The evolution of local schooling systems at the secondary level in Brazil between 1991 and 2010

In spite of the negative overall representa-tion of Brazilian secondary schools, the educational system at this level has shown remarkable quantitative developments. This paper proposes evolutionary paths of development of local secondary educational systems and addresses their determinants. It uses four schooling indicators - age speciﬁ c enrollment ratio, gross enrollment ratio, net enrollment ratio, and age-grade distortion - conjointly with the use of cluster analysis to determine development trajectories. Furthermore, it analyses the main determinants of the evolutionary paths with the use of logistic and multinomial logistic models. Regional aspects related to socioeconomic level, labor market returns to human capital, demographics, social stability, location and microenvironment were associated with educational evolution.

tries in Latin America and Caribbean, but they did not acquire more education due to high school postponement and high rates of repetition. Pontili and Kassouf (2008) analyzed the determinants of age-grade distortion in Brazil. They observed that individual factors, family characteristics, school infrastructure and location were associated with this indicator. They concluded that students from households with lower socioeconomic status would greatly benefi t from school infrastructure improvements and from an increase in their social status.
3 Methodological section

Databases
The Brazilian Demographic Censuses can be applied to municipalities, the basic geographical unit of analysis of the paper, and are suitable to address educational indicators such as those used here. The use of the last three, those of 1991, 2000 and 2010, is justifi ed by the necessity of observing the data in a time span of approximately two decades in order to evaluate evolutionary paths.

Educational indicators associated with enrollment and agegrade distortion
The use of stock variables are extremely useful to address points related to regional development, however, they represent the effects of cumulated educational attainment. Thus, the use of fl ow indicators tends to be more appropriate to analyze access to education, since these are more closely associated with the current characteristics of the educational system.
Among the fl ow variables, I selected four that can be estimated using Census data and that complement each other: age specifi c enrollment ratio, gross enrollment ratio, net enrollment ratio, and age-grade distortion. I briefl y present these indicators below. For further details see Riani and Golgher (2004) and UNESCO (2009).
The age specifi c enrollment ratio is the percentage of individuals in a specifi c age group that attended school at any schooling level. This pa-per analyzes secondary schooling level in Brazil, and the ideal age range for attending this level is between 15 and 17 years old. This indicator is particularly useful to give an overview of the retention capacity of the schooling system and to show the extent of educational participation of a specifi c age group.
The gross enrollment ratio is the ratio between the number of individuals of any age who attend a specifi c schooling level and the number of individuals in the population in the age group eligible for the level. In this paper, I consider the ratio between all students at the secondary level, irrespective of age, divided by the population aged between 15 and 17. This indicator describes the capacity of the educational system to enroll students of a specifi c level, and determines whether a region has an educational system at this level which is adequate to incorporate all potential local students.
A third indicator is net enrollment ratio. This indicator is defi ned as the percentage of individuals of the offi cial age for enrollment in a specifi c schooling level who actually attend the level. In this paper is the percentage of individuals aged between 15 and 17 that are studying at the secondary level. This indicator is appropriate to evaluate the effi ciency of the schooling system, particularly concerning the fl ow of students.
The last indicator is age-grade distortion, which represents the proportion of students who are older than they should be in any schooling year, in this paper, in any of the three years of the secondary level. Similarly to the last indicator, the age-grade distortion is also associated with the effi ciency of students´ progression.

Geographical unit of analysis
This paper has the Brazilian municipalities as the basic geographical unit of analysis. However, more than 1000 municipalities were created in the period: they were 4491 in 1991, 5507 in 2000, and 5565 in 2010. In order to make comparisons more insightful, I aggregated many municipalities in the last two Censuses and some in the fi rst, and I obtained the same areas in all years, which are known as minimum areas of comparison (MAC). Most of them represented one municipality in 1991, but some are groups of two or more municipalities in this year, with a total of 4253 areas.

The phases of development
This subsection describes how I defi ned the evolutionary phases of educational systems. Initially, I obtained the value for each indicator in each MAC for the three years. Thus, initially the data consisted of 4253 MACs x 3 years for each indicator. Then, the data in the three years were polled for each indicator. Because the indicators have distributions with different means and standard deviations, and this might affect the clustering process, I obtained a rank for each indicator, from one to 12759, representing from the best to the worst value, for each indicator.
After this, I classifi ed all MACs/Years in homogenous groups with the use of cluster analyses. Clustering methods are exploratory statistical procedures that classify the elements of information sets in internally homogeneous groups in order to fi nd structure in data (Hair et al., 2009). Given the nature of the used dataset, I chose to use the K-means clustering procedure. However, this technique has the drawback of requiring a previously defi ned number of clusters. I performed different analyses with a range of arbitrary defi ned numbers of clusters and, due to empirical outcomes, I chose the study with eight clusters. Notice that the clusters were obtained with the ranks of the four indicators, hence all of them had the same infl uence to determine these clusters. Finally, I classifi ed the eight clusters in fi ve phases of development, as detailed in the discussion of the results.

Econometric models
I used econometric models to verify which socioeconomic, demographic and geographic characteristics were signifi cantly associated with this diversity of evolutionary paths. The empirical analysis is divided in two parts: the fi rst discusses the main evolutionary paths between 1991 and 2000, and the second addresses those between 2000 and 2010. The dependent variable is binary or categorical and is the fi nal cluster membership in each period conditioned in the profi le of origin. For instance, regions classifi ed as cluster 1 in 1991 mostly developed to cluster 3 or 4 in 2000. Then I created a binary variable for the cluster achieved in 2000 (1 -For cluster 4, 0 -For cluster 3), and used logistic models. Similarly, regions categorized as cluster 2 in 1991 mostly evolved to clusters 3, 5, 6 or 7 in 2000. Thus, I created a categorical variable with the cluster achieved in 2000. The reference is always the cluster with the smaller number, representing the least remarkable evolution. For categorical dependent variables, I used multinomial logistics models. The objective is to analyze factors associated with the different likelihoods of evolving from a cluster in the beginning of the period to another at the end.

Explanatory variables
The independent variables of the econometric models consist of socioeconomic, demographic, geographical and political characteristics that might have an impact on educational indicators. Similar sets of explanatory variables were used by Goldin and Katz (1997) and by Meyer et al. (2012). Most explanatory variables were obtained for the beginning of the period being analyzed to minimize endogeneity problems. Therefore, the variables are from 1991 and 2000 when not specifi ed.
For urban structure, I included the logarithm of population. Moreover, an urbanization index was built using principal components analysis (PCA) applied to data for urbanization degree, and the presence or not in the household of piped water, electricity and a proper collection of sewage (Hair et al., 2009). A third independent variable consists of a socioeconomic index, also built using PCA, and based on the presence of assets in the households. These two indexes were normalized means of the variables composing the index.
Regarding local economic activity and labor market returns on human capital, the models incorporated data for university enrollment, representing returns of a high school diploma. Tertiary education in Brazil expanded remarkably in the last decades (Salata, 2018), however, many municipalities in Brazil do not have access to higher education institutions. Thus, it is expected that the return of a high school diploma may be lower in these places due to the greater diffi culties of local residents to attend a tertiary education institution.
Moreover, the models included the proportion of migrants in the population. In the Brazilian Census of 1991, 2000 and 2010, one of the questions defi nes a migrant as someone who lived in different municipalities fi ve years before the Census and in the Census data (Rigotti, 2011). I used this information to defi ne who was a migrant in this paper. High proportions of migrants are positively associated with positive characteristics of local labor markets; however, they can also be related to a lack of social stability. Other variables related to social stability included in the models are local unemployment rates and homicide rates. The data for homicide rates is a mean value of fi ve years around the years 1995 and 2005, indicating the values in the middle of each decade.
Demographics may infl uence educational outcomes, in particular the population's age structure and sex distribution. The models include the proportion of individuals aged under 15 in the population. Higher values for the proportion of this age group may indicate greater pressures to incorporate larger numbers of students in the educational system. Sex distribution, measured by sex ratios, was also included in the models. Girls in Brazil tend to achieve higher levels of formal education (Haussmann;Golgher, 2016).
Geography might also infl uence the development of the educational system. A dummy was created indicating whether or not the area was located in the North or Northeast regions, the two least developed in Brazil. The reference was if the area was localized in one of the most developed macroregions in Brazil: the Central-West, South or Southeast regions.
Homicide rates might represent social instability or may be spuriously correlated with positive features of a society depending on the level of development of a region. I included an interaction term between these rates and the dummy representing regions.
Moreover, spatial heterogeneity and/or dependence among the geographical units of analysis might exist (Elhorst, 2010;LeSage;Pace, 2009). In order to represent the potential infl uence of the microenvironment of the region, the neighbors' mean values of the four above-mentioned educational indicators were initially included in the models. After some analyses, the spatial lagged values of age specifi c enrollment ratio and of net enrollment ratio were dropped from the models.
Although the models were conditioned on the cluster of origin, and they represent approximately homogeneous groups, regions in each cluster were not identical. Hence, as a control, the models included the initial values for the four educational indicators.
I included two other variables for the analysis of the period between 2000 and 2010. Notice that in this second group of analysis, the areas are conditioned on the cluster achieved in 2000, and the regions classifi ed as cluster 1 or 2 in 1991 are analyzed together. Thus, the models include a dummy indicating whether the region was classifi ed in cluster one in 1991.
Finally, the Brazilian Federal Government implemented the Bolsa Família program in 2004, a conditional cash transfer (CCT) policy. This program integrated four cash transfer programs that already existed (Simões;Sabates, 2014). This program assists close to 25% of the Brazilian population and it is expected to have a direct positive impact on the children's learning conditions at home (Simões;Sabates, 2014). Nobre (2018) and Simões and Sabates (2014) observed that the Bolsa Família program reduced dropout rates and increased academic performance of children and adolescents. However, these last authors argue that most studies have found no effects of CCT on students´ academic achievement. In order to account for potential effects of this program on the development of local educational systems, the proportion of households assisted by this program in each area in 2004 was included in the models analyzing the transitions between 2000 and 2010.

Evolution of schooling indicators in Brazil between 1991 and 2010
This section presents a brief overview of the evolution of the four selected educational indicators for MACs in Brazil in the period between 1991 and 2010. Golgher (2010b) presents a lengthier presentation of descriptive statistics for these indicators for the years of 1991 and 2000. Table 1 shows the proportion of areas that improved in each indicator in each period. Nearly all areas improved the four indicators between 1991 and 2010, with values ranging from 97% of the total for age-grade distortion to 100% for net enrollment ratio. This indicates that despite the negative overall representation of Brazilian secondary schools, the educational system at this level exhibited remarkable quantitative development over this period.
From 1991 to 2000, similar numbers were observed for the enrollment indicators. The results for age specifi c enrollment ratio, gross enrollment ratio and net enrollment ratio respectively indicate that the proportion of the population aged 15 to 17 in school increased, more students were at the secondary level, and more students aged 15 to 17 were at the secondary level in nearly all MACs. However, given the results of the age-grade distortion indicator, many older students that ideally should be at the tertiary level were still in high school, or many were in the secondary level, but at a lower level than they should ideally have been.
Between 2000 and 2010, the proportion of individuals in the population aged 15 to 17 in school did not increase so remarkably, nor did the number of older students at the secondary level, as shown by the not so notable evolution of age specifi c enrollment ratio and gross enrollment ratio indicators, although the majority of the MACs also improved these indicators between these years. However, net enrollment ratio and age-grade distortion improved the most, indicating the increase in effi ciency of students´ progression.
This brief analysis suggests that the indicators do not evolve at the same pace: the age specifi c enrollment ratio and gross enrollment ratio apparently increase before the other two. That is, fi rst retention increases, then there is a correction in the students' progression. That is, in both decades there was a remarkable evolution of the Brazilian secondary system of formal education, but the dynamics of evolution of the indicators differ, as some evolve before than others.

Evolutionary phases of local educational systems
In the previous section, I discussed the evolution of the four indicators separately, when I observed that the temporal dynamics of the indicators differed. This section analyzes the joint dynamics of all four indicators. The questions being addressed here is: How do regions evolve from a less developed local schooling system to a more developed one? Table 2 shows the results of the clustering process in two panels. The upper panel shows the mean value for the ranks of each indicator for each cluster centroid. Notice that the values could potentially vary from one to 12759: the smaller the value, the better the indicator. The results should be analyzed relative to the other clusters. Additionally, the table includes a brief description of each profi le in the lower panel in order to facilitate the comprehension of the main characteristics of the clusters.
As already mentioned, I classifi ed the eight clusters into fi ve phases of development and they were numbered according to these phases; the fi rst cluster characterized the least developed regions, while the last represented the most developed areas. In the next paragraphs, I clarify how I defi ned these phases.
Cluster 1 characterized the regions with very low levels for all three indicators of enrollment and very high age-grade distortion when compared to other clusters. Notice that relative to the other clusters, the values for the cluster centroid are among the highest for all four indicators, all above 10,000. Thus, the cluster categorized areas with very few individuals aged 15 to 17 studying, very few secondary level students, and very low effi ciency of students' progression. Given these characteristics, it was the only cluster defi ned as phase one and was named the "Least developed areas." These features described 2,175 MACs/Years: 91% of the total in 1991, 1,988 MACs, and 9% of the total in 2000, only 187 MACs. Therefore, this profi le was a typical profi le of 1991, as very few regions had these characteristics in 2000 and none in 2010.
I considered the clusters numbered 2, 3 and 4 as phase two. They are clearly and unambiguously more developed profi les than cluster one. Notice, however, that these three clusters classifi ed as phase two show different development profi les. Each specifi c cluster has better values for some indicators and worse values for others when compared with the other clusters in the same phase of development, and no cluster is unequivocally more developed than the others.
Cluster 2 is similar to cluster 1 in the two fi rst enrollment indicators, age specifi c enrollment ratio and gross enrollment ratio, as the values for the centroid are similar. However, as shown by the results of net enrollment ratio and age-grade distortion, with smaller centroid values for both indicators, students´ progression was more effi cient. Hence, it can be considered as a potential initial step of an evolutionary path from the least developed regions with a correction in the students' progression. The profi le was named "least developed areas with lower age-grade distortion." Cluster 2 categorized more than 1000 MACs/Year, mostly also from 1991.
Cluster 3 is a typical profi le of 2000 and characterized over 1000 MACs/ Years. It mostly differs from cluster 1 in two indicators: the age specifi c enrollment ratio and the gross enrollment ratio, both higher. These differences suggest an evolution from the characteristics of cluster 1 with an increase in the number of students aged 15 to 17 at any schooling level and an increase of older students at the secondary level. However, students' progression continues to be ineffi cient, with low values for net enrollment ratio and very high values for age-grade distortion. I named this cluster "less developed areas with higher age-grade distortion." Cluster 4, named "less developed areas with lower age-grade distortion," characterized 1,264 MACs/Years, mostly from 1991 and 2000. It is a more advanced development profi le than that observed in cluster 1, with a slight evolution in all indicators: a greater proportion of students among the population aged 15 to 17, more students at the secondary level, more students at the secondary level aged 15 to 17, and less age-grade distortion. Notice that this cluster represents a general development when compared to cluster 1, unlike clusters 2 and 3, which show improvements in a limited set of indicators. However, cluster 4 was not considered a development from clusters 2 or 3, as some indicators are less developed in cluster 4 than in these two other clusters.
I classifi ed cluster 5 as phase three, because it is a clear development from clusters 2 and 4 in phase two. Comparing clusters 2 and 5, there was an increase in all enrollment indicators and a decrease in age-grade distortion. A comparison between clusters 4 and 5 shows the same low values for age specifi c enrollment ratio; however, there was an increase in gross and net enrollment ratios and a decrease in age-grade distortion.
Finally, comparisons between clusters 3 and 5 do not show such a clear dominance of the latter over the former as the last two mentioned comparisons. Regions classifi ed in cluster 5 had larger proportions of individuals in the secondary level, with less age-grade distortion, when compared to the areas categorized by cluster three; however, the proportion of individuals aged 15 to 17 in school was smaller. Nonetheless, given the ambiguities of the age specifi c enrollment ratio indicator, cluster 5 might be considered a potential development from cluster 3: due to an increase in the students' progression effi ciency, dropout rates among individuals of the age group between 15 and 17 might increase as the student fi nishes the elementary level. I characterized Cluster 5 as "areas of intermediate level of development" and it classifi ed regions in all three years.
Clusters 6 and 7 represented the fourth phase of development, and they show a more developed profi le than all clusters in the previous phases. Notice that both profi les mostly characterized MACs in 2000 and in 2010. The main difference between clusters 6 and 7 is the proportion of students aged 15 to 17 that are still in the elementary level, which is greater in the fi rst, with higher levels of age-grade distortion. Clusters 6 and 7 were respectively named "highly developed areas with high age-grade distortion" and "highly developed areas with low age-grade distortion." ASER = Age specifi c enrollment ratio; GER = Gross enrollment ratio; NER = net enrollment ratio; AGD = Age-grade distortion.
The evolution from cluster 5 to cluster 6 indicates an increase in the proportion of students aged 15 to 17, and of older students at the secondary level, with slight increases in age-grade distortion and in net enrollment ratios. That is, although age-grade distortion slightly increased, this was caused mostly because older students did not drop out of the educational system. From cluster 5 to cluster 7, the evolution is a general development in all indicators. The last cluster had good levels for all indicators, clearly dominated all others, and was defi ned as phase fi ve: the "most developed areas." This cluster grouped 2269 MACs/Years, most in 2010. The characteristics are a natural adjustment of students' progressions from clusters six and seven with an increase in the proportion of individuals aged 15 to 17 attending secondary school.

Evolutionary empirical paths of local educational systems
The discussion above presented some potential and theoretical steps in the evolution of educational systems. However, many steps might not be common, as some clusters typically characterized profi les in specifi c years. This section presents the most frequent evolutionary steps.
I begin the discussion with four clusters that represented most areas in 1991, those numbered 1, 2, 4 and 5. Very few areas in 1991 had the characteristics associated with the other clusters. Moreover, the regions classifi ed in clusters 4 and 5 in 1991 were much less numerous than those classifi ed in clusters 1 or 2, and their evolution was not so remarkable or diversifi ed. The areas were already more developed in the beginning of the analysis, and most evolved to cluster 8 in 2010. Therefore, the following analysis focuses on the regions that were classifi ed in clusters 1 or 2 in 1991, which represent 3,211 areas out of 4,253. Table 3 shows the empirical evolution of the areas categorized in clusters 1 or 2 in 1991 between 1991 and 2000. Cluster 1 categorized 1,988 regions in 1991, close to half of all areas in Brazil. Approximately 70% of these regions followed only two paths: 23.3% made the transition to cluster 3, and 45.6% evolved to cluster 4. These more common evolutionary paths respectively evolved from the "least developed areas" to "less developed areas with higher age-grade distortion" or to "less developed areas with lower age-grade distortion." In the fi rst path, there was a more remarkable increase in the proportion of individuals aged 15 to 17 who were studying; however, many of these were still attending the elementary level. In the second path there was an increase in the proportion of individuals aged 15 to 17 who were studying as well as an increase in the number of secondary level students and a decrease in age-grade distortion. That is, all indicators improved conjointly, an apparently more robust development than the previous path. Concerning the other transitions, some regions, 8.7% of the total, did not develop at all, while around 20% evolved more remarkably than in these more common paths. Cluster 2 classifi ed 1,223 areas in 1991. More than 80% of them followed four paths between this year and 2000: 13.2% evolved to cluster 3, 32.2% developed to cluster 5, 13.4% to cluster 6, and 24.4% to cluster 7. The fi rst of these paths, from "least developed areas with lower age-grade distor-tion" to "less developed areas with higher age-grade distortion," showed an increase in the number of students aged 15 to 17 in all levels, with an increase in age-grade distortion. In the path between the "least developed areas with lower age-grade distortion" to "areas of intermediate level of development" there was a more remarkable increase in the proportion of students in general, not accompanied by increasing age-grade distortion. Furthermore, some regions evolved from "least developed areas with lower age-grade distortion" to "highly developed areas with high age-grade distortion," while others evolved from this fi rst cluster to "highly developed areas with low age-grade distortion." In both cases, the development was substantial and, in this fi rst step, the increase in the proportion of students aged 15 to 17 in the elementary level was greater than in the latter step. Regarding the other paths, close to 14% evolved to clusters 4 or 8, and 2.4% did not apparently develop. Finally, notice in the last columns that regions classifi ed in 1991 as cluster 3 to 8 mostly evolved to cluster 6 to 8. Similarly to table 3, table 4 shows the evolution between 2000 and 2010. First, notice that the large majority of regions, 2,877 out of 3,211, were classifi ed in clusters 3 to 7 in 2000. Most of them achieved one of the three most developed profi les. The MACs classifi ed in 2000 as "less developed areas with higher age-grade distortion" or "less developed areas with lower age-grade distortion" mostly evolved to become highly developed areas or the most developed areas, with a general increase in the number of students at the secondary level and a correction of student progression. Regions that were already more developed in 2000, in clusters 5, 6 or 7, mostly achieved one of the two last clusters, also with a general improvement of all indicators.
The results above suggest that empirical evolutionary paths depend on the velocity of changes. On the one hand, for quicker evolutions, such as those observed in the 90s in Brazil, most regions begin their development of the secondary level with an increase in the retention capacity of students aged 15 to 17 and an increase in age-grade distortion. Then the gross enrollment ratio increases, as the retention capacity of older students is also improved. After this, students' progression becomes more effi cient, with an increase in net enrollment ratio and a decrease in age-grade distortion. A more homogeneous path is observed if there is a slower evolution in the indicators, as verifi ed in the 80s in Brazil. Because of the slower joint evolution of the indicators, I did not observe a very large enrollment ratio for those aged 15 to 17 with high levels of age-grade distortion before the other indicators progress.

Empirical analyses of the evolutionary paths
The last section emphasized that many areas initially classifi ed in clusters 1 and 2 in 1991 fully developed to cluster 8 in 2010, while others regions still lagged behind, mostly in clusters 6 and 7. This section addresses the question of which features might be associated with this diversity in evolutionary paths. Table 5 presents the results of the econometric models for the most numerous transitions between 1991 and 2000. The fi rst model is a logistic model and describes the results for the regions that were classifi ed in 1991 as the "least developed areas." As already discussed, most regions made the transition in 2000 to the clusters "less developed areas with higher age-grade distortion" or "less developed areas with lower age-grade distortion." The model compares these two outcomes, and the reference is the fi rst cluster. That is, it analyses factors correlated with the initial development steps of local educational systems with or without a greater effi ciency of the students' progression.
Most coeffi cients were signifi cant at 5%. Notice that controls for the initial values of the four indicators were included in the model, but the results are not shown.
Concerning urban structure, more populated municipalities, possibly due to larger schools, had a smaller propensity of belonging to the cluster with lower age-grade distortion. The variable for urban index was not signifi cant in this model nor in the next. Regions that had a better socioeconomic level, and a larger proportion of university enrollments, indicating greater returns on human capital, also had a greater propensity of belonging to the cluster with lower age-grade distortion.
Regarding social stability, areas with lower unemployment rates had a greater propensity of belonging to the cluster with lower age-grade distortion. The variable for homicide rate was not signifi cant in this model nor in the next. As described earlier, a higher proportion of migrants might indicate a local booming economy, but can also imply a higher level of social instability. The results indicate a positive correlation with the evolution of educational systems, suggesting that the fi rst factor may be more decisive.
Areas with greater proportions of males tended to develop more, suggesting that low levels of educational development favor men, possibly in part due to less sophisticated labor markets, lower levels of formal education and greater gender polarization. The variable for the proportion of the population aged 0 to 14, proxy for population pressure on the educational system, was not signifi cant in this model nor in the next.
Finally, location matters. The extremely small odds-ratio for the dummy North/Northeast regions indicate that macrolocation is greatly associated with the evolution of students' progression, possibly due to cultural factors, associations with local labor markets and differences in states' policies and priorities. Regions with low levels of educational development that are located in more advanced states and macroregions tend to develop more remarkably. Besides, the microenvironment is also related to corrections in students' progression, as shown by the value below one for the odds-ratio for the lagged age-grade distortion. Municipalities surrounded by regions with lower age-grade distortion also tended to show lower age-grade distortion, suggesting localized coevolution. The interaction between homicide rates and macroregions was non-signifi cant in both models. The lagged value for gross enrollment ratio was not significant in the fi rst model.
The next model has the same explanatory variables but compares the areas that were classifi ed as "least developed areas with lower age-grade distortion" in 1991 in a multinomial model. The reference is again the cluster "less developed areas with higher age-grade distortion," which is compared to three other profi les: areas with an intermediate level of development, or more developed areas with high or low age-grade distortion. Similarly to what was observed in the previous model, regions with better socioeconomic levels, greater proportions of enrollments in the tertiary level and of migrants, lower unemployment rates, and locations outside the North or Northeast regions tended to develop their educational systems more fully. But in this model, unlike the previous one, greater pro-portions of females were positively related to a greater development of the educational system. These results suggest that for regions with a very incipient schooling system, as in the fi rst comparison, greater proportions of males tend to promote a greater development until a reasonable level is attained; after this females take over, possibly due to lower participation in the labor market and because of cultural evolution towards women's empowerment (Hausmann; Golgher, 2016). Concerning the microenvironment, municipalities encircled by areas with greater proportions of students in the secondary level and with lower levels of age-grade distortion had a greater propensity to develop more. That is, local educational systems are infl uenced by what happens in their vicinities. The size of local population was signifi cant at low to intermediate levels of development, but not in the other comparisons. Table 6 shows the results for the transition between 2000 and 2010 for the fi ve clusters that were particularly common in 2000. Note that the models are conditioned on the cluster achieved in 2000. However, only those regions classifi ed in 1991 as cluster 1 or 2 were included in the models. Again, controls for the initial value of the four indicators are included in the models.
Before discussing any particular model, I present some general fi ndings. Notice in the last line of the table that most coeffi cients for the dummy indicating the cluster of origin in 1991 were non-signifi cant. That is, after controlling for initial values of age specifi c enrollment ratio, gross enrollment ratio, net enrollment ratio and age-grade distortion, the origin in 1991 did not account signifi cantly for the posterior trajectories between 2000 and 2010 in most cases. The origin in 1991 was signifi cant only in the fi rst model and with odds-ratio below one, indicating the lower propensity of regions that originated in this profi le to develop more fully.
Besides, all the coeffi cients for Bolsa Família program were non-signifi cant, indicating no signifi cant correlation between this policy and the evolution of educational systems at the municipal level, after controlling for the other variables in the model. Although I controlled for many socioeconomic factors, it should be clear that the least developed regions tend to have a greater proportion of their households as recipients of this CCT policy. Therefore, the initial expectation was that the coeffi cients would be positive and signifi cant. For instance, Nobre (2018) and Simões and Sabates (2014) verifi ed evidence that this type of policy increases schooling attainment of individuals. However, as emphasized by these last authors, most studies on the subject have found no effects of CCT on students´ academic achievement, as I observed here for the local development of schooling systems. Now I focus the discussion on each of the fi ve models. Among those classifi ed in 2000 in the profi le "less developed areas with higher age-grade distortion," most regions attained three clusters in 2010: "more developed areas with high age-grade distortion," "more developed areas with low age-grade distortion," and "most developed areas." Few variables were signifi cant at 5% and we present their results. Areas with greater proportions of students at the tertiary level and a more favorable microenvironment showed a greater propensity for major improvements in student progression or development of the education system in general. Urbanization and social stability were also slightly associated with these greater improvements. The other variables showed non-significant coeffi cients, including the dummy for macroregion.
The next model addresses those areas that were classifi ed in 2000 as "less developed areas with lower age-grade distortion." These areas had a lower age-grade distortion in 2000 than those addressed in the previous models; however, they had a similar evolution.
The coeffi cients for urban structure, for the socioeconomic index and for university enrollment were non-signifi cant. Similarly to the comparisons in previous table, areas with a higher proportion of immigrants, a location outside the North/Northeast regions, and a favorable microenvironment showed a greater likelihood of remarkably improving student progression or overall development of their education systems.
Concerning social stability, the lower the homicide rate, the greater the evolution of the educational system for areas located in the South/Southeast/Central-West regions. In the North/Northeast, as shown by the interaction term, the tendency is blurred. These results suggest that homicide rates in more developed areas are more associated with social stability, infl uencing educational outcomes, while in less developed ones this is not so straightforward.
Regarding the demographic variables, a higher proportion of females was related to lower levels of age-grade distortion, but not to greater general development. Females tend to be more focused on education (Hausmann; Golgher, 2016), resulting in lower dropout and repetition rates.
Lower population pressure, represented by smaller proportions of individuals aged 0 to 14 in the population, was associated with a greater development of the educational system.
The last three models address those regions that were classifi ed in 2000 respectively as "intermediate level of development areas," "more developed areas with high age-grade distortion" or "more developed areas with low age-grade distortion," the most developed main profi les in 2000. These areas mostly evolved to two profi les in 2010, which are this last one mentioned and the "most developed areas." The models compare these two profi les with logistic models analyzing the factors associated with a more remarkable educational development of the already most developed areas in 2000.
All coeffi cients for urban index, socioeconomic index, tertiary level enrollment and proportion of migrants were non-signifi cant. Differently from most other comparisons, macro location was not associated with the evolution of the educational systems. This suggests that more developed areas in less developed macroregions more closely resemble those in more developed regions.
Similarly to the previous comparisons, two measures of social stability were signifi cantly associated with the observed differences: homicide rates and unemployment rates. Lower population pressure was related to greater evolution, as in the previously discussed model. The microenvironment also seems to matter, as observed in previous comparisons. Similarly, regions surrounded by areas with higher gross enrollment ratio evolved more. Differently from the previous comparisons, however, those regions bordered by areas with higher age-grade distortion also evolved more. This seems contradictory; nonetheless, the regions analyzed here were already more developed in 2000, and hence age-grade distortion might occur at higher levels and continue for fewer years. Finally, in the last model, areas with a higher proportion of males evolved more, suggesting that more advanced labor markets interact with schooling systems favoring men. Fonte: Note: * signifi cant at 5%.

Conclusion
This paper proposed local evolutionary paths of development for secondary schooling systems in Brazil with the use of four indicators: age specifi c enrollment ratio, gross enrollment ratio, net enrollment ratio, and agegrade distortion. I defi ned evolutionary paths by the conjoint analysis of these four indicators, thus overcoming many of the limitations of more specifi c discussions focused on one or some of these indicators separately. Then, I observed the main empirical evolutionary paths of local educational development. Finally, I addressed some of the determinants associated with the diversity of paths with the use of logistic and multinomial logistic models.
Here are some of the main factors associated with differences in the evolutionary paths: for localities with low levels of educational development, macrolocation matters, possibly due to cultural and regional factors which are not as relevant in more developed areas. Besides, microenvironment matters, possibly because of localized regional cultures or comparison between close localities. Local socioeconomic levels were more positively associated with development in the initial stages of educational development, and social stability was positively related to evolution for all levels of evolution. Demographic factors might also affect development paths differently depending on the level achieved by the region. Population pressure was more associated with more developed evolutionary steps, while greater proportions of females were more associated with intermediary steps of evolution. Urban structure did not show a significant relation with educational evolution, nor did national policies, such as Bolsa Família.
The results observed in the paper indicate how local schooling systems evolve. This insight may facilitate the implementation of policies at the municipal and state levels designed to promote more advanced and encompassing educational systems. However, there were changes in the federal legislation that might have had direct impacts on the topics discussed in this paper, but they were not explicitly addressed here. The law nº 11.274 of 2006 amplifi ed the number of years of the elementary level implicating that the enrollment of children aged six years old became mandatory. Thus, the period for acquiring literacy increased, with potential positive benefi ts on academic performance in posterior levels of education (Schmidt;Furghestti, 2016). The law nº 13415 of 2017 modifi ed the secondary level, although it was posterior to the period analyzed here, it might impact on future studies concerning educational attainment (Hernandes, 2020). To analyze the effects of these policies are venues for future research.