Labor Force Transitions at Older Ages: Burnout, Recovery, and Reverse Retirement

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. Labor Force Transitions at Older Ages: Burnout, Recovery, and Reverse Retirement Lindsay Jacobs and Suphanit Piyapromdee 2016-053 Please cite this paper as: Jacobs, Lindsay, and Suphanit Piyapromdee (2016). “Labor Force Transitions at Older Ages: Burnout, Recovery, and Reverse Retirement,” Finance and Economics Discussion Series 2016-053. Washington: Board of Governors of the Federal Reserve System, http://dx.doi.org/10.17016/FEDS.2016.053. NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

Labor Force Transitions at Older Ages: Burnout, Recovery, and Reverse Retirement Lindsay Jacobs Suphanit Piyapromdee Federal Reserve Board University College London lindsay.p.jacobs@frb.gov s.piyapromdee@ucl.ac.uk Preliminary. Comments welcome. This version: April 29, 2016∗ Abstract: Partial and reverse retirement are two key behaviors characterizing labor force dynamics for individuals at older ages, with half working part-time and over a third leaving and later re-entering the labor force. The high rate of exit and re-entry is especially surprising given the declining wage profile at older ages and opportunities for re-entry in the future being uncertain. In this paper we study the effects of wage andhealthtransitionprocessesaswellastheroleofaccrueswork-relatedstrainonthe labor force participation on older males. We find that a model incorporating a work burnout-recoveryprocesscanaccountforsuchreverseretirementbehaviorthatcannot be generated by health and wealth shocks alone, suggesting re-entry patterns result in largepartfromplannedbehavior. Wefirstpresentdescriptivestatisticsofthefrequency and timing of re-entry and characteristics of those who re-enter using Health and Retirement Study (HRS) panel data. We then develop and estimate a dynamic model ofretirementthatcapturestheoccurrenceandtimingofre-entrydecisionsobservedin thedata—aswellasthetransitiontopart-timework—whileincorporatinguncertainty inearnings,health,andstressaccumulation. Theburnout-recoveryprocessallowsusto accountforabout40percentofre-entry,andone-quarteroftheshiftstopart-timework with age. We also consider the lower exit and re-entry rates after 2008, and attribute thistohighoptionvaluesofworkinanenvironmentwherefuturere-entryislesscertain. Consistent with our burnout-recovery model, we see that respondents are more likely to report high levels of job stress as they continue to work when they would have otherwise stopped working, recovered, and re-entered. This offers us some information about the relative option value of work versus the burnout-recovery process. ∗We appreciate the comments and suggestions of the University of Wisconsin–Madison and Federal Reserve Board applied micro lunch participants. The analysis and conclusions set forth are those of the authorsanddonotindicateconcurrencebyothermembersoftheresearchstaffortheBoardofGovernors. 1

1. Introduction Over one-third of men who identify themselves as retired later re-enter the labor force. The figure remains as high if we instead look at men who cease working and later begin working again. If it is indeed the case that marginal productivity relative to leisure is declining at older ages and that there is some cost associated with exiting and re-entering work,theproportionre-enteringseemssurprisinglyhighandwemaynotbeabletoaccount for this through only wage and health shocks. In this paper we model a burnout-recovery process that can generate a large share of these reversals in labor force participation in later life. Following Ruhm (1990), we refer to this behavior as reverse retirement. As a suggestion that there may be some burnout-recovery process happening, we can see in the Health and Retirement Study (HRS) data that (1) these re-entry rates remain nearly as high at older ages when excluding those who initially left work involuntarily and (2) respondents report much lower job stress levels upon restarting work than those who had been working and continue to work.1 We will see this and other relevant descriptive statisticswhichmotivateourchoiceofamodelthatcapturestheburnout-recoveryprocess. Because the degree ofburnout is naturally dynamic as the process may dependon previous labor supply decisions, and since we cannot observe directly the effects of such a burnoutrecovery process in the data—or what behavior would look like if this process did not exist—a structural model of its relationship with reverse retirement is well suited. To motivate our burnout-recovery explanation of exit and re-entry, we first consider why—among those who eventually do re-enter the labor force—the individuals stopped working initially. Looking at the responses to the HRS “reason for stopping work” question, which will be described in more detail below, we see that: 17.4 percent initially stopped working because of health, and presumably re-enter when their health improves; 23.5 percent stop working because they were laid off or their business closed, and presumably re-enter when they are able to find another job (though this means it took them possibly years to do so given that HRS surveys occur every two years); 38.2 percent say their reason for stopping work was that they “retired”, and may have found out they did not like being retired and went back to work or they don’t think of retirement as stopping work. (This is quite common, as we will show in Table A2.); 11.9 percent left work initially due to what they described as “burnout”, with, as we will model, perhaps the intention of taking a break, recovering, and going back to work, with the remainder giving “unknown” or one of many other miscellaneous reasons for stopping work. While we do account for the effects of health shocks on participation decisions, the later two reasons—“retirement” and “boredom or burnout”—are what we wish to focus on here. If an individual in some way plans to stop working (retires or quits due to stress or boredom), starting to work again is not necessarily what we would expect to see though it is very common. 1This is shown below in Table 10 and is true even when controlling for age. 2

In Section 2 we discuss some related work. Section 3 presents descriptive statistics and Section 4 describes our burnout-recovery model. We describe an estimation strategy in Section 5 and give simulation results using calibrated parameter values in Section 6. In Section 7 we discuss the option value of work at older ages before concluding in Section 8. 2. Related Work There are several studies directed at reverse retirement as well as partial retirement within the greater retirement literature. Our work complements the studies described here by formulating and estimating a structural model that can generate reverse retirement as the manifestation of a burnout-recovery process. Maestas and Li (2007) present a burnout and recovery process to explain reverse retirement, as we do here. They develop an index of burnout arising from work stressors from questionsintheHRS.Thisindexvariesovertimeanditspathlooksdifferentforthosewho eventually reverse retire, those who partially retire, and all others. They argue that higher burnout levels increase the likelihood of an individual retiring. Though methodologically our work goes in another direction, we use a similar burnout index in the descriptive portion of the paper for motivation. The effects of burnout we estimate, are not from the data directly but rather are uncovered in estimation of the structural model. Maestas (2010), also using HRS data, seeks to identify whether reverse retirement is a resultofinadequatefinancialplanningandhealthshocksorwhetherre-entryisanticipated before retirement occurs. Using different definitions, between 25 to 40 percent of retirees “unretire” and some of these individuals plus another quarter of the sample transition to full retirement through partial retirement or part-time work. She concludes that over 80 of all reverse retirements we planned prior to initial retirement. When conditioning on postretirement information in her multinomial logit model, little explanatory power is added relative to the model with pre-retirement information. An earlier related paper is Ruhm (1990), which focuses on later-life work transitions beyonddirectfull-timeworktoretirement. Theseincludepostcareer“bridge”jobs, partial retirementandpart-timework,andreverseretirement,characterizingtheworkchoicepaths for over half of all men at older ages. In his sample, about 25 percent reverse retire. This is lower than the 30-40 percent range we report here, though we use a different dataset and sample birth years.2 Cahill et al. (2011) find a lower rate of reverse retirement—15 percent—when looking at those who had left “career jobs” and re-entered. 2Ruhm (1990) uses Social Security Administration’s Retirement History Longitudinal Survey (RHLS) data, years 1969-1979. Our sample, as we will see, is made up of individuals observed up to 18 years and is reduced to those who are seen for at least five of the biennial HRS waves and were working in at least one of them, as we only see characteristics about their work and subjective job experience when they are working. 3

Blau (1994) uses quarterly data from the Social Security Administration’s Retirement History Longitudinal Survey (RHLS) to give a descriptive analysis of labor force transition sequences at older ages. The quarterly data allow him to capture more of these transitions, as well as the sharp spike in labor force exit at age 65. He suggests that there are dynamic features in labor supply decisions that do not operate through the budget constraint but rather through preferences. A structural economic model—which we attempt to provide here—is then, he concludes, the proper context for studying more complicated labor force transitions at older ages. Focusing on the effects of employer-tied health insurance, French and Jones (2011) is the basis on which we construct our model. They estimate a dynamic model of laterlife work decisions using a method of simulated moments (MSM) procedure, allowing for permanent preference heterogeneity in leisure and rate of time preference, as in Keane and Wolpin (2007). In Section 4, we add the burnout-recovery process to this and attempt to match, among many other moments, reverse retirement rates with the model. 3. HRS Data and Descriptive Statistics The data we use come from the Health and Retirement Study panel of men and women in the U.S. age 50 and older. There are 10 biennial waves available, with the survey years beginning in 1992 with the most recent available being from 2010. We include males from the HRS Cohort, born 1931-1941, who were observed for at least five waves and worked during at least one. This gives us a total of 3,241 respondents.3 The rationale behind selecting those who were observed at least five times is to get an idea of the proportion of individualstowhomthisisrelevant, aswewillmissfeweroccurrencesofreverseretirement this way. Table 1 gives a summary of our sample. InthefirstWavethesampleisobserved,nearly93percentreportthattheyare“working forpay”atthetimesurveyedwhilelessthan27percentreportworkingtheWave10, which means many changes in labor force participation status are captured over this time period. The proportion of those men who consider themselves retired corresponds to this fairly well, though, for reasons we will discuss below, we will be focusing on whether respondents report that they are working for pay to measure participation.4 Wecategorizeover35percentofthesampleasbeing“ReverseRetirees”orRR.Though the definition of retirement is not straightforward as retirement may or may not indicate labor force participation, we will use “Reverse Retiree” to identify an individual who, around what might be colloquially understood as retirement age, ceases to work for pay (“retires”)andlaterbeginsworkingforpayagain(“reverses”hisdecisiontostopworking). 3More details about our sample are found in the Appendix. Fewer are used in estimation of the model and some descriptive statistics as not all respondents answered all survey questions in every Wave. 4We use Rand HRS variable rWwork as the “working for pay” variable. 4

Table 1: Some Characteristics of the HRS Sample Respondents Time-Invariant Characteristics: Educational Category (3,229) Less than HS 22.3% HS or GED 34.6% Some College 19.6% College and Above 23.5% Percent Ever Reverse Retiring (3,241) 35.5% Time-Varying Characteristics: Wave 1 Wave 10 Average Age at Survey (3,117 and 2,287) 55.3 73.3 Self-Defined Retirement Status (2,865 and 2,187) Not Retired 89.2% 9.7% Partly Retired 7.6% 20.4% Completely Retired 3.3% 69.9% Percent “Working for Pay” (3,115 and 2,283) 92.9% 26.8% Self-Reported Health Status (3,117 and 2,286) Excellent 26.0% 9.3% Very Good 32.9% 28.9% Good 28.1% 37.2% Fair 10.5% 19.2% Poor 2.5% 5.3% Marital Status (3,117 and 2,287) Married or Coupled 86.9% 79.8% Divorced or Separated 8.8% 8.8% Widowed 1.3% 8.8% Never Married 3.0% 2.7% Percent with Spouse “Working for Pay” (2,641 and 1,748) 67.0% 23.2% Note: Number of responses in parenthesis above. 5

Figure 1: Labor Force Status by Age FT and PT Working Proportion 1.00 Part Time Full Time 0.80 0.60 0.40 0.20 0.00 53 55 57 59 61 63 65 67 69 71 73 75 77 79 Note: 26,926 person-years from HRS sample described in text. Individuals whom we do not observe exiting and subsequently re-entering work are “Non- Reverse Retirees” or non-RR.5 Next we will look at the relevant patterns around retirement and reverse retirement that we find in the HRS data. Though our main contribution is providing and estimating a model that can generate the unretirement phenomenon, these descriptive figures will help us better understand the behavior of our sample. 3.1. The Timing of Initial and Reverse Retirement First,inFigure1theproportionworkingbyage,aswellasthepercentofthoseworking who exit by age in Figure 2 on page 8.6 Over 90 percent are working in their early fifties; by age 65 about half are. At younger ages, few are working part time, though from their late 60s onward, the majority of those working are working part time. We have in Figure 2 the percent of respondents who begin to work after having previously stopped (as a proportion of those not working) by age, whom we refer to as the “reverse retirees”. The chance of re-entering the labor force is very high for those who are not working under age 60 and declines with age. Since re-entry is conditional on not working, this could be capturing the fact that those who stop working at relatively early ages(before62)aredifferentinotherwaysthatmakethemmorelikelytore-enterthelabor force (e.g., they had initially left work due to a layoff). It may also have to do with the fact that the better health people experience at younger ages means the odds of still being able to perform work-related tasks are higher. We suspect that re-entry at the youngest 5Usingthissurveyresponse,forapersontobecountedasareverseretireeoverthreeWaves(workingnotworking-working),timeoutofthelaborforcecouldconceivablyrangefrombeingoutofthelaborforce on the day of the second of the three survey Waves for up to the nearly four years between the first and third of the three surveys. 6UsingRandHRSvariablesrWworkandrWjhourshere. Part-timeworkinvolveslessthan30hoursper week. 6

ages is more likely a re-entry that occurs after unplanned exit or layoffs, whereas re-entry in later years arises from a burnout-recovery type of process as we model here. In Appendix Figure A1 on page 41, we have, among those who re-enter the labor force, whether their re-entry is into full-time or part-time work. At younger ages, re-entry is far more likely to be into full-time work (nearly 90 percent re-enter into full-time jobs at age 54). Again, this may indicate that those who re-enter at younger ages have circumstances very different from those re-entering when older. At older ages, re-entry is into part-time work for most, and re-entrants are much more likely to be working part time at those ages than those working overall. For instance, at age 75, 80 percent of re-entrants start part-time jobs, whereas just over 60 percent of all workers at age 75 are part time, as seen in Figure 1. While many spouses appear to coordinate the timing of retirement (Casanova, 2010), it’s not clear whether their decisions to return to work might be related. In our sample, about 16 percent of wives who were not working begin working again in the same period their husband reverse retires. We have excluded the spouses’ working decisions in this version of the model as a simplification, though the model could readily be extended to accountforjointdecisions,especiallyifcapturingtheprecisetimingofre-entryisofinterest. 3.2. How Do Reverse Retirees and Non-Reverse Retirees Differ? Now we will see whether there are significant differences we can observe in the data between those who will reverse retire and those who do not. We consider health and other reasons forstoppingwork, possibledifferences inassets, education, permanent income, and retirement enjoyment and re-entry. We find that, in many ways, reverse retirees and others are remarkably similar on these observable characteristics. Reasons for Stopping Work Here we look at some of the reasons respondents give for stopping work. Table 2 gives respondents’ reasons for stopping work, separated into those who eventually return (RRs) to work and those who do not (non-RRs). We can see that those who do return to work were slightly less likely to have stopped working due to being laid off (17.3 percent versus 18.2 percent), but somewhat more likely to have left work initially due to health reasons (20.3percentversus17.8percent). “Retired”wasamorecommonreasoncitedamongthose who never return to work (40.5 percent) than among those who do return (31.1 percent). Still, it is somewhat surprising that over 30 percent of those who ultimately reverse retire said they were stopping because they were retiring. We suspect they either do not think of retirement as the state of no longer working or they find that, unexpectedly, they do not like not working and would rather return to work.7 7Indeed, as we see in Table A2 of the Appendix, a high proportion—over three-quarters—of respon- 7

Figure 2: Transitions Out of and Back Into Work kroW TP fo tuO snoitisnarT gnikroW toN fo tuO snoitisnarT transitions out of FT 100% 80% 60% FT to Not Working Remain FT 40% FT to PT 20% 0% 53 55 57 59 61 63 65 67 69 71 73 75 transitions out of PT work 100% 80% 60% 40% PT to Not Working PT to FT 20% Remain PT 0% 53 55 57 59 61 63 65 67 69 71 73 75 Transition out of not working 100% Remain Not Working 80% FT Re-Entry PT Re-Entry 60% 40% 20% 0% 53 55 57 59 61 63 65 67 69 71 73 75 kroW TF fo tuO snoitisnarT Note: Includes 26,926 person-years. 8

Health, Exiting and Reverse Retirement Looking at the relationship between health status and changes and labor force exit, we can see that the labor force is associated with poorer health and changes for the worse in health, as seen in Table 3. This is important since leaving the labor force due to health means the chances of re-entering in the future are also low due to health. Those in worse health to begin with are more likely to exit whether their health is worse or better. Exiting the labor force is also associated with the respondent’s wife’s health status and Table 2: Why Respondent Stopped Working Reason for Stopping Work Non-Reverse Retirees Reverse Retirees Laid Off / Firm Reorg. 18.2% 17.3% Poor Health, Disability 17.8% 20.3% Business Closed 6.4% 6.2% Retired 40.5% 31.1% Bored 8.2% 11.6% Family 1.4% 1.7% Family Moved 1.1% 1.7% Find Better Job 0.6% 0.9% Other 5.8% 9.1% Observations 2,267 1,166 Notes: “Other” includes family reasons or relocation, refused, doesn’t know travel, pension incentive, and others. Table 3: Labor Force Exit by Self-Reported Health Status Percent Who Remain Working when Health Is Current Health Status∗ Worse or Much Worse Same, Better, or Much Better Excellent 75.58% (.10) 86.64% (.23) Very Good 77.88% (.24) 83.23% (.36) Good 73.53% (.37) 80.41% (.31) Fair 64.51% (.23) 76.65% (.09) Poor 58.23% (.06) 77.70% (.01) Note: 2,706 person-years forWorse or Much Worse and 12,761 person-years for Same, Better, or Much Better. ∗Parenthesized numbers sum to one in each column. In the first row of the first column, .10 indiscates that 10 percent of those whose health is Worse or Much Worse compared to last period currently report that they are in “Excellent” health. dents,whetherreverseretireesornot,saytheyintendto“continuepaidwork”post-retirement. Evidently, “retirement”doenotimply“notworking”tomostrespondentsexante. Atthesametime,responsesinthe HRS for whether the respondent considers himself retired line up quite well with whether he is “working for pay” or not. 9

changes in it, shown in Table 4. Again regardless of whether one’s spouse is in better or worse health compared to the previous period, those whose spouse is in poor health are less likely to remain in the labor force but not to a great extent. Table 5 shows that re-entering the labor force is also associated with one’s own health, but is less related to one’s spouse’s health status and change in health. Those whose own health became better were more likely to re-enter the labor force, while those whose wife’s health was much worse were more likely to re-enter. This might be suggesting that returning to work to help pay for medical expenses is chosen over remaining out the labor force in order to provide some in-home care. When faced with a negative health shock to one’s spouse—which presumably requires additional care taking and medical procedures—an individual can choose whether to work providingcareathomeortoworkandpayforcarethroughadditionalincome. Whenone’s own health unexpectedly worsens, he may want to work more to finance medical expenses or he may need to work less due to poor health. Medical expenses are shown in Table A7 of the Appendix by age category. While the maximum reported can be quite high, the median level even for the oldest age categories is only around $1,500 for out-of pocket medical expenses. Table 4: Labor Force Exit by Spouse’s Self-Reported Health Status Percent Who Remain Working when Spouse’s Health Is Spouse’s Health Status∗ Worse or Much Worse Same, Better, or Much Better Excellent 80.82 % (.08) 85.34 % (.24) Very Good 78.28 % (.24) 81.45 % (.37) Good 81.35 % (.32) 81.04 % (.29) Fair 78.36 % (.23) 76.98 % (.09) Poor 76.15 % (.13) 77.57 % (.02) Note: 2,758 person-years forWorse or Much Worse and 10,443 person-years for Same, Better, or Much Better. ∗Parenthesized numbers sum to one in each column. Table 5: Reverse Retirement by Self-Reported Change in Own and Spouse’s Health Change in Own Health Percent Re- Change in Spouse’s Health Percent Re- Since Last Period Entering LF∗ Since Last Period Entering LF∗ Much/Somewhat Better (.22) 14.29% Much/Somewhat Better (.20) 11.93% Same (.52) 11.96% Same (.54) 12.74% Somewhat/Much Worse (.26) 11.34% Somewhat/Much Worse (.25) 14.57% Note: 9,009 person-years for own-health changes and 6,903 for spouse health changes. ∗Using changes in rWwork status. 10

Table 6: Total Assets by Age Group and whether Reverse Retiree Total Assets (Including Housing) non-Reverse Retirees Reverse Retirees Age Category Mean Median Mean Median Obs. 50-54 $357,108 $142,417 $322,459 $159,167 2,278 55-59 460,596 193,056 381,729 175,000 5,978 60-64 567,724 223,953 486,295 213,284 7,519 65-69 652,218 260,760 570,851 249,454 6,985 70-74 641,595 273,369 644,357 251,965 4,399 75-79 515,784 238,384 761,379 252,000 1,321 In Figure A2 on page 41 of the Appendix, we can see that the probability of someone returning to work depends not only on changes in his health, but also his level of health in the past period as well as his age. This figure graphs the predictive margins resulting from probit estimates of the probability of returning to work given one’s change in health status, past self-supported health, and age. This figure gives the probability of re-entering the labor force for those whose health has improved by age. We can see that at all ages, those whose health had been good in the past are more likely to return at all ages relative to those whose health was fair and poor, and that the probability of returning decreases with age. A similar pattern holds for those whose health is the same or worse, though with the series representing the probability of returning being shifted down. This may be suggesting that voluntary time spent out of the labor force at these ages is not only intended to contribute to recovery from burnout but also physical convalescence. Assets, Education, Income and Reverse Retirement Now we will show the seemingly weak relationship between reverse retirees and nonreverseretireesonobservableassets,educationandincome. Thegreatestdifferencebetween the two groups is in assets, but the fact that reverse retirees and non-reverse retirees are are quite similar overall by these measures is one motivation for a model in which the unobservable effects of burnout and recovery generate reverse retirement. Table 6, gives total assets, including housing, by age category for both non-RRs and RRs. Mean assets grow until ages 65-69 (and to ages 70-74 for median assets) and decline after that for non-RRs, as labor force participation is quite low at that point. For reverse retirees, mean assets begin at a lower level than mean assets for non-RRs, but continue to increase for every age category; median assets start off slightly higher than non-RRs ages 50-54 and continue increasing, though the median assets are roughly similar for the two groups at all ages. Though not shown here, there are similar patterns for mean and median non-housing assets by age. 11

Table 7: Reverse Retirement by Education Category Percent Reverse Retiring Less than HS (.24) 33.12% GED (.06) 36.88% High School (.30) 36.82% Some College (.19) 35.78% College (.21) 35.30% Total (1.00) 35.43% Note: 2,681 individual responses. Table 8: Reverse Retirement by Earnings Category Quantile (Median in Quantile) Percent Reverse Retiring Lowest ($18,506) 34.48% 2 (35,304) 29.22% 3 (49,317) 32.00% 4 (67,341) 29.38% Highest (107,553) 34.69% Total 31.96% Note: 2,306 individual responses. Earnings quantile is based off of the average earnings for an individual when he is 50 to 60 years old. Those for whom we cannot observe average earnings somehow have higher rates of RR, as the 32% RR in this table is low. The probability of reverse retiring varies only slightly by educational attainment category and earnings when working between ages 50 and 60. Those in the educational attainment category of GED and High School were most likely to reverse retire (both nearly 37 percent), as seen in Table 7, while those with less than high school were only somewhat less likely (33 percent). Table 8 suggests that un-retiring may also have little to do with earnings history. In the first column is the earnings quantile based of of respondents’ average earnings when he is observed between ages 50 and 60 in the HRS. As we can see, while the probability of reverse retirement is quite high for those with the highest level of earnings, at nearly 35 percent, it is almost equally as high for those with the lowest level of earnings. This again points to financial constraints perhaps not be a universal driving force for reverse retirement as re-entry does not vary across those who have very different earnings histories. Retirement Enjoyment Surprisingly, individuals are actually somewhat less likely to return to work if they report in the preceding interview that they do not enjoy retirement, as we see in Table 9. This could be due to a number of factors that go beyond measurement error. For instance, 12

Table 9: Reverse Retirement by Prior Period’s Satisfaction with Retirement Percent Reverse Retiring Next Period Satisfied with Retirement? Unrestricted1 Enjoy Work2 Very 7.50% (.61) 10.86% (.59) Moderately 8.52% (.32) 13.54% (.34) Not At All 5.43% (.07) 10.48% (.07) Total (1.00) 7.68% 11.72% 1Entire sample. Includes 7,314 person-years. 2Includes 2,827 person-years. Sample is restricted to respondents who said they would work if the income was not necessary. it could be that some retirees do not enjoy retirement because, while they may prefer to work, they are not working due to health reasons. The same health factors that lead them to be less happy in retirement are the same factors that may preclude re-entry for this group. In any case, if re-entry rates are essentially the same across retirement enjoyment levels, this question is not likely to help us explain “unanticipated” reverse retirement arising from shocks in utility of leisure as opposed to shocks in the budget constraint. Even when we restrict the sample to respondents who have strong preferences for work, thereappearstobenoconnectionbetweenunsatisfactoryretirementandre-entrydecisions. The rightmost column inTable 9 shows that among those who reported that they “would continue working even if [they] did not need the income,” the reverse retirement rates are roughly the same regardless of whether they enjoyed or did not enjoy retirement in the precedingyear. Forthesereasons, wedonotincluderetirementexperienceasacontributor to reverse retirement in our model. Again, however, it is possible that the health factors thatleadsomeretireestobeunhappilyretiredconcurrentlyprecludethemfromre-entering the labor force. We capture this by allowing the quantity of leisure to depend on an individual’s health status both when he is and is not working. 3.3. Stress and Work Wewillclosethisdescriptiveportionofthepaperbylookingattherelationshipbetween work and stress. At this stage in our modeling, we have not made a distinction between the concepts of “burnout”, “boredom”, and “stress”. For the time being we will think of “burnout” as something that arises as work “boredom” and “stress” culminate, and diminishes when one is not working (and to a lesser extent when one works part-time as opposed to full-time). These stress measures, while related to the effect of burnout we would like to recover, give us insight possibly into the evolution while working, but cannot be observed when one is not working. We know how stressful one finds his job upon re- 13

Table 10: Job Stress for Re-Entrants and Continuous Workers Stressful Obs Continuous Work 50.8% 12,262 Re-Entrants 31.2% 932 Table 11: Job Stress by Occupation, Age and Whether Part-Time or Full-Time. Proportion Reporting Stressful Job: Occupation PT FT All .37 .71 .66 Managerial/Speciality (717) (4,264) (4,981) .37 .67 .60 Spec. Operator/Technical (1,015) (3,688) (4,703) .35 .63 .56 Sales (827) (2,422) (3,249) .23 .59 .52 Clerical/Admin. (289) (1,241) (1,530) .26 .56 .48 Farming/Forestry/Fishing (423) (1,142) (1,565) .26 .59 .55 Mechanics/Repair (217) (1,614) (1,831) .31 .49 .46 Construction/Extractors (297) (1,640) (1,937) .28 .59 .56 Precision Production (116) (1,090) (1,206) .19 .52 .43 Services (701) (1,883) (2,584) .30 .51 .47 Operators (963) (4,313) (5,276) Stress by Age Category: Age: 50-54 55-59 60-64 65-69 70-74 75-79 Stress: .64 .60 .51 .40 .34 .34 14

entering, however, and the fact that re-entrants find their jobs less stressful than those who were working continuously between waves suggests that there is some recovery process.8 That the recovery process and its effect on work decisions cannot be observed motivates our model. In Table 10 we can see that the job stress reported differs for those who just re-entered work and those who has been working the period prior. Those who have just re-entered are much more likely to report that their jobs are not stressful (nearly 51 percent) than those who had also worked the in the past period (31 percent). This might suggest that there was some burnout or stress recovery process happening for those who spent some time out of the labor market; they leave work due to high stress or burnout and re-enter when they have taken a break and recovered.9 Table 11 gives job stress reported by occupation category and whether working full time or part time, as well as the proportion within age categories who report that their job is stressful. While stress does differ somewhat across occupations, the difference between full-time and part-time workers’ stress levels within each occupation is much greater. This suggests that knowing occupation may not be more informative than knowing whether a respondentispart-timeorfull-time,whichisusefulasweincludethestressasacontributor to exit and subsequent reverse retirement and can more easily handle the full-time versus part-time work choice than we can occupation choice. In our model, working part-time not only gives more leisure time than working fulltime, we also allow for the possibility that working part-time contributes less to stress and burnout. We describe the model and this aspect of it in the next section. 4. A Model of Burnout and Recovery In this section we will describe the setup of the model. The present framework extends French and Jones (2011) by incorporating a burnout-recovery process, allowing preference parameters to vary across individual types. Our goal is to have a model that can generate overall participation levels and reverse retirement occurrences by age and health status among other dimensions, explaining especially reverse retirement rates that are beyond what can be explained by health, financial, or preference shocks alone. It will allow us to determine the extent to which a burnout-recovery process matters for generating the high levels of reverse retirement we see in the data. 8Atthesametime,re-entrantsalsogointopart-timeworkmoreoftenthanfull-timeworkatolderages and, as we will see, part-time workers report less job stress. Still, it is not clear why the reverse retirees would not instead go into part-time work earlier rather than stop work an restart. In any case, presenting further descriptive patterns on job stress could provide more insight. 9Job stress and other factors just before stopping work for RRs and non-RRs are shown in Tables A5 and A6 in the Appendix on page 38. 15

4.1. Preferences Inthisproblemwehaveahouseholdheadwhochoosesworkhours(0,part-time,orfulltime), consumption level and savings, and whether to apply for Social Security benefits10 in each year to maximize his expected lifetime utility at age t, t = 1,2,...,T +1. In each period the individual faces some survival uncertainty. If he lives, which occurs with some probability s , he receives utility from consumption C and leisure L . The t t t within period utility function takes the form 1 (cid:16) (cid:17)1−ν u(C ,L ,(cid:15) ,P ) = CγL1−γ +α (cid:15) (P ) (1) t t t t 1−ν t t S,p t t where (cid:15) (P ) is the preference shocks associated with the participation choice P and is t t t known by the individual at time t. The participation decision P can take on the values t FT (full-time work), PT (part-time work) or R (“retired” or not working) in all periods. The quantity of leisure he enjoys, which will also depend on health and whether he was working last period, is given by L = L−N −FC −φ 1 −φ 1 −φ RE (2) t t t HF {Ht=Fair,Pt(cid:54)=0} HP {Ht=Poor,Pt(cid:54)=0} RE t where L is the total annual time endowment measured in hours. The hours worked N is t equal to zero when P = R, 1,500 when P = PT, and 2,000 when P = FT. Workers who t t t leave the labor force re-enter at the time cost of φ where RE is a 0-1 indicator equal RE t to one when P = FT or PTandP = R.11 t t−1 To capture the empirical fact that health statuses are correlated with participation and reentry decisions, we allow the quantity of leisure to depend on an individual’s health status H ∈ {Good, Fair, Poor}. t Finally, to incorporate the burnout-recovery process into the model, we define the fixed cost of working, FC , as t FC = (α +α t)1 +α AP , (3) t P P,t {Pt=PTorFT} AP t The first coefficient α in (3) represents the fixed cost component to work. The second P term, α allows the fixed cost of work to increase linearly with age. The third coefficient P,t α captures the burnout-recovery process where AP is the accumulated work periods. AP t If an individual works full-time in period t then AP increases by α > 0 if the respont S dent reports that his work is stressful and by α > 0, while if he does not work then AP nS t 10In this version, Social Security application is deterministic: Every individual will apply at age 65 exactly. 11InFrenchandJones(2011),there-entrycostisequivalentto94hoursofleisureinayear. Individuals are allowed to reenter the labor force after retirement, and are heterogeneous in their willingness to work. The focus of their paper is to assess the effects of health insurance on retirement behavior. We suspect thatbymatchingthelevelsandtimingofreverseretirementbyage,health,andassetlevels,ourestimated re-entry cost should be lower than theirs. In Casanova (2010), switching cost is modeled as a permanent wage decrease when one switches from full-time to part-time or retired. 16

decreases by α in the following period. Formally, we define NW  AP +α 1 +α 1 if P = FT or PT AP = t−1 S {strt−1=1} nS {strt−1=0} t−1 (4) t AP −α if P = R t−1 NW t−1 as the accumulated participation units in time t. With probability s an individual remains alive at age t conditional on being alive at t age t−1. An individual values the bequests of his assets, A , upon his death, which occurs t with probability 1−s , according to the bequest function, t θ (A +K )(1−ν)γ b t 0 b(A ) = . (5) t 1−ν The parameter K measures the curvature of the bequest function. In estimation we will 0 allow the consumption weight γ, the subjective discount factor β and, the fixed cost of work parameters α ,α to vary across types of workers. P P,t 4.2. Budget Constraints The individual has three sources of income: current household income from working, YR, asset income rA where r is the pre-tax interest rate, and Social Security benefits ssR. t t t The asset accumulation equation is given by A = (1+r)A +YR+ssR×B −C (6) t+1 t t t t t where B is a 0-1 indicator equal to one if the individual is eligible for Social Security t benefits. For simplicity, we do not include pension benefits, government transfers other than Social Security, and medical expenses in the budget constraint. This will, however, be included in future versions. Post-tax income is defined as YR = Y (rA +W N ,τ) t t t t where τ is the income tax and W denotes annual wages. t Additionally, to both simplify the problem and reflect the difficulty in doing so at older ages, individuals cannot borrow, A +YR+ssR−C ≥ 0. (7) t t t t We estimate the (log) annual earnings for an individual i as lnW = W(H ,t)+ϕN +f +η (8) it it it i it where H is health status, N indicates full-time work, f represents an individual-specific it it i effect and η is an idiosyncratic error term at age (time) t. it 17

4.3. Value Function Let X denote the state variables, which include {t,A ,AP ,H ,P ,W ,ss }. The t t t t t−1 t t individual’s recursive problem can be written as (cid:26) V (X ) = max u(C ,L ,(cid:15) ,P )+β(1−s )b(A ) (9) t t t t t t t+1 t+1 Ct,Pt (cid:90) (cid:27) +βs V (X ,(cid:15) )dF (X |X ,C ,P ,(cid:15) ) . t t+1 t+1 t+1 t+1 t t t t subject to the borrowing constraint in equation (7). For simplicity, it is assumed in this version that workers receive Social Security benefits upon turning 65 years old and so B t is not a choice variable.12 The solution to the individual’s problem consists of the decision rules on consumption and participation choices that solve (9) backwards from terminal period T. To simplify the model solution, we assume that (cid:15) is drawn from an Extreme Value Type-1 distribution. t Following Casanova (2011), the individual’s problem can be solved in two steps as follows: (cid:26) V (X ) = max max[u(C ,L ,(cid:15) ,P )+β(1−s )b(A ) (10) t t t t t t t+1 t Pt Ct (cid:90) (cid:21) (cid:27) +βs V (X ,(cid:15) )dF (X |X ,C ,(cid:15) ) +(cid:15) (P ) . t t+1 t+1 t+1 t+1 t t t t t Inthefirststep, wesolvetheinnermaximizationbycomputingtheoptimalsavings(equivalent to solving for consumption) conditional on each discrete participation choice. Given the optimal consumption in the first step, the outer maximization is then solved by choosing the participation choice that yields the highest value given the realization of preference shocks. Table12summarizesthevariableswehaveincludedinthemodel. Nextwewilldescribe the procedure for estimating this model. 5. Estimation Procedure Through the method of simulated moments (MSM), we can find the preference parameters that generate simulated life-cycle decision profiles that best match the decision profiles found in our data. The model can be estimated using a two-stage approach similar to Gourinchas and Parker (2002), French (2005), French and Jones (2011) and others, which makes the problem easier computationally. In the first stage, the parameters that can be determined outside the model are estimated, which include the state transition 12In our sample, over 95 percent had claimed their Social Security benefits by the age of 65. As many claimed benefits before 65, however, it will be a priority in future versions to make applying for benefits a choice variable. 18

Table 12: Summary of Variables Description State Variables: t Age at time t P Participation decision last period t−1 A Total assets in 2010$ t H Health status: good, fair and poor t AP Accumulated work periods t SS Social Security earnings t str Work stress level t Choice Variables: P Labor force participation decision, P ∈ {R,PT,FT} t t C Consumption t Preference Parameters: Shared: β Time discount factor φ Leisure cost of fair health HF φ Leisure cost of poor health HP α Fixed cost: linear age trend P,t α Fixed cost: additional AP unit if job is stressful str α Fixed cost: additional AP unit if job is not stressful no str α Fixed cost: decrease in AP when not working no work Varying by Preference Type: ν Coefficient of relative risk γ Consumption weight θ Bequest weight B K Bequest shifter 0 φ Fixed cost of working P φ Reentry cost RE α Weight on burnout-recovery process AP 19

probabilities. In the second stage, he preference parameters of the model are estimated jointly with the type prediction parameters using first-stage estimates. 5.1. Moment Conditions and Identification The parameters we find will be those that generate moments from simulated data that are closest to the same moments from the HRS data using simulated method of moments techniques The moments for each age between 61-72 are matched to give identification of the behavioral parameters. Moments at ages 50-60 may be less informative about the burnout-recovery process since at these ages we have reason to think that transitions out of and back into work may be more due to layoffs or other involuntary exits as opposed to the burnout-recovery process that leads to reverse retirement at older ages. There are 51T moments, with T = 12: 1. Labor force participation by health status and age (2×2×T = 4T moments). 2. Assetsatthe25th, 50th, and75th percentilesbyhealthstatusandage(3×2×T = 6T moments). 3. Labor force participation by assets (2×3×T = 6T moments). 4. Transitions from full-time to not working and not working to full-time work by age (T +T = 2T moments). 5. Proportion decreasing work (FT to PT, FT to not working, or PT to not working) or increasingwork(notworkingtoPT,notworkingtoFT,orPTtoFT)byaccumulated stress level (1-10) and age (2×(10×T) = 20T moments). 6. Labor force re-entry by time out of labor force (1-5) and accumulated stress level (high or low) and age (5×2×T = 10T moments). 7. Participation by work preference index (high or low) and age (2T moments). 8. Labor force exit rates by age (T moments). The parameters of the model are identified through these moments. In particular: • Parameters for the consumption weight γ and the coefficient of relative risk aversion ν are identified through moments on savings rates and participation rates (whether full-time, part-time, or out of the labor force) by age and asset levels. • The utility cost of working while in poor health, ϕ , is identified by the proportion H working by age and health status. 20

• The fixed cost of labor force participation, ϕ , is identified by transition rates from P (to) full-time participation to (from) retirement, with no part-time work in between. • The coefficient on accumulated participation utility cost, or “burnout”, α , is iden- AP tified with the rate of exit from the labor force or the transition from full-time to part-timeworkbyaccumulatedparticipationlevelsbyagecategory. Ifα isgreater AP than zero, we should see higher exit rates when burnout is high. • Thecoefficientonthereductionofburnout—the“recovery”coefficientα —isiden- NW tified by the re-entry rates by accumulated participation, time out of the labor force, and age. • ϕ participation by age and health. P,t • The bequest weight θ and bequest shifter K are identified by asset levels by age b 0 (asset levels should be decreasing with age, with there being a lower probability of survival in the next period, if these parameters are low); K is also identified by 0 assets by age and health level, to distinguish bequests from precautionary saving in the expenses incurred or lost earnings in event of bad health. Returning to the estimation procedure, the parameters estimated in the first step are represented by χ. Further, let θ denote the vector of parameters estimated in the second (cid:98) step which includes parameters of utility function, fixed costs of work, and type prediction. The estimator θ(cid:98)is given by θ(cid:98)= argmin ϕ (cid:98) (θ,χ (cid:98) )(cid:48)Ω ϕ (cid:98) (θ,χ (cid:98) ) (11) θ where ϕ denotes the 51T vector of moment conditions, and Ω is a symmetric weighting (cid:98) matrix. We use a weighting matrix that contains the inverse of the estimated variancecovariance matrix of the estimates of the sample moments along the diagonal and zero elsewhere. The solution to (11) is obtained by the following procedure 1. Compute sample moments and weighting matrix Ω from the sample data. 2. From the same data, we generate an initial distribution for health, wages, AIME, assets, accumulated work periods and preference type assigned using our type prediction equation (described below). Many of the first-stage parameters contained in χ are also estimated from these data. 3. Using χ, we generate matrices of random health, wage, mortality, burnout from part- (cid:98) time work, and preference shocks. The matrices hold shocks for 10,000 simulated individuals. 21

4. Each simulated individual receives a draw of assets, health, wages, accumulated work periods,AIME,aswellaspreferencetypefromtheinitialdistribution,andisassigned one of the simulated sequences of shocks. 5. Given χ and an initial guess of θ, we compute the decision rules and simulate profiles (cid:98) for the decision variables. 6. Compute moment conditions by finding the distance between the simulated and true moments, which we seek to minimize as shown in (11). 7. Pick a new value of θ, update the simulated distribution of preference types, and repeat steps 4-7 until we find the θ(cid:98)that minimizes (11). 5.2. Preference Heterogeneity To account for unobservable differences among reverse and non-reverse retirees, we allow permanent preference heterogeneity across individuals. This approach was used in such influential papers as Heckman and Singer (1984) and Keane and Wolpin (1997) and adoptedbyFrenchandJones(2011). Inthesemodels, eachindividualisassumedtobelong to one of a finite number of preference types. The probability of belonging to a particular type is given by a logistic function of the individual’s initial state vector which includes age, initial wages, health status, AIME, and preference index. We estimate the type probability parameters jointly with the preference parameters in the second step. We have two types and allow for consumption weight γ, discount factor β, and fixed cost of work parameters α , α , α and α to differ by type. The probability 0 1 2 3 of being a certain type will depend on initial health, assets, income, age, AIME, and one’s work preference index level. We will describe this index briefly. Work Preference Index The work preference index is used as a measure of “willingness to work” as in French and Jones (2011). They construct a work preference index based on responses to three HRS questions given in Wave 1 interviews and our is very similar but not identical. While there may not be a strong connection with this preference index and re-entry, it will allow us to have types that better match levels of labor force participation. Here we present responses to these questions, also noting how the responses, and thus the preference index constructed from them, are independent of whether one is a “reverse retiree” or not in our categorization. The work preference index is constructed using three HRS questions. The first of the three questions asks whether the respondent would continue working even if he did not need the income from his job.13 Overall, nearly 70 percent of respondents either “agree” or 13Question V3319 in the HRS files. 22

“strongly agree” with the statement. We can see that if we look separately at those whom we identify as reverse retirees (RR) and those who are not (non-RR), there is almost no difference. These responses are given in Table 13. The second question used to construct the work preference index asks respondents whether the are looking forward to retirement.14 The results are in Table 14. While most people say theywouldcontinue toworkif the income from theirjobs was not needed, aswe saw in Table 13, at the same time a majority also look forward to their retirement. Fewer than 20 percent said the idea of retirement made them “uneasy”. But again, whether one looks forward to retirement or not does not differ on average across those who do and do not re-enter the labor force after exiting: There is less than one percentage point difference for each response across non-reverse retirees and reverse retirees. The third question that informs the French and Jones (2011) preference index asks respondents how much they enjoy their jobs on a scale of 0 (dislike) to 10 (like a great deal).15 This question was not asked of most respondents—only 146 in our sample. We will not use this as part of our index due to the low number of responses, though the results are in Table 15. These HRS questions were only asked in the 1992 Wave 1. As in French and Jones (2011),weconstructedtheindexbyfirstregressingparticipationinfutureWaves4onwards on responses to the “would work even if I didn’t need the money” and “look forward to retirement” questions, as well as age, average income ages 50 to 60, future participation levels, health, and interactions of these terms. The preference index is then the responses times the coefficient estimates. We divided the index into low (about 63 percent of the sample) and high, where the highest index individuals would have responded that they “strongly agree” with the statement “I would work even if I didn’t need the money” and that they do not look forward to retirement. The preference index will not inform reverse retirement directly, only whether the individual is more likely to work or not in any given period and which preference parameter type he is more likely to be assigned to.16 Table 13: Whether Respondent Would Work if the Income Was Not Necessary Would Work Even if Income Wasn’t Necessary non-RR RR Strongly Agree 14.1% 14.2% Agree 54.0% 54.9% Disagree 23.0% 22.6% Strongly Disagree 9.0% 8.4% Observations 2,170 705 14HRS question V5009. 15HRS question V9063. 16Some correlations between willingness to re-enter, measured by preference index, and health can be seen in Tables A8 and Table A9 on page 40 of the Appendix. 23

Table 14: Whether Respondent Looks Forward to Retirement Feelings about Retirement non-RR RR Looking Forward 69.1% 69.3% Mixed Feelings 13.7% 13.1% Uneasy 17.2% 17.6% Observations 1,670 648 Table 15: Whether Respondent Enjoys Job Like or Dislike Current Job? Dislike (0 to 3) 1.4% Neither Like nor Dislike (4 to 6) 15.0% Like (7 to 10) 84.6% Observations 146 5.3. First-Stage Estimates In the first stage we obtain parameters for what are determined outside of our model: wages, health transition probabilities, survival probabilities, and work stress. Health Transitions Health transitions are measured through an ordered probit, in which expectations on futurehealthstatusdependoncurrentself-reportedhealthstatusandage. Thestatusesare divided into “Good, Very Good, or Excellent”, “Fair”, and “Poor”. While, at most ages, the majority of respondents report that they are in the “Good, Very Good, or Excellent” category, we choose these groupings because movements among them may have significant consequencesforlaborforceparticipation. Inotherwords, achangefrom“Good” healthto “Poor” healthismoresignificantthanmovementsfrom“Good” to“Excellent”. Conditional health transition probabilities for ages 55, 65, and 75 are shown above in Table 16. Wage Estimates Table17givesestimatesofEquation(8),withtheoutcomebeinglogofannualearnings. All else equal, with these coefficients on age and age squared, wages are declining with age after 52. One can expect lower earnings with fair and poor health relative to the best health category (good, very good, end excellent self-reported health). Selection is on age, health, and dummies for ages 62 and 65 (the “early” and “full” Social Security retirement ages).17 17Casanova(2013): “Thesmoothlydecliningwageprofileoftenestimatedintheliteratureisareflection oftheincreasingproportionofpart-timeemployeesasworkersage.”(Thoughthisleadsustoaskwhythere 24

Table 16: Sample Health Transition Probabilities Next Period Health Current Health G/VG/E Fair Poor G/VG/E .87 .12 .01 Age=55 Fair .46 .37 .17 Poor .15 .36 .49 G/VG/E .84 .14 .02 Age=65 Fair .42 .39 .20 Poor .12 .34 .54 G/VG/E .82 .16 .02 Age=75 Fair .37 .40 .23 Poor .10 .32 .58 Table 17: Wage Estimates Outcome: lnAnnual Earning, n=13,064 Variable Coefficient (s.e.) Age (years) .1753 (.0651) Age2 -.0017 (.0006) Health Fair -.0702 (.0379) Poor -.1835 (.1120) Full-Time Work (ϕ) .7852 (.0230) Inv. Mills -.0152 (.1707) Constant 5.4025 (1.7257) ρˆ .4529 σˆ2 .7236 η σˆ2 (trans.) .6584 ξ Mortality Profiles Both Casanova (2010) and French (2005) compute their conditional survival probabilities using Bayes’ Rule, with P(H = h|Survive ) t−1 t s = P(Survive |H = H) = ×P(Survive ). t t t−1 t P(H = H) t−1 We adopt their method and will assume in the model that individuals die with probability one at age 90 regardless of health status, so P(Survive |H = H) = 0 for all 90 89 H =VE,F,P.18 aresomanypart-timeworkers—isitbecausepreferenceschangeordeclinesinproductivityreallytranslate into fewer hours rather than lower wages.) She concludes that the “correct specification for the offered wage profile is flat in age.” 18 SurvivalprobabilitiesareobtainedfromtheU.S.SocialSecurityAdministration’sOffice of the Chief 25

Stress Transitions An individual’s expected level of stress arising from work depends on whether he is working full- or part-time, his health, age, past participation status, and stress level when first observed.19 To clarify the role of stress in the model, whether one can expect to be stressed if he chooses to work is observed and is also predicted by observables, whereas the coefficient on stress in the utility function, in terms of equivalent leisure hours lost in (4), is unobserved. Table 18: Stress Estimates Outcome: lnReports Job is Stressful, n=42,195 Variable Coefficient (s.e.) Age -.024 .001 Acc. Work After 50 .005 .002 Initial Health Fair .192 .021 Poor .217 .047 Works Part-Time -.692 .027 Constant 1.69 .083 6. Simulation To examine whether the model can generate any of the reverse retirement seen in the data, we have simulated decisions for a given set of preference parameters, some of which are in the range of estimated parameters found in models similar to the model here. Using these values, we present some actual profiles from the HRS data and compare them with the simulated profiles using the estimated in Table 19 on page 27 to show the profiles most of interest here. 6.1. Simulated Profiles Figure 3.1 shows the simulated full-time, part-time, and non-participation decisions generated from the a model with the preference parameters in Table 19. The figures also include the actual participation by age. The model, with these parameters, is able to capture some of the patterns of declining full-time participation and modestly increasing Actuary reports: Actuarial Study 120, “Life Tables for the United States Social Security Area 1900-2100” byFelicitieC.BellandMichaelL.Miller. Availableathttp://www.ssa.gov/oact/NOTES/as120/LOT.html. These give one-year survival probabilities at age t by sex and birth year cohort, conditional on survival up to age t. We use the 1936 birth year cohort (the birth years in our sample range from 1931 to 1941). 19RAND HRS variable rWjstres. 26

Table 19: Parameter Estimates Shared Preference Parameters Estimates β Time Discount Factor .982 φ Leisure cost of fair health 270 HF φ Leisure cost of poor health 367 HP φ FC of Work: Linear Age Trend 31 P,t α AP Increase, Job Stress .63 str α AP Increase, No Job Stress .12 no str α AP Decrease, Not Working .88 no work Type-Specific Preference Parameters∗ Type 1 Type 2 Type 3 Type 4 (2.4%) (41.8%) (48.3%) (7.5%) η Risk Aversion 2.24 2.24 5.61 5.61 α Consumption Weight .52 .52 .49 .49 C α Bequest Weight 1.94 1.94 2.09 2.09 B K Bequest Shifter $12K $93K $12 $93 0 φ FC of Participation 180 391 180 391 P φ Re-entry Cost 217 289 217 289 RE α Weight on Stress/Recovery 10 17 10 17 AP ∗Type 1 interpretation: low risk aversion, low burnout Type 2: low risk aversion, high burnout Type 3: high risk aversion, low burnout Type 4: high risk aversion, high burnout part-time participation with age, though the levels are somewhat high for full-time and low for part-time work. In Figure 3.2, three graphs show both simulated and actual HRS assets at the 25th, 50th, and 75th percentiles. The simulated asset levels are close to the actual asset levels in the data, as they were selected to do so, though the pattern is somewhat different with age. In the HRS data, at all these percentiles there is an increase in assets with age. In the simulated behavior, only assets at the 25th percentile increases; there is, in the simulated behavior, more participation at older ages for those holding these levels of assets, adding to—oratleastnotsubtractingfrom—accumulatedassets. Forthe50th and75th percentiles, however, in the simulated behavior there is a very modest draw down of assets while in the actual data it continues to increase through age 72. Given that the simulated asset levels are somewhat close to the actual levels while the simulated participation is too high, the risk aversion parameter ν used may be too high. 27

Figure 3: Data and Simulated Labor Force Participation 555657585960616263646566676869707172737475 Age noitapicitraP emiT-lluF FT Participation by Age 0.9 Simulated 0.8 HRS Data 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 555657585960616263646566676869707172737475 Age noitapicitraP emiT-traP PT Participation by Age 0.22 Simulated 0.2 HRS Data 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 555657585960616263646566676869707172737475 Age )TP dna TF ni( gniretne-eR The proportion re-entering (FT and PT) by Age 0.15 Simulated HRS Data Figure 4: Data and Simulated Re-Entry Rates 0.1 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Age 0.05 0 noitapicitraP emiT-lluF FT Participation by Age 0.9 Simulated 0.8 HRS Data 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Age noitapicitraP emiT-traP PT Participation by Age 0.22 Simulated 0.2 HRS Data 0.18 0.16 0.14 0.12 0.1 0.08 0.06 0.04 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Age )TP dna TF ni( gniretne-eR The proportion re-entering (FT and PT) by Age 0.15 Simulated HRS Data 0.1 0.05 0 Figure 5: Data and Simulated Assets 555657585960616263646566676869707172737475 Age elitnecrep ht52 ta stessA 9#104 Assets at 25th percentile by Age Simulated 8 HRS Data 7 6 5 4 3 2 1 0 555657585960616263646566676869707172737475 Age elitnecrep ht05 ta stessA 3#105 Assets at 50th percentile by Age Simulated HRS Data 2.5 2 1.5 1 0.5 0 555657585960616263646566676869707172737475 Age elitnecrep ht57 ta stessA 7.5#105 Assets at 75th percentile by Age Simulated 7 HRS Data 6.5 6 5.5 5 4.5 4 3.5 3 28

Table 20: Type Prediction Parameters Coefficient Value Coefficient Value Bequest Intent High β 0.37 Risk Aversion Response β -1.89 1 5 Initial Health: Poor β -0.94 Initial Asset Level β -0.85 2 7 Initial Health: Fair β -0.21 SS Earnings β 0.11 3 8 *Variables are expressed in 10,000 dollars. Higher risk aversion is manifested not only in greater savings but also greater levels of participation. 6.1.1. Preference Type Prediction In the second stage of estimation we would also obtain type prediction parameters. Since we are simulating behavior for a given set of parameters, in this exercise we have chosen these parameters as well. There are two types: Type 1 and Type 2. The interpretation is that one type, Type 1, experiences lower disutility of working (relatively high consumption weight γ) and gets “burnt out” less quickly from work (lower α ). We AP estimate logistic function P(Type 1|X) = 1/(1+e−βX) where βX = β +β Bequest Intenthigh+β 1 +β 1 0 1 2 {H =Poor} 3 {H =Fair} initial initial +β Risk Aversion+β Assets +β SS Earnings. 4 5 initial 6 We expect that those with the higher work preference index (Indexhigh) are more likely to be Type 1, as are those in better health. As reverse retirement is one of the main behaviors we study here, we would like to see whether our model is able to generate it. A counterfactual exercise, we look at simulated labor-force re-entry behavior when all the stress-burnout related parameters (α , α , AP S α , and α ) are shut down, and compare this to the simulated behavior when these nS NW parameters are set as in Table 19 and reverse retirement in the HRS data. In Figure 7, we have the proportion, out of all simulated or HRS individuals, who transition from being out of the labor force back into it by age. The solid black line represents the re-entry rates in our HRS sample, which go from around 1.5 percent at the earlierages, upto over 2.5percent atages 66and67, goingback downto under1.5 percent at age 70. The simulated re-entry with Table 19 parameters gives rates that are within the range of real HRS re-entry; although the simulated participation rates are generally much higher than the true HRS participation in Figure 3, the re-entry (and exit) rates are much closer. The lowest line in Figure 7 represents the simulated re-entry rates when the burnout- 29

recovery part of the model is shut down, with the other parameters being unchanged. These re-entry rates are lower than both the series above, ranging from 0.5 to 0.8 percent at all ages. This suggest that, at least when holding the other selected parameters fixed, the burnout-recovery aspect of the model is indeed able to generate re-entry beyond what arises from shocks to wages, health, and preferences, giving re-entry behavior much closer to the true rates. Figure 6: Data, Simulated, and Counterfactual Re-Entry 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Age )TP dna TF ni( gniretne-eR The proportion re-entering (FT and PT) by Age 0.15 Simulated HRS Data No Burnout-Recovery 0.1 0.05 0 Figure 7: Data, Simulated, and Counterfactual Part-Time Participation 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 Age emiT-traP si taht noitapicitraP fo erahS Share PT Participation by Age 0.7 Simulated HRS Data 0.6 No Burnout-Recovery 0.5 0.4 0.3 0.2 0.1 0 30

Table 21: Work Transitions by Year Outcome: Working Outcome: Not Working to Not Working Transition to Working Transition Predicted Predicted Coeff. s.e. Margin Coeff. s.e. Margin Age .101 .006 - .105 .010 - Year 1996 .083 .087 .131 .182 .141 .048 1998 -.078 .091 .109 .073 .145 .042 2000 .171 .091 .131 .038 .151 .038 2002 .231 .098 .132 .338 .154 .049 2004 -.075 .109 .099 .241 .165 .045 2006 -.110 .118 .098 -.040 .183 .035 2008 -.474 .133 .071 -.019 .195 .037 2010 -.280 .142 .089 -.510 .225 .023 2012 -.618 .159 .064 -.535 .242 .023 2014 -.718 .175 .060 -.731 .267 .019 constant -7.84 .392 - -9.22 .593 - Note: Includes 26,045 person-year observations. Outcomes of multinomial logit regression. 7. The Option Value of Work at Older Ages In this section we use the decrease in job exit and re-entry rates to consider what the “option value of work”20 is at older ages, and possibly how valuable it is relative to the value of “recovery” of not working for some period of time. BosworthandBurtless(2011)useadministrativeSSAdataandCPStostudytheeffects and interaction of a weaker job market and losses in household wealth. They found that in the Great Recession, employment among males age 60 to 74 was up to 1.7 percent lower duetotheseeffects. Whileoverallemploymentislower, thereisalreadysomeevidencethat thosewhowereworkingwerelesslikelytoleavejobs,whichwealsoseeinoursampleduring this period. Gustman et al. (2015): study how the Great Recession affected wealth and retirement decisions in the HRS, the observe fewer people leaving jobs in Great Recession. Helppie McFall (2011) looks at changes in expected retirement age in this time period using CogEcon data, and finds that the effect due to losses in wealth alone accounted for 2.5 months of continued work. For descriptive motivation, in the table below, Table 21, are outcomes of a multinomial logit regression of work transitions on age and year. We can see that reverse retirement after 2008 generally declines, as there are lower initial exit rates due, we argue, to high 20Using the concept as in Stock and Wise (1990). 31

Table 22: Job Stress by Year Outcome: Stressful Job Coeff. s.e. Predicted Margin Age -.040 .009 - Year 2002 -.058 .099 .512 2004 .012 .115 .540 2006 -.109 .130 .491 2008 .086 .149 .569 2010 .097 .167 .573 2012 .094 .192 .572 2014 .239 .210 .628 Full Time .609 .056 - Income Quintile 2nd -.151 .067 3rd .102 .067 4th .201 .068 5th .480 .067 Acc. Work After 50 .015 .006 - Fair Health .162 .061 - Poor Health .437 .133 - Constant 1.83 .512 - Note: Includes 3,978 person-year observations. Outcomes of multinomial logit regression. option values of work in an environment where future re-entry is less certain. 21 We find support for the burnout-recovery model in Table 22: As people hold on to jobs longer than they otherwise would have, they accumulate more stress. 8. Discussion In this paper we developed a model of burnout and recovery to account for the high proportionofpeoplereverseretiring. Weshowedpatternsinreverseretirementandargued 21To help explain this change in reverse retirement behavior, we’ll use declines in the post-2008 jobfindingprobabilitiestodeterminetherelativeeffectoftheoptionvalueofworkversustheburnout-recovery process on initial exit and re-entry behavior. in future versions. 32

that the groups of those who do and do not reverse retire look very similar on many observable demographic characteristics. This motivated our use of a structural model that couldgeneratere-entryintoworkfromtheburnout-recoveryprocess,asopposedtore-entry arising from financial, health, or retirement enjoyment shocks. Through this model we can also account to some extent for the increasing fraction in part-time work at older ages. While models typically have part-time work giving more leisure,inourmodelchoosingpart-timeworkalsomeanschoosingalessstressfuljob—orat least one that has a lower probability of contributing to burnout. One question that could be addressed by this model is Social Security brings about periods of non-participation in between working periods. (I.e., to see how Social Security “subsidizes” periods of exit at certain times at the cost of taxing it on others, whereas agents would otherwise smooth work choices). We will determine this by changing eligibility ages. Another issue that could be considered is whether the lack of a being able to choose from a range of work hours would actually reduce rates of labor force exit followed by re-entry. Being able to choose only from “non-smooth” part-time or full-time hours, which is the case in our model and tends to be true in reality, may be contributing to this nonsmooth exit and re-entry behavior. Finally, it would be interesting to see the effects of “sabbaticals” and whether they are possibly less costly to employers than the turnover that could be generated when individuals are making participation decisions in the context of a burnout-recovery model. The phenomenon of reverse retirement—as well as increased part-time work with age— is worth understanding foremost due the fact that we observe such a high proportion of it occurring in the data. Additionally, the burnout-recovery model we develop and estimate here is process that can exist for any age: For older workers we see more labor force exits and re-entrances because their productivity puts them closer to the labor-leisure cutoff. We do not see this same in-and-out of the labor force action as much for younger workers because they are generally further from that cutoff. It could, however, explain why such a high number switch jobs or even careers for reasons beyond earnings. If instead of thinking of continued participation contributing to burnout (as we have here), we would have that continued work with the same employer or occupation contributes to burnout; switching diminishes the effect. In any case, the model may be relevant for all stages of work life. The final reason we think reverse retirement is worth understanding has to do with the cost of switching participation status. That we can generate high rates of exit and subsequent re-entry—along with fixed participation costs being low relative to what is found in related literature—suggests that the cost of switching participation status is not very high. Alternatively, the cost of switching may be high but is outweighed by the burnout-recovery process. 33

9. Appendix 9.A. Appendix: The HRS Data The main sample of respondents whose data used in estimations come from the HRS Cohort, born 1931 to 1941. This cohort was chosen for two reasons. First, this cohort was observed in every wave of the HRS. Second, they are observed over ages for which we observe wages when working as well as when might observe reverse-retirement activity: ages 51-83. Variable Descriptions. Below are descriptions of select RAND HRS variables used here. Further descriptions can be found through through RAND’s documentation.22 • Participation: A respondent is considered to be participating in the labor force if he answers that he is “working for pay” and not participating in the labor force if he is “not working for pay” (HRS variable RwWORK). These binary responses are fairly consistent with similar questions in the Study, such as whether the respondent considers himself retired (HRS variable RwSAYRET) or his labor force status (RwLBFR). There is no distinction here between part-time and full-time participation. • Non-Housing Financial Wealth: HwATOTF The net value of non-housing financial wealth is calculated as the sum of the appropriate wealth components less debt: Stocks, checking account balance, CDs, bonds, and other non-housing wealth minus debt. (HRS variables (HwASTCK + HwACHCK + HwACD + HwABOND + HwAOTHR) - HwADEBT.) • Earnings: Annual earnings come from the HRS variable RwIEARN. The nominal reported amounts are converted to 2010 dollars using the CPI. RwIEARN is the sum of a respondent’s wage or salary income, bonus and overtime pay, commissions, and tips. • Physical Health: IntheHRStherearefivecategoriesofself-reportedhealth(variables RwSHLT): Excellent, Very Good, Good, Fair, and Poor. In estimation, physical health statusisdividedintoonlythreecategories: “GE”, whichincludesExcellent, andVery Good, and Good, “F”, which includes Fair, and “P” for Poor self-reported health. • Retirement Earnings: Variable RwISRET includes annual Social Security income, includingretirement, spouse, orwidowbenefits, butnotincludingbenefitsreceiveddue to disability. RwIPENA gives income from pensions and annuities. 22Available at http://www.rand.org/content/dam/rand/www/external/labor/aging/ dataprod/randhrsL.pdf. 34

9.B. Appendix: Selecting the Estimation Sample ThesampleofrespondentsfromtheHRSthatareselectedformodelestimationismore restricted than the sample included in the descriptive statistics presented. Including only male respondents leaves us with 16,334 out of 37,495 total respondents found in all twelve waves. Keeping only those in the original HRS cohort, born 1931-1941 reduces the sample to 4,977. Excluding those observed in fewer than five waves or never observed working leaves us with 3,269; excluding those whose longest career is in ”Public Administration” leaves 2,995; keeping only married respondents whose wife is never observed working leaves 772 respondents in the model estimation sample. 9.C. Appendix: Primary Insurance Amount In future revisions, Average Indexed Monthly Income (AIME), which is used to determine an individual’s Social Security Primary Insurance Amount (PIA) will come from HRSrestricteddata. Inplaceofthis, wecurrentlytakeAIMEtobeanindividual’saverage earnings between the ages of 50 and 60. The (2010) formula for calculating PIA can be obtained at: http://www.ssa.gov/oact/cola/bendpoints.html. 9.D. Appendix: Additional Descriptive Statistics Participation Rates Those whom we categorize as reverse retirees overall have lowers rates of labor force participation at younger ages, and higher rates at older ages. Table A1: Proportion Working by Age and Whether Reverse Retiree Age Category non-RR RR 50-54 97.7% 77.6% 55-59 90.8 74.2 60-64 68.9 60.4 65-69 40.6 50.2 70-74 25.8 43.0 75-79 17.1 26.8 All Ages 59.2% 56.6% Person-Years 19,163 8,445 What Does Retirement Mean? Asurprisinglyhighproportionofpeople,whetherwecategorizethemasreverse-retirees or not, say that they plan to continue paid work after retirement, as seen in Table A2. 35

Table A2: Post-Retirement Intentions non-RR RR Stop Paid Work 23.0% 14.4% Continue Paid Work 77.0% 85.6% Observations 1,819 914 Table A3: What Does Considering Onesself Retired Mean for Future Participation? Percent Working... Next Wave +2 Waves +3 Waves +4 Waves Obs. All Not Retired .829 .719 .625 .537 11,276 Completely Retired .119 .134 .138 .145 9,575 Partially Retired .649 .555 .476 .411 4,536 non-RR Not Retired .863 .741 .631 .532 8,426 Completely Retired .026 .022 .020 .024 6,671 Partially Retired .688 .576 .484 .392 2,506 RR Not Retired .727 .655 .611 .553 2,850 Completely Retired .323 .363 .368 .359 2,904 Partially Retired .601 .529 .465 .434 2,030 In Table A3, we say whether one’s response to “Do you consider yourself retired?” tells us anything about participation in future Waves. We can see that, combining the respondents (to include RRs and non-RRs), 11.9 percent of this who consider themselves “Completely Retired” are working in the next Wave, while slightly higher numbers are working in future periods. Defining Reverse Retirement There are a number of possible ways to define reverse retirement occurrence. For instance, we could look at changes in the statuses of (1) whether one subjectively considers himself retired, (2) whether he reports working for any pay, (3) hours worked, or (4) level of income.23 We’ll compare responses for the first two definitions, as the later two require more judgement about what the cutoff levels should be, though we may look at these measures further in the future. Table A4 gives the percent who un-retire—which, in the data, we observe from 0 to 23These correspond to HRS variables (1) rWsayret, (2) rWwork, (3) rWhours, and (4) rWiearn. 36

Table A4: Reverse Retirement Occurrences: Comparing Definitions Reverse Change in Change in Retirement “Working “Considers Occurrences for Pay” Self Retired” 0 64.48 66.72 1 30.23 25.29 2 4.80 6.99 3 0.45 0.97 4 0.04 0.04 Note: 2,689 individual respondents. 4 times for an individual—during the time they are observed in the HRS under two definitions. Under the first, a change in the “Working for Pay” status from not working to working for pay, over 35 percent reverse retire at least once in our observations of them. Using the second definition, in which a respondent says he considers himself completely or partially retires one period and not retired in the next period, more than 33 percent reverse retire. The definition of reverse retirement we will use in many the descriptive statistics that follow, unless otherwise noted, is a change from “Not Working for Pay” to “Working for Pay”. In some ways a change in whether one considers himself retired is somewhat more interesting; if retirement is more a “state of mind” it’s surprising that there would be so many reversals. However, though it’s not immediately obvious why, the responses to whether one considers himself retired and whether he is working for pay line up quite well, and if we look at the later, we are more likely to get the wage observations necessary if looking at periods in which respondents say they are “Working for Pay”. Differences Just Before Stopping Work Next we look at responses given on income, hours worked, and job stress in the period before stopping work in Table A5 for non-RRs and RRs. Those who eventually returned to work had lower income, hours per week, and slightly lower stress just before leaving (and though not shown here, those in the RR category are somewhat older). Table A6 gives the percent who reported that their jobs were stressful for eventual RRs and non-RRs in the three Waves before stopping work. Medical Expenses and Reverse Retirement Out-of-pocket medical expenses are shown in Table A7, which include all payments for the two year proceeding the HRS interview. These expenses rise with age, but on average are not especially high relative to permanent income. The maximum out-of-pocket 37

expenses can be quite high, on the other hand. However, some of these tend to be incurred (necessarily) by people with rather high assets who self-insure against catastrophic events, so it’s not clear whether these expenses themselves should affect labor force decisions for this group. Un-Retirement Scenarios Re-entry into the labor force at older ages may by due to (unplanned) shocks and/or (planned) preferences. We’ll now list a few scenarios that fall under these categorizations inspired by descriptive statistics. Shocks: Either initial retirement or re-entry is not planned. • Unplanned retirement: Not working due to bad health (own or wive’s), re-enter LF when health is better. • Unplanned re-entry: Not working as planned, but then experience negative shock to Table A5: Responses Just Before Stopping Work non-RR RR Annual Income $49,385 $42,066 Hours per Week 38.5 35.9 Job is Stressful 52.8% 48.2% Observations 1,323 1,014 Table A6: Job Stress Before Stopping Work. Percent Reporting Stressful Job: Full-Time and Part-Time Workers: 3 Waves Prior 2 Waves Prior 1 Wave Prior non-RR 52.1 51.2 50.0 RR 54.2 48.3 44.4 Observations 1,834 2,171 2,876 Full-Time Workers Only: 3 Waves Prior 2 Waves Prior 1 Wave Prior non-RR 57.0 57.3 58.2 RR 62.8 59.0 56.5 Observations 1,436 1,626 1,906 Part-Time Workers Only: 3 Waves Prior 2 Waves Prior 1 Wave Prior non-RR 28.0 27.9 28.7 RR 26.5 22.5 25.3 Observations 348 488 834 38

Table A7: Out of Pocket Medical Expenses, Previous Two Years Out-of-Pocket Expenses Age Category Mean Median Maximum Obs. 50-54 $1,629 $491 $77,762 2,278 55-59 1,931 651 140,278 5,978 60-64 2,780 945 1,453,705 7,519 65-69 3,292 1,307 262,048 6,985 70-74 3,500 1,540 314,359 4,399 75-79 3,126 1,500 87,600 1,321 finances/wife’s health/own health that requires income from working. • Unplanned re-entry: Not working as planned, but the person does not enjoy retirement as much as he thought he would so he goes back to work. Preferences. Both initial retirement and re-entry are anticipated. • A leisurely job search: (This would apply to those who worked in jobs with less flexible hours and more rigid pension structures.) Before leaving his career job, a person expects that he will continue working afterwards, possibly part-time in work unrelated to his prior job, because he likes to stay busy and enjoys the additional income. He does not search for a new job at all before leaving his career employment, and after leaving he does not search intensely as there is no financial urgency. (Does not require utility of leisure declines with age.) • Taste for variety: In this scenario, a person likes retirement for a certain period of time,butknowsatsomepointhe’llgetboredwithitandwillfindanewjob(probably not the same as what he initially retired from) to keep life interesting or challenging. (Also does not require utility of leisure declines with age.) • Leisure time: Both productivity and utility of leisure decline with age, but at rates such that one is inclined to take time to vacation while utility is still high (even though earning potential is still high relative to later years). 39

Table A8: Health Status and Reverse Retirement Low Preference Index High Preference Index Current Health Status: Improved nonRR RR nonRR RR Excellent/Very Good/Good 87.76 12.24 87.27 12.73 Fair 92 8 92.96 11.32 Poor 96.46 3.54 92.96 7.04 Table A9: Retirement Satisfaction and Reverse Retirement Low Preference Index High Preference Index Retirement Satisfaction Last Period nonRR RR nonRR RR Very 91.27 8.73 90.61 9.39 Moderately 87.44 12.56 88.24 11.76 Not at all 95.61 4.39 85.34 14.66 9.E. Transitions Out of and Back Into Work Table A8 shows that people with the high preference index are more likely to return to work when their health improves, particularly when their health statuses are fair or poor. Table A9 shows that people with the high preference index are more likely to reenter the labor force when they do not enjoy retirement while there is no pattern between retirement satisfaction and work re-entry for people with low preference index. Figure 2 shows transitions out of full-time work, part-time work, and non working. We can see that at older ages, more individuals leave full-time work and enter into both part-time work and retirement at higher rates. At younger ages, those working part time are more likely to transition into full-time work at younger ages than they are beyond age 62. This may be capturing “underemployment” for younger part-time workers, who would prefer working full-time and take those offers when available. At older ages, part-time work could be considered more preferred. Transitions out of not working to either full-time or parttime work are highest at younger ages (where we suspect not working is more likely to be involuntary and re-entry thus more expected), but still over 10 percent in ages 60-70. 40

9.F. Additional Figures Figure A1: Labor Force Re-Entry into Part-Time versus Full-Time by Age 1.00 0.80 Re-Enter into PT 0.60 0.40 Re-Enter into FT 0.20 0.00 54 56 58 60 62 64 66 68 70 72 74 Note: 8,864 person-years. Figure A2: Labor Force Re-Entry Rates When Health Improves by Past Health and Age retteB si htlaeH fi kroW ot gninruteR fo ytilibaborP 6. 4. 2. 0 Good Past Health Fair Past Health Poor Past Health 55 60 65 70 Age Note: 8,864 person-years. 41

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