The influence of classroom characteristics on high school teacher turnover.

Mont, Daniel ; Rees, Daniel I.

I. INTRODUCTION

A number of authors have suggested that the U.S. will face a shortage of qualified teachers in the near future, especially in the areas of math and science.(1) School districts facing such a shortage could respond in a variety of ways. For instance, hiring standards could be lowered, teachers could be asked to teach outside their areas of certification, or, funds permitting, starting salaries could be increased in an effort to attract the most promising candidates.

Still another option would be to raise teaching loads (i.e., average class size or the number of classes taught), thus making do with fewer teachers. This option is particularly alluring in light of the fact that average class size has been falling rapidly in the U.S. over the last twenty years, and yet no strong connection between smaller classes and increased student learning has been established.(2)

There is, however, a possible hidden cost that needs to be investigated before recommending such a course of action. If teachers respond to larger or more frequent classes by quitting, then a district that tries to solve its hiring problems in this fashion could simply be increasing its demand for new teachers.

This paper uses data from the New York State Education Department's Personnel Master File for the years 1979 to 1989 in order to investigate whether an increased teaching load affects the likelihood that a teacher will leave his or her district. In order to obtain an unbiased sample of job lengths, the sample is restricted to full-time high school teachers who were newly hired in 1979.(3) We estimate a discrete-time hazard model in which teaching load is measured as the average class size taught by an individual, the number of classes taught, and the proportion of classes taught in the teacher's certified area. In interpreting our results we pay special attention to whether the behavior of math and science teachers differs from that of other teachers. This is an important issue because shortages of qualified teachers in these two areas are predicted to be especially acute.

II. BACKGROUND

The market for teachers differs from a well-functioning neoclassical labor market in that salaries are determined through a political process involving various levels of government, the public, and often teachers unions.(4) If the demand for teachers increases as retirements and student enrollment increase, then starting salaries cannot be counted on to quickly move to the market-clearing level, and thus a shortage of teachers becomes a possibility.(5) Few observers, however, believe that there will be an actual shortage of warm bodies. The more likely scenario is that there will be a lack of teachers trained in specific areas and of high-quality teachers in general (see Murnane et al. [1991,1-2]).

Given a limited budget, what are the options available to a school district facing this type of shortage? The district could settle for hiring lower quality teachers, but this might be seen as an unnecessary measure, with long-term implications, taken in response to what could be a temporary situation. Another option that has been suggested is to increase teacher workloads.(6) Whether this option is workable depends, in part, on the exit decisions of teachers.

A large number of empirical studies have investigated the determinants of teacher turnover. However, no work specifically directed toward capturing the effect of increased teaching responsibilities on turnover has been done.(7) Without knowing whether such an effect exists, and what the magnitude of it might be, informed policy decisions at the district level in response to a shortage of qualified teachers becomes impossible.

Past studies have shown that the probability of a teacher leaving his or her job is high in the first few years after entering the profession, falls after the third year,(8) and again increases as the teacher nears retirement age (Murnane et al. [1991, 5963]; Eberts [1987]; Greenberg and McCall [1974]). It is possible that as shortages materialize districts will be more reluctant to fire marginal teachers when they come up for tenure. Certainly the opposite is true: declining student enrollments during the 1970s led to increased terminations of younger teachers (Murnane [1981]).

Higher salaries are another factor associated with greater retention of teachers (Rees [1991]; Murnane and Olsen [1989; 1990]; Baugh and Stone [1982]). The effect of increased salaries is especially pronounced for beginning teachers (Murnane et al. [1991, 71-75]).

Studies by Murnane et al. [1991, 67-71] and Murnane and Olsen [1990; 1989] have emphasized the role of outside opportunities in a teacher's decision to leave the profession. They find that higher teacher test-scores are associated with a greater likelihood of leaving, and that high school physics and chemistry teachers are more likely to leave than their colleagues in other areas. These results suggest the possibility that increased teaching responsibilities could drive out those teachers who are the most difficult to replace.(9)

Finally, factors associated with unionization seem to affect teacher exit behavior. Eberts [1987] shows that teacher turnover is reduced by the presence of layoff and class size provisions in the collective bargaining agreement. He argues that these provisions acted as guarantees against layoffs, and so are viewed as a type of job benefit. Rees [1991] finds that stronger grievance procedures are associated with a lower probability of quitting, and argues that a union "voice effect" on quits is responsible. Both of these lines of research point to the importance of union rules and institutions in the exit decisions of teachers. Indeed, where there exist strong contract provisions with regard to the maximum number of hours in a day or students in a class, it would be difficult for a district to increase teaching loads in response to a shortage of qualified teachers.(10)

III. THE DATA

Data for this study were primarily drawn from the New York State Education Department's Personnel Master File.(11) Every year the New York Education Department surveys all public school teachers in New York State, asking a wide range of questions having to do with personal characteristics and working conditions. Each teacher is assigned an ID that is constant across years, so it is possible to collect information on a teacher over the course of his or her career.

Our sample consists of 525 individuals, all of whom were newly hired by a district outside of New York City in the fall of 1979.(12) Only full-time academic teachers with pupils in grades 9 through 12 were included in the sample.(13)

A job separation was defined as a teacher leaving his or her district. Teachers were defined as having left their original 1979 school district if they did not appear in the Personal Master File for two years running, or if their district code changed and did not change back in the next year. It is common for teachers to take a leave of absence or a sabbatic. Therefore an absence of two years instead of one was used to indicate a separation.(14) In fact, many teachers in the sample were absent for one year and then returned to teaching in the same district. Those teachers who were not separated from their original district were followed until 1987, at which time they were right-censored.(15)

IV. EMPIRICAL ANALYSIS

Survival Analysis

A discrete hazard model was estimated to determine the correlates of teacher job turnover. This model provides estimates for the probability of experiencing a job separation conditional on the number of years employed. For example, it estimates the probability of experiencing a job separation in one's third year of job tenure conditional on still being employed in that third year.

More formally, a discrete-time hazard rate at time f is defined as

[P.sub.it] - Prob ([T.sub.i]= t | [T.sub.i] [greater than or equal to] t, [X.sub.it])

where [T.sub.i] is the period job i terminates, and [X.sub.it] is a vector of explanatory variables. It can be shown that the log likelihood function for estimating a discrete-time hazard rate is simply

[Mathematical Expression Omitted]

where [y.sub.it] equals one if a separation occurs at time t and zero otherwise, and [t.sub.i] is the final period in which job i is observed.(16)

Since the above likelihood function is simply the likelihood function for the ordinary regression analysis of a limited dependent variable, it can be estimated using a standard maximum likelihood logit program. The only difference is that a unit of observation is no longer a job per se, but a job-year.(17)

Survival analysis was used previously to determine teacher job separations by Murnane and Olsen [1989; 1990], Willet and Singer [1988], Mark and Anderson [1978; 1985], and Whitener [1965], but these studies lacked information on class characteristics other than subject specialties.

Quits vs. Layoffs

There are basically two types of separations--involuntary and voluntary. The determinants of job quits versus job layoffs can be similar or quite different. We expect age to be correlated with fewer quits (as predicted by job-matching models) as well as fewer layoffs (as predicted by models with specific human capital or seniority), at least prior to retirement years. However, there are other variables, for example class size, that may act differently on quits than on layoffs. Smaller class sizes might be desirable and thus lessen quits. However, smaller class sizes might mean a school district's population is shrinking and it requires fewer teachers and so increases layoffs. Unfortunately, as in other studies of teacher turnover (Murnane and Olsen [1989; 1990], Eberts [1987], Grissmer and Kirby [1987], and Murnane [1981]) quits and layoffs can not be distinguished. This muddies the analysis, but the issue will be addressed at least partially by taking into account the institution of tenure within the teaching profession.

The Explanatory Variables

Economic research on quit behavior typically begins with the assumption that workers compare the expected utility from staying at their current job with the expected utility that could be realized at the next best alternative. Ideally, then, one would like to have information on current working conditions and pecuniary rewards, and at least some proxies for these variables at alternative jobs.

Because of data limitations, most empirical studies have employed only broad (school or district level) measures of working conditions at the current job. Our specification, however, includes a number of teacher-specific variables relating to current working conditions. Those of primary interest are average class size (CSIZE), number of classes taught (CNUMBER), and the proportion of classes taught in the teacher's certified area (CERT). They serve as measures of the amount of stress, preparation time, and grading time involved in class room teaching. Also included in the vector [X.sub.it] is a variable representing the average quality of students taught by a teacher (AQUAL).

In addition to the above measures, we employ a number of district-level explanatory variables, such as high school enrollment, the dropout rate, the percentage of students who go on to college, the percentage of white students, and the percentage of households in the district with children. These variables are intended as indirect measures of working conditions at the current job.(18) Other district-level explanatory variables can be thought of as indicators of the availability and/or desirability of alternative employment, as well as influencing conditions at the current job. Median household income and the percentage of residents who live in an urban area fall into this category.(19)

We use starting salary as our measure of the expected pecuniary returns to remaining at the current job. Thus, following Finnie and Mont [1991] and Meitzen [1986], the entire salary projection path is conceptually collapsed into one variable. A number of teacher turnover studies have used current salary to measure the pecuniary returns to remaining on the job. This alternative approach yielded similar results to those reported below.(20)

Finally, previous work has shown that many personal characteristics such as age, sex, and job tenure influence job separations, both for workers in general (Finnie and Mont [1991], Light and Ureta [1990], Meitzen [1986]) and teachers in particular (e.g., Jacobsen and Sweet [1982], Greenberg and McCall [1974]). A group of personal variables was therefore included in the empirical specification, although race and ethnic background variables were not available. A list of all independent variables employed in this study can be found in Table I. Means and standard deviations are shown in Table II.

TABLE I
Variable Definitions
From the New York State Education Department's Personnel Master File, 1979-1989
 Time Varying:
CNUMBER number of classes taught
CERT percent of classes taught in area of certification
AQUAL AQUAL is the average of a "quality of students" variable for each class
taught.
 The "quality of students" variable for each class is coded as follows:
 1 = below average
 2 = average
 3 = above average
 Class quality was determined by the teacher.
CSIZE average class size
CSIZESQ CSIZE squared
BELOW a dummy variable equal to one if a teacher's average class size is
below the
 mean class size of the sample
ABOVE a dummy variable equal to one if a teacher's average class size is
above the
 mean class size of the sample
YR1 dummy equal to one if the first year on this job
YR456 dummy equal to one if the fourth, fifth, or sixth year on the job
YR789 dummy equal to one if the seventh, eighth, or ninth year on the job
 (note: the ninth year is the last year observed)
 Time Invariant:
FEMALE dummy variable equal to one if female
SALARY starting salary in thousands of $1979
AGE age in years
EXPER years of teaching experience prior to starting the observed job
PHD dummy variable equal to one if teacher holds a Ph.D.

From the NYS Education Department's Institutional Master File, 1979-1987
 Time Varying:
ENROLL the high school enrollment of the teacher's school district in thousands
PDROP the percentage of high school students in a teacher's school district
that drop
 out of school each academic year
P4YEAR the percentage of high school seniors in a teacher's school district
that graduate
 and go on to attend a four year college
PWHITE percentage of high school students in a teacher's school district that
are white

From the 1980 Census of the Population: School District File
 Time Invariant:
PURBAN percentage of residents in a teacher's school district that live in an
urban area PHHWC percentage of families in a teacher's school district that
have children MHI79 The median household income of residents in a teacher's
school district in 1979,
 in thousands of 1979 dollars
TABLE II
Sample Means
(standard deviations in parentheses)
 Mean
FEMALE 0.631
 (0.48)
SALARY 14.988
 (4.63)
AGE 31.966
 (8.03)
CNUMBER 5.013
 (0.81)
CERT 0.983
 (0.10)
PHD 0.013
 (0.11)
EXPER 7.295
 (6.43)
AQUAL 2.035
 (0.45)
CSIZE 20.763
 (4.77)
CSIZESQ 453.839
 (192.70)
YR1 0.156
 (0.36)
YR456 0.215
 (0.41)
YR789 0.126
 (0.33)
ENROLL 1.285
 (3.24)
PDROP 0.027
 (0.02)
P4YEAR 0.172
 (0.20)
PWHITE 0.742
 (0.22)
PURBAN 0.507
 (0.47)
PHHWC 0.679
 (0.09)
MH179 19.753
 (5.86)
n = 1362

Results

Initially we divided the sample according to whether an individual taught in the math and sciences or in another discipline. A log-likelihood ratio test indicated that very little is gained in explanatory power by dividing the sample along these lines.(21) In other words, it would seem that the exit behavior of math and science teachers is not significantly different from their colleagues specializing in other academic areas. Thus the hazard model estimations, reported in Table III, are for the full sample of teachers. The first specification (column 1), which does not include district variables, is rejected at the 99 percent confidence level in favor of a specification in which district variables are included (column 2). This result indicates the importance of these variables as correlates of teacher attrition.

TABLE III
Hazard Estimation Results: Full Sample
 (1) (2)
CONSTANT 1.338 1.384
 (1.33) (1.10)
FEMALE -.202 -.324
 (1.57) (1.22)
SALARY -.077(**) -.069(**)
 (3.75) (2.34)
AGE .032(**) .051(**)
 (2.44) (3.37)
CNUMBER -.073 -.061
 (0.87) (0.66)
CERT -.983(*) -.982(*)
 (1.76) (1.69)
PHD .219 .137
 (.46) (0.23)
EXPER -.020 -.079(*)
 (1.04) (1.69)
AQUAL -.398(**) -.803(**)
 (2.79) (4.97)
CSIZE -.091(*) -.217(**)
 (1.81) (2.96)
CSIZESQ .0025(**) .0051(**)
 (2.07) (2.99)
YR1 1.490(**) .697
 (9.09) (2.47)
YR456 .022 -.104
 (.12) (0.52)
YR789 -.246 -.067
 (1.16) (0.27)
ENROLL -.007
 (0.27)
PDROP 5.888
 (1.15)
P4YEAR -1.172
 (1.09)
PWHITE -.602
 (1.15)
PURBAN -.276
 (1.08)
PHHWC -2.23(*)
 (1.81)
MHI79 .054(**)
 (2.11)
-2 Xlog likelihood 1758.01 1418.58
job endings 392 285
observations 2078 13262

(*) significant at 90% confidence level
(**) significant at 95% confidence level
absolute t-statistics in parentheses

Student Quality. Student quality is found to be significantly linked to the probability of observing a separation. As indicated by the negative coefficient, higher levels of student quality lessened the probability of a teacher leaving. No rationale could be developed for why student quality would be linked to layoffs. District characteristics such as income are controlled for, and the sample does not include special education teachers who might experience a different susceptibility to budget cuts than regular teachers. Therefore, it is hypothesized that higher student quality diminished quits. Teaching students with higher abilities might be associated with different amount of flexibility and variability in curriculum, fewer disciplinary problems, or a different level of personal satisfaction.

Average Class Size. The estimated coefficients of average class size (CSIZE) and class size squared (CSIZESQ) indicate that at low average class sizes, cutting class size would increase turnover, and at high levels of average class size cutting class size would decrease turnover. The turning point, in fact, occurs at just about the sample mean.(22) One explanation for this could be that the first effect is a result of layoffs and the second effect is the result of quits. In other words, when class sizes shrink to very small levels positions are eliminated, but when class sizes get too big teachers quit because of poor working conditions. Since we are interested in the determinants of teacher retention vis-'a-vis quits, this poses a problem.

One way to address this issue is to re-estimate the model separately for teachers with four or more years of experience and for teachers with less than four years of experience. All teachers in New York State who enter their fourth year of full-time permanent employment have tenure. It is very difficult to fire them, and they are less susceptible to layoffs then nontenured teachers. The coefficients for average class size and class size squared obtained using these subsamples (reported in Table IV) show no substantial difference from the results for the full sample. Although the tenured sample is not immune from layoffs, the results provide some support for the hypothesis that the observed effect of average class size is being driven by quits.

TABLE IV
Results from Sample Divided by Length of Job Tenure
 4 or more Less than 4
 years(a) years
CONSTANT 1.22 2.49
 (0.81) (0.83)
FEMALE -.197 -1.01
 (1.11) (1.40)
SALARY -.062(**) -.073(*)
 (2.27) (1.86)
AGE .047(**) .087(**)
 (2.49) (2.56)
CNUMBER -.031 -.164
 (0.29) (0.73)
CERT -.350 -2.479(*)
 (0.46) (1.65)
PHD .078 1.48
 (0.12) (0.64)
EXPERIENCE .025 -.851(*)
 (0.65) (3.21)
AQUAL -.818 -.627(*)
 (4.20) (1.83)
CSIZE -.124(*) -.165(**)
 (1.94) (2.82)
CSIZESQ .0047(**) .0046(**)
 (2.43) (2.04),
YR789 -.012 NA(b)
 (0.06)
ENROLL -.012 .002(**)
 (0.30) (2.17)
PDROP 8.47 1.58
 (1.36) (0.12)
P4YEAR -2.12(*) 4.52(**)
 (1.87) (3.62)
PWHITE -.333 -2.495(**)
 (0.46) (3.03)
PURBAN -.357 -.541
 (1.21) (0.86)
PHHWC -3.317(**) 5.376(*)
 (2.26) (1.83)
MH179 .089(**) -.002(**)
 (2.90) (2.30)
-2 X log likelihood 556.83 626.7
job endings 88 207
observations 761 601
(*) significant at 90% confidence level
(**) significant at 95% confidence level
absolute t-statistics in parentheses
(a) The sample for this specification consists of only those teachers who
were in the previous sample but did not experience a job separation prior to
their fourth year of teaching. This means that all teachers in this sample
are tenured. (b) not applicable for this sample.

To further investigate this issue, expected separation probabilities were estimated to examine the magnitude of the average class size effect above and below the turning point. Again, it turns out that this point is just below the sample mean in every case. Therefore, expected separation probabilities were computed using actual class size, and 60 percent, 80 percent, 120 percent and 140 percent of average class size. The expected separation probability estimated using actual class size, of course, preserves the sample mean.

The expected separation probabilities were estimated as follows: average class size was set equal to .6 x CSIZE and class size squared was set equal to the square of .6 x CSIZE for every observation in the sample used to estimate the model in column 2. Then the probability of observing a separation for every observation in the sample was computed using the parameter estimates in column 2. The mean of these probabilities is the predicted separation rate conditional on a 40 percent decrease in average class size. The same method was used for the other levels of average class size.

These results are presented in Table V. They demonstrate that the practical significance of the average class size effect is much larger above the mean (when increases in average class size are associated with a higher probability of a job separation) than they are below the mean (when increases in average class size are associated with a lower probability of a separation). Increasing average class size by 40 percent is predicted to increase the separation rate from .209 to .349, an increase of 67 percent. Decreasing average class size by 40 percent only increases the separation rate from .209 to .218, an increase of less than 5 percent.

In Table VI, we split average class size and average class size squared into four variables, allowing for unrelated effects of average class size above and below the mean. The results in Table VI suggest that there is no significant relationship between average class size and the probability of a job separation when average class size is below the sample mean. A positive relationship between job separations and increases in average class size is found above the sample mean. Although the coefficient on the above-average class size variable is negative, it must be remembered that this variable is equal to zero for every observation where average class size is less than the sample mean. When average class size is equal to or above the sample mean, the combined effect of above-average class size and its square is such that an increase in average class size leads to an increase in the probability of a job separation. This supports the hypothesis that small class sizes are not associated with layoffs, but large class sizes are associated with quits.(23)

Number of Classes. There was no statistically significant correlation between the number of classes taught and turnover. Teachers with smaller class loads might have more administrative duties and thus may be more likely to leave their jobs for administrative positions, whereas teachers with very high class loads might leave their jobs looking for better working conditions. It may be that these two effects counterbalance each other, leading to no relationship between class size and turnover.

Proportion of Classes Taught in Area of Certification. Although there was not much variance in this variable, it still was found to be significantly correlated with the probability of separation. The probabilities reported in Table V suggest, holding other factors constant, that decreasing the percentage of classes taught in one's area of certification by 10 percent is likely to increase the job separation rate by approximately 3 percent. Once again, teaching out of one's certification area could either be considered a poor working condition that inspires quits, or a sign that one's skills are not those required by a school district, inspiring layoffs. However, very few teachers taught less than 80 percent of their classes in their area of certification, so even in the most extreme case most classes were being taught within a teacher's specialty. This combined with the negative coefficient of CERT in the model using only tenured teachers (see Table IV), seems to suggest that this may be more of a quit effect than a layoff effect.

TABLE VI
Allowing for Different Effects of Class Size above and
below Its [Mean.sup.a]

BELOW x CSIZE -.087
 (0.92)
BELOW x CSIZESQ -.0033
 (0.79)
ABOVE x CSIZE -.217(**)
 (1.99)
ABOVE x CSIZESQ .0053(**)
 (2.06)
-2 x log likelihood 1236.51
job endings 285
observations 1362
(*) significant at 90% confidence level
(**) significant at 95% confidence level
absolute t-statistics in parentheses
(a) Other coefficients suppressed
TABLE V
Mean Probability of Job [Separation.sup.a]
[Baseline.sup.b] .209

Year 1 .331
Years 2-3 .229
Years 4-6 .167
Years 7-9 .091

Females .198
Males .230

.6 x Average Class Size .218
.8 x Average Class Size .214
Actual Average Class [Size.sup.C] .209
1.2 x Average Class Size .242
1.4 x Average Class Size .349

.8 x Salary .261
.9 x Salary .246
Actual [Salary.sup.c] .209
1.1 x Salary .196
1.2 x Salary .183

.8 x % Classes in Certification Area .227
.9 x % Classes in Certification Area .216
Actual % Classes in Certification Area .209
(a) The method for computing these mean probabilities is
described in section IV.
(b) Baseline is computed by taking the average of the predicted
probability of observing a job separation for each observation
in the sample. This is equivalent to the percentage of
observations experiencing a job separation, i.e. 285/1362 = .209.
(c) Equivalent to the baseline.

Job Length. As predicted by standard job-matching models and as found in numerous other job separation studies, the probability of job separations decreases with job length (Finnie and Mont [1991], Meitzen [1986]).(24) The expected separation probabilities generated for Table V predict that the turnover rate in the first year is .331. This drops to .229 for the next two years even before the tenure decision occurs. By years seven, eight, and nine, this drops further to .091. These predictions are in keeping with national statistics on teacher quit rates.(25)

Salary. As expected, higher salaries were associated with fewer quits. In the past there has been some conflicting evidence on the effect of salaries on teacher attrition. At least one study, Eberts [1987], was unable to find a statistically significant relationship between salary and attrition rates, while other studies have found strong evidence of a negative relationship between salary and the probability that a teacher leaves his or her district (Murnane and Olsen [1989; 1990]; Baugh and Stone [1982]). Our estimates suggest that, holding other factors constant, a 10 percent increase in starting salaries would lower attrition rates by approximately 6 percent.

District Variables. Estimates from the full and tenured samples suggest that as median household income in a district rises, teachers are more likely to leave their job. This result might be ascribed to the availability of better non-teaching opportunities in higher-income districts. In the sample of teachers with less than four years of experience, the opposite relationship is found. For these newer teachers it is possible that working conditions associated with the higher-income districts may out weigh the more attractive non-teaching alternatives.

Other results also suggest that teachers with less than four years of experience are quite sensitive to changes in workplace conditions. For these teachers, the relationship between high school enrollment and the probability of separation is positive, a result perhaps indicative of the increased bureaucracy in larger districts. Also, an increase in the percentage of students who are white is associated with a decrease in turnover for these teachers.

The results with regard to the percentage of students entering a four-year college after graduation and the percentage of families with children are somewhat puzzling. In the non-tenured sample the relationship between these variables and the probability of separation is positive, whereas in the tenured sample it is negative. An explanation for this pattern of results may be that tenure standards at the schools with better students and a more supportive public are higher, but after having received tenure these qualities are associated with an easier, more rewarding job.

Personal Characteristics. Age was found to be positively associated with job turnover, although the large bulk of the sample was not near retirement. This result is contrary to what has been found for the population in general, and is even at odds with studies of teachers' turnover.(26) However, upon closer observation these results are in line with prior expectations. The interpretation of the age variable must be made in light of the fact that previous teaching experience is included in the estimation. Given the same previous teaching experience, an older teacher is likely to have more nonteaching experience and thus more nonteaching opportunities.

Previous teaching experience was found to be negatively related to the probability of job separation, as expected. The estimated coefficients for female teachers and Ph.D.s were not statistically significant.

V. CONCLUSION

We included classroom characteristics in an estimation of the job separation rate of teachers, and found these to be significant correlates of job separation. In particular, average class size was found to be positively associated with the job separation of high school teachers, although this effect begins to occur at roughly the mean average class size in the sample. Similarly, teaching outside one's area of certification was also associated with higher job separation rates. It is reasonable to conclude, therefore, that efforts to reduce education costs by increasing class size and asking teachers to teach outside their areas of certification may be undermined by increased teacher turnover. However, controlling for average class size, the number of classes taught seems to have no effect on teacher separation rates.

Separate estimations were conducted for science and math teachers and for teachers of other academic subjects. Log likelihood ratio tests do not support the hypothesis that science and math teachers' turnover is structurally different from that of other high school teachers.

The population of high school age children in New York State is predicted to rise 6.8 percent from 1995 to the year 2000 (New York State Council on Children and Families [1988]). Without adjusting the number of teachers accordingly to maintain present average class sizes, the hazard function we estimate would predict a corresponding 7.2 percent increase in teacher turnover, from .209 to .224.(27) Our results suggest that to keep turnover rates constant without increasing teaching staff size would require an increase in starting salaries (and the corresponding salary scale for other teachers) by between 5 and 10 percent. In determining a cost-minimizing strategy, school districts will have to balance an increase in turnover costs with potential increases in labor costs.

There is an important caveat, however. Some teacher quits involve teachers moving to other districts, as opposed to leaving the profession. If all school districts raised salaries (or increased average class size, for that matter) the effect may not be as large as those predicted above. This is because the effects of higher salaries or class sizes estimated here reflect the impact of having a particular salary level or class size level relative to other districts. In order to more clearly address policy from a statewide or nationwide perspective, as opposed to a school district perspective, we would need data that enabled us to distinguish between teachers moving from one district to another and those leaving the profession altogether. Unfortunately, this information was not available to us. Therefore these estimates serve as an upper bound on teacher exit effects.

Nevertheless, we can conclude that class load variables, used here for the first time in a study of teacher job turnover, are important correlates of teacher attrition. Any future studies of teacher attrition or policy recommendations in this area should incorporate them into their analysis.

(1.) See, for instance, Murnane et al. [1991, 1-2] or Haggstrom et al. [1988, 2]. Predictions of teacher shortages are typically made on the basis of two facts: (1) the large cohort of teachers hired during the 1950s and 1960s is reaching retirement age, and (2) public school enrollment is rising as the children of the baby boomers enter and advance through the school system. (2.) According to a report by the National Education Association [1987, 34], the mean number of pupils taught per day by secondary and departmentalized elementary teachers fell from 134 in 1971 to 97 in 1986.

See Hanushek [1989] for a review of the literature m this area. Hanushek identified 152 studies in which the teacher/pupil ratio was used as an explanatory variable in an education production function. Of these 152 studies only 14 found a statistically significant positive relationship between the teacher/pupil ratio and student achievement. (3.) The sample was restricted to newly hired teachers in order to assure a random sample of job spells. The unit of analysis in hazard rate estimation is the job spell, not the teacher, per se (see Lancaster [1990], Allison [1984], Cox and Oakes [1984], Kalbfleisch and Prentice [1980]). Selecting a sample consisting of aR job spells currently in process in a given year oversamples long spells, and creates a non-random sample of job lengths. This type of sample is sometimes referred to as a stock, as by Lancaster [1990], or straddled sample, as by Sheps and Menken [1973]. If, for example, job tenure had no effect on termination rates whatsoever (i.e., an exponential distribution), a stock sample would have job lengths on average twice as long as a random sample of job lengths (Lancaster [1990, 95]). It is for this reason that only new hires were sampled (i.e., a flow sample that is random in job lengths) instead of all teachers employed in 1979. (4.) See Fogel and Lewin [1974] for a general discussion of public sector wage determination. Also see Ehrenberg and Schwarz [1986]. (5.) Weaver [1983, 5-19] identifies two twenty-year periods (1908-1928 and 1950-1970) in which there were general shortages of qualified teachers. Shortages of math and science teachers seem to be more frequent. Avoiding shortages in these areas

will inevitably require some form of

differentiating salary incentives...The resistance

to this solution will likely come from the

teaching profession itself...Merit pay and

other forms of differential compensation,

apart from seniority and credentials, have

had, to say the least, a less than enthusiastic

response from organized teacher groups

(Weaver [1983, 124]). (6.) For instance, according to Weaver [1983, 80],

[i]n the short term, adjustment m average

class size is the most probable policy action

[in response to a teacher shortage] because

of its direct and immediate effect...budget

savings. (7.) Rees [1991] found a small but positive effect of class size on the probability that a teacher left his or her district. His sample, however, included elementary as well as secondary school teachers. Because class size could potentially mean quite different levels of stress and effort for these two groups, it is not clear how to interpret his results. Also, Rees did not include a measure of the number of classes taught in his estimations which could have led to biased results. (8.) Tenure decisions are generally made at the end of a teacher's third year. (9.) Our data permit us to test if an increased teaching load has a particularly adverse impact on the retention of science teachers. However, because we have no test-score data, we cannot examine whether there is an interaction between "ability" and teaching load. (10.) In addition to the factors discussed in this section, personal and community characteristics have also been shown to be important determinants of teacher attrition. All teachers in this sample are unionized. (11.) Other data sources are detailed in Table 1. (12.) Some teachers arrived with experience from private schools or other public school districts. The rules governing inter-district movement within the New York City school system are unique, and it is for this reason that New York City teachers were excluded from the sample. (13.) Teachers specializing in physical, special, and industrial education, the fine arts, and various types of non-academic fields were excluded from the sample. Full-time was defined as a teacher who taught four or more classes in 1979 and was reported to be working at least 80 percent of a full work load. (14.) Models were estimated using a one-year absence as a job separation as well. The results were not significantly different from those reported below. Since some of these absent teachers re-appeared the following year (e.g., returning from a sabbatic) two-year absences were our preferred definition for a job separation. (15.) Determining if a teacher left his or her district in 1987 actually required examining the 1988 and 1989 Personnel Master Files. (16.) Some observed job spells were still in progress at the end of the sampling frame. That is, the beginning of the job was observed but not its ending. According to Lancaster [1990] these "right censored" observations do not typically lead to bias or consistency problems. (17.) It can be shown that estimates from the discrete-time hazard model are also estimates of the underlying continuous-time proportional hazard model. For the derivation of this log likelihood function and a discussion of its properties, see Allison [1982]. For a good introduction to survival analysis in general see Allison [1984]. For more formal treatments, see Lancaster [1990], Cox and Oakes [1984], and Kalbfleisch and Prentice [1980]. (18.) The percentage of households with children may be positively related to the level of support a school system receives from the community it serves. (19.) Of the district variables, the percentage of residents living in an urban area, the percentage of households with children, and median household income are time invariant and refer to 1979. (20.) The estimated coefficient of the salary variable changed from -.069 to -.081. The estimated coefficients and t-statistics of the other explanatory variables in the model did not change appreciably. (21.) This test was performed at a 95 percent confidence level. (22.) The turning point for the model with district variables is 20.98. The sample mean for class size for this sample is 20.76. The turning point for the model without the district variables is slightly below the mean at 18.2. (23.) Another way of trying to disentangle quit from layoff effects would be to split the sample into those districts with growing enrollments and those with declining enrollments. Districts with growing enrollments presumably face fewer layoff pressures. Unfortunately, the large majority of school districts in New York had falling enrollments over this time period and so this strategy was not used. Instead, a variable was constructed equalling the percent change in district enrollments over the time period. This variable was included in the analysis and interacted with CSIZE and CSIZESQ, (average class size and class size squared). The estimated coefficients of all three terms were negative, a result consistent with the hypothesis that there are fewer terminations when enrollments increase (or decrease less). However, only the coefficient of the percent change variable was statistically significant. The results with regard to the other explanatory variables in the model did not appreciably change.

Another possible criticism of this basic finding is that class size is endogenous. For instance, it may be that popular teachers draw large enrollments and are also more likely to be happy and well liked by administrators. This source of endogeneity would most likely mitigate against finding a positive relationship between class size and reacher turnover. (24.) Hazard functions with dummy variables for each year (one through nine) were also estimated. However, a log likelihood test failed to reject the restricted models reported in Table III. (25.) According to Grissmer and Kirby [1987, 38-39], at two years after entry just under 40 percent of all teachers have left their district, as compared to approximately 48 percent in our data. That is, .331 + (1.331) .229 = .484. (26.) For instance, Eberts [1987, 18] found a negative relationship between turnover and age until a teacher approached his or her fortieth birthday. (27.) A simulation was run similar to those reported in Table V with CSIZE and CSIZESQ being allowed to grow by 6.8 percent.

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DANIEL I. REES, Daniel Mont is an assistant professor at Cornell University. Daniel Rees is an assistant professor at the University of Colorado at Denver. They would like to thank Robert Avery, Ronald Ehrenberg, David Monk, Michael Rendall and two anonymous referees for their comments, and Shahbano Aliani for her excellent research assistance.