IDEAS home Printed from https://ideas.repec.org/a/eee/energy/v336y2025ics0360544225041416.html

Estimating elasticities of substitution and price elasticities of industrial demand using different levels of aggregation for energy inputs

Author

Listed:
  • Mardones, Cristian
  • Henríquez, Valentina

Abstract

Elasticities are key parameters in economic models to evaluate climate or energy policies, but estimates for disaggregated energy inputs are lacking in the empirical literature. This research estimates elasticities of substitution and price elasticities of demand for energy inputs in Chile through an industrial demand system based on the translog cost function. Additionally, the effect of aggregation levels on the values of elasticities is explicitly analyzed, a comparison that has typically been made in previous literature through sensitivity analysis. For the above, data from the National Annual Industrial Survey and econometric methods for nonlinear regression systems (NLS) are used. The demand system estimates are sensitized through regression with or without theoretical restrictions on the coefficients and four specifications that differ in the number of explanatory variables to determine the most precise and robust elasticities. The results show that the model with the greatest disaggregation of energy inputs (electricity, coal, coke, fuel oil No. 6, diesel, gasoline, kerosene, liquefied propane gas, natural gas, liquefied natural gas, and biomass) is the one that provides the most reasonable estimations for price elasticities, but elasticities of substitution do not necessarily improve with the finest level of detail. Finally, the usefulness of the elasticities obtained is exemplified by simulating the change in consumption and emissions at the firm level if a carbon tax of 50 USD/tCO2 is applied.

Suggested Citation

  • Mardones, Cristian & Henríquez, Valentina, 2025. "Estimating elasticities of substitution and price elasticities of industrial demand using different levels of aggregation for energy inputs," Energy, Elsevier, vol. 336(C).
    • Handle: RePEc:eee:energy:v:336:y:2025:i:c:s0360544225041416
    DOI: 10.1016/j.energy.2025.138499
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0360544225041416
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.energy.2025.138499?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Khalid, Waqar & Özdeşer, Hüseyin & Jalil, Abdul, 2021. "An empirical analysis of inter-factor and inter-fuel substitution in the energy sector of Pakistan," Renewable Energy, Elsevier, vol. 177(C), pages 953-966.
    2. Xu, Qi & Liu, Kui, 2024. "Hero or Devil: A comparison of different carbon tax policies for China," Energy, Elsevier, vol. 306(C).
    3. Sun, Xiaojun & Lei, Yalin & Wang, Xue-Chao & Zhao, Jun & Varbanov, Petar Sabev, 2024. "Directional nature of technological progress in the petrochemical industry prompting energy marginal substitution," Energy, Elsevier, vol. 310(C).
    4. Wei, Taoyuan, 2024. "Multiplier effect on reducing carbon emissions of joint demand and supply side measures in the hydrogen market," Energy, Elsevier, vol. 305(C).
    5. Henningsen, Arne & Henningsen, Geraldine & van der Werf, Edwin, 2019. "Capital-labour-energy substitution in a nested CES framework: A replication and update of Kemfert (1998)," Energy Economics, Elsevier, vol. 82(C), pages 16-25.
    6. Osorio-Aravena, Juan Carlos & Aghahosseini, Arman & Bogdanov, Dmitrii & Caldera, Upeksha & Ghorbani, Narges & Mensah, Theophilus Nii Odai & Khalili, Siavash & Muñoz-Cerón, Emilio & Breyer, Christian, 2021. "The impact of renewable energy and sector coupling on the pathway towards a sustainable energy system in Chile," Renewable and Sustainable Energy Reviews, Elsevier, vol. 151(C).
    7. Wang, Yubao & Zhen, Junjie, 2024. "Drivers and strategic options for renewable energy development in China: LMDI-elasticity analysis perspective based on photovoltaic and wind energy," Energy, Elsevier, vol. 309(C).
    8. Pindyck, Robert S, 1979. "Interfuel Substitution and the Industrial Demand for Energy: An International Comparison," The Review of Economics and Statistics, MIT Press, vol. 61(2), pages 169-179, May.
    9. Lifan Yang & Junhua Liu & Weixin Yang, 2023. "Impacts of the Sustainable Development of Cross-Border E-Commerce Pilot Zones on Regional Economic Growth," Sustainability, MDPI, vol. 15(18), pages 1-28, September.
    10. Muhammad Yousaf Raza & Songlin Tang, 2022. "Inter-Fuel Substitution, Technical Change, and Carbon Mitigation Potential in Pakistan: Perspectives of Environmental Analysis," Energies, MDPI, vol. 15(22), pages 1-20, November.
    11. Han Zhang & Jixian Meng & King Ning Yau, 2024. "Carbon pricing or non-pricing for developing countries? A dual-track strategy for decarbonization in China," Applied Economics Letters, Taylor & Francis Journals, vol. 31(5), pages 477-483, March.
    12. Acharya, Satish & Piantanakulchai, Mongkut, 2025. "The implications of production efficiency improvement and subsidy removal strategies during the transition to higher blends of biodiesel in Thailand’s transport sector," Energy, Elsevier, vol. 332(C).
    13. Lin, Boqiang & Liu, Weisheng, 2017. "Estimation of energy substitution effect in China's machinery industry--based on the corrected formula for elasticity of substitution," Energy, Elsevier, vol. 129(C), pages 246-254.
    14. Kat, B. & Şahin, Ü. & Teimourzadeh, S. & Tör, O.B. & Voyvoda, E. & Yeldan, A.E., 2024. "A new energy-economy-environment modeling framework: Insights from decarbonization of the Turkish power Sector towards net-zero Emission targets," Energy, Elsevier, vol. 302(C).
    15. Yue, Xianghua & Peng, Michael Yao-Ping & Anser, Muhammad Khalid & Nassani, Abdelmohsen A. & Haffar, Mohamed & Zaman, Khalid, 2022. "The role of carbon taxes, clean fuels, and renewable energy in promoting sustainable development: How green is nuclear energy?," Renewable Energy, Elsevier, vol. 193(C), pages 167-178.
    16. Shaik, Saleem, 2024. "Contribution of climate change to sector-source energy demand," Energy, Elsevier, vol. 294(C).
    17. Alan D. Woodland, 1993. "A Micro-Econometric Analysis of the Industrial Demand for Energy in NSW," The Energy Journal, , vol. 14(2), pages 57-89, April.
    18. Weixin Yang & Xiu Zheng & Yunpeng Yang, 2024. "Impact of Environmental Regulation on Export Technological Complexity of High-Tech Industries in Chinese Manufacturing," Economies, MDPI, vol. 12(2), pages 1-29, February.
    19. Dong, Jingrong & Zhang, Wenqing & Chen, Yuke & Li, Tingting, 2024. "Does technological progress mode affect just energy transition? A seemingly unrelated regression analysis based on Chinese provincial panel data," Energy, Elsevier, vol. 313(C).
    20. Berry, Audrey, 2019. "The distributional effects of a carbon tax and its impact on fuel poverty: A microsimulation study in the French context," Energy Policy, Elsevier, vol. 124(C), pages 81-94.
    21. Marie Hyland & Stefanie Haller, 2018. "Firm-level Estimates of Fuel Substitution: An Application toCarbon Pricing," The Energy Journal, , vol. 39(6), pages 71-98, November.
    22. repec:aen:journl:ej39-6-hylan is not listed on IDEAS
    23. Niklas Döbbeling-Hildebrandt & Klaas Miersch & Tarun M. Khanna & Marion Bachelet & Stephan B. Bruns & Max Callaghan & Ottmar Edenhofer & Christian Flachsland & Piers M. Forster & Matthias Kalkuhl & Ni, 2024. "Systematic review and meta-analysis of ex-post evaluations on the effectiveness of carbon pricing," Nature Communications, Nature, vol. 15(1), pages 1-12, December.
    24. Arcila, Andres & Baker, John D., 2022. "Evaluating carbon tax policy: A methodological reassessment of a natural experiment," Energy Economics, Elsevier, vol. 111(C).
    25. Bretschger, Lucas & Jo, Ara, 2024. "Complementarity between labor and energy: A firm-level analysis," Journal of Environmental Economics and Management, Elsevier, vol. 124(C).
    26. Antoszewski, Michał, 2019. "Wide-range estimation of various substitution elasticities for CES production functions at the sectoral level," Energy Economics, Elsevier, vol. 83(C), pages 272-289.
    27. Zha, Donglan & Zhou, Dequn, 2014. "The elasticity of substitution and the way of nesting CES production function with emphasis on energy input," Applied Energy, Elsevier, vol. 130(C), pages 793-798.
    28. Chen, Qian & Zha, Donglan & Salman, Muhammad, 2022. "The influence of carbon tax on CO2 rebound effect and welfare in Chinese households," Energy Policy, Elsevier, vol. 168(C).
    29. Jacobs, Leif & Quack, Lara & Mechtel, Mario, 2022. "Distributional effects of carbon pricing by transport fuel taxation," Energy Economics, Elsevier, vol. 114(C).
    30. Solow, John L, 1987. "The Capital-Energy Complementarity Debate Revisited," American Economic Review, American Economic Association, vol. 77(4), pages 605-614, September.
    31. Rivera, Nathaly M. & Ruiz-Tagle, J. Cristobal & Spiller, Elisheba, 2024. "The health benefits of solar power generation: Evidence from Chile," Journal of Environmental Economics and Management, Elsevier, vol. 126(C).
    32. Rentschler, Jun & Kornejew, Martin, 2017. "Energy price variation and competitiveness: Firm level evidence from Indonesia," Energy Economics, Elsevier, vol. 67(C), pages 242-254.
    33. Agostini, Claudio A. & Jiménez, Johanna, 2015. "The distributional incidence of the gasoline tax in Chile," Energy Policy, Elsevier, vol. 85(C), pages 243-252.
    34. Feng Wang & Yijie Jiang & Wulin Zhang & Fang Yang, 2019. "Elasticity of factor substitution and driving factors of energy intensity in China’s industry," Energy & Environment, , vol. 30(3), pages 385-407, May.
    35. Haller, Stefanie A. & Hyland, Marie, 2014. "Capital–energy substitution: Evidence from a panel of Irish manufacturing firms," Energy Economics, Elsevier, vol. 45(C), pages 501-510.
    36. Mortha, Aline & Arimura, Toshi H., 2024. "Purchase or generate? An analysis of inter-fuel substitution and electricity generation in Japanese manufacturing plants," Energy Economics, Elsevier, vol. 139(C).
    37. Runst, Petrik & Höhle, David, 2022. "The German eco tax and its impact on CO2 emissions," Energy Policy, Elsevier, vol. 160(C).
    38. Sakiru Adebola Solarin & Mufutau Opeyemi Bello, 2022. "Wind energy and sustainable electricity generation: evidence from Germany," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 24(7), pages 9185-9198, July.
    39. Mukhtarov, Shahriyar & Yüksel, Serhat & Dinçer, Hasan, 2022. "The impact of financial development on renewable energy consumption: Evidence from Turkey," Renewable Energy, Elsevier, vol. 187(C), pages 169-176.
    40. Boonman, Hettie & Pisciella, Paolo & Reynès, Frédéric, 2024. "The macroeconomic impact of policy measures, technological progress and societal attitude in energy transition scenarios," Energy, Elsevier, vol. 297(C).
    41. Phu Viet Le, 2019. "Energy demand and factor substitution in Vietnam: evidence from two recent enterprise surveys," Journal of Economic Structures, Springer;Pan-Pacific Association of Input-Output Studies (PAPAIOS), vol. 8(1), pages 1-17, December.
    42. Ara Jo, 2025. "Substitution Between Clean And Dirty Energy With Biased Technical Change," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 66(2), pages 883-902, May.
    43. repec:aen:journl:1993v14-02-a04 is not listed on IDEAS
    44. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-676, August.
    45. Ling, Long & Hu, Lu & Zhao, Xing, 2025. "How to achieve net-zero carbon emission? Evidence from energy-biased technical change," Energy, Elsevier, vol. 329(C).
    46. Clàudia Cruanyes & Olga Alcaraz & Bàrbara Sureda, 2024. "Evaluating long-term low emission development strategies and implications for the remaining global carbon budget," Climate Policy, Taylor & Francis Journals, vol. 24(5), pages 691-705, May.
    47. Pesaran, M Hashem & Pierse, Richard G & Kumar, Mohan S, 1989. "Econometric Analysis of Aggregation in the Context of Linear Prediction Models," Econometrica, Econometric Society, vol. 57(4), pages 861-888, July.
    48. Fu, Yupeng & Huang, Guohe & Zhai, Mengyu & Su, Shuai, 2025. "Factorial enviro-economic equilibrium analysis for the effects of hierarchical carbon policy on China's socio-economic and environmental systems," Energy, Elsevier, vol. 320(C).
    49. Zhang, Tianyuan & Tan, Qian & Cai, Yanpeng, 2024. "General equilibrium analysis of carbon tax policy on water-energy-food nexus efficiency," Energy, Elsevier, vol. 304(C).
    50. Jo, Ara & Miftakhova, Alena, 2024. "How constant is constant elasticity of substitution? Endogenous substitution between clean and dirty energy," Journal of Environmental Economics and Management, Elsevier, vol. 125(C).
    51. W. Erwin Diewert, 2022. "Duality in Production," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 3, pages 57-168, Springer.
    52. Lagomarsino, Elena, 2020. "Estimating elasticities of substitution with nested CES production functions: Where do we stand?," Energy Economics, Elsevier, vol. 88(C).
    53. Mardones, Cristian & García, Catalina, 2020. "Effectiveness of CO2 taxes on thermoelectric power plants and industrial plants," Energy, Elsevier, vol. 206(C).
    54. Fuss, Melvyn A., 1977. "The demand for energy in Canadian manufacturing : An example of the estimation of production structures with many inputs," Journal of Econometrics, Elsevier, vol. 5(1), pages 89-116, January.
    55. Devarajan Shantayanan & Go Delfin S & Robinson Sherman & Thierfelder Karen, 2011. "Tax Policy to Reduce Carbon Emissions in a Distorted Economy: Illustrations from a South Africa CGE Model," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 11(1), pages 1-24, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mei Lu & Michael G Pollitt, 2025. "Will high carbon prices reduce fossil fuel use in China? Evidence from price elasticity estimates using firm data," Working Papers EPRG2508, Energy Policy Research Group, Cambridge Judge Business School, University of Cambridge.
    2. Cao, Jing & Ho, Mun S. & Ma, Rong, 2020. "Analyzing carbon pricing policies using a general equilibrium model with production parameters estimated using firm data," Energy Economics, Elsevier, vol. 92(C).
    3. Lagomarsino, Elena, 2020. "Estimating elasticities of substitution with nested CES production functions: Where do we stand?," Energy Economics, Elsevier, vol. 88(C).
    4. Zhu, Xuehong & Zeng, Anqi & Zhong, Meirui & Huang, Jianbai, 2021. "Elasticity of substitution and biased technical change in the CES production function for China's metal-intensive industries," Resources Policy, Elsevier, vol. 73(C).
    5. Zhao, Hongli & Lin, Boqiang, 2019. "Resources allocation and more efficient use of energy in China's textile industry," Energy, Elsevier, vol. 185(C), pages 111-120.
    6. Elena Lagomarsino & Karen Turner, 2017. "Is the production function Translog or CES? An empirical illustration using UK data," Working Papers 1713, University of Strathclyde Business School, Department of Economics.
    7. Benmir, Ghassane & Mori, Aditya & Roman, Josselin & Tarsia, Romano, 2025. "Beneath the trees: the influence of natural capital on shadow price dynamics in a macroeconomic model with uncertainty," LSE Research Online Documents on Economics 128516, London School of Economics and Political Science, LSE Library.
    8. Fernández-López, Reinier & Mardones, Cristian, 2025. "Impact evaluation of the carbon tax in Chile using the difference-in-differences method," Energy, Elsevier, vol. 318(C).
    9. He, Yongda & Lin, Boqiang, 2019. "Heterogeneity and asymmetric effects in energy resources allocation of the manufacturing sectors in China," Energy, Elsevier, vol. 170(C), pages 1019-1035.
    10. Haller, Stefanie A. & Hyland, Marie, 2014. "Capital–energy substitution: Evidence from a panel of Irish manufacturing firms," Energy Economics, Elsevier, vol. 45(C), pages 501-510.
    11. Mardones, Cristian & Ortega, José, 2021. "Are the emissions trading systems’ simulations generated with a computable general equilibrium model sensitive to the nested production structure?," Applied Energy, Elsevier, vol. 298(C).
    12. Bataille, Chris & Melton, Noel, 2017. "Energy efficiency and economic growth: A retrospective CGE analysis for Canada from 2002 to 2012," Energy Economics, Elsevier, vol. 64(C), pages 118-130.
    13. Bello, Mufutau Opeyemi & Solarin, Sakiru Adebola & Yen, Yuen Yee, 2018. "Hydropower and potential for interfuel substitution: The case of electricity sector in Malaysia," Energy, Elsevier, vol. 151(C), pages 966-983.
    14. Mufutau Opeyemi Bello & Sakiru Adebola Solarin, 2022. "Searching for sustainable electricity generation: The possibility of substituting coal and natural gas with clean energy," Energy & Environment, , vol. 33(1), pages 64-84, February.
    15. Matthias Leuthard, 2025. "Equity and efficiency of carbon tax policies in Switzerland with endogenous energy substitution," Swiss Journal of Economics and Statistics, Springer;Swiss Society of Economics and Statistics, vol. 161(1), pages 1-24, December.
    16. Bardazzi, Rossella & Oropallo, Filippo & Pazienza, Maria Grazia, 2015. "Do manufacturing firms react to energy prices? Evidence from Italy," Energy Economics, Elsevier, vol. 49(C), pages 168-181.
    17. Marie Hyland & Stefanie Haller, 2018. "Firm-level Estimates of Fuel Substitution: An Application toCarbon Pricing," The Energy Journal, , vol. 39(6), pages 71-98, November.
    18. Wen, Feng & Wu, Kun & Wang, Wenfu & Chen, Xue-Li & Liu, Dandan & Song, Malin, 2026. "Do green tax policies shape China's household consumption structure? A production-side perspective," Energy Policy, Elsevier, vol. 208(C).
    19. Malliet, Paul & Reynès, Frédéric G., 2022. "Empirical estimates of the elasticity of substitution of a KLEM production function without nesting constraints: The case of the Variable Output Elasticity-Cobb Douglas," Conference papers 333423, Purdue University, Center for Global Trade Analysis, Global Trade Analysis Project.
    20. Bazhanov, Andrei, 2007. "The peak of oil extraction and consistency of the government's short- and long-run policies," MPRA Paper 2507, University Library of Munich, Germany.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:energy:v:336:y:2025:i:c:s0360544225041416. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/energy .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.