Abstract
In many situations, the dependence of the production or utility on the corresponding factors is described by the CES (Constant Elasticity of Substitution) functions. These functions are usually explained by postulating two requirements: an economically reasonable postulate of homogeneity (that the formulas should not change if we change a measuring unit) and a less convincing CSE requirement. In this paper, we show that the CES requirement can be replaced by a more convincing requirement—that the combined effect of all the factors should not depend on the order in which we combine these factors.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Kurowicka D, Joe H (eds) (2010) Dependence modeling: Vine copula handbook. World Scientific, Singapore
Aas K, Czado C, Frigessi A, Bakken H (2009) Pair-copula constructions of multiple dependence. Insurance Math Econ 44:82–198
Aczeél J (1965) Quasigroup-net-nomograms. Adv Math 1:383–450
Aczél J, Belousov VD, Hosszú M (1960) Generalized associativity and bisymmetry on quasigroups. Acta Math Acad Sci Hungar 11:127–136
Aczél J, Dhombres J (2008) Functional equations in several variables. Camridge University Press, Cambridge
Arrow KJ, Chenery HB, Minhas BS, Solow RM (1961) Capital-labor substitution and economic efficiency. Rev Econ Stat 43(3):225–250
Baltas G (2001) Utility-consistent brand demand systems with endogeneous category consumption: principles and marketing applications. Decis Sci 32(3):399–421
Bedford T, Cooke RM (2001) Monte Carlo simulation of vine dependent random variables for applications in uncertainty analysis. In: Proceedings of European safety and reliability conference ESREL’2001, Turin, Italy
Bedford T, Cooke RM (2002) Vines—a new graphical model for dependent random variables. Ann Stat 30(4):1031–1068
Buchanan BG, Shortliffe EH (1984) Rule based expert systems: the MYCIN experiments of the stanford heuristic programming project. Addison-Wesley, Reading
Czado C (2010) Pair-copula constructions of multivariate copulas. In: Jaworski P (ed) Copula theory and its applications. Lecture notes in statistics, vol 198. Springer, Berlin, pp 93–109
Dixit A, Steiglitz J (1977) Monopolistic competition and optimum product diversity. Am Econ Rev 67(3):297–308
Fisman R, Jakiela P, Kariv S, Markovits D (2015) The distributional preferences of an elite. Science 349(6254):1300. Artile aab096
Joe H (2010) Dependence comparisons of Vine copulae with four or more variables. In: Kurowicka D, Joe H (eds) Dependence modeling: Vine copula handbook. World Scientific, Singapore
Joe H, Hu T (1996) Multivariate distributions from mixtures of max-infinitely divisible distributions. J Multivar Anal 57(2):240–265
Joe H, Li H, Nikoloulopoulos AK (2010) Tail dependence functions and Vine copulas. J Multivar Anal 101:252–270
Jorgensen DW (2000) Econometrics. Economic modelling of producer behavior, vol 1. MIT Press, Cambridge
Klump R, McAadam P, Willaims A (2007) Factor substitution and factor augmenting technical progress in the US: a normalized supply-side system approach. Rev Econ Statisticsm 89(1):183–192
Kurowicka D, Cooke RM (2006) Uncertainty analysis with high dimensional dependence modelling. Wiley, New York
Nelsen RB (1999) An introduction to copulas. Springer, New York
Nikoloulopoulos AK (2012) Vine copulas with asymmetric tail dependence and applications to financial return data. Comput Stat Data Anal 56:3659–3673
Sklar A (1959) Fonctions de répartition á \(n\) dimensions et leurs marges. Publ Inst Statist Univ Paris 8:229–231
Solow RM (1956) A contribution to the theory of economic growth. Q J Econ 70:65–94
Sriboonchitta S, Kosheleva O, Nguyen HT (2015) Why are Vine copulas so successful in econometrics? Int J Uncertain Fuzziness Knowl Based Syst (IJUFKS) 23(Suppl 1):133–142
Taylor MA (1972) The generalized equations of bisymmetry, associativity and transitivity on quasigroups. Can Math Bull 15:119–124
Taylor MA (1973) Certian functional equations on groupoids weaker than quasigroups. Aequationes Mathematicae 9:23–29
Taylor MA (1978) On the generalized equations of associativity and bisymmetry. Aequationes Mathematicae 17:154–163
Varian H (1992) Microeconometric analysis. Norton, New York
Acknowledgements
This work was supported in part by the National Science Foundation grants HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence) and DUE-0926721, and by an award “UTEP and Prudential Actuarial Science Academy and Pipeline Initiative” from Prudential Foundation.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Kosheleva, O., Kreinovich, V., Dumrongpokaphan, T. (2017). How to Explain Ubiquity of Constant Elasticity of Substitution (CES) Production and Utility Functions Without Explicitly Postulating CES. In: Kreinovich, V., Sriboonchitta, S., Huynh, VN. (eds) Robustness in Econometrics. Studies in Computational Intelligence, vol 692. Springer, Cham. https://doi.org/10.1007/978-3-319-50742-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-50742-2_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-50741-5
Online ISBN: 978-3-319-50742-2
eBook Packages: EngineeringEngineering (R0)