EIO-LCA

An economic input-output life-cycle assessment, or EIO-LCA involves the use of aggregate sector-level data to quantify the amount of environmental impact that can be directly attributed to each sector of the economy and how much each sector purchases from other sectors in producing its output. Combining such data sets can enable accounting for long chains (for example, building an automobile requires energy, but producing energy requires vehicles, and building those vehicles requires energy, etc.), which somewhat alleviates the scoping problem of traditional life-cycle assessments. EIO-LCA analysis traces out the various economic transactions, resource requirements and environmental emissions (including all the various manufacturing, transportation, mining and related requirements) required for producing a particular product or service.
EIO-LCA relies on sector-level averages that may or may not be representative of the specific subset of the sector relevant to a particular product. To the extent that the good or service of interest is representative of a sector, EIO-LCA can provide very fast estimates of full supply chain implications for that good or service.
Background.
Economic input-output analysis was developed by the Nobel Prize-winning economist Wassily Leontief. It quantifies the interrelationships among sectors of an economic system, enabling identification of direct and indirect economic inputs of purchases. This concept was extended by including data about environmental and energy analysis from each sector to account for supply chain environmental implications of economic activity.
Theory.
Input-output transactions tables, which track flows of purchases between sectors, are collected by the federal government in the United States. EIO works as follows: If formula_1 represents the amount that sector formula_2 purchased from sector formula_3 in a given year and formula_4 is the "final demand" for output from sector formula_3 (i.e., the amount of output purchased for consumption, as opposed to purchased by other businesses as supplies for more production), then the total output formula_6 from sector formula_3 includes output to consumers plus output sold to other sectors:
formula_8
If we define formula_9 as the normalized production for each sector, so that formula_10, then
formula_11
In vector notation
formula_12
formula_13
formula_14
This result indicates that knowing only the final demand from each sector formula_15 and the normalized IO matrix formula_16, one can calculate the total implied production formula_17 from each sector of the economy. If data are available on a particular emissions release (or other attribute of interest) from each sector of the economy, then a matrix formula_18 can be compiled to represent various releases (columns) per $ output from each sector (rows). Total additional emissions formula_19 associated with additional final demand of formula_20 can then be calculated as:
formula_21
This simple result enables very quick analysis, taking into account releases associated with the entire supply chain requirements needed to provide a specific final demand, on average. The equations are based on average data in the current economy, but they can be used to make predictions for marginal changes in output (such as one more unit of a particular product) if 
Finally, if the researcher has estimates for valuation of externality costs associated with each item in formula_23 (or, alternatively, if weighting coefficients are available that represent the relative importance of each item in formula_23, using ecological indicators, for example) then the externality costs (or weights) per unit of releases could be compiled into a vector formula_25 in order to calculate the scalar "environmental impact metric" formula_26:
formula_27
Generally there is wide uncertainty associated with estimates of formula_25, so such aggregation should be done only with care, including sensitivity analysis. Typically, researchers examine specific elements of formula_23 rather than attempting to aggregate.
The big picture result is that by collecting data on average economic sector transactions formula_16 and average sector emissions formula_18, it is possible to make quick predictions about the full supply chain emissions associated with a product of interest by representing the product as marginal changes in production from relevant sectors formula_15.
Software.
Researchers at the Green Design Institute of Carnegie Mellon University began developing a web-based tool for performing an EIO-LCA in the 1990s. The underlying software traces out the various economic transactions, resource requirements and environmental emissions associated with the production of a particular product or service. The model captures all the various manufacturing, transportation, mining and related requirements to produce a product or service. For example, one might wish to trace out the implications of purchasing $ 46,000 of reinforcing steel and $ 104,000 of concrete for a kilometer of roadway pavement. Environmental implications of these purchases can be estimated using EIO-LCA. The current (2002) model is based upon the Department of Commerce's 428 sector industry input-output model of the US economy.
In 2018, VitalMetrics Group, an environmental consultancy, developed a web-based Spend Analysis Tool for quantifying the environmental impacts associated with an organization’s entire upstream supply chain. It is compliant with the approach for quantifying spend-based impacts defined in the Greenhouse Gas Protocol Corporate Value Chain Accounting and Reporting Standard. The tool utilizes the Comprehensive Environmental Data Archive (CEDA), a peer-reviewed EIO-LCA database with a base year of 2014. CEDA represents 389 industrial sectors, the commodities and the linkages between them, and over 2,700 environmental exchanges arising from them, including extraction of various natural resources, water consumption, land use, and emissions to air, water and soil. 
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