a ime B, he raio of he value o cos is given by 8

10 B 1 1 (1 + r) 1 + (1 + r) B = 0 = B D s s B 1 (1 + ρ) B D = 0 s (1 + r) where D is he maximum age of survival. This reduces o he firs expression when B = 0 and o he second expression when B = D. Tabulaions of he raio of annuiy value o cos for several scenarios are given in Table 2. For insance, he value of 1.38 in he firs row indicaes ha an individual currenly aged 62 whose asses will run ou a age 80 along he opimal consumpion pah would be willing o pay 38 percen more han he cos of an acually fair annuiy if he real ineres rae were 2% and he individual s discoun rae was 0. There are several hings o noe abou his able. If he individual s discoun rae is relaively low, he or she is likely o have accumulaed subsanial asses by reiremen, and because of he low discoun rae hese asses are likely o las very lae ino he life cycle. Therefore, for individuals wih a low discoun rae, he columns on he righ side of he able are mos likely o be relevan. These columns sugges ha annuiies are likely o be of considerable value o hese individuals. No only do hese individuals give relaively more weigh o laer years, bu he acuarially fair cos of providing he annuiy in hose years is relaively low. Recall also ha his value is on op of any acuarial advanage of Social Securiy delay, so for low discoun married individuals wih earnings higher han heir spouses, he value of he increased fuure benefis may well be double he value of he curren benefis foregone by delaying claiming. Individuals wih high discoun raes, on he oher hand, are unlikely o have amassed much in he way of asses by he ime of reiremen, and heir high preference for curren consumpion means ha whaever asses hey do have will no las for long. This means ha for individuals wih high discoun raes, he columns on he lef of he able are more likely o be relevan. As indicaed in he hird group of figures in he able, an individual wih few asses and a relaively high discoun rae (0.04) may find ha he value of he marginal annuiy is acually less han he acuarially fair cos of ha annuiy. In he limi, an individual wih a very high discoun rae and almos no asses may find ha he value of he marginal annuiy arising from delaying claiming would be almos 9

11 zero, in which case anyhing ha causes a delay in claiming (such as he earnings es) would ac effecively like a ax. The las hree rows of he able indicae ha increasing he ineres rae has differen effecs on differen groups of people. Compare hese rows wih he second group of hree rows, which have he same discoun rae bu a lower ineres rae. For individuals wih a lo of asses whose asses will las unil a relaively old age, an increased ineres rae will make he marginal annuiy less aracive. The reason appears o be ha he increased ineres rae downplays he laer years, when he annuiy is mos valuable relaive o is cos. On he oher hand, for individuals wih few asses who will deplee hose asses relaively quickly, he higher ineres rae makes he annuiy more valuable relaive o is cos. This appears o be because he higher ineres rae reduces he cos of he annuiy, whereas he value of he annuiy for hese individuals is governed more by he discoun rae, which has no changed. The ineres rae hus has an ambiguous effec on he value of an annuiy relaive o is cos, even among individuals wih he same discoun rae. In summary, he relaionship beween he amoun ha individuals would be willing o pay for he annuiy provided by delaying claiming and he amoun given up by foregoing curren benefis varies over a wide range. The higher earning individual in a couple wih subsanial asses and a low discoun rae will find delaying exremely advanageous, while a single individual over he normal reiremen age wih few asses and a high discoun rae may find i exremely disadvanageous o delay claiming. The commonly expressed feeling ha individuals wih relaively few asses should appreciae he opporuniy o insure hemselves agains living oo long is erroneous, especially if he cause of he low level of asses is ha he individuals have relaively high discoun raes. The opposie view, ha individuals wih low asse levels are likely o regard hemselves as over-annuiized and are willing o rade a leas some of heir fuure annuiy for an acuarially equivalen presen lump sum, is ofenimes more nearly correc. IV. The Srucural Model. 10

12 We now urn o he complee srucural model ha will be esimaed and simulaed in his paper. The core of he model is an expeced uiliy funcion D 3 1 = = EU = u(c0, L0) + sm, u(c, L ) ρ m 1 Where C is consumpion, L is leisure, m is an index ha indicaes he survival sae of he household, and s m, is he probabiliy ha he household survives o ime in sae m. The hree saes are ha boh spouses have survived, only he husband has survived, and only he wife has survived. Due o compuaional limiaions arising from he addiion of claiming variables ino he model, he wife s labor supply is aken as exogenous, so ha he leisure variable in he uiliy funcion is he husband s leisure. The wihin period uiliy funcion is given by 1 α α β0 + β a Age + β h Healh + ε u(c, L ) = C + e The coefficien in fron of he leisure erm indicaes he relaive weigh of leisure in he uiliy funcion. In his formulaion, leisure gradually ges more valuable relaive o work due o physical and menal exhausion, and a bou of bad healh adds o his relaive preference for leisure. The ε erm is an individual effec ha varies from individual o individual and reflecs ha individual s relaive preference for leisure. Consumpion and leisure are chosen o maximize expeced uiliy subjec o he budge consrain A + 1 = (1 + r ) A + E(L ) + S + P + O C, A+ 1 where E is earnings, S is Social Securiy benefis, P is pension benefis, and O is oher income. The reurn on asses r is aken o be sochasic and uncorrelaed over ime. Earnings depend on he amoun of leisure, and he wage rae may vary depending on he amoun of work he individual chooses. Social Securiy and pension benefis are he acual amouns paid in a year, and no a measure of accruals. As such, for insance, S is zero before he Social Securiy early enilemen age, and P is zero before he individual has reired from he job generaing he pension. The model is esimaed for a sample of married households in he original cohor of he Healh and Reiremen Sudy (HRS). The original HRS included individuals aged 11 L γ 0

13 51 o 61 in 1992 and surveyed hose individuals every wo years saring in In addiion o a large number of economic and labor force variables, he HRS has wo supplemens ha are useful for his sudy. The firs is he earnings records from he Social Securiy Adminisraion, and he second is he pension plan descripions from he providers of he pensions held by he respondens. These wo allow for much more precise measuremen of he economic incenives faced by he households. The wo main requiremens for a household o be included in our sample are ha he husband mus have been full-ime in he labor force mos years before age 50 wih a leas some indicaion of his wage eiher from he Social Securiy earnings records or self repors, and if he had a defined benefi pension in his curren job a he ime he survey sars, or he las job held before he sar of he survey, he pension mus be included in he pension provider survey. The laer exclusion arises because if an individual had a pension bu he deails of he pension are no available from he provider survey, i is very unlikely ha he incenives ha he individual faced o reire a paricular ages will be correcly refleced in he budge consrain. In he model, leisure is resriced o hree values: 0 for full ime work, ½ for parial reiremen work, and 1 for full reiremen. In he earnings funcion E, he wages may differ according o he amoun of work. For full-ime work before reiremen, wages for years no direcly observed are impued using coefficiens for experience and enure from a fixed effecs wage regression. Unobserved parial reiremen wages are inferred from a regression of observed parial reiremen wages on full-ime wages and oher variables. Wages for full-ime jobs which individuals have aken afer a period of eiher full or parial reiremen are inferred by reseing he enure variable o zero. The Social Securiy benefi amoun, which is cenral o he issues invesigaed in his paper, is aken o be deermined by hree sae variables in he model. The firs of hese is he level of he primary insurance amoun (PIA) of he husband, which is deermined by he age a which he husband leaves full-ime work iniially. The presumpion is ha parial reiremen jobs, which end o have lower wages han full-ime work, will no significanly impac he PIA. The oher wo sae variables are he adjusmen amouns for boh he husband and wife, reflecing boh any early reiremen 12

14 penalies and delayed reiremen credis. If he individual has he maximum adjusmen amoun relaive o his or her age, his indicaes ha he individual has no claimed any previous benefis, and ha individual may delay claiming furher if ha is he opimal sraegy. Once benefis are claimed, he adjusmen amoun may be recalculaed if he individual is subjec o he earnings es and loses benefis in a paricular year. The PIA of he wife eners implicily as an exogenous variable, since i is deermined by he exogenous work hisory of he wife. The pension benefi variable akes on a differen form depending on wheher he pension is defined benefi or defined conribuion. In boh cases, he pension benefi variable is zero before he individual reires from he pension job. In a defined benefi pension, he amoun of he benefi is fixed a he ime he individual leaves he job by applying he applicable formula from he pension provider documens o he earnings hisory and enure ha he individual had compiled in ha job. For defined conribuion pensions, a sae variable is creaed o reflec he balance in he defined conribuion accoun. Year by year, conribuions are made o he plan, and he accumulaed balance is augmened by he same rae of reurn ha is applied o he non-pension asses. The enire balance is presumed o be made available o he individual in he year following he las year in he job. A ha ime, he balance of he defined conribuion plan is effecively added o he non-pension asses. The oher income variable is primarily composed in mos cases of he earnings of he wife. I also includes any pension amouns due o he wife, calculaed on he same basis as he pension benefis due o he husband. A final inclusion in some cases is any inheriances ha he household receives. The model conains hree imporan elemens of preference heerogeneiy. The mos imporan of hese is he discoun rae reflecing ime preference. This is reaed as a fixed effec whose value for every household is calculaed as he value for which he asse amoun calculaed by he model maches he observed level of asses in he iniial year of he survey. As suggesed by he resuls of he previous secion, variaions in he discoun rae may play an imporan role in he differing responses of households o opporuniies o gain addiional annuiy amouns by delaying he claiming of Social 13

15 Securiy benefis. The second elemen of heerogeneiy is he iniial value of he leisure preference parameer ε. This value is presumed o be aken from a disribuion wih mean 0 and sandard deviaion σ ε. The hird elemen of heerogeneiy relaes o he relaive desire for parial reiremen. Recall ha leisure has he hree values 0, ½, and 1. For hese values of L, L γ has he hree values 0, (½) γ, and 1. Thus, γ effecively deermines he uiliy of parial reiremen. For he marginal uiliy of leisure o be declining, γ mus be beween 0 and 1, and (½) γ mus be beween ½ and 1. If (½) γ is closer o ½, he value of leisure will be proporional o he amoun of leisure, and individuals will end o choose eiher full reiremen or full-ime work depending on wheher he value of leisure exceeds he wage or no. If (½) γ is closer o 1, hen parial reiremen leisure is almos as valuable as he leisure in full reiremen, and he individual is more likely o go hrough a period of parial reiremen. This model supposes ha x = (½) γ is drawn from an exponenial disribuion f(x) = g(δ)e δx runcaed below ½ and above 1, where g(δ) is a erm of proporionaliy o make f(x) inegrae o 1 beween ½ and 1. The value of δ changes over ime according o δ = δ 0 + δ 1 Age o reflec ha parial reiremen may become more desirable over ime as he individual grows older. As he value of δ changes over ime, however, we assume ha he individual s relaive posiion wihin he disribuion says he same. The principal sochasic elemen in he model is he rae of reurn on asses, which comes from a normal disribuion wih a mean and sandard deviaion reflecing he observed behavior of a porfolio of roughly half socks and half shor erm governmen bonds over an exended period of ime. A second sochasic elemen is ha afer he individual iniially reires, he value of ε may unexpecedly change, reflecing ha reiremen may be more or less enjoyable han anicipaed. This is accomplished by inroducing a correlaion parameer ρ ε which measures he correlaion of ε in adjacen periods afer he individual reires. There are eigh parameers in he complee model: α (he exponen of consumpion), β 0, β a, and β h (which affec he weigh of leisure in he uiliy funcion), 14

16 σ ε and ρ ε (which influence he variance of leisure preferences and how hey change over ime), and δ 0 and δ 1 (which deermine he disribuion of parial reiremen preferences). Sae variables in he model, which mediae how pas decisions and sochasic evens affec he presen decisions and how presen decisions will affec fuure circumsances, include he following: he level of asses; wheher or no he individual is sill in he career job; he level of defined conribuion balances if he individual has a defined conribuion pension; he primary insurance amoun; he Social Securiy adjusmen amouns for boh he husband and wife; he pension benefi if he individual had a defined pension; and he value of leisure relaive o consumpion. Given values for he parameers, a value of he discoun rae ρ is calculaed using he observed or expeced reiremen daes and esimaing a consumpion model for he resuling income. Previous research has shown ha his gives a good approximaion o he median value of ρ. This approach has he advanage ha i guaranees ha he disribuion of asses from he model approximaely maches he observed disribuion, condiional on lifeime wages and oher measures of economic opporuniies. Given his value of ρ, he model is solved by backwards inducion in he usual process for dynamic sochasic models. Esimaion is achieved using he mehod of simulaed momens echnique. This echnique chooses he parameer values o bes mach he momens generaed by he model o he corresponding momens observed in he daa. Since here are many more momens han here are parameers, he model will be unable o fi all of he momens perfecly, bu if he model is correcly specified here should no be any insances where he momens generaed by he model are wildly differen from he observed momens. The momens ha are used are he reiremen percenages for boh full and parial reiremen by age and by healh saus and lifeime income level, and he percenages of ime ha individuals reurn o work afer an iniial period of full or parial reiremen. Momens relaing o claiming behavior of he individuals in he sample are no used in he esimaion, for wo reasons. Firs, one of he objecives of his projec is o see how close one can come o generaing realisic claiming behavior as a resul of opimizing a 15

17 model buil around a reiremen decision. And secondly, here are really no parameers in he model which can subsanially influence claiming behavior in any case. V. Esimaes and Base Simulaions. The model is esimaed for he HRS sample previously described, wih he resuls for he parameers being given in Table 3. Wih he excepion of δ 1, all of he coefficiens are individually significanly differen from zero a any reasonable level of significance. For a mehod of momens esimaion, if he model is correcly specified, he q saisic is randomly disribued according o a χ 2 disribuion wih degrees of freedom equal o he number of momens used minus he number of parameers esimaed. The curren esimaes use 43 momens and he model has 8 parameers, so he χ 2 disribuion has 35 degrees of freedom. A χ 2 disribuion wih 35 degrees of freedom has a 5% significance value of 49.8 and a 10% significance value of 46.1, as compared o he 43.9 value calculaed for he esimaes. Since low values of χ 2 are consisen wih he model being correc, his resul does no rejec he hypohesis ha he model is correc. By hemselves, hough, he parameers of he model are somewha difficul o inerpre. Therefore, we urn o a comparison of he resuls of simulaions wih he model o observed disribuions. These simulaions use 10,000 replicaions per observaion, so here should no be much sampling variance in he simulaed resuls. The firs se of simulaions racks he proporion of married men in work and reiremen. Figure 1 depics he difference beween he percenage of full-ime workers a one age and he corresponding percenage one year laer. This migh be called he pseudo-reiremen percenage, because i is he ne resul of individuals newly reired from full-ime work and a smaller group who were previously reired bu reurned o fullime work. The mos noable feaure of his figure is he large spike a age 62. Over 15 percen of he married men in he sample reired a his age, and his spike is fairly well capured in he simulaions. I should be emphasized ha here is nohing in he uiliy funcion which would produce his resul; i is he response o he incenives in he budge consrain. I does no occur simply because some individuals have no savings, since hey could always swich o a parial reiremen job and have a leas some income. Raher, i 16

18 occurs because individuals wih fairly high discoun raes and relaively low savings ofen find ha he earnings es serves o reduce heir effecive compensaion a age 62. A second considerably lower spike occurs in he daa a age 65, bu in he simulaions his spike is no much more han a bump. I is likely ha his spike arises in he daa because of Medicare eligibiliy, which is no included in he model. Figure 2 shows he corresponding ransiions ino full reiremen. The spike a age 62 is no quie so large here, eiher in he daa or in he simulaion. A plausible explanaion for his is ha because of he earnings disregard for he earnings es, he earnings es does no bie parial reiremen earnings quie so much as i does full-ime earnings. In his figure, also noe ha he age 65 spike is mued as well. This probably occurs because fewer parial reiremen jobs have healh insurance han do full-ime jobs, so ha eligibiliy for Medicare is no quie so imporan. Figure 3 indicaes he percenage of husbands claiming Social Securiy benefis by age, relaive o he observed percenages. The simulaed percenages are subsanially below he observed amouns, especially a he ages before he full reiremen age. I had been hoped ha he sochasic addiions o his model, including sochasic reurns o asses and he possibiliy ha some of he previous reired individuals reurn o work, would have increased he percenage of individuals claiming benefis in he simulaions, bu evidenly his is no he case. These resuls do reflec he common feeling of many who have examined his issue: ha claiming is higher han would be expeced, given he acuarial benefis of delaying claiming. (E.g., mos recenly, see Henriques, 2012.) The percenage of wives who claim benefis is subsanially higher, saring a 60 % a age 62 and rising o 90% by age 66. VI. Modificaions o he Model. There are several poenial explanaions as o why claiming in he model falls below he levels of claiming observed. In his secion, we will look a hree of hem, inroduce hem ino he model, and assess he degree o which hese explanaions can explain he relaively high levels of claiming. 17

19 The firs explanaion o be examined is ha individuals do no give full weigh o fuure Social Securiy benefis because hey quesion he solvency of he sysem and have some doubs wheher hey will acually receive he full benefis o which he presen rules enile hem. Figure 4 gives he resuls of a simulaion in which individuals assumed ha fuure Social Securiy benefis would be a fracion of he currenly legislaed benefis. The original simulaed resuls and observed resuls are repeaed from he previous figure, and he green line in he graph represens he new simulaion. In his simulaion, he β 0 parameer is adjused so ha he levels of reiremen remain a approximaely he same level as before. The simulaion srongly suggess ha he discrepancy beween he original simulaed resuls and he observed resuls can be accouned for if i is presumed ha individuals do no believe ha hey will receive heir legislaed benefis. The main problem is wih he magniude of he change required o achieve his effec: he simulaion supposes ha individuals believe ha beginning a age 70, hey will receive only 50 percen of heir legislaed benefis. This number would srike many people as low, paricularly for he HRS cohor whose reiremen occurred largely in he 1990 s. There is a second problem wih his explanaion. Over ime, i would seem ha doubs abou he fuure benefis would have increased as he projeced ime when he rus fund will be exhaused has crep ino he possible lifeimes of individuals currenly making claiming decisions. If a greaer likelihood of reducions in fuure benefis would cause individuals o be more likely o claim earlier so as o receive benefis before he reducions occur, he claiming rae should be increasing over ime. Bu his is no wha has been happening in recen years. A second explanaion of he underesimae of claiming by he curren model is ha individuals are more opimisic abou asse reurns han he model assumes. The mean reurn used in he model is he hisorical mean of he Ibboson series daing back o he 1926, bu individuals may be using a differen period wih a higher mean. The simulaion in Figure 5 uses a higher mean reurn han is used in he base simulaion. The resul of his simulaion almos overlays he observed daa. The main difficuly wih his simulaion is again wih he magniude: he mean rae of reurn is increased by 5 percenage poins over he hisorical series, a rae ha many migh regard as a bi high. 18

20 This explanaion, however, does have he advanage ha i is more or less consisen wih recen rends. The 1990 s, during which much of he reiremen of he original HRS cohor occurred, was a period of heady reurns. During ha ime, here was a lo of discussion abou he poor reurns of Social Securiy, and individuals were likely o claim as soon as possible in order o ake advanage of hose reurns. In he las dozen years, however, he picure has been much differen. Real reurns have been inching down ino negaive erriory, and he discussion abou he poor reurns o Social Securiy has largely ceased. The recen downurn in claiming would cerainly be consisen wih generally lower expecaions regarding he reurns o asses. The hird explanaion for why he model may underesimae claiming behavior has o do wih he assumpion in he model ha he husband provides equal weigh o his and his wife s uiliy, weighed only by he discoun rae and survival probabiliies. The experience wih pensions in pas decades cerainly gives some reason o suspec his assumpion. Before here were any regulaions, many if no mos husbands wih defined benefi pensions ook hose pensions as single life annuiies, even given a roughly acuarially fair opporuniy o conver hem o annuiies which would pay he wife in he case he died firs. The fac ha so many widows were lef desiue by his pracice led o regulaions which made i subsanially more difficul for a married person o ake a defined benefi pension as a single life annuiy. The same behavior may lead he husband o discoun he benefis o he wife afer his deah when making he claiming decision. Figure 6 shows he resuls of a simulaion wherein he husband does no give any weigh o he wife s survivor benefis afer he dies. Somewha surprisingly, he lack of concern for he wife s survivor benefis does no make a grea deal of difference in he claiming behavior in he simulaion, especially in he early years of eligibiliy for Social Securiy. To undersand his resul, recall ha he majoriy of survivor benefis will come only afer many years have passed. Any calculaion which gives much weigh o hese years will of necessiy have a fairly low discoun rae. Bu a low discoun raes, he value of he marginal Social Securiy annuiy relaive o is cos is probably fairly high, even if he wife s survivor benefis are ignored. Afer he normal reiremen age, his advanage sars o erode, and he simulaions predic claiming behavior closer o he observed 19

21 claiming behavior if he individual does no ake ino accoun he wife s survivor benefis. While all hree of hese explanaions have some weak poins, here is nohing which says ha hey are muually exclusive. I may be ha wo of hree of hem in combinaion would provide an adequae explanaion of he observed claiming behavior wihou invoking implausible assumpions. In he presen paper, we are no able o disinguish very well among hese explanaions, bu in he nex secion i is possible o ask wheher hese explanaions creae any differences in he resuls of poenial policy changes in which we migh be ineresed. VII. Policy Analysis. In his secion we explore he effecs of hree commonly proposed changes o he Social Securiy sysem in order o increase employmen and increase he solvency of he sysem. They are an increase in he early enilemen age, an increase in he normal reiremen age, and an eliminaion of he payroll ax afer an individual has reached he normal reiremen age. In each case, we will look a simulaions for he base case and also a simulaions which reflec he hree poenial explanaions for he underesimaion of claiming examined in he previous secion. Figure 7 looks a he resuls for he simulaions involving increasing he early enilemen age o 64. The base case and all hree modificaions of he model are in remarkable agreemen in his case: full-ime employmen will be lile affeced before age 62 or afer age 64, and a ages 62 and 63 full-ime employmen will increase by approximaely 12 percenage poins. Essenially, he spike in reiremen from full-ime work which presenly occurs a age 62 would be shifed o age 64 by his change. The solvency of he sysem will be increased by he exra wo years of payroll axes for he group ha delays, bu his mus be balanced agains he fac ha for mos of hese individuals, delaying benefis wih resul in more han acuarially fair adjusmens o laer benefis which will cos he sysem in he long run. Figure 8 examines he resuls for he simulaions involving increasing he normal reiremen age o 67, whereas i was age 65 for mos of he individuals in he sample. In 20

22 he figure, insolvency refers o he simulaion where individuals expec reduced fuure benefis due o solvency concerns abou he sysem, reurns refers o he simulaion wih he increased reurns on asses, and survivor refers o he simulaion wherein he husband discouns he benefis ha would be paid o his surviving spouse were he o die firs. These simulaions show somewha greaer variabiliy han he simulaions in Figure 7, bu in general hey show wo hings: he increases in full-ime work caused by increasing he normal reiremen age are subsanially less han he increases caused by raising he early enilemen age, and he impac of raising he normal reiremen age is generally posiive. The oulier appears o be he simulaion which reduces expecaions ha individuals will receive heir full legislaed benefis; he resuls of he oher hree simulaions are relaively much closer. In erms of relieving he Social Securiy shorfall, however, his is probably a much more effecive change han is raising only he early enilemen age. Whereas an increase in he early enilemen age mosly pospones benefis, an increase in he normal reiremen age wihou an offseing change in he full benefi serves effecively o reduce considerably he presen value of lifeime benefis. Figure 9 shows he resuls of simulaions for eliminaing he payroll ax afer he normal reiremen age. This simulaion shows he resul of eliminaing only ha par of he ax paid by he employee; if he employer s side of he ax were eliminaed and if ha saving were o be passed on o employees, one would expec he resuling magniudes o be roughly double he amouns shown. The simulaions also assume ha for ages for which he payroll axes are eliminaed, earnings for hose ages are no used in he PIA calculaions. These simulaions indicae a relaive agreemen beween he base simulaion and hose simulaions incorporaing he various explanaions for he claiming underesimaes in he base model. They all show a reducion in full-ime work of beween 0.5 and 1 percen beween age 60 and age 64 and an increase in full-ime work of beween 1 and 2 percen a age 65 and hereafer. Summed over all he ages, he ne resul seems o be an increase in full-ime effor, wih some shifing of work effor from he period when compensaion in unchanged o he period when effecive compensaion has increased. 21

23 VIII. Conclusion. This paper has examined he effecs of hree poenial policy changes: changes in he early enilemen age, in he normal reiremen age, and he eliminaion of he payroll ax for workers over he normal reiremen age. For wo of he changes, namely an increase in he early enilemen age and he eliminaion of he payroll ax, he model gives consisen answers regardless of which exension is used. There is more variaion in prediced effecs for an increase in he normal reiremen age, bu even here mos of he variaion is due o one of he exensions, namely he exension using a severe reducion in expeced fuure benefis. Of he hree poenial policy changes, an increase in he early enilemen age clearly has he mos impac on reiremen, alhough he increase in he normal reiremen age probably has he mos impac on he solvency of he sysem. Our esimaes reinforce he noion ha i is difficul o explain claiming behavior wih a sraighforward life cycle model, even one wih sochasic asse reurns and he possibiliy of reurning o work afer reiremen. However, several plausible exensions of he model exis ha permi i o beer mach simulaed claiming behavior wih observed behavior wihou much affecing oher posiive advanages of he model, including he abiliy o replicae he spike in reiremen a he early enilemen age. The exension ha bes appears o remedy he problem of underesimaing claiming and sill be consisen wih he reducion in claiming over he las few years is one in which individuals use shorer horizons in forming heir expecaions abou reurns o asses. Since expecaions regarding asse reurns have fallen considerably recenly, claiming relaively early is becoming less aracive agains he alernaive of waiing o claim benefis and having fuure Social Securiy paymens be larger. A recurring heme of our research is ha in designing policies, i is helpful o be cognizan of he heerogeneous populaion and ha policies may have differen impacs on differen pars of he populaion. For insance, an increase in he early enilemen age may have only limied effecs on hose wih low discoun raes who have a relaively higher level of asses relaive o earnings. They may well find ha i is advanageous o delay claiming anyway, since for hem he fuure benefi increases ouweigh he curren benefis foregone, and hey can live off heir asses in he meanime even if hey are 22

24 reired. For hose wih high discoun raes, he siuaion is much differen. They may no hink ha he fuure benefi increases are worh giving up he curren benefis, and wih few asses hey may be forced o work more han hey would find opimal. Of course, ha is he way hey feel during he period when he early enilemen is being delayed; en years laer, hey may feel glad ha hey are receiving higher benefis han hey would have received had hey been able o claim hose benefis earlier. Anoher example would be fuure medical expendiures. Financial planners have recenly been increasingly sounding he alarm abou poenial high ou-of-pocke expendiures for medical expenses in reiremen. Individuals wih low discoun raes may respond o high and variable poenial expendiures for medical expenses by increasing saving, working longer, and oher measures. Those wih higher discoun raes may no respond much a all o he prospec of higher medical expenses in wha is for hem he disan fuure. If hey do wind up wih subsanial medical expenses, hey will simply be forced o ighen heir bels and rely on whaever programs exis o keep hem ou of povery. The paper raises a number of quesions for fuure research. I invesigaed several explanaions why individuals migh wan o begin claiming Social Securiy benefis even hough acuarial and even uiliy calculaions migh sugges ha i would be advanageous o delay, and i is has noed a leas some recen evidence ha migh favor one of hese explanaions. Bu i would cerainly be helpful o have more evidence on his score. Also, he model emphasizes heerogeneiy in ime preference as an imporan aspec of modeling individuals behavior, and o a lesser degree heerogeneiy in leisure preferences. In he limi, wih preferences differing in unobservable ways, i is imporan o ry o ascerain wha unobserved dimensions of heerogeneiy are criical o answering he quesions a hand, and o ry o build hose dimensions of unobserved heerogeneiy ino he appropriae model. 23