1. INTRODUCTION

Trade liberalization and openness, combined with globalization and technological advances, allowed the internationalization of the global production of goods and services, which in turn led to the international division of production and the formation of global value chains (GVCs). GVCs are the product of a highly organized system of sources and destinations for value-added in a global production network (^{Koopmanet al., 2010}). Each country currently participates in production chains via those processes in which it is generally more efficient than other countries (^{Inomata, 2017}). Consequently, there has been a drastic global increase in the trade of intermediate goods that cross multiple international borders before becoming final goods and reaching the country of final consumption (^{Baldwin, 2013}).

Studying GVCs is crucial when tracing the various global production routes taken by goods and services, determining the role that different countries play in GVCs, and identifying their characteristics. In light of this, gross trade statistics must be distinguished from trade in value-added statistics. The disadvantage of using the former is that they incur double counting, by considering twice the value of intermediate goods embodied in final products that cross national borders more than once (^{Koopmanet al., 2010}).

Understanding the real value of exports and the trade balance between countries requires disaggregating by origin the value-added contained in a country's exports into its three sources: domestic, foreign, and pure double counting. This is particularly pertinent when seeking to contrast the trade balance between two countries in terms of domestic value-added (DVA) and gross value-added (GVA).

Recently, ^{Koopmanet al. (2014}) developed a decomposition method, which in addition to distinguishing between the sources of the value-added contained in exports, also identifies the destination of the DVA, that is, it recognizes how the recipient country makes use of exports and each countries’ type of insertion into GVCs.

The accounting framework adopted for the proposed decomposition is formulated according to interregional input-output matrices, which describe the flow of goods and services between economic sectors in different countries, whether for intermediate or final consumption.

This reality imbues the consolidation of trade blocs and the signing of trade agreements with additional importance. The Mexican economy entered into the General Agreement on Tariffs and Trade (GATT) in 1986, and the North American Free Trade Agreement (NAFTA, now renamed USMCA) launched in 1994, resulting in Mexico's economy becoming more closely integrated into the world economy, especially that of North America. Since then, the trade relationships between Canada, the US, and Mexico have been strengthened, giving rise to one of the most dynamic regions in terms of the flow of goods, services, and factors of production. As a result of USMCA, Mexico's trade flows with North America increased significantly, especially with the US. In 2020, 83.9% of total Mexican exports were destined for the North American region, of which 81.2% went to the US and 2.7% to Canada (^{Secretaría de Economía [Ministry of Economy], 2021}).

Although several studies assess USMCA’s impact on trade, foreign direct investment, development, employment, and the generation of productive linkages (for example, ^{Moreno-Bridet al., 2005}; ^{Boundi, 2017}; ^{Novelo, 2018}; ^{Torreet al., 2020}), few studies analyze value-added trade in the region (^{Fujii-Gambero and Cervantes, 2013}).

In a recent study focusing on Mexico and the US, ^{Fuenteset al. (2020}) found that in 2013 Mexico registered a trade deficit in DVA with the US, contrary to what conventional trade statistics show. According to the authors, this is explained by the high foreign value-added (FVA) content of Mexican exports. However, there are no studies that analyze bilateral trade among all USMCA members and, above all, that identify the source and use of the value-added content of exports.

This article sets out to disaggregate by origin and destination the value-added contained in the bilateral exports of the member countries of the United States-Mexico- Canada Agreement (USMCA) in the years 2005, 2010, and 2015, thereby identifying the share of DVA that each country exports and the nature of each country’s insertion into the region's value chains. Analysis was conducted using the inter-regional input-output methodology proposed by ^{Koopmanet al. (2010} and ²⁰¹⁴), applied to the 2005, 2010, and 2015 Inter-Country Input-Output (ICIO) matrices prepared by the ^{OECD (2018)}.

The article is divided into four sections, in addition to this introduction and the conclusions. The first section defines some fundamental concepts, such as production fragmentation and GVCs. The second section then presents some data on trade between the USMCA countries for the study period. The third section goes on to discuss the methodology used to fulfill and apply this article’s objectives. The fourth section presents findings and analyzes the results obtained from decomposition by origin and destination of the value-added contained in bilateral exports.

2. THE FRAGMENTATION OF PRODUCTION AND GLOBAL VALUE CHAINS

Economic and trade liberalization brought about major global transformations. One of the most important of these was the segmentation or fragmentation of production, which is directly related to the domestic location of industry and the supply of intermediate goods. According to ^{Minian (2009}), international segmentation seeks to reduce production costs and generate economies of scale.

Following on from the argument of production fragmentation, ^{Krugman (1995}) originally proposed the concept of GVCs, arguing that in international production networks, different countries generate added value through their participation in certain production stages of a good. GVCs divide the production process into stages, whereby different tasks are carried out in different countries.

Falling transport costs and advances in information and communication technologies enabled the formation of GVCs, which also reflect a system of sources and destinations of value-added in a global production network (^{Koopmanet al., 2010}). According to ^{Gereffi and Fernandez (2016}), GVCs link firms, workers, and consumers around the world; the authors describe the activities that go into making a product from conception to consumption, which can be concentrated in a single firm or across several firms. Currently, GVCs are dispersed around the world and different activities are carried out in different parts of the world.

For ^{Baldwin (2013}), meanwhile, the point of consumption has separated from the point of production, and goods now travel around the world in search of more profitable markets, accelerating the relocation of some production segments outside national borders where certain activities are performed more efficiently. How value is generated and transferred in global production chains is then a consequence of companies' efforts to optimize production networks (^{Inomata, 2017}).

^{Taglioni and Winkler (2016}), for their part, claim that an economy’s ability to insert itself into GVCs is a vital condition for the development and promotion of a country's competitiveness, one which depends both on the exporter's capacity and the capacity to import inputs from the rest of the world ((RoW). These authors argue that it is difficult for a country to become a major exporter in GVCs without first becoming a successful importer of intermediate goods.

It is also crucial to discern the stage of the production process in which each country participates. ^{Baldwinet al. (2014}) posit that developed economies engage in high value-added activities such as design, marketing, and post-sales services, while developing economies engage in lower value-added activities such as planning, production, and distribution, which is explained by the differentials in labor and raw material costs between developed and developing countries.

A recent study by ^{Xiaoet al. (2017}) suggests that, although the international flow of production inputs has increased significantly, the geographical distance between GVCs still matters, and regional value chains are more dynamic than global ones.

3. EXPORTS BETWEEN THE USMCA COUNTRIES

For Mexico, the signing of NAFTA represented the consolidation of the process of liberalization and economic and trade openness (^{Puchetet al., 2011}), which, in turn, consolidated the Mexican economy’s insertion into global dynamics, especially at the regional level. In its most recent version, the Mexico-United States-Canada Agreement (USMCA), launched in July 2020, is the regulatory framework that governs trade between these countries and seeks to maintain the strong trade, production, and investment links that have been in place since its inception.

The ^{Secretaría de Economía (2021)} points out that the region's trade links are a key factor for the competitiveness of the productive sectors of the USMCA, in addition to being considered indispensable for efficient productive chains in the region.

North America is one of the world’s most dynamic regions, with significant flows of goods, services, and factors of production, mainly generated by US economic activity. Data from the ^{World Trade Organization ([WTO], (2021)} indicate that North American countries’ trade represents approximately 13.2% of world trade, meaning that three countries account for one-eighth of global trade.

Exports in the T-MEC bloc grew between 2005 and 2015 at an average annual rate of 2.9%, while those of Mexico, the US, and Canada grew at a rate of 3.5 and 0.8%, respectively (see Table 1). Although Mexican exports grew at a higher rate than those of the other two countries, the US’s and Canada’s share of exports was higher; for example, in 2015, 43.5% of the region's exports came from the US, 29.2% from Canada, and 27.3% from Mexico.

The data reveal that Mexico's share increased by almost 5% during the study period, to the detriment of Canada's share. Moreover, 39.5% of US exports to the bloc went to Mexico, and the remaining 60.5% to Canada. In contrast, Mexico's and Canada's exports are concentrated in the US, representing 92.4% for the former and 97.4% for the latter.

Bilateral trade in the region takes place between the following pairs of countries: a) Mexico and the US, b) Mexico and Canada, and c) the US and Canada. In gross terms, bilateral trade in the years under analysis shows a clear trend; Mexico reports a surplus with the US and with Canada: with the former, it is growing, while with the latter it remains relatively constant (see Table 1). On the other hand, the US has a trade deficit with Canada.

It is worth mentioning that the gross value of these transactions, when considering the value of intermediate goods incorporated in the exported products may overestimate the real value of bilateral exports between these countries. In this sense, a distinction needs to be made between gross trade statistics and trade in value-added.

4. METHODOLOGY

This article’s analysis requires data on the productive and trade structure of Mexico, the US, and Canada, necessitating in turn an inter-regional accounting and methodological framework. Previously, the construction of interregional input-output matrices was a task that, besides being complicated and cumbersome, had to be carried out by the researcher on their own. In the last decade, however, renowned international institutions have made inter-regional input-output matrices available to the public, broadening the scope of research and facilitating the handling of information. Examples of such projects are a) the World Input-Output Database (WIOD), a project funded by the European Commission which provides a methodological and accounting framework for the countries of the European Union and 13 other countries, b) IDE-JETRO, a project funded by the Japan External Trade Organization, which, similar to the WIOD, presents interregional input-output matrices for Asian countries, and c) the OECD which provides a database of interregional input-output matrices (ICIO) for the period 2005-2015 with 64 countries worldwide (36 OECD members) from which the organization’s trade in value-added (TiVA) indicators are derived.

This article uses the ^{OECD (2018)} ICIO matrices for the years 2005, 2010, and 2015, which disaggregate economic activity into 36 activity sectors. To facilitate the estimation of the value-added matrices, analysis omitted the 36th sector of private households with employed persons, as these cells are empty. These matrices record trade flows between sectors in different economies around the world, whereby a country's production, whether for domestic consumption or for export, is carried out using inputs from other countries. These matrices show world production and their structure is presented in Figure 1.

Source: ^{OECD (2018)}.

Figure 1 Structure of an OECD ICIO Matrix. 

One of the advantages of using this methodology is the availability of data on the value of goods flows between countries, which makes it possible to trace the value-added generation process of each product in each country (^{Inomata, 2017}).

Following ^{Koopman et al. (2010}), and starting from the ICIO matrices, the interregional input-output model can be described by the equation of the general input-output model (equation 1), which in this case shows the sectoral output per country needed to satisfy final demand.

Where the matrix (A) of technical coefficients is of dimension (rN x rN)with r countries and N sectors, it is obtained from the matrix (Z) in Figure 1, (L) is the Leontief inverse of (rN x rN), and (y) is the final demand vector of magnitude (rN x 1).

With this structure and considering that the total exports of a country (e) comprise intermediate and final goods, the output required to satisfy total export demand is given by equation (2). It should be noted that vector (e) represents the total exports of each country to the RoW. Later, this vector will be adapted to show bilateral trade between countries.

Equation (2) represents the world production x ^e needed to satisfy export demand, and has dimension (rN x 1), where (e) is the vector of total exports of magnitude (rN x 1). The value-added contained in total exports is obtained by pre-multiplying equation (2) by the vector of value-added coefficients v. However, to identify the origin and use of the value-added contained in each country's exports, the diagonalized vectors of exports (ê) and value-added v^ of magnitude (rN X rN) (equation 3).

The value of gross exports is disaggregated according to the origin of the value-added contained in exports, which may be domestic or foreign, and according to the use, where the importing country may not be the destination country that consumes the final products, and rather the DVA is absorbed in other sections of the chain. To this end, a model is proposed that focuses on the bilateral trade relations of the three countries that make up the USMCA and the RoW, so that we work with four countries: the first country is Mexico, the second is the US, the third is Canada, and the fourth is the RoW Equation (3) and its components are matrix-represented in equation (4). To simplify the analysis, the matrix notation refers to vectors and matrices for each country; eachv _r represents the diagonalized vector of country r value-added coefficients of dimension (N x N), the sub-matrices L _rs of the matrix L of coefficients of direct and indirect requirements per unit of final demand are of dimension (N x N), and each diagonalized vector of exports e _s is also of dimension (N x N). Therefore, the matrices v^, L, ê, v^Lê are of dimension (rN X rN).

From the matrix of value-added contained in exports VAX (equation 4), the concepts of DVA and FVA contained in exports can be identified (^{Koopmanet al., 2010}):

The value of a country's exports must be equal to the gross value of exports, which requires examining the pure double counting (PDC). According to ^{Miroudot and Ming (2019}), PDC is defined as the value-added that crosses international borders more than once, and which according to ^{Koopmanet al. (2014}) accounts for the fraction of the DVA that was initially exported but eventually returns to the original country. This means that the sum of the terms DVA, FVA, and PDC results in 100% of the value of gross exports, and the PDC term records the difference between the value of gross exports and the sum of DVA and FVA contained in exports (equation 5).

The PDC term is only observed when both countries export intermediate goods. If these were zero for one or both countries analyzed, then gross exports would be equal to the DVA and FVA contained in exports (e _r = VAX _r ) i.e., the PDC term would be zero. This is because the PDC term accounts for value-added shipped back and forth as part of intermediate trade between countries (^{Koopman et al., 2014}). Similarly, when intermediate goods are exported between two countries and the PDC term is excluded, the accounting of gross exports will be incomplete, and will be less than 100%. ^{Koopman et al. (2014)} propose a further decomposition of the PDC term into its internal and external parts. However, since its application is beyond the scope of this article, only the total PDC term will be shown.

Likewise, the analysis of bilateral value-added exports allows us to disaggregate the exports of each economy by destination country (^{Stehrer, 2013}), which means, for example, that the scalar e1 that shows Mexico's total exports to the world can be disaggregated into Mexico's exports to the US (e ₁₂ ), to Canada (e ₁₃ ), and to the RoW (e ₁₄ ): e ₁ = e ₁₂ + e ₁₃ + e ₁₄. Then, the diagonalized vector of exports by destination country can be rewritten as in equation 6.

The matrix of value-added contained in exports VAX =v^Lê is:

According to this logic, the bilateral trade relationship between the analyzed countries is even more evident, e _st represents the exports from country s to t, hich at the same time are t's imports from s (^{Stehrer, 2013}). Bilateral trade in value-added between Mexico and the US is summarized by equation (8), where e ₁₂ is Mexican exports to the US and e ₂₁ is US exports to Mexico:

In this case, the equation shows for Mexico that DVA ₁₂ = v ₁ L ₁₁ e ₁₂ represents the DVA contained in its exports to the U.S.; the sum FVA ₁₂ = v ₂ L ₂₁ e ₁₂ + v ₃ L ₃₁ e ₁₂ + v ₄ L ₄₁ e ₁₂ represents the FVA (of countries 2, 3, and 4) contained in Mexican exports to the US. The same approach can be used to analyze bilateral exports between Mexico and Canada (e ₁₃ , e ₃₁ ), between the US and Canada (e ₂₃ , e ₃₂ ), and of each country with the RoW.

To determine the destination of the DVA contained in bilateral exports, a distinction is first made between exports of final goods (Y ₁₂ ) and intermediate goods, (A ₁₂ x ₂ ) e ₁₂ = Y ₁₂ + A ₁₂ x ₂ and then intermediate goods are disaggregated according to the use the importing country gives them (A ₁₂ x ₂ = A ₁₂ x ₂₁ + A ₁₂ x ₂₂ + A ₁₂ x ₂₃ + A ₁₂ x ₂₄), which in the case of country 1 is (^{Koopman et al., 2010}):

From the above definition it follows that: e ₁₂ = Y ₁₂ + Α ₁₂ x ₂₁ + Α ₁₂ x ₂₂ + Σ_t≠1,2 A ₁₂ x _2t , substituting in the expression of the DVA contained in exports DVA ₁₂ = v ₁ L ₁₁ e ₁₂ in equation 5, we obtain the total decomposition of the gross value of exports from country 1 to country 2 (equation 9).

This decomposition is also presented in Figure 2. In order of appearance and for the case of country 1, the terms of equation (9) indicate (^{Koopman et al., 2014}):

Recent literature on the subject indicates that one measure of a country's participation in GVCs is the type of chain it generates through its exports. And they can be simple or complex, depending on the number of times a product crosses the border. ^{Wang et al. (2017}) define the types of chains as follows: a) simple: observed when DVA or FVA crosses national borders for production only once. It is the value-added that once exported is not re-exported to third countries; b) complex: refers to the DVA or FVA contained in a country's exports used by the importing country to in turn produce exports of intermediate or final goods. A complex chain is observed when the value-added contained in exports crosses borders at least twice.

5. ORIGIN AND DESTINATION OF THE AGGREGATE VALUE CONTAINED IN BILATERAL EXPORTS FROM NORTH AMERICAN COUNTRIES

Value-added trade among the USMCA member countries is analyzed bilaterally. This means that the region's total trade is calculated using three models that factor in bilateral exports between pairs of countries as presented in equations (8) and (9). Based on these calculations, this section presents the decomposition of the value-added of total exports from one country to another (see Figure 2) by origin and destination. This is done to contrast the gross trade balance with the trade balance in DVA between Mexico and the US, Mexico and Canada, and the US and Canada, for the years 2005, 2010, and 2015. In terms of origin, value-added is divided into domestic, foreign, and double counting. In terms of destination, meanwhile, the value-added contained in exports can be absorbed directly in the recipient country via final goods, or in the case of intermediate goods, processed and then either consumed in the recipient country or re-exported back to the country of origin or to third countries. This decomposition provides valuable information on the insertion of each country in the regional value-added chain and the type of chain with which it participates. The findings reveal some crucial realities which are reviewed in detail in the following subsections.

Source: Compiled by the authors based on ^{Koopman et al. (2014}).

Figure 2 Complete decomposition of the value-added contained in exports. 

6. CONCLUSIONS

The insertion and participation of Mexico, the US, and Canada into the value chains of the USMCA region differ among countries. The US stands out as the country with the highest proportion of DVA contained in its exports to the region and the value of its exports is around 86%. For Canada, this figure averages 74%, while for Mexico it represents only 68%. These findings point to the high FVA contained in Mexican exports.

Although Mexico maintained a gross and value-added trade surplus with the US and Canada during the study period, this situation is very close to being reversed, especially with the US - a country with which the value-added surplus balance was drastically reduced between 2005 and 2015. This trend is due to the wide difference in the share of DVA in each country's exports.

Meanwhile, Mexico's and Canada's exports to the region contain a high FVA from the US, amounting to 12% and 11% of the value of total exports, respectively, suggesting a certain dependence on imports of intermediate goods from the US.

Regarding the type of each economy’s insertion into the region's value chains, the US’ participation in the bloc is complex, while that of Mexico and Canada is simple. The first country supplies the other two with intermediate goods, which, after processing, are re-exported to the US. In this scenario, Mexico and Canada provide the necessary services for transforming or assembling products at low costs to return then them to their final consumption destination. This means that Mexico and Canada are mainly exporters of final goods, which do not reach third countries. Even though the main destination for Mexican and Canadian exports is the US, these two countries manage to build complex value chains with each other to reach the US with an additional border crossing. These trade links should be strengthened to allow both economies to increase their participation in the process of fragmentation of production in the region.

Mexico is undoubtedly connected very superficially to the region's value chain; of the three countries, it has the lowest DVA content, exports the least in total to the region, and participates in a simple chain with its largest trading partner. All of the above suggests that the benefits of the USMCA will soon begin to dry up. To reverse this trend, it is essential to increase the DVA contained in exports, which requires strengthening productive linkages within the Mexican economy.

This study has yielded valuable data on Mexico's insertion into the NAFTA region. Future research on the subject could contrast the results of this work with those that would be obtained by using a different interregional database such as the WIOD, as well as analyze the value chains in the NAFTA region in the sectors, subsectors, or branches most relevant to the Mexican economy.