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* Correspondence regarding the article can be sent to matthew_kraft@brown.edu. This work was supported by the
Spencer Foundation and the Institute of Education Sciences, U.S. Department of Education grant [R305C090023] to
the President and Fellows of Harvard College. We also thank Heather Hill, Lawrence Katz, Susan Moore Johnson,
Richard Murnane, Doug Staiger, Eric Taylor, and John Willett for their valuable feedback on earlier drafts. Andrew
Baxter and Thomas Tomberlin at Charlotte Mecklenburg Schools and Eric Hirsch at the New Teacher Center
generously provided the data for our analyses. The opinions expressed are those of the authors and do not represent
views of the Institute, the U.S. Department of Education, or the Spencer Foundation.
Can Professional Environments in Schools Promote Teacher Development?
Explaining Heterogeneity in Returns to Teaching Experience
Matthew A. Kraft*
John P. Papay
Brown University
2014
Abstract
Although wide variation in teacher effectiveness is well established, much less is known about
differences in teacher improvement over time. We document that average returns to teaching
experience mask large variation across individual teachers, and across groups of teachers
working in different schools. We examine the role of school context in explaining these
differences using a measure of the professional environment constructed from teachers’
responses to state-wide surveys. Our analyses show that teachers working in more supportive
professional environments improve their effectiveness more over time than teachers working in
less supportive contexts. On average, teachers working in schools at the 75th percentile of
professional environment ratings improved 38% more than teachers in schools at the 25th
percentile after ten years.
Suggested Citation:
Kraft, M.A. & Papay, J.P. (2014). Can professional environments in schools promote teacher
development? Explaining heterogeneity in returns to teaching experience. Educational
Evaluation and Policy Analysis. 36(4), 476-500
Link to Publisher’s Version:
http://epa.sagepub.com/content/36/4/476.short
1
2
Research documenting the primary importance of effective teachers has shaped education
policy dramatically in the last decade, resulting in a broad range of reforms targeted at increasing
teacher quality. Federal, state, and local policy initiatives have sought to attract and select
highly-qualified candidates, evaluate their performance, and reward and retain those teachers
judged to be most effective. This narrow focus on individuals discounts the important role of the
organizational context in shaping teachers’ career decisions and facilitating their success with
students. In response, some scholars have argued that reforms targeting teacher effectiveness
would achieve greater success by also working to improve the organizational context in schools
(Johnson, 2009; Kennedy, 2010).
Mounting evidence suggests that the school context in which teaching and learning
occurs can have important consequences for teachers and students. Recent studies document the
influence of school contexts on teachers’ career decisions, teacher effectiveness, and student
achievement (Loeb, Hammond, & Luczak, 2005; Boyd et al., 2011; Ladd, 2011; Johnson, Kraft
& Papay, 2012). These studies capitalize on new measures of the school context constructed
from student, teacher, and principal responses to district and state-wide surveys. We build on this
work by investigating how the school context influences the degree to which teachers become
more effective over time. We refer to these changes in effectiveness of individual teachers over
time as “returns to teaching experience.”
Studies on the returns to teaching experience find that, on average, teachers make rapid
gains in effectiveness early in their careers, but that additional experience is associated with
more modest improvements (e.g. Rockoff, 2004; Boyd et al., 2008; Harris & Sass, 2011;
Wiswall, 2013; Papay & Kraft, 2012). Using a rich administrative dataset from Charlotte-
Mecklenburg Schools, we demonstrate that this average profile masks considerable
3
heterogeneity among teachers, as well as systematic differences in the average returns to
experience among teachers in different schools. We also find that this variation in returns to
teaching experience across schools is explained, in part, by differences in teachers’ professional
environments. Teachers who work in more supportive environments become more effective at
raising student achievement on standardized tests over time than do teachers who work in less
supportive environments. These findings challenge common assumptions made by education
policymakers and highlight the role of the organizational context in promoting or constraining
teacher development.
In the following section, we review the literature on returns to teaching experience and
describe the relationship between organizational contexts and worker productivity. We then
describe our data and our measure of the professional environment. Next, we explain our
empirical framework for measuring changes in effectiveness over a teacher’s career, present our
findings, and explore the sensitivity of these finding to our modeling assumptions. We further
examine alternative explanations for the relationship we observe between returns to teaching
experience and the professional environment in schools. Finally, we conclude with a discussion
of our results and their policy implications.
1. Organization Theory and Productivity Improvement in Schools
1.1 Heterogeneity in the Returns to Teaching Experience
Studies find that novice and early-career teachers are less effective than their more
experienced peers (Wayne & Youngs, 2003; Clotfelter, Ladd, & Vigdor, 2007; Rockoff et al.,
2011) and that, on average, individual teachers make rapid gains in effectiveness during the first
several years on the job (Rockoff, 2004; Boyd et al., 2008). However, it remains less clear how
much teachers continue to improve later in their careers (Harris & Sass, 2011; Wiswall, 2013;
4
Papay & Kraft, 2012). Scholars hypothesize that these returns to teaching experience result from
the acquisition of new human capital, including content knowledge, classroom management
techniques, and methods of instructional delivery. Teachers learn how to create and modify
instructional materials (Kaufman et al., 2002) and better meet the diverse instructional needs of
students (Johnson & Birkeland, 2003) as they gain experience on the job.
Clearly, though, these average patterns obscure potential heterogeneity in returns to
teaching experience. Just as there are large differences in the effectiveness of teachers at any
given level of experience, there are differences in the rate at which individual teachers improve
throughout their careers. Kane, Rockoff, and Staiger (2008) find initial evidence of this
heterogeneity in New York, as alternatively certified and uncertified teachers improve their
effectiveness over time more rapidly than their traditionally certified counterparts. Early
evidence on an urban teacher residency program also suggests that program graduates
underperform all other novice teachers but improve rapidly over time and eventually outperform
their peers after several years in the classroom (Papay et al., 2012). Two recent studies suggest
that differential returns to experience are related to school characteristics. Loeb, Kalogrides, and
Beteille (2012) document how, on average, teachers improve at faster rates in schools with
higher value-added scores. Sass and his colleagues (2012) find faster improvement among
teachers at schools with fewer low-income students.
1.2 The School Work Context and Teacher Development
That teachers might improve at different rates in different types of schools is not
surprising: for more than a century, scholars of organizational behavior have attempted to
explain differences in individual workers’ productivity and skill development across work
environments. They have developed a rich set of theories to explain how organizational
5
structures, practices, and culture affect the productivity of workers (Hackman & Oldman, 1980;
Kanter, 1983). In-depth qualitative studies of schools as workplaces illustrate how organizational
structures can facilitate or limit on-the-job learning for teachers (Johnson, 1990; Lortie, 1975).
Together, these organizational theories and qualitative studies predict that school environments
where teachers collaborate frequently, receive meaningful feedback about their instructional
practices, and are recognized for their efforts will promote teacher improvement at faster rates
than schools where such practices are absent.
A growing body of literature on the organizational context in schools has begun to bear
out these predictions. Both theory and empirical evidence point to several specific elements of
the school organizational context that, when practiced successfully throughout a school, can
promote teacher improvement. Principals play a key role in promoting professional growth
among teachers by serving as instructional leaders who provide targeted feedback and facilitate
opportunities for teachers to reflect on their practice (Blase & Blase, 1999; May & Supovitz,
2010; Waters, Marzano & McNulty, 2003). A principal’s ability to lead effectively and support
teachers’ practice stands out as a critical influence on teachers’ decisions to remain at their
school (Grissom, 2011; Boyd, et al., 2011).
Several studies find that measures of the social context of work, including principal
leadership and peer collaboration, relate to gains in student achievement. Ladd (2009) finds that
the quality of school leadership and the availability of common planning time predict school
effectiveness, as measured by contributions to student achievement. In a similar study using data
from Massachusetts, we find that stronger principal leadership, relationships among colleagues,
and positive school culture predict higher median student achievement growth among schools
(Johnson, Kraft & Papay, 2012). Jackson and Bruegmann (2009) find that teachers, especially
6
novices, improve their ability to raise standardized tests scores when they work in a school with
more effective grade-level colleagues. Furthermore, evidence shows that social networks among
teachers, particularly those with high-levels of expertise and high-depth substantive interactions,
enable investments in instructional improvement to be sustained over time (Coburn et al., 2012).
Over a decade of research by the Chicago Consortium on School Research (CCSR)
confirms these findings. Bryk and his colleagues find that for schools to be strong learning
environments for students and teachers, adults must work to create a culture of mutual trust and
respect (Bryk et al., 2010; Bryk & Schneider, 2002). They document the fundamental roles of
school culture and order and safety in creating an environment where teachers are willing and
able to focus on instruction. The large achievement gaps associated with measures of school
safety in Chicago schools illustrate the value of environments where teachers and students are
able to concentrate on teaching and learning (Steinberg et al., 2011).
The ways in which schools tailor and implement professional development and
evaluation also shape teachers’ opportunities for on-the-job learning. Over the past decades, a
growing consensus has emerged around the characteristics of effective professional development
programs. Studies find that professional development is most effective when it provides teachers
active learning opportunities that are intensive, focused on discrete skills, aligned with
curriculum and assessments, and applied in context (Correnti, 2007; Desimone, et al., 2002;
Desimone, 2009; Garet et al., 2001; Wayne et al., 2008). Many programs do not meet these
criteria and have largely been found to be ineffective when implemented at-scale (Garet et al.,
2008; Glazerman et al., 2008; Jacob & Lefgren, 2004). However, experimental evaluations of
programs that do, such as particular literacy coaching models, show measurable improvements in
teachers’ instructional practice and students’ performance on standardized assessments
7
(Matsumura et al., 2010; Neuman & Cunningham, 2009). For example, Allen et al. (2011) find
that teachers who were assigned randomly to participate in a program that used individualized
coaching to improve teacher-student interactions were more effective at raising student test
scores in the following year. Furthermore, teacher evaluation can also contribute to such
improvement. Taylor and Tyler (2012) find that participating in a rigorous teacher-evaluation
program promoted large and sustained improvements in the effectiveness of mid-career teachers.
Together, these studies suggest that a collection of specific elements of the school context
can play an important role in facilitating improvements in teacher effectiveness. Here, we
examine this relationship directly. Specifically, we pose three primary research questions:
i. Do the returns to teaching experience differ across individual teachers?
ii. Do the average returns to teaching experience differ across schools?
iii. Do teachers in schools with more supportive professional environments improve
more over time than their peers in less supportive environments?
2. Research Design
2.1 Site & Sample
We study teachers and schools in Charlotte-Mecklenburg Schools (CMS), an urban
district in North Carolina that is the 18th largest public school district in the nation. CMS serves
over 141,000 students across 174 schools and employs over 9,000 teachers. Teachers in CMS are
largely representative of U.S. teachers as a whole. Over 82% of teachers are female, 64% are
white, and 32% are African American. Thirty-four percent of teachers hold a master’s degree,
and teachers earn, on average, $42,320 annually. In recent years, the district has received
national recognition, including the 2011 Broad Prize for Urban Education.
We use a comprehensive administrative dataset from 2000-01 through 2009-10. These
data contain test records for state end-of-grade exams in mathematics and reading in 3rd through
8th grade as well as demographic characteristics, student enrollment records and teacher
8
employment histories. We link student achievement data to teachers using a course enrollment
file that contains both teacher and school IDs. Similar to past research, preliminary analyses
revealed both larger average returns to teaching experience and substantially greater individual
variation in mathematics than in reading (Boyd et al., 2008; Harris & Sass, 2011). This led us to
concentrate on returns to experience as measured by teachers’ contributions to students’
mathematics achievement.
We combine these data with teachers’ responses on the North Carolina Teacher Working
Conditions Survey, which was administered in 2006, 2008, and 2010. This 100-plus item survey,
developed by Eric Hirsch of the New Teacher Center, solicits teachers’ opinions on a broad
range of questions about the social, cultural, and physical environment in schools. These survey
data present new opportunities to measure elements of the work context that play a central role in
shaping teachers’ experiences, but that are much more difficult to quantify than indices of
traditional working conditions such as school resources and physical infrastructure. Survey
response rates in the district increased with each administration from 46%, to 67%, to 77%. The
survey contains identifying information on the schools where teachers work, but not unique IDs
for teachers. Thus, we merge these survey records to our administrative data using unique school
identifiers.
Our analytic sample consists of all students who can be linked to their mathematics
teachers in 4th through 8th grade, the grades in which the necessary baseline and outcome testing
data are available. This includes over 280,000 student-year observations and 3,145 unique
teachers.1
2.2 Measures
Our primary outcome consists of students’ scaled scores on their end-of-grade
9
examinations in mathematics, standardized within each grade and year (μ=0, σ=1). Although test
scores do not capture the full contribution that teachers make to children’s intellectual and
emotional development, we proceed with this narrow measure because it enables us to quantify
one aspect of teacher productivity.
Our primary question predictor is the interaction of teaching experience, EXPER, and an
overall measure of the professional environment in schools, PROF_ENV. We measure a
teacher’s level of experience using her step on the state salary scale. Because teachers receive
salary increases for each year of experience they accrue, this provides a reasonable measure of
actual on-the-job experience.
Because we examine the within-teacher returns to experience (i.e., we use teacher fixed
effects), we must make a methodological assumption to fit our models. The reason is that
teachers with standard career patterns gain an additional year of experience with every calendar
year. In other words, all teachers who start in the district in the fall of 2001 will have 10 years of
experience in the fall of 2011. Thus, within-teacher, we cannot separate the effect of differences
in achievement across school years (e.g., from the introduction of a new curriculum) from the
returns to teaching experience without making a methodological assumption (Murnane &
Phillips, 1981). The nature of this assumption can lead to substantial bias in the estimated returns
to teaching experience (see Papay & Kraft, 2012 for a detailed discussion).
However, in this paper, we focus on differences in the within-teacher returns to
experience across individual teachers and schools, not the shape of the average returns-to-
experience profile. Thus, the specific assumption we make is a second-order concern. As a result,
we adopt Rockoff’s (2004) simple and widely-used identifying assumption by censoring
experience at 10 years.2 This approach enables us to examine the returns to experience for early-
10
to mid-career teachers. We test the sensitivity of our results to alternative identifying
assumptions and find that they are unchanged.3 In our main models, we code experience as a
continuous predictor up to 10 years, while in supplementary models we use a set of indicator
variables to reflect teacher experience.
We create our measure of the professional environment by drawing on both the
theoretical and empirical literature concerning the work context in schools reviewed above. We
first identified elements of the work context characterized in the literature as important for
creating an environment that provides opportunities for teachers to improve their effectiveness.
We then restricted our focus to those elements for which we could find supporting empirical
evidence, and which were included as topics on the survey (see Johnson, Kraft & Papay, 2012
for a detailed description of this process). These elements of the professional environment
include:
ORDER & DISCIPLINE: the extent to which the school is a safe environment where rules
are consistently enforced and administrators assist teachers in their efforts to maintain an
orderly classroom;
PEER COLLABORATION: the extent to which teachers are able to collaborate to refine their
teaching practices and work together to solve problems in the school;
PRINCIPAL LEADERSHIP: the extent to which school leaders support teachers and address
their concerns about school issues;
PROFESSIONAL DEVELOPMENT: the extent to which the school provides sufficient time
and resources for professional development and uses them in ways that enhance teachers’
instructional abilities;
SCHOOL CULTURE: the extent to which the school environment is characterized by mutual
trust, respect, openness, and commitment to student achievement;
TEACHER EVALUATION: the extent to which teacher evaluation provides meaningful
feedback that helps teachers improve their instruction, and is conducted in an objective and
consistent manner.
To measure these elements, we selected 24 items from the survey, all of which were
administered with identical or very similar question stems and response scales across the three
years (see online Appendix A). A principal-components analysis of all 24 items suggested
11
strongly that teachers’ responses represented a single unidimensional latent factor in each survey
year.4 Internal-consistency reliability estimates across all items exceeded 0.90 in each year.
Consequently, we focused our analysis on a single composite measure of the professional
environment. We created this composite for each teacher in each year by taking a weighted
average of their responses to all 24 items, using weights from the first principal component.
Decomposing the variance of this composite measure, we find that differences in professional
environment across schools account for approximately 30% of the total variance in teachers’
responses in each year.
We then create a school-level measure of the professional environment by averaging
these composite scores at the school-year level. We restrict our school-year averages to those
derived from ten or more teacher survey responses in each year. To arrive at our preferred
overall measure of the professional environment in a school, we take the average of these school-
year values in 2006, 2008, and 2010 and standardize the result. Our preferred models include this
time-invariant average teacher rating of the overall professional environment in a school,
PROF_ENV. 5 Recognizing that some of the differences in the measure across years may be due
to real changes in the school’s professional environment, we conduct supplementary analyses
that use a time-varying measure. Results from these models are quite consistent with our primary
findings, although less precise because they are limited to three years of data.
Finally, we include a rich set of student, peer, and school-level covariates in our models
to account for observed individual differences across students as well as the sorting of students
and teachers across and within schools. Student-level measures include dichotomous indicators
of gender, race, limited English proficiency, and special-education status. Peer-level measures
include the means of all student-characteristic predictors, and prior-year achievement in
12
mathematics and reading for each teacher-by-year combination. School-level measures mirror
peer-level measures averaged at the school-by-year level and also include the percent of students
eligible for free or reduced price lunch in each year.6
2.3 Data Analysis
We examine the relationship between teacher effectiveness and teacher experience using
an education production function in which we model student achievement as a function of prior
test scores, student and teacher demographics, and school characteristics (Todd & Wolpin, 2003;
McCaffrey et al., 2004; Kane & Staiger, 2008). Following previous studies of returns to
experience using multilevel cross-classified data, we adopt a covariate-adjusted model as our
preferred specification, which we then modify to answer each of our research questions. Our
baseline model is as follows:
The outcome of interest,, is the end-of-year mathematics test score for student i in year t in
grade g taught by teacher j.7 We include cubic functions of prior-year achievement in both math
and reading, and allow the relationship between prior and current achievement in math to differ
across grade levels by interacting our linear measure of prior achievement with grade-level
indicators.8 The vector Xit represents the student, peer, and school-level covariates described
above. We include grade-by-year fixed effects, , to control flexibly for average differences in
achievement across grades and school years, such as the introduction of new policies in certain
grades. We specify the average effect of experience as a quartic function. We present results
below that demonstrate how a quartic polynomial approximates well a non-parametric
specification of experience.
Including teacher fixed effects, , in our models is critical because it isolates the within-
13
teacher returns to teaching experience, thereby avoiding many of the selection biases that arise in
cross-sectional comparisons of teachers with different experience levels. Models that omit
teacher fixed effects compare less-experienced teachers to their more-experienced peers. Instead,
we explicitly compare teachers’ effectiveness to their own effectiveness earlier their careers.
2.3.1 Estimating Heterogeneity
We modify the baseline specification described above in order to examine the variability
in returns to teaching experience across individual teachers and schools. Here, we are interested
in the variance of these estimated returns to experience. As a result, we depart from the fixed-
effect modeling approach described above and adopt a multilevel random-intercepts and random-
slopes framework that provides more robust, model-based variance estimates.9 In the new model,
we specify individual teacher effects as random (rather than fixed) intercepts, , and allow each
teacher’s return to experience to deviate from the average profile by including a random slope
for each teacher, . In other words, we estimate the returns to teaching experience separately for
each teacher and summarize the variation across these estimates by examining the variance of .
These additions result in the following generic multilevel model:
where
Here, the structural part of the model remains quite similar to equation (1).10 Again, we model a
common returns to experience profile as a quartic function of experience,
, but we
allow returns to experience to vary across individual teachers as linear deviations from this
average curvilinear trend. Sensitivity analyses presented below demonstrate this approach fits
our data well. The random coefficients, , characterize these individual deviations from the
14
average profile. If the variance of these random slopes,
, is statistically significant, it will
suggest that there is heterogeneity in returns to teaching experience across individual teachers. In
other words, it will indicate that some teachers do improve more rapidly than others. We extend
this framework to examine whether the average returns to teaching experience differ across
schools. We add a random effect for schools, , and replace the teacher-specific random slopes
for experience with school-specific random slopes, .
where
,
As before, estimates of the random slopes, , capture the average deviation from the average
returns to experience profile for all teachers in a given school. A statistically significant estimate
of the population variance of these random slopes,
, will suggest that there are systematic
differences in the pace at which teachers in different schools improve over time.
Here, our focus is on quantifying the total variance in returns to experience across
individuals or schools, rather than producing estimates for each individual teacher. As such, our
approach allows us to obtain consistent, model-based estimates of the true population variance.11
However, while this specification accounts for measurement and other error appropriately, it also
imposes several strong assumptions. First, we have assumed that all random effects are normally
distributed. Second, the model requires that the random effects (including teacher effects) are
independent of the large set of covariates we include in the model. This assumption would be
violated and could produce biased estimates of our parameters if, for example, more effective
teachers tended to teach certain types of students. As a result, we return to the widely-used fixed-
effect modeling framework in order to relax these assumptions as well as to facilitate a more
15
direct comparison of our results with related estimates from the prior literature.
2.3.2 Examining Heterogeneity across Professional Environments
We conclude our analyses by exploring whether differences in the professional
environment help to explain variation in returns to experience across schools. In other words, we
seek to understand whether teachers in more supportive environments improve more rapidly than
teachers in less supportive schools. We do this by adding our measure of the professional
environment and its interaction with experience (
) to model (I). This
specification allows us to answer our third research question by interpreting a single parameter of
interest, .
Estimates of capitalize on variation in the average returns to teaching experience of teachers
across schools with different professional environments. In effect, we are comparing the within-
teacher returns to experience of teachers in schools with more supportive professional
environments to those of their peers in schools with less supportive environments. A positive and
statistically significant estimate for then indicates that teachers become relatively more
effective over time when teaching in schools with more supportive professional environments.
As before, we estimate an average curvilinear return to experience using a quartic polynomial.
We assume that differences across professional environments accelerate (or decelerate) this
underlying pattern by the same amount per year over the first ten years of their career.
In addition to these primary analyses, we also test the robustness of our modeling
approaches and explore a variety of alternative explanations for our findings. We model
differences in returns to experiences across individuals, schools, and professional environments
16
using polynomial and non-parametric functional forms. We re-estimate our models across
different time periods and using alternative constructions of our professional environment
measures to test for non-response bias, self-report bias and reverse causality. We allow for
differential returns to experience across a variety of teacher and student-body characteristics.
Finally, we test for patterns of differential teacher retention related to rates of improvement and
dynamic student sorting that might account for our findings. As discussed below, these analyses
all confirm our central results.
3. Findings
We begin by presenting estimates of the average returns to experience in our sample as a
relative benchmark for our estimates of the variation in returns to experience, as well as an
illustration of the fit of our quartic function in experience. These estimates rely on a specific
identifying assumption that teachers do not improve after ten years. As we discuss in detail in a
separate paper (Papay & Kraft, 2012 ), we recommend that researchers who are concerned
primarily with estimating the exact magnitude and functional form of the average returns to
experience profile conduct parallel analyses using several alternative identifying assumptions.
We find that the average returns to teaching experience after ten years in our sample is almost
0.11 standard deviations (SD) of the student test-score distribution based on estimates from
model (I). In Figure 1, we illustrate the shape and magnitude the average returns to teaching
experience profile, showing that quartic function closely approximates the profile suggested by
the flexible, but less precisely estimated, set of indicator variables. Importantly, the magnitudes
of these returns to teaching experience are likely biased downwards because we assume that
teachers do not improve after 10 years.
The average returns to teaching experience after ten years are large when compared to the
17
overall distribution of teacher effectiveness in our sample estimated from model (II). Consistent
with prior estimates (e.g., Hanushek & Rivkin, 2010), we find that a one standard deviation
difference in the distribution of teacher effectiveness represents approximately a 0.18 SD
difference in student test scores (see Table 1 Column 1).Thus, a prototypical teacher who as a
novice was at the 27th percentile of the distribution of overall effectiveness moves to
approximately the median after ten years of experience. As Boyd and colleagues (2008) make
clear, it makes sense to compare the effects of interventions affecting teachers to the standard
deviation of gain scores (in effect, 0.18 SD here).
3.1 Do the returns to teaching experience differ across individual teachers and schools?
Estimates from model (II) confirm that the average returns-to-teaching-experience profile
obscures a large degree of heterogeneity in individual teachers’ changes in effectiveness over
time. In the first column of Table 1, we present the estimated standard deviations of each of the
random effects included in model (II). We find that the estimated standard deviation of the
random slopes for returns to experience across individual teachers () is 0.025 test-score
standard deviations (p<0.001). This suggests that a teacher who is at the 75th percentile of returns
to experience is improving her effectiveness by almost 2% of a test-score standard deviation
more annually than a teacher whose improvement follows the average returns to experience
trajectory. Specifying model (III) with random intercepts for schools leads to almost identical
results (column 2).
We illustrate this heterogeneity visually by plotting – in Panel A of Figure 2 – the fitted
returns-to-teaching-experience profiles for a random sample of 25 early-career teachers who had
taught for at least seven years. Each teacher’s predicted random intercept serves as an estimate of
her initial effectiveness level as a novice teacher. Individual returns-to-experience profiles are
18
obtained from our fitted models by combining the estimated average returns to experience and
the estimated teacher-specific deviations from this average pattern. In panel B, we center each
teacher’s random intercept on zero to focus attention on how much individuals improve relative
to their effectiveness as a novice teacher
Two overall patterns emerge from this figure. As is now widely documented in the
literature, Panel A depicts substantial differences in individual teacher effectiveness across
teachers. Secondly, the figure also demonstrates how returns to teaching experience differ widely
across teachers. The intersecting profiles in Panel A demonstrate how these differences in the
rate of improvement cause some teachers to become more effective than others over time. Panel
B helps to illustrate this point. Relative to each teacher’s initial effectiveness, some teachers
improve much more rapidly than others.
We also find strong evidence of variation in the average returns to experience among
teachers across individual schools. In the final column of Table 1, we present results from model
(III), in which we include both the random intercepts and slopes for schools. Here, we estimate
that the standard deviation of the school-specific random slopes is 0.007 SD (p<0.001), or almost
30% of the estimated variation in returns to experience across individual teachers. In other
words, teachers in certain schools tend to improve more than teachers in other schools.12
3.2 Descriptive Findings on Professional Environments in Schools
We now examine whether the quality of the professional environment in schools accounts
for the estimated differences in returns to experience across schools described above. Overall,
there exist meaningful differences in the quality of the professional environment in which
teachers work in Charlotte-Mecklenburg Schools. To illustrate this point, we present the sample
distribution of teachers’ average responses within a school to three individual survey items from
19
2008 in Figure 3. For example, teachers’ average perceptions of whether “There is an
atmosphere of trust and mutual respect within the school” and whether “School administrators
support teachers' efforts to maintain discipline in the classroom” differ widely across schools,
with long left-hand tails suggesting that some schools struggled in these areas. These
distributions also reveal that teachers on the whole, felt only slightly more positive than neutral
about these statements.
Not surprisingly, a school’s professional environment is also related to the characteristics
of its students and teachers. In Table 2, we compare school-level averages of selected student
and teacher characteristics by the quartiles of the overall rating of professional environment.
Schools with more supportive professional environments serve students who are higher-
achieving, more likely to be white, less likely to be from low-income families, and more likely to
attend school. On average, students at schools in the top quartile of the professional environment
outperform their counterparts in the lowest quartile by 3/4ths of a standard deviation in both
mathematics and reading and are absent over three days less per year. White students make up
over half of the student population at top quartile schools compared with less than 15% at bottom
quartile schools.
Schools with the most supportive professional environments also employ more highly-
qualified teachers. Teachers who are experienced, earned National Board certification, hold
master’s degrees, and graduated from competitive colleges are more likely to teach in top
quartile schools. Teacher sorting by race mirrors the same patterns found among students.
Schools in the bottom quartile of the professional environment employ less experienced teachers
on average and more than twice as many alternatively certified teachers as all other schools.
These strong associations between student characteristics – and to a lesser degree teacher
20
characteristics – and the professional environment in schools pose important challenges for
analysts using observational data. They illustrate the difficulties many past researchers have
faced when attempting to disentangle the effect of working conditions from the characteristics of
students or teachers in a school. They also highlight the importance of including our rich set of
controls for student characteristics and teacher fixed effects in our statistical models, as well as
examining whether the returns to experience differ by these teacher and student characteristics
(as we do in sensitivity tests).
3.3 Do teachers in schools with stronger professional environments improve more over time?
We find substantial heterogeneity in returns to experience across schools with different
professional environments. A one SD difference in the quality of the professional environment in
which teachers work is associated with an additional 0.0026 SD (p=0.024) increase in the annual
returns to teaching experience (Table 3, column 1). This becomes a 0.0052 SD difference after
two years, a 0.0078 SD difference after three years, and eventually a 0.0260 SD difference after
ten years. In Figure 4, we illustrate the magnitude of these differences as they compound over
time by plotting the within-teacher returns-to-teaching-experience profiles of three prototypical
teachers, those at schools which are rated as average as well as at the 75th and 25th percentiles of
the professional environment ratings.
On average, after three years, teachers working in schools at the 75th percentile of
professional environment ratings have improved their effectiveness by 0.010 SD more than
teachers working in schools at the 25th percentile, a 12% improvement gap. After five years,
teachers working at schools at the 75th percentile have improved their effectiveness by 0.017 SD,
on average, a 20% gap. As Figure 4 shows, by year ten, a prototypical teacher at a school with a
very strong professional environment will have improved by 0.035 SD more on average than a
21
teacher in a school with a very weak professional environment, a 38% gap. Thus, after ten years,
teachers at a school with a more supportive professional environment move upwards in the
distribution of overall teacher effectiveness by approximately one-fifth of a standard deviation
more than teachers who work in less supportive professional environments.
We extend this analysis by refitting model (IV) with each of our six conceptually distinct
elements of the professional environment and present these exploratory results in online
Appendix Table 1. Peer collaboration and school culture are among the strongest predictors, but
we emphasize that each element captures a large degree of common variance and that all six
parameter estimates are statistically indistinguishable from each other.
3.4 Assessing Model Assumptions
In Table 3, we present parameter estimates from our preferred model as well as
alternative specifications of our education production function which show that our primary
results are not driven by our modeling decisions.13 We begin by augmenting our preferred
specification of model (IV) by including school fixed effects, implicitly removing the effect of
all time-invariant student or teacher characteristics that differ systematically across schools.
Although we must remove the main effect of the professional environment from the model
because it does not vary within school, we can still estimate average differences in returns to
teaching experience across professional environments. We find that our parameter estimate
describing the differential returns to experience across professional environments remains
virtually unchanged (column 2).
Second, we replace teacher fixed effects with teacher-by-school fixed effects. Including
teacher-by-school effects restricts our estimates of the returns to experience to within teacher-
school combinations, eliminating the threat that specific patterns of teacher-transfer across
22
schools could create the effects we find. This approach produces somewhat larger and
statistically significant estimates of the differential returns to teaching experience across
professional environments, suggesting that the more conservative results from our primary
approach using model (IV) may understate the potential effect of the professional environment
(column 3).
Finally, we relax our assumption that the differential returns to experience across
professional environments are linear. In column 4, we report results from a model that allows for
the differential returns to experience to take on a quadratic functional form. Again, we continue
to specify the average returns-to-experience using a quartic polynomial; we simply model
deviations from this average trend using a quadratic relationship. The point estimate on the
interaction of our measure of the overall professional environment and the square of experience
is not statistically significant and is precisely estimated as very close to zero, which suggests that
the underlying pattern is linear. To be even more conservative, we also fit a model that uses a
completely flexible set of indicator variables to model these deviations. As seen above in Figure
4, these non-parametric point estimates are well approximated by our preferred model.
4. Alternative Explanations
The analytic methods discussed above allow us to show clearly that teachers in schools
with stronger professional environments experience greater returns to experience over time.
Ultimately, we also want to know whether it is the work environment itself that causes this
additional improvement over time. Thus, we examine the most plausible alternative explanations
for the patterns we observe in our data to further our understanding of the potential causes of this
observed relationship. However, we cannot make definitive causal statements about the
relationship between the professional environment and teacher development given the lack of
23
exogenous variation in the professional environment in our data.
Our construction and use of the professional environment measure presents several
possible alternative explanations. First, the relationship between returns to experience and the
professional environment could be a product of non-response bias, self-report bias or reverse
causality. Second, other unobserved characteristics that are correlated with the professional
environment in a school could be the underlying cause of the observed relationship. In addition,
a pattern where schools with more favorable professional environments recruit, select, and retain
teachers with greater potential for improvement over time could account for our results. A final
alternative explanation would be if student assignment patterns to individual teachers as they
gain experience differed across schools in ways that relate systematically to the work
environment.
4.1 Endogeneity in the Measurement of the Professional Environment
The construction of our measure of the overall professional environment using teacher
survey data presents the potential for three types of endogeneity: non-response bias, self-report
bias and reverse causality. We present evidence to assess the contributions of these biases to our
results in Table 4. First, it could be that the opinions of teachers who responded to the Working
Conditions Survey do not reflect the general opinion of teachers in their school. This issue would
be of particular concern in schools with low response rates. To test this, we restrict our sample to
include only those schools with at least a 50% response rate across the three survey
administrations. Results reported in column 1 of Table 4 demonstrate that our findings are
slightly stronger using this restriction, suggesting that measurement error due to low response
rates may be attenuating our results. We also examine the demographic characteristics of
teachers who responded to the survey and find that they are quite similar to those of the district’s
24
workforce as a whole.
A second concern is that, although the survey was both anonymous for teachers and its
results were not considered in any school evaluation process, individual teachers’ responses to
the working conditions survey may be systematically biased. Here, the issue is not that teachers
overall rated schools systematically higher (or lower), but that teachers in schools where early-
career teachers were improving at greater rates had systematically inflated responses. We
construct a test of this self-report bias by creating an alternative measure of PROF_ENV using
only the self-reported data from teachers with 11 years of experience or more. This allows us to
make inferences about the improvement of teachers in their first 10 years of the career without
relying on their own self-reported data to measure the professional environments in their schools.
As seen in column (2), results using this alternative measure of PROF_ENV are nearly identical
to our preferred estimates, demonstrating that our findings do not appear to be subject to a self-
reporting bias.
A third potential concern is that, by employing survey data from 2006 to 2010 to
characterize the professional environment in previous and concurrent years, our findings may be
the result of reverse causality. We examine this threat by refitting model (IV) in three ways.
First, we construct our measure of the professional environment using data from the first survey
in 2006 and limit our analysis to data from 2006 to 2010. Using this 2006 measure of the
working environment, we confirm that a prior measure of the work environment predicts large
and statistically significant differential returns to experience in future years (column 3). Here,
estimates are substantially larger than in our preferred model. Second, we then restrict our
sample to include only the three years during which the Working Condition survey was
administered (2006, 2008, and 2010). We fit two models in this restricted sample, one with our
25
preferred school-level average measure of the professional environment across these three years
and one with a time-varying measure. Parameter estimates in both models are quite similar in
magnitude to our preferred estimates, but are not statistically significant. These imprecise
estimates are likely the result of our reduced analytic sample from ten to three years of data,
although we cannot rule out the possibility that these coefficients are zero in the population
(columns 4 & 5). In short, the consistent pattern of results across these different specifications
suggests that non-response bias, self-report bias and reverse causality are not driving our
findings.
4.2 Omitted Variable Bias
Another concern is that that our estimates of the differential returns to experience may
not be driven by the professional environment in schools, but instead capture differences due to
unobserved teacher or student-body characteristics that are positively correlated with both the
quality of professional environment and student achievement. For example, it could be that
certain types of teachers are more likely than others to improve with experience and to work in
stronger professional environments. Or, perhaps teachers improve their effectiveness more
rapidly when they teach certain types of students who are likely to attend schools with stronger
professional environments. In order to test for these alternative explanations, we also allow for
differential returns to experience related to individual teacher characteristics as well as average
student characteristics in a school.
We refit model (IV) with an additional interaction term of and one of several
teacher or student-body characteristics and report the results in Table 5. If our estimates are the
result of omitted variable bias then including these terms should attenuate our point estimates
substantially. Instead, our estimates of the differential returns to experience across professional
26
environments remain practically unchanged by the addition of these interactions. Overall, these
results confirm that differences in returns to teaching experience across professional
environments are not driven by the strong correlations between the professional environment and
observed teacher characteristics or student-body characteristics in a school.
4.3 Dynamic Teacher Sorting across Schools
Finally, we must be concerned that teachers who will improve at greater rates selectively
sort into schools with stronger professional environments. Patterns of highly qualified teachers
sorting to more affluent, suburban, and white communities are widely documented in the
literature on teacher mobility (Lankford, Loeb, & Wyckoff, 2002; Clotfelter et al., 2007).
However, our inclusion of teacher fixed effects removes the possibility that a pattern where more
effective teachers sorting to schools with better professional environments would produce our
results. Instead, the concern is only that schools with more favorable professional environments
selectively recruit and hire teachers with greater potential for improvement over time. Although
we cannot rule out this alternative explanation, we find it more likely that schools would search
for effective teachers, rather than teachers who will improve. Furthermore, a large body of
literature documents the quite weak relationship between observable teacher characteristics and
future effectiveness (Wayne & Youngs, 2003; Clotfelter, Ladd, & Vigdor, 2007), as well
between measures of teachers’ conscientiousness and self-efficacy and future effectiveness
(Rockoff et al., 2011).
Positive estimates of the differential returns to teaching experience across professional
environments could also be the result of differential retention. Again, our results will only be
biased if schools are retaining teachers selectively who are improving more over time, not simply
that schools retain teachers who are more (or less) effective on average. We are able to examine
27
this possibility by testing whether the relationship between the probability of leaving a school
and estimates of an individual’s returns to teaching experience differ by the quality of the
professional environment in a school. To do this, we fit our teacher-specific random slopes and
intercepts model (model (II)) and obtain estimates of individual teachers’ pace of improvement,
relative to the average returns to experience, from the fitted model. We then use these best linear
unbiased predictions of the degree to which an individual teacher is improving) as a predictor
in the following linear probability model that at time t teacher j leaves school s:
We include fixed effects for calendar year and teacher experience to account for any district-
wide trends in student achievement or teacher employment patterns. The parameter estimate on
the interaction term, , tests whether teachers who are improving more
rapidly are less likely to leave schools with more supportive professional environments. We find
that teachers in more supportive professional environments are less likely to leave, but the
probability of leaving one’s school is unrelated to both changes in a teacher’s effectiveness over
time as well as the interaction of changes in effectiveness and our measure of the professional
environment. In other words, is not statistically different from zero (p=0.41).14 Thus, we find
no evidence that dynamic attrition explains our results.
4.4 Differential Student Sorting within Schools and Teachers
Finally, it is possible that our results are the product of differential student sorting
patterns to individual teachers as they gain experience, which are related to the professional
environment. Although more senior teachers and teachers in schools with better professional
environments are often assigned higher achieving students (Clotfelter, Ladd, & Vigdor, 2006;
Kalogrides, Loeb & Beteille, 2011), these patterns alone could not explain our results. Instead,
28
our findings could only be caused by a differential sorting pattern where schools with better
professional environments were more likely to assign such students to more experienced teachers
than schools with worse environments. Furthermore, because we include selected observable
student characteristics (including prior test scores) as covariates in our model, this alternative
explanation would require a pattern of differential sorting over time on unobserved
characteristics that are positively correlated with test scores. In fact, evidence suggests that the
opposite pattern may hold (Loeb, Kalogrides, & Beteille, 2012).
A true test of this alternative explanation is impossible to conduct because, by definition,
the variables we would like to examine are unobserved. Instead, we attempt to understand the
nature of dynamic sorting on observed student characteristics in order to gain insights into the
potential sorting on unobserved characteristics. To do this, we modify model (IV) by using
student characteristics as our outcomes, , and removing all student and peer level-
covariates as follows:
Again, the coefficient on the interaction of and , , is our parameter of
interest, as it examines whether certain types of students are more likely to be assigned to
teachers as they gain experience in schools with more supportive professional environments than
in schools with less supportive environments. In online Appendix Table 2, we show that
estimates of are near zero and not statistically significant across nearly all student
characteristics. The only statistically significant estimate points in the opposite direction than the
type of sorting that might indicate potential upward bias in our estimates. This suggests that
patterns of student sorting to teachers over time appear to be consistent across schools and
dynamic sorting on unobserved student characteristics is unlikely to explain away our findings.
29
5. Conclusion and Policy Implications
With this study, we have sought to document heterogeneity in the returns to teaching
experience and to examine whether this heterogeneity can be explained, in part, by the
professional environment in which teachers work. We find strong evidence of such
heterogeneity, establishing that there is not only substantial variation in teacher effectiveness, but
also in the pace at which teachers improve their effectiveness. Some teachers are improving two
or three times faster than others and continue these rapid gains in effectiveness throughout their
first five to ten years on the job. This large variation in returns to experience across teachers has
important implications for research and policy on teacher effectiveness.
Researchers often treat teacher effectiveness as fixed, attributing year-to-year fluctuations
to classroom-peer effects or sampling error. This approach assumes away an important element
of teacher effectiveness dynamics, how it changes over time with experience. Teachers are also
commonly characterized as having a fixed level of effectiveness in the popular press and in
education policy reform initiatives. For example, if Ms. Smith is an effective teacher, she should
be recruited, rewarded and retained. If Ms. Jones is an ineffective teacher, we should avoid
hiring her and she should not be granted tenure. That some teachers are far more effective than
others is an empirical fact. However, these characterizations fail to consider the substantial
degree to which individual teachers improve over their careers and the large variation in this
improvement. The frequent crossing of returns to experience profiles plotted in Panel A of
Figure 2 demonstrates how the rank order of teacher effectiveness changes as teachers improve
at different paces over time. A novice teacher who struggles at first but makes sustained
improvements over time may become more effective overall than an average novice teacher who
fails to improve with experience.
30
Our findings also illustrate how policies aimed at improving teacher effectiveness that
focus on the individual, ignoring the role of the organization, fail to recognize or leverage the
potential importance of the school context in promoting teacher development. We show that the
degree to which teachers become more effective over time varies substantially by school. In
some schools, teachers improve at much greater rates than in others. We find that this
improvement is strongly related to the opportunities and supports provided by the professional
context in which they work. For example, we estimate that teachers who work in schools at the
75th percentile of professional environment ratings increase their effectiveness by over 0.035
test-score SD more over the course of ten years than a similar teacher at a school at the 25th
percentile, a 38% difference in total improvement.
Although these findings are not definitive causal evidence that improving the
professional environment will accelerate teacher development, they are consistent with recent
evidence that the school context has lasting effects on teachers’ practice and career decisions.
For example, Ronfeldt (2012) finds that pre-service teachers who have field placements in
easier-to-staff schools become more effective teachers and are less likely to leave the profession
after five years, a result that is not driven by student characteristics or teacher sorting.
While our estimates of the differences in returns to experience across professional
environments are small in absolute magnitude, they are substantial given the overall distribution
of teacher effectiveness in the district. A difference of 0.035 test-score SD is approximately 20%
of a standard deviation in the distribution of overall teacher effectiveness and represents over
30% of the average total improvement teachers make in their first ten years on the job. As Boyd
and colleagues (2010) note, estimates of the effects of many interventions designed to improve
teacher effectiveness are overwhelmingly of similar or smaller magnitude (e.g., Boyd et al, 2008;
31
Goldhaber, Little & Theobald, 2012 ; Kane, Rockoff & Staiger, 2008; Koedel et al., 2010).
Furthermore, these results are likely to be a lower bound estimate for several important reasons.
First, measurement error inherent in the survey response data we use to quantify the professional
environments in schools will necessarily attenuate our findings. Second, CMS’s district-wide
efforts to improve schools’ professional environments are not captured by our estimates, as we
only examine variation in environments across schools. Finally, our measure of effectiveness
based on teachers’ contributions to student achievement on standardized tests does not fully
capture many aspects of teachers’ professional practice or the ways in which veteran teachers
contribute to the effectiveness of their peers and assume important leadership roles (Jackson &
Bruegmann, 2009; Johnson & Birkeland, 2003).
Ultimately, comparing point estimates across studies fails to capture a central difference
between supportive professional environments and many interventions intended to improve
teacher effectiveness. In contrast to a one-time investment in teacher skills, teachers have the
potential to benefit from the learning opportunities provided by a supportive professional
environment every day. Our findings suggest that working in a more supportive environment is
related to improvement which accumulates throughout the first ten years of the career.
Furthermore, our study’s findings that strong professional environments are related to
individual teachers’ improvements align with the growing recognition that such environments
benefit teachers and students systematically. For example, if teachers in more supportive
environments improve more and feel more successful because of this improvement, this “sense
of success” can increase the likelihood they remain at their schools (Johnson & Birkeland, 2003).
A large body of research finds that strong professional environments are directly related to
teacher retention (Allensworth et al., 2009; Boyd et al., 2011; Johnson, Kraft & Papay, 2012;
32
Ladd, 2011; Loeb, Darling-Hammond, & Luczak, 2005). As effective teachers remain in schools,
opportunities for meaningful peer collaboration and a positive organizational culture become
even more possible. This positive cycle can lead to effective school organizations, while, the
opposite pattern can occur in hard-to-staff schools. Poor working conditions may stifle teachers’
efforts to improve their practice, promoting turnover and contributing to staffing challenges.
Scholarly research is just beginning to discover why some teachers improve more than
others and the importance of school organizational environments for systemic improvement.
Practice and research have started to highlight promising avenues for promoting improvement
among teachers, such as providing teachers with actionable feedback about their instruction,
creating opportunities for productive and sustained peer collaboration, supporting teachers’
efforts to maintain an orderly and disciplined school environment, and investing in a school
culture characterized by high expectations, trust and mutual respect. Transforming schools into
organizations that support the learning of both students and teachers will be central to any
successful effort to increase the human capital of the U.S. teaching force.
33
Endnotes
1
We define teachers in our data as individuals in the Human Resources employment files who are paid based on the
teacher salary schedule, who have titles that indicate they are classroom teachers, and who are uniquely identified as
the math teacher of record in the course file. This results in a total of 3,922 4th through 8th grade teachers who taught
students in math. We restrict our sample to only those teachers who teach regular education classes and who have at
least five students with valid current and prior test scores in math, removing 2.6% of our sample. We then drop an
additional 1.1% of teachers who work in schools that do not have at least 10 respondents to the Working Conditions
Survey in any year. Next, we remove teachers from the data for whom we observe irregular jumps on the salary
experience scale in back-to-back years. These irregular jumps are likely caused by human resource processing delay,
retroactive credits awarded for relevant outside experience, or measurement error, and could bias our estimates of
the return to teaching experience. This eliminates 5.5% of our sample. Finally, we restrict our estimates to those
teachers who have continuous experience profiles, meaning that they do not leave the district and return. This
removes 10.5% of the sample. Importantly, relaxing either of these two final sample restrictions, or both, does not
change the character of our results.
2 Formally,
Rockoff justifies this assumption by citing previous literature that finds no evidence of returns to teaching
experience beyond the first several years on the job. We also choose 10 years because we are primarily interested in
early-career returns to experience, where we possess the most data; teachers with 10 years of experience or fewer
comprise 70% of our estimation sample.
3 We estimate models using two alternative identifying assumptions. First, we censor experience at 20 years.
Second, we adopt a two-stage modeling approach that we have developed in a separate paper (Papay & Kraft, 2012).
As expected, we find that our results are quite consistent across modeling approaches.
4 In each survey year, the Eigenvalue of the first principal component was greater than 12, with item loadings
ranging between 0.14 and 0.24 across all 24 times, while the Eigenvalue of the second principal component was less
than 2. Visual inspection of the corresponding scree plots shows a clear kink at the second Eigenvalue.
5 Several other factors contributed to this decision. It is unclear whether differences in our measure of the
professional environment across survey administrations are capturing true changes over time, or whether these
differences are due to the changing composition of survey respondents, differential survey response rates across
years, or changes in the response anchors across years.
6 We obtain these data from publicly available records maintained by the North Carolina Department of Instruction.
These state records cover 90.5% of the school-years observations in our analytic sample. We impute school-specific
values for missing data by taking the average of all available school-year observations for a given school. We
include a dichotomous indicator for school-years in which we imputed missing data in all our models.
7 We estimate standard errors after clustering students by school-by-grade-by-year to account for possible
unobserved correlations among the residuals of students in the same grade cohort within a school.
8 Including lagged student test scores, , as independent variables is potentially problematic because these
scores are an imperfect measure of true achievement. It is possible that measurement error in lagged test scores will
be correlated with measurement error in current-year test scores. This potential for serial correlation between
individual students’ error terms over time could result in biased estimates. We examine this potential threat by
instrumenting for lagged test scores using twice-lagged test scores as proposed by Todd and Wolpin (2003). This
alternative estimation strategy does not affect the character of our results.
9 See Murnane and Willett (2010) for a clear discussion of the trade-offs between using fixed and random effects
models.
34
10 We assume that the teacher-specific random intercepts and slopes are distributed non-independently, bivariate
normal with mean zero and appropriate population variances and covariance. Fitting our models results in moderate
to strong negative estimates of the correlations between the teachers’ initial effectiveness and their change in
effectiveness over time as reported in Table 1. These are asymptotically unbiased estimates of the population
correlation between teachers’ true initial status and change, estimated within the model rather than estimated by
predicting these values for individual teachers and then correlating these predictions ex-post. Our unbiased estimate
of a negative correlation between true change and initial status are consistent with Atteberry, Loeb and Wyckoff
(2012) who found that teachers in “the lowest two quintiles [of initial value-added] exhibit the most improvement.”
11 Estimating random-effects variance components within our model using full-information maximum likelihood
allows us to obtain consistent estimates of the true population variances and covariance. Alternative estimators such
as the corresponding sample variances of OLS or empirical Bayes estimates of individual teacher intercepts and
slopes would result in bias -- an overestimate and underestimate, respectively (see Bryk & Raudenbush, 2002 p.88).
12 We find nearly identical results across a variety of specifications. First, we change our identifying assumption by
censoring the main effect of experience at 20 years instead of ten. Second, we restrict our sample to include only
teachers who taught for at least five years in the district to ensure that teachers for whom we have very few years of
data are not inflating estimated variances. Lastly, we relax our assumption that individual and school-specific
deviations from the common returns to experience profile are linear by allowing these deviations to take on a
quadratic functional form.
13 An alternative approach to modeling these returns to experience involves estimating the model in two steps. Here,
we could fit a model similar to that in model (1), omitting the experience predictor and estimating teacher-year
effects rather than teacher fixed effects. We could then regress these teacher-year effects (which essentially reflect
an estimate of the teacher’s productivity in each year) on a quartic function of teacher experience (uncensored) and
an interaction between our measure of the professional environment and a linear measure of experience through the
first ten years of a teacher’s career. When we implement this approach, we find that our parameter of interest is
0.0023 (p=0.023), nearly identical to the estimate of 0.0026 from our preferred model. We estimate standard errors
using the bootstrap method to account appropriately for this two-stage modeling approach.
14 We estimate standard errors using the bootstrap method to account appropriately for the two-stage modeling
approach used in model (V).
35
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39
Figures
Figure 1: Estimated Average Returns to Teaching Experience, over Ten Years
Notes: This figure is based on parameter estimates from model (I), which specified achievement as a non-parametric
function of teaching experience, with results from the quartic functional form overlaid.
40
Figure 2: Estimated Individual Returns to Teaching Experience for a Random Sample of 25
Teachers with at least Seven Years of Classroom Experience
Notes: We depict in this figure the returns to experience profiles of 25 teachers based on post-hoc estimates from
model (II). In panel B, we center these profiles at zero to illustrate differences in the returns to experience over time
across teachers.
41
Figure 3: Sample Distributions of Unstandardized School-Average Responses to three Survey
Items from the 2008 Teacher Working Conditions Survey
Notes: Full item stems are “There is an atmosphere of trust and mutual respect within the school”, “Teachers have
time available to collaborate with their colleagues”, and “School administrators support teachers' efforts to maintain
discipline in the classroom”
0.2 .4 .6 .8
Density
Strongly
disagree Somewhat
disagree Neither
disagree
nor agree
Somewhat
agree Strongly
agree
Trust & Mutual Respect Time to Collaborate
Discipline Support
42
Figure 4: Fitted Returns to Teaching Experience for Prototypical Teachers, across School
Professional Environments
Notes: In this figure, we plot fitted estimates from model (IV) in which we specific the main effect of experience as
a quartic function, and allow for individual linear deviations from the average relationship between experience and
achievement. We also include fitted estimates from a model that in which we specify experience as a vector of
dichotomous indicator variables up to ten years interacted with our measure of the overall professional environment
for teachers at the 25th and 75th percentile schools.
43
Tables
Table 1: Standard Deviations of Random Intercepts and Slopes from Multilevel Models
Examining Heterogeneity in Returns to Teaching Experience
(1)
(2)
(3)
Teacher Intercepts (σαj)
0.177***
0.170***
0.143***
(0.004)
(0.004)
(0.002)
Teacher Slopes (σβj)
0.025***
0.024***
(0.001)
(0.009)
School Intercepts (σμj)
0.068***
0.073***
(0.006)
(0.007)
School Slopes (σβs)
0.007***
(0.001)
Residual (σ)
0.443***
0.443***
0.444***
(0.001)
(0.001)
(0.001)
Corr(σαj, σβj)
-0.625
-0.658
Corr(σμj, σβs)
-0.353
Observations
280,687
280,687
280,687
Notes: *** p<0.001, ** p<0.01, * p<0.05. Standard errors reported in parentheses.
44
Table 2: Sample Averages of Student and Teacher Characteristics by Quartiles of the Overall
Professional Environment in Schools
Mean
Quartiles of Professional
Environment
Bottom
2nd
3rd
Top
Panel A: School-Average Student Characteristics
Student Enrollment
807
889
639
844
837
Mathematics Achievement in Grades 4-8 (SD)
-0.09
-0.45
-0.38
0.03
0.36
Reading Achievement in Grades 4-8 (SD)
-0.09
-0.42
-0.37
0.03
0.35
Days Absent per Student
7.44
9.41
7.94
6.64
6.03
Limited English Proficient
0.15
0.17
0.17
0.15
0.12
Special Education
0.11
0.14
0.11
0.10
0.10
Free and Reduced Price Lunch
0.56
0.71
0.74
0.50
0.32
African American
0.45
0.61
0.59
0.38
0.24
White
0.30
0.13
0.15
0.36
0.53
Hispanic
0.16
0.18
0.18
0.16
0.13
Panel B: Teacher Characteristics
0 to 3 years of Experience
0.37
0.42
0.41
0.36
0.30
4 to 10 years of Experience
0.33
0.31
0.35
0.34
0.34
11 years of Experience or more
0.30
0.26
0.24
0.31
0.36
African-American
0.24
0.39
0.28
0.22
0.13
White
0.73
0.58
0.70
0.76
0.85
National Board Certified
0.07
0.04
0.06
0.06
0.12
Master's Degree
0.27
0.24
0.26
0.28
0.30
Alternative Pathway Certification
0.12
0.23
0.08
0.09
0.07
Less Competitive College
0.15
0.22
0.18
0.13
0.08
Competitive College
0.50
0.49
0.53
0.49
0.49
Very Competitive College
0.24
0.20
0.20
0.26
0.27
Highly Competitive College
0.07
0.06
0.06
0.06
0.11
Most Competitive College
0.04
0.03
0.03
0.05
0.05
Notes: We estimate statistics for student characteristics using school-year averages for those schools in
the analytic sample. We estimate statistics for teacher characteristics using all teacher-year observations
that are represented in the analytic sample.
45
Table 3: Parameter Estimates of the Differential Returns to Teaching Experience across Schools with
More Supportive and Less Supportive Professional Environments
Student Level
(1)
(2)
(3)
(4)
EXPER* x PROF_ENV
0.0026*
0.0025*
0.0039*
0.0027
(0.0011)
(0.0011)
(0.0016)
(0.0027)
EXPER*
0.0664***
0.0685***
0.0673***
0.0664***
(0.0087)
(0.0085)
(0.0087)
(0.0087)
EXPER*^2
-0.0174***
-0.0188***
-0.0180***
-0.0174***
(0.0039)
(0.0039)
(0.0040)
(0.0039)
EXPER*^3
0.0020**
0.0022***
0.0021**
0.0020**
(0.0006)
(0.0006)
(0.0006)
(0.0006)
EXPER*^4
-0.0001*
-0.0001**
-0.0001*
-0.0001*
(0.0000)
(0.0000)
(0.0000)
(0.0000)
PROF_ENV
-0.0087
-0.0090
(0.0083)
(0.0092)
EXPER*^2 x PROF_ENV
-0.0000
(0.0002)
Teacher Fixed Effects
Yes
Yes
Yes
School Fixed Effects
Yes
Teacher-by-School Fixed Effects
Yes
Observations
280,687
280,687
280,687
280,687
Notes: *** p<0.001, ** p<0.01, * p<0.05*, + p<0.10. Standard errors clustered by school-grade-year
reported in parentheses. All student-level models include grade-by-year fixed effect as well as vectors
of student, peer, and school-level covariates.
46
Restricted Sample of
School with Combined
50% Response Rate
Across Surveys (2001-
2010)
Prof. Env. Measure
Constructed Using Only
Veteran Teachers (2001-
2010)
2006 Measure of Prof.
Env. (2006-2010)
Avg. Prof. Env. Measure
in 2006, 2008, 2010
Time-varying Prof. Env.
Measure in 2006, 2008,
2010
(1) (2) (3) (4) (5)
EXPER* x PROF_ENV 0.0032* 0.0025* 0.0071* 0.0022 0.0024
(0.0013) (0.0012) (0.0031) (0.0022) (0.0023)
EXPER* 0.0637*** 0.0662*** 0.0748*** 0.0474* 0.0400*
(0.0094) (0.0087) (0.0142) (0.0199) (0.0192)
EXPER*^2 -0.0151*** -0.0174*** -0.0216*** -0.0083 -0.0080
(0.0042) (0.0039) (0.0061) (0.0081) (0.0080)
EXPER*^3 0.0015* 0.0020** 0.0029** 0.0009 0.0009
(0.0007) (0.0006) (0.0010) (0.0012) (0.0012)
EXPER*^4 -0.0001 -0.0001* -0.0001** -0.0000 -0.0000
(0.0000) (0.0000) (0.0000) (0.0001) (0.0001)
PROF_ENV -0.0138 -0.0077 0.0046 0.0024 0.0224
(0.0095) (0.0087) (0.0241) (0.0140) (0.0165)
Teacher Fixed Effects Yes Yes Yes Yes Yes
Observations 243,178 280,687 125,302 86,343 86,343
Notes: *** p<0.001, ** p<0.01, * p<0.05*, + p<0.10. Standard errors clustered by school-grade-year reported in parentheses. All models include grade-by-
year fixed effects as well as vectors of student, peer, and school-level covariates. Model 1 restricts the sample to the 91% of schools that have at least a 50%
combined response rate across all three Teacher Working Condition Surveys. Model 2 uses an alternative measure of the professional environment
constructed using only responses from teachers with eleven or more years of experience. Model 3 uses only data from 2006 to construct a measure of the
professional environment and only includes schools with a valid 2006 measure. Model 4 uses our preferred overall measure of the professional environment
in a restricted sample that includes the three years the Teacher Working Condition Survey was administered. Model 5 uses a time-varying measure of the
professional environment and restricts the sample to the same three years as model 4. In Model 5, we impute missing values of the time-varying measure of
the professional environment with the average professional environment among years with valid data for each school to facilitate a comparison of results
with model 4 which is not confounded by sample differences. We account for this imputation by including an indicator for school-years with missing values
for the professional environment and its interaction with EXPER*. Missing values are concentrated in 2006 and represen t 4.7% of the school-year
observations in Model 5.
Table 4: Parameter Estimates of Differential Returns to Teaching Experience across Schools Using Alternative Measures of the Overall Professional
Environment in Schools
47
White African
American
National Board
Certification
Alternative
Certification
Master's Degree
Competitive
College
(1) (2) (3) (4) (5) (6)
EXPER* x PROF_ENV 0.0028* 0.0028* 0.0024* 0.0026* 0.0026* 0.0030*
(0.0012) (0.0012) (0.0011) (0.0011) (0.0011) (0.0012)
EXPER* x Teacher Characteristic -0.0042 0.0046 0.0033 0.0013 -0.0007 -0.0021
(0.0029) (0.0030) (0.0033) (0.0013) (0.0028) (0.0028)
Observations 278,169 278,169 280,687 274,481 280,687 257,202
% FRPL
%African
American
% Limited
English
Proficient
% Special
Education
Average
Mathematics
Achievement in
Prior Year
Average
Reading
Achievement in
Prior Year
(1) (2) (3) (4) (5) (6)
EXPER* PROF_ENV 0.0021+ 0.0021+ 0.0025* 0.0025* 0.0022+ 0.0023+
(0.0012) (0.0013) (0.0011) (0.0011) (0.0013) (0.0013)
EXPER* x Student Body Characteristic -0.0014 -0.0009 -0.0006 -0.0032 0.0015 0.0018
(0.0011) (0.0010) (0.0010) (0.0025) (0.0023) (0.0030)
Observations 280,687 280,687 280,687 280,687 280,687 280,687
Table 5: Sensitivity Analyses of the Differential Returns to Teaching Experience across Schools with More Supportive and Less Supportive Professional
Environments
Notes: *** p<0.001, ** p<0.01, * p<0.05*, + p<0.10. Standard errors clustered by school-grade-year reported in parentheses. All models include teacher-
fixed effects and grade-by-year fixed effects as well as vectors of student, peer, and school-level covariates. We omit the main effect of time-invariant
teacher characteristics from models. We include the main effect of the respective student-body characteristic in all models that allow for differential
returns to experience by student-body characteristics.
Panel B: Models that also allow for differential returns by student-body characteristics
Panel A: Models that also allow for differential returns by individual teacher characteristics
48
Appendix
Appendix Table 1: Parameter Estimates of the Differential Returns to
Teaching Experience across Schools by Six Conceptually Distinct
Elements of the Professional Environment
EXPER* x Order & Discipline
0.0024*
(0.0010)
EXPER* x Peer Collaboration
0.0027*
(0.0011)
EXPER* x Principal Leadership
0.0022+
(0.0011)
EXPER* x Professional Development
0.0012
(0.0011)
EXPER* x School Culture
0.0026*
(0.0011)
EXPER* x Teacher Evaluation
0.0020+
(0.0011)
Notes: ** p<0.01, * p<0.05*, + p<0.10. Standard errors clustered by
school-grade-year reported in parentheses. Each cell represents results
from a separate regression. The number of observations in each regression
is 280,687.
49
Appendix Table 2: Parameter Estimates from Tests of Differential Within-teacher
Sorting of Students across Schools with More Supportive and Less Supportive
Professional Environments
Male
-0.0007
(0.0006)
[280,687]
African American Students
0.0002
(0.0007)
[280,687]
Limited English Proficient
-0.0004
(0.0004)
[280,687]
Special Education
-0.0004
(0.0005)
[280,687]
Retained in Grade (previous year)
0.0004*
(0.0002)
[262,063]
Total Tardies (previous year)
-0.0038
(0.0199)
[279,902]
Total Absences (previous year)
-0.0081
(0.0089)
[279,902]
Mathematics Achievement (previous year)
0.0007
(0.0027)
[280,687]
Reading Achievement (previous year)
-0.0004
(0.0024)
[280,687]
Notes: ** p<0.01, * p<0.05*, + p<0.10. Standard errors clustered by school-grade-
year reported in parentheses. Sample sizes reported in brackets. Each cell represents
results from a separate regression.
