In Table 4, we report the same models but include interactions with variables to capture the presence of heterogeneous effects, namely: (i) the ex-ante probability of dropout of the students (based on the predictive model described above); (ii) the school size; and (iii) the gender of the student. As in the previous table, the first panel reports the pooled model, and the second panel the corresponding coefficients for the three arms.<sup>12</sup> Table 4. Heterogeneity in the impact of the program on the probability of student dropout.

|||Interaction:<br>||
|---|---|---|---|
||(i) Pre-treatment<br>dropout probability|(ii) School size<br>(=1if large school)|(iii) Gender<br>(=1if boy)|
|**_Panel (i): Pooled Model_**||||
|ENTRE_j_+ (ENTRE_j_) x (_Interaction j_)|-0.029**|-0.020***|-0.019***|
||(0.012)|(0.006)|(0.007)|
|_ENTRE j_|0.001|-0.005|-0.007|
||(0.006)|(0.006)|(0.007)|
|Observations|145,628|145,628|145,628|
|R-squared|0.333|0.331|0.331|
|**_Panel (ii): Treatment arms_**||||
|ENTRE 1_j_ +(ENTRE 1_j_) x (_Interaction j_)|-0.032**|-0.026***|-0.032***|
||(0.015)|(0.008)|(0.009)|
|ENTRE 2_j_ +(ENTRE 2_j_) x (_Interaction j_)|-0.036**|-0.014**|-0.011|
||(0.014)|(0.007)|(0.008)|
|ENTRE 3_j_ +(ENTRE 3_j_) x (_Interaction j_)|-0.020|-0.021***|-0.013|
||(0.015)|(0.007)|(0.009)|
|_ENTRE 1 j_|0.000|-0.003|0.003|
||(0.008)|(0.008)|(0.009)|
|_ENTRE 2 j_|0.007|-0.007|-0.011|
||(0.007)|(0.008)|(0.009)|
|_ENTRE 3 j_|-0.005|-0.004|-0.013|
||(0.007)|(0.008)|(0.009)|
|Observations|145,628|145,628|145,628|
|R-squared|0.333|0.331|0.332|
|Controls at student level|YES|YES|YES|
|School fixed effects|YES|YES|YES|

Notes: 1) Standard errors clustered at school-year level in parenthesis; 2) *** p<0.01, ** p<0.05, * p<0.1. 3) The dependent variable is a dummy variable that is equal to 1 if student _s_ in school _j_ dropped out school between year t and year t+1. 4) _ENTREj_ represents the interaction _Entrejt_ x _Postt_ where _Entrejt_ : (1= Student _s_ attends a school _j_ in year _t_ that is in the treatment group) and _Postt_ : (1 = year of the intervention; 0 = year before the intervention); _ENTRE ij_ with i=1,2,3 captures the same interaction as _ENTREj_ but using assignment to the treatment arm _i_ instead of assignment to the general treatment group. 5) _Interaction j_ in column (i) is given by the variable _Risk sjt_ (Probability of dropout for student _s_ that attends school _j_ in year _t_ estimated in the Early Warning System); in column (ii) by _Large school sjt_ : (1=Large school: size in 2017 > median), and in column (iii) by _Man sjt_ : (1=Man). 6) All specifications in panel (i) include the corresponding _Postt_ , _Entrejt_ and _Interaction j_ dummies, while those in panel (ii) include the _Postt_ and _Entre i jt_ dummies; 6) Student characteristics used as control: age dummies, gender and risk (probability of dropout estimated in the Early Warning System).

12 In all these cases, to avoid any potential bias, we included interactions not only with the variable capturing the impact of the assignment to the program ((Entre)x(Post)) but also with both the program (when relevant) and year dummy, and we included the variable of interest as a direct control as well.

22