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370 Economic Growth and Per Capita Income Convergence among Municipalities of the Parana and Sao Paulo States (1999-2010) Jorge LeandroDelconte Ferreira, 1 José Luiz Parré and Maria LuziaLomba de Sousa Abstract: This work analyzes per capita GDP absolute and conditional convergence of Paraná and São Paulo States’ municipalities, between 1999 and 2010, as a guideline to investment opportunities in those regions. The study identified disparities in per capita income and different growth dynamics among municipalities. The analysis employed Exploratory Spatial Data Analysis (AEDE) techniques. The hypothesis of convergence was statistically supported, applying spatial correction. We found high-high clusters in São Paulo and low-low clusters in Paraná, suggesting the growth prospects of studied municipalities depend not only on the initial income, but also on the effect of the dynamics of neighboring municipalities. Keywords:Convergence of the per capita GDP, economy of Paraná, economy of São Paulo. 1. Introduction The economic growth of a country is an important indicator to assist in investment decisions. However, the degree of homogeneity of this growth in its geopolitical subdivisions (regions, states, municipalities) should also be considered. Several authors have tested, in the regional economic literature, the hypothesis of critics of the neoclassical economic theory that the degree of richness of these subdivisions tends to be approached in a process of convergence of per capita income, such as Russo, Santos &Parré (2012), Ferreira & Ellery Jr(1996), Azzoni (2001). For these analyses, the spatial econometrics allows considering the effects of geographic location on regional economic performance. Considering the scenario of two highly dynamic and bordering Brazilian states, Paraná and São Paulo, which together account for 38.9% Brazil's GDP, this study aimed to verify the hypothesis of absolute convergence of the per capita GDP among cities of those states, in the period 1999 - 2010.Researches grounded in new theories of economic growth incorporate the human capital to explain inequalities in per capita income, between countries, regions, or states of countries. Prominent authors in this area are Mankiw, Romer and Weil (1992), Barro and Sala-i-Martin (1995) at the international level, Azzoni (2001), Rocha and Vergolino (2002), at the national level and Justo (2004) at the regional level. The present study is made up of five sections, besides this introduction: the literature review addresses the economic growth theory and the absolute convergence of per capita income. The third section comments on the recent evolution of the economies of Paraná and São Paulo States. Subsequently is described the methodology used to examine the spatial convergence of income. In the fifth section, data are analyzed and results are discussed. Finally, the sixth section reports the final considerations. 2. Literature Review 1 Department of Economics, State University of Maringá (UEM).Av. Colombo, 5790 - Bloco: C34 - sala 5 - Maringá – PR.Tel: (44) 3011-4987 - Fax: (44) 3011-4744.

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Economic Growth and Per Capita Income Convergence among Municipalities of the Parana and Sao Paulo States (1999-2010)

Jorge LeandroDelconte Ferreira,1José Luiz Parré and Maria LuziaLomba de Sousa

Abstract: This work analyzes per capita GDP absolute and conditional convergence of Paraná and São Paulo States’ municipalities, between 1999 and 2010, as a guideline to investment opportunities in those regions. The study identified disparities in per capita income and different growth dynamics among municipalities. The analysis employed Exploratory Spatial Data Analysis (AEDE) techniques. The hypothesis of convergence was statistically supported, applying spatial correction. We found high-high clusters in São Paulo and low-low clusters in Paraná, suggesting the growth prospects of studied municipalities depend not only on the initial income, but also on the effect of the dynamics of neighboring municipalities. Keywords:Convergence of the per capita GDP, economy of Paraná, economy of São Paulo. 1. Introduction  

The economic growth of a country is an important indicator to assist in investment decisions. However, the degree of homogeneity of this growth in its geopolitical subdivisions (regions, states, municipalities) should also be considered. Several authors have tested, in the regional economic literature, the hypothesis of critics of the neoclassical economic theory that the degree of richness of these subdivisions tends to be approached in a process of convergence of per capita income, such as Russo, Santos &Parré (2012), Ferreira & Ellery Jr(1996), Azzoni (2001). For these analyses, the spatial econometrics allows considering the effects of geographic location on regional economic performance. Considering the scenario of two highly dynamic and bordering Brazilian states, Paraná and São Paulo, which together account for 38.9% Brazil's GDP, this study aimed to verify the hypothesis of absolute convergence of the per capita GDP among cities of those states, in the period 1999 - 2010.Researches grounded in new theories of economic growth incorporate the human capital to explain inequalities in per capita income, between countries, regions, or states of countries. Prominent authors in this area are Mankiw, Romer and Weil (1992), Barro and Sala-i-Martin (1995) at the international level, Azzoni (2001), Rocha and Vergolino (2002), at the national level and Justo (2004) at the regional level. The present study is made up of five sections, besides this introduction: the literature review addresses the economic growth theory and the absolute convergence of per capita income. The third section comments on the recent evolution of the economies of Paraná and São Paulo States. Subsequently is described the methodology used to examine the spatial convergence of income. In the fifth section, data are analyzed and results are discussed. Finally, the sixth section reports the final considerations.

2. Literature Review                                                             

1Department of Economics, State University of Maringá (UEM).Av. Colombo, 5790 - Bloco: C34 - sala 5 - Maringá – PR.Tel: (44) 3011-4987 - Fax: (44) 3011-4744.

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2.1. Growth Models with Income Convergence

Differences in growth and social and economic well-being are among the oldest and most traditional problems addressed by the Economic Theory. Some classical studies on this topic are Solow (1956; 1957), Romer (1986), Lucas (1988), Mankiwet al. (1992).Nevertheless, before discussing the income convergence, it is defined according to Galor (1996) who mentions the following typology of income convergence:

• Absolute or unconditional β convergence – the per capita incomes of any two economies tend to

the same level in the long term (steady state) regardless of their initial conditions; • Conditional β convergence – two economies with common structural characteristics (preferences,

technology, population growth rates, public policy etc.) will have the same level of per capita income in the long term, regardless of their initial conditions;

• Club convergence – per capita incomes of any two economies tend to the same level in the long term only if they share the same time of structural characteristics and similar initial conditions.

For Solow (1956; 1957), one of the forerunners on discussing convergence,in the long term, the level of per capita income of economies is explained by the amount of savings and technological level (positive forces), and by population growth and depreciation of physical capital (negative forces). He considered the exogenous technical progress, in the model below:

, 0 1 (1) In the model, K is the capital, L is the labor and A is the technology. The Solow model (1956; 1957) explains differentials in per capita income as a result of the difference in rates of investment and population growth, considered the technology. For him, poor economies will have higher growth rates than rich economies, which translate into the absolute convergence of per capita income between economies or regions. Baumol (1986) investigates convergence models by showing a narrowing of differences in GDP growth in sixteen industrialized economies in the period 1870-1979. Romer (1986) and Lucas (1988) question the formulation of the neoclassical model of absolute convergence, by adding to it the human capital. Romer (1986) argues that knowledge spillovers occur in the production, economies with greater human capital will achieve gains followed by productivity. Thus, the production function of such economies has increasing returns. Rich economies, with higher income and thus with higher human capital,continue richer compared with poorer economies, increasing the distance between them, leading to the existence of conditional convergence or to the formation of convergence clubs. With the incorporation of the human capital, this extended Solow model does not require high rates of saving and population growth to explain spatial differences in per capita incomes. In other words, people with higher education level and skill would imply in increased productivity (LUCAS, 1988; ROMER, 1990). While testing the extended Solow model, Mankiw, Romer and Weil (1992) concluded that the variables education, savings and population growth better explain differences in economic growth.Justo (2004) highlighted that the model with human capital has greater elasticity in the product with respect to its determinants than the traditional Solow model. Thereby, the extended model works with a broad concept that capital can explain better the spatial differences in income among municipalities. Various recent studies investigated the convergence of income for countries or regions. In the 1990s, some of the most prominent were those of Barros and Garoupa (1995), Persson (1997) and Lusigi and Thietle (1998). Bertussi and Figueiredo (2009)investigated the convergence of income in Latin America and East

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Asia for the period 1960-2000, concluding that the income convergence is a local phenomenon. In Brazil, Ferreira & Ellery Jr (1996) and Porto Jr&Souza (2002) examined the income convergence among Brazilian states, and the latter authors underlined the formation of convergence clubs among Brazilian regions.There are also several studies that investigated the convergence of income in southern Brazil, such as Porto Junior &Ribeiro (2000) and Esperidião, Meirelles&Bittencourt (2009). Both studies pointed out evidences of income convergence, either in absolute model or in club model. 2.2. Spatial Econometrics and Income Convergence According to Rey &Montouri (1999), analysis of spatial data allows a new understanding of the geographical dynamics for studying the income growth rate over time. Almeida (2012) emphasizes that the spatial econometrics includes into econometric models not only the pattern of socioeconomic interaction between agents of a system, but also the structural characteristics of this system in space. Thus, spatial econometrics captures effects of both the spatial dependence (Tobler law2) and of the spatial heterogeneity3. The spatial econometric regression usually starts with the exploratory analysis of collected data. Chi & Zhu (2008) argue that this step permits to visualize the spatial distribution of the data, admitting possible diagnoses of spatial aspects of statistical models, which may assist in the choice of regression models.In agreement with Pacheco et al (1995), the spatial dependence can be measured by several indices, among them the most applied is the Moran’s I. This index measures the degree of linear association between one attribute (y) at a given location and the weighted average of attributes in neighboring locations (Wy). The autocorrelation can be explained asthe slope of the regression of (y) on (Wy). According to Anselin (1998), the Moran’s I statistics describes the spatial dependence in data and presents a homogeneous spatial pattern, but it is not very informative when data present several spatial regimes. Anselin (1998) affirms that the Moran’s I is a gross measure of spatial dependence when is shown the scatter plot of the data, being possible to observe the presence of different spatial regimes. Moreover, the spatial heterogeneity or spatial structure describes the differences in the mean and/or variance and/or covariance including dependence within a spatial region. The spatial dependence requires the mean and variance of a particular attribute being constant in space, and two locations depend on a lag distance between two locations, but not necessarily of the very location (ALMEIDA, 2012). Anselin (1999) informs that tests to determine spatial dependence or heterogeneity can generate inconclusive results, that is, it is not always easy to distinguish the spatial heterogeneity from the spatial dependence. For instance, in some cases the presence of clusters may lead to spatial dependence between neighbors, but can also lead to spatial regimes. LeSageand Pace (2009) argue that to consider the spatial dependence in a given data set, it is essential to establish the structure of the neighborhood for each location by explaining the locations considered as neighbors.Particularly Anselin (1999) indicates that it is essential to specify a weight matrix corresponding to neighboring structure such that the variance-covariance matrix can be expressed as a function of a small number of estimable parameters compatible to the size of the studied sample. When studying the weight matrices, Chi & Zhu (2008) warn of two problems with the specification of spatial weights in practice: the weight structure can be affected by the quality of geo-referenced data and/or the use of some distance weight matrix may require a threshold value, which can be difficult to determine especially when there is a strong spatial heterogeneity.Chi & Zhu (2008) andAnselin (1999) elucidate that the simple linear regression model assumes that the error terms are independent and identically distributed. After

                                                            

2 Also known as the First Law of Geography: Everything depends on everything else but closer things more so (ALMEIDA, 2012, 21). It suggests that the closer in spatial terms, the more interrelated the subjects are. 3 Depending on the location or spatial scale, there may be structural instabilities, resulting in variations in responses.

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estimated a model, residuals are examined to check if they violate the assumptions. If the assumption is violated, the use of the estimation can be unsuitable for drawing inferences.Also, according to the authors, for the case of dependence on the dependent variable, estimations of Ordinary Least Squares (OLS) are biased and inconsistent; on the other hand when the correlation is present in the error term, there is no bias or inconsistency, but the OLS estimator is no longer the most efficient. Chi & Zhu (2008) mention that the linear regression model and the spatial linear regression model include, besides the coefficients of the explanatory variables (β) and the variance of the error term (σ²), a spatial autoregressive coefficient (ρ), which measures the strength of spatial dependence. In spatial regressions, a weight matrix (W) is included, corresponding to the neighborhood structure and the pre-specified weight matrix (D). Anselin (1998) claims that error terms in spatial linear regression models are more specific. Two models are more often used: in the spatial Lag model, Y is the vector of dependent variables, X is the matrix of explanatory variables, W is the spatial weight matrix, and ξ is the vector of error terms that are independent, but not necessarily equally distributed. If models are nested we can use a likelihood ratio test (LR) to compare models, and if models are not nested, one can use the AIC (Akaike’s Information Criterion) and the BIC (Schwartz’s BayesianInformation Criterion). Models with lower BIC and AIC are considered better. Other tests as the spatial Breusch-Pagan can also be applied (CHI & HU, 2008).According to Almeida (2012), the Exploratory Spatial Data Analysis (ESDA) precedes the spatial econometric modeling and aims to describe spatial distributions, identify outliers in space, discover patterns of spatial association, and suggest spatial clusters. The Exploratory Spatial Data Analysis uses tools for spatial visualization and analysis of global and local spatial autocorrelation to interpret the information gathered. The ESDA assumes that spatial phenomena tend to be correlated with others geographically close. 2.3. Recent Economic History

The evolution of the Brazilian economy over the last decades has been influenced by both the agricultural revolution of 1970 (modernization of inputs, incorporation of technological changes, strong rural exodus and the depletion of the agricultural frontier) and by the industrial decentralization from the Southeast to new regions, such as the Paraná State (ROLIM, 1995; DINIZ & LEMOS, 1990). According to Trintin (2002, p. 8), in the case of the industry of the Paraná State, there was a policy of the state government to promote industrial development. Trintin (2002) stresses the consolidationof the project Industrial City of Curitiba – CIC – as an emblematic example. The State Government has implemented policy of attracting investments, encouraging modern segments (metalworking, mechanical, oil refining) and traditional segments (wood, food, chemical - soybean oil), providing diversification of the industrial sector of the state. From the 1980s, changes in the secondary and primary sectors derived from mechanization and modernization and of processing grain and meat have expanded interstate commerce and export trade. This resulted in improvement of means of communication and transportation (roads, highways, railways, electricity) to the major urban centers. At the same time, the Paraná State slowed down the population growth, despite the emigration (IPARDES, 1997). Rippel (2005) points out that the economically active population, in the 1980s, fell 5%, given the recession period and modernization of the agricultural and industrial sectors of the state.This modernization accelerated the rural exodus, mainly to the Midwest and Southeast of Brazil. This was aided by the productive rearrangements due to the need for large properties for cultivation of soybean and wheat. Trintin (2006) tells thatthe modernization and growth of the industry of Paraná allowed the growth in the period 1985-1998, making the Paraná the fourth most important industrial state of the country. This State attracted large investments in the industrial sector(R$ 14 billion), benefiting metal mechanic and mechatronic industries,

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agroindustries, pulp industry, among others (JESUS & FERRERA DE LIMA, 2001).In the 1990s, the Paraná State promoted and diversified its export base by attracting new investments. For Moura&Kleinke (1999), the 1990s were marked by tax incentives and strengthening of infrastructure installation (duplication and maintenance of highways, implementing fiber optics and cellular telephony, advances in the energy sector).ForMatteo& Tapia (2002), in the 1980s, the maturation of Brazilian industrial matrix has decentralized the industry of the São Paulo State with theimplementation of investments outside the state (hydroelectric power plants, steel mills, chemical and petrochemical) or outside the metropolitan area, but keeping the highlight of being the largest Brazilian industrial core. For these authors, the industry of the São Paulo State has stagnated between 1985 and 1999, holding approximately 49.5% of the value of manufacturing of Brazil. Pacheco et al. (1995)agree that other states and the countryside of São Paulo have been benefited from such decentralization. Direct and indirect tax incentives had a key role in this process (exemptions, remissions, infrastructure, etc.). The lack of infrastructure in many regions, the reduction of logistics costs by locating near major metropolis (rather than being inside it) also have contributed to the increased decentralization of the density of the urban network. Thus, it was formed a dense network of highly sophisticated services, concomitantly with the depletion of natural resources and physical space for the implementation and expansion of new industrial plants(ARAÚJO, 2001). Matteo& Tapia (2002) emphasize industries which demand high technology and skilled labor remain consolidated in the metropolis. For these authors, the generation of manufacturing jobs in the countryside of the state results in an increase in urban population, income and quality of life in several micro-regions.Therefore, the states studied here showed a relative strength in terms of economic growth. 3. Methodology

This section describes the methodological procedures, divided into three parts: the data and variables, the models and theexploratory spatial data analysis. 3.1. Data and Variables

The present article used only four variables, namely: • LN_GDP_99: Municipal GDP per capita of 1999, converted into logarithm obtained from the

database of the Brazilian Institute of Geography and Statistics (IBGE); • HK: growth rate of Human Capital (indicated by the enrollment rate of Elementary and High

School per municipalityas a proxy), according to school census data published by National Institute of Educational Studies Anísio Teixeira (INEP);

• PhK: growth rate of Physical Capital (indicated by theindustrial consumption rate of electric energy as a proxy) according to data of IPARDES for the municipalities of the Paraná State, and of State System of Data Analysis for São Paulo.

• SLOPE_GDP: GDP growth rate4, from 1999 to 2010, considered the whole series, according to procedure suggested by Russo, Santos &Parré (2012).

These variables refer to 1044 municipalities, 399 from the Paraná State and 645 from the São Paulo State, for the years between 1999 and 2010. It was not possible to expand the database for previous periods because dozens of municipalities were created in São Paulo State in the mid-1990s. 3.2. Empirical Models

                                                            

4According to the equation: , where the regressed is the logarithm of Y and the regressor is the time, assuming values 1, 2, ..., n. (Gujarati, 2006, p.145). 

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The empirical models applied here were based on Russo, Santos &Parré (2012), and they are derived from the equation that shows the general model:

, ln , 1, … , ; 1, … , 2 Where Git is the SLOPE_GDP, X are the variables HK and PhK,  is the spacial lag, W is the matrix of spacial weight, ln(Yi,t-1) is the variable LN_GDP_99, and  and   are the parameters to be estimated. According to the general model, the speed of income convergence is obtained by the equation (2) and the half-life is given by the equation (3) below:

ln 1 3

ln 2ln 1

4

Where t is the total time of the estimation, θ is the speed of convergence and HL is the time in years that are necessary to reduce the inequalities of local income to half.There are six specific models, derived from the general model, mixing the absolute and the conditional convergence and the estimation with OLS, spatial lag and spatial error:

Table 1: Specific models of convergence of per capita income.

ABSOLUTE CONVERGENCE CONDITIONAL CONVERGENCE OLS ln , , ln , SPATIAL LAG

ln ,

, ln ,

SPATIAL ERROR

ln ,

, ln ,

Source: Elaborated by the authors. This paper tests all the models described above, selecting one of them that seemed to be the best fit to explain the income convergence. 3.3. Exploratory Spatial Data Analysis

The Exploratory Spatial Data Analysis (ESDA) is a set of techniques to statistical analysis of geographical information that allow identifying spatial patterns in data, reveal outliers, and shows clusters. The first of the techniques used was the Moran’s I. By calculating the Univariate Moran’s I, we tested the hypothesis that the growth of GDP per capita for each municipality in the studied region depends on the growth shown in neighboring municipalities, in the degree indicated by the coefficient calculated. The Moran’s I can be displayed in a scatter plot, which may have four different clusters: HH (high-high, when higher values of the interest variable are closer each other), LL (low-low, when low values of it are closer), HL (high-low, when high values are surrounded by low values) and LH (low-high, low values surrounded by high values). The Figure 1 below displays the possible clusters for the scatter plot of Moran’s I.

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Figure 1: Scatter plot of Moran’s I. Source: Russo, Santos &Parré (2012).

Nevertheless, the Moran’s I got some features that may mask a spatial association. Because of this, we also use the technique named Local Spatial Association (LISA), building with it a map of clusters in order to identify spatial units that feature local correlation significantly different from other observations in the data set. Thus, it illustrates the classification of statistically significant observations in the four categories of spatial association presented previously (HH, LL, HL, LH). 4. Results and Discussion The Exploratory Spatial Data Analysis (ESDA) aims to underline spatial characteristics of the data bases. Figure 2 reveals the spatial distribution of the per capita GDP growth of municipalities of the Paraná and São Paulo states in the study period. The distribution of per capita GDP evolution for the period is not homogeneous. The map reveals that municipalities of the São Paulo State presented greater dynamism in growth rate, highlighting the meso-regions of São José do Rio Preto, Bauru, Assis, Itapetininga and the Metropolitan macro-region. On the other hand, the Paraná State stands out by presenting several blocks of regions with low growth dynamism in the period, such as for example the Mid-South, East-Central and Southeast meso-regions. However, only these data are not enough to investigate the income convergence among municipalities. The verification of per capita income absolute convergence demands observation of the spatial distribution of the level of GDP per capita in locations in the beginning of the period, in 1999, which is depicted in Figure 3.

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Figure2: Spatial distribution of the per capita GDP growth (1999-2010).

Source: Elaborated by the authors.

Figure 3: Spatial distribution of the level of per capita GDP from 1999.

Source: Elaborated by the authors. In the initial period, 1999, the spatial concentration of incomes stands out on the axis Santos-São Paulo-Campinas, Piracicaba-RibeirãoPreto (concentration of high GDP), and in the axis called of ‘hunger

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corridor’ of the Paraná State (low GDP). Another highlight in terms of low per capita income is the region of Ribeira river valley, which includes part of both states. The first conclusion, that will be expanded later, is that the São Paulo State includes not only the major of municipalities with higher growth of GDP, as also the higher ones in the initial period. 4.1. Univariate and Multivariate Moran’s SI

By extending the spatial correlation analysis, it is important to establish the most adequate spatial weight matrix, that is, the most suitable contiguity ratio for the studied variables. It was evaluated six alternatives for establishing spatial correlation between variables: queen, rook, two, three, four and five neighbors. According to Moran’s I data, we chose to use the rook matrix that presented the best values, as shown in the table below:

VARIABLE WEIGHT

MATRIX MORAN'S

I EXPECTED

VALUE PROBABITLITY

SLOPE GDP 1999-2010 Rook 0.400485 -0.001 0.01 LN GDP 1999 Rook 0.341141 -0.001 0.01 LN GDP 2010 Rook 0.254467 -0.001 0.01

Table 2: Moran’s I for selected variables related to the São Paulo and Paraná municipalities. Source: Elaborated by the authors. The coefficient values suggest a high positive spatial correlation (ranging from 0.254 to 0.400 according to the variable). Combining these values with the plotted data in the Figure 4, it indicates a subtle concentration of municipalities in the quadrants HH and LL. It may suggest the occurrence of clusters of municipalities with high income and growth and other ones with low income and low growth of per capita income.

Figure4: Scatter plot of univariate Moran’s I for the logarithms of initial (1999) and final (2010) income per capita and of the growth rate in the period. Source: Elaborated by the authors. Nevertheless, this is not a conclusive assumption, and it can be more precisely explored by examining if there are any cluster, with the Local Spatial Association (LISA). This tool is appropriate to capture local patterns of linear association that can be statistically significant. In order to complement the spatial distribution analysis on per capita GDP growth, spatial clusters will be observed to detect points where spatial correlations identified by Moran statistics occur in a more incisive way. 4.2. Identification of Spatial Clusters

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With the use of the rook weight matrix, it was generated a spatial cluster map for the variable per capita GDP growth, as observed in Figure 4. It is seen that 693 municipalities have no significant correlation of clustering. Nevertheless, 198 municipalities had a strong clustering of the low-low type, i.e., municipalities with low dynamism in the period, surrounded by municipalities with similar characteristics. Of these, the vast majority are in the Paraná State, which confirms the statement made earlier that the municipalities of this state showed less dynamism than in the neighboring state. On the other hand, stands out the presence of 113 municipalities organized into a high-high cluster. Through the Figure 5 it can be verified that most are in the São Paulo State. Therefore, besides the greater dynamism in per capita GDP growth for the municipalities of this state in the period from 1999 to 2010, but it was also verified the occurrence of clusters, where municipalities of high dynamism are neighbors of municipalities with also high economic dynamism, measured by the per capita GDP.

Figure 5: Map of spatial clusters for the variation in per capita GDP (1999-2010). Source: Elaborated by the authors. Considering the regional development perspective, the situation of southeastern and central eastern meso-regions of the Paraná State is critical, because they combine low initial per capita GDP (Figure 2) and low growth rate of GDP (Figure 1), forming clusters of low dynamism (figure 4). In this context, these regions lack an effective strategy for a long-term regional development. 4.3. Income Convergence Estimated Models

The Table 3 below depicts estimated parameters for equations with and without correction spatial models, considering absolute and conditional convergence of per capita income.

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Table 3: β-Convergence Tests for Absolute and Conditional Convergence of per capita Income for the Municipalities of São Paulo and Paraná States, 1999-2010.

COEFFICIENTS ABSOLUTE CONVERGENCE CONDITIONAL CONVERGENCE OLS Spatial

Lag Spatial Error

OLS Spatial Lag

Spatial Error

0.13204 0.10260 0.19952 0.13164 0.10162 0.19510 (0.0000) (0.0000) (0.0000) (0.0000) (0.0000) (0.0000)Human Capital 0.04946 0.05559 0.04727 (0.3839) (0.2312) (0.3813)Physical Capital 0.039648 0.04481 0.04833 (0.000017) (0.00000) (0.0000)

0.60715 0.61778 (0.0000) (0.00000)

0.62939 0.64093 (0.0000) (0.0000)

-Convergence -0.00538 -0.00803 -0.01329 -0.00553 -0.00824 -0.01302 (0.0099) (0.0004) (0.0000) (0.0077) (0.00001) (0.0000)Speed of Convergence 0.0056 0.0084 0.0145 0.0057 0.0087 0.0142 Half-Life (Years) 128.8 86.3 52.2 125.4 84.1 53.2 R² 0.0064 0.3197 0.3419 0.0245 0.3451 0.3717

Adjusted R² 0.0054 0.0217 Akaike Criterion -4110.17 -4416.79 -4445.69 -4125.41 -4448.95 -4485.84Schwarz Criterion -4100.27 -4401.94 -4435.78 -4105.60 -4424.19 -4466.03F-Statistic 6.66827 8.70523 (0.0099) (0.0000) White Test 11.5533 69.8770 (0.0031) (0.0000) Jarque-Bera Test 1177.185 894.5769 (0.0000) (0.0000) Source: Elaborated by the authors. In the models for absolute convergence, all the estimated β-convergence showed significance, at a level of 1%, and his signal was negative in all the models, confirming the hypothesis that municipalities with lower per capita income tend to grow faster than other ones with a higher per capita income (which is named as income convergence). Attempting to identify the best econometric model, the Akaike and the Schwarz criteria reveal that the most suitable model for absolute convergence is obtained applying the spatial correction by using the Spatial Error Model ( ln , . According to the results of this model, the speed of convergence is estimated in 1,45% and the half-life is estimated in approximately 52 years, in the absence of changes in development policies, e. g., in 52 years, the income inequalities among studied municipalities will reduce in half. The explanatory power of the model is limited by the indication of the value of R², which suggests that only 34% of the changes in the slope of the income can be explained by the model. However, this is a reasonable estimate, according to the standards suggested by Anselin (1998).When it comes to conditional convergence, it is important to highlight that the variable Human Capital was not statistically significant in all three models (OLS, Spatial Lag and Spatial

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Error). In spite of this, all the estimated β-convergence parameters were negatives, and statistically significant at 1% level. This suggests that the differences among those municipalities reduced in the period of 1999-2010. The coefficient of the Physical Capital variable was significant in all three models, and the more appropriated model was again with the spatial correction with Spatial Error, as indicated by Akaike and Schwarz criteria. According to this model of Conditional Convergence of per capita Income Growth, the speed of convergence was 1.42%, which is similar with the model of absolute convergence. The estimated half-life is slightly higher in this model of conditional convergence than in the preceding model: 53,2 years to reduce in half the inequalities of income. Comparing these results with similar studies, Russo, Santos &Parré (2012) found 63 years of half-life to 1188 municipalities of Brazilian south region, between 1999 and 2008; and Vieira (2010) appointed 58.8 years for the municipalities of the Paraná State in the period 1996-2006. This comparison suggests that the adding of São Paulo State also added more speed of convergence. 5. Final Considerations

The present study sought to verify the absolute convergence of per capita GDP between municipalities of the Paraná and São Paulo State for the years between 1999 and 2010. To this end, it was used techniques related to Spatial Econometrics, specifically the Exploratory Spatial Data Analysis (ESDA).The analysis of the distribution of per capita GDP growth of municipalities of Paraná and São Paulo States in the years studied allowed observing that municipalities that had higher dynamism were predominantly those of the São Paulo State. Moreover, less dynamic municipalities in terms of per capita GDP were those of the Paraná State. In the cluster analysis, it became evident two most significant clusterings of the per capita income: high-high and low-low. The first prevailed in the municipalities of the São Paulo State, whereas the second was more representative in the Paraná State. The more suitable estimated statistical models were those with spatial correction by Spatial Error, and they appear to accord to the hypothesis of convergence of per capita GDP among municipalities in the period. For the absolute convergence, the half-life was estimated in 52.2 years, and for conditional convergence, 53.2 was the estimated half-life. In the second, the correlation between income growth and growth of Human Capital for the period was not statistically significant. In spite of that, the Physical Capital was significant in the regression.The results support the hypothesis of absolute and relative convergence of per capita GDP among municipalities, once municipalities with higher initial per capita GDP were precisely those that presented a greater dynamism in the period. Nevertheless, this study highlighted that the Paraná State clearly needs to change his development policies, in order to promote an acceleration in his growth rate of per capita income in his municipalities. References ALMEIDA, E.S. (2012) Econometria Espacial Aplicada. Campinas - SP: Alínea. ANSELIN, L. (1998) Exploratory Spatial Data Analysis in a Geocomputacional Environment. In: Longley P. et al. Geocomputation a primer. Chichester: John Willey & Sons Ltd, p.77-94. ANSELIN, L. (1999). Spatial Econometrics.Bruton Center, School of Social Sciences, University of Texas at Dallas, april. AZZONI, C. R. (2001). Economic growth and regional income inequality in Brazil. The Annals of Regional Science, 35(1):133–152. Available in: http://ideas.repec.org/a/spr/anresc/v35y2001i1p133-152.html.

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BARRO R., SALA-I-MARTIN X. (1997) Technological Diffusion, Convergence, and Growth. Journal of Economic Growth, 2(1), 1-26 CHI, G. ZHU, J. (2008). Spatial regression models for demographic analysis. Popul. Res. Policy Rev, 027, p. 17 -42. DINIZ, C. C.; LEMOS, M. B. (1990).A dinâmica regional e sua perspectiva de 90: propriedades e perspectivas de políticas públicas. v. 3, Brasília: IPEA/IPLAN. FERREIRA, A. & ELLERY Jr., R (1996). Convergência entre a renda per capita dos estados Brasileiros. Revista de Econometria, 16(1):83–104. GALOR, O. (1996). Convergence inferences from theoretical models. Economic Journal, 106(437):1056–69. Available in http://goo.gl/bwtO5. IPARDES (1997). Dinâmica demográfica da região Sul: anos 70 e 80. IE -Unicamp, Curitiba, PR. JESUS, G. E.; FERRERA DE LIMA, J. (2001). A indústria paranaense no Mercosul. O Prata e as controvérsias da integraçãoSul-Americana. Cascavel: Edunioeste. JUSTO, W. R. (2004). Crescimento Econômico e Convergência de Renda da Mesorregião do Araripe: uma abordagem espacial. LUCAS R E (1988).On the mechanics of economic development.Journal ofMonetary Economics, 22(1), 3-42. MANKIW, N G. et al.(1992). A Contribution to the Empirics of Economic Growth. Quarterly Journal of Economics 107 (may), p. 407-38. MATTEO, M. TAPIA, J. (2002).Características da Indústria Paulista nos anos 90: em direção a uma City Region? Revista de Sociologia e Política nº 18: 73-93 jun. MOURA, R.; KLEINKE, M. (1999). Espacialidades de concentração na rede urbana da região Sul. Revista Paranaensede Desenvolvimento. n.95, Curitiba: IPARDES, jan./abr. PACHECO, A.C.; et al. (1995) A nova realidade regional da indústria paulista: subsídios para a política de desenvolvimento regional. Ensaios FEE, Porto Alegre: Nº 16, volume 1, p. 242-276. PORTO JUNIOR, S. & SOUZA, N. (2002). Crescimento regional e novos testes de convergência para os municípios da região nordeste do Brasil. Available inhttp://www.ufrgs.br/ppge/pcientifica/2002_11.pdf. RIPPEL, R. (1995).Encadeamentos Produtivos de um Complexo Agroindustrial: estudo da Frigobrás-Sadia de Toledo e das empresas comunitárias. (Masters Degree),Curitiba. RUSSO, L. X. SANTOS, W. O. PARRÉ, J. L. (2012). Uma Análise da Convergência Espacial do PIB per capita para os Municípios da Região Sul do Brasil (1999-2008). Anais: XV Encontro de Economia da Região Sul - ANPEC SUL. Porto Alegre: Anpec. SOLOW, R. M. (1956).A Contribution to the Theory of Economic Growth. Quarterly Journal of Economics 70 (feb.), p. 65-94. SOLOW, R. M. (1957).Technical Change and the Aggregate Production Function.Review of Economics and statistics 39 (agosto), p. 312-320. TRINTIN, J. G. (2006).Desenvolvimento regional: o caso paranaense. Anais. XXI Encontro Nacional de Economia. ANPEC. Belo Horizonte. Vol. 2.

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TRINTIN, J. G. (2002).História E Desenvolvimento Da Economia Paranaense: Da Década de Trinta a meados dos anos noventa do Século XX. Available inhttp://www.fee.tche.br/sitefee/download/jornadas/2/e6-04.pdf. VIEIRA, F. L. (2010).Convergência de Renda e Desenvolvimento Regional no Paraná (1999-2006). Dissertação (Mestrado) – Programa de Pós-Graduação em Desenvolvimento Regional, Universidade Estadual do Oeste do Paraná – UNIOESTE, Toledo. About the Authors Jorge Leandro Delconte Ferreira,Masters degree in Strategy and Organizations, at Federal Univesity of Paraná (UFPR) from Curitiba – Brazil. Coursing the Doctorade degree in the Applied Economics Program, at State University of Maringá (UEM). Her main themes of research are Regional Development, Governance, Politics and Policies.Contact Information: [email protected] José LuizParré,Associated Professor in the Department of Economics at UEM. Doctor degree in Applied Economics at São Paulo University (USP). Has experience in the area of economics, with emphasis on Agricultural Economics, acting on the following topics: agribusiness, agricultural development, the Paraná state's economy, input-output matrix and factorial analysis.Contact Information: jlparré@uem.br Maria LuziaLomba de Sousa,Masters degree in Local Development, at Dom Bosco Catholic University from Campo Grande – Brazil. Coursing the Doctorade degree in the Applied Economics Program, at State University of Maringá (UEM). Her main themes of research are Regional Development and Local Development.Contact Information: [email protected]