NBER Retirement Research Center Working Paper NB How Fast Should the Social Security Eligibility Age Rise?

Transcription

1 NBER Retirement Research Center Working Paer NB04-05 Ho Fast Should the Social Security Eligibility Age Rise? David M. Cutler, Jeffrey B. Liebman, and Seamus Smyth Harvard University and NBER July 23, 2006 Abstract Many Social Security reform roosals recommend increasing the age at hich eole become eligible for Social Security retirement benefits as a ay to reduce future exenditures, maintain benefit adequacy in light of other benefit cuts, and increase labor suly. But the amount by hich the benefit eligibility age is increased in reform lans is rarely chosen based uon rinciles of otimal social insurance. In this aer e analyze the question of the otimal eligibility age using to models of otimal social insurance. In the first model, the eligibility age exists because of a aternalistic concern that some eole ill mistakenly retire too early if left to make decisions on their on. In the second model, the eligibility age reresents the age at hich it is no longer cost effective to screen eole for disability. We arameterize the models using ne estimates of ho the distribution of health status at each age has evolved in the U.S. over the ast four decades. This research as suorted by the U.S. Social Security Administration through grant #10-P to the National Bureau of Economic Research as art of the SSA Retirement Research Consortium. The findings and conclusions exressed are solely those of the authors and do not reresent the vies of SSA, any agency of the Federal Government, or the NBER. We thank Eric French for helful comments on an earlier draft and Mark Sheard for excellent research assistance.

2 1. Introduction Many Social Security reform roosals recommend increasing the age at hich eole become eligible for Social Security retirement benefits as a ay to reduce future exenditures, maintain benefit adequacy in light of other benefit cuts, and increase labor suly. For examle the Personal Security Accounts PSA lan of the Advisory Council on Social Security ould have raised the earliest eligibility age EEA from 62 to 65 by 2035 and the 1998 National Commission on Retirement Policy NCRP lan ould have raised the EEA to 65 by 2017 and then to higher ages thereafter. The amount by hich the benefit eligibility age is increased in reform lans is rarely chosen based uon rinciles of otimal social insurance. Instead, roosals motivate these changes as holding constant the number of years receiving benefits the NCRP lan or holding constant the ratio of retirement years to ork years the PSA lan. These ad hoc targets are unlikely to corresond to hat ould be recommended by a model of otimal social insurance. 1 In this aer e analyze the question of the otimal retirement age using to models of otimal social insurance. Both models have at their foundation the decision roblem of a reresentative forard-looking consumer and, in articular, the comarative statics of ho this consumer s choice of retirement date is affected by rising roductivity, a longer lifesan, and loer disability rates at each age. Rising roductivity ill lead to retirement at an earlier age if the income effect of higher age levels outeighs the substitution effect. Longer lifesans ill increase the marginal utility of income, leading 1 To scholarly reform roosals do aly logic similar to that of this aer in discussing reform otions. Aaron and Reischauer 2001 recommend raising the EEA, but note that the olicy ill create inners and losers. Their roosal ould kee the relacement rate constant for orkers ho send the same fraction of their adult lives in retirement as those reaching age 62 in Diamond and Orszag 2004 do not recommend raising the EEA, arguing that oulation heterogeneity makes it difficult to judge hether the benefits of doing so ould outeigh the costs. retirementage.july

3 to later retirement. Loer disability rates ill reduce the disutility of ork and also lead to later retirement. The to models then extend this reresentative consumer analysis by introducing heterogeneity in ages, retirement benefits, and initial eriod assets. Imortantly, one needs a rationale for Social Security to anser the eligibility age question -- hy eole are not simly ermitted to ta their Social Security benefits at hatever age they choose ith an aroriate actuarial adjustment for early receit of benefits. We consider to rationales. In the first model, the eligibility age exists because of a aternalistic concern that some eole ill mistakenly retire too early if left to make decisions on their on. The choice of an initial age at hich eole can access retirement benefits therefore involves balancing a desire to force myoic eole to kee orking against the cost of not ermitting eole for hom it ould be otimal to receive benefits before the retirement age to do so. In the second model, the eligibility age is set by considering the interaction beteen Social Security and Disability. If all e anted to insure ere health status, e ould have a disability rogram but no Social Security. In ractice, screens for disability are imerfect and costly. At some age the costs of screening outeigh the benefits. This is the age at hich universal access to Social Security should begin. We arameterize our models using ne estimates of ho the distribution of health status at each age has evolved in the U.S. over the ast four decades. These estimates allo us to make statements about ho fast the eligibility age should rise in the future if health gains in coming decades are similar to hat e exerienced in the ast. More generally, our health estimates allo us to make statements such as 70 year old males retirementage.july

4 today are as healthy as 62 year olds ere in This information is of use in thinking about eligibility-age olicy even in the absence of our secific modeling assumtions. 2. Background on the Social Security Eligibility Age The Social Security Act of 1935 set age 65 as the age at hich eole could first receive benefits. The 1889 German contributory ension system and the 1908 British means-tested system had both limited eligibility to eole age 70 and above Rodgers In the U.S., hoever, the 1890 ension system for Union army veterans and many other rivate and ublic ension lans established in the early 20 th century set age 65 as the age for benefit entitlement Costa, Indeed, Wilbur Cohen a staff member of Roosevelt s Committee on Economic Security has ritten that at no time in 1934 or 1935 did President Roosevelt, the Committee on Economic Security, or the key members of Congress handling the bill deem feasible or aroriate any age other than 65 as the earliest eligible age for receit of old-age insurance benefits. 3 The age at hich eole could first receive retirement benefits, termed the Early Eligibility Age or EEA, as reduced to 62 for female retirees beginning in Proonents of this change argued that omen ere on average several years younger than their husbands and deserved to be able to retire at the same time Meriam and Schlotterbeck, 1950,. 22. Older omen ere also seen as facing difficulties in the labor market. Then, in February 1961, President Kennedy roosed Social Security benefit exansions as art of his initial economic ackage. These roosals ere designed to address the eak emloyment situation and included a recommendation to 2 Germany reduced its retirement age to 65 in Hoever, this does not seem to have influenced the architects of the U.S. system. See htt://.ssa.gov/history/age65.html. 3 Cohen 1985,. 10. retirementage.july

5 loer the EEA for men to the same level as for omen. The EEA reduction for men as aroved by Congress and ent into effect in late Over time, a greater fraction of orkers have taken advantage of the oortunity to claim benefits before age 65. In 1965, a fe years after men first became eligible to claim at age 62, 16.6 ercent of men claimed benefits at age 62, 17.0 ercent claimed benefits at ages 63 or 64, and 66.5 ercent claimed benefits at ages 65 or older. By 1975, 29.2 ercent claimed benefits at 62, 26.1 ercent at ages 63 or 64, and 44.7 ercent at ages 65 or older. Today, 54 ercent claim benefits at age 62, 22 ercent at ages 63 or 64, and only 25 ercent at ages 65 or above. 5 There are several other Social Security olicy arameters related to retirement, including the full retirement age -- the age at hich one s benefits are not reduced for early retirement -- and the actuarial adjustment associated ith retirement at different ages. 6 Beteen 2000 and 2022, the full retirement age is to rise from 65 to 67. Workers ho choose to receive benefits before the full retirement age have their benefits reduced according to the actuarial adjustment factor of 6.7 ercent er year. 7 Workers ho claim benefits after the full retirement age receive a delayed retirement credit that increases their benefits by 8 ercent er year. While historically there as a strong financial incentive to retire by age 65, for a orker reaching age 62 today, these arameters are 4 We note that by reeatedly alternating these to rationales for adjusting the retirement age, e could quickly converge on an EEA of zero. 5 Diamond and Orszag These numbers exclude eole converting from disability benefits to retirement benefits at the full benefit age. There have been similar trends for females. 6 Though the age of full benefit entitlement is sometimes referred to as the normal retirement age NRA, Henry Aaron has ointed out that the term normal retirement age does not aear anyhere in the Social Security Act or regulations. Moreover, there is nothing normal about it since to-thirds of eole claim benefits before that age. Thus e join his crusade to eliminate this misleading term from discussions of Social Security olicy. See Diamond and Mirlees 1978 and Diamond and Mirlees 1986 for models of ho benefits should rise ith a orker s retirement date. 7 There is a slightly smaller adjustment for eole ho retire more than 36 months before the full benefit age. retirementage.july

6 aroximately actuarially fair on average. 8 Other rovisions including the ayroll tax rate, benefit calculation formulae, and earnings test affect retirement incentives as ell. 9 It is orth emhasizing that an increase in the full retirement age reresents a reduction in aggregate benefit ayments. In contrast, raising the earliest eligibility age has aroximately no effect on system finances since the benefits received later are increased to adjust for their delayed receit by an amount that is roughly actuarially fair. 10 While a full assessment of retirement-age olicy ould analyze tax and benefit levels and the rate at hich benefits rise ith age hen claiming is delayed, our emhasis in this aer is on the age at hich benefits availability begins, and therefore our olicy exeriments corresond to changing the EEA hile holding all other arameters of the Social Security system constant. For that reason, the changes e study kee exected lifetime benefit levels constant Theory To analyze otimal eligibility age olicy for Social Security, e need to combine a model of retirement decisions by individuals ith a rationale for government rovision of retirement income. In this section e first describe the model of individual decision making and sho some comarative statics for ho an individual's choice of a retirement 8 Coile and Gruber 2001 sho, hoever, that there is substantial heterogeneity in incentives across individuals. 9 For eole ages 65 and above, there is no necessary connection beteen benefit claiming and retirement. For eole beteen 62 and 64 ho continue to ork, benefits are reduced via an earnings test though the lost benefits are reaid in the form of higher later benefits. On the distinction beteen benefit claiming and retirement see Coile, Diamond, Gruber, and Jousten In this discussion, e ignore imacts of changes in the early eligibility age on income tax revenues. 11 This statement is only aroximately true. Our analysis holds exected lifetime benefits constant for each individual. An actual change in the EEA ould hold exected lifetime benefits constant for a cohort overall, but if an individual s mortality risk differed from the cohort average, there ould be distributional and incentive effects of a change in the EEA that are not catured in our model. retirementage.july

7 age varies ith roductivity groth, increases in longevity, and imrovements in health. 12 Then e combine this model ith to different rationales for Social Security one that hinges on orker myoia and another that hinges on the costs of verifying disability status. The Individual s Retirement Decision We model the retirement decision as a binary, annual, irreversible, choice. At each age, t, every erson ho is still orking faces a decision of hether or not to kee orking in that year as ell as a decision about ho much to consume. If the individual orks he or she receives additional income, t,. The retirement and consumtion decisions are made to maximize exected utility over the orker s remaining lifetime: V t A max = max E lt, ct t= current age [ v ct e ht, t lt ] tcurrent age 1 + r t 1 Utility in each eriod is an additively searable function of the utility of consumtion, vc t, and the disutility of labor effort, eh t,tl t. 13 The disutility of labor effort rises as health status declines and is zero if a erson does not ork l t =0. It may also deend on age for reasons other than health. t is the robability that an individual survives to age t. r is the discount rate. We assume that the only sources of uncertainty are health status and age of death. In articular, the age-varying age that ill be received by the orker in each year if the orker continues to ork is knon in advance, as are 12 Bloom, Canning, and Moore 2004 analyze similar issues in a model that lacks a rationale for Social Security. See also Sheshinski Although e follo conventional ractice in assuming that utility for each year is additively searable, this assumtion is not innocuous. For examle, there may be reasons other than declining health for hy eole bunch their leisure at the end of their lifetime. Some uses of leisure traveling around the orld, visiting grandchildren ho live in another city may require long contiguous blocks of leisure. In this case, the marginal value of leisure could deend on total lifetime leisure rather than simly on leisure in the current eriod. retirementage.july

8 retirement benefits hich are assumed to vary ith the date of retirement in a ay that is knon in advance. The exected future utility at time t can be exressed as a function of the three state variables: beginning of eriod assets, an indicator for hether the erson enters the eriod retired, and an indicator for hether the erson is in good health: t [ a I retired, I health ] V = V 2 t, t t An individual s choice of retirement date and the comarative statics associated ith changes in the economic environment can usefully be illustrated by considering an individual s exected retirement age vieed from the first eriod of the model in our emirical ork this ill be age 55. For each otential retirement age, R, it is ossible to calculate the difference, D R, beteen the exected value of continuing to ork through that year and ossibly continuing to ork in subsequent years and the exected value of orking through the rior year, but retiring in year R. An individual s exected retirement date, R*, ill be the age at hich this difference first becomes negative. This difference can be decomosed into three comonents. First, by orking an extra year a erson obtains extra income including the after-tax age for that year and additional entitlement to ension and Social Security benefits. The extra income results in higher consumtion and therefore higher utility in the current year and in all future years. This comonent of the difference can be calculated as the difference in value beteen coming into the eriod ith the initial asset level that ould occur if the erson lanned to retire in that eriod and coming in ith additional assets equal to the incremental income obtained by orking in that year. retirementage.july

9 EV R a R R +,1, I health R EV R [ a R,1, I health R ] 1 + r 3 Second, by continuing to ork a erson maintains the otion of orking in future. The utility benefit of the otion value is: 1 R 1 + ρ + 1 R { EV [ a,0, I health ] EV [ a,1, I health ]} R+ 1 R+ 1 R+ 1 R= 1 R+ 1 R+ 1 4 Third, the erson incurs the disutility of effort for the current year's labor, E[eh R, R]. If the exected consumtion benefits and otion value outeigh the exected disutility of effort, then the individual ill exect to ork rather than retire in year R. Figure 1 illustrates the three comonents of the individual s exected retirement decision, using a simulation from the dynamic rogramming imlementation of this model that is described belo. Curve AA shos the value of the additional year of income. As retirement is ostoned to later years, the value of an additional year of income falls because lifetime income is higher and therefore the marginal utility of additional consumtion is loer. 14 Line CC adds the otion value of continuing ork to the value of additional income and thus reresents the total benefits that accrue from orking an additional year. Otion value is greatest at earlier ages and falls to zero just before the age here the erson is certain to retire regardless of health status. Line BB reresents the disutility of from an additional year of effort hich is assumed to rise ith age as health deteriorates. The individual exects to retire at age R* -- here the CA and BB curves intersect. 14 At older ages t ill also likely fall ith age. retirementage.july

10 Consider no ho the curves ill shift over time. We simlify by ignoring otion value hich is small near the otimal retirement age. 15 Increases in roductivity raise age levels, hich results in offsetting income and substitution effects. Thus it is theoretically ambiguous hether the marginal utility of income curve ill shift left or right. The shift from line AA to line AA in Figure 2 shos an examle in hich the income effect dominates and so desired retirement ages ill fall. As longevity increases holding health at each age and the age level constant, consumtion er year of life ill fall as there ill be more years over hich to sread one's income. This change ill shift the marginal utility of income curve to the right and result in later retirement. Note, hoever, that the net imact of the income effect and the longevity effect is likely to be a shift in the AA curve to the left. Life exectancy at age 20 has increased by only about 0.25 ercent er year since 1960, hile real age groth has been roughly 1 ercent er year. Thus, on average, resources have exanded more raidly than the number of years they need to be sread over. Nonetheless, if the substitution effect of higher ages is sufficient, the AA curve could shift to the right. As health at each age imroves over time due to advances in medical care and changes in health behaviors, the disutility of effort falls, and the BB curve ill shift donard and to the right to BB in figure The net effect of income and health changes is thus likely to be a shift to the left of the marginal utility of income and a shift 15 In the model this is true because negative health shocks at older ages tend to ersist and because health status tends to shift the retirement date by only a fe years. In the real orld there is an additional reason for otion value to be small retirement decisions are not comletely irreversible. 16 Changes in job requirements over time could also shift the disutility of effort curve. If jobs require less manual effort, the curve ill shift further to the right. On the other hand, orklace changes such as increased cognitive demands or the increase in to-orker households could increase the disutility of ork effort over time. retirementage.july

11 to the right of the marginal disutility of effort. Both the magnitude of the shift in the individual's otimal retirement date and also the direction is theoretically ambiguous. The analysis so far has described the behavior of an individual orker. More generally, there ill be a searate set of curves for each orker, indexed by age level, initial-eriod assets, and health, and our analysis of retirement olicy ill involve summing social elfare over the full distribution of orker tyes. Before doing this, hoever, e need to discuss rationales for Social Security. Social Security Eligibility Age as a Cure for Myoia In our first model, the rationale for the Social Security eligibility age is to revent myoic eole from accessing their benefits too early and thereby ending u ith too lo a consumtion level in their later years. There are several different channels through hich the myoia might oerate. Myoia could oerate in the standard ay through individuals discounting the future at too high a rate erhas hyerbolically. In that case, myoic individuals ould tend to be the same individuals ho have inadequate rivate saving. Alternatively, otherise forard-looking individuals might simly retire at the first date Social Security benefits are available or the first date rivate ension benefits are available rather than going through the effort of otimizing, erhas assuming that the government or their emloyer has done the otimization for them. In this case, there might be little correlation beteen excessively early retirement and savings levels. Let R* i be the otimal retirement age for each individual if the individual ere forard-looking and could gain access to their retirement benefits at any age. Let R age be retirementage.july

12 the government-set age at hich eole can first access their benefits ith actuarially fair adjustments for delays in claiming. If credits for delayed retirement are actuarially fair, 17 forard-looking eole ith sufficient assets ill not be affected by R age ; they ill borro and lend to smooth income around the age at hich they can collect benefits. To other tyes of individuals ill be affected by Rage. First, some forard-looking individuals ith lo assets may ant to access their retirement benefits at a relatively young age. These eole ill be forced to ork longer than is otimal, and their ellbeing ill decline as the eligibility age rises. Second, some myoic individuals ould otimally ork longer than the earliest eligibility age, and these eole give u additional income by retiring earlier. As the eligibility age rises to a level closer to a myoic erson s otimal retirement age, the ell-being of these individuals imroves. The otimal eligibility age balances these to considerations, eighted by the number of eole and average er-erson utility loss of retiring at a subotimal age in each case. Social Security as Insurance Against Adverse Health Shocks Our second model interrets the Social Security retirement age as the age at hich orkers no longer need to meet a disability test to receive benefits. To analyze the issue from this ersective, e extend a model of Diamond and Sheshenski 1995 to incororate costs of screening for disability. 18 To begin, consider a oulation of orkers ith identical references and a distribution of ages, f, that ranges from to. In each eriod a orker has the 17 I.e. the exected resent value of retirement benefits is indeendent of the age at hich one claims them. 18 Waidman, Bound, and Nichols 2003 also extend Diamond and Sheshinski 1995 to incororate a more realistic model of the disability screening rocess. Their focus, hoever, is on variation in the screening mechanism and they do not address the issue of choosing an otimal retirement age. retirementage.july

13 otion of alying for disability insurance. The government screens orkers ho aly for disability. This screen costs the government A and the individual undergoing the screening B. Screening is imerfect. Thus agents ith oor health are successful at claiming disability ith robability >1/2, hile those in good health succeed ith robability g <1/2. The robability of being in oor health at each age, t, is φ t hich rises ith age. Workers receive utility from consumtion and leisure. uc is consumtion from orking and uc d is consumtion from receiving disability insurance. While orking, agents incur disutility from effort that varies ith their health status: vh >vh g. An agent in oor health ill aly for disability insurance if This simlifies to: [ u c B v h ] + [ u c B] > u c v h 1 d. 5 [ u c u c v h ] B. 6 d > The analogous condition for a healthy agent is: Define and [ u c u c v h ] B 7 g d g > g as the age levels at hich exressions 6 and 7 hold ith equality for agents in oor health and good health resectively. I.e. at ages above these levels eole do not aly for disability, hereas at ages belo these levels eole do aly. Because vh >vh g, e kno that >. g If the government does not screen for disability, orkers in oor health ill aly for benefits henever: [ u c v h ] 0 u c > 8 d retirementage.july

14 retirementage.july and orkers in good health ill aly for benefits henever [ ] 0 > g d h v c u c u. 9 Define n and ng as the age levels at hich exressions 8 and 9 hold ith equality -- at ages above these levels eole do not aly for benefits, even hen the government does not screen for disability. Assume that income transfers create deadeight loss and therefore the social cost of raising a dollar of revenue is MCF>1. Total social elfare ith screening is { } { } { } { } g g g g g d d g t d d t d f h v c u d f A B h v c u MCFc c u d f h v c u d f A B h v c u MCFc c u ] [ 1 ] [ 1 ] [ 1 ] [ φ φ,10 and total social elfare ithout screening is: { } { } { } { } ng ng n n g d d t d d t d f h v c u d f MCFc c u d f h v c u d f MCFc c u ] [ 1 ] [ φ φ 11 The difference in social elfare beteen screening and not screening consists of three comonents. First, under screening the government and alicants bear the cost of screening: Screening costs = g t t d f A B d f A B 1 φ φ 12 Second, under screening, some sick individuals ho aly for benefits are denied benefits, and some sick individuals are deterred from alying for benefits due to the alication cost. Assuming that the utility gain for individuals in oor health ho aly

15 for and receive disability benefits exceeds the marginal cost of funds, then this is a further cost of screening. Cost of denying benefits to sick= φt 1 n { u cd [ u c v h ] MCFcd } f d + { u cd [ u c v h ] MCFcd } f d 13 The benefit of screening is that it revents healthy individuals from claiming and ith robability g receiving benefits. Assuming that on average the utility gain for individuals in good health ho aly for and receive disability benefits is less that the marginal cost of funds, then this benefit is: 19 Benefit from denying ayments to healthy= 1 g f d g ng 1 φ t { MCFcd u cd + [ u c v hg ]} f d + { MCFcd u cd + [ u c v hg ]} 14 g At older ages, the fraction of the oulation in oor health, φ t, rises. This ill raise screening costs since it raises the fraction of the oulation that aly for benefits and need to be screened recall that >. It ill also raise the number of sick eole g ho are denied benefits. So both costs of screening rise ith age. Moreover, the benefits of screening denying ayments to the healthy decline ith age as there are feer healthy eole ho can otentially claim benefits. Thus at some age the costs of screening ill exceed the benefits of screening and at that age universal entitlement to retirement benefits should begin. As the oulation s health imroves over time, φ t at each age ill fall. This ill make screening orthhile u to higher ages than before raising the otimal age of universal entitlement to retirement benefits. 19 It is ossible that some healthy eole have lo enough age levels so that giving them disability benefits reresents an increase in social elfare. retirementage.july

16 4. Changes in the distribution of health In this section, e resent trends in the health of the elderly and near-elderly oulation, to identify ho health has changed over time. Health is, of course, multidimensional. While there are indices that try to combine various measures of health tyically on a 0 to 1 quality of life scale, e consider instead basic descritive data on several imortant dimensions. One can think about health differences at the high end of functioning or at the lo end. At the high end, there are questions about just ho vigorously a erson can exercise, and hat other strenuous activities they can engage in. At the lo end, questions revolve around hether the erson can care for themselves, undertake the normal activities of life, and function indeendently. For understanding the ability to ork, the relevant issue is health at the bottom end of the distribution. We focus on that dimension. Mortality is the end oint of oor health, so it is natural to begin there. Figure 3 shos the share of men at each age ho are near death hich e define as ithin to years of dying. 20 To years rior to death is a eriod in hich disability rates are very high. We reort results searately for men in 1960 and men in Because of our interest in social security retirement ages, e focus on the oulation of men in their early 60s. In 1960, the to-year mortality rate for men in their lo 60s as about 6 ercent. In 2000, the mortality rate as over 40 ercent loer. For our uroses, e care less 20 These data are from US life tables and reresent a ortrait of hat the tyical man of each age ould exerience in that year. retirementage.july

17 about changes in mortality at each age than in hat e term disability-adjusted age. We ask the question: at hat chronological age today ould one be in the same health as a erson of a given age 40 years reviously? An increase in disability-adjusted age is equivalent to an imrovement in health for that age grou. Figure 3 shos that the average 68 year-old in 2000 has the same robability of death in the next to years of life as the average 62 year-old in Thus, disability-adjusted age has increased by 6 years in the ast four decades. A similar analysis is true about life exectancy. The life exectancy of a 62 yearold in 1960 as 14.6 years. That is the life exectancy today of a erson aged 67. Thus, if one ere defining a Social Security retirement age based only on exected years until death, the retirement age ould have increased by about 5 years in the ast four decades. Mortality is not the only endoint, of course; non-fatal health may be even more imortant. We consider a number of dimensions of non-fatal health. The first is selfreorted general health status. Since the early 1970s, The National Health Intervie Survey has asked a question of the form: Would you say your health in general is excellent, very good, good, fair, or oor? 21 The tyical measure of oor health is hether the erson ansers fair or oor. Poor health measured this ay is strongly associated ith subsequent mortality Idler and Kasl, To ensure adequate samle size, e aggregate NHIS resonses for to time-eriods: and The former years are the earliest years of data availability; the latter years are toards the end of the data that have been released. Figure 4 reorts the share of men in fair or oor health over time. The jagged line is the ra data; the trend line is formed as the redictions from a quadratic in age. In the 21 The exact ording of the question has changed over time, but the meaning has been virtually the same. retirementage.july

18 mid-1970s, 29 ercent of men aged 62 reorted their health as being fair or oor. Over time, health has imroved, esecially at older ages. By the mid-1990s, one did not reach the same share of men reorting fair or oor health until ages in the lo 70s. By this measure, health has imroved by about 10 years. 22 It is notable that even ith the feer number of years in the intervening eriod, the gains in health status are larger than the gains in longevity. Healthy life is rising more raidly than are years of life. 23 This is articularly imressive because one ould exect some tendency for reorted health to remain stable over time if eole s exectations about hat they should be able to do increase ith imrovements in hysical functioning. In addition to self-reorts, one ould like to comare direct hysical assessments of health for examle, hether the erson can stand for a certain length of time or erform essential cognitive tasks. Some surveys of health do erform hysical assessments, but the questions asked are not the same over time. An alternative is to look at individual reorts of imairment in secific domains. The National Health Intervie Survey asks eole ho reort having a variety of different conditions ho many days the condition caused the erson to be in bed for all or most of the day. 24 We tabulate resonses for eole ho reort having a stroke, heart attack, ischemic heart disease, or other related conditions ICD-9 codes and These conditions are common and relatively severe. In this case, severity is a virtue: numerous studies sho that doctors diagnose less severe conditions more than they used to, and hence the set of 22 Another NHIS question asks hether eole are limited in the kind or amount of their major activity. The difficulty ith this question is that eoles major activity varies over time. The share of eole limited in their major activity, for examle, declines ith increasing age after retirement. 23 This is consistent ith the observation that disability rates among the young elderly are falling Cutler, In 1972, the secific question is about ho many days the erson as in bed for all or most of the day. In , the question is about ho many days the erson as in bed at least half the day. retirementage.july

19 eole ith less severe conditions such as arthritis or back ain ould not be the same over time. 25 Heart disease diagnoses, in contrast, seem to have matched trends in clinical measurement of disease incidence ell Cutler and Richardson, Figure 5 shos annual bed days for eole ith these conditions. We start at age 45, since heart disease is less common belo that age. Because our samle sizes are smaller, each individual observation is a three-year moving average. For the same reason, e ool men and omen. Imairment associated ith heart disease has fallen over time. In 1972, the average 62 year-old male ith heart disease reorted 20 days in bed in the revious year. By the mid-1990s, age-secific bed days ere about 5 days loer across the age sectrum. More general measures of disability suggest the same finding. The National Long-Term Care Survey has conducted assessments of disability among the elderly over the course of the ast to decades defined as the ability to erform basic activities of indeendent life such as dressing, bathing, and doing light houseork. The share of the 65 to 74 year-old oulation that is disabled in this ay fell from 12 to 9 ercent. Considering all the evidence, it is clear that health near traditional retirement ages has imroved markedly over time. Our best guess is that eole aged 62 in the 1960s or 1970s are in equivalent health to eole aged 70 or more today. 25 To rovide a sense of the magnitude of the increased diagnosis of chronic conditions, the average 62 year-old in the mid-1970s reorted about 0.7 chronic diseases. In the mid-1990s, that share of diseases as reorted by the average 47 year-old. retirementage.july

20 5. Emirical Imlementation of the Myoia Model Dynamic Programming Aroach We imlement a dynamic rogramming model using data from the Health and Retirement Survey to study the imlications of the theory discussed in section 3 in a more realistic setting. We build uon to recent aers that estimate similar models and exlore the behavioral resonses to changing the Social Security eligibility age. Our aroach is most similar to Gustman and Steinmeier In articular, e use the same secification for references, the same simulated method-of-moments estimatation technique, and the same HRS data set. Unlike Gustman and Steinmeier, ho treat only one s mortality date as uncertain, e treat both future mortality and health as uncertain; therefore our dynamic rogramming roblem is more comlicated than theirs. As a tradeoff, e make one major simlification relative to Gustman and Steinmeier in that e do not ermit a art-time ork otion. French 2005 estimates a life-cycle model of labor suly, retirement, and savings behavior in hich future ages, health, and mortality are uncertain. French s aroach is not suitable for our uroses because it does not allo for heterogeneity in references or heterogeneity in the data generating rocess for the state variables. Moreover, French uses non-searable references that constrain the income and substitution effect of an increase in age levels to cancel. Such a secification of references rules out the ossibility that the AA curve in figure 1 shifts to the left, something e ould like to be able to exlore. In articular e solve the folloing maximization roblem for each individual: retirementage.july

21 1γ ct Max + 1 lt e lt ct 1 γ h = P h a a t+ 1 t+ 1 t+ 1 = 1 + r a 0 t t + l t t β0 + β age age62 + β health bad health + εi c t + βφe V [ h. a, I retired ] here l t is an indicator that equals one if the erson orks in year t. In ords, each individual chooses consumtion and decides hether to ork or retire in the current eriod so as to maximizes the utility of the current eriod and discounted exected future utility. Current eriod utility is the sum of a consumtion term and a term that gives the utility of leisure. The latter is a function of health status, since the disutility of ork is greater ith orse health. The future is discounted for to reasons: time reference, β, and the chance of mortality, φ. There are three state variables in the model: health status, financial assets, and hether the individual has reviously made the irreversible decision to retire. Health status evolves according to a Markov rocess. Asset levels are determined by a standard asset accumulation equation and are constrained to be nonnegative. We solve the model from age 55 to age 100 using backard induction. We assume that everyone alive at 100 automatically dies at that age. Health status and retirement status are both discrete. In calculating the value function, e discretize over ossible asset levels and consumtion choices, interolate using Akima's shae reserving sline, and find the maximum using a non-linear interior oint solver maximization algorithm contained in the OPT++ toolkit. In order to let ages vary ith age and ension benefits to vary ith age of retirement, e solve the model searately for each individual in our data set. t+ 1 t+ 1 retirementage.july

22 Data Our data come from the RAND Health and Retirement Survey HRS version D and the HRS Imuted Data for Pension Wealth Calculations Version 1.0 for males in the original HRS cohort born beteen 1931 and The moments for our simulated methods of moments estimation rocedure are the fraction of samle members at each year of age from 54 to 68 ho are retired and in good health, retired in bad health, orking in good health, and orking and in bad health. Good health is defined as health that is excellent, very good, or good. Bad health is health that is fair or oor. A erson is retired if their self-reorted retirement status is fully retired or if self-reorted retirement status is artially retired and earnings are belo $10,000. To estimate the true moments, e use the entire data set. The number of observations er year of age ranges from 569 at age 68 to 2256 at age 59. To kee comutation costs reasonable i.e. to allo the model to be estimated in 8 hours using four rocessors oerating in arallel, e calculate our simulated moments using a random 132 erson subset of the data. Each orker s annual age is taken from the age in the 1992 HRS survey and is assumed to remain constant. Social Security benefits are calculated by alying the benefit formula to an imuted level of AIME based on 1992 earnings. 26 Defined Benefit ension benefits are taken from the ension benefit file described above and benefit levels are interolated for years beteen years available in that data set. Defined contribution ensions and other non-housing financial assets are assumed to earn a We have recently alied for access to the restricted version of the HRS ith SSA earnings records so as to imrove the accuracy of our Social Security benefit rojections. retirementage.july

23 ercent rate of return and can be consumed at any time Social Security benefits and ension benefits cannot be consumed until retirement. Mortality data come from Social Security Administration cohort mortality rojections for the 1940 and 1900 birth cohorts. The robability of transitioning beteen good and bad health states is estimated from to-year health transitions in the HRS. 27 Folloing Samick 1998 and Gustman and Steinmeier 2005, e assume that 40 ercent of the oulation has a discount rate of 2.5 ercent, 21 ercent has a discount rate of 7.5 ercent, 6 ercent has a discount rate of 12.5 ercent, and one-third has a discount rate of 80 ercent. We have estimated our model ith these discount rates correlated ith the initial asset-to-age ratio and ith it uncorrelated, and the to methods roduced very similar estimates. 28 Parameterizing and Estimating the Model The model has five arameters: γ, β 0, β age, β health, and σ ε.. Using only the moments described above, some airs of arameters are difficult to searately identify. In articular, as can been seen by referring to figure 1, γ and β 0 determine the location of the AA and BB curves and therefore jointly determine the average retirement age. Hoever, many airs of values of these to arameters generate essentially the same moments. Thus, some additional information needs to be brought in to identify these arameters. Gustman and Steinmeier 2005 identify γ=1.26 using the differential retirement rates of high and lo age individuals. This is an aealing aroach since it identifies the arameters from the same data as the rest of the estimation. There is of 27 We thank Amy Finkelstein for calculating these transition robability for us. 28 Once e obtain access to the restricted HRS e ill follo a rocedure like that of Gustman and Steinmeier to generate individual secific discount rates consistent ith lifetime earnings atterns and age 55 ealth. retirementage.july

24 course a large literature on values for the coefficient of relative risk aversion. Chetty 2003 argues that most microeconomic analysis suggests that γ must be beteen 1 log utility and 2, ith his referred value near 1. With log utility, the income and substitution effects cancel and the AA curve does not shift due to rising age levels. Since the AA curve ill shift right due to rising longevity and the BB curve ill shift right from imroved health, ith log utility e kno unambiguously that successive cohorts of forard-looking individuals ill choose later retirement dates all else equal. With γ=2, the income effect ill dominate the substitution effect. Simle simulations suggest that ith roductivity groth of 1 ercent er year, this ill shift the retirement date don by about 2 to 3 years every four decades the exact number deends on the sloe of the BB curve. When combined ith the longevity shift, shifts over time in the AA curve ith this arameter ill tend to reduce a forard looking individual s retirement age by about 1 to 2 years. Given that the BB curve ill shift right, the net effect is theoretically ambiguous. To sho the sensitivity of olicy conclusions to the value of γ, e fix γ at to values 1.26 and 2 and estimate the other four arameters. A second identification issue is ho to searately identify the effect of health status from other reasons that the disutility of effort might rise ith age given that oulation health deteriorates smoothly ith age. In articular, our binary measure of health status is unlikely to fully cature all health changes. Therefore, the age term in the model is likely to also be caturing some effects of health. In ractice, e find the ratio of the health coefficient to the age coefficient to be highly unstable ranging from 1.0 to over 20 deending on the other arameter values most of the estimates are beteen 5 and 10. In our olicy simulations, e resent both a loer bound estimate of the imact retirementage.july

25 of health, alloing imrovements in health to shift behavior only through the health term i.e. assuming that the age term has no health-related comonent and an uer bound estimate of the imact of health, alloing imrovements in health to shift behavior through both the health term and the age term i.e. assuming that the entire age term is attributable only to health. A third identification issue is distinguishing among different sources of heterogeneity in retirement dates. With γ and β 0 inning don the average retirement date, there are four remaining factors that can allo the model to match the emirical sread in retirement dates around the mean as ell as the sikes in retirement at age 62 and to a limited extent age 65: heterogeneity in tastes σ e, the magnitude of the age coefficient at high values everyone retires at the same date, heterogeneity in discount rates, and heterogeneity in ension lan incentives. We find that a model ith only a coule of these sources of heterogeneity can fit the basic retirement/health moments e use almost as ell as a model ith all four sources of heterogeneity and that the values of the age and heterogeneity arameters vary significantly in models ith different amounts of discount rate and ension lan heterogeneity. Thus, further rogress in identifying the model ill require, at the very least, the use of more moments for examle, matching searate retirement and health status means for those ith and ithout ensions or incororating evidence from outside the model such as from natural exeriment studies. Table 1 shos estimates from our model. These estimates are reliminary as e are currently using relatively crude measures of ension and Social Security benefits and have estimated each model ith only a fe starting values. The table also shos the estimates from Gustman and Steinmeier 2005 for comarison uroses. In our retirementage.july

26 estimates e are finding a somehat higher age coefficient than did Gustman and Steinmeier. Our health coefficients are much larger. With γ=1.26, oor health is the equivalent of 12 years of age comared ith 4 years in Gustman and Steinmeier. With γ=2.00 our health coefficient is imlausibly large. Because relatively fe eole transition from good to bad health in their mid 60s, are olicy simulations are not very sensitive to the estimate of the health arameter. Figure 6 shos the true data moments and the simulated moments for each of our to models. 6. Simulations of Otimal Policies This section reorts results of reliminary olicy simulations from each of our to sets of estimates. Figure 7 dislays the results of olicy simulations using our estimates ith γ=1.26. In order to avoid comlications associated ith conducting elfare analysis hen different individuals have different references, e conduct these simulations ith a discount rate of 2.3 ercent for all samle members. We start by solving the model for a samle of forard-looking individuals. Then e augment the samle to include a set of myoic individuals ho take the earliest-eligibility age as a cue and retire at the EEA rather than otimizing. The to left anel of figure 7 shos ho average lifetime utility varies ith the eligibility age for three different tyes of individuals. The first are forard-looking individuals ith asset to age ratios at age 55 of at least 5. We call these individuals unconstrained individuals because they have sufficient assets to consume out of if they retire before the EEA so that they are largely indifferent to the EEA. Thus their lifetime retirementage.july

27 utility is largely unaffected by varying the EEA. The second grou of individuals are forard-looking individuals ith asset to age ratios belo 5. Some of these individuals ould otimally ant to retire before the EEA esecially if they are in oor health if they could ta their Social Security benefits, but are harmed by not being able to do so. For this oulation it ould be best if there ere no EEA at all and eole could claim benefits ith aroriate actuarial adjustments in their level at any age they choose. The third grou are the myoes. At lo values of the EEA, many of them retire too early and have loer utility than if they ere constrained to retire later. As the EEA rises, average utility for this grou rises until it reaches a oint near the average retirement age that ould be desired by myoes if they ere forard-looking. At ages above this level, average utility falls as utility losses for eole ho are being constrained to retire after their otimal retirement age exceed the utility gains for eole ith high desired retirement ages ho are being brought closer to their otimum age. The otimal eligibility age for the government to set ill deend on the oulation share of these three grous. Since unconstrained individuals are essentially unaffected by the EEA, the key question is the relative size of the myoe and constrained forard-looking oulations. Three quarters of HRS samle members have asset-toage levels at age 55 that are belo 5. The bottom left anel of figure 7 shos overall average utility assuming that 50 ercent of the oulation are myoes, 37.5 ercent are constrained forard-looking individuals, and 12.5 ercent are unconstrained forardlooking individuals. With these fractions, the otimal eligibility age is Although the actual sike in retirement at age 62 is much smaller than ould occur if the oulation as half myoes, e think of myoia more broadly as reflecting eole ho retire both at the EEA and at their age of initial rivate ension entitlement -- so the fraction of eole ho retire too early could be much greater than the sike at age 62. retirementage.july