Constant elasticity of substitution functions for energy modeling in general equilibrium integrated assessment models: a critical review and recommendations

Abstract

Applying constant elasticity of substitution (CES) functions in general equilibrium integrated assessment models (GE-IAMs) for the substitution of technical factor inputs (e.g., replacing fossil fuels) fails to match historically observed patterns in energy transition dynamics. This method of substitution is also very sensitive to the structure of CES implementation (nesting) and parameter choice. The resulting methodology-related artifacts are (i) the extension of the status quo technology shares for future energy supply relying on fossil fuels with carbon capture, biomass, and nuclear; (ii) monotonically increasing marginal abatement costs of carbon; and (iii) substitution of energy with non-physical inputs (e.g., knowledge and capital) without conclusive evidence that this is possible to the extent modeled. We demonstrate these issues using simple examples and analyze how they are relevant in the case of four major CES-based GE-IAMs. To address this, we propose alternative formulations either by opting for carefully applied perfect substitution for alternative energy options or by introducing dynamically variable elasticity of substitution as a potential intermediate solution. Nevertheless, complementing the economic analysis with physical modeling accounting for storage and resource availability at a high resolution spatially and temporally would be preferable.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3

References

  1. Arrow KJ, Chenery HB, Minhas BS, Solow RM (1961) Capital-labor substitution and economic efficiency. Rev Econ Stat 43:225–250

    Article  Google Scholar 

  2. Ayres RU, Ayres LW, Warr B (2003) Exergy, power and work in the US economy, 1900–1998. Energy 28:219–273. https://doi.org/10.1016/S0360-5442(02)00089-0

    Article  Google Scholar 

  3. Barreto L, Kemp R (2008) Inclusion of technology diffusion in energy-systems models: some gaps and needs. J Clean Prod 16:S95–S101. https://doi.org/10.1016/j.jclepro.2007.10.008

    Article  Google Scholar 

  4. Bosetti V, Carraro C, Galeotti M, Massetti E (2006) WITCH: a world induced technical change hybrid model. Energy J 27:13–37

    Google Scholar 

  5. Bosetti V, Marangoni G, Borgonovo E et al (2015) Sensitivity to energy technology costs: a multi-model comparison analysis. Energy Policy 80:244–263. https://doi.org/10.1016/j.enpol.2014.12.012

    Article  Google Scholar 

  6. Breyer C, Bogdanov D, Gulagi A et al (2017) On the role of solar photovoltaics in global energy transition scenarios. Prog Photovolt Res Appl 6:545–520. https://doi.org/10.1002/pip.2885

    Google Scholar 

  7. Cai Y, Newth D, Finnigan J, Gunasekera D (2015) A hybrid energy-economy model for global integrated assessment of climate change, carbon mitigation and energy transformation. Appl Energy 148:381–395. https://doi.org/10.1016/j.apenergy.2015.03.106

    Article  Google Scholar 

  8. Carrara S, Marangoni G (2017) Including system integration of variable renewable energies in a constant elasticity of substitution framework: the case of the WITCH model. Energy Econ 64:612–626. https://doi.org/10.1016/j.eneco.2016.08.017

    Article  Google Scholar 

  9. Cheng AYC (2005) Economic Modeling of Intermittency in Wind Power Generation. MS thesis, Supervisor H. D. Jacoby. Massachusetts Institute of Technology. Retrieved from: http://web.mit.edu/globalchange/www/docs/Cheng_MS_05.pdf

  10. Christensen CM (1997) The innovator’s dilemma. When new technologies cause great firms to fail. Harvard Business School Press, Boston

    Google Scholar 

  11. Elliston B, MacGill I, Diesendorf M (2013) Least cost 100% renewable electricity scenarios in the Australian National Electricity Market. Energy Policy 59:270–282. https://doi.org/10.1016/j.enpol.2013.03.038

    Article  Google Scholar 

  12. Fouquet R (2010) The slow search for solutions: lessons from historical energy transitions by sector and service. Energy Policy 38:6586–6596. https://doi.org/10.1016/j.enpol.2010.06.029

    Article  Google Scholar 

  13. Frei CW, Haldi PA, Sarlos G (2003) Dynamic formulation of a top-down and bottom-up merging energy policy model. Energy Policy 31:1017–1031. https://doi.org/10.1016/s0301-4215(02)00170-2

    Article  Google Scholar 

  14. Gohin A, Hertel TW (2003) A note on the CES functional form and its use in the GTAP model (No. 2). Center for Global Trade Analysis, Purdue University, pp 1–14. Retrieved from https://www.gtap.agecon.purdue.edu/resources/res_display.asp?RecordID=1370

  15. Görig M, Breyer C (2016) Energy learning curves of PV systems. Environ Prog Sustain Energy 35:914–923. https://doi.org/10.1002/ep.12340

    Article  Google Scholar 

  16. Grubler A, Nakicenovic N, Victor DG (1999) Dynamics of energy technologies and global change. Energy Policy 27:247–280

  17. Grubler A, Nakicenovic N (1991) Long waves, technology diffusion, and substitution. Review (FernandBraudel Center) 14(2):313–343. https://doi.org/10.2307/40241184

  18. Hanoch G (1971) CRESH production functions. Econometrica 39:695–712

    Article  Google Scholar 

  19. Jacobson MZ, Delucchi MA (2011) Providing all global energy with wind, water, and solar power, Part I: technologies, energy resources, quantities and areas of infrastructure, and materials. Energy Policy 39:1154–1169. https://doi.org/10.1016/j.enpol.2010.11.040

    Article  Google Scholar 

  20. Jacobson MZ, Delucchi MA, Cameron MA, Frew BA (2015) Low-cost solution to the grid reliability problem with 100% penetration of intermittent wind, water, and solar for all purposes. Proc Natl Acad Sci 112:15060–15065. https://doi.org/10.1073/pnas.1510028112

    Article  Google Scholar 

  21. Joskow PL (2011) Comparing the costs of intermittent and dispatchable electricity generating technologies. Am Econ Rev:238–241

  22. Kriegler E, Petermann N, Krey V et al (2015) Diagnostic indicators for integrated assessment models of climate policy. Technol Forecast Soc Chang 90:45–61. https://doi.org/10.1016/j.techfore.2013.09.020

    Article  Google Scholar 

  23. Kuik O, Brander L, Tol RSJ (2009) Marginal abatement costs of greenhouse gas emissions: a meta-analysis. Energy Policy 37:1395–1403. https://doi.org/10.1016/j.enpol.2008.11.040

    Article  Google Scholar 

  24. Luderer G, Bosetti V, Jakob M et al (2011) The economics of decarbonizing the energy system—results and insights from the RECIPE model intercomparison. Clim Chang 114:9–37. https://doi.org/10.1007/s10584-011-0105-x

    Article  Google Scholar 

  25. Luderer G, Krey V, Calvin K et al (2013) The role of renewable energy in climate stabilization: results from the EMF27 scenarios. Clim Chang 123:427–441. https://doi.org/10.1007/s10584-013-0924-z

    Article  Google Scholar 

  26. Luderer G, Leimbach M, Bauer N, Kriegler E, Baumstark L, Bertram C et al (2015) Description of the REMIND model (Version 1.6) (pp. 1–44). Potsdam Institute. Retrieved from: https://www.pikpotsdam.de/research/sustainable-solutions/research/global-energy-systems/remind16_description_2015_11_30_final

  27. Luderer G, Pietzcker RC, Carrara S et al (2017) Assessment of wind and solar power in global low-carbon energy scenarios: an introduction. Energy Econ 64:542–551. https://doi.org/10.1016/j.eneco.2017.03.027

    Article  Google Scholar 

  28. Lund H, Mathiesen BV (2009) Energy system analysis of 100% renewable energy systems—the case of Denmark in years 2030 and 2050. Energy 34:524–531. https://doi.org/10.1016/j.energy.2008.04.003

    Article  Google Scholar 

  29. Maggio G, Cacciola G (2009) A variant of the Hubbert curve for world oil production forecasts. Energy Policy 37:4761–4770. https://doi.org/10.1016/j.enpol.2009.06.053

    Article  Google Scholar 

  30. Mansfield E (1961) Technical change and the rate of imitation. Econometrica 29:741–766

    Article  Google Scholar 

  31. Marchetti C, Nakićenović N (1979) The dynamics of energy systems and the logistic substitution model. International Institute for Applied Systems Analysis, Laxenburg

    Google Scholar 

  32. Mercure JF, Pollitt H, Chewpreecha U et al (2014) The dynamics of technology diffusion and the impacts of climate policy instruments in the decarbonisation of the global electricity sector. Energy Policy 73:686–700. https://doi.org/10.1016/j.enpol.2014.06.029

    Article  Google Scholar 

  33. Nagy B, Farmer JD, Bui QM, Trancik JE (2013) Statistical basis for predicting technological progress. PLoS One 8:e52669. https://doi.org/10.1371/journal.pone.0052669.g001

    Article  Google Scholar 

  34. Nordhaus WD (1992) An optimal transition path for controlling greenhouse gases. Science 258:1315–1319

    Article  Google Scholar 

  35. Norton JA, Bass FM (1987) A diffusion theory model of adoption and substitution for successive generations of high-technology products. Manag Sci 33:1069

    Article  Google Scholar 

  36. Paltsev S, Reilly J, Jacoby H, Eckaus R, McFarland J, Sarofim M et al (2005) The MIT emissions prediction and policy analysis (EPPA) model: version 4 (No. 125). MIT joint program on the science and policy of global change, pp 1–78. Retrieved from: http://dspace.mit.edu/bitstream/handle/1721.1/29790/MITJPSPGC_Rpt125.pdf?sequence

  37. Pearce J, Weyant JP (2008) Insights not numbers: the appropriate use of economic models. White Paper. Pew Center for Global Climate Change, pp 1–29. Retrieved from: http://www.c2es.org/docUploads/insights-not-numbers.pdf

  38. Pietzcker RC, Ueckerdt F, Carrara S et al (2017) System integration of wind and solar power in integrated assessment models: a cross-model evaluation of new approaches. Energy Econ 1–17. doi:https://doi.org/10.1016/j.eneco.2016.11.018

  39. Porter ME, Van der Linde C (1995) Toward a new conception of the environment-competitiveness relationship. J Econ Perspect 9:97–118. https://doi.org/10.1257/jep.9.4.97

    Article  Google Scholar 

  40. Rosen RA, Guenther E (2015) The economics of mitigating climate change: what can we know? Technol Forecast Soc Chang 91:93–106. https://doi.org/10.1016/j.techfore.2014.01.013

    Article  Google Scholar 

  41. Singer S (ed) (2010) The energy report: 100% renewable energy by 2050. WWF & Ecofys. Gland. Retrieved from: http://www.ecofys.com/files/files/ecofys-wwf-2011-the-energy-report.pdf

  42. Truong PT (2009) Constant elasticity of substitution (CES) production function can greatly overestimatethe economic costs of climate policies. (No. ITLS-WP-09-15). Institute of transport and logistics studies, University of Sydney, pp 1–24. Retrieved from: http://sydney.edu.au/business/__data/assets/pdf_file/0016/30634/itls-wp-09-15.pdf

  43. Trutnevyte E (2016) Does cost optimization approximate the real-world energy transition? Energy 106:182–193. https://doi.org/10.1016/j.energy.2016.03.038

    Article  Google Scholar 

  44. Ueckerdt F, Brecha R, Luderer G et al (2015) Representing power sector variability and the integration of variable renewables in long-term energy-economy models using residual load duration curves. Energy 90:1799–1814. https://doi.org/10.1016/j.energy.2015.07.006

    Article  Google Scholar 

  45. van Vuuren DP, Stehfest E, Elzen den MGJ et al (2011) RCP2.6: exploring the possibility to keep global mean temperature increase below 2°C. Clim Chang 109:95–116. https://doi.org/10.1007/s10584-011-0152-3

    Article  Google Scholar 

  46. Wilkerson JT, Leibowicz BD, Turner DD, Weyant JP (2015) Comparison of integrated assessment models: carbon price impacts on U.S. energy. Energy Policy 76:18–31. https://doi.org/10.1016/j.enpol.2014.10.011

    Article  Google Scholar 

Download references

Acknowledgements

We thank Joshua Msika and Maury Markowitz for their comments and editorial suggestions, as well as the careful reading of the two reviewers and the editor for their critical input. Finally, we acknowledge the financial support by Masdar Institute in conducting this study.

Author information

Affiliations

Authors

Corresponding author

Correspondence to Sgouris Sgouridis.

Electronic supplementary material

ESM 1

(DOCX 10009 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Kaya, A., Csala, D. & Sgouridis, S. Constant elasticity of substitution functions for energy modeling in general equilibrium integrated assessment models: a critical review and recommendations. Climatic Change 145, 27–40 (2017). https://doi.org/10.1007/s10584-017-2077-y

Download citation