(750c) Mathematical Models In Input-Output Analysis of Economic and Ecological Systems

Input-output analysis provides a network based tool for assessing the overall impact of industrial and consumer activities within interconnected agents in an economic system. It is widely used for various applications such as environmental and ecological modeling to determine the total (direct and indirect) resources required or pollution emitted to deliver a product. Over the years, many methods based on IO analysis have been proposed to calculate cumulative resource intensity from different perspectives. Each approach relies on different types of data and often uses different equations for the calculations. For example, some methods rely on supply side data while others rely on demand side data. Also, most methods calculate physical flows from IO data that are in monetary units. Deeper insight into these methods and their pros, cons and relationships can help to better understand the appropriateness of different tools for specific applications.

Physical-flow and monetary-flow IO tables are connected via price information. If price is homogeneous, the resulting resource intensities are equivalent, be any unit used for transactions. However, the price homogeneity assumption is not satisfied in real situations in which case the physical IO table is superior to monetary IO table and should be worth pursuing. Supply-driven and demand-driven model are two prevalent models quantifying total economic activity instigated by final demand or value-added. They have also been used for environmental modeling with corresponding supply-side and demand-side data. Supply-side data are the total mined resources from nature, while demand-side data are the resource consumption in each economic sector. Three methods were proposed to use supply-side data. Bullard and Herendeen set up the problem via energy and material balance. Miller and Blair sought a set of matrices analogous to economic counterpart but in physical units. Solving them also gives resource intensity. Ukidwe and Bakshi assumed resources as physical value-added and used Ghosh inverse to propagate resources into economy. The equivalence of these three methods can be proved by simple matrix manipulation. Then, their result is compared with that of demand-driven model. It can be shown that resource intensities calculated from both sides are identical except for the sectors whose products are still some forms of resources. The difference is due to the fact that the result of supply-driven model includes the resource content in products, while result of demand-driven model does not.

These findings are not only important from a theoretic point of view, they are useful to build better inventory data and calculate more accurate resource intensity. The equivalence of existing methods under certain assumptions have been proved, thereby it is possible to choose any of them. However, in reality data are not free of errors. The connection of supply-side method and demand-side method enables the use of both supply-side and demand-side data. Data rectification can be applied with help of additional mass/energy balance. On the other hand, although physical flows can better depict the resource consumption, it is not possible to collect enough data for a physical IO table as detailed as the existing monetary IO table in foreseeable future. A more practical expectation is to build a mixed-unit IO table with as many physical data as possible. Price information can also help convert monetary flow to corresponding physical flows. The use of such insight for improving LCA will be demonstrated via the Eco-LCA tool, which accounts for natural capital in LCA.

References

Bullard, C.W. and Herendeen, T.A., 1975, The energy cost of goods and services, Energy Policy, 3(4):268-278.

Miller, R.E. and Blair, P.D., 1985, Input-output Analysis: Foundations and Extensions, Prentice-Hall.

Ukidwe, N.U. and Bakshi, B.R., 2007, Industrial and ecological cumulative exergy consumption of the United States via the 1997 input-output benchmark model, Energy, 32(9):1560-1592.