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Imposing and testing curvature conditions on a Box-Cox function

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Author Info
Koebel, Bertrand M.
Falk, Martin
Laisney, Francois

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Abstract

We present a new method for imposing and testing concavity of a cost function using asymptotic least squares, which can easily be implemented even for cost functions which are nonlinear in parameters. We provide an illustration on the basis of a (generalized) Box-Cox cost function with six inputs: capital, labor disaggregated in three skill levels, energy, and intermediate materials. A parametric test of the concavity of the cost function in prices is presented, and price elasticities are compared when curvature conditions are imposed and when they are not. The results show that, although concavity is statistically rejected, the estimates are not very sensitive to its imposition. We find that substitution is stronger between the different types of labor than between any other pair of inputs. --

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Paper provided by ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research in its series ZEW Discussion Papers with number 00-70.

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Date of creation: 2000
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Handle: RePEc:zbw:zewdip:5352

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Related research
Keywords: input demands; concavity; inequality restrictions; Box-Cox;

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Find related papers by JEL classification:
J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data
J21 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Labor Force and Employment, Size, and Structure
E23 - Macroeconomics and Monetary Economics - - Macroeconomics: Consumption, Saving, Production, Employment, and Investment - - - Production

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  1. Kodde, David A & Palm, Franz C, 1986. "Wald Criteria for Jointly Testing Equality and Inequality Restriction s," Econometrica, Econometric Society, vol. 54(5), pages 1243-48, September. [Downloadable!] (restricted)
  2. Diewert, W.E. & Wales, T.J., 1990. "Quadratic Spline Models For Producer Supply And Demand Functions," UBC Departmental Archives 90-08, UBC Department of Economics.
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  3. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January. [Downloadable!] (restricted)
  4. Bertrand M. Koebel, 2002. "Can Aggregation Across Goods be Achieved by Neglecting The Problem? Property Inheritance and Aggregation Bias," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(1), pages 223-255, February. [Downloadable!] (restricted)
  5. Thompson, Peter & Taylor, Timothy G, 1995. "The Capital-Energy Substitutability Debate: A New Look," The Review of Economics and Statistics, MIT Press, vol. 77(3), pages 565-69, August. [Downloadable!] (restricted)
  6. Bergstrom, Villy & Panas, Epaminondas E, 1992. "How Robust Is the Capital-Skill Complementarity Hypothesis?," The Review of Economics and Statistics, MIT Press, vol. 74(3), pages 540-46, August. [Downloadable!] (restricted)
  7. Hardle, Wolfgang & Hildenbrand, Werner & Jerison, Michael, 1991. "Empirical Evidence on the Law of Demand," Econometrica, Econometric Society, vol. 59(6), pages 1525-49, November. [Downloadable!] (restricted)
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  8. Gagne, Robert & Ouellette, Pierre, 1998. "On the Choice of Functional Forms: Summary of a Monte Carlo Experiment," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(1), pages 118-24, January.
  9. Wooldridge, Jeffrey M, 1992. "Some Alternatives to the Box-Cox Regression Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(4), pages 935-55, November. [Downloadable!] (restricted)
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  10. Falk, Martin & Koebel, Bertrand M., 2000. "Outsourcing of services, imported materials and the demand for heterogeneous labour : an application of a generalised box-cox function," ZEW Discussion Papers 00-51, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research. [Downloadable!]
  11. Ryan, David L. & Wales, Terence J., 2000. "Imposing local concavity in the translog and generalized Leontief cost functions," Economics Letters, Elsevier, vol. 67(3), pages 253-260, June. [Downloadable!] (restricted)
  12. Berman, Eli & Bound, John & Griliches, Zvi, 1994. "Changes in the Demand for Skilled Labor within U.S. Manufacturing: Evidence from the Annual Survey of Manufactures," The Quarterly Journal of Economics, MIT Press, vol. 109(2), pages 367-97, May. [Downloadable!] (restricted)
  13. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January. [Downloadable!] (restricted)
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  14. 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 331-38, July.
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  15. Dhrymes, Phoebus J., 1994. "Specification tests in simultaneous equations systems," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 45-76. [Downloadable!] (restricted)
  16. repec:cup:etheor:v:8:y:1992:i:2:p:276-90 is not listed on IDEAS
  17. Kodde, David A & Palm, Franz C, 1987. "A Parametric Test of the Negativity of the Substitution Matrix," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 2(3), pages 227-35, July. [Downloadable!] (restricted)
  18. Moschini, Giancarlo, 1999. "Imposing Local Curvature Conditions in Flexible Demand Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(4), pages 487-90, October.
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