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Estimating The Characteristics Of Homogeneous Functionsusing Flexible Functional Forms

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  • O'Donnell, Christopher J.

Abstract

A flexible functional form can provide a second-order approximation to an arbitrary unknown function at a single point. Except in special cases, the parameters of flexible forms will vary from one point of approximation to another. I use this property to show that, in general, if an unknown function is homogeneous then i) Euler's Theorem gives rise to linear equality constraints involving both the data and a set of observation-varying flexible form parameters, ii) the common practice of imposing homogeneity on flexible functional forms is unnecessarily restrictive, and iii) it is possible to obtain estimates of the observation-varying parameters of approximating flexible forms using a Singular Value Decomposition (SVD) estimator. Two illustrations are provided: artificially-generated data is used to estimate the characteristics of a generalised linear production function; and Canadian data is used to estimate the characteristics of a consumer demand system.

Suggested Citation

  • O'Donnell, Christopher J., 2000. "Estimating The Characteristics Of Homogeneous Functionsusing Flexible Functional Forms," 2000 Conference (44th), January 23-25, 2000, Sydney, Australia 123713, Australian Agricultural and Resource Economics Society.
    • Handle: RePEc:ags:aare00:123713
    DOI: 10.22004/ag.econ.123713
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    1. Selvanathan, E A, 1989. "A Note on the Stochastic Approach to Index Numbers," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(4), pages 471-474, October.
    2. Bewley, R. A., 1983. "Tests of restrictions in large demand systems," European Economic Review, Elsevier, vol. 20(1-3), pages 257-269, January.
    3. Villezca-Becerra, Pedro A. & Shumway, C. Richard, 1992. "Multiple-Output Production Modeled With Three Functional Forms," Journal of Agricultural and Resource Economics, Western Agricultural Economics Association, vol. 17(1), pages 1-16, July.
    4. Swamy, P A V B, 1970. "Efficient Inference in a Random Coefficient Regression Model," Econometrica, Econometric Society, vol. 38(2), pages 311-323, March.
    5. Christopher J. O'Donnell & C. Richard Shumway & V. Eldon Ball, 1999. "Input Demands and Inefficiency in U.S. Agriculture," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 81(4), pages 865-880.
    6. Ryan, David L & Wales, Terence J, 1998. "A Simple Method for Imposing Local Curvature in Some Flexible Consumer-Demand Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(3), pages 331-338, July.
    7. Adolf Buse, 1998. "Testing Homogeneity in the Linearized Almost Ideal Demand System," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 80(1), pages 208-220.
    8. Griffiths, William E. & O'Donnell, Christopher J. & Cruz, Agustina Tan, 2000. "Imposing regularity conditions on a system of cost and factor share equations," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 44(1), pages 1-21.
    9. Terrell, Dek, 1996. "Incorporating Monotonicity and Concavity Conditions in Flexible Functional Forms," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(2), pages 179-194, March-Apr.
    10. David Blake & Angelika Nied, 1997. "The demand for alcohol in the United Kingdom," Applied Economics, Taylor & Francis Journals, vol. 29(12), pages 1655-1672.
    11. Doran, Howard E. & Rambaldi, Alicia N., 1997. "Applying linear time-varying constraints to econometric models: With an application to demand systems," Journal of Econometrics, Elsevier, vol. 79(1), pages 83-95, July.
    12. Toshiyuki Kako, 1978. "Decomposition Analysis of Derived Demand for Factor Inputs: The Case of Rice Production in Japan," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 60(4), pages 628-635.
    13. Diewert, W. E., 1973. "Functional forms for profit and transformation functions," Journal of Economic Theory, Elsevier, vol. 6(3), pages 284-316, June.
    14. Clements, Kenneth W & Izan, H Y, 1987. "The Measurement of Inflation: A Stochastic Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(3), pages 339-350, July.
    15. Ramon E. Lopez, 1980. "The Structure of Production and the Derived Demand for Inputs in Canadian Agriculture," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 62(1), pages 38-45.
    16. Deaton, Angus S & Muellbauer, John, 1980. "An Almost Ideal Demand System," American Economic Review, American Economic Association, vol. 70(3), pages 312-326, June.
    17. C.J. O'Donnell & A. D. Woodland, 1995. "Estimation of Australian Wool and Lamb Production Technologies under Uncertainty: An Error-Components Approach," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 77(3), pages 552-565.
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