Mario Montesino, Armando Álvarez, Juan José López and Meraris López*
This article inquires the relationship between the market prices and the analytical prices of the labor theory of value in El Salvador’s economy between 1990 and 2006. A new methodological perspective is proposed for the labor value and the production’s prices, measured with an emphasis on the distinction of the labor’s complexity of Marx and the importance of the full payment of the value of labor power. The data utilized for these estimations comes from El Salvador’s input-output tables from 1990 to 2006, obtained through the transformation of the supply and use tables with the model B of Eurostat. The article’s novelty is the theoretical approach for the values and production’s prices measuring; moreover, is one of the first research on this topic in a Central American country. The fundamental Marxian’s variables obtained are compared with the approach used by Shaikh (1984, 2016); Ochoa (1984) and Guerrero (2000); Sánchez, Álvarez and López (2017). Furthermore, the correlation coefficient between the market prices and the values is calculated.
(*) Department of Economics, Universidad Centroamericana José Simeón Cañas (UCA), El Salvador
During the eighties, the analyses that pretended to archive the labor value’s empirical measuring from the Marxist theory began to generalize. These analyses were based on Sraffa (1966) and Pasinetti’s (1984) approaches which proposed to use Input-Output Tables (IOT) and matrix algebra to measure labor-values, direct prices and prices of production. In this manner, the debate about the “transformation problem” provided new analytical tools and methodologies to continue looking for answers for Marx’s (1981) unsolved problems on Capital’s Volume III.
In this spirit, we present in this article a new proposal about this transformation process that would be appointed as “New Approach”. This proposal has focused on Marx’s distinction about simple and skilled labour and the importance of full payment of the labor power’s value. Moreover, this proposal has been elaborated considering El Salvador’s productive and labor market reality in specific, but Central and Latin-American countries’ in general, since our countries share many characteristics and limitations. Is plausible to think that this new approach fits better with our own economic conditions.
The second section of this article presents one proposal to the transformation problem, developed by Anwar Shaikh, Diego Guerrero and Edward Ochoa. This methodology will be the comparison point with our own proposal. The third section presents the “New Approach” methodology to this problem, explaining the main differences from Shaikh, Guerrero and Ochoa’s proposal in specific, but with others solutions to this problem in general. The forth section presents the data’s sources used in this research and also the methodology to calculate matrices and vectors required for labor-value’s measuring.
The fifth section presents the results from measuring labor-values and direct prices with both methodologies applied to El Salvador’s economy from 1990 to 2006, using the Input-Output Tables (OIT), while the direct prices are compared with the market prices to establish which methodology fits better with the Salvadorian market behavior. Also, the fundamental Marxian variables are calculated to study El Salvador’s economic behavior. Finally, conclusions and final thoughts are presented about the new approach’s explanatory capacity about the Salvadorian economy.
II. Shaikh, Guerrero and Ochoa’s solution on the transformation problem
One of the main theoretical and empirical proposals on the transformation problem is the one developed by the economist Anwar Shaikh (1984, 2016). As Guerrero points out (2000), Shaikh makes a reinterpretation of analytical tools of other authors –such as Leontief, Sraffa, Pasinetti- in a Classical-Marxist line of thought. Furthermore, he advised the PhD dissertation of Ochoa (1984), which is one of the main empirical calculates of the labor values using Shaikh’s approach for the United States’ economy.
In the chapter IV of this dissertation, Ochoa (1984) develops the expression for the labor-values, the direct prices, Sraffian prices of production and Marxian prices of production1. Through mathematical deductions, he shows that the labor-value vector (𝑣), which represents the labor-coefficients vector vertically integrated (Guerrero, 2000: 124), is obtained though the next expression:
𝑣 = labor-value vector
a₀= labor-coefficients vector
𝐼 = identity matrix
𝐴 = matrix of input coefficients
𝐷 = matrix of stock-discards coefficients
This labor-value vector clearly expresses the sectorial unitary values, that means, the direct and indirect labor requirements for monetary unit in each sector. So that, it is possible to calculate the sectorial values (Λ) which represent the total direct and indirect labor contain in each sector. To obtain Λ, 𝑣must be multiplied for the diagonal matrix of the sectorial gross value of production (𝑋)².
As Ochoa (1984: 49) points out, “these values cannot be directly compared to prices; the former are in units of (unskilled) labor-time and the latter in dollars”. So that, it is necessary to calculate the monetary expression of the value (edv) which express the quantity of monetary units contained in the unit of labor measure (human years, in this case). Mathematically, the edv is obtained through the ratio of the total gross value of production – total values (sectorial values added):
Once the edv is calculated, the direct prices (𝑑) and the unitary direct prices (𝑑𝑢), could be obtained. Both express the value in the monetary form:
After that, the circulating capital (CC), the fixed capital (CF), the fixed capital discarded (CFD), the variable capital (CV) and the surplus value are obtained (Pv):
Where K is the matrix of capital stock coefficients and B the matrix of labor consumption coefficients. It is important to remember that all these variables are in current prices. Since the analysis must be done with constant prices, it is necessary to multiply each one of these vectors with the inverse of the diagonal price vector (e). For example, the equation (11) express the circulating capital in constant prices, the subscript “k” express that the variable is in constant prices:
Finally, Ochoa (1984) develops the Marxian price of production. According to this author: “The essence of Marx’s concept of prices of production is that they are prices consistent with a uniform rate of profit on capital advanced. This means that prices consist of components: unit costs and profit on capital advanced per unit of output” (Ochoa, 1984: 89). In other words: “the prices of production are nothing more than the mass of benefits vertically integrated”³ (Guerrero, 2000: 124). Its expression in matrix algebra is as follows⁴:
We can rearrange the equation (12) to obtain an eigenvalue and eigenvector problem:
Where the variables that has not been defined yet, are:
𝑝 = Price of production vector
𝑏′ = transpose row vector of consumption per worker
𝑟= profit rate
For the Perron-Frobenius theorem, the profit rate must be the maximum eigenvalue and the prices of production must be the eigenvector associated to this eigenvalue. As Guerrero has pointed out, this method to understand the transformation problem places these authors on the New Interpretation, which “propose to interpret both [values and production prices] as inseparable from each other” (Guerrero, 2000: 43). Nevertheless, as has been shown, in this methodology the measure of the labor values and the price of production are totally independent from each other.
III. A new theoretical and empirical approach on the transformation problem
On this section, the theoretical and methodological approach that will be used in this article for the measure of the labor-values and prices of production will be developed. This approach pretends to overcome the independent treatment of the measure of these variables. Furthermore, the homogenization of labor to simple labor it is incorporate in the analysis.
The linear static method assumes a starting situation in which time does not count, since it is assumed that in the past periods the goods have been sold at their values. In this way, the iterative process represents an adequate description of the incorporation of direct and indirect inputs, this is present labor and past labor, since the labor force has the capacity to transfer and create value simultaneously (Montesino, 2011: 33).
The relative prices could be calculated with any commodity, including the labor. In the process of measuring the relative prices, is convenient to use a numeraire, that consist in making one of the variables equal to zero. This means that the other variables will be expressed in terms of the numeraire, just as Pasinetti (1984) does. Therefore, if we use the simple labor as numeraire, we obtain the labor-value coefficients, which is very important for Marx’s labor-value theory.
On the other hand, in the exchange process, the skilled labor is constantly transformed to simply labor. Marx (1979: 44) points out that human labor is the expenditure of simple labor power which “on average, apart from any special development, exists in the organism of every ordinary individual”. This simple labor is given in any society. Meanwhile, the skilled labor “counts only as simple labour intensified, or rather, as multiplied simple labour”, therefore, a certain amount of skilled labor equals a greater amount of simple labor. On this point, Marx indicate:
“The different proportions in which different sorts of labour are reduced to unskilled labour as their standard, are established by a social process that goes on behind the backs of the producers, and, consequently, appear to be fixed by custom. For simplicity’s sake we shall henceforth account every kind of labour to be unskilled, simple labour; by this we do no more than save ourselves the trouble of making the reduction” (Marx, 1979: 44).
It is on this point that this article will emphasizes the relevance of homogenize the different labor skills to simple labor in line with Marx’s ideas.
The simple labor is associated with a basket of basic goods (𝑑), strictly necessary for maintain the life of the worker, such as the salary of subsistence described by Pasinetti (1984). On Pasinetti’s words: “the men are treated as horses” (Pasinetti, 1984: 104). On the other hand, the skilled labor contemplates an improved basket with other goods and service.
With this starting point, the absolute prices or market prices in the economy are⁵:
Where the variables that has not been defined yet, express:
𝑑′ = vector of simple labor human consumption
𝜎= skilled labor coefficient
As is showed on the equation (15), the expression 𝑝(𝑑′𝑎0) just contemplates the fraction of the production that goes to the simple labor, therefore, what usually represents the benefits 𝜎𝑝[𝐾+(𝐴+𝑑′𝑎0)], reflects in this case all the surplus of the simple labor (including the remuneration to the skilled labor and the surplus value). So that, 𝜎expresses a skilled labor coefficient that contemplates all the new value created that excess the simple labor. Rearranging this equation, it is obtained an eigenvalue and eigenvector problem:
The eigenvalue gives us 𝜎. Then, it is possible to obtain the sectoral unitary values with the equation (15), in this way the direct prices and the prices of production will be calculated in a single process, as follow. To obtain the labor-value vector (𝑉) we use the simple labor as numeraire, 𝑝𝑑′=1, therefore the values calculated are homogenized to simple labor.
The analysis of the units of the variables makes easier the comprehension of the equation (17). At first, it is important to remember that the units of 𝑝 are monetary units for unit of good; 𝑑′, on the other hand, express unit of goods for unit of simple labor. Therefore, 𝑝𝑑′ is expressed as monetary units for unit of simple labor. Therefore, when 𝑝𝑑′ was defined as numeraire, the units of the expression (17) are simple labor for monetary unit. Rearranging the equation (17):
After the unitary labor-values have been calculated, the next steps are very similar to the approach used by Ochoa. First, we calculate the sectorial values (𝑉ˢ), then the monetary value expression for the new approach (edv𝑛𝑎), then the direct prices (𝑑𝑢𝑛𝑎) and finally is obtained the productive capital (CC, CF, CFD, CV) and the surplus-value (the subscript “𝑛𝑎” is used to differentiate the variables of the new approach).
Once again, these variables are expresses in current prices, to obtain these variables in constant prices must be followed the same process describe in Shaikh’s approach (equation 11).
On the other hand, the unitary new value created on the monetary form (𝑊ᵛ) and the sectorial new value created (𝑊ᵉ) are calculated with the following expressions:
A fraction of the previous expression corresponds to the value of the labor power and the rest represents the surplus-value. In underdeveloped countries, like El Salvador, is usual that the remuneration of the working class is less than the full value of the labor power. Therefore, is useful to estimate a human consumption basket of full value of the labor power, so that, this basket should contemplate the simple labor human consumption (𝑑′) basket and other goods and service needed in the reproduction of the total labor power (𝑏). On this way, the vector 𝑄of full coverage is obtained⁶:
To compare the results between both approaches, will be assumed that 𝑄 is equal to the human consumption observed, that means, 𝑄𝑎0 is equal to the matrix 𝐵⁷. With this information, the mean profit rate of the economy (𝑔′) is calculated:
In this case, X is the column vector of the gross value production. Meanwhile, the rate of surplus-value (𝑍) and the organic composition of capital (𝑛) are defined as follow:
On the other hand, the rate of surplus-value and the profits (not the rate of profit) for the sector j after the process of surplus-value redistribution are express in the next equations:
On the equation (33) , represents surplus-value rate after redistribution for the sector j, 𝑑𝑖 is the direct price of the sector i⁸, a𝑖𝑗 are the elements of the matrix A, 𝑤𝑗 is the mean salary of the sector j. The other variables have already been defined and the subscripts only represents the sectors.
Finally, the equation (35) represents the mean benefit after the redistribution of surplus-value for the sector j (g𝑚𝑗). The mean benefit will be higher (smaller) than the surplus-value generate on the same sector if the organic composition of that sector is higher (smaller) than the organic composition of all the economy. In this case is assumed the same wage for every sector.
IV. Data and methodology for different matrices and vector’s calculation
a. Labor values’ measure in El Salvador and statistical limitations
Sánchez, Álvarez y López (2017) used the methodology presented in section II for the labor value’s measure, direct prices and production prices for the Salvadorian economy for 1990 – 2006. However, there were two important statistical limitations. At first, due to the data available, the Supply and Use Tables (SUTs) were used instead of the intermediate transactions matrix form the Input Output Tables (IOTs). In second place, the labor for each sector was measured by weighting the total labor with the sectorial gross value of production of the economic activity. Both limitations are overcome in this article.
The IOTs that will be used were obtained by the UCA’s Department of Economics applying the Eurostat’s Model B (2008) with the SUTs from 1990 to 2006. For the sectorial labor, this has been measured through Encuesta de Hogares de Propósitos Múltiples (EHPM). For these reasons, the labor values from Shaikh (1984), Ochoa (1984) and Guerrero’s (2001) methodology are re-measured with the objective that the results could be compared with the labor values measured through the new approach’s methodology proposed in this article.
It should be noted that statistical limitations are always present. For example, the EHPM is not fully compatible with Salvadorian macroeconomics’ accounts, due to this some sectors will show labor even when the gross value of production is zero. On the other hand, while this article was being written, the Central Bank of El Salvador (BCR) updated the National Account System, offering a more precise picture of the economy’s interindustry relations. Nevertheless, this latest information will not be used due to time limitations. In upcoming researches this measuring will be improved.
b. Used matrices and vector’s calculation
For most of the matrices described above, we used the same information than Sánchez and Montibeler (2015) and Sánchez, Álvarez and López (2017); the methodology used is the one described by Guerrero (2000).
The methodology to calculate the matrix of technical coefficients A and the vector of labor requirements a₀ are well known. For the calculation of the matrix of stock-discards coefficients D it is used the matrix of capital stock coefficients K:
Where FBKF represents the gross fixed capital formation and j express the sector, that means that 𝑓𝑗 is the sectorial proportion of total investment. Meanwhile, 𝑓 is the vector of the las 𝑓𝑗 and is the row vector of the ratio capital – sectorial gross value production. Then the matrix D is obtained:
<𝐼𝐿> represents the diagonal column vector of the inverse of the average life of the capital goods used on every sector.
On the other hand, the vector d’ of simple labor consumption was obtained through information of the Dirección General de Estadísticas y Censos (DIGESTYC) from El Salvador. For this, the urban basic food basket that represents the minimum of calories necessaries to accomplish any human activity was used. The different goods of this basket were located on the sectors that produce them.
Finally, the matrix B was obtained with the vector 𝑄, this vector was calculated through the scalar of the participation of the salaries on the household consumption developed by the Departamento de Economía UCA (2016). This scalar was multiplied by the vector of final household consumption and the resulting vector was divided by the number of workers in the economy. Once again, it is possible to calculate an approximation of a basket of full payment of the labor power; this could be developed in further articles.
V. Empirical evidence for the labor values’ measuring, prices and fundamental Marxist variables
Once the methodologies to be compared in this article has been presented, the direct prices have been measured with both methodologies from 1990 to 2006. In this section, the respective results will be compared with the market prices to be able to establish which methodology presents a closer behavior to the market in this period.
a. Evidence on market prices in relation to direct prices and prices of production
At first, the scatter plot for 2006 between the market prices, the new approach’s direct prices and Shaikh’s direct prices is presented. Each dot represents one of 42 sectors from El Salvador’s IOT. It is shown in this graphic that the new approach’s direct prices are closer to the market prices in comparison to Shaikh’s direct prices for 2006. This is a first prove for the new approach’s explanation capacity.
To continue studding this situation, table 1 shows the regression analysis between direct prices with both methodologies and the market prices for 2006. These regressions are made with less ordinary squares, using natural logarithms to smooth out the variables.
According to these results, the new approach’s direct prices’ behavior determined 96.77% of the market prices’ behavior, while the Shaikh’s direct prices’ behavior determined 67.8%. Both models are statistically robust, since the F tests are above 4 in both cases, while the direct prices’ elasticities show student’s T-tests above 2, supporting their own statistical relevance. However, the bigger the F and t tests’ results are, the better the statistical relevance is. This means that the new approach’s behavior fits better with prices market’s.
Sánchez and Montibeler (2015: 340) has pointed out that the labor value’s measuring fit better in comparison to other values measured with different bases: electricity, chemistry, oil and agriculture. These results were obtained for China’s economy in 2002. It is plausible to think that this situation is valid for the Salvadorian economy as well.
To study the behavior through time between the different direct prices and the market prices, graphic 2 shows the correlation coefficient’s development from 1990 to 2006⁹, where the difference between the new approach is shown, presenting values between 96% and 98%, and the Shaikh’s method, with values between 74% and 82%. These results are reinforcing that the new approach’s direct prices give us a better explication of the behavior of the market prices.
b. Fundamental Marxist variables¹⁰
After the direct prices, prices of production and market price’s behavior have been analyzed, we proceed to study the fundamental variable’s behavior from Marx’s theory to understand the capitalist economic behavior, these are: profit rate (g’), organic composition of capital (n) and rate of surplus-value (z), all calculated with both methodologies. In first place, the following graphic shows the profit rate’s development between 1990 to 2006 for the Salvadorian economy:
Is clear that the behavior for both profit rates is to fall on this period, which is empirically proving Marx’s approaches (1981: 213): “The progressive tendency of the general rate of profit to fall is, therefore, just an expression peculiar to the capitalist mode of production of the progressive development of the social productivity of labour”.
Furthermore, Sánchez, Álvarez and López (2017: 12-13) has pointed out that the Salvadorian economy presented the highest growth rates between 1992 and 1995, with values above 6.0%. These years presented a mean profit rate of 10.17% for the new approach’s method, while Shaikh’s method presented 15.09% of mean profit rate, being one of the highest levels of the analyzed period. Nevertheless, these years also presented the greatest decreases for the profit rate.
In this situation, a possible explanation is the one proposed by the Departamento de Economía UCA (2016), which demonstrate that the highest growth rates did not implicate a full payment of the value of labor power, which generated disproportionality in the productive force’s development. As will be analyzed in the following, this implies elevated levels of organic composition as consequence of a low level of variable capital.
In the analysis of the rate of surplus-value, graphic 4 shows that, for both methods this rate had a growing trend, especially in the first years of the analyzed period, years with a high economic growth in El Salvador. However, since 1997 this rate of surplus-value reduces its growth and seems to stagnate (situation more evident in the new approach). This could be linked to situations that distort economic behavior, such as overexploitation of the labor power¹¹. For Shaikh’s method, this rate of surplus-value went from 1.50 in 1990 to 2.45 in 2006, while for the new approach’s method this rate went from 1.34 in 1990 to 1.70 in 2006.
A very important variable in Marx’s approaches is the organic composition of capital, which is a social-technology indicator of the economy, since it relates the constant capital’s quantity (machinery, raw material, technology, etc.) in relation with variable capital’s quantity (labor power) that manipulates this technology on the productive process (Marx, 1979: 612). This means that this indicator shows the constant capital’s quantity for each working person in the economy. This indicator’s development for El Salvador is presented in the following graphic.
Both methods have as result a growing organic composition in the analyzed period. A first, if full payment of the value of labor power is archived, this increase would be indicating a technological advance in the Salvadorian economy. Nevertheless, the reality is different, as the Departamento de Economía UCA (2016: 58) points out: El Salvador’s economy presents an important disproportionality given that the part of the GDP that goes to the working population is very low.
In other words, labor power is not fully paid, which means that the organic composition’s increase is due to the loss of labor power’s participation in production and its precariousness, situation that was anticipated since the rate of surplus-value’s analysis, showing a disproportionality in the productive force’s development, which is based on the study of a two-sector model presented by Departamento de Economía UCA (2016: 57 – 67). About this, Marx points out that:
“This mode of production produces a progressive relative decrease of the variable capital as compared to the constant capital, and consequently a continuously rising organic composition of the total capital. The immediate result of this is that the rate of surplus-value, at the same, or even a rising, degree of labour exploitation, is represented by a continually falling general rate of profit” (Marx, 1981: 212 – 213).
The Salvadorian economy’s behavior presented in this research would be in accordance with these Marx’s approaches, but it is important to consider that this situation has occurred under a productive force’s disproportionality, which would be distorting the economy’s development. In that sense, is plausible to think that an improvement on the Salvadorian working class’ coverage’s conditions not only would improve their situation as people, but besides would have a direct impact in their productive capacity and in the behavior of El Salvador’s economy in general.
The following graphics present the components of what Marx (1981: 26) called productive capital and the surplus-value that results from these capital’s productive activity. Is clear that for both methods, all these capitals and the surplus-value show very similar behaviors, valued to simple labor and where the variables measured by the new approach are above the variables measured by Shaikh’s method in almost all graphics (unless the surplus-value one)
On this article we presented the comparison between one of the main methodologies to solve the Marx’s transformation problem and a new approach with two emphasis: first, the idea to incorporate in a single process the measure of the direct prices and the prices of production; and second, the Marx’s distinction of simple labor and skilled labor.
Even though both direct prices calculated with the different methodologies offers a good explanation of the market prices, the new approach is the one that offers a better correlation with the actual prices, which implies a better explanation to Salvadorian economic behavior. As we have pointed out, the new approach’s direct prices’ behavior determined 96.77% of the market prices’ behavior, while the Shaikh’s direct prices’
On this point, the new approach offers a better description of the Salvadorian economy, since the labor power’s payment is below the full labor power’s value, so that the organic composition is artificially high, but does not implies an important impact on the surplus-value rate. This is what we have called disproportionality in the productive force’s development.
Is not this article’s objective to conclude the debate about the transformation problem, but rather to propose new analytical tools from and to underdevelopment countries –such as El Salvador-, since they present a higher propensity to paid the labor power below its value (demonstrated with higher levels of poorness, for example). Therefore, the new approach’s proposal fits better to explain this countries’ economic dynamics and it’s plausible to think that this methodology could offer a better approach to Latin American economies.
1 This article does not pretend to explain the details of the Shaikh’s and Ochoa’s approach, nevertheless, the methodology of these authors is described since it will be compared with the new approach.
2 In the following, any variable that appears with the form 〈𝑋〉, indicates a diagonalized vector.
3 The original document is in Spanish, the translate is exclusive responsibility of the authors of this document.
4 It will be assumed that the turnover time is equal to one.
5 Once again, it will be assumed that the turnover time is equal to one (T). The general case of the expression (8) is as follows: 𝑝=𝑝(𝐴+𝑑′𝑎0+𝐷)+𝜎𝑝[𝐾+(𝐴𝑇+𝑑′𝑎0𝑇)].
6 It is important to note that is not easy to express all the labor power value in monetary terms, nevertheless, in a mercantile economy it is relevant to do it to calculate the remuneration of the labor, this must include good and service that are expressed on monetary terms and others from sectors that do not produce goods on the material sense. Therefore, the calculation of the remuneration of full labor power value must be 𝑊=𝑑𝑢𝑛𝑎𝑄+𝑤𝑠𝑖, where 𝑤𝑠𝑖 expresses the fraction of the remuneration that cover services and intangibles.
7 The Departamento de Economía UCA (2017: 59-60) calculated the fundamental variables with the assumption of the full payment of labor power value. Even though the level of the profit rate and the surplus-value rate were less than those calculated with the actual payment of the labor power (less than the full payment), the tendencies of both variables with this assumption are a growing trend. On Montesino (2011: 40 – 57) could be deepened the theoretical impact on the productivity of the payment of the labor power below the full labor power value.
8 𝑑𝑖 represents the direct prices of the new approach, we write 𝑑𝑖 instead of 𝑑𝑢𝑛𝑎𝑖 to not overload the equation.
9 From 1995 to 1998, the cotton sector has been excluded for both methodologies, due to show zero gross production, which generates troubles when calculating the correlation coefficient.
10 For both methodologies, the profit rate is calculated based on equation (30), the rate of surplus-value based on equation (31) and the organic composition of capital based on equation (32), all using the direct prices.
11 About this, in the volume III of Capital, Marx (1981: 235) points out that the depression of wages below the value of labour-power is one of the most important factors checking the tendency of the rate of profit to fall. Nevertheless, he does not deepen on its effects on the productive process. In that sense, Montesino (2011: 40 – 52) has pointed out that a lack of coverage of the main productive force could implicate productivities below its potential.
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