The Labor Market Effects of an Educational Expansion. The case of Brazil from 1995 to 2014

Transcription

1 The Labor Market Effects of an Educational Expansion. The case of Brazil from 1995 to 2014 David Jaume June 2017 Preliminary and incomplete Abstract Most developing countries invest increasing shares of their GDP into education, expanding the educational level of their workforce. However, the labor market effects of such expansions have been heterogeneous across countries and within a country in different periods. This paper develops a simple general equilibrium framework to study the forces behind the labor market effects of an educational expansion. I focus on changes in real wages and the distribution occupations for the overall workforce and for each educational group. To do it, I use an assignment model of worker skills into occupations. I assume workers can be of three different types: low, medium and high educated (which maps into elementary, high school and college educated workers). An increase in education changes the assignment of workers types into occupations as well as their wages on those occupations. I show that an educational expansion in secondary schooling decreases wages of medium educated while wages for other groups could increase or decrease depending on the comparative advantage schedules. An expansion in tertiary education always increases wages of low educated workers and decreases wages of high educated, while wages of medium educated workers could increase or decrease. The key factor behind the direction and the extent of these changes is the comparative advantage schedule of workers types into different occupations. I apply this framework to explain the patterns in wages and occupations observed in Brazil during the period Brazil underwent a large educational expansion on secondary schooling until 2004, followed by an expansion in college educated workers. The model qualitatively predicts the wage and allocations patterns in those two distinct periods. I calibrate the model and show that it predicts most of the quantitative patterns from 1995 to I run counterfactuals to evaluate the contribution of an educational expansion to labor productivity and average wages. I find that returns to education on those dimensions decline rapidly, and further educational expansions in 2014 will have less than a third of the effect in JEL codes: I25; J24; O15. Keywords: Educational expansion; Occupations; Wages; Labor market. Ph.D in Economics Candidate, Department of Economics, Cornell University. djj56@cornell.edu.

2 1 Introduction Increases in human capital through formal educational is known to be one the key factors for economic development. Most developing countries invest increasing shares of their GDP into education, increasing the educational level of their workforce (Cruces et al. 2014). However, the labor market effects of such expansion have been heterogeneous across countries and within a country in different periods. An educational expansion has effects on to the jobs that are available in the economy, on which workers are employed in which jobs, and how much they earn in those jobs. Only a few papers provide a theoretical framework to consider the effects of an educational expansion in terms of wages and the distribution of occupations in a general equilibrium model. 1 Occupations play an important role on how an educational expansion affects the labor market. Since education increases human capital, its expansion changes the productive characteristics of the workforce. In any economy, workers differ from each other in their productive characteristics, and jobs differ in their complexity (and many other features such as amenities). Therefore, there exist an allocation problem of deciding which workers will perform which jobs (Sattinger 1993, 2012), and how much money they will get from them. A theoretical model of the labor market effects of an educational expansion should consider these effects. The aim of this paper is to develop a theoretical framework to evaluate the general equilibrium effects of an educational expansion, and to apply it to analyze the trends in Brazil during the period The questions that this research aims to answer are: How does an educational expansion affects real wages and the occupational composition of the workforce, overall and within each educational level? What are the differences in the effects of an expansion based on secondary schooling and one based on tertiary education? How much of the trends observed in Brazil in wages and occupations can be explained by its educational expansion? The main contributions of the paper are three. First, it provides a theoretical framework to evaluate the effects of an educational expansion, not only in terms of relative wages but also in real wages, as well as to study changes in the assignment of workers to occupations. Second, the paper shows that an educational expansion based on secondary education has distinctive effects than one based higher education. Third, it applies the framework to Brazil concluding that most of the patterns in wages and occupations can be explain by its large educational expansion. I discuss each one in turn. The recent literature on the effects of educational expansions has mainly focused on inequality, while this paper centers the attention on the evolution of real wages and occupations. It is a well establish result that relative wages between workers of different educational level are inversely related to relative supply (Katz & Murphy 1992). There are papers that evaluate 1 For example Fields (1995) and Teulings (2005). 1

3 the effects of educational expansions on inequality for Latin America (Gasparini et al. 2011) and Brazil (López-Calva et al. 2016, Ferreira et al. 2016), and found that the relative supply has been relevant to explain the decline on relative wages for the 2000s, especially for Brazil. However, inequality (or returns to education) can decline with wages of low, medium, and high educated workers decreasing at different rates, increasing at different rates, or wages increasing for one or more groups and decreasing for the others. In this paper, I provide conditions under which each of these situations can happen. The model provides a useful framework to think about some relevant issues regarding economic policies for developing countries. For example, to analyze conditions under which wages of low educated workers will raise with an educational expansion. This is important since wages of low educated workers are closely related with poverty, which is usually the prevailing economic problem in these countries (note, not inequality). In this case the model predicts that under certain conditions an expansion of medium education could reduce wages of low educated workers, while an expansion in higher education will always increase their wages. It is also economically relevant to analyze the changes in the occupational composition overall and for each educational level, since one might be interested in the occupational composition of employment in the economy. This paper considers the effect of an educational expansion on the assignment of workers to occupations. For example, it establishes conditions under which an educational expansion will improve or deteriorate the occupational composition of each group, and the whole economy. This is relevant for the economic literature given the importance that overeducation has received recently (Leuven & Oosterbeek 2011), and establish conditions under which, for example, an increase in the share of high educated workers will not be follow by a deterioration of the occupational composition of high educated workers. There are recent papers that evaluates changes on the occupational composition of employment. Those papers are mainly focused on changes in technology not in an educational expansion. Some examples are: Beaudry et al. (2016), Deming (2015), Autor & Dorn (2013), Acemoglu & Autor (2011). It is reasonable that the literature on occupational changes for developed countries has focused in technology. In these countries, the expansion in education took place in the past century, and technological progress is the main force behind recent changes in the assignment of workers type to occupations and their corresponding wages. In particular, there is a special interest in the effects of labor saving technologies that have polarized the labor market in developed countries (Autor 2014). For developing countries, including Brazil and most of Latin America, education has been increasing rapidly in the last 20 years, and it will likely continue to grow. And yet, the effects of an educational expansion on real wages and occupations are not fully understood since most of the related literature is mainly focused on technological changes. I now move to the second contribution of the paper, but first I need to briefly describe the model. The model is an extension of Acemoglu & Autor (2011). There is a unique good to be produced using different tasks, that can be ordered by its level of complexity, combined 2

4 by a Cobb-Douglas production function. These tasks can be thought as occupations in the empirical data. There are three types of workers, high, medium and low educated. Workers types differ in their productivity to perform each task, so that there is an optimal assignment of types to tasks. The model assumes that the comparative advantage of high to medium and that of medium to low educated workers increases with the complexity of the task. The competitive equilibrium determines: 1) the occupational structure of employment (the share workers performing each task), 2) the wages of each type of workers, and 3) the assignment of workers types to tasks. One of the main results of the model is the existence of two tasks thresholds, one that separates the bottom-level tasks performed by low educated workers from the medium-level tasks done by medium educated, and another that divides the medium-level tasks from the top-level occupations performed by high educated workers. These thresholds depend on the comparative advantage schedule in each task, and the relative supply of workers types, which changes with an educational expansion. The model describes two stages of an educational expansion. First, the educational expansion is concentrated on medium education. The occupational composition of high educated workers improve and those of low educated workers deteriorate since medium educated workers expand its range of tasks. 2. The model predicts that wages of medium educated will fall since they are more abundant now and employed in task with less comparative advantage than in the past, so there is a fall in the price for the tasks they perform. In the case of high educated workers, their wages can increase or decrease since they have two opposite effects on prices of the more selected tasks they now perform. On the one hand, they are more concentrated into the task they have the comparative advantage, the most complex tasks. On the other hand, the increase in the production of tasks by medium educated workers reduce the value of the most complex tasks. For low educated workers, their wages could increase or decrease also depending on what effect prevails. The fact that they now perform more low complex tasks where they have the comparative advantage increases their wages, while to opposite effect has the fact that medium educated workers now perform some task that were previously in hands of high educated workers. The second stage of an educational expansion consists on a more rapid increase in tertiary education. In this case the occupational composition of all educational groups deteriorates. However, wages of low educated workers largely increase given that they are now concentrated on task for which they have the comparative advantage, and it is also boosts by another improvement in the assignment of more productive workers (those with higher education) to tasks previously performed by medium educated workers. In the case of medium educated workers, wages could increase or decrease depending on the specific way the deterioration in the occupational composition took place. To replace low educated workers in tasks of low complexity 2 In the paper I used task and occupations indistinctly. This is because in the empirical application I rank occupations in terms of wages assuming that median wages inform with respect of how complex the occupations are. Based on this ranking a create an index of task complexity such that each occupation can be map one to one with a task complexity measure. More details are provided in section 4 3

5 implies that they are now employed in occupations with lower comparative advantage, decreasing their wages. To be replace for high educated workers in the most complex task increase their wages for the opposite reason. For high educated workers, wages decrease because they are now performing for which they have less comparative advantages. Now I turn to the specific results for Brazil. As in other developing countries, the educational expansion in Brazil has been very rapidly (Cruces et al. 2015). During the period 1995 to 2014, the share of workers with some secondary education (medium educated) doubled from 0.20 to 0.40, and the same happened for the share with some tertiary education that went from 0.11 to The period of 1995 to 2004 is characterized by a rapid increase in secondary schooling, while tertiary education expanded more rapidly in the years In the empirical section of the paper, I show the trends in wages and the assignment of workers to occupations during these two distinctive periods, which is consistent with the two stage prediction of the model. During the period we observe a reassignment of low, medium and high educated workers into occupations that resulted in a deterioration in the occupational distribution of low and medium educated workers, but not of high educated workers. Wages for all groups fell during this period of educational expansion. This is consistent with the predictions of the first stage in the model. During , we observe mainly a reassignment of medium and high educated workers characterized by a deterioration of their occupational distribution. For low educated workers that where already assigned to the lowest paid categories, only a decrease from agriculture related occupations towards low skilled services is observed. During this period wages of low educated workers largely increase, while wages of medium educated worker rise more moderately and wages of high educated workers declined, as predicted by the second stage in the model. I calibrate the model and show that it predicts most of the quantitative patterns from 1995 to I run counterfactuals to evaluate the contribution of an educational expansion to labor productivity and average wages. I find that returns to education decline rapidly, and further educational expansions in 2014 will have less than a third of the effect in labor productivity and wages than it had in The roadmap for the remaining of the paper is the following. Section 2 presents the model for two groups, which is useful for understanding of the main mechanisms in place in a simpler model. Section 3 develops the model for three groups. Section 4 presents the data for the empirical part of paper. Section 5 displays the empirical evidence for Brazil. Section 6 contains the calibration of the model. Section 7 presents the results from the calibrated model. Section 8 exhibit some robustness checks on the calibrated model. Section 9 discuss changes in the quality of human capital during an educational expansion. Section 10 concludes. 4

6 2 A theoretical model 2.1 Introduction The theoretical model presented in this section borrows heavily on Acemoglu and Autor (2011) (henceforth A&A). There are two main differences between my work and that of A&A. Firstly, I center the analysis on the effects of an educational expansion on the labor market, while the A&A are focus on skill based technological changes leading to job polarization. Secondly, my model also differs on the treatment of an educational expansion. In my model, the share of high educated workers can only increase if the share of low educated workers is reduced. A&A consider the case of an educational expansion as only affecting the number of high educated workers. This small change turns out to be key for the predictions of the model. In this section develop the model and the effects of an educational expansion for two educational groups, and in the next section I generalize it for three groups. The reason to start with two groups is because it is simpler to understand, and the generalization to three groups is easy to develop once the effect of an educational expansion is well understood in the two group model. The model can be briefly described as follows. There is a unique good to be produced using different tasks that can be ordered by its level of complexity. These tasks can be thought as occupations in the empirical data. There are two types of workers, high and low educated. Workers of different types differ in their productivity to perform each task, so that there is an optimal assignment of types to tasks. In particular, the model assumes that the comparative advantage of high educated workers increases with the complexity of the task. In the model, the competitive equilibrium will determine: 1) the occupational structure of employment (the share workers performing each task), 2) the wages of each type of workers, and 3) the assignment of workers types to tasks. One of the main results of the model is the existence of a task threshold that separates less complex tasks performed by low educated workers from more complex tasks done by high educated workers. This threshold depends on the comparative advantage schedule in each task, and the relative supply of high and low educated workers. The consequences of an educational expansion in the model can be summarized as follows. An educational expansion generates: a worsening in the task composition of employment of both high and low educated workers; a decrease in the wage differential between high and low educated workers, due to a decrease in wages of high educated workers and a raise in wages of low educated workers; and it predicts that the changes in the task or occupation composition of employment in the economy will be smaller the closer the increase in education is to the change in the threshold that determines the assignment of workers type to tasks. I discuss each of 5

7 these effects in turn. I will first discuss the change in the task-threshold. When education expands, high educated workers became more abundant and its wages fall in the tasks they were originally employed, while the opposite happens with low educated workers. Because of this, it becomes profitable for firms to employ high educated workers in some of the tasks that used low educated workers before the educational expansion. The more complex the task is the more the firm will benefit from substituting low educated workers for high educated (given the comparative advantage schedule). The substitution starts from the most complex tasks previously performed by low educated workers and goes down the job ladder until a new equilibrium is reached when no task could be produce at a lower cost by employing high educated workers. In the new equilibrium, the threshold that defines which task are assigned to each type of worker diminish: the now more abundant high educated workers start performing tasks of lower complexity, by pushing down low educated workers to even less complex tasks. Therefore, the average complexity of the tasks perform by high and low educated workers diminishes, so that there is a worsening on the tasks composition for both groups. By how much the threshold changes depends on the extent of the educational expansion and how different the worker s productivities are in each task. Next I discuss the effect on wages of different types of workers. The comparative advantage schedule of the model together with the Cobb-Douglas production function, determine that workers wages moves according to whether they are employed in occupations where they have better or worse comparative advantage. Since low educated workers moved into the worst occupations, but they are the ones where they have the comparative advantage, their wages increase. This effects is similar to a trade model where a country benefits by specializing in the production of one good, that for which it has the larger comparative advantage. The opposite happens to high educated workers, since they are now performing tasks for which they have less comparative advantages, and their wages drop. Finally, the changes in the task composition of employment will depend on the change in the task threshold relative to the educational expansion. With an educational expansion, there are more high educated workers but they also perform a larger number of tasks. There is also a lower share of low educated workers, but fewer tasks are assigned to them. The extent of the educational expansion and the change in the share of tasks performed by each type of worker will determine how the task composition changes in the whole economy. Note that the model is consistent with a small or no change in the task composition of the economy when an educational expansion takes place, despite its already described effects on the assignment of workers types to task and workers wages. With respect to the related theoretical literature (besides A&A), my model and my analysis is somehow close to Teulings (2005). His paper applies the same Ricardian principle of comparative advantage to analyze the labor market effects of an increase in human capital. He 6

8 aims to answer the following question: how do shifts in the distribution of worker types affect both the assignment of workers to task and the wages of various worker types? However, ours models differ in several ways. First, Teulings includes a continuum of worker and job types, which makes the model more elegant but much harder to bring to the data. Second, human capital is taken as separated from education. Third, the production technology satisfies the distance-dependent elasticity of substitution (DIDES) characteristic, that is the substitutability between types declines with their skill distance. I follow A&A assuming perfect suitability between types in each task. Despite the differences in the theoretical model, Teulingsś (2005) findings for an increase in the level of human capital are, in general, consistent with the ones that arise from my model with two educational groups. He finds that increases in human capital of a share of workers compress the wage distribution by reducing wages of the relative more abundant workers and increasing wages of low skill workers. However, this paper shows in section 3 than when you add another group (medium educated) educational expansions may not compress wages. 2.2 Environment There is a unique final good, the economy is closed and there is no trade in tasks. The unique final good is produced by combining a continuum of tasks represented in the unit interval [0, 1]. The final good is produced with a Cobb-Douglas technology mapping tasks to the final good as follows: [ 1 ] Y = exp ln y(i) di, (1) 0 where Y denotes the production of the unique final good, and y(i) is the production level of the task i. All markets are competitive and the final good is chosen to be the numeraire. In this version I work only with two factors of production, low and high educated workers. I assume that there is fix inelastic supply of the two types of labor, L and H (more details are given below). Educational levels change exogenously in this economy since workers do not decide whether to get education or not. Consider A J to be the factor-augmenting technologies of intput J and α J (i) to be its productivity schedules. The production of each task i is defined as follows y(i) = A L α L (i)l(i) + A H α H (i)h(i), (2) where L(i) and H(i) are the number of low and high educated workers allocated in task i. 7

9 I assume that the index i denote how complex the task is (task are ordered from less complex to more complex), so that comparative advantage of highly educated workers with respect to low educated workers is increasing in i. I also assume that relative productivity schedules are continuously differentiable. That is, α H(i) α L (i) i > 0. (3) This is a key assumption of the model since it establishes the structure of comparative advantage across tasks. There is no unemployment in the model, so that factor clearing requires that: 1 0 l(i)di L, 1 0 h(i)di H. (4) There is a continuum of workers whose labor supply has a mass of 1 in this economy. Let h be the fraction of high educated workers in the labor market. We can define: l(i)di + 0 h(i)di = (1 h) + h = 1. (5) Note that all the information about labor supply of each type of worker is collapsed into a single parameter h. With an educational expansion, h goes up so that there is an increase in the share of high educated workers and a decrease in the share of low educated workers at the same time. This is one of the main differences between my model and A&A, where L and H are considered separately so that one of them could increase while the other is constant. 2.3 Equilibrium Assignments to task An equilibrium is defined as an allocation such as producers maximize profits and labor markets clear. The characterization of the equilibrium is simple given the structure of the model. In particular, there exists some I L such that all tasks i < I H will be performed by low educated workers and all task i > I H will be performed by high educated workers. We can now state Lemma 1: Lemma 1. In any equilibrium there exist I H (0, 1) such that for any i < I H, l(i) > 0 and h(i) = 0, and for any i > I H, l(i) = 0, h(i) > 0. 8

10 Proof: See Acemouglu and Autor (2011). Intuitively, in an equilibrium where prices of labor are given by w H > w L there exist a unique task I H for which the cost of producing it with high and low educated labor is the same. By assumption α H (i)/α L (i) is strictly increasing in i, producers of task i > I H will find it more profitable to hire high educated labor rather than low educated labor, and the opposite will be true for task i < I H. The set of task are partitioned in Lemma 1 into two convex sets, one performed by low educated workers and another performed by high educated workers. A key aspect of this model is that this threshold is endogenous and will depend on labor supply of different educational levels and on technological parameters. Prices In this model workers with the same skills perform different tasks, but they will receive the same wage because of the competitive equilibrium assumption. Choosing the final good as the numeraire of this economy, [ 1 ] exp ln p(i) di = 1. (6) 0 Because the wage of low educated workers w L has to be the same in all tasks i < I H and similarly for wages of high educated workers, we can express: w L = p(i)a L α L (i) i < I H. w H = p(i)a H α H (i) i > I H. It implies that for two task i and i that are produced using the same type of labor it must be the case that price differences exactly offsets productivity differences. That is: p(i)α L (i) = p(i )α L (i ) P L i, i < I H. (7) p(i)α H (i) = p(i )α H (i ) P H i, i > I H. (8) Because the technology of the production function is Cobb-Douglas, the expenditure across all task should be equalized. That is, p(i)y(i) = p(i )y(i ) for any i,i. It implies that for any 9

11 two task produced by low educated workers, we have p(i)α L (i)l(i) = p(i )α L (i )l(i ) Because of equation (7), L(i) = L(i ) for all i,i < I H. Using the market clearing condition 4, we obtain H(i) = (1 h) I H, i, i < I H. (9) Similarly for tasks produced by high educated workers, H(i) = h (1 I H ), i, i > I H. (10) Comparing now tasks performed by low educated workers with those produced by high educated workers, and using the fact that total cost has to be the same across task (because the production is Cobb-Douglas), we have: p(i)a L α L (i)l(i) = p(i )A H α H (i )H(i ), for any i < I H, i > I H. Using equations (7), (8), (9), (10), we have: No arbitrage across skills P H P L = ( ) ( 1 IH AL (1 h) A H h As in Acemoglu and Autor (2011), I assume no arbitrage across skills. I H ). (11) That is, in the threshold I H the cost of producing this task with the two types of labor must be the same. We get the following no arbitrage condition: p(i H )A L α L (I H )L(I H ) = p(i H )A H α H (I H )H(I H ). By using (9) and (10), we get A L α L (I H )(1 h) = A Hα H (I H )h. I H (1 I H ) 10

12 Rearranging terms we have: (1 I H ) α L (I H ) I H α H (I H ) = A H h A L (1 h). (12) This equation provides a one to one mapping between the threshold task I H, which is a key element in the model, and the relative supply and relative productivities of high and low educated workers. Equilibrium wages Wages are equal to the value of the marginal products of different type of workers, that is: W L = P L A L. (13) W H = P H A H. (14) By equation 11, we get the following expression for relative wages: W H = P HA H = (1 I H) (1 h). (15) W L P L A L I H h Note that an increase in m will reduce the relative wage by two different effects. First, through a direct relative supply effect of the component (1 h)/h. Second, by the effect on the task threshold implied by the component (1 I H )/I H and equation (12). I will compute these effects in detail in another section below. To finalize characterizing the equilibrium, we need to compute price levels. Due to the [ ] choose of the numeraire, we established that 1 0 ln p(i) di = 0 (from equation (6)). By using equations (7) and (8), we have that IH 0 1 (ln P L ln α L (i)) di + (ln P H ln α H (i)) di = 0 I H (16) By using these equation together with (11), we can solve for price levels P L and P H. I will provide an analytical expression in the next section after characterizing the competitive equilibrium. 11

13 2.4 Characterization of the competitive equilibrium Proposition 1. There is a unique equilibrium given by (I H, P L, P H, W L, W H ) obtained by solving equations (12), (13), (14), (15) and (46). The block recursive structure of the model makes it easy to solve for the equilibrium. First, from (12) it is possible to solve for I H. Then, relative prices can be estimated by equation (11). Price levels are computed by a rearrangement of terms in equation (11) and replacing one of the price levels (and solving for the other) in equation (46). Wage levels are then estimated by (13) and (14). Figure 1: Determination of the task threshold I H Note: The figure shows the relationship between the threshold I H and the relative supply of high educated workers (h) and low educated workers (l = 1 h). The only claim of Proposition 1 that requires a formal proof is the uniqueness of the equilibrium. At this stage I will not provide a formal proof, but only an intuitive idea of it. A key determinant of the equilibrium is the threshold level I H. In Figure 1 we plot the two sides of equation (12). The RHS does not depend on I H, while the two terms of the LHS are decreasing in I H (the second term is decreasing in I H by assumption). When I H 0, the first term of the LHS goes to. When I H 1, it goes to 0. This structure ensures that there is a single point in which these two curves cross, so that we will have a unique threshold level I H that solves equation (12). Prices and wages 12

14 Solving for relative wages and relative prices is straightforward in the model once we have I H ; they are given be equations (11) and (15). To solve for wage levels is somehow more complicated, but we still can obtain an analytical expression for it. By using (15) to replace ln P H in (46), we get: IH 0 1 ( (ln P L ln α L (i)) di + ln P L + ln 1 I H (1 h) + ln ln A H I H I H h A L ) ln α H (i) di = 0. ( ln P L = A(I H ) + B(I H ) (1 I H ) ln 1 I H (1 h) + ln I H h ln A ) H, (17) A L where, A(I H ) = IH 0 ln α L (i) di, B(I H ) = 1 I H ln α H (i) di. We can now express the wages levels using equations (13), (14) and (15) as follows: ( ln W L = A(I H ) + B(I H ) (1 I H ) ln 1 I ) H (1 h) + ln ln A H + I H ln A L. (18) I H h ( ln W H = A(I H ) + B(I H ) + I H ln 1 I ) H (1 h) + ln + ln A L + (1 I H )ln A H, (19) I H h where the last expression arises by setting P H = ln 1 I H I H The gage gap can be defined as + ln (1 h) h + ln P L + ln A L ln A H. ln W H ln W L = ln 1 I H I H + ln (1 h). (20) h The expression above implies that the wage gap between high and low educated workers is compose by two effects, a task (occupational) composition effect given by the first term, and a pure relative supply effect denoted by the second term. Note that we could also derive this expression directly from (15). 2.5 Effects of an educational expansion through the lens of the model Summary of the effect of an expansion in education 13

15 The summary of the consequences of an educational expansion are stated in proposition 1 and in Table 1. Proposition 1 When an educational expansion of amount h = h h > 0 takes place in the model, the general equilibrium effects of an educational expansion are: (i) The occupational composition of employment did not change as much as the educational composition of the labor force did; (ii) Conditional on educational attainment, both those workers with high education and those workers with low education are employed on average in lower-level occupations than they were before the educational expansion took place; (iii) Wages of low educated workers increased and wages of high educated workers decreased, reducing the wage gap; I provide proof for (i),(ii) and (iii) in the following sections. I first define some objects of interest for the following sections. Given a threshold task I H, define low-level occupations for all i < I H and high-level occupations for all i > I H. Let Emp <IH be the share in low level occupations and Emp >IH be the share of high-level occupations, and Emp <IH and Emp <IH its change its. By definition, Emp <IH = 1 Emp >IH and Emp <IH = Emp <IH. (ii) Changes task composition within each educational level The threshold level I H define the task performed for low educated workers (i < I H ) from those performed by high educated workers (i > I H ). It determines the task composition within each educational level since it determines which tasks are performed for each type of worker. To prove that the task composition within each education level worsen is equivalent to show that when m increases I H decreases. Next I obtain simple mathematical expressions of this effect. Taking logs in (12) we have, ln 1 I H + ln α L(I H ) I H α H (I H ) = ln A H ln A L + ln h 1 h. By total differentiating we get: 1 IH 2 di H + α H(I H ) α L (I H ) d(α L(I H )/α H (I H )) = 1 da H 1 1 da L + A H A L (1 h) 2 dh. Assuming that da L = da H = 0 and rearranging terms we have, di H dh ( αh (I H ) d(α L (I H )/α H (I H )) 1 ) α L (I H ) di H IH 2 = 1 (1 h) 2. 14

16 Table 1: Labor market effects of an educational expansion. Two educational levels Threshold I L Average task within each group Low educated High educated Occupational composition (workforce) Low-level High-level Wages Low educated High educated Relative Wages High/Low h > 0,> h,< h Note: The figure shows the predicted effects of an educational expansion. The table contents should be interpreted as follows: denotes an increase for any value in the parameters of the model; denotes a decrease, ;< J (> J) denotes that it could increase or decrease depending on the parameters of the model but it will always be lower (larger) than J. 15

17 di H dh = 1 (1 h) 2 ( αh (I H ) d(α L (I H )/α H (I H )) 1 ) 1 α L (I H ) di H IH 2 < 0, (21) where the inequality arise from the assumption expressed by equation (3), which establishes that the comparative advantage α L (i)/α H (i) is decreasing in i. Figure 2 shows the effect of an increase in relative supply in the equilibrium threshold I H. An increase in the share of high educated workers from h to h increases relative supply from H/L to H /L and decreases I H from IH to I H. That is, higher educated workers will start performing less complex tasks that they did not used to do before the educational expansion (those between IH and I H ), displacing low educated workers towards tasks of lower complexity. Figure 2: Effect of an educational expansion on I H Note: The figure shows the effect on the threshold of an educational expansion h = h h, with l = 1 h and l = 1 h. Equation (2.5) is a key result of the model. It characterizes the different components affecting the assignment of workers to tasks (occupations) when an educational expansion takes place. Importantly, the change in the threshold will be larger with a lower starting point of the educational expansion (low m); a higher initial threshold (high I H ); a lower comparative advantage at the arbitrage task (low α L (I H )/α H (I H )); and the larger the change in the comparative advantage at the threshold. By looking at figure 2, it is clear that the change in threshold I H depends on the increase in relative supply (which is related to m), and the curvature of the line representing the LHS that depends on I H and the comparative advantage schedule. 16

18 The effect of the change in the comparative advantage at the threshold I H can be interpreted as follows. If at the threshold high educated workers are much more productive than low educated worker, there will be costly for firms to use them in lower tasks. In particular, if α H (I H )/α L (I H ) is very high, the threshold will barely move with an educational expansion. Thus, the model predicts that if high educated workers are already employed in task for which they are much more productive than low educated workers, an educational expansion will not change too much the assignment of workers to tasks. On the contrary, if high educated workers were already performing tasks for which they are barely more productive than low educated workers, an educational expansion will have a large effect on this threshold, since profit maximizing firms will not lose much productivity by hiring high educated workers to perform tasks of even lower complexity. (i) The effect of an educational expansion on the occupational composition of the workforce Next I analyze the changes in employment for task higher than I H. In particular, we are interested whether when an educational expansion h takes place if enough jobs are created in the original task performed by high skill workers. We can define: Emp >IH = 1 I H h (1 I H )di 1 I H h (1 I H ) di Emp >IH = h (1 I H) (1 I H ) h < h h = h, where the last inequality comes from the fact that I H < I H. It implies that the increase in employment in higher-level occupations is less than h, and the increase in employment in lower level occupations is greater than h. The extent to which Emp >IH is lower than h depends on how large the change in the threshold was as a consequence of the educational expansion. One could also be interested in the share of workers performing each task, not only on the share of employment above and below I H. Let j(i) be the changes in the share of workers performing each task (i), we have: l (i) l(i), if i < I H. j(i) = h (i) l(i), if I H < i < I H. h (i) h(i), if i > I H. 17

19 The model provides a clear prediction of the structure of the changes in the task composition of employment. Its sign depends on changes in m relative to the changes in I H. To see this, we can use equation (9) and (10) to write In particular, we have: 1 h I H j(i) = h 1 I H h 1 I H 1 h I H, if i < I H. 1 h I H, if I H < i < I H. h 1 I H, if i > I H. I H I H > 1 h 1 h, for i < I H. j(i) > 0 if: I H 1 I > 1 h H h, for I H < i < I H. 1 I H 1 I > h H h, for i > I H. (22) With an educational expansion, there are more high educated workers but they also perform a larger number of tasks. There is also a lower share of low educated workers, but less task are assigned to them. The extend of the educational expansion and the change in the share of tasks performed by each type of worker will determine how the task composition changes in the economy. We can only make some intuitive predictions for the cases where the changes in m and in I H are very different. Consider, for example, the case of a large decrease in I H with a small increase in m. A similar share of high educated workers will now need to be distributed in a larger set of tasks, so that the share of employment in tasks i > I H will diminished ( 1 I H 1 I < h H h ). On the contrary, a smaller number of task are filled with almost the same share of low educated workers, so that the employment in task i < I H will increase ( I H I H employment in tasks I H < i < I H will not have a definite sign. > 1 h 1 h ). Even in this case (iii) The effect of an educational expansion on wage levels and the wage gap The reduction in the wage wag as a concecuence of an educational expansion is easy to show. By equations (12) and (15) we can express the wage gap as follows: W H = α H(I H ) A H < α H(I H ) A H W L α L (I H ) A L α L (I H ) = W H A L W L. This proves that the wage gap decrease with an educational expansion. The extend to its decline depends only in relative productivities and in the comparative advantage at the threshold I H. It does not matter how productive high educated workers are on average with 18

20 respect to low educated workers, what determines the wage gap is the relative productivity at the threshold level I H. Now we have to proof that wages for high educated workers decreased and wages for low educated workers increase. From (18) and (19) it is possible to express the wage levels as follows: lnw L = A(I H )+B(I H )+I H lna L +(1 I H )lna H (1 I H )ln 1 I H I H (1 I H )ln 1 h h. (23) ln W H = A(I H ) + B(I H ) + I H ln A L + (1 I H )ln A H + I H ln 1 I H I H + I H ln 1 h h. (24) Note that the first fourth terms of both equations are the same, and can be expressed as: A(I H ) + B(I H ) + I H ln A L + (1 I H )ln A H = IH 0 1 ln A L α L (i) di + ln A H α H (i) di. I H Let P (j) = ln A H α H (j) ln A L α L (j). From the arbitrage condition (with logs) in equation (12), ln 1 I H I H + ln 1 h h = P (I H). Then ln W H can be expressed as follows: ln W H = IH 0 1 ln A L α L (i) di + ln A H α H (i) di. + I H P (I H ). I H Let ln W H = ln W H ln W H. An educational expansion will reduce wages of highly educated workers if ln W H < 0. To proof that this is the case, define: ln W H = I H 0 1 ln A L α L (i) di + ln A H α H (i) di. + I HP (I H). I H Using the fact that I H < I H, we can express ln W H as: ln W H = IH I H P (i) di ( I H P (I H ) I HP (I H) ). The interpretation of P (J) is the difference in productivity in task j between highly and low educated workers. Given the comparative and absolute advantage schedule, P (I H ) > P (i) > P (I H ), for all i = (I H, I H). We can establish the following inequalities: 19

21 IH I H Therefore, ln W H < 0. P (i) di < I H P (I H ) I HP (I H ) < I H P (I H ) I HP (I H). Similarly, define ln W L = ln W L ln W L. The change in wages for log educated workers can be expressed as ln W L = IH I H P (i) di + (1 I H )P (I H ) (1 I H)P (I H). Given that I H I H P (i) > I H P (I H ) I H P (I H ), ln W L > I H P (I H) I H P (I H ) + P (I H ) P (I H) = (1 I H )(P (I H ) P (I H)) > 0. 3 A theoretical model with three types: Low, medium and high educated In this section I present the results for three educational groups. The model is solved in the same way that a the two educational level model, and further details can be found in A&A. Here I concentrate my attention on the prediction of the model for an educational expansion. 3.1 Change in the environment There are three educational groups, low, medium and high. Let m be the share of medium educated workers and h be the share of high educated workers. The share of low educated workers is l = 1 h m. The production of each task i is defined as follows y(i) = A L α L (i)l(i) + A M α M (i)m(i) + A H α H (i)h(i), where L(i), M(i) and H(i) are the number of low, medium and high educated workers allocated in task i. I assume that the index i denote how complex the task is (task are ordered from less complex to more complex), so that comparative advantage of highly educated workers with respect to low educated workers is increasing in i. I also assume that relative productivity schedules are continuously differentiable. That is, 20

22 α M (i) α L (i) i > 0, α H(i) α M (i) i The supply of workers of each educational level is now defined as: > 0. (25) L(i)di M(i)di + 0 H(i)di = l + m + h = 1. (26) 3.2 Equilibrium The equilibrium with three educational groups is described by A&A. Here I display the elements of interest in this paper that are: the non arbitrage condition, which defines the assignment of workers to task, and real wages. I H. First it is necessary to define the thresholds fors task, that now are going to be two: I L and Lemma 2. In any equilibrium there exist I L andi H (0, 1) such that for any i < I L, L(i) > 0 and M(i) = H(i) = 0, for any I < i > I H, L(i) = H(i) = 0, and M(i) > 0, and for any i > I H L(i) = M(i) = 0and H(i) > 0. Proof: See Acemoglu & Autor (2011). In equilibrium, the non arbitrage conditions are: (1 I H ) I H I L α M (I H ) α H (I H ) = A H A M h m. (27) (I H I L ) α L (I L ) I L α M (I L ) = A M m A L (1 m h). (28) Wages levels are equal to: ln W H = AV P + I H P H (I H ) + I L P L (I L ) (29) ln W M = AV P (1 I H )P H (I H ) + I L P L (I L ) (30) ln W H = AV P (1 I H )P H (I H ) (1 I L )P L (I L ) (31) where, AV P = IL 0 IH 1 ln A L α L (i) di + I L ln A M α M (i) di. ln A H α H (i) di. I H 21

23 and P H (j) = ln A H α H (j) ln A M α M (j) P L (j) = ln A M α M (j) ln A L α M (j). The wages are selely determined by the terms AV P, P H (I H ), P L (I L ) and the thresholds I H and I L. The term AVP is the average productivity in the economy. P H (I H ) is the difference in productivity between high and medium educated workers at threshold I H, and P L (I L ) is the difference in productivity between medium and low educated workers at the task I L. The wages gaps are then equal to: ln W H ln W M = P H (I H ) (32) ln W M ln W L = P L (I L ) (33) ln W H ln W L = P H (I H ) + P L (I L ) (34) 3.3 Effects of an educational expansion In the case of the model with three educational levels the effects of an educational expansion on task and wages. First it is necessary to define an educational expansion in this case. Educational expansion: There exist an educational expansion between time t and t if m t m t and h t h t, with at least one of those relationship holds with strict inequality. Next I evaluate the effects of an educational expansion on the assignment of workers to task, that is, the thresholds levels. Changes task composition within each educational level The task composition within each educational level is determined by the thresholds levels I L and I H. I use comparative statics to estimate the effects of an educational expansion. I follow A&A by expressing (27) and (27) in logs: ln (1 I H ) ln (I H I L ) P H (I H ) ln h + ln m = 0 (35) ln (I H I L ) ln (I L ) P L (I L ) ln m + ln (1 m h) = 0. (36) Now consider the effect of a change in m by totally differentiate these equations. We thus 22

24 obtain: 1 (1 I H ) 1 (I H I L ) P H (I 1 H) (I H I L ) di H 1 (I H I L ) 1 (I H I L ) 1 I L P L (I = 1 m 1 L) di L m + dm (37) 1 (1 m h) The determinant of the first matrix, is positive (see A&A), therefore by Cramerś rule: di L dm = ( ) ( 1 m + 1 (1 m h) 1 (1 I H ) 1 ) (I H I L ) P H (I H) m (I H I L ) < 0 (38) ( di H dm = 1 m 1 (I H I L ) 1 ) I L P L (I L) ( ) 1 m + 1 (1 m h) 1 (I H I L ) > 0 (39) The inequality in the first equation is straightforward. For the second equation to be positive we need: P L(I L ) > m 1 (1 m h) (I H I L ) 1 I L From (36) the RHS is < 0, because m 1 (1 m h) (I H I L ) = 1 A L α L (I L ) I L A M α M (I L ) < 1. I L The result di H dm > 0 follows by the comparative advantage schedule, given that P L (I L) > 0. It is easy to see that with an increase in m the average task performed by low educated workers (I L /2) and that of high educated workers ((1 I H )/2) will increase. However,the changes in the average task performed by medium educated workers depends on the parameters of the model. An increase an increase in m leads to a larger share of task performed by medium educated educated workers, by increasing its participation in low-level and high-level tasks. We are also interested in d(i H+I L dm since the average task performed by medium educated workers can be defined as I L + (I H I L )/2 = (I H + I L )/2. Depending on which effect is stronger, d(i H+I L dm 0. The average task will increase or decrease depending on whether this inequality is positive or negative. We can write it as follows: 23

25 d(i H + I L ) = 1 m dm ( 1 m + 1 (1 m h) ( ) 1 I L P L (I 1 L) 1 (1 m h) (I H I L ) + ) ( ) 1 (1 I H ) 1 (I H I L ) P H (I H) m (I H I L ) 0 Now we can evaluate an educational expansion when h increases. Following a similar procedure than for changes in m we can write: di H dh = ( 1 h 1 (I H I L ) 1 ) I L P L (I L) 1 1 (1 m h) (I H I L ) < 0 (40) di L dh = ( 1 (1 m h) 1 (1 I H ) 1 ) (I H I L ) P H (I H) 1 1 h (I H I L ) < 0 (41) Again, the inequality in the first equation is straightforward since all terms are negative. For the second equation to be positive we need: P H(I H ) > (1 m h) h 1 (I H I L ) I H 1 (I H I L ) Which leads to a contradiction since P H (I H) > 0 and the RHS is positive. Therefore di L dh < 0. An increase in h leads to a reduction in both thresholds, since higher educated workers start performing medium-level tasks, and medium educated workers are pushed towards low-level tasks. With an increase in h, the average task performed by each educational level diminishes. Note that when m and h change simultaneously we will have a mixture of these effects. As a consequence, I L will diminish for sure but I H can increase or decrease depending on what effect is stronger. We can establish a necessary (but not sufficient) condition for I H to increase, given by the following proposition: Proposition 2 If I H > I H with an educational expansion m = m m > 0 and h = h h > 0, then it must be the case that m h > m h. Proof. Suppose that m h < m h and I H > I H. By equations (41) and (38) I L < I L. From (12), m h = N(I H)(I H I L ), where N (I H ) > 0. After the educational expansion m N(I H )(I H I L ) > m h, which is a contradiction. It means that I H cannot increase unless m h h = also increases. However, this condition does not 24

26 work in the other direction. Changes task composition of the economy In this section we are interested in the changes in the task composition of the economy as a consequence of the educational expansion. First we need to introduce some notation. Given a threshold level I L and I H, lower-level tasks are all i < I L, medium-level tasks are I L > i < I H and high level tasks are i > I H. Only a few cases the model provide sharp on the changes in the task composition of the economy that does not depend on the parameters of the model. For example, when there is an increase in I H, some medium educated workers will be added to tasks originally performed only by high educated workers, so that the share of these high-level tasks in the economy will increase. In fact, in the case that both m, h > 0 we know that the increase in high-level tasks is higher than h. In most cases it is possible to define boundaries of the changes, similarly to what has been performed for the two group model. For example, consider Empl < I L to be the change in the share of low-level task after an educational expansion. It can be estimated as: Empl < I L = I L 0 1 m h I L IL + I L m I H I L m IL 1 m di 0 I L = 1 m h + (I L I L) I H 1 m h > 1 m h = l. I L It establishes that the change in the share in low-level tasks is higher than the decrease in the share of low educated workers, since some medium educated workers start performing some of those task. Changes in the wages We now turn to the case of changes in the wage levels. From the wage equations (29), (30) and (31) we see that the threshold levels determine the wage levels. We saw that after an educational expansion I L always falls, while I H can increase or decrease depending in the case. We will consider these two cases separately. Case 1: DeltaI L < 0 and I H < 0 After and educational expansion we can express wages for high educated workers as: 25

27 ln W H = AV P + I HP H (I H) + I LP L (I L). Therefor, the wage gap ln W H = ln W H ln W H can be expressed as: ln W H = IH I H IL I L P L (i) di + I LP L (I L) I L P L (I L ) + } {{ } I L in W H effect< 0 P H (i) di + I HP H (I H) I H P H (I H ) < 0, } {{ } I H in W H effect < 0 Where the inequality comes from following similar procedures than in the estimation of changes in W H in the two educational level model. Both effects are negative in this case. Similarly, for medium and low educated workers we have: ln W M = IH I H IL I L P L (i) di + I LP L (I L) I L P L (I L ) + } {{ } I L in W M effect< 0 P H (i) di (1 I H)P H (I H) + (1 I H )P H (I H ) 0, } {{ } I H in W M effect > 0 ln W L = IH I H IL I L P L (i) di + (1 I L)P L (I L) (1 I L )P L (I L ) + } {{ } I L in W L effect > 0 P H (i) di (1 I H)P H (I H) + (1 I H )P H (I H ) > 0, } {{ } I H in W L effect > 0 In this case, in wages for medium educated workers can be negative or positive depending on the parameters of the model since there are two opposite effects. Case 2: I L < 0 and I H > 0 26

28 IL ln W H = I L P L (i) di + I LP L (I L) I L P L (I L ) + } {{ } I L in W H effect< 0 I H P H (i) di + I HP H (I H) I H P H (I H ) 0, } I H {{} I H in W H effect > 0 ln W M = IL I L P L (i) di + +I LP L (I L) I L P L (I L ) + } {{ } I L in W M effect< 0 I H P H (i) di (1 I H)P H (I H) + (1 I H )P H (I H ) < 0, } I H {{} I H in W M effect < 0 ln W L = IL I L P L (i) di (1 I L)P L (I L) + (1 I L )P L (I L ) + } {{ } I L in W L effect > 0 I H P H (i) di (1 I H)P H (I H) + (1 I H )P H (I H ) 0, } I H {{} I H in W L effect < 0 Changes in relative wages Relative wages are easy to estimate in the model. They will entirely depend on the changes in the thresholds. They can be expressed as follows. ln W H ln W M (ln W H ln W M ) = P H (I H) > 0, if I H P H (I H ) > I H. < 0, if I H < I H. ln W M ln W L (ln W M ln W L ) = P L (I L) P L (I L) < 0 ln W H ln W L (ln W H ln W L ) = P H (I H) P H (I H ) + P L (I L) P L (I L) 0, if I H > I H. < 0, if I H < I H. TO COMPLETE. EXPLAIN RESULT Summary of the effects of an educational expansion The summary of the labor markets effects in terms of wages and task (occupations) can be found in Table 2. Note that it is possible that because and educational expansion, the wages of all educational groups decrease (column 3), while only medium and low educated workers 27

29 experienced a decrease in the average task they perform. In this case, the wage premium between high and medium educated workers increased while it decreases between medium and low educated workers. Note that it is also possible that wages for low and medium educated workers to increase, while wages of high educated workers decrease, and all type of workers are employed, on average, on lower tier occupations. Wage gaps between all relevant groups decrease in this case. 3.4 The importance of comparative advantage schedules This section discuss the importance of comparative advantage schedules to changes in wages and in occupations. For that end, I evaluate the effects of increasing h under different comparative advantage schedules. The only condition presented in the model with respect to comparative advantage is that is has to be increasing in i, according to equation (25). However, the slope of this relationship is crucial to determine the effects of an educational expansion on wage levels and occupational composition of each group. I consider here four different combinations of comparative advantage schedules. The comparative advantage of high educated with respect to medium educated workers, α M (i), could largely increase when i increases, or increase by small amounts. Let each of these cases be called large CA H and small CA H respectively. The same is true for the comparative advantage of medium educated workers with respect to low educated ones, given by α M (i) α L (i). These cases are defined as large CA L and small CA L respectively. There are four possible combinations of high and low comparative advantages schedules. α H (i) The labor market effect of an increase in h under each of the four cases is presented in Table 3. The table shows the effect of an increase in h of 10 percent points, from 0.2 to 0.3. Figure 3 displays the 4 different comparative advantage schedules. The figure shows a numerical example on the curvature of P H (i) and P L (i) under different productivity schedules. This curves are used in the 28

30 Table 2: Summary of the labor market effects of an educational expansion. Model with three types of workers m > 0 h > 0 m > 0 and h > 0 I H I H Thresholds I L I H * * Average task within each group Low educated Medium educated High educated Occupational composition (workforce) Low-level,> m,> h,> m h,> m h Medium-level,< m,< m High-level,< h,> h,< h Wages Low educated Medium educated High educated Relative Wages High/Medium Medium/Low High/Low Note: The table shows the changes in the labor market in Brazil during the years and of four different educational expansion. Column one shows an increase in medium education. Column 2 an increase in high education. Columns 3 and 4 different scenarios for an increase in both medium and high education depending on its effect in the threshold I H. The table contents should be interpreted as in table 1. * Given by assumption. 29

31 Table 3: A numerical example on the differential effect of h for small and large comparative advantage schedules. Case 1 Case 2 Case 3 Case 4 Comparative adv. schedule CA H small large large small CA L small large small large Thresholds Initial I L Initial I H Final I L Final I H % in wages Low educated Medium educated High Educated mean occup. ranking Low educated Medium educated High Educated

32 Figure 3: Four different comparative advantage schedules Note: The figure shows P H and P L under a small and a large increase in comparative advantage with respect to the task index. Parameters are chosen such that initial I H and I L are the same. 4 Data In this section I present the main stylized facts that arise from analyzing the educational expansion, wages and the composition of occupations in Brazil during the period I use data from the Pesquisa Nacional por Amostra de DomicÃlios (PNAD), a nationwide household survey. I classify workers into low, medium and highly educated. Low educated workers are those with less than 9 years of education (completed primary education or less). Medium educated workers are defined as those with between 9 and 11 years of education (some or complete secondary education). Highly educated workers are those with more than 11 years of education (some or complete tertiary education). Occupations codes are harmonized using the International Standard Classification of Occupations of 1988 (ISCO-88). In the household surveys, occupations are classified according to the Classificação Brasileira de Ocupações (CBO), which changed between PNAD and PNAD I followed Salardi (2014) for recoding the occupations in the CBO for each period into ISCO-88 at 3 digits (further details can be found there). Hourly wages are expressed in 2005 purchasing power parity (PPP) dollars,and are estimated 31

33 by dividing monthly labor earnings by hours worked in the corresponding month. The analysis is performed on the following workers: employed, between 18 and 55 years old and living in regions that has been surveyed throughout the whole period (this excludes regions from rural north incorporated in the sample since 2004). 5 Empirical evidence: Brazil In this section I describe the general trends in Brazil in terms of the educational composition of the employed population, wages overall and for each educational group and the occupational composition of employed for all workers and by educational group. 5.1 Education In Brazil during the period the share of workers with medium and high education more than doubled. Figure 18 shows the evolution of the share of workers for each educational level. The share of low educated workers (less than 9 years of education) decreased steadily from 68.1 percent in 1995 to 36.4 percent in 2014, while the share of medium educated (between 9 and 11 years of education) increased from 20.5 to 40.0 and the share of ighly educated workers (more than 12 years of education) rose from 11.3 to 23.6 percent. This educational expansion took place in only 19 years. 3 To understand how large and rapid this expansion was, it is useful to compare the changes in enrollment rates in Brazil with other large educational expansions in other countries. Figure?? plots the 26 countries (and periods) with the fastest increased in secondary enrollment in a 20-year-period according to Barro & Lee (2013). Countries are sorted by the increase in percentage points in secondary enrollment. The enrollment ratios are defined as the ratio of students at a given level of schooling in the designated age group to the total population of that age group. Brazil is the second country with the largest educational expansion in history in terms of secondary school enrollment, going from 16.0 percent in 1990 to 86.2 percent in The increase in tertiary education during this period was more discrete when compared to other countries. Figure?? plots the evolution of enrollment rates since Except for a moderate increase in primary, enrollment rates were constant in Brazil between 1975 and From 1990 to 2010 enrollment in secondary schooling soared, while tertiary enrollment increased more steadily after The extent of the educational expansion is consistent with using hours of works instead of the share of employed persons. The share of hours worked by low educated workers went from 69.5 percent in 1995 to 36.3 percent in 2014, from 19.8 to 40.6 in the case of medium educated workers and from 10.7 to 23.0 for highly educated. 4 Other datasets find a lower increase in enrollment rates. For example, SEDLAC (CEDLAS and The World Bank) uses households surveys and estimate an increase of 50 percent points during the same period. 32

34 Figure 4: Educational expansion of the workforce Note: The figure shows the evolution of the shares of employed workers with low, medium and high education. Low education is defined as primary completed or less(< 9 years of education). Medium education is defined as secondary education uncompleted or completed (between 9 and 11 years of education). High education is defined by some tertiary education (12 or more years of education). Brazil implemented several important educational reforms aimed to increase the educational level of the population. In basic education, the government of Cardoso introduce and educational reform based on three pillars (Bruns et al. 2011): 1) Increasing and equalizing funding for basic education (primary and lower secondary schooling) across regions, states and municipalities, known as the FUNDEF reform ; 2) to applied a national learning policy by measuring and evaluating schools with a national yardstick (SAEB); and 3) increasing the educational opportunities of poor students by subsidizing their education (Bolsa Escola). Then in 2002 the goverment of Lula da Silva retain and expanded these policies. FUNDEF was extended to upper secondary schooling and preschool. Bolsa Familia was created by consolidating Bolsa Escola and other social programs, increasing the funds of cash transfers conditional on educational attainment and the coverage of the program. Bruns et al. (2011) estimate that, as a consequence of these reforms, a six-year-old Brazilian child born starting school in 2010 from the bottom quintile of the income distribution will on average complete more than twice as many years of schooling as her parents did. Data from the PNAD shows that the share of the population between 20 and 24 years old that finished secondary schooling increased from 24.0 percent in 1995 to 63.3 percent in

35 Figure 5: Largest educational expansions in history: changes in enrollment rates Note: The figure shows the 26 countries (and periods) with the fastest increased in secondary enrollment in history. Countries are sorted according to their increase in percentage points in secondary enrollment. Increases in enrollment in tertiary education are also shown. Enrollment ratios are defined as the ratio of students at a given level of schooling in the designated age group to the total population of that age group. Source: Barro & Lee (2013). In tertiary education, the government in introduce the ENEM (Exame Nacional do Ensino MÃ dio) in 1998, which is an aptitude test at the end of secondary education. It was created with the idea of leveling the playing field in admissions for students from low income families. The exam is an important part of the application to universities, especially after 2009, and it is the second largest exam of this type after the Gāo Kǎo applied in China. According to the data from Instituto Nacional de Estudos e Pesquisas Educacionais AnÃsio Teixeira (INEP), the number of students in tertiary education increased from 1.7 million in 1995 to 6.6 million in But selection become more though: 19 percent of the candidates where accepted 1995, and only 14 percent of them were accepted in The number of candidates increased from 2.6 million to 14.3 millions. Obviously the supply also increased, the number of institution offering tertiary education increased from 894 to 2,364. The large increase in enrollment had an impact in the educational level of the labor force after the new more educated cohorts were incorporated into the labor market. According to Bruns et al. (2011), the rise in the educational attainment of Brazil s labor force since 1995 has been one of the fastest on record, even faster than China s in the same period. It could be argue that with this large educational expansion, the quality of education went down in Brazil, which part of the labor market outcomes observed in the data. But Brazil 34