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Atlantic Review of Economics 

            Revista Atlántica de Economía

Colegio de Economistas da Coruña
 INICIO > EAWP: Vols. 1 - 9 > EAWP: Volumen 2 [2003]Estadísticas/Statistics | Descargas/Downloads: 6939  | IMPRIMIR / PRINT
Volumen 2 Número 14: The Financial Unlinkage of the Mexican Economy: A Social Accounting Matrix Multiplier Approach for a One-Sector Economy.

Andrés Blancas*
Instituto de Investigaciones Económicas, UNAM

Reference: Received 09th October 2003; Published 07th November 2003.
ISSN 1579-1475

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This paper addresses the financial unlinkage in Mexico through an accounting multiplier analysis derived from a SAM for a one-sector economy. Such an analysis provides a useful tool to quantify processes of structural financial change in terms of "stylized parameters". We identify and measure the financial unlinkage with financial backward and forward linkage indices derived from the accounting multipliers. The results can also help to the quality of policy decisions by identifying key and weak financial institutions and by giving a better understanding of how an impact of an initial financial injection travels within a structure.


Este artículo aborda la desvinculación financiera en México a través de un análisis multiplicador contable obtenido de una SAM (matriz de contabilidad social) y aplicado a una economía unisectorial. Dicho análisis nos proporciona una herramienta útil para cuantificar los procesos de cambio estructural financiero en términos de "parámetros estilizados". Identificamos y medimos la desvinculación financiera con índices de vinculación financiera futura y pasada, derivados de los multiplicadores contables. Los resultados pueden influir positivamente en la política de decisiones en tanto que nos facilitan la identificación de las instituciones financieras fuertes y débiles al tiempo que nos clarifican cómo el efecto producido por una inyección inicial financiera puede actuar dentro de una estructura.


   The main concern of this paper is to show the unlinked condition of the Mexican Financial System by means of an accounting multiplier analysis. Given the data at hand, this paper deals only with the structural financial factors of the Mexican economy under the key hypothesis that the Mexican financial system is structurally weak since it shows financial unlinkage amongst the institutional sectors. By means of a SAM framework for a one-sector economy and with the help of an accounting multiplier analysis, we get financial backward and forward linkage indices to identify and measure such a structural financial weakness. An accounting multiplier analysis within a social accounting matrix (SAM) scheme for a one-sector economy built up for 1990 provides a useful tool to quantify processes of structural financial change in terms of "stylized parameters".

   The analysis is mainly conducted by cross sectional representations of the economy, accounting identities, monetary and financial accounts, and standard empirical relations that typify developing countries. In section two, we define a SAM for a one-sector economy and depict the Mexican financial system through such a matrix. Some accounting multiplier generalities are considered in sections three and four. Section five presents an estimation of the accounting multipliers that permit to show the structural financial unlinkage of the Mexican economy in section six. The last section shows some concluding remarks of this work.


   A SAM is a double-entry bookkeeping table used to display national income and product, interindustry, flows of funds, and other combined sets of accounts. The rows of a SAM record incomes (receipts) and the column expenditures (payments). All entries of the matrix are set out in nominal terms and totals for corresponding rows and columns are the same; the SAM´s row-column identities hold only in current price terms. So, the base year prices can be normalized to unity and held in this condition for the SAM multiplier analysis, under de assumption of excess capacity and hence fix prices throughout.

   The SAM for a one-sector economy is meant to capture the financial structure, to focus on the flows of funds structural analysis; under this assumption, we sum up all transactions of production sectors just in a one row-column of production costs and uses of output activities. Another important assumption in such general outline is that the macroeconomic causality in developing economies runs from demand injections to leakages under conditions of endogenous finance, which implies to consider all the financial institutional accounts as endogenous. Table 1 shows the SAM for a one-sector economy, combining the real and financial parts of the Mexican economy and it tries to follow an outline designed for structural analysis in 1990. This table was elaborated with data presented by Vos (1997), BANXICO, INEGI, SHCP and CIE, and it contains 18 accounts grouped in a current and a capital account; each row and column pair represents an account with incomings in the row and spending in the column. The real side of the economy is represented in the current account by rows and columns 1 through 9; meanwhile, the financial side in the capital account by rows and columns 10 through 17.

DOWNLOAD TABLES (Menú de la derecha, Descargas - Download) 

   The account 1 shows the intermediate and final demand, input-output transactions among different sectors in the economy are aggregated in the total uses of output in row 1 and total production costs in column 1. Columns 5, 8 and 9 give uses of incomes in households and government consumption of domestic goods and exports, respectively. Columns 10 through 12 show national (row 1) and imported (row 9) investment goods. In this case public investment is split in public firms and government investment (columns 12 and 13), and column 17 shows the direct foreign investment. Accounts in rows 2 through 4 show the domestic and foreign income flows to factors of production from: labor (wages), unincorporated capital (self employed capital income) and corporate capital (operating surplus of corporate enterprises). These income flows to factors are transferred to domestic and foreign current institutions in columns 2, 3, 4 and 9.

   The domestic current institutions are households, private firms, public firms, and central Government. The account 5 shows the income and outlays flow of households, the income flow on row 5 comes from wages and salaries in column 2, self employed capital income in column 4, dividends from private firms in column 6, transfer payments and interest from public enterprises bonds in column 7, current transfers and interest from government bonds in column 8, and interest from investment abroad and current transfer payments from the rest of the world in column 9. Column 5 shows that households spend their income in final consumption (rows 1 and 9), direct taxes (row 8), and transfer payment to public enterprises (row 7).

   The account number 6 corresponds to private firms where incomes come from the operating surplus and the interest from government bonds, columns 3 and 8 respectively. Private firms spend their income in direct taxes (row 8), interest and other payments to the rest of the world (row 9), and dividends to households (row 5).

   In row 7 public firms receive incomes as corporate profits (column 3), transfer payments from households (column 5), and subsidies. In column 7 public firms spend their incomes in transfer payments to households (row 5), domestic interest payments and net transfer payments from government (row 8), and foreign interest payments (row 9).

   The account of central government shows in row 8 the income from indirect taxes (column 1), direct taxes from households and enterprises, and other incomes (columns 5 through 7). In column 8 central government spend its income in final consumption (row 1), subsidies to households and private firms (rows 5 and 6), domestic interest payments (row 5), and foreign interest payments (row 9).

   In row 9 foreigners get income from imports of intermediates and capital goods (columns 1, 11 and 12), and interest payments and other payments from private enterprises, public firms, and government (columns 6 through 8). In column 9 foreigners spend their income in exports (row 1), revenues, and transfer and interest payments to households (rows 2 through 5).

   The difference between income and spending in the current account leads to institutional saving which can be positive or negative registered in capital accounts in rows10 through 13, and 17 and columns 5 through 9. When flows of funds are included the identity between investment and domestic and foreign savings must add the financial transactions or the changes in liabilities and assets of institutions showed in rows and columns10 through 17. So, foreign transactions offset with the changes in reserves such that the accounting identity between incomes and spending holds. If flow of funds are not considered the accounting identity holds when foreign transactions offset with the deficit (surplus) in the current account of the balance of payment. In the last case, the private investment is financed with domestic private saving, foreign saving (the counterpart of which is the current account deficit), and the net public investment (operational fiscal deficit).

   The capital account shows in the rows institutional savings and liabilities adding to investment finance. The columns register the use of investment funds by institution in national and imported investment goods and institutional financial assets. This account permits us to determine the allocation of savings through different assets and to evaluate the role of financial intermediaries in making the private outlay possible. Across a row, saving goes into net accumulation of assets by the related income institution.

   In row 10, the saving of households goes completely toward building up net assets in column 10 with commercial (row 15) and development banks (row16) as deposits, with central bank as currency and coins (row 14), with private firms as stock exchange transactions or corporate stocks (row 11), with public sector as government securities (row 12), and with the rest of the world as foreign assets including capital fly (row 17). In row 10 also household liabilities include credit from commercial (column 15) and development (column 16) banks.

   In row 11 private firms take loans from both the domestic banking system and foreign sources (column 14 through 17) by direct indebtedness, money market and stock market transactions, which comprehend portfolio foreign investment. On the other hand, private firms buy government securities (row 12) and make deposits in the banks (rows 15 and 16).

   Table 1 shows in row 12 and 13 the public sector transactions of liabilities with domestic and foreign institutions. Public sector get financial resources from the placement or marketing of securities in the domestic and foreign markets (columns 10 through 17). This table shows public sector transactions of assets, column 10. In rows 15 and 16 Public firms have assets with commercial and development banks, in rows 12 and 14 government register negative asset transactions with public firms and central bank.

   The banking system´s net saving is set to zero (or accumulated in firms accounts), so there is no saving entry in their respective rows. The column of the central bank account shows the credit to private and public sectors, credit to banks (including banking rediscount), and foreign exchange reserves. The row of the central bank account registers the currency and coins, reserves for demand deposits from commercial, development banks, and private and public sector (including reserves for near money), and net debt with foreign sector.

   Assets of commercial banks include credit to private (rows 10 and 11, column15) and public sector (rows 12 and 13, column 15) and reserves for demand deposits on central bank (row 14) and near money. Liabilities registered in row 15 include demand deposits from private and public sector, near money and rediscount with the central bank, and net debt with the foreign sector (row 15, column 17).

   The development banks channel resources to private and public sectors by means of credit operations, and receive net resources from central bank. On the other hand, they have net debt with foreign sector (row 16, column 17) and hold monetary liabilities and saving instruments from the private and non financial public sector. In the row side, the foreign accounts show, the foreign exchange reserves hold by central bank (column 14) and the capital flight carried out by households (column 10); on the column side net direct indebtness of the private and non financial public sector and banking system, and portfolio investment and household foreign assets.


   By their properties pointed out above, a SAM table can be used to build up different sort of models in a well-behaved way into the structural change and policy analyses. Some development on these lines is given in Taylor (1990), Round J. (1999), Colatei and Round (2000), and Robinson, Yunez, Hinojosa, Lewis and Devarajan (1999) who elaborate different sorts of computable general equilibrium (CGE) models even like a complex set of simultaneous nonlinear CGE models with Jacobian multipliers.

   Into a SAM approach, the accounting multipliers are very simple indices, which contains important information about the structure of an economy and are built up directly from the SAM. However, they are not only measures of the effects of changes in exogenous injections on the levels of endogenous variables. Actually, they give an insight into the anatomy of the structure of an economy in terms of transfer effects and the full circular effects and cross-effects between different parts of the economy, corresponding to the circular flow of exogenous injections, which characterizes the multiplier process.

   At the beginning of the multiplier process, the matrix of accounting multipliers has the form of a Leontief inverse (Leontief, 1986) that can be applied to flows of funds and households as well as to industries. The accounting multiplier matrix, derived from a SAM table, links all endogenous income levels to exogenous injections. A SAM multiplier matrix can be decomposed into multiplicative components, each of which shows a specific sort of linkage into the system. We depict a la Stone (1985) an additive version of the multiplier matrix that links all endogenous income levels to exogenous injections.

   The accounting linear multiplier models are demand driven into the Keynesian tradition and do not incorporate supply constrains. The total impact of a particular set of final demand is described as process of round by round final demand in which given an initial change or financial injection into the system will lead to a process of multiplier effects.

   Let S be the matrix of column-normalized coefficients of the social accounting matrix for a one-sector economy with two subgroups: real accounts and financial accounts. Then S can be rearranged as follows:

where stands for the financial flow at a given year between real accounts, real intraflow, is the financial flow between the financial accounts, i.e. the financial intraflow. are investment and savings transactions respectively. After selecting some accounts as exogenous, in this case the public sector spending accounts, we proceed to rearrange S, the respective rows are taken into the leak matrix, and the columns are left out of the endogenous block to account for injections and intraexogenous financial flows. So,

   After this reclassification of exogenous and endogenous accounts, the submatrix [Intraendogenous Flows] is still a square matrix, since we removed out of it the same number of columns and rows, but still accounts belong to either subgroup,

but exclusively between endogenous accounts. Each represents the average expenditure propensities, i.e. the expenditures as proportions of total income.

   We may wonder how would the intraendogenous financial flows modify if financial flows were injected into the system? Such an answer clearly leads us to the usual structural multiplier analysis. Using the fact that total incomes received by endogenous accounts y equals expenditures by the endogenous accounts or intraendogenous accounts S*, plus injections x or expenditures by the exogenous accounts, we obtain:

where and is the number of exogenous accounts. Then a typical accounting multiplier inverse matrix. However, at first glance, it´s still impossible to discern the injection´s pathway through the accounts in . We decompose , based in a selection of endogenous accounts of more interest. In our case this subgroups will be the endogenous real accounts and the endogenous financial accounts. This leads us to an additive decomposition of as follows:

Analogously, from the geometric series we get

for n=2 we would obtain the classic decomposition, the value of n depends on the additional information from as well as their economic meaning. This is a multiplicative decomposition of the accounting multiplier inverse matrix, where we can observe the trajectory of the injection, as long as the inverse matrices exist,

   We have clearly obtained the partial intragroup multiplier effect of an exogenous injection to the system. We could define as the multiplier matrix of spillover effects and as the feedback one, but these are not unique.

   So far we have only discerned the path the injection follows trough the endogenous subgroups, (with the aid of the multiplicative decomposition) , and we are only interested in the net effect , then we write as a telescopic sum to obtain

which is an additive decomposition of the accounting multiplier inverse matrix, where we can observe the final destination of the financial injection. N1 shows the net intragroup effects, N2 represents the net spillover effects, and N3 describes the net feedback effects.


   The macro causality represented by the multiplier matrix can be broke down into several kinds of linkages in the economy. Since any SAM satisfies Walras´ Law with the receipt row and expenditure column for each account balancing, the complete network by means of which impact is conducted can be recognized and determined through structural multiplier analysis.

   As in any inverse matrix there are both backward and forward linkages: Backward linkage in the social accounting framework will mean: to increase an institution´s income, it will need more financial in-flow. Forward linkage will mean: there will be more financial resources to spend if an institution increases its income.

   The typical vector of accounting multipliers is given by , where is a row vector of ones and its dimension equals the number of accounts in the endogenous social accounting matrix. If we multiply this vector by a factor , where k is the number of endogenous accounts, what we get is the vector of average responses to exogenous injections. These average multipliers are clearly some measures of backward linkage. A measure of forward linkage is given by , a column vector, which components stand for how much the income of accounts would increase given a uniform exogenous injection. This is, how much the income of every account would increase if all the endogenous accounts had received the same amount of financial resources in an injection. If we multiply by , we obtain a measure of backward linkage response to a uniform total injection of say, one dollar.

   The number is the average multiplier of the whole accounting multiplier inverse, but it is also the average of backward and forward average multipliers, as constructed. Therefore from the vectors of ratios and we can see which accounts have the most significant backward and forward linkages, respectively, in the whole economy.

   So far, we are able to give some insight about the behavior of the whole economy based on the indices Besides the accounting multiplier inverse we can also use its additive decomposition, and the indices above to explore the exogenous injection path through the different multiplier matrices: intragroup, spillover, and feedback.

Since the inverse can be decomposed as follows:

we just decomposed the backward average linkages vector as a weighted average of the backward average feedback, backward average spillover, backward average intra-group linkages vectors plus the initial injection. Clearly a rough measure of weather the feedback, spillover or intra-group effects were more significant for the behavior of the whole economy is given by the numbers

   Lets decompose the forward linkages, analogously to the procedure above

   So that we just decomposed the forward average linkages vector as a weighted average of the forward average feedback, forward average spillover and forward average intra-group linkages vectors plus the initial injection.


   The next is to estimate the accounting multipliers according to the rules and assumptions stated above. After normalizing by column the SAM table and selecting the public sector accounts as exogenous, we proceed to rearrange the initial matrix; the respective rows are taken into the leak matrix and the columns are left out of the endogenous block.

   The result is a matrix with lesser dimension than the original SAM, but this new matrix is still a square matrix. This leads to an additive decomposition of intraendogenous flows in square and nonsingular matrices where after recursively substituting we obtain a multiplicative decomposition that shows the trajectory of the injection. However, we get only the path of the injections into the endogenous subgroups. With a telescopic sum of this multiplicative decomposition we get the additive decomposition that shows the final destination of the exogenous injection. So, the final result is a set of multiplier matrices showing the net intra-group, spillover, and feedback effects of the exogenous injection.

   All these accounting multiplier matrices capture the macro effects and reflect different types of linkages in the SAM for a one-sector economy at a given moment. With these accounting multiplier matrices we took pictures of linkages in the endogenous accounts. The accounting multipliers ignore any linkages that work through changes in prices. This kind of multiplier measures the grade of financial linkage and the relationships among different institutional accounts. The structural financial unlinkage is a signal of developing economies like Mexican economy, where there is an easy way to external and internal financial shocks to evolve very quickly toward a generalized economic crisis as in 1976, 1982, 1987, and 1994.

  The financial structure of the Mexican economy presented in the SAM table captures less structural financial vulnerability when it shows a higher degree of institutional linkages. A lower degree of intra-linkage, inter-linkage or extra-linkage of the financial and non-financial institutions show higher degree of structural financial vulnerability, a non complex and developing economy, that can be easily damaged by international fluctuations in row material prices, interest rates, capital flight, portfolio investment or terms of trade. The accounting multiplier matrices show these grades of institutional linkages.

   Under the assumption that when an account receives money it spends it in the proportions showed by the accounting multiplier matrices, the numbers in the columns of such matrices show the consequences for each account of a financial unit received exogenously by the respective account.

   The decomposition of accounting multipliers permits the policy-maker to get in a different and separated way the reaction mechanism of distinct economic agents within the complex system of structural relations. So, this can help to the quality of policy decisions by giving a better understanding of how impact travels within a structure. One can measure the strength and weakness of the backward and forward linkages of institutional accounts into the SAM scheme in terms of the total net effects, intra-group, spillover, and feedback multipliers.

   As we pointed out above, the SAM for a one-sector inverse, is a matrix multiplier for all effects. The multiplier effects contained in T matrix measure the net intra-group effects and flows from the impacts of the initial injection, represented by the identity matrix I, within the group of accounts which it initially penetrated. V matrix shows the net spillover effects and begin from the impacts of the initial injection when it has finished a round trip through all three groups and turned back to the one that it had originally entered. F matrix measures the feedback effects and starts from the repercussions of the initial exogenous injection when it has completed a tour outside its initial group without returning to it.

   By means of a program elaborated in a Windows version of Mathematica 3.0, we estimate the different accounting multiplier matrices. Tables 4 through 5 show the different accounting multiplier matrices. 

   When an account get financial resources, by an exogenous injection, it spends it in the proportions shown in the normalized matrix. The numbers in the matrix of Table 2 measure the all effects of such an injection; meanwhile, Table 3 measures the net intra-group effects (T matrix) and flows from the impacts of the initial injection within the group of accounts, which it initially entered. To this we add on in the matrix of Table 4 the net effects coming from the spillover multipliers. Finally, in the Table 5, we add the net effects coming from the feedback multipliers. So, the different accounting multiplier matrices show the consequences for each account of 1 financial unit acquired exogenously by the account at the head of the column.


   Since all these multiplier matrices are showing financial transactions between different accounts, then each number in this kind of matrices measure the grade of financial linkage of each account at different stages as a consequence of an exogenous financial injection. By the way, every matrix presents the backward and forward financial linkage as a result of a financial exogenous injection. If any of both the financial backward or the financial forward shows weakness then the account or set of accounts will be structurally vulnerable, that is, there is a case of structural financial vulnerability.

   The decomposition of accounting multipliers allows the identification of both the structural financial linked economic agents and the structural financial unlinked accounts. Such decomposition permits the decision-maker to capture the strength and weakness of each institutional account or a group of accounts, and in this manner contributes to the quality of policy decisions. Any linked account must satisfy both ub and to be considered a key account. Otherwise, if an account presents at least ub or it is enough to be defined as a partial unlinked or structural financial vulnerable account. In the case that both ub and then such an account can be considered financially weak account or total unlinked account. The degree of financial vulnerability is stated by the value of the weighted average multipliers within the complex network of structural relations. The lower weighted average multiplier, the greater structural financial vulnerability. At the bottom of each matrix of multipliers there is a resume table that shows the status of each account with different combinations of backward and forward unlinked values. It will have a number 1 at some account if the respective account was linked or was a key account, and there will have a number 0 if there is at least one kind of unlinked present, either backward or forward one.

   For a rapid view of the results see the financial backward and forward unlinkage status for all multiplier matrices in Table 6. What this table shows is that only a small number of accounts located mainly into the real side of the economy were key accounts in 1990. The "Product", "Private Firms" and the associated "Corporate Profits" accounts were the key accounts that stimulate the overall economy and they were also dragged by it as a result of a total net effect of an exogenous injection. It will read unlinked at some account and fixed year if the respective account was unlinked at that year, that is, if there is at least one kind of unlinked present, either a backward or a forward one. Figure 1 shows also the degree of link or unlink (backward or forward) an account has in the multiplier matrix for all effects.

   In contrast, all the other accounts show structural financial vulnerability. Households in the financial side, Wages, Unincorporated Profits, and Development Banks were total unlinked accounts. These accounts do not generate any important impact into the economic system and vice versa and they are more vulnerable to any kind of shock.

   Households in the current account, Foreign in both current and capital accounts, Central Bank and Commercial Banks were forward unlinked accounts; this means that all these accounts were growth promoters, by their backward linked status, but it could present bottlenecks that can lead to bankruptcy in the presence of external or internal shocks by their forward unlinkage status. Once financial institutions with forward unlinkage status (Uf<1) are "infected", as in the case of bankruptcy, they can become not growth promoters but they can facilitate the fast contagious of the financial disease as toward the rest of the financial system as toward the real side of the economy through the backward linkage, since they also present a backward linkage condition (Ub>1) at the same time. Because in the case of bankruptcy the increases in assets (international reserves, currency, deposits, government bonds and equities) can become "bad" financial assets that work like catalyst of generalized economic crisis. So, a financial account with forward unlinkage status and backward linkage condition can amplify the external and internal shocks toward the overall economic system.

   Table 6 shows the different financial linkage status in all the multiplier matrices. In the real side Private firms displayed a financial backward unlinked status in the spillover multiplier matrix. In the financial side, this account exhibited a backward and forward financial unlinked status in the intra-group and spillover multiplier matrices, respectively. Households showed a linked status in the intra-group matrix in the real side, but a total unlinked condition in the spillover and feedback matrices. In the financial side this account remains the same (total unlinked in all the different matrices). The Foreign accounts displayed a total unlinked status in the spillover and feedback multiplier matrices in the real and financial sides respectively.

   Central Bank exhibited a total unlinked status in the feedback multiplier matrix, and remained a forward unlinked in the other kind of matrices. Commercial Banks showed instability in their status: backward, total and forward financial unlinked condition in the intragroup, spillover and feedback multiplier matrices, respectively. Development Banks displayed a forward unlinked status in the feedback multiplier matrix, and remain the same total unlinked condition in all the other matrices.


   The result of the "picture´s analysis" is that the Mexican financial system in 1990 presents a generalized structural unlinkage. Since the majority (81%) of the entries in the SAM for a one-sector economy showed total (38%), forward (30%) and backward (13%) financial unlinked accounts in the net, intragroup, spillover and feedback multiplier matrices, then the Mexican economic system presented a structural financial weak system that facilitates the contagious from the financial side to the rest of the all economy in the presence of internal or external shocks.

   The Central Bank, commercial banks and development banks did not play any key role in the financial system. Although they were growth promoters, they also presented bottlenecks mainly in the role of lender of last resort and financial intermediaries. Such a condition permits that an individual bankruptcy and speculative attacks against the domestic currency can easily become a generalized economic crisis by their impact in the level of investment and employment. The total unlinked household accounts show the financial vulnerability into this sector, which also could be the result of a biased income distribution toward the richest groups.


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About the Author*

Autor: Andrés Blancas
Dirección: Instituto de Investigaciones Económicas, UNAM
Correo electrónico:

Helpful comments and suggestions from Ángel Calderón-Madrid, as well as research assistance from Jaime Blancas and Mario Mendieta are gratefully acknowledged. A preliminary version of this paper was presented at the ASSA meeting in New Orleans, 2001.



Derechos reservados 2002. El permiso para reproducir algún artículo está garantizado si Documentos de Trabajo en Análisis Económico lo acredita, las copias no son vendidas y es en acto de mayor difusión del documento.

Fernando González-Laxe. (Universidade da Coruña)
Venancio Salcines. (Universidade da Coruña)
Andrés Blancas. Instituto de Investigaciones Económicas (UNAM)
Editor Asociado para America Latina:
Luis Miguel Galindo. Facultad de Ecomomía (UNAM)


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