Advertisement

Journal of Economics

, Volume 102, Issue 3, pp 217–235 | Cite as

Global restrictions on the parameters of the CDES indirect utility function

  • Bjarne S. JensenEmail author
  • Paul de Boer
  • Jan van Daal
  • Peter S. Jensen
Article

Abstract

This paper extends the analytical and empirical application of the basic indirect utility function of Houthakker–Hanoch—called the CDES specification (constant differences of elasticities of substitution). The non-homothetic CDES preferences are the natural parametric extension on the global domain of the homothetic CES preferences with many commodities, and CDES can conveniently be used in specifying CGE multisector models with a demand side satisfying observable Engel curve patterns. Moreover, all Marshallian own-price elasticities are no longer restricted to exceed one, and positive and negative cross-price effects are allowed for in empirical demand analyses. Explicit calculations of the Allen elasticities of substitution are instrumental in demonstrating the economic implications of the parameters of indirect utility functions with global regularity properties and flexibility of the derived demand systems.

Keywords

Indirect utility functions Demand systems 

JEL Classification

D11 D00 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akin JS, Stewart JF (1979) Theoretical restrictions on the parameters of indirect addilog demand equations. Econometrica 47: 779–780CrossRefGoogle Scholar
  2. Allen RGD (1938) Mathematical analysis for economists. MacMillan, LondonGoogle Scholar
  3. Antony A (2010) A class of changing elasticity of substitution production functions. J Econ 100: 165–183CrossRefGoogle Scholar
  4. Arrow KJ, Chenery HB, Minhas BS, Solow RM (1961) Capital–labor substitution and economic efficiency. Rev Econ Stat 48: 225–250CrossRefGoogle Scholar
  5. Barnett WA, Lee YW (1985) The global properties of the miniflex Laurent, generalized Leontief, and translog flexible functional forms. Econometrica 53: 1421–1437CrossRefGoogle Scholar
  6. Barten AP, Boehm V (1982) Consumer theory. In: Arrow KJ, Intriligator MD (eds) Handbook of mathematical economics, vol 2. North-Holland, Amsterdam, pp 381–429Google Scholar
  7. Caves DW, Christensen LR (1980) Global properties of flexible functional forms. Am Econ Rev 70: 422–432Google Scholar
  8. Chai A, Moneta A (2010) Retrospectives: Engel curves. J Econ Perspect 24: 225–240CrossRefGoogle Scholar
  9. Chung JW (1994) Utility and production functions. Blackwell, OxfordGoogle Scholar
  10. Chung JW (1987) On the estimation of factor substitution in the translog model. Rev Econ Stat 69: 409–417CrossRefGoogle Scholar
  11. Deaton AS, Muellbauer J (1980a) Economics and consumer behavior. Cambridge University Press, CambridgeGoogle Scholar
  12. Deaton AS, Muellbauer J (1980b) An almost ideal demand system. Am Econ Rev 70: 312–326Google Scholar
  13. De Boer PMC, Paap R (2009) Testing non-nested demand relations: linear expenditure systems versus indirect addilog. Stat Neerlandica 63: 368–384CrossRefGoogle Scholar
  14. Diewert WE (1974) Applications of duality theory. In: Intriligator MD, Kendrick DA (eds) Frontiers of quantitative economics, vol 2. North-Holland, Amsterdam, pp 106–171Google Scholar
  15. Diewert WE, Avriel M, Zang I (1981) Nine kinds of quasiconcavity and concavity. J Econ Theory 25: 397–420CrossRefGoogle Scholar
  16. Diewert WE (1982) Duality approaches to microeconomic theory. In: Arrow KJ, Intriligator MD (eds) Handbook of mathematical economics, vol 2. North-Holland, Amsterdam, pp 535–599Google Scholar
  17. Diewert WE, Wales TJ (1987) Flexible functional forms and global curvature conditions. Econometrica 37: 43–68CrossRefGoogle Scholar
  18. Fisher D, Fleissig AR, Serletis A (2001) An empirical comparison of flexible demand system functional forms. J Appl Econ 16: 59–80CrossRefGoogle Scholar
  19. Frisch R (1959) A complete scheme for computing all direct and cross demand elasticities in a model with many sectors. Econometrica 27: 177–196CrossRefGoogle Scholar
  20. Gamaletsos T (1973) Further analysis of cross-country comparison of consumer expenditure patterns. Eur Econ Rev 4: 1–20CrossRefGoogle Scholar
  21. Gamaletsos T (1974) Reply—further analysis of cross-country comparison of consumer expenditure patterns. Eur Econ Rev 5: 307CrossRefGoogle Scholar
  22. Ginsberg W (1973) Concavity and quasiconcavity in economics. J Econ Theory 6: 596–605CrossRefGoogle Scholar
  23. Gravelle H, Rees R (2004) Microeconomics, 3rd edn. Prentice Hall, HarlowGoogle Scholar
  24. Guilkey DK, Lovell CAK (1980) On the flexibility of the translog approximation. Int Econ Rev 21: 137–147CrossRefGoogle Scholar
  25. Guilkey DK, Lovell CAK, Sickles RC (1983) A comparison of the performance of three flexible functional forms. Int Econ Rev 24: 591–616CrossRefGoogle Scholar
  26. Hanoch G (1975) Production and demand models with direct and indirect implicit additivity. Econometrica 43: 395–419CrossRefGoogle Scholar
  27. Heij C, de Boer PMC, Franses PH, Kloek T, van Dijk HK (2004) Econometric methods with applications in business and economics. Oxford University Press, OxfordGoogle Scholar
  28. Hertel TW, Preckel PV, Tsigas ME, Peterson EB, Surry Y (1991) Implicit additivity as a strategy for restricting the parameter space in computable general equilibrium models. Econ Finan Comput 1: 265–289Google Scholar
  29. Hertel TW, Tsigas ME (1997) Structure of GTAP. In: Hertel TW (eds) Global trade analysis: modelling and applications. Cambridge University Press, Cambridge, pp 13–73Google Scholar
  30. Hicks JR (1937) Théorie mathé matique de la valeur en régime de la libre concurrence, Hermann, Editeurs, ParisGoogle Scholar
  31. Hicks JR (1946) Value and capital, 2nd edn. Clarendon Press, OxfordGoogle Scholar
  32. Hicks JR (1969) Direct and indirect additivity. Econometrica 37: 353–354CrossRefGoogle Scholar
  33. Hotelling H (1932) Edgeworth’s taxation paradox and the nature of demand and supply functions. J Polit Econ 40: 577–616CrossRefGoogle Scholar
  34. Houthakker HS (1952) Compensated changes in quantities and qualities consumed. Rev Econ Stud 19: 155–164CrossRefGoogle Scholar
  35. Houthakker HS (1957) An international comparison of household expenditure patterns commemorating the centenary of Engel’s law. Econometrica 25: 532–551CrossRefGoogle Scholar
  36. Houthakker HS (1960a) The influence of prices and income on household expenditures. Bull Int Inst Stat 37: 9–22Google Scholar
  37. Houthakker HS (1960b) Additive preferences. Econometrica 28: 244–257CrossRefGoogle Scholar
  38. Houthakker HS (1961) The present state of consumption theory. Econometrica 29: 704–740CrossRefGoogle Scholar
  39. Houthakker HS (1965) A note on self-dual preferences. Econometrica 33: 797–801CrossRefGoogle Scholar
  40. Jensen BS, Larsen ME (2005) General equilibrium dynamics of multi-sector growth models. J Econ Suppl 10: 17–56CrossRefGoogle Scholar
  41. Katzner DW (1968) A note on the differentiability of consumer demand equations. Econometrica 36: 415–418CrossRefGoogle Scholar
  42. Lau LJ (1978) Testing and imposing monotonicity, convexity and quasi-convexity constraints. In: Fuss M, McFadden D (eds) Production economics: a dual approach to theory and applications, vol 1. North-Holland, Amsterdam, pp 409–453Google Scholar
  43. Lee LF, Pitt MM (1986) Microeconometric demand system with binding nonnegativity constraints: the dual approach. Econometrica 54: 1237–1242CrossRefGoogle Scholar
  44. Leser CEV (1941) Family budget data and price-elasticities of demand. Rev Econ Stud 9: 40–57CrossRefGoogle Scholar
  45. Mas-Colell A, Whinston MD, Green JR (1995) Microeconomic theory. Oxford University Press, New YorkGoogle Scholar
  46. Moschini G (1999) Imposing local curvature conditions in flexible demand systems. J Bus Econ 17: 487–490CrossRefGoogle Scholar
  47. Murty KN (1982) Theoretical restrictions on the parameters of indirect addilog demand equations: a comment. Econometrica 50: 225–227CrossRefGoogle Scholar
  48. Pollak RA (1969) Conditional demand functions and consumption theory. Q J Econ 83: 60–78CrossRefGoogle Scholar
  49. Rimmer MT, Powell AA (1996) An implicitly additive demand system. Appl Econ 28: 1613–1622CrossRefGoogle Scholar
  50. Roy R (1942) De l’utilité, contribution à la théorie des choix. Hermann, ParisGoogle Scholar
  51. Roy R (1947) La distribution du revenue entre les divers biens. Econometrica 15: 205–225CrossRefGoogle Scholar
  52. Ryan DL, Wales TJ (1998) A simple method for imposing local curvature in some flexible demand systems. J Bus Econ 16: 331–338CrossRefGoogle Scholar
  53. Samuelson PA (1965) Using full duality to show that simultaneously additive direct and indirect utilities implies unitary price elasticity of demand. Econometrica 33: 781–796CrossRefGoogle Scholar
  54. Samuelson PA (1969) Corrected formulation of direct and indirect additivity. Econometrica 37: 355–359CrossRefGoogle Scholar
  55. Samuelson PA (1974) Complementarity: an essay on the 40th Anniversary of The Hicks–Allen Revolution in demand theory. J Econ Lit 12: 1255–1289Google Scholar
  56. Shoven JB, Whalley J (1992) Applying general equilibrium. Cambridge University Press, CambridgeGoogle Scholar
  57. Silberberg E, Suen W (2001) The structure of economics—a mathematical analysis, Third edition. McGraw-Hill, SingaporeGoogle Scholar
  58. Slutsky EE (1915) Sulla teoria del bilancio del consumatore‘ Giornale degli Economisti, 51, 1–26; translation: on the theory of the budget of the consumer. In: AEA series, readings in price theory, 1953, George Allen and Unwin, London, pp 27–56Google Scholar
  59. Somermeyer WH, Langhout A (1972) Shapes of Engel curves and demand curves: implications of the expenditure allocation model, applied to Dutch data. Eur Econ Rev 3: 351–386CrossRefGoogle Scholar
  60. Somermeyer WH (1974) Further analysis of cross-country comparison of consumer expenditure patterns-comment. Eur Econ Rev 5: 303–306CrossRefGoogle Scholar
  61. Tobin J, Houthakker HS (1950) The effects of rationing on demand elasticities. Rev Econ Stud 18: 140–153CrossRefGoogle Scholar
  62. Uzawa H (1962) Production functions with constant elasticities of substitution. Rev Econ Stud 29: 291–299CrossRefGoogle Scholar
  63. Varian HR (1992) Microeconomic analysis, 3rd edn. Norton, New YorkGoogle Scholar
  64. Wold H, Jureen L (1953) Demand analysis. Wiley, New YorkGoogle Scholar
  65. Yoshihara K (1969) Demand functions: an application to the Japanese expenditure pattern. Econometrica 37: 257–274CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  • Bjarne S. Jensen
    • 1
    Email author
  • Paul de Boer
    • 2
  • Jan van Daal
    • 3
  • Peter S. Jensen
    • 4
  1. 1.Department of Environmental and Business EconomicsUniversity of Southern DenmarkEsbjergDenmark
  2. 2.Econometric InstituteErasmus University RotterdamRotterdamThe Netherlands
  3. 3.TrianGleUniversite de Lyon-2LyonFrance
  4. 4.Department of Business and EconomicsUniversity of Southern DenmarkOdenseDenmark

Personalised recommendations