Using Multi-Regional Input-Output models in health system emissions analysis

Who is this Decarbonization Analytics Guide for?

For analysts developing the expenditure-based component of a health system emissions assessment. It explains how to select and apply multi-regional input-output (MRIO) emission factors to estimate supply chain emissions. Use it alongside the WHO guidance on measuring greenhouse gas emissions in health systems (1) and the hybrid modelling guide, which explains how these estimates fit into a comprehensive assessment.

This Decarbonization Analytics Guide should be read alongside relevant greenhouse gas (GHG) accounting standards and the Healthcare Decarbonization Analytics Toolkit’s guidance on hybrid modelling and software and technology.

Health system emissions analysis that uses MRIO models must:

Account for the full international supply chain. Include domestic and international upstream emissions, and account for sources outside of MRIO coverage.
Select an MRIO model based on relevance and quality. Justify the model’s geographic, sectoral and GHG coverage, underlying data quality, reference years, transparency and continued access.
Match expenditure datasets to factors. Represent an appropriate mix of domestic and imported production, and align currency, price year and valuation basis.
Interpret results within their analytical limits. Account for uncertainty, sector averages and data limitations when drawing conclusions, comparing results or assessing changes over time.

1. Account for the full international supply chain

A health system emissions assessment must cover the full GHG footprint within its stated boundary, including all domestic and international upstream supply chain emissions.

Health systems purchase hundreds of thousands of pharmaceuticals, medical devices, utilities, construction materials, and other products and services through complex international supply chains. Comprehensive activity, product and supplier data are not yet available to calculate their entire footprints using process-based methods alone. Expenditure-based accounting using MRIO models provides a practical way to estimate these emissions and maintain broad coverage as more detailed information becomes available over time (Box 1).

Technical detail · Box 1What is an MRIO?

An input-output model describes the transactions between different sectors of an economy, together with purchases by final users such as households and governments. These models combine economic data from national accounts, supply-and-use tables, and trade statistics.

Models can cover one or many regions and countries. Single-region models often account for imported goods using a domestic technology assumption, assuming they were produced using the same technologies and emissions intensities as equivalent goods produced domestically.

A multi-regional input-output (MRIO) model connects countries or regions through international trade, representing sectors separately within each country. This is important in health system decarbonization analysis because production technologies, energy systems, labour markets and supply chains differ between countries that contribute to health systems’ supply chains.

An environmentally extended model links transactions to environmental satellite accounts, which use emissions inventories, energy statistics and other sources to quantify direct environmental impacts associated with production in each sector. Combining these accounts with transaction data allows emissions to be traced through domestic and international supply chains.

MRIO models combine economic transactions with emissions data to provide expenditure-based factors expressing average GHG emissions per unit of currency spent on goods or services from a specified sector. They support coverage across purchasing categories and successive supply chain stages, including production outside the country where health care is delivered (Fig. 1).

Fig. 1: Illustrative expenditure flows through a health system’s international supply chain — **Fig. 1:** Illustrative expenditure flows through a health system’s international supply chain

MRIO modelling provides three practical advantages:

Coverage across all purchased goods and services. All health system purchases can be mapped to economic sectors where product-specific data are unavailable. These estimates have limited product specificity but help identify major emissions sources and priorities for more detailed analysis.
Coverage across international supply chains. Models capture emissions across successive upstream production stages in different countries.
Compatibility with health system expenditure records. Financial records can be used to establish an organizational boundary for an emissions assessment, following WHO guidance Measuring greenhouse gas emissions in health systems (1). These datasets can be mapped directly to MRIO emission factors, with exclusions, gaps and duplication addressed as described in the Building hybrid models of health system emissions.

The factors applied must represent emissions from both the producing sector and all successive upstream supply chain stages. A supply chain multiplier captures these combined emissions per unit of expenditure and can be calculated directly from an MRIO model (Box 2). The producing sector’s direct emissions intensity alone is insufficient.

Technical detail · Box 2Calculating and interpreting supply chain multipliers

This box explains how expenditure-based emission factors are derived from an MRIO database. The calculations assume a square input-output table with matching environmental accounts. Databases supplied as supply-and-use tables may require transformation before calculations can be performed.

Manipulating MRIO tables that contain tens of thousands of rows and columns requires billions of calculations. This volume of data requires a dedicated programming environment such as Python or MATLAB, rather than use of spreadsheet software. The calculations described below can usually be defined in a few lines of code, but may take several hours to run. Processing time depends on the model size, calculations applied and hardware available. Teams applying suitable published factors do not need to perform these calculations themselves. Further advice on analytical tools and workflows is provided in the Toolkit’s guidance on software and technology.

Four components are needed to derive supply chain multipliers (Fig. 2):

MRIO component	Definition
Intermediate consumption, T	Transactions between sectors. Rows represent the supplying sector, and columns identify the purchasing sector.
Final demand, Y	Purchases by final users, including households and governments, and capital formation. Rows identify the producing sector, and columns identify the country and type of final demand.
Gross output, X	Total monetary output of each country-sector, equal to its intermediate sales plus final demand. In a balanced table, gross output equals gross input.
Environmental satellite accounts, Q	Direct GHG emissions associated with production in each country-sector, usually expressed in kg of carbon dioxide equivalent (CO₂e). Where gases are supplied separately, convert them to CO₂e using a documented, consistent set of global warming potentials before summing.

Fig. 2: Building blocks of an MRIO — **Fig. 2:** Building blocks of an MRIO

In the equations below, each index identifies a sector in a particular country or region. For transactions between country-sectors, $i\$ identifies the supplier and $j$ identifies the purchaser. Environmental satellite accounts may contain several indicators. For the calculations below, $\mathbf{Q}$ contains only direct GHG emissions, aggregated into mass of CO₂e for each country-sector.

Step 1: Calculate direct intensities

Divide each country-sector’s direct emissions by its gross output:

q_{i} = \frac{Q_{i}}{X_{i}}

(1)

The resulting direct intensity row vector $\mathbf{q}$ contains each country-sector’s direct emissions per monetary unit of output. This calculation does not yet include upstream emissions.

Step 2: Calculate supply chain requirements to meet final demand

The technical coefficient matrix $\mathbf{A}$ is calculated by dividing each column of $\mathbf{T}$ by the gross output of the purchasing sector:

A_{i,j} = \frac{T_{i,j}}{X_{j}}

(2)

Each column of $\mathbf{A}$ is a purchasing sector’s recipe of inputs to produce one unit of output. Each of those suppliers purchases their own inputs with their own recipe, represented by a different column of $\mathbf{A}$ .

These successive requirements are combined through the Leontief inverse:

\mathbf{L} = {(\mathbf{I} - \mathbf{A})}^{- 1}

(3)

which is equivalent to:

\mathbf{L} = \mathbf{I} + \mathbf{A} + \mathbf{A}^{2} + \mathbf{A}^{3} + \ldots

(4)

The identity term $\mathbf{I}$ represents one monetary unit of output from the sector supplying final demand. The term $\mathbf{A}$ represents the immediate inputs required to produce final demand; $\mathbf{A}^{\mathbf{2}}$ represents the inputs required to produce those inputs; and subsequent terms extend the calculation through all further upstream tiers (Fig. 3).

Each column of $\mathbf{L}$ therefore represents the output required from every country-sector to deliver one monetary unit of final demand for the selected country-sector.

Step 3: Calculate supply chain multipliers

Multiply these production requirements by the corresponding direct emissions intensities:

\mathbf{m} = \mathbf{qL}

(5)

Both $\mathbf{q}$ and $\mathbf{m}$ are expressed in emissions per monetary unit, but their coverage differs: only $\mathbf{m}$ includes the entire upstream supply chain.

These calculations produce a separate multiplier for each sector of production in each country (Fig. 3). The process of combining them is explained in section 3.

Fig. 3: Difference between direct intensity and a supply chain multiplier — **Fig. 3:** Difference between direct intensity and a supply chain multiplier

By default, MRIO factors do not capture use-phase emissions such as fuel combustion or releases of anaesthetic gases, inhaler propellants or refrigerants. They also exclude subsequent disposal, although purchased waste-treatment services may capture some of these emissions.

Sector-average factors should be applied to broad categories of expenditure. They may poorly represent individual products whose prices or emissions intensities differ substantially from the average. A high-cost drug does not necessarily generate proportionately higher emissions; a product made with a highly efficient low-carbon manufacturing process would have a true footprint that differs substantially from that implied by the sector average.

Assessments must account for fuel combustion, releases of anaesthetic gases and inhaler propellants, waste treatment, and travel outside purchasing records, preferably using activity-based methods. Existing coverage must be checked before incorporating these estimates to avoid double counting, following the Building hybrid models of health system emissions.

2. Select an MRIO model based on relevance and quality

MRIO models differ in geographic and sectoral coverage and detail, reference years, update frequency, environmental accounts and accessibility. Model selection must reflect the purpose of the assessment, the health system’s economic and trade relationships, and the capacity of the national team to access, maintain and use the data. Several selection criteria (Fig. 4 and Box 3) can help assess whether an MRIO database provides suitable economic and environmental coverage and a practical basis for continued use.

Fig. 4: Summary of key criteria for MRIO selection — **Fig. 4:** Summary of key criteria for MRIO selection

Technical detail · Box 3Criteria for MRIO model selection

Geographic coverage. Check whether the country of interest and its principal suppliers are represented individually. Factors for aggregated regions, such as “Rest of World”, cannot distinguish production in individual countries. Coverage of smaller and lower-income economies varies between databases and should be assessed against the health system’s trading relationships.

Sectoral resolution. Check whether major health care purchases and their upstream inputs are represented adequately. A distinct pharmaceuticals sector may be more appropriate than a broad chemicals sector with a different product and price mix. Expensive pharmaceuticals may have lower emissions per monetary unit because of their prices, without lower emissions per physical unit. Relevant sector definitions matter more than the total number of sectors.

Environmental accounts. Check which gases and emissions sources are included, their reference years and how emissions are allocated to economic sectors. A CO₂-only database requires supplementary estimates for other gases to provide a comprehensive GHG assessment. Differences in environmental coverage must be identified before comparing results from different models.

Recency and continuity. Distinguish publication dates from the underlying economic and environmental data years. Recent years may be estimated through extrapolation or nowcasting rather than observed directly. Check how these estimates were constructed. Regularly maintained databases support continued assessment; older models may remain appropriate for historical assessments.

Quality and transparency. Look for documented data sources, proxy assumptions, and methods for estimating missing data and reconciling inconsistencies. Published methodologies, validation results and independent applications support assessment of reliability. Accessible data and inspectable code enable reproduction and investigation of unusual factors. Established use alone does not demonstrate suitability for a particular health system.

Technical requirements. Establish whether the database provides input-output tables or supply-and-use tables requiring transformation. Labelled matrices, sector concordances and machine-readable files reduce analytical work and potential errors. Published factors may be sufficient for application, while deriving factors or undertaking further analysis may require underlying matrices, programming capability and suitable software.

Access and ownership. Check licence permissions for publishing results, sharing derived factors and retaining underlying data. National teams must retain access to the resources needed to maintain the assessment after external support ends. Prefer open sources where analytically suitable. Where paid access offers a material advantage, document the benefits, continuing costs and arrangements for national access.

Before deriving new emission factors, published sets of factors should be reviewed. Using existing factors may help avoid unnecessary analytical work, but their suitability should be assessed against the same criteria. Where no suitable set is available, factors can be derived from an appropriate MRIO database.

Models or factors already used in government reporting can support consistency with national statistics. For example, the footprint assessment of the National Health Service (NHS) in England (2) uses a model specific to the United Kingdom of Great Britain and Northern Ireland, which also underpins the United Kingdom’s consumption-based emissions accounts (3).

Analysts should document the selected database, the alternatives considered and the trade-offs that informed the decision. Comparing results from different models can help assess sensitivity to MRIO selection.

3. Match expenditure datasets to factors

Expenditure must be prepared and reconciled using the approach described in the Building hybrid models of health system emissions. Each expenditure category must be matched to factors representing the relevant goods or services.

Factors must represent an appropriate mix of domestic and imported production. A domestic-production factor must not be applied to all purchases without considering imports.

Where producing countries are known, the corresponding country-sector multipliers may be used. Where they are unknown, the model’s national sector-specific mix of domestic and imported purchases may provide a proxy. The resulting factors represent average direct and upstream GHG emissions per monetary unit of purchases from each sector, weighted by the national mix of imported and domestic sourcing (Box 4).

Technical detail · Box 4Combining domestic and imported production

Health care accounts usually identify expenditure by category, but not by country of production. It is therefore important to calculate factors that represent the mix of domestic and imported purchases for each purchasing sector in the consuming country. Final-demand data for the consuming country can be used as a proxy.

For sector $s$ in consuming country $c$ , a consumption-weighted factor is calculated by averaging the supply chain multipliers across producing countries $r$ , weighted by final demand for that sector’s output in the country of consumption:

{f_{s}}^{c} = \ \frac{\sum_{r}^{}{m_{s,r}Y_{s,r}^{c}}}{\sum_{r}^{}Y_{s,r}^{c}}

(6)

Here, $m_{s,r}$ is the multiplier for sector $s\$ produced in country $r$ , and $Y_{s,r}^{c}$ is expenditure by the selected final users in country $c$ on that output. The sum includes both domestic production and imports.

This step is particularly important for import-dependent countries. For the same sector, a domestic-production factor can differ considerably from a factor weighted across domestic and imported production (Fig. 5).

These weights represent the sourcing mix of the selected final users and are a proxy for health care purchasing. Health care providers’ operating purchases generally appear in intermediate transactions, and their sourcing mix may differ. Use representative health care procurement data to determine sourcing weights where possible.

Fig. 5: Illustrative comparison of emission factors for countries with low and high import shares — **Fig. 5:** Illustrative comparison of emission factors for countries with low and high import shares

Before factors are applied, expenditure and factors must have compatible currencies, price years and valuation bases. Adjustments should follow the methods used or recommended by the MRIO provider wherever possible.

Where no provider method is specified, local-currency expenditure should first be converted into the model’s reference currency. Purchasing-power-parity conversions must not be used unless the model explicitly uses that basis. Where price years differ, expenditure or factors must be adjusted to a common price year using an appropriate price index.

The valuation basis must also match. Purchasers’ prices can include trade and transport margins and product taxes that are absent from basic-price factors. Distribution services and tax adjustments must be treated consistently, either by adjusting expenditure or by deriving factors on a compatible purchasers’ price basis (Box 5).

Where suitable margin data are unavailable, applying basic-price factors to purchasers’ expenditure may support an initial estimate as a documented approximation. Its potential effect on major purchasing categories should be assessed.

Technical detail · Box 5Price bases and margins

Basic prices represent the producer’s receipt, excluding taxes on products and including subsidies on products. Purchasers’ prices also reflect trade and transport margins and applicable taxes less subsidies. National accounts generally exclude deductible value added tax (VAT) but retain non-deductible VAT.

Trade and transport margins pay for services with their own emissions. Applying a product-sector factor to the entire purchase value assigns that sector’s intensity to distribution services and taxes, potentially overestimating or underestimating emissions.

Provider margin tables or compatible national supply-and-use data may be used to separate the product value from distribution services and taxes. Alternatively, a suitably constructed purchasers’ price factor may be applied. Margin adjustments must not be repeated where already incorporated in the factor, and the treatment of taxes in expenditure records must be checked before amounts are removed.

Aligning price years and currencies alone does not update the production technologies, energy systems or trading relationships in an older model, which can remain a limitation even after alignment. Ideally, the model’s underlying economic and environmental data should be no more than five years older than the assessment year. Where older data are used, analysts must justify their suitability and assess the implications for the results. Recency must be judged from the underlying data years, rather than the publication date alone.

4. Interpret results within their analytical limits

The application of MRIO-derived emission factors should be appropriate to the question being asked. MRIO estimates can establish the broad scale and composition of supply chain emissions and identify purchasing categories that would benefit from further investigation. Sector-average factors do not distinguish the emissions intensities of individual products or suppliers within a sector. Changes in purchasing volumes and sector mix can affect expenditure-based estimates, but these estimates cannot capture all effects of operational changes. Confidence in a system-level assessment does not imply equivalent confidence in footprinting every individual product or expenditure line (Fig. 6).

Fig. 6: Appropriate and inappropriate uses of MRIO-derived estimates of emissions — **Fig. 6:** Appropriate and inappropriate uses of MRIO-derived estimates of emissions

Sector-average factors must not be used alone to rank individual products or suppliers, or to substantiate claims that a particular switch has reduced emissions. They can help identify where more specific assessment would be valuable. Small differences between categories must not be presented as definitive rankings where uncertainty could change their order.

Country-level multipliers must be interpreted in light of differences in prices, production systems and underlying data quality. Higher emissions per dollar do not, by themselves, demonstrate poorer environmental performance. Unusual factors must be investigated where they materially affect the assessment (Box 6).

Technical detail · Box 6MRIO uncertainty in low- and middle-income countries

MRIO uncertainty is not evenly distributed across countries and sectors. In places where economic or environmental statistics are incomplete or infrequently updated, including in some low- and middle-income countries, models may rely more heavily on proxy data, extrapolation and assumptions drawn from other economies.

The pharmaceutical sector example (Fig. 7) illustrates how lower-income countries usually have higher emission factors per dollar, including after weighting for domestic and imported sourcing. Differences in production technologies, energy systems and energy efficiency can affect emissions, while lower prices, potentially reflecting lower labour costs or a higher proportion of lower-cost products purchased within sectors, can increase emissions per dollar spent. Higher multipliers should therefore not automatically be interpreted as evidence of either poorer environmental performance or model error.

Data limitations can also cause unusual factors in some countries and sectors. Uncertainty tends to be greater in parts of the model with limited primary data coverage, including lower-income economies and smaller industries. In those places where primary data provide fewer constraints, balancing procedures can substantially adjust estimated transactions. Factors that are unexpectedly high or low relative to comparable country-sector estimates, other reference years or external sources must be investigated where they materially affect the assessment. One screening approach for identifying anomalous factors is described in the Lancet MedZero methodology (4).

Fig. 7: Emission multipliers for the pharmaceutical sector are negatively correlated with per-capita gross national income (GNI) of the country of production — **Fig. 7:** Emission multipliers for the pharmaceutical sector are negatively correlated with per-capita gross national income (GNI) of the country of productionSources: Lancet MedZero *(4,5)*; World Bank *(6)*; Industrial Ecology Virtual Laboratory *(7)* based on Lenzen et al. *(8,9)*.

Comparisons between health systems must consider consistency in boundaries, methods, reference years and data coverage. Total footprints and emissions per unit of expenditure must not be treated alone as measures of environmental performance or efficiency. Differences in prices, service provision, health care need, access and quality affect their interpretation.

Changes over time must be examined in relation to purchasing volumes, product mix, prices, production origins and changes to the model or factors. A reduction in expenditure-based emissions does not, by itself, demonstrate that a health system intervention reduced emissions. Where model revisions materially affect a trend, analysts should recalculate earlier estimates consistently or explain the break in comparability.

Analysts must test influential assumptions where these could change the conclusions. Sensitivity analysis should focus on consequential choices, such as the MRIO model, sourcing mix and monetary adjustments, and explain whether the findings remain sufficiently robust for their intended use.

Acknowledgements

This Decarbonization Analytics Guide was co-developed by WHO, NHS England and the Centre for Sustainable Medicine (CoSM) at the National University of Singapore as a contribution to the Health Systems Decarbonization Thematic Community of Practice.

Contributors: Lydia Loh, Sammy Bishop, Debbie Chan, Esa Chen, Reni Chng Cai Lok, Hiten Patel, Amy Savage, Aruzhan Shalabayeva, Robin Simpson, Jit Sohal, Olena Zotova, Nick Watts, Christopher Gormley, Elena Villalobos Prats, Diarmid Campbell-Lendrum and Thomas Andrew.

References

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2. Simpson R, Tennison VI, Episkopou E, Bagga Y, Patel H, Caunt M, et al. Five years of Greener NHS: improved carbon footprint assessment of the National Health Service in England. Lancet Planet Health. 2026;10(5):101464. doi:10.1016/j.lanplh.2026.101464.

3. UK and England’s carbon footprint to 2023 [website]. London: Department for Environment, Food & Rural Affairs; 2026 (https://www.gov.uk/government/statistics/uks-carbon-footprint, accessed 1 October 2026).

4. The Lancet MedZero: platform methodology. Carbon analytics for healthcare, by healthcare, at scale. Lancet MedZero; 2026 (https://www.medzerocarbon.com/files/The%20Lancet%20MedZero%20Methodology%20Overview%20-%20Final.pdf, accessed 1 October 2026).

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Using Multi-Regional Input-Output models in health system emissions analysis

Using Multi-Regional Input-Output models in health system emissions analysis

Who is this Decarbonization Analytics Guide for?

1. Account for the full international supply chain

Step 1: Calculate direct intensities

Step 2: Calculate supply chain requirements to meet final demand

Step 3: Calculate supply chain multipliers

2. Select an MRIO model based on relevance and quality

3. Match expenditure datasets to factors

4. Interpret results within their analytical limits

Acknowledgements

References

Alliance for Transformative Action on Climate and Health

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