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Singularity in the discrete dynamic Leontief model

Ábel, István and Dobos, Imre (2017) Singularity in the discrete dynamic Leontief model. Periodica Polytechnica Social and Management Sciences, 25 (2). pp. 158-164. DOI https://doi.org/10.3311/PPso.8432

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Abstract

A new wave of applications of the dynamic Leontief model brought into the forefront the singularity problem of the capital matrix. In these applications the singularity of the capital matrix is a common occurrence which complicates the solution of the model. In the singular case the model cannot be transformed in a direct forward recursive form. The method presented in this paper determines the length of a backward system (τ). Several applications stop at observing singularity while referring to the theoretical possibility of the solution. In particular, the singularity of the capital matrix played a prominent role in Bródy’s extensive contributions to the input-output literature but he never ventured into the details of its various solutions. We demonstrate that a number of papers dealing with the Leontief model with singular capital matrix based their solutions on similar regularity assumptions. Our formulation in this paper offers a brief overview of the approaches that can be followed in a wide range of applications confronting with the singularity problem.

Item Type:Article
Uncontrolled Keywords:Campbell regularity condition, dynamic Leontief model, Drazin inverse, matrix pencils, singularity, Weierstrass canonical form
Subjects:Economic development
Economics
DOI:https://doi.org/10.3311/PPso.8432
ID Code:3625
Deposited By: Ádám Hoffmann
Deposited On:28 Nov 2018 16:39
Last Modified:28 Nov 2018 16:39

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