Introduction⁶

The structural analysis, derived for the most part from the Leontief model, has been developed throughout more than eight decades since the first works by ^{Leontief (1936)}, and it is one of the methodologies used for the empirical analysis of real economies and for the design of economic policies. Virtually all the structural analysis tools-at first developed for the input-product analysis-can also be applied to the social accounting matrices.

However, despite the fact that the concept of Social Accounting Matrix (SAM) was developed and began to gain importance almost half a century ago, with at least one SAM having been developed in most countries based on the National Accounts, Mexico has had a marked backwardness due to various reasons-perhaps the main of which being that the INEGI abandoned the development of the Input - Output Table (IOT) for more than 30 years-, so that currently and in most cases each researcher in this area develops their own SAM, without the possibility of replicating the results, given that the SAM is not generally published. The main objective of this work is to build and present a SAM of the Mexican economy for the year 2003, based on the Domestic Input-Output Symmetric Table for the Total Economy, officially published by the INEGI, and using a transparent methodology, so that it can be used to carry out research with results that can be replicated and corroborated (or corrected). Furthermore, we did a basic study for the characterization of the productive sectors, and concluded with an application using the Leontief model to obtain the General Multipliers Matrix (GMM), with which we analyzed the structure of the productive sector of the country, and calculated the carry-over and dispersion indices to determine the relative importance of the productive activities in the Mexican economy.

While it is true that the OIT for 2008 is already available as well as an update for 2012,⁷ and therefore it is possible to update the SAM, this in no way undermines the usefulness and interest for a SAM for 2003 for various reasons.

Without being exhaustive, one of these is that the study of the evolution of variables throughout time is one of the fundamental interests of the economic analysis (this is the reason for the construction of time series), and the comparative studies of a set of data in two points of time is one of the basic approaches to the topic.

Another is that, insofar as the structural changes on the economy are not significant throughout a determined period, the conclusions could maintain their validity and, if there are indeed significant changes, their study could help understand how the different transmission mechanisms act on the economy.

In the practical field, the evaluation of the results of public policies and programs requires analyzing scenarios a posteriori (or ex post), regarding initial or reference situations, for which a SAM prior to the scenario of interest is of obvious importance.

Moreover, the fact that a set of data corresponds to a past period does not necessarily invalidate the results that could be derived from these. In other words, most (or all) of the work and the results obtained by past scientists, would lack validity.

On the other hand, the construction of this SAM is also intended to contribute elements that allow-along with the eventual contributions of other researchers interested in the topic- defining the methodology, or the most appropriate approach for the construction of Mexico’s SAM; both because the inter-temporal comparability is of central importance for the analysis of the evolution of variables, and because if each researcher builds their own database, then the results would not be comparable and thus, would be difficult to verify.

This work closely follows the methodology developed by ^{Núñez (2014)} for the construction of a macro-SAM, that is, an aggregated matrix at the macroeconomic level for the Mexican economy, and based on this macro-SAM we built the micro-SAM reported here. Furthermore, in this work we carried out a basic characterization of the productive structure, and calculated the General Multipliers Matrix, calculating the carry-over and dispersion indices to determine the relative importance of the sectors, and to identify key and strategic sectors.

We consider that the main advantage of this work is that it proposes a specific methodology for the Mexican System of National Accounts (MSNA), departing from the Input - Output Table (OIT) published by the INEGI, and data from the national accounts, to build a transparent SAM that can be replicated and corrected, or modified to carry out different researches; because as far as we know, this has not been done for Mexico, given that according to the work of ^{Barbosa-Carrasco et al. (2009)}:

"Despite its importance, there is no official SAM for Mexico and each researcher builds their own: 1) A SAM, in 1975, to analyze the function of the public sector in the economy of the country (Pleskovic and Treviño, 1985); 2) a SAM, with data from 1989, to calibrate the model to evaluate the impact of Mexico trade openness (Levy and Van Wijnbergen, 1992); 3) a SAM, based on 1985, to calibrate the computable general balance models to analyze the consequences of the North American Free Trade Agreement and fiscal policies (Sobarzo, 1992 and 1994); and 4) a SAM with data from 1996 (Harris and Robinson, 2003) (McDonald and Thierfelder, 2004). Of these matrices, only those by Pleskovic and Treviño (1975), Harris and Robinson (2003), and a SAM of the GTAP with data from 1997 (Trejos et al., 2004) were published. Due to there not being a more recent SAM that is available for Mexico, this work was done with the objective of building one for 2004".

More recent works such as that by ^{Aguayo et al. (2009)} are based on updates made to considerably old matrices,⁸ and others such as the cited work of ^{Barbosa-Carrazco et al. (2009)} resort to econometric techniques to estimate a great quantity of unavailable data.⁹ The proposal followed in this work allows building a SAM based on current and complete data, therefore, it is possible to apply this methodology to the 2008 input-product matrices, and to the 2012 update published by the INEGI,¹⁰ as well as to future matrices and supplementary data of the national accounts, without having to resort to updating old data or estimating inexistent data. Both works cited in this paragraph-published in the same year (2009), regarding two matrices for the same year (2004), built with different methodologies, and thus non-comparable-also show the need for a consistent approach that avoids the duplication of efforts and, above all, the need to have a framework that allows replicating and comparing the results of different researches.

The article is organized as follows. In the first section, we considered the matrix to be used and we take the Domestic Input-Output Symmetric Table(OIT-Mx03ETD), adding the productive sectors to obtain the macro matrix from which the SAM-Mx03 will be built. In the second section, the Activities are disaggregated to carry out the basic study of the sectors and their characterization. In the third section, we select the exogenous accounts and apply the Leontief model to obtain the General Multipliers Matrix (GMM) and elaborat the Rasmussen indices. Finally, the fourth section presents some closing remarks.

Construction of the Social Accounting Matrix SAM-Mx03.

Table 1 partially compares, from the production point of view, the 4 input-product symmetric matrices published by the INEGI. The basic differences consist, on the one hand, on the disaggregation done on the imports, and on the other, the Maquila Export Industry (MEI). For this work, we have opted to use the Domestic Input-Output Symmetric Table for the Total Economy (OIT-Mx03ETD, which simply follows the OIT), given that the additional objective will be to carry out a sector analysis. The methodology used is immediately applicable to any of the other input-product matrices of Table 1 for the construction of the corresponding SAM. Throughout the article, the figures are expressed in millions of pesos for the year 2003, unlike the national accounts, where these are expressed in thousands of pesos.

Table 1 Input-Output Symmetric Tables 2003 of the INEGI. (Millions of pesos). 

Source: Own elaboration based on the Mexican Input-Product Matrices for 2003 (^{INEGI, 2008}).

Elaboration of the macro matrix.

First, we added the 20 sectors of the OIT into a single one to facilitate the elaboration of the macro matrix, since once this is squared, according to the national accounts, the subsequent disaggregation will maintain the consistency. The OIT with the aggregated productive sectors is shown in Table 2.

Table 2 OIT with the added productive sectors into a single one. (Millions of pesos). 

Source: Elaborated based on the Domestic Input - Output Table of the Total Economy of Mexico for 2003 (^{INEGI, 2008}).

Although the SAM can be seen as an extension of the OIT, conceptually, it is an accounting framework that has two fundamentally different implications: while the OIT focuses on the productive sectors, specifying all of their inputs and the destination of the production, the SAM reflects the circular flow of the economy and specifies the balance of all the accounts of the economy, focusing on the institutions of the same (namely, Households, Government, and Companies or Partnerships, thus it is denominated Social Accounting Matrix) and thus on the balance of the economy as a whole. Consequently, the SAM contains more information than the OIT due to necessity. Furthermore, according to the conventional standard format, each account has a row that specifies its incomes (resources) and a column that specifies its expenses (uses); meaning that the SAM is a squared matrix where the total per row is exactly the same as the total per column (income=expense) (^{Defourney and Thorbecke, 1984}). Table 3 shows the information of the OIT contained in Table 2, using the previously mentioned standard SAM format.

Table 3 makes obvious that with the information from the OIT, only the account of the productive Activities is balanced. All the others show greater or lesser imbalances, because the OIT does not contain the necessary information that must be integrated into the SAM. For example, in the case of Households, the incomes must also include the transfers and payments of the RoW to the productive factors, and for expenses, the taxes paid by the households must also be included, mainly the ISR. In the case of the Government, there are also certain elements missing with regard to its income and others regarding public expenses, and such is the case for the other accounts. In other words, the difference between a SAM and a OIT is both conceptual and informative, and not a matter of format, thus, it is not possible to make an OIT using the SAM format.

Subsequently, we resort to the data of the Mexican System of National Accounts (MSNA) to balance the accounts of the matrix in Table 3, to obtain a squared (balanced) macro matrix, from which we can build a fully consistent micro matrix. During the process, we will introduce new accounts to build a matrix that adequately shows the data of our economy, resorting mainly to the data reported in the Goods and Services Accounts (^{Inegi, 2010a}) and the Accounts by Institutional Sector ^{(Inegi, 2010b}). The macro matrix obtained is shown in Table 4.

Following the order proposed in Table 3, we begin with the balance of the account for the Households. For this, it is necessary to previously introduce three more accounts: the Capital and Labor to disaggregate the Value Added, and the Partnerships to systematically make use of the data of the Accounts by Institutional Sectors (AIS).

According to Table 3 of the Goods and Services Accounts (GSA) Employee remuneration (including Social contributions) increases to 2 370 474 (as noted above, all figures are in millions of pesos for 2003), and the Gross operating surplus (GOS) increases to 4 487 421. Adding both we obtain 6 857 895, the difference of which regarding the Gross Value Added of the total economy reported by the OIT gives us 310 631, which are the Other taxes on production paid by the Activities to the Government (in addition to the net taxes on the products already mentioned). The GOS goes to the Capital account, which transfers it to the Partnerships, which shall subsequently distribute it. The Employee remuneration goes to the Labor account, minus the Social contributions that the Activities pay to the Government, given that according to the AIS the "Net social contributions" perceived by the government are of 147 621, and thus the remaining 2 222 853 must correspond to the Households.

On the other hand, according to the AIS, the Social transfers (Social benefits different to the transfers in kind) are of 117 510, from which we subtract the Other social transfers (net) 4 269, to obtain the total transfers that the government makes to the Households: 113 241. In this case, we wish to obtain only the gross income of the Households, thus we subtract the Other social transfers that the government makes.

Also, according to the AIS the Other current transfers (net) of the RoW are of 167 223, (which constitute the remittances that the Households receive), and the payment of the RoW to the labor factor is of 16 353, with which the Households incomes are completed, missing only what they receive as capital income (GOS) from the partnerships.

Before obtaining the GOS that the Households receive from the Partnerships, we can observe their additional expenses to obtain their GOS as a balance. According to the AIS the Gross savings of the Partnerships is of 779 607, of 116 046 for Government, of 757 902 for the Households and the ISFLSH, and of 76 071 for the RoW.

Finally, according to the AIS, the ISR paid by the Households is of 226 509, (in addition to the consumer tax mentioned above). The ISR paid by the Partnerships (financial and non-financial) is of 170 107.

Since we already have the total expenses of the Households, and all of the elements of their income, we can obtain the GOS they obtain as the difference given by the balance: 3 513 249, with which the Households account is balanced.

The next account is that of Partnerships, for which we have practically obtained all the elements, observing that it has a balance of 24 458 corresponding to the Property income that the Partnerships pay to the RoW, which is consistent with the AIS data. With this, the Partnerships account is now also balanced.

Here we can observe that all the other accounts are already balanced, except that of Government, showing an imbalance of 124 766, which corresponds to the payment of the Property income of the Government to the RoW. It is worth noting that this payment, plus the payment made by the Partnerships that we obtained previously, add up to 149 224, an amount equal to the (net) Property Income of the RoW, as reported by the AIS. With this, all of the accounts of the macro matrix are balanced and we can proceed to disaggregate the Activities.

Disaggregation of the Activities and basic characterization

To disaggregate the Activities, we return to the OIT to reestablish the data that we added to elaborate the macro matrix, and shall subsequently use the information of the GSA to disaggregate the remaining data.

Previously, we introduced four more accounts to separate the social taxes (ISR, Social contributions, Sale taxes, and Other taxes on the production) to adequately carry out their disaggregation by productive sector.

Once the taxes have been reorganized, we open the 20 accounts necessary to disaggregate the Activities, where we can immediately copy the data from the OIT: inter-industrial exchanges submatrix, and the columns for Private Consumption, Government Consumption, FBCF plus Change in Stocks, and Exports. This done, the assignment of all the goods and services provided by the Total supply is completely disaggregated.

We can also immediately disaggregate the data from the rows of Imports and Sales Tax, copying the data from the OIT to the SAM, thus including in the SAM all the information of the IMP that is advantageous for its construction as has been mentioned, and we proceed to using the data reported by the GSAs.

Tables 55, 58, and 59 of the GSAs contain figures, by productive sector, of the Employee remuneration, of the Other taxes on the production, and the GOS respectively. As in said tables sectors 48 and 49 are aggregated, and considering that the importance of sector 49 is relatively small to maintain the transparency of the data, we also added these two sectors to the SAM (it is always possible to disaggregate them later if the necessary information becomes available). The three listings mentioned comprise the Gross Value Added (GVA), however, unlike the IMP, the GOS reported in the GSAs includes the "Indirectly measured financial intermediation services", which are not disaggregated. Therefore, to calculate the GOS per Activity, we first added the Remunerations, the Other taxes, and the GOS of the GSAs to obtain a GVA that includes the Financial services, and subsequently subtracted the GVA from the IMP to obtain the Financial services per sector, which we in turn subtracted from the GOS of the GSAs to obtain the net GOS per Activity of the Financial services.

The Other taxes on production in Table 58 of the GSA are the net taxes (304,878), which differ from those calculated for the macro matrix (310 631); this is a relatively small (1.85%) unexplained difference, and to distribute it we assume that it is proportionally allocated between the sectors.

On the other hand, we must separate the Social contributions from the Remunerations, for which we will also assume that the payment of the Social contributions is proportional to the Remunerations paid by each sector, which is equivalent to assuming that the Social contributions paid for each Activity are similar.

Once we included the Other taxes on the production, the Remunerations, and the Social contributions by sector in the SAM, the remaining balance must then correspond to the GOS per sector, with which the SAM-Mx03ETD is left completely balanced. We present the SAM-Mx03ETD in Appendix A.

We created Table 5 to evaluate the accuracy of the abovementioned balance, regarding the GOS per sector that we obtained previously from the GSA.

Therefore, the constructed SAM shows an inconsistency in the disaggregation of the GOS regarding the figures of the IMP, however, this is a transparent error and is not quantitatively significant, given that in most cases it only increases to 3.3% for the GOS of Activity 2 (Mining), and can be immediately corrected once the necessary data are available.

Basic study and characterization of the productive sectors

Foreign trade

Another important indicator to evaluate the performance of the economy is given by the degree of foreign trade, that is, the measure in which goods and services are imported and exported, also known as the degree of integration with the global economy.

We begin with the imports, presenting the demand for national inputs in Table 8, followed by the demand of imports and, in the last column, the import of inputs as a ratio of the national inputs.

The first thing that calls our attention is that manufacturing, the most important sector of the economy, imports inputs for an equivalent of 61.9% of the national inputs, significantly above the other sectors, which implies a high degree of integration (or dependence) of the global economy. In the lower extreme, we have five sectors with input imports that, due to their own nature, represent less than 10% of the national inputs: Real Estate services (7.9%), Educational services (8.9%), Recreational services (8.5%), Lodging services (5.0%), and Government activities (4.3%). For the rest of the Activities, the percentage varies, more or less uniformly, between 11.7% (Financial services) and 30.2% (Other services).

Table 8 Imported inputs. (Millions of pesos 2003). 

Activity	National inputs (A)	Imported inputs (B)	Imported inputs as a percentage of the national inputs (B/A)*100
Agriculture, livestock, forestry, fishery and hunting	135 281	26 618	19.7
Mining	94 399	16 028	17.0
Electricity, Water, Gas (end consumption ducts)	121 468	22 675	18.7
Construction	422 822	68 481	16.2
Manufacturing Industries	1 703 222	1 054 394	61.9
Commerce	314 052	59 933	19.1
Transport, Post Office and Storage	238 969	53 314	22.3
Information in mass media	101 206	20 661	20.4
Financial and Insurance Services	111 565	13 035	11.7
Real Estate and Rental Services	76 380	5 999	7.9
Professional, scientific, and technical services	92 393	19 312	20.9
Company and Corporate Management	15 937	3 284	20.6
Business support and waste management services	41 560	8 978	21.6
Educational services	39 570	3 513	8.9
Health and social assistance services	59 456	11 197	18.8
Recreation, cultural, and other services	11 157	948	8.5
Lodging, food and drink services	72 334	3 597	5.0
Other services except government activities	54 593	16 503	30.2
Government activities and international agencies.	100 632	4 309	4.3
Total	3 806 997	1 412 778

Source: Own elaboration with data from the Mexican System of National Accounts.

Let us now consider the exports. In Table 9, we present the total final demand per sector, the exports and, in the last column, the exports as a percentage of the total final demand. The highest percentage observed, 74.6%, corresponds to Mining, explained by the presence of Pemex with its oil exports. In second place we have Manufacturing, with exports that increase to close to half of its total net production of inputs (45.9%). In absolute terms, Manufacturing is also the most important exporting sector of the economy; the exports of the previously seen Mining sector only represent 13.8% of the exports from Manufacturing. In third place we have Commerce, which contributes 18.4% of its final consumption production. The rest of the Activities do not have significant exports.

Table 9 Exports. (Millions of pesos 2003). 

Source: Own elaboration with data from the Mexican System of National Accounts.

General Multipliers Matrix (GMM)

In this section, we used the SAM-Mx03ETD to carry out an identification exercise for the accounts of our economy, based on the General Multipliers Matrix (GMM)-thus called because it generalizes Leontief multipliers to a SAM-and using the definition of Rasmussen indices.

Possibly, the most important utility -or at least the most exploited one of Leontief model- is that it allows the quantification of the interrelations between the sectors of the economy and, therefore, the identification of those that have the most intense relations with the others (key sectors). In this manner, it could be argued that such sectors, should they receive significant investments, would generate a higher growth for the economy.

Although various methods have been developed for the identification of key sectors, mainly based on their "backward" and "forward" chaining (^{Iráizoz, 2006}), and even when Rasmussen indices have received some critiques (^{Sonis et al., 1995}, p. 234), in this work we calculated the General Multipliers Matrix (GMM) and classified the accounts of our economy according to said indices-due to their broad use and because they comprise a first approximation to the study of the structure of a real economy.

We will not go into detail regarding the specification of the model, as it is well known and many texts discuss it in detail (in particular, ^{Miller and Blair, 2009}, Ch. 6); it suffices to specify that the general form of the model is:

()1

Where y represents the income vector (equal to expense) of n=1, ..., N endogenous accounts; M=(I-A)^-1 is the multipliers matrix (equal to Leontief inverse when the endogenous accounts are only the productive sectors); and x is an endogenous accounts vector (equal to the final demand in Leontief model).

Each M element of column j is interpreted as the impact of an exogenous unitary increase directed to account j, over the income of each endogenous institution, so that the sum comprises the total multiplying effect.

Rasmussen indices simply compare the impact of each account or sector with the average impact, both by column (carry-over) and by row (dispersion), so that when a particular impact is higher to the average there is an index greater than one. Otherwise, the carry-over or impact index per column is defined as:

()2

Where is the average impact of the sector or account j over the other endogenous accounts, and N is the number of endogenous accounts or sectors. Similarly, the dispersion per row of the index is defined as:

()3

To carry out this exercise, we performed the follow modifications to the SAM, with the purpose of simplification. We eliminated the Societies account, making it so that the Capital account directly does the distribution of the GOS. We also eliminated Private consumption, so that the Activities directly transfer the goods and services to the Households. Finally, we considered the Rest of the World and the Government as endogenous accounts along with the tax accounts.

Appendix B presents the table with the obtained GMM, and in Table 10 we can observe the Rasmussen indices that can be interpreted as a summary of the GMM, with the identification of the 23 endogenous accounts of our economy.

According to these results, the productive factors have an above average impact, both in the carry-over and the dispersion, which is logical if we consider that all the productive sectors utilize them, and the income is generated from these. In the strategic sectors, the multiplier effect that the households have with the dispersion of their income is notable, which increases to 5.24, that is, each peso spent by the households generates a total dispersion of 5.24 pesos, an interesting result if a strengthening policy of the income of the households is considered.

Table 10 Rasmussen carry-over and dispersion indices. 

Source: Own elaboration.

Final comments

In this work, we built and presented a Social Accounting Matrix (SAM), proposing and developing a transparent methodology to make it possible to clearly track-up to the statistical sources of the national accounts-the origin of all the data contained in the SAM; therefore detecting errors, making corrections, and adapting the matrix to specific research purposes. It is worth noting that this SAM can be immediately extended to the next level of disaggregation reported by the INEGI-which comprises 79 sectors of the NAICS-to carry out more detailed analyses of the productive sectors.

Once specified, the SAM can be used to apply a broad range of multi-sectoral models to the analysis of the Mexican economy, particularly the structural analysis and Applied General Equilibrium Models, with the advantage that the results can be replicated by different researchers and, consequently, can be discussed and validated or corrected.

Additionally, we carried out an analysis of the productive sectors, followed by the calculation of a generalized multipliers matrix that provides the total effects that a boost would have on each productive sector. Finally, we identified the productive sectors based on Rasmussen carry- over and dispersion indices.

According to other similar studies (Beltrán et al. 2016 and ^{Sobarzo 2011}), the classification of the productive sectors is consistent and comprises a useful guide for the economic policy analysis. Especially, the identification of strategic sectors allows preventing bottlenecks that could hinder the growth of the economy, and that of booster sectors allows the identification of investments that could have the highest multiplier effects and thus the best return to planned investments.