Estimating elasticity of substitution between energy and other inputs for Iran using a multi-stage CES production function

Document Type : Research Article



The main goal of this paper is to estimate the elasticity of substitution between energy and other factors of production by using a multi-stage CES production function. In order to achieve this goal, we design a nested CES production function with four inputs, labor, capital, energy and investment in research and development for Iranian economy. This nonlinear production function is estimated by continuous genetic algorithms method. This method is relatively more efficient than traditional econometrics approach. In the first stage, three different functions are estimated and the best one is selected.    In the next stage, we have calculated the elasticity of substitution between energy and other inputs of production. Our choice of nonlinear production function, the explanatory variables, and also the estimation method make this research different from those already done for Iran. The results indicate that one percent increase in labor force reduces energy consumption by 0.56 percent.  We also find that one percent increase in physical capital decreases energy use by 0.59 percent, and similarly one percent increase in investment in R&D (Research and Development) might reduce energy consumption by 0.46 percent. Furthermore, we calculate marginal products of different input for various years and observe that the marginal product of labor has increased after Iran-Iraq imposed war. Moreover the marginal product of energy has increased since 1995. This might be a result of energy saving policy implemented in Iran after this year. 


آذربایجانی، کریم؛ راکی، مولود و رنجبر، همایون (1390)؛ تأثیر متنوع­سازی صـادرات بر بهره­وری کل عوامل تولید و رشد اقتصادی (رویکرد داده­های تابلویی در کشورهای گروه دی هشت)، پژوهش­های رشد و توسعه اقتصادی، شماره 3: 165-201.
بانک مرکزی جمهوری اسلامی ایران، نماگرهای اقتصادی، سال­های مختلف.
 بانک مرکزی جمهوری ایران، گزارش اقتصادی و ترازنامه، سال­های مختلف.
خدادادکاشی، فرهاد و جانی، سیاوش (1390)؛ بررسی پویای رفتار تولید کنندگان در استفاده از نهاده­ها بر مبنای تابع تولید دو مرحله­ای CES، با تأکید بر اصلاح الگوی مصرف انرژی در تولید و ارتقای اشتغال، مطالعات اقتصاد انرژی، سال هشتم، شماره 30: 97-124.
دلیری، حسن و رنانی، محسن (1389)؛ سرمایه اجتماعی چگونه وارد تابع تولید می­شود؟ (طراحی یک الگوی نظری و آزمون آن در چارچوب یک مدل رشد درونزا)، اقتصاد تطبیقی، سال اول، شماره اول: 41-68.
عاقلی­کهنه­شهری، لطفعلی (1385)؛ برآورد تابع تولید معادن کشور، پژوهشهای اقتصادی، شماره 6 (1): 33-49
مشیری، سعید و نیک­پور، سمیه (1386)؛ تأثیر فن­آوری اطلاعات و ارتباطات و سرریزهای آن بر رشد اقتصادی کشور های جهان، پژوهش­های اقتصادی ایران، سال نهم، شماره 33: 75-103.
محمودزاده، محمود (1389)؛ اثرات فناوری اطلاعات و ارتباطات بر بهره‌وری کل عوامل تولید در کشور‌های درحال­توسعه منتخب، پژوهشنامه بازرگانی، شماره 57: 64 – 29.
وزارت نیرو، ترازنامه انرژی (سال­های مختلف).
Alan, S.M. and G.R. Richard (1992); Buying Greenhouse Insurance: The Economic Costs of CO2 Emission Limits, MIT Press
Arrow K.J., H.B. Chenery, B.S. Minhas B and R.M. Solow (1961); Capital-Labor Substitution and Economic Efficiency, Review of Economics and Statistics, 43(3), 225- 250.
Burniaux, J. M.; Martin, J.; Nicoletti, G. and J.O. Martins (1991); GREEN a Multi-Sector, Multi Region General Equilibrium Model for Quantifying the Costs of Curbing CO2 Emissions: A Technical Manual, OECD Economics Department Working Papers, No. 116,
Backus, D. K., Crucini, M. J., February (2000); Oil prices and the terms of trade. Journal of International Economics 50 (1), 185–213.
Beckman, J., Hertel, T., (2010); Why previous estimates of the cost of climate mitigation are likely too low. GTAP Working Paper 54 (version 3).
Bodenstein, M., Erceg, C. J., Guerrieri, L., March (2011); Oil shocks and external adjustment. Journal of International Economics 83 (2), 168–184.
Burniaux, J.-M., Truong, T., (2002); GTAP-E: an energy-environmental version of the GTAP model. GTAP Technical Paper 16.
Chang, K. P. (1994); Capital-Energy Substitution and Multilevel CES Production Function." Energy Economics, 16(1), 22-26.
Chang, K.-P., (1994); Capital-energy substitution and the multi-level production function. Energy Economics 16 (1), 22–26.
David, P., van de Klundert, T, (1965); Biased efficiency growth and capital-labour substituion in the U.S., 1899-1960. American Economic Review 55, 357–394.
De La Grandville, O., (1989); In quest of the Slutsky diamond. American Economic Review 79, 468–481.
De La Grandville, O., (2009); Economic growth: a united approach. Cambridge, UK: Cambridge University Press.
De Miguel, C., Manzano, B., July (2006); Optimal oil taxation in a small open economy. Review of Economic Dynamics 9 (3), 438–454.
Dhawan, R., Jeske, K., Silos, P., (2010); Productivity, energy prices and the Great Moderation: a new link. Review of Economic Dynamics 13 (3), 715–724.
Dupuy, A. and de Grip A. (2006); Elasticity of Substitution and productivity, Capital and Skill Intensity Differences Across Firms, Economics Letters 90, 340-347.
Haupt R. L. and S. E. Haupt (1996); Practical Genetic Algorithms, Second Edition, A JOHN WILEY & SONS, INC., PUBLICATION
Jacoby, H. D., Reilly, J. M., McFarland, J. R., Paltsev, S., November (2006); Technology and technical change in the MIT EPPA model. Energy Economics 28 (5-6), 610–631.
Kemfert, C., (1998); Estimated substitution elasticities of a nested CES production function approach for Germany. Energy Economics 20 (3), 249–264.
Kemfert, C., Heinz, W., (2000); Energy-capital-labour substitution and the economic effects of CO2 abatement: Evidence for Germany. Journal of Policy Modeling 22 (6), 641–660.
Kazuo S. (1967); Two Level Constant – Elasticity of Substitution Production Function, 34(2), 201-218
Klump, R., Saam, M., (2007); Calibration of Normalized CES Production Functions in Dynamic Models. Goethe University Frankfurt.
Kwon, Hyeog Ug and Tomohiko Inui (2003); R&D and productivity growth in Japanese manufacturing firms. Economic and Social Research Institute Discussion Paper No. 44.
Klump, R., de la Grandville, O., (2000); Economic growth and the elasticity of substitution: Two theorems and some suggestions. American Economic Review 90 (1), 282–291.
Kuper, G., van Soest, D., (2003); Path-dependency and input substitution: Implications for energy policy modelling. Energy Economics 25, 397–407.
Lecca, P., Swales, K., Turner, K., (2011); An investigation of issues relating to where energy should enter the production function. Economic Modelling 28 (6), 2832–2841.
Lv, Z.; Guo, J. and Y. Xi (2009); Econometric Estimate and Selection on China Energy CES Production Function. China Popul Resources Environ, 19(4), 156–16
Li, Z. (2000); Econometrics, Higher education press, Beijing, China Kmenta J. (1967), One the Estimation of the CES Production Function, International Economic Review, 8, 180-189.
Markandya, A. and S. Pedroso-Galinato (2007); How Substitutable is Natural Capital? Environment Resource Economic, 37, 297–312.
Mishra, S.K. (2006); Globalization and Structural changes in the Indian Industrial Sector: An Analysis of Production Functions, MPRA Paper No. 1333.
Michalewicz, Z. (1994); Genetic Algorithms + Data Structures = Evolution Programs, Second Edition, New York, Springer Verlag.
Prywes, M., January (1986); A nested CES approach to capital-energy substitution. Energy Economics 8 (1), 22–28.
Sato, K. (1967); Two level constant elasticity of substitution production function, Review of Economics and Statistics, 34(2), 201-18.
Schubert, S., Turnovsky, S., (2011); The impact of energy prices on growth and welfare in a developing open economy. Open Economies Review 22 (3), 365–386.
Sue Wing, I., (2003); Induced technical change and the cost of climate policy. Tech. rep., MIT Joint Program on the Science and Policy of Global Change Report 102.
Van der Werf, E., November (2008); Production functions for climate policy modeling: an empirical analysis. Energy Economics 30 (6), 2964–2979.
Vinals, J.M., Oct-Nov (1984); Energy-capital substitution, wage flexibility and aggregate output supply. European Economic Review 26 (1-2), 229–245.
Wang, Jiann-Chyuan and Kuen-Hung Tsai (2003); Productivity Growth and R&D expenditure in Taiwan's manufacturing firms, NBER Working Paper No 9724.