Singularity in the Discrete Dynamic Leontief Model

  • Imre Dobos Corvinus Univeristy
  • István Ábel


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
How to Cite
DOBOS, Imre; ÁBEL, István. Singularity in the Discrete Dynamic Leontief Model. Periodica Polytechnica Social and Management Sciences, [S.l.], may 2017. ISSN 1587-3803. Available at: <>. Date accessed: 26 sep. 2017. doi: