Human capital quality and regional growth in Brazil

By the end of the 1950s, economic theory, mainly influenced by classical economics, considered that the different levels of regional economic growth depended on existing production factors in each region, that is, capital, labor and natural resources (Solow, 1956). Many studies discussed and demonstrated its importance for economic growth (Mincer, 1958; Schultz, 1961; Becker, 1964; Lucas, 1988), but traditionally, only the quantitative aspect has been considered. In most cases, human capital is measured by proxies related to the average level of education of the adult population, as in Mincer (1974), Mankiw et al. (1992) and Krueger and Lindahl (2001).

However, considering only the quantitative aspect of human capital involves making unlikely hypotheses: first, that worker productivity is strictly proportional to their years of study; second, that workers with a certain level of education are perfect substitutes for workers at all other levels and the elasticity of replacement between workers from different levels of education is always constant; and third, that one extra year of education generates the same increase in skills, regardless of the area of study or quality of different education systems (Mulligan & Sala-I-Martin, 2000). In this sense, studies such as Hanushek and Kimko (2000), Barro (2000), Barro and Lee (2001), Bosworth and Collins (2003) and Jamison, Jamison, and Hanushek (2007) consider the importance of human capital quality in their estimations. There are many empirical studies relating human capital growth and convergence of per capita income between countries and regions. Wößmann (2003) provides an excellent review of the literature, focusing on different specifications of human capital.

The literature is also abundant in applied studies for Brazilian regions. Among these, a first division that can be made is regarding the type of human capital modeling: MRW or Mincer-type specification. Cangussu, Salvato, and Nakabashi (2010) and Ferreira, Issler, and Pessôa (2004) comparatively analyze these specifications and conclude in favor of Mincerian. However, there seems to be no consensus in the literature regarding this, with studies using only one or both specifications.

Another division that can be established is regarding the use of spatial models to capture neighborhood effects. Most studies applied to Brazilian regions do not use spatial models, therefore disregarding possible spillover effects of economic growth between regions. This can harm the robustness of the results, making the estimates inconsistent or inefficient (Anselin, 2002; Ertur & Koch, 2007; Firme & Simão Filho, 2014). Among the works that use these models, we can point out (Silveira Neto & Azzoni, 2006; Montenegro, Lopes, Ribeiro, Cruz, & Almeida, 2014; Cravo, Becker, & Gourlay, 2015; Firme & Simão Filho, 2014).

A third division that can be made is regarding the disaggregation of human capital, aiming to differentiate the effects between the quantity (generally measured by the average number of years of study of the adult population) and the quality of human capital (generally represented by the performance of students in tests and/or the quality of school infrastructure). The idea is that a school year can have different results in terms of student learning in different regions (Gundlach, Rudman, & Wößmann, 2002; Wößmann, 2003). Among the studies applied to Brazil that incorporate the quality of human capital, Nakabashi and Salvato (2007) and Firme and Simão Filho (2014) can be highlighted.

To contribute to this debate, this article proposes an analysis of the importance of human capital quality for regional economic growth in Brazil. Based on the model of Mankiw et al. (1992), an alternative version of the model is proposed, with the inclusion of human capital quality, applied to the 558 Brazilian micro-regions in the period between 2009 and 2017.

We use spatial econometric techniques that offer greater robustness to the results and control effects of spatial autocorrelation, as the literature suggests that investments in quantity and quality of human capital can generate externalities for the individual or region, and for individuals or neighboring regions (Barros & Mendonça, 1998). Due to the existence of these spatial interactions between neighboring areas, regions cannot be treated as spatially independent in economic growth models (Ertur & Koch, 2007), as educational performance in a given region is positively associated with the performance of neighboring regions (Fujita, Bagolin & Fochezatto, 2021).

This work uses a model with an MRW specification, uses spatial modeling and disaggregates human capital into quantity and quality. In relation to spatial units, this study uses the geographic section of micro-regions, while most of the studies consulted use the state or municipal section of specific states. The level of geographic disaggregation is relevant, as in general, the smaller the spatial unit, the greater the effects of spatial spillovers tend to be (Anselin, 2002; Ertur & Koch, 2007). Regarding the disaggregation of human capital into quantity and quality, it is also possible to find important differences between the works, both in terms of proxies used (performance indicators in school tests or combination of test performance and school infrastructure) and in terms of the returns of education, linear or diminishing returns (Psacharopoulos, 1994; Hanushek & Kimko, 2000; Gundlach et al., 2002; Wößmann, 2003). In this work, the quality of regional human capital is represented by a multidimensional indicator combining student performance in tests and quality of school infrastructure, with log-linear specification. Thus, this work contributes to the literature in three aspects: it uses quality as a latent variable that reflects multiple dimensions, it uses a greater geographic disaggregation (micro-regions) covering the whole of Brazil and it uses a spatial model to capture possible spillover effects.

In general, the results of this study are in line with works that analyze the effects of human capital on regional economic growth in Brazil, showing that both quantity and quality are important (Nakabashi & Salvato, 2007; Firme & Simão Filho, 2014). The inclusion of a quality proxy reduces the effect of human capital quantity. Furthermore, the use of spatial models reduces the impact of human capital (Firme & Simão Filho, 2014). Therefore, separating the effects of these two measures is relevant especially in the presence of educational disparities between regions, as is the case in Brazil.

This article is divided into four sections, in addition to this introduction. In Section 2, the theoretical framework is presented, which starts with a brief literature review and finishes with the presentation of the proposed model. In Section 3, the econometric methodology and the database are presented. In the following section, the results are discussed. Finally, in Section 5, the final considerations, limitations, implications for public policies and possible future studies are discussed.

The economic growth model used in this study is strongly supported by the groundbreaking work of Mankiw et al. (1992). However, modifications are proposed that include a new quality measure of human capital. We will present a brief history of the evolution of growth models and the concept of human capital in economic theory, in addition to the proposed model.

The work of Solow (1956) is the main work with a neoclassical approach that began the important debate on economic growth, and the author won the Nobel Prize in Economics in 1987 for his contributions. This model uses a relatively simple Cobb–Douglas function, in which economic growth is explained by savings rate, population increase and technical progress. One of its main contributions was to demonstrate that capital accumulation is not the only factor capable of explaining economic growth, which Solow (1956) demonstrated through the residual of regressions – also known as total factor productivity.

Subsequently, other studies began to incorporate human capital as a factor capable of explaining economic growth and increased productivity. Mincer (1958) conducted a groundbreaking study, demonstrating that different levels of human capital accumulation can generate differences in income levels. The author performed an analysis of the relationship between investment in the formation of workers and income, concluding that income varies according to different professions, age and individuals' choice to invest in human capital.

Schultz (1961) held an important discussion that suggests the existence of a positive relationship between economic growth and investment in human capital. The study also pays attention to qualitative and quantitative dimensions.

Becker (1964) defines human capital as a set of productive capabilities that an individual acquires by accumulation of general and specific knowledge. Dedicating more time to studying has direct costs, when it comes to paying for studies, and indirect costs, when it comes to giving up a salary that the individual could receive if they chose to devote their time to work instead of studying. On the other hand, education is considered an investment, as it allows the worker to increase their productive capacity and increase their wage throughout life.

Lucas (1988) presents a model in which human capital accumulation is important for economic growth, as it affects the worker's skill and indirectly affects production. The author argues that human capital has positive externalities, capable of mitigating the decreasing income of capital.

Mankiw et al. (1992) present a model similar to Solow's (1956), but include the human capital factor in the production function, which is then expressed by:

Where Y represents the product, H is the stock of human capital, K is the capital, L is the labor, A is the level of technology, t is the time and $(1−α−β)$ represents the role of work, physical and quantity of human capital, respectively. As in Solow (1956), it is assumed that L and A grow at exogenous rates, n and g, respectively. A common assumption is that physical and human capital depreciate at δ rates.

Based on the previous equation, this study proposes an expansion of the MRW model (1992) through the inclusion of the quality of human capital as a factor capable of explaining economic growth. If Q is the quality of human capital and H is the quantity of human capital, Equation (1) is expressed as:

Following the traditional MRW model, the number of effective work units $AtLt$ grows at an $n+g$ rate. Transforming the terms into work units, they are expressed by:

Just as (4) and (5) reflect the fractions of income invested in physical capital (⁠$Sk$⁠) and quantitative human capital (⁠$Sh$⁠), equation (6) represents the fraction of the income invested in qualitative human capital, and, assuming that they depreciate at the same δ rate, the evolution of the economy is determined by:

Converging to the steady state, we will have:

Where * represents the variable at the steady state. In this proposed model, technological progress is considered to be different among regions. Then, by replacing the equations above in the production function (2) in work units, and applying a natural logarithm, the per capita product equation becomes:

The above equation represents the main innovation of the proposed model, in which economic growth depends on the quality of human capital in addition to the variables of the traditional model. To put it simply, the parameters of the equation are defined as:

By adjusting Equation (13) to the parameters defined in Equations (14) to (17), the estimated model is defined as:

Where $ϵ$ represents the residuals of the regression.

The main objective of the estimated model is to test whether the quantity and quality of the human capital stock are important for regional economic growth. This result is crucial to broaden the debate in this area, as the results are not definitive in the existing literature.

By using an economic model with spatial lags, it should be possible to test the existence of spatial spillovers of human capital, showing its importance for the economic development of the region (both for micro-regions themselves and for neighboring micro-regions). In addition, the hypothesis is raised that a multidimensional measure for the qualitative aspect of human capital can capture effects (both direct and indirect) not captured by the proxies usually employed in the literature (performance in specific tests).

Furthermore, we aim to broaden the debate on human capital, considering that its development depends on various circumstances on both quantitative and qualitative aspects. In particular, we expect to assess whether the formation of human capital stock is in fact a qualitative process, developed by different regional conditions that accompany individuals along their lives.

The period between 2009 and 2017 was chosen due to the availability of information. The data are gathered from the 558 micro-regions of Brazil. We chose to use this type of aggregation to control possible daily migration effects among workers living close neighboring areas. For example, if the study considered only the municipalities, the results would probably need to be observed with caution, as the local population could migrate daily to neighboring cities. Although using micro-regions does not fully eliminate this possibility, this type of aggregation allows us to mitigate the problem. In addition, the spatial economy model can capture indirect effects of neighboring regions.

The quality variable was generated from the factor analysis method, capturing several circumstances that affect individuals from birth through adulthood. The procedure follows the study by Saraiva, Silva, and França (2017), with updated data until 2017. As in Golgher (2008), this variable was standardized between zero and one. In the present study, this standardization was necessary to apply the natural logarithm and for comparability purposes between the variables of human capital quantity and quality, considering that it originally had negative values. For the quantitative aspect, a measure usually used in the literature is applied. Figure 1 summarizes the variables in each aspect.

In the case of the quantitative proxy, we used a measure usually applied in the literature, based on data from the Annual Report on Social Information (RAIS). Although RAIS does not indicate the worker's level of education, it is possible to assign weights of average levels of education based on each education range: illiterate (0 years); up to 5th grade incomplete (2.5 years); complete 5th grade (5 years); incomplete 6th to 9th grade (7 years); complete elementary school (9 years); incomplete high school (10.5 years); complete high school (12 years); incomplete higher education (14 years); complete higher education (16 years); Master's Degree (18 years) and Doctorate Degree (22 years) ^[1].

As for the other variables of the economic growth model, the following proxies are used: (i) GDP (Gross Domestic Product) per capita corrected by the implicit GDP deflator (IBGE – Brazilian Institute of Geography and Statistics), as an endogenous variable; (ii) variation of the resident population (IBGE), to measure population growth n; (iii) fleet of trucks and tractors (DENATRAN – National Traffic Department), as a proxy for physical capital K ^[2]; (iv) variation in Internet access (ANATEL – National Telecommunications Agency), to represent technological progress g and (v) capital depreciation rate, which this study assumes to be constant equal to 0.025, considering that Mankiw et al. (1992) assume that $g+δ$ is equal to 0.05 and justify that this assumption has a small effect on estimations. Table 1 (below) presents the description, the source, the expected sign and the descriptive statistics of the variables. The expected signs follow the model of Mankiw et al. (1992).

Spatial econometrics is a branch of traditional economics, which aims to specify, estimate, test and predict theoretical models influenced by spatial effects using cross-section or panel data (Almeida, 2012). In the previous section, studies that demonstrate the need to control spatial effects were discussed. Thus, this technique is used in this study to estimate the expanded MRW theoretical model with human capital quality. According to tests that will be presented, the econometric model with estimated panel data in this work will be the spatial lag fixed effects of the dependent variable (spatial autoregressive model – SAR), given by:

Where $ρ$ represents the spatial autoregressive coefficient and W represents a spatial weights matrix that is assumed to be invariant in time procedure, we chose to use the k-nearest neighbors spatial weights matrix = 5); i refers to each of the N micro-regions and t refers to time in a total of T periods; $yit$ is the dependent variable in each micro-region and in a specific period; $xit$ is a vector of K variables for each micro-region and period; $β$ are the K coefficients estimated in the model; $μi$ represents a specific effect invariant over time for each i, whose omission would cause bias in the estimates of a cross-section model; and $εit$ is an element of the error term identically and independently distributed to i and t, with mean zero and constant variance. The coefficient ρ indicates the effect of the endogenous variable (economic growth) in neighboring micro-regions on the micro-region in question. Therefore, this coefficient can be interpreted as the spillover effect of regional economic growth.

Based on Equations (18) and (19) and the definition of variables in Table 1, the model estimated in this study can be defined by the following equation:

where: according to Equation (18), $Kit=sk,Hit=sh,Qit=sq,Dit=(n+g+δ)$⁠; $β$ = are estimated parameters; $μi$ = individual fixed effect constant in time (unobserved heterogeneity per unit i); $εit$ = are the residuals. The other variables were defined after Equation (19) and in Table 1.

For estimation of the model (20) by maximum likelihood, the log-likelihood function has the following form (Elhorst, 2010). However, in the SAR model, the interpretation of parameters is more complex, because when incorporating the existence of spatial spillovers, a change in the explanatory variable in a given region will affect not only the region itself, but also the neighboring regions. In this sense, the reach of a shock becomes global. However, the advantage of the model is to allow measuring the effects of a change in the explanatory variable on the explained variable in the region itself (direct effect), in other regions (indirect effects) or the total marginal effect (Almeida, 2012).

The choice of the most appropriate econometric model was based on the specification tests and procedures proposed in Almeida (2012). The initial tests are presented in Table 2. Initially, we chose to perform the variance inflation factor (VIF) test to rule out possible collinearity problems in the matrix of explanatory variables that could cause problems in the interpretation of the estimated results. There was a concern that the variables of human capital quantity and quality were strongly related, but the VIF found equal to 2.36 does not confirm this hypothesis.

The Breusch-Pagan test suggests the presence of unobserved effects, rejecting the null hypothesis that residual variance due to individual effects is zero. Then, knowing that the unobserved effects are relevant to the estimation, the Hausman test is required to determine which model is the most appropriate: fixed or random effects. The results make it possible to reject the null hypothesis of this test, indicating that the most appropriate model is fixed effects.

The next step is to test the presence of spatial autocorrelation in nonspatial estimation residuals, using Moran's I in cross-sections. The results in Table 3 make it possible to reject the null spatial randomness hypothesis in the residuals in all years of the model without incorporated spatial lags (at 1% significance). This result contrasts with Ertur and Koch (2007), as the authors say that in growth models the regions cannot be treated as spatially independent, and spatial interactions between nearby regions should be considered.

Traditionally, there are two main economic models that have been used in studies that incorporate spatial aspects: the SAR and the spatial error model (SEM). The first incorporates the spatial lag into the dependent variable, assuming that it is influenced by its mean in the nearest regions. In the second model, the spatial effect is manifested in the regression error term, capturing effects that show a spatial pattern. Incorrect nonincorporation of the spatial effects assumed in these models would cause bias and inconsistency (SAR) or bias of standard errors and inefficiency (SEM) of regression estimates, and therefore justifies the use of spatial econometrics in this study.

Then, it is necessary to choose the spatial model of fixed effects that will be estimated. The tests in Table 4 make it possible to choose between the SAR or SEM models using the Akaike and Schwarz information criterion – the smaller the criterion, the more appropriate the model. Based on the results below, we chose to use the SAR model.

The results of the expanded MRW Model estimation with quality of human capital are presented in Table 5. All coefficients follow the expected signs.

Initially, it appears that the coefficients associated with physical capital and the effective depreciation of physical capital – represented by $ln(K)$ and $ln(D)$⁠, respectively – present the same sign expected by Mankiw et al. (1992). Regarding variables of interest, the quality and quantity of human capital are positive and significant, either with or without the inclusion of the spatially lagged variable. Several other studies also find this relationship between human capital quality and economic growth, mainly Hanushek and Kimko (2000) and Barro and Lee (2001), indicating that these two aspects of human capital positively influence economic growth.

In addition, they have positive effects on both the micro-region itself (direct) and through spillovers to neighboring (indirect) micro-regions. These results are supported by Barros and Mendonça (1998), as they argue that investments in human capital are able to generate positive externalities for both individuals and those around them. According to the authors, the effects of investment in education can be realized by both improvements in quality and quantity of education. Along the same lines, similar results about externalities are found in Ertur and Koch (2007).

There are different approaches in the literature for the positive relationship between human capital and economic growth. Neoclassical interpretation is that intellectual skills resulting from education are a form of capital, so that the increase in the amount of skills directly increases production (Lucas, 1988).

As Nakabashi and Figueiredo (2005) explain, a more qualified worker can do the same service, using the same techniques and equipment, obtaining a larger end product than other workers who are not so well prepared. Human capital also indirectly affects production, given the externalities generated by it, which attenuate the effects of the decreasing income of capital, as in the model of Lucas (1988). In addition, more qualified workers accelerate the diffusion process, a crucial issue for developing countries, as noted by Nelson and Phelps (1966) and Barro and Sala-I-Martin (1997). A fourth possibility is the training of individuals who are engaged in R&D processes or any other process that affects technology creation. This is an indirect effect of education on growth. Thus, R&D depends on the quantity of human capital of the people involved in this process, as stressed by Romer (1990) apud Nakabashi and Figueiredo (2005).

An alternative interpretation from the technology gap literature is that intellectually qualified workers facilitate technology transfer (Benhabib & Spiegel, 1994). This suggests that a high level of intellectual skills is associated with increases in production (Foley & Michl, 1999).

Finally, indirect effect coefficients are higher than direct effects, suggesting that human capital is more important for neighboring regions than only for the micro-region individually. In addition, stock and physical capital are important for regional economic growth, both in the region itself and in the neighboring areas. By analyzing effects of spillovers in economic growth, the study by Ertur and Koch (2007) also concludes that spatial externalities are significant.

The role of human capital as a source of growth received little attention in the literature until the late 1950s. From then on, several important studies revolutionized the theoretical discussion about human capital and the neoclassical theory of economic growth. By introducing endogenous growth models, studies initially began to point out the mechanisms and incentives linked to the dynamics of growth itself. One of the most striking characteristics of these growth theories has been the increasing importance attributed to human capital, productive knowledge and interaction between these two factors.

However, most studies used human capital indicators that assume strictly quantitative and unidimensional characters, such as school enrollment rates or average years of study. In addition, most of these indicators contain some measurement error, which may lead to biased estimates. Therefore, there is a challenge to present better measures for human capital and determine whether human capital has a multidimensional character. With the evolution of studies in this area, a small number of new authors have argued that the quality of human capital is also an important aspect to explain different performances in economic growth. This work aimed to evaluate the importance of the quantity and quality of human capital for economic growth.

Initially, there was a literature review of growth models, starting with the Solow (1956) model and then moving to the model proposed by Mankiw et al. (1992), which includes human capital. Then, a change was proposed in this model to include the variable quality of human capital, in addition to quantity. Then, using a database for the 558 micro-regions of Brazil, for the period between 2009 and 2017, spatial econometrics techniques were used to estimate regressions.

The results found the expected signs, suggesting that the quantity and quality of human capital are important factors for regional economic growth. In addition, there were direct (region) and indirect (neighboring regions) effects, indicating that the larger stock of human capital in a given area is able to influence the economic growth of this region and also its neighboring areas.

From the point of view of public policies, the results of this study stress the importance of investing in human capital for economic growth, which has been measured in several other studies. Moreover, they indicate that investing in the quality of human capital is critical for the economic growth of regions. In this sense, it is possible to suggest, for example, investment in health conditions and the quality of elementary, secondary and higher education as ways to promote regional economic growth.

Although it is expected that the use of this spatial approach in micro-regions has been able to mitigate the problem of human capital migration between regions, the main limitation of this article is related to labor mobility, as it is possible for workers with greater qualifications to move to neighboring areas in search of better living and salary conditions. In this regard, the ideal approach would be to incorporate into human capital quality variables some control for human capital migration between regions, but there is a great difficulty due to the unavailability of this information in the databases.

Nonetheless, this article opens possibilities for new studies to evaluate the role of the quality of human capital as an element that stimulates economic growth. In this sense, Islam (1995) apud Nakabashi and Figueiredo (2005) argues that disregarding the quality factor can lead to insufficient or incorrect results that would suggest that this factor is not directly important to economic growth, especially in studies using time series. In order to analyze this relationship, it is possible that new approaches use the economic model that was suggested in this article, employing different qualitative variables and thus deepening the discussion in human capital literature.