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A New Vision of Classical Multi-regional Input–Output Models

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Abstract

We present classical multi-regional multi-sectoral input–output trade structures from the perspective of networks. Unlike existing approaches by which dynamic changes in structures are studied, here, emphasis is given on recovering the stable structure architecture of interrelations in the input–output model. By self-explanatory visual outputs we display the connectivity patterns, interactions of the trading partners, the number of trade linkages per trader and the density of interrelations of the network. Our network analysis traces causal relationships, feedback loops and examines certain global structural properties. The whole computational approach is implemented in Mathematica. Our programming style allows for the creation of iterative schemes explaining the the linkage development among sectors, the influence of regions and sectors system-wise, aspects of the nature of trade and, the evolution of spatial trading/production cycles in growing trading networks.

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Notes

  1. Mathematica software is tradable from Wolfram Research, Inc.

  2. The study and analysis of the interregional trade flows in interregional economic activities often reveal interregional and inter-activity linkages, referred to as “feedback loops” and/or spatial production cycles in interregional level (see also Sonis et al. 1993, 1995; Sonis and Hewings 2001). A sophisticated approach to measure the impact of loops and regional feedbacks by Lantner and Carluer (2004) relies on matrix algebra and its application requires several mathematical skills.

  3. A wide range of analytical methods has been reported, (see Higashida and Managi 2014; Mensi et al. 2013; etc.).

  4. Two graphs are called isomorphic if they have the same number of vertices and the adjacency is preserved (Kaveh 2013, p. 18).

  5. A graph is called regular if all its vertices have the same degree. If the degree is k then it is a k-regular graph (Diestel 2005; Kaveh 2013).

  6. A graph is called connected if all pairs of its vertices are connected (Diestel 2005; Kaveh 2013).

  7. The set S\(\subseteq \)N is autonomous if and only if there are not any edges from the vertex of N\(\backslash \)S to a vertex of S.

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Acknowledgments

Thanks are due to the Editor Professor Dr Hans Amman and to three anonymous reviewers for their helpful and constructive comments on an earlier version of our paper. Any reaming errors are solely the authors responsibility.

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  1. Laboratory of Operations Research, Department of Economics, University of Thessaly, Korai 43, 38333, Vólos, Greece

    George E. Halkos & Kyriaki D. Tsilika

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Correspondence to George E. Halkos.

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Halkos, G.E., Tsilika, K.D. A New Vision of Classical Multi-regional Input–Output Models. Comput Econ 51, 571–594 (2018). https://doi.org/10.1007/s10614-016-9624-x

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