The Matrix as a Tool in Macro-Accounting - Fuerst, E. (The Review of Economics and Statistics, 1955)
THE purpose of this paper is to analyze the formal structure of the matrix as an accounting tool (I to 7), to review actual inputoutput matrices under the aspect of their formal structure (8), and finally to construct an income-product matrix (g to I 2 ). i. A matrix, as used in macro-accounting, is a form of presentation of accounting material. It is distinguished from other forms of presentation mainly by four technical features: economy in figures, consolidation of interaccount flows, absence of narrations, and specific grouping of the accounting material. The economy in figures is obtained by making one figure serve two purposes simultaneously. According to the direction in which it is read, either vertically or horizontally, a figure is either a debit entry or a credit entry. This feature has the advantage that the number of figures required to communicate a given volume of information is in a matrix roughly one-half of that required in any other form of accounting statement. On the other hand, difficulties arise if the volume of information becomes large. The usual device of making statements manageable in size, which is to relegate part of the information to subsidiary schedules, is not available in the case of a matrix, because, in consequence of the double purpose served by each figure, figures cannot be taken out of the context within the matrix. A matrix grows therefore in direct proportion to the volume of information and, after a certain point, becomes an unwieldy instrument. The second feature is the necessity of consolidating inter-account flows. Transactions affecting any two accounts have to be contracted into two figures, because the framework of a matrix has only two places available for the record of flows affecting two accounts. One is the place of intersection of the row representing the credit entries to the first account with the column representing the debit entries to the second account; in this place, the flows from the first to the second account are recorded. The other place is the intersection of the row of the second account with the column of the first account, which is the place for the flows from the second to the first account. The matrix thus allows an expression of the direction in which transactions flow between any two accounts. But no more. If the transactions between two accounts are for instance composed of a number of heterogeneous flows and that occurs quite regularly in macro-accounting the social accountant faces an inconvenient choice. One alternative is to consolidate different transactions among the same transactors. This entails a loss of information or even of meaning, though the macro-accountant may help himself to some extent by cumbersome devices such as double rows 1 or footnotes. The other alternative is to split one transactor into as many accounts as different intertransactor-relations are to be recorded. This entails a loss of institutional or other transactor unity. In any case, the number of meaningful flows between two transactors which can be shown in a matrix is technically limited by the number of available accounts. The third feature of a matrix is the absence of what accountants call narration, that is a short explanation of the meaning of an entry. An economy in text is thus added to the economy in figures, making the matrix a still more concise form of presentation. Without the guidance of narrations, the reader of a matrix can derive the meaning of an entry solely from the captions of the row and column at whose intersection the figure stands. In this way, captions in a matrix are charged with two functions. They have to describe not only the account as a point of reference, but also the kind of transactions entered in the account. To call a personal account by the name of the transactor, or the impersonal account by the subject-matter assembled in it, is not sufficient. A way must also be found to describe the transactions entered in the account; otherwise