Opportunity wages, classroom characteristics, and teacher mobility.
Recent evidence suggests that teachers are the most important factor in promoting student achievement (Rivkin, Hanushek, and Kain 2005), yet public schools face two major problems in the retention of qualified teachers. First, there are systemic losses as teachers move into other occupations, as well as to other schools. On a national level, 7.7% (close to 0.2 million) of teachers stop teaching every year, and nearly as many teachers move from one school to another (U.S. Department of Education 2004). For teachers with less than three years of experience, the corresponding statistics are 8.5% and 13.3%, respectively. Using the lower-end turnover estimates from Milanowski and Odden (2007), taxpayers are paying at least four billion dollars each year to replace teachers. (1) Second, schools in urban areas, as well as those serving primarily disadvantaged student populations, have particular difficulty in staffing their classrooms. Previous studies in both New York and North Carolina showed that schools with greater percentages of minority and poor students usually had fewer qualified teachers (Lankford, Loeb, and Wyckoff 2002; Clotfelter, Ladd, and Vigdor 2005). Even worse, teachers in those schools were very likely to transfer to a new school district (Ingersoll 2001; Imazeki 2004; Hanushek, Kain, and Rivkin 2004).
Not only can schools in urban and high-poverty areas lose teachers to other districts, teachers can transfer to more desirable schools within a district. Intra-district mobility has been largely ignored in the literature; however, a study by Boyd et al. (2005) showed that intra-district mobility occurs as frequently as teacher exits. Additionally, the distinctions between different types of employment changes are important for policy makers. While attrition from teaching reduces the total teacher labor force, intra-district and inter-district movement may leave certain schools better off and others worse off. Furthermore, the appropriate policy will depend on the relative magnitude of the alternative choices made by teachers and the determinants of each choice. For example, schools serving disadvantaged populations cannot change the population of students they serve, but a district could choose to implement differential pay policies if intra-district mobility is a significant problem. However, such a policy may not be efficacious if inter-district mobility dominates.
This paper utilizes a unique administrative database from the state of Florida that tracks public school teachers in the state over time. The analysis is based on a sample of 17,935 new teachers who have no prior teaching experience in Florida public schools. These teachers are among six cohorts who began their teaching careers during the 1997-1998 through 2003-2004 school years and were followed for the complete duration of the 2003-2004 school year--seven years for the earliest cohort. Over 31,000 teacher-year observations are included in the data. Focusing on the mobility pattern of teachers in the first few years of teaching is important because previous studies have indicated that rookie teachers are associated with lower student achievement (Rockoff 2004; Harris and Sass 2007). Previous publications have not been able to focus on rookie teachers either because of sample size or the lack of longitudinal data (Dolton and van der Klaauw 1995, 1999; Stinebrickner 1998: Smith and Ingersoll 2004).
The administrative database I employ allows me to investigate previously unexplored determinants of teacher labor market decision. For example, previous research has focused on school characteristics, demonstrating that teachers' attrition and mobility decisions are closely related to their schools' minority enrollment and average achievement level (Hanushek, Kain, and Rivkin 2004, Imazeki 2004). With the linkage between teachers and their classroom students, this article examines the inner workings of schools in terms of classroom assignments within a school and their impact on teacher mobility. Similar, past research has employed school district level indicators to control for alternative teacher wages or has used the average of all other districts' wages to proxy for teachers' opportunity wages (Gritz and Theobald 1996; Hanushek, Kain, and Rivkin 2004). This study extends the field by focusing on the "pull" (e.g., pay and working conditions in competing districts or competing professions) and "push" (e.g., pay and working conditions in one's own school) factors that influence teacher mobility and retention.
2. Theoretical Model and Empirical Methodology
Often, a teacher's decision to quit or change a job is modeled as an individual's utility maximizing decision over a number of job choices. Similar to Hanushek, Kain, and Rivkin (2004), I define the problem a teacher faces in the following way: A teacher will select among a group of schools based on her individual preferences and the characteristics of the job, including both pecuniary aspects (e.g., salary) and nonpecuniary components (e.g., working conditions). A teacher will compare the available options and select the school that yields the highest present value of expected utility. This paper extends the model to a multi-period context and includes additional considerations of "pull" factors, such as relative salaries of teachers in other districts, relative salaries of individuals in other professions, and relative working conditions in both the teacher's own school district and other districts.
Early teacher attrition studies used cross-sectional data, such as the School and Staffing Survey and the Teacher Follow-up Survey (Ingersoll 2001; Smith and Ingersoll 2004). Cross-sectional data is only a snapshot of teacher characteristics. However, from these earlier studies, teacher attrition and mobility were found to occur at the beginning of a teacher's career. To model such an inter-temporal dependence on outcome, it is important to have panel data to determine the inertia and habit persistence in the teacher decision-making process.
The decision facing a teacher during each time period t is represented by Equations 1 and 2:
U = f([X.sub.ijkt], [C.sub.ijkt], [W.sub.ijkt], [RC.sub.ijkt]), (1)
max PV[[U.sub.S], [U.sub.W], [U.sub.I], [U.sub.L]], (2)
where [X.sub.ijkt] is a vector of demographic characteristics of teachers, such as race and gender. In order to control the impact of family circumstances on teacher attrition and migration decisions, age and interactions with female teachers are included to reflect women's reproductive decisions. (2) [C.sub.ijkt] represents the working conditions for teacher i in school j and district k at time t, including teacher-specific classroom characteristics, such as the demographic makeup of the student body, the poverty level of the students, student performance on exams, and student behavior. Similar information at both the school and district levels is also available. [W.sub.ijkt] represents the salaries earned for individual i at school j and district k at time t. [RC.sub.ijkt] is a vector of relative salaries from other districts or other professions and the relative working conditions in other schools within a district and in other districts, in which the conditions of other districts are weighted based on historical teacher migration. Details are provided in the data section.
The utility a teacher obtains from working at a particular school is a function of both the teacher's working conditions and salary. A teacher maximizes his utility by selecting the option that provides the highest utility out of four possibilities: stay at the present school (S), move to a different school within the school district (W), move to a new school in a new school district (I), or leave teaching (L).
It is assumed that all moves are the results of utility-maximizing choices. While this assumption may not be correct in cases of involuntary separations because of poor performance or the need by schools to reduce their workforces, such instances are relatively rare. According to teacher exit interviews conducted by the Florida Department of Education, 85-90% of teachers exit voluntarily. In addition, involuntary separations included in the estimation may bias against finding significant results because involuntary separations are primarily unrelated to pay and working conditions.
There are two ways that time can be handled in the survival model: continuous and discrete. Most of the earlier studies on teacher attrition or mobility use discrete time (Murnane and Olsen 1990; Singer and Willet 1993; Stinebrickner 1998; Podgursky, Monroe, and Watson 2004; Boyd et al. 2005). For teachers, most moves and exits occur at the end of semesters. In addition, information on schools and districts is typically only available at yearly intervals. Given this discreteness of the data, this paper employs a discrete multinomial-logit-hazard model with both time-variant and time-invariant coefficients.
Only new teachers with no prior teaching experience are included in the analysis. Including experienced teachers would produce left-censoring problems because their teaching careers are already in progress. Generally speaking, the discrete-time hazard function is the probability of transition at discrete time t, given survival up to time t, in Equation 3:
[h.sub.ijkt] = Pr[[T.sub.ijkt] = t | [T.sub.ijkt] [greater than or equal to] t]. (3)
In the current paper, the discrete-time hazard function models the probability that any of the four events--staying, moving within the district, moving to a new district, or leaving--happened to teacher i during period t, which is conditional on the event not occurring until that time. Specifically, Equation 3 can be updated to Equation 4:
[h.sub.ijkt] = Pr[[T.sub.ijkt] = t | [T.sub.ijkt] [greater than or equal to] t, [X.sub.ijkt], [C.sub.ijkt], [W.sub.ijkt], [RC.sub.ijkt]]. (4)
Given the independence of irrelevant alternatives, assuming the error terms are independently and identically extreme value distributed, a multinomial logit hazard model specifies the probability of choosing each alternative as a function of teacher, school, and district characteristics. (3) A multinomial logit model makes the analysis of specific employment transition possible. The cumulative probability of leaving a particular school is a summation of the transition probability of exiting teaching, the probability of intra-district moving, and the probability of inter-district moving. Equations 5a-5c represent the set of the multinomial-logit-hazard model. Details of the discrete-time hazard model estimation procedure are provided in Jenkins (1995, 2005).
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5a)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5b)
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (5c)
For policy purposes, it is necessary to determine the factors that affect the transition from teaching in a given school to each of the three alternatives. It is quite likely that different factors drive different employment transitions. For example, for teachers who consider moving within a given district, the relative working conditions of schools within the same district, such as the current school's percentage of students on free and reduced-price lunches (FRLs) relative to the FRL percentages at other schools within the same district, will likely be influential. Similarly, teachers who consider moving to a new school district will pay attention to the relative salaries and working conditions between school districts.
The data come from the Florida Education Data Warehouse (FL-EDW), an integrated longitudinal database with information on both students and teachers. Current dataset covers the years 1997-1998--2003-2004 and contains rich information on Florida public school teachers. For each year, each teacher record has detailed information on their demographic characteristics, certification status, experience, salary, and the school and district in which they are employed. More importantly, teachers can be linked to their classroom, and thus enable the analysis of classroom characteristics on teacher mobility.
One obvious factor affecting decisions to change employers or occupations is the potential for increasing one's salary. The lower a teacher's current salary, the more likely it is that the teacher will move. Therefore, annual base teaching salaries, excluding bonuses, are included as an explanatory variable. To account for differences in the cost of living across counties at a point in time within Florida, nominal salaries are divided by the Florida Price Level Index (FPLI), published by the University of Florida Bureau of Economic and Business Research (BEBR). The FPLI is a county-level spatial cost-of-living index with a population-weighted average of 100 for the entire state. Since the FPLI only takes into consideration geographic differences in the cost of living, additional inter-temporal adjustments based on the Consumer Price Index (CPI) were performed to convert the nominal salary measure to constant dollars in 1997. (4) The net result of the two adjustments was the teacher's salary, expressed in terms of the statewide population-adjusted average cost of living in 1997.
A priori, I expect that the more challenging students a teacher has in his or her classroom, the more likely this teacher is to leave the school. For example, having a greater number of high-achieving and well-behaving students in one's classroom will reduce the stress of teaching and, thus, reduce teacher exits. Prior studies have found that the percentage of minority and low-income students in a school are also associated with more teacher exits. I expect the same force will be at work at the classroom level.
One important student characteristic is student academic ability. Every spring, Florida administers the Florida Comprehensive Assessment Test (FCAT) in both reading and math to students in grades 3 through 10. (5) Two types of tests are administered. The first is the FCAT Norm Referenced Test (NRT)--a version of the Stanford-9 achievement test. This test is a vertically scaled exam where students who make normal progress will achieve higher scores in each successive grade level. The second test--the FCAT Sunshine State Standards Test (SSS)--is a criterion-referenced test, where the mean score is equivalent across grade levels. Thus, a student who makes normal progress would earn the same FCAT-SSS score in successive years. To avoid complications with different grade-level mean scores, I employed the FCAT-SSS score as the metric of student ability. Earlier research indicated that mathematics is a better predictor of a complete set of student outcomes, such as college graduation and earnings later in life (Rose and Betts 2001). In order to avoid potential multi-co-linearity between reading and math scores, I only use the score from the mathematics portion of the statewide exam.
In addition to achievement test scores, I include the classroom averages of numerous other student characteristics that are likely to affect the perceived cost of teaching, including the number of disciplinary incidents per student, proportion of students eligible for free or reduced lunch, and the shares of students who are black and who are Hispanic. In addition, the teacher-specific number of discipline incidents per student is included to reflect the teaching environment at the classroom level. (6) Disciplinary incidents will measure another important aspect of the teaching environment because of two related reasons. On one hand, low-performing students tend to be kept out of school during the high-stakes testing period (Figlio 2006); therefore, merely including a student's test performance will not provide an accurate picture of the teaching environment. On the other hand, behavioral problems are associated with increased peer disciplinary problems and reduce peer performance (Figlio 2007). All of these factors make teaching less enjoyable.
One concern with using classroom averages as indicators of working conditions for teachers is potential endogeneity. Enthusiastic and motivated teachers may be both more effective at boosting student test scores and less likely to leave teaching. Similarly, highly motivated teachers may work particularly hard to manage their classroom, strictly enforcing disciplinary rules. To test the possible endogeneity of these two variables, I carried out separate instrumental variable probit regressions for each pair of outcomes of interest (intra-district moving versus staying, inter-district moving versus staying, and leaving versus staying) and then conducted Basmann overidentifying-restrictions tests. (7) Two sets of instruments are used in these instrumental variable probit regressions. The first set of instruments includes only the class average of prior-year test scores and the class-average disciplinary incidents the year before. The second, and more complete, set of instruments includes additional classroom variables, such as the teacher-specific percentage of female students, percentage of repeating students, percentage of gifted students, the birth month of students, the class average of prior-year test scores, and the class-average disciplinary incidents the year before. For both sets of instruments, the overidentifying test of exogeneity cannot reject the null hypothesis that the teacher-specific mean math test score and discipline incidents are exogeneous.
There are other reasons to believe that class-average tests scores and disciplinary incidents per student are exogenous. It is more likely that math teachers will have the most impact on classroom average math achievement. In the estimation sample, there are only a small fraction of math teachers (about 15%). Arguably, other teachers will not affect students' math performances, and thus weaken the endogeneity argument. As to the disciplinary incidents, Figlio (2006) has argued that administrators may enforce selective discipline, thus mitigating a specific teacher's impact on per-student disciplinary incidents.
Within a single district, teachers' salary schedules are constant and working conditions become the prominent consideration for teachers. As argued above, key aspects of a teacher's work environment are the numbers and types of students they are required to teach. While the composition of a teacher's classroom indicates their current work environment, the school-wide student body characteristics may be indicative of expected future classroom environments. Further, the overall school environment may be an important consideration in terms of perceived safety for teachers. However, only one prior study (Ingersoll 2001) clearly indicates that schools with fewer student discipline problems have lower teacher turnover rates.
To the extent that the racial/ethnic characteristics and economic status of students are correlated with their ease of instruction or behavior, average student characteristics may partly determine the employment choices of teachers. However, teachers may also exhibit preferences for working with students of their own race or ethnic group. For example, a black teacher who grew up in poor neighborhood may find it more personally rewarding to teach economically disadvantaged black students than white students from affluent families, even though the latter group may in a sense be "easier to teach." Indeed, Hanushek, Kain, and Rivkin (2004), Imazeki (2004), and Boyd et al. (2005) all found that minority teachers favor schools with higher percentages of minority student enrollment.
Besides the characteristics of students, the physical location of a school may be important to teachers and, thus affect their employment choices. Previous research indicates that teachers in urban inner-city schools are more likely to migrate and leave their schools compared with teachers in other areas (Ingersoll 2001; Lankford, Loeb, and Wyckoff 2002). However, it is not clear whether it is the location preference of teachers or the student characteristics that drive these employment changes. Using the Public Elementary/Secondary School Universe Survey Data in 2003 from the Common Core of Data, I identified geographic location with a categorical variable that indicated the rural or urban location of the school.
Each of the 67 school districts in Florida set their own salary schedule and each district faces unique challenges in retaining teachers. It is possible that many districts may have changed their salary schedules and other policies relating to teachers' working conditions during the study period. Therefore, to capture differences across school districts I avoid using time-invariant district indicators and instead employ time-varying district-level characteristics. This approach also allows me to investigate how district-level tradeoffs between salary and working conditions play a role in teachers' employment choices.
To capture differences in working conditions among school districts, I employed the following district-level measurements: student performance on the FCAT-SSS, the number of disciplinary incidents per student, the percentage of black students, the percentage of Hispanic students, and the percentage of students in the FRL program.
If there are rigidities in labor markets, alternative job prospects will depend on the availability of jobs, as well as prevailing salaries. Therefore, the county-level unemployment rate is used as an additional dimension of the opportunity cost of teaching. Since higher unemployment rates means fewer outside options for teachers, the county unemployment rate is expected to be negatively correlated with the likelihood of leaving and moving.
Relative Salaries and Working Conditions
Next I consider the "pull" factors that will attract teachers away from the school where they initially work. Better wages in other professions will entice teachers to abandon teaching and seek employment in other occupations. Similarly, better wages in other districts will tend to lure teachers into other schools or school districts. Given the fixed within-district salary schedule, teachers who decide to stay within the same district will tend to be drawn toward schools with better test scores, and a smaller share of disruptive kids and salary should be relatively unimportant.
Wages in Non-Teaching Occupations
Previous studies have used a variety of non-teaching salaries to represent the opportunity cost of remaining in teaching. Beaudin (1993) used the average salary of new college graduates with a bachelor's degree as the opportunity cost of staying in teaching. Rickman and Parker (1990) adopted two different measurements: i) the wage differential between teaching and all other occupations, and ii) the wage differential between teaching and occupations to which teachers in the Current Population Survey (CPS) move. They found that teachers were more responsive to changes in the wages of the occupations to which teachers in the CPS moved rather than to changes in wages across all occupations. Using a one-in-six sample of British college graduates from 1980-1987, Dolton and van der Klaauw (1999) constructed a measure of expected starting salaries in the non-teaching sector from the salaries of ex-teachers to obtain relative outside wages.
Combining the approaches used by Rickman and Parker (1990) and Dolton and van der Klaauw (1999), I created an opportunity cost measure based on historical teacher movements across occupations. Since the FL-EDW does not follow ex-teachers once they leave Florida public schools, I used two national representative data sources (Baccalaureate and Beyond 1993, 1997, 2003; and the School and Staffing Survey 1999) to determine the sectors into which teachers move when they leave teaching. The sectors to which teachers most frequently move are retail trade, information, finance and insurance, services, and public administration. Using county-level data from the Quarterly Census of Employment and Wages for each year, I calculated the simple salary average in these sectors to obtain an alternative wage for teachers outside education.
Inter-District Relative Wages
Not only does the salary a teacher currently makes affect the probability of staying at their current school, the salaries at other schools in which a teacher could potentially work could determine their opportunity cost and, hence, the likelihood of a move. Three previous studies included a measurement of the opportunity cost of staying in a particular school district. Gritz and Theobald (1996) estimated a teacher's alternative teaching salary by the teacher-weighted average of the annual salary the teacher would earn in all school districts in the state of Washington, excluding the teacher's current district. Brewer (1996) investigated how promotion prospects affected the decisions of teachers to quit. He utilized the ratio of the starting salary for an administrator in the district and the teacher's current teaching salary. Imazeki (2004) employed two measurements of the opportunity cost of staying in one's current school district. The first measurement is the ratio of a teacher's current salary to the average salary in the Cooperative Education Service Agencies (CESA) and the adjacent CESA weighted by the number of vacancies in a teacher's subject area. The second measurement is the same as for a teacher with a master's degree and 10 years of experience.
Rather than treating all districts equally (as in Gritz and Theobald 1996) or assuming that movement is based solely on distance (as in Imazeki 2004), I used historical teacher flows across districts within Florida to weight alternative salaries in other school districts. The historical teacher flows take into account both the number of teaching positions and physical proximity, as well as other factors, such as available amenities, that affect location choice. Relative frequencies of moves are then used as district weights to determine the alternative wages for each year.
Inter-District Relative Working Conditions
Given that a teacher's utility is a function of both salary and working conditions, potential working conditions in other districts will impact the probability that a teacher stays at a particular school. If two districts offer the same salary for the same education level and experience, teachers will select the school district with better working conditions. Indeed, past research shows that non-monetary working conditions affect a teacher's decision to leave a particular school district or to exit teaching entirely (Hanushek, Kain, and Rivkin 2004; Imazeki 2004; Smith and Ingersoll 2004).
Using the same historic teacher-flow methodology described in the previous section, I create a weighted average of working conditions in alternative school districts. Working conditions included measurements of student ability (proxied by test scores), family income (measured by FRL status), and race/ethnicity, as described above.
Within-District Relative Working Conditions
Within the same district, all teachers face the same salary schedule; therefore, the decision to move within a district will primarily be influenced by working conditions. Previous research has found that teachers prefer schools with smaller percentages of minority and poor students and larger percentages of high-achieving students (Hanushek, Kain, and Rivkin 2004; Boyd et al. 2005; Scafidi, Sjoquist, and Stinebrickner 2007). As with the alternative district salary measurements, the historic frequency of moves to other schools in a district are used to weight the alternative working conditions at other schools in a district.
[FIGURE 1 OMITTED]
Descriptive Statistics: Survivor Function for Initial Placement
Figure 1 shows the Kaplan-Meier survivor functions for new teachers who began teaching during the period 1997-1998--2003-2004. The survivor curves display the proportion of teachers who are still teaching in year t. Four survivor functions are displayed. The cumulative survivor rate for leaving the initial placement is represented by a dark solid line. Three individual survivor rates for leaving Florida public schools, transferring to a different district, and transferring schools within a district are represented by diamonds, squares, and triangles, respectively.
As shown in Figure 1, approximately 25% of new teachers remained at their initial schools for six years. The median survival time, during which half of the new teachers left a particular school, is approximately three years. By year three, 73% of teachers were still teaching, including 9% who moved to a new school district and 24% who changed schools within their original school district. Except for the first year, the proportion of those who left is always higher than those who moved within or between districts. Within-district movement is more common than inter-district movement. This is not surprising because inter-district movements, which sometimes involve changing residences, are much more disruptive than within-district movements.
Descriptive Statistics: Classroom Characteristics and Opportunity Wages
How different are teachers' assignments within a school? Do differential classroom assignments have any impact on teachers' employment choices? Despite the recent literature indicating that minority students are more likely to be exposed to novice teachers (Clotfelter, Ladd, and Vigdor 2005), little is presently known about the impact of teacher assignments within a school on a teacher's employment decisions. Table 1 shows the median survival time (i.e., where half of the new teachers are found to be still teaching in their initial placement), broken down by the working conditions teachers face. School-level characteristics and classroom characteristics are split into four quartiles. Top and bottom quartile of school characteristics are listed in column one while column two displays ranges of teacher-specific classroom characteristics. Median survival time is displayed together with the 95% confidence intervals.
Table 1 shows that the median survival time differs widely for teachers in different schools and in different classrooms. The most dramatic differences in median survival time are related to student math achievement. Within the same lowest quartile math schools, the median survival time for teachers with the top quartile students is five years, compared to the median survival time of four years for teachers with the lowest quartile students in their classrooms. This difference in classroom assignment is even more pronounced in the schools with the highest-performing students. The median survival time for teachers with the highest-performing students is seven years, three more years than the median survival time for teachers with the lowest-performing students in their classroom. These summary statistics point out the necessity of modeling classroom assignments within a school. These results also suggest that the lowest achieving students within a school are more likely to be taught by new teachers, who tend to be less effective than their more experienced colleagues (Rivkin, Hanushek, and Kain 2005; Clotfelter, Ladd, and Vigdor 2007; Harris and Sass 2007).
Comparisons across schools also show that low-performing schools face tough challenges in keeping their teachers. For example, teachers with the best draw (top quartile-performing students) in the lowest-performing schools will on average stay for five years, while teachers with the best draw (top quartile-performing students) in the highest-performing schools will on average stay for seven years. Although there is no difference in median survival time between a low-performing school and a high-performing school for teachers with the worst draw (bottom achievement quartile of students), the upper 95% survival time for teachers with the worst draw in a high-performing school is five years, instead of four years for teachers with the worst draw in a low-performing school. Apparently, the distribution of student achievement both across schools and across classrooms within schools are important factors to consider when determining optimal policies for retaining teachers.
Table 2 shows that various opportunity wages are used in this paper. These opportunity wages signify the "pull" factors in other competing districts and in other competing professions within the same county. Opportunity wages are usually estimated using the nearby district average salaries or the average of all other district salaries (Gritz and Theobald 1996; Imazeki 2004). The average district-level salary from all other districts in the state, excluding the current employer, namely, the Gritz and Theobald opportunity wage, is approximately $36,580. Using the historical teacher flow method, the opportunity wages (district-level salaries in other competing districts) that a teacher could potentially make declines by $712. After adjustments for individual-specific degree attainment, the average relative wage in other competing districts is approximately $33,584, which is $2,996 lower than the Gritz and Theoblad opportunity wage. The district-level salaries in other competing districts, after adjustments, are the preferred measurements of opportunity wages within the teaching profession and are used in the main specification of the paper.
Table 2 also shows two opportunity wages that measure the potential earnings outside of the teaching profession. The county-level alternative wages for former teachers in other occupations were based on the average salaries in those sectors into which teachers frequently move. This opportunity wage measurement is much more precise than county-level alternative wages for all occupations. The average alternative salaries for all other professions within the county are approximately $30,113, which is $1,000 more than the average opportunity wages in competing professions within the county.
The following tables report the results of the multinomial logit hazard estimations. Each table shows the odds ratios (i.e., hazard ratios), calculated as exp ([beta]), where [beta] is the estimated coefficient from Equations 5a-5c. (8) Just as in regular logistic regression, the antilog of a dichotomous predictor estimate yields the estimated odds ratio associated with a one-unit difference in the predictor. Similarly, the antilog of a continuous predictor yields the estimated odds ratio associated with a one-unit difference in the predictor. In general, an odds ratio greater than one suggests an increased probability of leaving or moving, compared with the default, which is staying at the initial placement, while an odds ratio less than one implies a decreased probability of leaving or moving, compared with the default.
In order to compare the current study with earlier studies that used school-level information on student characteristics (Hanushek, Kain, and Rivkin 2004; Scafidi, Sjoquist, and Stinebrickner 2007), Table 3 shows the impact of average school measurements of student demographics, behaviors, and test scores on teacher decisions. This model specification is closely aligned with earlier studies, except that the current model distinguishes intra-district versus inter-district moving; whereas, the earlier studies do not.
Higher percentages of black students in a school increase all risks of leaving: exit to other professions, inter-district moving, and intra-district moving. This finding is consistent with previous research; Boyd et al. (2005) found that teachers in New York City tended to move away from schools with higher percentages of minority students. A similar pattern was found for teachers in both Georgia (Scafidi, Sjoquist, and Stinebrickner 2007) and Texas (Hanushek, Kain, and Rivkin 2004). The behavior of minority educators shows a different pattern, however. The probability that a minority teacher will move (either inter-district or intra-district) decreased as the percentage of minority students in their initial school increased. Similar patterns were uncovered in both Texas (Hanushek, Kain, and Rivkin 2004) and Wisconsin (Imazeki 2004).
Table 4 shows the estimates from the preferred model for this paper. (9) Model 2 adds teacher-specific classroom characteristics to Model 1. In addition, Model 2 replaces the district-fixed effects in Model 1 with district-level covariates, such as the district-level mean math score, mean discipline incidents, etc. Lastly, Model 2 adds the relative working condition variables, such as the district-level covariates in other competing districts, within-district covariates in other competing schools, and two opportunity wage measurements. The first opportunity wage measurement is the district-level salaries that teachers would have earned in other districts after adjustments for education level, while the second opportunity wage measurement is the county-level alternative wages for former teachers in other occupations. I discuss the effects of teacher characteristics, salary, and student characteristics on each of the three teacher mobility choices.
Teacher Educational Attainment
Previous research has produced mixed evidence on the relationship between the educational attainment of teachers and their likelihood of leaving the teaching profession. Some studies have found that teachers with an advanced degree are more likely to quit or transfer (Rees 1991; Kirby, Berends, and Naftel 1999; Imazeki 2004), while other studies found the opposite result (Shin 1995; Adams 1996).
While in general one would expect that increases in educational attainment would tend to make a worker more mobile, the effect on mobility depends on the specificity of the human capital that is obtained. The vast majority of teachers' master's degrees are in education and, thus, may not increase the teacher's productivity in alternative occupations. Since teacher salary schedules are typically based on two factors--education and experience level--there are strong incentives to obtaining a master's degree, even if it has no impact on productivity. If the wages of teachers with master's degrees bestow some economic benefit, this observation could make the teacher with an advanced degree less likely to change occupations. Furthermore, if differences in salary schedules across districts yield differential returns to a teacher with an advanced degree, then possession of advanced degrees would enhance incentives to seek employment in a different district.
Data presented in Table 4 reveal that once the education-attainment-adjusted opportunity wage that a teacher would be earning in another district is properly taken into account, the possession of an advanced degree actually reduces the likelihood of moving to a new district and exiting the Florida public school system. This finding is consistent with prior expectation and points out the importance of controlling the individual-specific opportunity wage.
Teacher's Own Salary and Opportunity Wages
Unlike Model 1, once adjustments for both cost of living and inflation are made, a teacher's own salary affects the decision to stay in teaching but has no significant impact on their decision to move to a new district. This difference could be due to inclusion of opportunity wages. Model 1 does not account for variations in opportunity wages, while Model 2 incorporates opportunity wages into moving to a new district and leaving Florida public schools.
In contrast, the levels of alternative salaries have positive and statistically significant effects on the probabilities of moving and leaving. A teacher's opportunity cost of staying in teaching is measured by county-level alternative wages for teachers in other occupations. The higher this measure is, the higher the probability of all three departure decisions. If other districts (to which there have been historical movements of teachers from the original school district) decide to increase teacher salaries, then the probabilities of leaving and inter-district moving both increase. Consistent with prior expectation, district-level salaries in other districts have no impact on the decision to move within a district because wages in other districts are only relevant when moving outside of one's initial school district.
Student Characteristics at Class, School, and District Level
At the classroom level, an increase in the number of disciplinary incidents in one's classroom is associated with an increase in all risks: exit to other professions, inter-district moving, and intra-district moving. Like crime statistics, the probability of an incident being reported may be higher in "better" schools. If that fact is the case, estimates of the impact of disciplinary incidents may be attenuated. Therefore, estimates of the impact of disciplinary incidents presented here should be considered a lower-bound estimate. The impact of teacher-specific average math scores exhibits an interesting pattern. A higher teacher-specific classroom average math test score is associated with a lower likelihood of moving, while the same increase is associated with a higher likelihood of inter-district moving. The former example is consistent, with a priori expectation, while the latter is not. Since more teachers move within a district, it is expected that higher test scores are associated with higher teacher retention in general.
In contrast to Model 1, only one school-level covariate affects the transfer and exit decisions of teachers. Increases in the poverty rate at a school are associated with a greater likelihood of leaving the public school system in Florida. Specifically, a one-percentage-point increase in the school poverty rate is associated with a 57% increase in hazards/odds of leaving. Once the classroom level covariates are included, the school-level covariates, such as the percentage of black students, are no longer statistically significant. This finding indicates the specific classroom environment has a much stronger effect on teachers' employment decisions than student characteristics throughout the school.
Though not shown in Table 4, black teachers are found to be more likely to leave teaching and Hispanic teachers are found to be more likely to transfer to a new school district. Black teachers are less likely to leave the Florida public school system if they have a greater proportion of black students in their classrooms. The same can be said about the inter-district mobility of Hispanic teachers. Earlier studies found this interaction between minority teachers and students at the school level (Hanushek, Kain, and Rivkin 2004; Imazeki 2004; Boyd et al. 2005).
At the school-district level, higher average performances on the math portion of the FCAT are associated with a lower likelihood of teachers moving or exiting teaching. Thus, school districts with low-performing students find it particularly difficult to retain teachers in their schools. Past research has shown that the quality of teachers is important in improving student achievement (Goldhaber, Brewer, and Anderson 1999; Rivkin, Hanushek, and Kain 2005; Burke and Sass 2006). Furthermore, teachers with less experience are not as effective in improving student performance (Rockoff 2004; Rivkin, Hanushek, and Kain 2005; Clotfelter, Ladd, and Vigdor 2006; Harris and Sass 2006). Teacher attrition and mobility could make the problem of low performance in these school districts even worse.
School districts with a large proportion of students in the FRL program have more internal teacher turnover; teachers are more likely to change schools within a district if a high proportion of district students receive FRLs. Additionally, a higher percentage of minority students in a district are associated with a lower likelihood of intra-district mobility or exit.
Relative working conditions in other schools within the district or in other school districts play a role in teachers' occupational decisions, even accounting for salary differentials. For example, holding the number of disciplinary incidents per student constant, the higher the number of competing district disciplinary incidents, the less likely teachers are to leave or move. The greater the proportion of minority or poor students in competing districts, the less likely a teacher is to leave his current school. Surprisingly, the higher the number of competing district math scores, the less likely a teacher is to move or leave. One possibility is that school districts are clustered geographically in terms of student math scores. Another possibility is that the high-performing districts may not prefer teachers to transfer from low-performing districts.
For intra-district movers, holding current school environment constant, more disciplinary incidents per student in competing schools within the district are associated with a decreased likelihood of intra-district moves. This result fits prior expectations: the worse the working conditions in competing schools, the lower the likelihood of a move. Given the presence of district-wide salary schedules (and thus, little within-district variation in salaries for a given teacher), it is not surprising that salaries do not have a significant effect on within-district teacher mobility. These results are consistent with those of Boyd et al. (2005), who found that within-district moves are primarily affected by school working conditions.
[FIGURE 2 OMITTED]
5. Policy Simulations
As demonstrated in the previous section, classroom characteristics, such as the teacher-specific mean math test scores, the racial composition of students and teachers in a classroom, and the behavior of students, are important determinants of teacher labor market decisions. Similarly, the interplay of a teacher's own salary, opportunity wages in other districts, and opportunity wages in other professions are important influences on teacher job choices. Consequently, both salaries and working conditions are potential tools for the promotion of teacher retention. In the following subsections, I present simulations that indicate the net effects of potential policy changes. Unless otherwise stated, the policy simulation is for a 32-year-old, white, female teacher with a bachelor's degree, who is professionally certified and teaching in a self-contained classroom in an elementary school located at the edge of a mid-size city. She has two years of teaching experience with students who possess average characteristics.
Figure 2 shows the impact of raising teacher salaries to various benchmarks on teacher retention rates. 10 Unlike earlier studies, this study has four meaningful benchmarks for teacher salaries. The first two benchmarks are based on the opportunity wages a teacher could potentially earn in other professions, while the remaining two benchmarks are based on the opportunity wage a teacher could potentially earn in another district. With an average actual teacher salary of $25,796, the retention rate is 82.12%. If teacher salaries were raised to the average salary in competing professions ($28,956), equivalent to a $3,160 increase, the retention rate would increase by 0.48 percentage points. Similarly, if teacher salaries were raised to the average salary in competing school districts ($33,583), the retention rate would increase to 83.27%. This calculation translates into a 1.15-percentage-point increase from the retention rate of 82.12% for teachers with average actual salaries.
Table 5 presents the simulated probabilities for both average and "hard-to-staff" schools based on model estimates in Table 4. There is no consensus in the literature on the definition of "hard-to-staff" schools. In the current paper, a school is classified as "hard to staff" when both the proportion of black students at the school exceeded the district average and the proportion of students receiving FRLs was greater than the district average. Based on this definition, a typical (average) hard-to-staff school has 47% black students and 69% poor students, while the average for all schools is 26% black students and 48% poor students.
If teachers in "hard-to-staff" schools were paid an average salary ($25,796 in 1997 terms), the retention rate would be 80.63%, compared to 82.12% in an average school. If teacher salaries in "hard-to-staff" schools were raised to the average salary in competing professions ($28,956) or a $3,160 increase in average salary, the retention rate increases by 0.52 percentage points. Similarly, if teacher salaries were raised to the average salary in competing school districts ($33,583), the retention rate would increase to 83.27%. This calculation translates into a 1.26-percentage-point increase from the retention rate of 80.63% for teachers with average actual salaries.
To maintain the teacher retention rate in "hard-to-staff" schools at the same level as average schools (81.12%), a teacher in a "hard-to-staff" school would have to be paid an additional $10,000. In other words, a $10,000 salary premium is required to neutralize turnover effects associated with increasing the proportions of black and poor students by 21%.
Another means to improve retention rates in "hard-to-staff" schools is to change the work environment. If student behavior can be improved, it would have a significant impact on teacher retention. Within "hard-to-staff" schools, the assignment of teachers to a classroom with 0.4938 fewer average discipline incidents per student (which is half a standard deviation) is equivalent to raising teacher salaries by between $3,160 and $4,309 (which is 30-40% of a standard deviation). Even if it is not possible to improve overall student behavior at a school, altering classroom assignments could have a net positive effect on teacher retention within a school. The current paper only examines the choices of teachers in their early careers. However, other research indicated that classroom assignment is not a zero-sum game. Specifically, teachers with more years of experience are not as responsive as their younger counterparts to having more unruly students in their classrooms (Feng 2005), suggesting that assigning relatively more unruly students to veteran teachers would lower the overall attrition rate within a school.
One nice characteristic of reducing the number of incidents is that its impact on all three types of turnover is the same. However, altering classroom assignments based on student exam performance is not a straightforward way to promote retention. Student academic achievement is found to have a differential impact on both mobility and attrition. For example, if a teacher is assigned to teach in a class with an average test score of 428, or three standard deviations higher than an average class with an average test score of 283, then the probability of intra-district mobility and exiting the Florida system decreases, while inter-district mobility increases, compared with the baseline of teaching in an average-achieving class.
The federal No Child Left Behind Act's mandates for highly qualified teachers in every classroom, along with state class-size limitations and accountability standards, have exacerbated the challenges that school districts face in hiring and retaining teachers. In addition to the systemic problem of attrition from the teaching profession, many schools, particularly those serving disadvantaged students, are plagued by high faculty turnover caused by teachers moving to other schools. This study uses a unique statewide administrative database from Florida that tracks six cohorts of new public school teachers over time to study why teachers transfer within a district, move to a new district, or exit teaching altogether.
This paper contributes to the growing literature on teacher employment choice in several ways. First, it includes intra-district teacher mobility, which is quantitatively important, and which has been largely ignored in the literature. Second, this paper examines not only school-level working conditions, but also the impact of within-school classroom assignments on the employment choices of teachers early in their careers. Third, an innovative methodology was employed to infer salaries in competing districts and in other professions within the district. Additionally, the same methodology provides a mechanism to examine how the working conditions in other schools within a district affect intra-district mobility.
The estimates of the determinants of teacher labor market decisions provide important guidance for public policy. First, the labor supply of teachers, once they enter the profession, is relatively inelastic. Raising average teacher salaries to levels equivalent to wages in alternative occupations (a 12% increase) would only increase the retention rate by 0.48 percentage points (from 82.12% to 82.60%), suggesting that even fairly substantial across-the-board salary increases would have only a modest impact on teacher attrition. Second, teachers are relatively sensitive to working conditions. Teachers are significantly more likely to move away from schools with high proportions of minority, low-income, and low-achieving students. Offering differential pay to teachers willing to teach in such "hard-to-staff" schools could overcome the non-monetary disadvantages these schools face but would be costly. In Florida, equating the retention rate in schools serving above-average proportions of black and poor students with that in schools serving average proportions of black and poor students would require a $10,000 salary premium. A potentially less costly alternative would be to find ways to improve the school environment by reducing disciplinary problems or redistributing unruly students to veteran teachers.
While the current study sheds new light on teacher labor markets and the efficacy of alternative policy options, it has limitations as well. In particular, the relationship between teacher quality and teacher job choice has not been explored. Some attrition is good if those exiting the profession are relatively ineffective teachers. Potentially value-added estimates of the teacher impact on student achievement could be used to measure quality and allow investigation of the relationship between attrition, mobility, and the distribution of teacher quality. With value-added estimates, it may also be possible to investigate whether highly effective teachers respond to classroom characteristics and local labor market conditions differently than do less effective teachers.
Appendix: Robustness Checks
Alternative Measurements of Opportunity Wages Table 6 shows abbreviated results with an alternative opportunity cost measurement. As discussed above, Gritz and Theobald (1996) use a simple average of the mean teacher salary in other school districts within a state as their metric of alternative teaching wages, rather than the historic-teacher-flow weighted average used here. Overall, the results presented in Table 6 are qualitatively consistent with the preferred model in Table 4 but differ in magnitude. The estimated impact of a $1,000 increase in alternative salaries on inter-district mobility using teacher-flow weighted average measurements is a 21% increase in the hazards/odds ratio of inter-district mobility (Table 4); whereas, the average employed by Gritz and Theobald produces a much larger increase of nearly double the original hazards/odds ratio (Table 6).
This is not surprising because the Gritz and Theobald (1996) alternative wage measurement uses all salaries in a state; whereas, the measurement used in Table 1 only considers those salaries from school districts into which teachers have historically moved. The Gritz and Theobald (1996) alternative wage measurement may exaggerate the benefits of moving because the transaction cost of moving from one part of the state to another may be prohibitive. For example, moving from Orlando to Tampa will be less costly compared with moving from Orlando to Ft. Lauderdale. Gritz and Theobald (1996) treat salaries in Tampa and those in Ft. Lauderdale the same, while the measurement used in the current analysis weights the salaries in Ft. Lauderdale if there is less historical teacher movement between Orlando and Ft. Lauderdale. In addition, the district-level competing salaries in Table 4 adjust for individual teacher education level in the calculation of the opportunity wage a teacher could potentially earn in the new school district, while the Gritz and Theobald (1996) alternative wage measurement does not. Compared with the preferred model, Gritz and Theobald alternative wage measurements may overstate the benefits of moving.
Using data from the Current Population Survey, Rickman and Parker (1990) found that teachers are more responsive to the salaries of the occupations into which teachers move compared with the general level of salaries. Instead of using the opportunity wages of other occupations based on inter-occupation movement patterns, I also estimate the model using county-level alternative wages for all occupations in Table 7. Results in Tables 4 and 7 are similar. Table 7 indicates that the average wages for all occupations in a county have greater impacts on leaving teaching and within-district migration than the average wages of competing professions. Specifically, a $1,000 increase in countylevel alternative wages in Table 7 will increase the initial hazards/odds ratio of leaving by 10%, while the same increase for the measurement in Table 4 induces a reduction of 9%.
Adjusting for Teacher Quality
Although it is not always clear what observable characteristics determine teacher effectiveness in improving student achievement, Ferguson and Ladd (1996) indicated that ACT scores are an important factor. The data on college entrance exam scores come from the student records of Florida public universities and community colleges, which are only available from 1995 to present. Thus, the sample is limited to teachers who entered a Florida public university or community college in the 1995-1996 school year or later and possess a valid test score. Though not shown here, a teacher's SAT-equivalent college entrance exam score has a positive statistically significant effect on the decision to move to a new district and exit Florida public schools. Caution is warranted when interpreting these results, however, because the number of teachers with test-score information (5841 teacher-years) is low compared with the full sample of teachers (31,129 teacher-years).
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(1) The turnover cost per teacher per year for a teacher with one year of experience is estimated to range between $9,061 and $23,088.
(2) Commuting time to school is possibly an important aspect of teachers' employment choices. Unfortunately, the available data do not provide such information.
(3) One may suspect that intra-district and inter-district moves are not independent, as they may represent a decision to stay in teaching; whereas, leaving is distinct from these two alternatives. To test the multinomial logit model's assumption of the independence of irrelevant alternatives (IIA), I carry out both a Hausman test of the IIA assumption and the Small and Hsiao test of the IIA assumption. Both tests confirm that the null hypothesis of any pair of outcomes as independent of the other cannot be rejected.
(4) Consumer Price Index for All Urban Consumers (CPI-U) for South Urban 1997-2003 is used.
(5) For details on the Florida Comprehensive Assessment Test, see the following website: http://www.firn.edu/doe/sas/fcat/ handbk/fcathandbook.html.
(6) A disciplinary incident is a situation that results in disciplinary action being taken. Possible actions include corporal punishment, in- or out-of-school suspensions, expulsions, or placement in an alternative educational facility. Incidents can include gang involvement, drug or alcohol use, possession of weapons, hate crimes, or other problems.
(7) Results are not shown here but are available upon request.
(8) Homsmer and Lemeshow (1999) called the product of the antilog of the coefficients a hazard ratio while Singer and Willet (2003) defined the product as the odds ratio.
(9) Included in the appendix are some alternative specifications of the preferred model that examine the robustness of other alternative measurements of opportunity wage and take a preliminary look at the teacher quality issues.
(10) Several states have proposed increases in teachers' salaries in order to reduce attrition (Education Commission of States 2005). For example, Georgia will increase the pay for all Georgia public school teachers by 4%, or roughly $1,000 to $2,000 per teacher. Kentucky, Oklahoma, and Virginia will increase their teacher salaries to match the regional or national average salary.
Li Feng, Department of Finance and Economics, McCoy Hall 561, McCoy College of Business and Administration, Texas State University-San Marcos, 601 University Drive, San Marcos, TX 78666, USA; E-mail LF20@txstate.edu; corresponding author.
I am grateful to Tim Sass for his comments and suggestions. I would like to thank two anonymous referees, Christopher Bollinger, Peter Gregory, David Macpherson, Thomas McCaleb, Douglas Harris, Stefan Norrbin, Susan Averett, Lisa Dickson, Matthew G. Nagler, Melanie Guldi, Rhonda Sharpe, and other participants at the 2007 Eastern Economic Association Annual Meeting, the 2007 CEMENT Eastern Economic Mentoring Workshop, and the 2007 American Education Finance Association Annual Meeting. I appreciate Florida Department of Education's K-20 Education Data Warehouse and the National Center for Education Statistics for providing the data. Any views expressed in this paper are solely my own.
Received August 2007; accepted April 2008.
Table 1. Median Survival Times at First Placement School by Distribution of School Characteristics and Classroom Characteristics School- Teacher- Median Level Mean Specific Mean Number of Survival Math Score Math Score Subjects Time Lowest quartile Lowest quartile 4385 4 Lowest quartile 2nd quartile 3578 4 Lowest quartile 3rd quartile 1469 4 Lowest quartile Highest quartile 548 5 Highest quartile Lowest quartile 942 4 Highest quartile 2nd quartile 1299 5 Highest quartile 3rd quartile 2553 5 Highest quartile Highest quartile 4436 7 School- Lowest 95% Highest 95% Level Mean Confidence Confidence Math Score Interval Interval Lowest quartile 3 4 Lowest quartile 4 4 Lowest quartile 4 5 Lowest quartile 4 5 Highest quartile 3 5 Highest quartile 4 5 Highest quartile 4 7 Highest quartile 7 NA (a) School- Teacher- Level Mean Specific Mean Median Discipline Discipline Number of Survival Incidents Incidents Per Subjects Time Per Student Student Lowest quartile Lowest quartile 8523 4 Lowest quartile 2nd quartile 4241 4 Lowest quartile and quartile 522 4 Lowest quartile Highest quartile 83 2 Highest quartile Lowest quartile 193 3 Highest quartile 2nd quartile 513 4 Highest quartile 3rd quartile 3758 4 Highest quartile Highest quartile 8605 3 School- Level Mean Lowest 95% Highest 95% Discipline Confidence Confidence Incidents Interval Interval Per Student Lowest quartile 4 5 Lowest quartile 4 5 Lowest quartile 3 4 Lowest quartile 2 NA Highest quartile 2 4 Highest quartile 3 NA Highest quartile 4 4 Highest quartile 3 4 (a) NA: not applicable. Table 2. Comparison of Various Opportunity Wage Measurements within the Teaching Occupation with Other Comparable Professions (a) Standard Variables Mean Deviation District-level salaries in other competing districts adjusting for individual- specific degree 33.58408 1.573397 District-level salaries in other competing districts 35.86756 0.7139261 County-level alternative wages for former teachers in other occupations 28.96639 4.7739 County-level alternative wages for all occupations 30.11255 3.72079 District-level salaries in other districts (Gritz and Theobald 1996) 36.5806 0.3486289 Variables Minimum Maximum District-level salaries in other competing districts adjusting for individual- specific degree 30.45996 43.53058 District-level salaries in other competing districts 32.85959 39.33326 County-level alternative wages for former teachers in other occupations 7.783797 42.76956 County-level alternative wages for all occupations 19.78664 40.2448 District-level salaries in other districts (Gritz and Theobald 1996) 35.26492 37.73061 (a) All opportunity wages are measured in terms of thousands of constant 1997 dollars based on statewide population-adjusted average costs of living. Table 3. Multinomial Logit Hazard Estimates (in Odds Ratios) of the Determinants of the Probability That Public School Teachers Exit Teaching, Move to a New School District, or Move within the District with District Fixed-Effects (a) Model 1 Intra-District Move Inter-District Move Teacher holds advanced 0.9607 [0.0686] 1.6348 *** [0.1682] degree Teacher salaries 1.0000 [0.0021] 0.9923 ** [0.0038] (adjust for COLI and inflation) School-level mean math 0.9982 * [0.0010] 0.9997 [0.0018] score School-level mean 0.9941 [0.0355] 1.1091 * [0.0620] discipline incidents per student School-level percent 1.7038 *** [0.2595] 2.2559 *** [0.6276] black students School-level percent 0.7614 [0.1483] 0.8179 [0.2816] Hispanic students School-level percent 1.2120 [0.1632] 1.5275 * [0.3660] free-lunch students Black teacher x 0.5340 *** [0.0995] 0.2538 *** [0.0910] school-level percent black students Hispanic teacher x 0.7694 [0.2117] 0.1707 *** [0.0990] school-level percent Hispanic students Black teacher x 0.7848 [0.2221] 0.9973 [0.4793] school-level percent Hispanic students Hispanic teacher x 1.1430 [0.2767] 0.6274 [0.2801] school-level percent black students Teacher-year 47,344 47,344 observations Model 1 Exit Florida Public School Teacher holds advanced 1.0913 [0.0820] degree Teacher salaries 0.9790 *** [0.0017] (adjust for COLI and inflation) School-level mean math 1.0011 [0.0010] score School-level mean 1.0227 [0.0332] discipline incidents per student School-level percent 1.4537 ** [0.2141] black students School-level percent 0.8566 [0.1552] Hispanic students School-level percent 1.0449 [0.1340] free-lunch students Black teacher x 0.7118 * [0.1238] school-level percent black students Hispanic teacher x 0.9447 [0.2318] school-level percent Hispanic students Black teacher x 0.6325 * [0.1529] school-level percent Hispanic students Hispanic teacher x 0.9224 [0.2190] school-level percent black students Teacher-year 47,344 observations (a) Salaries are measured in terms of thousands of constant 1997 dollars based on statewide population-adjusted average costs of living. Other excluded variables include the following parameters: teacher age, age squared, female, female and age interaction term, teacher race, professional certification, reading certification, middle school math certification, high school math certification, indicator variables for special education teachers, middle school education teachers, high school teachers, English teachers, math or science teachers, self-contained class teachers, social studies teachers, indicator variable for regular and full-time teachers, the number of working days, urbanicity of the school (seven categories: large city, mid-size city, urban fringe of a large city, urban fringe of a mid-size city, large town, small town, rural inside of a Metropolitan Core Based Statistical Area (CBSA), and rural outside of a CBSA), and dummy variables indicating cohort year and school district dummy variables. *** = p < 0.01; ** = p < 0.05; * = p < 0.10. Table 4. Multinomial Logit Hazard Estimates (in Odds Ratios) of the Determinants of the Probability That Public School Teachers Exit Teaching, Move to a New School District, or Move within the District with Classroom, School, and District-Level Covariates (a) Model 2 Intra-District Move Inter-District Move Teacher holds advanced 0.9643 [0.2525] 0.4795 * [0.1997] degree Teacher salaries 0.9970 [0.0024] 0.9946 [0.0042] (adjust for COLI and inflation) Teacher-specific mean 0.9989 [0.0030] 1.0045 [0.0051] class size Teacher-specific mean 0.9986 ** [0.0007] 1.0023 * [0.0012] math score Teacher-specific mean 1.0766 ** [0.0343] 1.1321 *** [0.0537] discipline incidents per student Teacher-specific mean 1.2437 [0.3075] 1.2832 [0.5723] percent black students Teacher-specific mean 0.9586 [0.2231] 1.2090 [0.5098] percent Hispanic students Teacher-specific mean 1.1520 [0.2348] 0.8782 [0.3156] percent free-lunch students Black teacher x 0.6728 [0.3574] 1.0739 [1.0191] teacher-specific mean percent black students Hispanic teacher X 0.7653 [0.4491] 0.4726 [0.4663] teacher-specific mean percent Hispanic students Black teacher x 0.5849 [0.4167] 1.9617 [2.7184] teacher-specific mean percent Hispanic students Hispanic teacher x 0.5320 [0.3508] 0.0365 ** [0.0534] teacher-specific mean percent black students School-level mean math 0.9981 [0.0016] 1.0011 [0.0028] score School-level mean 0.9196 [0.0543] 0.9417 [0.0968] discipline incidents per student School-level percent 1.5132 [0.4832] 2.4285 [1.4578] black students School-level percent 1.0461 [0.3457] 0.7889 [0.4959] Hispanic students School-level percent 0.6596 [0.1755] 1.9835 [0.9909] free-lunch students Black teacher x 1.1506 [0.6371] 0.3166 [0.3227] school-level percent black students Hispanic teacher x 0.7650 [0.4937] 0.1603 [0.1990] school-level percent Hispanic students Black teacher x 1.2564 [0.9280] 0.4288 [0.6369] school-level percent Hispanic students Hispanic teacher x 2.0703 [1.3841] 6.0556 [9.4550] school-level percent black students District-level mean 0.9907 ** [0.0043] 0.9860 * [0.0072] math score District-level mean 1.0774 [0.2405] 1.4368 [0.4881] discipline incidents per student District-level percent 0.1440 *** [0.0910] 0.5050 [0.4831] black students District-level percent 0.0876 *** [0.0549] 0.3751 [0.3874] Hispanic students District-level percent 2.1176 * [0.9209] 0.4717 [0.3037] free-lunch students County unemployment 1.0468 ** [0.0209] 1.0605 * [0.0342] rate District-level math 0.9355 *** [0.0091] 0.9260 *** [0.0134] score in other districts District-level mean 0.4326 * [0.1978] 0.4462 [0.3020] discipline incidents per student in other districts District-level percent 0.0055*** [0.0046] 1.4389 [1.8835] black students in other districts District-level percent 0.1712 ** [0.1307] 0.0040 *** [0.0049] Hispanic students in other districts District-level percent 0.0700 *** [0.0702] 1.8531 [3.0759] free-lunch students in other districts Within-district 0.9992 [0.0011] 0.9972 * [0.0015] relative math score Within-district mean 0.8584 * [0.0673] 0.9295 [0.1244] discipline incidents per student Within-district percent 0.5650 [0.2412] 0.6155 [0.4624] black students Within-district percent 2.1544 [1.0765] 1.8571 [1.7253] Hispanic students Within-district percent 2.1277 *** [0.6103] 1.5975 [0.7938] free-lunch students District-level salaries 1.0021 [0.0414] 1.2057 *** [0.0786] in other districts County-level 1.0900 *** [0.0122] 1.0452 *** [0.0170] alternative wages for former teachers in other occupations Observations 31,129 31,129 Model 2 Exit Florida Public School Teacher holds advanced 0.5909 ** [0.1530] degree Teacher salaries 0.9833 *** [0.0020] (adjust for COLI and inflation) Teacher-specific mean 1.0010 [0.0028] class size Teacher-specific mean 0.9999 [0.0007] math score Teacher-specific mean 1.0843 *** [0.0338] discipline incidents per student Teacher-specific mean 1.2796 [0.3286] percent black students Teacher-specific mean 0.9617 [0.2608] percent Hispanic students Teacher-specific mean 0.8423 [0.1693] percent free-lunch students Black teacher x 0.4370 * [0.2174] teacher-specific mean percent black students Hispanic teacher X 1.2116 [0.7110] teacher-specific mean percent Hispanic students Black teacher x 1.4552 [0.8840] teacher-specific mean percent Hispanic students Hispanic teacher x 0.5025 [0.3479] teacher-specific mean percent black students School-level mean math 1.0010 [0.0015] score School-level mean 0.9559 [0.0506] discipline incidents per student School-level percent 1.1314 [0.3634] black students School-level percent 0.7171 [0.2619] Hispanic students School-level percent 1.5724 * [0.4079] free-lunch students Black teacher x 1.5999 [0.8135] school-level percent black students Hispanic teacher x 0.6474 [0.4038] school-level percent Hispanic students Black teacher x 0.3693 [0.2381] school-level percent Hispanic students Hispanic teacher x 1.9597 [1.3583] school-level percent black students District-level mean 0.9830 *** [0.0041] math score District-level mean 1.2353 [0.2709] discipline incidents per student District-level percent 0.2840 ** [0.1547] black students District-level percent 0.1018 *** [0.0614] Hispanic students District-level percent 1.0170 [0.3972] free-lunch students County unemployment 1.0458 ** [0.0205] rate District-level math 0.9206 *** [0.0089] score in other districts District-level mean 0.1737 *** [0.0773] discipline incidents per student in other districts District-level percent 0.3343 [0.2631] black students in other districts District-level percent 0.1546 ** [0.1133] Hispanic students in other districts District-level percent 0.0146 *** [0.0136] free-lunch students in other districts Within-district 0.9949 *** [0.0010] relative math score Within-district mean 0.9383 [0.0652] discipline incidents per student Within-district percent 0.7772 [0.3219] black students Within-district percent 2.4509 * [1.2256] Hispanic students Within-district percent 0.8025 [0.2253] free-lunch students District-level salaries 1.1291 *** [0.0466] in other districts County-level 1.0982 *** [0.0112] alternative wages for former teachers in other occupations Observations 31,129 (a) Salaries are measured in terms of thousands of constant 1997 dollars based on statewide population-adjusted average costs of living. Other excluded variables include the following parameters: teacher age, age squared, female, female and age interaction term, teacher race, professional certification, reading certification, middle school math certification, high school math certifcation, indicator variables for special education teachers, middle school education teachers, high school teachers, English teachers, math or science teachers, self-contained class teachers, social studies teachers, indicator variable for regular and full-time teachers, the number of working days, urbanicity of the school (seven categories: large city, mid-size city, urban fringe of a large city, urban fringe of a mid-size city, large town, small town, rural inside of a Metropolitan Core Based Statistical Area (CBSA), and rural outside of a CBSA), and dummy variables indicating the cohort year. * p < 0.10; ** p < 0.05; *** p < 0.01. Table 5. Probabilities of Retention, Moving, and Quitting for Teachers in "Hard-to-Staff Schools Based on Model 2 in Table 4 (a) Average Schools Percent Percent Remaining Intra-District Teachers' Own Salaries in School Move 25.79596 80.63 6.70 28.95632 81.15 6.68 30.10479 81.34 6.67 33.58252 81.89 6.64 36.58128 82.34 6.62 Teacher-specific mean Percent remaining Percent discipline incidents in School intra-district per student Move 0.0497 81.48 6.44 0.2143 81.27 6.51 0.3789 81.06 6.57 0.5435 80.85 6.63 0.7081 80.63 6.70 Teacher-specific mean Percent remaining Percent math score in School intra-district Move 282.6492 80.63 6.70 331.218 80.83 6.27 379.7868 80.98 5.87 428.3556 81.07 5.49 476.9244 81.12 5.13 Average Schools Percent Inter-District Percent Exiting Florida Teachers' Own Salaries Move Public School System 25.79596 2.21 10.47 28.95632 2.18 9.99 30.10479 2.17 9.82 33.58252 2.15 9.32 36.58128 2.13 8.91 Teacher-specific mean Percent Percent exiting discipline incidents inter-district Florida public per student Move school system 0.0497 2.05 10.02 0.2143 2.09 10.13 0.3789 2.13 10.24 0.5435 2.17 10.35 0.7081 2.21 10.46 Teacher-specific mean Percent Percent exiting math score inter-district Florida public Move school system 282.6492 2.21 10.46 331.218 2.47 10.43 379.7868 2.76 10.40 428.3556 3.09 10.35 476.9244 3.45 10.30 Average Schools Teachers' own salaries Percent remaining Percent in School intra-district Move 25.79596 82.12 6.83 28.95632 82.60 6.81 30.10479 82.77 6.80 33.58252 83.27 6.77 36.58128 83.69 6.74 Teacher-specific mean Percent remaining Percent discipline incidents in School intra-district per student Move 0.0497 82.90 6.57 0.2143 82.71 6.63 0.3789 82.51 6.70 0.5435 82.32 6.76 0.7081 82.12 6.83 Teacher-specific mean Percent remaining Percent math score in School intra-district Move 282.6492 82.12 6.83 331.218 82.38 6.40 379.7868 82.59 5.99 428.3556 82.77 5.61 476.9244 82.90 5.25 Average Schools Teachers' own salaries Percent Percent exiting inter-district Florida public Move school system 25.79596 1.61 9.44 28.95632 1.60 9.00 30.10479 1.59 8.85 33.58252 1.57 8.39 36.58128 1.55 8.02 Teacher-specific mean Percent Percent exiting discipline incidents inter-district Florida public per student Move school system 0.0497 1.50 9.03 0.2143 1.53 9.13 0.3789 1.56 9.23 0.5435 1.59 9.33 0.7081 1.61 9.44 Teacher-specific mean Percent Percent exiting math score inter-district Florida public Move school system 282.6492 1.61 9.44 331.218 1.81 9.41 379.7868 2.02 9.39 428.3556 2.27 9.36 476.9244 2.53 9.32 (a) The policy simulation is for a 32-year-old, white, Female teacher with a bachelor's degree, professionally certified, teaching in a contained classroom in an elementary school located at the urban fringe of a mid-size city with two years of teaching experience with mean student characteristics. Simulation for "hard-to-staff" schools is For teachers teaching in a school with 47% black students and 69% poor students, while simulation For average schools is for teachers teaching in a school with 26% black students and 48% poor students. Table 6. Multinomial Logit Hazard Estimates (in Odds Ratios) of the Determinants of the Probability That Public School Teachers Exit Teaching, Move to a New School District, or Move within the District with Classroom, School, and District-Level Covariates Using the District-Level Relative Wage Measurement in Gritz and Theobald (1996) Intra-District Move Teacher holds advanced degree 0.9766 [0.0838] Teacher salaries (adjust for 0.9981 [0.0023] COLI and inflation) District-level salaries in other 2.4030 *** [0.2541] districts (Gritz and Theobald 1996) County-level alternative wages for 1.0831 *** [0.0119] teachers in other occupations Teacher year observations 31,129 Inter-District Move Teacher holds advanced degree 1.4877 *** [0.1887] Teacher salaries (adjust for 0.996 [0.0042] COLI and inflation) District-level salaries in other 2.8259 *** [0.5231] districts (Gritz and Theobald 1996) County-level alternative wages for 1.0442 *** [0.0167] teachers in other occupations Teacher year observations 31,129 Exit Florida Public School Teacher holds advanced degree 1.2096 ** [0.1064] Teacher salaries (adjust for 0.9846 *** [0.0020] COLI and inflation) District-level salaries in other 2.4473 *** [0.2715] districts (Gritz and Theobald 1996) County-level alternative wages for 1.0958 *** [0.0109] teachers in other occupations Teacher year observations 31,129 Same as Table 4. Same model specification otherwise. ** p < 0.05 *** p < 0.01. Table 7. Multinomial Logit Hazard Estimates (in Odds Ratios) of the Determinants of the Probability That Public School Teachers Exit Teaching, Move to a New School District, or Move within the District with Classroom, School, and District-Level Covariates Using the County-Level Relative Wage Measurement for All Occupations Intra-District Move Teacher holds advanced degree 0.6667 [0.1733] Teacher salaries (adjust for 0.9955 * [0.0024] COLI and inflation) District-level salaries in other 1.0716 * [0.0437] districts County-level alternative wages for 1.0988 *** [0.0123] all occupations Teacher year observations 31,129 Inter-District Move Teacher holds advanced degree 0.4363 ** [0.1834] Teacher salaries (adjust for 0.9946 [0.0043] COLI and inflation) District-level salaries in other 1.2271 *** [0.0807] districts County-level alternative wages for 1.007 [0.0188] all occupations Teacher year observations 31,129 Exit Florida Public School Teacher holds advanced degree 0.4059 *** [0.1053] Teacher salaries (adjust for 0.9816 *** [0.0020] COLI and inflation) District-level salaries in other 1.2106 *** [0.0496] districts County-level alternative wages for 1.1012 *** [0.0119] all occupations Teacher year observations 31.129 Same as Table 4. Same model specification otherwise. * p <0.10 ** p < 0.05 *** p < 0.01.