Participation of the sector in the region (P _ij )

It represents the percentage that the sector “i” occupies in the region “j”; therefore, it can be used to determine the intra-regional distribution. The values of this indicator can be less than or equal to 100 %.

The expression of P_ij, is the following:

where V _ij : Value of the variable V corresponding to the sector i in the region j; ∑iVij: Sum of the value of the variable V corresponding to the regional total.

Participation of the region in the sector (P _ji )

It represents the percentage that the region j occupies within the sector i; therefore, it can be used to determine the inter-regional distribution of the sector. The values of this indicator in each region can be less than or equal to 100 %.

The expression (P_ji), is the following:

where V _ij : Value of the variable V corresponding to the sector i in the region j; ∑jVij: Sum of the value of the variable V corresponding to the national total of the sector i.

Localization quotient (Q _ij )

It indicates the proportion of the sector i in the region j, compared to the relative size of the same activity in the national sphere. This quotient is used as a measure of relative or inter-regional specialization in the sectors being analyzed.

The expression of Q_ij is the following:

where V _ij : Value of V corresponding to the sector i in the region j; ∑iVij: Value of V corresponding to the regional total; ∑iVij: Value of V corresponding to the national total of the sector “i”; ∑i∑jVij: Value of V corresponding to the national total of the sector i and the region j.

The values that Q_ij adopts are Q _ij : 1 Indicates that the relative size of the sector i in a region j is identical to the relative size of the same sector in the country; therefore, there is no regional specialization in this sector. Q _ij <1 Indicates that the relative size of the sector i in a region j is less than the relative size of the same sector in the country; as consequence, there is no regional specialization in this sector. Q _ij >1 Indicates that the relative size of the sector i in a region j is greater than the relative size of the same sector in the country. In this case, it is a regional specialization in the sector i.

Results from the indicators of relative participation and specialization are interpreted according to the theory established by the methodology and were explained jointly with other economic variables obtained in various scientific studies.

The production value of grains for livestock consumption in Mexico

In 2003, the real production value of grains for livestock consumption in Mexico was 69 868.62 billion pesos. Of this amount, maize contributed 48 682.83 billion pesos, while the other grains as a whole generated 21 185.80 million pesos (Table 1).

In the territorial sphere, the CW region generated the highest amount (20 566.53 billion pesos) of the national production value, followed by the regions CE, NW and S, whose values were similar among one another. The PE region contributed the lowest amount, for it generated 846.81 billion pesos. Maize generated the highest value in all the regions, except in the NE region, where it was surpassed by sorghum.

In 2013, the national production value of grains for livestock consumption in Mexico was 104 768.36 billion pesos. This amount increased 49.95 % in relation to 2003 (Table 2).

Maize continued to be the one which made the highest contribution to the national production value of grains, followed by sorghum, and in the last place oats, since it barely generated 309.26 billion pesos. However, wheat was the grain whose value showed the highest increase (104.59 %), compared to the rest of them, because the price of the product increased 65.49%, the yield 17.81 %, and the surface harvested 4.89%.

In the regional sphere, the productive structures of the grains for livestock consumption were modified in different proportions in relation to 2003, because the values that these products generated increased unevenly.

Maize remained as the grain with the highest contribution within the production value of grains in all the regions, except in the NE region, where sorghum continued in first place in value generation. The highest increase of the maize production value was found in the regions PE, NE and NW, whose percentages were 116.24, 108.29 and 94.98 %, compared to 2003.

The higher increase of sorghum and wheat was found in the regions NW and N, whose percentages were 174.84 and 88.70 %, for the case of the first grain; meanwhile, for wheat they were 134.77 and 409.85 %.

Relative participation of grains for livestock consumption in regions of Mexico

In 2003, the relative participation of each of the feed grains for livestock consumption in the national production value was diverse. Maize contributed in greater proportion than the rest of the grains, by representing 69.68 % of the national total, because it occupied the highest percentage of participation destined to the agricultural sector (^{Guzmán et al., 2012}), followed by sorghum and wheat (Table 3).

In most of the regions (except the NE region), maize contributed the highest percentage of the regional production value of grains for livestock consumption, while sorghum did in the NE region. This last grain was the second in relative importance in the regions N, CW, S, E and PE. In the NW region, wheat was the grain that made the second highest contribution to the total regional value (34.09 %), while in the CE region it was barley (10.87 %). In the N region, oats was the third grain that contributed the highest percentage to the total regional value (4.59 %); meanwhile, in the other regions this product was the one that made the lowest contribution to the total value of grains.

By virtue of the higher relative participation of maize, sorghum and wheat in the real production value in the regions of Mexico, it is undeniable that the behavior of these products defined the dynamics of the productive structures of grains in the territorial sphere (^{Mejía et al., 2010}).

During 2013, the relative compositions of the grains for livestock consumption at the national and regional level evolved in different proportions; this caused changes in the position of some products in terms of their contribution to the production value.

In the national sphere, maize, sorghum and wheat continued being the grains that made the highest contribution to the total production value. However, the first of them contributed with a similar percentage in relation to 2003, while sorghum decreased its relative participation and wheat increased it (Table 4).

The change in relative position of sorghum was due to the lower growth of the production value of this product (38.80 %), compared to the increase that the totality of the grains experienced (49.95%). This lower growth of sorghum is explained in part by the decrease of 6.67 % in the production volume, which indicated going from 6.75 million tons in 2003 to 6.73 million tons in 2013; this decrease was because of the increase of 14.38 % in the surface harvested of this product (^{Financiera Rural, 2014a})

The increase of the relative participation of wheat was due to the increase of 104.59 % of the national production value, since the price increased 65.49 % and the production volume 23.62 %, as consequence of the increase of international prices caused by droughts in the United States and Australia, as well as winter in Russia, which caused a fall in the global offer of this grain (^{Financiera Rural, 2014b}).

In the territorial sphere, specifically in the NW region, maize reduced its contribution since it went from 55.69 % in 2003 to 50.29 % in 2013. This decrease was because of the lower increase in the production value of this product (94.98 %), compared to the growth that the totality of the grains experienced (115.90 %). In turn, sorghum and wheat increased their relative participation in similar proportion, due to the growth from 174.84 and 134.77 % of the production value, caused by the increase of 71.23 and 67.49 % in the prices of these products; in addition, 75.82 and 26.88 % in their yield. The rest of the grains in this region decreased their contribution in a lower percentage.

In the N region, oats decreased its relative participation, due to the lower increase of the production value of this product (7.79 %), compared to the one found in the totality of the grains (75.11%). The reduction of this grain was associated in part to the decrease in 16.56 % of the surface harvested and the growth of 1.44 % in the yield.

In the same region, wheat increased its relative participation of 3.02 % in 2003, to 8.78 % in 2013; this is because of the higher growth (409.85 %) of this grain, compared to the growth of the totality of the grains (75.11 %). The higher growth of wheat was associated to the increase of 163.04 % of the surface harvested and 60.50 % in the price of this grain. The rest of the products were modified in reduced percentages.

In the NE region, maize and wheat increased their relative participation while that of sorghum decreased. This increase in the first grain was explained in part by the increases in price (42.96 %) and in yield (65.05%), while the relative increase of wheat took place because the price of this product increased by 83.20 % and the surface harvested increased 6.54%. The decrease in sorghum was associated with the 29.38 % decrease of the surface harvested in the region, since it went from 1043.71 thousand hectares in 2003 to 737.06 thousand hectares in 2013.

In the CW region, maize increased its contribution to the regional production value, because the production volume and the price of the product increased 13.19 and 36.44 %, compared to 2003. The rest of the grains experienced changes in their reduced relative participation.

In the rest of the regions of Mexico, the relative participations of the other grains in the value of regional production maintained a similar proportion, because the increase in production value of most of these was akin to the growth that the grains in their totality experienced.

Relative participation of the regions in the grains for livestock consumption in Mexico

In 2003, the national production value of maize was 48.68 million pesos, of which the CW and S regions contributed with the highest proportion (27.01 and 22.05 %), followed by the CE and NW regions. The NE region was the one that made the lowest contribution (1.72 %), because its productive vocation was directed at the production of sorghum, when contributing 12.74 million pesos to the national production value of grains, where the CW and NE regions participated with 40.56 and 40.29 % of the total value of the grain. The rest of the regions participated in lower percentages (Table 5).

Within the value of the national production value of wheat, the NW region contributed the highest percentage (70.55 %), while the CW and CE regions, jointly, contributed with 24.47 %. The rest of the regions, as a whole, participated with nearly 5% of the total.

For barley, whose national production value was 2.59 million pesos, the CE and CW regions contributed 96.57 % of the total value. The remaining percentage was contributed by the N and NW regions.

The production value that oats generated was the smallest compared to the value of the grains for livestock use in Mexico, which reached 0.25 million pesos. Of this amount, the N region contributed 83.49 %. In turn, the CE region contributed 14.86%. These two regions together generated 98.35% of the national total.

In 2013, the inter-regional distribution of the production value of grains for livestock consumption in Mexico was different compared to 2003, since the contributions that the territories made evolved in different proportions. Some showed increases, while others reduced their relative participation (Table 6).

Regarding the production value that maize generated in Mexico, the CW and CE regions continued contributing the highest percentages; however, the magnitude of its participation was similar to the one found in 2003. The NW and S regions experienced changes in their participation. The first region increased the percentage due to the higher increase of the production value in the region (94.98 %), compared to the growth found by the same region in the country (50.48 %). The S region decreased its participation, which was associated to the scarce growth in value that the product generated in the region (1.21 %), compared to its growth in the country.

Concerning the national value generated by sorghum, the CW and NE regions remained as the territories with the highest contribution; however, none of these increased their participation. The first contributed with a similar percentage than in 2003, while the NE region decreased its contribution, since the value that it generated increased only 3.68 %, compared to its 38.80 % of increase at the national level. Other regions like NW and CE increased their relative participation in different proportions.

Regarding the production value of wheat, the NW region contributed 80.96 % of the total national value of this grain. This percentage represented an increase in value of 134.77 % compared to 2003. The percentage of the remaining value was contributed mostly by the CW and CE regions.

Barley generated a national production value of 2.06 million pesos, of which the CE and CW regions contributed 98.84 % of the total. However, the first region increased its participation and contributed with 76.79 %, due to the increase in value that it generated (25.03 %), while CW decreased its contribution, since its value decreased by 66.50 %.

Concerning the national value generated by oats, the N and CE regions continued contributing the highest percentage, since, jointly, they participated with 97.06 % of the total. However, the participation that the first showed was lower, while the one obtained by the CE region was higher, compared to 2003. These changes in the relative participations were explained by the differences in growth of the production value of this grain in each region, which were 7.79 and 97.38 %.

Regional localization quotients of the grains for livestock consumption in Mexico

During the study years, all the regions obtained localization quotients higher than or lower than one, distributed in the different grains for livestock consumption. These values indicated presence or absence of regional specialization, given that the relative size of the production value generated by each of the grains in the regions was higher or lower than the production value of the same product in the national sphere (Table 7).

During 2003, the CE, S, W, PE and N regions obtained localization quotients higher than one in maize; and they indicated that the percentage contribution of the production value that this product made in the regions (85.96, 81.82, 96.08, 95.06 and 98.92 %), was higher than the relative participation of the same grain in the national sphere (69.68 %); therefore, these regions were specialized in maize.

The vocation of these territories towards maize is because this crop was the most widely disseminated and important in Mexican agriculture, not only because of its relevance in matters of the population’s diet, but also due to its multiple uses as input in industry, whether directly or as byproduct (^{SIAP, 2013a}).

In the S region, participation by Chiapas in the regional production value of maize was notable, since during the year of reference, it contributed 4.49 billion pesos, equivalent to 41.86 % of the regional total. In the W region, Veracruz generated 2.89 billion pesos and represented 89.96 % of the total value of the territory. On the other hand, the PE region benefitted from the contribution to the production value made by Campeche, with 433.02 million pesos, equivalent to 51.69 % of the regional total.

The highest specialization of the N region was oats, due to the significant contribution made by Chihuahua, because of its importance in surface sown devoted to this crop. The production in this state during the study year reached a real value of 146.78 million pesos, corresponding to 69.88 % of the regional total (^{SAGARPA, 2014}).

The CE region also showed productive vocation for barley, even greater than maize, same as the CW region, whose corresponding values for this product were also higher than one in these territories.

It should be highlighted that the national production of barley is carried out in two cycles: spring-summer, where the rainfed modality predominates and Hidalgo, Tlaxcala, Puebla and Zacatecas stand out; and in fall-winter with irrigation, where Michoacán and Guanajuato stand out (^{SAGARPA, 2008}).

In the CW region, the contribution by Guanajuato was important, since it generated 1.05 billion pesos, equivalent to 85.01 % of the regional total. In the CE region, Hidalgo reached a value of 488.57 million pesos, that is, 38.47 % of the territory’s total.

The NE region was specialized in sorghum, with the contribution by Tamaulipas as the one of highest impact, since the geographic and temporal participation, at the national level, was higher than the rest of the states, with a production value of 4.99 billion pesos, which in relative terms meant 97.29 % of the regional total (^{SAGARPA, 2003}).

The NW region was specialized in wheat, because the percentage contribution of the value that this grain made in the region (34.09 %) was higher than the contribution made by this product at the national level (8.01 %). In this territory, Sonora was the state that had the highest participation, by contributing 2.64 billion pesos, corresponding to 66.97 % of the regional total; this was in part because the state was the one that showed the highest productivity in Mexico, while its yield per hectare was among the highest, in addition to presenting favorable climate conditions, an abundance of lands with good quality, with irrigation and prone to using machinery, and with government support for infrastructure (^{Márquez et al., 2014}).

In 2013, some regions continued with their productive vocation and stayed specialized in the same grains for livestock consumption than in 2003, while others modified their vocation and changed their specialization to other grains different from those that they were specialized in (Table 8).

The NW region had a localization quotient higher than one in wheat (3.39); however, of lower magnitude compared to 2003 (4.25); this indicated that this territory continued specializing in this product, but in lower proportion, since the increase in percentage participation of this grain in the region was lower than the increase that it showed in the national sphere.

The permanent vocation of this territory for wheat responds to the production achieved by Sonora, as principal producer, since its participation in the last decade was around 44 % of the national total. This contribution is due in part to the fact that all the production of this grain is obtained under irrigation, whose yield was 5.70 t per hectare, as a result of higher productivity (^{Financiera Rural, 2011}).

In their turn, the S, W and PE regions continued specializing in maize, since the localization quotients obtained by these remained with similar values to those from 2003; this indicated that the relative participation of this grain in these regions continued being higher than the one shown by this product in the country.

The CE region increased its specialization in barley and maize; in addition, it added its specialization in oats. In the latter, the increase of the relative participation in the region was higher than the increase that was found in the national sphere.

The N region continued with quotients higher than one in oats and maize, whose values indicated that it remained specialized in these products; however, its relative specialization was lower than in 2003, because the value of the quotients was lower.

The constant productive vocation for maize in these territories is explained by the agro-climate conditions that are adequate for it, and its use is not only centered in human consumption, but rather it is an important input in production for the livestock sector (^{Guzmán et al., 2014}). From the dietary point of view, maize is the most important crop in Mexico (^{De los Santos et al., 2017}), whose national production in the last decade was concentrated in ten states, among them Sinaloa, Jalisco and Estado de México, which contributed 43.50 % of the total. Chiapas, Guerrero, Michoacán and Puebla expanded their surface by adding new lands as a result of policies and programs to foster agricultural production (^{FIRA, 2016a}).

In addition, the vocation of the N region in oats was because Chihuahua is the main producer and with the highest productive potential for oat grain in Mexico, with around 69.30 % of the national volume found in the last five years; this crop is also a key input for the production of balanced meals for livestock use, and livestock activity is strategic in this state (^{SAGARPA, 2016}).

The permanent and superior specialization of the CE region in barley was due in part to the main producing zones of this cereal in Mexico being located in the center of the country: Guanajuato, Hidalgo, Tlaxcala, Estado de México, Puebla and Michoacán, which in average contribute approximately 90 % of the national production. The main areas of current and potential production are located in semi-dry and sub-humid temperate regions with summer rains and adapt to climates with precipitation higher than 500 annual millimeters (Zamora et al., 2008).

In turn, the NE region continued specializing in sorghum, whose productive vocation did not experience significant changes, given that the localization quotients of this grain obtained in both years were similar. A similar condition arose in the CW region, which acquired the vocation in maize, in addition to sorghum; however, it ceased to be specialized in barley, since the localization quotient obtained by this grain was lower than the unit.

The continuous specialization of these two territories in sorghum responds to the fact that during the agricultural year 2015, five states concentrated around 82 % of the national production of sorghum, where Tamaulipas stood out with 40.20 % and Guanajuato with 15.90 %. The seasonality of the sorghum production in Tamaulipas is peculiar, since 88.40 % of its harvest is performed in fall-winter and in spring-summer in the other states (^{FIRA, 2016b}).