2.1 Computing DB pension wealth at retirement

DB pensions typically pay retired workers an annuity – that is, an income flow until death.Footnote ⁴ Denote the annual benefit paid out each year after retirement in year t as b _t, b _t+1, b _t+2, …. In turn, this benefit flow can be assigned a cash value B_t that represents expected future benefits. Pension wealth B _t^DB in DB plans equals the expected present value of future pension benefits if the worker retires in year t:

Pension wealth equals the discounted sum of expected future benefits. Benefit payments are discounted by the future interest rate . The expectations operator E[.] reflects four possible sources of uncertainty, the first two of which are represented in this formula. First, the cumulative benefit flow is uncertain because the date of death is unknown. To deal with this uncertainty, the formula discounts benefits in year t+j, for example, by including the probability π_{t +j} of surviving until future period t+j, conditional on having reached t+j−1. Second, the future interest rate is uncertain today. The approximation after the expectations term abstracts from this uncertainty. Third, the real value of future pension benefits is uncertain in pension plans that do not automatically adjust for inflation.Footnote ⁵ Fourth, political uncertainty over the likelihood of receiving future benefit payments may arise if pensioners anticipate that states may cut promised benefits in the event of underfunding. This is not allowed by some state constitutions and is politically difficult even when allowed.Footnote ⁶

Pension wealth B_t can be viewed as the value of leaving one's job today and claiming the resulting pension benefits. A worker who is deciding whether to retire this year or to delay should also consider the value of waiting to claim benefits at a future retirement date. This can be defined in terms of pension wealth accrual ΔB _t+1, the difference between the discounted value of waiting one more year and then retiring and gaining B _t+1 and retiring today and gaining B_t:

2.2 The evolution of DB pension wealth

Pension wealth evolves non-linearly as workers move through their career because benefits depend in complicated ways on the path of career earnings and on job tenure and age upon retirement. To see this in a snapshot, Figure 1(A) shows pension wealth B _t^DB in the Teacher Retirement System of Texas and Figure 1(B) shows pension wealth accrual ΔB _t+1 in the same plans.

Source: Author's calculations.

Fig. 1. Pension wealth stock and accrual under the Teacher Retirement System of Texas. (A) Pension wealth. (B) Pension wealth accrual

As people work longer in a job offering a DB pension, DB pension wealth rises in a starkly non-linear fashion, with occasional jumps upward and, in many cases, a late drop-off. There are often between one and three crucial dates when the path of DB pension accrual spikes upward, for example with one very large spike in Figure 1(B) and two small ones, and most plans show later losses in pension wealth.

The first jump occurs at the vesting date, when a worker first qualifies for future benefits. The modal vesting period in teacher plans is 5 years, as in Texas, although Arizona and Wisconsin vest immediately, whereas 13 states have vesting windows of 10 years (NEA, 2006). Pension wealth in 1-A jumps to a value of about $40,000 upon vesting.

The other spike in Figure 1(B) occurs when someone reaches full years of service at the plan's normal retirement age (NRA). In Texas, the NRA is either aged 65 with 5 years of service or follows a ‘rule of 80’, where age and years of service (for 5 or more years of service) must at least equal 80. In Illinois, the NRA is 62 with 5 years of service, 60 with 10 years, or 55 with 35 years. If a worker retires at the NRA, then her DB plan will start to pay out benefits immediately. The initial benefit b _t at the NRA is typically a proportion of the worker's recent salary, with the proportion increasing in tenure, along the following lines:

The benefit b _t^NRA is proportional to the final average salary , which is average earnings in the τ years before retirement, where τ generally ranges between 1 and 5 years. The proportional factor α_t that multiplies final average salary usually rises with service credits, measured as each year of service since the starting year θ in the job. Virginia, for example, pays α=2.3% multiplied by each year of service multiplied by the average salary over the τ=5 highest consecutive years, whereas in Illinois, α=2.2% and τ=4, and in addition b _t cannot exceed 75% of .

Retiring before the NRA often reduces pension wealth for a few reasons. Many plans have an early-retirement age (ERA); upon reaching that age, one can immediately receive benefits, but they will be reduced from the value in the formula above. Plans with an ERA exhibit a middle spike between vesting and the NRA. In Texas, retiring at the ERA of age 55 with 5 years of service or at any age with 30 years of service reduces annual benefits according to an actuarial formula; in other states, the reduction rate varies between 3% and 6% for each year before the NRA. Whether or not a plan offers early retirement, retiring before the NRA erodes pension wealth because fewer service credits are accumulated (so α_t is smaller) and because final average salary is not adjusted for inflationary gains after retirement and before benefits begin (so is smaller, whereas staying in the job would yield those gains). These factors account for the gradual increase in pension wealth after the vesting date in Figure 1.

Lastly, retiring after the NRA reduces the number of years that full benefits are received and hence reduces the present value of benefits at retirement – one gives up current pension benefits income without replacing them later on, as benefits cease upon death. This accounts for the decline in pension wealth after the NRA.

2.3 DC pension wealth

Some states offer add-on mandatory or optional DC plans, whereas Alaska has replaced its DB with a DC plan for all new employees. More importantly, DC plans are now the norm in the private sector and are under discussion in many state houses. While DC plans come in several varieties, the focus here is on the smooth accrual patterns that are typical across them and are also common to cash balance plans.Footnote ⁷ The path of pension wealth accrual in DC plans, like 401(k) accounts, stands in sharp contrast. In a DC plan, an annual contribution is made to a retirement account and that account belongs to the worker whenever she leaves her job, possibly after a vesting period. The funds grow at the rate of return . Pension wealth after vesting is simply , the amount of accumulated funds plus this period's contribution c_t.Footnote ⁸ Pension wealth accrual is therefore constant if there is no change in the rate of return or in the contribution rate. The smooth path of DC pension wealth accrual shown stands in stark contrast to the bumpy path of DB accrual. While DB plans reward long-tenure workers, DC plans insure pension wealth for workers who are at risk of job switches early in their careers.

3.1 Empirical limitations in studying pensions

A common theme throughout this review is that the empirical evidence is inadequate to confirm or refute theoretical implications of pensions on labor markets. I will discuss some major reasons for this here, as they are common across various questions of interest. I will then show how these issues have been addressed in studying labor market effects of pensions and finish by suggesting ways in which studying state and local pension plans may provide additional opportunities to surpass these limitations.

3.2 Evidence about pensions and retirement

As little analysis has focused on public-sector workers, this section and the next review evidence from the labor economics literature about mobility responses of workers in general (Friedberg and Turner, Reference Friedberg and Sarah2010). This literature suggests that the timing of retirement responds strongly to the timing of DB pension wealth peaks.

3.2.2 Evidence from nationally representative surveys

Subsequent papers made advances by using data from large, broadly representative longitudinal surveys that contacted employers of respondents to obtain pension data. The SCF and the HRS have done this.

Samwick (Reference Samwick1998) used the SCF, which obtained pension data for respondents in 1983 and had a short panel that re-surveyed respondents in 1986, yielding observations on some retirements. Samwick used the Option Value measure developed by Stock and Wise.Footnote ¹⁰ He found that neither the level of pension wealth nor the 1-year measure of pension wealth accrual significantly affects retirement, while the full path of accruals strongly does. This result has been confirmed in later papers, discussed next. Samwick also confirmed that the Option Value measure, capturing the full path of future pension accruals, does a superior job in explaining retirement as compared to the 1-year pension wealth accrual measure in this large sample of workers from numerous firms. His estimates suggest that extending DB pension coverage, using a representative plan, to all workers in the SCF would raise the probability of retirement between ages 50 and 70 by 4.9%. As this corresponds to roughly the increase in DB coverage observed in the post-war period, it suggests further that DB pensions account for over a quarter of the total decline in the average U.S. retirement age. The estimates indicate that altering Social Security incentives would have smaller effects on retirement.

Coile and Gruber (Reference Coile and Gruber2007) and Friedberg and Webb (Reference Friedberg and Webb2005) studied retirement using data from the HRS, the most current and comprehensive dataset that follows workers into retirement. Each emphasized distinct aspects of the relationship between retirement and the accrual of retirement wealth. The innovation in Coile and Gruber was to use a simpler measure of retirement incentives, which they termed Peak Value, instead of the utility-based Option Value measure from Stock and Wise. Peak Value is similar to the annual pension wealth accrual measure defined in Section 2, but it subtracts current pension wealth from the peak of pension wealth that is available in the future, rather than subtracting it from next year's pension wealth. Thus, the Peak Value PV of pension wealth is defined as

where m represents the number of years from today until the peak in pension wealth is reached. If a person has reached or passed her pension's peak, then Coile and Gruber define Peak Value as simply the annual pension wealth accrual, and so m=1 above.

The attraction of Peak Value is that, first, it abstracts from numerous functional form assumptions that Stock and Wise required in order to estimate the utility function and, second, it avoids directly incorporating earnings into the same measure as pension accruals, which Option Value does. Coile and Gruber make a point of controlling separately for earnings and job tenure, and so these possibly endogenous variables only influence pension wealth, and indirectly retirement, through the idiosyncrasies of the pension formula. Otherwise, the estimated relationship between pension wealth or pension wealth accruals and retirement might result spuriously from a true correlation between, say, earnings and retirement.

Coile and Gruber use Peak Value to measure Social Security incentives and sometimes include Peak Value from employer pensions as well. In their probit estimates, controlling for either the Peak Value or Option Value measures of Social Security accruals yields statistically significant estimates. The estimation with Option Value raises the log likelihood, but not by a great deal; Coile and Gruber argue that this may occur because earnings do in fact add explanatory power, although it may be spurious, in the model. In models that included both, they estimated that Social Security and employer pension accruals have similar effects on retirement. Specifically, a one standard-deviation increase in someone's Peak Value from either Social Security or their pension raises their likelihood of retirement by 1% point, or 14% of the baseline retirement hazard.

Friedberg and Webb (Reference Friedberg and Webb2005) explored the effects of the major shift from DB to DC plans that began in the early 1980s. They clarified the definition of Peak Value and explored the further impact of other pension plan details. Coile and Gruber applied the Peak Value definition above to both DB and DC plans. Friedberg and Webb only defined Peak Value for DB plans, as DC pensions never reach a peak as long as DC plan contributions remain constant and the individual's time discount rate does not exceed the interest rate. As long as these reasonable assumptions hold, then simply controlling for DC pension wealth incorporates the full information about the path of DC pension wealth accruals. They also defined Peak Value as zero after the peak is passed, adding a separate dummy variable indicating that the peak has past, so as not to impose linear effects of Peak Value even after pension wealth has passed its peak. Lastly, they explored the sensitivity of the empirical specification to additional related pension controls.Footnote ¹¹

The estimates in Friedberg and Webb for the HRS sample indicate that having the mean Peak Value for stand-alone DB plans, rather than a Peak Value of zero (which happens upon reaching or passing the peak or if one has a DC plan), reduces the annual retirement hazard by 1.7 percentage points at ages 55–59, a 29% reduction compared to the observed hazard. Based on this, they simulated the effect of the ongoing shift in pension structure from DB to DC plans. The results imply that this will raise the median retirement age of full-time employees with a pension by about 10 months when comparing cohorts aged 53–57 in 1983 and in 2015.

Finally, Asch et al. (Reference Asch, Haider and Zissimopoulos2005) use administrative data and employ the Peak Value and Option Value measures to analyze retirement among federal civil service workers. Their results suggest that the probability of retirement falls by 4% for each additional $10,000 of expected pension wealth they would gain by working another year. This estimate is very similar in magnitude to the Coile and Gruber estimates for the impact of Social Security in the HRS sample – giving us reason to think that public-sector workers respond similarly to pension incentives as private-sector workers.

3.3 Evidence about pensions and worker mobility at younger ages

The evidence described in the previous section indicates that retirement timing is strongly influenced by the timing of peaks in DB pension wealth accumulation. At younger ages, we should see the inverse relationship – workers should have a lower propensity to exit jobs with DB pensions so that they can gain access to these future peaks. The present value of those peaks is relatively small early in a career (Gustman and Steinmeier, Reference Gustman and Steinmeier1993). These deterrents then grow, with an average pension loss associated with switching jobs for workers aged 35–54 of approximately half a year's earnings, computed for representative workers in the mid-1980s (Allen et al. Reference Allen, Robert and Ann1988). Thus, mobility should be increasingly inhibited as tenure rises.

Empirical evidence from the labor economics literature about this response is suggestive but not definitive. The empirical limitations discussed earlier account for the less substantive evidence in this case, compared to the analysis of retirement. Mobility at younger ages has been more difficult to study than retirement because the HRS only covers people aged 50 and over, and the SCF pension data are quite dated. Firm-level administrative data have not been used to examine younger workers either. The only alternative in the literature has been to use other nationally representative datasets, relating simple indicators of pension coverage or pension-type to exit from or years of tenure in the current job – forgoing the chance to gain identification from idiosyncratic variation in mobility incentives across workers with DB plans.

Early attempts, as in Allen et al. (Reference Allen, Robert and Ann1988), compared mobility of workers with and without pensions. More recently, the spread of DC pensions has offered the opportunity to compare mobility of workers with DB and DC plans. Such workers are more similar in other observable characteristics than are workers with and without pensions, reducing (but not eliminating) concerns that workers with different characteristics, and hence different propensities to leave later, choose jobs based partly on pension type. This type of comparison underlies the strategies in Gustman and Steinmeier (Reference Gustman and Steinmeier1993) and Friedberg and Owyang (Reference Friedberg and Owyang2005). Gustman and Steinmeyer used the Survey of Income and Programme Participation (SIPP), observing job changes between 1984 and 1985. Friedberg and Owyang used the 1983–2001 releases of the SCF and the 1993 pension supplement of the Current Population Survey (CPS), both of which asked workers about job tenure.Footnote ¹²

Friedberg and Owyang found that workers with DB pensions in the SCF have significantly longer job tenure, as measured by both current tenure and expected future tenure, than do workers without pensions and workers with DC pensions. Workers with a DB pension have total expected tenure that is 5.0–7.0 years longer on average than workers without a pension, whereas workers with a DC pension have total expected tenure that is 2.5–4.0 years longer, with very similar findings in the CPS. They found further that workers with higher DB pension wealth (although imperfectly measured, as it is based on self-reported and not employer-reported pension parameters) have longer tenure, controlling for the level of earnings. Thus, workers with DB plans stay in jobs considerably longer than do other workers, although it is puzzling to find that workers with DC plans also stay in jobs somewhat longer than workers without pension coverage – possibly reflecting some unobserved heterogeneity in worker type.

The results from Friedberg and Owyang differ importantly from the earlier estimates of Gustman and Steinmeier (Reference Gustman and Steinmeier1993). Gustman and Steinmeier found similar mobility rates for workers with DB and DC pensions, apparently undermining the hypothesis that DB plans deter mobility relative to DC plans. They used a short panel from the first SIPP, observing job changes from a much earlier time period when DC plans were only beginning to proliferate, possibly one reason why they do not find mobility differences across pension types. Another difference is that Gustman and Steinmeier included a control for compensation in alternative jobs for each worker. They did so by using compensation changes associated with observed job switches to impute alternative compensation for workers, with an adjustment for selection bias, who did not change jobs. The results then hinge on specifying this relationship correctly. Yet, they obtain an anomalous result that a dollar of delayed pension compensation has a much greater effect in deterring mobility than does a dollar of current compensation, when measured in equivalent present value terms. In Friedberg and Owyang, current earnings having a greater effect than pension wealth on job tenure.

To sum up, the evidence that DB pensions deter worker mobility at younger ages is less definitive than evidence about their influence on the timing of retirement. Econometric identification of the estimates is less straightforward without the opportunity to exploit idiosyncratic variation in mobility incentives across workers with DB plans. Hence, this remains an open question, one that may be possible to answer by studying teachers' careers.

3.4 Evidence about public school teachers

Recently, researchers have begun to apply the tools developed in the labor economics literature to study how retirement of public school teachers responds to DB pension incentives. These tools include using longitudinal data to track job exits, measuring pension wealth accruals over long horizons, and estimating models that match the timing of pension wealth peaks and job exit. Two types of data are employed in this ongoing work. Costrell and McGee (Reference Costrell and McGee2010), Ni and Podgursky (Reference Ni and Michael2010), Brown (Reference Brown2009) and Ferguson et al. (Reference Ferguson, Strauss and Vogt2006) use administrative data from particular states, and Friedberg and Turner (Reference Friedberg and Sarah2010) use nationally representative teacher survey data.

In the earliest effort along these lines, Ferguson, Strauss and Vogt use Pennsylvania teacher records to study a temporary retirement incentive programme. Using a simple reduced-form strategy, the authors estimate that the substitution elasticity of retirement is significant and quite negative, so that retirement responses were substantial. It is not clear, though, that responses to a temporary programme can tell us much about the effects of permanent pension reform.

Costrell and McGee estimate the effect of Peak Value on retirement of Arkansas teachers. One of their explanatory variables is an indicator that a teacher chose to participate in the Arkansas ‘T-DROP’ programme, which allows teachers with at least 28 years of service to save a portion of their pension benefits if they continue to work. While this variable is recognized as endogenous, the authors' goal is to control for a revealed preference to delay retirement. Also, the authors are able to include some characteristics of the school environment in which teachers work, finding that teachers in districts that are larger and have higher math scores retire later. They use estimates from their random-effects probit model to simulate pension reforms. Interestingly, eliminating early retirement, currently available at 25 years of service, would lead some teachers to work until full retirement at 28 or 30 years but would lead others to retire earlier, as they face a reduced incentive to wait until 25 years and find waiting even longer unappealing. With the two effects moving in opposite directions, the average retirement age is predicted to increase by a half-year overall. Ni and Podgursky (Reference Ni and Michael2010) are undertaking a similar effort for Missouri teachers, and their analysis compares the simple Peak Value measure with Stock and Wise's full structural estimation approach.

Brown uses novel empirical strategies that are more closely related to the income tax literature. These methods are applicable here when viewing pensions as altering the lifetime budget constraint that a worker faces when deciding in which year to retire; however, they are less suited for capturing year-to-year variation in circumstances such as classroom characteristics or health status. She applies them for studying California teachers and gains identification from an unexpected boost policy change in 1999 designed to induce teachers to delay retirement. One estimation strategy in the paper uses a reduced-form approach and then infers the elasticity of retirement at the kink in the lifetime budget constraint that shifted at 60 years in age and/or 30 years of service (Saez, Reference Saez2002). The other strategy in the paper estimates a piecewise linear budget constraint model of retirement (Burtless and Hausman, Reference Burtless and Hausman1978). The resulting estimates from the two approaches are similar, indicating an elasticity of retirement with respect to its price of 0.02 in the medium-run and 0.10 in the long-run (within 5 years). Brown describes this as a surprisingly price-inelastic response and shows that the average retirement age will increase by only 1.5 months if the annual financial return to working increases by 10%. Teachers may make their retirement plans over a relatively long time horizon, which would explain the relative unresponsiveness over the time horizon examined here. The small aggregate change may also mask the contradictory effects at the micro level that Costrell and McGee uncovered, with some teachers delaying retirement as its price is reduced but others perhaps retiring earlier as the gains from waiting have been reduced as well.

Lastly, Friedberg and Turner (Reference Friedberg and Sarah2010) use the Teacher Follow-Up Survey (TFS) component of the Schools and Staffing Survey (SASS). The SASS offers repeated cross-sections of approximately 50,000 teachers per year and has been undertaken every 3–4 years since 1987. The TFS follows up with respondents a year later, revealing whether they have exited from their jobs and retired or taken another job. In addition to demographic information, the SASS asks a full battery of questions about teaching credentials, characteristics of the schools in which teachers work, subject matter taught, type of students instructed, classroom autonomy and job satisfaction. These provide measures of teacher quality and satisfaction that will help determine what kinds of teachers respond to retirement incentives. Friedberg and Turner compute Peak Value using publicly available pension data. They estimate probit models of retirement as a function of Peak Value, and preliminary results indicate significant and strong responses.

Future work in this area can be extended in at least two directions. One approach will be to link student and teacher personnel records. The education literature has used longitudinal test score data to form measures of value-added, using average test-score gains of students to compute the effects coming from being in a particular classroom that year. This offers a promising way of examining whether better or worse teachers respond most readily to retirement incentives. Of relevance to this point is a set of previous studies on retirement at universities. These have found that faculty with relatively low pay or recent pay growth (and who may be, therefore, less productive) retire earlier following the elimination of mandatory retirement in 1994 (Ashenfelter and Card, Reference Ashenfelter and Card2002), the introduction of phased retirement incentives in North Carolina (Allen et al. Reference Allen, Robert and Linda2004), and pension buyouts in California (Pencavel, Reference Pencavel2001).Footnote ¹³Kim (Reference Kim2003) used another measure of faculty productivity and found similarly that California professors with fewer recent publications had a significantly greater response to the pension buyout. The Ashenfelter and Card sample consists only of faculty with DC plans and therefore not facing sharp retirement incentives from their pensions; the differential retirement response underlines the importance of personnel management tools that could induce less productive workers to retire optimally, especially as the elimination of mandatory retirement substantially reduced retirement rates overall. The chance to observe student test scores in public schools while controlling for numerous other school characteristics offers the best chance yet to measure how more versus less productive workers respond to retirement incentives.

The other approach will be to examine mobility of younger teachers. One unanswered question is whether the long delay in substantive pension wealth accrual for new teachers impedes optimal mid-career entry into the teaching labor force by people who have built up private-sector experience. Another is whether the lack of portability across pension programmes for schools operating under different organizational control impedes entry of young teachers or encourages their rapid exit. These questions involve not just mobility across public school systems but also across public, private and charter schools.

4.1 Theories of DB pensions

Why is part of compensation commonly deferred in the form of a pension? Individuals should prefer to receive cash up-front rather than waiting for it. The prevalence of pensions suggests that they must make employers or employees or both better off (Friedberg and Owyang, Reference Friedberg and Owyang2002, Reference Friedberg and Owyang2005). A theory of pensions as a form of deferred compensation was developed in a series of papers by Lazear and summarized in Lazear (Reference Lazear, Ashenfelter and Layard1986) and is also related to Becker and Stigler (Reference Becker and George1974).

Lazear viewed pensions as a component of an implicit contract that alters the incentives for long-term employment. While employers often avoid explicit long-term contracts because they hamper flexibility and are subject to limited enforceability, many nonetheless wish to encourage workers to stay in a job or to devote greater effort to a job. Several benefits may arise from longer time horizons in jobs. Less turnover reduces hiring costs and allows employers to gain the benefits of investing in the human capital formation of particular workers. The expectation of longer tenure then raises the rate of job training and results in higher productivity and profits, which the employer can share with the worker in the form of a DB pension. Alternatively, deferred compensation may function as an efficiency wage, encouraging workers to devote greater effort to their jobs. In some jobs, it is difficult or costly for employers to monitor workers who may shirk their responsibilities. Paying an efficiency wage that is higher than the going wage in other jobs can deter shirking, because a worker will lose her high-wage job if shirking is detected. Deferred compensation can also function as an efficiency wage – in that case the DB pension is like a bond – because a shirking worker can lose her job before qualifying for a pension.

One form of deferred compensation is the implicit promise of future wage increases. If a fixed amount of wages are to be paid over some duration, wages can be structured to rise over time by paying a worker less than her marginal product early on and more later. However, two problems arise with implicit or explicit promises of wage increases. First, they encourage workers to stay too long in a job. An aging worker should retire when her marginal utility of leisure, which likely increases with age, exceeds her wage; the promise of rising wages leads her to retire later than is efficient.Footnote ¹⁴ Second, the rising wage profile creates an incentive for employers to violate the implicit promise by firing workers as their marginal wage gains begin to exceed their marginal productivity gains. This credibility problem undermines the implicit contract; workers will not agree to a rising wage profile if they anticipate getting fired when their wages rise. DB pensions help resolve both of these problems (Akerlof and Katz, Reference Akerlof and Katz1989; Ippolito, Reference Ippolito1991, Reference Ippolito1994). A DB pension encourages the worker to retire when the real value of her pension accruals is turning negative, even if wages continue to rise. That, in turn, reduces the incentive of employers to fire older workers, which helps maintain the credibility necessary for the implicit contract.

An alternative to the Lazear framework proposes that DB pensions are designed to attract workers who value stability and are also productive in other unobservable ways (Viscusi, Reference Viscusi and Wise1985; Ippolito, Reference Ippolito1994). Productive workers may also have high private moving costs or a low discount rate – characteristics that are difficult to observe in the job application process. Jobs that offer part of their compensation in the form of a DB pension will attract workers with long time horizons but not mobile or myopic workers.

4.2 Reconciling the existence of DB and DC pensions

While one or both of the explanations discussed in this section may explain the existence of DB pensions, they are quite difficult to distinguish empirically. In the Lazear framework, pensions make workers more productive, and in the sorting model, pensions attract more productive workers. Papers that have sought to test one or the other of these explanations have encountered severe identification problems (Allen et al. Reference Allen, Robert and Ann1993; Even and Macpherson, Reference Even and David1990). However, consider the contrast between DB plans and the DC plans that have replaced them – with the exception of generally short vesting periods, DC plans are neutral with respect to tenure incentives. The trend away from DB and towards DC plans may be informative about the purposes of deferred compensation.

This trend implies two things that may point the way toward future research. First, whatever motives governed the use of DB pensions in the first place, perhaps along the lines that Lazear suggested, have diminished. Friedberg and Owyang (Reference Friedberg and Owyang2005) suggest a connection between the decline in DB pensions and a decline in current and expected future job tenure over a similar period. In the SCF, total expected job tenure (current plus expected future tenure) declined from 27.2 years in 1983 to 22.3 years in 2001 among male full-time employees.Footnote ¹⁵ They are not able to establish the direction of causation – reduced DB pensions causing declines in job tenure or reductions in desired job tenure reducing the appeal of DB pensions – but these patterns are consistent with more rapid obsolescence of job-specific skills (Friedberg and Owyang, Reference Friedberg and Owyang2005; Aaronson and Coronado, Reference Aaronson and Coronado2005) or reduced costs of job search (Friedberg et al. Reference Friedberg, Owyang and Sinclair2006).

Second, the shift in pension structure implies that pensions must serve an additional purpose besides influencing worker mobility. Here, I will mention candidate explanations involving taxes, motives for saving, government regulations and unions, although none of them can fully explain both the existence of pensions and the shift from DB to DC.

Pension contributions by employers or employees are tax-preferred, which may explain the existence of pensions but not the form they take. Tax preferences for DC plans were codified and extended in the 1970s and very early 1980s, leading to the use of some types of DC plans, such as 401(k) accounts. Other DC plans existed previously, however, and the tax explanation for pensions does not account for the form that DB pension accruals take – smoothly accruing DB pensions would enjoy the same tax preferences. Government may offer tax preferences in order to promote deferred compensation as a way of encouraging workers to save for retirement. One possible reason for government involvement is that optimal long-term saving plans might otherwise be neglected due to the self-control and planning problems that have been emphasized in behavioral economics (Thaler and Sunstein, Reference Thaler and Sunstein2008).

Apart from the tax preferences, the government has frequently altered and tightened pension regulations since ERISA passed in 1974. These changes have established funding standards for DB pensions, extended tax incentives for DC pensions, and constrained the structure of pensions, primarily DB plans. As a result, the costs of administering pension plans have increased, but at a similar rate for all but the smallest plans (Ippolito, Reference Ippolito1995; Kruse, Reference Kruse1995). Moreover, enhanced funding standards may increase the appeal of DB pensions to workers. Some of the regulatory changes have limited the extent to which DB plans can be designed as incentive contracts (Clark and McDermed, Reference Clark and Ann1990). Yet, it is not clear how binding these restrictions are, as DB pension wealth can still accrue highly non-linearly through various manipulations of the pension formulas described earlier. Moreover, these regulatory changes may have responded to, rather than caused, increases in worker mobility that brought attention to losses by workers of claims to future pension benefits.Footnote ¹⁶

Another explanation has focused on the prominent role of unions in negotiating DB pensions. In labor economics models, unions represent workers with an interest in staying with the firm, and they use DB pensions to appropriate surplus from short-tenure workers (Freeman, Reference Freeman and Wise1985). It follows that the decline in unionization rates might explain the declining use of DB pensions. A problem with this argument is that DB pensions were also prevalent in non-unionized private-sector and federal-government jobs as well in unionized jobs, and they have become less common universally (Friedberg and Owyang, Reference Friedberg and Owyang2005).

5.1 Pensions and total compensation

In the productivity or selection theories of pensions, lifetime compensation with a pension need not exceed the lifetime total if, say, pay were constant and no compensation were deferred. Yet, the theories above suggest that deferring compensation will raise productivity, generating additional surplus in the employment relationship that can be shared between workers and firms, perhaps in the form of a Nash bargaining model that is sometimes posited in the matching literature.

A relevant empirical test, then, is whether an extra dollar in deferred compensation results in an offset to current pay of zero (the employee gets all the surplus), one (the employer gets all the surplus) or something in between. From a practical perspective, though, the complexities of the pension accrual formulas make it difficult for employers to offset future benefits exactly for each worker, because wage changes typically depend on civil service formulas that apply to all workers. The identification problems of obtaining estimates of the wage-pension offset are acute, moreover, as a model in which employers choose current and deferred compensation simultaneously makes it impossible to estimate the causal effect of deferred compensation on current compensation in a simple econometric framework.

It has been some time since there has been an active literature estimating the trade-off between pension benefits and current wages. Ehrenberg (Reference Ehrenberg1980) and Smith (Reference Smith1981) estimate the relationship between current and deferred compensation using data on local public pensions. Ehrenberg uses two city-level datasets on police, fire and sanitation employees in the early–mid-1970s. He estimates how pay scales (in the former dataset) and average pay (in the latter) relate to some observable pension plan parameters; using data on pay scales is preferable, as it is unrelated to the composition of the labor force in terms of age. Many of the pension variables have the expected sign and some have statistically significant associations with pay. A higher minimum age for claiming benefits has a positive relationship with current pay in some regressions, as expected, and a negative relationship in others, whereas a higher compulsory retirement age has a positive relationship and a higher minimum pension benefit has a negative relationship. The analysis thus suggests that there may be a trade-off between current and deferred pay. Smith (Reference Smith1981) estimates similar regressions using data from Pennsylvania cities and counties in 1976. He estimates the relationship between the average wage and both the value of pensions, as measured by the average actuarial value of accumulated pension funds per employee, and the likelihood of receiving them, as measured by the degree to which the 1976 contribution was greater or less than the required contribution. The current pension value is further instrumented with plan parameters involving vesting, age and years of service requirements. The results suggest the possibility of a one-to-one trade-off between average pension benefits and average pay, but the confidence intervals are wide. The estimates also suggest a significant relationship between worse underfunding and higher current pay. Smith and Ehrenberg both acknowledge the problem with their analysis that current pay, deferred pay and pension funding levels are likely to be jointly determined.

One way to extend research on this question is to build on the studies mentioned here by seeking plausibly exogenous changes in pension compensation – for instance, in response to federal regulations (for private-sector plans), income tax rate changes or state budget crises (although this will affect current compensation as well). In this way, one may observe whether, for example, mandates which increase pension benefits (like the 1974 decrease in maximum vesting dates) lead to higher pensions and subsequent reductions in pay.

5.2 Other features of pension plans

The pension literature has not yet provided evidence about the impact of other differences between DB and DC plans. Understanding the impact of these differences is critical as state governments consider shifting workers into DC plans. Besides those related to accrual patterns and portability, a key distinction is that, under DB plans, employers bear the risk of managing pension fund accumulation and decumulation, whereas employees bear these risks under DC plans.

5.3 Interactions between pension and health insurance benefits

The funding of retiree health insurance is in an even greater crisis than is the funding of pension benefits (Clark, Reference Clark2009). Increasing evidence also shows that retirement of private-sector workers is influenced by the availability of health insurance coverage after retirement (Gruber and Madrian, Reference Gruber and Madrian1995). Consequently, any steps to shift greater costs of retiree health insurance onto state and local government workers may affect retirement decisions and hence the drain on pension funds as well. Using administrative or survey data and exploiting variation in retiree health insurance contributions across states and, possibly, within states over time, should yield some insight into the interaction of pension and health insurance benefits on retirement.