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Flexible Functional Forms and Global Curvature Conditions

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  • W. Erwin Diewert
  • T.J. Wales

Abstract

Empirically estimated flexible functional forms frequently fail to satisfy the appropriate theoretical curvature conditions. Lau and Gallant and Golub have worked out methods for imposing the appropriate curvature conditions locally, but those local techniques frequently fail to yield satisfactory results. We develop two methods for imposing curvature conditions globally in the context of cost function estimation. The first method adopts Lau's technique to a generalization of a functional form first proposed by McFadden. Using this Generalized McFadden functional form, it turns out that imposing the appropriate curvature conditions at one data point imposes the conditions globally. The second method adopts a technique used by McFadden and Barnett, which is based on the fact that a non-negative sum of concave functions will be concave. Our various suggested techniques are illustrated using the U.S. Manufacturing data utilized by Berndt and Khaled

Suggested Citation

  • W. Erwin Diewert & T.J. Wales, 1989. "Flexible Functional Forms and Global Curvature Conditions," NBER Technical Working Papers 0040, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberte:0040
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    1. Barnett, William A, 1983. "New Indices of Money Supply and the Flexible Laurent Demand System," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(1), pages 7-23, January.
    2. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1973. "Transcendental Logarithmic Production Frontiers," The Review of Economics and Statistics, MIT Press, vol. 55(1), pages 28-45, February.
    3. Elbadawi, Ibrahim & Gallant, A Ronald & Souza, Geraldo, 1983. "An Elasticity Can Be Estimated Consistently without A Priori Knowledge of Functional Form," Econometrica, Econometric Society, vol. 51(6), pages 1731-1751, November.
    4. Gallant, A. Ronald & Golub, Gene H., 1984. "Imposing curvature restrictions on flexible functional forms," Journal of Econometrics, Elsevier, vol. 26(3), pages 295-321, December.
    5. Barnett, William A & Lee, Yul W, 1985. "The Global Properties of the Miniflex Laurent, Generalized Leontief, and Translog Flexible Functional Forms," Econometrica, Econometric Society, vol. 53(6), pages 1421-1437, November.
    6. Shoven, John B & Whalley, John, 1984. "Applied General-Equilibrium Models of Taxation and International Trade: An Introduction and Survey," Journal of Economic Literature, American Economic Association, vol. 22(3), pages 1007-1051, September.
    7. McFadden, Daniel, 1978. "The General Linear Profit Function," Histoy of Economic Thought Chapters,in: Fuss, Melvyn & McFadden, Daniel (ed.), Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 5 McMaster University Archive for the History of Economic Thought.
    8. White, Halbert, 1980. "Using Least Squares to Approximate Unknown Regression Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 21(1), pages 149-170, February.
    9. Wales, Terence J., 1977. "On the flexibility of flexible functional forms : An empirical approach," Journal of Econometrics, Elsevier, vol. 5(2), pages 183-193, March.
    10. Caves, Douglas W & Christensen, Laurits R, 1980. "Global Properties of Flexible Functional Forms," American Economic Review, American Economic Association, vol. 70(3), pages 422-432, June.
    11. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
    12. Lau, Lawrence J., 1978. "Applications of Profit Functions," Histoy of Economic Thought Chapters,in: Fuss, Melvyn & McFadden, Daniel (ed.), Production Economics: A Dual Approach to Theory and Applications, volume 1, chapter 3 McMaster University Archive for the History of Economic Thought.
    13. Berndt, Ernst R & Khaled, Mohammed S, 1979. "Parametric Productivity Measurement and Choice among Flexible Functional Forms," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1220-1245, December.
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