The indirect transactions between sectors of an economic system has been a long-standing open problem. There have been numerous attempts to define and mathematically formulate this concept in various other scientific fields in literature as well. The existing indirect effects formulations, however, cannot quantify the indirect transactions between any two sectors of an economic system. Consequently, although the directand total requirement matrices are formulated and used for economic system analysis, the indirect requirements matrix has never been formulated before. Based on the system decomposition theory , the indirect transactions and the corresponding indirect requirements matrix are introduced in the present article for the first time. This novel concept of the indirect transactions is also compared with some existing indirect effect formulations, and the theoretical advancement brought by the proposed methodology is discussed. It is shown theoretically and through illustrative examples that the proposed indirect transactions accurately describe and quantify the indirect interactions and relationships , unlike the current indirect effects formulations. The indirect requirements matrices for the US economy using aggregated input-output tables for multiple years are also presented and briefly analyzed.
The indirect transactions between sectors of an economic system has been a long-standing open problem. There have been numerous attempts to define and mathematically formulate this concept in various other scientific fields in literature as well. The existing indirect effects formulations, however, can neither determine the direct and indirect transactions separately nor quantify these transactions between two individual sectors of interest in an economic system. The novel concepts of the direct, indirect and total transactions between any two sectors are introduced, and the corresponding requirements matrices are systematically formulated relative to both final demands and gross outputs, based on the system decomposition theory . It is demonstrated theoretically and through illustrative examples that the proposed requirements matrices accurately define and quantify the corresponding direct, indirect, and total interactions and relationships . The proposed requirements matrices for the US economy using aggregated input-output tables for multiple years are then presented and briefly analyzed.
R
cannot quantify the indirect transactions between any two sectors of
can neither determine the direct and indirect transactions separately nor quantify these transactions between two individual sectors of interest in
R
Consequently, although the directand total requirement matrices are formulated and used for economic system analysis, the indirect requirements matrix has never been formulated before. Based
The novel concepts of the direct, indirect and total transactions between any two sectors are introduced, and the corresponding requirements matrices are systematically formulated relative to both final demands and gross outputs, based
R
, the indirect transactions and the corresponding indirect requirements matrix are introduced in the present article for the first time. This novel concept of the indirect transactions is also compared with some existing indirect effect formulations, and the theoretical advancement brought by the proposed methodology is discussed. It is shown
. It is demonstrated
R
indirect transactions accurately describe
requirements matrices accurately define
R
indirect
corresponding direct, indirect, and total
R
, unlike the current indirect effects formulations. The indirect
. The proposed
R
also
then