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The effects of teacher quality on the robustness of the racial interaction effects can be assessed by using classroom fixed effects in place of school fixed effects in the regression (Dee 2004). This will result in the racial interaction effects being identified using within-classroom variation; therefore, any potential teacher sorting across schools by quality and race will no longer be conflated with the racial interaction effect. This is because the estimate of the effect is no longer also capturing any potential within-school quality differences of a low-quality teacher whose students are mostly of the opposite race with a high-quality teacher whose students are largely of the same race (which is a potential danger if the racial interaction effects are identified using within-school variation—i.e., by using a school fixed effect). An additional benefit of including classroom fixed effects is that it also controls for other unobservable teacher inputs and classroom effects (such as peer effects). Estimating the system of equations using classroom fixed effects, I find no substantive differences in the results, which are displayed in table 6.19

Table 6. 
Own-race Teacher Effect on Achievement, Using Classroom Fixed Effects
MathematicsReadingWord Recognition
Kindergarten    
 15.39** 6.00** 5.28* 
 (2.63) (1.76) (2.05) 
Observations 5,782 5,701 5,762 
First grade    
 17.12** 13.01** 13.15** 
 (2.69) (2.86) (3.40) 
 5.57* 10.94** 10.28** 
 (2.55) (2.93) (3.79) 
Observations 3,958 3,865 3,359 
Second grade    
(1,1,1)(0,0,0) 13.76** 8.46* 9.22* 
 (3.36) (3.40) (4.11) 
(1,1,0)(0,0,0) 7.89** 3.28 4.01 
 (3.00) (2.95) (3.81) 
(0,1,1)(0,0,0) 6.68* 3.55 5.26 
 (3.31) (3.27) (4.42) 
Observations 2,336 2,338 2,348 
Third grade    
(1,1,1,1)(0,0,0,0) 13.68** 17.85** 26.94** 
 (3.25) (3.26) (5.13) 
(1,1,1,0)(0,0,0,0) 16.90** 18.52** 25.26** 
 (3.39) (3.77) (5.63) 
(1,1,0,0)(0,0,0,0) 11.32** 14.50** 20.01** 
 (3.18) (3.05) (4.43) 
(0,0,1,1)(0,0,0,0) 2.36 3.35 6.93 
 (3.38) (3.22) (4.30) 
Observations 1,840 1,852 1,877 
MathematicsReadingWord Recognition
Kindergarten    
 15.39** 6.00** 5.28* 
 (2.63) (1.76) (2.05) 
Observations 5,782 5,701 5,762 
First grade    
 17.12** 13.01** 13.15** 
 (2.69) (2.86) (3.40) 
 5.57* 10.94** 10.28** 
 (2.55) (2.93) (3.79) 
Observations 3,958 3,865 3,359 
Second grade    
(1,1,1)(0,0,0) 13.76** 8.46* 9.22* 
 (3.36) (3.40) (4.11) 
(1,1,0)(0,0,0) 7.89** 3.28 4.01 
 (3.00) (2.95) (3.81) 
(0,1,1)(0,0,0) 6.68* 3.55 5.26 
 (3.31) (3.27) (4.42) 
Observations 2,336 2,338 2,348 
Third grade    
(1,1,1,1)(0,0,0,0) 13.68** 17.85** 26.94** 
 (3.25) (3.26) (5.13) 
(1,1,1,0)(0,0,0,0) 16.90** 18.52** 25.26** 
 (3.39) (3.77) (5.63) 
(1,1,0,0)(0,0,0,0) 11.32** 14.50** 20.01** 
 (3.18) (3.05) (4.43) 
(0,0,1,1)(0,0,0,0) 2.36 3.35 6.93 
 (3.38) (3.22) (4.30) 
Observations 1,840 1,852 1,877 

Notes: The table displays the dynamic average treatment on the treated estimates for exposure to a teacher of the same race for a given treatment path (). Standard errors clustered at the level of the classroom are given in parentheses. Scaled test scores are used as the response variable. Regressions only include free lunch status as additional covariates, since the classroom fixed effects absorb all classroom-invariant control variables. Student fixed effects are included in the specification. Observations are weighted using inverse probability weights; see section A.3 of the online appendix.

*Statistical significance at the 5% level; **statistical significance at the 1% level.

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