Table 12: Heckman model to adjust for Selection Bias due to Attrition

|Dependent variable|Selection<br>variables: all<br>controls|
|---|---|
|A. Instructional activities|0.0615***<br>(0.00706)|
|B. Classroom management activities|-0.0279***<br>(0.00580)|
|C. Off-task activities|-0.0270***<br>(0.00420)|
|D. Instructional activities all students engaged|-0.00314<br>(0.0109)|
|E. Big group (>6) of student off-task|-0.0358***<br>(0.00942)|

_Note_ : Sample size 3178. Variables D and E only consider the time teacher was instructing and thus assumes missing values if the teacher did not spend any time instructing. * p<0.10 ** p<0.05 *** p<0.01 A second robustness check is to estimate bounds for the average treatment effects based on weaker assumptions about the sample selection process. We estimated the bounds using the Lee trimming method that relies on the monotonicity of the outcomes if the individuals participate in the treatment (Lee, 2002 and 2009). These bounds involve excluding a fraction of the observations from the part of the sample that had less attrition (in this case, the treatment group) to equalize its size with that of the control group. In other words, the Lee bounds are generated by trimming the sample to equalize attrition rates between the treatment and control groups (Fryer, 2013). The excluded observations are the ones most likely to bias the results. Table 13: Results for sample trimmed with Lee bounds

||<br>ITT<br> (no controls)|<br>ITT<br> (all controls)|<br>Lower Bound<br>Lee Bounds|Upper Bound<br>- No Tight|Lower Bound<br>Lee Bounds|Upper Bound<br>- With Tight|
|---|---|---|---|---|---|---|
|Dependent variable|(1)|(2)|(3)|(4)|(5)|(6)|
|A. Instructional activities|0.0589***<br>(0.0124)|0.0470***<br>(0.0122)|0.0375***<br>(0.0139)|0.0816***<br>(0.0142)|0.0555***<br>(0.0127)|0.0555***<br>(0.0127)|
|B. Classroom management activities|-0.0334***<br>(0.00896)|-0.0235***<br>(0.00897)|-0.0515***<br>(0.0111)|-0.0195*<br>(0.00996)|-0.0310***<br>(0.00950)|-0.0280***<br>(0.00935)|
|C. Off-task activities|-0.0254***<br>(0.00650)|-0.0269***<br>(0.00647)|-0.0378***<br>(0.00768)|-0.0175**<br>(0.00773)|-0.0258***<br>(0.00680)|-0.0245***<br>(0.00672)|
|D. Instructional activities all students engaged|0.00347<br>(0.0216)|-0.0147<br>(0.0213)|-0.0454*<br>(0.0265)|0.00125<br>(0.0217)|0.0402<br>(0.0291)|0.00255<br>(0.0220)|
|E. Big group (>6) of student off-task|-0.0492***<br>(0.0159)|-0.0344**<br>(0.0149)|-0.0850***<br>(0.0194)|-0.0299*<br>(0.0170)|-0.0473***<br>(0.0172)|-0.0448***<br>(0.0172)|
|Sample Size<br>_Note_: Standardized dependent variables (z-score|292<br>s). * p<0.10 **|292<br>p<0.05 *** p<0|350<br>.01|350|350|350|

Table 13 presents the lower and upper bounds results for two specifications of the Lee bounds, without any covariates and with dummy or categorical covariates that allow for tightening the bounds (Lee, 2002). We used the quintile distribution of schools based on student performance in the previous year. In the model with no tightening, columns (3) and (4), the lower bounds are significant for instructional activities (0.0375), for classroom management (-0,0515), off-task activities (-0.0454), and student off-task (-0,085). The upper bounds are significant for instructional activities (0.0816), for classroom management (-0,0195), off-task activities (-0.0175), and student off-task (-0.0299). All of our ITT estimates fall within the intervals of the Lee bounds, which suggests that selection bias due to attrition did not affect our impact estimates. In the model with tight bounds, shown in columns (5) and (6), the estimates were positive for instructional activities and negative for classroom management, off-task activities, and big group of students off-task. In a few model specifications, our ITT estimates are not within the bounds intervals. However, all of the bounds estimates have the same sign and are close to the ITT estimates. In summary, this analysis provides further assurance that our sample attrition did not bias the comparability of our treatment and control groups, because we are able to control for a large range of observable covariates.

Finally, we conducted a more intuitive exercise to adjust for attrition. In the balance check analysis in Section 2, we showed that the treatment and control groups are balanced across covariates. However, 20 more schools were observed in the treatment group than in the control group. The fact that a higher share of our initially-defined treatment sample was observed (89% of the original treatment sample against 78% of the 22