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Imposing and Testing Curvature Conditions on a Box-Cox Cost Function

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  • Koebel, Bertrand
  • Falk, Martin
  • Laisney, Francois

Abstract

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

Suggested Citation

  • Koebel, Bertrand & Falk, Martin & Laisney, Francois, 2003. "Imposing and Testing Curvature Conditions on a Box-Cox Cost Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(2), pages 319-335, April.
  • Handle: RePEc:bes:jnlbes:v:21:y:2003:i:2:p:319-35
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    2. Chen, Qiu & Mirzabaev, Alisher, 2016. "Evaluating the Impacts of Traditional Biomass Energy Use on Agricultural Production in Sichuan, China," Discussion Papers 250213, University of Bonn, Center for Development Research (ZEF).
    3. Lichter, Andreas & Peichl, Andreas & Siegloch, Sebastian, 2015. "The own-wage elasticity of labor demand: A meta-regression analysis," European Economic Review, Elsevier, vol. 80(C), pages 94-119.
    4. Andreas Lichter & Andreas Peichl & Sebastian Siegloch, 2017. "Exporting and labour demand: Micro-level evidence from Germany," Canadian Journal of Economics, Canadian Economics Association, vol. 50(4), pages 1161-1189, November.
    5. Fitzenberger, Bernd & Kohn, Karsten, 2006. "Skill wage premia, employment, and cohort effects: are workers in Germany all of the same type?," ZEW Discussion Papers 06-044, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
    6. Cox, Michael & Peichl, Andreas & Pestel, Nico & Siegloch, Sebastian, 2014. "Labor demand effects of rising electricity prices: Evidence for Germany," Energy Policy, Elsevier, vol. 75(C), pages 266-277.
    7. Falk, Martin & Koebel, Bertrand M., 2004. "The impact of office machinery, and computer capital on the demand for heterogeneous labour," Labour Economics, Elsevier, vol. 11(1), pages 99-117, February.
    8. De Palma, Francesco & Seegmuller, Thomas, 2005. "Dual Labor Market And Endogenous Fluctuations," Macroeconomic Dynamics, Cambridge University Press, vol. 9(03), pages 398-411, June.
    9. Arne Henningsen & Christian Henning, 2009. "Imposing regional monotonicity on translog stochastic production frontiers with a simple three-step procedure," Journal of Productivity Analysis, Springer, vol. 32(3), pages 217-229, December.
    10. Yang, Sansi & Shumway, C. Richard, 2015. "Asset Fixity under State-Contingent Production Uncertainty," 2015 AAEA & WAEA Joint Annual Meeting, July 26-28, San Francisco, California 205256, Agricultural and Applied Economics Association;Western Agricultural Economics Association.
    11. 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.
    12. Klaus Conrad & Andreas Löschel, 2005. "Recycling of eco-taxes, labor market Effects and the true cost of labor - A CGE analysis," Journal of Applied Economics, Universidad del CEMA, vol. 8, pages 259-278, November.
    13. Xi Chen & Bertrand M. Koebel, 2017. "Fixed Cost, Variable Cost, Markups and Returns to Scale," Annals of Economics and Statistics, GENES, issue 127, pages 61-94.
    14. Koebel, Bertrand M., 2004. "First-order serial correlation in seemingly unrelated regressions," Economics Letters, Elsevier, vol. 82(1), pages 1-7, January.
    15. Henning, Christian H.C.A. & Henningsen, Arne, 2005. "Modeling Price Response of Farm Households Under Imperfect Labor Markets: A Farm Household Approach to Family Farms in Poland," 94th Seminar, April 9-10, 2005, Ashford, UK 24431, European Association of Agricultural Economists.
    16. Barbara Hutniczak, 2014. "Increasing Pressure on Unregulated Species Due to Changes in Individual Vessel Quotas: An Empirical Application to Trawler Fishing in the Baltic Sea," Marine Resource Economics, University of Chicago Press, vol. 29(3), pages 201-217.
    17. Le-Yu Chen & Jerzy Szroeter, 2009. "Hypothesis testing of multiple inequalities: the method of constraint chaining," CeMMAP working papers CWP13/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Valeria Cosmo, 2013. "Ownership, Scale Economies and Efficiency in the Italian Water Sector," Journal of Industry, Competition and Trade, Springer, vol. 13(3), pages 399-415, September.

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