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Factors Affecting Labor Supply Decisions and Retirement Income

Robin L. Lumsdaine

Recent retirement research has focused on factors affecting the retirement decision, reflecting the notion that retirement has become voluntary (Quinn, Burkhauser, and Myers, 1990, document the transition over the last four decades from ''involuntary" retirement due to health reasons to the current situation in which most people choose to retire). Leonesio (1993a) cites the "life-cycle view of work, saving, and consumption" as the motivating influence behind the behavioral focus of the retirement literature, particularly with regard to decisions about Social Security, pensions, leaving a career job, and accepting post-retirement work. Recognizing the life-cycle view, economists have concentrated not just on the final decision to retire but on the individual's whole history of labor force participation decisions.

Owing to both the projected shortfall in Social Security and an overall anticipated labor shortage, recent policy has focused on ways to alter these labor supply decisions, particularly with regard to affecting retirement behavior and income. Gustman, Mitchell, and Steinmeier (1994) and Hurd (1993) identify some of the factors that influence the retirement decision. Gustman, Mitchell, and Steinmeier consider factors affecting the individual, such as health status, retirement status of spouse, additional family needs, and the individual's savings

Financial support for this paper from the National Institute on Aging, grant number R37-AG00146, and the Center for Economic Policy Research at Princeton University is gratefully acknowledged. This paper has benefited substantially from comments on earlier drafts by Constance Citro, Marjorie Honig, John Rust, and participants at the panel conference.



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Assessing Knowledge of Retirement Behavior 3 Factors Affecting Labor Supply Decisions and Retirement Income Robin L. Lumsdaine Recent retirement research has focused on factors affecting the retirement decision, reflecting the notion that retirement has become voluntary (Quinn, Burkhauser, and Myers, 1990, document the transition over the last four decades from ''involuntary" retirement due to health reasons to the current situation in which most people choose to retire). Leonesio (1993a) cites the "life-cycle view of work, saving, and consumption" as the motivating influence behind the behavioral focus of the retirement literature, particularly with regard to decisions about Social Security, pensions, leaving a career job, and accepting post-retirement work. Recognizing the life-cycle view, economists have concentrated not just on the final decision to retire but on the individual's whole history of labor force participation decisions. Owing to both the projected shortfall in Social Security and an overall anticipated labor shortage, recent policy has focused on ways to alter these labor supply decisions, particularly with regard to affecting retirement behavior and income. Gustman, Mitchell, and Steinmeier (1994) and Hurd (1993) identify some of the factors that influence the retirement decision. Gustman, Mitchell, and Steinmeier consider factors affecting the individual, such as health status, retirement status of spouse, additional family needs, and the individual's savings Financial support for this paper from the National Institute on Aging, grant number R37-AG00146, and the Center for Economic Policy Research at Princeton University is gratefully acknowledged. This paper has benefited substantially from comments on earlier drafts by Constance Citro, Marjorie Honig, John Rust, and participants at the panel conference.

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Assessing Knowledge of Retirement Behavior and consumption patterns, while Hurd surveys some of the institutional causes that lead individuals to retire at different ages, such as fixed employment costs, the Social Security earnings test, and pre-existing condition clauses in health insurance. In addition, the perceived financial condition of the employer may play a role in an individual's decision to leave a firm. This paper examines the determinants of some of the key labor supply decisions and their relationship to retirement behavior and retirement income. In order to determine which policies will have the most desirable effects at the lowest cost, we need to assess the relationships and interactions among direct and indirect influences. Some of the questions that have been debated are the following: Will increasing the Social Security early and normal retirement ages create a substitution toward increased disability applications? Have increasing life expectancies resulted in more productive years of life or just prolonged years of nonwork life? Is the relationship between longevity and the ability to work becoming weaker as labor-intensive jobs are a smaller proportion of available jobs? How do individuals formulate expectations about the future and how do they incorporate uncertainty into their decisions? What would be the impact of universal health coverage on labor force participation? This paper will investigate the data and research methodology needed to answer questions such as these. The first section summarizes some of the trends in factors affecting labor force participation decisions and retirement income. The ability to predict future trends is critical to forecasting the success of proposed changes in policy aimed at ensuring adequate retirement income. The next five sections focus on specific key areas that potentially affect the labor supply decision, the transition to retirement, and associated retirement income: Social Security, pensions and early retirement "window" plans, disability, Medicare and other forms of health insurance, and job characteristics. Each of these sections begins with a summary of questions and currently available techniques for addressing them. I then identify future research priorities, focusing on data and methods necessary to understand the extent of the interaction among these areas and how policies aimed at specific areas will ultimately affect retirement behavior and income. I present conclusions in the final section. SUMMARY OF TRENDS While legislation over the last few decades has aimed to reduce the incidence of poverty among the elderly, the threat of poverty has not been eradicated, as shown in Figure 3-1. As individuals age, the probability of being at or near the poverty line increases substantially. One group of elderly particularly at risk are the nearly one-third of Americans over age 65 that live alone, most often women: For the millions of elderly people who live alone, the threats of impoverishment, loss of independence, loneliness and isolation are very real. Many have serious health and economic problems that our society and our governments are

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Assessing Knowledge of Retirement Behavior FIGURE 3-1 Percentage of persons below poverty and near poverty thresholds, by age, 1990. SOURCE: Radner (1993a). neglecting. These conditions persist despite the substantial improvements that Social Security and health and income assistance programs have made in the lives of most older Americans over the past 20 years (Kasper, 1988). Women currently account for more than four-fifths of the elderly living alone, as seen in Figure 3-2. Poverty rates for the elderly are also expected to be concentrated on single women in the future, despite expectations that the elderly as a group will have higher standards of living than previous cohorts (Kingson, 1992). Radner (1993b) considers income, wealth, and combined income-wealth measures and finds that the economic status of widows living alone is significantly worse than that of other groups of elderly. Across all ages, uncertainty about Social Security is increasing. Concerns

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Assessing Knowledge of Retirement Behavior FIGURE 3-2 Percentage of elderly women and men living alone. SOURCE: Kasper (1988). over the budget deficit have threatened the current levels of Social Security benefits. Even if benefits are held at their current levels, the aging of the baby boom population poses an additional strain on the Social Security Trust Fund. Combined, these two concerns have undermined confidence regarding adequate income for future generations of elderly. Despite concerns over the adequacy of Social Security retirement income, the wealth of the elderly remains surprisingly low. The typical American family with a household head age 60 to 65 has very little retirement saving, with median liquid wealth equal to about $6,600 (Venti and Wise, 1992). Lumsdaine and Wise (1994) document various components of elderly wealth and labor force participation and discuss their interaction. Auerbach, Kotlikoff, and Weil (1992) note that the incomes of the elderly are becoming increasingly annuitized as a result of increases in pension benefits and Social Security during the early 1980s. They note that the fraction of elderly income attributable to these two sources

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Assessing Knowledge of Retirement Behavior rose from 40 percent in 1967 to 55 percent in 1988, a 37 percent increase. Increased annuitization could make retirement income planning easier by reducing future uncertainty. However, it is not the fraction of annuitization that is important for the adequacy of retirement income, but the amount. There is additional evidence that the elderly will continue to find themselves with inadequate income to carry them through retirement. The American Society of Pension Actuaries (ASPA) found that employees receive only limited investment advice when it comes to retirement planning. What advice is given often occurs within 1 or 2 years of retirement. ASPA recommends four vehicles for improving one's retirement income. At the individual level, income is expected to come from personal savings, Social Security, pension, and supplemental work after retirement. At the macro level, they emphasize a need for universal coverage and replacement rates targeted as high as 85 percent of final pay for low-income workers and 73 percent for higher income workers. In 1990, average replacement rates for Social Security varied from 28 percent for maximum earners to 56 percent for low wage earners. Currently only 12 percent of employers surveyed have pension plans that are designed around specific replacement rate goals. Of those that do have specific replacement rate goals, the target replacement rate falls far short of those recommended by ASPA (Employee Benefit Plan Review, 1994a). Figure 3-3 shows average replacement rates for defined benefit plan participants in 1989. Evidence in Mitchell (1992) concurs; for representative workers in defined benefit plans with 30 years of service, replacement rates ranged from 34.6 percent for individuals with final earnings of $15,000 to 29.8 percent for individuals with final earnings of $40,000. Fewer years of service substantially lowered replacement rates at all levels; for example, a worker with only 10 years of service could expect a maximum replacement rate of 12.1 percent. According to reports in Employee Benefit Plan Review (1994b), using the Consumer Expenditure Survey, replacement rates for lower income individuals in 1993 were nearly the same as in 1988; the replacement rates for higher income individuals had gone up dramatically. Of particular concern is the adequacy of retirement income for women (for a review of the literature, see Weaver, 1994). Although the proportion of elderly living alone is expected to remain constant in the future, the percentage that are women is projected to increase, as seen in Figure 3-4. In addition to having longer life expectancies, women have traditionally been more likely to experience gaps in service, leading to reduced Social Security and pension benefits. As more women enter the labor force, concern over adequacy of retirement income for women may decrease. In 1959, 40 percent of women above age 16 were in the labor force, compared with 60 percent in 1989 (U.S. Department of Labor, 1992). Additional evidence suggests improvements in earnings that will lead to higher Social Security benefits. Over roughly the same time period, the percentage of women over 62 receiving Social Security benefits on the basis of their own work history has increased from 43.3 percent to 59.7 percent (see Table 3-1). It

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Assessing Knowledge of Retirement Behavior FIGURE 3-3 Average replacement rate for defined benefit pension plan participants, medium and large private establishments, 1989. NOTE: Calculations based on retirement at age 65 with annual salary of $35,000 in final year. SOURCE: U.S. Department of Labor (1992:Chart 20). is not clear that there have been similar improvements in pension benefits. Even and MacPherson (1994) note that "pension coverage for women is less likely to convert into pension receipt at retirement" (p. 562). In addition, the average level of benefits for women is between 55 percent and 62 percent of the average level of benefits for men. Even and Macpherson estimate that one-third of the gap in coverage between men and women is attributable to women's absence from the labor force (their work history). Some of the policies that have been proposed to address this disparity are earnings sharing, homemaker credits, and caregiving credits (Employee Benefit Plan Review, 1994a, from Ferber, 1993). While an obvious solution to the threat of inadequate retirement income is a shortened retirement phase (through either prolonged work, delayed retirement, or earlier mortality), trends both in labor force participation and life expectancies suggest that retirement savings will need to be stretched over more years of life

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Assessing Knowledge of Retirement Behavior FIGURE 3-4 Composition of elderly people living alone. NOTE: Asterisked years are projections. SOURCE: Kasper (1988). rather than fewer. Labor force participation rates of the elderly are decreasing, particularly among men. Table 3-2 compares labor force participation rates of men and women at various ages between 1970 and 1990. While male labor force participation rates have decreased dramatically, corresponding rates for women have increased in the first three groups but have declined in the 62-to-64 and 65+ age groups. As a result, the gap between male and female labor force participation has narrowed over the last two decades, by about 15 percentage points for those aged 50 to 62 (Peracchi and Welch, 1994). In addition, the modal labor TABLE 3-1 Percentage of Women Over Age 62 Receiving Social Security on the Basis of Their Own Work History Year Percent 1960 43.3 1970 50.6 1980 56.9 1988 59.7   SOURCE: U.S. Department of Labor (1994) and Lingg (1990) (primary source).

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Assessing Knowledge of Retirement Behavior TABLE 3-2 Labor Force Participation Rates (percent)   Age Gender and Year 45–54 55–59 60–61 62–64 65+ Men   1970 94.3 89.5 82.6 69.4 26.8 1990 90.7 79.8 68.8 46.4 16.4 Women   1970 54.4 50.4 41.4 32.3 9.7 1990 71.2 55.3 42.9 30.7 8.7   SOURCE: Bureau of the Census (1992, Table 622). TABLE 3-3 Life Expectancy and Projections Among White Men and Women, Age 65 (in years)   Actual Projected Gender and Scenario 1980 1990 2000 2020 Men 14.2 15.2   I   15.3 15.6 II   15.9 16.7 III   16.4 18.0 Women 18.4 19.1   I   18.9 19.1 II   19.6 20.4 III   20.2 21.9   SOURCE: U.S. National Center for Health Statistics (1990) (actual) and Hurd (1994b) (projections). force participation transition age moved from 65 in 1968 to 62 in 1991 (Quinn and Burkhauser, 1992; Peracchi and Welch, 1994). In addition to declining labor force participation trends, life expectancies are also increasing. Table 3-3 shows life expectancies and projections for white men and women under three different demographic scenarios (these are described in Hurd, 1994b). In the last decade, the life expectancy for men has increased by 1 year. Depending on the projection used, even scheduled increases in the Social Security eligibility age, aimed at encouraging later retirement, will not keep up with the increasing life expectancies. The elderly population is itself aging. In 1980, 40 percent of individuals 65+ were over age 75. It is expected that by 2000,

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Assessing Knowledge of Retirement Behavior FIGURE 3-5 Recipients of Social Security payments, 1940–1990. SOURCE: U.S. Department of Labor (1992:Chart 25). this proportion will rise to 50 percent. As individuals age, the threat of poverty rises substantially. In 1990, one-fifth of persons age 85 or older had income levels at or below the poverty threshold (Radner, 1993b). Because of these trends, the ratio of the retired population to the working population is expected to rise from 0.21 in 1990 to 0.27 in 2020 to 0.37 in 2035 (Congressional Budget Office, 1993). The number of Social Security beneficiaries has also increased dramatically, as shown in Figure 3-5. To remain solvent, the current Social Security system will have to impose an increasingly large tax burden on the shrinking working population in order to support the growing elderly population.

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Assessing Knowledge of Retirement Behavior SOCIAL SECURITY In 1990, nearly 40 percent of the income of the elderly (65+) was from Social Security (Congressional Budget Office, 1993). In addition, 57 percent of the elderly obtained more than half their income from Social Security; 24 percent obtained more than 90 percent from this source (Hurd, 1994a). Almost 95 percent of elderly households reported receiving Social Security benefits (Hurd, 1994a; Congressional Budget Office, 1993); these benefits are an especially important component of income for households in the lower income brackets and are the largest single source of income for all but the highest income quintile of the elderly (Reno, 1993). It is projected that for retirees in the bottom half of the income distribution in 2019, 60 percent to 70 percent of retirement income will come from Social Security (Kingson, 1992). As a result of pressures on the Social Security system and rising health care costs, concern that the income of the elderly will be inadequate has created debate over how to increase retirement income, accompanied by legislation aimed at effecting such an increase. Because Social Security affects so much of the elderly population, it is the obvious place to start in discussing broad-based policy changes that influence retirement behavior and income. Previous research considering the effects of changes in Social Security policy on retirement and labor force participation includes Gustman and Steinmeier (1991) and Feldstein and Samwick (1992). As Table 3-2 showed, it is clear that labor force participation rates decline precipitously among individuals that have reached the Social Security early and normal retirement ages (62 and 65, respectively). Using aggregate time series data, Stewart (1995) provides further evidence of the influence of Social Security, demonstrating that ratios of primary insurance amount (PIA) to earnings closely mirror the nonparticipation rate of men ages 65 and older, as shown in Figure 3-6. However, evidence in Bondar (1993) suggests that individuals with high pre-retirement earnings (as estimated based on PIA amount) are most likely to continue to work and earn high post-retirement earnings. In addition, replacement rates (PIA/earnings) are higher for low wage individuals, suggesting that the labor force participation decline is being driven by precisely the individuals for whom concerns over retirement income adequacy are the largest. Therefore, discussions about the government's role in ensuring adequacy of retirement income have focused on the Social Security program and its ability to meet the needs of a growing elderly population. Researchers have also become increasingly aware of the Social Security system's inability to adequately provide for many women in their retirement. This is due partly to the societal norms under which the system was designed (i.e., around the "traditional" one-earner family) and to differences in men's and women's labor force history and attachment. Ferber (1993) provides evidence that the earnings gap, along with male/female differences in labor force participation and tenure, has declined, but not disappeared.

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Assessing Knowledge of Retirement Behavior FIGURE 3-6 The PIA/earnings ratio and the nonparticipation rate of men aged 65–69 in the labor force. NOTE: PIA is the primary insurance amount. SOURCE: Stewart (1995). In order to increase labor force participation and decrease the burden on the Social Security system, current Social Security policy dictates an increase in the normal retirement age from 65 to 67. Those born in 1937 will be the last group with a normal retirement age of 65. Those born in 1960 will be the first with a normal retirement age of 67. Many believe that this increase is too gradual. In addition, the level of benefit reduction at age 62 will gradually increase from 20 percent to 30 percent. The earnings test will be liberalized; it currently affects only individuals below age 70. To try to reduce some of the perceived inadequacies of the Social Security system, an earnings-sharing proposal (where the Social Security benefit is based on the earnings of the household, not just on individuals) and a two-part payment system have also been suggested. The latter is an attempt to meet the dual roles of the Social Security system—to provide a basic amount of coverage to all elderly (not just wage earners and their spouses) and to provide an additional payment proportional to wages. As mentioned earlier, additional proposals include caregiving and homemaker credits, but the current design (of supporting wage earners in retirement based on revenues from current wage earners) does not suggest an obvious answer to the question of who will pay for such credits.1 The earnings test component of Social Security, which applies to individuals below age 70 (the age limit was 72 prior to 1983), is viewed as a significant barrier to continued work. In addition, the earnings test is more liberal for Social

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Assessing Knowledge of Retirement Behavior With improved technology comes an ability to accommodate the proliferation of choices in our economic models. Besides choosing a retirement date, many individuals are faced with having to decide how to receive a pre- or post-retirement distribution (annuity or some other form); these decisions might be modeled in a simultaneous decision framework. Virtually the only attempt to model all interactions is Rust (1989), where an astounding quantity of (admittedly discrete) transitions are modeled. Given that data are often in discrete units, however, this does not seem like an unrealistic approximation, even though behavioral decisions are more accurately modeled as continuous processes. In addition, Rust specifies dynamic processes for marital status, employment, health status, wealth, and so forth. The problem is the computational burden involved. This is a problem with dynamic programming models in general, where, without simplifying assumptions, the number of nodes in the decision tree increases exponentially with the number of time periods (i.e., nodes = CT, where C is the number of choices and T is the number of time periods). Future models, therefore, must focus on adequately modeling transitional behavior and conditional probabilities, where the conditioning information set incorporates the complete history of choices available to the individual. The emphasis should be on this as a means of reducing computational time and more closely approximating actual behavior. Still, there are a number of limitations to the model in Rust (1989); these are recognized by Rust himself and also outlined in Burtless (1989) and Rust and Phelan (1993). Many modeling limitations are the fault of data limitations; in Rust's case, the limitation is inadequate information on pensions and caregiving responsibilities and computational burden. Burtless (1989) notes that most studies examine a single issue; more advanced ones consider a subset of the determinants, allowing for some interaction. Rust (1989) has laid out a comprehensive framework that, in principle, allows assessment of all determinants at once. Of course, it too is limited by data, computational burden, and assumptions about stochastic processes that describe the evolution of these factors over time. However, it defines the state of the art in terms of what models should, it is hoped, ultimately achieve—a way of mimicking behavior and mirroring the dynamic nature of decision making. Another form of endogeneity arises when one tries to draw inferences about policy changes. To the extent that policy and behavior are jointly determined, parameter estimates obtained from a base model under the current policy regime will not accurately reflect effects in an alternative policy state (see Lucas, 1981, and discussion therein). A final form of endogeneity is sample selection. As discussed in each of the sections above, heterogeneity between a sample population and a reference population will render inferences useless. It is important, therefore, to assess the extent of sample selection and its role in affecting inferences and, if necessary, to attempt to correct biases that may arise.

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Assessing Knowledge of Retirement Behavior Uncertainty Few models of retirement behavior have allowed for uncertainty in the specification. Even dynamic models such as Gustman and Steinmeier (1986) assume perfect markets, and Stock and Wise (1990a, 1990b) assume perfect foresight in imputed earnings computations. Capturing individual uncertainty (including, but not limited to, modeling expectations, as discussed above), such as the probability of finding a new job or of qualifying for disability insurance, is crucial to understanding and modeling behavior. It is also important in dynamic models to control for aggregate uncertainty; in the case of pension plans this could include the financial condition of the firm or the termination of the plan. At more macroeconomic levels, this includes concerns over solvency of public programs such as Social Security, disability insurance, and Medicare. One way to incorporate uncertainty into dynamic models is by simulation methods such as those in Keane and Wolpin (1994). This usually requires specifying an error distribution. When individual-specific correlation is introduced into a dynamic programming specification, a multidimensional integral results, often rendering the model intractable.9 Keane and Wolpin use Monte Carlo integration to approximate the integral and suggest that such approximations perform well, both in being able to mimic behavior and in terms of providing plausible structural parameter estimates. Data Issues Rust (1989:371) raises the issue of approximating continuous processes with discrete variables, distinguishing between the discrete employment state and the continuous employment decision. Similarly, application for disability benefits (like Social Security) is dichotomous, but the decision process is not. It is therefore important to consider how to model the transition to disability, perhaps an even more continuous process than the transition to retirement. Discretizing health status is equally tricky. In general, models need to accommodate both decision variables, which are continuous, and associated behavioral states, which are discrete. Current research still does not adequately model both jointly. Many of the shortcomings of previous literature, as well as the failure to adequately model the multiple factors influencing the retirement decision, stem from insufficient data sets. Two of the most promising data sets for future researchers are the HRS and the Asset and Health Dynamics Among the Oldest Old (AHEAD) survey. Improving data accuracy and eliminating systematic biases should be a top priority. Evidence in Parsons (1991c) suggests that workers are reluctant to admit they have applied for disability insurance; similarly, virtually all surveys of

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Assessing Knowledge of Retirement Behavior income exhibit signs of underreporting of income by respondents. Linkages across data sets improve the ability to check responses for consistency and accuracy. New techniques were employed to improve the response rate for the HRS. Besides asking the same questions a number of times with slightly different phrasing, interviewers also used unfolding brackets and card brackets to encourage responses. Juster and Smith (1994) argue that these techniques provide significantly more accurate imputations of financial variables, such as nonhousing wealth. They also propose using an ''optimal brackets" method of threshold determination, where the optimality criterion is to maximize the between-group sum of squares. They find that asset imputations "are almost twice as large as those currently being obtained in SIPP"; this suggests that previous studies that have used SIPP's imputations have understated nonhousing wealth by 22 percent. Extending the bracketing techniques of Juster and Smith (1994) to other survey data sets still in progress is another way in which we can improve the quality of data for studying questions related to retirement and retirement income. Other Concerns As noted in the Introduction, concerns exist over income inadequacy of the elderly and projected funding inadequacy among government programs such as Social Security, Medicare, and disability insurance. The interactions among decisions related to retirement behavior and income suggest that inadequacy may affect an increasingly concentrated proportion of the population. If current demographic trends continue and policy emphasis does not address their needs, this population will most likely be elderly women living alone. Correlations among the variates considered in this paper point to the development of a bimodal distribution of elderly (Reno, 1993)—those who were high wage earners in their work lives and who therefore have adequate retirement income (in the form of pension benefits, a post-retirement job, low medical expenditures, and high levels of savings) and those who were not (having less attachment to the labor force, lower probability of a pension, and being in poorer health). In terms of policy directed at alleviating poverty among the elderly, as well as targeting public assistance to where scarce resources are most needed, the focus should be on this lower cluster of the distribution. NOTES 1.   For more discussion on these topics, see Ferber (1993). 2.   From 1985 to 1988, there were 3.3 million participants in defined benefit plans that were terminated (Beller and Lawrence, 1992). 3.   Or the workers agree to engage in the implicit labor contract that is offered. For theories of pension, plans, see, for example, Ippolito (1985), Kotlikoff and Wise (1985), Viscusi (1985), and Lazear and Moore (1988).

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Assessing Knowledge of Retirement Behavior 4.   In a true dynamic programming framework, individuals choose the expected maximum given a variety of choices in each time period. Thus the approximation in the Stock-Wise model induces a bias towards early retirement (Emax > maxE from Jensen's Inequality). 5.   Woods (1993:6) notes that "while the gender gap is relatively small among workers under the age of 40, it diverges sharply among older workers." 6.   In 1986, a 10 percent penalty tax was imposed; this tax was increased to 20 percent in 1993. For this and more details on lump-sum distributions, see Woods (1993). 7.   In fact, the correlation in Parsons' data from 1947 to 1979 is 0.91. 8.   I am grateful to John Ausink for providing the numbers and information in this paragraph. 9.   A multidimensional integral will also arise with a multichotomous decision variable. Keane and Wolpin provide a four-dimensional example, where an individual's labor force participation decision is between two occupations, schooling, and staying home. REFERENCES Allen, S.G., R.L. Clark, and A.A. McDermed 1993. Pensions, bonding and lifetime jobs. Journal of Human Resources 28(3):463–481. Anderson, K.H., R.V. Burkhauser, and J.F. Quinn 1986. Do retirement dreams come true? The effect of unanticipated events on retirement plans. International Labor Relations Review 39:518–526. Auerbach, A.J., L.J. Kotlikoff, and D.N. Weil 1992. The Increasing Annuitization of the Elderly—Estimates and Implications for Intergenerational Transfers, Inequality, and National Saving. NBER Working Paper #4182. Cambridge, Mass.: National Bureau of Economic Research. Ausink, J.A. 1991. The Effect of Changes in Compensation on a Pilot's Decision to Leave the Air Force. Unpublished Ph.D. dissertation. Harvard University. Ausink, J.A., and D.A. Wise 1993. The Military Pension, Compensation, and Retirement of U.S. Air Force Pilots. NBER Working Paper #4593. Cambridge, Mass.: National Bureau of Economic Research. Bai, J., R.L. Lumsdaine, and J.H. Stock 1994. Testing for and Dating Breaks in Integrated and Cointegrated Time Series. Unpublished manuscript. Department of Economics, Massachusetts Institute of Technology. Barron, J.M., and A. Fraedrich 1994. The implications of job matching for retirement health insurance and leave benefits. Applied Economics 26:425–435. Beller, D.J., and H.H. Lawrence 1992. Trends in private pension plan coverage. Pp. 59–96 in J.A. Turner and D.J. Beller, eds., Trends in Pensions 1992. Washington, D.C.: U.S. Department of Labor, Pension and Welfare Benefits Administration. Berkovec, J.C., and S. Stern 1991. Job exit behavior of older men. Econometrica 59(1):189–210. Bernheim, B.D. 1989. The timing of retirement: A comparison of expectations and realizations. Pp. 335–355 in D.A. Wise, ed., The Economics of Aging . Chicago, Ill.: University of Chicago Press. 1994. Do Households Appreciate Their Financial Vulnerabilities? An Analysis of Actions, Perceptions, and Public Policy. Unpublished manuscript. Department of Economics, Stanford University. Bernheim, B.D., and L. Levin 1989. Social Security and personal saving: An analysis of expectations. AEA Papers and Proceedings 79(2):97–102.

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