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Imposing and testing curvature conditions on a Box-Cox function

  • Koebel, Bertrand M.
  • Falk, Martin
  • Laisney, François

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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  8. Wooldridge, J.M., 1989. "Some Aleternative To The Box-Cox Regression Model," Working papers 534, Massachusetts Institute of Technology (MIT), Department of Economics.
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  14. 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.
  15. 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.
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  19. Diewert, W E & Wales, T J, 1992. "Quadratic Spline Models for Producer's Supply and Demand Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 705-22, August.
  20. 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.
  21. 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.
  22. 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.
  23. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(02), pages 179-191, August.
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