level. Also, there is a positive effect on high school mathematics achievement from certified teachers only when the certification is in mathematics. Finally, reports that the training institution attended by the teacher has a positive effect on student achievement, particularly at the secondary level, but points out that this can be a reflection of the cognitive ability of the teacher.

Harris and Sass (2011) carry out a survey of the researches developed up to 2010, highlighting the fragility of previous work to control the heterogeneity among students only by their characteristics observed (covariates of students). The authors cite evidence that students who present greater learning capacity and fewer disciplinary problems tend to be allocated in classes with more experienced and qualified teachers, so that the lack of appropriate controls for the unobservable characteristics tends to generate biased estimates of the effects associated with the training of teachers.

Regarding the studies that have addressed the problem of selection bias, Harris and Sass (2011) point out eight studies that used fixed effects at the student level to control for the heterogeneity not observed, and five that explored random assignment experiments between students and teachers or that use natural experiments. None of the studies finds positive and statistically significant effect of the nature of higher education on the future teacher performance and the majority finds no relationship between the selectivity of higher education institution and teacher performance. Finally, with the exception of two studies that have identified significant and positive effects of master’s degree education of teachers on students’ math scores, all other studies either indicate absence of statistically significant effect or even negative effect of holding a postgrad degree on math and language students’ performance.

Since unobservable characteristics of teachers (like their IQ) can influence their pre-service training and also affect their future performance in the classroom, Harris and Sass (2011) incorporate in their study the teachers grade in the college admission exam as a way of controlling the effect of higher education for the pre-college skills, thus avoiding a major source of bias.<sup>10</sup> The authors found no robust evidence that pre-service teachers training affects the productivity of the future teacher.

For Brazil, Louzano (2010) did not find a significant correlation between pre-service training of teachers and the performance of students. Menezes Filho (2007), on the other hand, reported significant impact of teacher's education only on third grade secondary education students, and for teachers with a degree in mathematics. The author also reports that teachers with 50 years or more of age positively affect students' learning. Such studies, however, do not use methods capable of dealing with various issues, in particular with the existing selection bias in the allocation between students, teachers and schools.

# **4. Data and Descriptive Analysis**

In this study we use data from the National Examination of Secondary School (ENEM) and from the School Census for the years 2009 and 2015, which covers proficiency indicators and a broad set of covariates at student and school levels, for potentially all Brazilian schools.<sup>11</sup> In total, there were 20,979 public secondary schools in ENEM microdata, of which 17,214 appeared in the year 2009, 19,847 appeared in the year 2015, and 16,082 occurred in both years. Following the MEC criteria for disseminating the ENEM results, schools with fewer than 10 students from the 3rd grade participating in the exam were excluded, which resulted in 11,506 schools remaining in the sample. Of these, 151 schools with a participation rate above 100% were also excluded, leaving 11,355 schools at the base in both years.

Based on the School Census data, two school-level variables were constructed to characterize teachers’ education for each field or discipline (math and Portuguese): (i) _Percentage of classes taught by teacher with higher education_ , and (ii) _Percentage of classes taught by teacher with higher education in the field_ . The calculation was restricted to the schools with at least three upper secondary school classes for each discipline, so that the indicators reflect at least one class for each series of this teaching stage.<sup>12</sup>

> 10 Harris and Sass (2011) investigate the effects of the specific areas of higher education of teachers ( _Education Major, Math Education Major, English Education Major, Math Major_ e _English Major_ ) so as to take advantage of the greater variability of these variables to try to capture some effects that are statistically significant on student performance.

> 11 ENEM incorporate the Item Response Theory for scores calculation in 2009, when a proficiency scale with an average of 500 points and standard deviation of 100 points was defined, which allowed comparing results of different editions of the exam. Moreover, since this year students’ performance in ENEM has become the main access route to public university, which has significantly enlarged the number participants. The year of 2015 was the last year in which microdata are available. 12 Resulted in 11,336 and 10,857 schools with, respectively, at least three high school math and Portuguese classes in 2009, and in 11,317 and 11,323 schools with, respectively, at least three high school math and Portuguese classes in 2015.

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