The United Nations System of National Accounts includes an input or use table U = (uij) of commodities i consumed by industries j and an output or make table V (vj) of industries producing commodities]. This paper is on the construction of an input-output or table A = (aij) of commodities i for commodities]. The established constructs are criticised. The current favourite, the industry technology model, is rejected on the ground that the choice of base year prices affects the results in more than a scaling fashion. The paper presents an alternative to the existing constructs which cancels out the shortcomings and amounts to a rich representation of technology. THE United Nations (1967) System of National Accounts includes an input or use table U = (u1J) of commodities i consumed by industries j and an output or make table V = (Vij) of industries i producing commoditiesj. This paper is on the construction of an input-output or table A = (aij) of commodities i for commodities j. (Industry tables and mixed tables are not considered.) Section I reviews the established constructs. Section II evaluates them. Special attention is given to the so-called industry technology model which is now used by the United States (1980). Section III derives a new construction of a requirements table. Section IV applies the analysis. For convenience we have chosen the well organized tables of Canada (1981) for our experiment. Section V discusses the results. Section VI concludes the paper. 1. The Established Constructs The established constructs are the commodity technology model, the by-product technology model, the industry technology model, and the mixed technology model of Gigantes (1970). Some notation facilitates the presentation of these models. e denotes the unit colunm vector. ' denotes transposition. denotes diagonalization either by suppression of the off-diagonal elements of a square matrix or by placement of the elements of a vector. denotes off-diagonalization by suppression of the diagonal elements of a square matrix. (Thus for a square matrix, A = A + A.) The commodity technology model (C) rests on the assumption that each commodity has its own input structure. Industries are independent combinations of outputs j with their input structures (ac), i = 1,..., n. Thus, industry j needs for the production of Vik units of output k an amount a,v1k of input i. Summing over outputs k yields industry j's total demand for input i: uij= EkaikVjk. Hence U = ACV'. Thus the commodity technology requirements table is given by Ac = UV'-'. Note that existence may be guaranteed only if the number of commodities equals the number of industries. The by-product technology model (B) rests on the by-product assumption that each industry produces outputs in a fixed proportion. All secondary products are by-products and therefore can be treated as negative inputs, yielding net input structures (a/B), i = 1,..., n for the primary outputsj. Thus, industry j needs for the production of Vjj units of its primary output a net amount ui1 vJj =a,Bvjj of commodity i. Hence U= ABV. Thus the by-product technology requirements table is given byAB = (U V')V -1. Note that again existence may be guaranteed only if the number of commodities equals the number of industries. The industry technology model (I) rests on two assumptions. One is the industry technology assumption that each industry j has the same input requirements for any unit of output. Here output is measured in value. The other assumption is that of fixed commodity market shares of industries. Thus, industry k needs uik/lIVkl of input i per unit of output-in particular for commodity j-and its market share Vkj/lIVIj is fixed. Taking the (market share) weighted average over industries k yields the amount of input i required for Received for publication September 17, 1981. Revision accepted for publication April 6, 1983. * New York University and Erasmus University; Jadavpur University; and New York University, respectively. The application of the analysis was suggested by Wassily Leontief to the authors when they were at the Institute for Economic Analysis, New York. A first version of the paper was presented at the Seventeenth General Conference of the International Association for Research in Income and Wealth held at Chateau de Montvillarg&re, Gouvieux, France, August 16-22, 1981. The authors are grateful to Kishori Lal, Jean H. P. Paelinck, Ashok Parikh, and an anonymous referee for valuable comments, to Henk Gravesteijn and Jimmy Younkins for computational assistance, and to the Sloan Foundation for financial support.
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Nov 1, 1997
S Chaudhuri 
Open Access