6

Sudipto Banerjee is a research associate at Employee Benefi t Research Institute (EBRI). David Blau is a professor of economics at The Ohio State University. Blau is grateful to the Social Security Administration for fi nancial support via a grant to the Michigan Retirement Research Center. Helpful comments were received in presentations at the Population Association of America 2011 Annual Meeting and the Michigan Retirement Research Center annual conference in 2012. Any views expressed in this paper are those of the authors, and should not be ascribed to the offi cers, trustees, or other sponsors of EBRI, EBRI- ERF, or their staffs, or to the Social Security Administration. The data used in this article can be obtained beginning August 2016 through July 2019 from David Blau, Department of Economics, Arps Hall, 1945 N. High Street, Columbus OH 43210- 1172, [email protected]. [Submitted January 2014; accepted September 2014] ISSN 0022- 166X E- ISSN 1548- 8004 © 2016 by the Board of Regents of the University of Wisconsin System

T H E J O U R N A L O F H U M A N R E S O U R C E S • 51 • 1

Employment Trends by Age in the United States Why Are Older Workers Different?

Sudipto Banerjee David Blau Banerjee and Blau

ABSTRACT

In the 1960s, 1970s, and 1980s, male employment rates were declining or fl at at all ages, and female employment rates were rising or fl at at all ages. But employment trends diverged more recently, with employment rising at older ages and falling at younger ages. We estimate labor supply models for men and women, allowing differences in behavior across age groups. The results indicate that changes in the educational composition of the population, the increase in age at fi rst marriage, and Social Security reforms can account for a modest proportion of the divergence. However, much of the divergence remains unexplained.

I. Introduction

Perrachi and Welch (1994) summarize empirical fi ndings from their analysis of U.S. labor force behavior from the 1960s through the 1980s as indicat- ing that “. . . the forces shaping employment for younger men do not appear to be fundamentally different from the forces determining the participation behavior of the oldest.” (p. 238). On the basis of this interpretation of the evidence they argue that “. . . [T]he search for explanations of trends in the labor force behavior of older people should primarily emphasize the larger question surrounding participation in general, and only secondarily should the peculiarities of advancing age be addressed. . . . [W]e

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believe that the retirement literature is too specialized. Obviously, old age has its dis- tinguishing aspects, but it seems that the major trends in the data cannot be attributed to them.” (p. 212).

These recommendations may seem strange to researchers who study labor force be- havior at older ages. Younger workers rarely withdraw permanently from the labor force, but the great majority of workers do exactly this at older ages.1 Older workers often leave the labor force around the time at which they become eligible for Old Age and Survivors Insurance (OASI) benefi ts from Social Security, benefi ts from an employer- provided pension, or health insurance coverage from Medicare. Obviously, these institutions were created precisely to deal with the “distinguishing aspects” of old age, and there is abun- dant evidence that labor force behavior is infl uenced by these programs.

Nevertheless, the trends in employment documented by Perrachi and Welch did in fact show many similarities across age groups. Figures 1a (for men) and 1b (for women) present our replication of a graph in their paper (Figure 7) illustrating trends in full- time equivalent weeks worked per year (divided by 52), using data from the 1966–90 March supplements to the Current Population Survey. The trends are easily summarized: Male employment generally declined until the 1980s, with larger drops at older ages. Female employment generally increased, with larger increases at younger ages. Female em- ployment at older ages began to increase in the 1980s. The levels and rates of change differ by age group, but the trends are mainly in the same direction: down (or fl at) for men, up (or fl at) for women. These data do not prove that common forces have shaped employment trends across the life cycle, but they demonstrate that there were common trends in employment by age that in principle could be explained by broad economic, demographic, and social forces without resorting to age- specifi c explanations.

There are at least two specifi c arguments as to why a common- forces explanation is plausible. First, while OASI and Medicare are intended deal with the distinguishing aspects of old age, there is another social insurance program intended to deal with the distinguishing aspects of younger ages: Social Security Disability Insurance (SSDI). SSDI is an increasingly important source of support for individuals who are deemed unable to work and are not yet eligible for retirement benefi ts. Furthermore, SSDI benefi ciaries become eligible for Medicare coverage after two years of benefi t receipt. This suggests that the institutional environment facing older and younger workers may not be as different as one might think at fi rst glance.

Second, PW and others have pointed out that the characteristics of older workers who tend to retire relatively early are similar to those of younger workers who with- draw from the labor force: poor health, low education, black, and, for men, unmarried. Not coincidentally, these characteristics are associated with low wage rates. The op- portunity cost of withdrawing from the labor force is relatively small for low- wage workers, regardless of age (Juhn 1992). Older and disabled low- wage workers face an especially low opportunity cost of labor force exit because the progressivity of the Social Security benefi t schedule results in a relatively high replacement rate of earn- ings for low- wage workers.

The last year of data used by Perrachi and Welch was 1990. Since 1990 there have been major changes in labor force behavior at both older and younger ages. These

1. There is some variation in the classifi cation of younger and older age groups across studies. We defi ne our categorization below.

Banerjee and Blau 165

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52

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Figure 1b Trends in Full- Time Equivalent Weeks Worked by Age Group, Women, 1965–89

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Figure 1a Trends in Full- Time Equivalent Weeks Worked by Age Group, Men, 1965–89

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changes are illustrated in Figures 2a and 2b, which update Figures 1a and 1b, respec- tively, through 2010. Between 1990 and 2010, the employment rate has increased substantially for older men and decreased for younger men. Aggregating the three older groups shown in Figure 2a (62–64, 65–67, 68–69), the male employment rate rose from around 30 percent in 1990 to 36.2 percent in the prerecession years of 2005–2007, and to 37–38 percent in 2008–2010. Aggregating over ages 25–39 and 40–54, the employment rate of younger men declined from around 84 percent in 1990 to 82.9 percent in 2005–2007 and 77.3 percent in 2008–2010.2 The middle group, ages 55–61, experienced little change. The changes for women were also quite strik- ing. The long trend of rising female employment at ages 25–54 ended around 2000, and has been declining since then. But, at older ages, female employment has been increasing at a rate very similar to that of older men. If common forces were driv- ing employment trends across the age distribution pre- 1990, those forces have either ended or been swamped by age- specifi c factors in the last two decades.

Changes in the institutional environment facing older workers have been proposed as explanations for the rise in employment at older ages. Social Security reforms that affected cohorts reaching their 60s during the 1990s and 2000s raised the Full Retire- ment Age (FRA) from 65 to 66, eliminated the Social Security Earnings Test for work- ers at or above the FRA, and increased the actuarial adjustment in benefi ts for delayed claiming past the FRA (the Delayed Retirement Credit, or DRC). These reforms all encourage employment at older ages (Blau and Goodstein 2010). Defi ned Benefi t pen- sion plans have become increasingly scarce in the private sector, largely replaced by Defi ned Contribution plans such as the 401k (Poterba, Venti, and Wise 2007). Defi ned Benefi t plans typically encourage early retirement, while Defi ned Contribution plans have no specifi c retirement incentives. In addition, the increase in employment of older married women has resulted in a large increase in the proportion of older married couples in which both spouses have had signifi cant attachment to the labor force. This makes joint labor force decisions of greater importance and may encourage employ- ment of older men (Schirle 2008).

Potential explanations for employment declines at younger ages are less obvious. Moffi tt (2012) shows that part of the drop for men aged 16–64 in recent years can be explained by falling wages and part by demographic changes. The end of the upward trend for women and the beginning of the recent decline have been more diffi cult to explain (Goldin 2006, Macunovich 2010). Blau and Kahn (2007) and Heim (2007) have shown that the elasticity of women’s labor supply with respect to the wage rate declined substantially in the 1980s and 1990s, and Moffi tt (2012) reports a negligible elasticity for women in the 2000s. But this does not explain a reversal of the age- specifi c employment trends for women.

Understanding trends in employment by age is important because these trends de- termine the future size and age composition of the U.S. labor force, and have impor- tant implications for the Social Security system. The United States experienced an unprecedented decline in the employment- population ratio beginning in 2000 (Moffi tt 2012), even before the deep recession of the last few years. This was largely due to the decline in employment of younger workers noted above, as well as less educated

2. The low employment rate in 2009 and 2010 is obviously a result in large part of the Great Recession, but it is likely that some portion of the decline will persist.

Banerjee and Blau 167

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Figure 2b Trends in Full- Time Equivalent Weeks Worked by Age Group, Women, 1965–2010

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Figure 2a Trends in Full- Time Equivalent Weeks Worked by Age Group, Men, 1965–2010

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workers. This decline has been widely discussed, but analysis has been fairly lim- ited (Aaronson et al. 2006, Moffi tt 2012). The literature has focused mainly on labor supply of younger workers, but the rising employment trend at older ages will help offset the decline among younger workers. There will be a large increase in the share of the elderly population in the next two decades, increasing the importance of under- standing labor supply at both younger and older ages.

In this paper, we evaluate potential explanations for the divergence in employ- ment trends between younger and older workers in recent years. Like Moffi tt (2012) and others, we use a labor supply framework to motivate the empirical specifi cation, but, unlike other papers, we focus on differences in labor supply behavior across age groups.3 We analyze the effects on labor supply by age group of two broad sets of driving forces: economic factors, including the wage rate, Social Security policy, pen- sion coverage, and the income tax rate; and demographic factors, including education, marital status, race and ethnicity, number of children, and health.4 The effects of these variables are allowed to differ by age group, and we use the results to analyze the contribution of age- specifi c trends in the explanatory variables to explaining differ- ences in employment trends across age groups. We use data from 1965 through 2010 to estimate the labor supply models. The models are specifi ed and estimated in levels, and the results are used to explain trends—that is, growth and decline, as well as lev- els. For most of the paper we follow a dichotomous age classifi cation. For men, ages 25–61 and 62–69 are referred to as the younger and older age groups, respectively. For women, the respective age groups are 25–54 and 55–69. The reason for the dif- ference by gender is discussed below.

We have three main fi ndings. First, changes in demographic composition can explain most of the decline in employment of younger men. The two main drivers are changes in marital status and race / ethnicity. We estimate that never- married and divorced, sepa- rated, and widowed men are 19–27 percentage points less likely to work than their married counterparts, other things equal. The share of younger men who were never married increased by ten percentage points from 1965–88 to 1989–2010, and the share widowed, divorced, or separated rose by 4 percentage points. The increase in the share never- married is the result of a delay in fi rst marriage; there was no increase in the share never- married at older ages. So this difference is an important age- specifi c de- mographic trend that clearly contributed to the divergence in employment trends across younger and older men. Black, other race, and Hispanic men have lower employment rates than white men, and the share of these groups in the population increased sub- stantially, contributing to the decline in younger male employment. Changes in marital status and racial and ethnic composition each can explain about half of the decline in the employment growth rate of men aged 25–61 from 1965–88 to 1989–2010.

Second, Social Security reforms can explain a modest portion, 9 percent, of the increase in employment of men at older ages, and can explain 27 percent of the decline in employment of younger men and 6 percent of the decline in employment of younger

3. Aaronson et al. (2006) estimate employment models by age group using aggregate data. They have an extensive discussion of trends in employment by age group, but their analysis focuses on how age- specifi c trends affect the aggregate employment rate, rather than on explaining age- specifi c trends. 4. We also analyze the effects of the minimum wage, life expectancy, the SSDI award rate, and net imports. However, these variables vary only in the aggregate, so we do not have much confi dence in our ability to identify their effects.

Banerjee and Blau 169

women. For given lifetime earnings, Social Security benefi ts have declined for recent cohorts as a result of the increase in the FRA, and the incentive structure has tilted to favor later claiming. Our estimates indicate that these changes resulted in increased male employment at older ages, confi rming results of other recent studies (Blau and Goodstein 2010, Mastrobuoni 2009). A novel contribution of our paper is to show that Social Security reforms also contributed to the decline in employment of younger men, and to a lesser extent younger women. The decline in benefi ts is predicted to cause an increase in LFP at all ages, but in the presence of a borrowing constraint less generous benefi ts could induce lower work effort at younger ages in anticipation of greater work effort at older ages. In the presence of a liquidity constraint, the inability to borrow against future benefi ts may prevent a worker from retiring as early as he would like. This will result in a constrained optimum in which retirement occurs at the earliest age at which benefi ts are available. Depending on preferences (intertemporal comple- mentarity in hours worked), this could lead to adjustments in labor supply at younger ages as well. A cut in benefi ts reduces the likelihood that the liquidity constraint binds, causing later retirement and reinforcing the wealth effect at older ages. But the ef- fect on labor supply at younger ages depends on preferences and could be positive or negative. If the effect is negative and large enough to offset the wealth effect, the net effect of the benefi t cut on labor supply at younger ages could be negative. We do not have any direct evidence on this mechanism, but the reduced form results suggest that recent benefi t cuts help explain divergence in employment trends across age groups.

Third, changes in the educational composition of the labor force account for a small share of the increase in employment at older ages: 11 percent for older men and 14 percent for older women. Cohorts that experienced large increases in high school graduation and college attendance reached their 50s and 60s in recent years, while more recent cohorts have had a much slower rate of increase in educational attainment.

The effect of Social Security reforms on the divergence in labor supply by age will very likely persist and perhaps increase in magnitude as cohorts with an FRA of 67 reach their 60s in the 2020s. In contrast, the effects of rising educational attain- ment will be transitory, as future cohorts of older workers will be as well- educated as their younger counterparts. We think it is unlikely that the proportions never- married and divorced, widowed, or separated at older ages will ever approach the proportions observed at younger ages. If this is correct, the effects of the increase in age at fi rst marriage on the divergence in employment trends by age likely will be persistent.

The next section briefl y reviews related literature and highlights our contributions. Section III describes the employment data, and Section IV discusses model specifi ca- tion and measurement of the explanatory variables. Section V presents and discusses the results, and Section VI concludes. We discuss implications of the fi ndings for Social Security policy reforms in the conclusion.

II. Related Literature

Our analysis is related to three main areas of the labor supply litera- ture: the effects on labor supply of (a) the wage rate, (b) OASI, and (c) SSDI. We discuss these in turn, followed by a brief discussion of other employment determinants that do not fi t neatly into the labor supply framework.

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A. Wages The labor market returns to skill have increased substantially over the last four de- cades (Acemoglu and Autor 2011). Low- skill workers have faced declining relative wages and in many cases declining absolute real wages as well. Changes in the wage structure affect workers of all ages, but the effects may differ by age, as suggested by the life cycle model. We analyze the effect of the wage rate on labor supply at different ages, but we fi nd that wage effects on labor supply are small and differences in wage trends across age groups cannot account for divergence in employment trends. These fi ndings are similar to those of Moffi tt (2012) for women, but Moffi tt fi nds somewhat larger explanatory power of wages for men, most likely because he includes men aged 16–24 in the population analyzed while we do not. We verify previous fi ndings indicating that changes in wages are not a major factor behind changes in employment trends.

B. OASI Social Security retirement benefi ts became increasingly generous from the beginning of the program in the 1930s through the mid- 1970s. However, the evidence suggests that increased generosity of OASI was not the main cause of the decline in employ- ment of older men during this period (Blau and Goodstein 2010, Krueger and Pischke 1992). Social Security reforms in 1977 and 1983 reduced the benefi t available at a given age of claiming, increasing the incentive to work at older ages, as discussed above. Blau and Goodstein (2010) estimate that changes in Social Security can explain between one quarter and one half of the increase in employment of older men since the 1980s. Our contributions are to analyze how OASI benefi ts affect employment behavior at younger ages as well as at older ages, and for women as well as men.

C. SSDI If an individual successfully applies for disability benefi ts, the SSDI benefi t is equal to his Primary Insurance Amount (PIA), which is determined by average indexed earn- ings. Unlike in the case of OASI, the benefi t does not depend on the age of claiming. The OASI benefi t for a retired worker is equal to his PIA if he claims the benefi t at his FRA but is reduced if he claims early. The earliest claiming age is 62, and the reduc- tion for claiming at 62 is 20–30 percent depending on the FRA, which is determined by year of birth. For example, an individual with an FRA of 67 can receive an OASI benefi t equal to his PIA if he claims it at age 67, a benefi t equal to 0.7*PIA if he claims at age 62, and a benefi t equal to his PIA if he is awarded disability benefi ts, regard- less of age at the time of SSDI eligibility.5 Thus a decline in the OASI benefi t as a result of an increase in the FRA increases the relative attractiveness of SSDI (Duggan et al. 2007). The increase in the FRA effectively cut the OASI benefi t for claiming at a given age, but did not affect the SSDI benefi t. Von Wachter et al. (2011) found that 30 percent of new awards and over half of rejected applications in 2007 were from

5. The benefi t will differ in each scenario to the extent that average indexed earnings at the time of claiming differ. For example, if earnings rise with age then the PIA will be larger for claiming at a later age, for both OASI and SSDI.

Banerjee and Blau 171

individuals aged 30–44. There is no evidence of a decline in health of younger men, suggesting that a growing share of applications is “induced” by the program.

A large literature analyzes the effect of SSDI on labor supply, but few studies ana- lyze the effect of the SSDI benefi t. This is because the SSDI benefi t varies only in the time series, conditional on average lifetime earnings, so there is no cross- cohort varia- tion available for identifi cation. For this reason, we are not able to analyze the impact of the SSDI benefi t level, but we explore the impact of the SSDI award rate. Almost all studies fi nd a negative effect of being awarded SSDI benefi ts on labor supply but most conclude that the effect is relatively small.6 However, Autor and Duggan (2003) and Black, Daniels, and Sanders (2002) argue that labor supply of low- skill workers is more sensitive to the relative value of SSDI benefi ts, likely because the benefi t sched- ule is progressive, replacing a higher proportion of earnings at low levels of earnings.

D. Other Determinants of Employment Employment is affected by demand- side factors that are not fully captured by the wage rate, and labor- demand effects on employment may differ by age. For example, older workers are less likely to experience loss of a job due to layoff or business closing, but the consequences of job loss are more severe for older workers. Older workers are much less likely to be reemployed within one to three years, and experience much larger wage losses upon reemployment (Johnson and Mommaerts 2010, Farber 2005). Age discrimination in employment is another example of a demand- side factor that has differential effects by age. Employment protection aimed at older workers may reduce age discrimination in fi ring but also alters hiring incentives (Lahey 2008, Neu- mark and Song 2012). We do not directly analyze the effects of labor demand and related policies except for the minimum wage, so it is important to bear in mind that what we interpret as labor supply effects could be partially a consequence of labor demand factors. This of course affects the interpretation of our estimates but not their consistency.

III. Employment Data

The main source of data for the analysis is the March supplement to the CPS. We use data from the 1966 through 2011 surveys on individuals aged 25–69.7 To facilitate computation and merging with data from other sources, we aggregate the

6. Recent studies that take a structural approach to estimation have estimated the effect of the SSDI ben- efi t on labor supply: Bound et al. (2010), Kim (2014), and Low and Pistaferri (2015). Other recent studies estimate the treatment effect of being awarded SSDI benefi ts without identifying the impact of the amount of the benefi t: Chen and van der Klaauw (2005); French and Song (2014); and Maestas, Mullen, and Strand (2013). 7. Alexander, Davern, and Stevenson (2010) report that the Census Bureau inadvertently introduced errors in age and sex in the CPS public use fi les in several years in the 2000s as part of their procedures to avoid disclosure. These errors apply to the population aged 65 and above, and the authors report that there may have been a signifi cant effect on studies of the older population. Fisher (2010) uses Social Security administrative records matched to the CPS for 2001–2006 to explore the extent of age misclassifi cation. She fi nds that the probability of misclassifi cation of age by more than one year increases linearly with age beginning at 65, reaching about 15 percent for men at ages 68–69 and 10 percent for women. She also reports that there are

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individual data into cells defi ned by gender, single year of age, single calendar year, and education group. Calendar year refers to the year prior to the March survey, and age is measured as age at the March survey minus one.8 The four education groups are high school dropout, high school graduate, college attendee, and four year college graduate.9

The dependent variable is the number of full- time- equivalent weeks worked in the calendar year, divided by 52, with weeks worked part- time (35 or fewer hours) treated as half of full- time weeks. This measure, which we refer to as Full Time Weeks worked (FTW), combines the intensive and extensive margins of labor supply behavior. 10

A useful way to characterize changes in trends across age groups is in the form of growth rates. We compute the average annual growth rate in FTW for two subperiods, 1965–88 and 1988–2010, for three age groups: 25–54, 55–61, and 62–69. Figures 3a (for men) and 3b (for women) show the results. For men, there is little difference in growth across the periods for the two younger groups but at older ages the contrast is stark: a 2.2 percent average annual rate of decline in FTW in the earlier period and an increase of 1.2 percent in the more recent period. The contrast is sharp for women as well, in this case for both the youngest and oldest age groups. In the earlier period growth was most rapid for the youngest group at 2.4 percent per year and declined with age, while in the more recent period the age pattern was reversed, with essentially no growth for the youngest group, 1.1 percent for the middle group, and 2.6 percent at ages 62–69.

In the analysis that follows we further aggregate the age groups in order to simplify the analysis. Based on Figures 3a and 3b, we defi ne younger men as ages 25–61 and older men as ages 62–69. For women, we use ages 25–54 as the younger age group and ages 55–69 as the older group. We estimate models of FTW in levels, and then use the results to derive implications for the growth rate.

IV. Model Specifi cation and Measurement of Explanatory Variables

We specify an empirical model of employment behavior based loosely on the static labor supply framework. As noted above, we aggregate the individual data to cell means in order to combine data from different sources (described below), with cells defi ned by single year of age, education group, and single calendar year. The analysis is carried out separately for men and women, so we omit gender from the

errors in years that were not subject to inadvertent Census Bureau errors, so the net effect of the misclassifi ca- tion introduced by the change in disclosure practices was 12 and 7 percent for men and women, respectively. 8. Birth year is an important variable in our analysis because it determines the applicable Social Security rules. We assume that individuals were born after the March survey date, which implies that birth year equals calendar year minus age minus one. This introduces some measurement error. Blau and Goodstein (2010) indicate that their results are not very sensitive to alternative assumptions. See Mastrobuoni (2009) for an alternative approach to inferring birth year in the CPS, using monthly data. 9. There is a great deal of variation over time and across age groups in educational wage differentials and other explanatory variables, so it is useful to incorporate education in the defi nition of the cells in order to exploit this variation in the analysis. 10. The trends in alternative employment measures such as labor force participation in the survey week are very similar to those reported here for FTW. Parameter estimates and simulation results are also very similar.

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Figure 3b Average Annual Rate of Change in Full- Time Equivalent Weeks Worked by Period and Age Group, Women

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defi nition of the cells. The model is linear in order to facilitate aggregation. Using the cell as the unit of observation, the dependent variable is Ejat, the weighted mean value of FTW for the population in education group j observed at age a in year t.11 Defi ne c = t – a as birth year, and let g denote an age group. The model is (1) Ejat = β

gXjat + γ gZjc + α

gYt + δa + f g(c) + hg(t) + θj + εjat,

where Xjat is a vector of education- age- and- time- varying variables (for example, the wage rate), Zjc is a vector of variables that varies across birth cohorts and education groups but not by age within a cohort (for example, the OASI benefi t, for a given claiming age), Yt is a set of variables that vary only in the time series, δa is an age fi xed effect, fg(c) is a function of birth cohort, hg(t) is a function of calendar year, θj is an education- group fi xed effect, and εjat is a disturbance. All coeffi cients are allowed to differ by age group but not by period.

The coeffi cients of most interest are βg and γg. The specifi cation of cohort, age, and time effects is crucial for identifi cation and interpretation. Unrestricted age fi xed ef- fects are included in order to account for persistent life cycle patterns of labor supply. Unrestricted education fi xed effects are included because there may be differences across education groups in unmeasured factors such as preferences that would cause bias in estimates of the effects of wages and other variables that vary with educa- tion. Birth cohort effects are included in order to avoid confounding the effects of cohort- specifi c variables such as OASI benefi ts with unobserved cohort trends. We seek to explain time trends in employment, so one might think that time trends should not be included and that time- varying variables should be forced to explain the trends in employment. But there are undoubtedly omitted time- trending variables associated with the included time- varying variables such as wages, health, and others. Hence, some controls for such unobserved trends should be included. However, we cannot be completely fl exible in specifying cohort and time effects, given the well- known age- cohort- period relationship.

First, consider identifi cation of γg, the effects of cohort- education specifi c variables such as OASI benefi ts that are independent of age. OASI rules differ only by cohort, but benefi ts vary within birth cohorts as a result of differences across education groups in lifetime earnings. However, this source of variation does not identify the effects of changes in the OASI rules, which do not vary across education groups. We include lifetime earnings in Zjc as a control variable, so the effect of OASI benefi ts is identi- fi ed by changes in the benefi t formula and nonlinearity of the formula with respect to lifetime earnings. An unrestricted set of cohort fi xed effects would eliminate changes in OASI rules as a source of identifi cation, leaving only nonlinearity of the benefi t formula as a source of identifi cation. As long as cohort effects are not completely unre- stricted, the effects of OASI benefi ts (an element of γg) are identifi ed by discontinuous changes in cohort- specifi c OASI rules such as changes in the FRA and DRC men- tioned above. These changes are described more fully below. Our main specifi cation of the birth cohort function f is a third order polynomial. Alternative specifi cations, including two- year and four- year fi xed effects and no cohort effects, are discussed in the next section. The key identifying assumption is that unobserved cohort effects

11. We use the CPS March supplement weight to construct cell means. In the regression analysis we weight each cell by the number of individual- level observations used to construct the cell mean.

Banerjee and Blau 175

can be adequately captured by less- than- fully- nonparametric specifi cations, such as a smooth polynomial function or a set of two- year or four- year dummies.

Now consider identifi cation of βg, the effects of age- time- and education- specifi c variables such as the wage rate, marital status, number of children, and health. Given the specifi cation of age and cohort effects described above, identifi cation of βg depends crucially on the specifi cation of calendar time effects. The most fl exible specifi cation of time effects is age- group- specifi c individual year fi xed effects, say hg(t) = πgt. In this case identifi cation of βg is mainly from differences in time trends in the explanatory variables by age group within education group (or equivalently, by education group within age group). For example, wage trends differ considerably by education within age groups. This is illustrated for men in Figure 4 and women in Figure 5. For each of the four education groups, there was a large increase in the wage gap between younger and older men, refl ecting the well- known increase in returns to work experience. The increase in the wage gap for women was smaller but still evident.

A more restrictive specifi cation limits year fi xed effects to be common across age groups: hg(t) = πt. Some variables are independent of education, such as the SSDI ac- ceptance rate. The acceptance rate varies by age and time, but the age trends are very similar over time, so the effects of the acceptance rate are not identifi ed even with a restricted set of time effects. Also, this specifi cation does not permit identifi cation of the effects of aggregate variables such as the minimum wage and life expectancy.12 The most restrictive specifi cation excludes time effects altogether and includes a set of variables that vary only by time. We estimate all three specifi cations and compare results.

The key explanatory variables of interest are the hourly wage rate, the average income tax rate, OASI benefi ts, the SSDI award rate, pension coverage, and demo- graphic variables. The specifi cation is motivated by the standard static labor supply model, but we do not adhere to the model rigidly because our aim is to explain changes in trends rather than estimate behavioral parameters. For example, given the focus on older workers, we incorporate Social Security benefi ts rather than nonwage income or household wealth. We discuss measurement of the key variables, followed by a brief discussion of other variables and some limitations of the specifi cation.13

A. Wage Rate and Tax Rate The hourly wage rate net of taxes is a key variable in any labor supply model.14 We compute average hourly earnings of full time year round workers (at least 45 weeks and 35 hours per week) from CPS data.15 The sample is limited to ages 25–59 in order to reduce the potential for selection bias from participation decisions at older ages.16

12. Life expectancy differs by age, but the trends are virtually identical across age groups. Life expectancy by age and education is not available. 13. The specifi cation ignores joint labor supply issues. In one of the extensions discussed below, we include spouse characteristics and spouse earnings or employment as explanatory variables. 14. The results were very similar using the weekly wage rate in place of the hourly wage rate. 15. Cases were dropped if average hourly earnings were less than $5 or greater $500 in 2010 dollars. 16. Wages at ages 60 plus are assumed to be equal to the age- 59 wage. Selection bias could be important at younger ages, especially for women. We attempted to generate a correction for selection into the wage sample following the linear probability model approach of Moffi tt (2012), but we were unable to fi nd exclu-

The Journal of Human Resources176

2. 2

2. 4

2. 6

2. 8

1965 1975 1985 1995 2005 Year

Ages 25–39 Ages 40–54 Ages 55–61

High School Dropouts

2. 5

2. 6

2. 7

2. 8

1965 1975 1985 1995 2005 Year

High School Graduates

2. 6

2. 7

2. 8

2. 9

3

1965 1975 1985 1995 2005 Year

Some College

2. 8

3 3.

2 3.

4

1965 1975 1985 1995 2005 Year

College Graduates

Ages 25–39 Ages 40–54 Ages 55–61

Ages 25–39 Ages 40–54 Ages 55–61

Ages 25–39 Ages 40–54 Ages 55–61

Figure 5 Trends in the Log Wage for Women by Education and Age Groups

2. 7

2. 8

2. 9

3 3.

1 3.

2

1965 1975 1985 1995 2005 Year

Ages 25–39 Ages 40–54 Ages 55–61

High School Dropouts

2. 9

3 3.

1 3.

2 3.

3

1965 1975 1985 1995 2005 Year

High School Graduates 3

3. 1

3. 2

3. 3

3. 4

1965 1975 1985 1995 2005 Year

Some College

3. 23

.3 3.

43 .5

3. 6 3

.7

1965 1975 1985 1995 2005 Year

College Graduates

Ages 25–39 Ages 40–54 Ages 55–61

Ages 25–39 Ages 40–54 Ages 55–61

Ages 25–39 Ages 40–54 Ages 55–61

Figure 4 Trends in the Log Wage for Men by Education and Age Groups

Banerjee and Blau 177

In order to eliminate composition effects on wage rates, the log wage is regressed on a quadratic in age, and dummies for race, ethnicity, marital status, and census division, separately by the combination of education group, gender and single calendar year. The explanatory variables are a subset of the variables in the labor supply equation, but each variable is (implicitly) interacted with a full set of year dummies. Thus, al- lowing all coeffi cients of the wage equation to differ by year while restricting year effects to the intercept in the labor supply equation provides identifi cation of the wage effects. The estimates are used to compute the fi tted value of the log wage, holding the explanatory variables other than age and education constant (the baseline values are white, non- Hispanic, married, and Census geographic division 1). This approach preserves variation in the wage rate by education, age, and year, the three main dimen- sions of interest. We also constructed a measure of the fi tted log wage that incorporated variation in race, ethnicity, marital status, and region, and found very similar results.

We compute the income tax rate facing each individual based on marital status, number of children, and the predicted wage rate. The combined federal income, state income (beginning in 1977), and payroll average tax rate (ATR) is computed using the NBER TAXSIM program under the following assumptions: (a) income from sources other than earnings, interest, dividends, and rent is ignored, (b) hours of work are assumed to be 2,000 per year, and (c) married couples fi le jointly and single individu- als fi le as singles or head of household depending on whether they have dependent children. Tax rates for married individuals are computed under two alternative as- sumptions: The spouse works 2,000 hours and the spouse does not work. The coef- fi cient estimates differed quite a bit, but the simulation results were very similar for the two alternative measures, so we report results only for the former case. There is a noticeable drop in the average tax rate on earnings at younger ages beginning in the mid- 1980s (not shown here), around the time of the Tax Reform Act of 1986. We in- clude the wage rate and tax rate as separate explanatory variables because preliminary results showed a better fi t than in a specifi cation in which they are restricted to have the same effect.

B. Social Security Retirement Benefi ts Social Security benefi ts are computed using birth- cohort- specifi c Social Security rules, and birth- cohort- and- education- specifi c mean age- earnings profi les derived from the CPS, supplemented by published Social Security Administration (SSA) data for years before CPS data are available. The appendix describes the computation of these earn- ings profi les in detail. The earnings profi les are input to the anypia program provided by the SSA to compute benefi ts for several alternative scenarios: work continuously (from an assumed age of labor force entry that depends on education) through age 61 and claim at 62; work through 64 and claim at 65; and work through 69 and claim at 70. In each case, it is assumed that exit from employment is permanent. We compute

sion restrictions that could produce stable and plausible selectivity- corrected wage equation estimates. As an alternative, we employed a more standard Heckman selectivity correction approach. The selection correction is identifi ed only by functional form because there were no plausible exclusion restrictions. For example, the Social Security variables discussed below might have served as exclusion restrictions, but they are not available at the individual level. The results using this approach were very similar to the main results with the exception of one case, discussed in the results section.

The Journal of Human Resources178

the present discounted value (PDV) of benefi ts as of age 55, using life table mortality and a real interest rate of 3.0 percent. The PDVs of benefi ts for claiming ages 62 and 70 are included in the model in the form of differences from the PDV of the benefi t for claiming at age 65. In this specifi cation, the age- 65 benefi t captures the wealth effect of benefi t generosity for a given payroll tax, while the differences between the age- 62 and age- 65 and age- 70 and age- 65 PDV of benefi ts capture incentives to claim and retire early and late, respectively (Blau and Goodstein 2010).17 The earliest age of eligibility for OASI benefi ts is 62, but behavior at younger ages may be infl uenced by expectations of future benefi ts, so we allow the benefi t to affect employment decisions at younger ages. Social Security has wealth and substitution effects on labor supply. We expect the wealth effect on employment to be negative, while the sign of the substitution effect depends on age. In order to ensure that the SS variables are captur- ing the effects of changes in benefi t rules rather than changes in lifetime earnings, we control for a sixth order polynomial function of the average earnings variable used to compute the benefi t.

We assume perfect foresight about future rule changes. For example, a 1983 Social Security reform increased the FRA for cohorts reaching age 62 in 2000 or later, ef- fectively cutting benefi ts. The fi rst cohort affected by the rule change was born in 1938 and was age 45 in 1983. This cohort had at least 17 years to respond to the new rules; we assume that they behave as if they knew about the rule change from the time of labor force entry. Blau and Goodstein (2010) explored this and alternative assumptions and found that the perfect foresight assumption yielded the most sensible results.18

Figure 6 illustrates the trend in the present discounted value of real benefi ts for claiming at age 65. In order to focus on rule changes, the fi gure shows benefi ts calcu- lated holding the lifetime earnings profi le fi xed while applying the rules for each birth cohort.19 There were many ad hoc benefi t increases in the early years of Social Secu- rity, but there was no automatic adjustment for infl ation. Benefi ts rose irregularly until the famous “notch” that reduced benefi ts beginning with the 1917 cohort (Krueger and Pischke 1992). There were additional ad hoc benefi t cuts that affected cohorts born in the 1920s, and a major reform in 1983 cut benefi ts for cohorts born after 1937 by increasing the FRA. The increases in the FRA were phased in irregularly, beginning with the 1938 cohort and ending with the 1960 cohort.20 The benefi t is adjusted auto- matically for infl ation, but slow projected wage growth leads to a decline in benefi ts for cohorts born after 1960.

Figure 7 illustrates changes in claiming- age incentives, calculated as the gain in PDV from claiming at 62 relative to 65, and from claiming at 70 relative to 65.

17. This approach to measuring benefi ts is arbitrary, but Blau and Goodstein (2010) show that benefi t mea- sures computed under a variety of alternative assumptions are highly correlated with the benefi t measures used here. 18. The elimination of the Social Security Earnings Test for workers who have reached their FRA was enacted unexpectedly in 2000. We do not analyze the impact of this policy change. See Haider and Loughran (2008) for a recent analysis and summary of the evidence. 19. The fi gure uses the earnings profi le of male high school dropouts born in 1937, but the results are very similar using profi les of other groups. The regression analysis uses the actual (predicted) profi le for each cohort. 20. The full retirement age is 65 for individuals born in or before 1937; 65 + x / 6 for birth years 1937+x, x=1, . . . ,5; 66 for birth years 1943–54; 66 + x / 6 for birth years 1954+x, x=1, . . . ,5; and 67 for birth years 1960+. Each one year increase in the FRA is equivalent to a 6.67 percent benefi t cut for a given claiming age.

Banerjee and Blau 179

Until 1972, there was no increase in the benefi t from claiming after age 65, so the gain for many of the earliest cohorts was negative in PDV terms. A Delayed Retire- ment Credit (DRC) was instituted in 1972, providing a permanent 1 percent increase in the benefi t per year of claiming past age 65 (up to age 70). This was increased to 3 percent in 1977, and then increased by 0.5 percent per two- year birth cohort, from 3.5 percent for the 1925–26 cohorts to 8.0 percent per year for the 1943 and subsequent cohorts. The possibility to claim before age 65 was instituted in 1956 for women and 1961 for men. This explains the large negative values for the gain from claiming at 62 until the 1901 cohort, which was the fi rst (male) cohort to have this opportunity. The gain from claiming at age 62 was not affected by most subsequent reforms, which tended to change benefi ts between ages 62 and 65 by roughly equal amounts.

C. Social Security Disability Insurance The incentive to apply for SSDI benefi ts is likely to be infl uenced by the probabil- ity of a successful application, known as the award rate (Low and Pistaferri, 2015). We have aggregate time series data on the award rate for the entire period, and age- group- specifi c data beginning in 1992.21 Figure 8 shows that the award rate increases

21. We are grateful to the Social Security Administration for providing unpublished tabulations on age- specifi c award rates.

.0 2

.0 4

.0 6

.0 8

.1 .1

2 PD

V B

E N

65

1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 Birth Year

Based on lifetime earnings for high school droput men born in 1937. Millions of year 2010 $

Figure 6 Expected Present Discounted Value of Lifetime Old Age and Survivors Insurance Benefi ts for Claiming at Age 65, by Birth year

The Journal of Human Resources180

with age, but the time trends in the award rate are very similar across age groups. Thus, in practice we have only time series variation, so as discussed previously we can analyze the effect of the award rate only in specifi cations without time effects. The award rate may be endogenous to labor supply if the composition of the applicant population with respect to severity of disability is infl uenced by the award rate. We cannot account for this directly, but we include the fraction of the insured population that applied for SSDI in a given year to control for the composition of the applicant population.22

D. Pension Coverage Employer- sponsored pension plans are quite heterogeneous, and it is diffi cult to com- pute benefi ts without knowing the details of each plan. We use the CPS to compute a binary indicator of pension coverage that varies by birth cohort and education but not by age, as described in the appendix. This is a crude proxy for the infl uence of pen- sions. Unfortunately, data on pension type are not available in the CPS.

22. In a specifi cation without time effects we could include the SSDI benefi t as well as the award rate. However, in practice the benefi t effect is poorly identifi ed even in this specifi cation as a result of the high- order polynomial control for the average earnings used to compute the benefi t and the absence of benefi t rule variation affecting SSDI since the late 1970s.

–. 06

–. 04

–. 02

0 .0

2

1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 Birth Year

pdvgain62 pdvgain70

Based on lifetime earnings for high school droput men born in 1937. Millions of year 2010 $

Figure 7 Gain in Expected Present Discounted Value of Lifetime Old Age and Survivors Insur- ance Benefi ts for Claiming at 62 and 70 Relative to 65, by Birth year

Banerjee and Blau 181

E. Other Variables The specifi cation includes race (black, other), marital status (widowed, divorced or separated, and never married), Hispanic ethnicity, and number of children younger than 6 and younger than 18, all derived from the CPS. We also include measures of self- reported health and work days lost as a result of illness, derived from the National Health Interview Survey. These data are aggregated to the sex- age- education- year cell level and merged with the CPS data. The appendix provides further details.

V. Results

A. Coeffi cient Estimates Table 1 shows coeffi cient estimates from models of FTW estimated for age groups 25–61 and 62–69 for men, and 25–54 and 55–69 for women. In addition to the vari- ables shown in the table, the specifi cation includes a sixth order polynomial in average indexed earnings used to compute OASI benefi ts, age and year fi xed effects, a cubic polynomial in birth year, and geographic division dummies (full results are available on request). The upper panel shows results for the economic variables. The log wage coeffi cient estimate is 0.09 for younger men and 0.001 for older men. The implied elasticities at the sample mean values of FTW (see the bottom of the table) are 0.11 for younger men and zero for older men. The coeffi cient estimates for women are

0 .2

.4 .6

.8

1960 1970 1980 1990 2000 2010 year

25–29 30–34 35–39 40–44 45–49 50–54 55–59 All ages

Fraction of SSDI Applications Accepted

Figure 8 Trend in Social Security Disability Insurance Award Rate by Age Group

The Journal of Human Resources182

Table 1 Coeffi cient Estimates from regressions of Full- Time Equivalent Weeks Worked / 52 (FTW)

Men Women

25–61 62–69 25–54 55–69

Economic variables Log wage 0.09 0.001 0.05 –0.07

(0.01) (0.04) (0.02) (0.04) Average tax rate –0.56 0.03 –0.14 0.22

(0.06) (0.22) (0.09) (0.17) PDVBEN65 0.64 –0.72 1.98 –0.29

(0.16) (0.59) (0.49) (0.38) Gain from early claiming 0.24 –1.17 0.43 –0.31

(0.16) (0.41) (0.26) (0.29) Gain from later claiming –0.11 0.54 0.89 0.65

(0.13) (0.30) (0.22) (0.19) Pension coverage 0.07 –0.01 0.20 0.16

(0.02) (0.07) (0.02) (0.04) Demographic variables

Divorced, widowed, or separated –0.19 –0.05 0.13 0.17 (0.01) (0.03) (0.02) (0.02)

Never married –0.27 –0.10 0.16 0.12 (0.01) (0.05) (0.02) (0.04)

Black –0.05 –0.02 0.07 –0.06 (0.02) (0.05) (0.02) (0.03)

Other race –0.18 0.09 –0.15 0.01 (0.03) (0.08) (0.03) (0.06)

Hispanic –0.17 –0.02 –0.13 –0.07 (0.01) (0.06) (0.02) (0.04)

Number of kids < 6 –0.02 –0.06 –0.08 0.02 (0.004) (0.06) (0.01) (0.04)

Number of kids < 18 0.01 –0.03 –0.03 –0.10 (0.002) (0.02) (0.002) (0.02)

Health very good 0.04 –0.01 0.04 0.03 (0.01) (0.03) (0.01) (0.02)

Health good –0.07 –0.01 –0.03 0.01 (0.01) (0.03) (0.01) (0.02)

Health fair –0.12 –0.06 –0.11 0.04 (0.01) (0.03) (0.02) (0.02)

Health poor –0.19 –0.02 –0.26 0.02 (0.02) (0.05) (0.04) (0.04)

Fraction of year unable to work due to illness

–0.07 –0.05 0.01 –0.02 (0.01) (0.03) (0.02) (0.02)

(continued)

Banerjee and Blau 183

0.05 and –0.07. The negative effect for older women is anomalous. The wage rate was predicted assuming full- time year- round employment, which could produce mis- leading results for women. As noted above (Footnote 16), we reestimated the wage models correcting for selection on employment (specifi cally, observing a wage rate for year- round full- time employment). The effects for men were similar to those shown in Table 1. For younger women, the positive effect becomes essentially zero, and for older women the effect changes from –0.074 to –0.035. This is still anomalous but smaller quantitatively.

The average tax rate has negative effects for younger men and women, but the estimates are positive for older individuals. The implied elasticities at the means are –0.26 and –0.09 for younger men and women, and 0.04 and 0.25 for older men and women (see Appendix Table A2 for the sample means of the explanatory variables).

The estimated effects of the PDV of Social Security benefi ts at age 65 are posi- tive at younger ages and negative for the older groups. The elasticities at the sample means for younger men and women are 0.11 and 0.47, and for older men and women are –0.20 and –0.08. At older ages we would expect a negative wealth effect, while at younger ages the sign of the effect is theoretically ambiguous. There is a negative wealth effect, but in the presence of a borrowing constraint more generous benefi ts could induce greater work effort at younger ages in anticipation of less work effort at older ages. We expect the gain from claiming at 62 relative to 65 to have a negative ef- fect on labor supply, and the results show this for older ages but not for younger ages. We expect the gain from claiming at 70 relative to 65 to have a positive effect on labor supply, and the results show this except for younger men. In both cases the effects are quite small, with elasticities of 0.04 or less in absolute value.

Men Women

25–61 62–69 25–54 55–69

High school dropout –0.04 –0.20 –0.02 –0.12 (0.01) (0.03) (0.02) (0.03)

High school graduate –0.01 –0.13 0.03 –0.06 (0.004) (0.02) (0.01) (0.02)

Some college –0.008 –0.09 0.02 –0.02 (0.003) (0.01) (0.01) (0.01)

Mean of dependent variable 0.815 0.349 0.546 0.315 R2 0.89 0.94 0.94 0.95 (number of cells) (6808) (1472) (5520) (2760)

Notes: PDVBEN65 = Present Discounted Value of OASI benefi t if claimed at age 65 (discounted to age 55). Gain from early claiming = PDVBEN62 – PDVBEN65. Gain from later claiming = PDVBEN70 – PD- VBEN65. Reference groups for categorical variables are white, married, health excellent, and college gradu- ate. All monetary amounts except the log wage are measured in millions of year- 2010 dollars. Coeffi cients on the sixth order polynomial in the average earnings variable used to compute OASI benefi ts, age- and time- fi xed effects, the cubic in birth year, and geographic dummies are not shown.

Table 1 (continued)

The Journal of Human Resources184

Pension coverage has a positive effect on labor supply for all groups except older men, with small elasticities for men (0.05 and –0.02), and modest elasticities for women (0.15 and 0.23). These pension effects are diffi cult to interpret in economic terms because of the absence of measures of benefi ts or even pension type.

The results for demographic and health variables shown in the lower panel of Table 1 are similar to those reported in many other studies: Unmarried men work less and unmarried women work more than their married counterparts; blacks, members of other racial groups, and Hispanics generally work less than whites, with the notable exception of younger black women; men and women with children present in the household work less; individuals who report fair or poor health and more days lost due to illness generally work less; and less- educated individuals work less, especially at older ages.

B. Counterfactual Simulations Table 2 shows the results of counterfactual simulations of the change in the average annual growth rate of FTW from 1965–88 to 1989–2010. We use the regression re- sults to simulate the level of FTW under alternative assumptions, and then compute the implied growth rates. We focus on growth rates because they are more directly informative about changes in trends (results for levels, reported in Appendix Table A1, are briefl y discussed below). The fi rst three rows of Table 2 show the observed average annual growth rate of FTW in each period, and the change in the growth rate from the earlier to the later period. For example, the column for older men indicates that in the earlier period FTW declined by 2.23 percent per year on average, while in the later period it rose by 1.21 percent. The change in the average annual growth rate from the earlier to the later period was 3.44 percent. The fourth row shows that the model predicts the difference in growth rates perfectly (thanks to the year fi xed effects), using the observed values of the explanatory variables.

The subsequent rows show the predicted change in the growth rate holding constant the value of each variable or group of variables at their 1965–88 means, one at a time. The percent of the observed change that can be accounted for by changes in the ex- planatory variables is shown in parentheses for cases in which the explanatory power is non- negligible (at least 5 percent) and is in the right direction. For example, the row labeled “education” at the bottom of the table indicates that if the educational com- position of the older male population had remained at its average 1965–88 value dur- ing 1989–2010, the change in the employment growth rate would have been 0.0305 instead of the observed increase of 0.0344. So the change in education can account for 11 percent ([0.0344 – 0.0305)] / 0.0344) of the decline in the employment growth rate of older men and 14 percent for older women.23

Table 3 shows the changes in the mean values of the explanatory variables from 1965–88 to 1989–2010. The share of men aged 62–69 who were high school dropouts decreased by 29 percentage points, and Table 1 indicates that high school dropouts work substantially less than their more educated counterparts. As a result, the increase

23. The entries in Table 2 are rounded, so the percent change in the table, which is based on unrounded fi gures, is slightly different in some cases from the percent change calculated from the rounded entries.

Table 2 Counterfactual Simulations of the Average Annual Growth Rate of FTW

Men Women

25–61 62–69 25–54 55–69

1965–88 annual growth rate –0.0020 –0.0223 0.0240 0.0040 1989–2010 annual growth rate –0.0047 0.0121 0.0004 0.0184 Observed change –0.0027 0.0344 –0.0236 0.0144 Predicted change –0.0027 0.0344 –0.0236 0.0144

Counterfactual predicted change, replacing 1989–2010 values of explanatory variables with 1965–88 values

Economic variables Wage rate –0.0032 0.0341 –0.0240 0.0178 Average tax rate –0.0056 0.0367 –0.0243 0.0149 OASI –0.0016 0.0357 –0.0205 0.0154 (percent of total change explained) (27) (9) (6) [base] [–0.0022] [0.0390] [–0.0218] [0.0154] PDVBEN65 –0.0016 0.0355 –0.0199 0.0145 (percent of total change explained) (27) (8) [base] [–0.0022] [0.0361] [–0.0216] [0.0144] Gain from early claiming –0.0027 0.0352 –0.0236 0.0156 [base] [–0.0027] [0.0351] [–0.0236] [0.0155] Gain from later claiming –0.0026 0.0338 –0.0242 0.0142 (percent of total change explained) (8) [base] [–0.0026] [0.0365] [–0.0238] [0.0144] Pension coverage –0.0025 0.0345 –0.0234 0.0137 (percent of total change explained) (8)

Demographic variables Marital status –0.0012 0.0347 –0.0249 0.0143 (percent of total change explained) (54) Race / ethnicity –0.0014 0.0343 –0.0223 0.0144 (percent of total change explained) (48) (5) Number of children –0.0028 0.0363 –0.0221 0.0180 (percent of total change explained) (6) Health –0.0027 0.0337 –0.0235 0.0142 Education –0.0029 0.0305 –0.0234 0.0123 (percent of total change explained) (11) (14)

Notes: FTW = (Full- time equivalent weeks worked) / 52. The counterfactual change for all variables except OASI and its components replaces the observed value of each variable or group of variables (one at a time) in 1989–2010 with its 1965–88 mean value. The OASI simulations replace the 1989–2010 values with the values for the 1937 birth cohort but using observed lifetime earnings of each cohort to compute the benefi t. The predicted change is used as the base to compute percent of the total explained. The OASI counterfactual cannot be computed using the anypia program, so we used our own approximation of the Social Security benefi t formula. In order to ensure that the baseline and counterfactual simulations are comparable, we also used our code to simulate the baseline values for OASI. These values are shown in brackets for OASI and its components. The text provides more discussion. Health is not measured before 1972, so the means for the earlier period use 1972–88 values (the very good category was not introduced until 1982, so the mean is measured from 1982–88). Hispanic ethnicity is not available until 1970, so the mean is measured for 1970–88. State tax rates are not available until 1977, so the mean tax rate is measured for 1977–88. OASI = Old Age and Survivors Insurance. PDVBEN65 = Present Discounted Value of OASI benefi t if claimed at age 65 (discounted to age 55). Gain from early claiming = PDVBEN62 – PDVBEN65. Gain from later claiming = PDVBEN70 – PDVBEN65. The OASI simulation changes PDVBEN65 and the gains from early and late claiming jointly. All monetary amounts except the log wage are measured in millions of year- 2010 dollars.

The Journal of Human Resources186

in educational attainment can account for a modest part of the increase in employment of older men.24

Table 3 indicates that the mean real wage rate increased by 9–16 log points for men across periods, and by 24–27 log points for women. However, these wage increases cannot explain changes in employment growth for any of the groups. The positive wage coeffi cients are too small for the wage changes to make much difference, and the negative coeffi cient for older women implies that their wage increase should have

24. The large changes in educational attainment over this period were probably accompanied by changes in the average unobserved skill of the education groups. For example, as high school completion approaches 90 percent, the remaining dropouts may be more negatively selected than when the high school graduation rate was only 75 percent. We reestimated the models allowing education effects to differ across the two periods. The explanatory power of education increased from 14 percent to 47 percent for older women, and was unchanged for the other groups.

Table 3 Change in means of the explanatory variables from 1965–88 to 1989–2010

Men Women

25–61 62–69 25–54 55–69

Log wage 0.093 0.162 0.243 0.269 Average tax rate –0.088 –0.079 –0.092 –0.075 PDVBEN65 –0.0163 –0.0030 –0.0184 –0.0043 Gain from early claiming 0.0015 0.0003 0.0023 0.0006 Gain from later claiming 0.0112 0.0044 0.0113 0.0057 Pension coverage –0.063 –0.009 0.014 0.042 Divorced, widowed, or separated 0.043 0.039 0.025 0.0001 Never married 0.090 –0.008 0.083 0.002 Black 0.015 0.004 0.020 0.015 Other race 0.038 0.026 0.039 0.034 Hispanic 0.068 0.033 0.061 0.049 Number of kids<6 0.036 0.053 0.067 0.064 Number of kids<18 0.006 0.156 0.030 0.192 Health very good 0.044 0.055 0.036 0.057 Health good –0.064 –0.036 –0.099 –0.070 Health fair –0.013 –0.043 –0.021 –0.047 Health poor –0.009 –0.032 –0.003 –0.014 Fraction of year unable to work due to illness

–0.027 –0.105 –0.008 –0.035

High school dropout –0.147 –0.295 –0.136 –0.268 High school graduate –0.021 0.066 –0.121 0.034 Some college 0.095 0.097 0.128 0.122

Notes: Each entry is the mean value of the indicated variable in 1989–2010 minus the mean value in 1965– 88. See Table 2 for additional notes. Monetary amounts except the log wage are measured in millions of year- 2010 dollars.

Banerjee and Blau 187

caused a decline in their labor supply rather than the observed increase. The decline in the average tax rate of 0.07–0.09 shown in Table 3 also cannot account for the observed changes in employment growth between periods. Overall, changes in the net reward to working in a given year cannot help explain the observed changes in employment.

We use a different approach for the counterfactual simulations for OASI benefi ts. The anypia program cannot be used to compute benefi ts for a given earnings history and a counterfactual OASI formula. Instead, we use the PIA produced by anypia as input into our own program that computes benefi ts for alternative policy regimes. This introduces some measurement error since our program does not produce the same benefi ts as anypia using our approximation of the actual rules for each cohort. We do not have the code for the anypia program and cannot determine the source of the error. Nevertheless, our calculations yield benefi ts that are very highly correlated with the benefi ts produced by anypia (0.98). We use the benefi ts from anypia in estimation, and we use our program to generate both counterfactual and baseline benefi ts (shown in brackets) for the simulations, to ensure that any errors in calculations cancel out when we take the difference.

The OASI counterfactual simulation assigns the benefi t computation rules for the 1937 cohort to everyone but uses each cohort’s observed (predicted) lifetime earnings. This approach isolates the effect of rule changes, holding average indexed earnings constant for each cohort. The 1937 cohort was the last to have an FRA of 65.25 As indi- cated in Table 3, the PDV of lifetime OASI benefi ts if claimed at age 65 (discounted to age 55) would have been higher by 16–18K in 1989–2010 for the younger cohorts if the 1937 SS rules had remained in effect for subsequent cohorts, and by 3–4K for the older groups.26 Table 2 shows that the decline in benefi ts can account for 27 percent of the decline in employment growth of younger men and 8 percent of the decline for younger women (shown in the row labeled PDVBEN65). The small changes in the gains from earlier and later claiming had little impact on employment except for older men. The OASI reforms as a group cannot explain any of the increase in employment growth of older men and women, and can account for 27 percent and 6 percent of the declines for younger men and women, respectively (shown in the row labeled OASI, which sums the effects of PDVBEN65 and the gains to early and late claiming).27

Concerning the demographic characteristics in Table 2, the row labeled “marital status” indicates that if the marital status composition of the younger male population had remained unchanged from 1965–88 to 1989–2010, the decline in the employ- ment growth rate would have been only –0.0012 per year instead of the actual de- cline of –0.0027. So changes in marital status can account for 54 percent ([–0.0027 –

25. Alternative counterfactuals based on the rules for other cohorts yielded very similar results. Results using benefi t levels in place of the present discounted value of benefi ts were qualitatively similar, but the explana- tory power of OASI rule changes was smaller. 26. These are declines of 11 percent, 3 percent, 14 percent, and 5 percent for the four groups, using the overall sample means reported in the Appendix as the base. The magnitude of the decline depends on the mix of birth years in the period two samples. 27. This differs from the results for older men in Blau and Goodstein (2010), who found that changes in OASI could explain one quarter to one half of the rise in LFP of older men. Our results were closer to theirs when we estimated a specifi cation that included only a linear term in lifetime earnings, as in their specifi ca- tion.

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(–0.0012)] / –0.0027) of the decline in the employment growth rate of younger men over this period. This was a consequence of substantial increases in the proportion of the younger male population that was never- married, divorced, widowed, or sepa- rated. There were increases of similar magnitudes for women, but they cannot explain changes in employment since never- married women work more at younger ages than their married counterparts, while female employment growth declined at younger ages. The only other change in the demographic characteristics that can help account for changes in employment growth (aside from education, which was discussed above) is the change in the racial and ethnic composition of the younger male population. The black, other race, and Hispanic shares of the population increased for all groups (see Table 3), but the effects of these variables on labor supply are largest at younger ages. These composition changes can explain about half of the slowdown in employment growth for younger men. For younger women, blacks work more than whites, so the increased share of blacks offset the effects of the increased shares of the other groups.

C. Alternative Specifi cations and Simulations (1) As discussed above, we simulate the growth rate of employment, because this is more informative about trends than are employment levels. Nevertheless, it is worth examining simulation results for employment levels briefl y. These are reported in Ap- pendix Table A1, using the estimation results from Table 1. Qualitatively, the results are very similar. The explanatory power of several of the variables is much larger for younger men but similar in magnitude for the other groups.

(2) A key issue discussed in the previous section is how to control for time- trending unobservables that could be correlated with the explanatory variables. The results re- ported in Table 1 are from a specifi cation that includes age- group- specifi c year fi xed effects, which control for such unobserved factors in a very fl exible way. In fact, this specifi cation might be too fl exible for our purposes, since we are interested in common trends. We estimated two other specifi cations to gauge the importance of this issue. The fi rst incorporates a full set of year fi xed effects with coeffi cients constrained to be equal across age groups, by sex. The simulation results from this specifi cation are shown in Table 4 (coeffi cient estimates are not shown). An important point to note is that the model does not predict the observed changes as well as in the specifi cation with unre- stricted year fi xed effects. The predicted change reported in row four of Table 4 is used as the baseline for the counterfactual simulations, to ensure that the counterfactual and base simulations are comparable. Most of the simulation results are quite similar quali- tatively to the results in Table 2. The main exception is that the explanatory power of OASI is smaller for younger men and women, while it is larger for older women. There are also modest increases in the explanatory power of health for older men and women, and a moderate increase in the explanatory power of pensions for older women.

The second alternative specifi cation omits all calendar year effects, replacing them with a set of observed aggregate variables. These include the minimum wage, SSDI award and application rates,28 net imports, life expectancy, and GDP growth. The

28. The award rate is determined in part by the composition of the applicant population, so other things may not be equal as the award rate varies. We use the application rate (the share of the insured population that ap- plies in a given year) as a rough proxy to control for changes in the composition of the applicant population.

Banerjee and Blau 189

Table 4 Counterfactual Simulations of Annual Average Growth Rate of Full- Time Equivalent Weeks Worked / 52 (FTW), Restricted Year Fixed Effects

Men Women

25–61 62–69 25–54 55–69

1965–88 annual growth rate –0.0020 –0.0223 0.0240 0.0040 1989–2010 annual growth rate –0.0047 0.0121 0.0004 0.0184 Observed change –0.0027 0.0344 –0.0236 0.0144 Predicted change –0.0022 0.0251 –0.0221 0.0073

Counterfactual change, replacing 1989–2010 values with 1965–88 values of explanatory variables

Economic variables Wage rate –0.0027 0.0237 –0.0221 0.0073 (percent of total change explained) (5) Average tax rate –0.0043 0.0214 –0.0218 0.0075 (percent of total change explained) (15) OASI –0.0016 0.0241 –0.0215 0.0061 (percent of total change explained) (15) (14) [base] [–0.0019] [0.0028] [–0.0217] [0.0071] PDVBEN65 –0.0017 0.0244 –0.0211 0.0076 (percent of total change explained) (13) [base] [–0.0020] [0.0238] [0.0215] [0.0071] Gain from early claiming –0.0022 0.0246 –0.0221 0.0073 [base] [–0.0022] [0.0246] [–0.0221] [0.0073] Gain from later claiming –0.0021 0.0253 –0.0225 0.0057 (percent of total change explained) (21) [base] [–0.0021] [0.0245] [–0.0222] [0.0072] Pension coverage –0.0020 0.0255 –0.0219 0.0165 (percent of total change explained) (10) (6)

Demographic variables Marital status –0.0008 0.0266 –0.0235 0.0068 (percent of total change explained) (64) (7) Race / ethnicity –0.0010 0.0262 –0.0210 0.0082 (percent of total change explained) (56) Number of children –0.0022 0.0249 –0.0207 0.0092 (percent of total change explained) (6) Health –0.0022 0.0222 –0.0219 0.0065 (percent of total change explained) (11) (11) Education –0.0024 0.0237 –0.0223 0.0062 (percent of total change explained) (6) (14)

Notes: Simulations are based on a specifi cation with year effects restricted to be the same across age groups for each sex. The coeffi cient estimates from this specifi cation are not shown, and are available upon request. All monetary amounts except the log wage are measured in millions of year- 2010 dollars. See Table 2 for additional notes.

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Table 5 Counterfactual Simulations of Annual Average Growth Rate of Full- Time Equivalent Weeks Worked / 52 (FTW), No Controls for Calendar Time

Men Women

25–61 62–69 25–54 55–69

1965–1988 annual growth rate –0.0020 –0.0223 0.0240 0.0040 1989–2010 annual growth rate –0.0047 0.0121 0.0004 0.0184 Observed change –0.0027 0.0344 –0.0236 0.0144 Predicted change –0.0021 0.0306 –0.0191 0.0176

Counterfactual change, replacing 1989–2010 values with 1965–88 values of explanatory variables (percent of total change explained)

Economic variables Wage rate –0.0023 0.0305 –0.0193 0.0186 Average tax rate –0.0017 0.0281 –0.0171 0.0177 (percent of total change explained) (20) (8) (11) OASI –0.0017 0.0329 –0.0126 0.0184 (percent of total change explained) (10) (13) (19) [base] [–0.0019] [0.0377] [–0.0155] [0.0185] PDVBEN65 –0.0017 0.0327 –0.0117 0.0176 (percent of total change explained) (12) (22) [base] [–0.0019] [0.0340] [–0.0151] [0.0175] Gain from early claiming –0.0022 0.0316 –0.0192 0.0188 [base] [–0.0021] [0.0315] [–0.0192] [0.0186] Gain from later claiming –0.0021 0.0298 –0.0202 0.0171 (percent of total change explained) (10) [base] [–0.0021] [0.0335] [–0.0196] [0.0175] Pension coverage –0.0021 0.0306 –0.0191 0.0165 (percent of total change explained) (6)

Demographic variables Marital status –0.0008 0.0311 –0.0211 0.0174 (percent of total change explained) (61) Race / ethnicity –0.0007 0.0303 –0.0178 0.0179 (percent of total change explained) (66) (7) Number of children –0.0023 0.0303 –0.0182 0.0193 (percent of total change explained) (5) Health –0.0021 0.0297 –0.0190 0.0177 Education –0.0025 0.0245 –0.0184 0.0168 (percent of total change explained) (20)

(continued)

Banerjee and Blau 191

counterfactual simulation results based on these estimates are shown in Table 5, using the predicted values as the baseline. Qualitatively, the results are quite similar to those in Table 4. The simulated effects of the aggregate variables are shown at the bottom of Table 5. The results suggest that changes in the minimum wage and the SSDI award rate can account for part of the changes in employment growth. However, these results should be interpreted cautiously given that they are identifi ed by the very strong as- sumption of the absence of unobserved aggregate trends correlated with the included variables.29

(3) Another issue of interest is the sensitivity of the results to the sample period used in estimation. We use all available years (1965–2010), but it is possible that behavior has changed over time, and as a result the restriction that the coeffi cients do not vary over time could be incorrect. This seems plausible given the relative lack of explana- tory power of many of the explanatory variables. We reestimated the models for two subperiods: 1965–91 and 1992–2010. This choice of periods is motivated by the avail- ability of some additional data on the SSDI award rate beginning in 1992. Many of the coeffi cient estimates (not shown) are qualitatively and quantitatively similar in the two periods, but there are some notable differences as well. The simulation results (not shown) are quite different in some cases. This is not surprising: If changes in the values of the explanatory variables cannot account for much of the employment trends, changes in the effects of the explanatory variables are likely to have played a role.

(4) As noted above, the specifi cation of cohort effects is important for identifi ca- tion. The results reported so far use a cubic polynomial in birth cohort. We tried sev- eral other specifi cations, including two- year fi xed effects, four- year fi xed effects, and

29. Beginning in 1992, data on SSDI applications and awards are available by age group. This provides an additional source of variation beyond the pure time series available back to 1965. As noted above, we expect a negative effect of the award rate on employment, other things equal. The results (not shown here) reveal small positive effects of the award rate on employment for men, a negative effect for younger women, and no effect for older women. Unfortunately, a counterfactual simulation is not possible because we lack age- specifi c award rate data before 1992.

Men Women

25–61 62–69 25–54 55–69

Aggregate variables Minimum wage –0.0014 0.0275 –0.0182 0.0182 (percent of total change explained) (32) (10) (5) SSDI award and application rates 0.0011 0.0258 –0.0153 0.0174 (percent of total change explained) (154) (16) (20) Net imports –0.0025 0.0295 –0.0199 0.0174 Life expectancy –0.0029 0.0467 –0.0195 0.0200

Notes: Simulations based on a specifi cation with no year effects. The coeffi cient estimates from this specifi cation are not shown. See Table 2 for additional notes.

Table 5 (continued)

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no cohort effects. The results (not shown here) indicate that the explanatory power of OASI is smaller in the fi xed effects specifi cation for men, but larger for younger women.

(5) To check if the results are sensitive to the choice of periods for the simulations, we recomputed the simulations for an alternative pair of periods: 1980–88 as Period 1 and 1998–2006 as Period 2. These periods correspond to the turning point for labor supply at older ages (Period 1) and a recent period before the Great Recession (Period 2). The results (not shown) are qualitatively very similar to the original analysis. For older men, OASI and education are still the only factors that can explain a signifi cant part of the change in the annual average growth rate between periods. For young women, race / ethnicity and number of kids continue to be the only factors that can explain the change in growth rates. But for this set of periods, the percentage changes in growth explained by these factors are much higher. For older women also, the same factors as in the original analysis continue to have the most explanatory power. For younger men, marital status, race, and pensions have increased explanatory power.

(6) Finally, we estimated several specifi cations that included spouse variables for married individuals.30 A family or collective labor supply model implies that the spouse’s wage rate should be included in the specifi cation. The spouse’s predicted wage rate had a statistically signifi cant coeffi cient estimate for two of the four groups, but changes in the spouse’s wage rate had no explanatory power in simulations (results not shown here). In another specifi cation, the spouse’s age, education, employment. and / or earnings were included. Counterfactual simulations (not shown here) indicated that changes in the spouse’s education could explain 6–12 percent of observed em- ployment changes for all four groups, and changes in spouse’s employment status could explain 9 percent of the increase in employment for older men. The explanatory power of the other variables remained unchanged. These are interesting fi ndings, but it is quite likely that spouse earnings and employment are endogenous, so these results are mainly of descriptive interest.

D. Discussion The main goal of this paper is to explain the divergence in employment trends by age group in recent years. Our results suggest three partial explanations for men. The fi rst is demographic change (other than educational composition, discussed below), specifi - cally the delay in fi rst marriage and increases in the population share of nonwhite and Hispanic men. Most men eventually marry, and despite the large increase in the share of younger men who have never married, there has been no increase among older men (see Table 3). Never- married men are much less likely to work at any age, so the delay in marriage can explain reduced employment growth of younger men but had no im- pact on older men. In addition, while the increase in the share of divorced, widowed, and separated men was about the same for both age groups (four percentage points), there is a negative effect of this marital status on employment only for younger men.

30. The spouse’s age, education, predicted wage rate, observed employment (FTW), and observed annual earnings (including spouses outside the 25–69 age range) were added to each married individual’s record be- fore collapsing the data to the cell level, with means taken over the married subsamples. The spouse variables are included in the regression interacted with the fraction married in the cell.

Banerjee and Blau 193

In quantitative terms, the change in the rate of employment growth is much larger for older men. The increase across periods in the annual rate of male employment growth at older ages was 0.0344 and the decline at younger ages was –0.0027, so the difference across age groups in the rate of change was 0.0363. The results in Table 2 indicate that the change in marital status can explain a large share of the small decline in growth at younger ages but only a very small share (3 percent) of the much larger difference in the change in growth rates by age. The same logic implies that the change in racial and ethnic composition can explain only a small share of the divergence in employment growth for older and younger men. Thus, demographic change was not a major factor in the divergence in employment growth by age.

The second explanation is the increase in educational attainment. This can account for 10 percent of the observed divergence in employment growth by age for men, also a rather small share of the change.31

The third explanation is Social Security reform. Our results add to a growing body of evidence indicating that the decline in benefi ts and the increased incentive to delay claiming have contributed to the increase in employment at older ages. Our study is the fi rst to investigate the impact of these reforms at younger ages. The results show that OASI benefi ts have a positive impact on labor supply at younger ages, and the decline in benefi ts contributed to the reduction in employment at younger ages. As noted above, a positive effect of benefi ts at younger ages is consistent with the lifecycle framework, although our reduced form approach does not reveal whether a lifecycle explanation for the fi nding is warranted. The contribution of OASI reform to the 0.0412 difference in the change in the average annual growth rate is 9 percent.32 Thus, the combination of changes in marital status, educational attainment, and Social Security policy can explain only about one- fi fth of the observed age difference in the change in employment growth for men.

For women, OASI reform contributed to the divergence in growth across age groups, but only via increasing employment at older ages. The estimates indicate that OASI benefi ts have a positive impact on labor supply at younger ages, but the effect is too small to matter. Using the OASI baselines, the increase in employment growth for women at older ages was 0.0154 and the decline at younger ages was –0.0218, so the difference in the change across age groups was 0.0372. The results in Table 2 indicate that the change in OASI reform can explain 0.0013 of this difference, or 3.5 percent.33 Education can explain 0.0023, or 6 percent of the observed change. So we can explain only about 10 percent of the observed change for women.

VI. Conclusions

Social Security reforms, the delay in fi rst marriage, and changes in the education distribution can account for about 20 percent of the recent divergence in employment growth by age. As discussed in the introduction, the impact of Social

31. This is calculated as (0.0344 – 0.0305) – (–0.0027 –[–0.0029]) = 0.0037, which is 10 percent of 0.0363. 32. (0.0390 – 0.0357) – (–0.0022 – [–0.0016]) = 0.0039 out of the observed 0.0412. See the OASI row in Table 2. 33. (0.0154 – 0.0154) – (–0.0218 – [–0.0205]) = 0.0013 out of the observed 0.0372. See the OASI row in Table 2.

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Security reforms should persist, because all future cohorts are affected. The impact of increases in educational attainment is unlikely to persist because the major changes of recent decades have ended, and in the absence of unforeseen changes future retir- ing cohorts will have an educational composition similar to today’s retirement- age cohorts.

The future effects of delayed marriage are more diffi cult to predict. Median age at fi rst marriage increased by two full years from 2000 to 2010 for men, and increased by four and half years from its low point in the 1950s and 1960s (Elliott et al. 2012). The share of the male population that was never married by age 45 increased by three per- centage points from 1990 to 2010. Even if these trends have run their course, they will have persistent effects as long as the share never married remains low at older ages.

OASI reforms have contributed modestly to the age divergence, but they are clearly not the main factor. We have been unable to convincingly analyze the impact of SSDI policy, but we speculate that it might have played a signifi cant role in reducing labor supply at younger ages, as suggested by Autor and Duggan (2003), Duggan et al. (2007), and others. If this is correct, the main implication is that SSDI policy reforms to tighten screening criteria may be of more importance than OASI reforms. However, Low and Pistaferri (2015) have argued that tighter screening criteria would reduce social welfare. Further research on the role of SSDI should be a priority.

Another important area for future research is the impact of labor demand and insti- tutional factors on the divergence in employment growth by age. Age discrimination and policies intended to counteract it is one example of such a factor. These factors are more diffi cult to measure than the determinants studied here, but the payoff to such an effort could be high.

Appendix

Data

A. Dependent Variables The main outcome analyzed in this paper is full- time- equivalent weeks worked per year (FTW), defi ned as weeks worked in the previous calendar year if usual hours worked were at least 36, and weeks worked divided by two if usual hours worked were between one and 35. The measure is divided by 52 to restrict it to the unit interval for ease of interpretation. An alternative outcome analyzed is a categorical measure of labor force status in the week prior to the survey date. An individual is defi ned as employed if the employment status recode indicates that he was employed or search- ing for work.

B. Social Security We use CPS earnings from ages 25–59 to compute OASI benefi ts, assuming continu- ous employment at cell- specifi c average annual earnings (truncated at the maximum taxable amount), as in Blau and Goodstein (2010). The CPS data are augmented with

Banerjee and Blau 195

published Social Security Administration data on median covered earnings by age prior to the availability of CPS data. Cells are defi ned by gender, age, education, and year. We use ages 25–59 because most individuals are fi nished with schooling by age 25 and have not yet retired by age 59. Thus we do not have to deal with issues of selec- tion on entry to and exit from employment, at least for men. This provides the 35 years of earnings used in the computation of Average Indexed Monthly Earnings (AIME), the basis for determining the Social Security benefi t. This is an arbitrary approach, but the resulting benefi t is highly correlated with benefi ts computed using alternative as- sumptions about the earnings history (see Blau and Goodstein 2010). We do the same for women, despite the fact that many women do not work continuously. For women the assumption of no selection bias is implausible, but there is no straightforward way to deal with this.

Benefi ts are computed under three alternative assumptions about the age of claim- ing: 62, 65, and 70. We use the batch version of the SSA computer program “anypia” to compute the OASI benefi t for each of the three OASI claiming ages. We compute the Expected Present Discounted Value (EPDV) of benefi ts using standard mortality schedules and an assumed real interest rate of 3 percent. Benefi ts are assumed to be constant in real terms (as they have been since the automatic COLA was introduced). Benefi ts are discounted to the year in which the individual turns age 55. This is arbi- trary but has no impact on the results.

The details of the earnings and benefi t calculations are as follows. We use data on wage- salary income, with the bottom and top 1 percent within each cell trimmed. Earnings are capped at the taxable maximum earnings applicable in each year. Earn- ings data from the CPS for calendar years1961–2010 (from March 1962–2011 fi les) are used to compute the cell mean of positive values of capped earnings. We use pub- lished SSA median earnings data for various years and ages from 1937–60, prior to the availability of CPS data. The medians are transformed to means using mean / median ratios from the CPS. The means are then capped, and data are fi lled in for missing years and ages using regression imputations. Combining CPS and SSA data, we have information for birth years 1878–1985 at ages 25–59. The specifi c steps involved in combining CPS and SSA data are as follows:

1. Compute the CPS mean / median ratio, and run sex- age- group- specifi c regres- sions to project backward.

2. Compute the ratio of education- specifi c mean earnings to overall mean earn- ings using the CPS 1961–2010, for use in adjusting 1937–60 SSA data, which are not available by education. Regress the ratio on year by sex and age group.

3. Apply the adjustments from steps a and b to the SSA data on median earnings, which are available only for selected ages and years. Interpolate missing years and ages.

4. Run sex- education- group- specifi c log earnings regressions for ages 25–59 on a cubic in age, a cubic in birth year, and interactions, in order to smooth earn- ings profi les.

5. Use the regression coeffi cients to generate predicted earnings paths for each of the alternative retirement age scenarios, assuming constant real earnings at ages 60 and above (using the age- 59 value). We also use average earnings

The Journal of Human Resources196

Table A1 Counterfactual Simulations of the Level of Full- Time Equivalent Weeks Worked / 52 (FTW)

Men Women

25–61 62–69 25–54 55–69

1965–88 mean FTW 0.830 0.379 0.450 0.266 1989–2010 mean FTW 0.807 0.327 0.613 0.355 Observed change –0.023 –0.053 0.163 0.089 Predicted change –0.023 –0.053 0.163 0.089

Counterfactual change, replacing 1989–2010 values with 1965–88 values of explanatory variables (percent of total change explained)

Economic variables Wage rate –0.032 –0.059 0.155 0.128 (percent of total change explained) (5) Average tax rate –0.071 –0.018 0.146 0.090 (percent of total change explained) (66) (10) OASI –0.014 –0.044 0.180 0.087 (percent of total change explained) (52) [base] [–.029] [–0.039] [0.155] [0.087] PDVBEN65 –0.014 –0.046 0.194 0.088 (percent of total change explained) (52) [base] [–.029] [–.045] [.0156] [.088] Gain from early claiming –0.024 –0.054 0.163 0.089 [base] [–0.023] [–0.054] [0.163] [0.088] Gain from later claiming –0.022 –0.048 0.149 0.090 (percent of total change explained) (6) (8) [base] [–0.023] [–0.045] [0.162] [0.090] Pension coverage –0.019 –0.052 0.159 0.085 (percent of total change explained) (18) (5)

Demographic variables Marital status 0.009 –0.052 0.147 0.089 (percent of total change explained) (137) (10) Race / ethnicity –0.006 –0.053 0.175 0.087 (percent of total change explained) (74) Number of children –0.022 –0.047 0.167 0.103 (percent of total change explained) (11) Health –0.034 –0.061 0.156 0.091 Education –0.028 –0.084 0.166 0.069 (percent of total change explained) (23)

Notes: Simulations are based on the coeffi cient estimates shown in Table 1. See Table 2 for additional notes.

Banerjee and Blau 197

growth by year for future years implied by the predicted earnings paths to generate wage index and price index values in future years (2011+).

C. Other Variables Data on pensions and health insurance are available beginning with the 1980 CPS survey. However, we do not use the health insurance data because the trends show unexplained breaks related to changes in the survey. Pension coverage is measured by enrollment, and we limit the universe for measuring coverage to nonagricultural private sector workers. Pensions are important only if an individual is covered for a long period of time and expects to receive a benefi t. We approximate this by measur-

Table A2 Sample Means for Estimation Samples

Men Women

25–61 62–69 25–54 55–69

FTW 0.815 0.345 0.546 0.315 Log wage 3.195 3.179 2.803 2.732 Average tax rate 0.370 0.380 0.350 0.360 PDVBEN65 0.136 0.099 0.129 0.087 Gain from early claiming –0.0053 –0.0082 –0.0087 –0.0084 Gain from later claiming –0.0053 –0.0071 0.0041 –0.0006 Pension coverage 0.547 0.603 0.468 0.456 Divorce, widowed, or separated 0.116 0.149 0.172 0.318 Never married 0.175 0.054 0.138 0.052 Black 0.103 0.086 0.124 0.099 Other race 0.041 0.028 0.045 0.029 Hispanic 0.097 0.050 0.098 0.057 Number of kids<6 0.339 0.058 0.391 0.069 Number of kids<18 1.101 0.235 1.363 0.263 Health very good 0.313 0.256 0.322 0.268 Health good 0.258 0.330 0.282 0.345 Health fair 0.072 0.173 0.0788 0.164 Health poor 0.026 0.079 0.0216 0.063 Fraction of year unable to work due to illness 0.125 0.334 0.110 0.272 High school dropout 0.190 0.375 0.169 0.325 High school graduate 0.344 0.297 0.378 0.374 Some college 0.210 0.142 0.228 0.163 Age 41.4 65.3 38.8 61.5 Sample size 6,808 1,472 5,520 2,760

Notes: FTW = (Full- time equivalent weeks worked) / 52. PDVBEN65 = Present Discounted Value of OASI benefi t if claimed at age 65 (discounted to age 55). Gain from early claiming = PDVBEN62 – PDVBEN65. Gain from later claiming = PDVBEN70 – PDVBEN65.

The Journal of Human Resources198

ing pension coverage at ages 45–55 and assigning coverage at those ages as a perma- nent characteristic. The type of pension is not recorded.34

We use data on self- reported health and days lost due to illness from the National Health Interview Survey, downloaded from the Minnesota Population Center’s IHIS web site. Data on work days lost due to illness are available beginning in 1969. The reference period changed from the previous two weeks to the previous calendar year in 1997. The self- reported health measure is available as a four- point scale (poor, fair, good, excellent) from 1972–81 and as a fi ve- point scale (poor, fair, good, very good, excellent) beginning in 1982.

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