the dynamics of teacher salary expense

The Dynamics of Teacher Salary Expense 13

The Dynamics of TeacherSalary Expense

Hamilton Lankford, Peter Ochshorn, andJames Wyckoff

State University of New YorkUniversity at Albany

About the Authors

Hamilton Lankford is Associate Profes-sor of Economics and Public Policy at the StateUniversity of New York at Albany. He re-ceived his Ph.D. in Economics from the Uni-versity of North Carolina at Chapel Hill, andwas a dissertation fellow at the Brookings In-stitution. Professor Lankford’s current re-search focuses on the economics of education.He has collaborated with Jim Wyckoff on aseries of projects examining public/privateschool choice and the allocation of schoolexpenditures. He was awarded an NSF/ASSA/Census Fellowship to examine the ef-fects of school choice and residential locationchoice on the racial composition of urbanschools. He is also engaged in research ex-amining the implicit subsidy to school districtsfrom the property tax deduction on federal andstate income taxes.

Peter Ochshorn is an economics consult-ant. Peter received his Ph.D. in Economicsfrom the University of Michigan. Prior to hisconsulting career, Dr. Ochshorn was AssistantProfessor of Economics at the State Univer-sity of New York at Albany and was an eco-nomic researcher at the New York State De-

partment of Taxation and Finance. Dr.Ochshorn specializes in econometrics and isthe author of several articles that apply econo-metrics to various substantive areas.

James Wyckoff is Associate Professor ofPublic Administration and Policy and Econom-ics at the State University of New York at Al-bany. He received his Ph.D. in Economicsfrom the University of North Carolina atChapel Hill. Professor Wyckoff’s research isfocused largely on the economics of education.Over the last several years, in collaborationwith Hamp Lankford, he has pursued two linesof research. The first addresses issues of pub-lic and private school choice, examining fac-tors relevant to these choices and how thesechoices affect the racial and economic charac-teristics and the academic quality of studentsin public and private schools. The second areaof research examines how public schools al-locate resources. This work explores chang-ing resource allocations over time, with par-ticular focus on teacher compensation and spe-cial education. It is from this research that thechapter in this volume is drawn.

14 Selected Papers in School Finance, 1996



Selected

Papers in

School

Finance



Hamilton Lankford, Peter Ochshorn,and James WyckoffState University of New YorkUniversity at Albany

Although growth rates are expected to declinesomewhat during the late 1990s and early nextcentury, enrollment increases and the accom-panying budgetary pressure will continue. Al-though school district budgets do not increaseproportionately to enrollment increases, re-search indicates that there are few economiesof scale with respect to enrollment increases.Thus, enrollment increases are a real and siz-able source of concern for many school dis-tricts.

Another, less noticed trend has the poten-tial to offset the fiscal effects of increased en-rollment. In many school districts, teacherswho were hired to teach the students from thebaby boom have recently begun to retire.These retirements will continue over the next10 years. As these teachers retire, they will bereplaced with new, substantially lower paidteachers. Figure 2 shows the experience dis-

Much has been made of the budgetaryimpact of the so-called baby boom enrollmentecho on school districts. It is estimated thatthe nation will need an additional 190,000teachers by the year 2006 and that to main-tain current service levels public schools willneed to spend an additional $15.1 billion dol-lars just to keep pace with increasing enroll-ments.1

Indeed, over the period from 1985 to 2005enrollments in elementary and secondaryschools are estimated to increase by just un-der 25 percent, with most of this growth oc-curring before 1997. Figure 1 shows the an-nual enrollment growth for the United Statesover the 1969–2005 period. From 1970 to1984 U.S. enrollments fell, reducing fiscalpressure in many school districts. Since 1984,fiscal pressure has been increasing, withgrowth rates peaking during the mid-1990s.2

Introduction

1 U.S. Department of Education (1996).2 For a detailed analysis of the effect of school district enrollment trends on school district budgets in the U.S., see Hanushek

and Rivkin (1996). Grissmer and Kirby, in a series of papers, analyze teacher supply in Indiana and the nation (1987, 1991,1992, 1993). For an analysis of these trends in New York, see Lankford and Wyckoff (1995).


for only 6 percent of all teachers. This is adramatic shift in the experience distributionof teachers.

The aging teacher workforce offers thepotential for substantial salary savings. Anexample of a district’s salary schedule isshown in figure 5. Since teacher salaries arelargely determined by experience in the school

tribution for all New York state teachers in1970, 1980, and 1995.3 The 1970 spike ofteachers with 1 to 5 years of experience hiredin response to the baby boom enrollment surgegradually worked its way through the system.By 1995, the cohort of teachers with 20 to 30years of experience (veterans) accounted forone-third of all teachers in New York. Teach-ers with similar experience in 1970 accounted

Figure 1.—Annual school enrollment growth rates for the United States andNew York

3 Information on the age distribution for a national sample of teachers is provided by the Schools and Staffing Survey (SASS).In addition, there is limited age information provided by the American Federation of Teachers regarding the teachers in itsunions. The information from both sources is consistent with that provided for New York State. For example, informationfrom the SASS (U. S. Department of Education, 1996a) indicates that the average age of teachers has increased between1987–88 and 1993–94. In addition, the portion of New York teachers who are at least 50 years old is only slightly greater thanthe national average. Many school districts across the United States find themselves with an aging workforce in which a largenumber of teachers are at or near retirement.

SOURCE: U.S. Department of Education, National Center for Education Statistics, Digest of EducationStatistics 1995 and Projections of Education Statistics to 2006.

SOURCE: Based on calculations by authors using New York State Education Department PersonnelMaster File (NYSED PMF).

Figure 2.—Years of teaching experience of New York state teachers

-6

-4

-2

0

2

4

1965 1975 1985 1995 2005

YearG

row

th r

ates

US

NY

0

5

10

15

20

1 11 21 31 41

Years of teaching experience

Per

cent

age

of te

ache

rs

1970

1980

1995


Table 1.—Teacher salary structure

Entry level Veteran

United States $23,956 $40,517

New York 30,289 56,125

SOURCE: U.S. salary information comes from U.S. Department of Education (1996a) and reflects 1993–94 averages for public school teachers with a master’s degree and no experience and highest step of theschedule. New York information from the New York State Education Department Personnel Master File(NYSED PMF) represents state averages in 1994–95 for the same categories.

district, the cohort of aging teachers representsa substantial portion of school district salaryexpense. Table 1 shows the salaries paid toentry level teachers and teachers at the top endof the experience distribution for the UnitedStates and New York. As the veteran teachersretire, their replacements will earn from$15,000 to $30,000 less. With such a largepercentage of the teacher population in thiscohort, the potential savings are substantial.

In this paper we examine the potential sal-ary savings from teachers aging through theexperience distribution and compare this to thesalary costs associated with the increasing en-rollment from the baby boom echo. In gen-eral, we find that few districts are likely toexperience meaningful salary savings as a re-sult of the retirement of the baby boom cohortof teachers. Thus, the increasing enrollmentsof the baby boom echo are likely to continueto force difficult decisions in most school dis-tricts.

Teacher Retirement

The literature on teacher retirement gen-erally examines two issues—work describingthe structure of teacher retirement programs4

and statistical models of the factors relevantto the retirement decisions of teachers.5

Through the collective bargaining process,teachers have won generous retirement in-creases over the last 20 years. Until recently,

the vesting requirements and a lack of port-ability of many of these plans had the effect oftying teachers to particular districts. During theperiod of declining enrollments from 1970until the mid-1980s, many districts employedearly retirement incentive programs to replacehighly paid veteran teachers with entry levelteachers. While the research regarding retire-ment programs provides a useful understand-ing of teacher retirement policies, the analysisis largely descriptive and aggregative. It is notintended to examine the behavioral responsesto policy changes.

Statistical models of teacher quits typicallyemploy data for a sample of teachers over timeto understand the individual and school-levelvariables that cause some teachers to leaveteaching. This work largely focuses on teacherretention during the early years of teaching ca-reers, rather than factors relevant to retirementdecisions.


Teacher compensation in most districts isbased on salary schedules in which salarieslargely reflect teacher in-district experienceand educational attainment. Thus, total teachersalary expense is determined by the numberand education-experience distribution of teach-ers6 together with the salary matrix. The num-ber of teachers is given by the desired student-

4 Examples of this type of research include Auriemma, Cooper, and Smith (1992), and Tarter and McCarthy (1989).5 Recent examples include Brewer (1996), Theobald and Gritz (1996), Mont and Rees (1996), and Murnane and Olsen (1990).6 Although teachers in a district receive compensation associated with other factors, such as extra-curricular activities, their

salaries largely reflect their educational attainment and years of experience.


teacher ratio and enrollments. Throughout thefollowing analysis we take student-teacher ra-tios as given by the actual district level valuefor historical years (1987–88 through 1994–95), and we assume the 1994–95 values holdconstant through 2003–04 when making pro-jections. With regard to the salary matrix, weassume that the rewards to experience are asgiven in the 1987–88 salary matrix for eachdistrict.7 As we age and replace the teachingworkforce, we assume that the education lev-els of teachers in each district remain con-stant throughout.

Within a district, our analysis turns on twovariables, enrollment changes and an agingteacher workforce. Enrollment changes di-rectly affect the number of teachers hired. Anaging workforce produces higher salaries asteachers move up the salary schedule. It alsoproduces teacher quits which produce salary

savings through the substitution of new teach-ers for veteran teachers. The analysis ofchanging enrollments is straightforward. Forexample, increasing enrollments in any givenyear lead to new hires, who then begin to worktheir way through the salary schedule.8 Un-derstanding the effects of the evolving teacherexperience distribution is more complicated.

How the experience distribution of teach-ers changes over time is a function of teacherquit rates, the initial experience distribution,and whether the total number of teacherschanges. A district’s annual quit rate for teach-ers in a particular experience category is de-fined to be that proportion of the teachers whoretire, resign or are terminated in a year. 9 Thethree hypothetical cases shown in figure 3 il-lustrate several features typical of teacher quitrates. Quit rates are relatively high for newteachers. After declining over approximately

7 Alternative assumptions (e.g., using the 1994–95 salary schedule for experience) has almost no effect on the results.8 A portion of the initial new hires quit and are replaced by other new hires. Others continue teaching, thereby gaining

experience and higher salaries. It follows that the salary expenditure associated with the teachers hired to teach the addi-tional students will increase over time as these teachers move through the experience distribution.

9 Quit rates are defined in terms of separations from a particular district. Alternative measures could be based on individualsleaving teaching altogether, leaving the public sector, or leaving the public sector, in a particular state. The appropriatedefinition depends upon the questions of interest. Since salary schedules in individual districts are based on in-districtexperience, and we are interested in budgets at the district level, district-level quit rates are employed in this analysis. Toallow for the common practice of teachers taking leaves of absence, a quit is operationally defined to be a teacher notreturning to teach in the district within 3 years. In reality, the rates at which teachers in a district quit will be subject torandom fluctuations. The deterministic quit rates represent average quit patterns.

SOURCE: Hypothetical cases constructed by authors.

0

0.2

0.4

0.6

0.8

1 11 21 31


Ann

ual q

uit r

ates

Case A

Case B

Case C

Figure 3.—Examples of quit rates, by years of teaching experience


the first 10 years of teaching, the rates remainrelatively constant over a range of years andthen rise.10

When the total number of teachers in adistrict is constant over time, the number ofteachers quitting at a point in time determinesthe number of new teachers that must be hired.Thus, the number of replacement teachersneeded depends upon the initial experiencedistribution and teacher quit rates, since thesedetermine the number of quits. For example,with a large number of highly experiencedteachers having relatively high quit rates, thenumber of replacements will be larger than ifthe experience distribution is such that the bulkof teachers are in stages of their careers wherequit rates are relatively low (i.e., the middlerange of experience). In general, the numberof new hires in a year together with the num-ber of returning teachers in each experiencecategory imply the new experience distribu-tion.

Figures 4a and 4b show the hypotheticalcase of a district initially having the experi-ence distribution labeled “year-00”. This isthe actual experience distribution for all NewYork public school teachers in 1970, and isroughly characteristic of the experience dis-tributions found in districts across the countyat the end of the baby-boom era. Considerhow the experience distribution would changeover time for the case where the total numberof teachers hired remains constant and annualquit rates were as represented by case-C in fig-ure 3. Those teachers hired around year-00who continue to teach (i.e., the year-00 co-hort) have a marked effect on the teacher dis-tribution in subsequent years. This is certainlytrue for the distribution in year-10, although

the relatively high quit rates for inexperiencedteachers have altered the shape of the distri-bution of teachers who remain from the year-00 cohort. Between years 10 and 20 the“boomer” cohort continues to move throughthe experience distribution, with no change inthe shape of the bubble, and only a modest re-duction in its size. This results from teachersin this range of experience having quit rateswhich are both relatively constant and low. Asshown in figure 4b, the change between year-20 and year-30 is more marked as a result ofthose remaining from the “boomer” cohorthaving experience levels such that quit ratesare relatively large and increasing.

The dark solid line in figure 4b shows theasymptotic distribution of experience. “As-ymptotic” is used to describe this distributionsince the actual experience distributions of thedistrict asymptotically approach this distribu-tion over time, provided that the total numberof teachers and the set of quit rates remainedunchanged.11 Higher quit rates, especially forlow levels of experience, would result in fasterconvergence. As is shown in figure 4b, theevolving experience distribution is relativelyclose to the asymptotic distribution even as thelast of teachers in the year-00 cohort reach re-tirement. Once achieved, the asymptotic dis-tribution would be self perpetuating; at eachexperience level, the number of teachers em-ployed in year t+1 would be the same as thenumber employed in year t.

Even if the set of quit rates were constantover time, changes in the total number of teach-ers—due either to enrollment changes orchanges in pupil-teacher ratios—would“shock” the system, thereby perturbing theconvergence to the asymptotic distribution.

10 This pattern has important implications. For example, the quit rates for case A in figure 3 imply that only 42 percent of thoseteachers newly hired will be teaching in the district after 10 years. However, 89 percent of those teachers who have alreadytaught in the district for 10 years continue to teach there another 10 years. For teachers with 20 years of experience, 61percent continue to teach another 10 years.

11 It is possible that convergence will not occur. Consider the case where there is a zero quit rate for all teachers having less thanT years of experience and a quit rate of one at experience level T. In this case, any bulges in the experience distribution wouldcycle through unchanged over time. In contrast, non-zero quit rates over a wide range of experience levels have the effect of“stirring-up” the distribution, resulting in bulges being dissipated and the actual experience distribution converging to theasymptotic one. The dampening of the “boomer bubble” is clearly seen in figures 4a and 4b.


0

2

4

6

8

10

12

14

16

1 11 21 31


Per

cent

age

of te

ache

rs

Year-00

Year-10

What is relevant here is that the experiencedistribution subsequent to a shock will evolveover time following a pattern dictated by theinitial distribution of quit rates.

As a result of the experience distributionchanging over time, the total expenditure onteacher salaries in the district will typicallychange even if the total number of teachers ina district and its salary schedule are constant.Reconsider figures 4a and 4b, which providesnap shots of the evolving experience distri-bution. This along with the salary scheduleshown in figure 5 implies the pattern of aver-age salaries shown in figure 6.

If the asymptotic experience distributionhad been in place in year-00, average salaryexpenditure would have remained constant at$33,068 through time, shown by the horizon-tal line in figure 6. However, as a result ofthe relatively large cohort of new teachershired just prior to year-00, the average salaryexpenditure of $28,771 in year-00 is 13 per-cent smaller. How average salaries change asthis cohort retires is more pertinent here. Inthe simulation, salary expenditures in year-30 are almost 5 percent lower than that asso-ciated with year-20, even though the numberof teachers remains unchanged. A compari-son of the experience distributions for theseyears in figure 4b reveals why. Many of the

Figure 4a.—Teacher experience distributions over time

Figure 4b.—Teacher experience distributions over time

SOURCE: New York State Education Department Basic Education Data System (NYSED BEDS), 1970,and simulation by authors.

SOURCE: Simulation by authors.

0

2

4

6

8

10

12

14

16

1 11 21 31


Per

cent

age

of te

ache

rs

Year-20

Year-30

Asymptotic


teachers having 20+ years of experience andsalaries exceeding $40,000 in year-20 are re-placed with inexperienced teachers havingsalaries of approximately $25,000 in year-30.

The example demonstrates how teacherretirements can lead to reductions in salaryexpenditures. Savings occur after the averagesalary initially over-shoots its asymptoticvalue. The extent to which there are savingswill depend upon the experience distributionin place as the boomer cohort approaches re-tirement, the set of quit rates (e.g., the rates atwhich they retire), and the salary schedule inplace. Before considering these factors, it ispertinent to note that the experience distribu-tion at any point in time reflects past quit rates.

Both experience distributions shown infigure 7 were generated with the initial expe-rience distribution in year-00 shown in figure4a. The cases differ as a result of assumeddifferences in quit behavior, represented bycases A and C in figure 3. Because of the cu-mulative effect of higher quit rates, figure 7shows that relatively fewer teachers are closeto retirement in case C. It follows that anysubsequent salary savings associated with re-tirements will be smaller, other things equal.Again, this results from the high quit rates dis-sipating the bulge more quickly, which in turnreduces the extent to which the average salaryovershoots and subsequently falls. In termsof the situations currently faced by publicschool districts, the extent to which there will

Figure 5.—Example of a district salary schedule

SOURCE: Hypothetical case.

05,000

10,00015,00020,00025,000

30,00035,00040,00045,00050,000

0 10 20 30 40


Sal

ary

$


Figure 6.—Average yearly and asymptotic (real) salaries

20,000

22,000

24,000

26,000

28,000

30,000

32,000

34,000

36,000

0 20 40 60 80 100Years from start of simulation

Ave

rage

teac

her

sala

ry

$

Asymptotic average salary

Yearly average salary


be savings associated with boomer-teachersretiring depends upon the extent to which theboomer bulge dissipated before the teachersreached retirement, which in turn dependsupon quit rates.

For a given experience distribution inplace at a point in time (e.g., year-25), quitrates also have a direct effect on the extent towhich total salary expenditures fall in subse-quent years. Suppose that the current experi-ence distribution is as shown in figures 8a and8b. The experience distributions for the twocases in 5 and 10 years out differ as a result ofdifferences in quit rates, cases A and B, in fig-ure 3, respectively. The sets of quit rates arethe same for teachers having no more than 20years of experience. The retirement pattern incase A corresponds to the case where fewteachers teach beyond 30 years. In case B,relatively more teachers continue teaching be-yond that experience level. As shown in fig-ure 8a, the relatively higher rates of retirementin case A result in the “boomer bulge” dissi-pating more quickly. This has important im-plications for the change in salary expendi-tures. Figure 9 shows how the average salaryexpenditures in both cases would change overtime.

Over the first 10 years, salary expendituresin case A fall at a rate of approximately 1 per-

cent annually. The expenditure reduction incase B is smaller so that by the end of 10 yearsannual salary expenditures for case A are over5 percent lower than for case B. This wouldbe expected for the early years given that theretirement of the boomer cohort is more con-centrated in case A. To some extent the sav-ings due to the retirements in case B are onlydelayed. Annual salary expenditures continueto fall between years 10 and 15 in case B butbottom out and then rise slightly in case A.However, it is striking that at each point intime the average salary for case A is eitherapproximately equal to or below that for caseB. Even though the initial experience distri-bution is the same in the two cases, the inter-action of this distribution with the two sets ofquit rates leads to accumulated salary savingsthat are systematically different.

The horizontal lines in figure 9 show theaverage salaries for the asymptotic experiencedistributions implied by the quit rates in casesA and B. The average salary in case A is lowerthan that in case B by approximately $500 asa result of quit rates for teachers approachingretirement being relatively higher in case A;the higher quit rates imply an asymptotic ex-perience distribution with relatively fewer ex-perienced teachers. A less obvious result re-lates to the short-run salary difference. Formuch of the initial 15 year period, average


Figure 7.—Experience distributions resulting from quit rates A and C

0

2

4

6

8

10

12

14

0 10 20 30 40 50


Pro

port

ion

of te

ache

rs

Year-25—AYear-25—C


teacher salaries in the two cases differ by morethan the asymptotic salary difference, due tothe dynamics of the salary adjustments pro-cess in the short-run. For example, after 10years average teacher salaries for case A arenearly $2,000, or 5 percent, lower than thoseunder case B.

How salary expenditures change over timealso depends upon the salary structure. Con-sider the situation identical to case A with theexception that the salary schedule is as shownin figure 10, rather than figure 5. With the al-ternative salary schedule, the reduction in sal-ary expenditures are only half as large.

The above examples have all maintaineda constant number of teachers in order to iso-late the factors affecting salary expenditures

through the “aging” of an existing experiencedistribution. In each example, new teacherswere hired only to replace those quitting. Ex-tending the analysis to allow for an increasein the total number of teachers is straightfor-ward. Suppose that the number of teachersemployed increased from N

t in period t to N

t+s

s periods later. With a fixed salary schedule,the total change in salary expenditures can berepresented as follows:

.

The variable is the average salaryin year t+s with the number of teachers heldconstant at N

t. Thus, has been

the focus of the above examples. is themean salary of those teachers hired to increase

Figure 8a.—Simulated distributions of experience: Case A

Figure 8b.—Simulated distributions of experience: Case B

0

1

2

3

4

5

6

7

8

9

0 10 20 30 40 50


Per

cent

age

of te

ache

rs Initial distribution

Year +5

Year +10

0

1

2

3

4

5

6

7

8

9

0 10 20 30 40 50


Per

cent

age

of te

ache

rs Initial distribution

Year +5

Year +10



( ) sttsttstttst S)N(NSSNSS ++++ −+−=−

stS +

( )tstt SSN −+

stS +


the total number of teachers from Nt to N

t+s. In

the case where s=1, equals the salaryfor starting teachers. When s>1, is aweighted average of the salaries in the first ssteps of the salary schedule. The weights de-pend upon the number of “expanders” at eachstep, either teachers hired to increase the totalnumber of teachers or to replace hired expand-ers who quit.

Consider case A discussed above with themodification that the total number of teachersincreases by 1 percent per year. It can be shownthat the salary expense 10 years out associ-ated with the expanders equals approximatelyseven percent of the total salary expenditurein the initial period. As discussed above, the“aging” of the initial distribution of teacherswould result in salary expenditures 10 yearsout being lower by approximately 10 percent.In this example, the annual salary savings as-sociated with the retirement of the boomer co-hort would more than offset the annual expenseof increasing the number of teachers for a num-ber of years.

The above examples help clarify the chan-nels through which current trends in studentenrollment and teacher retirement could affectschool budgets. If the salary schedule and stu-

dent-teacher ratios remain constant, the netbudgetary effect of these trends depends upona complex interplay of the initial experiencedistribution of teachers, quit rates and the sal-ary schedule in each district. The remainderof the paper explores how these relationshipsplay out in New York school districts duringthe period 1987–88 to 2003–04.

Data and Method

The New York state teacher-level dataused in this study have been extracted fromthe Basic Educational Data System (BEDS).The BEDS is an annual census of publicschool personnel, and provides a snapshot ofdemographic characteristics, assignments andsalaries of teaching and non-teaching staff.Files for the 8 years, 1987–88 through 1994–95, are employed to examine actual behaviorhistorically. Using estimated quit rates, theexperience distribution is extrapolated to theyear 2005. In a typical year, the file containsdata for each of about 200,000 teachers.

To estimate quitting behavior for extrapo-lation of the dataset, the files are merged byschool district and individual, a quit being in-dicated if the individual is not present for 3subsequent years. A quit function by the levelof experience in the district is then estimated


Figure 9.—Simulated changes in average salary: Cases A and B

stS +

stS +

30,000

31,000

32,000

33,000

34,000

35,000

36,000

37,000

38,000

39,000

40,000

0 10 20 30 40 50

Years from start of simulation

Ave

rage

teac

her

sala

ry

Case B

Case A

$


0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

40,000

45,000

0 10 20 30 40 50


Tea

cher

sal

ary

$

for the years 1987–88 through 1991–92, ag-gregated into seven major location groups:New York City, Rochester, Syracuse, Buffalo,and Yonkers (the large cities), small city andsuburban districts, and rural districts. Thefunctions are then averaged and smoothedwhere necessary using moving averages. Asteachers quit and enrollments change, newteachers are hired into the extrapolated dis-tricts. To estimate these extrapolated salaries,it is necessary to estimate the total teachingexperience outside the district for newly hiredteachers. This is done, again by major loca-tion group, and averaged over the 8 years ofdata. For reasons of consistency of the data,33 school districts involved in mergers or con-solidations between 1987 and 1995 have beendropped from the study. To project the num-ber of teachers beyond the year 1994–95, nec-essary in order to calculate the rate of hiringof new teachers, student enrollment projec-tions are employed (New York State Educa-tion Department, 1994). These growth rates,by county, are applied to the teaching staffsof districts in the respective counties, thus im-plicitly holding teacher-student ratios con-stant.

In order to control for changing salaryschedules, including the effects of price in-flation, in the historical record, and to esti-

mate salaries in the extrapolation beyond1994–95, two salary schedules are estimatedfor each district: one based on the years 1993–95 and a second for the years 1987–89. Thecreation of the 1993–95 schedule is illustra-tive: starting with 692 major districts from1994–95, 141 have been set aside due to ex-cessive missing values for salary, 70 districtshave been removed due to too few teachers(fewer than 30); and 6 districts are not suit-able for our salary regression model (below)due to inadequate distribution of experiencelevels or college degrees among the teachers,leaving 475 suitable districts. The 141 dis-tricts with missing salary information are thenexamined using 1993–94 data. Of these, 41districts still had missing salaries, 5 have lessthan 30 teachers, and 2 suffer problems withexperience and/or degrees, adding 93 moresuitable districts to the first batch, and result-ing in a total of 568 usable districts. A regres-sion model of the salary schedule is estimatedby district in a manner similar to that employedin Lankford and Wyckoff (1997). The salarystructure is fit to a piecewise-linear functionof in-district experience, with adjustments forhighest degree obtained (the data limited theestimation to BA plus 30 credits; MA; and MA+ 30) and for out-of-district experience. Thekink points are set at 5, 10, 15, 20, and 25 yearsof experience, with a constant salary forced

Figure 10.—Alternative salary schedule

SOURCE: Hypothetical case.


above 25 years. For example, the New YorkCity school district in 1994–95 yields the fol-lowing: base salaries of $28,319, $29,598 and$34,009 for BA+30, MA, and MA+30 de-grees, respectively; plus $960 for each yearof experience up to 5 years (the first yearcounts as 1 year of experience); plus $1,270for each additional year up to 10 years; plus$918 per year up to 15; plus $759 per year upto 20; plus $454 per year up to 25 years; andfinally an additional $550 for each year of priorexperience teaching outside of the district.

To control for the effects on district schoolbudgets of changing salary schedules, in or-der to better view the effects of the changingdistribution of experience, a fixed district sal-ary schedule is used to estimate the teachingbudget for each of the years 1987–95. To con-trol for the changing number of teachers, inorder to ask what might have happened to thebudget were the number unchanged, the newlyhired and returning teachers are apportionedto the category of “replacer” or “expander,”according to the number of teachers leavingthe district. The full-time-equivalent (FTE)of each entrant is divided proportionately inthis way. A leaving “expander” was alwaysreplaced by another “expander.”

To extrapolate school budgets from 1994–95 out to 2003–04, average quit rates are ap-plied to each teacher FTE. Growth rates areused to calculate the FTE deficit to be madeup of created new hires with average charac-teristics. New FTEs are apportioned betweenthose replacing quits and those expanding thenumber of teachers. Thus the effect of expan-sion of the teaching staff can be separated fromchanging distribution of experience on the bud-get, as in the historical analysis. Again, a con-stant salary structure is used to estimate sala-ries over time.

Teacher Salary Expense in NewYork Districts

We have divided teacher salary expenseinto a component attributable to the aging of

the original workforce, including replacementof retiring teachers with new teachers, and acomponent attributable to increased enroll-ment. As described above, the salary expenseattributable to the aging of the workforce de-pends on the interaction of teacher quit rates,the teacher experience distribution and thesalary schedule. On average, teacher quit ratesover the 20–35 year experience range are rela-tively low (see figure 11), and the teacher ex-perience distribution moves a significant num-ber of teachers through relatively steep por-tions of the salary schedule. Although the babyboom cohort largely works its way throughthe system by 2003–04 (see figure 12), theseretirements do not result in substantial salarysavings in most districts.

In fact, over the 1987–88 to 1994–95 pe-riod, the aging of the original workforce re-sults in an increase in salary expense in themedian district of about one half percent peryear (see the “without early retirement incen-tive” columns of table 2). A district at the10th percentile of salary growth saves aboutone half percent per year, while districts atthe 90th percentile actually see their salariesgrow by more than 1 percent per year. Oncethe enrollment growth that occurred over thisperiod (see figure 1) is included, the total ef-fect on teacher salary expense is 1.7 percentper year in the median district. Salary savingsdo occur over the 1994–95 to 2003–04 pe-riod, although they are quite modest. We es-timate that the median district has its teachersalary budget reduced by about one half per-cent per year, or slightly more than 6 percentover the period. This result is very similar tothat implied by Case B in figure 10. Districtsat the 10th percentile experience savings ofmore than 1.2 percent per year, which overthe 9 year period amounts to significant sav-ings. However, few districts find themselvesin this situation. When the enrollment growthis accounted for, the median district has a sal-ary expense that increases only marginallyover the next 9 years.


How might these results be altered if dis-tricts were to offer early retirement incentivesto teachers? Would such incentives enticeteachers near retirement, who otherwise wouldhave continued to teach, to retire in sufficientnumbers to provide meaningful salary savingsto districts? This is a complicated questionthat requires a behavioral model of teacher

retirement decisions and how early retirementincentives would affect retirement decisions.Our data do not support such a model and therehas been very little research that has devel-oped such models.12 We can explore theseeffects by making some reasonable assump-tions about the effect of early retirement in-centives on teacher quit behavior.

Figure 12.—New York teacher experience distribution


Figure 11.—New York teacher quit rates, by years of teaching experience

SOURCE: Based on calculations by authors using New York State Education Department PersonnelMaster File (NYSED PMF) data.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

1 11 21 31 41


Qui

t rat

es

0

4

8

12

1 11 21 31 41


Per

cent

age

of te

ache

rs

1988

2004

1995

12 Grissmer, Eisenman, and Taylor (1995) examine early retirement incentive plans for the military. They develop models totarget retirement among specific age cohorts. It is analysis of this sort that is missing for teachers. Their work suggests thatsuch plans are effective cost management tools for the military.


Table 2.—Annual average growth rates in New York teacher salary expense 1

Without early retirement incentive With early retirement incentive2

Original workforce Original workforcereplacement Total effect replacement Total effect

1988 to 1995Median 0.49 1.76 — —

10th percentile -0.42 -0.48 — —

90th percentile 1.25 3.98 — —

1995 to 2000

Median -0.45 0.54 -1.18 -0.16

10th percentile -1.32 -0.83 -2.61 -2.1090th percentile 0.27 1.81 -0.22 1.30

1995 to 2004

Median -0.49 0.11 -0.49 0.09

10th percentile -1.21 -1.15 -1.29 -1.12

90th percentile 0.09 1.37 0.09 1.38

— Not applicable.

1 Employs the 1987–88 salary schedule.

2 Increase the quit rates for teachers with at least 25 years of experience by 25 percent for the 1995–96year only.

SOURCE: Based on simulation by authors.

New York school districts have offeredearly retirement plans in 4 of the 6 years from1991 to 1996. The plans work as follows.Teachers who are at least 50 years old andhave 10 years of experience are provided withan extra month of service toward retirementbenefits for each year of actual service com-pleted, up to 36 months of extra experience.Thus, a teacher with 24 years of experiencecould retire under the early retirement incen-tive with benefits comparable to someone with26 years of experience retiring without the in-centive. During years with early retirementincentive plans, the incidence of retirementamong those who were eligible was about 4percent greater than in years without early re-tirement incentive plans (an increase from 14.5to 15.1 percent). These effects may be some-what muted because plans were offered fourtimes in 6 years and the plans do not have largeincentives.

To provide some sense of the effect of in-centive plans on salary savings we experiment

with a plan that has the effect of increasingquit rates for teachers with at least 25 yearsof experience by 25 percent, but only for the1995–96 year. As shown in table 2, the effectof such a plan on district salary expense ismodest. Over the first 5 years, the medianannual growth in total salary expense is esti-mated to be about 0.7 percent lower (from 0.54to -0.16) with the early retirement incentivethan without it. Most of these savings accruein the first few years. For cash strapped dis-tricts these savings may be important, althoughour calculations do not include the increasein retirement payments resulting from theearly retirement plan. The effects of early re-tirement plans on district salary expense is animportant issue that deserves additional re-search attention.

Conclusion

The results of this research surprise us.We had expected that the retirement of mostof the teachers hired in the late 1960s and early


1970s would yield considerable savings inmany districts, and would offset the additionalexpense of enrollment increases. Instead thereseems, at best, to be only modest savings fromretirements. The simulations that examine theinterplay of quit rates, experience distribu-tions, and salary schedules illustrate why sav-ings can be very illusive. They also show thatrelatively small changes in quit rates, espe-cially in the high experience tail of the distri-bution, can change salary savings substan-tially. This would suggest that early retire-ment incentive policies can be effective indelivering salary savings. Even though be-yond the scope of this research, it would beinformative to explore the determinants of quitbehavior and, in particular, the effects thatsteepness of salary schedules, the changingpool of individuals drawn into teaching, re-tirement plans, and early retirement incentivepolicies have on teacher quit rates.

Even though actual data employed in thispaper comes from school districts in New

13 Clearly there are many districts in the south and west that are experiencing enrollment growth at a substantially faster pacethan that in New York.

York, there is good reason to believe that theresults generalize to many other places. First,as noted in the introduction, trends in NewYork are similar to those in many other areasof the country. Enrollment growth in NewYork is very similar to that occurring on aver-age throughout the country.13 In addition, weexpect that the New York salary schedule andexperience distribution are similar to thosefound elsewhere. Quit rates, conditioned onexperience, may also be similar. Second, thesimulations suggest that under a broad rangeof circumstances sizable salary savings due toretirements are unlikely.

As a result, we are now convinced of theaccuracy of the projections that enrollmentgrowth will continue to be a source of fiscalpressure on many school districts. It is likelythat in most cases savings from the retirementof an aging teacher workforce will be verysmall.


References

Auriemma, F., Cooper, B., and Smith, S. 1992. Graying Teachers, A Report on State Pension Systemsand School District Early Retirement Incentives, ERIC Clearinghouse on Educational Management,Eugene, Oregon.

Brewer, D. 1996. “Career Paths and Quit Decisions: Evidence from Teaching,” Journal of LaborEconomics, 14(2): 313–339.

Grissmer, D. and Kirby, S. 1987. Teacher Attrition: The Uphill Climb to Staff the Nation’s Schools.Rand Corporation.

Grissmer, D. and Kirby, S. 1992. Patterns of Attrition Among Indiana Teachers, 1965–1987. RandCorporation.

Grissmer, D., Eisenman, R., and Taylor, W. 1995. Defense Downsizing: An Evaluation of AlternativeVoluntary Separation Payments to Military Personnel. Rand Corporation.

Hanushek, E. and Rivkin, S. 1997. “Understanding the Twentieth-Century Growth in U.S. SchoolSpending.” Journal of Human Resources, 35–68.

Kirby, S., Grissmer, D., and Hudson, L. 1991. New and Returning Teachers in Indiana. Rand Corpo-ration.

Kirby, S. and Grissmer, D. 1993. Teacher Attrition: Theory, Evidence, and Suggested Policy Options.Rand Corporation.

Lankford, H. and Wyckoff, J. 1995. “Where has the Money Gone? An Analysis of School DistrictSpending in New York State, 1979–80 to 1991–92.” Educational Evaluation and Policy Analysis, 195–218.

Lankford, H. and Wyckoff, J. 1997. “The Changing Structure of Teacher Salary Compensation, 1970–94, ”Economics of Education Review, 371–382

Mont, D. and Rees, D. 1996. “The Influence of Classroom Characteristics on High School TeacherTurnover,” Economic Inquiry, 152–167.

Murnane, R. and Olsen, R. 1990. “The Effects of Salaries and Opportunity Costs on Length of Stay inTeaching, ”Journal of Human Resources, 25: 106–124.

National Education Association. 1992. Retirement and Retiree Health Benefits Provisions Survey,1990–91.

New York State Education Department. 1994. “Projections of Public and Nonpublic School Enroll-ment and High School Graduates to 2003–04 New York State.” Table 7.

Tarter, S. and McCarthy, M. 1989. “Early Retirement Incentive Programs for Teachers,” Journal ofEducation Finance, 119–133.

Theobald, N. and Gritz, R. 1996. “The Effects of School District Spending Priorities on the Exit Pathsof Beginning Teachers Leaving the District,” Economics of Education Review, 11–22.


U.S. Department of Education, National Center for Education Statistics. 1996. Projections of EducationStatistics to 2006. NCES 96–661. Washington, DC.

U.S. Department of Education, National Center for Education Statistics. 1996a. Schools and Staffing inthe United States: A Statistical Profile, 1993–94. NCES 96–124. Washington, DC.

U.S. Department of Education. 1996b. “A Back to School Special Report: The Baby Boom Echo.”

U.S. Department of Education, National Center for Education Statistics. 1995. Digest of EducationStatistics 1995. NCES 95–029. Washington, DC.

U.S. Department of Education, National Center for Education Statistics. 1991. Characteristics ofMovers, Leavers, and Stayers: Results from the Teacher Followup Survey, 1988–89. NCES 91–128.Washington, DC.

Wood, R. 1982. “The Early Retirement Concept and a Fiscal Assessment Model for Public SchoolDistricts,” Journal of Education Finance, 262–276.

the dynamics of teacher salary expense

Documents