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.

Keywords: Campbell regularity condition, dynamic Leontief model, Drazin inverse, matrix pencils, singularity, Weierstrass canonical form
Published online
How to Cite
Ábel, I. and Dobos, I. (2017) “Singularity in the Discrete Dynamic Leontief Model”, Periodica Polytechnica Social and Management Sciences, 25(2), pp. 158-164. doi: