I/O Database

x= + +(I A A²+A³+… = −)y (I A y)⁻¹ (4.8) where I is the identity matrix, and the total output vector x is the total amount of goods and services in each sector needed to meet the demand y.

The environmental matrix B multiplies the total output x to yield the quantities of emitted substances and extracted resources (ũ) corresponding to the demand (e.g., in kgCO2/FU, Equation 4.9).

u = B x = B (I A y = E y− )⁻¹ (4.9) where E = B (I A − )⁻¹ is the matrix of environmental emissions and resource extrac-tions from each economic sector over the entire production chain. The elements of

E are expressed as ekj: the total elementary flow k extracted from or emitted into the environment per monetary demand of sector j (e.g., in kgCO2/$).

4.4.2 i/O d^ataBase

Calculating emissions with the I/O method requires two types of data: the expenses of each sector in every other economic sector (Ã), and the emission factors per dollar for each sector and pollutant (B ). These data are generally calculated using national statistics, as detailed further below.

74 Environmental Life Cycle Assessment

4.4.2.1 Determining Economic I/O Matrix

The key advantage of the I/O approach is its use of national economic statistics to systematically determine the use of goods and services among different indus-tries. Figure 4.5 shows a simplified national transactions matrix Z, which represents the total expenses of each sector in every other sector, and is available to varying degrees for most countries. The entry in column j and row i represents the expen-diture of industry j in sector i to produce the total output of sector j. If Industry 2 corresponds to the aluminum sector and Industry 4 corresponds to the electricity sector, Figure 4.5 shows that the aluminum sector spends $3.33 billion in the elec-tricity sector to produce $11.5 billion of output. The difference between its sum of intermediary expenses ($8.17 billion) and its total industrial output ($11.5 billion) is

$3.3 billion worth of added value, used for such payments as salaries and benefits.

For the national transactions matrix to be applied generically to a given amount of spending in a sector, it needs to be normalized to express the amount a given sec-tor spends in each secsec-tor for a dollar of output. Each element ã_ij in the normalized economic matrix à is obtained by dividing each element z_ij in the national transac-tions matrix Z by the total output xj of that column’s sector. In the aluminum and electricity example, we find that the aluminum sector spends $0.29 on electricity per dollar of aluminum produced.

The sum of elements in each sector’s row of the transaction matrix is the total sec-tor production that is used by other industrial secsec-tors ($11.0 billion for Industry 2).

By definition, the product of à with the total industrial output vectorx gives this total industrial use. Since the economic system is closed, the total industrial output ($11.5 billion) is the sum of the industrial use with the final demand y of consumer and government spending in each industry ($0.5 billion for Industry 2). In terms of matrices, this is expressed as A x y x + = . By solving for x, we redefine the funda-mental equation of the I/O approach: x= −(I A y)^–1.

National economic transaction matrices are available for most countries, with varying levels of sector and time resolution, in ways that do not necessarily corre-late with LCA data availability. Switzerland has relatively detailed and comprehen-sive data on LCA processes, but possesses an economic matrix of only 42 sectors (Nathani et al. 2006). The United States, on the other hand, is relatively poor in LCA process data, but differentiates 500 sectors in its economic matrix. Several multire-gional input–output (MRIO) approaches have also compiled economic I/O matrices in a consistent manner for a majority of countries of the world (Section 4.4.2.4).

4.4.2.2 Determining I/O Environmental Matrix

Once the final demand is combined with the economic matrix to yield the indus-trial output (Equation  4.8), this must be multiplied by the environmental impacts per dollar output. Databases provide pollutant emissions and energy and resource use for each sector of the economy. So, each emission factor is calculated by divid-ing the total emissions for each sector by that sector’s total output. Figure 4.6 com-pares the direct emissions of CO₂ per dollar spent in each U.S. economic sector for the Open-LC (Norris 1999) and Comprehensive Environmental Data Archive (CEDA) (Suh et al. 2004; Suh 2005) databases. The correspondence between the

Inventory Analysis of Emissions and Extractions 75

Supplying IndustriesUsing IndustriesIndustrial UseConsumers & Govt. Transaction Matrix ZInd. 1Ind. 2Ind. 3Ind. 4Ind. 5Ind. 6Total intermediate input

+Final demand=Total industrial output (M$)(M$)(M$)(M$)(M$)(M$)(M$)(M$)(M$) Industry 114002000575014203595667910274 Industry 222001700012827066781097649411470 Industry 3342503330120038781100514883 Industry 40333044500007780649314273 Industry 515928504920587060001439939114790 Industry 6890907802200720077011930463816568 Total intermediate input8074817010483877381908868Ãx+y=x + Value added220033004400550066007700 = Total industrial output102741147014883142731479016568 Ind. 1Ind. 2Ind. 3Ind. 4Ind. 5Ind. 6 Economic matrixÃ($/$)($/$)($/$)($/$)($/$)($/$) Industry 10.1360.01700.04000.086 Industry 20.2140.14800.0090.0180.403 Industry 30.33300.02200.0080 Industry 400.2900.299000 Industry 50.0150.2480.3310.4110.0410 Industry 60.0870.0080.0520.1540.4870.046 FIGURE 4.5Sample calculation of economic I/O matrix from the national transaction matrix. (Adapted from Norris, G., personal communication. With permission.)

76 Environmental Life Cycle Assessment

two databases is limited, with the Open-LC emission factors smaller than the CEDA factors for the majority of sectors. However, the sectors with the highest emissions per dollar have more consistent factors between the two databases, particularly the electricity sector.

Figure  4.7 plots the same comparison, but accounting for emissions over the entire supply chain, resulting in much better correspondence between the two. This is because the cumulative coefficients are dominated by sectors with high emission levels, which have the best correspondence of direct emissions.

4.4.2.3 I/O Country-Specific Databases

Some software programs and databases directly provide the emissions or impacts associated with expenses in different sectors (see Appendix  I for websites from which the information in this subsection was extracted and to access more detailed information).

For the United States, several databases extend the Bureau of Economic Analysis (BEA) economic I/O matrix for environmental assessment and LCA applications. Carnegie Mellon University provides the “Economic Input–Output Life Cycle Assessment (EIO-LCA) method to estimate the materials and energy resources required for, and the environmental emissions resulting from, activities in the US economy, with summary results for various environmental impacts”

(Appendix  I). The MIET freeware software, developed at Leiden University, provides an I/O database for the United States in 2002, with 1170 environmen-tal inventory flows. CEDA is a “suite of environmenenvironmen-tally extended input–output

1E–03 1E–02 1E–01 1E+00 1E+01 1E+02

1E–03 1E–02 1E–01 1E+00 1E+01 1E+02

Direct equivalent CO2 emissions-Open-LC (kg/$)

Direct equivalent CO₂ emissions-CEDA (kg/$)

Other goods an processes Semiconductors Chemicals Electricity Primary nonferrous metals

Plating and polishing Fitted line 1:1 line

FIGURE 4.6 Comparison of direct CO2 emissions for the American economic sectors, as modeled by Open-LC and CEDA. (Adapted from Loerincik, Y., Environmental Impacts and Benefits of Information and Communication Technology Infrastructure and Services, Using Process and Input–Output Life Cycle Assessment, PhD thesis, École polytechnique fédérale de Lausanne (EPFL), n° 3540, 2006, doi:10.5075/epfl-thesis-3540. With permission.)

Inventory Analysis of Emissions and Extractions 77

databases that covers a comprehensive list of over 1500 environmental interven-tions including fossil fuels, water, metals ores and minerals, and various emis-sions to air, water and soil” (Appendix I; North American I/O CEDA database described in Suh et al. 2004; Suh 2005). Integrated into the SimaPro software, it consists of a commodity matrix from 2002, supplemented with data for capital goods. The I/O matrix is linked to a large environmental intervention matrix compiled from several data sources. By using the databases mentioned, the impacts of small and medium enterprises (SME) have been added to the envi-ronmental intervention matrix, along with those from diffuse sources such as transport.

In Asia, the Japanese I/O database (Nansai et al. 2012) was developed by the Environmental Technology Laboratory of the Corporate Research & Development Center of Toshiba Corporation. It utilizes the Japanese I/O table from the year 2000, as published in 2004, and it contains approximately 400 domestic industrial sectors in Japan exclusively.

On the European level, Danish and Dutch institutions have also created databases that have been integrated into the SimaPro LCA software. The I/O database for EU27 and Denmark (2003) is based on statistical data from 1999, which have been modi-fied and improved by 2.0 LCA Consultants to make the I/O data more relevant to LCA applications. It is based on the hybrid I/O model FORWAST that provides com-plete balanced monetary and physical supply-use tables. The Dutch Input Output 95 library is based on a survey of average consumer spending in 350 categories grouped by economic sector (Goedkoop 2004). The I/O table was extended to also account for imports from both Organisation for Economic Co-operation and Development (OECD) and non-OECD regions. CML-LCA also allows a combination with the

1,E-01 1,E+01

1E–03 1E–02 1

1E–04 1E–01 1E+01 1E+02 1E+03

1E–03

Cumulative CO2 emissions – Open-LC (kg/$)

Other goods and processes

Cumulative CO₂ emissions – CEDA (kg/$)

FIGURE 4.7 Comparison of cumulative CO₂ emissions for the American economic sectors, as modeled by Open-LC and CEDA. (Adapted from Loerincik, Y., Environmental Impacts and Benefits of Information and Communication Technology Infrastructure and Services, Using Process and Input–Output Life Cycle Assessment, PhD thesis, École polytechnique fédérale de Lausanne (EPFL), n° 3540, 2006, doi:10.5075/epfl-thesis-3540. With permission.)

78 Environmental Life Cycle Assessment E3IOT database (see Appendix I), which distinguishes approximately 500 produc-tion sectors.

4.4.2.4 I/O Multiregional Databases

Several methods have combined national I/O matrices into MRIO databases cov-ering the whole world. Developed at the University of Sydney, the EORA MRIO (Lenzen et al. 2013) provides the highest level of detail, with data for 187 individual countries comprising more than 15,000 industry sectors. It has been applied to car-bon, water, ecological footprinting (Lenzen et al. 2013), and employment, with a detailed study of uncertainties.

The EXIOPIOL project has developed a new series of European matrices directly coupled to environmental data, and then extended the system to a global scale to create the global commercial EXIOBASE (see Appendix I). Based on the year 2000, it covers 43 countries (95% of the global economy) and distinguishes 129 industry sectors and products by country, covering 30 emitted substances and 80 resources by industry. Peters and Hertwich (2008) used this data to determine the influence of global trade on CO2 emissions.

The WIOD database includes 40 countries and a model for the rest of the world (see Appendix I). It includes data on employment capital stocks, gross output, and value, as well as on energy use, CO2 emissions, and emissions to air at the industry level (Timmer 2012).

Finally, the tracking environmental impacts of consumption (TREIC) project (Friot 2009) combined matrices from the Global Trade Analysis Project with the emissions database for global atmospheric research (EDGAR) and an impact assess-ment model to evaluate the public health impacts associated with global consump-tion. Using the matrices to link a consuming region to the supply chain regions of production and emission, the TREIC project estimates health impacts due to each consuming region of the world, both locally and in the other regions.

4.4.3 e^xaMpleOf i^nput–O^utput lCa: a^luMinuM