|(42.9%, 69.2%]|**374**|136|174|228|169|1,081|
|---|---|---|---|---|---|---|
|[0%, 42.9%]|**304**|97|154|251|280|1,086|
|Total|5,441|1,292|1,500|1,509|1,085|10,827|

_Note._ Strata were constructed based on 10th, 20th, 30th, and 40th percentiles. Blue (red) color indicates schools that moved the indicator to a superior (inferior) stratus between years 2009 and 2015.

In Table 6, for example, note that some schools that had high _percentage of classes taught by teachers with higher education_ in 2015 (above 87.5% for math classes and above 94% for Portuguese classes) was in lower strata of the distribution in 2009 (below 87.5% for math classes and below 94% for Portuguese classes): 1,254 of 9,799 schools and 1,262 of 9,527 schools, respectively, considering the indicator for math and Portuguese classes. On the other hand, other schools that had a high _percentage of classes taught by teachers with higher education_ in 2009 passed to lower levels of distribution in 2015: 1,040 from 9,585 schools and 935 from 9,200 schools, respectively for math and Portuguese classes.

These transitions from lower strata to the highest stratum of the distribution can be used to characterize school treatment condition in the following sense: schools that went from a lower strata to the greater stratum of the distribution are considered to have being treated, since they showed improvement in the indicator in the period; and schools that went from the highest stratum to a lower strata of the distribution are considered to have undergone a _negative treatment_ . Due to its large number, schools that remained in the highest stratum of the distribution are considered as control group.

Based on the above strategy we constructed a set of variables that characterize different degrees of exposure to treatment, here understood as the increase (or decrease, for _negative_ treatment) in the _percentage of classes taught by teachers with higher education_ and _by teachers with higher education in the field_ . We subdivide the exposition to treatment into three degrees (and four degrees, for the _higher education in the field_ indicator) according to the stratum in which the school was in year 2009: treatment group 1 ( _Treated_ 1) is composed of schools whose indicator was in the stratum immediately below the highest, treatment group 2 ( _Treated_ 2) is composed of schools whose indicator was in the next stratum, and so on; so that the greater the order of treatment, the greater its intensity is. Similarly, the degree of _negative_ treatment can also be characterized in degrees, according to the stratum of the school in 2015.

We see in Table 8 that for both years and disciplines the average scores are higher among students from untreated schools, and are smaller for more intensively treated schools. This is consistent with the hypothesis of positive correlated between teachers’ education and students learning. It would be also expected a higher increase in outcome among treated schools, especially among the most intensively treated ones. Data on Portuguese scores corroborate with this hypothesis, but not for math, as students from treated and untreated schools perceived similar reduction in the average scores.

<u>Table 8 – Mean score on ENEM by condition of exposure to treatment</u>

||||Math<br>||||<br>|Portuguese<br>|<br>||
|---|---|---|---|---|---|---|---|---|---|---|
||20|09|20|15|∆ Mean|20|09|20|15|∆ Mean|
|Treatment|Mean|SD|Mean|SD||Mean|SD|Mean|SD||
||||_Te_<br> <br>|_achers w_<br>|_ith higher edu_<br>|_cation_<br>||<br>|||
|Control|479.1|(81.0)|<br>454.4|(87.0)|-24.7|480.7|(90.2)|<br>493.3|(66.2)|12.6|
|Treated 1|463.5|(72.2)|<br>439.0|(77.5)|-24.5|463.7|(87.5)|<br>478.6|(65.8)|14.9|
|Treated 2|461.1|(72.2)|<br>437.2|(80.1)|-23.9|460.8|(88.6)|<br>477.5|(66.8)|16.7|
|Treated 3|455.6|(69.9)|<br>431.1|(74.2)|-24.5|448.5|(85.0)|<br>469.7|(64.6)|21.2|
|Treated 1,2,3|461.0|(71.8)|<br>436.7|(77.8)|-24.3|459.4|(87.5)|<br>476.3|(66.0)|16.9|
|Treated 2,3|458.9|(71.4)|<br>434.9|(78.0)|-24.0|456.0|(87.4)|<br>474.6|(66.1)|18.6|
||||_Teache_<br> <br>|_rs with hi_<br>|_gher educatio_<br>|_n in the field_<br>|<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|472.2|(76.8)|<br>446.8|(83.2)|-25.4|477.8|(90.4)|<br>491.4|(67.6)|13.6|
|Treated 2|470.4|(76.1)|<br>444.6|(81.4)|-25.8|472.1|(90.2)|<br>486.4|(67.1)|14.3|
|Treated 3|466.5|(73.4)|<br>441.9|(80.0)|-24.6|465.4|(88.3)|<br>481.2|(66.0)|15.8|
|Treated 4|460.8|(72.7)|<br>437.2|(78.5)|-23.6|448.1|(85.9)|<br>469.5|(65.9)|21.4|
|Treated 1,2,3,4|468.7|(75.3)|<br>443.6|(81.3)|-25.1|469.5|(89.8)|<br>484.5|(67.3)|15.0|
|Treated 2,3,4|467.0|(74.5)|<br>442.0|(80.4)|-25.0|464.7|(89.2)|<br>480.8|(66.8)|16.1|

_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.

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