PHYS5033

Environmental Footprints and IO Analysis

Reading Material

Week 9

Week 9      Production layer decomposition

The mathematical characteristics of the fundamental input-output equation allow for more sophisticated analyses of the economic system within a given input-output table, and any associated satellite accounts associated with it. The first of these analysis techniques is production layer decomposition (PLD), which reveals the consumption footprint at a particular layer (or tier) within a supply chain. The point of consumption, or final demand, represents the first production layer and the footprint calculated here represents the direct impact due to the consumption being analysed. The second production layer captures the expenditure that each sector makes on the goods and services provided by its suppliers, the third production layer captures the expenditure of those suppliers on their suppliers, and so on. Any footprint calculated due to expenditure at these layers will be indirect in relation to the point of consumption.

Information on each of these layers can be found within our footprint equation:

                  equation (9)

which can also be written as:

and we know that the values of the elements in A will always be less than 1 (see week 4). The Taylor series expansion is a mathematical ‘tweak’ that allows us to write an equation in the form  as:

and if we use this form, remembering that I is the matrix equivalent of 1, our footprint equation can be expressed as:

            equation (10)

The values calculated for each of the 3rd and subsequent production layers will be smaller than the previous layer due to the characteristics of A. As noted in week 4, each of the elements in A will be less than 1. This means that as A is raised to subsequent powers, the values of the elements within A diminish, and since q and y remain unchanged with each production layer, the footprint values calculated for each production layer will become smaller, and eventually converge towards the value of the total footprint. To illustrate this, a plot can be made of the cumulative values of the production layers, such as in Figure 9.1, which has been plotted from the production layer calculations in Table 9.1.

Table 9.1: Hypothetical GHG emissions footprint calculations by production layer

Figure 9.1: Example production layer decomposition chart based on the data in Table 9.1. Note that the cumulative footprint converges towards the total footprint value of 31.6 as the production layer increases.

An interesting example of the use of production layer decomposition in sustainability research can be seen in Figure 9.2, where the labour requirements for two different scenarios related to a vehicle are compared along the related supply chains. Scenario 1 shows the labour requirements (as measured by employment hours) per $1,000 worth of expenditure against a new car while scenario 2 shows the labour requirements per $1,000 worth of expenditure on repairs for an existing car. As can be seen in Figure 9.2, the total labour requirements are higher for the new car purchase once higher production layers are included, even though at the first production layer this requires less labour.

Figure 9.2: Production layer decomposition chart comparing the labour requirements per $1,000 expenditure on 1) a new vehicle and 2) repairs. Figure is sourced from Lenzen, 2002.

Expanding the methodology to calculate sector-level production layer decomposition allows researchers to understand the sectors and regions which make the greatest contribution to food-mile GHG emissions, as seen in Figure 9.3, which is sourced from Li et al., 2022, and to identify the regions which experienced employment reduction and loss of value-added due to a natural disaster, as seen in Figure 9.4 which is sourced from Lenzen et al., 2019. As can be seen from these figures, the direct impact of consumption (at the first production layer) is often significantly lower than the cumulative impact across the supply chains which support that consumption.

Figure 9.3: Production layer decomposition charts related to an analysis of GHG emissions and food-miles, with a) plotting the region which is contributing to GHG emissions, and b) plotting the sector which is contributing to GHG emissions. Note the contribution that food-miles makes to the GHG emissions associated with vegetables and fruits, representing their dependence on temperature-controlled environments as they move around the globe. Figures are sourced from Li et al., 2022.

Figure 9.4: Production layer decomposition charts related to the impact of cyclone Debbie on a) employment across Australian regions and b) value-added cross Australian regions. Note for example that the NSW Tweed region experienced much higher employment losses relative to its value-added losses, while the Mackay region (where the cyclone was most intense) experienced higher value-added losses than employment losses. Figures are sourced from Lenzen et al., 2019.

References

Heihsel, M, Lenzen, M, Malik, A & Geschke, A, 2019, ‘The carbon footprint of desalination: An input-output analysis of seawater reverse osmosis desalination in Australia for 2005–2015’, Desalination. 454, 71–81. doi:10.1016/j.desal.2018.12.008.

Lenzen, M 2000, ‘Errors in Conventional and Input‐Output—based Life—Cycle Inventories’, Journal of Industrial Ecology, 4 (4), 127–148. doi:10.1162/10881980052541981.

Lenzen, M 2002, 'Differential Convergence of Life-Cycle Inventories toward Upstream Production Layers: Implications for Life-Cycle Assessment', Journal of Industrial Ecology, vol. 6, no. 3-4, pp. 137-160.

Lenzen, M & Dey, C 2000, ‘Truncation error in embodied energy analyses of basic iron and steel products’, Energy, 25 (6), 577–585. doi:10.1016/S0360-5442(99)00088-2.

Lenzen, M, Malik, A, Kenway, S, Daniels, P, Leung Lam, K & Geschke, A 2019, 'Economic damage and spillovers from a tropical cyclone', Natural Hazards and Earth System Sciences, vol. 19, no. 1, pp. 137-151.

Lenzen, M & Treloar, G 2002, ‘Embodied energy in buildings: wood versus concrete—reply to Börjesson and Gustavsson’, Energy Policy, 30 (3), 249–255. doi:10.1016/S0301-4215(01)00142-2.

Li, M, Jia, N, Lenzen, M, Malik, A, Wei, L, Jin, Y & Raubenheimer, D 2022, 'Global food-miles account for nearly 20% of total food-systems emissions', Nature Food, vol. 3, no. 6, pp. 445-453.

Rodríguez-Alloza, A M, Malik, A, Lenzen, M & Gallego, J, 2015 ‘Hybrid input–output life cycle assessment of warm mix asphalt mixtures’, Journal of Cleaner Production, 90, 171–182. doi:10.1016/j.jclepro.2014.11.035.

Wiedmann, T O, Lenzen, M & Barrett, J R, 2009, ‘Companies on the scale comparing and benchmarking the sustainability performance of businesses’, Journal of Industrial Ecology, 13 (3), 361–383. doi:10.1111/j.1530-9290.2009.00125.x.