Why a Popular Accounting Trick May Be Breaking Carbon Footprint Math

A quiet but consequential fight is unfolding in the world of environmental accounting, and its outcome could shape how companies, governments, and consumers understand the true carbon footprint of nearly everything they buy. At stake is a technique called substitution, a method used in life cycle assessment to deal with products that come bundled together, such as corn ethanol and the animal feed left over from its production. In a new reply published in the Journal of Industrial Ecology, Matthew Brander of the University of Edinburgh Business School argues that substitution is fundamentally incompatible with attributional life cycle assessment, directly challenging a 2024 paper by Arianne Provost-Savard and Guillaume Majeau-Bettez that had claimed the two could be reconciled. The dispute may sound arcane, but the numbers involved are anything but: the technique is permitted by influential standards including the Greenhouse Gas Protocol and ISO 14044, and it has been used in a large body of published studies.

To understand the clash, it helps to start with the problem substitution is meant to solve. Many industrial processes produce more than one useful output. A corn ethanol refinery, for example, yields not only fuel but also dried distillers’ grains with solubles, a protein-rich animal feed known as DDGS. When an analyst wants to calculate the footprint of just one of these co-products, the shared upstream emissions, in this case everything from fertilizer manufacture to the energy consumed by the refinery, must somehow be divided between them. One option is allocation, which partitions the shared burdens according to some rule, such as relative mass or economic value. Substitution takes a different route: it identifies the products that the co-products displace in the market, quantifies the environmental burdens of those displaced products, and credits the avoided burdens to the product under study. In the ethanol example, because DDGS displaces dedicated soy meal production as animal feed, the emissions associated with that soy meal are subtracted from the ethanol’s ledger.

Brander’s argument rests on a precise statement of what attributional life cycle assessment, or ALCA, is supposed to represent. He identifies two defining features. First, ALCA describes the material and energy flows, and their associated impacts, from the processes that are actually used in the life cycle of the product being studied. Second, ALCA estimates the share of total absolute anthropogenic impacts that belongs to that product, a property often visualized as a slice of a pie chart. This second feature gives rise to additivity, the principle that if you calculated attributional footprints for every final product in the economy and added them up, the total should approximate the sum of all human impacts. Consequential life cycle assessment, by contrast, answers a different question entirely: it models how the world changes in response to a shift in demand, linking in whatever activities are expected to change as a consequence.

The heart of the new reply is a worked example using corn ethanol, drawing on data from a 2011 paper by Brander and Colleen Wylie. Producing a tonne of ethanol alongside 1.03 tonnes of DDGS generates 2.18 tonnes of carbon dioxide equivalent in upstream emissions. Because each tonne of DDGS displaces soy meal, the avoided burden credited to the system works out to 3.51 tonnes of carbon dioxide equivalent per tonne of ethanol. Applying substitution, the ethanol is assigned a result of minus 1.33 tonnes, a negative footprint. Provost-Savard and Majeau-Bettez had proposed a fix for the additivity problem: assign the 3.51 tonnes of avoided burden to the DDGS instead, so that the assigned values sum back to the true total of 2.18 tonnes. On the surface, the arithmetic balances.

But Brander shows that this solution fails both tests of what ALCA is meant to represent. Consider the figure of 3.51 tonnes assigned to the DDGS. That number describes the emissions from processes used in the life cycle of soy meal, not the processes used in the life cycle of DDGS, which are the refinery operations and corn cultivation that actually produced it. The result therefore does not describe the supply chain of the product it is attached to. Provost-Savard and Majeau-Bettez, Brander notes, accept this entailment of their proposal but do not appear to recognize how profound a departure it represents. If practitioners want to adopt such an alternative normative rule, he argues, they owe the community an explicit statement of what the resulting method would represent, something their paper does not provide.

The second failure is even more visually striking. A share of total impacts cannot exceed 100 percent or fall below zero. Yet the value assigned to the DDGS, 3.51 tonnes, is greater than the entire absolute impact of the combined system, 2.18 tonnes. And the value assigned to the ethanol, minus 1.33 tonnes, is negative. As Brander puts it, when dividing a pie it is impossible to give one person a negative slice. He is careful to pre-empt a misunderstanding here: the objection is not that life cycle results can never be negative, since genuine carbon removals or albedo effects can produce net negative totals, but rather that a share of any effect, positive or negative, cannot logically be less than zero percent or more than 100 percent of that effect. Notably, Provost-Savard and Majeau-Bettez themselves state that ALCA should represent shares of total impacts, without recognizing that their own solution produces values that cannot be shares.

The reply also tackles the argument that any absolute value can be expressed as a change relative to some reference state, which was central to the 2024 defense of substitution. Brander shows that this framing creates a strange hybrid when substitution results are carried into further analyses. If the change value is assigned to one product and the reference value to another, summing them recovers only the total for the described state, not separate absolute values for each co-product, which lands the analyst back at the original multifunctionality problem. Alternatively, treating displacement as a property of the state, suitable for allocation like mass or economic value, fails because substitution is not actually apportioning shares of the absolute flows, as the out-of-range results demonstrate. On the question of marginal data, he observes that the rationale for using it, representing the market mechanism of a transition, is inherently consequential, answering what changes rather than what exists.

Perhaps the most technically interesting section addresses functional unit expansion, a rival technique that Provost-Savard and Majeau-Bettez had invoked to argue that substitution must be legitimate. Functional unit expansion widens the object of study to include the functions of the co-products, so the functional unit becomes one tonne of ethanol plus 1.03 tonnes of DDGS, avoiding allocation altogether. It is a long-established result, dating to work by Anne-Marie Tillman and colleagues in 1994, that substitution and functional unit expansion yield identical outcomes in comparative analyses, because comparing ethanol with petrol requires ensuring both systems deliver the same functions, including animal feed. Brander confirms the numerical equivalence in this context but insists it does not make the techniques methodologically equivalent. Outside comparisons, ALCA serves other purposes, such as quantifying contributions to absolute sustainability thresholds or feeding into further assessments. If a negative ethanol result were used as an input to another product’s footprint, the final number would simply fail to describe the emissions of the processes involved. Functional unit expansion does not create this problem; substitution does.

The stakes of this methodological quarrel extend well beyond the journals. Brander and Wylie called fifteen years ago for standards and guidance documents to state clearly that substitution should not be used in attributional assessment, yet the recommendation was never implemented, and practitioners continue to report results whose coherence the new paper calls into question. The reply closes with a renewed call for the life cycle community to confront the issue and for existing standards, including ISO 14044, which has been criticized elsewhere for conflating substitution with system expansion, to be updated. Whether the appeal gains traction may depend on whether the field agrees with Brander’s central claim: that before defending a technique, its advocates must first say, precisely, what the numbers are supposed to mean. Until then, some of the carbon footprints printed on products and enshrined in corporate reports may rest on arithmetic that cannot describe any share of the world’s actual impacts.

Subject of Research: The compatibility of substitution with attributional life cycle assessment methodology

Article Title: Substitution is not consistent with attributional life cycle assessment: reply to Provost-Savard and Majeau-Bettez (2024)

Article References: Brander, M. (2026). Substitution is not consistent with attributional life cycle assessment: reply to Provost-Savard and Majeau-Bettez (2024). Journal of Industrial Ecology, 30(4), 1779-1785. https://doi.org/10.1007/s44498-026-00121-0

Image Credits: AI Generated

DOI: 10.1007/s44498-026-00121-0

Keywords: life cycle assessment, substitution, attributional LCA, consequential LCA, carbon footprint, multifunctionality, allocation, system expansion, ISO 14044, Greenhouse Gas Protocol, industrial ecology, methodology