Singularity in the Discrete Dynamic Leontief Model


  • István Ábel

    Institute of Finance and Accounting, Budapest Business School, Hungary

  • Imre Dobos

    Institute of Business Economics, Corvinus University Budapest, Hungary


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.


Campbell regularity condition, dynamic Leontief model, Drazin inverse, matrix pencils, singularity, Weierstrass canonical form

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How to Cite

Ábel, I., Dobos, I. (2017) “Singularity in the Discrete Dynamic Leontief Model”, Periodica Polytechnica Social and Management Sciences, 25(2), pp. 158–164.