Research. Michigan. Center. Retirement. The Adequacy of Economic Resources in. Retirement. Working Paper MR RC. Michael D. Hurd and Susann Rohwedder

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1 Michigan Universiy of Reiremen Research Cener Working Paper WP The Adequacy of Economic Resources in Reiremen Michael D. Hurd and Susann Rohwedder MR RC Projec #: UM08-11

2 The Adequacy of Economic Resources in Reiremen Michael D. Hurd RAND and NBER Susann Rohwedder RAND Sepember 2008 Michigan Reiremen Research Cener Universiy of Michigan P.O. Box 1248 Ann Arbor, MI hp:// (734) Acknowledgemens This work was suppored by a gran from he Social Securiy Adminisraion hrough he Michigan Reiremen Research Cener (Gran # 10-P ). 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, Bingham Farms; Olivia P. Maynard, Goodrich; Rebecca McGowan, Ann Arbor; 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

3 The Adequacy of Economic Resources in Reiremen Michael D. Hurd and Susann Rohwedder Absrac The mos common meric for assessing he adequacy of economic preparaion for reiremen is he income replacemen rae, he raio of income afer reiremen o income before reiremen. However boh economic heory and common sense say ha someone is adequaely prepared if she is able o mainain her level of economic well-being, which is no he same as mainaining her level of income or some fixed proporion of income. Economic well-being is ypically measured by consumpion, which is he measure we use. We define and esimae measures of economic preparaion for reiremen based on a complee invenory of economic resources, paricularly wealh, which we compare wih opimal consumpion pahs. We find ha a subsanial majoriy of hose jus pas he usual reiremen age are adequaely prepared for reiremen in ha hey will be able o finance a pah of consumpion ha begins a heir curren level of consumpion and hen follows an age-paern similar o ha of curren reirees. This is no rue, however, for all groups in he populaion. In paricular, almos half of singles who lack a high school educaion are likely o be forced o reduce consumpion. Couples are much beer prepared han singles. Bu because of axes a subsanial number of married college graduaes will have o reduce consumpion. Auhors Acknowledgemens The research repored herein was pursuan o a gran from he U.S. Social Securiy Adminisraion (SSA) funded as par of he Reiremen Research Consorium (RRC). 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 RRC. We graefully acknowledge research suppor from he Social Securiy Adminisraion via he Michigan Reiremen Research Cener (UM06-03), from he Deparmen of Labor (J-9-P ), and from he Naional Insiue on Aging (P01AG08291 and P01AG022481). We hank Joanna Carroll for excellen programming assisance.

4 1. Inroducion The mos common meric for assessing he adequacy of economic preparaion for reiremen is he income replacemen rae, he raio of income afer reiremen o income before reiremen. This meric is usually applied wihou regard o family circumsances or o he complee porfolio of economic resources, paricularly wealh. Thus, i is saed ha a single person or a couple is adequaely prepared if heir pos-reiremen income is in some fixed raio (such as 80%) o heir pre-reiremen income. However boh economic heory and common sense say ha someone is adequaely prepared if she is able o mainain her level of economic well-being, which is no he same as mainaining her level of income or some fixed proporion of income. Well-being or uiliy is prey accuraely measured by he level of consumpion no by he level of income a some paricular poin in ime. From his poin of view we would wan o ask wheher someone has he economic resources in reiremen o consume a he same level as prior o reiremen and o mainain ha consumpion level wih adjusmen for possible widowing and moraliy. Bu, he relaionship of consumpion afer reiremen o consumpion before reiremen is no a all well measured by he relaionship of income afer reiremen o income before reiremen, which is he income replacemen raio. Consumpion before reiremen will ypically be subsanially less han income before reiremen because of axes (and Social Securiy conribuions) and work-relaed expenses, bu mos imporanly because of saving for reiremen. 1 Consumpion afer reiremen will ypically be greaer han income because of he abiliy o spend ou of saving. Furhermore, many reired households pay lile or no axes and make no Social Securiy conribuions. The implicaion is ha income could change by a grea deal a reiremen, ye consumpion could be mainained. 2 The overall goal of his paper is o assess economic preparaion for reiremen in a way ha akes ino accoun many of he deficiencies of he income replacemen rae concep. 3 We define a wealh replacemen rae which shows he amoun by which bequeahable wealh a reiremen eiher exceeds or falls shor of he amoun needed o finance a consumpion plan from reiremen hrough he end of life. The consumpion plan begins a an observed saring value and follows a pah whose shape is deermined by observed consumpion change wih age in panel daa. To he exen ha curren reirees are opimizing heir consumpion choices he consumpion plan is opimal. We define a consumpion replacemen rae which is he amoun by which consumpion could be increased in he case where economic resources are more han adequae, or he amoun by which consumpion would have o be reduced in he case where economic resources are less han adequae. We recognize ha because he age of deah is unknown and because wealh is no compleely annuiized, someone who dies unexpecedly early may have been adequaely prepared ex pos, ye someone who survives o exreme old age will have no have been 1 We do no coun work-relaed expenses as producing uiliy. 2 An addiional complicaing facor is wheher individuals have had children: if so, hey will wan o spend relaively more of heir lifeime income during heir working lives and hus will reach reiremen wih less wealh han someone who did no have children. 3 Work similar in spiri o his paper bu very differen in execuion is VanDerhei (2006).

5 adequaely prepared ex pos. To accoun for his randomness we find via simulaion he fracion of imes ex pos a household was adequaely prepared. Economic resources are a combinaion of pos-reiremen income, housing wealh and nonhousing wealh. The replacemen raes accoun for moraliy, and, in he case of couples, he lifeime of he couple and he subsequen loss of reurns-o-scale in consumpion on he deah of he firs spouse. I recognizes ha consumpion need no be consan wih age. Our implemenaion is a combinaion of model-based simulaions and daa-based simulaions. The advanage of his approach is ha we can accoun for more economic facors han we could were he analysis compleely model based. 2. Concepual framework Our saring poin is opimal consumpion planning over he lifeime. For illusraive purposes, suppose someone begins work a age 20 wih zero wealh, and plans and execues an opimal life-cycle consumpion pah over his or her lifeime. Illusraive consumpion and wealh pahs are shown in Figure 1. Iniially he or she consumes more han income. Thus, wealh (W) soon becomes negaive. Evenually income increases, exceeding consumpion (C) so ha wealh begins o increase a abou age 30. Saving coninues and wealh becomes posiive a abou age 40. Consumpion begins o decline when moraliy risk becomes imporan. The worker reires a age R wih maximum wealh and receives annuiy A. He or she consumes unil T when wealh is exhaused and hen consumes A. These are he opimal consumpion and wealh pahs condiional on lifeime earnings and on annuiies. Now suppose ha anoher person mainained he same consumpion pah bu had lower income. Then he enire pah of wealh would be lower as shown by he doed line in Figure 2. A reiremen he person would no be able o finance consumpion unil T bu would exhaus wealh a abou age 87. We would say ha he observed consumpion level a reiremen is no opimal given he wealh and annuiies a reiremen. This oucome is evidence for under saving: wealh is oo low o mainain he consumpion pah associaed wih observed consumpion following reiremen. Said differenly, given he level of income over he lifeime, his worker over-consumed. We will es for his by finding wheher consumpion shorly following reiremen is consisen wih an opimal pah over he res of he lifeime. Assuming ha we know he shape of he opimal consumpion pah, we ask: in our daa se how many persons can afford he opimal pah associaed wih he observed consumpion level a reiremen? And by how much would he iniial level of consumpion have o change o keep he chance of he household will run ou of wealh a he end of he life reasonably low? 3. Daa Our analyses are based on daa from he Healh and Reiremen Sudy (HRS) and daa from he Consumpion and Aciviies Mail Survey (CAMS). The HRS is a biennial panel. Is firs wave was conduced in The arge populaion was he cohors born in (Juser and Suzman, 1995). Addiional cohors were added in 1993 and 2

6 1998 so ha in 2000 i represened he populaion from he cohors of 1947 or earlier. In 2004 more new cohors were added making he HRS represenaive of he populaion 51 or older. In Sepember, 2001, CAMS wave 1 was mailed o 5,000 households seleced a random from households ha paricipaed in HRS In households wih couples i was sen o one of he wo spouses a random. The fac ha he sample was drawn from he HRS 2000 populaion allows linking he CAMS daa o he vas amoun of informaion colleced in prior waves in he core survey on he same individuals and households. In Sepember, 2003, and in Ocober 2005, CAMS wave 2 and wave 3 were sen o he same households. 4 The srucure of he quesionnaire was almos he same so as o faciliae panel analysis. In his paper we will use daa from all hree waves. Descripive saisics of daa qualiy are similar across waves. We will herefore resric heir discussion o he firs wave of CAMS. CAMS wave 1 consiss of hree pars. In Par A, he responden is asked abou he amoun of ime spen in each of 32 aciviies such as ime spen waching TV or ime spen preparing meals. Par B collecs informaion on acual spending in each of 32 caegories, as well as anicipaed and recolleced spending change a reiremen (Hurd and Rohwedder, 2005). Par C asks abou prescripion drugs and curren labor force saus. The insrucions requesed ha for Par B he person mos knowledgeable abou he opics be involved in answering he quesions. The addressee answered Par B in 88% of households, possibly wih he assisance of he spouse; 5% of he cases repor explicily ha he spouse answered he quesions; 2% had heir children or children-in-law of he addressee help ou in answering he quesions, and he remaining 5% was a mix of miscellaneous responses including nonresponse. Of he 5,000 mailed-ou quesionnaires in 2001 here were 3,866 reurned quesionnaires giving a uni response rae of 77.3 percen. The second wave of CAMS had a uni response rae of 78.3 percen (no adjused for moraliy and undeliverable quesionnaires). 5 To accoun for uni nonresponse, we use weighs when calculaing populaion averages. The Consumer Expendiure Survey (CEX) is he survey in he U.S. ha collecs he mos deailed and comprehensive informaion on oal spending. Bu CAMS could no ask abou spending in as many caegories as he CEX, which in he recall componen of he survey asks abou approximaely 260 caegories. The design sraegy adoped for CAMS was o choose spending caegories saring from he CEX aggregae caegories ha are produced in CEX publicaions, so as o have direc comparabiliy wih he CEX. However, o reduce he burden o respondens he caegories had o be aggregaed furher. The final quesionnaire colleced informaion on 6 big-icke iems (auomobile; refrigeraor; washer or dryer; dishwasher; elevision; compuer) and on 26 non-durable spending caegories. 4 CAMS 2005 included in addiion a sub-sample of he newly added cohor of he Early Baby-Boomers ha was firs recruied ino he HRS sample as par of he HRS 2004 core survey. 5 A oal of 4,156 quesionnaires were mailed ou for he second wave of CAMS in 2003, resuling in 3,254 reurned quesionnaires. The remainder of he original sample was los due o deah (n=372), due o loss o follow-up (n=173), and some respondens (n=298) paricipaed in anoher HRS supplemenal sudy and were herefore excluded from CAMS wave 2. 3

7 The reference period for he big-icke iems is las 12 monhs. For he nondurables i varied: he responden could choose he reference period beween amoun spen monhly and amoun spen yearly for regularly occurring expendiures like morgage, ren, uiliies, insurance, propery axes where here is lile or no variaion in amouns, and amoun spen las week, amoun spen las monh, and amoun spen in las 12 monhs for all oher caegories. 6 For all non-durable caegories here was a box o ick if no money spen on his in las 12 monhs. The quesionnaire had no explici provision for don know or refuse so as no o invie iem nonresponse. Table 1 shows he spending caegories and he rae of iem response. Iem response in CAMS is much higher han i is for ypical financial variables such as he componens of wealh or income where i can be as low as 60%. A consequence of he high response raes is ha 54% of households in CAMS wave 1 were complee reporers over all 32 caegories of spending. An addiional 26% had jus one or wo nonresponse iems. Niney percen of he sample were complee reporers of 26 caegories or more. Furhermore, in he spending caegories wih he highes rae of nonresponse, we have informaion from he HRS core ha we can use for impuaion. For example, ren has almos he highes rae of nonresponse. However, we have responses in he HRS abou homeownership which we can use wih considerable confidence o impue ren. Of he 512 who were nonrespondens o he ren query, 427 owned a home in HRS We believe we can confidenly impue zero ren o hese households. Similarly among nonrespondens o he quesion abou homeowners insurance and who owned a home wih morgage in 2000, 66% repored ha heir insurance was included in heir morgage paymen. Apparenly hey did no respond in CAMS because hey had already included ha amoun in he morgage repor. Using he HRS core daa we impued (mosly zeros) for some households in up o 18 spending caegories. The number of households impued in a paricular caegory ranged from jus a few o 470. Based on hese and similar impuaions ha use HRS core daa o provide household-level informaion, 63.5% of CAMS respondens are complee reporers over all 32 caegories of spending. 7 A naural validaion exercise for he spending daa in CAMS is o compare hem o he CEX. Table 2 has comparisons beween spending in CAMS and spending in he CEX. The oals are almos idenical among hose 55-64, which is somewha surprising in view of he grea dispariy in he number of spending iems queried. 8 A older ages CAMS shows greaer spending. There are a leas hree possible reasons for his difference: (1) Differences in he survey insrumens, bu his is unlikely because of he close agreemen in he lowes age band. (2) The reference person. The CEX and he CPS inerview one person in he household (he reference person) who answers for everyone in he household. The HRS inerviews boh spouses in he case of a couple. However, he very close agreemen beween HRS and CPS income suggess ha using a reference person is unlikely o be he explanaion. (3) Differenial uni nonresponse wih age. Tha is, higher consuming households do no respond o he CEX. Almos by 6 In CAMS wave 2 and 3 he las week opion was eliminaed o reduce he risk of observing ouliers ha arise from unusually high values repored as las week ha are subsequenly muliplied by 52 o arrive a annualized values. 7 Because of he small amoun of iem nonresponse ha remains we used simple impuaion mehods from he mean of he repored amoun. See Hurd and Rohwedder (2005) for furher deails. 8 A common view in survey mehodology is ha he more deailed are he caegories, he higher he oal will be. Thus we would expec ha CEX oals would be subsanially greaer han CAMS oals. 4

8 eliminaion we come o his explanaion. In addiion i is clear ha spending in he CEX in he highes age band is oo low because, when compared wih HRS or CPS income, i implies a high rae of saving. 9 Such a high rae of saving is no consisen wih eiher heoreical predicions or wih observed raes of change in wealh. 10 We applied he same cleaning and impuaion mehods o all hree waves of CAMS. Descripive saisics of daa qualiy are similar o hose shown in wave one: iem non response is jus slighly lower in wave 2 and wave 3, while he overall uni response rae in wave 3 was lower (71 percen vs. 78 percen). 4. Mehods Our approach relies on simulaing consumpion pahs over he remaining life cycle for a sample of households observed shorly afer reiremen. For his purpose we need he iniial level of consumpion, which we observe direcly in he CAMS daa, and he slope of he consumpion pah which we esimae from observed panel ransiions based on CAMS wave 1 o 2 and CAMS wave 2 o 3. For he simulaions we consruc life-cycle consumpion pahs for each household: we begin wih he observed consumpion level a reiremen age and hen apply he observed raes of change o race ou a life-cycle pah whose slope is given by he esimaed raes of change. Whereas a model based on a paricular uiliy funcion would specify ha he slope of he consumpion pah depends on he ineres rae, he subjecive ime-rae of discoun, moraliy risk and uiliy funcion parameers, we esimae hese slopes direcly from he daa. Pracically all model esimaion uses he consan-relaiverisk-aversion uiliy which specifies ha he slope of log consumpion is independen of he level. The observed pahs do no necessarily have ha shape and we do no impose ha. Thus our esimaions are model-based in ha we use he framework of lifeime uiliy maximizaion bu hey are essenially nonparameric in ha we allow he consumpion pah o be deermined direcly by he daa. In his paper we propose wo relaed mehods for finding replacemen raes: (a) wealh-based replacemen raes; and (b) consumpion-based replacemen raes. We will sar ou by illusraing he approach for singles. We observe he resources a reiremen of a single person. We ask: can he resources suppor he projeced consumpion pah. The consumpion pah is anchored a he iniial pos-reiremen consumpion level and follows he pah given by he slopes of consumpion pahs ha we have esimaed from he CAMS panel. If he consumpion pah canno be suppored by he economic resources we find he level of bequeahable wealh ha would permi he person o follow he opimal pah. The wealh replacemen rae is he raio of acual wealh o his required wealh. If he replacemen rae is greaer 9 Income in he CEX is no reliable because i is only repored for complee reporers; ha is, hose who give answers o all income quesions. Only saring wih he 2004 daa does he CEX impue missing values on income o produce saisics compued over he enire sample as opposed o jus over complee reporers. 10 Panel wealh change shows approximaely consan wealh among couples unil he oldes spouse reaches his/her 80s when wealh declines slowly. Among single persons, wealh declines afer abou age 70 a increasing raes wih age. CEX spending when combined wih HRS afer-ax income would, in conradicion, predic seadily increasing wealh. 5

9 han one, acual wealh is more han sufficien o finance he consumpion pah. If i is less han one, here is a wealh shorfall. Because lifeime is uncerain, and wealh is no ypically annuiized, we also find he resources ha will permi he consumpion pah o be followed wih a high degree of probabiliy. Here he uncerainy is lengh of life, so he quesion is equivalen o finding wheher he resources will susain he pah unil advanced old age where he probabiliy of survival is very small. Someone wih a moderae level of pre-reiremen consumpion could susain pos-reiremen consumpion wih a moderae level of Social Securiy benefis, some pension income and a moderae amoun of wealh. Someone wih low pre-reiremen consumpion may only need Social Securiy and a small amoun of savings. These requiremens are likely o differ subsanially from wha would be required o consume a he pre-reiremen income level. We do his calculaion for each single person in our CAMS sample who is in his or her early reiremen years. For couples he basic mehod is similar. However, he consumpion pah followed while boh spouses survive will differ from he consumpion pah of single persons, so i is separaely esimaed from he CAMS daa. The couple will follow ha consumpion pah as long as boh spouses survive, and hen he surviving spouse will swich o he consumpion pah of a single person. The shape of he single s pah is esimaed as described above, bu he level of consumpion by he surviving spouse will depend on reurns-o-scale in consumpion by he couple. A he deah of he firs spouse, he surviving spouse reduces consumpion o he level specified by he reurns-o-scale parameer. We assume a reurns-o-scale parameer ha is consisen wih he lieraure and wih pracice. For example, he povery line specifies ha a couple wih 1.26 imes he income of a single person who is a he povery line will also be a he povery line. This implies ha consumpion by he surviving spouse should be 79% of consumpion by he couple o equae effecive consumpion. 11 Knowing he consumpion pah of he surviving spouse we find he expeced presen value of consumpion for he lifeime of he couple and surviving spouse. We compare populaion averages of he expeced presen value of consumpion wih average resources a reiremen o find wheher he cohor can finance he expeced consumpion pah. We also deermine he fracion of households ha can finance wih, say, 95% probabiliy heir expeced consumpion pah, and by how much a household would have o adjus consumpion o keep he chances of running ou of wealh owards he end of he life cycle reasonably small. 5. Model for singles In his secion we develop he ideas discussed previously more formally. Suppose a single person reires a age R. Call ha = 0. He or she reires wih real annuiy S and nominal annuiy P 0, he inflaion rae is f, and he nominal ineres rae F, which implies a real ineres rae r = F f. Then he real annuiy a some laer ime is 11 We discuss laer he sensiiviy of our analysis o his reurns-o-scale parameer. 6

10 P0 A = S0 +. When he only source of uncerain is moraliy risk and ignoring any (1 + f ) beques moive, a single person will choose opimal consumpion o saisfy dln c 1 (1) = ( r ρ h ) d γ as long as bequeahable wealh is posiive, where γ is risk aversion (which in general need no be consan), r is he fixed real ineres rae, ρ is he subjecive ime rae of discoun, and h is moraliy risk. Because h is approximaely exponenial, a some (relaively young) age consumpion will decline wih age. The consumpion level will be deermined by adjusing he consumpion pah so ha a he age when consumpion has declined o equal annuiy income, bequeahable wealh is zero. If, in Figure 3, he area under he consumpion pah bu above he annuiy pah were equal o iniial bequeahable wealh, he consumpion pah would be opimal. We consruc he consumpion pah { c } such ha iniial consumpion, c 0, is given by observed consumpion a or near reiremen and he change in consumpion from one Δ c period o he nex,, is observed in he CAMS panel daa by age band. The siuaion c is illusraed in Figure 3 for R = 65. Consumpion will follow his pah unil consumpion equals annuiies, ct = AT. If he consumpion pah is opimal wealh will be zero a T and consumpion will remain a he level of annuiies a greaer ages. T c A The presen value of spending in excess of annuiies is PVc =. If PV T = 1 (1 + r) equals iniial wealh we say he consumpion pah is he opimal consumpion pah alhough he shape is no derived from any uiliy funcion. By his we mean ha he level and shape are consisen wih economic resources and spending change in panel daa. 12 We ask wheher PV c is less han or greaer han iniial wealh. If i is greaer han iniial bequeahable wealh, he opimal consumpion pah is no feasible. The wealh w acual iniial wealh replacemen raio is = and if he opimal consumpion is PV c necessary iniial wealh feasible he wealh replacemen rae is greaer han 1.0. We define a consumpion replacemen rae which is similar o he income replacemen rae: wha fracion of iniial consumpion can be afforded by economic resources? To find he consumpion replacemen rae we find ĉ 0 such ha he consumpion pah { c ( c ˆ0 )} wih iniial consumpion ĉ 0 is opimal; ha is, he associaed wealh replacemen raio is 1.0. ĉ 0 is found by searching: given some iniial guess find PV * of he associaed consumpion pah. If PV * c c > w reduce * c * c and search again 12 The pah which is illusraed in Figure 3 is similar o a pah derived from he assumpion of CRRA uiliy and esimaed over wealh change daa (Hurd, 1989). 7

11 unil PV * = w. Once we have found he opimal consumpion ĉ c 0 condiional on iniial wealh we calculae he consumpion replacemen raio ĉ0 c0 If his raio is less han 1.0 he person canno afford he opimal consumpion pah. Calculaing he consumpion replacemen rae in his way ignores he fac ha someone may die before exhausing wealh even if on an unsusainable consumpion pah. We can find he probabiliy ha someone survives o he age when wealh is exhaused by finding τ such ha τ c( c0) A = w (1 + r) = 1 τ is he age when wealh is exhaused. In a life able we find he probabiliy of surviving o τ condiional on iniial age R. This will give he probabiliy of exhausing wealh before dying. 6. Model for Couples The life-cycle model for couples is considerably more complicaed. Under he same assumpions as for he singles model he firs-order condiion for consumpion by a couple is dln C 1 1 Ω = ( r ρ h ) + d γ γ C γ where h = he couple s moraliy risk (he probabiliy densiy ha one of hem will die a given ha neiher has died before ), C is consumpion by he couple, γ is he risk aversion parameer in he couple s CRRA uiliy funcion, r is he fixed real ineres rae, and ρ is he subjecive ime rae of discoun of he couple. The las erm accouns for bequess o he surviving spouse: Ω is he expeced marginal uiliy of wealh should one of he spouses die. I is composed of wo erms: he marginal uiliy of wealh of he widower weighed by he moraliy hazard of he wife and he marginal uiliy of wealh of he widow weighed by he moraliy hazard of he husband. Ω varies from couple o couple according o he marginal uiliy of wealh of he survivor should one of he spouses die. The marginal uiliy of wealh of he survivor varies by he wealh of he couple (which he survivor will inheri ), he moraliy risk of he survivor, and he level of pension and Social Securiy benefis ha he survivor will have. Predicions abou he slope and level of he consumpion pah are complex because of Ω. Bu consumpion should decline if boh spouses are old because he marginal uiliy of wealh will be small for an old surviving spouse. The slope of he consumpion pah should be greaer algebraically when one spouse is young because he marginal uiliy of wealh is large for a young spouse. To find he prediced consumpion pah of a couple we begin wih C 0, which is observed consumpion by a couple a baseline. Then we projec consumpion o he nex period by C = 1 C(1 + + G) where G is he annual growh rae of consumpion by couples 8

12 as esimaed by age and educaion bands beween waves 1 and 2, and beween waves 2 and 3 of CAMS. The associaed wealh pah is W+ 1 = W(1 + r) C + A where r is an assumed real rae of ineres. The couples model differs from he singles model in ha one spouse will die before he oher and he surviving spouse will coninue o consume, bu he consumpion level will change according o reurns-o-scale. Suppose he husband dies. Then he widow will inheri he wealh of he couple, an annuiy which is some fracion f a of A, and an opimal consumpion level ha reflecs reurns-o-scale. According o he povery line, he widow would need 1/1.26 = of he consumpion of he couple; according o scaling of he wife s and widow s benefis in Social Securiy, he widow would need 1/1.5 = From ha poin on he widow will follow he singles model aking as iniial condiions he inheried wealh, he reduced annuiies and he reduced consumpion level. Figure 4 has an example under he assumpion ha boh spouses are iniially 65 and ha he husband dies a age 80. Iniial wealh is 500. Prior o age 80 consumpion by he couple follows C+ 1 = C(1 + G). Consumpion declines when he husband dies because of reurns-o-scale, and hen i follows he pah of singles. In he case shown, he couple and surviving spouse could jus exacly afford he iniial consumpion of Should he widow survive o 94 or beyond, wealh would be exhaused. Now suppose iniial consumpion is slighly greaer a 55.5 as shown in Figure 5. Then he surviving spouse runs ou of money a abou 87. The presen value of spending ou of bequeahable wealh is given by he area beween he consumpion curve (boh couple and widow) and he annuiy curve (boh couple and widow). In his case he excess presen value of spending o age 94 is abou 21.7 more han iniial wealh so ha he wealh shorfall rae is 21.7/500 = 4.3%. The foregoing assumes widowing a 80, bu we need o allow random widowing. Take he same couple where boh are iniially 65. Randomly choose wheher boh, one or neiher spouse survives wih probabiliies given by life able survival hazards. If boh survive coninue calculaing he couple s consumpion and wealh pah. If he husband dies, we swich o he widow s consumpion and wealh pah and follow ha as in he case of a single. We find he expeced presen value of spending in excess of annuiies. If he wife dies we perform he same calculaion. If boh die, we sop he calculaions. The oucomes of one simulaion are: Did he household die wih posiive wealh? If so, how much compared wih iniial wealh. If no, wha is he wealh shorfall? By repeaing he simulaions a number of imes for he same household we can find he probabiliy ha he household will die wih posiive wealh or negaive wealh and he disribuion of hose excesses or shorfalls in wealh. As described for he case of singles, we will also compue he consumpion replacemen rae for couples based on muliple simulaions. 7. Differenial Moraliy A large lieraure on he gradien beween socioeconomic saus (SES) and healh documens ha individuals wih high SES such as high educaion live longer han hose wih low SES. Because households are no fully annuiized, long-lived households have o be prepared o finance consumpion over a longer remaining ime horizon. We ake his ino accoun in our simulaions by applying survival probabiliies ha differeniae by 9

13 educaion as well as by age, sex and marial saus. Given he exended ime horizon high SES households may also follow differen consumpion pahs han low SES households. Economic heory predics a flaer consumpion pah when moraliy risk is lower. We herefore also sraify by educaion when esimaing he consumpion pahs for singles and couples. Esimaion of differenial moraliy We obain our esimaes of differenial moraliy based on seven waves of HRS daa spanning he years 1992 o We esimae he probabiliy of survival a ime +1 condiional on being alive a ime, pooling he six ransiions we observe in he HRS. The logi model yields he esimaes shows in Table 3 for separae esimaions for males and females as a funcion of age, marial saus and educaion. For males he odds of survival beween waves for college graduaes is 79% higher han he odds of survival for high school dropous. For boh men and women he survival odds increase in educaion, bu he profiles are differen: for men here is a large gain from compleing college, much larger han he gain for women. From hese esimaes we consruc survival curves by sex, marial saus and educaion and normalize hese o life ables so ha he average survival probabiliy given age and sex equals ha given in he life ables. Figures 6 and 7 show he resuling survival curves for males and females. Esimaion of consumpion pah Because survival differs by age, sex and educaion he slope of he consumpion pah should vary by hose characerisics. Furhermore, here is no reason o impose he consancy of γ ha would be required were we o base our esimaion on wealh alone. Therefore we esimae he model c + 1 c = αi + β j + θk + u c wherei indicaes age caegory, j indicaes educaion caegory and k indicaes sex. We have four educaion caegories: less han high school, high school, some college and college graduae. For singles we have five age caegories 65-69, 70-74, 75-79, and 85 or over. We observed 781 consumpion ransiions among singles 65 or older beween he hree waves of CAMS. For couples we have jus four age caegories because of small sample size in he op age caegory. Bu in addiion we enered caegorical variables for he age of he spouse. We observed 2817 consumpion ransiions among couples where boh spouses were 62 or older. We esimaed by median regression because observaion error on consumpion produces large ouliers in he lef-hand variable which makes OLS esimaes unreliable. Examples of fied consumpion pahs for single women from hese esimaes are in Figure The pahs are normalized a 100 a age 65. College graduaes have much flaer consumpion pahs han hose wih less educaion where here is lile difference. For comparison we have graphed he opimal consumpion pah based on CRRA uiliy where he pah is generaed by equaion (1). We use moraliy risk of women. Risk aversion, γ, is 1.12 which Hurd (1989) esimaed on wealh change daa in he RHS. In 13 The pahs for single men are approximaely he same as so we do no show hem. 10

14 his simulaion r = ρ. The pahs generaed by he CAMS consumpion change are remarkably similar o he pah generaed by he model. Figure 9 shows consumpion pahs of couples where boh spouses are he same age. The mos obvious difference from he consumpion pahs of single women is ha consumpion by couples shows much less decline. This is o be expeced because he couples has a srong desire o leave wealh o a surviving spouse as refleced in subsanial marginal uiliy of wealh o he survival spouse. There is lile difference in he pahs by educaion Oher sources of uncerainy The model we have oulined only explicily includes moraliy risk. However, he esimaes implicily accoun for oher uncerainies alhough hey are no separaely idenified. To see his consider he second-order approximaion o he firs-order condiion for lifeime uiliy maximizaion for singles when here is uncerainy (Carroll, 2001). I is 1 γ E( Δ ln c) = δ h + V( Δ ln c) γ 2 where Δ ln c is he change in log consumpion; h is moraliy risk; γ is risk aversion (which in general need no be consan); δ is a combinaion of he (fixed) ineres rae, he subjecive ime rae of discoun and risk aversion, and V( Δ ln c ) is he variance in he change in he log of consumpion. The expecaion operaor on Δ ln c arises because when choosing consumpion a ime an individual can only have an expecaion abou consumpion a ime + 1: for example, a large healh shock may lead he individual o choose greaer han average spending, or he lack of any shock a all may permi less han average spending. In he absence of uncerainy, he variance erm is zero, and he consumpion pah will be downward sloping because h becomes large a old age. Spending will exceed income so ha wealh will decline. Wih uncerainy he pah is flaened and consumpion mus iniially be reduced o mee he lifeime budge consrain. Therefore wealh will be decumulaed a a slower rae. The resuling greaer amoun of wealh is buffer sock saving. In our esimaions V( Δ ln c ) is a lef-ou variable. Because our righ-hand variables are caegorical variables is effec on reducing he slope of he (downward sloping) consumpion pah will be absorbed ino our esimaed effecs of hose caegorical variables. Thus, o he exen ha individuals reduce iniial consumpion in he face of uncerainy our esimaed consumpion pah will flaened. We do no, of course, separaely idenify any flaening due o uncerainy. 9. Resuls Because we wan o observe Social Securiy and pension income we selec a sample shorly afer reiremen and of a sufficien age ha hey are likely o be receiving Social Securiy if hey are eligible. We selec couples where one spouse is 66, 67, 68 or 14 Educaion is he educaion of he responden o he CAMS survey 11

15 69, and he oher is 62 or older; hey were respondens in CAMS wave 1, 2 or 3; and hey were a couple in he HRS surrounding waves. We make he age resricion on he younger spouse because spouses younger han 62 would no ye be receiving Social Securiy benefis and so we would miss a significan fracion of reiremen resources. We selec singles who were Table 4 gives he iniial condiions for couples and Table 5 gives hem for singles. The ables show he disribuions of iniial consumpion, Social Securiy income, pension income, and annuiy income (Social Securiy plus pension income). Noe ha hese are populaion disribuions of each variable. However, excess income is he difference beween he quaniles of consumpion and oal annuiy income. This is a beer measure of he amoun of consumpion ha will have o be financed ou of wealh han he quaniles of excess income: households end o occupy similar poins on he disribuions of consumpion, annuiy income and wealh whereas ha is no he case wih excess income. For example, he 25 percenile of excess income is -$17 housand (no shown) which could be someone wih considerable wealh. The las column is he disribuion of oal wealh which includes housing wealh. 15 We can already see ha on average and for mos of he disribuion, couples have adequae resources o finance heir consumpion in reiremen. For example, average consumpion is $42.0 housand, average annuiy income (Social Securiy + pensions) is $37.9 housand leaving jus $4.1 housand per year o be financed ou of wealh, which is $652 housand. A he median he numbers are smaller bu jus $6.6 housand per year needs o be financed ou of $291 housand of wealh. Even a he 25 h percenile consumpion is jus $5.3 housand more han income, so a small adjusmen o spending or a small draw-down of wealh would permi consumpion o be mainained. The siuaion wih singles is very differen. A he mean wealh is adequae o finance excess spending, bu a he median wealh could only finance abou 10 years of excess spending. A he 25 h and 10 h perceniles consumpion would have o be reduced subsanially from heir iniial low levels. We perform 20 simulaions of he consumpion and wealh pahs of each married person who is in he age range By consumpion we mean he consumpion by he couple as long as boh spouses survive and also he consumpion by he survivor. Alhough we begin wih 757 households as shown in Table 4, we only have 924 married persons who are age eligible (66-69), he oher spouses being ouside he given age range. The economic circumsances of he 924 age-eligible persons will ener he ables. In hese simulaions we use he povery line reurns-o-scale and assume ha he annuiy of he survivor is 0.67 imes he annuiy of he couple. The ables 6 and onward show he resuls of he simulaions, incorporaing differenial moraliy by educaion level and differenial raes of consumpion change by educaion level. Because we are ineresed in he fracion of individuals ha runs ou of resources a he end of he lifecycle we have arranged all subsequen ables a he individual level. They show he characerisics and resuls for year olds living in couple households and in single households a baseline. Table 6 shows ha iniial average wealh, he average presen value of earnings and he average presen value of annuiies for couples oal abou $1.1 million. The 15 Fuure work will make a disincion beween housing and nonhousing wealh. 16 We have also run previous versions wih 100 simulaions and resuls were closely comparable. 12

16 presen value of consumpion is abou $474 housand so ha average excess wealh is $669 housand. A leas on average couples are well prepared financially for reiremen. The median of he household-level amoun of excess wealh is abou $324 housand, indicaing ha he household of he median person is also well prepared. As would be expeced, he measures increase srongly wih educaion bu even hose wih less han a high school educaion are a he median adequaely prepared. In abou 87% of he simulaions, he surviving spouse dies wih posiive wealh. For singles he resuls are much less opimisic (Table 7). Median excess wealh is jus $74 housand, and in he lowes educaion band i is essenially zero. In 68% of he simulaions he single person dies wih posiive wealh. Our individual-level meric for he probabiliy of dying wih posiive wealh is based on he fracion of simulaions for which an individual in a couple or a single person dies wih posiive wealh. In his meric we say ha he individual is adequaely prepared if he chances are 95% or greaer. Table 8 shows ha overall abou 83% of married persons are adequaely prepared. The average for males and females is he same, which is somewha surprising because husbands ypically die before wives, so ha hey are more likely o die before asses have been depleed. However, i should be kep in mind ha here are 757 households in our sample, ye jus 924 individuals. The implicaion is ha in 77% of hese households only one of he spouses mees our selecion crieria for age, Thus, he males and females generally come from differen households which have differen economic resources and have chosen differen iniial consumpion levels. Among singles abou 64% are adequaely prepared (Table 9). In he lowes educaion band only 43% of women are adequaely prepared compared wih 63% of men. The preceding ables measured adequae preparaion for reiremen in erms of residual wealh a deah. This measure does no disinguish wheher he required adjusmen o a household s consumpion pah is big or small relaive o curren consumpion. For example, a household wih generous annuiies, say of eighy housand dollars per year, may have similar shorfalls in excess wealh as a household wih very low annuiy enilemens. Ye, he consumpion floor ha eiher of hese households faces is very differen and so are he welfare implicaions. If a household wih a consumpion level of 10 housand dollars per year has o reduce consumpion by a housand dollars o keep he probabiliy of running ou of wealh sufficienly low his implies a drop in consumpion of 10 percen a an already very low level of consumpion. For a household wih a consumpion level of 80 housand dollars per year a drop in consumpion by a housand dollars is equivalen o a drop of only 1.25 percen a a much higher level of consumpion. Due o he concaviy of he uiliy funcion he welfare loss for he laer household will be even smaller in comparison. In he nex ables we will answer he quesion: By how much does he household have o adjus iniial consumpion compared o curren iniial consumpion o keep he probabiliy of running ou of wealh a he end of life below a desired hreshold? This measure will reflec he changes o sandard of living required for a household o achieve adequae preparaion for reiremen. 13

17 Table 10 shows ha for all couples, he average affordable consumpion is $98 housand, ye average iniial consumpion is jus $42 housand. Thus on average couples could increase heir consumpion subsanially. The average of he raios of affordable consumpion o iniial consumpion (mean raios in he able) is 2.32, bu his raio is heavily influenced by he wealhy and/or hose wih very low iniial consumpion possible he resul of measuremen error. Even he median of he individual raios of affordable consumpion o acual consumpion, which is relaively robus o measuremen error, is Among singles, consumpion could be increased on average a all educaion levels, bu he median of he affordable consumpion raio in he lowes educaion band is jus 1.02 (Table 11). This indicaes ha he ypical person in ha educaion band could jus afford iniial consumpion in abou half he simulaions. As wih he wealh simulaions we repored on earlier, we now pu consumpion shorfalls or excesses in a probabilisic framework. We say ha an individual is inadequaely prepared if iniial consumpion of he household would have o be reduced by 15 percen or more o keep he individual s chance of running ou of wealh a 5 percen or less. Table 12 shows ha for married persons abou 88.6% are adequaely prepared, and ha females are slighly more likely o be prepared han men. Even among high school drop-ous abou 81% are adequaely prepared. Among singles (Table 13) he overall rae is 74%. An especially inadequaely prepared group is females in he lowes educaion caegory: jus 52% are adequaely prepared. Our definiion of adequae preparaion makes some ad hoc choices regarding he cu off poins. I is no clear how small he chances of running ou of wealh should be kep. We have presened resuls for a cu off of 5 percen or less, bu some migh argue ha his could also be higher or possibly smaller. Similarly we have chosen a required reducion of iniial consumpion by 15 percen or more o signal inadequae preparedness. We have esed he sensiiviy of our resuls wih respec o hese cu offs. Tables 14 and 15 show a marix for couples and singles, respecively, wih differen cu off poins. The resuls are no very sensiive o hese definiions. The reason is ha mos households eiher fall subsanially shor of he hresholds of adequacy or hey exceed hem by a large margin, resuling in floor and ceiling effecs in he saisics for preparedness. Reurns-o-scale We performed sensiiviy analyses o our assumpion abou reurns-o-scale. Because our esimaes of preparaion for reiremen by couples show ha mos couple are very well prepared we anicipaed ha he resuls would no be sensiive. In addiion widowing occurs on average abou 10 years afer he sar of he simulaions so ha he consumpion level of he surviving spouse is discouned fairly heavily. We used wo alernaives: he implici reurns-o-scale in he Social Securiy survivors benefi where he benefi of he surviving spouse is 2/3 of he couple's benefi, and he observed consumpion change in he CAMS panel a widowing, which is close o he povery line reurns-o-scale. Boh alernaive reurns-o-scale assumpions produced resuls ha are similar o our main resuls. Taxes 14

18 Taxes, which include Social Securiy conribuions, influence economic preparaion for reiremen via four roues. The firs is federal and sae ax paid on ordinary income such as earnings, capial income and pension income. The second is Social Securiy conribuions paid on earnings. The hird is ha Social Securiy income is only parially couned as axable income and he fracion depends on he level of oher axable income and on he amoun of Social Securiy income. The fourh is ha wihdrawals from axadvanaged accouns such as IRAs are axed. We have accouned for hese axes in a somewha simplified manner, which, noneheless addresses all of hese elemens. 17 Table 16 shows he effec of axes on economic preparaion for singles. For comparison he column labeled no axes is copied from Table 13. In our populaion of recenly reired singles, accouning for axes reduces economic preparaion for reiremen by a fairly small amoun, from 74.1% o 70.1%. Among hose lacking a high school educaion he reducion is jus a lile over wo percenage poins. The reason for his insensiiviy o axes is ha economically vulnerable single persons pay lile if any axes. For example, he median ax rae among hose in he lowes annuiy income quarile (pension plus Social Securiy) is zero, and i is jus 1% in he second annuiy income quarile. In addiion ofen hose who pay some income ax pay no ax a all on Social Securiy benefis. There is a srong gradien by educaion, which is a good proxy for economic saus. Accouning for axes reduces he number of single persons wih a college educaion who are adequaely prepared by 9.5 percenage poins. Accouning for axes among married persons has a fairly small overall effec reducing preparaion from 88.6% o 83.2% of married persons. Because of heir low incomes, hose lacking a high school educaion (abou 18% of he sample) are very lile affeced by axes. A he oher exreme is college graduaes (19% of he sample). In he absence of axes 92% are adequaely prepared, bu axes reduce his number o 74% making his group he leas well prepared among married persons. 10. Fuure research Our mehod of assessing he adequacy of reiremen resources involves comparing resources wih spending levels and spending paerns ha we observe in oday s daa. If spending requiremens increase subsanially faser han hey have in he pas, hen resources ex pos will look inadequae whereas ex ane hey looked adequae. Ou-ofpocke spending on healh care is an obvious area where his could happen. Accouning for his would require he esimaion of a model of consumpion ha includes healh care expenses, and, mos imporanly, a sound mehod of forecasing wha fuure healh care expenses will be. Alhough he firs ype of model can be specified and possibly esimaed from curren economic heory and daa, he second ype of model is, o say he leas, a dauning ask. However, as shown in Figure 10, we do no ye see any dramaic increase in he share of he budge of he reired populaion ha is spen on healh care. Among hose 65-74, he share has remained fairly consan a approximaely 10.5%. For hose 75 or over here has possibly been an upward rend, alhough i is small: in 1989 he share was 14.8% and in 2004 i was 15.5%. The implicaion is ha a model ha 17 We use sandard deducions and esimae he relaionship beween federal and sae income axes for each household based on he NBER ax calculaor, TAXSIM. We use his relaionship o esimae sae axes. 15

19 relies on hisorical daa on budge shares would no forecas any dramaic increase in spending on healh care. In addiion, as we discussed earlier, our esimaes of he slopes of he consumpion pahs include pas increases in healh care spending beween 2001 and 2005, a period of high and increasing healh care spending. Fuure healh care spending would have o accelerae for our resuls o be inaccurae. We have reaed housing wealh in he same manner as nonhousing wealh. However, available evidence suggess ha housing wealh is decumulaed more slowly han nonhousing wealh. This is no an imporan issue as long as a household has nonhousing wealh o decumulae o mainain he desired consumpion pah. Bu if some households are relucan o downsize or o oherwise moneize he value of heir house hey may be forced o deviae from heir desired consumpion pah. In fuure work we will separae ou housing wealh and develop rajecories of home equiy. 11. Conclusions Our conclusion is ha a subsanial majoriy of hose jus pas he usual reiremen age are adequaely prepared for reiremen in ha hey will be able o follow a pah of consumpion ha begins a heir curren level of consumpion and hen follows an agepaern similar o ha of curren reirees. Thus we do no find inadequae preparaion for reiremen on average or even a he median. This is no rue, however, for all groups in he populaion. In paricular, many singles lacking a high school educaion are likely o be forced o reduce consumpion: almos half could reduce iniial consumpion subsanially (15%) ye hey would sill face a probabiliy of running ou of wealh greaer han 5 percen. Economic preparaion by couples is much beer han preparaion by singles. However, a noeworhy group is college graduaes: when axes are aken ino accoun he proporion adequaely prepared falls subsanially, by abou 18 percenage poins. 16