An Alternative Treatment of Secondary Products in Input-Output Analysis
An Alternative Treatment of Secondary Products in Input-Output Analysis
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投入产出分析中二次产品的另类处理
DOI：
10.2307/1924699
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发表时间：
1984
期刊：
影响因子：
--
通讯作者：
J. Anthony Small
中科院分区：
文献类型：
--
作者：
Thijs ten Raa;D. Chakraborty;J. Anthony Small
联合国国民账户体系包括一个投入或“使用”表U =（uij），列示各行业j消费的商品i，以及一个产出或“制造”表V（vj），列示生产商品的各行业]。本文件是关于编制一个投入产出或“需求”表A =（aij）的问题。已建立的结构受到批评。目前最受欢迎的行业技术模型被拒绝，理由是基准年价格的选择对结果的影响不仅仅是按比例缩放。本文提出了一种替代现有的结构，取消了缺点，相当于一个丰富的技术代表。联合国（1967年）国民账户体系包括一个投入或“使用”表U =（u1 J）的商品i消费的产业j和一个产出或“制造”表V =（Vij）的产业i生产的商品j。本文件是关于为初级商品j编制初级商品i的投入产出表或“需求”表A =（aij）（不考虑工业表和混合表）。第一节回顾了既定的结构。第二节对它们进行评价。特别要注意的是美国现在使用的所谓工业技术模式（1980）。第三节重新编制了一个所需经费表。第四节进行了分析。为了方便起见，我们选择了加拿大（1981）的组织良好的表进行实验。第五节讨论了结果。第六节是本文的结论。1.已建立的结构已建立的结构是商品技术模型、副产品技术模型、工业技术模型和吉格尔（1970）的混合技术模型。一些符号便于这些模型的表示。e表示单位列向量。'表示换位。表示通过抑制方阵的非对角元素或通过放置向量的元素来对角化。表示通过抑制方阵的对角元素的非对角化。(Thus对于正方形矩阵，A = A + A。）商品技术模型（C）建立在每种商品都有自己的投入结构的假设之上。产业是输出j与其输入结构（ac）的独立组合，i = 1，.，n.因此，为了生产Vik单位的产出k，工业j需要输入i的量a，v1 k。对输出k求和得出行业j对输入i的总需求：uij= EkaikVjk。因此U = ACV '。因此，商品技术要求表由Ac = UV“-”给出。注意，只有当商品的数量等于产业的数量时，才能保证存在。副产品技术模型（B）建立在副产品假设上，即每个产业都以固定的比例生产产出。所有次级产品都是副产品，因此可以被视为负投入，产生净投入结构（a/B），i = 1，.，n表示主要输出j。因此，产业j为了生产Vjj单位的初级产品，需要商品i的净量ui 1 vJj =a，Bvjj。所以U= ABV。因此副产品技术要求表由AB =（U V '）V-1给出。要注意的是，只有当商品的数量等于工业的数量时，才能保证存在。工业技术模型（I）基于两个假设。一个是产业技术假设，即每个产业j对任何单位产出都有相同的投入需求。在这里，产出是以价值来衡量的。另一个假设是各行业的固定商品市场份额。因此，工业k每单位产出需要投入i的uik/lIVkl--特别是商品j--其市场份额Vkj/lIVIj是固定的。对行业k取（市场份额）加权平均值，得到1981年9月17日出版的《接收》所需的输入量i。修订版于1983年4月6日接受出版。* 分别是纽约大学和伊拉斯谟大学;贾达夫普尔大学;和纽约大学。在纽约的经济分析研究所工作时，瓦西里·列昂惕夫向作者们提出了这种分析方法。1981年8月16日至22日，在法国古维约的蒙维拉尔城堡举行的第十七届国际收入与财富研究协会大会上，提交了这篇论文的第一版。作者感谢Kishori Lal，Jean H。P. Paelinck，Ashok Parikh和一位匿名裁判提供了宝贵的意见，Henk Gravesteijn和Jimmy Younkins提供了计算帮助，Sloan基金会提供了财政支持。
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 " requirements" 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 "requirements" 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.