# Developing an Input-Output Based Method to Estimate a National-Level Energy Return on Investment (EROI)

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. A National-Level EROI: The Concept

#### 2.1. Background

#### 2.2. The Benefits of a National-Level EROI

#### 2.3. Conceptual Issues and Choices

#### 2.3.1. Boundary of Analysis

#### 2.3.2. Accounting for Embodied Energy Inputs

#### 2.3.3. Temporality

#### 2.3.4. Accounting for Energy Quality

## 3. A national-Level EROI: The Data and the Methodology

#### 3.1. Input-Output and Energy

#### 3.2. EROI_{nat(UK)}: Data

#### 3.3. EROI_{nat(UK)}: Methodology

## 4. Results and Discussion

_{iE}) in the calculation of ${\mathrm{EROI}}_{\mathrm{nat}\left(\mathrm{UK}\right)}.\text{}$ An ${\mathrm{EROI}}_{\mathrm{nat}}$ calculation, using only energy industry’s own use as the energy inputs gives higher values because there is an element missing in the denominator. By including indirect energy use (E

_{iE}), using the IO methodology described in Section 3.3, we obtain a more complete view of the energy invested into the energy producing sectors. This is the key contribution of the methodology we outline here and a step forwards in the EROI literature. Our calculations for the UK without including indirect energy (E

_{iE}) are the same order of magnitude to King et al.’s [23] calculations of EROI (or net power ratio—NPR as they call it).

_{out}) and the energy invested (denominator E

_{in}) are shown in Figure 6. Since 1999 the UK’s production of energy has been declining steadily (compensated by increased imports that are not included in ${\mathrm{EROI}}_{\mathrm{nat}\left(\mathrm{UK}\right)}$). For a national-level EROI from a production perspective, this means that we are extracting/capturing less energy by using a relatively stable stream of energy inputs. Thus the steady decline of ${\mathrm{EROI}}_{\mathrm{nat}\left(\mathrm{UK}\right)}$ from 2003 onwards.

## 5. Conclusions and Policy Implications

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix A

#### Appendix A.1. A Note on Notation

#### Appendix A.2. Multi-Regional Input-Output Matrix Structure, with an Energy Extension

**Z**(Figure A1). In the top left hand corner of

**Z**is the UK data, followed by 5 world regions (the Rest of Europe, the Middle East, China, the Rest of the OECD, and the Rest of the World). Each region contains 106 industry sectors.

**Z**displays sales by each industry in rows and the columns represent purchases by each industry. In other words, reading across a row reveals which other industries a single industry sells to and reading down a column reveals who a single industry buys from in order to make its product output. A single element, ${\mathrm{z}}_{\mathrm{ij}}$, within $Z$ represents the contributions from the ith supplying sector to the jth producing sector in an economy. The $Z$ matrix is in monetary units.

#### Appendix A.3. Basic Calculations: Obtaining the A, L and F Matrices

#### Appendix A.4. EROI_{nat} Specific Calculations: Obtaining Indirect Energy

## Appendix B

## References

- Hall, C.A.S.; Kiltgaard, K.A. Energy and the Wealth of Nations. Understanding the Biophysical Economy; Springer: New York, NY, USA, 2012. [Google Scholar]
- Cleveland, C.J. Biophysical Economics: Historical Perspective and Current Research Trends. Ecol. Modell.
**1987**, 38, 47–73. [Google Scholar] [CrossRef] - Dale, M.; Krumdieck, S.; Bodger, P. Net energy yield from production of conventional oil. Energy Policy
**2011**, 39, 7095–7102. [Google Scholar] [CrossRef] - Gagnon, N.; Hall, C.A.S.; Brinker, L. A preliminary investigation of energy return on energy investment for global oil and gas production. Energies
**2009**, 2, 490–503. [Google Scholar] [CrossRef] - Lambert, J.G.; Hall, C.A.S.; Balogh, S.B. EROI of Global Energy Resources. Status, Trends and Social Implications; Department for International Development: London, UK, 2013. [Google Scholar]
- Hall, C.A.S.; Lambert, J.G.; Balogh, S.B. EROI of different fuels and the implications for society. Energy Policy
**2014**, 64, 141–152. [Google Scholar] [CrossRef] - Dale, M.; Benson, S.M. Energy Balance of the Global Photovoltaic (PV) Industry—Is the PV Industry a Net Electricity Producer? Environ. Sci. Technol.
**2013**, 47, 3482–3489. [Google Scholar] [CrossRef] [PubMed] - Raugei, M.; Fullana-i-Palmer, P.; Fthenakis, V. The energy return on energy investment (EROI) of photovoltaics: Methodology and comparisons with fossil fuel life cycles. Energy Policy
**2012**, 45, 576–582. [Google Scholar] [CrossRef] - Kubiszewski, I.; Cleveland, C.J.; Endres, P.K. Meta-analysis of net energy return for wind power systems. Renew. Energy
**2010**, 35, 218–225. [Google Scholar] [CrossRef] - Cleveland, C.J. Net energy from the extraction of oil and gas in the United States. Energy
**2005**, 30, 769–782. [Google Scholar] [CrossRef] - Brandt, A.R. Oil depletion and the energy efficiency of oil production: The case of California. Sustainability
**2011**, 3, 1833–1854. [Google Scholar] [CrossRef] - Smith, D.M. The yield and energy content of milk and the energetic efficiency of sows on different levels of nutrition during gestation and lactation. New Zeal. J. Agric. Res.
**1960**, 3, 745–763. [Google Scholar] [CrossRef] - Hall, C.A.S. Migration and metabolism in a temperate stream ecosystem. Ecology
**1972**, 53, 585–604. [Google Scholar] [CrossRef] - Hall, C.A.S.; Lavine, M.; Sloane, J. Efficiency of energy delivery systems: I. An economic and energy analysis. Environ. Manag.
**1979**, 3, 493–504. [Google Scholar] - Cleveland, C.J.; Costanza, R.; Hall, C.A.S.; Kaufmann, R.K. Energy and the U.S. Economy: A Biophysical Perspective. Science
**1984**, 225, 890–897. [Google Scholar] [CrossRef] [PubMed] - Murphy, D.J.; Hall, C.A.S. Year in review—EROI or energy return on (energy) invested. Ann. N. Y. Acad. Sci.
**2010**, 1185, 102–118. [Google Scholar] [CrossRef] [PubMed] - Murphy, D.J.; Hall, C.A.S.; Dale, M.; Cleveland, C.J. Order from Chaos: A Preliminary Protocol for Determining the EROI of Fuels. Sustainability
**2011**, 3, 1888–1907. [Google Scholar] [CrossRef] - Murphy, D.J.; Hall, C.A.S. Energy return on investment, peak oil, and the end of economic growth. Ann. N. Y. Acad. Sci.
**2011**, 52–72. [Google Scholar] [CrossRef] [PubMed] - Poisson, A.; Hall, C.A.S. Time series EROI for Canadian oil and gas. Energies
**2013**, 6, 5940–5959. [Google Scholar] [CrossRef] - Leach, G. Net energy analysis—Is it any use? Energy Policy
**1975**, 3, 332–344. [Google Scholar] [CrossRef] - Peet, N.J.; Baines, J.T.; Macdonald, M.G.; Tohili, J.C.; Bassett, R.M. Energy supply and net energy in New Zealand. Energy Policy
**1987**, 15, 239–248. [Google Scholar] [CrossRef] - Lambert, J.G.; Hall, C.A.S.; Balogh, S.B.; Gupta, A.; Arnold, M. Energy, EROI and quality of life. Energy Policy
**2014**, 64, 153–167. [Google Scholar] [CrossRef] - King, C.W.; Maxwell, J.P.; Donovan, A. ComparingWorld Economic and Net Energy Metrics, Part 2: Total Economy Expenditure Perspective. Energies
**2015**, 8, 12975–12996. [Google Scholar] [CrossRef] - King, C.W. Comparing World Economic and Net Energy Metrics, Part 3: Macroeconomic Historical and Future Perspectives. Energies
**2015**, 8, 12997–13020. [Google Scholar] [CrossRef] - King, C.W.; Maxwell, J.P.; Donovan, A. ComparingWorld Economic and Net Energy Metrics, Part 1: Single Technology and Commodity Perspective. Energies
**2015**, 8, 12949–12974. [Google Scholar] [CrossRef] - Fizaine, F.; Court, V. Energy expenditure, economic growth, and the minimum EROI of society. Energy Policy
**2016**, 95, 172–186. [Google Scholar] [CrossRef] - Herendeen, R.A. Connecting net energy with the price of energy and other goods and services. Ecol. Econ.
**2015**, 109, 142–149. [Google Scholar] [CrossRef] - Raugei, M.; Leccisi, E. A comprehensive assessment of the energy performance of the full range of electricity generation technologies deployed in the United Kingdom. Energy Policy
**2016**, 90, 46–59. [Google Scholar] [CrossRef] - Dale, M.; Krumdieck, S.; Bodger, P. Global energy modelling—A biophysical approach (GEMBA) Part 1: An overview of biophysical economics. Ecol. Econ.
**2012**, 73, 152–157. [Google Scholar] [CrossRef] - Heun, M.K.; Santos, J.; Brockway, P.E.; Pruim, R.; Domingos, T.; Sakai, M. From Theory to Econometrics to Energy Policy: Cautionary Tales for Policymaking Using Aggregate Production Functions. Energies
**2017**, 10, 203. [Google Scholar] [CrossRef] - Brockway, P.E.; Heun, M.K.; Santos, J.; Barrett, J.R. Energy-Extended CES Aggregate Production : Current Aspects of Their Specification and Econometric Estimation. Energies
**2017**, 10, 202. [Google Scholar] [CrossRef] - Kümmel, R. Why energy’s economic weight is much larger than its cost share. Environ. Innov. Soc. Transit.
**2013**, 9, 33–37. [Google Scholar] [CrossRef] - Ayres, R.U.; van den Bergh, J.C.J.M.; Lindenberger, D.; Warr, B. The underestimated contribution of energy to economic growth. Struct. Chang. Econ. Dyn.
**2013**, 27, 79–88. [Google Scholar] [CrossRef] - Brandt, A.R.; Dale, M. A General Mathematical Framework for Calculating Systems-Scale Efficiency of Energy Extraction and Conversion: Energy Return on Investment (EROI) and Other Energy Return Ratios. Energies
**2011**, 4, 1211–1245. [Google Scholar] [CrossRef] - Herendeen, R.A. Net Energy Analysis: Concepts and Methods. Encycl. Energy
**2004**, 4, 283–289. [Google Scholar] - International Energy Agency (IEA). Energy Statistics Manual; IEA: Paris, France, 2005. [Google Scholar]
- Brandt, A.R.; Dale, M.; Barnhart, C.J. Calculating systems-scale energy efficiency and net energy returns: A bottom-up matrix-based approach. Energy
**2013**, 62, 235–247. [Google Scholar] [CrossRef] - Hall, C.A.S.; Balogh, S.B.; Murphy, D.J. What is the Minimum EROI that a Sustainable Society Must Have? Energies
**2009**, 2, 25–47. [Google Scholar] [CrossRef] - Brandt, A.R.; Englander, J.; Bharadwaj, S. The energy efficiency of oil sands extraction: Energy return ratios from 1970 to 2010. Energy
**2013**, 55, 693–702. [Google Scholar] [CrossRef] - Harmsen, J.H.M.; Roes, A.L.; Patel, M.K. The impact of copper scarcity on the efficiency of 2050 global renewable energy scenarios. Energy
**2013**, 50, 62–73. [Google Scholar] [CrossRef] - Arvesen, A.; Hertwich, E.G. More caution is needed when using life cycle assessment to determine energy return on investment (EROI). Energy Policy
**2015**, 76, 1–6. [Google Scholar] [CrossRef] - Dale, M. The Energy Balance of the Photovoltaic (PV) Industry: Is the PV industry a net electricity producer? Environ. Sci. Technol.
**2013**, 47, 3482–3489. [Google Scholar] [CrossRef] [PubMed] - Cleveland, C.J.; Kaufmann, R.K.; Stern, D.I. Aggregation and the role of energy in the economy. Ecol. Econ.
**2000**, 32, 301–317. [Google Scholar] [CrossRef] - Brockway, P.E.; Barrett, J.R.; Foxon, T.J.; Steinberger, J.K. Divergence of trends in US and UK Aggregate Exergy Efficiencies 1960–2010. Environ. Sci. Technol.
**2014**, 48, 9874–9881. [Google Scholar] [CrossRef] [PubMed] - Warr, B.; Ayres, R.U.; Eisenmenger, N.; Krausmann, F.; Schandl, H. Energy use and economic development: A comparative analysis of useful work supply in Austria, Japan, the United Kingdom and the US during 100years of economic growth. Ecol. Econ.
**2010**, 69, 1904–1917. [Google Scholar] [CrossRef] - Brockway, P.E.; Steinberger, J.K.; Barrett, J.R.; Foxon, T.J. Understanding China’s past and future energy demand: An exergy efficiency and decomposition analysis. Appl. Energy
**2015**, 155, 892–903. [Google Scholar] [CrossRef] - Williams, E.; Warr, B.; Ayres, R.U. Efficiency dilution: Long-term exergy conversion trends in Japan. Environ. Sci. Technol.
**2008**, 42, 4964–4970. [Google Scholar] [CrossRef] [PubMed] - Kostic, M.M. Energy: Physics. Encycl. Energy Eng. Technol.
**2012**, 2, 808–823. [Google Scholar] - Gaggioli, R.A.; Wepfer, W.J. Exergy economics. Energy
**1980**, 5, 823–837. [Google Scholar] [CrossRef] - Wall, G. Exergy—A Useful Concept; Chalmers University of Technology: Göteborg, Sweden, 1986. [Google Scholar]
- Wall, G. Exergy—A Useful Concept within Resource Accounting; Chalmers University of Technology and University of Göteborg: Göteborg, Sweden, 1977. [Google Scholar]
- Wall, G. Exergy tools. Proc. Inst. Mech. Eng. Part A J. Power Energy
**2003**, 217, 125–136. [Google Scholar] [CrossRef] - Kanoglu, M.; Cengel, Y.A.; Dincer, I. Efficiency Evaluation of Energy Systems; Springer: London, UK, 2012. [Google Scholar]
- Dincer, I. The role of exergy in energy policy making. Energy Policy
**2002**, 30, 137–149. [Google Scholar] [CrossRef] - Rosen, M.A. Benefits of exergy and needs for increased education and public understanding and applications in industry and policy—Part I: Benefits. Int. J. Exergy
**2006**, 3, 202–218. [Google Scholar] [CrossRef] - Rosen, M.A. Energy crisis or exergy crisis? Exergy Int. J.
**2002**, 2, 125–127. [Google Scholar] [CrossRef] - Sciubba, E.; Wall, G. A brief Commented History of Exergy From the Beginnings to 2004. Int. J. Thermodyn.
**2007**, 10, 1–26. [Google Scholar] - IEA. Statistics: Frequently Asked Questions. Available online: http://www.iea.org/statistics/resources/questionnaires/faq/#one (accessed on 2 February 2017).
- Casler, S.; Wilbur, S. Energy Input-Output Analysis. A Simple Guide. Resour. Energy
**1984**, 6, 187–201. [Google Scholar] [CrossRef] - Bullard, C.W.; Penner, P.S.; Pilati, D.A. Net energy analysis. Handbook for combining process and input-output analysis. Resour. Energy
**1978**, 1, 267–313. [Google Scholar] [CrossRef] - Bullard, C.W.; Herendeen, R.A. The energy cost of goods and services. Energy Policy
**1975**, 3, 268–278. [Google Scholar] [CrossRef] - Wright, D.J. Goods and services: An input-output analysis. Energy Policy
**1974**, 2, 307–315. [Google Scholar] [CrossRef] - Brandt, A.R. How Does Energy Resource Depletion Affect Prosperity? Mathematics of a Minimum Energy Return on Investment (EROI). Biophys. Econ. Resour. Qual.
**2017**, 2, 2. [Google Scholar] [CrossRef] - IEA. World Energy Balances: Extended Energy Balances, 1960–2014. Available online: http://dx.doi.org/10.5257/iea/web/2015 (accessed on 15 October 2015).
- ONS Supply and Use Tables. Available online: http://www.ons.gov.uk/ons/taxonomy/index.html?nscl=Supply+and+Use+Tables (accessed on 6 October 2016).
- Lenzen, M.; Moran, D.; Kanemoto, K.; Geschke, A. Building Eora: A Global Multi-Region Input-Output Database At High Country And Sector Resolution. Econ. Syst. Res.
**2013**, 25, 20–49. [Google Scholar] [CrossRef] - Lenzen, M.; Kanemoto, K.; Moran, D.; Geschke, A. Mapping the structure of the world economy. Environ. Sci. Technol.
**2012**, 46, 8374–8381. [Google Scholar] [CrossRef] [PubMed] - Roberts, F. The aims, methods and uses of energy accounting. Appl. Energy
**1978**, 4, 199–217. [Google Scholar] [CrossRef] - Guevara, Z.H.Z. Three-Level Energy Decoupling: Energy Decoupling at the Primary, Final and Useful Levels of Energy Use; Universidade de Lisboa: Lisboa, Portuguese, 2014. [Google Scholar]
- International Energy Agency (IEA). World Energy Investment Outlook 2014; IEA: Paris, France, 2014. [Google Scholar]
- Berndt, E.R. From Technocracy to Net Energy Analysis: Engineers, Economists and Recurring Energy Theories of Value; Sloan School of Management, Masachusetts Institute of Technology: Cambridge, MA, USA, 1982. [Google Scholar]
- Carbajales-Dale, M.; Barnhart, C.J.; Brandt, A.R.; Benson, S.M. A better currency for investing in a sustainable future. Nat. Clim. Chang.
**2014**, 4, 524–527. [Google Scholar] [CrossRef]

**Figure 1.**Types of EROI. ${\mathrm{EROI}}_{\mathrm{stnd}}$: standard EROI. ${\mathrm{EROI}}_{\mathrm{pou}}$: EROI at the point of use. ${\mathrm{EROI}}_{\mathrm{ext}}$: extended EROI.

**Figure 2.**National level EROI—UK case. Black and dotted arrows represent what we measure, while white arrows represent flows that occur but that are not included in this approach to EROI

_{nat}given its boundary of analysis.

**Figure 5.**${\mathrm{EROI}}_{\mathrm{nat}\left(\mathrm{UK}\right)}$ (1997–2012): Comparison of results with and without indirect energy (E

_{iE}).

**Figure 7.**UK energy production: share of energy sources 1997–2012. Data taken from IEA [64].

**Figure 8.**Financial investments in the production of UK’s energy by source (1974–2012). Data taken from IEA [70].

Energy Source | Change in Production (%) | |
---|---|---|

1997–2010 | 2010–2012 | |

Coal and coal products | −0.6 | 0.0 |

Crude, NGL and feedstocks | −0.5 | −0.1 |

Natural gas | −0.3 | −0.2 |

Nuclear | −0.4 | 0.1 |

Hydro | −0.1 | 0.4 |

Solar/wind/other | 13.5 | 14.2 |

Biofuels and waste | 1.6 | 0.7 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Brand-Correa, L.I.; Brockway, P.E.; Copeland, C.L.; Foxon, T.J.; Owen, A.; Taylor, P.G. Developing an Input-Output Based Method to Estimate a National-Level Energy Return on Investment (EROI). *Energies* **2017**, *10*, 534.
https://doi.org/10.3390/en10040534

**AMA Style**

Brand-Correa LI, Brockway PE, Copeland CL, Foxon TJ, Owen A, Taylor PG. Developing an Input-Output Based Method to Estimate a National-Level Energy Return on Investment (EROI). *Energies*. 2017; 10(4):534.
https://doi.org/10.3390/en10040534

**Chicago/Turabian Style**

Brand-Correa, Lina I., Paul E. Brockway, Claire L. Copeland, Timothy J. Foxon, Anne Owen, and Peter G. Taylor. 2017. "Developing an Input-Output Based Method to Estimate a National-Level Energy Return on Investment (EROI)" *Energies* 10, no. 4: 534.
https://doi.org/10.3390/en10040534