Estimating the Total Pollution Generation by Means of the General Relation between Two Different Inverse Matrices

다국어 초록 (Multilingual Abstract)

Until now, in estimating the total pollution generation resulting from economic activities, the Leontief inverse matrix of the traditional input-output model has been used. As it is well known, each element of the Leontief inverse, , represents the direct and indirect output requirements to support a unit of final demand.
Moreover, I verified the general relation between the notion of direct and indirect input requirements of commodity i to support a unit of final demand of commodity j,, and that to produce a unit of gross output of commodity j,, in the open static input-output model. Accordingly, the identical meaning cannot exist between two different notions of direct and indirect input requirements.
In the same way, we can find the difference between the total requirements matrix for a unit of final demand and that for a unit of gross output. Therefore, we cannot consider two different notions as identical because there is a difference between the notion for a unit of final demand and that for a unit of gross output. The general relation easily helps us convert the Leontief inverse into the other inverse matrix expressed as a unit of output.
On the basis of the issues mentioned above, the study objectives of this paper are as follows. (1) Through introducing and understanding the exact theoretical and economic meanings of the general relation, we can apply this relation to estimate another concept of the total pollution generation as an alternative method distinguished from the traditional method using the Leontief inverse. (2) We can obtain three different concepts of the total pollution generation: one from the Leontief inverse and the other two from the general relation. Through three different total amounts of pollution generation, we can analyse theoretically and empirically the impact and difference of the economic meaning between
them, and then we can compare the results and findings to get the best-fitting total pollution generation which coincides with the analysis objectives.
This research is mainly limited to estimating the total pollution generation by the general relation; however, we hope and expect that the general relation between two different inverse matrices will be used in many different applications: especially in environmental and energy input-output models, intensity analysis of resources, and impact analysis for one unit of output, etc.

다국어 초록 (Multilingual Abstract)

1. Introduction
2. The General Relation^1 and Interpretation
3. Estimating the Total Pollution Generation
4. Numerical Illustration
5. Conclusions