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Energy Policy

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A review of EROEI-dynamics energy-transition models

Craig D. Rye⁎, Tim JacksonCentre for the Understanding of Sustainable Prosperity (CUSP), University of Surrey, 388 Stag Hill, Guildford GU2 7XH, United Kingdom

A R T I C L E I N F O

Keywords:EROEINet-EnergyModelTransitionDynamicsBiophysical

A B S T R A C T

The need for an environmentally sustainable economy is indisputable but our understanding of the energy-economy interactions (dynamics) that will occur during the transition is insufficient. This raises fascinatingquestions on the future of economic growth, energy technology mix and energy availability. The crucial inter-actions between energy and economy systems can be usefully described in terms of the Energy Returned onEnergy Invested (EROEI) metric (the energy cost of primary energy production). Multiple authors have used thismetric to explore the behaviour of the economy over the transition to lower carbon energy sources. The fol-lowing text is a review of energy-economy models that incorporate the EROEI metric. In particular, the EROEI-dynamics literature is found to describe a common set of dynamics associated with the transition to lower EROEIprimary energy resources. These include: the rising resource-cost of primary energy production, the short-termmisallocation of resources, the short-term overproduction of energy and the potential decline in economicstability. The literature can be divided into groups of related models. Following the review, a number of keyareas for additional work are identified and discussed.

1. Introduction

The Energy Returned on Energy Invested (EROEI; aka efficiency) ofprimary energy production has declined markedly over recent decades(Murphy, 2014). Furthermore, the EROEI of primary production isprojected to decline further in the early half of the current century,associated with the continuing depletion of fossil fuel reserves and thetransition away from conventional fossil fuels (IPCC, 2014; Sterman,1982; Gagnon et al., 2009; Grandell et al., 2011; Murphy and Hall,2010). For example, Guilford et al., (2011) find that the EROEI forUnited States Oil and Gas has declined by around a half, between 1930and present. The continuing decline of EROEI is a significant academicand political concern posing impacts on energy futures and the dy-namics of the transition to a low carbon economy.

EROEI is estimated as the energy produced by an energy-gatheringactivity divided by the energy required for that production (Eq. (1)).The energy produced by energy gathering activity is refered to here asprimary energy. Typical EROEI values are provided in Table 1. A si-milar useful metric of primary energy efficiency is Net Energy (NE). NEis estimated as the energy produced by primary energy minus the en-ergy required for that production (Eq. (2)). Both the EROEI and NEmetrics indicate the efficiency of energy production. EROEI is a parti-cularly interesting term because its name explicitly refers to the energythat is ‘used up’ or ‘invested’ in the process of producing useful energy

for society.

=EROEIEnergy ReturnedEnergy Invested (1)

= −NE Energy Returned Energy Invested (2)

Many of the core insights of the EROEI (or NE) metric are intuitivebut poorly accounted for. For example, an energy carrier (such as ga-soline) must provide more energy when it is used than it requires inproduction. Otherwise, it would not make ‘economic sense’ to produceit. The greater the energy return, or net energy, the greater the positiveeffect on the economy. Unfortunately, this kind of argument is oftenneglected. For example, green energy subsidies typically support bio-fuels and wind energy equally, however, wind power usually providessignificantly greater energy and economic return. Therefore subsidiesare often biased towards low EROEI renewables. EROEI provides apowerful approach for examining the efficiency of primary energygeneration technologies.

Charles Hall and collaborators provide many early works on EROEIin economics (e.g. Hall and Cleveland, 1981; Cleveland et al., 1984;Hall et al., 2008; Hall et al., 2009). Notably, Murphy and Hall (2010)highlight that the relationship between Net Energy and the EROEI isexponential where NE declines rapidly as EROEI falls below approxi-mately ~10:1. The relationship between EROEI and NE is commonlyreferred to as the ‘Net Energy cliff’ (see Fig. 1). This relationship

https://doi.org/10.1016/j.enpol.2018.06.041Received 8 November 2017; Received in revised form 26 June 2018; Accepted 27 June 2018

⁎ Corresponding author.E-mail address: craig.d.rye@gmail.com (C.D. Rye).

Energy Policy 122 (2018) 260–272

Available online 01 August 20180301-4215/ © 2018 Elsevier Ltd. All rights reserved.

T

suggests that advanced economies require EROEI values of at least 5 tomaintain key infrastructure and avoid economic decline. From a similarargument, it is suggested that the Net Energy cliff could play a key rolein the growth rate of an economy.

Following the work of Hall and Murphy, numerous authors haveconducted empirical analyses of the relationship between EROEI andother economic indicators. For example, Heun and de Wit (2012) Kingand Hall (2011) and Brandt (2017) find interesting relationships be-tween EROEI and energy prices. Heun and de Wit (2012) suggest thatthese relationships may break down as EROEI becomes small. Hall et al.(2008) suggest that during periods of energy shortage (i.e. low EROEI,such as the 1970s ‘energy crisis’ or the rising prices of 2000–2007)discretionary spending typically declines. Finally, Rubin (2012) andHamilton (2009) use empirical analysis to argue that the rising energyprices (declining EROEI) of 2000–2007 contributed to the recent 2008financial crisis. Empirical works therefore typically suggest an inverserelationship between EROEI and energy prices, and a link betweenEROEI and economic health.

Numerical models have been developed to explore the related set ofsystem behaviours accompanying the transition towards lower EROEI(e.g. Sterman, 1982; Hounam, 1979; Baines and Peet, 1983; Bodger andBaines, 1988). These models typically simulate the behaviour of theenergy-economy during a period of declining resource quality, or en-ergy technology transition. The emergence, nuance, evolution and as-sociation of these EROEI-dynamics models are the subject of this re-view.

The structure of this review is as follows: Section 2 outlines thehistory of EROEI-Dynamics models. Section 2.1: discusses formativework (1970–1980). Section 2.2: covers a period of rapid development(1980–2000). Section 2.3: highlights the most recent literature(2000–2017). Section 3 outlines the closely related field of resource-

curve models. Each model is described (typically in 3 paragraphs) interms of its novelty, technical detail and main findings. Section 4 pro-vides a discussion and Section 5 gives concluding remarks.

2. Numerical models of EROEI-dynamics

In this section, we review the history of energy-economy modelsthat specifically explore EROEI dynamics. Emphasis is given to seminalworks. There are unavoidably a number of limitations to this review.During the development of the literature, models are often documentedinconsistently therefore it is challenging to provide a consistent outlineof technical detail. Further, choosing the boundaries of the review ischallenging. For example, this review does not explore the broaderIntegrated Assessment Modelling (IAM) literature. The accuracy of theIAM literature in simulating EROEI-dynamics is debated (e.g. Daleet al., 2013) and this discussion is beyond the scope of this review.However, some of the EROEI-dynamics models may be considered asbelonging to the IAM literature and vice-versa. This review particularlyemphasises research that directly refers to EROEI.

2.1. Early Models (~1970 to 1980)

World3 is perhaps the earliest model to (implicitly) simulate EROEIdynamics (Meadows et al., 1972). It is associated with the Limits toGrowth study (Meadows et al., 1972) and was designed to explore theintegrated environmental challenges facing the global economy in the21st century. The model was derived from the earlier work of Forester(1970) on Industrial Dynamics and has had a defining impact on thefollowing energy-economy-environment debate.

The World3 model can be technically described as a globally ag-gregated, system dynamics framework, where well-chosen simplifiedequations are used to represent large complex systems. The modelimplicitly simulates EROEI-dynamics by assuming that the cost of ex-tracting non-renewable resources increases as resources are depleted.Therefore as the model consumes non-renewable resources, their costincreases and this drives a downward pressure on economic growth.However, the model does not explicitly simulate energy systems.

The main results (or dynamics) of World3 are relatively consistentfor a range of reasonable model parameters. The ‘standard run’ ofWorld3 suggests that the current growth trend of the global economy isunsustainable; leading to the encroachment of environmental limits andultimately ‘overshoot and collapse’ (Fig. 2). In this case, industrialoutput and food production peak around 2015 and decline thereafter.Population and pollution peak around 2030 and decline thereafter. Thesimulation stabilises around the beginning of the 22nd century with aglobal population of around a half of the peak value. However, ac-counting for the models’ uncertainty, its precise predictions are lessimportant than the underlying dynamics (Jackson and Webster, 2016).

Table 1Typical EROEI values (derived from Hall and Klitgaard, 2011).

Primary energy production technologies Approximate EROEI

Hydropower > 100:1Historic oil and gas 100:1Coal 80:1Current global oil and gas 20:1Wind (no storage) 20:1Nuclear 15:1Current US oil and gas 10:1Solar (no storage) 10:1Unconventional oil and gas 5:1Biofuels 2:1

Fig. 1. The relationship between Net Energy (expressed as a percentage) EnergyReturn on Energy Invested: ‘the net-energy cliff’ (Murphy 2013).

Fig. 2. The distribution of core variables for the World3 ‘Standard Run’, takenfrom (Meadows et al., 1972).

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Shortly after publication World3 was heavily criticised (see Hall andDay, 2009; Bardi, 2011; Jackson and Webster, 2016 for more details).But the results of World3 were revisited by Turner (2008), who con-cluded that the behaviour of the global economy 1972–2008 agreeswell with the ‘standard run’ scenario. Furthermore, World3 was re-cently re-calibrated by Pasqualino et al. (2015), who argue that recentimprovements in pollution and food productivition may have delayedbut not negated Meadows et al. (1972) prediction of ‘overshoot andcollapse’.

Following World3, Roger Naill and collaborators (in association withthe U.S. Department of Energy; Naill, 1973) developed a progression offive models, COAL 1 and 2, FOSSIL 1 and 2, and IDEAS. Unfortunately,these models are sparsely documented. However, these models are wellcited and considered influential on following work (Sterman, 1982).COAL and FOSSIL are perhaps the earliest System Dynamics models toincorporate energy market dynamics, investment time lags and priceelasticities. Later iterations of the group, such as FOSSIL2 and IDEAS wereused by the U.S. Department of Energy between 1973 and 1995, as policydesign and testing tools (Qudrat-Ullah, 2013).

From a technical perspective, early iterations of COAL follow anaggregated (‘top-down’) approach similar to World3. However, lateriterations of FOSSIL emphasise greater detail in primary energy pro-duction (‘bottom-up’ approach). FOSSIL 2 and IDEAS may be classedprincipally as bottom-up models (Qudrat-Ullah, 2013), where eachsector, and often subsectors are described explicitly with individualbehavioural equations.

Following World3, the COAL-FOSSIL studies, the STER (System,Time, Energy and Resources) model, documented by Hounam (1979),presents an innovative EROEI-dynamics approach. STER is one of theearliest models to explore the behaviour of the energy sector during aperiod of resource depletion, and therefore also one of the first to di-rectly focus on EROEI-dynamics. It may also be one of the earliest ex-amples of a ‘biophysical’ EROEI model, where all capital flows andproduction are defined in terms of energy. In addition, the researchquestion posed by STER is novel; STER is designed to determine themaximum possible (resource constrained) growth rate that an economycan achieve in a given time period. In this regard, the model designavoids the uncertainty of many parameters by framing results in termsof the maximum economic potential. Unfortunately, STER is onlydocumented by a single conference paper where it is described as a pilotstudy (Hounam, 1979).

It is difficult to discuss the technical detail of STER because of sparsedocumentation. The structure is shown in Fig. 3. STER is a simplified,aggregated, top-down model with a production function articulated interms of energy, capital, labour, and technology. The model simulatesEROEI dynamics by assuming that the demand for resources by theprimary energy sector increases (i.e. the resource cost of primary en-ergy production increases) as energy resources are depleted.

The results of STER suggest that, if energy use is held constant, therelative resource consumption of the energy sector must increase asresources are depleted, so as to keep up with demand. The rising cost ofenergy production then leads to the crowding out of (non-energy) in-dustrial production and the growth of the energy sector relative to thenon-energy industry (Fig. 4). This (relative) expansion of the energysector during the transition to low EROEI is an important process dis-cussed by the EROEI-dynamics literature.

Directly following World3 and the COAL-FOSSIL studies, JohnSterman of the MIT System Dynamics group developed a seminal en-ergy-economy model, referred to here as the Sterman model (e.g.Sterman, 1982). In line with STER, the Sterman model is one of theearliest models designed to specifically simulate the energy-economydynamics associated with a transition from high to low EROEI primaryenergy. Furthermore, the model provides one of the earliest direct re-ferences to EROEI-dynamics (Sterman, 1982; Section 2.1 para. 8). Adiagram of the structure of the Sterman model is shown in Fig. 5.

The Sterman model is a globally aggregated, top-down, system

dynamics framework that uses a nested, constant elasticity of sub-stitution production function in technology, capital, labour and en-ergy.1 The model characterises the energy sector in terms of two ag-gregated technology groups, conventional and unconventional energy.This simplification supports the inclusion of complex economic detailand allows the examination of many interesting energy-economy dy-namics. For example, the model includes inflation, monetary policy andinternational trade. It also provides a complex representation of in-vestment and capital depreciation. Conversely, for simplicity, the modelexcludes many interesting factors that may play important roles inenergy-transition dynamics, such as business inventories and environ-mental interactions.

The Sterman model simulates EROEI-dynamics using two key as-sumptions. In principle, it assumes that the cost of producing conven-tional energy increases as reserves are depleted (whereas the reserves ofunconventional energy are infinite). Further, it assumes that the initialEROEI of conventional fossil fuels is greater than the EROEI of un-conventional fossil fuels. Therefore, as the economy consumes con-ventional energy or transitions from conventional to unconventionalenergy, the resource cost of energy production increases. This in-creasing demand for resources by the energy sector ‘crowds out’ in-vestment in the non-energy economy and provides a downward pres-sure on economic growth. It is noted that the EROEI-dynamics of themodel follow from similar core assumptions made by the World3.

The conclusions of Sterman (1982) emphasises three key energy-economy dynamics:

1. As previously stated, the depletion of conventional energy leads toincreasing resource requirements for the energy sector, leading to adownward pressure on economic growth by ‘crowding out’ invest-ment in the non-energy economy.

2. Energy price increases are expected to drive an increase in economy-wide energy efficiency, however, it is argued that this will occurmore slowly than investment in energy production. Therefore, in theshort-term energy may be over-produced and capital misallocated.In the long run, the misallocation of capital will constitute in-efficiency.

3. Due to the capital-intensity of energy production, significant in-vestment will be required in the short-run at the start of the tran-sition; the initial cost of transition will facilitate a short-termdownward pressure on economic growth and may slow the transi-tion.

Fig. 3. Schematic illustration of the structure of Gilliland (1978) theory, andthe STER model (Hounam, 1979).

1 The constant elasticity of substitution (CES) production function is a simpleaggregate model of production (Solow, 1956). The function is characterised byconstant elasticity’s for its factors (e.g. capital and labour) regardless of pro-duction scale. The role of energy in production is well discussed; authors suchas Cantillon (1730) and Georgescu-Roegen (1971) make notable contributions.Early modelling studies that incorporate energy as a factor of production in-clude: Tintner et al., 1974; Hudson and Jorgenson, 1974; Berndt and Wood,1979).

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The distribution of energy production over the transition as pro-jected by Sterman is illustrated by Fig. 6. Sterman concludes: ‘the roadto the economy freed from dependence on non-renewable energysources is likely to be quite long and rocky’ (Sterman, 1982, page 352).

2.2. Intermediate models (~1980 to 2000)

Following the Sterman model and the STER model, Baines and Peet(1983), and Bodger and Baines (1988) developed a system dynamicsmodel to explore the role of historical energy transitions (e.g. frombiomass, to coal, to oil and gas) in long-run (inter-decadal) economicvariability (e.g. Kondratieff, 1979). This is referred to here as the BPBmodel. A schematic of the BPB model and an illustration of the energyavailability over recent energy transitions are shown in Figs. 7 and 8respectively (Baines and Peet, 1983).

In a technical regard, the BPB model is a globally aggregated, top-down, biophysical approach that uses constant values for the EROEI ofenergy technologies. The model simulates historical energy transitionsby assuming that the economy has a preference to consume the highestEROEI resources available. Therefore economies typically transition tohigher EROEI resources as they become available. The model contains asimilar level of energy production detail to the STER model. The BPBmodel was not thoroughly calibrated to historical data (Dale, et al.,2012). Furthermore, it does not appear to include a complex re-presentation of the economy such as the Sterman model.

The results of the BPB model suggest that EROEI-dynamics have

Fig. 4. STER model output. Left: Sectorial percentage of capital. Right: capacities of energy sectors. Hounam (1979).

Fig. 5. Schematic illustration of the Sterman model structure (Sterman, 1982).

Fig. 6. An example of output from the Sterman model, highlighting the energytransition envisioned by Sterman (1981).

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played a plausible role in long-run (inter-decadal) economic variability,particularly in association with energy technology transitions. This ar-gument is supported by the work of other notable authors, such asSchumpeter (e.g. Schumpeter, 1939), Sterman (1985) and King et al.(2015).

In the early 90s Malcolm Slesser and colleagues developed theEnhancement of Carrying Capacity Options (ECCO) modelling frame-work in association with UNESCO (e.g. Slesser, 1992). ECCO was ori-ginally developed to assist supply-side growth in low-GDP nations andhas been applied to a range of economies including Kenya (Owino,1991), China (Wenhua, 1991; Xiaohui, 1995) and the Netherlands(Noorman, 1990, 1995). ECCO is a biophysical system dynamics ap-proach that draws directly from the approaches of World3, FOSSIL2,and STER (Gilliland, 1978). In particular, following STER, it is designedto determine the maximum growth potential of an economy as afunction of its resource constraints.

The core ECCO model is a top-down aggregated simulation of anational economy. The structure of ECCO follows the Natural CapitalAccounting methods of Slesser (1989). This basis leads to a strongemphasis on the efficiency of primary resource production, and there-fore emphasis on EROEI. The model defines three types of natural ca-pital, depletable (e.g. fossil fuels), recyclable (e.g. aluminum) and re-newable (e.g. solar power). Similar to STER, ECCO is classed as abiophysical model and describes all the interactions in the economy interms of energy. Following Dürr (1994), ECCO has a novel productionfunction with factors in terms of operational energy and capital-em-bedded energy. The ECCO production function interestingly neglectsthe role of labour. Further, ECCO explicitly calculates the EROEI ofmultiple primary resources, including energy resources.

ECCO models typically incorporate an aggregated world model,referred to as CORECCO or GlobECCO. A diagram of the CORECCOstructure is shown in Fig. 9. Similar to the ECCO national models,

CORECCO explicitly simulates EROEI dynamics at an aggregate level.The standard implementation of CORECCO suggests that industrialoutput of the global economy will peak in the early half of the currentcentury and decline thereafter.

In the late 90s, Fiddaman (1997) developed the Feedback RichEnergy Economy model (FREE) in association with the MIT SystemDynamics group that draws directly from World3 and the Stermanmodel (Fig. 10). FREE is designed to highlight the role of complex non-linear feedbacks in energy-economy systems, particularly over a periodof energy transition. Furthermore, it is designed to explore the responseof the energy-economy to policy proposals.

The FREE model simulates a large range of economy-energy-en-vironment interactions, it therefore can be considered an IntegratedAssessment Model, as well as an EROEI-dynamics model. The economystructure of FREE is derived from the highly cited DICE IntegratedAssessment Model (Nordhaus, 1992). The energy systems and energy-economy coupling of FREE is derived from the Sterman model (e.g.Sterman, 1982). FREE uses a Cobb-Douglas production function withfactors in Labour, Capital, Energy and Technology. Unlike the Stermanand World3 models, the population and total factor productivity areestimated exogenously. FREE explicitly accounts for EROEI dynamicsand resource constraints, as well as climate interactions (Fiddaman,1997, 1998).

The ‘business as usual’ results of the FREE model suggest that thenet energy output of the global economy will decline between 2020 and2045. However, unlike the Sterman or World3 models, the GDP of theeconomy does not appear to decline. This distinction for GDP highlightsa potential rigidity in the model that may be associated with exogenousparameters, such as population or total factor productivity growth.Similar to Sterman (1982), Fiddaman argues: ‘Much of the harm fromdepletion actually arises from the difficult period of transition awayfrom oil and gas, rather than from the long-run effects of losing theservices of those fuels’. This is due to the cost of building new andretiring old energy systems (pg. 15, Fiddaman, 1997). Fiddamantherefore additionally supports Sterman (1982)’s emphasis on the roleof the misallocation of capital during the transition, both in the energyindustry and in the none-energy industry. Fiddaman argues ‘Depletionleads to suboptimal capacity utilization in the goods producing sector,because energy prices are far from the levels for which the capital stockwas designed. In extreme scenarios, when depletion suddenly becomessevere, a near-shutdown of the economy is possible.’ (pg. 15, Fiddaman,1997). Fiddamen argues that a depletion tax on oil and gas improvesthe economic stability of the transition by increasing the price of oil andgas earlier; therefore, by spreading the economic cost and risk of sys-temic failure.

2.3. Recent models (2000–2017)

Following from STER and ECCO, the Global Energy Modelling – aBiophysical Approach model (GEMBA; Dale et al., 2012) is a recentdirect effort to explore EROEI dynamics over the renewable energytransition. GEMBA’s description of EROEI-dynamics is highly intuitiveand engaging. Furthermore, GEMBA is notably well constructed forcalibration with empirical data.

GEMBA can be technically described as a globally aggregated top-down, biophysical model that utilises a highly simplified economymodel with a production function in terms of capital and a capital tooutput ratio (Fig. 11). In particular, GEMBA simulates a detailed rangeof production technologies, including coal, oil, gas, wind, hydro andsolar. GEMBA estimates

EROEI in terms of resource depletion and technological develop-ment (Dale et al., 2010).

The main results of the GEMBA model suggest that the relativecapital requirement of the energy sector may increase over the energytransition to around half the capital in the economy (Fig. 12a; similar toSTER and the Sterman model). Over the same period, the total available

Fig. 7. A schematic showing the BPB model view of EROEI dynamics (Bodgerand Baines, 1988).

Fig. 8. A schematic showing the distribution of capital between competingenergy technologies over a series of transitions, as Envisioned by Bodger andBaines (1988), associated with the BPB Model.

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energy is suggested to peak mid-21st century, eventually stabilising ataround half current values in 2200 (Fig. 12b).

Dale et al. (2013) compare the MESSAGE (common Integrated As-sessment Model) projections, associated with the Special Report on

Energy Scenarios (SRES; IPCC) with the GEMBA projections. GEMBA’sprojections provide lower future estimates of energy availability thenMESSAGE. It is argued that this is because GEMBA utilises more rea-listic primary resource estimates.

Fig. 9. Outline of CORECCO (Slesser, 1992) taken from Dale (2010).

Fig. 10. A schematic of the FREE model, taken from Fidderman (1997).

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Finally, a recent work by Brandt (2017) focuses on the dynamics ofthe ‘Net Energy Cliff’. The Brandt approach is novel for the distinctionthat it makes between GDP and ‘material prosperity’. This emphasis on‘material prosperity’ provides a strong link with the Biophysical ap-proach, however, the Brandt model is not biophysical.

The Brandt model is a bottom-up globally aggregated model thatuses a neoclassical production function, with factors in, capital, labour,energy and resources. The economy component of the Brandt model isderived from the KLEMS economy model (Van Ark et al., 2007) and itsrepresentation of energy production uses an input-output model of theenergy industry. The Brandt model explicitly simulates EROEI-dy-namics, where a decline in the EROEI of production is shown to drive adecline in the material prosperity of the economy.

The results of Brandt (2017) are used to explore the concept of aminimum EROEI. As suggested by Hall and Murphy (2011) Brandt findsa consistent behaviour in all runs, where below a specific level of

EROEI, typically ~7, the material wealth of the economy declines ra-pidly.

3. Resource curve methods

In addition to the EROEI-dynamics models, a related body of lit-erature utilises resource curve methods (e.g. Hubbert, 1956) to explore21st century energy futures. Studies within this group include: Brecha(2008), Doose (2004), Nel and Cooper (2009), Macías and Matilla-García (2015). Resource curve methods simulate resource depletion butdo not explicitly include EROEI-dynamics. The approach uses empiricalobservations of resource depletion and global geological data to esti-mate the future global depletion of resources. Resource curve methodstypically apply these distributions as exogenous constraints. The re-source curve literature is extensive and often overlaps with EROEI-dy-namics models, it includes some influential studies that are well cited

Fig. 11. A schematic of the GEMBA model (Dale et al., 2013).

Fig. 12. GEMBA model output: Left (a): the distribution of capital between the energy sector and the industrial sector. Right (b): the projected energy production ofthe global economy (Dale et al., 2013).

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by the EROEI-dynamics modelling literature. The following sectionoutlines a number of notable studies that use these methods.

Following World3, Capellán-Pérez and collaborators (e.g. Capellán-Pérez et al., 2014; Mediavilla et al., 2013) developed the World LimitsModel (WoLiM). WoLiM is a biophysical system dynamics model thatuses resource curve methods. WoLiM is designed to explore the feasi-bility of 20th century growth trends (Fig. 13).

WoLiM is a bottom-up model with notable detail in primary energyproduction (Fig. 14). The model is driven primarily by a group of GDPand population scenarios that are set externally (exogenous). ThereforeEROEI decline is not able to influence GDP and the model is not able toproperly simulate EROEI dynamics. The model simulates the depletionof resources with resource depletion curves (e.g. Mohr, 2012, Patzekand Croft, 2010). WoLiM’s results typically predict resource constraintsin the early half of the 21st century. The majority of WoLiM runs exceedenvironmental limits leading to dangerous climate change. WoLiMmaybe be thought of as a model that is designed to test for resourcelimitations as a result of optimistic 21st century growth projections.

Kumhof and Muir (2014) and Benes et al. (2015) provide relatedmodelling studies that are more closely aligned with resource curvemodels then with the EROEI dynamics models. Kumhof and Muir(2014) use a top-down, Dynamic Stochastic General Equilibrium Modelto explore the behaviour of the global economy responding to a declinein oil production. The model simulates energy scarcity using a resourcedepletion curve, which is expressed in terms of the oil price. Benes et al.(2015) use an econometric model of the global oil market to explore theresponse of the economy to a decline in oil production. The Benesmodel simulates EROEI dynamics through a rising oil price, associatedwith a depletion curve. The Kumhof model suggests that a realisticdecline in the global oil production may drive a significant decline inthe GDP growth rate of both importer and exporter countries. Thisdecline is notable since the growth rates of the high GDP countries arecurrently declining and additional decline may constitute stagnation ordecline (Summers 2011). The Benes model similarly predicts that re-source depletion with drive oil prices to almost double over the comingdecade. Benes notes that this scale of increase would have a dramaticimpact on the global GDP, further supporting the arguments of Kumhofand Muir (2014) and the EROEI dynamics models.

Finally, Sgouris et al. (2016) developed the NETSET resource curvemodel. The NETSET model uses a novel inverse approach to simulate arange of feasible transition pathways. The framing of the approach iswell illustrated by the title: ‘… quantifying the narrowing net-energypathways to a global energy transition’ (Sgouris et al., 2016).

The NETSET model is a globally aggregated, top-down, biophysicalsimulation model. The model uses an exogenous projection of futurepopulation to estimate future energy demand. It then integrates back-wards to estimate a range of transition pathways that satisfy emissionstargets and minimum energy per capita requirements. NETSET uses

three core pre-conditions. First, carbon emissions must not surpass le-vels chosen to limit global warming to 2 °C (between 510-1505 Gt CO2;IPCC, 2014). Second, energy availability must not decline below levelsdeemed as unrealistic (between 600 and 6000 Watts per person). Third,the rate of transition to low-carbon technologies should not exceed thatwhich fully depletes none-renewable resources.

The results of the NETSET model suggest that there are a number ofbiophysically feasible pathways to transition to a low carbon economy(Fig. 15). Sgouris et al. (2016) uses a ‘feasibility indicator’ to determinewhich pathways are most likely. It intuitively suggests that the transi-tion becomes more difficult if it is delayed, or if the carbon emissiontargets are relatively stringent. However, the model does not simulatemacro-economic variables. The model, therefore, does not discuss theeconomic or social implications of the projected energy pathways.

4. Discussion

In the spirit of organising our discussion, it is useful to present ahistorical synthesis of the models discussed in this paper. An overviewof the key literature is shown in Fig. 16 and a summary table is shownin Appendix I. Four model groups are evident: the MIT System Dy-namics group (red), the US department of energy group (blue), the BPBgroup (green), and the STER-ECCO group (orange). These four groupscan be additionally linked. The red and blue groups are interconnectedthrough the work of authors such as Sterman and Fidderman. The greenand orange groups show strong association both through common au-thors and model design.

As previously stated, the World3 model is one of the earliest modelsto directly explore the inter-related global challenges associated withunsustainable 20th century growth trends, having a defining impact onfollowing work. It is also perhaps one of the earliest models that im-plicitly simulates EROEI dynamics. It is important to note that World3follows World2 and the formative work of Forester in IndustrialDynamics (Forrester, 1970).

Following World3, the development of EROEI models can be de-scribed in terms of the MIT (red-blue) group and the Biophysical (or-ange-green) group. A divergence between the MIT and Biophysicalgroups occurs around 1980 associated with the STER model and theSterman model. These models are perhaps the earliest to directly si-mulate EROEI dynamics; both make significant contributions to theliterature.

The Sterman model signifies a more direct development of World3but also draws influence from the COAL and FOSSIL models. The modelhas a stylised description of the energy sector and a more complex re-presentation of the economy that provides a good platform for ex-ploring energy-economy interactions. One may argue that many fea-tures of the Sterman model, such as the misallocation of capital, or therole of inflation and unemployment have been insufficiently exploredfollowing its publication. The Sterman model is followed by the FREEmodel, which integrates the Sterman approach with recent economictheory and explores a range of policy options.

At a similar time to the Sterman model, the STER model introducesmultiple novel features to EROEI modelling, including the biophysicalapproach. It is unfortunate that the STER model is only documented bya brief preliminary paper. STER is followed by a series of biophysicalmodels: BPB, ECCO and GEMBA (green and yellow). The BPB modeluses a similar approach to STER but explores a distinctive question onthe role of EROEI in historical inter-decadal energy transitions. TheECCO framework develops the STER approach and applies it to a rangeof national economies, with a particular interest in understanding theresource constraints of economic growth. Finally, GEMBA continues theapproach of this group but returns to focus directly on the renewableenergy transition and provides an intuitive structure that is well de-signed for calibration with empirical data. Of this group, the GEMBAmodel is perhaps the most directly interested in EROEI dynamics andprovides a critique of the highly cited integrated assessment models

Fig. 13. A comparison of a global carbon emissions scenario estimated byBrecha (2008) and the IPCC Integrated Assesment Model scenarios. Brecha(2008) scenarios are shown by full lines, IPCC scenarios are shown by dashedlines.

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that appear to neglect EROEI dynamics.Following the progression of the MIT, and the biophysical modelling

groups, a number of relatively independent models have made sig-nificant contributions. For example, WoLiM provides an alternativeapproach to the problem outlined by World3. It utilises more recentapproaches to economic theory and highlights that current resourceconsumption growth trends are unsustainable, both in terms of resourceand pollution limits.

Despite the diversity in the EROEI-dynamics literature, there areseven key arguments or dynamics that run through all material. Thesedynamics are listed below, along with the dates of their first doc-umentation.

1. EROEI declines during the low carbon transition – during the transitionto low carbon technology, primary energy production becomes lessefficient (this is first implied by Meadows et al., 1972; this is fun-damental to all models in this review except the BPB model).

2. The energy sector outgrows the economy (aka. energy cannibalism) - asthe EROEI of primary energy production declines, the energy sector

requires increasing resources (including energy) to maintain supplywith demand (Hounam, 1979; Sterman, 1982; Slesser, 1992;Fiddaman, 1997; Dale, 2010; Capellán-Pérez et al., 2014; Kumhofand Muir, 2014; Benes, 2015).

3. Short-term confusion - during the transition to low-carbon tech-nology, a short-term misallocation of capital and labour occurs dueto imperfect information (Sterman, 1982; Fiddaman, 1997).

4. Short-term over production - energy scarcity drives both an increase inenergy efficiency and investment in energy production. Sterman(1982) argues that this leads to a short-term overproduction ofprimary energy.

5. Short-term scarcity - a decline in EROEI is expected to drive scarcityand inflation (Sterman, 1982).

6. Energy transition ‘long wave’ - ‘long wave’ (inter-decadal) economicvariability may be associated with energy transitions and EROEI(Baines and Peet, 1983).

7. ‘Net Energy Cliff’ - economic systems become unstable as EROEIdeclines below 10:1 associated with the ‘Net Energy Cliff’ (Brandt,2017; Murphy and Hall, 2010).

Fig. 14. Schematic illustration of the structure of the WoLiM model (Capellan-Perez et al., 2014) IB stands for Industrial Buildings sector. The WoLiM structure can bedescribed as follows: GDP growth drives energy demand. Energy demand is divided into three categories. Demand drives production through a number of technologyoptions. The optimal pathway for generation is a function of resource limits and environmental pollution.

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These dynamics may be usefully re-framed into three groups:Scarcity (1, 2, 6), Instability (5, 6, 7) and Uncertainty (3, 4). From thisview, ‘Scarcity’ encompasses the driving dynamics that lead to a declinein resource availability. Dynamics 1 and 2 of this group are the mostconsistent across the literature. ‘Instability’ encompasses potential sys-temic failures where systems are forced to sustain unanticipated re-source constraints. Finally, ‘Uncertainty’ encompasses the period ofchange or adjustment, where unavoidable unknowns (imperfect in-formation) lead to the misallocation of capital. Scarcity is the primarydriver of Instability and Uncertainty, however, these dynamics areinter-related and constitute feedbacks that are difficult to simulate.From this framework, the issues of Instability and Uncertainty in en-ergy-economy dynamics are notably poorly understood.

The issue of instability is an interesting topic of divergence in theliterature. Multiple authors, particularly in the MIT group, suggest thatthe low carbon transition is likely to drive a period of instability(Sterman, 1982, Fiddaman, 1997). However, dedicated modelling stu-dies such as Jackson and Victor (2015), Jackson (2017), suggest thatthe transition to a steady state or low carbon economy does not ne-cessitate instability. Further work is required to explore the role ofEROEI in systemic instability and the macro policy levers available tofacilitate a stable energy transition.

In addition, the issue of late 21st century energy availability is animportant topic in the literature. Models such as GEMBA and WoLiMpredict a mid 21st century decline in energy availability (Dale, 2013;

Capellán-Pérez et al., 2014). This behaviour is similar to the ‘systemcollapse’ described by World3 and CORECCO (Meadows et al., 1972;Slesser, 1992). However, models such as the Sterman (1982) and Fid-derman (1997) predict short-term instability instead of long-run de-cline. Here, it is important to account for model design factors andconsider the research questions being explored by given papers. Forexample, the Sterman model is highly idealised. It is not designed topredict future energy availability from empirical data. The models thatare more directly designed to explore empirical estimates of resourceconstraints such as CORECCO, GEMBA and WoLiM typically predict along-run decline in energy availability in the mid 21st century(Meadows et al., 1972; Slesser, 1992; Dale, 2013; Capellán-Pérez et al.,2014). Here it is argued that this issue requires further direct analysesof model code and empirical data.

Following models such as GEMBA and WoLiM, multiple authorshave expressed concern that the highly cited Integrated AssessmentModelling or Energy-Economy modelling literature does not effectivelysimulate or discuss EROEI-dynamics (e.g. Dale et al., 2013) andtherefore presents optimistic scenarios for future energy availability.Moreover, Keepin and Wynne (1984), Schneider (1997) and Schneiderand Lane (2005) argue that the subcomponents of Integrated Assess-ment Models are often poorly coupled suggesting EROEI dynamics arepoorly simulated. This concern is also crucial, requiring directed re-search and review. It is argued that it is beyond the scope of this review.

The Energy-Economy modelling literature is critiqued in general fordocumentation issues (Pindyck, 2015; Beck and Krueger, 2016;Pfenninger, 2017; Schneider, 1997). It is argued that the EROEI-dy-namics literature could also benefit from improved documentation andarchiving. For example, research papers (and/or manuals) for COAL,FOSSIL and STER are not readily accessible. However, these models arehighly cited by later work. Model descriptions, terminology and sche-matics are often used inconsistently. For example, common challengingterms include, ‘Top-Down’, ‘Bottom-Up’, ‘Hybrid’, ‘Simulation’, ‘Opti-misation’ and ‘General Equilibrium’. This issue is compounded by theconcern that model code is rarely available for scrutiny, even decadesafter original research publications. It is further suggested that the lit-erature may benefit greatly from an improved effort in review andsynthesis.

Further research in energy-economy dynamics is vital, consideringthe urgency of the transition to a sustainable economy (IPCC, 2014;Sverdrup et al., 2015). Particularly considering that the current eco-nomic climate is characterised by declining economic growth rates(Summers, 2013), increasing instability (Rye and Jackson, 2016) andincreasing uncertainty (Baker et al., 2016), all of which are plausiblyrelated to EROEI dynamics. There is therefore a notable requirement forfurther empirical studies in EROEI-dynamics. For example, it may bepossible to find signatures of EROEI dynamics in Secular Stagnation, orin international trade. Further work is required to provide an improvedlink between empirical work, such as Heun and de Wit (2012) and themodelling literature.

There are multiple a-priori EROEI dynamics identified by our dis-cussion that are not discussed by the current literature. These provideinteresting subjects for further research. Examples of these dynamicsinclude:

• The role of EROEI in financial instability – e.g. As EROEI declinescurrently highly valued resources may become unprofitable to ex-tract. A sudden loss in value would provide a significant destabi-lising perturbation/s to financial systems (e.g. stranded assets:Carbon Tracker, 2013).

• The role of EROEI in Secular Stagnation – Following e.g. Slesser(1992), EROEI plays a significant role in determining the growthrate of an economy. Therefore, the decline in EROEI over recentdecades may have played a primary role in Secular Stagnation.

• The role of international trade in global EROEI and global energy prices –Resource exploitation and international trade strategies are likely to

Fig. 15. An example of a NETSET simulated energy future, providing 2000 Waverage net power per capita by 2100 to a population of 10.8 billion. Fossil fuelemissions do not exceed 990 GtCO2. The dashed line represents the net avail-able energy. Values above this line represent energy invested.

Fig. 16. The recent history of EROEI models. Colours denote studies with thesame or related authors. Relatively independent models are black. Full line:strong link between authors. Dotted line: significant influence from a paper.

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change as EROEI declines and the nation state’s concerns of resourcescarcity increase. It is possible that changes in trade may lead to adecline in oil price during a period of declining EROEI.

5. Concluding remarks

The literature discussed by this review is diverse and spans almost50 years from the initial publications of the Limits to Growth study. It ispossible to map the development of the EROEI-dynamics models overthis period, to identify seminal works and provide a historical catalogueof blueprints for future work. Notable early works include: Meadows(1973), Hounam (1979) and Sterman (1982). The consistency of thekey arguments stemming from these papers and running through theEROEI-dynamics literature is strongly supportive of their validity. Themost widely established arguments suggest that geological resourceconstraints will drive a relative expansion of the energy sector in thecoming century, and a downward pressure on material prosperity (ar-guments 1, 2, 3 and 5).

It is clear that considerable work is required to further our under-standing of EROEI-dynamics. Perhaps the most significant concernfollowing this review is the divergence in the literature, where thewidely cited Integrated Assessment Modelling literature poorly citesEROEI-dynamics literature. It is possible that better integration ofEROEI-dynamics could have a significant impact on the discussion ofenergy futures and therefore a significant impact on government policy.

Greater research is required to explore this concern.Regardless of this concern many of the immediate-term policy im-

plications are consistent throughout the literature. These suggest thatrapid investment in renewable energy and energy efficiency are re-quired, some form of carbon or resource tax would be beneficial anddelayed actions are likely to increase the chance of dangerous climatechange. Further, there is a significant risk of systemic collapse.However, policy implications differ in the medium to long-term, wherethe EROEI-dynamics literature often advocates a low-growth or steadystate economy. This is discussed both in terms of a mitigation strategyand a biophysical inevitability. It is clear that greater research is re-quired to explore the dynamics of the steady state economy, as theEROEI-dynamics literature consistently projects that it may become aprominent feature of the current century.

Acknowledgements

The financial support of the Economic and Social Research Councilfor the Centre for the Understanding of Sustanable Prosperity (ESRCgrant no: ES/M010163/1) is gratefully acknowledged. We would alsolike to thank researchers at the Centre for the Understanding ofSustainable Prosperity (CUSP.ac.uk) for their support. We would like tothank Iñigo Capellán-Pérez, Roberto Pasqualino, Sarah Hafner andAngela Druckman for their insightful comments and supportthroughout.

Appendix I. Model Summary Table

Summary of models discussed by the review. The models are classified by the year of their first major publication as well as the developmentgroup assigned by this review. Red: MIT group. Blue: US government group. Orange: STER-ECCO group. Green: BPB group. Grey: no clear group. Themodels are also classified by the key dynamics. Further, by novel conclusions and their earliest reference.

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