Analytical Assumptions and Causal Ordering in Interindustry Modeling

Abstract

Since the publication of Leontief's path breaking work, the overwhelming majority of applications of inter-industry models have relied on the standard model of demand-driven production functions -even when the exogenous perturbation originated on the supply side [13]. For some time now, in fact, some economists have been suggesting an alternative to the standard model in situations of supply constraints [8, 58-64; 9; 1, 249 -69; 10; 5, 447 54; 6, 281 89]. However, this alternative model relying on supply-constrained allocation functions, is not based on the precepts of standard microeconomic theory. Rather than assuming that input shares are constant, as in the standard model, the alternative model assumes that output shares are constant-an assumption which is not tied to any demonstrated optimizing behavior on the part of firms. Both models would seem to be somewhat limited -the standard model due to its demand-only orientation, the alternative model due to its untested analytical underpinnings.1 In fact, as this paper demonstrates, there is an inherent symmetry underlying interindustry analysis. The standard Leontief interindustry model can be formulated to directly analyze supply-constrained perturbations just as the Ghoshian allocation model can be formulated to directly handle demand-induced perturbations. That is, there actually exist four frameworks for employing interindustry models that are differentiated by the analytical assumptions (i.e., production or allocation function) and the causal ordering (i.e., demand-driven or supply-contrained) employed. This paper demonstrates the four frameworks, discusses the rationales for their use, and provides illustrative results based on their application to the 1967 U.S. interindustry table. Section II of this paper develops the four theoretical frameworks and demonstrates their symmetry. Simple empirical results are presented in section III together with some recommended potential applications. Conclusions are offered in the final section.

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