Economy-wide accounts (incl. MFA, EE-IOA, DSM)

Suggested citation: Fischer-Kowalski, M., Schaffartzik, A., Pauliuk, S. (2014). Economicy-wide accounts. LIAISE Toolbox. Retrieved date, from


Human societies are encroaching on “planetary boundaries” (Rockström et al., 2009), it becomes increasingly important to monitor both growth and size of resource use. Based on the concept of societal metabolism, according to which a society requires biophysical inputs of material and energy, processes these, and eventually discharges wastes and emissions (Fischer-Kowalski and Haberl, 1998), the tool of material flow accounting (MFA) was developed (Fischer-Kowalski and Hüttler, 1998). MFA tracks those material flows which enter a socio-economic system when they are extracted domestically or imported as well as those flows which exit the system as exports or waste and emissions. Material flows are commonly categorized into four main groups – biomass, fossil energy carriers, metals, and non-metallic minerals – and reported in metric tonnes. While material flow accounts are most commonly compiled at the national level, the concept may also be applied at the subnational (e.g. for regions or cities) or the international level (country groupings or global totals). Today, material flow accounts are conducted annually for all member countries of the European Union (European Commission, 2011) and for a number of other countries internationally. Economy-wide material flow accounts document material use in mass units, most commonly metric tons. The material flows considered include all materials an economy extracts from its domestic environment, imports from and exports to other economies as well as discharges to the environment (Eurostat, 2012).

Both the spatial disconnect between production and consumption and the high fragmentation of international supply chains have added complexity to a society’s metabolism: In many economies, a relevant share of the resources extracted domestically is used in the production of traded goods while at the same time highly processed goods with substantial amounts of embodied materials and energy are imported. Within the internationally harmonized methodological framework of material flow accounting, it is not possible to distinguish whether resources are extracted to satisfy domestic or foreign final demand. In that regard, the structure of production and the origin of material inputs remains a ‘black box’. Based on the work of economist Wassily Leontief (Leontief, 1970), environmentally extended input-output analysis (EE-IOA) has rapidly become the tool of choice for opening up this black box and taking production structure into account.

Both material flow accounting and environmentally extended input-output analysis cover the flows of material, energy, and money within the economy, but not the accumulated physical and monetary capital, or the stocks of products, infrastructure, and buildings. These in-use stocks play a central role in society: They provide physical services such as shelter and mobility, they represent large accumulations of material and capital, their lifetime and/or depreciation rates determine material flows required to maintain them and influence when new technologies can penetrate the market, and their technical properties link service provision with energy and material throughput (Pauliuk and Müller, 2013). Understanding the dynamic properties of in-use stocks is the subject of dynamic stock modelling (DSM).

Material flow accounting (MFA)

Material flow accounting provides economy-wide data on material use. Through international standardization, this data has become reliable and comparable across countries (Eurostat, 2012; Fischer-Kowalski et al., 2011). Increasingly, the data are also being made available in medium- to long-term time series allowing for the analysis of past trends as well as potential future developments. Material flow accounts provide information on the material inputs into, the changes in material stock within, and the material outputs in the form of exports to other economies or discharges to the environment of an economy. Aside from calculating the net additions to stock (NAS) as a balancing item, flows within the economy are not considered. MFA covers all solid, gaseous, and liquid materials, mobilized by humans or by their livestock, with the exception of bulk water and air. The unit of measurement is most commonly (metric) tonnes per year (t/a). Flows are distinguished by whether they are extracted domestically (domestic extraction, DE) or are trade flows (imports or exports). Materials are most commonly grouped according to four main material categories: biomass, fossil energy carriers, metals, and non-metallic minerals. The former category may be further differentiated by type of use into industrial and construction minerals. It is very important to note that MFA seeks to provide a complete picture of an economy’s material use so that materials are included in these accounts irrespective of whether or not they have direct market value. The most prominent non-market flows covered by MFA are grazed biomass and used crop residues as well as waste rock extracted during mining activities. In 2010, these material flows accounted for 21% of global extraction.

The data collected in MFA is used to calculate several different standardized indicators:

Direct Material Input (DMI) is a measure of the total material inputs into an economy and is calculated as the sum of domestic extraction (DE) and imports.

The Physical Trade Balance (PTB) is a measure of net-imports and is calculated as the difference between imports and exports. Reflecting that material and money flow in opposite directions during trade, this is a contrast to the monetary trade balance which calculates net-exports.

Domestic Material Consumption (DMC) is a measure of apparent consumption and calculated from domestic extraction plus imports minus exports (or DE plus PTB).

Economy-wide MFA is a satellite system to the system of national accounts and provides a rich empirical database for analytical studies.

Environmentally Extended Input-Output Analysis (EE-IOA)

Material flow accounting follows a production-based perspective: Resources used and emissions generated during the production of goods for export are attributed to the producing country and not to the country of final consumption; only the weight of the traded product itself is included in material flow accounts. In recognition of the increasing importance of global resource use mediated by international trade for environmental accounting and policy, new perspectives have been and are currently being developed within environmental accounting. The most prominent among these are consumption-based accounts compiled using environmentally extended input-output analysis. Consumption-based indicators of material use are commonly referred to as “material footprints” (Wiedmann et al., 2013) or as raw material equivalents (RME) for imported and exported goods (e.g., Schaffartzik et al., 2013; Schoer et al., 2012). Raw material equivalents or material footprints of traded goods comprise the material inputs required along the entire supply chain associated with their production. This includes both direct and indirect flows: For example, the ore mined to extract the metal contained in a mobile phone as well as the coal needed to generate the electricity needed to produce the metal concentrates would be included. In order to allocate domestic extraction to exported goods, information on the production and trade structure of an economy is required. In monetary terms, information on the production structure is contained in commonly available economy-wide input-output tables (IOT) which recently have been combined with trade statistics to form multi-regional IO (MRIO) tables

In the following, a short introduction to input-output analysis and its environmental extension for the calculation of material footprints or RME indicators is provided. For an in-depth guide to input-output analysis, please refer to (Miller and Blair, 2009). The inter-industry flows within an economy form an n x n matrix Z and the total output of each industry is forms an n x 1 vector x. By dividing each flow into an industry (i.e., each element of Z) by the total output of that same industry, we obtain an n x n matrix of so-called technical coefficients A. In matrix algebra, where x̂ indicates that vector x has been diagonalized, this reads as follows:


A = Z * x̂ ^(-1)


Matrix A contains the multipliers for the inter-industry inputs required to supply 1 unit of industry output. A certain total economic output x is required to satisfy a given level of final demand y. This final demand may be domestic (for private households as well as the public sector) or foreign (exports) and can be written as an n x 1 vector. When this vector of final demand y is multiplied by the Leontief inverse (I-A)^(-1), we obtain total output x. I is the identity matrix so that the following matrix equation is the result of equivalence operations in our previous equation:


x = ((I-A)^(-1))*y


The Leontief inverse contains the multipliers for the direct and indirect inter-industry inputs required to provide 1 unit of output to final demand. Next to the inter-industry flows recorded in Z, each industry requires additional inputs (e.g. energy, materials, capital, labour) and outputs (e.g. emissions) which can be introduced into the calculation with the help of an environmental extension. This commonly takes the shape of an m x n matrix M of total factor inputs or outputs: Factors are denoted in a total of m rows and the industries by which they are required are included along n columns. Allocation of factors to the different industries in the compilation of the extension matrix requires careful review of industry statistics and national emissions inventories. In case of lacking data, expert opinions or additional modelling may be required to estimate the extension. Once completed, M can be transformed into a direct factor requirements matrix per unit of useful output F, and the calculation is analogous to determination of the monetary direct multipliers matrix A (see first equation):


F = M*x̂^(-1)


Consumption-based accounting of resource use and emissions can be performed by post-multiplying the monetary input-output relation by the industry-specific factor requirements:


F = F*((I-A)^(-1))*y


This formula is the core of environmentally extended input-output analysis: The final demand vector y can be split up into a domestic and a foreign (exports) component, which makes it possible to calculate the material inputs associated with each.

The matrix F integrates material flow data into input-output analysis. It allows us to allocate economy-wide material requirements to specific industries. With the help of the coefficients contained in the Leontief inverse (I-A)^(-1), the material requirements can be allocated to domestic or foreign (exports) final demand. In order to consider variations in production structures across different economies or regions, national input-output tables are combined to form so-called multi-regional input-output (MRIO) models. In these models, the sum total of resources allocated to final consumption equals the sum total of resources extracted, as recorded in the material flow accountings for each of the regions. An account of and a reflection on the current MRIO state-of-the-art has been provided by Wiedmann and colleagues (2011) and by Tukker and Dietzenbacher (2013).

Environmentally extended input-output analysis comes with a number of assumptions which have to be kept in mind when interpreting the results of such studies:

  1. Homogeneity of products: Calculations based on the standard IO model make it necessary to assume that each economic activity produces only one physically homogenous product. In reality, however, the high level of aggregation of activities (e.g., in most European IO tables, all mining is included in the same activity irrespective of the specific material) leads to inhomogeneous outputs. In addition, many industries generate by-products (e.g., a paper mill may also produce saw dust); and this additionally violates the assumption of homogeneity of outputs.
  2. Homogeneity of prices: In using the standard IO model, it is also necessary to assume that each industry sells its characteristic output to all other economic activities and to final consumers at the same price. In reality, however, this is not always true as illustrated by the example of electricity which costs less in the primary than in the tertiary sectors and/or final consumption. In addition, the aforementioned heterogeneity of industry output will cause this assumption to be violated: For example, a sector buying mostly aluminum from the non-ferrous metal industries is likely to pay a different price than a sector that mostly buys rare earth metals.
  3. Allocation of investments: In creating a consumption-based account of material flows, it is necessary to decide how investments are allocated within the production and consumption structure. In national accounting, investments are reported as part of final demand. From a consumption-based perspective, they can also be thought of as an input into the production process (e.g., machinery and production infrastructure are necessary inputs to production). The manner in which capital investments are included and how (or if) they are depreciated, significantly impacts the results obtained for the raw material equivalents of exports (see, for example, work by Schoer and colleagues (2012)). If infrastructure investments (whether in monetary terms or as domestic extraction of construction materials) are not depreciated over time, importing one and the same product from an emerging economy currently building up its infrastructure will be associated with more embodied material than importing it from a mature economy which has significantly invested into its infrastructure in the past.

Understanding the impact and eventually resolving these methodological issues will become important items on the environmental accounting research agenda. At the same time, interest is already growing in the interpretability of the results of such consumption-based approaches. It has yet to be determined how responsibility for material investments into the production of exports should be shared in general: While it is true that the importing economy receives the benefit of the ready-made product, it is also true that the exporting economy receives the benefit of income (for a discussion of these political implications for CO2 emissions embodied in trade, refer to the work by Jakob and Marschinski (2012)). These very recent developments within material flow accounting methodology clearly show that the impacts of increasing globalization make it necessary to constantly re-examine the system boundaries upon which environmental accounting methods are based.

Dynamic Stock Modelling (DSM)

In-use stocks of buildings, infrastructure, and (durable) products play several important roles in social metabolism (Pauliuk and Müller, 2013):

  • They supply physical services such as transportation or shelter to people.
  • They are ‘capital containers’ and ‘resource repositories’ representing large accumulations of fixed capital and materials; for example, steel and concrete in buildings.
  • They are ‘dynamics determiners’; their lifetime determines replacement flows and when new technologies can penetrate the market.
  • They are ‘wealth watchers’ and can serve as an indicator of the amount of services utilized within a given socio-economic system.
  • They are ‘consumption couplers’ because their technical properties determine the energy and material throughput required to operate them.
  • They are ‘city shapers’ as the location and density of buildings determines transport patterns and other parameters of the urban fabric.

Dynamic stock modelling explicitly considers these different roles of in-use stocks. DSM has a long tradition in modelling population and fixed capital; over the last twenty years, applications for product and material stocks have been developed (Müller et al., 2014). Age-cohort-based models, state-of-the-art in DSM, are of a descriptive nature: Each age-cohort is assigned an expected lifetime and the cohort’s use phase ends when its lifetime elapses. At any given point in time, in-use stocks are composed of different age-cohorts, each with its specific material content and energy efficiency (Elshkaki, 2005; van der Voet et al., 2002). In DSM, the assumed total stock size is determined by exogenously specified parameters such as population and per capita service level (Müller, 2006) and the age-cohort lifetime model can be used to adjust the inflows into and the outflows from stocks.

DSM is the basis for many other types of modelling; examples include integrated assessment models, system dynamics models, population balance models, and dynamic material flow analysis models. The latter are an important manner in which the material and technological detail of MFA is enhanced. DSM of materials additionally allows for the modelling of the end-of-life product flow which is the sum of all discarded products leaving the use phase according to the lifetime distribution chosen. This enables forecasting of waste volume and recycling potential and provides essential information for resource and energy use reduction strategies. The connection between dynamic DSM and waste-input-output models, a special IO model type designed for handling waste, is currently under development and will allow for simultaneous assessment of environmental impacts of material production and recycling. An extensive overview of the literature on dynamic modelling of material stocks is provided by Müller and colleagues (2014).

Further Reading

Elshkaki, A., 2005. Dynamic stock modelling: A method for the identification and estimation of future waste streams and emissions based on past production and product stock characteristics. Energy 30, 1353–1363.

European Commission, 2011. Communication from the Commission to the European Parliament, the Council, the European Economic and Social Committee and the Committee of the Regions: Roadmap to a Resource Efficient Europe, /* COM/2011/0571 final */.

Eurostat, 2012. Economy-wide Material Flow Accounts (EW-MFA) - Compilation Guide 2012. Eurostat, Luxembourg.

Fischer-Kowalski, M., Haberl, H., 1998. Sustainable development: socio-economic metabolism and colonization of nature. Int. Soc. Sci. J. 50, 573–587.

Fischer-Kowalski, M., Hüttler, W., 1998. Society’s Metabolism. J. Ind. Ecol. 2, 107–136.

Fischer-Kowalski, M., Krausmann, F., Giljum, S., Lutter, S., Mayer, A., Bringezu, S., Moriguchi, Y., Schütz, H., Schandl, H., Weisz, H., 2011. Methodology and Indicators of Economy-wide Material Flow Accounting. J. Ind. Ecol. 15, 855–876.

Jakob, M., Marschinski, R., 2012. Interpreting trade-related CO2 emission transfers. Nat. Clim. Change 3, 19–23.

Leontief, W., 1970. Environmental repercussions and the economic structure: an input-output approach. Rev. Econ. Stat. 52, 262–271.

Miller, R.E., Blair, P.D., 2009. Input-output analysis: foundations and extensions. Cambridge University Press.

Müller, D.B., 2006. Stock dynamics for forecasting material flows - Case study for housing in The Netherlands. Ecol. Econ. 59, 142–156.

Müller, E., Hilty, L.M., Widmer, R., Schluep, M., Faulstich, M., 2014. Modeling metal stocks and flows-a review of dynamic material flow analysis methods. Environ. Sci. Technol.

Pauliuk, S., Müller, D.B., 2013. The role of in-use stocks in the social metabolism and in climate change mitigation. Global Environmental Change.

Rockström, J., Steffen, W., Noone, K., Persson, Å., Chapin, F.S., Lambin, E.F., Lenton, T.M., Scheffer, M., Folke, C., Schellnhuber, H.J., Nykvist, B., de Wit, C.A., Hughes, T., van der Leeuw, S., Rodhe, H., Sörlin, S., Snyder, P.K., Costanza, R., Svedin, U., Falkenmark, M., Karlberg, L., Corell, R.W., Fabry, V.J., Hansen, J., Walker, B., Liverman, D., Richardson, K., Crutzen, P., Foley, J.A., 2009. A safe operating space for humanity. Nature 461, 472–475.

Schaffartzik, A., Eisenmenger, N., Krausmann, F., Weisz, H., 2013. Consumption-based Material Flow Accounting. J. Ind. Ecol.

Schoer, K., Weinzettel, J., Kovanda, J., Giegrich, J., Lauwigi, C., 2012. Raw Material Consumption of the European Union - Concept, Calculation Method, and Results. Environ. Sci. Technol. 46, 8903–8909.

Tukker, A., Dietzenbacher, E., 2013. Global Multiregional Input-Output Frameworks: An Introduction and Outlook. Econ. Syst. Res. 25, 1–19.

Van der Voet, E., Kleijn, R., Huele, R., Ishikawa, M., Verkuijlen, E., 2002. Predicting future emissions based on characteristics of stocks. Ecol. Econ. 41, 223–234.

Wiedmann, T., Wilting, H.C., Lenzen, M., Lutter, S., Palm, V., 2011. Quo Vadis MRIO? Methodological, data and institutional requirements for multi-region input–output analysis. Ecol. Econ. 70, 1937–1945.

Wiedmann, T.O., Schandl, H., Lenzen, M., Moran, D., Suh, S., West, J., Kanemoto, K., 2013. The material footprint of nations. Proc. Natl. Acad. Sci.