A note on the differences between process-based LCA and MRIO.

Process-based life cycle assessment (LCA) and monetary multiregional input-output (MRIO) models are widely applied to study telecoupling, that is, to quantify the supply chains of goods and services consumed. They are both suitable to quantify embodied environmental impacts, also called environmental footprints, and are often combined into so-called hybrid models (Crawford et al. 2018). They share a common mathematical framework (Heijungs and Suh 2002), a bipartite system structure (Pauliuk, Majeau-Bettez, and Müller 2015), and can be constructed from balanced supply and use tables (Majeau-Bettez, Wood, and Strømman 2014).

LCA and MRIO obviously differ in their resolution (regional, product, and industry coverage) as well as their unit of measurement (monetary units are widely used in MRIO, whereas process and life cycle inventory (LCI) databases are quantified in mass, energy, or number of items). Next to those distinct features MRIO and LCA show a number of more subtle differences that one needs to know when comparing the results of the two methods or when combining them. While working with both model frameworks, I still ‘discover’ new features from time to time, and here is a list of what I have come across so far:

MRIO and LCA databases show different degrees of completeness: The national IO tables that form the basis of MRIO models are compatible with the System of National Accounting (SNA) and the System of Environmental-Economic Accounting (SEEA), meaning that they depict the entire economy and emissions of a region. All market transactions and all emissions are included (barring reporting gaps such as informal economic sectors), which means that all economic sectors and their emissions appear in the carbon footprints of consumption. In LCI and process databases there is no criterion regarding completeness; instead, unit process data are filled in according to their availability. That practice leads to coverage gaps (Majeau-Bettez, Strømman, and Hertwich 2011) and hence to truncation errors for supply chains where significant fractions of a product carbon footprint are not captured simply because some relevant industries and products are not included and the respective supply chain links are void (Lenzen 2001).

This difference in completeness between LCA and MRIO, combined with the differences in granularity, is the main motivation for conducing hybrid LCA.

MRIO and LCA databases contain data from different years: An MRIO table is determined for one reference year, and ideally, the large majority of the data in there was actually obtained for that year (and is not inferred or extrapolated using proxy data from previous years). When calculating footprints with an MRIO table the current world trade network and intermediate requirements serve as proxy for the actual supply chain of the commodities, which may be spread out over several years. (The materials in the products we consume may have been produced more than one year ago, before they were shipped, stored, and finally manufactured.) On the contrary, the process and LCI databases contain process data from different years, and some datasets may be more than 15 years old. This difference in coverage is reflected in the naming of the databases: We speak of the EXIOBASE 2007 or the WIOD 2014 table and of ecoinvent 3.2 or 3.3 but not of ecoinvent 2010, as each ecoinvent version contains process data and market mixes from many different years.

The Leontief IO model does not make any difference between the different reference years. All process or sectoral data, whether they are up to date or not, are linked together to form a constructed supply chain.

Neither MRIO nor LCA can reconstruct the actual supply chains of the commodities consumed: That is just not possible a) because the actual supply chain is much more granular than either database (specific alloys, plastics, chemicals, transport distances, production technologies used), b) because the regional diversity of production, emissions, and impacts is much greater than what is described by the databases, and c) because the actual time of production and disposal does not match with the years for which the datasets were recorded. While ‘your’ product may contain 15 kg of x alloy steel from the y steel mill in China produced in year z, the LCA database typically replaces this inflow with average steel from average Chinese (or just non-European!) steel mills over the year 2005-2010 or so. Depending on the resolution the MRIO database would link to the Chinese steel sector or just the Chinese metal sector for the reference year. If one is very serious about tracing the ‘true’ life cycle inputs to the products we consume, one easily can go back deep into the history of the industrial system, as Figure 1 illustrates. Neither MRIO nor LCA databases contain the information to compute such deeply rooted impacts, and use recently (LCA) or currently (MRIO) produced capital to do that.

Figure 1: The deep historic roots of the goods we consume. The capital stocks (steel mills, power plants, bridges, …) often were produced decades ago, using inputs that again came from assets that were decades ago back then…

 Follow-up question: Do the LCAs of all commodities add up?: In an attributional setting with complete data, the LCAs of all commodities consumed added together should yield the total emissions and resource uptake of the world economy, same as the MRIO-based footprint calculation of total final demand. In practice this equality will not hold because a) the process databases are not complete, leading to truncation, and b) because the product systems of the goods we consume contain inputs from many different years. I therefore like to think that with a complete time series of process LCA databases, all attributional LCIs from all years will add up to the total cumulative emissions, but not the attributional LCAs from the goods consumed within any given year.

MRIO and LCA databases differ in their treatment of capital stocks: In ecoinvent you will find many processes that require 10E-11 steel mills or 10E-10 incineration plants to function. These tiny inflows represent the physical capital requirements, which are modelled by allocating 1/(total cumulative lifetime output) to the amount of material required for your product system. In that sense ecoinvent has a capital closure, meaning that the impacts of producing the capital that is required to produce ‘your’ reference flow are accounted for. In the currently available MRIO tables there is no such capital closure by default, meaning that if you calculate the footprint of household consumption with EXIOBASE, for example, the capital requirements will not be included. Instead, the databases contain the current capital formation, which represents current investments, and which are included in the calculation of national consumption footprints. Capital consumption can be included in different ways in IO, with the so-called augmentation method being the easiest to implement (Lenzen and Treloar 2005). I do not have an overview about how well capital services are included in the many footprint studies that use MRIO, but there likely is a systematic gap in system boundaries between process-based LCA and MRIO results.

Unlike in process-based LCA the total output vector x of your product system does not describe the actual (final) sectoral output: In the process databases each unit process has a clearly defined homogenous reference product. Not so in IO, where the output of a sector is a mix of a) the output of the different products aggregated together (e.g., the different crops in the agricultural sector), and b) both final and intermediate sectoral output (e.g., pig iron, cast steel, semi-finished steel, finished steel, and steel products for the iron and steel sector). That inhomogeneity of the IO output vector links back to an old question of what the meaning of the x-vector in IO is. While there is a clear interpretation of x (total final and intermediate sectoral output placed on the markets), it cannot be used as an output indicator or for comparison among countries. In the SNA the total output x depends on how many intra-sectoral transaction steps are recorded (Fig. 2). For an integrated steel mill, for example, the pig iron product directly goes into the steel converter and does not change ownership, and the pig iron as intermediate product is never placed on the market. If, in another country, pig iron production and steel making are carried out by two separate companies, there will be a market transaction in the IO table. In one case the steel sector output contains pig iron that is consumed by another process in the same sector (flows f or g in Fig. 2 are recorded) and in another case it doesn’t (f or g are not recorded).

Figure 2: Recording of process chains in process-based LCA (top) and IO (bottom), where a sector comprises several processes. Depending on the geographical proximity of the processes and the ownership the internal flows f and g may or may not be recorded in the IO table, which means that the total sectoral output x may comprise both final output and intermediate output.

One can assume that national statistical offices make an effort to harmonize the reporting of internal flows across their supply and use tables, but when combining IO tables from different countries into an MRIO table there will be a mix of different degrees of internal sectoral linkages. As an example, Table 1 shows the own consumption coefficients ((f+g)/x in Figure 2) of the iron and steel sector of EXIOBASE2 for selected countries.

There is apparently a large difference in the sectoral reporting structure across countries. In Japan about 44% of the intermediate and value added input into the steel sector comes from other companies and processes within that sector, whereas in the UK that share is less than 1%. One possible explanation is that the Japanese steel sector is split into a number of smaller companies, whereas in the UK it is governed by a few highly integrated businesses.

Table 1: Relative intermediate consumption of own output for the steel sectors in selected regions of EXIOBASE 2. The table shows the diagonal elements of the multiregional A matrix of technical coefficients for the iron and steel sector in the different regions.


In process-based LCA the resolution of the output vector x depends on the granularity of your database. If pig iron is included as a product all pig iron output will be present, if it is not included there will be no pig iron flows at all and steel will directly be linked to iron ore. In IO the sectoral produce contains a number of different final and intermediate outputs and the presence of intermediate outputs in your x vector, such as pig iron, depends on whether or not they are recorded as market transactions within the different sectors.

 Unlike in process-based LCA the columns of the A-matrix cannot be interpreted as unit process descriptions. When teaching I like to speak of the A-matrix columns as production recipes to make an analogy with a cooking book, where each page describes the making of one dish. A production recipe, or a Leontief production function, in IO is not the same as a unit process description in LCA. The reason is the difference in meaning of the x vector: In LCA, the output x comprises final sectoral output only, like finished steel, vehicles, or bottled milk. The technical coefficients in LCA then have only the final output as their reference and can directly be interpreted as specific requirements per unit of final sectoral output. In an LCA database I can directly compare different unit processes that have the same product type (e.g., non-alloyed steel) as their reference product. In IO, I can’t: the output x comprises final sectoral output and may comprise intermediate output, and the technical coefficients have the sum of both as their reference. You cannot look at the A-matrix entries for electricity in the steel sector in Japan and the UK and conclude from these coefficients what the difference in energy intensity of the two sectors is, because both A-matrix elements have different reference products: in Japan the steel output contains significant intermediate output whereas in the UK it doesn’t.

Unlike in process-based LCA the columns of the S-matrix cannot be interpreted as per unit emissions coefficients. That is a corollary of the finding that x cannot be interpreted in the same manner across the same sector in different regions, and the argumentation goes analogue to the A-matrix case. In the simplest constructs, the stressor s is the ratio of emissions h over total output x:

s = h/x

From figure 2 we then read that

s = (h1+h2+h3)/(b+f+g)

While the emission flows hi are present in all countries, the internal flows f and g may or may not be part of x. Hence the stressor s includes both actual differences in relative emissions and the different degrees of coverage of internal output in the x vector.

The inclusion of intermediate output flows in the calculation of s means that I can’t look at the stressor matrix in MRIO, compare the entries for one stressor in a sector across regions, and conclude on the relative environmental performance of those sectors. On the contrary, in an LCA database I can directly compare the unit process emissions if the reference products are of the same kind.

An important observation is that despite the difficulties we face when interpreting the x vector and S matrix in MRIO the calculation of footprints via S·L·y is insensitive to the magnitude of internal flows f and g. If you change your x vector and Z matrix to correct for internal flows within sectors such as the ones shown in Table 1, the L matrix and the S matrix will change, but the product footprints will remain the same.



Crawford, Robert H, Paul-Antoine Bontinck, André Stephan, Thomas Wiedmann, and Man Yu. 2018. “Hybrid Life Cycle Inventory Methods – A Review.” Journal of Cleaner Production 172: 1273–88. doi:10.1016/j.jclepro.2017.10.176.

Heijungs, Reinout, and Sangwon Suh. 2002. Computational Structure of Life Cycle Assessment. Dordrecht, The Netherlands.: Kluwer Academic Publications.

Lenzen, Manfred. 2001. “Errors in Conventional and Input-Output – Based Life-Cycle Inventories.” Journal of Industrial Ecology 4 (4): 127–48. doi:10.1162/10881980052541981.

Lenzen, Manfred, and Graham J Treloar. 2005. “Endogenising Capital: A Comparison of Two Methods.” Journal of Applied Input-Output Analysis 10: 1–11.

Majeau-Bettez, Guillaume, Anders Hammer Strømman, and Edgar G. Hertwich. 2011. “Evaluation of Process- and Input-Output-Based Life Cycle Inventory Data with Regard to Truncation and Aggregation Issues.” Environmental Science & Technology 45 (23): 10170–77. doi:10.1021/es201308x.

Majeau-Bettez, Guillaume, Richard Wood, and Anders Hammer Strømman. 2014. “Unified Theory of Allocations and Constructs in Life Cycle Assessment and Input-Output Analysis.” Journal of Industrial Ecology 18 (5). Trondheim, Norway. Accepted for publication in the Journal of Industrial Ecology: 747–70. doi:10.1111/jiec.12142.

Pauliuk, Stefan, Guillaume Majeau-Bettez, and Daniel Beat Müller. 2015. “A General System Structure and Accounting Framework for Socioeconomic Metabolism.” Journal of Industrial Ecology 19 (5). Accepted for publication in the Journal of Industrial Ecology.: 728–41. doi:10.1111/jiec.12306.

2 thoughts on “A note on the differences between process-based LCA and MRIO.

  1. It is true that the calculation of footprints via S·L·y is insensitive to the magnitude of internal flows f and g, if we only want the aggregate footprint results. But if we want to allocate aggregate footprint to individual products represented in y, it will be sensitive to internal flows, right?

    1. Hi Ming! Also on the product level footprints will not change. When the internal flows for a sector change, the respective column in the A matrix will change, and the respective row in the L matrix (only this one row!), and the respetive column in the S matrix. The output vector x will change but not the emissions b = S \cdot x. Emissions by product and by industry b = S \cdot \hat{x_yi}, where x_yi = L \cdot yi, where yi = [0,0,..0,1,0,0,…], will also remain the same. Cheers, Stefan

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