This work aims to verify the correlation between income inequality and economic growth in Brazilian states using the Kuznets inverted U hypothesis for the time period from 1995 to 2012. The assumption of the inverted U hypothesis – Kuznets (1955) – signals that in the short term, there is a positive correlation between income inequality and per capita income levels. In the long term, however, the inverted U relationship emerges, as the relationship is reversed. These types of income inequality indicators, as well as the Gini and Theil indices and dynamic panel data econometrics, were included in this work to empirically examine the relationship between income inequality and economic growth. This work confirms the Kuznets hypothesis in Brazilian states, among other findings.

1. INTRODUCTION

Debates on the relationship between economic growth and income inequality were more prevalent in the 1950s, thanks to the pioneering work of Simon Kuznets. Since then, other studies and methods have been proposed to measure income inequality, both in developed and developing countries.

In 1955, Simon Kuznets drafted a theoretical framework based on an analysis of the process of change in agricultural economies for the industrial economies of England, Germany and the United Kingdom. This theory ascertains that the economic development process should lead to an initial period of income concentration as people and resources migrate from agriculture to urban and industrialized areas, but this trend should be reversed as the migration process is attenuated.

This is due to the difference in income between two sectors that can be studied through average per capita industrial income, the share of sector income with respect to total income and inequality in the shares of populations, which tend to be higher in the urban sector than the rural (Salvato et al., 2006).

Kuznets (1955) discusses income distribution, aiming to determine whether inequality in income distribution increases or decreases in the course of a country’s economic growth, and what factors determine this in the long term, as well as whether its origin is linked to economic growth.

The correlation between and weighting of economic growth and income inequality is an extremely important, although also controversial, topic in the history of economic thought. Studies by Deininger and Squire (1996, 1998), Ravallion and Chen (1997), Easterly (1999) and Dollar and Kraay (2002) indicate that economic growth is not related to high levels of income inequality. By contrast, Alesina and Rodrick (1994) and Alesina and Perotti (1996) found that income inequality is indeed related to economic growth.

The Kuznets inverted U hypothesis has also been proven by some authors using data on Brazil, as is shown in works by Barros and Gomes (2007), Júnior et al. (2007), Bêrni, Marquetti and Kloeckner (2002) and Salvato et al. (2006).

The estimates vary depending on the different per capita incomes, both linearly and quadratically, using the Gini index and Theil's L to measure income inequality for all the econometric methods. With that in mind, the main objective of this article is to verify, in Brazilian states, the correlation between income inequality and economic growth using the Kuznets inverted U hypothesis, from 1995 to 2012, considering that Brazil is among the nations with the strongest economic indices, despite the fact that inequality in the income distribution is considered a serious problem in the country and a cause of rising poverty and criminality.

As such, all states in Brazil, including the Federal District, for the time period 1995 to 2012, were used as the database for this work. The analysis included data on income inequality – Gini index and Theil’s L – per capita household income, years of schooling and life expectancy at birth. The database was constructed using data from the National Household Sample Survey (PNADS), the Brazilian Geography and Statistics Institute (IBGE) and the Applied Economic Research Institute (IPEADATA).

Unlike the previous articles that worked on this topic, this text uses a dynamic panel data model, developed by Arellano and Bond (1991), Arellano and Bover (1995) and Blundel and Bond (1998), and also considers the most updated data. Although this study focuses on a commonly debated topic in the academic world, the evolution of inequality in Brazil is once again important in light of the paradoxes of its economic growth model.

With that said, this study includes an introduction and six sections. The second section describes the theoretical and empirical framework used to address the issue suggested here, including an article by Kuznets (1955) and a review of the literature produced on this subject. The third section presents the econometric model and estimation methods used. The fourth section defines and discusses the database. The fifth section analyzes the results obtained from the estimate of the econometric model and, finally, the sixth section offers a conclusion with some final considerations.

2. THE KUZNETS PROPOSAL

2.1 Economic Growth and Income Inequality, the article

The classic article Economic Growth and Income Inequality, by Simon Kuznets, shows the relationship between income inequality and economic growth. Kuznets (1955) scrutinizes this topic in a unique way, exploring the nature and consequences of long-term changes in income distribution.

The author believes that there are at least two groups of forces in the long-term development of countries that lead to increasing inequality in the distribution of income – the industrial structure of the income distribution and the concentration of savings in the upper-income brackets.

As a result of industrialization and urbanization, rural migration came about in search of better living conditions. With that, to analyze the income distribution of the population in its totality is essential to understand the way in which income is shared between cities and rural environments, considering that the inequality of distribution and average rural per capital income are commonly lower than in urban settings, mainly due to the lower productivity inherent to activities in each realm.

Because the distribution of savings is more unequal than the distribution of personal income and assets, only the wealthiest strati of society have the capacity to save and this leads, ceteris paribus, to the concentration of a growing proportion of income in the hands of the upper groups.

In this same work, Kuznets (1955) poses a few questions on income distribution, including the following. Does inequality in the distribution of income increase or decrease in the course of a country’s economic growth? What factors determine long-term income inequality? Generally speaking, these questions confirm his concern with the degree of inequality in the income distribution, whose origin may be associated with economic growth.

According to the author, the aforementioned questions are broad, in a field of study that has few definitions, scarce data and the pressure of strongly defended opinions. Moreover, he points out that while the resulting difficulties cannot entirely be avoided, it may be helpful to specify the characteristics of the size of income distributions to be examined and the movements to explain.

The empirical data in the Kuznets study suggest that inequality is reduced in developed countries only in the later phases of the growth process and as a function of its benefits. Society gains greater access to healthcare networks and education, which leads to greater productivity, which leads to rapid industrialization and urbanization. It also reasons that as economies experience growth, access to education can provide better opportunities, reduce inequalities and make the poorest strati of the population more political and able to modify government policies.

The consequences of the shift from the agricultural revolution to the industrial age, along with population growth due to rapidly declining mortality rates and the maintenance, or in some cases increase, of birth rates, leads to the increase in inequality, principally in early stages.

According to Kuznets, the population growth rate can be considered as part of both the cause and effect of the long shift in income inequality. In addition, in the words of Kuznets, it is worthwhile to note that in this phase there may have been a preponderance of factors favoring maintenance or increase in the shares of top-income groups, insofar as their position was bolstered by gains arising out of new industries.

In light of the above, a dynamic inequality model can be proposed, dependent on a specific growth regime able to characterize the secular structure of income distribution, in which inequality increases in the early stages of economic growth, is consolidated for a time and then decreases in later phases.

This temporal model is adjusted to the poorest population, but the results acquired indicate that this process of decreasing inequality, analyzed in developed countries, is marked by the eventual upswing of inequality over time, simulated in the inverted U curve.

Various studies and methods have been created to explore the nature of the relationship between income distribution and growth, both for developed and developing countries. Aiming to illuminate the proposal of this work, the next section will offer a literature review of work related to the Kuznets proposal, describing its theoretical foundation and the empirical evidence found.

2.2 Literature Review

According to Kuznets (1955), the study of the secular trend in income structure is extremely important, as well as the factors that determine it, with an evaluation of the features and origins of long-term change, given that any insight obtained from observing changes in countrywide aggregates over time will be valid, if explained in terms of the movements of shares of the various income groups, and can be measured by percentile, decile or quintile.

In Economic Growth and Inequality (1955), with regard to the dynamic of income distribution during industrialization and urbanization, Kuznets illustrates his theory through a dualist economic model, working with one agricultural and one non-agricultural sector to analyze the relationship between income inequality and economic growth. He conjectured that income inequality would increase in the short term and, with economic growth, it would decrease, making an inverted U.

Switching the population from one sector to another, from a traditional agricultural population to a modern industrialized sector, income inequality would increase, given that this more dynamic sector is also wealthier and more unequal. This phenomenon happens due to the income differential of the populations between two sectors, which can be analyzed as average per capita industrial income of the share of sector income, with respect to total income and inequality in the two population shares, which tends to be higher in urban populations than in rural (Salvato et al., 2006).

With regard to the data, Kuznets (1955) attempts to classify income into different categories with various dimensions, despite the setbacks resulting from the lack of data for long time periods. To study this dynamic, the author uses time series from the United States, United Kingdom and a limited sample for Germany (Prussia and Saxony), and suggests that relative income distribution, estimated by annual income incidence in rather broad classes, revealed greater changes in equality in the 1920s, with evidence also in the time period before the First World War.

In the United States, it was found that income between groups was similar between the 1929 crisis and after the Second World war. The same development was noted in England between 1910 and 1947, as a result of the wealthier becoming poorer, while the income value of the poorest remained constant until 1919 and then rose between 1929 and 1947.

After these influential works by Simon Kuznets were published in the 1950s and 1960s, debates on the relationship between per capita income and income inequality played a larger role in the broader economic discussion. Since then, various studies and methods have been created to measure income inequality, both in developed and developing countries (Taquez and Mazzutti, 2010).

Fields (2002) ascertains that the literature has divided into two groups with regard to these Kuznets studies, one that tends to use models that analyze the shape of the inverted U – based on level of economic development – and the other that uses empirical methods to corroborate or refute the Kuznets proposal.

Aiming to prove the inverted Y hypothesis, various estimates have been made. Cross-sectional and time series methods were widely used in subsequent decades, at the suggestion of Kuznets, but other authors continued to point out their limitations. As an alternative, panel data estimates have been broadly adopted and produce more statistically significant results (Taques and Mazzutti, 2010).

According to Bêrni, Marquetti and Kloeckner (2002), cross-sectional data is better for the current purposes, because they may be able to identify uniform models, which would be indicative of the problem in different countries. That identification could help establish averages, where levels of inequality observed in specific countries could be compared.

By choosing data on developed and developing countries, Fields and Jakubson (1994) assume that some countries are either above or below the Kuznets curve. Then, the central line can be estimated using the fixed effects approach. Various results of other authors have challenged this based on the econometric method used, because the difference could be explained by observing the results between countries and in a single country.

The majority of empirical studies that include groups of both developed and developing countries in the international literature mention or praise the Kuznets hypothesis, even if they use other approaches. With that said, Kravis (1960), Oshima (1962), Adelman y Morris (1974), Paukert (1973), Ahluwalia (1976), Robinson (1976), Ram (1989), Perotti (1993), Dawson (1997), Ogwang (2000) and Sylvester (2000) are all studies based on cross-sectional data, which report evidence favorable to the hypothesis in question.

In addition, Hsing and Smith (1994), using time series data for the American economy, do not reject the Kuznets hypothesis. The same is true in studies by Forbes (2000), Deininger y Squire (1998), Barro (2000) and Thornton (2001), which used panel data. And Fields and Jakubson (1994), one of the principal works that does not support the inverted U hypothesis, drew on estimates for panel data with fixed effects.

Other studies have offered alternative explanations for the shape of the inverted U and the correlation between inequality and economic growth, subsequent to Kuznets (1955) and Robinson (1976). In that line, Barro (2000) attributes this peculiarity to deficiencies in the financial market that exist in underdeveloped economies. Deficiencies in the credit market would significantly affect the poorest swath of the population, which faces greater difficulties in accessing credit, reducing their capacity to make investments that would lead to the accumulation of physical or human capital.

On the national level, there are also works that would appear to provide proof of the inverted U behavior espoused by Kuznets. Using Fiscal Aggregate Value (FAV) data and the Theil index, Bêrni, Marquetti and Kloeckner (2002) showed the existence of a Kuznets curve for the industrial and services sectors of Rio Grande do Sul in 1991, but they did not find statistically significant results for the agricultural and livestock sector.

Using panel data for municipalities in Rio Grande do Sul, Bagolin, Gabe and Pontual (2003) also demonstrated the inverted U relationship between per capita income and the Theil index, for the time period of 1970, 1980 and 1991. Jacinto and Tejada (2004) used cross-section and panel data for cities in northeastern Brazil, analyzing the years 1970 and 1971 and also finding evidence of the aforementioned curve. Salvato et al.(2006), looking at 1991 and 2000, also found evidence that in municipalities in Minas Gerais, the correlation between income inequality and economic development is in accordance with the Kuznets theory.

In cross-sectional estimates, Porto Júnior et al. (2007) used liner and quadratic per capita income as metrics, aiming to capture directional shifts in the distribution of income in accordance with its level. The authors verified that for panel data in Rio Grande do Sul, the fixed effects estimate showed that initial development was overcome and income inequality was not as high as compared to the state of Paraná.

For cities in Rio Grande do Sul, Bêrni, Marquetti and Kloeckner (2002) observed the Kuznets inverted U hypothesis in cross-sectional data. Using a non-parametric local regression, they looked at municipal demographic density and per capita income by sector and inequality, both for agricultural and livestock income as well as industrial and service sector income. The results confirmed the Kuznets inverted U, but only for some municipalities, when the explanatory variable of municipal demographic density was included.

Moreover, in Brazil, local economic inequality indices grew in the 1970s and remained high until the mid-1990s. This situation began to change after the implementation of the "Real Plan," when inequality indices began to fall. Despite this recent decrease, inequality in Brazilian income remains fairly high. The portion of total income appropriate by the wealthiest 1% of the population is of the same magnitude as the amount appropriated by the poorest 50% (Kakwani et al., 2006).

3. METHODOLOGY

Aiming to determine the correlation between income inequality and the factors that determine it, with dynamic panel data, the generalized method of moments (system GMM) were used as set forth in works by Arellano and Bond (1991), Arellano and Bover (1995) and Blundell and Bond (1998).

This work analyzes the behavior of inequality in 27 Brazilian states as related to income, education and life expectancy of individuals from 1995 to 2012.

The model assumes that current income inequality tends to be perpetuated and/or influence the behavior of inequality in the future. The relationship between income inequality and economic growth is analyzed with a panel data regression model, in the following equation:

(1)

Where the dependent variable y_it is the measure of income inequality (Gini or Theil coefficient); renta_it is per capita income; edu_it is average years of schooling of individuals; edu_it is the life expectancy of individuals; η_i are the non-observable fixed effects of individuals and ε_it represents random disturbances. The subscript i represents the state and t the time period.

Arellano and Bond (1991) discuss what happens with two econometric problems when the model is calculated using traditional estimation methods. First, the problem of the non-observable effects of individuals, η_i, together with the lagged dependent variable y_it-1, on the right side of the equation. In this case, omitting the individual fixed effects in the dynamic panel model returns deformed and inconsistent ordinary least squares (OLS) estimators. Meanwhile, the within group estimate, which corrects for the presence of fixed effects, produces a downward biased estimate β₁ for panel data with small temporal dimension.

Second, there is the problem of the likely endogeneity of the explanatory variables. In this case, the endogeneity on the right side of the equation (2) should be treated to prevent possible deformation due to problems of simultaneity.

One way to solve this problem, according to Arellano and Bond (1991) is to use the generalized method of moments estimator (difference GMM), which consists of eliminating the fixed effects through the first difference of the equation (1).

(2)

Thus we have, for any variable y_it, Δy_it = y_it - y_{it - 1}. It is noted that in equation (2), Δy_it-1 and Δε_it are correlated, and since that is such, the OLS estimators for its coefficients will be distorted and inconsistent. It will then be necessary to use instrumental variables for Δy_it-1

The adoption of the hypothesis in equation (1) refers to the fact that the conditions of moments E [ Δy_it-S Δε_it ] = 0 for t = 3, 4, ...T and s ≥ 2, are valid. Arellano and Bond (1991), based on those moments, indicate to apply y_{it - S} for t = 3, 4, ...T and s ≥ 2 as instruments for equation (2).

The other explanatory variables can be considered as (a) strictly exogenous, if not correlated with past, present and future error terms, (b) weakly exogenous, if correlated only with past values of error terms and (c) endogenous, if correlated with past, present and future error terms. In the second case, the values of the lagged variable in one or more periods are valid instruments in estimating equation (2) and, in the latter case, the lagged values in two or more periods are valid instruments in estimating that equation.

According to Arellano and Bover (1995) and Blundell and Bond (1998), these instruments are weak when the dependent and explanatory variables exhibit strong persistence and/or the relative variation of the fixed effects increases. In that way, they produce an inconsistent and distorted difference GMM estimator for panels with small T.

With that said, Arellano and Bover (1995) and Blundell and Bond (1998) recommend a system that combines the set of equations in differences, equation (2) with the set of equations in level, equation (1), to reduce this issue of distortion. This system has been designated as the generalized method of moments system (system GMM).

For equations in differences, the set of equations is the same as previously mentioned. For the regression in levels, the appropriate instruments are the lagged differences of the respective variables. For example, assume that the differences of the explanatory variables are not correlated with individual fixed effects (for t = 3, 4, ...T) and E [ Δy_i2 v_i ] = 0 , for i = 1, 2, 3, …, N. Then, for the explanatory variables in differences and Δy_{it - 1}, if they are exogenous or weakly exogenous, they are valid instruments for the equation in levels. The same is true if they are endogenous, but with instruments that are explanatory variables in lagged differences for a period and Δy_{it - 1},

The system GMM estimates described in the next section derive from an estimate with an estimator corrected by the Windmeijer (2005) method to prevent the respective estimator of variances from underestimating the true variances in a finite sample.

As such, the estimator used was suggested by Arellano and Bond (1991) in two steps. The first stage supposes that the error terms are independent and homoscedastic across states and over time. And in the second period, the residuals obtained in the first stage are used to build a consistent estimate of the variance-covariance model, thereby relaxing the hypotheses of independence and homoscedasticity. The estimator for the second period is asymptotically more efficient than the estimator of the first stage.

The consistency of the system GMM estimator depends on the assumption of the absence of serial correlation in the error term and the validity of additional instruments. In that way, initially, null hypotheses on the absence of first and second order autocorrelation of the residuals are proved.

In order for the estimators of the parameters to be consistent, the hypothesis of the absence of first order autocorrelation must be rejected and the second order accepted. Then, the Hansen test is conducted to verify if the additional instruments required by the system GMM method are valid, as Arellano and Bond (1991) recommend.

4. DATABASE

The data for this work to evaluate the relationship between income inequality and economic growth were obtained from the National Household Sample Survey (PNADS) and taken from the Applied Economic Research Institute (IPEADATA), and they cover all Brazilian states and the Federal District, making up a balanced panel that encompasses the time period 1995 to 2012.

According to Vanhoudt (2000), studies with a global scope make it difficult to compare data, as research methodologies and data collection are carried out differently in each country. As such, this work benefits from only using variables that were calculated with the same methodology in each state, which makes it possible to more precisely estimate the indicators and compare the data.

The Gini coefficient, used as a measure of inequality, is taken from per capita household income. This index is frequently used to express the degree of income inequality and may be associated with the Lorenz curve determined by the set of points which, based on incomes ordered by increasing level, relate the cumulative proportion of people and income.

Both the Gini and Theil indices were used to observe the evolution of inequality in each Brazilian state, as well as the strength of the econometric results. Average per capita household income of the population was used as a measure of economic growth levels, and the series for these variables were calculated based on responses to the National Household Sample Survey (PNAD/IBGE).¹

Education was used as an explanatory variable, defined by number of years of schooling of residents in the various Brazilian states, constructed based on PNAD data, as well as life expectancy of individuals at birth, obtained from the Brazilian Geography and Statistics Institute (IBGE).

5. RESULTS AND DISCUSSION

This section presents and discusses the results of the estimated econometric model introduced in section 4, relating income inequality as measured by the Gini and Theil indices and their determining factors.

Besides the results of OLS and within-group measurements, this work also introduces the estimates made with the system GMM method. As shown before, this method is an extension of the original Arellano and Bond (1991) estimator, proposed in Arellano and Bover (1995) and developed in Blundell and Bond (1998).

In column [a] of Table 1, the values of the coefficients of the variable 〖gini〗_(it-1) and 〖gini〗_(it-2) estimated by OLS are, in fact, higher than the values estimated in column [b] for this same variable for within group. This being the case, if the instruments used are appropriate, the values of the coefficients of that variable estimated by the system GMM should fall between the limits of the coefficients estimated by the other two methods earlier. The values obtained by system GMM for that variable in column [c] show that this condition is indeed satisfied, indicating that the distortion caused by the presence of endogenous variables on the right side of the regression and the non-observable fixed effects were corrected by system GMM.

The levels of lagging to adjust the model are represented by the terms gini_it-1 and gini_it-2 in the first and second row of Table 1. The lagged variables are statistically significant, and significant at 1% for the values of column [a] and [c], which indicates the proper adjustment for the dynamic behavior model of the estimated variables.

Of the various models estimated, the choice was made to use the model in column [c] of Table 1, where the dependent variable gini_it lagged in one period and the variable edu_it were used as endogenous variables. The other explanatory variables were considered weakly exogenous.

The tests carried out in the system GMM model showed that the statistical properties were acceptable. The Hansen test, which checks whether the instruments used and required by this model are valid, was satisfactory. Statistical tests from Arellano and Bond (1991) were included to detect the existence of first and second order autocorrelation. It was noted that the absence of second order autocorrelation is essential for the system GMM to be consistent and the test did not reject the first order autocorrelation hypothesis, although it did reject the second order autocorrelation.

In column [a] of Table 1, all variables returned significant signs as expected. The model was estimated by OLS, and when lagging the Gini variable for two periods, went from a total of 486 to 432 observations, including all Brazilian states between 1995 and 2012.

In column [c] of Table 1 of the system GMM model, the coefficient of the lagged dependent variable in a period returned a highly significant value, relatively lower than the OLS estimator, confirming the expectation of the persistence of income inequality in Brazil for the time period analyzed.

The existence of a negative relationship between inequality and average number of years of schooling was found, significant in all estimated models, columns [a], [b], [c], with respective values of: -0.00334, -0.00819, -0.00171. In this way, even though the values are not so expressive, they corroborate what diverse authors, such as Shultz (1961) and Enreberg and Smith (2000), have found, by showing that the increase in number of years of schooling leads to more skills and knowledge, thereby increasing productivity. This helps people earn higher salaries and reduces income inequalities and poverty.

In column [c] of Table 1 there is a negative and significant relationship between life expectancy and income inequality, with an approximate estimated value of -0.0049.

Average per capita household income of the population, as in its quadratic form, in the regressions estimated, was used as a measure of economic growth. The values and signs found – statistically significant for within-group and system GMM – for these variables, indicate evidence of the Kuznets curve in Brazil for the time period analyzed, in agreement with Bêrni, Marquetti y Kloeckner (2002), Bagolin, Gabe and Pontual (2003), Jacinto and Tejada (2004) and Salvato et al. (2006).

Aiming to confirm the previously discussed results, the same methodology was applied to the Theil index, and Table 2 shows that for the system GMM, column [c], there is a negative relationship, -0.02893, significant at 1%, between inequality and average years of schooling. This validates the results found by using the Gini index and the literature mentioned in section 2.

Looking closely at the regression done by system GMM in Table 2 using the Theil index as the measure of inequality, we see that there is also a significant relationship at 1% with the values and signs expected for life expectancy with respect to income inequality in the country. This is further evidence that an increase in life expectancy of individuals reduces the panorama of income inequality in Brazil.

Column [c] of Table 2 shows that the explanatory variable that represents a measure of economic growth, per capita household income in its quadratic form, is inversely related to the Theil index, confirming the same inclination found in the previous model in Table 1. To Sen (2000), the measure of economic development should take into account socioeconomic variables such as access to education, availability of healthcare and sanitation services and life expectancy. Using variables exclusively related to income would not be enough to measure the level of economic development.

With that said, the results found in Table 2 followed the same leaning as Table 1, in which for regressions with the Theil coefficient, the system GMM returned values with the expected signs, statistically significant for all variables. Later on, the conditions of concavity are met for this inequality index, indicating that the existence of an inverted U shaped curve cannot be rejected.

The choice of two income inequality indicators (Gini and Theil indices) and the linearity of the variables aimed to make the estimated models more robust. It could be said that this objective was attained, given that the majority of estimates made converged for the desired result.

In the static approach to the system GMM model, column [c] of Table 2, the signs of the coefficients that were significant are in accordance with expectations. In decreasing order, the inequality measured by the Theil index is more sensitive to the average years of schooling (-0.02893), years of average life expectancy (-0.01910) and income (-1.05e-07).

The results of the models estimated for both the Gini and Theil indices point towards the fact that economic growth reduces income inequality. In this way, as has been seen already, in the least restrictive version of the concept, in the short term, there is a positive connection between income inequality and per capita income. But in the long term, there is an inverted U relationship, as the relationship is inverted.

6. FINAL CONSIDERATIONS

Aiming to demonstrate the existence of an inverted U relationship between income inequality and economic growth, as proposed by Simon Kuznets (1955), between 1995 and 2012 in Brazil, this work highlighted some studies on a variety of theoretical and econometric debates relevant to the topic at hand. Using different estimates, some of these corroborated and others rejected the Kuznets hypothesis.

In the search for an answer to research the Kuznets hypothesis on the course of income inequality in developing countries, this study proposed to use a panel data approach, employing the system generalized method of moments method (system GMM), which sets it apart from previously published works. This method made it possible to mitigate the econometric problems that affect the majority of work in this area, such as the endogeneity of explanatory variables.

By analyzing the behavior of inequality, as measured by the Gini and Theil coefficients, in all Brazilian states in relation to average per capita household income of the population and, in its quadratic form as well, the estimated regressions returned the expected values and signs, statistically significant for the system GMM, confirming the positive connection between income inequality and per capita income in the short term, although this relationship is inversed in the long term.

However, life expectancy also showed an inverse and significant relationship with the Gini and Theil coefficients. That said, an increase in the life expectancy of individuals was correlated with a decrease in income inequality.

Looking at average years of schooling, education, as well as the other variables analyzed, there is a positive effect to the detriment of income inequality. More years of schooling afford individuals training and the chance to develop skills and knowledge that may increase their productivity and by extension their salaries. Income then goes up and income inequalities and poverty go down.

The econometric estimates also allowed us to verify that the series showed signs of autocorrelation, that is, the present results depend on past results. The results showed, for all series, specific cyclical behavior for the period analyzed, where increases in income, education and life expectancy of individuals pushed income inequality in the opposite direction.

The empirical evidence found for both inequality coefficients used suggests that the relationship between income inequality and economic development in Brazil in the time period analyzed follows the inverted U model as proposed by Kuznets in his studies. This work also agrees with literature whose authors corroborate the Simon Kuznets (1955) hypothesis, where income inequality in Brazil increases in the early stages of economic development and in later stages of growth, inequality tends to fall off.

Although this research did achieve its objective, it would be useful to expand the number of physical and economic features of the country taken into account, looking at other explanatory variables to prove the aforementioned Kuznets hypothesis in future studies on the various Brazilian states and regions.

BIBLIOGRAPHY

Adelman, I. and Morris, C. (1974), Economic Growth and Social Equity in Developing Countries, Stanford, California, Stanford University Press.

Ahluwalia, M. S. (1976), "Income Distribution and Development: Some Stylized Facts", American Economic Review, vol. 66, no. 2, pp. 128-135.

Alesina, A. and Rodrik, D. (1994), "Distributive Politics and Economic Growth". The Quarterly Journal of Economics, vol. 119, no. 2.

______, and Perotti, R. (1996), "Income Distribution, Political Instability and Investment". European Economic Review, vol. 40, no.6.

Arellano, M., Bover, O. (1995), "Another Look at the Instrumental-variable Estimation of Error-components Model", Journal of Econometrics, vol. 68, pp. 29-52.

______ y Bond, S. (1991), "Some Tests of Specification for Panel Data: Monte Carlo Evidence and Application to Employment Equations", The Review of Economic Studies, vol. 58, no. 2, pp. 277-297.

Bagolin, I. P; Gabe, J. and Pontual, R. E. (2003), Crescimento e Desigualdade no Rio Grande do Sul: uma revisão da Curva de Kuznets para os municípios gaúchos (1970-1991). Mimeo. Porto Alegre, UFRGS.

Barros, L. C.; Gomes, F. A. R. (2007), "Desigualdade e Desenvolvimento: a hipótese de Kuznets é valida para os municípios brasileiros?", Ibmec. São Paulo, Working Paper, no. 28, (consulted October 28, 2013), available at: <www.ibmecsp.edu.br/pesquisa/download.php?recid=3101>.

Barro, R. J. (2000), "Inequality and Growth in a Panel of Countries", Journal of Economic Growth, vol. 5, pp. 5-32.

Bêrni, D. A.; Marquetti, A. and Kloeckner, R. (2002), "A Desigualdade Econômica do Rio Grande do Sul. Primeiras Investigações sobre a Curva de Kuznets". In: 1º Encontro de Economia Gaúcha, Anais... Porto Alegre.

Blundell, R. and Bond, S. (1998), "Initial Conditions and Moment Restrictions in Dynamic Panel Data Models", Journal of Econometrics, vol. 87, pp. 115- 143.

Dawson, P. J. (1997), "On Testing Kuznets’ Economic Growth Hypothesis", Applied Economic Letters, vol. 4, pp. 409-410.

Deininger, K. and Squire, L. (1996), "A New Data Set Measuring Income Inequality", World Bank Economic Review, vol. 10, pp. 565-591.

______ (1998), "New Ways of Looking at the Olds issues: Inequality and Growth". Journal of Development Economics, vol. 57, no. 2, pp. 256-287.

Dollar, D.and Kraay, A. (2002), "Growth is Good for the Poor", Journal of Economic Growth, vol. 7, no. 3, pp. 195-225.

Easterly, W. (1999), "Life during Growth: International Evidence on Quality of Life and per cápita Income", Journal of Economic Growth, no. 4.

Enrenberg, R.G and Smith, R.S. (2000), A moderna economia do trabalho – Teoria e política pública, São Paulo, Makron Books, pp. 319-409.

Fields, G. S. (2002), Distribution and Development, Cambridge, MA. MIT Press.

Fields, G. and Jakubson, G. (1994), The Inequality-development Relationship in Development Countries, Mimeo.

Forbes, K. J. (2000), "A Reassessment of the Relationship between Inequality and Growth", American Economic Review, vol. 90, no. 4, pp. 869-887.

Hsing, Y. and Smith, D. (1994), "Kuznets’ Inverted-U Hypothesis Revisited", Applied Economic Letters, pp. 111-113.

Jacinto, P. A. and Tejada, C. A. O. (2004), "Desigualdade de renda e crescimento econômico nos municípios da região nordeste do Brasil: o que os dados têm a dizer?", In: Encontro Nacional de Economia da ANPEC, 32, João Pessoa, PB. Anais … Belo Horizonte: ANPEC.

Júnior, S. S. P. and Ribeiro, E. P. (2007), "Um estudo exploratório sobre a curva de Kuznets e a lei de Zipf ". In: X Encontro de Economia da Região Sul Da ANPEC. 10.2013, Porto Alegre, RS. Anais. Porto Alegre, ANPEC.

Kravis, I. B. (1960), "International Differences in the Distribution of Income". Review of Economics and Statistics, vol. 42, no. 4, pp. 408-416.

Kuznets, S. (1955), "Economic Growth and Income Inequality", American Economic Review, vol. 45, núm. 1, pp. 1-28.

Kakwani, N.; Neri, M.and Son, H. (2006), "Linkages between Pro-poor Growth, Social Programmes and Labour Market: The Recent Brazilian Experience", Brasil, PNUD, Working Paper, no. 26.

Ogwang, T. (2000), "Inter-country Inequality in Human Development Indicators", Applied Economic Letters, vol. 7, no. 7, pp. 443-446.

Oshima, H. T. (1962), "The International Comparison of Size Distribution of Family Incomes with Special Reference to Asia", Review of Economics and Statistics, vol. 44, no. 4, pp. 439-445.

Paukert, F. (1973), "Income Distribution at Different Levels of Development: a Survey of Evidence", International Labour Review, vol. 108, no. 2-3, pp. 97-125.

Perotti, R. (1993), "Political Equilibrium, income Distribution and Growth", Review of Economics Studies, vol. 60, no. 4, pp. 755-756.

Ram, R. (1989), "Level of Development and income Inequality: an Extension of Kuznets-Hypothesis to The World Economy", Kyklos, vol. 42, pp. 73- 88.

Ravallion, M and Chen, S. (1997), "What can New Survey Data tell us about Recent Changes in Distribution and Poverty? World Bank Economic Review, Oxford University Press, vol. 11, no. 2, pp. 357-382.

Robinson, S. (1976), "A Note on the U Hypothesis Relating income Inequality and Economic Development", The American Economic Review, vol. 66, no. 3, pp. 437-440.

Salvato, M. A.; Alvarenga, P. S.; França, C. S.and Araújo Jr, A. F. (2006), Crescimento e Desigualdade: evidências da Curva de Kuznets para os municípios de Minas Gerais – 1991/2000. Ibmec MG Working Paper. WP33.

Sen, A. (2000), Desenvolvimento como liberdade, São Paulo: Cia. Das Letras.

Sylvester, K. (2000), "Income Inequality, Education Expenditures and Growth", Journal of Development Economics, vol. 63, no. 2, pp. 379-398.

Taques, F. C. and Mazzutti, C. C. T. P. C. (2010), "Qual a Relação entre Desigualdade de Renda e Nível de Renda per capita? Estando a hipótese de Kuznets para as Unidades Federativas Brasileiras", Planejamento e Políticas Públicas. no. 35.

Thornton, J. (2001), "The Kuznets inverted-U hypothesis: panel data evidence from 96 countries", Applied Economics Letters, vol. 8, no. 1, pp. 15-16.

Windmeijer, F. (2005), "A Finite Sample Correction for The Variance of Linear Efficient Two-step GMM Estimators", Journal of Econometrics, vol. 126, pp. 25-51.

Vanhoudt, P. (2000), "An Assessment of the Macroeconomic Determinants of Inequality", Applied Economics, vol. 32, no. 7, pp. 877-883.