Carbon Emissions Model
March 2024

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Wilshire Indexes Carbon Emissions Model

Contents
1 Introduction.............................................................................................................................................. 2
2 Definitions ................................................................................................................................................ 2
2.1 Common Definitions .............................................................................................................................................2
2.2 Specific Definitions................................................................................................................................................3

3 Sources and Input Data ............................................................................................................................ 3
3.1 Reported Carbon Emissions Data..........................................................................................................................3
3.1.1 Self-Reported Carbon Data ................................................................................................................................................................................3
3.1.2 Reported-Derived Carbon Data .........................................................................................................................................................................3

3.2 Wilshire Indexes Global Asset Taxonomy System .................................................................................................4
3.3 Fundamental Data ................................................................................................................................................4
3.3.1 Net Sales or Revenues in USD ............................................................................................................................................................................4
3.3.2 Other Data ...........................................................................................................................................................................................................4

3.4 Environmentally Extended Multi-Regional Input Output model (EE-MRIO) .........................................................5

4 Methodology ............................................................................................................................................ 5
4.1 Overview ...............................................................................................................................................................5
4.2 Notational Definitions ...........................................................................................................................................6
4.3 Quality Control of Reported Data (Scope 1&2) .....................................................................................................7
4.4 Estimated Data from a Third Party........................................................................................................................7
4.5 Estimated Data from Wilshire Indexes ..................................................................................................................7
4.5.1 Median-based estimated data for Scope 1 and Scope 2 ..................................................................................................................................7
4.5.2 EE-MRIO-based estimated data for Scope 1 and Scope 2: overview...............................................................................................................8
4.5.3 Estimated data for Scope 3 ................................................................................................................................................................................8

4.6 Final Estimated Data .............................................................................................................................................94.6.1 Final estimated data for Scope 1 and Scope 2 ..................................................................................................................................................94.6.2 Final estimated data for Scope 3 .................................................................................................................................................................... 10

4.7 Selection Algorithm............................................................................................................................................ 10

Approval .................................................................................................................................................... 10
Appendix A: Example of the Adjustment Size from the Median-based modelling strategy...................... 11
Appendix B: Carbon Intensity Coefficients by NAICS Sector ..................................................................... 12
Appendix C: Scope 3 Categories ................................................................................................................ 14
Appendix D: Countries and Geographic Regions from Exiobase ............................................................... 15
D.1 Countries ........................................................................................................................................................... 15
D.2 Rest of World regions ........................................................................................................................................ 16

Legal Notices ............................................................................................................................................. 17

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Wilshire Indexes Carbon Emissions Model

1 Introduction
The Wilshire Indexes Carbon Emissions Model provides comprehensive data on Scope 1, Scope 2 and Scope 3 emissions forany company. The emissions data results from a rigorous hierarchical selection process that combines both reported andestimated data (when no reported data is available or validated). The process and input data used are detailed in the next
sections.

2 Definitions
2.1 Common Definitions
The following definitions are based on the GHG Protocol 1.
GHG (Greenhouse Gas): GHG are gases in the atmosphere such as carbon dioxide, methane and nitrous oxide that absorb
and emit radiant energy, thus causing the greenhouse effect.
Carbon emissions: the GHG emissions caused by a company expressed in terms of CO2 equivalent (CO2eq) units, according to
the IPCC and related official documentation.
Scope 1: direct carbon emissions emitted by a company during the production process.
Scope 2: indirect carbon emissions of a company linked to its energy-use during the production process. Note that Scope 2
emissions can be either “location-based” (calculated from the energy that the company has physically drawn from the energygrid) or “market-based” (calculated from the proportion and type of energy purchased by the company on the market) 2. For
reporting companies, the sustained value is “market-based”. For non-reporting companies, estimates are “location-based”.
Scope 3: indirect GHG emissions that occur upstream or downstream of the production chain of a company. These include
emissions required to produce raw material used by a company or emissions associated with using products sold by acompany. Scope 3 emissions are divided into 15 categories as detailed in Appendix C.
Reported carbon emissions: carbon emissions figures disclosed by a company.
Carbon intensity: the carbon emissions produced per unit of a monetary or physical metric. , The most common monetary
metrics are carbon intensity per unit of sales or revenues, market value (MV), or enterprise value (EV, or EVIC if cash isincluded).
Fiscal year: the one-year period that companies use for accounting purposes to prepare financial statements. Note that not
all fiscal years correspond with the calendar year.
NAICS (North American Industry Classification System) 3: The North American Industry Classification System (NAICS) is thestandard used by Federal statistical agencies in classifying business establishments for the purpose of collecting, analyzing,and publishing statistical data related to the U.S. business economy. NAICS was developed under the auspices of the Office ofManagement and Budget (OMB) and adopted in 1997 to replace the Standard Industrial Classification (SIC) system. It wasdeveloped jointly by the U.S. Economic Classification Policy Committee (ECPC), Statistics Canada, and Mexico's Instituto
Nacional de Estadistica y Geografia, to allow for a high level of comparability in business statistics among the North Americancountries.

1 https://ghgprotocol.org/standards
2 https://ghgprotocol.org/scope_2_guidance
3 https://www.census.gov/naics/

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NACE 4: The Statistical classification of economic activities in the European Union (EU), abbreviated as NACE,is derived fromthe French Nomenclature statistique des Activités Economiques dans la Communauté Européenne. Various NACE versions
have been developed since 1970.
Multi-Regional Input Output (MRIO) model: a MRIO model gathers all monetary flows between the major economic sectorsof geographic regions. It is one of the most powerful tools used in macroeconomics to illustrate, calculate, and predict theinterrelations between various activities and economic players.
Environmentally-Extended MRIO (EE-MRIO) model: an EE-MRIO model associates environmental accounts to monetary flows
from MRIO, such as the direct GHG emissions from each economic sector of each geographic region during the production
process.

2.2 Specific Definitions
Specific definitions are the definitions that are used by Wilshire Indexes in its internal processes.
Self-Reported data: carbon emission data that is publicly disclosed by the emitters (companies), whether they have been
quality-checked or not by an external third-party. Self-Reported data is collected from time to time by various data providers
and vendors, and is usually attached to a specific fiscal year.
Reported-Derived data: carbon emission data that is not directly disclosed by emitters, but is derived directly from SelfReported data using basic interpolation (between two years) or extrapolation (derived from the two years immediately
before), according to a general proxy (net sales or revenues). For Scope 3, given the limited historical coverage, we
extrapolate backwards or forwards from the latest known reported emissions. Reported-Derived data is considered as part of
the Reported data family, and not Estimated data. Reported-Derived data only depends on data specifically linked to theemitter (net sales or revenues, previous carbon emissions).
Estimated Data: Estimated data encompasses all carbon emissions data that is neither Self-Reported nor Reported-Derived
data. Estimated data is the output of specific modelling based on macro-economic perspectives or statistical analysis of peergroups.
Final Dataset: refers to the final dataset which assigns emission data to a company and a fiscal year, either reported or
estimated.

3 Sources and Input Data
3.1 Reported Carbon Emissions Data
3.1.1 Self-Reported Carbon Data
Self-Reported corporate carbon emissions data is sourced from the ISS Climate Core dataset. It contains self-reported
emissions data collected by ISS from all available sources, including company CSR and annual reports, and other directsources of emissions data. The dataset also integrates carbon emissions data from the Carbon Disclosure Project (CDP).
3.1.2 Reported-Derived Carbon Data
To expand the coverage of reported carbon emissions, Reported-Derived emissions data is computed either by interpolating
data between two reported years or by extrapolating previous carbon emission data, using computed revenue carbon
intensity and current net sales or revenue in USD from no earlier than two years previously. For Scope 3, given the limited
historical coverage, we extrapolate backwards or forwards from the latest known reported emissions.

4 https://ec.europa.eu/eurostat/statistics-

explained/index.php?title=Glossary:Statistical_classification_of_economic_activities_in_the_European_Community_(NACE)

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3.2 Wilshire Indexes Global Asset Taxonomy System
The Wilshire Indexes Global Assets Taxonomy System (GATS) is a hierarchical industry classification system that iscomprehensive, adaptive, flexible and incorporates green technology identification. GATS classifies companies according totheir specific use case or utility within a given industry enabling a more nuanced view of an economy to be obtained.
GATS has a hierarchical structure:••••

11 industries,
35 supersectors,
59 sectors,
181 subsectors.

Companies are classified via an automated process:
1.
2.
3.

Raw product segments 5 disclosed by companies are translated into NAICS segments
NAICS segments are aggregated at subsector level
The primary subsector assigned to a company is the subsector from which its revenue mainly comes.

For more details, see Wilshire Indexes Global Assets Taxonomy System.

3.3 Fundamental Data
3.3.1 Net Sales or Revenues in USD
For industrials, “Net Sales or Revenues” represents gross sales and other operating revenue less discounts, returns andallowances. For banks, insurance, and other financial companies, it represents the total operating revenue of the company.
Note that all the financial statements reported by companies in local currency are converted to USD using the exchange rate
given in the statements, or where it is not available, using the fiscal year-end exchange rate linked to the country of primarylisting of the shares traded by the company.
3.3.2 Other Data
Companies are assigned to the country in which the corporate office of a company is located.
Fiscal years and associated fiscal periods start and end dates that are used in the process are initially sourced from our data
provider. However, when there are missing fiscal years for a company, a fiscal period is created which starts at the end of thelatest available fiscal period and ends at the beginning of the next available one. Note that before applying this, checks are
made to ensure that the company is active during the created period and that the dates of the initial periods are notconsecutive.

5 Raw product segments represent the revenue as disclosed by a company from each of its product lines.

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3.4 Environmentally Extended Multi-Regional Input Output model (EE-MRIO)The Exiobase 6 v.3 dataset is the Environmentally Extended Multi-Regional Input Output model (EE-MRIO) used, in part, toestimate non-reported carbon emissions. Key features of this dataset can be found in the table below:
Key features of Exiobase3
Number of countries andgeographic regions

Number of economic
sectors

Economic sectors
classification

Currency of monetary data

44 countries*

163 industries

NACE Rev. 1.1 except
energy-linked sectors

EUR 7

5 Rest of World regions*

Source: Exiobase. *See Appendix A for a detailed list of Exiobase countries and regions.

4 Methodology
4.1 Overview
There are a variety of models and approaches available for estimating missing carbon emission data. The fundamental reason
why these models are still employed lies with the limited proportion of companies reporting and disclosing their emissions
for the various scopes. Despite significant progress over time and increased regulation asserting the material risk either inproducing emissions (climate change risk) or failing to report such emissions (transparency & litigation risk), investors
wanting a comprehensive view of the investment universe must continue to make substantial use of models that estimate
non-reported emission data.
Such models are usually characterized according to two perspectives:
1.
2.

Is the model derived from a top-down, macro-economic view linking economies, sectors, and emitters together? Or
is it derived from bottom-up observations related to some peer-group average?
Regarding the potential breakdown of activities of the emitter and its specific carbon intensity factors, is theemitting company considered as a portfolio of separate activities (multi-segment) or as a pure play (one-segmentonly)?

6 Exiobase is a global, detailed Multi-Regional Environmentally Extended Supply-Use Table (MR-SUT) and Input-Output Table (MR-IOT). It

was developed by harmonizing and detailing supply-use tables for a large number of countries, estimating emissions and resource
extractions by industry. Exiobase was developed by a consortium of several research institutes in projects financed by the European
research framework programs. Three versions of Exiobase are available. (https://www.exiobase.eu/)
7 To make Exiobase data, in EUR, comparable with segments data, in USD, the EUR to USD exchange rate from the OECD exchange ratetable (https://data.oecd.org/conversion/exchange-rates.htm) is applied to the Exiobase monetary figures.

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Wilshire Indexes Carbon Emissions Model

This is summarized in the following table.
Comparing the modelling strategies
Top-Down Approach

Examples:Corporates as One-Segment Only

Corporates as Multi-Segment Portfolio-

Meta Sector Analysis (factor
coefficients)

Bottom-Up Approach

Examples:-Median/Mean
1Factor / Multifactor Regression
analysis

Examples:Examples:--EE-MRIO

Interpolation

Source: Wilshire Indexes (NB. The list of solutions presented here is not exhaustive and displayed only for illustrative purpose).

The Wilshire Indexes Carbon Emissions model covers the two main, complimentary types of solutions:-

A Bottom-Up Approach applied to companies viewed as One-Segment Only, with multi-level weighted adjustedmedian estimates, and
A Top-Down Approach applied to companies viewed as Multi-Segment Portfolios, with the EE-MRIO-based
estimated data and the model for estimating Scope 3 emissions.

Additionally, a third-party estimate (from ISS) is also introduced into the final estimate computation, to increase the stability
across sectors and over time.

4.2 Notational Definitions
The following definitions are used throughout this methodology document:𝑟𝑟𝐶𝐶𝑖𝑖,𝑡𝑡: self-reported 𝑟𝑟 carbon emissions of a company 𝑖𝑖 for the fiscal year 𝑡𝑡 (see section 3.1.1),

𝑟𝑟𝑟𝑟: reported-derived 𝑟𝑟𝑟𝑟 carbon emissions of a company 𝑖𝑖 for the fiscal year 𝑡𝑡 (see section 3.1.2),
𝐶𝐶𝑖𝑖,𝑡𝑡𝑒𝑒: estimated 𝑒𝑒 carbon emissions of a company 𝑖𝑖 for the fiscal year 𝑡𝑡 (see sections 4.4, 4.5 and 4.6),
𝐶𝐶𝑖𝑖,𝑡𝑡

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖,𝑡𝑡 : Net Sales or Revenue in USD of a company 𝑖𝑖 for the fiscal year 𝑡𝑡,
𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

𝐶𝐶𝐶𝐶𝑖𝑖,𝑡𝑡=

𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒𝑒 𝑡𝑡𝑡𝑡𝑡𝑡𝑡𝑡

𝐶𝐶𝑖𝑖,𝑡𝑡

𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖,𝑡𝑡: revenue-based carbon intensity of a company 𝑖𝑖 for the fiscal year 𝑡𝑡. Note that “emissions

type” may be either self-reported, reported-derived or estimated.

Each symbol can refer to scope 1, scope 2 or scope 3 emissions.

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4.3 Quality Control of Reported Data (Scope 1&2)
Before integrating reported data into the Final Dataset, the influence of outlier carbon data points is moderated through theapplication of the following Winsorisation process performed at GATS sector Level 3.
For each GATS sector with at least 2 companies reporting revenue-based carbon intensity, 1st and 95th percentiles arecalculated. Any company’s reported carbon intensity below the 1st percentile is then set to the 1st percentile. Any company’s

reported carbon intensity above the 95th percentile is set to the 95th percentile.

For GATS sectors with fewer than 2 reporting companies the company’s revenue-based carbon intensities are left
unchanged.

4.4 Estimated Data from a Third Party
The ISS Climate Core dataset includes estimated carbon emissions data for non-reporting companies. These estimates are
based on the ISS classification system which allows benchmarking of non-reporting companies against their reporting peers.
𝑖𝑖𝑖𝑖𝑖𝑖
They are denoted below by 𝐶𝐶𝑖𝑖,𝑡𝑡.
For an overview of the methodology used by ISS, please see their Carbon Footprint Assessments methodology document
available on request from ISS Climate Solutions.

4.5 Estimated Data from Wilshire Indexes
In addition to third-party data, Wilshire Indexes has developed its own estimation model for assigning carbon emissions data
to non-reporting companies. Data is estimated using a process based on the combination of three strategies detailed below.
Note that the process estimates Scope 1 and Scope 2 location-based emissions and Scope 3 emissions for all companies. In
particular, Scope 2 emissions estimates are mainly derived from intensity factors based on the location of the company.
4.5.1 Median-based estimated data for Scope 1 and Scope 2This estimation strategy is based on the various medians of reported revenue-based measure of carbon intensity computedat each GATS sectoral level, whether it is industry, supersector, sector, or subsector.
The principle is that each company’s carbon intensity can be approximated by various peer groups that can be considered at
different levels within the GATS taxonomy (industry, supersector, sector and subsector).
A wider peer group (e.g. at industry level) will give a carbon intensity proxy which will be more stable, while a narrower peergroup will give a carbon intensity proxy likely more representative of the specific characteristics of similar companies but lessstable over time.
With a multi-level weighted median (described below), a corporate carbon intensity will be simultaneously approximated by
the four sector level intensity medians, according to the merits (peer group size, representativeness) of each level.
Adjusted median of reported carbon intensity
Based on controlled reported revenue-based measure of carbon intensities, we compute medians for each sectoral activity 𝑠𝑠
at each GATS level 𝑙𝑙 (𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶𝐶𝐶 𝑠𝑠𝑙𝑙 ). We also count the overall size of each sectoral activity in each GATS level (𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑠𝑠𝑙𝑙 ) as wellas the number of companies with an available controlled reported revenue intensity figure (𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 𝑠𝑠𝑙𝑙 ).

As stated in section 3.2, GATS has a hierarchical structure with four levels: 𝑙𝑙 = [1,2,3,4]. Therefore, a company is assigned aunique subsector 𝑠𝑠4 at level 4, a unique sector 𝑠𝑠3 at level 3, a supersector 𝑠𝑠2 at level 2 and an industry 𝑠𝑠1 at level 1.
For each company 𝑖𝑖 and fiscal period 𝑡𝑡, we derive from the size and the number of companies with reported data in each of
the sectoral levels 𝑠𝑠𝑙𝑙 assigned to the company, an adjustment coefficient regarding the size of its subsector 𝑠𝑠4 :𝑠𝑠

𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖,𝑡𝑡𝑙𝑙 =𝑠𝑠

𝑠𝑠

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖,𝑡𝑡4 ∗ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖,𝑡𝑡𝑙𝑙
𝑠𝑠(𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖,𝑡𝑡𝑙𝑙 )2

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This coefficient reflects the representativeness of each sectoral level in GATS regarding the corresponding subsector. Please
see Appendix A for a detailed example of the computation.
Furthermore, to minimize the impact of potential abnormal changes of the sectoral median from one fiscal period to thenext, we use a 3-year trailing average to smooth every median of each sectoral level assigned to a company:
𝑠𝑠

𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶𝐶𝐶𝑖𝑖,𝑡𝑡𝑙𝑙 =𝑠𝑠∑3𝑡𝑡=1 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶𝐶𝐶𝑖𝑖,𝑡𝑡𝑙𝑙
3

The adjusted median of reported carbon intensity of company 𝑖𝑖 for a fiscal period 𝑡𝑡 is then the average of the smoothed
medians of the four sectoral levels assigned to it, weighted by the corresponding adjustment size coefficients:
𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶𝐶𝐶𝑖𝑖,𝑡𝑡 =Multi-level weighted adjusted-median estimates𝑠𝑠𝑠𝑠∑4𝑙𝑙=1 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖,𝑡𝑡𝑙𝑙 ∗ 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆ℎ 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶𝐶𝐶𝑖𝑖,𝑡𝑡𝑙𝑙
𝑠𝑠∑4𝑙𝑙=1 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖,𝑡𝑡𝑙𝑙

The median-based estimated carbon emissions data for a company 𝑖𝑖 and a fiscal period 𝑡𝑡 is the product of its adjusted
median of reported carbon intensity and its net sales or revenue in USD:
𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚= 𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴𝐴 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶𝐶𝐶𝑖𝑖,𝑡𝑡 ∗ 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖,𝑡𝑡
𝐶𝐶𝑖𝑖,𝑡𝑡

4.5.2 EE-MRIO-based estimated data for Scope 1 and Scope 2: overview

The second carbon model, used to compliment the multi-level weighted adjusted-median estimates described in Section
4.5.1, is based on an Environmentally-Extended Multi-Regional Input-Output (Exiobase) table; this allows sectors andcountries to be linked together with the Greenhouse Gas emissions generated and exchanged between them.
In this model, a vector of carbon coefficients per monetary unit can be computed for each sector / country in the table andthen applied to the vector of revenues (revenue segment breakdown) of each company. The dot product of those two
vectors is computed and aggregated for assessing and estimating the total GHG (in CO2eq) corresponding to the total
revenues generated by the company.
The sector classification here is NAICS, the US industrial classification that supports GATS.
For technical details on how Exiobase is used and for the matrix computation, please see Appendix B.
Adjusted MRIO estimates
The final set of MRIO-based carbon emissions data are derived from the raw MRIO estimates by adjusting them by theirdistance from reported peers at the industry level. More precisely, based on the companies with both reported and MRIObased figures in each GATS industry (level 1), an MRIO adjustment coefficient (𝛽𝛽 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 ) is derived from the distance
between MRIO-based figures and their reported peers.

Finally, this adjustment coefficient is applied to the raw MRIO estimates to obtain the final MRIO-based carbon emissions:
𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖

𝐶𝐶𝑖𝑖𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 = 𝑅𝑅𝑅𝑅𝑅𝑅 𝐶𝐶𝑖𝑖𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 ∗ 𝛽𝛽𝑖𝑖

𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖

where 𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 is the GATS industry assigned to the company 𝑖𝑖 and 𝛽𝛽𝑖𝑖
company 𝑖𝑖.

the adjustment coefficient associated to the

4.5.3 Estimated data for Scope 3

Modeling Scope 3 emissions poses challenges due to its scope falling beyond a company's direct activities, leading to limited
reported data availability. To enhance accuracy and coverage, we integrate various models. These include:
Third-party estimates
In addition to self-reported emissions, we receive Scope 3 GHG emissions estimates from the ISS Climate Core dataset. The
methodology was established in 2010 in collaboration with researchers from ETH Zurich; sector and sub sector specificwilshireindexes.com © 2024 Wilshire OpCo UK Limited or affiliates. All Rights Reserved.

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Wilshire Indexes Carbon Emissions Model

models were developed. Readers interested in the full Carbon Footprint methodology can request it here ISS Climate
Solutions.
GHG emissions estimates are refined by computing the average between the intensity and median intensity over thepreceding three years. This process serves to mitigate year-on-year fluctuations. To address outliers, any intensity falling
below one-third or exceeding three times the median intensity is substituted with the median intensity.
Multi-level weighted median estimates
A limitation of the median approach is the choice of the peer group used for estimation. A wide group, at the industry level, ismore stable over time but does not account for sectoral specificities. A narrow group, at the subsector level, will give moreaccurate results but is sensitive to outliers if the subsector’s size is limited.
As such, the Scope 3 median-based carbon emissions model follows a similar logic to Scope 1&2’s estimation strategy. We
leverage the reported revenue-based carbon intensity to account for the relationship between emissions and revenues andcontrol for the limited reporting by using different sector levels.
The multi-median revenue-based carbon intensity is calculated using the median intensity at the subsector and sector level(respectively GATS level 4 and 3). To control for potential outliers at the subsector level, intensities are weighted with respect
to the number of reporting companies in the following manner:

𝐶𝐶𝐶𝐶𝑡𝑡𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚,𝑠𝑠 =(𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡𝑠𝑠 ∗ 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶𝐶𝐶𝑡𝑡𝑠𝑠 ) ∗ (𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡𝑠𝑠3−𝑠𝑠 ∗ 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶𝐶𝐶𝑡𝑡𝑠𝑠3 ))𝑠𝑠(𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡 3 )where:•••

𝑠𝑠
is the number of companies in subsector s with reported emissions,𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑖𝑖,𝑡𝑡
𝑠𝑠3 −𝑠𝑠
𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑡𝑡
is the number of companies in the corresponding sector (GATS level 3) that are not in
subsector 𝑠𝑠,
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐶𝐶𝐶𝐶𝑡𝑡𝑠𝑠 is the median revenue carbon intensity of subsector 𝑠𝑠 (or corresponding sector 𝑠𝑠3 ).

In addition, if no reported emissions can be found at the subsector level the intensity at the supersector level is assigned.
Adjusted MRIO estimates
Scope 3 MRIO estimates are calculated for downstream and upstream emissions in a similar fashion to Scope 1 & 2.
The Scope 3 estimates aggregation rule is detailed in the next section.

4.6 Final Estimated Data
4.6.1 Final estimated data for Scope 1 and Scope 2
The final estimated carbon emissions data for Scope 1 and Scope 2 assigned to a non-reporting company 𝑖𝑖 for a fiscal period
𝑡𝑡 results from the combination of the estimates of the 3 modelling strategies such as:𝑒𝑒=𝐶𝐶𝑖𝑖,𝑡𝑡𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖
𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚
𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚+ 𝐶𝐶𝑖𝑖,𝑡𝑡+ 𝐶𝐶𝑖𝑖,𝑡𝑡
𝐶𝐶𝑖𝑖,𝑡𝑡
3

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4.6.2 Final estimated data for Scope 3
𝑒𝑒
The final estimated Scope 3 GHG emissions 𝐶𝐶𝑖𝑖,𝑡𝑡
is defined below:
𝑒𝑒=𝐶𝐶𝑖𝑖,𝑡𝑡𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖
𝑒𝑒 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤ℎ𝑖𝑖𝑖𝑖𝑖𝑖
𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖
𝑒𝑒 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤ℎ𝑖𝑖𝑖𝑖𝑖𝑖
𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖
𝐶𝐶𝑖𝑖,𝑡𝑡
if 𝐶𝐶𝑖𝑖,𝑡𝑡< 𝐶𝐶𝑖𝑖,𝑡𝑡
or 𝐶𝐶𝑖𝑖,𝑡𝑡> 1.5 ∗ 𝐶𝐶𝑖𝑖,𝑡𝑡
� 1 𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖
𝑒𝑒 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤ℎ𝑖𝑖𝑖𝑖𝑖𝑖
�𝐶𝐶+ 𝐶𝐶𝑖𝑖,𝑡𝑡�
otherwise
2 𝑖𝑖,𝑡𝑡

𝑒𝑒 𝑤𝑤𝑤𝑤𝑤𝑤𝑤𝑤ℎ𝑖𝑖𝑖𝑖𝑖𝑖
𝑒𝑒 𝑖𝑖𝑖𝑖𝑖𝑖
is defined as the median or MRIO estimate that is closest in value to 𝐶𝐶𝑖𝑖,𝑡𝑡.
𝐶𝐶𝑖𝑖,𝑡𝑡

4.7 Selection Algorithm

The final carbon emissions data for a company and a fiscal period is selected as below:
Final carbon emissions data selection process

1
Final Carbon Emissions
𝑪𝑪𝒊𝒊,𝒕𝒕

2
3

Self-Reported Carbon Emissions
𝑪𝑪𝒓𝒓𝒊𝒊,𝒕𝒕
Reported-Derived Carbon Emissions
𝑪𝑪𝒓𝒓𝒓𝒓𝒊𝒊,𝒕𝒕Estimated Carbon Emissions
𝑪𝑪𝒆𝒆𝒊𝒊,𝒕𝒕

𝑟𝑟
if 𝐶𝐶𝑖𝑖,𝑡𝑡
is available𝑟𝑟
if 𝐶𝐶𝑖𝑖,𝑡𝑡
is not available𝑟𝑟𝑟𝑟𝑟𝑟
if both 𝐶𝐶𝐶𝐶𝑖𝑖,𝑡𝑡
and 𝐶𝐶𝐶𝐶𝑖𝑖,𝑡𝑡
are not available

The final carbon emissions values are used in the determination of the FT Wilshire Climate Change Indexes through theirincorporation into company Emission Intensities (see Section 2.1.1 of FT Wilshire Climate Change Indexes Methodology).

ApprovalThis Carbon Emissions Model was approved by the Wilshire Indexes Index Management Committee.

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Appendix A: Example of the Adjustment Size from the Medianbased modelling strategy
This Appendix provides an example of the computation of the Adjustment Size coefficient for a company which is assigned to
the GATS subsector “Electronic Entertainment Goods”. This subsector sits within the sector “Digital and Electronic Goods”
which itself is part of the supersector “Digital Goods and Services”. The industry associated with this supersector is “Digital
Information and Services”.
Example of the Adjustment Size Process

GATS level

GATS name

Size

Reporting Proportion Size

Adjusted Sizeweightingcoefficient

Subsector (4)ElectronicEntertainment Goods

40

14

0.35

Sector (3)Digital and Electronic
Goods

65

36

0.34

Supersector (2)Digital Goods andServices

112

53

0.16

Industry (1)Digital Information andServices

434

161

0.03

40*(14/(40)2)

40*(36/(65)2)

40*(53/(112)2)

40*(161/(434)2)

Source: Wilshire Indexes

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Appendix B: Carbon Intensity Coefficients by NAICS Sector
Introduction
As set out in section 4, EE-MRIO details the monetary values 𝑍𝑍 exchanged between, and the user demand 𝑌𝑌 within, theeconomic sectors of each geographic region with other sectors and regions during the whole production process, and the
direct GHG emissions associated with the consumption of these quantities 𝐸𝐸.

Note that 𝑍𝑍 and 𝑌𝑌 are sparse matrices and 𝐸𝐸 is a vector such that:1,1𝑧𝑧𝑖𝑖,𝑗𝑗

𝑍𝑍 = � ⋮𝑚𝑚,1𝑧𝑧𝑖𝑖,𝑗𝑗

𝑦𝑦𝑖𝑖1,1

𝑌𝑌 = � ⋮𝑦𝑦𝑖𝑖𝑚𝑚,1

1,𝑚𝑚
𝑧𝑧𝑖𝑖,𝑗𝑗⋯𝑟𝑟,𝑘𝑘𝑧𝑧𝑖𝑖,𝑗𝑗𝑟𝑟,𝑘𝑘⋮ � where 𝑧𝑧𝑖𝑖,𝑗𝑗
is the monetary input from sector 𝑖𝑖 in region 𝑟𝑟 to sector 𝑗𝑗 in region 𝑘𝑘;

𝑚𝑚,𝑚𝑚
𝑧𝑧𝑖𝑖,𝑗𝑗⋯

𝑦𝑦𝑖𝑖1,𝑚𝑚⋯𝑟𝑟,𝑘𝑘⋮ � where 𝑦𝑦𝑖𝑖 is the final demand of region 𝑘𝑘 of the product of sector 𝑖𝑖 in region 𝑟𝑟;

𝑦𝑦𝑖𝑖𝑟𝑟,𝑘𝑘

𝑦𝑦𝑖𝑖𝑚𝑚,𝑚𝑚⋯

𝑒𝑒𝑖𝑖1
𝐸𝐸 = � ⋮ � where 𝑒𝑒𝑖𝑖𝑚𝑚 is the direct GHG emissions demand of sector 𝑖𝑖 in region 𝑚𝑚.
𝑒𝑒𝑖𝑖𝑚𝑚
EE-MRIO GHG intensity factors

From the above matrices, the gross output 𝐺𝐺𝐺𝐺 vector can be derived, which is the overall monetary quantities consumed
both as intermediary input by other sectors and regions and by final users of other regions:1,1+ ⋯ + 𝑦𝑦𝑖𝑖1,1 + ⋯ + 𝑦𝑦𝑖𝑖1,𝑚𝑚
𝑔𝑔𝑔𝑔𝑖𝑖1 = 𝑧𝑧𝑖𝑖,𝑗𝑗
𝐺𝐺𝐺𝐺 = ��.
⋮𝑚𝑚,1+ ⋯ + 𝑦𝑦𝑖𝑖𝑚𝑚,1 + ⋯ + 𝑦𝑦𝑖𝑖𝑚𝑚,𝑚𝑚
𝑔𝑔𝑔𝑔𝑖𝑖𝑚𝑚 = 𝑧𝑧𝑖𝑖,𝑗𝑗

The key assumption in an MRIO framework is that the gross output vector must be equal to the total input vector. Because ofthis, a matrix of technical coefficients 𝐴𝐴 can be derived, which expresses the monetary quantities from a sector in a regionused to produce one unit of total input:
1,1𝑧𝑧𝑖𝑖,𝑗𝑗⎛ 𝑔𝑔𝑔𝑔𝑖𝑖1⎜
𝐴𝐴 = ⎜ ⋮⎜⎜ 𝑚𝑚,1𝑧𝑧𝑖𝑖,𝑗𝑗⎝ 𝑔𝑔𝑔𝑔𝑖𝑖1⋯

𝑟𝑟,𝑘𝑘𝑧𝑧𝑖𝑖,𝑗𝑗
𝑔𝑔𝑔𝑔𝑖𝑖𝑘𝑘⋯

1,𝑚𝑚
𝑧𝑧𝑖𝑖,𝑗𝑗

𝑔𝑔𝑔𝑔𝑖𝑖𝑚𝑚 ⎞⎟⋮ ⎟.
⎟𝑚𝑚,𝑚𝑚 ⎟
𝑧𝑧𝑖𝑖,𝑗𝑗
𝑔𝑔𝑔𝑔𝑖𝑖𝑚𝑚 ⎠Using the total input vector, the GHG direct multiplier vector 𝑀𝑀𝑀𝑀 can be derived, which represents the direct GHG emitted
from the production of one unit of total input:⎛
𝑀𝑀𝑀𝑀 = ⎜⎝𝑚𝑚𝑚𝑚𝑖𝑖1 =⋮𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚 =

𝑒𝑒𝑖𝑖1

𝑔𝑔𝑔𝑔𝑖𝑖1

⎞
⎟.
𝑚𝑚

𝑒𝑒𝑖𝑖

𝑔𝑔𝑔𝑔𝑖𝑖𝑚𝑚⎠𝑚𝑚
The rows of the 𝑀𝑀𝑀𝑀 matrix constitute the Scope 1 MRIO intensity factors for a sector 𝑖𝑖 in a region 𝑚𝑚: 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1𝑚𝑚
𝑖𝑖 = 𝑚𝑚𝑚𝑚𝑖𝑖 .

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In economic analysis, MRIO is used to track the ripple effects in an economy where sectors and regions are fullyinterconnected. These interconnections are shown in the so-called “Leontief inverse” matrix 𝐿𝐿. This matrix expresses all
direct and indirect effects on output in one sector from one region required to produce a unit of output from another sectorof another region. In other words, it summarises the entire production chain (direct and indirect). It is defined by:
𝐿𝐿 = (𝐼𝐼 − 𝐴𝐴)−1 where 𝐼𝐼 is the identity matrix and 𝐴𝐴 the matrix of technical coefficients.

Therefore, the dot product of the Leontief inverse matrix and the GHG direct multiplier vector gives both direct and indirect
GHG emissions associated to each sector and region of the whole production chain:
1,1
𝑚𝑚𝑚𝑚𝑖𝑖1
𝑙𝑙𝑖𝑖,𝑗𝑗
𝑀𝑀𝑀𝑀 = (𝐿𝐿 ∗ 𝑀𝑀𝑀𝑀) = �⋮𝑚𝑚,1𝑚𝑚𝑚𝑚𝑖𝑖1
𝑙𝑙𝑖𝑖,𝑗𝑗

⋯
⋱
⋯

1,𝑚𝑚
𝑙𝑙𝑖𝑖,𝑗𝑗
𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚
�⋮𝑚𝑚,𝑚𝑚
𝑙𝑙𝑖𝑖,𝑗𝑗
𝑚𝑚𝑚𝑚𝑖𝑖𝑚𝑚

Note that, by construction, the direct GHG multipliers vector is only included in the diagonal of 𝑀𝑀𝑀𝑀.

Based on the 𝑀𝑀𝑀𝑀 matrix, we deduce Scope 2 MRIO intensity factors for a sector 𝑖𝑖 of a region 𝑚𝑚 as the sum of all the rows of
𝑀𝑀𝑀𝑀 associated with energy producing sectors 𝑗𝑗:
𝑚𝑚,𝑚𝑚
𝑚𝑚
𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2𝑚𝑚
𝑖𝑖 = ∑𝑗𝑗 𝑙𝑙𝑖𝑖,𝑗𝑗 𝑚𝑚𝑚𝑚𝑖𝑖

where 𝑗𝑗 includes only energy producing sectors of the production chain of the sector 𝑖𝑖.

Raw MRIO estimates

The first set of MRIO-based estimates is obtained by combining the previous MRIO outcomes with NAICS segments data.
Before computing estimated carbon emissions, we associate each NAICS activity to a single Exiobase industry and eachcountry to an Exiobase region thanks to tables of correspondence provided by the Exiobase working group 8.
Note that an Exiobase industry can be associated with various NAICS activities. From these tables, we derive intensity factors
for each NAICS activities 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 and country 𝑐𝑐 as:
𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐺𝐺𝐺𝐺𝐺𝐺 𝑐𝑐𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 =∑𝑖𝑖 𝑔𝑔𝑔𝑔𝑖𝑖𝑚𝑚 ∗ 𝐺𝐺𝐺𝐺𝐺𝐺𝑖𝑖𝑚𝑚∑𝑖𝑖 𝑔𝑔𝑔𝑔𝑖𝑖𝑚𝑚

where 𝐺𝐺𝐺𝐺𝐺𝐺 represents either 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 1 or 𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆𝑆 2 intensity factors, 𝑚𝑚 is the Exiobase region associated with country 𝑐𝑐, and 𝑖𝑖
represents the Exiobase sectors associated with the 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 activities.
For a company 𝑘𝑘, the raw MRIO-based carbon emissions results from the sum of its NAICS segments weighted by the
associated NAICS-Country MRIO intensity factors:
𝑅𝑅𝑅𝑅𝑅𝑅 𝐶𝐶𝑘𝑘𝑒𝑒 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 =𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁� 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝐺𝐺𝐺𝐺𝐺𝐺 𝑐𝑐𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 ∗ 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛

𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛

where 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 represents the revenue of the company in the segment 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛, 𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁𝑁 represents all its 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛
segments, and 𝑐𝑐 is the country associated to the company.

8 https://ntnu.app.box.com/s/ziox4zmkgt3cdsg549brr0qaecskgjsd

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Appendix C: Scope 3 Categories
The Scope 3 GHG emissions categories as referred to by the GHG Protocol are shown below.
Upstream categories
1. Purchased goods and services
2. Capital goods
3. Fuel – and energy – related activities
4. Upstream transportation and distribution
5. Waste generated in operations
6. Business travel
7. Employee commuting
8. Upstream leased assets

Downstream categories
9. Downstream transportation and distribution
10. Processing of sold products
11. Use of sold products
12. End of life treatment of sold products
13. Downstream leased assets
14. Franchises
15. Investments

Source: GHG Protocol.

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Appendix D: Countries and Geographic Regions from Exiobase
D.1 Countries
Exiobase CodeISO3 Code

Name

AT

AUT

Austria

AU

AUS

Australia

BE

BEL

Belgium

BG

BGR

Bulgaria

BR

BRA

BrazilCA

CAN

CanadaCH

CHE

Switzerland

CN

CHN

China

CY

CYP

CyprusCZ

CZECzech Republic

DE

DEU

Germany

DK

DNK

Denmark

EE

EST

Estonia

ES

ESP

Spain

FI

FIN

FinlandFR

FRAFranceGB

GBR

United Kingdom

GR

GRC

GreeceHR

HRV

Croatia

HU

HUN

HungaryID

IDN

Indonesia

IE

IRL

Ireland

IN

IND

India

IT

ITA

Italy

JP

JPN

Japan

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KR

KOR

South Korea

LT

LTU

Lithuania

LU

LUX

Luxembourg

LV

LVA

Latvia

MT

MLT

Malta

MX

MEX

MexicoNL

NLD

Netherlands

NO

NOR

NorwayPL

POL

PolandPT

PRT

Portugal

RO

ROM

Romania

RU

RUS

RussiaSE

SWE

SwedenSI

SVN

SloveniaSK

SVK

Slovakia

TR

TUR

TurkeyTW

TWN

TaiwanUS

USA

United States

ZA

ZAF

South Africa

Source: Exiobase.

D.2 Rest of World regions
Exiobase Code

Name

WA

RoW Asia and Pacific

WE

RoW Europe

WF

RoW Africa

WL

RoW America

WM

RoW Middle East

Source: Exiobase.

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