Singularity in the discrete dynamic Leontief model

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

Solving an analytic dynamic Leontief model with time dependent capital matrix

[EN] This paper deals with the construction of power series solutions of dynamic Leontief input–output models with possibly singular capital matrix function, assuming that data functions are analytic in a neighbourhood of the origin. Using the majorant method a convergence interval for the power series solution is obtained. An illustrative example is included.Jódar Sánchez, LA.; Merello Giménez, P. (2010). Solving an analytic dynamic Leontief model with time dependent capital matrix. Mathematical and Computer Modelling. 51(5-6):400-404. doi:10.1016/j.mcm.2009.12.008S400404515-