From the perspective of the _negative_ treatment, it would be expected that the mean increase (decrease) in the outcome indicator would be smaller (greater) among treated schools, the most intensively treated schools performing relatively worse. However, with the exception of the exposition of the students of math classes to higher educated teachers, there is no clear pattern indicating adherence to the hypothesis (Table 9). Average scores in math decreased most for treated students, as expected. Also, average scores in Portuguese increased the least for treated students, except for the most intensively treated school ( _Treated_ 3), which showed similar advance in scores. Similar results are found when analyzing the treatment in terms of _percentage of classes taught by teacher with higher education in Portuguese_ ( _Treated_ 3 and 4), which may reflect schools’ strategy of exchanging higher educated but lower performance teachers by newer teachers, who perform better despite the lower schooling.

<u>Table 9 – Mean score on ENEM by condition of exposure to</u> _<u>negative</u>_ <u>treatment</u>

||2009||Math<br>2015|||2009||Portugues<br>2015|e||
|---|---|---|---|---|---|---|---|---|---|---|
||||||||||||
|Treatment|Mean|SD|Mean|SD|ean|Mean|SD|Mean|SD|ean|
||||<br> <br>|_Teachers w_<br>|_ith higher ed_<br>|_ucation_<br>||<br>|||
|Control|479.0|(81.0)|<br>454.4|(87.0)|-24.7|480.7|(90.2)|<br>493.3|(66.2)|12.6|
|Treated 1|474.6|(78.1)|<br>448.3|(85.1)|-26.3|477.8|(88.5)|<br>488.2|(65.1)|10.4|
|Treated 2|472.9|(75.0)|<br>445.0|(81.6)|-27.9|475.8|(91.4)|<br>486.5|(67.7)|10.7|
|Treated 3|466.5|(74.4)|<br>440.1|(78.3)|-26.4|468.7|(87.3)|<br>481.1|(64.4)|12.4|
|Treated 1,2,3|473.1|(76.7)|<br>446.3|(83.2)|-26.8|475.8|(89.4)|<br>486.6|(66.0)|10.8|
|Treated 2,3|471.4|(74.9)|<br>443.9|(80.8)|-27.5|473.8|(90.4)|<br>485.1|(66.9)|11.3|
||||_Teach_<br> <br>|_ers with hi_<br>|_gher educatio_<br>|_n in the fiel_<br>|_d_<br>|<br>|||
|Control|481.8|(82.6)|<br>457.5|(89.0)|-24.3|487.1|(90.6)|<br>498.4|(65.8)|11.3|
|Treated 1|479.4|(80.3)|<br>454.9|(87.4)|-24.5|487.4|(89.3)|<br>496.6|(65.2)|9.2|
|Treated 2|478.1|(79.3)|<br>452.6|(84.8)|-25.4|486.2|(91.1)|<br>496.6|(65.7)|10.4|
|Treated 3|471.1|(75.6)|<br>446.7|(81.3)|-24.4|480.8|(89.0)|<br>492.4|(65.7)|11.6|
|Treated 4|475.9|(86.8)|<br>446.6|(81.1)|-29.3|467.5|(87.1)|<br>487.5|(64.6)|19.9|
|Treated 1,2,3,4|477.4|(79.7)|<br>452.4|(85.3)|-25.0|482.8|(89.7)|<br>494.5|(65.5)|11.7|
|Treated 2,3,4|475.7|(79.2)|<br>450.3|(83.5)|-25.4|480.5|(89.9)|<br>493.5|(65.6)|13.0|

_Note._ Students in the 3rd year of public regular secondary school that participate in ENEM in the years 2009 or 2015. _Source. ENEM_ , 2009 and 2015, microdata.

# **5. Causal inference strategy**

What effect did the growth in higher education schooling of upper secondary school teachers have on students’ learning? One way to answer this question would be to compare the performance of the students in schools with high percentage of teachers with a degree (treated group) with the performance in schools that did not raise this percentage (comparison group). The main challenge we confront by doing this, however, is to address the problem of selection bias that may affect the estimation of this effect. This bias occurs when schools with certain characteristics, like the presence of more motivated and intelligent students, which have higher chances to achieve higher performance, are the most attractive ones for teachers with higher education. This entails in an overestimation of the treatment effects due to reverse causality.<sup>13</sup> Does being enrolled in treated schools imply better student performance? Or do characteristics related to the performance of students imply more treatment schools?

In this sense, it is necessary to compare the performance of treated schools with a group of schools that have similar chances to be treated, even if they were not. We do this by applying difference-indifference estimation on matched samples obtained by propensity score matching, which allows us to control for several observed and unobserved school characteristics that may contribute to selection bias. Adapted from Cameron and Trivedi (2005), in a model of differences-in-differences, considering a school panel of two periods, the _ATT_ can be obtained from the  parameter in equation (1):

> 13 It is expected that better schools attract or select higher performance teachers. As an example, Hanushek et al (2004) find that teachers in Texas tend to move to schools with more proficient students, especially the more experienced ones, who often have the option of going through districts and choose the school within the district in which they teach. Thus, it is necessary to isolate the characteristics of students and schools in order to guarantee that the odds of attracting/retaining teachers with higher education are similar for both treatment and control schools. In this sense, the treatment status between schools with same characteristics would be random (conditional independence assumption).

12