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Linear and Quadratic Spline Models for Consumer Demand Functions

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  • W. E. Diewert
  • T. J. Wales

Abstract

This paper combines flexible functional form techniques, which provide local approximations to indirect preferenc es with respect to prices and incomes, with spline techniques that provide global approximations with respect to real income. The main technical problem is that real income or utility is an unobserved variable. Starting with the normalized quadratic expenditure functio n, linear and quadratic spline models are introduced theoretically and are empirically estimated using Japanese consumer data for four goods fo r the years 1970-87. The semi-nonparametric literature initiated by A. R. Gallant is reviewed and a limited semi-nonparametric property is claimed to hold for the spline models presented in the paper.

Suggested Citation

  • W. E. Diewert & T. J. Wales, 1993. "Linear and Quadratic Spline Models for Consumer Demand Functions," Canadian Journal of Economics, Canadian Economics Association, vol. 26(1), pages 77-106, February.
    • Handle: RePEc:cje:issued:v:26:y:1993:i:1:p:77-106
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    Citations

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    Cited by:

    1. William A. Barnett & Ikuyasu Usui, 2007. "The Theoretical Regularity Properties of the Normalized Quadratic Consumer Demand Model," International Symposia in Economic Theory and Econometrics, in: Functional Structure Inference, pages 107-127, Emerald Group Publishing Limited.
    2. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    3. Koop, Gary & Osiewalski, Jacek & Steel, Mark F J, 1994. "Bayesian Efficiency Analysis with a Flexible Form: The AIM Cost Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 339-346, July.
    4. 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.
    5. Diewert, W. E. & Wales, T. J., 1995. "Flexible functional forms and tests of homogeneous separability," Journal of Econometrics, Elsevier, vol. 67(2), pages 259-302, June.
    6. Robert H. Beach & Matthew T. Holt, 2001. "Incorporating Quadratic Scale Curves in Inverse Demand Systems," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 83(1), pages 230-245.
    7. Diewert, W. Erwin & Fox, Kevin J., 2016. "Kevin J. Fox Interview of W. Erwin Diewert," Microeconomics.ca working papers erwin_diewert-2016-6, Vancouver School of Economics, revised 02 Jun 2016.
    8. Chambers, Robert & Färe, Rolf & Grosskopf, Shawna & Vardanyan, Michael, 2013. "Generalized quadratic revenue functions," Journal of Econometrics, Elsevier, vol. 173(1), pages 11-21.
    9. Diewert, Erwin, 2009. "Cost of Living Indexes and Exact Index Numbers," Economics working papers erwin_diewert-2009-6, Vancouver School of Economics, revised 13 Feb 2009.
    10. Feng, Guohua & Serletis, Apostolos, 2008. "Productivity trends in U.S. manufacturing: Evidence from the NQ and AIM cost functions," Journal of Econometrics, Elsevier, vol. 142(1), pages 281-311, January.
    11. Hans G. Bloemen & Arie Kapteyn, 2008. "The estimation of utility-consistent labor supply models by means of simulated scores," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(4), pages 395-422.
    12. Bloemen, H.G. & Kapteyn, A.J., 1993. "The estimation of utility consistent labor supply models by means of simulated scores," Other publications TiSEM d6bdd830-0b82-4200-97a4-7, Tilburg University, School of Economics and Management.
    13. William A. Barnett & Jane Binner & W. Erwin Diewert, 2005. "Functional Structure and Approximation in Econometrics (book front matter)," Econometrics 0511006, University Library of Munich, Germany.
    14. Rossella Bardazzi & Marco Barnabani, 2001. "A Long-run Disaggregated Cross-section and Time-series Demand System: An Application to Italy," Economic Systems Research, Taylor & Francis Journals, vol. 13(4), pages 365-389.
    15. Diewert, W. Erwin, 2015. "A Note on the Flexibility of the Barnett and Hahm Functional Form," Economics working papers erwin_diewert-2015-1, Vancouver School of Economics, revised 09 Jan 2015.
    16. Kevin Fox, 1998. "Non-Parametric Estimation of Technical Progress," Journal of Productivity Analysis, Springer, vol. 10(3), pages 235-250, November.
    17. Srikanta Chatterjee & Claudio Michelini & Ranjan Ray, 1994. "Expenditure Patterns and Aggregate Consumer Behaviour: Some Experiments with Australian and New Zealand Data," The Economic Record, The Economic Society of Australia, vol. 70(210), pages 278-291, September.
    18. McKitrick, Ross R., 1998. "The econometric critique of computable general equilibrium modeling: the role of functional forms," Economic Modelling, Elsevier, vol. 15(4), pages 543-573, October.
    19. Jalil, Muaz, 2009. "Measuring Switzerland's Productivity Performance (1960-2008)," MPRA Paper 65321, University Library of Munich, Germany.
    20. Rana Bose, 2005. "Total Factor Productivity Growth in Finland 1960 − 1999," Econometrics 0508014, University Library of Munich, Germany.

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