Productive effi ciency and the future of regional disparities in Brazil

We use Stochastic Production Frontiers to estimate the recent levels and the evolution of productive effi ciency across regions in Brazil. Results are available for agriculture, industry and services, as well as for total production. We observe a substantive effi ciency growth exhibited by agriculture at the national level, which is counterbalanced by the poor performance of services. The regional results show that effi ciency levels still replicate, in general, the regional inequality that marked the country’s history through decades. However, the effi ciency growth reveals new signs of convergence among states, especially for industry, with effects on the aggregate production. This indicates that inequality trends in productive effi ciency may be starting to change.


Introduction
Brazil is a well-known case of a large country displaying quite stable levels of regional concentration and regional inequality (Baer, 2007;Azzoni;Haddad, 2018). 1 In 2014, the Northeast region hosted 28% of the population, and less than 13% of the GDP, and is thus the most visible aspect of the "regional problem" in the country, given its political infl uence.The South and Southeast regions are richer, accounting for 74% of GDP in 2014, and 56% of population.In the last three decades of the 20 th century, some important changes occurred, mainly within the North and Midwest regions, with the expansion of the agricultural and mining frontiers.The fi rst region more than doubled its share in population and doubled its share in GDP, based on logging and mining activities, and cattle ranching.The second more than tripled its share in population, and multiplied by a factor of more than four times its share in GDP, led by the expansion of the agricultural frontier and the establishment of the nation's capital (Brasília) in the region.Even with those events, the levels of disparity have not changed substantially.Monasterio and Reis (2008) indicate that as far back as 1872 the levels of disparities were similar to the present situation.
However, changes occurred in the fi rst decade of the 21 st century in the economic environment within which its regional economies operate that have potential to introduce important elements to change the longlasting disparity scenario.These changes include the opening up of the economy, the reduction and stabilization of the infl ation, with differentiated infl uence in space according to the concentration of poor population, the real growth of the minimum wage, the important social programs of income transferences2 associated to a growth path led by internal consumption and the favorable scenario of commodity prices experienced in the fi rst decade of this century (Ferreira et al., 2006;Silveira-Neto;Azzoni, 2011 and2012).The reversal of the commodity prices trends, in conjunction with the ineffi cacy of the internal economic policy, as well as the political unrest associated with it, led to a serious recession, now in its fourth year in a row, with zero or negative GDP growth rates.This could also produce structural changes with regional repercussions, but it is too early to judge.
Regional inequality within a country is produced by decades of differences in competitiveness among its regions, and changes in this scenario can only come out if the relative competitiveness of regions is altered in a signifi cant way.Studies of regional performance typically use data on GDP, employment or investment shares.These are relevant aspects to be considered, but they only inform on the established competitiveness scenario resulting from decisions taken by productive units in the past.Following the trend in GDP shares to predict future competitiveness could be misleading, for the regional distribution of new investments is not considered.This paper assumes that the future regional distribution of investments follows the recent regional distribution of competitiveness and that it is infl uenced by its trend.In deciding on where to invest, entrepreneurs take into account the observed levels of productivity, and its recent evolution.
As such, regional competitiveness is a better indicator of the future evolution of regional shares in GDP than the regional shares.Productivity is a major indicator of competitiveness and sustainable economic growth (Kaldor, 1970;Jacinto;Ribeiro, 2015).This sets the background for this investigation, which is intended to measure the productivity levels of its regions and how they have changed in recent years.We provide estimates of productive effi ciency levels and trends for the period 2000-2014 for three broad sectors of activities -agriculture, industry (manufacturing and extractive) and services -, as well as for aggregated production.
Most authors reviewed produced results only for specifi c sectors, without considering events occurring in other parts of the economy.This paper contributes to the literature by producing indicators of effi ciency levels and effi ciency trends for the three broad sectors of economic activity simultaneously.We bring information for a period of 15 years after the turn of the century, thus providing evidence on a more recent period, one in which important changes in the national economy were present.We use Stochastic Frontiers to estimate the effi ciency levels, which is also not common in the literature on Brazil.In line with the recent literature on regional studies, we introduce spatial effects in the estimations.Finally, we deal with states, thus providing a fi ne geographical disaggregation of the national results.
The paper is organized in seven sections.After this introduction, section 2 reviews the literature on the measurement of effi ciency at the national level in the country.Section 3 presents the methodology used to obtain regional productivity estimates by sector.Section 4 shows the data and presents the descriptive statistics.Section 5 discusses the estimated levels and growth rates of productive effi ciency.Section 6 debates the possible existence of regional effi ciency convergence.Finally, section 7 concludes the paper.

Effi ciency in the Brazilian economy
Many studies indicate very low, or even negative, growth rates of the Total Factor Productivity (TFP) for the country during recent decades (Gomes et al., 2003;Bonelli;Veloso, 2012;Bonelli;Bacha, 2013;Ferreira;Veloso, 2013).In the 2000s, the studies agree in observing productivity growth, especially from 2008-2010, but at a low pace.From 2010 on, there was even a decrease or close to zero evolution, as a refl ection of the world economic crisis (Bonelli, 2014).De Negri and Cavalcante (2014) explain that, contrary to what happened during the 90s, just half of the per capita GDP growth during 2001-2009 could be explained by productivity gains.According to IPEA (2012), these gains were mostly due to the performance of agriculture.In fact, this sector is a relevant case to look at, given the success of the country in terms of expanding its market share in the international markets.TFP grew at around 2.3% per year in the 1980s, 3.37% in the 1990s and 4.7% from 2000 to 2008 (Bragagnolo et al., 2010;Brigatte;Teixeira, 2012;Gasques et al., 2012).
Most studies analyze productivity at the country level, but very few are able to include the regional dimensions of the problem.Agriculture received the attention of several researchers.Gasques and Conceição (2000) and Gasques et al. (2004aGasques et al. ( , 2004b) ) verifi ed that nontraditional states in the Center-West (MT and MS3 ) and Northeast (PI and CE) were the area that enhanced TFP growth in agriculture between 1985 and 1995.Marinho and Carvalho (2004), despite confi rming the result for the Center-West and adding the South, do not agree with the good result for the Northeast.Vicente (2011) estimated TFP and effi ciency in agriculture in Brazilian states and verifi ed regional convergence of TFP levels between 1995 and 2006, but the states of the poor North and Northeast regions continued to present lower-than-average TFP performance.Felema et al. (2013), using data from the 2006 Census of Agriculture, confi rmed the low performance of those regions and the positive situation of the South and Center-West regions.Bragagnolo et al. (2010) used a Stochastic Frontier model to estimate agricultural effi ciency for Brazilian states from 1975 to 2006.They concluded that strong technical progress and positive effi ciency growth were responsible for expanding the agricultural frontier in the Northeast and Center-West regions.Without specifying any region, Gasques et al. (2004aGasques et al. ( , 2004bGasques et al. ( and 2013)), Gray et al. (2011), Vieira Filho et al. (2005) and Gonçalves and Neves (2007) suggest that intense technological innovations and research, reductions in the labor/capital ratio and improvements in seeds, fertilizers and pesticides were responsible for the substantial TFP growth observed in agriculture.
Studies for manufacturing at the national level stress the high impact of trade liberalization and monetary stabilization on TFP during the 1990s (Kupfer, 1998;Quadros et al., 1999;Feijó;Carvalho, 2002;Rossi;Ferreira, 1999;Bonelli;Fonseca, 1998).According to Bonelli (1992) and Rossi and Ferreira (1999), TFP had an annual increase of 0.8% from 1975 to 1985 and 2.15% from 1991 to 1997.Recent estimates, however, show a decline in performance.Barbosa Filho et al. (2010) observed an annual TFP growth of only 0.72% from 1992 to 2007.Squeff (2012) compares the GDP per capita growth of 1.9% per annum from 2000 to 2009 to the labor productivity growth of the economy of 0.8%; productivity in manufacturing decreased 1.2% per year, leaving to agriculture and services the job of keeping the path of aggregate productivity growth in recent years.Messa (2015) estimates a sharper drop of 1.68% per year from 2002 to 2010.Galeano and Wanderley (2013) separate the industry estimates between manufacturing and extractive activities and conclude that as the former exhibits decreases in labor productivity from 1996 to 2010, the latter increased its performance.As for the regional dimensions of manufacturing, Schettini and Azzoni (2013) indicate that the traditional manufacturing centers are the ones with the highest productivity levels, and that there are no signifi cant signs of changes in this situation between 2000 and 2006.Galeano and Wanderley (2013) consider that despite having enhanced its competitiveness due to trade liberalization, the poor Northeast region presented the lowest labor productivity indicators in 2010, compared to other regions.
Finally, some studies on the service sector highlight the great heterogeneity of its activities, which affect the estimation of productivity (Arbache, 2015;Nogueira et al., 2014;Jacinto;Ribeiro, 2015).Arbache (2015) emphasizes the low performance of this sector and indicates labor productivity growth between 1998 and 2000, followed by a decline from 2000 to 2005, turning positive again since then.Jacinto and Ribeiro (2015) argue that services performed better than manufacturing in the 2000s.Labrunie and Saboia (2016) go further, affi rming that the positive results may have contributed to gains in productivity in manufacturing.Given the recognized heterogeneity of services, results vary substantially across sub-sectors.Technology-intensive sub-sectors are expected to present high rates of productivity growth, and they usually have a low proportion of labor employed, which may explain the positive performance of the service sector.
According to McMillan and Rodrik (2011), developing countries tend to show asymmetry of productivity indicators across economic sectors.As indicated by the results shown above, this seems to be the case in Brazil.Therefore, it is important to consider the different performance of sectors in analyzing aggregate productivity growth.On the other hand, regions are heterogeneous and develop at different paces.Estimating productivity by states provides information on the levels and evolution of regional inequalities.This is the standpoint of this paper, since we consider levels and evolution of productive effi ciency in three sectors across regions in Brazil.We use a panel of 27 regions for the period 2000-2014 to estimate the levels and growth of productivity for agriculture, industry and services.

Methodology
According to Bonelli (1996), productivity can be defi ned as the ratio between the output (goods or services) and the inputs used in the production process, resulting in a Total Factor Productivity indicator.The neoclassical theory considers two main productivity measures: i) marginal productivity, when only one factor of production is contemplated and ii) TFP, which accounts for all the factors of production, in addition to the effi ciency in the production process.Thus, the TFP refl ects improvements in technology, organization of production and change in the use rate of resources and their effi ciency.
Economic effi ciency is the result of two components: i) technical effi ciency -maximization of output, given a level of inputs and ii) allocative effi ciency, which is the ability to combine output and input in great proportions, according to their prices (Farrel, 1957).The technical effi ciency, which is also called productive effi ciency in the literature, is an indicator obtained through the use of Stochastic Frontiers, and relates observed inputs and outputs to an optimal performance.Several authors investigated the different types of effi ciency and the decomposition of productivity changes in technical and allocative changes and technological frontier shifts (Balk, 2001;Lovell, 1993;Färe et al., 1994).From this debate, it is possible to establish a direct relationship between economic effi ciency (and each one of its components) and productivity (TFP).Other factors remaining constant, an increase in technical or allocative effi ciency leads to an increase in productivity.
In this article, we use the technical effi ciency given by the Stochastic Frontier methodology as a measure of productivity.We use Stochastic Frontier Analysis, originally developed by Aigner et al. (1977) and Meeusen and Van Den Broeck (1977) to estimate regional productive effi ciency.For each sector, the general estimated model is: where GDP is the output, L it and K it are the labor and capital inputs, all measured in natural logs.The subscript i represents the units of observation and t represents the year; ds j is the dummy for industry (j=2) and services (j=3); regional fi xed effects are 26 state dummies:4 t is the general trend, assuming values from 1 to 15 (years 2000 to 2014); t k is the general trend interacted with the sectorial dummies (t 2 is the industry trend and t 3 is the services trend). 5he production function indicates the output produced with a given technology and a certain amount of inputs.We use a Cobb-Douglas production function, with the natural logarithm of GDP as the output and the natural logarithm of labor and capital as the inputs.Since we work with panel data (regional sates over time), we add regional and sectoral fi xed effects to account for unobservable and constant effects (Greene, 2004a(Greene, , 2004b)).A general trend component and its interactions with sectoral dummies account for the productivity growth rates for each sector.
The error term is the sum of a symmetric random component and a one-sided ineffi ciency component. 6This implies that the productive unit produces according to its production function, but it is subject to some technical ineffi ciency that takes it away from the frontier.Jondrow et al. (1982) proposed a method to estimate the technical effi ciency for each individual, with the indicator varying between zero (minimum effi ciency) and one (maximum effi ciency).
Finally, since we work with regional data, it is important to check and control for spatial dependence, so we add spatial controls.Franzese and Hays (2007) explain the consequences of estimating non-spatial Ordinary Least Squares in the face of spatial dependence.Ignoring spatial processes in data creates the omitted variable bias, leading to wrong standard errors estimates and the inference invalid (Anselin, 1988;Ward;Gledtisch, 2008;Klotz, 2004).We considered a Spatial X model (SLX), since neighboring independent variables may be affecting the outcome of a certain region.There are six spatial controls, at most, given by the interactions of a spatial weight matrix W with each input (labor and capital).The spatial controls are also distinct by sectors, through the interaction with sectoral dummies.We use the inverse of the distance between regions as weights.

Data
The database is a panel composed of 27 Brazilian states (regions) and three economic sectors (agriculture, industry and services), over the period 2000-2014, resulting in 1,215 observations. 7We use the value added, from the Gross Domestic Product of National Accounts, of each sector/state as the output.The number of employees is the measure of the labor input.For agriculture, we used the censuses of 1996 and 2006, and have interpolated with data from annual surveys; these surveys were also used to extend the series to 2014.For industry and services, we used the population censuses of 2000 and 2010, interpolating the annual values with employment data from yearly surveys on samples of population and fi rms (PNAD and PIA). 8 Due to the lack of better data, the consumption of electricity is used as a proxy for capital in industry and services. 9The proxy for capital in agriculture is the total number of tractors and agricultural machinery. 10We interpolate the stocks measured in the 1996 and 2006 censuses with the annual sales of tractors in each state. 11In order to correct for the different 7 As defi ned by the regional accounts produced by the Brazilian Institute of Geography and Statistics (IBGE), the offi cial statistics offi ce.In our sample, agriculture includes farming and ranching; industry includes manufacturing and extractive activities; services include commerce but exclude public health, social security, education and administration activities.8 Value added is measured in BRL millions of 2013.PNAD -Pesquisa Nacional por Amostras de Domicílios (National Survey on Samples of Households) and PIA -Pesquisa Industrial Anual (Annual Industrial Survey) are also produced by IBGE.We have used PNAD variations in employment by sector/region to interpolate census data for agriculture and services.For industry, we have applied the value added/labor ratio from PIA to the value added given by the Regional Accounts.9 For industry, we used the sum of electricity and fuel consumption from PIA.For services we use data from Ipea, Ministry of Planning, and the Statistical Yearbook of Electrical Energy (Ministry of Mines and Energy), measured in GWH.State proportions are based on the consumption of automotive fuel (gasoline, diesel, ethanol), provided by the Agência Nacional de Petróleo, Gás Natural e Biocombustíveis (ANP).Despite limitations, some authors use electricity as a proxy to capital stock (Barreto et al., 1999;Cangussu et al., 2010;Noronha et al., 2010;Figueredo et al., 2003;Nakabashi;Salvato, 2007).10 Vicente et al. (2001) and Marinho and Carvalho (2004) also use the number of machines.11 Data from the Yearbook of the Brazilian Automotive Industry of Anfavea (National Association of Automobile Manufacturers).The capital stock in agriculture was constructed with data from the agricultural censuses of 1996 and 2006 and annual sales of tractors from Anfavea.We took the stock registered in the 1996 Census and added the state annual sales through 2006.This produced state stocks for this later year that were different from the ones registered by the 2006 census, resulting in distinct growth rates for each state.In order to generate annual values, we have introduced the yearly oscillations in sales of tractors in each state into the geometric growth rates observed in the between censuses data.We did it in such a way that the number of tractors and agricultural machines in 1996 and 2006 in each state are exactly the same as reported in the censuses, but the oscillations in this stock measures of capital (energy, measured in Reais (R$) for industry and in Gwh for services, and number of tractors for agriculture), we have included dummy variables for industry and services interacting with capital. 12By doing so, we take into account the characteristics of each sector in terms of capital usage. 13 Table A2 in the appendix shows the evolution of value added (VA), labor (L) and capital (K) at the national level and some descriptive statistics.The high values of the standard errors reveal the great diversity across regions in each sector. Figure 1 exhibits maps displaying value added, labor and capital levels by states in 2014, the last year of our period of analysis, measured in relation to the national average.With few exceptions, it is clear that the Southeastern and Southern states concentrate the economic activity of the country in all sectors.
Table A3 in the appendix details the annual average of labor productivity by state and sector.Shaded cells are states with an above-average labor productivity.This happens mostly in the states of the Southeast, South and Center-West to agriculture and services and Southeast and South to industry.Bahia and Amazonas are the only ones to have above-average labor productivity in industry outside those regions and Rondônia, Acre and Tocantins to agriculture.from year to year replicate the oscillations in sales observed in each state.From 2006 on, we simply added to the observed stock in 2006 the state annual sales reported by Anfavea.The possibility that tractors could be sold in one state and used in another state is not a problem in the period 1996-2006, since the methodology makes sure the stocks in each state are exactly those reported in the censuses.From 2007 on, this could be a problem.However, the effi ciency results would be biased only if some states had systematic tractor trade defi cits and others, superavits.Our analysis of the period within censuses indicates that the problem is not important, but we really do not have ways to access how serious of a problem this could be from 2007 on.In any case, we found no better alternative to generating state level series of capital stocks in agriculture.12 Several empirical tests were made using different measures of capital for each sector before choosing the best model.For instance, energy consumption was also considered for agriculture and services, but it led to poorer results.According to Arbache (2015), who investigated productivity in the Brazilian service sector between 1998 and 2001, 89% of the fi rms have from 0 to 10 employees.The subsector of surveillance, security and valuable transportation is the largest in terms of number of employees.This is why we used state fuel consumption to distribute energy consumption in the service sector.Not only did this mean we had consistent data, but also better results.13 Since we work with a pooled database for the three sectors, the coeffi cient of capital would represent an average estimate for the three sectors.Since we have different ways of measuring capital across sectors, it is necessary to take that into consideration in the estimations.We did so by interacting capital with sectorial dummies.

National
Table 1 reports the estimated Cobb-Douglas production function frontiers.The fi rst model includes labor and capital as inputs and a trend effect, to account for national macroeconomic shocks in the economy.Given that we use different proxies for capital across sectors, we have inserted sectoral dummies interacting with capital. 14We also differentiate productivity levels and trends by interacting with the sectoral intercept dummies for industry and services.As such, the general productivity level and trend refers to agriculture; the productivity levels and trends for industry and services are given by adding the respective sectoral dummy coeffi cients to the general coeffi cient. 15 As the results from Model 1 show, the coeffi cients of labor and capital are signifi cant, with the expected signs and values.The positive and signifi cant trend coeffi cient indicates the expansion of the agricultural frontier through time.The trend for industry is similar to that of agriculture, and the trend for services is signifi cantly lower.The signifi cant sectoral intercepts (ds2 and ds3) indicate that industry and services present larger productivity levels, as compared to agriculture (constant term). 16 The residual test for spatial autocorrelation using Moran's I statistic indicates the presence of spatial autocorrelation.Therefore, we added regional fi xed effects through intercept dummies to account for unobservable and constant regional effects.We also include two spatial controls as independent variables, as in a SLX spatial model, interacting each input with an inverse distance spatial weight matrix (Model 2).There is no spatial autocorrelation in the residuals of this model, but the spatial controls 14 "2" refers to industry and "3" to services.15 In production functions, the constant term is an estimate of the general productivity level.If we had no intercept dummies in the model, the constant would represent the average productivity level for all sectors.By including sectoral intercept dummies, we differentiate the productivity level of each sector.As explained for the sectoral trend, when the dummies for industry and services are both zero, the constant represents the productivity in agriculture.The productivity level for industry is given by the sum of the industry dummy coeffi cient and the constant.The same goes for services.16 The estimated productivity level for agriculture is -1.695, according to Model1.The estimated productivity levels for industry and services are higher, 3.645 and 5.105 (ds2 and ds3 coeffi cients), respectively.Since we also consider regional fi xed effects, the estimated constant coeffi cient cannot just refl ect the agricultural productivity level.
were not signifi cant.Since Model 1 indicated spatial autocorrelation for agriculture, we differentiate the spatial effects sector by sector (Model 3).The coeffi cients of interest are not substantively different from those in Models 1 and 2. In Model 3, the general trend coeffi cient indicates that effi ciency in agriculture is growing (1.3% per year); the estimated trend for industry, although with a negative coeffi cient (-0.3% per year), is not statistically different from that of agriculture.The trend coeffi cient for services is signifi cantly lower that for agriculture, and shows a negative value (1.3% -2.9% = -1.6%).
The results indicate that a 1% increase in labor causes an increase of 0.58% in output.An increase of 1% in capital leads to an increase of 0.67% in output for services (0.428 + 0.240), 0.52% for industry (0.428 + 0.089) and 0.43% for agriculture (0.428).This is our preferred specifi cation and it will be the one employed in the subsequent regional and sectoral analysis.The intercept dummies for the sectors (ds2 and ds3) indicate that the annual average levels of productivity for industry and services are higher than that of agriculture. 17However, the frontier for agriculture expands at a faster pace compared to the other sectors (although the difference to industry is not signifi cant).This suggests a sort of productive convergence within sectors.The general trend coeffi cient indicates that agriculture experienced the strongest productivity growth in the period, 1.3% per year.
A direct comparison of our results with those presented by other studies is not straightforward.We use both capital and labor as inputs, while the majority of analyses are based on a partial concept of productivity, value added per worker.Moreover, we use state-level data to estimate the national results, which is distinct from the majority of the studies revised.Another source of diffi culty is the fact that we estimate the three sectors simultaneously, while all of the studies reviewed produce estimates for individual sectors.A fourth issue lays on the periods considered, which do not match ours.In spite of these methodological differences, our results are in line with the main fi ndings of those studies at the national level.
The results for agriculture are compatible, in general terms, with the literature presented in the introduction.Gasques et al. (2014), estimating TFP 17 Since the coeffi cients of ds2 (estimated productivity level for industry) and ds3 (estimated productivity level for services) are positive, while the constant term (estimated productivity level for agriculture) of Model 3 is negative.using only data on agriculture, indicate a higher growth rate in the period 2000-2012, but the results point in the same direction as ours.Industry is growing at a similar pace (the difference is not signifi cant, although negative), which replicates the results of Barbosa et al. (2010).Britto et al. (2015), estimating partial productivity (VA/L) only for industry, found that productivity in 2011 was 6.1% lower than in 2003 in that sector.Again, the conclusions are the same as in our case.Galeano and Feijó (2013) indicate declining productivity in manufacturing, especially in lowtech sectors, but their period of analysis is 1996-2007.Productivity in services declined at 1.6% per year, which is compatible with the fi ndings of Arbache (2015) and Jacinto and Ribeiro (2015).
Thus, our national results, which are based on regional data, are consistent with the results obtained in studies developed with national data, giving us confi dence to proceed with the regional analysis.

Effi ciency Levels
The model produces effi ciency level indicators for each state, by year and by sector.Table 2 presents the ranking of states in terms of the average of effi ciency in the whole period.The continuous horizontal line positions the states in terms of the national average; the dotted lines indicate the top, middle and lower thirds.The sectoral average is reported at the bottom of the table.
These estimates provide a rich framework of regional productive effi ciency.It can be seen that the top tier of effi ciency in agriculture includes states in the core of agricultural production in the country, mostly in the extended savannah area in the Center-West (MT, MS, GO) and North regions (TO, AC, AP, PA), which also involves some areas of the Northeast region (MA).The highest effi ciency level, however, occurs in MG, in the Southeast region.The top performer state in Industry is AM, in the North.It hosts a very active free import zone, congregating the world top producers of electronics, pharmaceuticals and motorbikes, with state-of-the-art plants.Traditional industrial states of the Southeast (SP, RJ) and South (RS, PR) regions belong to the upper third, as well as the oil-related states of BA and SE.States which excel in agriculture belong to the lower tier in industry.The situation in services is more heterogeneous.The top performer in these activities is the nation's capital (Brasília -DF), which is the poorest performer in agriculture and is in the lower third in industry.The top performers in industry are typically in the middle tier in services, and the top performers in agriculture are in the lower third.These sectoral levels of effi ciency were aggregated for each state, using the sector's participation in the state value added as weights.Thus, in order to excel at the aggregate level, a state must show high effi ciency in its important economic sectors.The fi nal aggregate effi ciency ranking results are displayed in Figure 2. The top performer is DF, due to its top position in services, its most relevant activity.SP and RJ, which constitute the manufacturing core of the country's economy, come next.Other traditional industrialized states from the South are also in this group (RS, PR).Good performance in services granted four states from the poor Northeast region (PB, PE, CE, RN) a position in the upper tier of aggregated effi ciency.
Figure 2 Aggregate Estimates of Regional Effi ciency Levels Horizontal line represents the national average.
Source: Elaborated by the authors.

Effi ciency Growth
The model provides estimates of average effi ciency growth rates for each state and sector in the period.The results are presented in Table 3.

Economic Efficiency Level
The fast-growers in agricultural effi ciency include states in the Center-West and North regions (AC, AM, RO, MT and MA in the savannah part of the Northeast), where this activity leads the state's economies, and some states in the Southeast (SP) and South (PR, RS).The important states in industrial production do not show high effi ciency growth, which is observed in non-industrialized states (with the exception of MG).Services, again, present a distinct situation, with a mix of rich and poor states in the top tier.
The results allow us important considerations.For decades, the Northeast region experienced low performance indicators, while the Southeast led the high performance of the country.The numbers indicate that the Northeast continues to perform poorly in the period as a whole, but some states from Center-West and North are growing in effi ciency.All the states in the Center-West and Southeast, with the exception of Rio de Janeiro, exhibit above-average growth.Only two states in the Northeast (BA and AL) are in that situation (a petrochemical complex in BA and an ethanol and sugar complex in AL).Despite the high level of effi ciency in services, states in that area have lost effi ciency through time.
The aggregate rates presented in Table 3 are the weighted average of the sectoral rates, using the sectoral participation in the state's value added as weights.The top fi ve growth rates are awarded to states which do not belong to the main economic core of the country, in spatial terms.States in this area come after, with growth rates much smaller than that of the fi rst group.At the other end of the distribution, only states in the Northeast and North regions belong to the group with low growth rates.
Few states actually have rates above the national average, and these are concentrated in the southern regions.Only nine states present positive effi ciency growth in all sectors (RO, AC, BA, RJ, PR, RS, MT, MS and DF).PA is the only with negative rates in all sectors.
The strong positive performance of agriculture in AM was not enough to counterbalance the negative rates of industry and services.The same happens to AP, MA and SE, and, in the case of high growth rates in industry, with PI, CE and PB.Services were responsible for the negative effi ciency growth of TO and RN.On the positive side, services, for ES, and industry, for SC, were the sectors that accounted for the aggregate positive growth of these states.In SP, BA and RS, the above-average aggregate growth rates are led by the performance of agriculture and services.In the poor Northeast region, poor performance is observed in all sectors, but typically agriculture shows the worst performance in this region, followed by services.Figure 3 shows the rank of the growth rates of aggregate effi ciency for the states.Again, a comparison of these results with those produced by other authors is plagued by the diffi culties pointed out earlier.Gasques et al. (2013) estimated TFP in agriculture in the period 2000-2012 for some states, using labor, land and capital as inputs.They found that MG, BA, GO, PR and MT presented above-average TFP growth rates.These states are in the above-average group also in our study, but only PR and MT are in our topgrowing group.In industry, Britto et al. (2015) considered the period 1996-2011, using a partial productivity indicator (VA/L).They found negative growth rates for all macro regions, but the Center-West and the Northeast presented better performance.AM and PA are in the lower tier of our results, a result in line with their fi nding that the North macro region had the most intensive decrease in productivity.The states of MT, GO and MS are in our upper tier, which is compatible with their result for the Center- West macro region.Their conclusion that the Northeast macro region had better-than-average performance is not contradicted by our fi nding that PE, PB, RN and CE are in the upper tier of productivity growth.In spite of the differences in methodology and periodicity, our regional results, in general, are in line with the available evidence.

Regional effi ciency convergence
As mentioned before, some effi ciency results are compatible with the regional disparity levels observed in the country in many aspects, as GDP per capita, poverty, education, as well as in regional concentration.Changing this situation requires that low performing regions improve at a faster rate than high performing regions.The presence of convergence indicates that differences in productivity levels across states will reduce over time.This could happen both at a national upper or lower level, depending on the national trend.If productivity is growing at the national level, as is the case of agriculture, the resulting equality will occur at a higher level of productivity.In the case of services, which show declining productivity, equality would happen at a lower effi ciency level.
In order to analyze signs of convergence in each sector, we have correlated the initial (average of 2000-2002) levels of effi ciency in each state with the estimated effi ciency growth rates, as presented in Figure 4 to 7.
The results for agriculture are in Figure 4.The six states with high initial effi ciency levels and positive growth rates belong to the North and Center-West regions.Two northeastern states, PI and PE, are in the third quadrant, exhibiting low initial effi ciency levels and negative growth rates.While SE, BA and RN, in the same region, exhibit positive growth rates, the Southeastern and Southern states of PR, DF, RS, RJ and SP, show below-average effi ciency levels and positive growth rates.Thus, the situation in agriculture shows slight signs of convergence.A simple regression of the growth rates on the initial levels (2000-2002 average) indicates that convergence cannot be ruled out at the 5% signifi cance level.As can be seen in Figure 4, the larger states in terms of production are in the fi rst quadrant, meaning high effi ciency levels and high growth rates.This indicates that the convergence process will result in higher effi ciency rates in general at the national level.The situation with industry (Figure 5) is closer to convergence, since states with low initial effi ciency levels tend to present higher growth rates, and states at the other extreme, negative rates.AM, home of the free import zone, was the most effi cient in industry, and depicted a negative growth rate.In the same region, AP also presented a negative growth rate.The upper left-hand quadrant receives northern (RO, AC, RR) and center-western states (MT, MS, GO), which, together with the northeastern state of RN and southeastern state of MG, show below-average initial levels and positive growth rates.The economically important states of the rich Southeast (RJ, SP) and South (RS, PR, SC) show above-average initial levels and negative growth rates.A simple regression of the growth rates on the initial levels (2000-2002 average) indicates that, at the 1% signifi cance level, convergence cannot be ruled out.As can be seen in Figure 5, the most representative states in terms of industrial production are in the fourth quadrant, meaning high effi ciency levels and negative growth rates.Thus, the ending result of the convergence process comes with a decrease in the national effi ciency level.The heterogeneous service sector is more complex to analyze (Figure 6).Of the 17 states with above-average initial effi ciency levels, seven presented positive, and ten negative growth rates.The same proportion (60/40) situation is repeated with the below-average states.All the four negative cases of low levels and negative rates belong to the northern region, and GO, in the Center-West, but some positive cases are also from those regions (RO, AC, MT, MS).A simple regression of the growth rates on the initial levels (2000-2002 average) did not indicate signs of convergence.

Initial Efficiency Level
Considering the aggregate of all sectors, displayed in Figure 7, it seems that some convergence is taking place.The northern states of RO, AC and MT display low average initial effi ciency levels, but experienced the highest effi ciency growth rates.However, AP and AM, in the same region, with similar average initial effi ciency, presented negative effi ciency growth rates.States in the right-hand side of the horizontal axis display above-average initial effi ciency levels.In this case, we observe more states presenting negative growth rates.Seven out of the nine northeastern states showed negative effi ciency growth rates.A simple regression of the growth rates on the initial levels (2000-2002 average) indicates that convergence cannot be ruled out at the 10% signifi cance level.These results

Conclusions
We have tackled the question of regional inequalities in Brazil from the fundamental point of view of the evolution of regional competitiveness.

Initial Efficiency Level
Efficiency 0,42 0,52 0,72 0,92 0,62 0,82 years, in order to gather information on their relative positions and the evolution of productivity, as a sign of potential future competitiveness.
We use state-level data for the fi rst time in this type of estimative procedure.Our results show that agriculture is leading the growth in effi ciency at the national level, followed by industry, probably due to the extractive activities.The tertiary sector experiences a decrease in productivity.These aggregate results are compatible with the available estimates based on national data.Thus, our approach provides regional estimates that are compatible with the established national results.
Other contributions of this study relate to the simultaneous estimation of effi ciency for the three main sectors of activity.Other authors have estimated similar measures for individual sectors, ignoring the interaction between sectors of activity.By dealing with a period already into the XXI century, we provide evidence on the possible effects of important changes in the national economy.We use Stochastic Frontiers to estimate the effi ciency levels, introducing spatial effects in the estimations, which is new in the literature of both topics.
The estimated productivity levels indicate that the most productive states are in the richer part of the country, although some exceptions appear in the Center-West and North, mostly related to agriculture.The estimated efficiency growth rates reveal the possibility of changes in the inequality scenario, with some signs of convergence, especially in industry, which may be changing the observed disparity in the aggregate of the economic activities.
Some exceptional cases of success outside the traditional economic center of the country are, in a way, related to government initiatives.These are the cases of the free-trade zone in the North, the petrochemical complex in Bahia, but the most impressive case is the performance of the agricultural states of the Center-West and some border states in the North (RO, AC) and Northeast (MA, RN, BA).The technological development led by Embrapa, the government-owned research institution in agriculture, has created the conditions for states in that region to go from the low productivity agriculture in the past into a state-of-the-art and highly competitive modern activity.More recently, social programs targeting poor families have created a growing demand for wage goods in poor areas, leading to some movement of part of the production of this sort of goods in the vicinity of the new consumption centers.New private investments supported by government programs in the Northeast reinforced this movement, such as automobile assembling plants in Bahia and Recife, the naval industry and a massive petrochemical complex in Recife.Since these factors exerted their infl uence mostly in the 21 st Century, their consequences might only be starting to appear in the most recent trends.
The recent changes are good news, in terms of the excessive concentration of production in the country, as well as in terms of regional inequality indicators.But the changes are too soft to produce relevant changes in the highly concentrated situation observed in the country.Even after two decades of a stabilized and more open economy, the competitiveness situation still, on average, favors the traditional economic core.In spite of the recent progress, the competitive position of peripheral regions is limited by the lack of infrastructure, especially in comparison to the core region (Schettini;Azzoni, 2015).The maintenance of the scenario of high demand for wage goods, propelled by social programs and the implementation of large scale projects, could increase the stress on the limited infrastructure present outside the core region.Surpassing this barrier is a challenge to government, which is locked into a tight budgetary situation.Creative ways of fi nancing infrastructure expansion will have to be designed and implemented, with the necessary participation of the private sector.But the positively changing scenario might make investments in infrastructure in the peripheral regions more attractive to private investors, provided a clean and safe regulatory apparatus is established.Maybe the challenge lies in providing such apparatus in a sound way.

Figure 1
Figure 1 Value added, labor and capital across states, 2014

Figure 3
Figure3Aggregate Estimates of Regional Effi ciency Growth Rates (% per year)

Figure 4
Figure 4 Regional Effi ciency Levels and Growth Rates in Agriculture

Figure 5
Figure 5 Regional Effi ciency Levels and Growth Rates in Industry Azzoni and Silveira-Neto (2005), who, in spite of the difference in period of analysis, concluded that agriculture and services acted in favor of divergence, while industry (especially manufacturing) favored the convergence.

Figure 6
Figure 6 Regional Effi ciency Levels and Growth Rates in Services

Figure 7
Figure 7 Regional Effi ciency Levels and Growth Rates -All Sectors

Table 1
Frontier Results