INTRODUCTION

Since the implementation of the North American Federal Trade Agreement (NAFTA), perhaps the most important result has been the drastic change in the trade relationship between Mexico and the United States (U.S.), with Mexico’s prior trade deficit turning into a surplus. In response, U.S. President Donald Trump (2017–2021) proposed the renegotiation or cancellation of the trade agreement during his election campaign (2015–2016).

The U.S. trade deficit with Mexico, however, only reflects the gross trade value of final goods and does not accurately reflect the complexities of trade flows of intermediate goods between the two countries. Notably, trade between the U.S. and Mexico is based on supply chains of binational intermediate goods (inputs), meaning that intermediate goods often cross the border several times before a final good is produced. At each intermediate crossing, value can be added to a good before it is exported again. Consequently, the traditional metrics based on recording the exchange of final goods tend to double gross bilateral trade flows, resulting in increasingly biased measurements of the contribution of each nation to production.

The main purpose of the present study was to carry out a binational sector analysis of the value- added flows in the gross value of exports between the U.S. and Mexico in 2013 using a bilateral input-output table (IOT). The advantage of this approach is that production components can be integrated and weighted without resorting to ad hoc classifications concerning their intermediate or final destination (^{Amar & García Díaz, 2018}).⁴

The utilized methodology is mainly based on the recent work of ^{Koopman, Wang, and Wei (2012}; ²⁰¹⁴⁾; ^{Stehrer (2013)}, and ^{Wang, Wei, and Zhu (2013)}. The technique proposed by the first authors makes it possible to divide gross export flows at the multilateral level into their value- added components, group them according to origin and destination, and identify duplicate records. ^{Koopman, Wang, and Wei (2014)} and ^{Stehrer (2013)} propose extensions of this technique to address the breakdown of exports at the bilateral and sector-bilateral levels, respectively.

Thus, the present study aimed to answer a number of questions currently on the bilateral agenda: How do the input-output tables of the U.S. and Mexico integrate with each other and the rest of the world? How are the economic benefits of participating in bilateral co-production chains distributed? Furthermore, how would the renegotiation or cancellation of NAFTA affect participation in bilateral co-production chains?

The article is organized as follows: After the introduction, the essential literature on the subject is reviewed in section two. The statistical sources and construction of the bilateral or inter-country input-product matrix are described in section three. The breakdown of value-added proposed by ^{Wang, Wei, and Zhu (2013)} is explained in section four. Then, an empirical analysis of the value- added component of export flows is carried out using the “decompr” module included in R software. The last section presents our conclusions.

LITERATURE REVIEW

The importance of global value chains (GVCs) for the production of goods and services in the global economy has increased over the past few decades. In this regard, the trade of final goods has lost importance to trade in intermediate goods. To reach the final consumer, many of the components of these goods cross several borders on multiple occasions. We can find one notable example in ^{Xing and Detert (2010)}, who show how the production of a product invented and designed in the U.S., such as Apple’s iPhone, can increase the trade deficit. Of more than 750,000 workers involved in the design, sale, commercialization, manufacturing, and assemblage of the iPhone, only 63,000 work directly with Apple (^{West, 2018}).

Following the creation of GVCs, the national accounts no longer have the same meaning. When the same components cross the border several times, there is a double accounting that does not occur if only final goods are traded. Also, it is difficult to know how much value was added to previously imported goods. Since some of this added value comes from other economies, bilateral trade balances no longer have the same interpretation in the absence of GVCs.

There is a growing international literature on the participation of countries in GVCs according to a structural input-output framework. For example, we can highlight the seminal work of Hummels, Ishii, and Yi (2001), which adopts a global inter-country input-output (GICIO) framework. Similarly, ^{Trefler and Zhu (2010)}; ^{Daudin, Rifflart, and Schweisguth (2011)}; ^{Johnson and Noguera (2012a}; ^2012b), and ^{Koopman, Wang, and Wei (2008}, ²⁰¹², and ²⁰¹⁴⁾ use a GICIO. Other authors such as ^{Timmer, Stehrer, and de Vries (2013)}; ^{Baldwin and Lopez-Gonzalez (2015)}; ^{Johnson (2014)}; and ^{Solaz (2016)} use a world input-output database (WIOD).

^{Koopman, Wang, and Wei (2008}, ²⁰¹², and ²⁰¹⁴⁾ integrate vertical specialization measures and the breakdown of value-added in international trade use a multi-country input-output framework, while ^{Stehrer (2013)} and ^{Wang, Wei, and Zhu (2013)} propose extensions to address the breakdown of exports at the bilateral and sector-bilateral levels, respectively. ^{Koopman, Wang, and Wei (2012)} use a multilateral input-output model to develop a unified conceptual framework from which various indicators to measure the degree of vertical integration of productive processes among countries are derived. We can highlight the following indicators:

Thus, the conceptual framework provides a breakdown of gross export flows in terms of their value-added components, which are grouped by origin, destination, and double accounting. Following these authors, the value-added content of gross exports can be broken down into the three categories shown in Figure 1. Each category is in turn subdivided into three subcategories, including those that reflect the value of the “double registration” that is generated in customs as a result of having crossed the border several times.

Source: Translation by the authors of the scheme of ^{Koopman, Wang, & Wei (2014, p. 482)}.

Figure 1. Conceptual Framework of Koopman’s Export Decomposition  

The previously defined block of exported value-added (VAX) can be subdivided into three types of goods:

The previously defined block of returned domestic content that is exported and then re-imported (vS1*) can be subdivided into three subcategories:

The previously defined block of vertical integration (VS), or foreign content of exports, can be subdivided into three subcategories:

It is important to note that the methodology of ^{Koopman, Wang, and Wei (2012}; ²⁰¹⁴⁾ was designed for the breakdown of the value-added content in total aggregate exports in the multilateral case.

^{Stehrer (2013)} proposes three modifications to the methodology of ^{Koopman, Wang, and Wei (2014)} to enable the components of value-added to add up precisely to the value of total bilateral exports. The three modifications in the multilateral and aggregate case are as follows:

Thus, the RE-X—or proportion of value-added that passes through the trading partner and is later re-exported—may or may not have a bilateral trade flow as a counterpart. That is, only the fractions of bilateral VAX (IV) and RE-X will reach the trading partner through a bilateral export flow. Therefore, to ensure that the breakdown of total value-added adds up exactly to the bilateral gross exports, the transited value-added that the destination country received indirectly must be subtracted. However, this approach presents a disadvantage at the sectoral-bilateral level.

^{Wang, Wei, and Zhu (2013)} propose another method for dividing value-added at the sectoral- bilateral level. This methodology modifies the disaggregation components of value-added that can be grouped in the three previous categories. In the section showing the breakdown of ^{Wang, Wei, and Zhu (2013)}, we present the breakdown of this concept in 16 terms for the sectoral-bilateral case.

STATISTICAL SOURCES AND CONSTRUCTION OF THE BILATAERAL INPUT-OUTPUT TABLE

To conduct a sectoral-binational analysis of participation in the value chain using an input-output framework, we must ask the following: How should the input-output tables of the U.S. and Mexico be integrated and with the rest of the world? The answer is to develop a bilateral/inter-country input-output table between the U.S. and Mexico. In undertaking this task, it was considered appropriate that sectoral aggregation had the highest possible level of detail. For the U.S., the table constructed by IMPLAN (^{Minnesota Implan Group, 2017}) for 2013 was used, with a sectoral structure of 526 sectors.

In the case of Mexico, we used the official national table for 2013 (^{INEGI, 2014}) of the North American Industrial Classification System (Sistema de Clasificación Industrial de América del Norte [SCIAN]) composed of 261 sectors and disaggregated to the four-digit level. The official matrix was updated to 2013 to coincide temporally with the matrix for the U.S. and with the data for the year reflected in the 2014 Economic Census (^{INEGI, 2014}).

The official update to the RAS methodology⁵ which, based on the base matrix and availability of the aggregate values by row and column for 2013, applied an iterative bi-proportional process with the aim of making the sum of the values of the sectoral interactions in the matrix coincide with the aggregates for the year to be estimated (^{Lahr & de Mesnard, 2004}; ^{INEGI, 2014}). The aggregate data for the borders in 2013 were taken from the 2014 Economic Censuses (^{INEGI, 2014}).

The first step to generate the integrated U.S.-Mexico model was to ensure the sectoral compatibility of the individual models. Of the 526 sectors, 488 corresponded fully at the four-digit level of the SCIAN, and the remaining 38 combined activities from several sectors. These were assigned a weight according to their relative participation in the aggregated data using data from the economic censuses. This process resulted in 259 sectors. Finally, to ensure the compatibility of activities between both models, minor adjustments of the classifications were required, resulting in 247 sectors of economic activity.

After both national models have a compatible classification, the second step was constructing the integrated model for the estimation of the trade flows between both countries at the level of individual sector interaction. However, for this, we have the aggregate flows of U.S.-Mexico trade as part of the matrix of import flows at the level of sector interaction and total aggregate exports by sector. A similar problem was faced when estimating the multiregional models in ^{Canning and Wang (2005)}.

The reasoning behind the estimation of the foreign trade matrices begins by considering that trade between the two countries already forms part of the import and export aggregates of each country’s matrices. Therefore, their incorporation to the matrix initially requires subtracting the values of the trade flows from the total imports and exports in the matrices of both countries as appropriate.

With this procedure, we can incorporate these amounts to the trade matrices by making an initial distribution based on the structural composition of the import matrices for each country as appropriate. The consistency of the aggregates is achieved by considering that the sum of the rows of the trade flows between both countries and the exports should coincide with the exports by sector of the individual models; and, in turn, the sum of the columns of the trade flows between the U.S. and Mexico and the imports of the rest of the countries should add up by sector to the total imports of the individual matrices. Finally, the adjustment of the trade values and imports and exports of the rest of the countries can be achieved using the RAS method, which adjusts the sum of the previous values to the total aggregates by row and column.

The scheme of the bilateral input-output table is shown in Table 1. It is a combination of the sector interactions (xi,js,r) and economic aggregates of final demand (yi,js,r) for each country (s, r) and includes the records for bilateral trade flows (eis,r) and exports from the rest of the world (eiw) for 247 sectors (i = 1,…, 247).

The balance sheet equations can be derived from Table 1 in matrix form as follows:

where x^s is the total gross production in country s destined as intermediate or final goods domestically or internationally; x^ss is the intermediate demand in country s for intermediate goods or inputs in country s; y^ss is the final demand in country s for final goods in country s; x^rs is the intermediate demand in country r for intermediate goods or inputs from country s; y is the final demand in country r for final goods from country s; and xis,w are exports from the rest of the world from country s. The same interpretation can be used for country r.

Based on Leontief’s assumption about the linearity of the parameters of the cost function, i.e., aij=xijxj, we obtain the bilaterally defined structural equations as follows: 

Equations (2) and (4) represent the direct intra-country coefficients, and equations (3) and (5) are the inter-country trade coefficients. Substituting these structural equations into the balance equation and arranging them in the matrices, we obtain the following:

By rearranging the previous matrices, we obtain the following:

where b_i,j are the Leontief inverse coefficients or total coefficients, y^s = y^sr + y^sssup>, and y^r = y^sr + y^rr. Thus, we obtain the solution for the Leontief system of equations for the intercountry case.

WANG, WEI, AND ZHU DECOMPOSITION

The division of sector-bilateral flows of the gross value-added of exports proposed by ^{Wang, Wei, and Zhu (2013)} is long and tedious. Because of the limited space, it is not possible to present the complete derivation. However, we show the breakdown of the 16 terms of gross export value- added and a simple interpretation of each component.

The breakdown of exports from country s to country r (e^rs) according to their value components by origin, destination, and final and intermediate goods, is as follows:

where vⁱ is the value-added matrix of country i, b^ij is the sub-matrix of the inverse Leontief matrix, l^ij is the local Leontief inverse of the sub-matrix x^ij , T is transposed, and # refers to the multiplication of “element by element” similar to the point product of two vectors.

The terms can also be grouped as domestic value-added (DVA), foreign value-added (FVA), return value-added (RVA), and pure double counting (PDC).

EMPIRICAL ANALYSIS

The passage of NAFTA led to an increase in trade flows between member countries. It is currently a challenge to measure bilateral trade volumes because of the boom in global co-production chains at the bi-national level.

Given this context, we ask how the economic benefits of participating in bilateral co-production chains are distributed. Table 2 shows the results of the breakdown of the origin of the value-added of the gross exports of the U.S. and Mexico in 2013. For this, the “decompr” module developed by ^{Quast and Kummritz (2015)} integrated to the R software (^{R Core Team, 2018}) was used.

In 2013, of the U.S. $236 billion exported from the U.S. to Mexico, U.S. $120.2 billion corresponds with value-added directly in the U.S. and another U.S. $62.1 billion with value-added in the U.S. of inputs exported as intermediate goods that returned to the U.S. as exports. Additionally, U.S. $6.4 billion correspond with duplicate counting but are integrated to the national value-added of gross exports totaling U.S. $188.7 billion.

The other components of U.S. exports to Mexico are U.S. $2.5 billion of value-added in Mexico and U.S. $1.4 billion of duplicate accounting generated in Mexico. Finally, U.S. $43.3 billion of the value-added is imported by the United States from other nations to be integrated in exports to Mexico.

The results show that of the U.S. $287 billion in exports from Mexico to the U.S., the value- added directly in Mexico reaches U.S. $140.5 billion. To this, we must add U.S. $22.5 billion of value-added that returned to Mexico and U.S. $1.5 billion of double counting forming part of the U.S. $164.4 billion of domestic production contained in gross exports. The rest is made up of the U.S. $50.2 billion of value-added in the U.S. and a double counting in the U.S. of U.S. $6.4 billion. The U.S. $65.9 billion of imports from third countries must also be considered. These results are consistent with those of the Bank of Mexico (^{BANXICO, 2017}).

In terms of domestic value-added, that of the gross exports from the U.S. reaches U.S. $188.7 billion dollars, while that of Mexico is around U.S. $164.4 billion. This has significant implications because it means that after discounting the imported amount from gross exports, the U.S. domestic content exceeds that of Mexico. Likewise, in terms of trade between both partners, the implication would be that the U.S. maintains a surplus in the trade balance with Mexico, as opposed to the conclusions derived from the traditional analysis of gross foreign trade between both countries.

In addition, there is a large difference between the domestic and foreign components of the value-added in exports. For the U.S., the foreign value-added in its exports reaches U.S. $2.5 billion dollars, whereas for Mexico, this amount reaches U.S. $50.2 billion, more than 20 times the amount for the U.S.

It can also be observed that the amount of imports from other countries is greater for Mexico, reaching U.S. $65.9 billion dollars, in comparison to U.S. $43.3 billion for the U.S. This means that a significant proportion of the gross bilateral trade surplus (U.S. $22.5 billion, or 44%) comes from other countries in the form of intermediate imports. In other words, the gross bilateral surplus does not take into account that, through GVCs, Mexico imports U.S. $22.5 billion in excess of what the U.S. imports for the production of exported goods and, consequently, the trade surplus increases considerably.

On the other hand, the analysis of these figures in aggregate per concept and in relative terms can be carried out by calculating the indexes used by the abovementioned authors (^{Koopman, Wang, & Wei, 2012}) who previously researched the extent of value-added content in exports. The results are presented in Table 3.

The table shows that, in both domestic value-added content and total domestic content, the trade relationship favors the U.S. and indicates a surplus for the country given that the value of its exports exceeds that of its imports. There are also notable differences in the foreign value-added content of each country’s exports. For the U.S., it only reaches U.S. $4 billion of the content of imports in its exports. For Mexico, the import content from the U.S. in its exports reaches U.S. $56.7 billion, which is only 30% of the domestic content of exports to the U.S.

In terms of the proportion of value-added proposed by ^{Johnson and Noguera (2012b)} (VAX ratio) applied to U.S.-Mexico trade figures, the value reaches 51% for the U.S. and 50% for Mexico. In regard to the proportions of domestic value-added and domestic content in gross exports, these reach nearly 80% in the U.S. and 57.3% in Mexico.

The results of the relative indices show how the consideration of trade volumes in terms of value-added only partially accounts for a country’s participation in international trade. Also, after integrating the returned value-added, a country’s trade position can change, as occurs in the U.S.-Mexico trade relationship. In addition, it is important to recognize how imports from other countries are an important figure that can explain part of the trade in gross terms between countries. The integration of these figures enables a closer examination of the contributions of each country and third parties in international trade relations.

The findings per sector are shown in Table 4. The information in the table shows how trade between the two countries is highly concentrated, with exports in the top 15 sectors accounting for more than 58% of exports of the total 247 sectors. In terms of value-added, for most sectors, the percentage is lower than average, although these produce inputs to a wide variety of processes.

In that sense, as stated above, the largest difference rests in the exports returned to the U.S. economy as intermediate products that are then integrated into U.S. products and exported again. This is the case, for example, of electronics components manufacturing (sector 3344), which accounts for 46.5% of the U.S. $18 billion of gross exports. However, of this amount, U.S. $5.7 billion is domestic value-added, U.S. $8.5 billion is returned value-added, and U.S. $3 billion is imports from third countries. These latter amounts explain U.S. $17 of the U.S. $18 billion dollars traded.

We must also consider sectors such as motor vehicle parts manufacturing (sector 3363), which have low added value but have strong sectoral links with other sectors of the Mexican economy. This sector can generate U.S. $7.3 billion dollars of domestic value-added of the U.S. $16.8 billion dollars exported, of which an additional U.S. $5.9 billion dollars are returned value-added. That is, of the U.S. $16.8 billion exported, although less than 50% is domestic, more than 75% is value- added in the U.S. during the GVC process.

The correct measurement of the value-added in exports between these two countries is a basic starting point for assessing the effects of any changes to trade policy. How would the renegotiation or cancellation of NAFTA affect participation in bilateral co-production chains? The answer can be found in the following graph in which the circles on the line indicate sectors for which the proportion of value-added is equal between countries. In this case, there is no domestic value returning in intermediate imports. The majority of the sectors in the case of Mexican exports are located near this line. In contrast, in the case of U.S. exports, a large part of the sectors are located above the line, especially the sectors with lower domestic value on the horizontal axis, thus increasing the domestic content considerably.

Source: Own elaboration based on the results.

Graph 1. Total Domestic Value-Added of Mexican and U.S. Exports.  

This result is relevant because it means that during NAFTA an important part of the income from Mexican exports was destined to remunerate productive factors employed in the U.S. As a consequence, the multiplier effect—direct and indirect—associated with any change in binational exports is greater for the U.S. than Mexico.

CONCLUSIONS

In the present analysis, we highlight that, although Mexico has officially had a surplus trade balance with the U.S. during the NAFTA period, there is evidence of a deficit in terms of the value- added in gross exports. The figures describing the flow of added value gross exports from Mexico to the U.S. reach 164.4 billion dollars, while the domestic content of gross exports from the U.S. is $188.7 billion.

The main difference is between the domestic and foreign components of the value-added in exports. For the U.S., the foreign value-added in its exports reaches $2.5 billion, while for Mexico it is around $50.2 billion, or 20 times higher than the amount of the U.S. One conclusion directly derived from this finding is that, as a consequence of NAFTA, a significant part of the income from Mexican exports goes to remunerate production factors employed in the United States.

Bilateral trade is highly concentrated in 15 export sectors that account for more than 58% of exports. In particular, the electronics manufacturing sector stands out, representing 46.5% of trade, of which U.S. $18 billion dollars correspond with gross exports, U.S. $5.7 billion with domestic value-added, $8.5 billion with returned value-added, and $3 billion with imports from third countries, explaining $17 of the $18 billion dollars traded.

In addition, the vehicle parts manufacturing sector (sector 3363) also has a high domestic content of gross exports. Of the U.S. $16.8 billion exported, $7.3 billion are domestic value-added and 5.9 billion are returned value-added. Based on these findings, the importance of the difference in the consumption of intermediate goods between both countries can be highlighted in addition to the consequences for the added value generated in certain sectors of activity.

Therefore, the correct measurement of the value-added in bilateral sectoral exports should be a basic starting point for assessing the appropriateness or effects of any changes to binational trade policy. On the Mexican side, where a greater amount of foreign content is generally observed in production (and exports), the electronics, oil refining, chemical and plastic production, base metals, and metal-mechanics sectors stand out with a proportion of approximately 40%. The contribution of the U.S. side, which is usually the main source of this foreign content, has generally been on the rise.

For the U.S., the proportion of foreign content in all cases is around 20%, whereas that explained by Mexico never exceeds 3% (the highest being in the automotive sector). This is partly explained by the asymmetric economic relationship. As a result, the multiplier effect—direct and indirect—associated with any change in binational exports is greater for the U.S. than for Mexico.

Finally, an important limitation to be taken into account in future studies that aim to estimate the value-added in the trade relations between the two countries is the need to incorporate the impact of the rest of the world endogenously in the net balance of the distribution of value-added at the disaggregated level presented herein. In the case of the countries considered herein, the importance of this aspect is truly evident and, ultimately, it cannot be said that third countries are taking advantage of trade agreements without taking into account their impact. However, without a doubt, the estimation is complex.