How Fast Should the Social Security Retirement Age Rise? David M. Cutler, Jeffrey B. Liebman, and Seamus Smyth Harvard University and NBER

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1 How Fas Should he Social Securiy Reiremen Age Rise? David M. Culer, Jeffrey B. Liebman, and Seamus Smyh Harvard Universiy and NBER April 28, 2006 Absrac Many Social Securiy reform proposals recommend increasing he age a which people become eligible for Social Securiy reiremen benefis as a way o reduce fuure expendiures, mainain benefi adequacy in ligh of oher benefi cus, and increase labor supply. Bu he amoun by which he benefi eligibiliy age is increased in reform plans is rarely chosen based upon principals of opimal social insurance. In his paper we analyze he quesion of he opimal reiremen age using a model of opimal social insurance in which he reiremen age exiss because of a paernalisic concern ha some people will misakenly reire oo early if lef o make decisions on heir own. We paramerize he model using exising esimaes from he empirical lieraure coupled wih our own esimaes of how he disribuion of healh saus a each age has evolved in he U.S. over he pas four decades. This research was suppored by he U.S. Social Securiy Adminisraion hrough gran #10-P o he Naional Bureau of Economic Research as par of he SSA Reiremen Research Consorium. The findings and conclusions expressed are solely hose of he auhors and do no represen he views of SSA, any agency of he Federal Governmen, or he NBER. We hank Eric French for helpful commens on an earlier draf.

2 1. Inroducion Many Social Securiy reform proposals recommend increasing he age a which people become eligible for Social Securiy reiremen benefis as a way o reduce fuure expendiures, mainain benefi adequacy in ligh of oher benefi cus, and increase labor supply. For example he Personal Securiy Accouns (PSA) plan of he Advisory Council on Social Securiy would have raised he earlies eligibiliy age (EEA) from 62 o 65 by 2035 and he 1998 Naional Commission on Reiremen Policy (NCRP) plan would have raised he EEA o 65 by 2017 and hen o higher ages hereafer. The amoun by which he benefi eligibiliy age is increased in reform plans is rarely chosen based upon principals of opimal social insurance. Insead, proposals moivae hese changes as holding consan he number of years receiving benefis (he NCRP plan) or holding consan he raio of reiremen years o work years (he PSA plan). These ad hoc arges are unlikely o correspond o wha would be recommended by a model of opimal social insurance. 1 In his paper we analyze he quesion of he opimal reiremen age using a model of opimal social insurance. The foundaion of he model is he decision problem of a represenaive forward-looking consumer and, in paricular, he comparaive saics of how his consumer s choice of reiremen dae is affeced by rising produciviy, a longer lifespan, and lower disabiliy raes a each age. Rising produciviy will lead o reiremen a an earlier age if he income effec of higher wage levels ouweighs he subsiuion effec. Longer lifespans will increase he marginal uiliy of income, leading 1 Two scholarly reform proposals do apply logic similar o ha of his paper in discussing reform opions. Aaron and Reischauer (2001) recommend raising he EEA, bu noe ha he policy will creae winners and losers. Their proposal would keep he replacemen rae consan for workers who spend he same fracion of heir adul lives in reiremen as hose reaching age 62 in Diamond and Orszag (2004) do no recommend raising he EEA, arguing ha populaion heerogeneiy makes i difficul o judge wheher he benefis of doing so would ouweigh he coss. 1

3 o laer reiremen. Lower disabiliy raes will reduce he disuiliy of work and also lead o laer reiremen. The model hen exends his represenaive consumer analysis by inroducing heerogeneiy in wages, reiremen benefis, iniial period asses, and ime preferences, and by providing a raionale for he exisence of a Social Securiy reiremen age -- i.e. for why people are no simply permied o ap heir Social Securiy benefis a whaever age hey choose wih an appropriae acuarial adjusmen for early receip of benefis. In our model, he reiremen age exiss because of a paernalisic concern ha some people will misakenly reire oo early if lef o make decisions on heir own. The choice of an iniial age a which people can access reiremen benefis herefore involves balancing a desire o force myopic people o keep working agains he cos of no permiing people for whom i would be opimal o receive benefis before he reiremen age o do so. We parameerize our model using exising esimaes from he empirical lieraure coupled wih our own esimaes of how he disribuion of healh saus a each age has evolved in he U.S. over he pas four decades. When combined wih our model, hese esimaes allow us o make saemens abou how fas he reiremen age should have risen since 1962, assuming i was se opimally in ha iniial year. They also le us make saemens abou how fas he reiremen age should rise in he fuure if healh gains in coming decades are similar o wha we experienced in he pas. More generally, our healh esimaes allow us o make saemens such as 70 year old males oday are as healhy as 62 year olds were in This informaion is of use in hinking abou reiremen-age policy even in he absence of our specific modeling assumpions. 2

4 2. Background on he Social Securiy Reiremen Age The Social Securiy Ac of 1935 se age 65 as he age a which people could firs receive benefis. The 1889 German conribuory pension sysem and he 1908 Briish means-esed sysem had boh limied eligibiliy o people age 70 and above (Rodgers 1998). 2 In he U.S., however, he 1890 pension sysem for Union army veerans and many oher privae and public pension plans esablished in he early 20 h cenury se age 65 as he age for benefi enilemen (Cosa, 1998). Indeed, Wilbur Cohen a saff member of Roosevel s Commiee on Economic Securiy has wrien ha a no ime in 1934 or 1935 did Presiden Roosevel, he Commiee on Economic Securiy, or he key members of Congress handling he bill deem feasible or appropriae any age oher han 65 as he earlies eligible age for receip of old-age insurance benefis. 3 The age a which people could firs receive reiremen benefis, ermed he Early Eligibiliy Age or EEA, was reduced o 62 for female reirees beginning in Proponens of his change argued ha women were on average several years younger han heir husbands and deserved o be able o reire a he same ime (Meriam and Schloerbeck, 1950, p. 22). Older women were also seen as facing difficulies in he labor marke. Then, in February 1961, Presiden Kennedy proposed Social Securiy benefi expansions as par of his iniial economic package. These proposals were designed o address he weak employmen siuaion and included a recommendaion o 2 Germany reduced is reiremen age o 65 in However, his does no seem o have influenced he archiecs of he U.S. sysem. See hp:// 3 Cohen (1985), p

5 lower he EEA for men o he same level as for women. The EEA reducion for men was approved by Congress and wen ino effec in lae Over ime, a greaer fracion of workers have aken advanage of he opporuniy o claim benefis before age 65. In 1965, a few years afer men firs became eligible o claim a age 62, 16.6 percen of men claimed benefis a age 62, 17.0 percen claimed benefis a ages 63 or 64, and 66.5 percen claimed benefis a ages 65 or older. By 1975, 29.2 percen claimed benefis a 62, 26.1 percen a ages 63 or 64, and 44.7 percen a ages 65 or older. Today, 54 percen claim benefis a age 62, 22 percen a ages 63 or 64, and only 25 percen a ages 65 or above. 5 There are several oher Social Securiy policy parameers relaed o reiremen, including he full reiremen age -- he age a which one s benefis are no reduced for early reiremen -- and he acuarial adjusmen associaed wih reiremen a differen ages. 6 Beween 2000 and 2022, he full reiremen age is o rise from 65 o 67. Workers who choose o receive benefis before he full reiremen age have heir benefis reduced according o he acuarial adjusmen facor of 6.7 percen per year. 7 Workers who claim benefis afer he full reiremen age receive a delayed reiremen credi ha increases heir benefis by 8 percen per year. While hisorically here was a srong financial incenive o reire by age 65, for a worker reaching age 62 oday, hese parameers are 4 We noe ha by repeaedly alernaing hese wo reiremen age raionales, one could quickly converge on an EEA of zero. 5 Diamond and Orszag (2004). These numbers exclude people convering from disabiliy benefis o reiremen benefis a he full benefi age. There have been similar rends for females. 6 Though he age of full benefi enilemen is someimes referred o as he normal reiremen age (NRA), Henry Aaron has poined ou ha he erm normal reiremen age does no appear anywhere in he Social Securiy Ac or regulaions. Moreover, here is nohing normal abou i since wo-hirds of people claim benefis before ha age. Thus we join his crusade o eliminae his misleading erm from discussions of Social Securiy policy. 7 There is a slighly smaller adjusmen for people who reire more han 36 monhs before he full benefi age. 4

6 approximaely acuarially fair on average. 8 Oher provisions including he payroll ax rae, benefi calculaion formulae, and earnings es affec reiremen incenives as well. 9 I is worh emphasizing ha an increase in he full reiremen age represens a reducion in aggregae benefi paymens. In conras, raising he earlies eligibiliy age has approximaely no effec on sysem finances since he benefis received laer are increased o adjus for heir delayed receip by an amoun ha is roughly acuarially fair. 10 While a full assessmen of reiremen-age policy would analyze ax and benefi levels and he rae a which benefis rise wih age when claiming is delayed, our emphasis in his paper is on he age a which benefis availabiliy begins, and herefore our policy experimens correspond o changing he EEA while holding all oher parameers of he Social Securiy sysem consan. For ha reason, he changes we sudy keep expeced lifeime benefi levels consan Theory To analyze opimal reiremen age policy for Social Securiy, we need o combine a model of reiremen decisions by individuals wih a raionale for governmen provision of reiremen income. In his secion we firs describe he model of individual decision making and show some comparaive saics for how an individual's choice of a reiremen 8 Coile and Gruber (2001) show, however, ha here is subsanial heerogeneiy in incenives across individuals. 9 For people ages 65 and above, here is no necessary connecion beween benefi claiming and reiremen. For people beween 62 and 64 who coninue o work, benefis are reduced via an earnings es (hough he los benefis are repaid in he form of higher laer benefis). On he disincion beween benefi claiming and reiremen see Coile, Diamond, Gruber, and Jousen (2002). 10 In his discussion, we ignore impacs of changes in he early eligibiliy age on income ax revenues. 11 This saemen is only approximaely rue. Our analysis holds expeced lifeime benefis consan for each individual. An acual change in he EEA would hold expeced lifeime benefis consan for a cohor overall, bu if an individual s subjecive moraliy risk differed from he cohor average, here would be disribuional and incenive effecs of a change in he EEA ha are no capured in our model. 5

7 age varies wih produciviy growh, increases in longeviy, and improvemens in healh. Then we combine his model wih a raionale for Social Securiy ha hinges on worker myopia. The Individual s Reiremen Decision We model he reiremen decision as a binary, annual, irreversible, choice. A each age,, every person who is sill working faces a decision of wheher or no o keep working in ha year as well as a decision abou how much o consume. If he individual works he or she receives addiional income, w,. The reiremen and consumpion decisions are made o maximize expeced uiliy over he worker s remaining lifeime: V A max = max E l, c = curren age [ v( c ) e( h )] curren ( 1 + r) p age (1) Uiliy in each period is an addiively separable funcion of he uiliy of consumpion, v(c ), and he disuiliy of labor effor, e(h ). 12 Labor effor depends on healh saus, h, and is zero if a person does no work. The amoun of effor required o work rises as healh saus declines, so e (h )<0. p is he probabiliy ha an individual survives o age. r is he discoun rae. We assume ha he only sources of uncerainy are healh saus and age of deah. In paricular, he (age-varying) wage ha will be received by he worker in each year if he worker coninues o work is known in advance, as are reiremen benefis (which are assumed o vary wih he dae of reiremen in a way ha is known in advance). 12 Alhough we follow convenional pracice in assuming ha uiliy for each year is addiively separable, his assumpion is no innocuous. For example, here may be reasons oher han declining healh for why people bunch heir leisure a he end of heir lifeime. Some uses of leisure (raveling around he world, visiing grandchildren who live in anoher ciy) may require long coniguous blocks of leisure. In his case, he marginal value of leisure could depend on oal lifeime leisure raher han simply on leisure in he curren period. 6

8 I is useful o express he expeced fuure uiliy a ime as a funcion of hree sae variables: beginning of period asses and indicaors for wheher he person eners he period reired and in good healh: [ a I ( reired ), I ( healh )] V = V (2), The difference in expeced uiliy a a given age beween working and reiring is a resul of hree facors. Firs, by working a person obains exra income (including he afer-ax wage for ha year and addiional enilemen o pension and Social Securiy benefis) The exra income resuls in higher consumpion and herefore higher uiliy in he curren year and in all fuure years. The uiliy benefi of his exra income is he derivaive of he value funcion wih respec o wealh imes he incremenal income. a [ a 0, I ( healh ] w V, ) (3) Second, by coninuing o work a person mainains he opion of working in fuure. The uiliy benefi of he opion value is: [ a 0, I ( healh )] V [ a,1, I ( healh )] V (4) + 1, Third, he person incurs he disuiliy of effor for he curren year's labor, e(h ).. If he consumpion benefis and opion value ouweigh he disuiliy of effor, hen he individual will choose o work raher han reire. Figure 1 illusraes he hree componens of he individual s reiremen decision. Line AA shows he value of he addiional year of income, V a [ a 0, I ( healh )] w,. As reiremen is posponed o laer years, he value of an addiional year of income falls because lifeime income is higher and herefore he marginal uiliy of addiional 7

9 consumpion is lower. 13 Line CC adds he opion value of coninuing work o he value of addiional income and hus represens he oal benefis ha accrue from working an addiional year. Opion value is greaes a earlier ages and falls o zero a he age where he person is cerain o reire regardless of healh saus. Line BB represens he marginal disuiliy of effor, e(h ), which is assumed o rise wih age as healh deerioraes. 14 The individual chooses o reire a age R* -- where he CC and BB curves inersec. Consider now how he curves will shif over ime. We simplify by ignoring opion value which is likely o be small since many negaive healh shocks a older ages persis and because reiremen decisions are no, in fac, compleely irreversible. Produciviy increases raise wage levels, which resuls in offseing income and subsiuion effecs. A higher wage levels, [ a 0, I( healh )] Va, will be lower (he income effec), bu w will be higher (he subsiuion effec). Thus i is heoreically ambiguous wheher he marginal uiliy of income curve will shif lef or righ. The shif from line AA o line AA in Figure 2 shows an example in which he income effec dominaes and so desired reiremen ages will fall (we will argue in a laer secion ha his is wha he empirical evidence suggess). As longeviy increases (holding healh a each age and wage levels consan), annual consumpion will fall and [ a 0, I( healh )] V will rise as here will be more years a, over which o spread one's income. This change will shif he marginal uiliy of income curve o he righ and resul in laer reiremen. Noe, however, ha he ne impac of he income effec and he longeviy effec is likely o be a shif in he AA curve o he lef. 13 A older ages w will also likely fall wih age. 14 More generally, we could draw wo marginal disuiliy of effor curves one for good healh and one for poor healh. Opion value incorporaes he possibiliy ha someone currenly in poor healh experiences an improvemen in healh. 8

10 Life expecancy a age 20 has increased by only abou 0.25 percen per year since 1960, while real wage growh has been roughly 1 percen per year. Thus, on average, resources have expanded more rapidly han he number of years hey need o be spread over. Noneheless, if he subsiuion effec of higher wages is sufficien, he AA curve could sill shif o he righ. As healh a each age improves over ime due o advances in medical care and changes in healh behaviors, he disuiliy of effor falls, and he BB curve will shif downward and o he righ (o BB in figure 2). 15 The ne effec of income and healh changes is hus likely o be a shif o he lef of he marginal uiliy of income and a shif o he righ of he marginal disuiliy of effor. Boh he magniude of he shif in he individual's opimal reiremen dae and also he direcion is heoreically ambiguous. The analysis so far has described he behavior of an individual worker. More generally, here will be a separae se of curves for each worker, indexed by wage level, iniial-period asses and healh, 16 and our analysis of reiremen policy will involve summing social welfare over he full disribuion of worker ypes. Before doing his, however, we need o discuss he raionale for Social Securiy. Social Securiy Reiremen Age as a Cure for Myopia In his model, he raionale for he Social Securiy reiremen age is o preven myopic people from accessing heir benefis oo early and hereby ending up wih oo low 15 Changes in job requiremens over ime could also shif he disuiliy of effor curve. If jobs require less manual effor, he curve will shif furher o he righ. On he oher hand, workplace changes such as increased cogniive demands or he increase in wo-worker households could increase he disuiliy of work effor over ime. 16 In acual daa, wealh near reiremen age will vary as well, eiher by design or by luck. We ignore his in he model. 9

11 a consumpion level in heir laer years. There are several differen channels hrough which he myopia migh operae. Myopia could operae in he sandard way hrough individuals discouning he fuure a oo high a rae (perhaps hyperbolically). In ha case, myopic individuals would end o be he same individuals who have inadequae privae saving. Alernaively, oherwise forward-looking individuals migh simply claim Social Securiy benefis a he firs dae hey are available raher han going hrough he effor of opimizing, perhaps assuming ha he governmen has done he opimizaion for hem. In his case, here migh be lile correlaion beween excessively early reiremen and savings levels. In our work o dae, we simplify by assuming ha myopic individuals always reire a he firs dae ha Social Securiy benefis are available, bu oherwise save he same as non-myopic individuals. We hen explore how he resuls change as he share of reiremen-myopic individuals who are savings-myopic varies. I will be sraighforward o insead implemen a model wih a bimodal disribuion of discoun raes. Le r* i be he opimal reiremen age for each individual if he individual were forward-looking and could gain access o heir reiremen benefis a any age. Le r age be he governmen-se age a which people can firs access heir benefis (wih acuarially fair adjusmens for delays in claiming). Assuming ha credis for delayed reiremen are acuarially fair, 17 raional people will no be affeced by r age ; hey will borrow and lend o smooh income around he age a which hey can collec benefis. Myopic people will be affeced by he reiremen age. For simpliciy, we assume ha myopes ake he reiremen age as a cue and always reire a he reiremen age. 17 And ha he presen value of reiremen benefis is independen of he age a which one qualifies for hem. 10

12 Deciding on he opimal reiremen age involves balancing wo consideraions. The firs is ha some myopic people would opimally work longer han he reiremen age he governmen would se (r* i >r age ), and hese people give up addiional income by reiring earlier. On he oher side, some people would opimally reire before he formal reiremen age. If hey have inadequae savings o allow hem o reire before hey receive heir Social Securiy benefis, hen hese people will be forced o work longer han is opimal. The opimal reiremen age balances hese wo consideraions, weighed by he uiliy loss of being wrong in each case. 4. Changes in he disribuion of healh In his secion, we presen rends in he healh of he elderly and near-elderly populaion, o idenify how healh has changed over ime. Healh is, of course, mulidimensional. While here are indices ha ry o combine various measures of healh ypically on a 0 o 1 qualiy of life scale, we consider insead basic descripive daa on several imporan dimensions. One can hink abou healh differences a he high end of funcioning or a he low end. A he high end, here are quesions abou jus how vigorously a person can exercise, and wha oher srenuous aciviies hey can engage in. A he low end, quesions revolve around wheher he person can care for hemselves, underake he normal aciviies of life, and funcion independenly. For undersanding he abiliy o work, he relevan issue is healh a he boom end of he disribuion. We focus on ha dimension. 11

13 Moraliy is he end poin of poor healh, so i is naural o begin here. Figure 3 shows he share of men a each age who are near deah which we define as wihin wo years of dying. 18 Two years prior o deah is a period in which disabiliy raes are very high. We repor resuls separaely for men in 1960 and men in Because of our ineres in social securiy reiremen ages, we focus on he populaion of men in heir early 60s. In 1960, he wo-year moraliy rae for men in heir low 60s was abou 6 percen. In 2000, he moraliy rae was over 40 percen lower. For our purposes, we care less abou changes in moraliy a each age han in wha we erm disabiliy-adjused age. We ask he quesion: a wha chronological age oday would one be in he same healh as a person of a given age 40 years previously? An increase in disabiliy-adjused age is equivalen o an improvemen in healh for ha age group. Figure 3 shows ha he average 68 year-old in 2000 has he same probabiliy of deah in he nex wo years of life as he average 62 year-old in Thus, disabiliy-adjused age has increased by 6 years in he pas four decades. A similar analysis is rue abou life expecancy. The life expecancy of a 62 yearold in 1960 was 14.6 years. Tha is he life expecancy oday of a person aged 67. Thus, if one were defining a Social Securiy reiremen age based only on expeced years unil deah, he reiremen age would have increased by abou 5 years in he pas four decades. Moraliy is no he only endpoin, of course; non-faal healh may be even more imporan. We consider a number of dimensions of non-faal healh. The firs is selfrepored general healh saus. Since he early 1970s, The Naional Healh Inerview 18 These daa are from US life ables and represen a porrai of wha he ypical man of each age would experience in ha year. 12

14 Survey has asked a quesion of he form: Would you say your healh in general is excellen, very good, good, fair, or poor? 19 The ypical measure of poor healh is wheher he person answers fair or poor. Poor healh measured his way is srongly associaed wih subsequen moraliy (Idler and Kasl, 1991). To ensure adequae sample size, we aggregae NHIS responses for wo ime-periods: and The former years are he earlies years of daa availabiliy; he laer years are owards he end of he daa ha have been released. Figure 4 repors he share of men in fair or poor healh over ime. The jagged line is he raw daa; he rend line is formed as he predicions from a quadraic in age. In he mid-1970s, 29 percen of men aged 62 repored heir healh as being fair or poor. Over ime, healh has improved, especially a older ages. By he mid-1990s, one did no reach he same share of men reporing fair or poor healh unil ages in he low 70s. By his measure, healh has improved by abou 10 years. 20 I is noable ha even wih he fewer number of years in he inervening period, he gains in healh saus are larger han he gains in longeviy. Healhy life is rising more rapidly han are years of life. 21 This is paricularly impressive because one would expec some endency for repored healh o remain sable over ime if people s expecaions abou wha hey should be able o do increase wih improvemens in physical funcioning. In addiion o self-repors, one would like o compare direc physical assessmens of healh for example, wheher he person can sand for a cerain lengh of ime or 19 The exac wording of he quesion has changed over ime, bu he meaning has been virually he same. 20 Anoher NHIS quesion asks wheher people are limied in he kind or amoun of heir major aciviy. The difficuly wih his quesion is ha peoples major aciviy varies over ime. The share of people limied in heir major aciviy, for example, declines wih increasing age afer reiremen. 21 This is consisen wih he observaion ha disabiliy raes among he young elderly are falling (Culer, 2001). 13

15 perform essenial cogniive asks. Some surveys of healh do perform physical assessmens, bu he quesions asked are no he same over ime. An alernaive is o look a individual repors of impairmen in specific domains. The Naional Healh Inerview Survey asks people who repor having a variey of differen condiions how many days he condiion caused he person o be in bed for all or mos of he day. 22 We abulae responses for people who repor having a sroke, hear aack, ischemic hear disease, or oher relaed condiions (ICD-9 codes and ). These condiions are common and relaively severe. In his case, severiy is a virue: numerous sudies show ha docors diagnose less severe condiions more han hey used o, and hence he se of people wih less severe condiions such as arhriis or back pain would no be he same over ime. 23 Hear disease diagnoses, in conras, seem o have mached rends in clinical measuremen of disease incidence well (Culer and Richardson, 1997). Figure 5 shows annual bed days for people wih hese condiions. We sar a age 45, since hear disease is less common below ha age. Because our sample sizes are smaller, each individual observaion is a hree-year moving average. For he same reason, we pool men and women. Impairmen associaed wih hear disease has fallen over ime. In 1972, he average 62 year-old male wih hear disease repored 20 days in bed in he previous year. By he mid-1990s, age-specific bed days were abou 5 days lower across he age specrum. 22 In 1972, he specific quesion is abou how many days he person was in bed for all or mos of he day. In , he quesion is abou how many days he person was in bed a leas half he day. 23 To provide a sense of he magniude of he increased diagnosis of chronic condiions, he average 62 year-old in he mid-1970s repored abou 0.7 chronic diseases. In he mid-1990s, ha share of diseases was repored by he average 47 year-old. 14

16 More general measures of disabiliy sugges he same finding. The Naional Long-Term Care Survey has conduced assessmens of disabiliy among he elderly over he course of he pas wo decades defined as he abiliy o perform basic aciviies of independen life such as dressing, bahing, and doing ligh housework. The share of he 65 o 74 year-old populaion ha is disabled in his way fell from 12 o 9 percen. Considering all he evidence, i is clear ha healh near radiional reiremen ages has improved markedly over ime. Our bes guess is ha people aged 62 in he 1960s or 1970s are in equivalen healh o people aged 70 or more oday. 5. Calibraing he Models We implemen a dynamic programming model using daa from he Healh and Reiremen Survey o sudy he implicaions of he heory discussed in secion 3 in a more realisic seing. In paricular we solve he following maximizaion problem for each individual: 1 γ c Max + η( h, ) l R 1 γ h = P( h ) a a = (1 + r) a > 0 + w l + βφe V c [ ( h. a, I( reired) ] In words wha his means is ha each individual decides wheher or no o reire in he curren period so as o maximizes he uiliy of he curren period (which is he sum of a consumpion erm and a erm ha gives he uiliy of leisure as a funcion of healh saus and age) and discouned (due o boh ime preference and he chance of moraliy) expeced fuure uiliy which depends on hree sae variables: healh saus, financial asses, and wheher he individual has previously made he irreversible decision o reire. 15

17 Healh saus evolves according o a markov process. Asse levels are deermined by a sandard asse accumulaion equaion and are consrained o be non-negaive. We solve he model from age 55 o age 100 using backward inducion. Sae variables are healh saus and reiremen saus (boh discree) and asse level (which is coninuous). In calculaing he value funcion, we discreize over possible asse levels and consumpion choices, inerpolae using Akima's shape preserving spline, and find he maximum using a non-linear inerior poin solver maximizaion algorihm conained in he OPT++ oolki. In order o le wages vary wih age and pension benefis o vary wih age of reiremen, we solve he model separaely for each individual in our daa se. We parameerize he single-period uiliy funcion using esimaes from Gusman and Seinmeier (2005). 24 Specifically, our uiliy funcion is: U =.26 c + e.26 l *( age 62) +.298( healh= poor) +ε l is an indicaor ha equals one if he person is reired. Thus, he value of leisure in his equaion rises wih age and he impac of being in poor healh is equivalen o being four years older. We also follow Gusman and Seinmeier (and Samwick, 1998) in assuming heerogeneous discoun raes. In paricular we allocae 46 percen of he sample o discoun raes below 0.05, 21 percen o discoun raes beween.05 and.10, and 33 percen o discoun raes above Our healh ransiion marices, which give he probabiliy of moving from poor healh o good healh, are esimaed from he HRS separaely for hree age ranges. Our moraliy probabiliies come from SSA cohor life ables. 24 French (2005) conains an alernaive appealing model of reiremen and healh saus. 16

18 Our main microdaa come from he HRS and War Baby cohors of he RAND Healh and Reiremen Survey files (version D). These include people born beween 1931 and 1947 and we adjus he daa o represen healh and asse saus a age 55. For our curren simulaions, we assume ha he individual s annual earnings levels say consan above age 55, if hey coninue o work. We calculae pension benefis using he Impued Daa for Pension Wealh Compuaions (version 1.0) available from he HRS web sie. Finally, we consruc Social Securiy benefis by assuming ha a person s AIME is 7/120hs of heir curren wage, applying he PIA formula, and adjusing benefi levels appropriaely for early or delayed reiremen. In a fuure revision, we are planning o implemen more sophisicaed projecions of pension and Social Securiy benefis using he resriced version of he HRS conaining lifeime earnings records and more deailed pension informaion. 6. Simulaions of Opimal Policies This secion repors resuls of preliminary policy simulaions from our model. We assume ha 30 percen of he populaion are reiremen myopes and reire a he firs available opporuniy. This assumpion is broadly consisen wih he Gusman and Seinmeier esimae ha 33 percen of he populaion has very high discoun raes. Figure 6 shows he sum of he value funcion (expeced lifeime social welfare) for he enire sample a differen Social Securiy reiremen ages under hese assumpions and based on curren daa. The opimal EEA is around 64. Figure 7 disaggregaes he value funcion ino hree groups. The firs group consiss of people who are reiremen myopes. Because hey will reire earlier han is 17

19 opimal if given he chance, we see ha heir lifeime uiliy is rising wih he EEA unil very high levels of he EEA (ages in which hey would opimally reire before he EEA). People who are forward-looking and have significan asses a age 55 should be relaively unaffeced by he EEA because hey can live off of heir asses unil heir Social Securiy benefis become available. In conras, people who are forward-looking and have few financial asses a age 55 could be hur by no being able o access heir Social Securiy benefis early, especially if hey are in poor healh. To look a hese wo groups we spli he forward-looking porion of he sample ino people wih asses ha are greaer han heir annual earnings ( unconsrained ) and people whose asses are below ha level ( consrained ). For boh groups uiliy falls wih he EEA, bu he figure clearly shows ha he sum of values is flaer for he unconsrained group (if hey were ruly unconsrained i would be compleely fla bu i akes asses of more han one imes earnings o be ruly indifferen o he iming of Social Securiy benefis). Figure 8 shows a similar simulaion designed o replicae he environmen in he 1960s. Wage levels and benefi levels are shrunk by 40 percen o represen he lower produciviy level. Moraliy raes are higher and healh a each age is assumed o be equivalen o healh a decade laer oday. Under hese assumpions he opimal age EEA is 62 raher han Conclusions This paper has analyzed he opimal choice of an eligibiliy age for Social Securiy a model of opimal social insurance. When combined wih empirical evidence 18

20 abou healh improvemens over ime, preliminary simulaions sugges ha he EEA should rise by 3 o 6 monhs per decade. We are currenly working in four exensions o he work presened in his paper. Firs, we are developing a second model ha can jusify a social securiy reiremen age. In his second model, he reiremen age is he age a which one no longer needs o mee a disabiliy es in order o receive benefis. Second, we are in he process of applying for he resriced version of he HRS so as o incorporae beer esimaes of lifeime earnings and expeced pension benefis ino our empirical simulaions. Third, we are working o esimae he parameers of our uiliy funcion raher han using ones from oher people s work. Esimaing hem ourselves is preferable because i will make he esimaes fully consisen wih he simulaion model. Fourh, we are doing empirical analysis of how he correlaion beween healh saus and asse levels on he verge of reiremen has changed over ime. If he correlaion beween poor healh and low asse levels is rising hen he case for raising he EEA is weakened. 19

21 References Aaron, Henry J. and Rober D. Reischauer (2001). Coundown o Reform: The Grea Social Securiy Debae (Washingon, DC: Cenury Foundaion). Cohen, Wilbur J (1985). The Social Securiy Ac of 1935: Reflecions Fify Years Laer, in The Repor of he Commiee on Economic Securiy of 1935 and Oher Basic Documens Relaing o he Developmen of he Social Securiy Ac (Washingon, DC: Naional Conference on Social Welfare). Coile Courney C. and Jonahan Gruber (2001). Social Securiy Incenives for Reiremen, in Themes in he Economics of Aging, David A. Wise, ed. (Chicago: Universiy of Chicago Press). Coile, Courney C., Peer Diamond, Jonahan Gruber, and Alain Jousen (2002). Delays in Claiming Social Securiy Benefis. Journal of Public Economics 84(3): Cosa, Dora (1998). The Evoluion of Reiremen: An American Economic Hisory (Chicago: Universiy of Chicago Press). Culer, David (2001). "Declining Disabiliy Among The Elderly", Healh Affairs, 20(6), Culer, David and Elizabeh Richardson (1997). "Measuring he Healh of he Unied Saes Populaion", Brookings Papers on Economic Aciviy, Microeconomics, 1997, Diamond, Peer and Peer Orszag (2004). Saving Social Securiy: A Balanced Approach. (Washingon, DC: Brookings Insiuion). French, Eric (2005). The Effecs of Healh, Wealh, and Wages on Labor Supply and Reiremen Behavior, Review of Economic Sudies, 72: Gusman, Alan L. and Seinmeier, Thomas L. (2005). "The Social Securiy Early Reiremen Age in A Srucural Model of Reiremen and Wealh". Journal of Public Economics, 89: Idler, Ellen L. and Sanislav Kasl (1991). "Healh Percepions and Survival: Do Global Evaluaions of Healh Saus Really Predic Moraliy?" Journals of Geronology 46:S55- S65. Meriam, Lewis and Karl Schloerbeck (1950). The Cos and Financing of Social Securiy (Washingon, DC: The Brookings Insiuion). Rodgers, Daniel T. (1998). Alanic Crossings: Social Poliics in a Progressive Age (Cambridge, MA and London: Belknap Press 1998) 20

22 Samwick, Andrew (1998). New Evidence on Pensions, Social Securiy, and he Timing of Reiremen. Journal of Public Economics 70:

23 Figure 1: The Reiremen Decision Marginal Uiliy A C Value of an addiional year of income + opion value Marginal disuiliy of effor B B C Value of an addiional year of income A R * Age 22

24 B Figure 2: Effecs of Improvemens in Produciviy, Longeviy and Healh Uiliy A A Marginal disuiliy of effor B B B B Value of an addiional year of income A A Age 23

25 Figure 3: Share of Men in he Las Two Years of Life 10.0% 9.0% 8.0% % Percen 6.0% 5.0% 4.0% % 2.0% 1.0% 0.0% Age Source: Life ables from he Naional Cener for Healh Saisics. 24

26 Figure 4: Share of Men in Fair or Poor Healh Percen Mid-1970s Mid-1990s Age 25

27 Figure 5: Beds Days in he Pas Year for People wih Hear Disease

28 Figure 6 Sum of Values for Given Reiremen Ages Value a Age Reiremen Age All 27

29 Figure 7 Values for Differen Agen Types Value for ypes Reiremen Age Myopes Unconsrained Consrained 28

30 Figure 8 Sum of Values for Given Reiremen Ages Value a Age Reiremen Age 29