Measures of equity for multi-capital accounting

Inequity is one of the primary economic and societal risks posed by the global food system, yet measures of inequity are missing from prominent corporate tools that aim to account for the impact of the economic activities associated with food production, manufacturing and retail. Here we suggest new metrics to measure socio-economic, gender, racial, generational and risk divides between the bearers of natural, social and human capital costs and those of benefits. Corporate reporting tools should incorporate equity considerations if they are to cover the true costs of operating in the food system. Looking at natural, social and human capital costs, this study proposes integrated metrics to account for the impact of economic activities across socio-economic, gender, racial, generational and risk-bearing domains.

T he activities and outcomes of the global food system contribute 30% of annual anthropogenic CO 2 -equivalent emissions 1 , use 70% of fresh water 2 and are responsible for over 50% of nitrogen and phosphorous emissions 3 . Globally, 33% of adults are obese, while 9% of the global population are hungry and many more are undernourished 4 . While providing livelihoods for at least a billion people 5 , 66% of the 740 million people living in extreme poverty globally are agricultural workers 6 .
There is a large global disparity between who receives the benefits of the production, processing and retail in the global food sector, and who pays the costs. Climate change and biodiversity loss 7,8 , health burdens 9 and scarcity of resources 10 are among the impacts disproportionately affecting marginalized and poorer groups. The same groups have less power to affect market correction due to corruption and their proportionately lower representation, ownership and share of profits 11,12 . Economic costs include 1.3% of gross domestic product lost to developing countries from profit shifting 12 and 2% of gross domestic product through malnutrition in low-paid agricultural workers and lost productivity 13,14 . The costs are likely to magnify through the reinforcing effects of inequity, climate change, biodiversity loss and health impacts 15,16 .
Companies are seeking to report their impacts 17,18 , and to demonstrate pledges on the Sustainable Development Goals (SDGs) and science-based trajectories to a low-impact food system 19,20 . In 2020, 73% of approximately 420 agriculture, food and beverage companies in the top 100 companies by revenue in 52 countries published a sustainability report, with the Global Reporting Initiative (GRI) multi-capital accounting standard used in 66% of the reports 21 .
Despite the ultimate economic costs and risks of inequity to society there are few, if any, summary measures of inequity in the accounting standards or reports 22 . SDG-linked reporting on human rights and inequality is increasing, but agri-food sector sustainability reports have few specific indicators of value sharing and social outcomes in the supply chain 23 , have practically no spatially explicit indicators 23 and report few negative results 21 .
This is a problem as multi-capital corporate reporting plays an increasing role in bridging the monitoring of impacts and the allocation of sustainability-linked funds for the agri-food sector [24][25][26] . In 2020, US$10 trillion in new environmental, social and governance (ESG) managed capital (growing at >30% yr −1 ) was added, including a 9% share of the food and agriculture sector of around US$300 billion in impact investments 24,27,28 . In the same year, US$750 billion of sustainability-linked debt was issued (growing >50% yr −1 ), with 3% of green bonds associated to agriculture and forestry 26,29 . In February 2021, food and beverage company Anheuser-Busch InBev was issued a record US$10.1 billion sustainability-linked loan 30 .
A majority of respondents in a 2020 GRI survey indicated their trust in corporate reporting 31 , implying that irrespective of the actual confluence between reports, disclosure and achieving science-based sustainability targets or the SDGs, investors are allocating capital guided by reports and ESG data 24,32 . Missing equity in broader accounting of benefits and costs risks a misallocation of the growing pool of funds that could enable a just transition to sustainable and health-producing food systems 33,34 .
This Perspective introduces quantitative inequity indices for multi-capital accounts based on the 'true' costs and benefits of activities in the food sector. The true cost of food has been introduced by researchers, civil society and business groups to describe the recognition and rectification of costs that are not reflected in corporate accounting and market transactions [35][36][37] , including externalized environmental costs 38,39 , issues around fair wages and justice 40 , and inequitable exchanges of natural and social capital 19,41,42 .
Inequity is commonly defined as an unfair or unjust outcome associated with an inequality 43 . The indices we introduce measure asymmetry in costs and benefits disaggregated by dimensions of inequality and unaccounted for in market exchanges. This provides summary measures of the socio-economic, gender, race, generational and risk-bearing divides between the receivers of uncompensated natural, social and human capital costs and the receivers of free benefits. Value chains in the food system, and companies and investments in those value chains, can be compared, tracked and given equity targets to achieve using these indices.
Example indices are illustrated by the unaccounted costs and benefits of cocoa product value chains in international dollars 44 disaggregated by the United Nations Development Programme (UNDP) Human Development Index (HDI) and Gender Inequality Index (GII) 45,46 . Optimal transport 47 is used to quantify the asymmetry of the distribution of costs and benefits across the HDI and GII. The resulting statistic is a measure of the uncompensated costs disproportionately paid by women and by actors in countries at lower HDI and the free benefits disproportionately received by men and by actors in countries at higher HDI.

Valuation in multi-capital accounting
In response to pressure from civil society and investors, the corporate sector has developed multi-capital accounting to report on a company's impact on natural, social and human capital 17,18 . Accounting firms (for example, KPMG 48 , EY 49 , PwC 50 ) and food companies produce-or sell services to produce-reports for multi-capital accounts and non-financial annual statements. Valuation of impacts is used in some accounts to demonstrate an overall non-financial

Measures of equity for multi-capital accounting Steven Lord ✉ and John S. I. Ingram
Inequity is one of the primary economic and societal risks posed by the global food system, yet measures of inequity are missing from prominent corporate tools that aim to account for the impact of the economic activities associated with food production, manufacturing and retail. Here we suggest new metrics to measure socio-economic, gender, racial, generational and risk divides between the bearers of natural, social and human capital costs and those of benefits.
position 18,51,52 . The accounting has appeared under names such as integrated profit and loss.
Present approaches to the valuation of impacts offset negative amounts (for example, the costs of natural capital loss) with positive amounts (such as benefits from social and human capital gain) without considering substitutability of capital 53 . This is a flawed approach to non-financial accounting. Whereas net costs and benefits are usually separated under broad terms such as environmental and social before calculating totals ( Fig. 1), there is little or no indication of where and by whom the main costs are incurred versus where and to whom the main benefits are distributed. Why or how natural capital negative externalities in a developing country, for instance, are offset by social capital positive externalities in a developed country remains unexplained.
Better accounting should indicate the degree to which social benefits occur in the communities experiencing natural costs, offering the possibility that benefits offset some costs. The accounting should indicate where there is a considerable distance between the costs and benefits, and substitutability of capital becomes much less clear. In theory, this could apply to all non-financial capital exchanges, between national and subnational economies separated by socio-economic, cultural, legal, racial, gender, spatial and temporal dimensions. Although estimation and disaggregation of unaccounted costs and benefits is challenging in practice 52 , a financial reporting community that genuinely embraces a multi-capital approach should be able to track exchanges in different capital classes linked to the largest inequities.

Statistics for reporting inequity
The net natural capital costs and benefits bars in Fig. 1 contain, for example, costs from carbon emissions, biodiversity loss through land-use, nutrient emissions and water consumption. The net social and human capital costs and benefits bars contain, for example, multipliers on wages and taxes and productivity losses.

The Supplementary Information discusses common inclusions of unaccounted costs and benefits in the valuation of impacts and references to published examples by companies.
Concerns about inequity should be reflected in a further disaggregation of costs and benefits by dimensions of inequality.
The HDI measures socio-economic differences between countries. Splitting the costs and benefits in Fig. 1 using the HDI reflects a distribution of costs in low human development countries (LHDCs, low HDI) versus benefits in high human development countries (HHDCs, high HDI) that can be plotted in a histogram ( Fig. 2a shows distributions from the accounts in Tables 1 and 2).
The first inequity statistic proposed, called the socio-economic spatial (SES) statistic, is a measure of the distance between the cost distribution in terms of the HDI and the benefit distribution in terms of the HDI. A concrete implementation of the SES statistic is given by optimal transport 47 . In non-mathematical terms, optimal transport measures the total shift required until a unit of cost and a unit of benefit are, after the shift, at the same HDI and only then cancel (Fig. 2a).

an example of cocoa value chains
A fraction of the revenue from final cocoa products sold and made in HHDCs goes to about 40-50 million people involved in cocoa production, mainly smallholders in LHDCs 54 . Growth in demand for chocolate, especially from rising incomes in Asia, is expected to drive biodiversity loss and the continued presence of child labour in LHDCs 54 .
Tables 1 and 2 provide an example of costs and benefits for two hypothetical value chains of cocoa products, disaggregated by HDI and not normally accounted for in market exchanges. The two value chains have the same 'net impact' . Their net natural and social capital costs and benefits aggregated match Fig. 1b Fig. 1 | a common approach to valuation of impacts. a, Separated costs and benefits. b, Net cost or benefit as the difference between costs and benefits in a. this approach displays either unaccounted natural (green) and social and human (blue) capital aggregated costs and aggregated benefits, or net unaccounted costs or benefits, as an adjustment to a financial position according to the accounting methodology used in KmpG 48 . Divisions into finer environmental, social or operational categories are not based on inequality and spatial occurrence of impact in practice. the numerical amounts are hypothetical amounts for the value chain of cocoa products and reflect currencies that have already been exchanged at purchasing power parity (ppp) rates; see tables 1 and 2. ppp facilitates comparison between unaccounted costs and the welfare from produced capital implicit in the net financial position (grey). total costs or benefits are shown in red.
Value chain A (Table 1) reflects an industry baseline of production in Ghana as a major African cocoa producer. The value chain is characterized by agriculture practice involving deforestation, low-paid agriculture workers and the presence of child labour, driven by demand for final products in China with large profit shifting to US and EU investors; bean grinding occurs in the EU (the Netherlands) and manufacturing in the United States. Value chain B (Table 2) reflects moving to proportional human and economic development benefits in return for resources in Indonesian cocoa production, effective procurement policies for deforestation, a policy on profit-shifting and investment in local ownership (bean grinding in Indonesia 55 ), minimum living incomes and standards, and a value chain with South-South trade and some manufacturing in mid-HDCs (manufacturing in Mexico 56 ), for final consumption in EU supermarkets with the major retail profit flow returning to Germany.
Unaccounted costs and benefits distributed in the HDI for value chains A and B are in the top panels of Fig. 3. Reduced social costs from production in Indonesia at higher HDI (0.707) can be seen for value chain B. Despite the higher level of social benefits in chain A at lower HDI (0.758) produced by Chinese retail compared with the benefits of profit flow to Germany (HDI ≈ 0.939) from retail in value chain B, the SES index of value chain A is 3.766 versus 1.537 for value chain B. The residual costs of child labour in Ghana are shifted twice as far to cover the benefits to the EU and US of grinding and manufacture in value chain A. In value chain B, costs in Indonesia are cancelled by grinding in Indonesia and manufacturing in Mexico at living wages.
A second statistic, called SES-G, relates disparity in the gender of receivers of benefits compared with the bearers of costs within and across countries. As an illustration of the G dimension, Figs. 2b and 3 show capital costs disaggregated by HDI and the GII. Note that the GII is reflected with a negative sign on the GII axis for benefits, to account for women bearing more of the costs and receiving fewer of the benefits in the optimal transport (Fig. 2b) in capital exchanges within and between countries.
Unaccounted costs and benefits distributed in the GII and HDI-GII for value chains A and B are in the middle and bottom panels, respectively, of Fig. 3. Value chain A fairs better on the GII and in the SES-G statistic, from benefits at higher gender equality in the EU (GII ≈ 0.04), versus grinding and manufacturing in Indonesia and Mexico at worse GII (0.34, 0.41) in value chain B. Despite the improvement, and that some portions of the chain value in value chain A had better outcomes than value chain B, chain A still clearly requires more costs to be shifted across HDI and GII combined to cancel benefits, with a SES-G index of 14.893 versus 8.596 for value chain B.
The Supplementary Information discusses more sophisticated cost functions than the Manhattan distance that can account for trade-offs between the HDI and GII.  Costs 10 Hypothetical unaccounted costs and benefits associated with production, manufacturing and retail of cocoa products are shown (see Supplementary Information). Cost and benefit amounts are assumed to be exchanged with a reference currency using ppp. productivity loss from overconsumption refers to labour productivity losses from the contribution of consumed cocoa products to the burden of malnutrition in the country of consumption (human health impacts of consumption). Environmental costs of greenhouse gas (GHG) emissions are attributed to the country of emissions-the text describes using country-level social cost of carbon to distribute the costs of emissions in practice. productivity loss from overconsumption refers to labour productivity losses from the contribution of consumed cocoa products to the burden of malnutrition in the country of consumption (human health impacts of consumption). Environmental costs of GHG emissions are attributed to the country of emissions-the text describes using country-level social cost of carbon to distribute the costs of emissions in practice. Hypothetical unaccounted costs and benefits associated with production, manufacturing and retail of cocoa products are shown (see Supplementary Information). Cost and benefit amounts are assumed tobe exchanged with a reference currency using ppp. productivity loss from overconsumption refers to labour productivity losses from the contribution of consumed cocoa products to the burden of malnutrition in the country of consumption (human health impacts of consumption). Environmental costs of GHG emissions are attributed to the country of emissions-the text describes using country-level social cost of carbon to distribute the costs of emissions in practice.

additional statistics for reporting inequity
Statistics for the distance between unaccounted costs and benefits disaggregated by race, generation and risk-bearing follow the same idea. Statistical divisions in the race of receivers can be indicated in a statistic termed SES-R, or added as a third dimension in SES-G, resulting in SES-GR. A socio-economic temporal statistic, using the disintegration of costs and benefits over the dimension of time when impacts are received, would measure inequity in capital exchanges crossing generations.
A capital exchange risk (CER) statistic would measure the volatility of benefits compared with costs. Risk can be quantified by the right-sided standard deviation for costs and left-sided standard deviation for benefits 57 , and CER would reflect where more risk of higher costs is exchanged for less risk of lower benefits. An SES-CER statistic could capture that, during the 2007/2008 food price crises, western food prices were relatively stable whereas poorer or exposed demographics in the same value chain faced higher food prices, volatile agricultural yields from extreme weather, and volatile labour and input costs from social unrest and geopolitical responses 58 .

discussion
The food sector faces an immediate challenge to provide a growing global population with healthy diets while reducing negative impacts. Although acknowledging natural, social and human capital impacts is positive, current attempts by the sector do not capture equity concerns in capital exchanges. Given the position of the food sector as a driver of global inequity, and the role inequity plays in the inability of the sector to correct itself, the omission jeopardizes the allocation of capital for a just transition to a sustainable and health-producing food system.
Market exchanges reflect compensation for, or mitigation of, costs by those that receive benefits. Asymmetry in disaggregated unaccounted costs and benefits reflects market failure coinciding with differences in power or opportunity. The SES and SES-G statistics are measures of inequity, in that uncompensated or unmitigated costs being borne disproportionately by those who are poor or women while free benefits derived from paying those costs go disproportionately to richer demographics or men, simply because one group is poor or women and another is richer or men, is unfair.
The GRI standards, other non-financial corporate reporting initiatives including the UN Global Compact and emerging ESG indices provide information relevant to inequality and achievement of the SDGs. Summary performance on inequity is difficult to extract from this information, disclosure is often incomplete, non-specific or inconsistent, and equity-relevant data are scattered across tens or hundreds of qualitative and quantitative metrics 23 .
As summary indices of disaggregated multi-capital accounts, the SES and SES-G metrics do not change the underlying multi-capital accounts or their valuations, except for the level of disaggregation. The indices allow complex value chains, and investments and activities of companies in them, to be compared and tracked. The lower the SES and SES-G values, the more equitable the value chains are. A collection of desirable or exemplary value chains representing sustainable development and a just transition by 2050 can be used to derive context-based benchmark values for the indices. This would contribute to guiding an estimated US$350 billion yr −1 in new public and private annual investment required for the transformation of the global food system 33,59 .
Companies in the value chains can assess their performance in several ways: assessing the value chains they are involved in against benchmarks or alternatives; calculating the SES and SES-G statistics for the distribution of benefits specific to the company (to employees, investors, through paid taxes and so on); and scaling the cost distribution by the proportion of the company benefits to the value chain benefits. The inequity statistics applied to these sub-distributions of the value chain's benefit and cost provide an attributable portion for the company.
The indices also signal wider economic benefits implied by achievement of the SDGs. Benefits include reducing the economic risks to the agri-food sector, and society broadly, associated with inequity and capitalizing on the opportunities that exist in a more equitable food system. Opportunities such as infrastructure for more sustainable and increased agricultural production in LHDCs 60 and value-adding (in both economic and nutritional terms) by small-and medium-enterprise manufacturing in developing countries 61 , would add external benefits at lower HDI and GII and be visible in the inequity indices.
Disaggregating by HDI and GII has advantages and limitations that are discussed further in the Supplementary Information. The HDI is applicable for global food value chains involving international trade and broad economic impacts. It can capture profit shifting 62 and the asymmetry of climate change costs and benefits by using the social costs of carbon distributed by HDI 63 . The HDI and GII do not capture inequality within national boundaries. Agri-food production and trade between LHDCs and HHDCs is increasing but, by value, 76% of food sector value chains are domestic 64 . When a value chain has a widely adopted voluntary sustainability standard, the HDI and GII cannot reflect the specific development and gender position of benefits and costs due to the voluntary sustainability standard. Subnational and value-chain contextual inequity indices should be developed further for practice.
The estimation and disaggregation of unaccounted costs and benefits for food system impacts is a known challenge. Broad stakeholder initiatives are seeking to develop standardized valuations for use 52 . This hurdle is decreasing in height. Measures of economic impact such as the social cost of carbon and valuation of ecosystem services are reaching the scientific, financial and economics mainstream 65,66 .

Conclusion
If multi-capital accounting continues to gain traction, tracking capital exchanges as suggested would offer a way for agri-food sector companies and investors to gain insights into impact, risk and inequity.
Equity statistics based on disaggregated valuation of impacts would address a gap in multi-capital accounting. This would increase assurance for impact investors and public bodies that investments are contributing towards food system transformation targets with the least social harm and reducing capital risks. Without consideration of equity, multi-capital accounting risks tasting like the old wine of corporate responsibility in a new bottle.

data availability
The datasets generated during the current study are available in the Oxford Research Archive at https://ora.ox.ac.uk/objects/ uuid:50c88e3a-071e-4835-a8af-9ceb945c496e. HDI and GII data are publicly available from the UNDP at http://hdr.undp.org/en/data.  chains. a,c,e, Value chain A. b,d,f, Value chain b. a,b, the value chains for capital costs (light green for natural capital and light blue for social and human capital) and benefits (dark green for natural capital and dark blue for social and human capital) disaggregated by HDI. c,d, Costs and benefits disaggregated by HDI and GII, where GII is negative for benefits. e,f, the costs or benefits for HDI-GII pairs in three dimensions. the SES and SES-G statistics quantify differences in inequity between the two value chains. the lower the SES or SES-G statistic, the better the performance on equity. the SES for value chain A is 3.766, and that of value chain b is 1.537, a quantification of the difference in the distribution of benefits and costs across HDI that can be seen in a and b. the SES-G for value chain A is 14.893, and that of value chain b is 8.596, quantifying in e and f the difference between the value chains in GII and HDI.