Journal of Macroeconomics 77 (2023) 103542
A0
(Contents lists available at ScienceDirect
Journal of Macroeconomics
journal homepage: www.elsevier.com/locate/jmacro
Misallocation of talent, teachers’ human capital, and developmentin Brazil✩Fernando Barros Jr a,∗, Bruno R. Delalibera b, Luciano Nakabashi a, Marcos J. Ribeiro a
a FEARP/USP, Brazilb Universitat de Barcelona, BEAT and CREB, Spain
A R T I C L E I N F O
JEL classification:J20J24O11O40Keywords:MisallocationHuman capitalLaborExternalitiesGrowth
A B S T R A C T
In this study, we investigate the allocation of talent in an economy where teachers play acritical role in developing the human capital of the workforce. To this end, we formulate aRoy model with externality in the occupational choice, as the quantity and quality of teachersare key determinants of workers’ human capital. Our analysis suggests that when individualswith greater abilities opt for teaching careers, the entire workforce benefits. However, frictionsin the labor and educational goods markets may lead to a suboptimal allocation of talent andhinder economic growth and development. Our model is calibrated to the Brazilian economy,and our findings reveal a negative correlation between frictions in the teacher’s occupation andper capita output in the Brazilian states. Our results indicate that eliminating friction in thelabor market could result in a 16.94% increase in Brazilian income.
1. Introduction
Many studies analyze the hindrances to economic growth, and one relevant approach is that of resources misallocation.Misallocation of capital, credit, and talent has been pointed out as possible barriers to growth (Banerjee and Duflo, 2005; Restucciaand Rogerson, 2008; Hsieh and Klenow, 2009; Hsieh et al., 2019). Misallocation of talent across occupations and sectors may be aconsequence of race and gender discrimination, social norms and culture, and barriers to the human capital formation (Restuccia andRogerson, 2017).1 In the present paper, we study the allocation of talent in an economy where individuals choose their occupationfacing different barriers among professions, and teachers play an explicit role in the human capital formation of all workers.Based on Hsieh et al. (2019), we build a general equilibrium model where individuals choose consumption, time at school,investment in education, and the sector to work. We introduce two barriers that influence individuals’ occupational choices, affectingtalent allocation in the economy. First, we consider frictions in the labor market, which can be interpreted as the relative difficulty
✩ We thank the co-editor, Chong K. Yip, and an anonymous referee for their insightful and constructive comments that have significantly improved the paper.We also thank Luiz Brotherhood, Tiago Cavalcanti, Pedro Ferreira, Fábio Gomes, Vahagn Jerbashian, Lourenço Paz, Xavier Raurich, and seminar participantsat FEARP/USP-RP and 44th Meeting of the Brazilian Econometric Society for their helpful comments. The remaining errors are our own. This research wascarried out with the support of Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brazil - Financing Code 001. Fernando Barros Jr thanksCNPq-Brazil for partial financial support. Delalibera thanks the financial support from AGAUR-Generalitat de Catalunya through grant 2021 SGR 00862.
∗ Correspondence to: Faculdade de Economia, Administração e Contabilidade de Ribeirão Preto da Universidade de São Paulo, Avenida Bandeirantes, 3900 -Vila Monte Alegre, Ribeirão Preto SP, 14040-905, Brazil.E-mail addresses: fabarrosjr@usp.br (F. Barros Jr), bruno.delalibera@ub.edu (B.R. Delalibera), luciano.nakabashi@gmail.com (L. Nakabashi),mjribeiro@usp.br (M.J. Ribeiro).1 In the context of developing economies, Hnatkovska et al. (2012) show that the misallocation of talent in India comes from the caste system. In Brazil, Café(2018) shows an overqualification of workers in the public sector in relation to the private sector, especially when the evaluation in the public sector is notrelated to the worker’s performance.vailable online 16 June 2023164-0704/© 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license
http://creativecommons.org/licenses/by/4.0/).
https://doi.org/10.1016/j.jmacro.2023.103542Received 10 February 2023; Received in revised form 10 May 2023; Accepted 31 May 2023
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
ofa
bdm
wcs
siFow
tBpo
trd(mWf
eeFlecmbc
ott
WaatTe
r
pof finding a job in a given occupation and region. This barrier can result from social status or discrimination. The second barrierappears in the educational market. It is related to the costs of human capital formation in a given region and occupation.In our model, the number of workers choosing an occupation decreases with higher barriers. Moreover, frictions in the teacher’sccupation would harm the whole economy since it is essential to the human capital formation of all workers. Furthermore,ollowing Eckstein and Zilcha (1994), we consider the quality of teachers as an input to human capital formation. Based on Gilpinnd Kaganovich (2012) and Hatsor (2012), we also consider the number of teachers as input.Our model is calibrated to the Brazilian economy, where our baseline calibration demonstrates a positive correlation betweenarriers to the teacher’s occupation and per capita output in the Brazilian states. Specifically, these barriers are lower in the lesseveloped regions of Brazil, leading to the accumulation of more human capital among teachers in these areas. Conversely, theore developed states exhibit higher levels of productivity, owing to elevated Total Factor Productivity (TFP).Brazil confronts several microeconomic challenges, such as a distortionary tax burden, high levels of labor market regulationith expensive firing costs, varying regulations across different sectors, different levels of union market power across sectors, limitedompetition in several industries (like the energy sector), regional disparities in infrastructure quality, and a significant informalector. These obstacles make Brazil an important country for research and analysis.Barros and Delalilbera (2018) have also identified an inverse relationship between the relative wage of teachers and the Braziliantates’ economic development. They point out that the occupational choice of workers with multiple skills is driven by labor marketncentives (net wage) and the costs of investing in education. Our study differs from Barros and Delalilbera (2018) in two ways.irst, in addition to considering that teachers’ human capital is a source of positive externalities, we explicitly model the importancef the number of teachers in the workforce’s human capital formation. Second, we use our model to study differentials in the relativeorkers’ wages to better understand the relationship between market frictions and the misallocation of talent in Brazil.We show that the frictions related to the teacher’s occupation have a more relevant influence on the economy’s output thanhose of other occupations. We run a series of counterfactual exercises, and we find that the complete removal of frictions in therazilian economy would generate an increase of 16.94% in GDP. Furthermore, we calibrate our model with data from differenteriods to study the evolution of the allocation of talent in Brazil. We argue that the reduction of the barriers over time could bene of the drivers of absolute income convergence across the Brazilian states.2Although we based our model on Hsieh et al. (2019), we are interested in understanding the impact of misallocation of talent inhe teacher’s occupations. In contrast, Hsieh et al. (2019) study the economic performance related to the reduction in gender andace discrimination over time in the United States. They find that between 20% and 40% of GDP per capita growth over the last fiveecades is due to declining occupational barriers, causing women and blacks to occupy highly qualified positions over time. Abdulla2019) also investigates the misallocation of talent in Brazil and India. Their results show that removing all frictions of the laborarket and human capital accumulation in Brazil and India would increase average output by 22%–52% and 38%–53%, respectively.e extend the analysis of the above studies by modeling the tradeoff between quality and quantity of teachers in human capitalormation.The misallocation literature has traditionally focused on the role of individual choices in explaining the economic outcome. How-ver, recent studies have highlighted the importance of financial constraints in shaping the educational choices of families (Soarest al., 2012; Ponczek and Souza, 2012; Hanushek et al., 2014; Delalibera and Ferreira, 2019; Brotherhood and Delalibera, 2020).or example, Soares et al. (2012) provide micro-evidence that children from disadvantaged families are associated with more childabor and less schooling, while Ponczek and Souza (2012) shows that twins in the family have adverse consequences for children’sducation. Hanushek et al. (2014) provide an overlapping generations model that demonstrates how different college funding rulesan affect aggregate outcomes and individual welfare. Brotherhood and Delalibera (2020) also build an overlapping generationodel to study the optimal allocation of public expenditure across schools and universities.3 Our findings complement this literaturey studying how barriers in educational markets, which can also be viewed in part as financial constraints, can affect the occupationalhoice of multi-ability workers and generate a misallocation of talent.Human capital is crucial for economic development by increasing labor productivity, besides facilitating innovation and diffusionf technology as in Romer (1990), Mankiw et al. (1992), Borensztein et al. (1998), and Benhabib and Spiegel (2005). We contributeo this literature by showing how regional disparities in the labor and educational markets can generate talent misallocation in theeacher’s occupation and, in turn, affect aggregate human capital.The recent literature has emphasized the relevance of education quality in economic growth. For example, Hanushek andoessmann (2012) argue that Latin American countries lagged behind because of their students’ poor performance in educationalchievement. In addition, many studies point to the relevance of teachers in the students’ learning process (Woessmann, 2016; Barrosnd Delalilbera, 2018; Hanushek et al., 2019). Indeed, Hanushek et al. (2019) find a robust and positive relationship between theeachers’ cognitive skills and student performance measured by the Programme for International Student Assessment (PISA) scores.he cognitive skills of teachers are even more critical to students’ performance than the cognitive skills of their parents (Hanushekt al., 2019).Using the PISA’s mathematics test score, Woessmann (2016) points to the relevance of teachers’ quality measured by theirelative wage and human capital on students’ performance. Woessmann (2016) argues that higher teacher wages positively influence
2 See Ferreira (2000) and Ribeiro and Almeida (2012) for evidence of income convergence in Brazil.3 In this context, Brotherhood et al. (2022) claim that when there is a high proportion of credit-constrained students, a reallocation of expenditure towardsublic schools positively affects GDP.2
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
ccsccsh
ecb
2
w
2
nrecruiting higher-ability individuals into teaching. For Brazil, Menezes-Filho and Pazello (2007) find that the relative wage ofteachers positively affects the proficiency of public school students. Machado and Scorzafave (2016) point out that wages mayaffect the decision of the most talented individuals to become teachers. In addition, after an individual becomes a teacher, thewages affect their effort in the classroom and the turnover rate. Several other studies also indicate that the ability of teachers isrelated to their relative wage, as Stoddard (2003), Lakdawalla (2006), and Bacolod (2007).Tamura (2001) examines the role of education and the quality and quantity of teachers in economic growth and incomeonvergence. Following Card and Krueger (1992a) and Card and Krueger (1992b), Tamura (2001) formulates a function of humanapital formation, where teachers’ quality and class size interact with private investment to produce human capital. Then, the authorhows that human capital convergence across regions occurs if teachers’ quality is relatively more important than class size in humanapital production. He argues that poor school districts have relatively better teachers than wealthier districts, driving the incomeonvergence observed in the data. We also consider teachers’ quality and quantity to study income convergence across the Braziliantates. We find that income convergence is due to human capital convergence because teachers of poorer Brazilian states have aigher quality.Besides this introduction, the present paper is organized as follows. Section 2 presents our general equilibrium model. Section 3xplains how this model is calibrated using data from the Brazilian economy. The calibration results, some stylized facts, and theounterfactual exercises are presented in Section 4. Section 5 presents the robustness checks of our main exercises. Finally, Section 6rings our final remarks.
. Model
This section provides an overview of the model and its fundamental assumptions. We discuss the behavior of both firms andorkers and highlight the main implications of the model. Additionally, we define the competitive equilibrium.
.1. Firms
We begin by considering a country divided into 𝑅 ∈ N independent regions (states). Each region comprises a continuum ofworkers who choose one of the 𝑁 ∈ N available occupations in the economy. It is assumed that workers born in a particular region,
𝑟, can only work there.4 Multiple homogeneous competitive firms hire workers from all regions and occupations to produce a singleproduct. The production function for each firm is defined by
𝑌 =
𝑅∑
𝑟=1
𝑁∑
𝑖=1
𝐴𝑟𝐻𝑖𝑟, (1)
where 𝑌 is output, 𝐴𝑟 is Total Factor Productivity (TFP) of region 𝑟, and 𝐻𝑖𝑟 is the aggregate human capital of people working inoccupation 𝑖 at region 𝑟. Output can be consumed or used as an educational good. The firm’s problem is choosing labor in terms ofefficient units (aggregate human capital) to maximize profit, taking wages (𝑤𝑖𝑟) of each occupation in each region as given.
max
𝐻𝑖𝑟≥0
[ 𝑅∑
𝑟=1
𝑁∑
𝑖=1
𝐴𝑟𝐻𝑖𝑟 −
𝑅∑
𝑟=1
𝑁∑
𝑖=1
𝑤𝑖𝑟𝐻𝑖𝑟
]
. (2)
The solution to the problem described above is simple. The demand for human capital is given by:
𝐻𝑑𝑖𝑟 =
⎧⎪⎨⎪⎩
0 if 𝐴𝑟 < 𝑤𝑖𝑟
𝑥 ∈ R+ if 𝐴𝑟 = 𝑤𝑖𝑟
∞ if 𝐴𝑟 > 𝑤𝑖𝑟
. (3)
2.2. Workers
Each worker in our model has idiosyncratic abilities for each occupation. In a world with multiple occupations, some workerspossess a high talent for many occupations, while others may lack the skills for any occupation. Individuals value both consumptionand leisure, which we model as the time not spent at school. Each worker is endowed with one unit of time, which can be allocatedto either studying or leisure. The following equation gives the utility of a worker:
𝑈 (𝑐, 𝑠) = 𝑐𝛽 (1 − 𝑠), (4)
where 𝑐 represents consumption, 𝑠 is time spent at school, and 𝛽 is a parameter giving the relative importance of consumption toleisure.We adopt the approach of Hsieh et al. (2019) and introduce two frictions in our model. First, we assume that a person workingin occupation 𝑖 in region 𝑟 is paid a net wage of (1 − 𝜏𝑤𝑖𝑟 )𝑤𝑖𝑟, where 𝜏𝑤𝑖𝑟 is a barrier specific to occupation 𝑖 and location 𝑟. This can
4 In Appendix D, we discuss migration and argue that the fraction of the Brazilian population that migrates is relatively small. Therefore, our assumption of3
o migration is consistent with the available data.
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
csf
ch
wcTw
F
w
a
w
c
o
fP
P
tmobe interpreted as an unobserved cost (or benefit) of working in occupation 𝑖 at region 𝑟, which can arise due to various factors suchas social status or barriers to finding a job in a given occupation and region.The educational market in our model also experiences friction in the form of 𝜏ℎ𝑖𝑟, which captures the barriers to acquiring humanapital for different occupations and regions. These barriers may include difficulties in finding quality educational institutions oruitable training programs for a particular occupation. Additionally, 𝜏ℎ𝑖𝑟 may represent the costs of developing the necessary skillsor specific occupations.Following Tamura (2001) and Barros and Delalilbera (2018), we assume that the quality of teachers is a crucial input to humanapital formation. In addition, we extend the existing literature by incorporating the number of teachers as a determinant of workers’uman capital formation. Therefore, the human capital of workers in each region can be represented by the following expression:
ℎ𝑖𝑟(𝑒, 𝑠) = 𝑇 𝜑𝑟 𝑠
𝜙𝑖
𝑖 𝑒
𝜂
𝑖𝑟, (5)here 𝑒 represents the consumption of educational goods, 𝑠 is the time spent at school, 𝜂 is the elasticity of the human capitaloncerning the consumption of educational goods, and 𝜙𝑖 > 0 is the elasticity of human capital concerning the time spent at school.his parameter varies among occupations and generates differences in schooling. Finally, 𝑇𝑟 represents the role of teachers in theorkers’ human capital formation. We set 𝑇𝑟 = 𝑝𝛼𝑡𝑟𝐻1−𝛼𝑡𝑟 where 𝛼 ∈ (0, 1), 𝑝𝑡𝑟 is the fraction of people working as teachers, and 𝐻𝑡𝑟is the teachers’ aggregate human capital. We use this functional form to incorporate the quality and quantity of teachers into theworkers’ human capital formation.5Following McFadden (1974), Eaton and Kortum (2002), and Hsieh et al. (2019), abilities dispersion is modeled as a multivariateréchet distribution. Let 𝜖𝑖 be the ability of an individual in occupation 𝑖, then the distribution of abilities across occupations is:
𝐹 (𝜖1,… , 𝜖𝑁 ) = exp
[
−
𝑁∑
𝑖=1
𝜖−𝜃𝑖
]
, (6)
here 𝜃 governs the skill dispersion.The individual decision is made in two steps. First, given the occupational choice 𝑖, for which the individual has an idiosyncraticbility 𝜖𝑖, and taking wage 𝑤𝑖𝑟 as given, each worker chooses 𝑐, 𝑒, and 𝑠, to solve the following problem:
max
𝑐,𝑠,𝑒
𝑐𝛽 (1 − 𝑠) (7)
s.t. 𝑐 = (1 − 𝜏𝑤𝑖𝑟 )𝑤𝑖𝑟ℎ𝑖𝑟(𝑒𝑖𝑟, 𝑠𝑖)𝜖𝑖 − (1 + 𝜏ℎ𝑖𝑟)𝑒𝑖𝑟,Solving the problem above yields the optimal time spent on school and the amount of educational goods purchased6:
𝑠∗𝑖 =
(
1 + 1 − 𝜂
𝛽𝜙𝑖
)−1 (8)
𝑒∗𝑖𝑟(𝜖) =
[
𝜂
(
1 − 𝜏𝑤𝑖𝑟
1 + 𝜏ℎ𝑖𝑟
𝑤𝑖𝑟
)
(𝑝𝛼𝑡𝑟𝐻
1−𝛼
𝑡𝑟 )
𝜑
(
1 + 1 − 𝜂
𝛽𝜙𝑖
)−𝜙𝑖
𝜖𝑖
]𝜅 (9)
here 𝜅 = 1∕(1 − 𝜂).A higher elasticity of human capital with respect to time for a given occupation (𝜙𝑖) leads to more time allocated to humanapital accumulation. Individuals in occupations with a high 𝜙𝑖 acquire more schooling and have higher wages as compensation.Using Eqs. (8), (9) and the budget constraint into the utility function, we have the following indirect utility function forccupation 𝑖:
𝐷𝑖𝑟 =
[
?̄?
(
1 − 𝜏𝑤𝑖𝑟
(1 + 𝜏ℎ𝑖𝑟)𝜂
𝑤𝑖𝑟
)
(𝑝𝛼𝑡𝑟𝐻
1−𝛼
𝑡𝑟 )
𝜑𝑠𝜙𝑖𝑖 (1 − 𝑠𝑖)
1
𝛽𝜅 𝜖𝑖
]𝛽𝜅 (10)
where ?̄? = 𝜂𝜂(1 − 𝜂)1−𝜂 .Therefore, the occupational choice problem reduces to picking the occupation that delivers the highest 𝐷𝑖𝑟.7 Since talent is drawnrom an extreme value distribution, the highest utility can also be characterized by an extreme value distribution (McFadden, 1974).roposition 1 states that the share of the workers in each occupation can be obtained by aggregating the individuals’ optimal choices.
roposition 1 (Occupational Choice). Let 𝑝𝑖𝑟 be the fraction of workers in occupation 𝑖 in region 𝑟. Then, aggregating the solution ofindividual’s occupational choice problem across workers, we have:
𝑝𝑖𝑟 =
?̃?𝜃𝑖𝑟∑𝑁
𝑗=1 ?̃?
𝜃
𝑗𝑟
(11)
5 See Krueger (2003) and Lakdawalla (2006) for a discussion on teachers’ quality and quantity.6 For a complete solution of the model, refer to the Online Appendix.7 Our model assumes a deterministic path for every feasible occupational choice without inherent risk. Additionally, we assume that there is no variation inhe pre-existing wealth of workers. However, empirical evidence suggests that less wealthy individuals tend to select less risky income paths due to the higherarginal utility of consumption (Guo and Leung, 2021). For example, Cagetti and De Nardi (2006) find that restrictive borrowing constraints reduce the number4
f people engaging in (risky) entrepreneurial activities.
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
P
T
T
Pwhere
?̃?𝑖𝑟 = ?̄?
(
1 − 𝜏𝑤𝑖𝑟
(1 + 𝜏ℎ𝑖𝑟)𝜂
𝑤𝑖𝑟
)
(𝑝𝛼𝑡𝑟𝐻
1−𝛼
𝑡𝑟 )
𝜑𝑠𝜙𝑖𝑖 (1 − 𝑠𝑖)
1
𝛽𝜅
roof. Let:
?̃?𝑖𝑟 = ?̄?
(
1 − 𝜏𝑤𝑖𝑟
(1 + 𝜏ℎ𝑖𝑟)𝜂
𝑤𝑖𝑟
)
(𝑝𝛼𝑡𝑟𝐻
1−𝛼
𝑡𝑟 )
𝜑𝑠𝜙𝑖𝑖 (1 − 𝑠𝑖)
1
𝛽𝜅
hen, we can rewrite Eq. (10) as:
𝐷𝑖𝑟 = [?̃?𝑖𝑟𝜖𝑖]𝛽𝜅
herefore, the individual decision problem for worker 𝑖 in region 𝑟 consists of choosing the occupation that yields the highest valueof ?̃?𝑖𝑟𝜖𝑖. Without loss of generality, let us consider the probability of an individual choosing occupation 1:
𝑝𝑖𝑟 = 𝑃𝑟(?̃?1𝑟𝜖1 > ?̃?𝑖𝑟𝜖𝑖) ∀ 𝑖 ≠ 1
= 𝑃𝑟
(
𝜖𝑖 <
?̃?1𝑟
?̃?𝑖𝑟
𝜖1
)
∀ 𝑖 ≠ 1
= ∫ 𝐹1(𝛼1𝜖, 𝛼2𝜖,… , 𝛼𝑁 𝜖)𝑑𝜖 (12)where 𝐹1 represents the derivative of Eq. (6) with respect to its first argument, and 𝛼𝑖 = ?̃?1𝑟∕?̃?𝑖𝑟 for 𝑖 ∈ {1, 2,… , 𝑁}. Taking thederivative of Eq. (6) with respect to 𝜖1, and evaluating in 𝜖:
𝐹1 = 𝜃𝜖−𝜃−11 exp
(
−𝜖1?̂?
)
𝐹1(𝜖) = 𝜃𝜖−𝜃−1 exp
(
−𝜖?̂?
)
where ?̂? = ∑𝑛𝑖=1 𝛼−𝜃𝑖 . Then, Eq. (12) can be written as:
𝑝1𝑟 = ∫ ?̂??̂? 𝜃𝜖−𝜃−1 exp
(
−𝜖−𝜃?̂?
)
𝑑𝜖
= 1
?̂? ∫ ?̂?𝜃𝜖−𝜃−1 exp
(
−𝜖−𝜃?̂?
)
𝑑𝜖
This expression is the derivative of Eq. (6) with respect to 𝜖. Hence:
𝑝1𝑟 =
1
?̂? ∫ 𝑑𝐹 (𝜖)
= 1
?̂?
=
?̃?𝜃1𝑟∑𝑁
𝑖=1 ?̃?
𝜃
𝑖𝑟
□
We can interpret ?̃?𝑖𝑟 as a net reward of a person from region 𝑟 and occupation 𝑖 with average ability. Therefore, ?̃?𝑖𝑟 is composedof wage per efficiency unit, schooling, teachers’ human capital, and barriers. In this context, occupations with high 𝑤𝑖 will attractmore workers in all regions. On the other hand, differences in occupational choices are driven by frictions in the educational goodsand labor markets. Therefore, the fraction of individuals choosing sector 𝑖 is low when there are considerable barriers in humancapital formation (𝜏ℎ is high) and in the labor market (𝜏𝑤 is high). The following proposition defines the workers’ human capitalin each occupation in a given region.
Proposition 2 (Average Quality of Workers). For a given region, the human capital of workers in occupation i is:
𝐻𝑖𝑟 = 𝑝𝑖𝑟E[ℎ(𝑒𝑖𝑟, 𝑠𝑖)𝜖𝑖|person choices 𝑖], (13)
The average quality of workers is:
E[ℎ(𝑒𝑖𝑟, 𝑠𝑖)𝜖𝑖|person choices 𝑖] = 𝛤 [(1 − 𝜏𝑤𝑖𝑟1 + 𝜏ℎ𝑖𝑟 𝑤𝑖𝑟
)𝜂
ℎ̃𝑖𝑟𝑝
− 1𝜃
𝑖𝑟
]𝜅 (14)
where 𝛤 = 𝛤 (1 − 𝜅∕𝜃) is related to the mean of the Fréchet distribution for abilities, ℎ̃𝑖𝑟 = [(𝑝𝛼𝑡𝑟𝐻1−𝛼𝑡𝑟 )𝜑𝑠𝜙𝑖𝑖 𝜂𝜂]𝜅 and 𝜅 = 1∕(1 − 𝜂).
roof. We have:
ℎ(𝑒𝑖𝑟, 𝑠𝑖)𝜖𝑖 = (𝑝𝛼𝑡𝑟𝐻
1−𝛼
𝑡𝑟 )
𝜑
[
𝜂
(
1 − 𝜏𝑤𝑖𝑟
ℎ 𝑤𝑖𝑟
)
(𝑝𝛼𝑡𝑟𝐻
1−𝛼
𝑡𝑟 )
𝜑𝑠𝜙𝑖 𝜖𝑖
]𝜂𝜅
𝑠𝜙𝑖𝑖 𝜖𝑖 (15)
5
1 + 𝜏𝑖𝑟
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
i
tOatt
C
dg
𝑊o𝐻𝑖𝑟 is the total labor supply in efficiency units of occupation 𝑖 in region 𝑟. Then,
𝐻𝑖𝑟 = 𝑝𝑖𝑟E
{
(𝑝𝛼𝑡𝑟𝐻
1−𝛼
𝑡𝑟 )
𝜑
[
𝜂
(
1 − 𝜏𝑤𝑖𝑟
1 + 𝜏ℎ𝑖𝑟
𝑤𝑖𝑟
)
(𝑝𝛼𝑡𝑟𝐻
1−𝛼
𝑡𝑟 )
𝜑𝑠𝜙𝑖𝑖 𝜖𝑖
]𝜂𝜅
𝑠𝜙𝑖𝑖 𝜖𝑖
||||person choices 𝑖
}
= 𝑝𝑖𝑟
{
(𝑝𝛼𝑡𝑟𝐻
1−𝛼
𝑡𝑟 )
𝜑
[(
1 − 𝜏𝑤𝑖𝑟
1 + 𝜏ℎ𝑖𝑟
𝑤𝑖𝑟
)
𝜂(𝑝𝛼𝑡𝑟𝐻
1−𝛼
𝑡𝑟 )
𝜑𝑠𝜙𝑖𝑖
]𝜂𝜅
𝑠𝜙𝑖𝑖 E
[
𝜖𝜅𝑖
||||person choices 𝑖
]}
= 𝑝𝑖𝑟ℎ̃𝑖𝑟
(
1 − 𝜏𝑤𝑖𝑟
1 + 𝜏ℎ𝑖𝑟
𝑤𝑖𝑟
)𝜂𝜅
E
[
𝜖𝜅𝑖
||||person choices 𝑖
] (16)
To calculate this last conditional expectation, we use the Fréchet distribution. We suppress the region index 𝑟 because thiscalculation is similar across all regions. Let 𝑦𝑖 = ?̃?𝑖𝜖𝑖. Since we are maximizing 𝑦𝑖, it also has the extreme value distribution:
𝐏𝐫
(Max𝑖𝑦𝑖 < 𝑧) = 𝐏𝐫(𝜖𝑖 < 𝑧∕?̃?𝑖) ∀𝑖
= 𝐹 (𝑧∕?̃?1,… , 𝑧∕?̃?𝑁 )
= exp
[
−
𝑁∑
𝑖=1
(𝑧∕?̃?𝑖)−𝜃
]
= exp
[
−𝑘𝑧−𝜃
]
where 𝑘 = ∑𝑁𝑖 ?̃?𝜃𝑖 .After some algebraic manipulation, we conclude that the distribution of 𝜖∗ (the workers’ ability in their chosen occupation) hasa Fréchet distribution:
𝐺(𝑥) = 𝐏𝐫(𝜖∗ < 𝑥) = exp
[
−𝑘∗𝑥−𝜃
] (17)
where 𝑘∗ = ∑𝑁𝑖=1(?̃?𝑖∕?̃?∗)𝜃 = 1∕𝑝∗.Finally, we calculate the expectation of Eq. (16). Let 𝑖 be the occupation an individual chooses, and 𝜆 a positive exponent.
E(𝜖𝜆𝑖 ) = ∫
∞
0
𝜖𝜆𝑖 𝑑𝐺(𝜖)
= ∫
∞
0
𝜃
(
1
𝑝∗
)
𝜖(𝜆−𝜃−1) exp
[(
1
𝑝∗
)
𝜖−𝜃
]
𝑑𝜖
We set 𝑥 = ( 1𝑝∗ ) 𝜖−𝜃 and rewrite the last expression as:
E(𝜖𝜆𝑖 ) =
(
1
𝑝∗
) 𝜆
𝜃
∫
∞
0
𝑥−
𝜆
𝜃 exp(−𝑥)𝑑𝑥
=
(
1
𝑝∗
) 𝜆
𝜃
𝛤
(
1 − 𝜆
𝜃
)
Using this result in Eq. (16) completes the proof. □
This finding suggests that there is a selection effect at play in the economy. Eq. (14) reveals that the average quality of workersn occupation 𝑖 and region 𝑟 is inversely related to the proportion of workers in that occupation (𝑝𝑖𝑟). When there are significantfrictions in occupation 𝑖 and region 𝑟, only the most skilled workers are selected for that occupation. For example, if becoming aeacher is relatively easy in a particular region, the average human capital of teachers in that region will be low (intensive margin).n the other hand, if we keep the average human capital constant and increase the proportion of workers in an occupation, theggregate human capital will be higher (extensive margin). The net effect depends on the values of the parameters. When 𝜃(1−𝜂) > 1,he extensive margin dominates, while the intensive margin dominates otherwise. Having established this, we solve the model forhe average wage in occupation 𝑖 and region 𝑟.
orollary 1 (Gross Average Wages). Let 𝑊𝑖𝑟 be the gross average wage in occupation 𝑖 in region 𝑟. Then:
𝑊𝑖𝑟 = 𝑤𝑖𝑟E[ℎ(𝑒𝑖𝑟, 𝑠𝑖)𝜖𝑖] = 𝛤𝜂
(1 − 𝑠𝑖)−1∕𝛽
(1 − 𝜏𝑤𝑖𝑟 )
( 𝑁∑
𝑖=1
?̃?𝜃𝑖𝑟
) 𝜅
𝜃 (18)
This result is a consequence of Proposition 2. As Eq. (18) indicates, the gross average wage varies across occupations in a regionue to differences in schooling and labor market frictions. Occupations with higher levels of human capital offer more substantialross average wages. Using Eq. (3), we deduce that in equilibrium, 𝐴𝑟 = 𝑤𝑖𝑟. As a result, ?̃?𝑖𝑟 is a function of 𝐴𝑟, and consequently,
𝑖𝑟 depends on regional TFP. This implies that labor market frictions, average human capital, and TFP are all critical determinants6
f regional average wage disparities. Finally, we adopt a standard competitive equilibrium definition.
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
3
2
iNo
(awcr
Tt
𝜑(
3
aohoog
lam
GG2.3. Equilibrium
Definition 1 (Competitive Equilibrium). A competitive equilibrium in this economy consists of:
(i) Given an occupational choice, 𝑤𝑖𝑟, and the idiosyncratic ability 𝜖, each worker chooses c, e, s to maximize utility in Eq. (7).(ii) Given market friction, 𝑤𝑖𝑟, 𝐻𝑖𝑡, and 𝜖, a worker chooses the occupation that maximizes 𝐷𝑖𝑟.(iii) A representative firm hires 𝐻𝑖𝑟 to maximize profits.(iv) The occupational wage, 𝑤𝑖𝑟, clears the labor market in each occupation and region.(v) Total output is given by the production function in Eq. (1).
. Empirical investigation
This section describes how we calibrated the model to fit the Brazilian data. We used data from two distinct periods (2003 and015) to investigate the convergence of income and human capital across the Brazilian states.8Our calibration strategy involved identifying appropriate values for frictions and TFP to ensure that the competitive equilibriums consistent with the dataset of the Brazilian states in 2015. To achieve this goal, we used individual-level data from the Brazilianational Household Sample Survey (PNAD) for the following variables: years of schooling; work hours; gross earnings; and the sharef workers in occupations.After some adjustments,9 our dataset consisted of 109,038 individuals belonging to eight occupational groups: (1) managersexcluding those in the public sector); (2) professionals in the fields of science and the arts; (3) middle-level technicians; (4)dministrative service workers; (5) individuals in the service sector; (6) professionals in sales and service provision; (7) agriculturalorkers; and (8) workers in the goods and industrial production, services, and repairs/maintenance. To simplify our analysis, weombined groups 4, 5, and 6 into the service sector. Additionally, we separated individuals working as teachers in another category,esulting in the following list of occupational categories:
1. Managers (except public sector);2. Professionals of sciences and arts (except teachers);3. Middle-level technicians (except teachers);4. Service sector;5. Agriculture;6. Goods and industrial production, services and repairs-maintenance;7. Teachers.
he 26 Brazilian states and the Federal District (DF) are considered in the empirical analysis.10 Therefore, the dataset contains aotal of seven different occupations (𝑁 = 7) spread across twenty-seven regions (𝑅 = 27).We divided the parameters into three distinct groups. The first group contains the preferences and technology parameters (𝜂, 𝜃,, 𝛽, 𝛼). The second group consists of the elasticity of human capital in relation to time spent at school (𝜙𝑖), as well as the frictions
𝜏𝑤𝑖𝑟 and 𝜏ℎ𝑖𝑟). The third group includes TPF (𝐴𝑟).
.1. Preferences and technology parameters
The model’s parameters define the functional forms of various equations, such as those governing the distribution of abilitiesnd the utility function. We set the first group of parameters (𝜂, 𝜃, 𝜑, 𝛽, 𝛼) to evaluate income convergence by taking the meanf specific statistics from the period between 2003 and 2015. To estimate the skill dispersion parameter (𝜃) and the elasticity ofuman capital to educational goods (𝜂), we follow the approach of Hsieh et al. (2019). We assume that wages within a specificccupation and region follow a Fréchet distribution shaped by 𝜃 and 𝜂 in a multiplicative form: 𝜃(1 − 𝜂). Therefore, the dispersionf wages depends on 1∕𝜃 and 1∕(1 − 𝜂), and the coefficient of variation (𝐶𝑉 ) of wages within a particular occupation and region isiven by:
𝐶𝑉 =
𝛤
(
1 − 2𝜃(1−𝜂)
)
(
𝛤
(
1 − 1𝜃(1−𝜂)
))2 − 1, (19)
where 𝛾 represents the Gamma function.
8 We chose this period because the Brazilian National Household Sample Survey (PNAD) methodology underwent changes before 2003 and after 2015.9 We removed individuals with no occupation and those whose wages were less than 60% of the minimum wage to eliminate cases of underreported wages,eading us to drop individuals receiving considerably less than the minimum wage. We also limited our sample to individuals between the ages of 25 and 65,nd excluded individuals in occupations that were not well-defined or in the military. In Appendix E, we present the results of an alternative calibration of ourodel, which demonstrates the robustness of our results to the data filtering process, including individuals that earn less than 60% of the minimum wage.10 Acre (AC), Alagoas (AL), Amapá (AP), Amazonas (AM), Bahia (BA), Ceará (CE), Espírito Santo (ES), Goiás (GO), Maranhão (MA), Mato Grosso (MT), Matorosso do Sul (MS), Minas Gerais (MG), Pará (PA), Paraíba (PB), Paraná (PR), Pernambuco (PE), Piauí(PI), Rio de Janeiro (RJ), Rio Grande do Norte (RN), Rio7
rande do Sul (RS), Rondônia (RO), Roraima (RR), Santa Catarina (SC), São Paulo (SP), Sergipe (SE), Tocantins (TO).
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
sTable 1Baseline constant parameters.Parameters Value Description Source
𝜂 0.129 Elasticity of educational goods in the human capital function Estimated using data from PNAD 2015 and 2003
𝜑 0.48 Elasticity of teacher’s human capital in the human capital function Tamura (2001)
𝜃 2.52 Dispersion of skills Estimated using data from PNAD 2015 and 2003
𝛼 0.31 Weight of the share of teachers in 𝑇𝑟 Tamura (2001)
𝛽 0.231 Consumption preference Hsieh et al. (2019)
Table 2Descriptive statistics of years of schooling among occupations and implied 𝜙.Source: Elaborated by the authors with data from PNAD 2015.Occupation Parameter Schooling statistics
𝜙𝑖 Mean 1◦ Quartile Median 3◦ Quartile VarianceManagers 0.28 11.77 11 11 15 3.36Sciences and arts 0.35 13.98 15 15 15 2.39Middle-level technicians 0.28 11.67 11 11 14 2.58Service-sector 0.22 8.91 6 11 11 3.79Agriculture 0.12 5.07 2 4 8 3.92Industrial production and services 0.18 7.75 5 8 11 3.69Teachers 0.35 14.13 14 15 15 1.69
Each 𝜙𝑖 is computed using Eq. (8).
Afterward, we compute the mean and variance of the exponent of the regression residuals and use a root-finding algorithm toolve Eq. (19) for 𝜃(1 − 𝜂). The value for 2003 is 2.39, for 2015 it is 2.00, and the average of the two years is 2.19.We adopt the approach of Hsieh et al. (2019) to estimate 𝜂 as the ratio of educational expenditure to labor compensation. Thetotal amount of public and private educational expenditures as a share of GDP was 0.064 in 2003, 0.079 in 2015, and its averagewas 0.072. The ratio of labor compensation to GDP was 0.53 in 2003, 0.58 in 2015, and averaged 0.56.11 We set 𝜂 to 0.129 basedon these values. With 𝜃(1 − 𝜂) and 𝜂 in hand, we can easily compute 𝜃 as 2.52.Table 1 presents the remaining functional parameters of the model. To specify the parameters related to the teacher’s rolein human capital formation, we adopt the values suggested by Tamura (2001): 𝛼 = 0.31; and 𝜑 = 0.48. We also set 𝛽 = 0.231,following Hsieh et al. (2019). In Section 5, we investigate the robustness of our results by varying the values of 𝛼, 𝛽, 𝜃, 𝜂, and 𝜑.
3.2. Estimation of 𝜙𝑖’s
To calculate the second group of parameters, which represents the elasticity of human capital to time spent at school for eachoccupation (𝜙𝑖’s), we begin by computing the average years of schooling for each occupation and then the study hours. We assumethat a typical individual studies six hours a day on weekdays, so the number of study hours in a year is 252 × 6 = 1512. Therefore,of the 8760 h available in a year, the time studying represents 17.26%.We assume that the schooling period occurs in the first 25 years of an individual’s life, which is the upper bound of years ofeducation in our model. We then divide the average years of schooling in the dataset by 25 and multiply it by the share of studyingtime in a year (0.1726). Finally, we use Eq. (8) to calculate the 𝜙𝑖’s.12 Table 2 brings the results.
3.3. Calibration of 𝜏’𝑠 and 𝐴’𝑠
We calibrate the remaining parameters, 𝜏’s and 𝐴’s, using the Method of Moments, which involves minimizing the differencebetween the statistics of our model and those of the Brazilian data. In the calibration procedure, we use two statistics groups foreach occupation and region: the workers’ share; and the average gross wage.We utilize the PNAD microdata to compute the average hourly wage for each occupation in each region.13 In our model, thosestatistics are described by Eqs. (11) and (18). We use the First Order Conditions (FOC) of the firm’s maximization problem, where
𝑤𝑖,𝑟 = 𝐴𝑟 ∀ 𝑖, 𝑟, to recover the equilibrium wage rate, which allows us to use Eqs. (11) and (18) to compute the model’s statistics thatrepresents the competitive equilibrium.The sum of the occupations’ share in each region equals one, ∑𝑁𝑖=1 𝑝𝑖𝑟 = 1, implying that each region has (𝑁 − 1)𝑅 independentstatistics. Thus, we assume that 𝜏ℎ1𝑟 = 0, ∀ 𝑟. Also, we assume that 𝜏𝑤1𝑟 = 𝜏𝑤1 for all regions, implying that the frictions in occupation1 are equal across regions. Also, we fix the TFP of the last region to a constant value, denoted as 𝐴𝑅.
11 The data for labor compensation as a share of GDP was obtained from the PennWorldTable10.0.
12 By rewriting Eq. (8) as 𝜙𝑖 = (1 − 𝜂)𝑠𝑖𝛽(1 − 𝑠𝑖) , we can substitute the time spent on education, as calculated previously, and the other parameters into this expression.13 Appendix A brings the average hourly wage and the share of workers by occupation and region.8
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
4
acpr
4
t
A
t
ipFig. 1. Model adjustment to data - wages and share of workers.
We define the following objective function to our numerical routine:
 = 𝑁,𝑅∑
𝑖=1,𝑟=1
(
𝑊𝑀𝑖𝑟 −𝑊
𝐷
𝑖𝑟
𝑊 𝐷𝑖𝑟
)2
+
𝑁−1,𝑅∑
𝑖=1,𝑟=1
(
𝑝𝑀𝑖𝑟 − 𝑝
𝐷
𝑖𝑟
𝑝𝐷𝑖𝑟
)2 (20)
The superscripts 𝑀 and 𝐷 in Eq. (20) represent the model and target statistics, respectively.14 We utilize the Nelder–Mead algorithmto minimize Eq. (20), resulting in  = 0.00092, which is considered to be a small number, as we have a total of 378 different targets.Fig. 1(a) displays the average hourly wage from the empirical data (vertical axis) and the estimated average hourly wage fromthe model (horizontal axis). Fig. 1(b) presents the empirical data (vertical axis) and model-estimated data (horizontal axis) for theshare of workers in each occupation and region. The model fits the empirical data well, as indicated by the points being close tothe 45◦ line. Appendix B brings the calibrated values of 𝜏𝑤𝑖𝑟 , 𝜏ℎ𝑖𝑟, and 𝐴𝑟.
. Results
This section presents and discusses the results of the numerical exercises. Firstly, we compare the results of our simulations withset of stylized facts. Additionally, we perform a series of counterfactual exercises to assess the sensitivity of simulated GDP tohanges in the labor market and educational frictions. Furthermore, we calibrate the model using 2003 data and compare it to therevious calibration to analyze the income convergence process across Brazilian states. Finally, we evaluate the robustness of ouresults.
.1. Comparing model results with a set of stylized facts
The calibrated model produces a good fit for GDP per worker, as illustrated in Fig. 2(a). Moreover, as expected, Fig. 2(b) showshat the model’s results indicate a positive correlation between GDP and TFP.Fig. 3 presents the model’s results and data on teachers’ wages relative to other occupations.15 The model’s results also displaya good fit for relative wages, and as shown in Fig. 3, on average, teachers have a higher relative wage in low and middle-incomestates16 than in high-income states.17
14 We apply the logarithm in Eq. (20) to improve the algorithm’s numerical stability.15 In Brazil, the LawN11.738 of 2008 regulates the national minimum wage for public teaching professionals in basic education. However, Table A.1 inppendix A shows that there is wage dispersion among teachers across regions.16 We rank the 27 Brazilian states using 2015 GDP per capita data. The first nine states are considered high-income, the middle nine are middle-income, andhe last nine are low-income.17 To further investigate the relationship between teachers’ relative wages and GDP per capita, we conduct a panel regression analysis with the results presentedn Appendix F, which provides a more rigorous analysis than our earlier findings. The results of the econometric estimations support our earlier findings and9
rovide additional evidence of the negative relationship between teachers’ relative wages and GDP per capita.
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.Fig. 2. GDP - Model.
Fig. 3. Teachers’ relative wages.
As argued by Barros and Delalilbera (2018), one possible reason for the negative relationship between teachers’ relative wagesand GDP per capita is that the teaching profession is labor-intensive and less affected by technological and structural changescompared to other occupations. Therefore, in states with more advanced technologies, the relative teachers’ wage is lower than inless developed states.In low-income states, the teaching profession may be more accessible to individuals due to lower labor and educational marketbarriers compared to richer states. As a result, a higher share of talented people may choose the teaching profession in these statescompared to high-income ones, as illustrated in Fig. 4. Therefore, providing more incentives for talented individuals to become
10
teachers in high-income states may lead to even higher incomes in these regions.
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
E
tt
faFig. 4. GDP per worker and teachers’ human capital.
Fig. 5. Share of students in teaching courses, and share of teaching courses offered. Note: The data used to create this figure was obtained from the Higherducation Census of 2015, which was provided by the National Institute of Educational Studies and Research Anísio Teixeira (INEP).
The results obtained are consistent with the available data. Fig. 5(a) illustrates that, on average, more students are enrolled ineaching courses in the poorest states than in the wealthiest ones, which can be explained by the fact that the poorest states tendo have a greater number of institutions offering teaching courses, as depicted in Fig. 5(b).Additional data findings support the calibration of our model. For instance, in the model, agriculture has the highest averagerictions in the educational market, which is consistent with the fact that around 65% of workers in this occupation lived in ruralreas in 2015 (PNAD), where access to education is often more challenging.18 In addition, research has shown that the quality
18 See Appendix B for more details.
11
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
o
m
oe
4
ampaFig. 6. GDP before and after placing state barriers with the highest and lowest ATHC in all states.
f education in rural schools is generally lower than that in urban areas.19 On the other hand, at least 92% of workers in otheroccupations reside in urban areas.
4.2. Frictions and GDP
To investigate the economy’s sensitivity to frictions, we conduct counterfactual exercises. In Fig. 6(a), we assume that all stateshave the same frictions (𝜏𝑤 and 𝜏ℎ) as the one with the highest Average Teachers Human Capital (ATHC), which is Roraima (RR).In this case, our results show that all states would have a significantly higher GDP, with the Brazilian GDP increasing by 87.85%.Moreover, the relative wage of teachers in all states would be equal to the level observed in Roraima.Conversely, if all states had the same frictions as São Paulo (SP), the state with the lowest ATHC, the GDP of all states woulddecrease (Fig. 6(b)), with the Brazilian GDP declining by 59.62%. Finally, in 6(c), we explore a counterfactual scenario where allfrictions are eliminated, resulting in a 16.94% growth in the Brazilian output.The above counterfactual exercises illustrate the significant impact that frictions have on the economy. However, these exercisesinvolve changing the entire structure of economic incentives, which is a complex matter of public policy. While the results makesense, they cannot be easily implemented.Based on this exercise, we can infer that labor misallocation is a significant issue across Brazilian states. When the barriers toentry in the teaching profession are altered, the relative wage for teachers changes, which leads to a reallocation of talent acrossdifferent occupations. Since becoming a teacher has an externality, meaning that it impacts society as a whole, a modification infrictions that encourages more talented individuals to choose this occupation significantly impact regional GDP.In the next exercise, we examine how market frictions across all occupations affect GDP per capita:1. We calculate the GDP per capita assuming no frictions in both labor and educational markets.2. We set the educational market frictions to zero and vary the labor market friction from −0.9 to 0.9.3. Similarly, we conduct an exercise where labor market frictions are set to zero, and we analyze the impact of educational goodsarket frictions.Frictions in the educational market act as a ‘‘price’’, enabling consumers to adjust their demand for educational goods. On thether hand, due to the inelastic labor supply, frictions in the labor market only affect the net wages. Therefore, alterations inducational frictions tend to exert a more substantial influence on GDP. Fig. 7 shows the results.
.3. Teacher’s human capital
This section examines the impact of changing frictions in each occupation while keeping the frictions in the other occupationst zero. Fig. 8 reveals that changes in frictions in the teacher’s occupation, particularly in the educational goods market, have aore significant effect on GDP than changes in other occupations’ frictions. Hence, public policies should incentivize more qualifiedeople to become teachers to promote GDP growth. It should be noted that reducing frictions in other occupations could adverselyffect economic performance by reducing the incentives for individuals to become teachers.
19 See, for example, Williams (2005) and Zhang (2006).12
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
t
(tFig. 7. Increases in the frictions of all occupations and the percentage effects on GDP - Model.
Fig. 8. Increases in the frictions of each occupation and the percentage effects on GDP.
In Fig. 9, we shift the focus from GDP sensitivity to the impact of frictions on teachers’ human capital and the proportion ofeachers in the workforce.The teaching profession becomes more attractive with lower barriers, and as a result, more individuals choose this career pathextensive margin). However, the decrease in barriers may also lead to individuals with lower idiosyncratic skills choosing to becomeeachers, resulting in a lower average quality of teachers (intensive margin).Although there is a trade-off between the quality and quantity of teachers in our model, a lower 𝜏ℎ results in a lower ‘‘price’’ ofeducational goods (see Eq. (9)). As a result, all workers who choose to become teachers invest more in human capital, compensatingfor the potential decrease in quality due to the increase in quantity (extensive margin). Therefore, the net effect of reducing barriers
13
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
it
4
wacFig. 9. Increases in frictions and percentual effects on 𝐻𝑡𝑟 and 𝑝𝑡𝑟. Note: 𝐻𝑡𝑟 = Human capital of teachers, 𝑝𝑡𝑟 = proportion of workers in teacher occupation.
s an increase in the average quality of teachers (intensive margin). It is important to note that all these effects are amplified dueo the positive externality of teachers on the entire workforce.
.4. Income convergence
According to the research conducted by Barro and Sala-i-Martin (1992), absolute income convergence happens when economiesith lower income grow faster than those with higher income per capita, leading to a decrease in the income gap between poornd wealthy regions over time. To test whether income convergence occurs across the Brazilian states, we utilize data from a modelalibrated for 2015 and 2003. To achieve this, we estimate the following equation using Ordinary Least Squares (OLS):
1
𝑇
log
(𝑌𝑟,2015
𝑌𝑟,2003
)
= 𝑎 + 𝑏 log(𝑌𝑟,2003) + 𝜖𝑟 (21)
Here, 𝑌𝑟,2015 and 𝑌𝑟,2003 represent the GDP of region 𝑟 in the years 2015 and 2003, respectively. The model is estimated over 𝑇years, with 𝑎 and 𝑏 being constants and 𝜖𝑟 representing the error term. A negative value of 𝑏 provides support for the convergencehypothesis.The findings in Table 3 support the hypothesis of absolute income convergence among the Brazilian states since the estimated 𝑏 isnegative and statistically significant. In addition, we have calculated the speed of convergence of this economy, which is 𝛽𝑠 = 4.01%.20The half-life concept can be used to interpret this result, which represents the time required to reduce the income gap by half. Thehalf-life is calculated as 𝐻𝐿 = log(2)∕𝛽𝑠, and we find that it equals 17.3 years.The occurrence of absolute income convergence among Brazilian states from 2003 to 2015 is further evidenced by Fig. 10.This plot clearly shows that low-income states, such as Paraíba (PB), Rio Grande do Norte (RN), Maranhão (MA), Alagoas (AL),Piauí(PI), and Ceará (CE), experienced relatively fast income growth in this period. Conversely, high-income states, including theFederal District (DF), São Paulo (SP), Santa Catarina (SC), Rio de Janeiro (RJ), and Rio Grande do Sul (RS), exhibited slower growthrates.The occurrence of absolute income convergence among Brazilian states from 2003 to 2015 can be explained by multiple factors,including a reduction in educational market frictions and an increase in Total Factor Productivity (TFP).21 Our analysis reveals thateducational frictions have decreased more sharply in the poorest states and Rio de Janeiro. Additionally, there has been an averagereduction in frictions for occupations in the teaching occupation. However, the most substantial reduction in friction occurred inthe agriculture sector, likely due to the increase in the average years of education of Brazilian agricultural workers.Our analysis also indicates a slight increase in labor market barriers from 2003 to 2015, on average. However, as depicted inFig. 7, the impact of increases in labor market barriers on GDP is relatively small compared to reductions in educational marketfrictions.
20 The formula for the speed of convergence is given by: 𝛽𝑠 = − log(𝑇 𝑏+1)𝑇 .21 Appendix B provides the calibrated frictions and TFP for 2003.14
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
aTable 3Absolute income convergence across Brazilian states from 2003 to 2015.Source: Search results.
1
𝑇
log
(
𝑌𝑟,2015
𝑌𝑟,2003
)
a 0.0880***(0.0114)b −0.0318***(0.0049)
R-squared 0.6284R-squared Adj. 0.6136
Notes: Standard errors in parentheses. Single (*), double (**) and triple (***) asterisk denotestatistical significance at 10%, 5% and 1%, respectively.
Fig. 10. Growth rate from 2003 to 2015 and Log of GDP 2003.
5. Robustness check
We present the results of our robustness analysis in Table 4. To conduct this analysis, we performed a counterfactual exercisesimilar to that presented in Section 4.2, where we set the market frictions (𝜏𝑤 and 𝜏ℎ) to match those of the states with the highestnd lowest Average Teachers’ Human Capital (ATHC).In our counterfactual exercise, when we change the educational goods elasticity in the human capital function 𝜂 using thefrictions of the state with the highest ATHC (Roraima), GDP increases substantially from 2.71% (𝜂 = 0.05) to 87.85% with ourbaseline 𝜂 = 0.129, and up to 162.36% when 𝜂 = 0.25. The results are analogous when we use the frictions of the state with thelowest ATHC (São Paulo). Therefore, we can conclude that changes in 𝜂 substantially impact GDP, regardless of the specific stateused in the counterfactual exercise. Among all parameters tested in our robustness analysis, we find that GDP is most sensitive tochanges in 𝜂 and 𝜑.In the following two lines of Table 4, we analyze the sensitivity of skill dispersion, represented by the parameter 𝜃. In the secondcolumn, we observe that when skill dispersion is given by 𝜃 = 2, GDP is 57.95% higher and 90.41% greater when 𝜃 = 3. Thethird column shows that changes in 𝜃 have a more significant impact on GDP in an economy with higher frictions. Moreover, theparameter 𝛽 also positively affects GDP.One critical parameter in the human capital function is the one measuring the trade-off between the quantity and quality ofteachers. By increasing 𝛼, we place more weight on the number of teachers in relation to their quality (average human capital ofteachers).22 When we set 𝛼 = 0.2, GDP increases by 107.55%, and it is 57.87% higher when 𝛼 = 0.6.Finally, we examine the sensitivity of our results to the teacher’s contribution to human capital formation, denoted by 𝜑. Asshown in Table 4, an increase in this parameter has a significant positive influence on GDP. Therefore, teachers play a critical rolein driving economic performance in our economy.
22 Recall that 𝑇 = 𝑝𝛼𝐻 (1−𝛼), where 𝐻 is the average human capital of teachers and 𝑝 is the proportion of teachers in region 𝑟.
15
𝑟 𝑡𝑟 𝑡𝑟 𝑡𝑟 𝑡𝑟
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
Table 4Robustness check for constant parameters.Source: Search results.Parameter GDP variation (Largest ATHC) GDP variation (Lowest ATHC) GDP variation (Zero frictions)
𝜂 = 0.05 2.71% −14.07% 9.31%
𝜂 = 0.25 162.36% −108.50% 20.22%
𝜃 = 2.0 57.95% −48.50% 21.19%
𝜃 = 3.0 90.41% −60.59% 16.68%
𝛽 = 0.1 80.46% −52.38% −0.29%
𝛽 = 0.3 88.52% −61.37% 18.35%
𝛼 = 0.2 107.55% −73.20% 18.29%
𝛼 = 0.6 57.87% −38.79% 14.41%
𝜑 = 0.1 8.44% −16.06% 20.20%
𝜑 = 0.6 162.13% −99.39% 13.19%
Benchmark 87.85% −59.62% 16.94%
Notes: ATHC is Average teacher human capital. The baseline values are 𝜂 = 0.129, 𝛽 = 0.231, 𝜃 = 2.52, 𝜑 = 0.48 and 𝛼 = 0.31.
6. Final remarks
In this paper, we develop a Roy model to investigate the influence of market frictions on labor and educational markets in Brazil.Additionally, we incorporate a function where teachers play a crucial role in the human capital formation of the entire workforce.After calibrating the model to Brazilian data, we find a positive correlation between barriers related to the teacher’s occupation andGDP across Brazilian states. We also show that increasing the attractiveness of the teaching occupation results in higher GDP. Whenmore individuals with higher idiosyncratic abilities pursue teaching careers, they directly affect the workforce’s productivity. Thesefindings highlight the importance of addressing market frictions in the education and labor sectors and underscore the critical roleof teachers in promoting economic growth.Furthermore, our calibrated model for 2015 suggests that the main driver of absolute income convergence was the reductionof frictions related to the teaching profession. This reduction led to an increase in the average human capital and productivity ofthe entire economy. Therefore, policymakers should focus on increasing incentives for individuals to pursue teaching as a career,particularly for those with higher idiosyncratic abilities, to attract more talented people.Due to the practical challenges involved in selecting high-quality teachers, it is important to interpret our findings with caution.Identifying individuals with high ability in this occupation is a challenging task. For instance, Rivkin et al. (2005) estimateteacher quality using a detailed micro dataset and find that factors such as teachers’ experience and education explain verylittle of teacher quality. Further research is needed to determine the most effective strategies for enhancing the attractiveness ofthe teaching profession. For instance, policymakers could consider implementing strategies to enhance the attractiveness of theteaching profession, such as creating career paths for teachers based on their performance and offering salaries comparable to thoseof similarly qualified professionals in other fields. Additionally, providing a work environment that fosters collaboration amongteachers, investing in their training, and offering a good retirement plan could also be effective incentives. Further research isnecessary to better understand the factors that drive individuals to choose a career in teaching and how to improve the quality ofthe teacher workforce.There is potential for further research that accounts for differences in risk levels across occupational options and incorporatesheterogeneity in workers’ wealth. Such an extension could shed light on how wealth, risk, and the marginal utility of consumptioninfluence occupational choices, and it is a promising direction for future research. Furthermore, investigating the misallocationof teachers across different educational stages could offer further insight into the efficiency of the education system and provideopportunities for targeted policy interventions. For instance, analyzing the allocation of teachers between primary, secondary, andtertiary education, and evaluating how this allocation affects human capital accumulation could be a fruitful area of research.Therefore, future studies could explore these extensions to expand upon our findings and provide a deeper understanding of thedynamics of occupational choices and teacher allocation, which would help inform policy decisions to improve the allocation ofhuman capital and promote economic growth.
CRediT authorship contribution statement
Fernando Barros Jr: Conceptualization, Methodology, Investigation, Writing – original draft, Writing - review & editing. BrunoR. Delalibera: Conceptualization, Methodology, Software, Investigation, Writing – original draft, Writing – review & editing.Luciano Nakabashi: Investigation, Writing – original draft, Writing – review & editing. Marcos J. Ribeiro: Methodology, Software,Data curation, Investigation, Writing – original draft, Writing – review & editing.
Data availability
Data will be made available on request.16
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
Table A.1Descriptive statistics of teachers’ hourly wages by state.Source: Elaborated by the authors with data from PNAD 2015.State Relative wage Mean 1◦ Quartile Median 3◦ Quartile Variance Income group
AC 1.57 17.53 9.72 14.29 23.81 10.46 Middle incomeAL 1.45 16.04 9.38 13.91 20.37 9.65 Low incomeAM 1.30 16.13 9.52 14.29 20.24 8.63 Middle incomeAP 1.48 19.77 13.17 17.80 23.53 10.03 Middle incomeBA 1.33 15.40 8.33 11.90 17.86 11.97 Low incomeCE 1.21 14.04 8.33 11.90 15.87 11.17 Low incomeDF 1.49 27.93 13.69 23.81 35.71 17.42 High incomeES 1.29 18.16 9.68 15.01 21.33 12.99 High incomeGO 1.42 19.30 10.19 14.29 22.55 15.18 Middle incomeMA 1.30 15.93 8.93 11.90 20.40 12.50 Low incomeMG 1.37 18.42 9.52 14.29 21.65 13.78 Middle incomeMS 1.45 21.84 11.11 17.86 26.19 16.22 High incomeMT 1.31 18.93 11.90 17.06 21.43 10.58 High incomePA 1.50 17.81 9.38 14.29 21.71 13.82 Low incomePB 1.37 17.13 9.04 12.50 21.60 12.55 Low incomePE 1.29 14.99 7.28 11.43 19.05 11.57 Low incomePI 1.28 14.24 9.52 13.10 15.67 7.72 Low incomePR 1.36 21.04 11.90 17.27 23.81 14.86 High incomeRJ 1.33 20.00 9.52 15.87 23.81 15.05 High incomeRN 1.24 15.53 7.37 11.90 18.45 13.25 Low incomeRO 1.25 16.21 10.39 14.07 17.86 10.30 Middle incomeRR 1.62 22.34 9.72 20.22 29.17 14.21 Middle incomeRS 1.38 20.40 10.84 15.16 23.81 15.12 High incomeSC 1.21 18.15 11.90 14.88 20.83 11.36 High incomeSE 1.70 19.61 9.40 16.67 26.19 13.52 Middle incomeSP 1.13 18.61 9.52 14.88 23.15 14.07 High incomeTO 1.30 17.32 9.38 14.58 19.05 13.09 Middle income
Notes: Relative wage is the average hourly wage of teachers divided by the average hourly wage of other six occupations. Acre (AC), Alagoas (AL), Amapá (AP),Amazonas (AM), Bahia (BA), Ceará (CE), Distrito Federal(DF), Espírito Santo (ES), Goiás (GO), Maranhão (MA), Mato Grosso (MT), Mato Grosso do Sul (MS),Minas Gerais (MG), Pará (PA), Paraíba (PB), Paraná (PR), Pernambuco (PE), Piauí(PI), Rio de Janeiro (RJ), Rio Grande do Norte (RN), Rio Grande do Sul (RS),Rondônia (RO), Roraima (RR), Santa Catarina (SC), São Paulo (SP), Sergipe (SE), Tocantins (TO).
Table A.2Logarithm of average hourly wages by occupation and state.Source: Elaborated by the authors with data from PNAD 2015.Managers Sciences and arts Middle-level technicians Service sector Agriculture Industrial production and services Teachers
AC 2.87 2.86 2.19 2.00 2.04 2.06 2.86AL 2.68 2.99 2.29 1.95 2.06 1.95 2.77AM 2.97 3.05 2.46 2.02 1.91 2.07 2.78AP 3.11 3.13 2.50 2.08 1.86 2.10 2.98BA 2.81 3.10 2.37 1.92 1.78 2.02 2.73CE 2.83 3.13 2.44 1.92 1.53 1.87 2.64DF 3.42 3.47 2.97 2.36 2.24 2.36 3.33ES 2.92 3.21 2.74 2.06 2.03 2.27 2.90GO 2.97 3.02 2.64 2.14 2.24 2.26 2.96MA 3.10 2.99 2.44 1.99 1.75 1.95 2.77MG 2.92 3.20 2.63 2.04 2.00 2.17 2.91MS 3.05 3.27 2.70 2.14 2.29 2.26 3.08MT 2.93 3.22 2.56 2.16 2.37 2.36 2.94PA 2.94 2.92 2.48 1.96 2.00 1.99 2.88PB 2.80 3.24 2.45 1.95 1.91 2.01 2.84PE 2.91 3.07 2.36 1.89 1.72 1.94 2.71PI 2.92 3.00 2.29 1.88 1.65 1.92 2.66PR 3.10 3.23 2.79 2.23 2.26 2.32 3.05RJ 3.03 3.42 2.65 2.15 1.88 2.27 3.00RN 2.97 3.13 2.51 2.00 1.77 1.92 2.74RO 2.89 3.00 2.56 2.08 2.20 2.28 2.79RR 3.04 3.26 2.66 2.03 1.80 2.11 3.11RS 3.05 3.24 2.68 2.19 2.22 2.22 3.02SC 3.01 3.18 2.73 2.30 2.33 2.34 2.90SE 2.92 3.02 2.39 1.91 1.65 1.97 2.98SP 3.25 3.30 2.83 2.22 2.22 2.35 2.92TO 2.90 3.20 2.54 2.10 2.01 2.19 2.8517
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
Table A.3Average years of schooling by occupation and state.Source: Elaborated by the authors with data from PNAD 2015.Managers Sciences and arts Middle-level technicians Service sector Agriculture Industrial production and services Teachers
AC 9.82 10.82 10.69 8.71 4.26 6.79 14.40AL 10.33 13.24 11.91 7.83 3.70 6.20 14.13AM 11.48 13.48 11.24 9.09 4.39 8.40 14.20AP 10.82 13.50 11.84 8.88 4.92 7.38 13.95BA 11.09 13.51 11.27 8.80 3.52 7.19 13.69CE 10.57 13.45 11.46 8.65 3.69 7.44 14.19DF 12.76 14.18 11.88 9.55 5.61 7.90 14.47ES 11.07 13.85 11.83 8.82 5.82 7.91 14.59GO 11.69 13.43 11.47 8.77 5.85 7.73 14.45MA 11.35 13.62 11.27 8.60 4.32 7.07 13.36MG 11.57 13.97 11.54 8.62 5.02 7.41 14.11MS 11.71 13.98 11.48 8.58 5.39 7.42 14.11MT 11.08 13.79 11.37 9.14 5.71 7.54 14.39PA 10.82 12.58 10.68 8.63 4.05 7.01 14.09PB 11.88 13.82 10.81 8.51 3.41 6.29 14.32PE 11.09 14.06 11.50 8.58 4.38 7.02 14.13PI 11.03 13.35 11.37 8.21 4.05 6.13 14.27PR 11.93 13.81 11.79 9.01 6.32 8.02 14.29RJ 11.99 14.17 11.76 9.02 5.29 8.16 14.02RN 10.47 13.57 11.13 8.85 3.67 7.09 14.03RO 10.08 14.03 10.69 8.78 5.45 7.03 14.28RR 10.83 12.95 12.05 9.34 4.83 7.23 14.16RS 11.66 13.92 11.73 8.98 6.10 7.75 14.42SC 11.60 13.69 11.57 9.20 6.57 8.18 14.37SE 11.07 13.68 11.11 8.53 3.27 6.30 14.20SP 12.48 14.27 12.02 9.18 6.46 8.38 14.09TO 10.40 13.34 11.34 8.98 5.13 8.05 14.20
Table A.4Share of workers in each occupation by state.Source: Elaborated by the authors with data from PNAD 2015.Managers Sciences and arts Middle-level technicians Service sector Agriculture Industrial production and services Teachers
AC 0.04 0.03 0.05 0.42 0.13 0.25 0.09AL 0.04 0.04 0.07 0.41 0.12 0.25 0.07AM 0.05 0.05 0.08 0.38 0.07 0.29 0.08AP 0.04 0.03 0.07 0.44 0.07 0.25 0.10BA 0.05 0.04 0.06 0.45 0.08 0.26 0.06CE 0.05 0.03 0.06 0.44 0.05 0.31 0.07DF 0.06 0.10 0.10 0.48 0.01 0.17 0.08ES 0.07 0.06 0.07 0.35 0.12 0.29 0.05GO 0.05 0.05 0.06 0.42 0.08 0.29 0.05MA 0.04 0.04 0.06 0.37 0.14 0.27 0.09MG 0.06 0.06 0.06 0.39 0.10 0.28 0.06MS 0.06 0.06 0.05 0.38 0.12 0.27 0.06MT 0.05 0.05 0.06 0.35 0.16 0.28 0.05PA 0.03 0.04 0.05 0.44 0.11 0.27 0.06PB 0.05 0.05 0.07 0.42 0.08 0.25 0.08PE 0.05 0.06 0.07 0.46 0.05 0.25 0.06PI 0.04 0.03 0.05 0.40 0.10 0.30 0.08PR 0.08 0.07 0.07 0.36 0.07 0.29 0.06RJ 0.05 0.08 0.08 0.46 0.01 0.25 0.06RN 0.06 0.05 0.07 0.42 0.06 0.26 0.07RO 0.06 0.04 0.05 0.35 0.16 0.28 0.06RR 0.05 0.03 0.07 0.39 0.11 0.24 0.11RS 0.06 0.08 0.08 0.39 0.06 0.28 0.05SC 0.08 0.06 0.07 0.32 0.09 0.31 0.06SE 0.04 0.04 0.05 0.43 0.14 0.25 0.06SP 0.07 0.09 0.08 0.41 0.03 0.27 0.05TO 0.05 0.04 0.05 0.33 0.21 0.23 0.0918
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
S
A
A
Sb2
aT
A
wbwTable B.1Labor market frictions 𝜏𝑤𝑖𝑟 - 2015.ource: Search results.State Managers Sciences Middle-level Service Agriculture Industrial Teachers Mean Incomeand arts technicians sector production friction leveland services by state
AC 0.56 0.53 0.43 0.43 0.50 0.47 0.53 0.49 Middle incomeAL 0.56 0.58 0.49 0.45 0.54 0.47 0.55 0.52 Low incomeAM 0.56 0.54 0.48 0.42 0.45 0.45 0.50 0.49 Middle incomeAP 0.56 0.53 0.46 0.41 0.41 0.43 0.51 0.47 Middle incomeBA 0.56 0.57 0.48 0.42 0.44 0.47 0.52 0.50 Low incomeCE 0.56 0.58 0.50 0.41 0.35 0.42 0.50 0.47 Low incomeDF 0.56 0.54 0.50 0.43 0.47 0.45 0.52 0.50 High incomeES 0.56 0.57 0.54 0.44 0.49 0.51 0.53 0.52 High incomeGO 0.56 0.54 0.51 0.45 0.53 0.50 0.53 0.52 Middle incomeMA 0.56 0.51 0.45 0.38 0.38 0.39 0.47 0.45 Low incomeMG 0.56 0.57 0.52 0.43 0.49 0.49 0.53 0.51 Middle incomeMS 0.56 0.56 0.51 0.43 0.53 0.48 0.53 0.52 High incomeMT 0.56 0.57 0.50 0.46 0.56 0.53 0.53 0.53 High incomePA 0.56 0.53 0.49 0.41 0.48 0.44 0.52 0.49 Low incomePB 0.56 0.60 0.51 0.43 0.49 0.47 0.54 0.51 Low incomePE 0.56 0.56 0.47 0.39 0.40 0.43 0.50 0.47 Low incomePI 0.56 0.54 0.45 0.38 0.38 0.42 0.48 0.46 Low incomePR 0.56 0.55 0.52 0.45 0.52 0.49 0.52 0.52 High incomeRJ 0.56 0.59 0.50 0.44 0.44 0.49 0.53 0.51 High incomeRN 0.56 0.56 0.49 0.41 0.41 0.41 0.49 0.48 Low incomeRO 0.56 0.55 0.51 0.45 0.54 0.52 0.51 0.52 Middle incomeRR 0.56 0.56 0.50 0.41 0.41 0.45 0.54 0.49 Middle incomeRS 0.56 0.56 0.51 0.45 0.52 0.48 0.52 0.51 High incomeSC 0.56 0.56 0.52 0.48 0.54 0.51 0.51 0.53 High incomeSE 0.56 0.55 0.47 0.39 0.38 0.43 0.54 0.48 Middle incomeSP 0.56 0.54 0.50 0.42 0.48 0.47 0.48 0.49 High incomeTO 0.56 0.58 0.50 0.45 0.49 0.49 0.52 0.51 Middle income
Mean by occupation 0.56 0.56 0.49 0.43 0.47 0.46 0.52
Acre (AC), Alagoas (AL), Amapá (AP), Amazonas (AM), Bahia (BA), Ceará (CE), Distrito Federal(DF), Espírito Santo (ES), Goiás (GO), Maranhão (MA), MatoGrosso (MT), Mato Grosso do Sul (MS), Minas Gerais (MG), Pará (PA), Paraíba (PB), Paraná (PR), Pernambuco (PE), Piauí(PI), Rio de Janeiro (RJ), Rio Grandedo Norte (RN), Rio Grande do Sul (RS), Rondônia (RO), Roraima (RR), Santa Catarina (SC), São Paulo (SP), Sergipe (SE), Tocantins (TO).
Appendix A. Descriptive statistics
See Tables A.1–A.4.
ppendix B. Calibrated 𝝉′𝒔 and 𝑨′𝒔 to 2015 and 2003
See Tables B.1–B.6.
ppendix C. Public and private spending on education
We estimated private education expenditures in Brazil for 2003, 2009, and 2018 using data from Table 49 of the Family Budgeturvey (POF).23 Our estimates indicate that private education expenditures were approximately R$ 32.4 billion in 2003, R$ 40.5illion in 2009, and R$ 145.4 billion in 2018. The private education expenditures as a percentage of GDP were 1.8%, 1.2%, and.0% for the respective years, with an average of 1.7%.The National Institute of Educational Studies and Research Anísio Teixeira (INEP) provides data on public spending on educations a percentage of GDP. In 2003, public spending on education accounted for 4.6% of GDP, while in 2015, it increased to 6.2%.herefore, Brazil’s total public and private spending on education, as a share of GDP, was 6.4% in 2003 and 7.9% in 2015.
ppendix D. Migration between states
We analyzed the PNAD microdata from 2015 to assess the extent of worker migration, finding that, on average, 20.36% oforkers moved to another state or country. Table D.1 presents the proportion of workers who relocated to another state or countryy occupation. As illustrated, only a small proportion of employees relocated from their home state to another. Thus, assuming thatorkers do not migrate in the theoretical model is reasonable.
23 Details about the POF can be found on the Brazilian Institute of Geography and Statistics (IBGE) website: https://www.ibge.gov.br/.
19
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
S
Table B.2Education market frictions 𝜏ℎ𝑖𝑟 - 2015.ource: Search results.State Managers Sciences Middle-level Service Agriculture Industrial Teachers Mean Incomeand arts technicians sector production friction leveland services by state
AC 0 0.09 1.83 −0.70 1.72 −0.35 −0.72 0.27 Middle incomeAL 0 −0.52 −0.12 −0.77 0.92 −0.48 −0.69 −0.24 Low incomeAM 0 −0.22 0.21 −0.55 9.96 −0.30 −0.47 1.23 Middle incomeAP 0 0.14 0.43 −0.67 11.87 −0.18 −0.70 1.56 Middle incomeBA 0 −0.46 0.29 −0.69 7.44 −0.34 −0.45 0.83 Low incomeCE 0 −0.25 0.32 −0.68 33.70 −0.29 −0.46 4.62 Low incomeDF 0 −0.62 −0.10 −0.60 170.40 0.95 −0.43 24.23 High incomeES 0 −0.42 0.34 −0.35 4.88 −0.31 0.12 0.61 High incomeGO 0 −0.16 0.36 −0.68 3.88 −0.48 −0.26 0.38 Middle incomeMA 0 −0.03 0.59 −0.57 4.48 −0.15 −0.60 0.53 Low incomeMG 0 −0.51 0.44 −0.49 6.16 −0.24 −0.16 0.74 Middle incomeMS 0 −0.32 1.11 −0.45 2.91 −0.15 −0.26 0.41 High incomeMT 0 −0.38 0.70 −0.59 0.62 −0.53 −0.27 −0.06 High incomePA 0 −0.27 0.12 −0.77 1.93 −0.47 −0.62 −0.01 Low incomePB 0 −0.57 0.19 −0.62 6.90 −0.19 −0.60 0.73 Low incomePE 0 −0.43 0.56 −0.54 26.38 0.13 −0.09 3.72 Low incomePI 0 0.17 1.17 −0.56 9.07 −0.28 −0.54 1.29 Low incomePR 0 −0.25 0.58 −0.31 9.78 −0.05 0.11 1.41 High incomeRJ 0 −0.76 0.03 −0.70 129.70 −0.34 −0.33 18.23 High incomeRN 0 −0.24 0.51 −0.52 20.34 0.30 −0.27 2.88 Low incomeRO 0 0.10 0.79 −0.54 1.11 −0.49 −0.22 0.11 Middle incomeRR 0 0.17 0.22 −0.52 8.05 −0.04 −0.75 1.02 Middle incomeRS 0 −0.55 0.20 −0.53 11.59 −0.17 0.01 1.51 High incomeSC 0 −0.13 0.79 −0.32 6.14 −0.21 0.43 0.96 High incomeSE 0 −0.36 0.36 −0.71 3.96 −0.32 −0.63 0.33 Middle incomeSP 0 −0.49 0.46 −0.39 51.65 0.08 0.61 7.42 High incomeTO 0 −0.29 0.79 −0.54 0.93 −0.27 −0.60 0.00 Middle income
Mean by occupation 0 −0.28 0.49 −0.57 20.24 −0.19 −0.33
Table B.3Total productivity factors - 2015.Source: Search results.State 𝐴𝑟 State 𝐴𝑟 State 𝐴𝑟AC 24.68 MA 26.59 RJ 38.49AL 26.75 MG 41.38 RN 34.65AM 30.76 MS 40.28 RO 38.19AP 25 MT 39.83 RR 24.22BA 33.07 PA 29.81 RS 45.89CE 30.61 PB 28.79 SC 49.75DF 35.99 PE 39.56 SE 30.90ES 46.65 PI 27.93 SP 51.25GO 40.42 PR 46.44 TO 28.03
Notes: Recall that in our model TFP is equal across occupations. The average of TFP is 35.4.
Appendix E. Alternative calibration
There are many microeconomic issues in Brazil, and informal work is an important one. Scholars have conducted extensiveresearch to understand the relationship between economic development and the informal sector. For instance, Franjo et al. (2022)built a life-cycle model to explore the interplay between informality and financial development in Brazil. They also conductedcross-country data analysis, highlighting the importance of considering the informal sector when studying the relationship betweenfinancial and economic development.The prevalence of informal employment is not unique to Brazil; it is a common feature in many developing countries. Researchconducted by Bacchetta et al. (2009) reveals that informality negatively correlates with GDP and GDP growth in developingcountries. During the 2000s, the proportion of informal employment in total employment was 52% for Latin America, 78% forAsia, and 56% for Africa. The informal sector (excluding agriculture) accounted for 26% of Latin America’s GDP in 2006. Moreover,the research suggests that informal employment tends to attract low-educated workers, with approximately 65% of all informalworkers in Latin America classified as such.The decision to exclude individuals earning less than 60% of the minimum wage could raise concerns as it may disproportionatelyimpact workers in the informal sector. To address this concern and ensure the robustness of our findings, we provide an alternativecalibration of our model that incorporates data from all workers with positive wages. Our primary analysis focused on a sample20
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
S
STable B.4Labor market frictions 𝜏𝑤𝑖𝑟 - 2003.ource: Search results.State Managers Sciences Middle-level Service Agriculture Industrial Teachers Mean Incomeand arts technicians sector production friction leveland services by state
AC −0.05 −0.06 −0.28 −0.72 −0.98 −0.68 −0.36 −0.45 Middle incomeAL −0.05 0.10 −0.34 −0.76 −0.94 −0.50 −0.38 −0.41 Low incomeAM −0.05 −0.12 −0.65 −0.82 −0.92 −0.75 −0.47 −0.54 Middle incomeAP −0.05 −0.15 −0.36 −0.68 −0.74 −0.45 −0.31 −0.39 Middle incomeBA −0.05 −0.08 −0.22 −0.69 −0.77 −0.54 −0.42 −0.40 Low incomeCE −0.05 −0.06 −0.22 −0.67 −1.00 −0.68 −0.38 −0.44 Low incomeDF −0.05 −0.02 −0.16 −0.50 −0.22 −0.45 −0.16 −0.22 High incomeES −0.05 −0.15 −0.19 −0.58 −0.53 −0.50 −0.28 −0.33 High incomeGO −0.05 −0.05 −0.15 −0.57 −0.38 −0.48 −0.30 −0.28 Middle incomeMA −0.05 −0.01 −0.39 −0.63 −0.61 −0.54 −0.28 −0.36 Low incomeMG −0.05 −0.06 −0.20 −0.61 −0.58 −0.45 −0.20 −0.31 Middle incomeMS −0.05 0.02 −0.18 −0.50 −0.14 −0.52 −0.28 −0.24 High incomeMT −0.05 −0.06 −0.30 −0.64 −0.41 −0.47 −0.36 −0.33 High incomePA −0.05 −0.02 −0.25 −0.64 −0.38 −0.54 −0.25 −0.30 Low incomePB −0.05 −0.06 −0.25 −0.74 −0.87 −0.76 −0.34 −0.44 Low incomePE −0.05 −0.07 −0.29 −0.67 −0.93 −0.64 −0.41 −0.44 Low incomePI −0.05 0.02 −0.39 −0.74 −1.00 −0.93 −0.50 −0.51 Low incomePR −0.05 −0.10 −0.21 −0.54 −0.29 −0.41 −0.22 −0.26 High incomeRJ −0.05 −0.04 −0.19 −0.53 −0.92 −0.38 −0.13 −0.32 High incomeRN −0.05 0.01 −0.22 −0.61 −1.00 −0.53 −0.23 −0.38 Low incomeRO −0.05 0.01 −0.15 −0.58 −0.18 −0.40 −0.16 −0.22 Middle incomeRR −0.05 −0.18 −0.27 −0.60 −0.61 −0.61 −0.29 −0.37 Middle incomeRS −0.05 −0.04 −0.18 −0.50 −0.34 −0.44 −0.19 −0.25 High incomeSC −0.05 −0.05 −0.10 −0.36 −0.14 −0.31 −0.19 −0.17 High incomeSE −0.05 0.04 −0.27 −0.61 −0.78 −0.57 −0.41 −0.38 Middle incomeSP −0.05 −0.11 −0.19 −0.49 −0.45 −0.39 −0.25 −0.28 High incomeTO −0.05 0.01 −0.18 −0.72 −0.56 −0.46 −0.38 −0.34 Middle income
Mean by occupation −0.05 −0.05 −0.25 −0.62 −0.62 −0.53 −0.30
Table B.5Education market frictions 𝜏ℎ𝑖𝑟 - 2003.ource: Search results.State Managers Sciencesand arts Middle-leveltechnicians
Servicesector Agriculture Industrialproductionand services
Teachers Meanfrictionby state
Income level
AC 0 0.49 2.93 0.23 155.73 3.97 0.03 23.34 Middle IncomeAL 0 −0.19 1.75 0.73 14.16 1.50 −0.15 2.54 Low IncomeAM 0 0.71 3.83 0.24 205.14 1.32 0.80 30.29 Middle IncomeAP 0 −0.00 0.49 −0.15 77.86 −0.16 −0.68 11.05 Middle IncomeBA 0 0.33 1.24 0.34 16.33 1.66 0.86 2.97 Low IncomeCE 0 −0.11 0.82 −0.17 51.68 0.99 0.13 7.62 Low IncomeDF 0 −0.58 0.32 −0.02 253.03 3.08 −0.20 36.52 High IncomeES 0 0.37 1.60 0.46 12.16 1.39 0.92 2.41 High IncomeGO 0 0.27 1.01 0.19 10.03 1.01 1.14 1.95 Middle IncomeMA 0 −0.06 2.00 −0.05 5.79 0.68 −0.40 1.14 Low IncomeMG 0 0.05 1.46 0.39 23.15 0.93 0.26 3.75 Middle IncomeMS 0 0.78 3.69 0.35 7.17 2.07 1.26 2.19 High IncomeMT 0 0.31 3.40 1.29 5.16 1.41 1.18 1.82 High IncomePA 0 −0.34 0.82 −0.26 28.28 0.52 0.03 4.15 Low IncomePB 0 0.38 1.39 0.56 28.44 3.18 −0.16 4.83 Low IncomePE 0 −0.19 0.93 0.00 54.79 2.18 0.45 8.31 Low IncomePI 0 −0.13 1.17 0.29 27.12 5.69 −0.22 4.84 Low IncomePR 0 0.21 1.20 0.55 14.87 1.27 0.83 2.70 High IncomeRJ 0 −0.63 0.28 −0.33 360.08 0.31 −0.18 51.36 High IncomeRN 0 −0.45 1.66 −0.32 28.81 0.43 −0.55 4.23 Low IncomeRO 0 1.20 1.11 0.00 7.43 0.29 −0.28 1.39 Middle IncomeRR 0 0.13 4.32 0.38 50.15 3.63 −0.41 8.32 Middle IncomeRS 0 −0.08 0.86 0.39 21.53 1.06 0.78 3.51 High IncomeSC 0 0.78 1.27 0.56 8.81 0.76 1.24 1.92 High IncomeSE 0 −0.19 1.01 −0.13 16.92 0.81 −0.21 2.60 Middle IncomeSP 0 −0.24 1.11 0.20 81.56 1.02 1.25 12.13 High IncomeTO 0 0.30 1.87 1.62 13.17 2.16 0.37 2.79 Middle Income
Mean by occupation 0 0.12 1.61 0.27 58.49 1.60 0.3021
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
o1amo
dFTable B.6Total productivity factors - 2003.Source: Search results.State 𝐴𝑟 State 𝐴𝑟 State 𝐴𝑟AC 25 MA 19.65 RJ 28.93AL 20.95 MG 31.16 RN 18.05AM 31.24 MS 36.08 RO 24.47AP 15.60 MT 34.85 RR 19.02BA 30.05 PA 27.16 RS 37.54CE 24.95 PB 21.09 SC 39.91DF 26.92 PE 26.77 SE 19.57ES 35.74 PI 17.88 SP 40.71GO 36.73 PR 36.03 TO 25.16
Notes: Recall that in our model TFP is equal across occupations. The average of TFP is 27.82.
Table D.1Share of workers who migrated and did not migrate to another state or country.Source: Elaborated by the authors with data from PNAD 2015.Managers Sciencesand arts Middle-leveltechnicians Servicesector Agriculture Industrialproduction andservices
Teachers
Migrated 0.21 0.18 0.19 0.22 0.20 0.22 0.15Not migrated 0.79 0.82 0.81 0.78 0.80 0.78 0.85
Table D.2Main counterfactual exercises – Sample with wages filter (Original calibration) vs. sample without wagesfilter. Main counterfactuals (%)
Main calibration Alternative calibration
Highest ATHC 87.85 87.51Lowest ATHC −59.62 −53.74Without frictions 16.94 18.30
Notes: This table compares the main counterfactuals of the main calibration of our model to thecounterfactuals computed using the extended sample.
f 109,038 individuals after applying specific filters described in the main text. Here, we constructed a broader dataset comprising15,994 individuals and compared the filtered (With filter) and unfiltered (Without filter) samples in terms of wages, educationalttainment, and worker proportions, as shown in Fig. D1, where the red points represent teachers’ statistics. We observedinor differences between the two samples for teaching professions, with the most significant disparities occurring in low-wageccupations, such as those in the agricultural sector.We recalibrated our model using the extended sample. Fig. D2 demonstrates that the alternative calibration effectively fits theata. We also compared the calibrated parameters from the main text to those computed with the extended sample, as shown inig. D3. The parameters linked to teachers’ occupations (marked in red) showed no substantial alterations. Moreover, the TPF (𝐴𝑖)and educational market barriers (𝜏ℎ) are almost indistinguishable in both calibrations. While there are some differences in labormarket barriers (𝜏𝑤), a high correlation is observed between the alternative calibration of these parameters.We have verified that many important results from our analysis remain robust when using the alternative calibration. Table D.2presents the outcomes of counterfactual experiments using both the primary and alternative calibrations. In the first scenario, weassumed that all states have the same frictions (𝜏𝑤’s and 𝜏ℎ’s) as Roraima (RR), the state with the highest Average Teachers’ HumanCapital (ATHC). Using the alternative calibration, we find that the Brazilian GDP would increase by 87.51% (compared to 87.85%in our primary exercise).Suppose all states had the same frictions as São Paulo (SP), the state with the lowest ATHC. In that case, we find that the GDPof all states would decrease, and the Brazilian GDP would decline by 53.74% according to the alternative calibration (compared to59.62% in our primary calibration).Finally, in the exercise where we eliminate all frictions in the economy, the alternative calibration suggests that the GDP couldincrease by 18.3% (compared to 16.94% predicted by the same exercise using our primary calibration).Therefore, the results in Table D.2 show that the main findings are not significantly affected by the different calibration choices,indicating that our model’s results are not sensitive to excluding individuals earning less than 60% of the minimum wage.
Appendix F. Teachers’ relative wages and economic development
In this section, to further investigate the link between economic development and the relative earnings of teachers, we conducted
22
a panel regression analysis using all available data from the household survey (PNAD) covering the period from 2002 to 2015
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
wt
(tc
affpodFig. D1. Data – Sample with wages filter vs. sample without wages filter. Notes: This figure compares our main calibration data (With filter) and the data withoutage filters (Without filter). In the figure, the red dots represent observations of teachers, while the blue dots denote other occupations. (For interpretation ofhe references to color in this figure legend, the reader is referred to the web version of this article.)
excluding 2010 due to lack of data). Our analysis includes information on the average wage of teachers relative to other occupations,he proportion of teachers in public institutions, and the ratio of teachers with labor municipality contracts to teachers with stateontracts for all years and states.The structure of the Brazilian education system differs from that of other economies. The Organization for Economic Cooperationnd Development (OECD) notes that funding for different levels of education in Brazil is divided among the municipality, state, andederal governments. Typically, the municipal government provides funding for the lowest level of education, the state governmentunds the intermediate level, and the federal government funds higher education, such as colleges and universities. Moreover, theroportion of teachers financed by each administrative level also varies. In 2015, across the Brazilian states, the average percentagesf teachers in public institutions were 55%, 39%, and 6% for the municipal, state, and federal levels, respectively. The standardeviations for these percentages were 16%, 15%, and 3%, respectively.
23
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
atpwm
ip
pTmp
mbFig. D2. Model adjustment to data with full sample- wages and share of workers.
Table D.3The effect of teachers from public institutions on relative wages of teachers.(1) (2) (3)
Share of pub. teachers −0.21 −0.21 −0.14(0.27) (0.27) (0.26)
Municipality to state pub. teachers 0.001 −0.004(0.02) (0.021)
GDP per capita −0.04***(0.01)
Constant ✓ ✓ ✓Time fixed effect ✓ ✓ ✓State fixed effect ✓ ✓ ✓
Observations 351 351 351
Note: We report robust 𝑡-statistics in parentheses. Statistical significance is indicated at the ∗∗∗ 𝑝 < 0.01, ∗∗ 𝑝 < 0.05, and ∗ 𝑝 < 0.1 levels. Our dataset comprisesll household surveys conducted after 2000 with a consistent methodology (2002–2009, 2011–2015). We compute the weighted average of the relative wage ofeachers to other occupations and the proportion of teachers in public institutions for all years and states. Our sample includes individuals aged 25 to 65 withositive wages, yielding 351 observations (13 years multiplied by 27 states). Our panel regression analysis consists of three models. In Model 1, we examinehether the proportion of public teachers explain differences in relative wages, controlling for time and state-fixed effects. Model 2 introduces the ratio ofunicipal to state-funded teachers across states. Finally, in Model 3, we extend the analysis by including the log of GDP per capita in the second model.
These numbers suggest significant variations in the distribution of teachers across administrative levels and regions. As teachersn different states or municipalities within the same state may receive different salaries, we consider the proportion of teachers inublic institutions and the ratio of teachers with labor municipality contracts to teachers with state contracts in our analysis.The dependent variable in our panel regression is the relative wage of teachers to other occupations. We explore whether theroportion of public teachers can account for the observed differences in relative wages, controlling for time and state-fixed effects.he first model (Model 1) examines this relationship. The second model (Model 2) expands on the first by adding the ratio ofunicipality teachers to state teachers. Finally, the third model (Model 3) further extends the analysis by including the log of GDPer capita as an additional regressor.The regression results presented in Table D.3 indicate that neither the proportion of teachers in public institutions nor the ratio ofunicipality teachers to state teachers significantly impact the relative wages of teachers. However, we do find a negative correlationetween GDP per capita and relative wages, which is consistent with our earlier findings.
24
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.Fig. D3. Calibrated parameters – Sample with wages filter vs. sample without wages filter. Notes: This figure compares the calibrated parameters obtained fromthe original calibration (with filter) to those obtained from the calibration without wage filters (without filter).
References
Abdulla, Kanat, 2019. Productivity gains from reallocation of talent in Brazil and India. J. Macroecon. 62, 103160.Bacchetta, Marc, Ernst, Ekkehard, Bustamante, Juana P., et al., 2009. Globalization and Informal Jobs in Developing Countries. International Labour Organization,Geneva.Bacolod, Marigee P., 2007. Do alternative opportunities matter? The role of female labor markets in the decline of teacher quality. Rev. Econ. Stat. 89 (4),737–751.Banerjee, Abhijit V., Duflo, Esther, 2005. Growth theory through the lens of development economics. In: Handbook of Economic Growth, Vol. 1. Elsevier, pp.473–552.Barro, Robert J., Sala-i-Martin, Xavier, 1992. Convergence. J. Polit. Econ. 100 (2), 223–251.Barros, Fernando Jr., Delalilbera, Bruno R., 2018. Market frictions, misallocation of talent and development. Econ. Bull. 38 (4), 2410–2430.Benhabib, Jess, Spiegel, Mark M., 2005. Human capital and technology diffusion. In: Handbook of Economic Growth, Vol. 1. Elsevier, pp. 935–966.Borensztein, Eduardo, De Gregorio, Jose, Lee, Jong-Wha, 1998. How does foreign direct investment affect economic growth? J. Int. Econ. 45 (1), 115–135.Brotherhood, Luiz, Delalibera, Bruno R., 2020. Minding the gap between schools and universities. J. Econom. Dynam. Control 120, 104010.Brotherhood, Luiz, Delalibera, Bruno R., Torres de Mello Pereira, Luciene, 2022. Public overspending in higher education. Bull. Econ. Res..Café, Renata Motta, 2018. A Alocação de Talentos No Setor Público Brasileiro (PhD dissertation).Cagetti, Marco, De Nardi, Mariacristina, 2006. Entrepreneurship, frictions, and wealth. J. Polit. Econ. 114 (5), 835–870.Card, David, Krueger, Alan B., 1992a. Does school quality matter? Returns to education and the characteristics of public schools in the United States. J. Political25
Econ. 100 (1), 1–40.
Journal of Macroeconomics 77 (2023) 103542F. Barros Jr et al.
GG
HH
HHHHHKLM
MM
M
P
RRRRRS
S
TWWZCard, David, Krueger, Alan B., 1992b. School quality and black-white relative earnings: A direct assessment. Q. J. Econ. 107 (1), 151–200.Delalibera, Bruno Ricardo, Ferreira, Pedro Cavalcanti, 2019. Early childhood education and economic growth. J. Econom. Dynam. Control 98, 82–104.Eaton, Jonathan, Kortum, Samuel, 2002. Technology, geography, and trade. Econometrica 70 (5), 1741–1779.Eckstein, Zvi, Zilcha, Itzhak, 1994. The effects of compulsory schooling on growth, income distribution and welfare. J. Public Econ. 54 (3), 339–359.Ferreira, Afonso, 2000. Convergence in Brazil: recent trends and long-run prospects. Appl. Econ. 32 (4), 479–489.Franjo, Luis, Pouokam, Nathalie, Turino, Francesco, 2022. Financial frictions and firm informality: a general equilibrium perspective. Econ. J. 132 (645),1790–1823.ilpin, Gregory, Kaganovich, Michael, 2012. The quantity and quality of teachers: Dynamics of the trade-off. J. Public Econ. 96 (3–4), 417–429.uo, Naijia, Leung, Charles Ka Yui, 2021. Do elite colleges matter? The impact on entrepreneurship decisions and career dynamics. Quant. Econ. 12 (4),1347–1397.anushek, Eric A., Leung, Charles Ka Yui, Yilmaz, Kuzey, 2014. Borrowing constraints, college aid, and intergenerational mobility. J. Hum. Cap. 8 (1), 1–41.anushek, Eric A., Piopiunik, Marc, Wiederhold, Simon, 2019. The value of smarter teachers international evidence on teacher cognitive skills and studentperformance. J. Hum. Resour. 54 (4), 857–899.anushek, Eric A., Woessmann, Ludger, 2012. Schooling, educational achievement, and the Latin American growth puzzle. J. Dev. Econ. 99 (2), 497–512.atsor, Limor, 2012. Occupational choice: Teacher quality versus teacher quantity. Labour Econ. 19 (4), 608–623.natkovska, Viktoria, Lahiri, Amartya, Paul, Sourabh, 2012. Castes and labor mobility. Am. Econ. J.: Appl. Econ. 4 (2), 274–307.sieh, Chang-Tai, Hurst, Erik, Jones, Charles I., Klenow, Peter J., 2019. The allocation of talent and US economic growth. Econometrica 87 (5), 1439–1474.sieh, Chang-Tai, Klenow, Peter J., 2009. Misallocation and manufacturing TFP in China and India. Q. J. Econ. 124 (4), 1403–1448.rueger, Alan B., 2003. Economic considerations and class size. Econ. J. 113 (485), F34–F63.akdawalla, Darius, 2006. The economics of teacher quality. J. Law Econ. 49 (1), 285–329.achado, Laura Muller, Scorzafave, Luiz Guilherme Dácar da Silva, 2016. Distribuição de salários de professores e outras ocupações: uma análise para graduadosem carreiras tipicamente ligadas à docência. Rev. Bras. Econ. 70 (2), 203–220.ankiw, N. Gregory, Romer, David, Weil, David N., 1992. A contribution to the empirics of economic growth. Q. J. Econ. 107 (2), 407–437.cFadden, Daniel, 1974. Conditional logit analysis of qualitative choice behavior. In: Zarembka, P. (Ed.), Frontiers of Econometrics. Academic Press, New York,NY, pp. 105–142.enezes-Filho, Naércio, Pazello, Elaine, 2007. Do teachers’ wages matter for proficiency? Evidence from a funding reform in Brazil. Econ. Educ. Rev. 26 (6),660–672.onczek, Vladimir, Souza, Andre Portela, 2012. New evidence of the causal effect of family size on child quality in a developing country. J. Hum. Resour. 47(1), 64–106.estuccia, Diego, Rogerson, Richard, 2008. Policy distortions and aggregate productivity with heterogeneous establishments. Rev. Econ. Dyn. 11 (4), 707–720.estuccia, Diego, Rogerson, Richard, 2017. The causes and costs of misallocation. J. Econ. Perspect. 31 (3), 151–174.ibeiro, Erika Cristina Barbosa de Almeida, Almeida, Eduardo Simões de, 2012. Convergência local de renda no Brasil. Econ. Apl. 16, 399–420.ivkin, Steven G., Hanushek, Eric A., Kain, John F., 2005. Teachers, schools, and academic achievement. Econometrica 73 (2), 417–458.omer, Paul M., 1990. Endogenous technological change. J. Polit. Econ. 98 (5, Part 2), S71–S102.oares, Rodrigo R., Kruger, Diana, Berthelon, Matias, 2012. Household choices of child labor and schooling: A simple model with application to Brazil. J. Hum.Resour. 47 (1), 1–31.toddard, Christiana, 2003. Why has the number of teachers per student risen while teacher quality has declined?: The role of changes in the labor market forwomen. J. Urban Econ. 53 (3), 458–481.amura, Robert, 2001. Teachers, growth, and convergence. J. Polit. Econ. 109 (5), 1021–1059.illiams, J.H., 2005. Cross-national variations in rural mathematics achievement. J. Res. Rural Educ. 20 (5), 20–25.oessmann, Ludger, 2016. The importance of school systems: Evidence from international differences in student achievement. J. Econ. Perspect. 30 (3), 3–32.hang, Yanhong, 2006. Urban-rural literacy gaps in Sub-Saharan Africa: The roles of socioeconomic status and school quality. Comp. Educ. Rev. 50 (4), 581–602.26