**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**32451

##### Measurement of CES Production Functions Considering Energy as an Input

**Authors:**
Donglan Zha,
Jiansong Si

**Abstract:**

Because of its flexibility, CES attracts much interest in economic growth and programming models, and the macroeconomics or micro-macro models. This paper focuses on the development, estimating methods of CES production function considering energy as an input. We leave for future research work of relaxing the assumption of constant returns to scale, the introduction of potential input factors, and the generalization method of the optimal nested form of multi-factor production functions.

**Keywords:**
Bias of technical change,
CES production function,
elasticity of substitution,
energy input.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1340280

**References:**

[1] Blanchard, O.J., Nordhaus, W.D., and Phelps, E.S., 1997. The medium run. Brookings Papers on Economic Activity, 89-158.

[2] Jones, C.I., 2003. Growth, Capital Shares, and a New Perspective on Production Functions. Mimeo, University of California Berkeley.

[3] Jones, C.I., 2005. The shape of production functions and the direction of technical change. Quarterly Journal of Economics, 120(2): 517-549.

[4] Solow, R.M., 1956. A contribution to the theory of economic growth. The Quarterly Journal of Economics, 70(1): 65-94.

[5] Temple, J., 2012. The calibration of CES production functions. Journal of Macroeconomics, 34(2): 294-303.

[6] Klump, R., McAdam, P., and Willman, A., 2012. The normalized CES production function: theory and empirics. Journal of Economic Surveys, 26(5): 769-799.

[7] Cantore, C., León-Ledesma, M., and McAdam, P., 2010. Shocking stuff: technology, hours, and factor substitution. ECB Working. Paper Series No. 1278.

[8] Dickinson, H.D., 1954. A note on dynamic economics. The Review of Economic Studies, 22(3): 169-179.

[9] Pitchford, J.D., 1960. Growth and the elasticity of factor substitution. Economic Record, 36(76): 491-504.

[10] Arrow, K.J., Chenery, H.B., Minhas, B.S., and Solow, R.M., 1961. Capital-labor substitution and economic efficiency. The Review of Economics and Statistics, 43(3): 225-250.

[11] David, P.A., and Van de Klundert, T., 1965. Biased efficiency growth and capital-labor substitution in the US, 1899-1960. The American Economic Review, 55(3): 357-394.

[12] Frondel, M., and Schmidt, C.M., 2004. Facing the truth about separability: nothing works without energy. Ecological Economics, 51(3-4): 217-223.

[13] Greening, L.A., Greene, D.L., and Difiglio, C., 2000. Energy efficiency and consumption-the rebound effect-a survey. Energy Policy, 28(6): 389-401.

[14] Dimitropoulos, J., 2007. Energy productivity improvements and the rebound effect: An overview of the state of knowledge. Energy Policy, 35(12): 6354-6363.

[15] Hanley, N., McGregor, P.G., Swales, J.K., and Turner, K., 2009. Do increases in energy efficiency improve environmental quality and sustainability?. Ecological Economics, 68(3): 692-709.

[16] Sue Wing, I., 2006. Representing induced technological change in models for climate policy analysis. Energy Economics, 28(5-6): 539-562.

[17] Zha, D.L., and Zhou, D.Q., 2014. The elasticity of substitution and the way of nesting CES production function with emphasis on energy input. Applied Energy, 130(1): 793-798.

[18] Burniaux, J.M., Martin, J.P., and Nicoletti, G., 1992. GREEN a multi-sector, multi-region general equilibrium model for quantifying the costs of curbing CO2 emissions: a technical manual. OECD Publishing.

[19] Carraro, C., and Galeotti, M., 2004. Does Endogenous Technical Change Make a Difference in Climate Change Policy Analysis? A Robustness Exercise with the FEEM-RICE Model. Fondazione Eni Enrico Mattei, Working Paper N.152.04.

[20] Clarke, L., and Weyant, J., 2002. Modeling induced technological change: an overview. In A. Grübler, N. Nakicenovic, W. Nordhaus (Eds.), Technological change and the environment, Resources for the Future Press, Washington, DC.

[21] Löschel, A., 2002. Technological change in economic models of environmental policy: a survey. Ecological Economics, 43(2-3):105-126.

[22] de La Grandville, O., 1989. In quest of the Slutsky diamond. The American Economic Review, 79(3): 468-481.

[23] Klump, R., and de La Grandville, O., 2000. Economic growth and the elasticity of substitution: Two theorems and some suggestions. American Economic Review, 90(1): 282-291.

[24] Klump, R., McAdam, P., and Willman, A., 2007. Factor substitution and factor-augmenting technical progress in the United States: a normalized supply-side system approach. The Review of Economics and Statistics, 89(1): 183-192.

[25] Klump, R., and Irmen, A., 2009. Factor substitution, income distribution and growth in a generalized neoclassical model. German Economic Review, 10(4): 464-479.

[26] Xue, J., and Yip, C.K., 2012. Factor substitution and economic growth: A unified approach. Macroeconomic Dynamics, 16(4): 625-656.

[27] Saam, M., 2008. Openness to trade as a determinant of the macroeconomic elasticity of substitution. Journal of Macroeconomics, 30(2): 691-702.

[28] Kmenta, J., 1967. On estimation of the CES production function. International Economic Review, 8(2): 180-189.

[29] Hoff, A., 2004. The linear approximation of the CES function with input variables. Marine Resource Economics, 19(3): 295-306.

[30] Chetty, V.K., and Sankar, U., 1969. Bayesian estimation of the CES production function. The Review of Economic Studies, 36(3): 289-294.

[31] Van der Werf, E., 2008. Production functions for climate policy modeling: An empirical analysis. Energy Economics, 30(6): 2964-2979.

[32] Berndt, E.R., 1991. The practice of econometrics: classic and contemporary. Reading, MA: Addison-Wesley.