However, the founders of our modern system of economic theory chose the firm, rather than the household, as the basic unit of

MATRICES OF INTERDEPENDENCE

An open letter to Filipino econometricians

On Dec. 1, 1991, an online article by Dr Sixto K. Roxas appeared on the website of PCDForum (column #22) entitled “COMMUNITY CENTERED CAPITALISM: AN NGO ALTERNATIVE.” It contained this observation:

<<However, the founders of our modern system of economic theory chose the firm, rather than the household, as the basic unit of analysis>>

This it a very important observation in the context of world poverty and the danger of another Great Depression. I should think that the NEDA or the NSCB would immediately respond constructively to this observation in their Social Accounting Matrix (SAM). But it seems that in 1994, they still followed the format of their 1990 SAM. This is extremely risky for the Philippine economy, especially during the present global conditions.

The U.S. economy, on which our accounting models are still based, depended on the obsolete input-output tables (constructed by Wassily Leontieff in 1966) that chose firms as the basic unit of analysis. As a result, those models failed to give warning signals early enough for the large corporations to take prompt remedial actions that could have prevented the downturn. There was a tremendous expansion during the preceding decade, but it was this addicitive overexpansion that led to the downturn. (A domino effect of this is their recourse to deceptive accounting.) This is now making things even more risky than honest but incomplete accounting.

The present accounting methods are incomplete because the undifferentiated lumping of data (on household demands with the productivity of firms) conceals the dynamic interactions between firms and households. These interactions include the quantifiable effects of production-velocities with payment-velocities. It is analogous to the mathematical relationships between two linear functions with one another, between these and their first derivative, between this with the second derivative, and so on. The analogy with calculus derivatives reveals information that can help decision-makers maintain dynamic equilibrium between rising (or falling) demand of households and rising (or falling) supply from firms. Dynamic equilibrium is the goal of Lonergan’s “Macroeconomic Dynamics: An Essay in Circulation Analysis” (or MD-ECA, first published in 1999 after a series of studies since the Bretton Woods Conference of 1944).

Contrary to first impressions, Lonergan’s proposal is not just one model among many models. It is a method of quantitatively analyzing the many microeconomic models described in Schumpeter’s “History of Economic Analysis” (first published in 1954). These are models of economic states that from year to year keep reproducing themselves in a static context. Schumpeter saw the challenging need for quantitative analysis in a dynamic context, but did not undertake this. Responding to this challenge, Lonergan saw that it is only by finding empirical and quantitative verification (or falsification) of successive aspects of these models that significant features can be analytically selected by those decision-makers whose primary purpose is to maintain dynamic equilibrium.

Dynamic dis-equilibrium leads to recurrent “business cycles” of booms and busts together with their harmful effects. Maintaining dynamic equilibrium can transform the business cycle into a “pure cycle” of sustained growth with fast booms continuously alternating with slow booms (or stationary states) and with no busts. Such transformation can be promoted only by prompt (interval-by-interval) adaptations of decision-makers to the velocities and accelerations between rising and falling demands of households and the rising and falling production-rates of firms. Firms must maintain themselves in dynamic equilibrium for the sake of the households. Firms are for households and not vice-versa.

After the death of Lonergan in 1984, the study was continued by his research associates who updated Lonergan’s series of typescript essays with a more consistent terminology fit for publication in 1999. This version contains a brief reference to a phrase “matrices of interdependence” on page 36 but did not include these matrices in the 1999 version. It is possible to integrate these matrices with attempts (if any) with the SAM format of NSCB such as to change the unit of analysis from firms to households while maintaining dynamic equilibrium for all households and firms..

{It is important to note that Lonergan’s technical language translates “households” into a mathematical function denoting the flow-rates of goods and services demanded by a “standard of living.” [Households or their living standards are commonly divided into A, B, C, D and E classes, with upward (or downward) mobility among them.] Moreover, operations of “firms” are further distinguished and more finely-tuned with quantifiable interactions between (1) the production-rates of consumer goods and services called the “basic sectors”; and (2) the production-rates of producer goods and services called the “surplus sectors.” There can be several stages of surplus sectors}

It is possible to compare Lonergan’s original concept of his "matrices of interdependence" with NCSB’s 1994 IO matrices described in http://www.nscb.gov.ph/technotes/io_tech.htm (and their MAKE and USE matrices). The fundamental difference between the two concepts is that Lonergan posits a functional distinction between "surplus" (producer goods and services) and "basic" (consumer goods and services), whereas NSCB (and its counterparts in U.S. and other countries that use the 1966 Leontieff input-output tables) ignore such distinction. To ignore this distinction is to ignore the measurable effects of "acceleration" (whether positive or negative) of the production-rate of surplus products on the production-rate of basic products, as well as the effects on the flow rates of payments for surplus products with flow rates of payments for basic products. These measureable effects should provide data useful for economic modeling, forecasting and optimizing decisions about quantities and types of products demanded by a changing standard of living.

Page 15 of MD-ECA describes "acceleration" with an example from shoe making. An ordinary user of shoes may demand 2 pairs of shoes per year, and an Imeldific user of shoes may demand 200 pairs of shoes per month. To supply that demand, the production of shoes may be accelerated by the production of shoe-factories and their equipment when the demand for shoes rises from ordinary to Imeldific quantities. The shoe-factories may demand an increasing supply of leather. When the supply of leather becomes smaller, "canvas uppers and wooden soles become more common." And similarly for other types of footwear and for other commodities.

In a commodity-X-commodity matrix of which shoes constitute one of many outputs of basic goods and services, a matrix of industry-X-commodity would be associated with each commodity. This may be similar to the MAKE matrix of the 1994 NSCB. There can be a series of MAKE matrices whose outputs provide inputs for each commodity.

I cannot find any Lonergan counterpart for the USE matrix. Presumably, this is because the USE matrix entails some pricing mechanism. For Lonergan, pricing begins in a later chapter where he treats of payments and their classification. He treats the payment process as a process that must be adapted by producers to the demand and supply in the producton process, not vice-versa. For production firms are for the sake of supplying demands of household for goods and services, not vice-versa.

Now, he uses q_i to symbolize the ultimate product (e.g. shoe). The subscript can be 1, 2, 3 … to denote a pair of shoes, a watch, a ganta of rice, etc.) Other subscripts are: j to denote unit of enterprise (shoe-factory, watch factory, rice field, etc.) ; and k to denote factors of production (e.g. labor, management, capital equipment in use).

[However, the editors now use k to denote human factor and production skills like workers’ use of a particular kind of equipment, workers’ performance of tasks like sales management, financial management, personnel managements, etc. These editors see this as differentiations of Leontieff’s "labor" arising from "innovations". (such as innovations in accounting methods.)]

Next, the editors introduce 4 matrices: q, r, A, B, where

q = final product matrix (1X m)

r = total skill-contribution matrix (1 X n)

A_ij = fraction of enterprise j’s total productive activity contributed to product i;

B_jk = fraction of total man-hours expended during enterprise j

so that q = A(Br) = "state" of the production process (minus the pricing mechanism, to be discussed in later chapters)

The editors then infer from Lonergan’s "double summation" (p. 30) that

q_ijk= A_ij. B_jk. r_k

_{----------------------------------------------------}

The editors add the 3 concluding paragraphs:

'Now the value of such matrix equations is that they communicate something of the intricacy of the network of interdependences involved in the productive process of any class of final products. They are, however, of limited usefulness for two reasons. First, as Lonergan pointed out, no "common measure" for "ultimate products and contributions to ultimate products" (p.__) has yet been introduced. That is to say, the double summations and matrix equations merely equate the total number of person-hours involved in the production of product "i" to its total quantity "q_I" . No distinctions are made among the relative importances of the different contributions, "r_k" . In order to achieve this, not only the prices of final products but also the prices of human contributions "o_ij" (p. 65 ff) would have to be introduced.

'Second, while the determination of the matrix elements is a "Herculean" but not impossible task, it is worth undertaking only for periods of static equilibrium, not of dynamic change. The matrix elements shift more or less with every innovation in production. And not only to the numerical, fractional value of the elements change, but even the shape, size, dimensions, classification and components of the matrices also undergo transformations. Moreover, when the dynamic change is a long-term acceleration, this transformation of the matrices will be complex, rapid and prolonged. (Still, this need not necessarily be a "Herculean" task for innovative and interactive computer programs like advanced and finely-tuned Parallel Processing. V.M.)

'Finally, we note the contrast between this type of matrices of interdependence and those of Wassily Leontieff. Leontieff received the Nobel Prize for Economics for his detailed classification and empirical determinations of the matrix elements for the various economic regions. However, his resource-input matrix -- which parallels r above – includes labor as but one factor, in addition to the numerous classes of raw materials. (See Wassily Leontieff, Input-Output Economics, (New York: Oxford Univsersity Press, 1966, especially p. 237 for matrix notation applied to this context.) Lonergan, on the other hand is concerned with the complexities of the productive process insofar as they impact accelerations, and hence is concerned with the differentiation of labor into different skills which is effected by innovations. (Innovations are needed for accounting methods. V.M.) Finally, since Leontieff matrices concern "raw material" inputs rather than productive skills (that have not yet been innovatively updated), they may be more relatively stable over periods of time than Lonergan’s matrices of interdependence. Still, Leontieff’s input-output matrices mediate between raw materials and products, and hence they too may have limited usefulness in dynamic periods where final products are shifting rapidly.'

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Vicente Marasigan, S.J.

Loyola House of Studies

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