New Developments in Input-Output Analysis

In this chapter, a new temporal approach to the classical Leontief input–output analysis is elaborated that avoids the assumption of the constant direct input coefficients. The presentation builds on earlier work (Sonis & Hewings, 1989, 1991, 1992) that examined a variety of issues surrounding error and sensitivity analysis, decomposition and inverse important parameter estimation. These ideas are now brought into a general form as a basis for a more complete, general fields of influence approach that is the main vehicle for describing the overall changes in economic relationships between industries created by combinations of changes in technological coefficients caused by diffusion of technological, organizational and administrative innovations. The most important new concept based of the notion of the direct fields of influence is the multiplier product matrix and the corresponding artificial economic landscape which represents the classical key sector analysis and hierarchies of sectoral backward and forward linkages. The multi plier product matrix is the main part of the fundamental minimal information decomposition of Leontief inverse in the form of the difference between the global presentation of direct effects of the changes in inputs coefficients and the syner getic effects of the overall interaction of the changes. The new Temporal Leontief inverse is constructed such that it can serve as the basis for the temporal analysis of an evolving input–output system; the inverse depends on an evolutionary tail of changes in a highly non-linear manner. The detailed analytical structure of the Temporal Leontief inverse addresses the possibilities of tracing the impact of each change in the individual direct inputs in each time period through to the final state of the economy. This dynamic approach provides the basis for a new perturbation theory for matrix inversion.