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Peer-reviewedCC BY 4.0Axioms

AMatrix-Algebraic Framework and Pairwise Asymmetry Multiplier for Quantifying Shock Propagation in Complex Production Networks

  • Özlem Orhan1
  • Oya Mert Coşkun2
  • Yasemin Demirel3,4
4 affiliations
  1. 1Department of Engineering Sciences, Faculty of Engineering and Natural Sciences, Bandırma Onyedi Eylül University, 10200 Balıkesir, Türkiye
  2. 2Department of Mathematics, Faculty of Arts and Sciences, Tekirdağ Namık Kemal University, 59030 Tekirdağ, Türkiye
  3. 3Department of Data Science and Analytics, Faculty of Economics, Administrative and Social Sciences, İstanbul Topkapı University, 34662 İstanbul, Türkiye
  4. 4Department of Information Security Technology, Faculty of Computer and Information Sciences, Yeditepe University, 34755 İstanbul, Türkiye
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Abstract

Scalar centrality measures assign one score to each sector of a production network and cannot compare its exposure to two shock sources. We develop a matrix-algebraic framework for this comparison. The Asymmetry Multiplier γj(α,β)=Ljα⊤/Ljβ⊤, the ratio of the price responses of a target sector to equal increments in unit value added at two sources, factors into a direct ratio and a network amplification ratio. Using sub-eigenvectors of the technical coefficient matrix, we derive lower and upper bounds that hold for every productive network and reduce to Perron–Frobenius bounds under irreducibility. We also prove that linear price responses bound those of competitive constant-returns economies from above and that no labeling-independent node-level measure determines the multiplier. A symmetric structural decomposition separates technological and final demand effects. As a proof of concept, the framework is applied to electricity and mining cost shocks in Türkiye. In 2022, the multiplier ranges from 0.20 to 1.86 across eleven sectors, indirect paths attenuate the direct ratio by a factor of 8 to 22 in six sectors, and Basic Metals is more exposed to mining than to electricity cost shocks, through imported mining inputs. For most sectors, the dominant channel is robust to disaggregation, coefficient perturbation and the annual tables of 2012–2022.

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Cite

BibTeXRIS
BibTeX
@article{orhan2026amatrixalgebraic,
  title = {{AMatrix-Algebraic Framework and Pairwise Asymmetry Multiplier for Quantifying Shock Propagation in Complex Production Networks}},
  author = {Özlem Orhan and Oya Mert Coşkun and Yasemin Demirel},
  journal = {Axioms},
  year = {2026},
  month = nov,
  doi = {10.3390/axioms15110832},
  url = {https://www.mdpi.com/2075-1680/15/11/832},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - AMatrix-Algebraic Framework and Pairwise Asymmetry Multiplier for Quantifying Shock Propagation in Complex Production Networks
AU  - Özlem Orhan
AU  - Oya Mert Coşkun
AU  - Yasemin Demirel
PY  - 2026
DA  - 2026/11/06
JO  - Axioms
DO  - 10.3390/axioms15110832
UR  - https://www.mdpi.com/2075-1680/15/11/832
AB  - Scalar centrality measures assign one score to each sector of a production network and cannot compare its exposure to two shock sources. We develop a matrix-algebraic framework for this comparison. The Asymmetry Multiplier γj(α,β)=Ljα⊤/Ljβ⊤, the ratio of the price responses of a target sector to equal increments in unit value added at two sources, factors into a direct ratio and a network amplification ratio. Using sub-eigenvectors of the technical coefficient matrix, we derive lower and upper bounds that hold for every productive network and reduce to Perron–Frobenius bounds under irreducibility. We also prove that linear price responses bound those of competitive constant-returns economies from above and that no labeling-independent node-level measure determines the multiplier. A symmetric structural decomposition separates technological and final demand effects. As a proof of concept, the framework is applied to electricity and mining cost shocks in Türkiye. In 2022, the multiplier ranges from 0.20 to 1.86 across eleven sectors, indirect paths attenuate the direct ratio by a factor of 8 to 22 in six sectors, and Basic Metals is more exposed to mining than to electricity cost shocks, through imported mining inputs. For most sectors, the dominant channel is robust to disaggregation, coefficient perturbation and the annual tables of 2012–2022.
SN  - 2075-1680
ER  -