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Introduction
During the past 20 years, the debate in the literature about the construction of regional input-output matrices has solely centered in the use of a top-down approach, and concentrated in its limitations and possibilities, without exploring new ways to identify a proper methodology for the construction of a regional input-output matrix (I-O matrix) using a bottom-up approach with its reliance on regional data. Furthermore, the discussion was based on the improvement of the implementation of the location quotient and on the application of the restricted additive Schwarz method (RAS), Stone (1963). In fact, it astonishes, that no effort has been done in order to construct a regional I-O matrix using a bottom-up approach.
In spite of this, we began to explore this research topic and elaborated three preliminary articles concerning different methodologies based on bottom-up approaches1, and four articles with miscellaneous topics and the same approach for the construction of regional I-O matrices2.
Thus, to some extent, this article is the outcome of a set of methodological experiences and exploratory analyses whose results were favorable, despite the fact that it is still under development. However, we consider that it has solid elements to support our bottom-up theoretical and methodological approach.
Hence, in this article, our main concern is to develop and implement a methodology for the construction of a multi-sub-regional I-O matrix using a bottom-up perspective. Our proposal is not only concerned with the improvement of the technicalities, but also with taking up the essentials of the regional economic behavior, particularly, the spatial economic concentration at a sub-regional level and its spatial unity, which we propose to be the spatial economic functional unit and the basis under which the regional input-output matrix should be constructed. Furthermore, we pretended to make a comparative analysis between both bottom-up and top-down approaches as well as between their statistical assessments using as a case study the state of Sonora in Mexico.
To make this study, we used the 2008 national input-output matrix, and data from the 2008 national economic census of Mexico, which provides information by state and municipalities3. It is worth mentioning, that the missing information was estimated with data given by the government. In the case of the construction of the regional input-output matrix using a bottom-up approach, we first identified 10 functional economic sub-regions, which are the main spatial economic units. Consequently, we constructed 10 sub-regional input-output matrices with a size of 20 by 20 economic sectors, which led us to construct 100 input-output matrices, 10 sub-regional and 90 inter sub-regional matrices, which were integrated into a regional matrix. It is also noticeable, that the construction of the regional matrix was based on inter sub-regional interactions, that is on intra-regional interactions, in order to compare it, to the matrix constructed by the Sonoran government using a top-down approach. Furthermore, we assume that the main challenge in the construction of a regional matrix has to do with intra-regional interactions, which are at the core of the economic region, given that this is required for the incorporation of the sub-regional spatial differentiation in their analysis, instead of only taking into account the inter-regional interactions. We also believe that inter-regional interactions are very important, but they can never replace the intra-regional attributes. Of course, we have to incorporate them later in our analysis, in order to have the whole picture of the regional economic performance, which means that we have to consider both intra-regional and inter-regional economic interactions.
On the other hand, we analyzed the regional input-output matrix that was constructed, with a top-down approach, and that used the 2008 national input-output matrix as a reference. This matrix was created by the Sonoran government, using a top-down approach based on Flegg and Webber location quotients and the RAS technique as a supplementary tool to compensate for the lack of data.
It is important to mention that the development of our methodology required a considerable amount of analysis and information. Consequently, we present only the most important results of the methodology and the comparative analysis of the economic linkages in the region, differentiating their results according to the implemented approaches.
Literature review
Research problem
The original application of the input-output model was done initially at a national level. However, the interest in extending this application to different spatial units -usually sub-national regions-, led to modifications in the national model, which originated a set of regional input-output models (Sargento, 2009).
The first studies about the construction of regional matrices were carried out using to some extent a combination of both regional and national data and, using in their analysis political and administrative units, such as state, counties, urban and metropolitan developments. According to Miller and Blair (2009, p. 70) the most important theoretical developments were made by Isard (1951) and Leontief (1955). Then, came the studies of Leontief and Strout (1963), Morrison (1974), Morrison and Smith (1974), Round (1983) and Richardson (1985); and finally those of Round (1983), Miller and Blair (1985), Hewings and Jansen (1986).
Miller and Blair (2009), pointed out that there has been an enormous amount of work related to regional input-output. Nevertheless, despite this permanent interest in the literature for methodologies and technics for the construction of regional I-O matrices, there is still nowadays a lack of bottom-up approaches, as well as considerations for the spatial units, which are the basis with which the regional matrices should be constructed.
However, an important exception is the article of Lahr and Stevens (2002), in which they explicitly take into account the economic spatial dimension as well as the concept of spatial economic functional areas in order to discuss the problems that arise from the generation of aggregation errors created in the traditional regionalization of input-output models.
Despite the latter, there is still widespread preference for the use of national data via top-down approaches. Traditionally, regional input-output matrices had been created using national matrices; that is the top-down approach without taking into account the spatial economic units. Despite that it was already pointed out how hybrid methods must be based on regional data (Lahr, 1993; Brand, 1997; McCann and Dewhurst, 1998; Lahr and Stevens, 2002; Tohmo, 2004; Lehtonen and Tykkyläinen, 2014, and Kowalewski, 2015).
Therefore, the debate emerged with the notion of how a regional matrix should be constructed using a perspective of hybrid methods, through a top-down approach, focusing on the one hand in the improvement of the accuracy of Stone's (1963), RAS algorithm, and on the other in the revision of the traditional location quotients, mainly Flegg's 1995 and 1997 quotients.
However, Lahr (1993) had pointed out, that hybrid model constructors should pursue a non-survey model as accurate as possible for any region -using adequate regional purchase coefficients and minimizing data aggregation, as well as using a rigorous methodology-. Actually, we support Lahr's proposal and we also believe in the use of spatial economic units as the basis of the construction of regional matrices, instead of using administrative-political entities, such as states, municipalities, provinces or counties4.
In Mexico, the traditional top-down approach has been applied to most states, geographical regions and municipalities (Dávila, 2002; Fuentes and Brugués, 2001; Callicó López, González, and Sánchez, 2003; Fuentes, 2003 y 2005; Armenta, 2007; Chapa Cantú, Ayala, and Hernández, 2009; Aroche, 2013, and Dávila, 2015).
There is no doubt that these works are very important for the improvement of the knowledge of the construction of regional I-O matrices in Mexico using a top-down approach. However, as it is the case at international and national levels, there are no methodologies for the construction of regional matrices using a bottom-up approach. In fact, from our literature review, we found no empirical evidence of such line of research both at international and national levels, and of any comparative analysis of both methodologies, in order to identify their advantages and limitations. It is generally assumed that the construction of regional input-output matrices should be done using a top-down approach, due to the lack of regional data and a sound methodology for the construction of a regional input-output from "below" -that is, from the region itself-. However, from our point of view, what is really needed is a spatial, theoretical and methodological approach from "below", in order to address the regional analysis and to create a database, from which a regional input-output matrix could be constructed. So, we assume, that the construction of the regional input-output matrix using a top-down approach is inadequate for the comprehension of the economic behavior, structural attributes and spatial characteristics of an economic region, and consequently, it is unsuitable for decision-making in terms of regional and territorial economic policy, due to its inability to grasp the spatial heterogeneity of the regional economic structure and its spatial interactions. Furthermore, it distorts the estimation of the technical coefficients and economic linkages within the region. This is due, mainly to the lack of the spatial localization of sales and purchases between places of origin and destination within the region and between sub-regions, which arises from a sectorial bias, which in turn, is it inherent to regional input-output matrices constructed according to a top-down approach.
Hence, our main interest is to develop and apply a line of research for the construction of regional I-O matrices using a bottom-up approach, and thus show its differences and advantages when compared to the top-down approach. We do this by presenting a methodological proposal for the construction of a regional input-output matrix using a bottom-up approach and its statistical assessment.
Location quotients and the debate about the construction of a regional I-O matrix using a top-down approach
The essence of its application
The traditional location quotient (r ij ), as an estimator of regional trade5, is a function of the regional propensity to consume (C ), of the inputs (j ), bought from national suppliers (i ), multiplied by the national technical production coefficients (a ij ), which is denoted as follows:
(1)
where c ijaij = (1 - m ij )a ij ; i are the sales; j are the purchases; c ij is the regional propensity to consume, 0 ≤ c ij ≤ 1; m ij is the regional propensity to import, 0 ≤ c ij ≤ 1.
However, non-survey methods for the estimation of r ij , typically make the assumption that the coefficients a ij can be obtained from the national input-output matrix. This implies that there are no differences in technology levels between region and nation, which means that the only task when specifying the regional intermediate matrix is the estimation of regional propensities to consume, through the calculation of a simple location quotient (SLQ), that in its simplest form, states the following:
(2)
where
Finally, the cross industrial location quotient (CILQ) is used to estimate the regional propensity to consume, and is calculated as the ratio between both i and j simple location quotients, which is expressed as follows:
where
The use of the RAS technique as an estimator of regional trade, is applied when regional data is incomplete, whereas the location quotient is commonly implemented without regional information derived from regional transactions (West, 1990).
Main discussions and proposals
Consequently, Flegg, Webber, and Elliot (1995), pointed out that the use of the traditional location quotients (LQ) for the estimation of the regional input-output coefficients from national data leads to an overestimation of the regional multipliers, caused by the disregard of the relative size of the regional sales and purchases and by wrong and inadequate estimations of data aggregation. Thus, in order to improve the location quotient to generate regional input-output matrices, they proposed a set of changes in the traditional LQ, using as a case study the English county of Avon.
They adjusted the traditional LQ when incorporating the economic size of regions, compared to the countr's size: and created the Flegg's location quotient (FLQ).
The Flegg's location quotient, FLQ ij , is a function of the product of the crossed-holding location coefficient, CILQ ij , multiplied by lamda (λr∂), and by the national technical coefficients, a ij , which is denoted as:
(4)
where λr ∂ is an algorithm that takes into account the economic size of the sub-region.
The interpretation of the FLQ is related to the definition of a degree of the provision of regional's supplies (t ij ) with the following relationships:
Thus the regional trade coefficients r ij , are estimated with:
(5)
The estimation of the crossed-holding location coefficient is stated as follows:
(6)
If CILQ ij > 1, then the requirements for input i by the industry j , are obtained inside the region.
If CILQ ij < 1, then the requirements for input by the industry j , are imported.
The regional economic size λ is estimated essentially with regional economic specialization coefficient with respect to the nation's, which is the ratio of regional total output (Et r) to national total output (Et n), and weighted by the factor log2,
which is derived as: where
However, Flegg's methodology was criticized by Brand (1997), who pointed out that the FLQ has a weak theoretical base and poor empirical pedigree. He believes the FLQ offers little to cure the fundamental deficiencies of the genre., and that research funds would be much more effectively employed in any form of survey-based analysis.
The response of the authors, was that the foundation of the FLQ's cross-holding quotients are theoretically appropriate, and that their approach provides a rigorous basis for the testing of the traditional assumption of identical regional and national technology levels.
However, they actually accepted the need to improve the FLQ, in order to give more importance to the different weights of both national and regional economic sizes.
Thus, they developed a reformulation of the FLQ, the RFLQ, Flegg and Webber (1997), which attempted to improve the measurement of the economic size of the region and to avoid the underestimation of regional imports, as well as not allowing the overestimation of the regional multipliers. Hence, the original FLQ was changed, first by improving the estimation of the scalar λ in the original FLQ and second by substituting the crossed holding coefficients, CILQ ij , with the simple location quotient, SLQ i , which is derived as:
(8)
where
However, the interpretation of the RFLQ was similar to the FLQ ij , so they derived the following relationships:
Thus, the regional trade coefficients, r ig , are estimated with:
(9)
Flegg and Webber consider that a value of δ must be near 0.3 in order to minimize the regional differences; this appears to have empirical evidence according to Sánchez Torres (2014) 6.
Despite this improvement, McCann and Dewhurst (1998) raised some concerns about the FLQ formula for the estimation of regional coefficients from national data. They argued there is a need to consider regional specialization when modeling regional economies. As a response, Flegg and Webber (2000) in "Regional size and regional specialization and the FLQ formula", pointed out "(...) empirical work using Scottish data shows that the inclusion of a measure of regional specialization in lq-based formulae does not yield more accurate estimates of regional coefficients. We find too that the FLQ invariably outperforms its main rivals, the SLQ and CILQ".
In an applied research to Finland, Tohmo (2004) validated the conclusions of Flegg and Webber (2000) when comparing the survey-based regional input-output coefficients and production multipliers published by Statistics Finland, to estimates obtained through the application of LQ to national data for the construction of the Keski-Pohjanmaa region. The results led him to support the FLQ quotient as a much better regional input-output coefficient and multiplier than the SLQ and CILQ.
However, contrary to the last argument, Lehtonen and Tykkyläinen (2014) concluded that the core of the problem is the lack of regional information when estimating the simple location quotients. They presented an evaluation of four location quotient regionalization techniques applied in twenty Finnish regions, and addressed the issue of the impacts of the region's properties on the results of the regionalization process. They concluded that the results do not allow for a generalization in any of the four location quotient techniques and would always yield the best results, but they do indicate that the attributes of regions can give information that should be taken into account when selecting the best possible regionalization technique.
Controversially, Kowalewski (2015) in a study applied to Federal Germany, gave empirical evidence on the use of the FLQ formula, pointing out the advantages of the industry-specific FLQ (SFLQ).
Finally, Flegg and Tohmo (2016) re-examined the evidence presented by Lehtonen and Tykkyläinen (2014) about the use of the lqs for the estimation of regional input coefficients and multipliers and stressed out that their evidence is erroneous and that the Flegg's location quotient, yields far superior results, so it should provide a more satisfactory way to generate an initial set of input-output coefficients. The choice of a value for the parameter δ is also examined.
From this review it is clear that the debate has only focused in the advantages and limitations of the main location quotients for the construction of a regional I-O matrix, using only a top-down approach, without any attempt to construct regional matrices using a bottom-up approach, showing their results and making statistical assessments concerning their differences, limitations and advantages.
Methodology for the construction of regional input-output matrices, using a bottom-up approach and its interpretation
The analytical orientation of the construction of regional input-output matrices is based on a theoretical and methodological approach of the economic concentration, which is part of the broader perspective of the spatial dimension of the economy, that we have been developing (Asuad Sanén, 2014, pp. 312-319; Asuad, 2001, pp. 137-158). The main concept of this approach is economic space as well as its derivative economic concepts, territory and region.
Therefore, we assume that economic development and growth tend to be unbalanced, due to the heterogeneity of both natural and economic space; it is not homogeneous or politically bounded to states or municipalities, and given that the spatial distribution of economic activity is highly concentrated in very few areas, economic and population nodes emerge. These are characterized by their economic interactions through production, exchange and consumption. Thus, a node or hub is defined as a site or place, whose economy is characterized by its economic dominance over and connection with a set of minor economic sites that interact and compete with each other, whereas a traditional economic site is defined as a place on the economic space, where economic activities are highly concentrated and from which a set of economic impulses are exerted through economic exchanges; this guides the spatial economic behavior as a whole.
Economic nodes are spatial economic sub-units distributed in a given geographical or political space, with extremely dense economic activity and demographic concentration. Indeed, they behave as the centers of a given market area where most of the spatial concentration of production and consumption are located. Furthermore, they are connected by the economic flows established among them, which as a whole integrate the economic space.
The economic importance of nodes depends on their economic interaction, which is an outcome of the type of connection and market relationships they establish. These can be thought of as economic complementarities or competition among themselves, or just a mixture of both economic interactions. If these interactions were relevant, they would lead to the creation of sub-economic spaces. Therefore, economic space, in order to exist, requires at least the existence of a pair of economic sites or nodes, interacting with each other. Of course, they do not coincide with any geographical or political unit, despite their influence on economic decision-making processes. Only those economies based on market behavior and territorial development define how the economy as a whole is structured in space.
These can be measured with their economic interactions, mainly purchases and sales carried out by companies and consumers. This sectorial-spatial economy and its synergy with the natural and territorial space in a given area, leads to the development of region or sub-regions, integrated by a system of cities and networks of transportation routes, that link them.
In a generic way, the development of regions as spatial economic units is defined as spatial economic functional units , SEFU7, which are an outcome of economic growth and development on space, that is to say, the economic space as a whole. Thus, the development of this spatial unit allows us to know how economic activities have been spatially distributed, defining the spatial structure and behavior of their economy.
According to this theoretical framework, we propose a methodology for the construction of a regional input-output matrix using a bottom-up approach, which has the following steps:
Identification and demarcation of SEFU
The identification and demarcation of the spatial economic functional units of the spatial economic system within a region, requires the specification of the importance and economic specialization within the region as well as its spatialization, by pointing out the particularities of their location. We do this, first, through the identification of nodes and areas of influence, using an index of concentration of economic activity and population, and second, through the establishment of areas of influence, assuming that the pair of nodes which are spatially near are in competition with each other, and taking into account their size and distance with the application of a Reilly index. Actually, as already mentioned, this is the economic space. However, in the first step, we analyzed the economic structure of Sonora, and later we characterized the role and importance of its economic and population nodes as well as their areas of influence. This led us to identify the functional economic spatial units within the region of Sonora. The concentration index is just a result of a ratio between the share of the output of a sub-region (q ir ) in total sub-regional output (q jr ) divided by the same national proportion, which is denoted as:
(10)
where r represents the region or sub-region, and n represents the nation.
The Reilly Index (Asuad, 2016, pp. 362-364), which measures the border between two a pair of nodes that compete with each other, is a function of an inverse relationship between size and distance between them, and is denoted as:
(11)
where BP is the border point; Pa is the population site a ; Pb is the population site b ; Da is the distance to the site a , and Db is the distance to the site b .
Construction of a sub-regional matrix using a bottom-up approach
In order to do this, we used the Mexican economic census to gather regional data from each sub-region at the sub-sector level, or in other words, data coded with three digits according to the Industrial Classification System of North America (NAICS). Then, we estimated the trade coefficients between subsectors at sub-regional level including the sub-regional economic specialization index, which was complemented with a basic accounting framework, in order to apply a set of identities of the regional input-output matrix, at sub-regional level, as the basis for the construction of the sub-regional I-O matrix.
The estimation of the trade coefficients within sub-regions is done with a crossed relative economic specialization quotient (WCLQ) between any pair of economic sectors of the sub-regions, in order to assess the probable economic importance of the transactions of economic sectors given their economic specialization and taking into account their possible economic association as an indirect weight for the calculation of the technical coefficients of production of the economic sectors. This is done just by the transposition of the weighted quotient in a matrix form by economic sector, using in this analysis, the traditional array of rows and columns. In the case of the size of the economic activity, we applied a semi logarithmic quotient in order to measure the relative size of the economic sub-region in terms of the region, which is denoted as:
(12)
For the analysis of the regional economic specialization of Sonora, we used the quotient of economic specialization (Iee), which is the ratio between the economic specialization of the sub-region in the economic activity i and the same ratio at regional level; this is defined as follows:
(13)
However, this was developed taking into account the average value of the economic activities of the Sonora sub-region compared to the total production of the sub-region. Notwithstanding, the interpretation of the location quotient is the same, thus the coefficient value is equal to or greater than 1.
Thus, the interpretation of the WCLQ ij
has to do with the definition of a degree of the provision of sub-regional's
Therefore, the sub-regional trade coefficients, r ij , are estimated as the product of the sub-regional provision of supplies, t ij , multiplied by the sub-regional output (P i ) of the subsector, and defined as:
(14)
Hence, in a matrix form, we have the following expressions:
(15)
Basic sub-regional economic accounts
With the economic data from the most recent Mexican economic census, we formulated four basic sub-regional economic accounts, in order to estimate the most important economic transactions of the economic sub-regions of the Sonora region. This is the basis for the construction of the identities from which in turn, we constructed the sub-regional matrices with data from the municipalities (Sonora has 72 municipalities).
i) Sub-regional product account.
It is worth mentioning that the consumption of families and companies (C ) is obtained with the differential between production (P ) and local investment (I ) plus net exports (Xn ).
P = Production, C = Consumption, I = Investment; Xn = Net exports
ii) Sub-regional income and expenditure account.
(18)
(19)
(20)
Thus, regional income, Y , is equal to consumption, C , plus savings (S ); and the total of regional savings, S , results from the difference between production, P , and consumption, C .
Y = Income, S = Savings, G = Expenditure
iii) Sub-regional savings and investment account.
(21)
(22)
This account is based on the assumption that savings, S , are equal to investment, I , so that, when local savings are insufficient to finance investment, the difference will be borrowed from outside of the region.
Ii = Local investment, Ie = External investment
iv) Sub-regional exports and imports account.
(23)
This account is nothing more than the net balance (Bc ) between regional exports (X i ) and imports (M m ) in which regional exports are assumed to be related to national exports and imports to a mixture of purchases outside the region, both national or international.
Bc = Net commercial balance, X i = Regional exports, M m = Regional imports
Therefore, the sub-regional accounts, lead to the establishment of the following accounting identities of the sub-regional input-output matrix.
Total sub-regional supply:
(24)
R s = Regional supply, M = Imports
Total sales:
(25)
V = Sales, Vi = Intermediate sales, Vf = Final sales
Total sub-regional demand:
(26)
Total purchases:
(27)
v) Sub-regional production at factor costs.
(28)
(29)
I = Intermediate cost, VA = Value added, W = wages,
P = profits, t = taxes and subsidies, m = imported inputs
The construction of a multi sub-regional matrix of the economic region of Sonora
At this stage, purchases and sales between sub-regions are identified through the application of a Moran index of economic interactions, which is validated by the measurement of the spatial dependence between the data of the economic sub-regions. Subsequently, the multi sub-regional matrix was constructed with the use of the technical coefficients of the sub-matrices as a diagonal matrix of the set of the sub-regional matrices of Sonora. Hence, this diagonal matrix integrates estimated purchases and sales of the region, and it is shown above and below the main diagonal of the arrangement of the system of sub-regional matrices. Finally, the RAS method (Appendix 3) was applied in order to obtain the values of the region, applying the traditional way, so purchases were estimated using the total production and purchases through value added.
The construction of the weighted distributions of the sectorial participation in each of the sub-regions, in order to have a measure of the importance of both economic sectors and subsectors in the sub-regions, and use it in order to have a measure of the relative size of the sectors and subsectors in the economy of the sub-regions.
where SEI is the spatial economic interaction;
This stage has the following steps:
For the construction of the multiple sub-regional matrix (MSE), we started with the sub-regional input-output matrices [15] and converted them into technical coefficients in the main diagonal on [30], or
(31)
2. Find the values of the matrices of sales
The economic activities are differentiated by their diverse economic distribution among sub-economic regions, so we have an unbalanced economic participation of the economic activities.
The economic interaction between a pair of sites can be thought of as spatial dependence if it is established that purchases and sales between two sites are economic flows that are determined by the functional economic interaction of the two sites.
3. Find an economic specializacion indicator
4. The estimation of the spatial dependence between economic sub-regions and their economic activities, which is done first, through the application of a local Moran Index (I) (Appendix 2), that identifies the spatial correlation between sectors of a pair of sites, based on their physical distance. This coefficient is essential since it allows us to identify purchases and sales between subsectors and between sub-regions, as it is shown in a spatial correlation, which in literature is known as spatial dependence. We assume that this measure accurately reflects the flows of trade of the subsectors of economic activity between sub-regions.
5. The estimation of the economic interactions between economic sub-regions, through purchases and sales of their economic activities, taking into account in their analysis a pair of economic sub-regions. In order to do this, we multiplied matrix I (spatial correlation matrix), with matrix Eijrs(the weighted participation of the economic activities matrix), in order to obtain the SEI of purchases and sales of the economic sub-regions.
6. The estimation of the MSE through the integration of the sub-regional matrices of the region, Rijrs, matrices of purchases, Cijrs, and sales, Vijrs, from SEI, into the traditional matrix arrangement for the multi-regional matrix, which consists of the following:
(32)
where mse represents the multiple sub-regional matrix in terms of coefficients of intra-sub-regional and inter-sub-regional trade.
7. Finally, the application of the RAS technique (Appendix 3) to the mse matrix, in order to convert it into the spatial economic interactions matrix, based on the transformation of the spatial economic interactions coefficients into production, commerce and consumption, in monetary terms.
Statistical assessment of both bottom-up and top-down regional matrices of the sonora region
Type of analysis
We did a comparative analysis between both approaches through the identification of chains and economic links. Therefore, two input-output matrices were analyzed: 1) The regional input-output matrix constructed by the Government of Sonora (Bracamontes Sierra and Sánchez G., 2011), using a top-down approach, without sub-regional divisions, and 2) The regional input-output matrix of Sonora constructed with a bottom-up approach, integrated with 10 economic sub-regional units.
In order to evaluate these chains and their linkages we used the traditional approach of sectorial classification of Chenery and Watanabe (1958). For this, we calculated the effects of complete interdependence, through the input-output inverse matrix, which is designated as Z ij .
The traditional classification of Chains, whose effects are above average are classified as follows:
Base sectors refer to industrial activities with high forward linkages and low backward linkages.
Key sectors refer to economic activities with strong linkages both forward and backward.
Sectors of strong drag refer to activities with low forward linkages and high backward linkages.
Independent sectors are activities with low linkages, both backward and forward.
Thus, the sectorial classification of the activities was established, taking into account the use of each branch of intermediate inputs according to their average value of production (μ), and the final destination of the average value of intermediate products (ω) of each branch of economic activity. Thus, we have the following indexes:
where Z j is the production of branch j , and Z ij are uses of branch j of inputs of branch i .
where Z j is the production of branch i , and Z ji are uses of branch i of inputs of branch j .
Therefore, according to the relationships between μ and ω we have the following classification:
Comparative analysis of backward and forward economic linkages of the economic sectors in both national and regional matrices
The statistical assessment of the regional input-output matrices was done by applying the Watanabe and Chenery approach first to the 2008 national input-output table published by INEGI, and second, to the regional matrices constructed by implementing the bottom-up approach and to the regional matrix constructed by Government of Sonora, using a top-down approach.
Analysis of the economic linkages in each matrix
The results of these economic linkages are analyzed in order to compare them to the observed economic structure of Sonora. In consequence, four tests of hypotheses were applied to see whether the regional matrices constructed using both top-down and bottom-up approaches showed similar averages in their economic sectorial linkages to the national matrix.
We expected that the regional matrix constructed using a top-down approach had a similar economic structure and linkages to the national matrix. However, in the matrix constructed with a bottom-up approach, not only did we expect it to be different to the national matrix, but also to describe the economic structure of Sonora with greater accuracy, because in its construction it takes into consideration the observed elements of the economic structure of the State of Sonora. These assumptions are confirmed in the following 1.
As shown in Table 1, the national matrix has seven key chains and two linkages while the regional matrix constructed using a top-down approach has three key chains, three linkages, and two base chains. Finally, the matrix constructed using a bottom-up approach has four key chains and one base chain.
Table 1
| Sector | National | Sonora top-down | Sonora bottom-up | Sonora | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| BL | FL | Type | BL | FL | Type | BL | FL | Type | Product share % | |
| Primary sector | 2.2 | |||||||||
| _112 | 0.4 | 0.4 | Ind. | 0.2 | 0.1 | Ind. | 0.3 | 0.3 | Ind. | 1.5 |
| _114 | 0.1 | 0.1 | Ind. | 0.0 | 0.0 | Ind. | 0.1 | 0.1 | Ind. | 0.7 |
| _115 | 0.0 | 0.0 | Ind. | 0.1 | 0.0 | Ind. | 0.0 | 0.0 | Ind. | 0.0 |
| Secondary sector | 64.7 | |||||||||
| _2 | 3.0 | 3.5 | Key | 0.7 | 5.1 | Pull | 3.5 | 2.2 | Key | 25.9 |
| _311 | 1.8 | 3.4 | Key | 1.5 | 3.8 | Key | 0.6 | 0.7 | Ind. | 6.0 |
| _312 | 0.3 | 0.5 | Ind. | 0.7 | 0.8 | Ind. | 0.7 | 0.6 | Ind. | 3.1 |
| _327 | 0.7 | 0.3 | Ind. | 0.1 | 0.2 | Ind. | 1.9 | 2.2 | Key | 2.2 |
| _331 | 1.5 | 0.7 | Pull | 0.7 | 0.3 | Ind. | 0.5 | 0.5 | Ind. | 6.6 |
| _332 | 0.9 | 0.4 | Ind. | 0.5 | 0.2 | Ind. | 0.6 | 0.7 | Ind. | 2.7 |
| _334 | 1.8 | 1.4 | Key | 1.8 | 0.8 | Pull | 4.7 | 5.9 | Key | 3.1 |
| _336 | 1.1 | 1.6 | Key | 6.3 | 0.5 | Pull | 0.2 | 0.1 | Ind. | 13.2 |
| _339 | 0.5 | 0.4 | Ind. | 0.8 | 0.3 | Ind. | 1.0 | 0.9 | Pull | 1.9 |
| Tertiary sector | 33.0 | |||||||||
| _43-46 | 3.3 | 1.0 | Key | 2.6 | 1.6 | Key | 1.1 | 1.0 | Key | 15.0 |
| _48_49 | 1.2 | 1.3 | Key | 1.0 | 0.7 | Pull | 0.5 | 0.6 | Ind. | 1.9 |
| _51 | 1.2 | 0.5 | Pull | 0.4 | 0.9 | Ind. | 0.7 | 0.9 | Ind. | 3.6 |
| _52 | 1.3 | 1.1 | Key | 0.6 | 0.5 | Ind. | 0.0 | 0.0 | Ind. | 0.3 |
| _53_56 | 0.0 | 0.8 | In. | 1.4 | 1.6 | Key | 0.7 | 0.8 | Ind. | 4.9 |
| _6 | 0.0 | 0.6 | Ind. | 0.1 | 1.3 | Pull | 0.3 | 0.3 | Ind. | 2.3 |
| _7 | 0.4 | 0.7 | Ind. | 0.2 | 0.8 | Ind. | 0.6 | 0.8 | Ind. | 3.3 |
| _8 | 0.5 | 0.2 | Ind. | 0.2 | 0.3 | Ind. | 0.3 | 0.3 | Ind. | 1.7 |
Note: BL = backward linkages; FL = foward linkages.
Source: own elaborations base don data from the 2008 national input-output the 2008 matrix of Sonora and the Censos Económicos 2009 of the INEGI. See Apendix 5 for the code of the economic sectors.
However, if we look at the following graphics we see clearer similarities between the information generated from the matrix constructed using a top-down approach with the national matrix, and differences between the latter and the one constructed using a bottom-up approach.
The key sectors for both the regional and national matrices are Food industry (311) Wholesale trade and retail (43-46), Professionals in Real Estate services, Corporate and Business Support and Waste management and Waste.
While the comparison of the graph of sectoral linkages with information from the national grid and built from below, it is observed that in key sectors have in common only two on Mining (2), Wholesale trade and retail (43-46). This comparison is true but given the importance of mineral at the regional level, as well as services in general.
However, this analysis is not rigorous enough to find out the statistical differences between the regional matrices with the national one, thus we apply the two -tailed test hypothesis, in order to look for them.
Statistical assessment of the two-tailed test hypothesis
This test is also known as non-directional hypothesis , and it is a standard test of statistical significance, which means that the differences in the results do not occur randomly. Succinctly, two-tailed tests divides the 0.05 probability value (p) into two and puts each half on each side of the bell curve in order to determine if there is a relationship between variables in one of the directions (See Appendix 4). So, it does not predict whether the parameter of interest is greater or less than the reference value specified in the null hypothesis. Hence, with this statistical assessment of the regional matrices constructed using both bottom-up and top-down approaches we wanted to determine if their economic linkages are on average different or similar than the national matrix, in order to identify if the regional matrices were similar to the nation, assuming that if this is the case there would be no difference between the region and the nation. Therefore, we concluded that is just a change of scale from regional level to national, and inadequate for economic regional modeling or regional policy and planning.
According to the results of the two-tailed test hypothesis analysis, we have the following results:
Test I. Backward linkages:
1.The average backward linkages observed in the state matrix constructed using a top-down approach are very similar to the backward linkages of the national matrix.
2.The backward linkages observed in the matrix constructed using a bottom-up approach are on average, different than the observed linkages in the national matrix.
Test II. Forward linkages:
3.The forward linkages observed in the state matrix constructed using a top-down approach are very similar to the forward linkages observed in the national matrix.
4.The forward linkages observed in the matrix constructed using a bottom-up approach are on average, different that the observed linkages in the national matrix.
Test III. No linkages:
5.The independent sectors observed in the state matrix constructed using a top-down approach are very similar to the independent sectors in the national matrix.
6.The independent sectors observed in the matrix constructed using a bottom-up approach are different on average to the observed sectors in the national matrix.
Test IV. Forward and backward linkages
Concluding remarks
It is observed that there are important differences between both regional matrices. The top-down regional matrix is more similar to the national matrix in terms of economic linkages. Furthermore, significant differences arise from the regional matrices, in terms of the backward linkages and independent sectors, which is closer to the national case (top-down matrix). Therefore, we conclude that this article shows empirical evidence to support the need for the construction of regional input-output matrices constructed using a bottom-up approach. This is already in a methodological proposal we made, despite the need for more simplification and operationalization procedures for its application. We think this shows a more accurate perspective of regional structures than the top-down matrices.
Although this article is an outcome of a set of methodological experiences that are still in process of review and discussion, we believe we present solid elements to support our bottom-up theoretical and methodological approaches; we also believe there is still a need to use this topic as a new line of research for the construction of regional input-output matrices.
According to our view, the main theoretical and methodological challenge, which was already achieved, is the construction of regional input-output matrices at intra-regional level, given that in the literature, the construction of inter-regional matrices has important theoretical and technical proposals and that it also has enough empirical evidence related to their application at national and international levels (See Miller and Blair, 2009; Sargento, 2009; Lahr, 2001).
Finally, it is important to stress out that this work is part of a line of research developed over a long period of time and still continues in CEDRUS, applying in to the construction and analysis of the regional input-output matrices with the use of a bottom-up approach. This already has opened up new research proposals for applied studies, the development of spatial economic analyses and experimental researches of regional and urban economic studies.
