mean peer characteristics.
j
3
x||
A fourth model, which does not control for student baseline scores, students’ baseline demographics, or mean peer characteristics.The first column uses our primary model,
x||
0j, to predict teacher effects. It is possible that we “overcontrolled”in this model, and the component that was removed by peer effects could also predict additional differences in teacher performance under randomization.35
Therefore, the second column includes
x||
0j as well asx||
1j-x||
0j, the portion of the teacher effect that was sub-tracted off when controlling for peer effects. We estimate the coefficient on this additional component in the same way as we have in other specifications, using the additional component for the assigned teacher as an instrument for the additional component of the student’s actual teacher. The coefficient on this component is also near one and significantly different from zero. In other words, the component removed by controls for peer effects does seem to reflect causal teacher effects—not just factors outside a teacher’s control. It is a significant predictor of teacher impacts on student test scores following randomization. This suggests that we may have been overcontrolling when we added controls for peer effects, capturing a portion of the effect attributable to teachers.
Column (3) repeats the exercise for the component removed by student demographics. It includes three vari- ables:
x||
0j,x||
1j-x||
0j,x||
2j-x||
1j. Although the coefficients onx||
0j andx||
1j-x||
0j are both statistically differentfrom zero and not statistically different from one, the component associated with student demographics,
j j
2 1
x||
-x||
, is not statistically different from zero. In other words, the component removed by controls for stu-dent demographics does not seem to contain a portion that is associated with causal teacher effects—it is not
35 It is somewhat counterintuitive that our primary measure could accurately predict a one-unit difference in student outcomes yet still be overcontrolling for peer effects. Here’s the intuition. One can decompose a teacher’s true causal effectiveness into two components: One component that is correlated with classroom peer characteristics (due to sorting of effective teachers to classrooms with higher prior achievement scores); and the remaining component that is independent of peer characteristics. Our primary measure of effectiveness removes the component that is related to peer characteristics, but the remaining component is still correct on average because it is not related to peer characteristics by construction—some teachers (teaching classrooms with higher prior achievement scores) will have causal effects greater than our primary measure, while others (teaching classrooms with lower prior achievement scores) will have casual effects less than our primary measure. If we had not overcontrolled, we could have identified these additional causal differences between teachers that are related to peer characteristics.
TESTIng FOR bIaS In COMPOnEnTS REMOVED by ValUE-aDDED MODElS WITh InCREaSIngly RICh COnTROlS
(1) (2) (3) (4)
Variable Math and ELA Stacked Math and ELA Stacked Math and ELA Stacked Math and ELA Stacked Expected student achievement
in teacher’s class based on teacher’s effectiveness in prior year, controlling for student baseline scores, demographics, and peer effects
0.955***
(0.123) 0.947***(0.115) 0.934***(0.127) 0.879***(0.131)
Component removed by controls
for peer effects 1.150***(0.336) 0.932***(0.337) (0.424)0.636
Additional component removed by controls for student demographics
-0.025
(0.521) (0.508)0.015
Additional component removed by controls for student baseline scores
0.047 (0.042)
Observations 27,255 27,255 27,255 27,255
R-squared 0.684 0.684 0.684 0.685
Number of randomization blocks 619 619 619 619
Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
Note: The sample consists of all randomized students in grades 4 through 8. The dependent variable is student achievement on state tests following random assignment in 2011, standardized by grade and district. Expected student achievement in a teacher’s class is the prediction of the teacher’s value-added in that subject, based on value-added, student surveys, and observations in the prior school year. See text for description of how additional components were calculated. The coefficients are LIML IV estimates of the effect of actual teacher effectiveness and each of the components, using the effectiveness and components of randomly assigned teachers interacted with school-level indicators as instruments. All specifications also included fixed effects for randomization block and controls for students’ prior achievement and demographics as described in the text. Standard errors were calculated allowing for clustering within teacher.
a significant predictor of teacher impacts on student test scores following randomization. However, because the standard error is quite large and the confidence interval includes one, we also cannot reject the view that this component contains a sizable portion attributable to teacher effectiveness.36 Unfortunately, our evidence
cannot resolve the long debate over the inclusion of student demographics.
Column (4) adds the component associated with student baseline scores,
x||
3j-x||
2j. As with student demo-graphics, the component associated with the baseline scores of individual students was not significantly related to the performance of students following random assignment. Unlike with student demographics, however, the effect of this component could be estimated fairly accurately (with a standard error of .04). This provides strong evidence that controls for student baseline scores are removing variation that is not attribut- able to teacher effectiveness.
In sum, we are comfortable recommending that school systems should control for student baseline scores, since this component is not predictive of outcomes following random assignment. At least for making com- parisons within schools, the evidence also recommends against controlling for mean characteristics of stu- dents, since this component does seems to be predictive of outcomes following random assignment. However, the peer effect controls may be important to eliminate bias in between-school comparisons—a possibility we could not test. As a result, we cannot make a recommendation on the use of peer effects without fur- ther evidence. Finally, the case for or against controlling for demographic characteristics of students remains ambiguous.