Where

LQ_i and LQ_j = simple location quotients.

PRT= Total Remunerated Product.

Once the value of t_i,j is obtained, it is multiplied by the corresponding national coefficient (a_i,j) to estimate the regional coefficients of intersectoral trade (r_i,j).

In turn, the regional input-output model is formulated and resolved in a manner similar to the basic model. According to Dávila (2015), the solution is expressed in the following terms:

X ^r = (I - A^rr)^-1 Y ^r

where

A^rr = matrix of regional coefficients of intersectoral trade (rij),

X ^r= column vector of gross production values for region r,

I = identity matrix, and

(I - A ^rr)= Leontief matrix for the regional model.³

Domestic interregional flows are obtained as a residual between the total domestic inputs of the national IOM and those within the region. Thus, in matrix notation,

where

A^rr = matrix of regional coefficients for region r,

A^sr = matrix of coefficients for interregional imports of domestic inputs from r to the rest of the country (region s),

A^rs = matrix of coefficients for interregional exports of domestic inputs from r to s, and

A^ss = matrix of regional coefficients for region s.

where

X ^r = column vector of gross production values for region r, and

X ^s = column vector of gross production values for region s.

where

Y ^r = column vector of final demand for region r, and

Y ^s = column vector of final demand for region s.

where

I ^r = identity matrix for r, and

I ^s = identity matrix for s.

The system solution is obtained in the same way as in the standard model.

Production, Employment, Employee Compensation and Value-added Multipliers

One of the main uses of an input-output model is determination of the effect of exogenous changes on an economy. This process is called impact analysis, and the aggregate measures used in this analysis are called input-output multipliers. The most commonly used multipliers are those that estimate the effects of exogenous changes on industrial production, employee compensation due to increased production, employment generated in each industry due to new production, and the added value created by each productive sector due to increased production (Miller & Blair, 2009).

The production multiplier for sector j is defined as the total value of the production of an economy’s industries needed to satisfy the final demand for the production of sector j when demand increases by one monetary unit. The total “backward” multipliers indicate the necessary increase in the gross value of production of an economy’s various sectors due to an increase in the final demand of a sector of activity. The total “forward” multipliers indicate the regional increase in the gross production value of a sector needed to satisfy a one-unit increase in the final demand of all sectors of the local economy (Miller & Blair, 2009).

Direct effects represent the additional demand for inputs generated by an increase in sectoral final demand, while indirect effects result from the chain reaction of all economic sectors as a result of the additional demand for inputs from the sector that initially changed its final demand. However, not all economic activities have the same capacity to produce multiplier impacts on others (Dávila, 2015).

Per Dávila (2015), the production model solution can be expressed as follows:

x = (I - A)^-1 y

If

L = (I - A)^-1

then

x = Ly

The elements for the inverse Leontief matrix (L) can be grouped in four submatrices:

Based on the above, the total production multipliers (m) (subscript o) for the region analyzed (superscript r), are obtained by adding the columns with the elements (L₁₁ and L₂₁) of the inverse Leontief matrix (L) of the interregional model:⁴

Therefore, to calculate the total employment multipliers (l_c), a diagonal matrix must first be computed using the coefficients of the share of remunerated jobs in the gross output of each sector. To do this, the row vector of remunerated jobs is multiplied by the inverse of a diagonal matrix made up of the gross production values:

l´c = l´

-1

Next, this matrix must be multiplied by the inverse Leontief matrix (L) of the interregional model, and the result is multiplied by the inverse of the previously calculated matrix:

mlII=i´l´cL(

´c)-1

The sum of the columns of the resulting matrix shows the total employment multipliers. Lastly, to calculate the total multipliers of the value added and of employee compensation, we proceed in a similar manner by replacing the values corresponding to each variable in the two previous equations (Dávila, 2015).⁵

Analysis of the Productive Chains

Classical structural analysis focuses on the identification of backward (BLR) and forward (FLR) productive linkages that quantify direct and indirect effects. In other words, the linkages enable the identification of the sectors with the greatest potential pulling effect or sectors that are associated with many other sectors. Backward linkages measure a sector’s capacity for stimulating the development of other sectors that use its inputs. Forward linkages occur when one sector provides an output that is the input of another sector, which in turn is a stimulus for a third sector that is the input of the first sector (Chenery & Watanabe, cited in Schuschny, 2005).

Productive chains have their origins in studies by Chenery & Watanabe (1958), Rasmussen (1956), and Ghosh (1958), who established a four-part sector classification:⁶

Rasmussen (1956), in particular, suggests two measures based on Leontief's inverse matrix to quantify the direct and indirect backward (BLR) and forward (FLR) effects that a sector may experience. The normalized measures are obtained from the following expressions (Table 1):

BLR= (ni'(I - A)^-1) / (i'(I - A)^-1i)

FLR= (n (I - A)^-1i) / (i'(I - A)^-1i)

where

(I - A)^-1 is the Leontief inverse matrix,

i’ is a row vector with values equal to the unit,

A is the matrix of technical coefficients,

i is a vector column with values equal to one, and

n is the total number of sectors.

Results

Building the Reynosa 2013 Input-Output Matrix: Context of the Starting Point

To determine how the industrial sector in Reynosa’s economy is structured, this section incorporates some regional economic analysis techniques, including the average annual growth rate of the total gross output, the location quotients of the total remunerated personnel, the input-output multipliers, and an analysis of the productive chains.

Average Annual Growth Rate of the Total Gross Output

Mexico’s northern border is made up of six states that represent 24% of Mexico’s total gross output. There are 80 municipalities along the border with the U.S.; eight of these represent 18% of the border state output. Therefore, the output of the other 72 municipalities is not significant. The municipalities of Tijuana, Mexicali, Nogales, Ciudad Juárez, Piedras Negras, Reynosa, Nuevo Laredo, and Matamoros account for more than 75% of the total gross output of Mexico’s northern border region (Inegi, 2014).

When examining the average annual growth rate (AAGR) of the total gross output (TGO) of the most important border municipalities from 2003-2013,⁷ Piedras Negras, Coahuila (9.7%) stands out as the highest performer, followed by Reynosa (6.79%), with Tijuana (6.51%) and Nuevo Laredo (5.79%) close behind. Reynosa’s estimated growth exceeded that of Nogales (5.18%), Mexicali (4.94%), Ciudad Juárez (3.49%), and Matamoros (2.64%).

In contrast, when examining the relationship between AAGR and municipal share of the national TGO, Tijuana (1.13%) and Ciudad Juárez (0.99%) were the border cities with the highest contributions, followed by Reynosa (0.85%) and Mexicali (0.75%). These four cities far exceeded the contributions of Matamoros (0.26%), Nuevo Laredo (0.21%), Piedras Negras (0.13%), and Nogales (0.13%) (see Figure 2).

Figure 2: Mexican Border Cities: Average Annual Growth Rates of Gross Domestic Output (2003-2013) and Share of the National Total Gross Output (2013) in Percentages

Source: Created by the authors based on Inegi’s data (2004; 2014).

The relationship between the AAGR of the municipal TGO and its share of the national TGO suggests that Reynosa is frequently considered by companies looking for places to invest and locate. Of all the border cities, Reynosa is considered the most important in the northeastern region. This raises two key questions: 1) Considering national sectoral behaviors, which subsectors of the economy were identified in Reynosa by the end of the study period (2013)? 2) Which of these subsectors exhibited the highest productive linkages by having a better capacity for structuring a buying and selling network in the local economy? To answer the first question, the location quotient tool was used. To address the second question, we built an interregional input-output matrix for Reynosa based on Flegg et al. (1995) and Flegg & Webber (1997).

Location Quotients

Location Quotients (LQ)⁸ are used to explore the evolution of the municipal economic structure and to identify the relative importance of each economic sector in terms of production. The LQ is ideal for comparing the weight of a sector in a region (Reynosa) to the weight of that same sector in a reference economy (Mexico); three results can be produced: strong regional presence (LQ > 1) , weak regional presence (LQ < 1), and self-sufficiency (LQ = 1)

Figure 3 shows Reynosa’s location quotients for 2003 and 2013. It is very clear that in terms of paid personnel, computer equipment and electronic component manufacturing is the dominant sector in the municipality, followed by oil and gas extraction activities. This is confirmed by the weak presence in the region of most of the subsectors corresponding to the tertiary economy, with the exception of cargo transport services.

Figure 3: Reynosa: Location Quotients (LQi) 2003 and 2013

Note 1: The nomenclature for the corresponding subsector can be found in Table 2. Note 2: The 2003 database does not contain information on the total employee compensation in Reynosa for subsectors 211, 213, or 314.9 Source: Created by the authors based on data from Inegi (2014).

Before proceeding with the interregional input-output model, the location quotients confirm that the manufacturing, maquiladora, and export services industries have been dominant since 2003 and that the region has maintained its hegemony in computer and peripheral equipment manufacturing as well as in motors and electric generators manufacturing (Dávila & Escamilla, 2013; Esqueda, 2018; Esqueda & Trejo, 2014; Pérez, Ceballos & Cogco, 2012).¹⁰

Interregional Input-Output Model

This section presents the analysis of the production multipliers (multiplier effect) and the total multipliers (weighted multiplier effect) for the main macroeconomic variables, which are employee remuneration, employment, and value added. The results are summarized in Table 2.

Once the two effects have been measured, the table of multipliers is organized by grouping economic activities according to their sector classification: a) secondary, nonmanufacturing, b) secondary, light manufacturing, c) secondary, heavy manufacturing, and d) tertiary activities.

Secondary, Nonmanufacturing Sector

Although oil and gas extraction is an activity that boosts the economy through the direct and indirect jobs it generates, the results as of 2013 showed that this activity’s productive interdependencies were not very influential in the local economy (they did not show significant multipliers). In contrast, construction-related activities (building and civil engineering construction) maintained above-average values, particularly in terms of output. In other words, each additional peso in the value of their output increases the total output of the rest of the Reynosa sectoral economy by 1.3 pesos.

Secondary, Light Manufacturing Sector

This sector consists of a number of industrial activities that involve the processing of consumer goods and that do not involve a successive productive process of transformation. Beverage and tobacco product manufacturing stood out among the industries in this group because its influence on the local economy was significant in terms of employment and employee compensation. For example, a one-unit increase in employment in this industry generates 1.7 new jobs in Reynosa’s overall economy. Similarly, a one-unit increase in employee remuneration increases the remuneration of employees in Reynosa’s other productive activities by 1.6 pesos.

Secondary, Heavy Manufacturing Sector

The activities with the largest production multipliers were found in heavy manufacturing. In this group, the manufacture of computer equipment and communication and electronic accessories was the most dynamic of the four macroeconomic groups studied. The results show that for each job added in this subsector, 2.1 jobs are added to the local economic system.

Another dynamic subsector is the manufacture of transportation equipment, which was ranked among the highest in terms of output, employee compensation, and value added. For each peso added to this subsector, 1.4 pesos (output), 1.7 pesos (employee compensation), and 1.4 pesos (value added) are created in the overall economy of Reynosa. Also noteworthy is the performance of the chemical industry, which achieved above-average multipliers in the four macroeconomic variables.

Tertiary Activities Sector

When a new job is created in the radio and television subsector, Reynosa’s employment grows by 3.7 jobs. This industry is so buoyant that when there is a one-peso increase in the variable of employee compensation, the employee compensation for all local economic activities increases by 3.2 pesos. Similarly, bonding companies, insurance carriers, and pension funds are also highly ranked in terms of their employment and employee compensation multipliers; this shows their ability to influence the behavior of the local economy.

It is worth noting that the economic subsectors with the lowest values are in the Tertiary Activities group, particularly with regard to value added and employee compensation. The results indicate that services do little to stimulate Reynosa’s economy. It is important to point out that in developed economies the tertiary sector is a very significant catalyst of economic growth due to its intersectoral linkages (Berlingieri, 2014).

Productive Chains

Figure 4 presents the results of the sectoral classification of productive chains based on the Rasmussen criteria (Rasmussen, 1956): seven of them are classified as base activities, 24 are classified as independent, eight are classified as driving forces, and six activities comprise the group of key sectors.

Figure 4: Reynosa: Classification of Economic Subsectors According to Production Linkages

Source: Created by the authors based on the Reynosa IOM, 2013.

The Rasmussen model enables us to extract two alternatives for the industrial policy profile to be implemented in a region.

One alternative acknowledges that poor sectoral diversification is reflected in the breakdown of numerous local productive chains, which diminishes the potential for reinforcing the internal market (González & Barajas, 2004; Pérez, Ceballos & Cogco, 2014, pp. 201-202). This alternative does not discriminate against industries that are unattractive (independent sectors), or those that do not have a significant impact on the sectors that demand their products.

The other alternative acknowledges that specialization in a few industries leads to better regional competitive advantages, thereby stimulating exports (Porter, 2003). Thus, advocates of specialization want to promote subsectors with growth potential, and that can bring along other economic areas that can become key industries. This ideology highlights the regional vocation by viewing the manufacturing sector as the main engine of growth, but it also excludes certain economic activities and territorial distributions (Becerril, 2012).

The influence of manufacturing on regional productive interdependencies is obvious in Reynosa. Some examples are seen in the key subsectors dedicated to the manufacture of computer equipment, machinery and equipment, electrical appliances, transportation equipment, and the chemical industry. These subsectors are notable not only for their strong demand for intersectoral inputs but also as suppliers of intermediate products. They are also a necessary waystation for the economy’s diverse sectoral flows. From the perspective of regional economic specialization, these industries would have to be considered when developing local public policy, despite the risk of allocating resources to sectors heavily dependent on the U.S. economic cycle.

However, if the aim is to reduce the dependence of the local economy on a few subsectors, those that are in the base and driver quadrants must be considered due to the significance of their intersectoral sales and purchases, respectively. Tertiary economic activities, in particular storage services, repair and maintenance services for motor vehicles, and telecommunications, stand out among the driver subsectors. Regarding the base subsectors, the importance of metal product manufacturing is noteworthy. From the perspective of sectoral diversification, these activities must be included in the local public agenda since their presence in the economic system stimulates the production and consumption of intermediate goods, thereby reducing dependence on manufacturing, maquiladoras, and export services. The diversification strategy would involve focusing institutional efforts on local enterprises to reduce foreign trade risks.

Conclusions

In this study of the historical performance of the average annual growth rate (2003-2013) of the total gross output (TGO) of the most important border cities in northern Mexico (Tijuana, Ciudad Juárez, Reynosa, Mexicali, Matamoros, Nuevo Laredo, Piedras Negras, and Nogales), it was confirmed that during this period Reynosa was among the cities with the best performance both in terms of growth and in TGO share. Reynosa’s performance was comparable to those of Tijuana, Mexicali, and Ciudad Juárez. These four cities have become the border cities with the most economic influence in terms of the value of their TGOS.

The regional performance data analyzed here perpetuate the ongoing debate between specialization (a group of companies in the same sector that support the argument that growth is driven by industries with regional competitive advantages) and economic diversification (companies from different sectors that provide services for firms and workers, advocating growth resulting from the development of the industrial base).

If the aim is to reinforce the manufacturing sector’s position as the main driver of economic growth in Reynosa, one would have to consider the influence of heavy manufacturing on regional productive interdependencies. This is supported by the high levels of employment generated by the manufacturing of computer equipment, electrical accessories and transportation equipment (heavy manufacturing). This study demonstrated that the manufacturing capacity installed in this region produces strong demand for intersectoral inputs and the supply of intermediate products, creating a necessary waystation for the rest of the economic flows.

Despite the above, caution must be exercised regarding the specialization of the manufacturing, maquiladora, and export services industries. Industry concentration has not fostered a virtuous mechanism that develops local integration through commercial exchanges. This is reflected in I) the marginal value of the multipliers for production, employment, employee compensation, and value added for the rest of the productive activities; II) the weakness of the productive chains in nonmanufacturing activities; and III) the inadequate presence of the tertiary sector (in terms of production) with respect to its national counterpart.

When examining the system’s flows and productive chains using an interregional input-output matrix, it was demonstrated that heavy industry does not necessarily imply that all subsectors generate high multipliers. An example of this is the results obtained for the plastic and rubber industry and industries linked to the manufacture of metal products.

Furthermore, if the intention is to reduce the local economy’s dependence on a few subsectors, the hegemony of light manufacturing (manufacture of textiles and clothing) and tertiary economic activities (storage services, bonding companies, and companies linked to telecommunications) must be considered. The results showed that the presence of these activities in the economic system stimulates the production and consumption of intermediate goods. Thus, by supporting the performance of these activities, Reynosa’s economic growth would be fostered by solidifying the local supply chains.

In view of the above and regardless of the preferred approach (specialization or diversification), we recommend a forward-looking regional growth policy that promotes the system’s different expressions.

Regarding the methodology used, it is noted above that the lack of information on gross internal output at the municipal level thwarts a detailed analysis of the operation of the productive framework. Furthermore, the lack of current information (data are only available up to 2013) limits the accuracy of the estimated results. However, the models based on Flegg et al. (1995), Flegg & Webber (1997), and Rasmussen (1956) are suitable for examining the behavior of a city’s productive sector structure.

Although agriculture does not dominate Reynosa’s productive sector, we recommend incorporating information on this sector (compatible with the economic census). This would lead to improved estimates in the regional input-output model. In any case, what is needed is a comprehensive tool that can examine the production of goods and services in detail. With such a tool, the development of a municipal social accounting matrix or a general equilibrium model would be very useful as a reference framework for a regional structural analysis.

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Notas

¹ Indirect and hybrid methods incorporate better information (quantitative and qualitative) from official sources, specialized partial surveys, and expert opinions in the area as well as a mathematical process for balancing external data (Bravo & Castro, 2006; Chapa, Ayala & Hernández, 2009; Fuentes, 2005).

² Due to space limitations, the results of the application of the interregional Leontief model to Reynosa are presented in the appendices. Interested readers may request the authors to provide the databases that support the results and were used to produce the input-output multipliers in Table 2.

³ For clarity, to estimate the results presented in this article, the analysis was limited to the matrix of regional coefficients of intersectoral trade A^rr.

⁴ For clarity, to estimate the results presented in this article, the analysis was limited to sub-matrix L₁₁. so as to be consistent with the delineation of the previously mentioned A^rr matrix.

⁵ The multipliers for employee compensation and value added are obtained from the national IOM data for 2013 regarding employee compensation and gross value added.

⁶ It is acknowledged that there are alternative techniques for calculating productive interdependencies and establishing sectoral classifications for both national and sub-national economies. These alternatives include the hypothetical extraction method developed by Dietzenbacher, Linden & Steenge (1993) and network theory. The studies by Chraki (2016) and Llano (2009) stand out as the best examples of the hypothetical extraction method, while network theory has evolved out of many contributions, notably the seminal work of García & Ramos (2003) and studies by Hurtado & Martínez (2017), Molina & Gutiérrez (2015), and Fuentes, Cárdenas & Brugués (2013).

⁷ The analysis of the AAGR of the TGO is based on economic census data published by Inegi (2004; 2014).

⁸ The formula for estimating the location quotient is as follows: LQi = ((ei / et) / (Ei / Et)) where “e” is the total employee compensation for the region (Reynosa), “E”; is the national total employee compensation, “i” refers to the subsector of economic activity, and “t” refers to the total economy.

⁹ Due to the unavailability of the sectoral vector for gross domestic product, per Miller & Blair (2009), sectoral information on total employee compensation was used to calculate the location quotients. The data are from the economic census conducted by Inegi for 2003 and 2013 (Inegi, 2004; 2014). The total employee compensation variable was selected to avoid inconsistencies between the location quotients and the indirect method used to regionalize the national IOM.

¹⁰ When manufacturing is in a procyclical condition, it is a sign of future contractions, as was the case for the electronics industry in Reynosa. From 2008 to 2013, the number of jobs declined from 42 232 to 33 392. In addition, the value of its gross output decreased from 11 billion to 9 billion pesos (Inegi, 2009; 2014).

Rodrigo Vera Vázquez
Mexican. Dean of El Colegio de Tamaulipas. Doctorate in Social Sciences from El Colegio de Michoacán and a Master’s Degree in Integrated Environmental Management from El Colegio de la Frontera Norte. Both programs are registered with Conacyt’s PNPC at an international level. His areas of research include cross-border economic geography and regional development. He is an assessor for Conacyt’s research projects and public sector social programs. Among his most recent publications is Eagle Ford Shale Play: Petroleum-Mining Industrial Geography in South Texas, 2008-2015. Trayectorias, 19(45), 3-36.

Miguel Angel Langle Flores
Mexican. Bachelor’s Degree in Chemical Engineering and a Master’s Degree in Economics (PNPC) from the Universidad de Guanajuato. Doctorate in Regional Economics (PNPC) from the Universidad Autónoma de Coahuila. He is currently a professor and researcher at El Colegio de Tamaulipas and a member of the Regional and Urban Economics Research Network. His areas of research include regional economies and regional multisectoral models. Among his most recent publications is Langle M., Dávila A. & Valdés M. (2019). Productive displacement in the southern region of Mexico. In A. Dávila (Coord.), Modelos económicos de las regiones de México. Mexico: Universidad Autónoma de Coahuila, Miguel Ángel Porrúa.

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