Peaks, Cliffs and Valleys:
Robert M. Costrell
November 19, 2007
This paper examines the pattern of incentives for work versus retirement in five state teacher pension systems. We do this by examining the annual accrual of pension wealth from an additional year of work over a teacher’s career. Accrual of wealth is highly non-linear and heavily loaded at arbitrary years that would normally be considered mid-career. One typical pattern exhibits low accrual in early years, accelerating in mid-late fifties, followed by dramatic decline, or even negative returns in years that are relatively young for retirement. We consider five states for specific analysis: We identify key factors in the defined benefit formulas that drive such patterns, and likely consequences for employee behavior. We examine the efficiency and equity consequences of these systems and lessons that might be drawn for pension reform.
The authors wish to acknowledge support from the National Center for Employment Incentives at Vanderbilt University, the Center for the Analysis of Longitudinal Data in Education Research at the Urban Institute, and the Thomas B. Fordham Institute. An abridged, non-technical version of this paper was published in the Winter 2008 issue of Education Next. The usual disclaimers apply.
This highlights the growing disconnect between the operation of state teacher pension systems and the larger public discussion of pension and Social Security solvency in an era of longer life spans and the impending bulge of retirees. Nearly all proposed remedies for fixing Social Security involve raising retirement ages as part of the menu. By contrast, there is little discussion of the incentives to retire even earlier in teaching; indeed, early retirement schemes are commonplace.
The cost side of employee benefits also affects labor markets by driving a wedge between the amount paid by employers and the take-home pay received by teachers. The sharp rise in that wedge due to employee health insurance costs is well documented. However, less well known are the growing costs and large unfunded liabilities for teacher pension plans and retiree health insurance. In Ohio, for example, where public school teachers are not covered by Social Security, the combined contributions of teachers and school districts for retirement benefits currently stand at 24 percent. But even this large “tax wedge” falls well short of what is needed and pension officials are recommending a phased increase to 29 percent, to shore up funding for pensions and retiree health benefits. At this level, retiree benefits for teachers and other professionals would be consuming well over $1,000 of the annual per student expenditures. The costs of school retiree benefits are consuming a growing share of K-12 spending in much the same way that the benefit overhang of GM, Chrysler and Ford finally forced them to overhaul their retiree benefits.
As teacher retiree benefit costs spiral ever upward, it is important to begin asking what effect these systems have on recruitment, retention, and workforce quality, and whether these are efficient expenditures. A substantial literature in labor economics demonstrates that the incentives in pension systems matter, not only for the timing of retirement, but for labor turnover and workforce quality (Friedburg and Webb, 2005; Asch, Haider, and Zissimopoulos, 2005; Ippolito, 1997; Stock and Wise, 1990 ). Unfortunately, little of this literature pertains to teacher pensions. While there have been many studies of the effect of current compensation on teacher turnover (e.g., Murnane and Olsen, 1990; Stinebrickner, 2001; Hanushek, Kain, and Rivkin, 2004; Podgursky, Monroe, and Watson, 2004), the econometric literature on teacher pensions is very slender. The only published econometric study to date is Ferguson, et. al. (2006), who find that Pennsylvania teachers’ retirement decisions were highly responsive to incentives for early retirement.
In this article, we analyze the incentives embedded in teacher pension systems by examining the pattern of pension wealth accumulation over a teacher’s career. As we shall see, these systems feature dramatic peaks, cliffs and valleys in pension wealth accumulation that can greatly distort career decisions – or punish teachers for not adapting their plans to the system’s benefit structure. In many states, teachers will accumulate very little pension wealth until their early 50s, at which point they can suddenly reap very large increases. But if they stay much beyond such a pension “peak”, they can suffer declines in pension wealth – punishing them for staying too long. This is one simple pattern, with no compelling rationale, but systems can also exhibit even more bizarre accumulation patterns, which reward or punish teachers at arbitrarily chosen points in their career.
Our main contribution in this paper is to illustrate graphically the peaks and valleys in pension wealth accumulation that operate over the course of a teacher’s career in a representative set of state systems. They are in contrast with the much smoother path of pension wealth accumulation under more modern professional pension plans that tie benefits more closely to contributions, and which, as a result, provide more neutral incentives for career decisions.
How Teacher Pensions Work
Typically, a DB teacher pension plan requires that both teachers and employers make a contribution each year to a pension trust fund. In general these contributions (and the associated benefits) are larger for the 30 percent of teachers who are not part of the Social Security system and smaller for those who are covered. For example, in Maryland, a state in which teachers are part of the Social Security system, during the 2005-06 school year, employees contributed 2 percent and school districts paid 11 percent for a combined total of roughly 13 percent. This was in addition to the 12.4 percent combined employer and employee contribution to the Social Security system. By contrast, in Ohio public school teachers are not covered by Social Security. Teachers contribute 10 percent and districts 14 contribute percent, for a combined total of 24 percent.
In theory, at any point in time, these contributions and the investment returns they have earned, should equal or exceed actuarial accrued liabilities; however, this is rarely the case. In many states the teacher pension systems have large unfunded liabilities. And as large as these are, they do not include future costs for retiree health insurance -- an issue that is now beginning to appear on education finance radar screens.
Once a teacher is vested (usually 5 or 10 years), she becomes eligible to receive a full pension upon reaching a certain age and/or length of service. Different versions of these eligibility rules are discussed below, but they typically allow a teacher to draw a full pension well before age 65, especially if she has been working since her mid-20s.
(1) Annual Benefit = r(S,A)∙S∙FAS.
In this expression, S denotes years of service, the final average salary (FAS) is an average of the last few years of salary (typically three) and r is a percentage that we will call the “replacement factor” that may be constant, but is often a function of service and age (A). In Missouri, for example, teachers at normal retirement earn 2.5 percent for each year of teaching service. Thus, a teacher with 30 years of service would earn 75% of the final average salary. So if the final average salary were $60,000 she would receive:
Annual Benefit = .025 x 30 x $60,000 = $45,000,
payable for life. If the teacher were to separate from service prior to being eligible to receive the pension, the first draw would be deferred and the amount of the pension would be frozen until that time. Once the pension draw begins, there is typically some form of inflation adjustment, although the nature of it varies from state to state.
Table 1 summarizes some of the key parameters of DB pension plans in five states. While not randomly chosen (we inhabit two of these states), they are broadly representative of the universe of teacher pension funds. More complete such tables are published by the NEA and others, showing similar variation in these pension parameters across states. While these types of comparative tables provide useful information about the individual pieces of the pension system, they do not tell us about the composite effect of the system when it is fully assembled and running. To appreciate the powerful incentive effects of these systems, and thus make informative comparisons among states, we use the data in Table 1 to examine the way in which teachers accumulate pension wealth with each year of employment.
Pension Wealth and Earnings Wealth
Formally, consider an individual’s pension wealth, P, at some potential age of separation, As. The stream of expected payments may begin immediately, or may (perhaps must) be deferred until some later retirement age. The present value of those payments is:
where B(A│As) is the defined benefit one will receive at age A, given that one has separated at age As, and ƒ(A׀As) is the conditional probability of survival to that age.
The benefit stream may itself be a choice among alternative streams open to the individual, based upon the choice of when to begin receiving payments, since receipt prior to “normal” retirement may entail a penalty, depending on age and years of service. In modeling pension wealth below, we assume that individuals separating at age As will choose the stream of payments that maximize present value.
In principle, P(As) represents the market value of the annuity. If, instead of providing a promise to pay benefits, the employer were to provide a lump sum of this magnitude upon separation, the employee could buy the same annuity on the market. The teacher’s pension wealth, P(As), is the size of the 401k that would be required to generate the same stream of payments the individual would be owed upon separation at age As.
Figure 1 depicts the pension wealth, in inflation-adjusted dollars, for a 25-year-old entrant to the Ohio teaching force who works continuously until leaving service at various ages of separation. The salary schedule assumed is that of the state capital (Columbus, Ohio) and we assume all cells of this schedule grow at 2.5%. We assume a 5% interest rate, and use a Federal unisex mortality table.
Clearly, the accumulation of pension wealth is not smooth and steady, but rises with fits and starts after age 50, due to rules of eligibility for early retirement and the like. During her first 24 years in the classroom, this teacher accumulates about $315,000 in pension wealth. However, over the next six years she accumulates more than $100,000 per year and crosses the million dollar mark at age 56. Pension wealth reaches a peak by her early sixties and then starts to decline.
For purposes of comparison, it is useful to define one’s earnings wealth analogously to that of pension wealth:
where W(A) is one’s annual wage at age A. Thus E(As) is simply cumulative earnings with accrued interest. It can be thought of as the lump sum that would have been sufficient to fund the stream of earnings, as evaluated at the age of separation. Since pension wealth is the present value of a stream of payments going forward and earnings wealth is the present value of a stream of payments going backwards, both evaluated at the same point in time (at age As), they are comparable measures, capitalizing these two components of compensation.
Figure 2 depicts pension wealth as a percentage of cumulative earnings, P(As)/E(As). This measure has a fairly intuitive interpretation, expressing deferred compensation as a percent add-on to compensation during one’s working life. The pension wealth measure P(As)/E(As) also has a more concrete interpretation, from the funding side. It represents the percentage of earnings that must be set aside each year (from employer and/or employee) in order to fully fund the pension benefits, for any given age of separation. Clearly, those individuals who retire in their mid-to-late 50s receive significantly more in benefits than has been contributed to the system on their behalf, while those who separate from service earlier in their career do not. Figure 2 therefore illustrates the inequities that are built into the system. Since all Ohio teachers contribute 10 percent of their earnings to the pension fund, the net benefits are even more unequally distributed than the gross benefits.
Comparable diagrams for other states typically show a single peak in pension wealth, as a percent of cumulative earnings, but there is significant variation due to the specifics of each state’s benefit formula. In addition, a state’s pension wealth curve often has distinct segments, with markedly different slopes, which means the annual increments to pension wealth at different ages can vary quite dramatically, as we shall presently show.
Annual Change in Pension Wealth, as a Measure of Deferred Compensation
Formally, the annual income from deferred compensation is the change in pension wealth net of interest on the prior year’s pension wealth:
Let us examine (5) in more detail. The first term represents the increase in expected pension payments from As forward. We see from the bracketed expression, which is positive, that this is due to the rise in benefits from the pension formula (B(A│As) > B(A│As-1)), as well as the higher probability of surviving to receive each benefit payment (ƒ(A│As) > ƒ(A│As-1)).
Note that if As is at an age or service level where the formula allows one to accelerate the first pension draw (e.g. age 50 in Arkansas or age 46 in Missouri, as shown in Figures 4 and 5 below), then one or more of the B(A│As-1) terms are zero while the corresponding B(A│As) terms are positive. Thus, at such an age the annual income from deferred compensation includes the sudden addition of one or more years of pension payments, frontloaded. Conversely, if one was already eligible to receive a pension the previous year, at age As-1, then deferring separation forgoes that benefit payment, as shown in the last term in (5).
In sum, the income from deferred compensation in any given year has several conceptual pieces: (i) the rise in expected benefit payments due to the formula (more years of service, higher final average salary, and, in some states, a higher replacement factor); (ii) at certain break points in the formula, additional years of pension eligibility; and (iii) later in one’s career, the loss of a year of benefits from deferring separation.
Consider Ohio, depicted in Figure 3. A teacher who enters service at age 25 accrues pension wealth during her early years on the job starting at roughly ten percent of annual earnings and gradually rising to 34 percent in her 24th year (age 49). However, her 25th year of experience yields quite a bonanza in pension wealth. In that year her pension wealth jumps by 176 percent of her annual earnings. And each of the next five years also yield deferred income that equals or exceeds her current income. The growth of pension wealth drops off sharply over the next few years, followed by yet another sharp spike at age 60 (35 years experience). Beyond age 60, and in spite of the fact that both she and her employer are continuing to make large contributions to the retirement fund, pension wealth actually shrinks (net of interest), and at an accelerating rate.
Note that every one of the five state systems displays sharp pension spikes. In Arkansas, a particularly sharp spike occurs at age 50, as depicted in Figure 4. In that year, our teacher would earn an increase in pension wealth worth almost five times her salary. In other words, a teacher with a $50,000 salary would earn total compensation of nearly $300,000 for that year of teaching, before dropping off precipitously the next year.
The spikes for our representative teacher in Missouri, California, and Massachusetts also occur in her early to mid-50’s, as depicted in Figure 5-7.
What gives rise to such sharp spikes in pension wealth, followed by reductions? At first blush one might imagine that pension wealth accrual would be fairly steady. After all, both the teacher and employer are making the same contributions year after year. But that is the wrong way to think about these teacher pension funds. Teacher pension wealth is only loosely tied to contributions. The primary drivers in changing pension wealth are changes in the annual annuity payment (determined by equation (1)) and the number of years the teacher can expect to collect. It is the latter that is often the wild card in these systems.
For example, during the first 24 years of teaching (to age 49), our Ohio teacher had to wait until age 60 to collect her full pension. However, her 25th year of teaching (at age 50) allows the teacher to begin drawing her pension five years earlier, thereby producing a sharp spike in wealth accrual. Spikes in several of these systems are triggered by the fact that beyond a certain number of years of experience, teachers can start collecting their pension at an earlier age. In other states, spikes are created by enhancements to the benefit formula at specified ages or years of experience.
Finally, and quite importantly, note that once teachers get past the spike (or spikes), pension wealth accrual turns negative. For all these states this occurs by the early sixties, and in some states it does so much earlier. This is not because the annual pension annuity falls. In fact, it is rising (although eventually teachers hit a pension cap typically set at 100 percent of earnings). Rather pension wealth falls because the teacher collects the pension for one fewer years and the annual payment is not enhanced sufficiently to offset this loss.
These charts also illustrate how legislatures alter these incentive structures periodically, even if the public policy impact may not always have been fully understood at the time. In the cases of California and Massachusetts (see Figures 6 and 7), these spikes were created by benefit enhancements enacted when pension funds were flush, following the bull market of the 1990s. Ohio’s multiple-spiked system also reflects benefit enhancements enacted over the years – it used to have a single spike at age 60.
Incentive Effects of Pension Spikes
Second, once a teacher is beyond the spike and into the region of negative wealth accrual, the pension system creates a disincentive to stay on – a push out the door – even if one excels at the job. At this point, the pension system serves as a two-fold tax on earnings, first by the required employee contribution and second by the negative deferred income; together, these can easily offset much or even all of one’s salary. That is, the reduction in pension wealth from working an additional year can approach or exceed the teacher’s take-home pay, in which case her total compensation is little or nothing: she may even be paying for the privilege of teaching.
There is ample evidence that such incentives affect behavior. Anecdotal evidence is commonplace of teachers (and others) timing their retirement decisions to the parameters of the benefit formula; pension systems routinely provide on-line pension calculators to help their members do so. Labor economists have developed more systematic evidence of the behavioral impact of defined benefit pensions in other fields, particularly in the private sector. There has been much less research on teacher pensions, but that which is available indicates strong incentive effects.
Consider the case of Missouri. Missouri’s pension system features a “rule of eighty,” under which a teacher is eligible to receive a full pension once the sum of age and service equals eighty. This feature drives the pension spike depicted in Figure 5. Figure 8 shows the retirement patterns in Missouri, by graphing the frequency of retirements against the sum of age and service. Clearly there is a strong peak of retirements in the vicinity of eighty years, consistent with the incentives created by the benefit formula.
Pension Accrual Patterns at Different Entry Ages
At first blush, it might seem that the spikes would simply be displaced to the left or right depending on the entry age of the teacher. Things are not that simple, however, since the spikes depend in part on the interaction of age and service years. For example, if a teacher is eligible for regular retirement at age 60 or service years equal to thirty, then the magnitude of the spike when service years hit 30 will depend on the difference between a teacher’s age at that point and age 60. In this section, we illustrate some of these complexities by analyzing the Ohio pension scheme.
Figure 9 shows the pattern of deferred income over the careers of three entrant groups. The red curve is the three-peaked pattern of the 25-year-old entrant depicted previously, in Figure 3. The blue curve represents a 22-year-old entrant – an entry age that is actually a bit more common than age 25. It, too, has three peaks, but they are moved three years to the left, appearing at ages 47, 52, and 57. The peak at age 52 is particularly pronounced: a 22-year-old entrant will, in her 30th year of service, raise her pension wealth by the equivalent of four times her salary. This is a bigger spike than for the 25-year-old entrant because her 30th year of service now qualifies her for three extra years of pension payments (starting at age 52 instead of 55). Finally, the green curve represents the 30-year-old entrant. For her, the first two peaks collapse into one at age 55, and the final peak occurs 10 years later, upon her 35th year of service.
Our analysis of Ohio and other states suggests that the curves for 25-year-old entrants are, in fact, indicative of the patterns for entry at the most common entry ages. The accrual patterns for older entrants, such as age 30, are not quite as striking, but those for younger entrants, such as age 22, are even more idiosyncratic, and more strongly tilted toward early retirement.
Unintended Consequences: Employment After “Retirement”
1. Part time employment. All of the pension systems considered here allow teachers who have retired to continue to work in covered employment on a part time basis (without accruing additional benefits).
3. Break in employment. Some states allow teachers to return to full-time employment and collect their pension after a specified break in service. In California the required break is 12 months. In Ohio, a retired teacher can return to work the next day, but must wait two months before receiving pension benefits.
4. DROP plans. Many states have implemented Deferred Retirement Option Plans (DROP’s). These permit teachers to continue working full time for a specified period of time (one to ten years), during which all or most of their pension check goes into what amounts to an individual retirement account. These provide an incentive for teachers to retire and return to work.
Figure 10 provides an example using the Arkansas T-DROP plan. Under this plan, a teacher can keep working after “retirement,” with 72% of her pension check going into a retirement account for her and accumulating interest until she actually leaves teaching. Figure 10 assumes the teacher exercises this option beginning at age 53 (after 28 years of service). Under this simulation, the T-DROP essentially eliminates the pension penalty for continuing to teach beyond 28 years. The impact may be different under other states’ DROP systems.
Of course, there is no obstacle to retirees resuming employment in other fields, or even in teaching itself, by crossing a state line or a district boundary to work in a different pension system. For example, Missouri teachers in the state pension system can retire and work full time in the St. Louis or Kansas City systems, or they can cross the border and work in Kansas.
The result of all of these practices is that the decision to “retire” (i.e., collect a retirement check) is not necessarily the same as a decision to quit teaching in public schools. Unfortunately, we are aware of no comprehensive national data on this topic. Limited data from a national survey conducted by the U.S. Department of Education suggest that at least five percent of the public school teaching workforce is also collecting a teacher pension. A longitudinal study of Missouri teachers found that 12 percent of teachers worked at least one year part- or full-time following retirement.
The significance of these practices has not been fully explored. They have no parallel in the private sector, since early retirement incentives there are always part of a downsizing effort, not one that offers re-employment. In teaching, by contrast, early retirement incentives have a completely different origin, namely legislatively enacted benefit enhancements, typically under heavy union lobbying. Re-employment provisions are often a delayed response to the unintended (if often predictable) problems created by these incentives. In other words, these provisions are ad hoc fixes to some of the perverse incentives created by enhanced pension spikes.
Post-retirement employment blurs the distinction between current and deferred compensation. At the very least, this calls into question the meaning of published data on teacher compensation. In addition, as re-employment becomes easier, the incentive to “retire” at or near a pension spike becomes more pronounced – there is no downside if employment can continue. It might also be in the district’s interest, if the pension costs are borne by the state. One might expect, therefore, that “retirements” would become further concentrated at those points, maximizing the total cost to taxpayers.
More Unintended Consequences: Health Insurance
The consequences of early teacher retirements for publicly-funded health liabilities have not been studied. The shift from active employee to retiree does not, in itself, increase the demand for health insurance. However, to the extent that early retirement increases the total number of individuals – active and retired – relying on the school system for health insurance, the cost to taxpayers is increased.
Options for Reform: Cash Balance or Defined Contribution Plans
CB plans are very similar to DC plans, in that both systems tie benefits closely to contributions. Under a CB plan, employees and employers contribute a certain percentage of earnings to an individual retirement account, the same as under DC. The main difference is that in a CB plan, the return is guaranteed by the employer (typically at a rate comparable to risk-free Treasury bonds), so the market risk is not borne by the employee. Often the debate over DB vs. DC plans focuses on the issue of who bears the market risk, rather than retirement incentives. Since our subject here is the incentives, we focus here on CB plans, where the question of employee risk-bearing does not arise.
The neutrality of CB plans with regard to age of separation can be simply depicted. In the pension wealth accrual graphs (Figures 3 – 7), the irregular curves would simply be replaced with flat lines, at a percentage given by the sum of employee and employer contributions (see Figure 3). There are no spikes, inducing teachers to stay to their mid-fifties and then to leave. Pension wealth never declines: if a teacher wants to work another year, the account grows by the contributions, plus the investment return. This can then be converted to an annuity (many CB plans do this automatically). If a teacher works another year, the starting annuity is increased in an actuarially fair manner, since there is one less year of retirement to cover.
Such a retirement-neutral plan leaves the employee much more latitude to decide when to retire or switch careers, based on individual preferences. It also makes it easier for schools to retain effective teachers, who might otherwise be driven by the pull-push incentives of pension spikes. In our view, this is preferable to the heavy-handed DB formulas, supplemented by makeshift DROP formulas or other re-employment provisions. Finally, it is fiscally more stable, since benefits are tied closely to contributions. Unfunded liabilities do not arise so readily, and legislatures have less opportunity to enhance benefits by shifting costs to future generations of taxpayers and teachers.
In addition, pension policy has powerful effects on K-12 school finance. Teachers who retire in their mid-fifties draw pension benefits for periods of time that are likely to equal or exceed their years of classroom service. A teacher retiring at age 55 with a $50,000 annual pension (indexed) has received an annuity valued at over $1 million. In addition, she may well receive heavily subsidized retiree health insurance for a good while.
A new or reworked retirement system should embody several key features:
• Neutrality. Each additional year of work should increase additional pension wealth in a fairly uniform way. There should be no spikes or cliffs at any particular years of service. Longevity decisions by individuals and their employers should be based on personal priorities and education needs.
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Footnotes (click on a footnote number to return to the paper)
Key Features of Selected State Defined Benefit Teacher Pension Plans
Sources: State pension fund web sites.
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