THE BRAZILIAN STRUCTURE OF INTERDEPENDENCE: AN INPUT- OUTPUT APPROACH FOR THE PERIOD

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1 THE BAZILIAN STUCTUE OF INTEDEPENDENCE: AN INPUT- OUTPUT APPOACH FO THE PEIOD Fernando Salgueiro Perobelli Eduardo Amaral Haddad Guilherme Armando de Almeida Pereira Marina de Lemos Pierini odrigo Antonio Farinazzo TD. Mestrado em Economia Aplicada FEA/UFJF 00/2008 Juiz de Fora 2008

2 The Brazilian structure o interdependence: an input-output approach or the period Fernando Salgueiro Perobelli Eduardo Amaral Haddad 2 Guilherme Armando de Almeida Pereira 3 Marina de Lemos Pierini 4 odrigo Antônio Farinazzo 5 This paper wants to analyze the Brazilian structure o interdependence among the Brazilian states during the period to classiy and identiy the role that each state plays in interregional trade. In order to reach this aim we will use the structure o an interregional input-output matrix or the Brazilian economy. We will use the ollowing measures to analyze the structure o interregional trade: a) direct and indirect interregional interdependence this idea will be developed through the Chenery and Watanabe (958) coeicients; b) the order o interdependence we will use the Streit (969) index; c) asmussen (963) index; and d) the extraction method (Dietzenbacher et al, 993). The empirical results are based on the 996 and 2002 interregional input-output table or the Brazilian states. The nature o this type o data enables us to ocus on the sectoral as well as the spatial dimension o the interdependence.. Introduction The input-output model enables us to analyze the lows o goods and services in an economy. This model is a suitable ramework to identiy interdependence among regions in a country. The model can be regional and interregional. In this paper we will deal with the interregional structure that is appropriate to model the trade pattern. According to Pavia et al (2006) the interregional approach is good to very which are the impacts o a speciic region upon others and which region presents the highest multiplier eect. Furthermore it enables us to better understand the degree o interactions among regions. The literature presents a range o indicators to make the analysis o interaction among regions. We can highlight the contributions rom Chenery-Watanabe; asmussen, Dietzembacher, and others. The Chenery-Watanabe indicators capture only the direct eect (orward the dependence o a region by the supply side and backward the dependence o a region by the demand side). It is well know that the trade lows between regions can, at the same time, induce transactions in other regions. For example, i region i demand inputs rom region j, that We would like to thanks the inancial support rom FAPEMIG and CNPq to develop this research. Department o Economics FEA/UFJF Brazil CNPq Scholar. 2 Department o Economics FEA/USP Brazil CNPq Scholar. 3 esearch Assistant FEA/UFJF CNPq Scholar. 4 esearch Assistant FEA/UFJF. 5 esearch Assistant FEA/UFJF CNPq Scholar.

3 demand inputs rom region k to produce demanded inputs by region i, the region i is indirectly dependent upon region k. In order to improve the analysis, asmussen constructs a new indicator using the Leontie Inverse. This indicator measures the direct and indirect eects. This paper will deal with the idea o interdependence using a wide range o indicators: a) Chenery-Watanabe; b) asumessen; c) Key sector and d) Extraction Method 6. It is important to highlight that we will implement the study in an interregional matrix or the Brazilian economy or the years 996 and Those matrices were elaborated by FIPE (Fundação Instituto de Pesquisas Econômicas). 2. Methodological Aspects and Database In a basic interregional input-output model the total demand can be divided into exports to the rest o the country, exports to the rest o total domestic demand (including inal and intermediate demand). The supply is classiied in imports rom the rest o the country, rom other countries and total domestic production (including inal production X and intermediate). Thus the exports o region i to other countries is denoted by x i, the total domestic demand in region i is d i, the imports o region j to other countries is, the local total production o region j is, and the exports o region i to region j is with =0 and the own use o region I products is included in d i. Thus the equilibrium is: Where represents the number o regions and x i represents the total demand in the region i. The trade between regions can be expressed by an input-output matrix, where the inter-sectoral transactions are changed by interregional ones. In this way, i an interregional transactions and transers matrix x is deined by T, a linear relation or o equation () can be expressed as: Ax y x, 2 Where is a matrix o technical coeicients, is a vector x o total supply, is a diagonal matrix x o total regional demand and y is a vector x o total internal and external demand. The coeicient o matrix A show the marginal propensity o region j to import products o region i and captures the degree o relationship between regions j and i. This matrix shows the direct eects o interregional trade lows. Thus the Leontie inverse shows the indirect eects. 6 For a complete reerence about the dierent types o extraction methodology see Miller and Lahr (200)

4 2. Chenery-Watanabe Indicators: The backward eects were calculated by the sum o each column o matrix A and relect the direct dependence o region j upon the imports rom other regions. In this way, the region that presents a high value or shows a high degree o dependence o imports rom the rest o the country meaning that needs the exports o other regions to satisy the increase in its own domestic demand. egions that present, in relative terms, a high value or will be identiied as imports regions. On the other side, regions that j present a small value or will be considered regions with a small imports potential. j j Backward Eects: 3 The orward eects are calculated through the sum o rows in the matrix.the coeicient measure the relative importance that the demand or the rest o the country has upon the total demand o region i and shows the direct dependence that interregional trade has upon region i. Thus, a high value or the coeicient means that this regions exports more than the others. The regions that present a high value or this coeicient will be classiied as exporter regions. On the other side, regions with small values or the coeicient show a low capacity to export. The coeicient values and its averages enable us to classiy them in our groups. Forward Eects: 4 Table These indicators and its classiications show important inormation. Despite the inormation the Chenery-Watanabe coeicients have a range o restrictions: () the coeicients do not have weight. They do not take into account the relative potential that

5 each region has to modiy the interregional trade low; (2) The coeicients are unable to dierentiate a concentrated trade low in a small group o regions rom disperse trade lows; (3) They measure only the direct eects. (4) It is a general indicator and do not take into account de degree o interactions among regions. Actually we use the Chenery-Watanabe coeicients to show general aspects o dependence instead o show speciic aspects. 2.2 asmussen Indicator: Up to this moment, the analysis takes into consideration only the direct eects. In other to have more precise conclusions, the indirect eects have to be incorporated. asmussen considers explicitly the indirect eects. For doing this the author uses the Leontie Inverse. Backward Eects: 5 Forward Eects: (6) Tem term Iij is the element o Leontie Inverse and means the additional quantity o exports o region i that is necessary, direct and indirectly, due to an additional unit upon the domestic and external demand in region j. In this sense, the condition Ci will happen or regions with high capacity to satisy, through exports, the increase in the domestic demand in all the regions. This kind o region will be considered with a high capacity to impact, orward, the interregional trade. On the other side, regions with G j are regions that to cover an increase in its domestic demand induces impacts above the average in the interregional trade lows. Those regions are classiied with strong backward eects. Using those coeicients is possible to elaborate new regional classiications:

6 2.3 Extraction Method 7 Consider the general case o an inter-regional input-output model with N regions and n productive sectors in each region 8. The model is given by: x Ax where: x the nn-element column output vector. A the nn x nn matrix o input coeicients. the nn-element column vector o inal demand. () The solution o equation () will be: x ( I A) or L where L ( I A) is the Leontie Inverse The output vector is partitioned as ollows 9. ' I ' N ' x ( x,..., x,..., x ) where x I ( x I,... x I i,... x I n The coeicient matrix is constructed as ollows: ) ' A A A N A A N NN (2) The extraction method considers the eect o hypothetically isolate one region upon the output o the rest o the economy. Without loss o generality, let s suppose that the irst region was extracted. Thus, the remaining N- regions will represent the rest o the ' ' ' 2' I ' N ' ' economy0. Hence, we can write x ( x, x ) with x ( x,..., x,..., x ) a n(n-) element column vector. In a similar way, we have: 7 This section is based on Dietzenbacher, et al (993) and Dietzenbacher (997). 8 The regions will be represented by superscripts I,J=,,N and the products by subscripts i, j=,, n. 9 The vector can be partitioned in the same way. 0 In order to represent these regions we will use the superscript.

7 A A A A A (3) Analogous to the equation (3), the Leontie inverse in its partitioned orm is given by L L ( I A) L L L (4) Based on the equation (4) we have: x x L L L L (5a) (5b) With the hypothetical extraction o region, the model in equation () will be reduced and will assume the orm: x A x The vector x represents the product o the rest o the economy or the reduced model. The solution o the reduced equation is: x ( I A ) (6) The dierence between x (equation 5b) and x (equation 6) will give the extraction eect o region upon the product o the rest o the economy. In order to interpret the elements o vector x x, we have to calculate the matrix L as the inverse o partitioned matrix as ollows: L L L L A ( I A ) ( I A ) A L ( I A ) ( I A ) A L A ( I A ) (7a) (7b) (7c) Hence we have: x x L L I A ( ) (8a) ( I A ) A L A ( I A ) The interpretation o the expression x x can be divided into two parts: a) the irst one L describes the production in the rest o the economy that is necessary to (8b)

8 satisy the inal demand in region and b) the second part, L describes the production in the rest o the economy the inal demand in the rest o the economy. L ( I A ) that is necessary to satisy We can observe that the elements o vector x x show the interdependence between the region and the other regions. According to Dietzenbacher et al (993), these interdependencies are undamentally backward in their nature. These can be demonstrated using the matrix A (whose elements indicate the backward dependence o on ) and A (whose elements indicate the backward dependence o on ). In order to better understand the expression x x, we will use the equation (8b) and examine this equation using the idea o interregional spillover eect and interregional eedback eects developed by Miller and Blair (985). To satisy the inal demand in region, this region must produce L. egion does not have all the inputs necessary to reach this level o production. So, with the aim o achieving this production, it is necessary that region purchases inputs direct rom the other regions. The amount o inputs purchased will be A L. To provide these inputs, the production in the rest o the economy is required to I A A L become o the economy.. The same analysis can be made or the demand in the rest Applying the traditional idea o inter-regional eedbacks to region, it is possible to airm that the eedbacks or this region will be obtained by comparing the outputs o region within the inter-regional model to the outputs o region, within the singleregion model. In a mathematical orm we have: x I A x L L (9) Taking the equations (7) and (8) and interchanging the superscripts and we will have: x I A A L A I A x (0) Based on the regional extraction ramework it is possible to airm that the vector x x measures the backward dependence o the rest o the economy on the region. In other words, the vector enables us to measure the impact o extracting, rom the economy, all the N- regions in upon the output o the remaining region., 3. esults 3. Chenery-Watanabe

9 We can veriy that during the period 996 to 2002 the indicator presents signiicant changes in the pattern o interregional trade. Minas Gerais, during the period presents an increase in the imports indicator meaning that the state has a high degree o dependence in the exports o the rest o the country to satisy its domestic demand. On the other side, states as Goias and Santa Catarina do not need the demand rom the other states. We can veriy that, in 2002, Pernambuco state leaving the cluster (exporter region and non importer region) in 996 to classiy in the cluster no importer and exporter region. Despite the existence o Zona Franca de Manaus, Amazonas states present an exports index below the national average. São Paulo presents a high index o exports and a small imports index meaning that the state has a high degree o sel-suiciency. Table Table 2 The results presented above enables us to classiy the Key regions. These regions are regions that have their imports and exports aected by variations in the domestic

10 demand or in the demand o the other regions. In the year 996, Goiás, Paraná and Santa Catarina were classiied as key region. In the year 2002, Minas Gerais was classiied as Key region but Goias and Santa Catarina were not. Amapá and Paraíba presented in 2002 imports index above the national average meaning that those states are dependent rom the exports o the rest o the country. 3.2 Extraction Method In this section we will present the results or the extraction method. There is a wide range o results. The methodology enables us to veriy the ollowing aspects: a) Which is the impact upon all the sectors and regions due to the extraction o industry? b) Which is the impact upon all the sectors and regions due to the extraction o agriculture? c) Which is the impact upon the industry sector located at a speciic region due to the extraction o industry sector? d) Which is the impact upon the agriculture sector located at a speciic region due to the extraction o agriculture sector? It is also relevant to consider the dierences between the bilateral linkages o two states. Thus, in this paper we present results or net backward and net orward dependencies. It is important to emphasize that these dependencies are calculated, or this paper, in intrasectoral terms. More speciic we present the dierences between linkages o two states or the industrial sector. The literature airms that the eect on a small state (or region, or country) o isolating a large state is larger than the reversed eect. For example, i a state F depends more on state I than the other way round, it is possible to airm that F shows a net dependence on I. The net dependence at Brazilian economy is given in Tables 3 to 6. We would like to emphasize that all the results could be checked upon request Net Backward Dependence (Demand side or buying side) We can view the structure o net dependencies or industry by the demand side on Tables 3 and 4. We can highlight that: a) For 996 and 2002 each state shows a net dependence on São Paulo; b) In contrast, oraima is at the other end and shows a net dependence on each other state; c) We can note that, or 996 and 2002, the states located at regions Southeast and South are the states that show a good result in terms o net dependence. In other words the majority o other Brazilian states (located at Northeast, North and Center-west) show a net dependence on those states and d) The structure o dependencies do not present a big change during the period. It should be emphasized that this structure o bilateral dependencies is quite remarkable. Since there are no cycles, the linkages show a clear hierarchical structure o net dependencies. At the bilateral level o the backward application, we ound or the year 996 and 2002 a clear hierarchy o net dependencies between the Brazilian states, with São Paulo being A irst application o this method to the Brazilian economy was Perobelli, et al (2006).

11 at the top and oraima being at the bottom. For example, the net backward dependence o oraima on São Paulo in Table 3 and 4 expressed that, in absolute numbers, oraima dependes more on São Paulo inputs than the São Paulo depends on oraima inputs Net Forward Dependence (Supply side or selling side) Tables 5 and 6 show the results or net orward dependence or the period 996 and It is important to emphasize that this approach is make using the output side. In other words the suppllier s point o view is taken, implying the use o output coeicients. Thus the main results are: a) the hierarchy is quite dierent rom the backward dependence; b) For the year 996 and or the year 2002 oraima is located on the top meaning that oraima do not supply any good or the rest o the economy; c) São Paulo show a net dependence on the majority o the other Brazilian states meaning that the state is an important supplier o goods or the rest o the country.

12 Table 3. Net backward dependencies 996 Net Backward dependence o SP MG J P SC S BA ES PE AM PA GO CE SP MG J P SC S BA ES PE AM PA GO CE MT MS DF MA SE N PB AL O PI AP AC TO Source: Elaborated by the authors

13 Table 3. Net backward dependencies 996 Net Backward dependence o MT MS DF MA SE N PB AL O PI AP AC TO SP MG J P SC S BA ES PE AM PA GO CE MT MS DF MA SE N PB AL O PI AP AC TO Source: Elaborated by the authors

14 Table 4 Backward Dependencies 2002 Net Backward dependence o SP MG S P J SC BA GO ES AM CE PA PE SP MG S P J SC BA GO ES AM CE PA PE MS MT MA PB AL N PI DF O SE TO AC AP Source: Elaborated by the authors

15 Table 4 Backward Dependencies 2002 Net Backward Dependece o MS MT MA PB AL N PI DF O SE TO AC AP SP MG S P J SC BA GO ES AM CE PA PE MS MT MA PB AL N PI DF O SE TO AC AP Source: Elaborated by the authors

16 Table 5 Forward Dependencies 996 Net Forward Dependencies o BA PB AP AL CE O PE AC MA PI N MT BA PB AP AL CE O PE AC MA PI N MT MS SE DF AM TO PA GO ES P MG J SP SC S Source: Elaborated by the authors

17 Table 5 Forward Dependencies 996 Net Forward Dependence o MS SE DF AM TO PA GO ES P MG J SP SC S BA PB AP AL CE O PE AC MA PI N MT MS SE DF AM TO PA GO ES P MG J SP SC S Source: Elaborated by the authors

18 Table 6 Forward Dependencies 2002 Net Forward Dependence o PA MA AC PB PI DF MT AL TO GO O SC PA MA AC PB PI DF MT AL TO GO O SC MS N P AP SE ES CE PE S J AM SP MG BA Source: Elaborated by the authors

19 Table 6 Forward Dependencies 2002 Net Forward Dependence o MS N P AP SE ES CE PE S J AM SP MG BA PA MA AC PB PI DF MT AL TO GO O SC MS N P AP SE ES CE PE S J AM SP MG BA Source: Elaborated by the authors

20 Final emarks The study o economic networks is important, because changing network dynamics are invariably an expression o changes in productivity and competitiveness. This paper tried to understand the role played by the interactions (Brazilian states network) in a broad sense. We use a range o indicators to better understand the Brazilian structure o trade. In this sense we could veriy the importance o São Paulo as an exporter and also an importer. The results also emphasize the dierences among the Brazilian regions. This dierence does not change during the period o analysis. It is important to highlight that this paper is under construction and we can discuss all the other results generated by the extraction methodology. eerences Dietzenbacher, E and Van Der Linder, J.A. Sectoral and Spatial Linkages in the EC production structure. Journal o egional Science, vol 37, n.2, pp (997) Dietzenbacher, E; Van Der Linden, J.A. and Steenge, A. E. The egional Extraction Method: EC Input-Output Comparisons. Economic Systems esearch, vol 5, n. 2. pp (993). Miller,. E and Lahr, M.L A Taxonomy o Extractions. egional Science in Economic Analysis. Chapter 2. pp Elservier Science B.V (200) Pavía, J.M; Cabrer, B and Vila, L.E. Interregional trade linkages and the commercial role: the Spanish case. International Advances in Economic esearch, n. 2 p (2006) Perobelli, F.S; Haddad, E.A and Domingues, E.P. Interdependência entre os estados brasileiros: uma análise de insumo-produto. Economia. Edição SELECTA. (2006).