PHYS5033

Environmental Footprints and IO Analysis

Reading Material

Week 6

Week 6      Footprint calculations

Once a satellite matrix (Q) has been created from the relevant raw datasets and manipulated into a structure that matches that of the input-output table being used, footprint calculations of the indicator/s included in that matrix can be undertaken. The satellite matrix provides an account of the indicator against the sector which directly ‘produces’ it – a production-based account. In the case of GHG emissions this is the sector which generates the emissions, in the case of employment it is the sector which employs the workers, and in the case of waste it is the sector which generates the waste.

The term ‘footprint’ is used to denote consumption-based accounting of those same indicators, this time connecting those indicators to the sector of consumption. The act of consumption creates demand for all the economic activities required to produce the end good or service, all the way through the supply chains to the various points of production. This means that the sector of highest consumption impact is not necessarily the same as the sector of highest production impact for a given indicator. A simplistic illustration of this is included in Figure 6.1, which represents a 4-sector input-output table and a GHG emissions satellite matrix (Q), with the size of the icon representing the relative size of emissions. The electricity sector produces the most GHG emissions, yet from a consumption perspective it is the Food sector that is responsible for the highest emissions, as many elements within the supply chains which support that final consumption rely on electricity production, and many of the intermediate outputs from the Agriculture sector are used as inputs to the Food sector.

Figure 6.1: A simplistic illustration of the connection between a production-based account and consumption-based account for GHG emissions. Note that the total production-based emissions and the total consumption-based emissions must be equal.

Connecting the matrices

The input-output table and its components T, Y, and v contain economic data and are measured in monetary units. The satellite matrix Q contains information on the environmental, social, and/or economic inputs to production, and will be measured in the units associated with the chosen indicators within the satellite matrix.

In order to connect these different elements together, we apply some more mathematics to the fundamental input-output equation derived in Week 4. Consider a satellite matrix Q containing information on the GHG emissions by sector, measured in kilograms of CO2-e.

This provides information on the total emissions required as inputs to production for each sector to deliver its total output. To calculate how much of these emissions are required to produce $1 worth of total output, or the ‘direct intensities’, we di ide the emissions in Q by the total output x, remembering that these are matrices nd so simple m them tic l di ision won’t work. We c lcul te the direct intensities m trix q in the same way that we calculated A by multiplying T by (see equation 2 in week 4):

                         equation (7)

The direct intensities (q) matrix provides us with information on the emissions required as direct inputs to production for a given sector to deliver $1 worth of total output, similar to how the A matrix provides us with information on the direct requirements needed from each sector for a given sector to deliver $1 of total output. However, we know that each sector requires more than just direct requirements to produce its outputs, since each input sector also requires inputs to produce its output. The total requirements matrix, or L matrix, provides us with this information (see week 4). Taking advantage of this, we can calculate the total intensities matrix m, as follows:

m = qL                          equation (8)

This provides us with information on the total emissions required as input to production for a given sector to deliver $1 worth of total output, similar to how the L matrix provides us with information on the total requirements needed from each sector for a given sector to deliver $1 of total output.

We now return to our fundamental input-output equation:

x = (I – A) -1y

                              = Ly                      equation (6)

where L = (I – A)-1. If we multiply both sides of this equation by q, we arrive at our footprint equation:

qx = qLy

qx = my

                                   Footprint = qLy                           equation (9)

and we also know that from equation (7), so this can also be written as:

Applications of footprinting – Australian Households

Lenzen & Peters developed a consumption-based account of two environmental indicators (GHG emissions and water use), one social indicator (employment), and one economic indicator (turnover) in their 2010 paper ‘How City Dwellers ffect their Resource Hinterl nd: p ti l mp cts tudy of ustr li n Households’ (Lenzen & Peters, 2010). This consumption-based account shows the locations around Australia impacted by the consumption of an average Sydney household and an average Melbourne household for each indicator ssessed, representin the ‘flow’ of e ch indic tor from the point of production (the re s sh ded in the following figures) to the point of consumption (Sydney or Melbourne, as noted in the Figures).

Figure 6.2: Extract from Lenzen & Peters (2010) showing the location of production of GHG emissions required to support consumption based in Sydney (on the left) and Melbourne (on the right).

Figure 6.3: Extract from Lenzen & Peters (2010) showing the location of production of water (ie where the input water is sourced from) required to support consumption based in Sydney (on the left) and Melbourne (on the right).

Figure 6.4: Extract from Lenzen & Peters (2010) showing the location of production of employment (ie where people are doing the work) required to support consumption based in Sydney (on the left) and Melbourne (on the right).

References

Lenzen, M & Peters, GM 2010, 'How City Dwellers Affect Their Resource Hinterland', Journal of Industrial Ecology, vol. 14, no. 1, pp. 73-90.

Other reading

Fry, J, Lenzen, M, Giurco, D & Pauliuk, S 2016, 'An Australian Multi‐Regional Waste Supply‐Use Framework', Journal of Industrial Ecology, vol. 20, no. 6, pp. 1295-1305.

Hertwich, E & Peters, G 2009, 'Carbon Footprint of Nations: A Global, Trade-Linked Analysis', Environmental Science & Technology, vol. 43, no. 16, pp. 6414.

Hoekstra, A & Chapagain, A 2007, 'Water footprints of nations: Water use by people as a function of their consumption pattern', Water Resources Management, vol. 21, no. 1, pp. 35-48.

Irwin, A, Geschke, A, Brooks, TM, Siikamäki, J, Mair, L & Strassburg, BBN 2022, 'Quantifying and categorising national extinction-risk footprints', Scientific Reports, vol. 12, no. 1, pp. 5861.

Lenzen, M, Li, M, Malik, A, Pomponi, F, Sun, Y-Y, Wiedmann, T, Faturay, F, Fry, J, Gallego, B, Geschke, A, Gómez-Paredes, J, Kanemoto, K, Kenway, S, Nansai, K, Prokopenko, M, Wakiyama, T, Wang, Y & Yousefzadeh, M 2020, 'Global socio-economic losses and environmental gains from the Coronavirus pandemic', PLOS ONE, vol. 15, no. 7, pp. e0235654.

Lenzen, M, Moran, D, Kanemoto, K, Foran, B, Lobefaro, L & Geschke, A 2012, 'International trade drives biodiversity threats in developing nations', Nature, vol. 486, no. 7401, pp. 109-112.

Oita, A, Malik, A, Kanemoto, K, Geschke, A, Nishijima, S & Lenzen, M 2016, 'Substantial nitrogen pollution embedded in international trade', Nature Geoscience, vol. 9, no. 2, pp. 111-115.

Shilling, H-J, Wiedmann, T & Malik, A 2021, 'Modern slavery footprints in global supply chains', Journal of Industrial Ecology, vol. 25, no. 6, pp. 1518–1528.

Wilting, H & Vringer, K 2009, 'CARBON AND LAND USE ACCOUNTING FROM A PRODUCER'S AND A CONSUMER'S PERSPECTIVE – AN EMPIRICAL EXAMINATION COVERING THE WORLD', Economic Systems Research, vol. 21, no. 3, pp. 291-310.

Wiedmann, TO, Schandl, H, Lenzen, M, Moran, D, Suh, S, West, J & Kanemoto, K 2015, 'The material footprint of nations', PNAS, vol. 112, no. 20, pp. 6271.

Wiedmann, T, Wood, R, Minx, JC, Lenzen, M, Guan, D & Harris, R 2010, 'A CARBON FOOTPRINT TIME SERIES OF THE UK - RESULTS FROM A MULTI-REGION INPUT-OUTPUT MODEL', Economic Systems Rresearch, vol. 22, no. 1, pp. 19-42.

Xiao, Y, Lenzen, M, Benoît‐Norris, C, Norris, GA, Murray, J & Malik, A 2018, 'The Corruption Footprints of Nations', Journal of Industrial Ecology, vol. 22, no. 1, pp. 68-78.