Opportunity wages, classroom characteristics, and teacher mobility.

• Author: Feng, Li

1. Introduction

   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...