Leontief Meets Markov: Sectoral Vulnerabilities Through Circular Connectivity

Wirkierman, Ariel Luis; Bianchi, Monica and Torriero, Anna. 2022. Leontief Meets Markov: Sectoral Vulnerabilities Through Circular Connectivity. Networks and Spatial Economics, 22(3), pp. 659-690. ISSN 1566-113X [Article]

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Abstract or Description

Economists have been aware of the mapping between an Input-Output (I-O, hereinafter) table and the adjacency matrix of a weighted digraph for several decades (Solow, Econometrica 20(1):29–46, 1952). An I-O table may be interpreted as a network in which edges measure money flows to purchase inputs that go into production, whilst vertices represent economic industries. However, only recently the language and concepts of complex networks (Newman 2010) have been more intensively applied to the study of interindustry relations (McNerney et al. Physica A Stat Mech Appl, 392(24):6427–6441, 2013). The aim of this paper is to study sectoral vulnerabilities in I-O networks, by connecting the formal structure of a closed I-O model (Leontief, Rev Econ Stat, 19(3):109–132, 1937) to the constituent elements of an ergodic, regular Markov chain (Kemeny and Snell 1976) and its chance process specification as a random walk on a graph. We provide an economic interpretation to a local, sector-specific vulnerability index based on mean first passage times, computed by means of the Moore-Penrose inverse of the asymmetric graph Laplacian (Boley et al. Linear Algebra Appl, 435(2):224–242, 2011). Traversing from the most central to the most peripheral sector of the economy in 60 countries between 2005 and 2015, we uncover cross-country salient roles for certain industries, pervasive features of structural change and (dis)similarities between national economies, in terms of their sectoral vulnerabilities.

Item Type:


Identification Number (DOI):



Input-output analysis, Markov chains, Betweenness centrality

Departments, Centres and Research Units:

Institute of Management Studies
Institute of Management Studies > Structural Economic Analysis


7 July 2021Accepted
30 August 2021Published Online
September 2022Published

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Date Deposited:

07 Sep 2021 15:32

Last Modified:

26 Feb 2024 13:34

Peer Reviewed:

Yes, this version has been peer-reviewed.



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