## Abstract

Using unique administrative data from North Carolina that allow us to separate classroom teacher turnover during the school year from end-of-year turnover, we find students who lose their teacher during the school year have significantly lower test score gains (on average −7.5 percent of a standard deviation unit) than those students whose teachers stay. Moreover, the turnover of other teachers during the year lowers achievement gains, whereas end-of-year teacher turnover appears to have little effect on achievement. The harmful effects of within-year turnover cannot be explained by other extraneous shocks or the quality of departing teachers. Teachers who depart from December through April have the most harmful effects on achievement, although these vary somewhat by level of schooling and subject.

## 1.  Introduction

Researchers have long identified systematic patterns in the teacher labor market whereby teachers leave schools with high concentrations of traditionally underserved racial/ethnic groups and low-income students at higher rates than other schools (Lankford, Loeb, and Wyckoff 2002; Hanushek, Kain, and Rivkin 2004a). The result of this pattern is that more qualified and effective teachers are less likely to teach the students most in need (Goldhaber, Lavery, and Theobald 2015; Redding and Henry 2018). Summarizing the relationship between teacher effectiveness and teacher mobility, Boyd and colleagues (2008, p. 2) write: “the more effective transfers tend to move to higher achieving schools, while less effective transfers stay in lower-performing schools, likely exacerbating the differences across students in the opportunities they have to learn.” In addition to exacerbating the inequitable distribution of teachers across schools, teacher turnover negatively impacts student learning (Ronfeldt, Loeb, and Wyckoff 2013).

Studies from New York City and Texas provide the first credible estimates of the effect of teacher turnover on student achievement. Ronfeldt, Loeb, and Wyckoff (2013) find that fourth- and fifth-grade students in a grade where all teachers turned over the previous year scored between 8.2 and 10.2 percent of a standard deviation lower in math and 4.9 to 6.0 percent of a standard deviation lower in English language arts (ELA) compared with a grade in which all teachers return the next year. Hanushek, Rivkin, and Schiman (2016) find results smaller in magnitude and less consistent across model specification, ranging from 2.2 (and not significant) to 7 percent of a standard deviation in math, with no results reported for ELA. Even with evidence that turnover affects student achievement to a nontrivial extent, both studies may attenuate the true effect of turnover for two reasons. First, their measure of teacher turnover is somewhat distal to the timing of student testing at the end of the academic year. In New York City, for example, turnover is measured as the proportion of teachers to have turned over between October of the previous school year and October of the current year. Second, their identification strategy leverages idiosyncratic variation in turnover between grades in the same year and school and, as an alternative, between years within the same grade and school.

Using unique administrative data from North Carolina that allow us to measure monthly individual teacher turnover, we are able to distinguish the effect of teacher turnover that occurs before the school year begins from turnover during the school year. In addition, we are able to estimate the direct effect of students losing their classroom teacher during the school year and how this effect compares with overall grade-level instability, either before or during the current school year. Whereas most research on teacher turnover has focused on annual measures of turnover, elsewhere we show that roughly a quarter of all teacher turnover takes place within the school year, with an average of 4.6 percent of teachers turning over during each school year (Redding and Henry 2018). As losing a teacher midyear is likely quite detrimental to students’ learning, it is unquestionably important to quantify its effect and understand how the direct effect of losing a classroom teacher compares with the turnover that occurs between school years.

The goal of this study is to estimate the effect that within-year teacher turnover has on student achievement, including how this relationship may change over the course of the school year. We also examine the extent to which the turnover that occurs during the school year differentially affects student achievement from the turnover that occurs at the end of the year. We address three specific research questions:

1. What is the average effect of teacher turnover on student achievement?

2. Does grade-level turnover affect student achievement more or less than when it occurs within versus the end of the school year?

3. What is the effect of within-year classroom teacher turnover on student achievement? Does the timing of teacher turnover cause the effect to vary?

In the next section, we describe three distinct mechanisms by which teacher turnover may harm student achievement—(1) classroom disruption, (2) staff instability, and (3) differences in quality of replacement and replaced teacher—and how these effects may vary over the course of the school year and by school level. We then describe the data and measures used for this study, as well as the empirical strategy used to estimate the effect of teacher turnover. In our Results section, we begin by distinguishing the effect of the teacher turnover that occurs during the school year from when it occurs at the end of the year. With evidence that the negative effect of teacher turnover is driven by the turnover that occurs during the school year, we estimate a series of models to better understand how much the effect of within-year turnover is influenced by the quality of the departing teacher and how it differs for student subgroups, as well as the month in which it occurs. We conclude with implications for policy.

## 2.  Teacher Turnover and Student Achievement

### Classroom Disruption

We define classroom disruption as the interruption to students’ learning that results from their teacher turning over during the school year. The classroom disruption caused by within-year turnover is driven by two main factors. First, the midyear departure of a teacher disrupts student–teacher relationships and the continuity of a child's learning experience. In a review of the literature on the impact of instability on child development, Sandstrom and Huerta (2013, p. 5) write, “Children thrive in stable and nurturing environments where they have a routine and know what to expect. Although some change in children's lives is normal and anticipated, sudden and dramatic disruptions can be extremely stressful and affect children's feeling of security.” Within-year teacher turnover can be a destabilizing experience for a child in that it separates the child from a teacher with whom he has built a relationship and who may understand how to tailor instruction to meet his individual needs.

Second, when a teacher leaves midyear, he or she also severs the social capital that has accumulated between the child and the child's parents/guardians, weakening the child's academic support system, which may increase the impact on students with fewer supports. The literature on student mobility highlights how the loss of social capital associated with nonstructural mobility results in an adjustment period where students underperform in school and have a greater risk of dropping out (Rumberger and Larson 1998; Pribesh and Downey 1999; Swanson and Schneider 1999; Hanushek, Kain, and Rivkin 2004b; Welsh 2016). That being said, in the case of students moving schools midyear, the adverse effects are attributable to switching teachers as well as changes in peers and schools.

When a teacher turns over at any time throughout the school year, it is likely to be consequential for the disruption it causes students. We expect the effects of within-year classroom teacher turnover will be larger in the spring due to the proximity to the testing period and disruption of longer relationships. Research on teacher absences suggests that students perform worse in school when assigned to a teacher who is absent more frequently (Miller, Murnane, and Willett 2008; Gershenson 2016), with the absences occurring in the spring being more detrimental than those occurring in the fall, given their proximity to annual testing (Clotfelter, Ladd, and Vigdor 2009).

When teachers leave school early in the year, they would likely not have developed an in-depth relationship with their students and the replacement teacher would still have the majority of the school year to develop such a connection and reestablish instructional routines. However, it is also possible the disruption caused by turnover early in the school year may extend for a period of days or even weeks if a permanent replacement teacher is not immediately available and assigning substitute teachers or doubling up classes is necessary (Papay and Kraft 2016).

### Staff Instability

The second mechanism by which teacher turnover may impact student achievement is staff instability. The instability caused by teacher turnover can inhibit the formation of a cohesive organizational culture that is capable of implementing a coherent instructional program (Bryk et al. 2010; Holme and Rangel 2012). When teachers leave a school, they take with them institutional knowledge about their students, the curriculum, and school programs and policies (Simon and Johnson 2015). Less shared knowledge among the remaining teachers weakens their ability to form a cohesive instructional culture. Further, stability of the teaching staff is vital for the development of staff collegiality and a culture of trust in the school (Little 1982; Bryk and Schneider 2002). The social capital that results from the network of interrelationships forms the basis of professional relationships aimed at improving instruction (Louis and Marks 1998). Recent research on the school conditions needed for teacher instructional improvement affirm that working in a school with a strong culture of collaboration and high-quality peers can affect student achievement (Jackson and Bruegmann 2009; Kraft and Papay 2014; Ronfeldt et al. 2015; Papay et al. 2016).

The formation of collaborative relationships that foster instructional improvements would be undermined by both within- and end-of-year teacher turnover, although turnover is likely most detrimental to school operations when it occurs during the school year. Immediately following a teacher's departure, class sizes may bulge before the teacher is replaced and long- or short-term substitutes may staff the recently vacated classroom. When a replacement is hired, teachers may be assigned to help orient and mentor the new teacher, reducing the time they can dedicate to their own students (Guin 2004). In schools where teachers leave midyear, administrators must dedicate time to re-staff classrooms throughout the year that could be used for improving teacher instruction or working conditions.

### Turnover and Changes in Teacher Quality

Finally, differences in the quality of the original and replacement teacher are another path through which teacher turnover can affect student achievement. Adverse effects from this mechanism are triggered when a less-effective teacher replaces the departing teacher, resulting in lower quality of instruction. Although research has generally shown that lower-performing teachers are most likely to exit teaching (Hanushek, Kain, and Rivkin 2004a; Boyd et al. 2008; Goldhaber, Gross, and Player 2011), evidence of the extent to which these exits lead to improvements in the composition of the teacher workforce is somewhat mixed. Results from Hanushek, Rivkin, and Schiman (2016) suggest that, even though less-effective teachers are most likely to turn over (which would imply compositional improvements in the teacher workforce), replacement teachers are even less effective. Teachers new to the school or assigned to a different grade are less effective than teachers who stayed in their same assignment within the school, with estimates ranging from −0.053 to −0.068 of a standard deviation.

In contrast, Adnot et al. (2017) show, in the context of the Washington, DC, IMPACT teacher evaluation and performance incentive system, that replacement teachers improved student achievement by an average 8 percent of a standard deviation in math and 5 percent of a standard deviation in reading. However, it remains to be seen the extent to which these findings generalize to contexts without a high-stakes evaluation system that includes significant financial incentives and with a smaller pool of high-quality replacement teachers, particularly in rural districts.

We expect that there is also an important temporal element to these dynamics of replacement teacher quality. When teacher turnover occurs during the school year, administrators choose replacement teachers from a diminished applicant pool composed mainly of teachers not previously hired to work elsewhere, which is likely to yield less-effective replacements. In their study of teachers hired late in the school year, Papay and Kraft (2016) find evidence of this “labor market effect” in mathematics, whereby math teachers hired after the start of the school year performed 0.02 standard deviation units worse than teachers employed by the beginning of the school year. The diminished applicant pool could also result in assignment to a long-term substitute teacher who fills the vacancy indefinitely, likely resulting in diminished instructional rigor (Miller, Murnane, and Willett 2008). That being said, certain exits, such as those for planned health leave of absence or retirement, may be less disruptive and also result in less drastic changes in the quality of the original and replacement teacher. It could also be that, even with a diminished labor pool of replacement teachers, the teachers who leave midyear may perform so poorly with their students that their departure could be beneficial, regardless of replacement teacher quality.

### School Organization and the Effects of Teacher Turnover

The effects of teacher turnover may differ by school level. In elementary schools, teachers often spend all or at least most of the day with a classroom of students. Therefore, the direct effect from classroom disruption may be greater than the effect in middle schools, where students spend time with several classroom teachers each day. Further, the negative effects that arise from staff instability may be particularly detrimental when concentrated in a particular grade. Elementary teachers often meet in grade-level teams to coordinate lesson planning, align their pacing, discuss strategies to engage students, and receive collegial encouragement (Louis, Marks, and Kruse 1996). Just as schools with high levels of teacher turnover struggle to form a cohesive organizational culture, the challenges of maintaining instructional continuity in elementary schools may be more difficult when turnover occurs at the grade level.

In middle schools, students’ instruction in other classes is not disrupted when one teacher leaves, which may reduce the harmful consequences of classroom disruption. We also expect the teacher instability mechanism to operate somewhat differently. In particular, the basis for teacher collaboration may be either subject-specific or grade-level teams, leaving a more ambiguous relationship. Middle school teachers also tend to report lower-quality collaboration than elementary school teachers, including collaboration focused on instructional strategies and students (Ronfeldt et al. 2015). If teacher turnover is more harmful to collaboration in elementary schools, we would expect the negative effects that arise from staff instability to be weaker in middle schools than elementary schools.

## 3.  Data and Measures

We use administrative data from the state of North Carolina that link students, teachers, and test scores. We draw on a six-year panel of data from the 2008–09 to 2013–14 school years.1 The analytic sample is limited to fourth- through eighth-grade students who took end-of-grade tests in ELA and mathematics. Third grade students are not included in the analysis in order to estimate test score gains. In elementary school, our sample includes 2,496,694 student-year observations for ELA and 2,052,965 observations in math. In middle school, our sample includes 1,623,216 student-year observations for ELA and 1,582,019 observations in math.

Four independent variables are used in this study to measure the turnover that occurs at different times (i.e., within-year versus end-of-year). To create these different turnover variables, we draw on monthly teacher pay files, which give detailed information on the school in which teachers are employed in each month. End-of-year grade-level turnover is the fraction of teachers who were employed at a school at the end of the school year t − 1 and no longer employed at that school at the start of the school year in year t. For instance, if two of the four teachers in fourth grade turned over during the summer, the end-of-year grade-level turnover would be 50 percent. Within-year grade-level turnover is measured as the fraction of teachers to turnover from a school during the current school year. If these two teachers were replaced but one of the four teachers in fourth grade turned over during the school year, the within-year grade-level turnover would be 25 percent. In supplementary analysis, we estimate the effect of total grade-level turnover, which includes end-of-year and within-year grade-level turnover.2

Within-year grade-level turnover can be further separated for those students who lost their teacher midyear. We term this final type of turnover within-year classroom teacher turnover, which is measured as a variable for each specific student whose classroom teacher left the school during the year. In some analyses, we differentiate this measure based on the month when a teacher left her current school. We assume that midyear exit—transferring to other schools, temporarily leaving the school, or leaving the profession—would have similar effects on student learning in the schools the teachers leave and focus our analysis on teacher turnover without regard to the exiting teacher's destination.3

In some models, we include a rich set of covariates for student demographic characteristics and school characteristics. We report sample means in table 1. Time-varying student variables include an individual student's prior test scores in reading and mathematics, gifted status, disability status, whether the child is currently or was previously classified as limited English proficient, mobility (within-year and between-year), and indicators for whether the child was overage or underage for the grade. Time-invariant covariates include student gender and race/ethnicity (black, Hispanic, Asian, American Indian, and multiracial).

Table 1.
Descriptive Statistics
 Student and School Characteristics Mean Black 0.26 Hispanic 0.13 Other race/ethnicity 0.21 Male 0.50 Eligible for free lunch 0.44 Eligible for reduced price lunch 0.07 Gifted 0.17 Disability 0.11 Currently limited English proficient 0.06 Previously limited English proficient 0.04 Between year mobility 0.08 Within year mobility 0.06 Underage for grade 0.01 Overage for grade 0.21 Prior reading test (std) −0.00 Prior math test (std) 0.01 Percentage Black students 26.01 Percentage Hispanic students 13.13 Teacher salary supplement 32.74 Total per-pupil expenditures 84.64 City 32.41 Rural 81.32 Town 0.30 Student enrollment (100s) 6.88 Short-term suspension rate 54.82 Violent acts per 1,000 students 17.92 Teacher characteristics Total grade-level turnovera 0.16 End-of-year grade-level turnover 0.15 Within-year grade-level turnover 0.03 Female 0.87 Black 0.14 Hispanic 0.01 Other race 0.03 In-state, traditional preparation 0.49 Alternate entry 0.12 Teach For America 0.01 Out-of-state prepared 0.34 Other entry pathway 0.04 Years teaching experience 10.33 Average teacher test 0.14 Median principal evaluation score (lagged) 3.69
 Student and School Characteristics Mean Black 0.26 Hispanic 0.13 Other race/ethnicity 0.21 Male 0.50 Eligible for free lunch 0.44 Eligible for reduced price lunch 0.07 Gifted 0.17 Disability 0.11 Currently limited English proficient 0.06 Previously limited English proficient 0.04 Between year mobility 0.08 Within year mobility 0.06 Underage for grade 0.01 Overage for grade 0.21 Prior reading test (std) −0.00 Prior math test (std) 0.01 Percentage Black students 26.01 Percentage Hispanic students 13.13 Teacher salary supplement 32.74 Total per-pupil expenditures 84.64 City 32.41 Rural 81.32 Town 0.30 Student enrollment (100s) 6.88 Short-term suspension rate 54.82 Violent acts per 1,000 students 17.92 Teacher characteristics Total grade-level turnovera 0.16 End-of-year grade-level turnover 0.15 Within-year grade-level turnover 0.03 Female 0.87 Black 0.14 Hispanic 0.01 Other race 0.03 In-state, traditional preparation 0.49 Alternate entry 0.12 Teach For America 0.01 Out-of-state prepared 0.34 Other entry pathway 0.04 Years teaching experience 10.33 Average teacher test 0.14 Median principal evaluation score (lagged) 3.69

Notes: Student and school characteristics: 1,500,071 observations; Teacher characteristics: 48,835 observations. Average teacher test observations = 47,437. Median principal evaluation score (lagged) observations = 37,262.

aUnduplicated count of turnover, which includes one exit for a teacher who moves multiple times or moves then leaves the database.

Some models include the following time-varying, school-level covariates: average student enrollment, total per-pupil expenditures, the district's teacher salary supplement, urbanicity (with suburban schools as the reference group), the percentage of students within a school by race/ethnicity, and the percent of students receiving free or reduced-price lunch. Measures of school climate include the reported violence rates per 1,000 students, and the short-term suspension per 100 students.

Also in table 1, we include means for several teacher characteristics. For our sample of teachers, we estimate an unduplicated count of 16 percent of teacher turnover each year. Whereas 4.64 percent of teachers in North Carolina turn over during the school year, the study sample, which is limited to elementary and middle grade teachers, turns over at approximately 3 percent annually. Because a small percentage of teachers move multiple times or move and leave, the unduplicated count is less than the sum of within-year and end-of-year turnover.

## 4.  Empirical Strategy

We begin with a series of models that estimate the impacts that within- and end-of-year grade-level turnover have on student achievement. The end-of-year turnover measure combines the staff instability and replacement mechanisms, averaged across all students within the grade. The within-year turnover measure captures both of these mechanisms, as well as the classroom disruption mechanism. To estimate the effect of grade-level turnover, we implement a school-by-year fixed effect specification. Using this equation, we are able to exploit idiosyncratic variation in turnover in different grades and remove potentially confounding shocks, such as the turnover of a principal, which may affect both teacher turnover and student achievement gains. An equation for the school-by-year model can be written as:
$Yijgst=β0+β1WithinTurnovergjst+β2EOYTurnovergjst+β3Yit-n+β4Xijgst+β5Wst+φgs+uijgst,$
(1)
where $Yijgst$ is the test score for student i in classroom j in grade g in school s at time t; $WithinTurnovergjst$ is the proportion of within-year grade-level teacher turnover; $EOYTurnovergjst$ is the proportion of end-of-year grade-level teacher turnover; $Yit-n$ represents the prior test scores for student i; $Xijgst$ represents the set of student covariates; $Wst$ represents a set of time-varying school covariates; $φgs$ is a school-by-year fixed effect; and $uijgst$ is an error term. In this model, as in others described below, standard errors are clustered at the level of analysis.

This school-by-year fixed effect controls for any shock that occurs in a year that affects both teacher turnover and student achievement. A limitation of this model is that it does not account for the bias linked to nonrandom student sorting into schools with higher turnover rates. In particular, these models do not account for sorting of students into high turnover schools based on unobserved student characteristics that may also influence teacher turnover. Estimates could be biased if, for example, students with fewer educational resources at home attended schools in which teachers were more likely to turn over.

To account for the unobserved non-time varying student and school characteristics, we specify a model with student-by-school fixed effects:
$Yijst=β0+β1WithinTurnovergjst+β2EOYTurnovergjst+β3Xijst+β4Wst+δis+γt+uijst,$
(2)
where $Yijst$ is the test score for student i in classroom j in school s at time t; $β1$ and $β2$ estimate the average difference in test performance in a school in which all teachers in the grade turn over within or at the end of the year; $Xijst$ represents the set of time-varying student covariates; $Wst$ represents a set of time-varying school covariates; $δis$ is a student-by-school fixed effect to adjust for time-invariant student and school characteristics; $γt$ is a year fixed effect; and $uijst$ is an error term.
We hypothesize that the negative effects of teacher turnover are likely most detrimental for the students assigned to a teacher who leaves midyear—the classroom disruption hypothesis. Therefore, we leverage our measure of within-year classroom teacher turnover to estimate the effect turnover has on individual students in classrooms of teachers who leave midyear. Within-year classroom teacher turnover is likely correlated with unmeasured determinants of student test performance. In particular, we are concerned with the quality of the departing teacher due to the prior research that indicates lower-performing teachers are more likely to leave. To isolate the plausibly exogenous variation in within-year classroom teacher turnover, we adopt two fixed effects modeling strategies. First, our preferred strategy for estimating the effect of within-year classroom teacher turnover uses teacher fixed effects ($ljt)$, which remove the stable effects of the departing teachers on their students’ achievement from the estimate of the effect of within-year classroom teacher turnover ($Turnoverijst)$. This model can be expressed as:
$Yijgst=β0+β1Turnoverijst+β2WithinTurnovergjst+β3EOYTurnovergjst+β2Yit-n+β3Xijgst+β4Wst+ljt+uijgst,$
(3)
where $β1$ estimates the average difference in student test performance in school years when a teacher turns over during the year compared with years when the teacher remains in her school for the whole year; $β2$ estimates the average difference in test performance in school years when a student is enrolled in a grade in a school with different proportions of teachers turning over within the school year; $β3$ estimates the average difference in test performance in school years when a student is enrolled in a grade in a school with different proportions of teachers turning over at the end of the previous year.

As the teacher fixed effects model can be biased by uncontrolled-for time-varying school factors, any spillover effects from other grade-level turnover would bias these estimates. To address this concern, we retained the measures of end-of-year and within-year grade-level turnover in the model.4 This operationalization allows us to estimate the magnitude of the effect of within-year classroom teacher turnover controlling for the effect of the other turnover that occurs during the school year or over the previous summer. This model is our preferred estimation strategy for the effect of within-year classroom teacher turnover, as these within-teacher estimates account for unobserved but fixed quality of the teacher and the spillover effects of other turnover, which allows us to better isolate the effect of classroom disruption.

As a robustness check, we estimate the student-by-school fixed effect with an indicator for within-year classroom teacher turnover and measures of the proportion of within-year and end-of-year turnover. This model is identified for students who experience two particular turnover conditions within the same school: assignment to a teacher who remains in the school the whole year and, in another year, assignment to a teacher who leaves during the school year. In cases where this model is identified, the student essentially serves as her own comparison group, and her deviations from her average test performance are compared in years with and without a teacher who left midyear while the student remained in the same school. This model has the benefit of removing stable student and school characteristics as potential confounders. Also, it allows us to see how the effects of within-year teacher turnover averaged across all students in the grade (equation 3), divide between students who experience loss of their teacher and other students in their grade. In addition, we reestimate this model with different measures of teacher performance or background characteristics to control for the quality of the exiting teachers. For the experience and average teacher test specifications, this model allows us to retain first-year teachers who are excluded from the teacher fixed effects model.

## 5.  Results

### The Effect of Grade-Level Turnover on Student Achievement

In this section, we present the results from a series of models that estimate the effects of within- and end-of-year teacher turnover on student achievement for elementary and middle school students. Estimates from table 2 indicate that within-year grade-level turnover has a negative effect on ELA achievement in elementary and middle schools.5 In our preferred specification, the school-by-year fixed effect, losing all teachers in a grade during the school year reduces ELA student achievement gains by an average 0.071 standard deviation in the grade experiencing the turnover in elementary schools. The negative effect of within-year grade-level turnover in elementary schools is somewhat larger in mathematics, −0.089 standard deviation. Turnover during the prior summer is consistently smaller in magnitude and, when significant, positive for elementary ELA and mathematics, with estimates ranging from 0.017 to 0.019. However, neither estimate is consistent across the two estimation strategies.

Table 2.
Estimates Comparing the Effect of End-of-Year and Within-Year Grade-Level Turnover
ElementaryMiddle
English Language ArtsMathematicsEnglish Language ArtsMathematics
(1)(2)(3)(4)(5)(6)(7)(8)
Within-year grade-level turnover −0.071*** −0.051*** −0.089*** −0.069*** −0.045* −0.042*** −0.065* −0.106***
(0.018) (0.010) (0.025) (0.010) (0.020) (0.012) (0.030) (0.010)

End-of-year grade-level turnover 0.017* 0.005 0.019 0.019*** 0.008 0.002 −0.008 −0.002
(0.008) (0.004) (0.011) (0.004) (0.007) (0.004) (0.013) (0.004)
School-by-year fixed effects
Year fixed effects
Student-by-school fixed effects
Student controls
School controls
Observations 2,497,549 2,497,549 2,053,616 2,053,616 1,662,623 1,662,623 1,582,700 1,582,700
Unique student observations 867,131 867,131 876,062 876,062 1,013,283 1,013,283 1,017,930 1,017,930
ElementaryMiddle
English Language ArtsMathematicsEnglish Language ArtsMathematics
(1)(2)(3)(4)(5)(6)(7)(8)
Within-year grade-level turnover −0.071*** −0.051*** −0.089*** −0.069*** −0.045* −0.042*** −0.065* −0.106***
(0.018) (0.010) (0.025) (0.010) (0.020) (0.012) (0.030) (0.010)

End-of-year grade-level turnover 0.017* 0.005 0.019 0.019*** 0.008 0.002 −0.008 −0.002
(0.008) (0.004) (0.011) (0.004) (0.007) (0.004) (0.013) (0.004)
School-by-year fixed effects
Year fixed effects
Student-by-school fixed effects
Student controls
School controls
Observations 2,497,549 2,497,549 2,053,616 2,053,616 1,662,623 1,662,623 1,582,700 1,582,700
Unique student observations 867,131 867,131 876,062 876,062 1,013,283 1,013,283 1,017,930 1,017,930

Notes: Models include controls for time-varying student and school characteristics and year fixed effects. Standards errors clustered at either the school-by-year level or student-by-school level in parentheses.

*p < 0.05; ***p < 0.001.

Similar to elementary school, we find middle school within-year grade-level turnover to be more detrimental to math achievement than ELA. For ELA, the effect is −0.045 standard deviation. For math, the effect is −0.065 standard deviation. The results from our preferred specification are consistent with our hypothesis that grade-level teacher turnover would be more detrimental in elementary schools. In middle schools, however, we find no effect of end-of-year grade-level turnover on student achievement.6 Taken as a whole, these results suggest that the classroom disruption caused by within-year teacher turnover is likely a primary driver of the negative effect that teacher turnover has on student achievement. In the next set of analyses, we separate the effect caused by classroom disruption from grade-level teacher instability.

### Within-Year Classroom Teacher Turnover

Across both levels of schools and subjects presented in table 3, we find a consistent, negative effect of within-year classroom teacher turnover with effects from our preferred specification, ranging from approximately −0.05 to −0.11 standard deviation. The effect for within-year classroom teacher turnover is −0.100 standard deviation on elementary math gains with the teacher fixed effects. This coefficient translates to losing roughly 72 instructional days or 40 percent of the 180-day school year (CREDO 2015). The coefficient is almost identical for middle school math. These findings suggest that when math teachers turn over during the school year, it makes a sharp departure from their stable performance level. This specification likely yields a less-biased estimate of the effect of within-year classroom teacher turnover as it adjusts for the stable quality of the departing teachers. Although it is possible this negative effect of within-year classroom teacher turnover is driven by the low quality of the replacement teacher, these results suggest that the effect caused by classroom disruption plays a substantial role in the observed negative effects on student achievement. In the robustness check, the student-by-school fixed effect estimates are smaller than the preferred specification estimates in three of the four school-level and subject combinations but consistently negative and significant. This may raise concerns that the students assigned to classrooms of teachers who are expected to leave during the year may be lower performing, and this sorting produces larger effects in the teacher fixed effect specification.

Table 3.
Estimates of the Effect of Within-Year Classroom Teacher Turnover on Student Achievement
Elementary SchoolMiddle School
ELAMathELAMath
(1)(2)(3)(4)(5)(6)(7)(8)
Within-year classroom teacher −0.045*** −0.042*** −0.100*** −0.048*** −0.049*** −0.014*** −0.106*** −0.073***
turnover (0.010) (0.004) (0.013) (0.004) (0.008) (0.003) (0.015) (0.003)
Within-year grade turnover −0.004 −0.045*** −0.052** −0.052*** −0.042* −0.033* −0.034 −0.072***
(adjusted) (0.013) (0.011) (0.017) (0.010) (0.019) (0.013) (0.025) (0.011)
End-of-year grade turnover −0.009* 0.005 0.004 0.020*** 0.001 0.002 0.007 −0.002
(0.005) (0.004) (0.006) (0.004) (0.006) (0.004) (0.008) (0.004)
Teacher fixed effects
Student-by-school fixed effects
Observations 2,496,694 2,496,694 2,052,965 2,052,965 1,662,321 1,662,321 1,582,019 1,582,019
Unique student observations 867,006 867,006 875,847 875,847 1,013,241 1,013,241 1,017,834 1,017,834
Elementary SchoolMiddle School
ELAMathELAMath
(1)(2)(3)(4)(5)(6)(7)(8)
Within-year classroom teacher −0.045*** −0.042*** −0.100*** −0.048*** −0.049*** −0.014*** −0.106*** −0.073***
turnover (0.010) (0.004) (0.013) (0.004) (0.008) (0.003) (0.015) (0.003)
Within-year grade turnover −0.004 −0.045*** −0.052** −0.052*** −0.042* −0.033* −0.034 −0.072***
(adjusted) (0.013) (0.011) (0.017) (0.010) (0.019) (0.013) (0.025) (0.011)
End-of-year grade turnover −0.009* 0.005 0.004 0.020*** 0.001 0.002 0.007 −0.002
(0.005) (0.004) (0.006) (0.004) (0.006) (0.004) (0.008) (0.004)
Teacher fixed effects
Student-by-school fixed effects
Observations 2,496,694 2,496,694 2,052,965 2,052,965 1,662,321 1,662,321 1,582,019 1,582,019
Unique student observations 867,006 867,006 875,847 875,847 1,013,241 1,013,241 1,017,834 1,017,834

Notes: The adjusted measure of within-year grade turnover is the proportion of teachers to turn over from a grade, not including the current teacher. Models include controls for time-varying student and school characteristics and year fixed effects. Standard errors clustered at the student-by-school or teacher level in parentheses. ELA = English language arts.

*p < 0.05; **p < 0.01; ***p < 0.001.

Evidence of the indirect effect of grade instability on student achievement gains is much less consistent across model specification. Within-year grade-level turnover has effects of −0.052 and −0.042 for elementary math and middle grade ELA, respectively. When adjusting for the stable quality of the teacher, we find no evidence of an indirect effect of within-year grade-level turnover in elementary ELA achievement, but losing all teachers in a grade at the end of the previous school year has a −0.009 standard deviation effect. For middle school math, only the direct effect of within-year classroom teacher turnover is significant, within-year and end-of-year grade-level turnover are not statistically significant. However, the within-year turnover effect estimates for the alternative specification, student-by-school fixed effects, are all negative and significant, perhaps indicating that lower quality of departing teachers is responsible for these larger negative effects.

When comparing the results for elementary and middle school ELA and mathematics from the teacher fixed effects models, the estimates are remarkably consistent. Compared with the years in which a teacher does not turn over midyear, his students’ ELA achievement is 0.045 standard deviation lower in elementary school and −0.049 in middle school. Compared with the years in which a teacher does not turn over midyear, his students’ math achievement is 0.100 standard deviation lower in elementary school and −0.106 in middle school.7

There may also be an interactive effect of being in a grade that experiences high turnover and being in a classroom with a teacher who leaves midyear. To test for this hypothesis, we estimate a model with the interaction between within-year classroom teacher turnover and within-year grade-level turnover (see table A.6 in the online appendix). In elementary schools, we find no evidence of an additional combined effect of losing one's teacher and experiencing higher levels of within-year teacher instability in other classrooms in the same grade within the school. In middle schools, however, the coefficient on the interaction between within-year classroom teacher turnover and within-year grade-level turnover is positive and significant in all models except the teacher fixed effects model for ELA. That being said, the negative effect of within-year teacher turnover remains mainly driven by the classroom disruption caused to students by losing a teacher during the school year.8

With strong evidence that a negative effect of within-year classroom teacher turnover—an effect that appears to be largely driven by the classroom disruption faced by students, and possibly the quality of the replacement teacher—we extend these analyses in three ways. First, we test the degree to which the effect of within-year classroom teacher turnover can be explained by different measures of teacher quality or background characteristics. Second, we examine whether or not the negative effect of losing a teacher differs for different student subgroups. Third, we leverage our monthly observations of within-year classroom teacher turnover to examine the extent to which the effect of turnover differs throughout the course of the school year.

### Within-Year Classroom Teacher Turnover and Teacher Quality

As the previous analysis accounts for the stable component of teacher quality, it provides strong evidence that the negative effect of within-year classroom teacher turnover is driven by the classroom disruption mechanism and, possibly, the low quality of the replacement teacher. The teacher fixed effect is limited by the fact that the model is not identified for first-year teachers, a concern given that first-year teachers turn over at higher rates during the school year (Redding and Henry 2019). To further understand the extent to which the effect of within-year classroom teacher turnover can be explained by the quality of the departing teacher, we add to the student-by-school fixed effects model four measures related to teacher quality or background: teaching experience, average teacher test score, lagged evaluation score, and teacher background characteristics (gender, race/ethnicity, and entry pathway [in-state, traditional preparation, alternate entry, Teach For America, out-of-state prepared, and other pathway]).9 The average teacher test score is an average test score measure of all available tests, separately standardized, including college entrance and teacher certification exams. The lagged evaluation score takes the teacher's median evaluation score from the previous school year across five domains on which teachers are evaluated in North Carolina. In these models, if the effect of within-year classroom teacher turnover is being driven by any of these measures of teacher quality, the coefficient on the within-year classroom-level turnover measure would attenuate to zero. If the estimate on within-year classroom teacher turnover remains consistent and statistically significant, it would provide additional evidence that the negative effect of losing a teacher during the school year is not driven by the quality of that teacher. Because this includes teachers in their first year, we are able to include more departing teachers in the effect estimate than the teacher fixed effects model.

No evidence in table 4 supports this hypothesis. Controlling for teacher experience fails to explain the effect of within-year classroom teacher turnover on student achievement in ELA or math. Similarly, when the average teacher test score is added to the model, the estimate on within-year classroom teacher turnover remains consistent. When we control for the lagged median evaluation score, the estimate on within-year classroom teacher turnover is less consistent across models. With currently available data, we cannot confidently link replacement teachers to the students within their classrooms and therefore are unable to examine the extent to which the negative effect of within-year classroom teacher turnover is driven by the quality of the replacement teacher.

Table 4.
Estimates of the Effect of Within-Year Classroom Teacher Turnover on Student Achievement Controlling for Teacher Quality
Panel A. Elementary School Student Achievement
English Language ArtsMath
(1)(2)(3)(4)(5)(6)(7)(8)
Within-year classroom teacher −0.039*** −0.037*** −0.033* −0.026*** −0.047*** −0.050*** −0.045** −0.044***
turnover (0.004) (0.005) (0.014) (0.003) (0.003) (0.004) (0.015) (0.003)
Teaching experience
Average teacher test
Lagged evaluation score
Teacher characteristics
Student-by-school fixed effects
Observations 2,500,973 2,185,564 1,144,334 2,500,973 2,055,970 1,795,861 981,260 1,586,614
Unique student observations 867,905 799,661 502,479 753,134 876,850 809,700 505,246 761,949
Panel B. Middle School Student Achievement
English Language Arts Math
(1) (2) (3) (4) (5) (6) (7) (8)
Within-year classroom teacher −0.014*** −0.020*** 0.021 −0.014*** −0.071*** −0.083*** −0.067*** −0.073***
turnover (0.003) (0.003) (0.013) (0.003) (0.003) (0.003) (0.012) (0.003)
Teaching experience
Average teacher test
Lagged evaluation score
Teacher characteristics
Student-by-school fixed effects
Observations 1,663,945 1,424,879 828,609 1,344,634 1,583,834 1,388,431 813,006 1,285,680
Unique student observations 1,013,600 912,653 560,467 751,029 1,018,119 930,046 572,466 756,860
Panel A. Elementary School Student Achievement
English Language ArtsMath
(1)(2)(3)(4)(5)(6)(7)(8)
Within-year classroom teacher −0.039*** −0.037*** −0.033* −0.026*** −0.047*** −0.050*** −0.045** −0.044***
turnover (0.004) (0.005) (0.014) (0.003) (0.003) (0.004) (0.015) (0.003)
Teaching experience
Average teacher test
Lagged evaluation score
Teacher characteristics
Student-by-school fixed effects
Observations 2,500,973 2,185,564 1,144,334 2,500,973 2,055,970 1,795,861 981,260 1,586,614
Unique student observations 867,905 799,661 502,479 753,134 876,850 809,700 505,246 761,949
Panel B. Middle School Student Achievement
English Language Arts Math
(1) (2) (3) (4) (5) (6) (7) (8)
Within-year classroom teacher −0.014*** −0.020*** 0.021 −0.014*** −0.071*** −0.083*** −0.067*** −0.073***
turnover (0.003) (0.003) (0.013) (0.003) (0.003) (0.003) (0.012) (0.003)
Teaching experience
Average teacher test
Lagged evaluation score
Teacher characteristics
Student-by-school fixed effects
Observations 1,663,945 1,424,879 828,609 1,344,634 1,583,834 1,388,431 813,006 1,285,680
Unique student observations 1,013,600 912,653 560,467 751,029 1,018,119 930,046 572,466 756,860

Notes: Models include controls for time-varying student and school characteristics and year fixed effects. Lagged evaluation score is the median evaluation score the teacher receives from their principal. Teacher characteristics include gender, race/ethnicity, and entry pathway (in-state, traditional preparation, alternate entry, Teach For America, out-of-state prepared, and other pathway). Standard errors clustered at the student-by-school level in parentheses.

*p < 0.05; **p < 0.01; ***p < 0.001.

### Heterogeneity of the Effects of Within-Year Classroom Teacher Turnover

Elsewhere, we show that schools with the greatest concentrations of underserved student populations tend to have the highest within-year teacher turnover (Redding and Henry 2018). To examine the extent to which the negative effect of within-year classroom teacher turnover is greater for black, Hispanic, and economically disadvantaged students, we estimate the teacher fixed effects model separately for each group. In addition, we also separate students into three groups based on their prior achievement: below the 25th percentile (lower performing), between the 25th and 75th percentiles (moderately performing), and above the 75th percentile (higher performing), and examine the effects of losing a classroom teacher on each group.

Our main results indicate that losing a teacher during the school year causes a 0.045 decrease in ELA achievement for elementary school students. In panel A of table 5, counter to the hypothesis that black and economically disadvantaged students would be more adversely affected by within-year classroom teacher turnover, we find a −0.039 standard deviation effect for economically disadvantaged students, −0.052 effect for Hispanic students, and no evidence of an effect for black students. In panel B, in contrast, within-year classroom teacher turnover causes a larger decrease in math achievement for black and Hispanic students than white students. Compared with an overall effect of −0.100 standard deviation, the effect for black students is −0.122 and Hispanic students is −0.114. The most consistent finding for elementary school students relates to prior student performance, where we find moderately performing students to be most negatively affected by the loss of a teacher during the school year. Within-year classroom teacher turnover causes a 0.060 decrease in ELA achievement and a 0.115 decrease in math achievement for these students.

Table 5.
Estimates of the Effect of Within-Year Teacher Turnover on Elementary School Student Achievement by Student Characteristics
Panel A. Student Achievement in English Language Arts
OverallWhiteBlackHispanicEconomically DisadvantagedLower PerformingModerately PerformingHigher Performing
Within-year classroom −0.045*** −0.066*** −0.004 −0.052* −0.039** −0.026 −0.060*** −0.042*
teacher turnover (0.010) (0.014) (0.017) (0.021) (0.013) (0.018) (0.011) (0.017)
Teacher fixed effects
Observations 2,496,694 1,118,237 633,505 332,441 1,145,852 611,891 1,261,432 628,180
Unique student 867,006 364,426 219,406 116,955 419,989 233,080 494,128 243,103
observations
Panel B. Student Achievement in Mathematics
Within-year classroom −0.100*** −0.090*** −0.122*** −0.114*** −0.104*** −0.096*** −0.115*** −0.086***
teacher turnover (0.012) (0.017) (0.018) (0.024) (0.016) (0.018) (0.016) (0.019)
Teacher fixed effects
Observations 2,052,965 888,737 528,608 281,232 947,229 503,672 1037,342 515,306
Unique student 875,847 367,197 221,601 119,165 426,161 240,571 495,553 244,714
observations
Panel A. Student Achievement in English Language Arts
OverallWhiteBlackHispanicEconomically DisadvantagedLower PerformingModerately PerformingHigher Performing
Within-year classroom −0.045*** −0.066*** −0.004 −0.052* −0.039** −0.026 −0.060*** −0.042*
teacher turnover (0.010) (0.014) (0.017) (0.021) (0.013) (0.018) (0.011) (0.017)
Teacher fixed effects
Observations 2,496,694 1,118,237 633,505 332,441 1,145,852 611,891 1,261,432 628,180
Unique student 867,006 364,426 219,406 116,955 419,989 233,080 494,128 243,103
observations
Panel B. Student Achievement in Mathematics
Within-year classroom −0.100*** −0.090*** −0.122*** −0.114*** −0.104*** −0.096*** −0.115*** −0.086***
teacher turnover (0.012) (0.017) (0.018) (0.024) (0.016) (0.018) (0.016) (0.019)
Teacher fixed effects
Observations 2,052,965 888,737 528,608 281,232 947,229 503,672 1037,342 515,306
Unique student 875,847 367,197 221,601 119,165 426,161 240,571 495,553 244,714
observations

Notes: Models include student and school controls and year fixed effects. Standard errors clustered at the teacher level in parentheses. Lower-performing students scored at the bottom quartile on the lagged English Language Arts or mathematics test; moderately performing include the middle quartiles; higher performing includes students who scored in the top quartile.

*p < 0.05; **p < 0.01; ***p < 0.001.

The results for middle school students generally follow a similar pattern as elementary school. In table 6, the negative effect of classroom teacher turnover on ELA achievement is slightly larger for white students compared with black and Hispanic students. The negative effect of classroom teacher turnover on math achievement is slightly larger for Hispanic students. We find no difference in the effect of within-year classroom teacher turnover for economically disadvantaged students. In terms of prior student performance, the pattern is similar to elementary student achievement in that losing a teacher within the year is most detrimental to moderately performing students. In middle schools, within-year classroom teacher turnover has the smallest effect on lower-performing students in both ELA and math.

Table 6.
Estimates of the Effect of Within-Year Teacher Turnover on Middle School Student Achievement by Student Characteristics
Panel A. Student Achievement in English Language Arts
OverallWhiteBlackHispanicEconomically DisadvantagedLower PerformingModerately PerformingHigher Performing
Within-year classroom −0.049*** −0.059*** −0.044*** −0.048** −0.050*** −0.033* −0.064*** 0.045**
teacher turnover (0.008) (0.012) (0.012) (0.018) (0.011) (0.014) (0.010) (0.013)
Teacher fixed effects
Observations 1,662,321 701,712 450,956 207,872 752,478 411,375 835,508 417,514
Unique student 1,013,241 410,214 265,631 120,724 449,651 254,914 552,113 293,363
observations
Panel B. Student Achievement in Mathematics
Within-year classroom −0.107*** −0.104*** −0.103*** −0.128*** −0.107*** −0.079*** −0.116*** −0.103***
teacher turnover (0.015) (0.020) (0.018) (0.022) (0.016) (0.017) (0.017) (0.02)
Teacher fixed effects
Observations 1,582,019 683,684 416,155 194,585 708,109 393,546 793,663 397,618
Unique student 1,017,834 410,743 265,296 123,091 454,080 271,893 557,500 276,125
observations
Panel A. Student Achievement in English Language Arts
OverallWhiteBlackHispanicEconomically DisadvantagedLower PerformingModerately PerformingHigher Performing
Within-year classroom −0.049*** −0.059*** −0.044*** −0.048** −0.050*** −0.033* −0.064*** 0.045**
teacher turnover (0.008) (0.012) (0.012) (0.018) (0.011) (0.014) (0.010) (0.013)
Teacher fixed effects
Observations 1,662,321 701,712 450,956 207,872 752,478 411,375 835,508 417,514
Unique student 1,013,241 410,214 265,631 120,724 449,651 254,914 552,113 293,363
observations
Panel B. Student Achievement in Mathematics
Within-year classroom −0.107*** −0.104*** −0.103*** −0.128*** −0.107*** −0.079*** −0.116*** −0.103***
teacher turnover (0.015) (0.020) (0.018) (0.022) (0.016) (0.017) (0.017) (0.02)
Teacher fixed effects
Observations 1,582,019 683,684 416,155 194,585 708,109 393,546 793,663 397,618
Unique student 1,017,834 410,743 265,296 123,091 454,080 271,893 557,500 276,125
observations

Notes: Models include student and school controls and year fixed effects. Standard errors clustered at the teacher level in parentheses. Lower-performing students scored at the bottom quartile on the lagged English Language Arts or mathematics test; moderately performing include the middle quartiles; higher performing includes students who scored in the top quartile.

*p < 0.05; **p < 0.01; ***p < 0.001.

### Timing of Within-Year Classroom Teacher Turnover

In other work, we find notable variation in the frequency of within-year turnover throughout the school year (Redding and Henry 2018). Within-year teacher turnover is most common during the first two months of the year and at the transition between the first and second semesters, and likely results from districts reassigning staff to meet shifting student enrollments. Teachers are most likely to transfer schools within the same district during the first months of the school year. Teachers are most likely to leave teaching in January and February. The rate at which teachers move to a school in a different district in the state is consistent throughout the school year, with roughly 0.1 percent of teachers moving each month.

As we explain earlier, we expect within-year teacher turnover to be most detrimental for students when it occurs in the spring, given the proximity to annual testing and the harm to longer running student–teacher relationships. That being said, other factors are likely also at play that are unrelated to this disruption hypothesis. The exit of a teacher during the school year is conflated with the quality of the replacement teacher. If a teacher leaves early in the school year, the replacement teacher may be able to establish instructional continuity and minimize the disruptive effect of losing a teacher early in the school year. This outcome would suggest that we would find less of an impact of the within-year teacher turnover that occurs in the first couple months of the school year. Regardless of the replacement teacher's quality, we would expect the replacement mechanism to play less of a role later in the school year, as a replacement teacher hired late in the school year would need to have a very strong influence over the short period of time she is assigned to her students.10

In figure 1, we plot the coefficients and confidence intervals from a teacher fixed effects model that replaces the within-year classroom teacher turnover indicator with a series of monthly turnover indicator variables. First, we find the negative effect of within-year classroom teacher turnover is larger when losing a teacher in the spring. Compared with a teacher who remains in the same school, we find evidence that teachers who turn over in November, January, February, April, May, and the end of the year negatively impact student achievement in elementary school ELA. We find an even more consistent pattern for elementary school math. Within-year teacher turnover that occurs after November is detrimental to elementary school math achievement. It is worth noting that even though the negative effect of turnover is largest in the spring, none of the monthly estimates are significantly different from one another. In other words, these results only provide evidence that the turnover that occurs after the first semester is most disruptive.
Figure 1.

Effect of Within-Year Classroom Teacher Turnover on Student Achievement, by Month of the School Year

Notes: Estimates from teacher fixed effects model (online table A.7). Estimates reported in reference to teachers who remained in the school the entire year. ELA = English language arts; EOY = end of year.

Figure 1.

Effect of Within-Year Classroom Teacher Turnover on Student Achievement, by Month of the School Year

Notes: Estimates from teacher fixed effects model (online table A.7). Estimates reported in reference to teachers who remained in the school the entire year. ELA = English language arts; EOY = end of year.

Second, we find no evidence that teachers who turned over in the first two months of the school year are more or less effective than teachers who did not turn over. The direction and magnitude of these estimates is inconsistent and they are measured with little precision. Third, we also find evidence for the hypothesis that teachers who knew they were going to turn over after the school year were less productive and resulted in a negative effect on their students’ academic achievement. Teachers who turn over at the end of the school year have a small, negative impact on their students’ performance during the prior school year. The effect of an end-of-year departure is −0.009 standard deviation in ELA and −0.010 standard deviation in math, which is consistent with an Ashenfelter dip due to a withdrawal of effort prior to leaving.

Results for middle school ELA and math achievement follow the same general pattern, although the magnitude of the estimates is less consistent. In ELA, within-year classroom teacher turnover results in lower achievement in January through April. In math, within-year classroom teacher turnover has a negative effect beginning in November, with the magnitude of the coefficients decreasing through April. Again, we find end-of-year turnover to result in lower ELA and math achievement. We find slight evidence of a relationship between within-year classroom teacher turnover and student achievement in the first months of the school year, with turnover in September negatively related to ELA achievement.

## 6.  Conclusion

The goal of this paper was to estimate the direct effects of losing a classroom teacher during the school year and to better understand the effects of teacher turnover by distinguishing these direct effects from turnover at the end of the year. In doing so, we sought to elucidate three mechanisms by which teacher turnover harmed student achievement: classroom disruption, staff instability, and lower replacement-teacher quality. We describe two main contributions from this paper.

First, our results bring increased clarity around the mechanisms driving the negative effect of teacher turnover. In our preferred specification with teacher fixed effects, we found consistently negative effects of within-year classroom teacher turnover on ELA and mathematics achievement across elementary and middle schools. In ELA, within-year classroom teacher turnover had an effect of −0.045 standard deviation in elementary school and −0.049 standard deviation in middle school. In math, within-year classroom teacher turnover had an effect of −0.10 standard deviation in elementary school and −0.107 standard deviation in middle school. As these models condition on unobserved but fixed teacher quality, they account for the quality of the departing teacher, suggesting that the negative effect is driven most strongly by the classroom disruption faced by students, and possibly the quality of the replacement teacher. We also provide evidence of an indirect effect of grade-level teacher turnover—the grade-level instability mechanism. Although students who lose a teacher midyear are most harmed by this turnover, there are larger spillover effects from losing a teacher midyear and, as a result, other students in the grade suffer academically.

Second, our results point to the importance of considering the timing of teacher turnover when assessing its impacts. When separating the effect of the grade-level turnover that occurs within versus at the end of the year, we find consistent evidence of an adverse effect of within-year grade-level turnover. In addition, the turnover at the end of the school year was largely unrelated to student achievement gains in elementary and middle schools. In addition, we find suggestive evidence that losing a teacher later in the school year is more detrimental. In ELA, the effect of losing a teacher in April ranged from −0.040 to −0.057 standard deviation. In math, the effect of losing a teacher in April ranged from −0.114 to −0.151 standard deviation. Because the negative effects are larger and more consistent when classroom teacher turnover occurs closer to the end of the year, this pattern provides further support for the classroom disruption mechanism—as a replacement teacher entering the classroom late in the year would spend less time with the students—reducing the possibility that the adverse effects are due to a lower-quality replacement.

In addition to these overarching contributions, separating our results by school level and student subgroups provides additional evidence of how these mechanisms operate. When examining grade-level turnover, our results were consistent with the hypothesis that teacher turnover is more detrimental in elementary schools than middle schools. This finding points to the importance of grade-level collaboration promoting student achievement and offsets the negative effect of grade instability (Jackson and Bruegmann 2009; Kraft and Papay 2014; Ronfeldt et al. 2015; Papay et al. 2016). That being said, the consistently negative effect of within-year classroom teacher turnover across elementary and middle schools suggests that the differences in school organization does not cause this direct effect of turnover to vary.

When looking at the effect of within-year classroom teacher turnover on student subgroups, the pattern is not readily explainable. Although the performance of marginalized students might be expected to suffer the most from within-year classroom teacher turnover, we find within-year classroom teacher turnover to be most consequential for moderately performing students, a finding that is consistent across ELA and math for both elementary and middle school students. It is possible that moderately performing students are more dependent on the relationship they developed with their teacher and therefore are more affected by their teacher's departure. On the other hand, the lowest-performing students are less affected by their teacher's departure, perhaps because they were not well served by the teacher who departed.

Two limitations of this study should be noted. First, this study relies on a series of fixed effect estimation strategies to identify the effect of teacher turnover. The consistency of the estimated effect of within-year classroom teacher turnover when controlling for the departing teacher's quality suggests that we are estimating a plausibly causal effect of the disruption from within-year turnover. The robustness check, student-by-school fixed effect, reduced the magnitude of the effects in three out of four cases, perhaps indicating that these may be viewed as more conservative estimates, and all of them were negative and statistically significant. Still, even with results robust to a student-by-school fixed effect, our results do not rule out unobserved factors that occur within a grade that led to a teacher's departure and students in that class to underperform, but we believe the consistency of the estimates across identification strategies and the plausibility of this within-grade phenomena increase the credibility of our estimates.

Second, given data limitations, we are unable to confidently distinguish the extent to which losing a teacher midyear is driven by the disruption it causes for students or his replacement. We determined the negative effect of turnover was not driven by the quality of the departing teacher. Yet, by not being able to identify replacement teachers, we are unable to measure their quality. Addressing this issue of replacement teacher quality is an area for measurement development for future research that will help to better distinguish the mechanisms that drive the effect of teacher turnover.

Despite these limitations, this study makes important contributions to the ongoing debate of the degree to which teacher turnover harms student academic performance. A recent shift in this literature has been to identify the conditions in which turnover might be beneficial to the teacher workforce composition, and when it is detrimental. Initial evidence of the implementation of more rigorous teacher evaluation systems has begun to show that policies promoting the selective retention of effective teachers or the contract nonrenewal of less effective teachers can improve the overall quality of the teacher workforce (Grissom, Loeb, and Nakashima 2013; Dee and Wyckoff 2015; Springer, Swain, and Rodriguez 2016; Adnot et al. 2017). Evidence from our study on the lack of negative effect of teacher end-of-year grade-level turnover suggests that any grade-level instability caused by end-of-year turnover may be counteracted by replacement with better teachers.

The concentration of the negative effect of teacher turnover at particular times within the school year points to the need for policy makers and school leaders to become more cognizant of the ways in which certain policies may promote within-year turnover or, when it occurs, to reduce its harmful effects. Evidence of the indirect effect of grade instability points to the continued importance of collaboration and peer learning opportunities among elementary and middle school teachers that may help to deter turnover (Ronfeldt, Loeb, and Wyckoff 2013). Recent research points to the value of a supportive administrator in deterring teacher turnover, including the turnover that occurs during the school year (Redding and Henry 2018). That being said, many of the personal factors driving within-year teacher turnover are unlikely to be amenable to change: a teacher takes time in the middle of the school year for parental leave; a veteran teacher retires midyear; a beginning teacher leaves a few months into the school year after realizing teaching is a poor occupational fit. As a result, school leaders could do more to reduce the disruption of losing a teacher midyear. In cases of planned family or medical leave, interventions—including more student interactions with school staff who will remain in the school—could be beneficial in efforts to reduce the disruption of losing a teacher during the school year.

Our results also suggest that when in the school year teachers and administrators receive information on teacher performance may be consequential. First, evaluations during the school year could send signals to a teacher about the extent to which administrators feel he is fit for the teaching profession or the school community. Second, full performance evaluations, including value-added scores, are often not available until the subsequent school year has begun (Goldring et al. 2015). In other work, we show that teachers with lower summative evaluation scores are more likely to turn over during the following school year (Redding and Henry 2018). When school leaders do not receive this information until the beginning of the school year, any consideration of dismissing a teacher once the school year has begun would have to weigh against the negative effect the teacher's exit causes his students. An implication drawn from this study is that all measures of teachers’ performance, including their value-added scores, should be provided during the summer to allow teachers and administrators to attend to employment decisions without disrupting classes that have already begun.

Another type of within-year teacher turnover occurs when a teacher is transferred by the district at the beginning of the school year to keep pace with shifting student enrollment patterns. Descriptive evidence suggests the majority of interdistrict teacher transfer occurs in the first two months of the school year. Given our finding suggesting that within-year turnover is more detrimental when it occurs later in the school year (when districts are forced to transfer teachers based on changes in student enrollment), teachers would be advised to do so as early in the school year as possible and avoid it, when possible, later in the school year.

Our previous work has found leaving teaching within the academic year to occur most frequently at the beginning and end of teachers’ careers (Redding and Henry 2018). Yet, descriptive evidence shows that Teach For America Corps members turn over at very low rates during the school year. For other early career teachers who struggle with the transition into teaching and become demoralized with their efforts to manage their classroom and deliver effective classroom instruction, principals would be advised to begin observing new teachers very early in the school year and provide them with feedback. These processes may aid in identifying less-effective teachers who are at risk of leaving later in the school year and improving their effectiveness or counseling them out as early in the school year as possible. For teachers who become eligible for retirement benefits during a school year, incentives could be introduced for these teachers to stay until the end of the school year rather than retire in the middle of the school year when they become eligible. However, more research would need to be done to establish that they don't begin to withdraw effort during the months they agree to stay on.

Teacher turnover is a diverse phenomenon, with teachers leaving their schools and the teaching profession for a variety of reasons, both voluntarily and involuntarily. In recent years, researchers have come to better understand how turnover can be beneficial for school systems when it occurs as part of the strategic management of a district's human capital (Grissom et al. 2013; Adnot et al. 2017). Although it is possible for turnover to be beneficial for school systems, an extensive body of research points to the ways that teacher turnover disrupts school organizational processes and the continuity of a child's learning experiences (Ingersoll 2001; Lankford, Loeb, and Wyckoff 2002), particularly in underserved schools (Simon and Johnson 2015). By considering the timing of when in the school year teacher turnover occurs, our results speak to both points in the literature. We find that end-of-year turnover does not seem to affect student achievement but turnover that occurs during the year is harmful for the students who lose their teacher and, to a lesser degree, other students in the same grade. As such, these results can help policy makers and school leaders alike understand the specific conditions under which turnover is most detrimental, on average, and consider policies, practices, and personnel actions in light of whether the situation justifies the risk of these average effects on students.

## Notes

1.

During this time period, North Carolina began school turnaround efforts in the state's lowest-performing schools. In supplementary analysis, we exclude schools in the top percentile of school turnover (greater than 81.7 percent) to account for such schools, as well as other schools that were closed or reconstituted. When replicating our main analysis on this restricted sample, results are qualitatively similar.

2.

For comparison with Ronfeldt, Loeb, and Wyckoff (2013), we create their measure of “lagged attrition,” which is measured as the fraction of teachers to turn over from a particular grade in October of year t − 1 compared with October in year t. These results are presented in table A.4, which is available in a separate online appendix that can be accessed on Education Finance and Policy's Web site at https://www.mitpressjournals.org/doi/suppl/10.1162/edfp_a_00274

3.

We examined differences of whether within-year movers or leavers were more or less detrimental to student achievement. We found little evidence of differences by the type of turnover and thus do not include these results.

4.

To avoid double counting teachers who turn over during the school year, the measure of within-year grade-level turnover includes all teachers in the grade at the school other than the teacher who turned over that year when estimating the effects on students whose teacher turned over. Table A.5 in the online appendix presents the results using the original, unadjusted measure of within-year grade-level turnover.

5.

Tables A.1 and A.2 in the online appendix run separate models for end-of-year and within-year grade-level turnover. The results are qualitatively similar compared to when both measures are included in the same model.

6.

To compare our results with previous studies that have examined the effect of teacher turnover, we estimate models with two additional measures of grade-level turnover: total grade-level turnover and October-to-October grade-level turnover. Table A.3 in the online appendix reports the estimates from a model with total grade-level turnover are somewhat smaller than reported in these studies. In elementary school, the effect ranged from −0.019 to −0.044 standard deviation unit in ELA, with no evidence of an effect on math achievement. In middle school, the effect of total grade-level turnover was −0.027 standard deviation unit in ELA and between −0.052 and −0.057 standard deviation unit in math. When we use an October-to-October measure of annual, grade-level teacher turnover that is comparable to the Ronfeldt, Loeb, and Wyckoff (2013) measure, we find effects similar to those we find in terms of magnitude and significance on ELA for both elementary and middle schools (see table A.4 in the online appendix). However, the effects on mathematics are −0.021 in elementary school and slightly smaller and not significant in middle schools.

7.

Online appendix table A.5 reports the estimates that do not adjust the within-year grade-level turnover measure. In general, when we control for the unadjusted measure of within-year grade-level teacher turnover, the estimates decrease slightly in magnitude but maintain the same direction and level of significance.

8.

Holding all variables in the model at their sample mean, when a student is in a grade with no other within-year turnover but his own teacher, he is predicted to score 0.045 standard deviation lower in ELA. When he is in a grade where 22 percent of other teachers turn over—the 99th percentile of within-year turnover for this adjusted measure—the student's predicted achievement is −0.034. In the teacher fixed effects model predicting middle school math achievement, when a student is in a grade with no other within-year turnover but his own teacher, he is predicted to score 0.104 standard deviation lower. When in a grade where 22 percent of other teachers turn over, the student's predicted achievement is −0.063.

9.

In addition to these measures of teacher quality, we examined a teacher value-added measure. This measure was only available for 18 percent of the teacher observations. After running regressions with this reduced sample of teachers with and without including the teacher value-added measure, the regression surfaces for the reduced sample were substantially different than the full sample, leading to the conclusion that the differences in the estimated coefficients were attributable to sample differences and, therefore, are not presented here.

10.

A teacher may leave midyear because she is failing, and the effect of within-year turnover is driven by the low quality of her teaching rather than the disruptive effect of a teacher leaving midyear or the quality of the replacement teacher. As we condition on teacher fixed effects, unless there are unobserved, time-varying factors that influence a teacher's decision to leave during the school year and student achievement, we are not particularly concerned that the quality of the departing teacher is driving these results. Furthermore, measured teacher effectiveness does not systematically vary throughout the school year (see table A.8 in the online appendix).

## Acknowledgments

We wish to thank Jason Grissom, Matthew Springer, and Thomas Smith for reviewing an earlier draft of this paper. We thank conference participants at the 2017 meeting of the Association for Education Finance and Policy.

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