1. Introduction
1.1 question
Does the impact of teachers extend beyond the students in their classroom?
1.2 motivation
(1) the importance of teachers
the impact of teachers on their students’ short-term achievement ( test scores, attendance, or discipline), as well as longer-term outcomes ( high school graduation, college attendance, and earnings)
a teacher’s “value-added” (VA): the estimated effect of a teacher on her or his students’ test scores, increasingly used in school districts as one of the inputs into the district’s personnel decisions
(2) the value of teachers potentially extends beyond the impact they have on their own students.
[By increasing the ability of their own students, effective teachers increase the peer ability for a much larger group of students. If students are affected by their peers’ ability, teachers then indirectly affect their students’ future peers. ]
it is unlikely that applying the estimates from the literature on peer effects to the existing VA estimates will accurately quantify the importance of this channel.
the endogenous peer effect: the direct effect of a student’s peers’ test score on the student
the exogenous or contextual peer effect: the effect of other aspects of the peers’ background such as their parental involvement or socioeconomic status
[identifying a teacher’s indirect effect on their students’ future peers requires isolating the endogenous peer effect.]
1.3 Approach and Data
multiple elementary schools feed into the same middle school
suppose two elementary schools (Elementary School A and Elementary School B) feed into one middle school, and that in 2008 an effective teacher (Teacher X) enters Elementary School A.
By comparing the students who attended Elementary School A after 2008 to those who attended before 2008, it is possible to estimate the direct effect of Teacher X on her students.
This approach is valid as long as teacher turnover in a student’s neighboring elementary school is uncorrelated with unobservable determinants of her test scores. A natural concern is the existence of unobserved neighborhood shocks that both draw high-quality teachers to the local schools and lead independently to higher test scores.
a comprehensive administrative dataset covering more than 585,000 students who attended a New York City public middle school from 1990–2010.
1.3 major findings
(1) an effective teacher (as measured by teacher value-added) also affects individuals who later share a class with the teacher’s students. This effect is both statistically and economically significant, with an increase in the average quality of a student’s peers’ previous teachers being found to affect the student’s test score by around 50 percent as much as a similar increase in her own teacher’s quality.
(2) ignoring a teacher’s effect on their student’s future peers underestimates a teacher’s value by anywhere from 30 percent to 90 percent, depending on which assumptions are made about how to handle the dynamic nature of the comparisons and the precise definition of the peer group.
(3) a method of moment estimator that simultaneously estimates teacher value-added and the spillover parameter: By comparing these teacher value-added measures to the traditional measures of teacher value-added, in New York City at least, accounting for the spillovers does not have a large effect on the ranking of teachers.
(4) The spillovers occur mainly within-subjects and not across-subjects.
The estimated spillovers seem to occur mainly within groups of students who are the same race and gender, as opposed to occurring within the entire grade.
1.4 innovations
(1) the measurement of teacher value:
While these studies lead to relatively precise estimates of the bias in teacher VA when comparing teachers at the same school, these approaches are less able to determine whether VA measures are accurate predictors of teacher quality when comparing teachers at different schools.
Instead of trying to directly estimate the bias in VA measures, I take a different approach and show that there is a mechanism (peer spillovers) that theoretically causes the estimated VA measures to diverge from the teachers’ true VA. However, I also show that in New York City these spillovers do not lead to a large change in the way teachers are ranked based on their VA estimates, even when comparing teachers across very different schools.
(2) the importance of teachers on student outcomes:
a new channel through which teachers can add value to the school system that extends beyond the effect they have on their own students. This is in contrast to the vast majority of papers that study the importance of teachers.
the peer effect channel
(3) how students are affected by their peers:
cannot separately identify the causal effect of increasing a student’s test scores on her peers’ test scores (i.e., endogenous peer effect) from the effect of the student’s other characteristics on her peers’ test scores (i.e., the exogenous or contextual peer effects).
Since the variation in peer test scores that I exploit is unrelated to changes in other peer characteristics, this paper differentiates itself by its ability to isolate the endogenous peer effect.
2. Data
2.1 data in general
student-level administrative data from the New York City Department of Education
yearly information on the roughly 1.8 million students who attended grades 3–8 in New York City from the 1990–1991 school year until the 2010–2011 school year.
each student: his or her school and grade; his or her math teacher and English teacher; the year-end math and English test scores (standardized by year, grade, and subject); some demographic information (gender and race).
2.2 Sample Restrictions
(1) focus on the transition from elementary school to middle school.
there are a number of K–8 schools in New York City
the makeup of elementary schools and middle schools in New York City has changed over time, with the number of K–6 schools falling and the number of K–5 and K–8 schools increasing
include in the regressions information from each student’s first year at middle school, regardless of what grade this is.
do not include any student in a K–8 school.
(2) any students who make a non-traditional elementary-to-middle school transition are implicitly dropped from the regressions, since there is no comparison group of students who made the same elementary-to-middle school transition in the previous year
This restriction also leads to dropping anyone who did not attend elementary school in a New York City public school.
(3) all students who are missing middle school test scores are by necessity excluded from regressions.
I also drop students in separate special education classrooms, which are usually co-taught and in which many students are exempt from the year-end tests.
In addition, the regression sample drops an entire cohort of students (i.e., a group of students who transition from the same elementary to the same middle school in the same year) if all of the students are missing the control variables in the particular specification.
[TABLE 1]
2.3 Teacher Value-Added
the same technique as in Chetty, Friedman, and Rockoff (2014a)
(1) removing the determinants of students’ test scores that a teacher cannot affect, which is done by regressing students’ test scores on a vector of fixed student observables and a flexible cubic function of students’ lagged math and English test scores.
(2) The regression results in student-subject-year residuals, which are then averaged at the teacher-subject-year level.
These teacher-subject-year measures combine the impact of the teachers on their students with all the unobserved determinants of the students’ test scores, which means that these teacher-subject-year measures can be thought of as being the true teacher’s VA plus an error term.
(3) To remove the contemporaneous error terms from the teacher VA estimates, the Chetty, Friedman, and Rockoff (2014a) technique predicts the teacher-subject-year aggregate residuals with the teacher-subject-year residuals from the same teacher-subject in different years.
[FIGURE 1]
3. Empirical Strategy
c(e, m, t)
the average test scores on subject s of these students in year t
a measure of the difference in average test scores between subsequent cohorts
the average teacher VA on subject s for the teachers in the highest grade at elementary school e in year t − 1
a measure of how the average teacher VA in the highest grade at elementary school e changed between year t − 1 and year t − 2.
use information on the outcomes of the students they taught in every year but t − 1 and t − 2
the teachers for whom I cannot estimate teacher VA at elementary school e in year t − 1 are the same quality as the teachers for whom I cannot estimate teacher VA at the same elementary school in the previous year.
a shrunken leave-out-average
the leave-out-average is shrunken toward 0 by an amount that corresponds to the size of the left-out group.
for two reasons: First, using the shrunken leave-out average as a covariate in an ordinary least squares (OLS) regression is asymptotically equivalent to using the traditional leave-out-average as an instrument for the overall average in an IV regression.
Second, using the shrunken leave-out average gives more precise coefficient estimates than the traditional leave-out average; the intuition behind this is that the shrunken leave-out average incorporates variation in the size of the left-out group into the variable, leading to a stronger relationship between it and the overall average than between the traditional leave-out average and the overall average.
估计值与真实情况有两点不同：(1) fix the weights on each elementary school. This means it ignores variation caused by students at middle school m coming from different elementary schools in year t than in year t − 1.
(2) it constructs the average teacher VA at each elementary school using all teachers in the top grade at the elementary schools, rather than focusing on the teachers of the students who go on to attend middle school m.
only reflects changes in the average VA at the neighboring elementary schools and is not affected by changes in the sorting patterns of students to middle schools or students to teachers within-elementary schools.
weighted-least squares regression
cluster the standard errors at the middle-school level and weight the regressions by the number of students in each cohort who take the year-end test for the relevant subject
4. identifying assumptions
(1) the main peer variable needs to be exogenous: teacher turnover in a student’s neighboring elementary schools is uncorrelated with unobservable determinants of her test scores
(2) there needs to be meaningful variation in the year-to-year changes in average teacher quality in the top grade at a student’s neighboring elementary schools.
Constructing the peers’ average therefore involves averaging over a relatively small number of teachers, as opposed to averaging over a large number of students. This means that there is more variation, for example, in the year-to-year changes in a cohort’s peers’ average previous teacher VA than there is in the year-to-year changes in a cohort’s peers’ average baseline test scores.
(3) the method of moments estimator discussed in Section IV provides unbiased estimates of true teacher VA, or equivalently that the only bias present in traditional teacher VA estimates is due to the spillovers studied in this paper.
5. results
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