IDEAS home Printed from https://ideas.repec.org/p/zbw/zewdip/5352.html
   My bibliography  Save this paper

Imposing and testing curvature conditions on a Box-Cox function

Author

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

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.

Suggested Citation

  • Koebel, Bertrand M. & Falk, Martin & Laisney, François, 2000. "Imposing and testing curvature conditions on a Box-Cox function," ZEW Discussion Papers 00-70, ZEW - Leibniz Centre for European Economic Research.
    • Handle: RePEc:zbw:zewdip:5352
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/24418/1/dp0070.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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 935-955, November.
    2. 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.
    3. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    4. 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 565-569, August.
    5. B. Ripley & Philippa Pattison & Paul Thompson & Jan Leeuw & Ludovic Lebart & Brian Everitt & Roderick McDonald & Jeffrey Banfield & Richard Hathaway, 1990. "Book reviews," Journal of Classification, Springer;The Classification Society, vol. 7(2), pages 287-316, September.
    6. 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 - Leibniz Centre for European Economic Research.
    7. 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 227-235, July.
    8. Eli Berman & John Bound & Zvi Griliches, 1994. "Changes in the Demand for Skilled Labor within U. S. Manufacturing: Evidence from the Annual Survey of Manufactures," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(2), pages 367-397.
    9. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(2), pages 179-191, August.
    10. Fuss, Melvyn & McFadden, Daniel (ed.), 1978. "Production Economics: A Dual Approach to Theory and Applications," Elsevier Monographs, Elsevier, edition 1, number 9780444850133.
    11. Kodde, David A & Palm, Franz C, 1986. "Wald Criteria for Jointly Testing Equality and Inequality Restriction s," Econometrica, Econometric Society, vol. 54(5), pages 1243-1248, September.
    12. 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.
    13. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (I): The Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 1, number fuss1978.
    14. 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 118-124, January.
    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.
    16. 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 705-722, August.
    17. Fuss, Melvyn & McFadden, Daniel, 1978. "Production Economics: A Dual Approach to Theory and Applications (II): Applications of the Theory of Production," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, volume 2, number fuss1978a.
    18. Hardle, Wolfgang & Hildenbrand, Werner & Jerison, Michael, 1991. "Empirical Evidence on the Law of Demand," Econometrica, Econometric Society, vol. 59(6), pages 1525-1549, November.
    19. Härdle, Wolfgang & Hart, Jeffrey D., 1992. "A Bootstrap Test for Positive Definiteness of Income Effect Matrices," Econometric Theory, Cambridge University Press, vol. 8(2), pages 276-292, June.
    20. Moschini, Giancarlo, 1999. "Imposing Local Curvature Conditions in Flexible Demand Systems," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(4), pages 487-490, October.
    21. Wolak, Frank A., 1989. "Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(1), pages 1-35, April.
    22. 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.
    23. 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 540-546, August.
    24. repec:cup:etheor:v:8:y:1992:i:2:p:276-90 is not listed on IDEAS
    25. Badi H. Baltagi & James M. Griffin & Weiwen Xiong, 2000. "To Pool Or Not To Pool: Homogeneous Versus Hetergeneous Estimations Applied to Cigarette Demand," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 117-126, February.
    26. Dhrymes, Phoebus J., 1994. "Specification tests in simultaneous equations systems," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 45-76.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Henningsen, Arne & Glauben, Thomas & Henning, Christian H.C.A., 2003. "Farm Household Decisions Under Various Tax Policies: Comparative Static Results And Evidence From Household Data," 2003 Annual Meeting, August 16-22, 2003, Durban, South Africa 25889, International Association of Agricultural Economists.
    2. Falk, Martin, 2002. "Diffusion der Informations- und Kommunikationstechnologien und die Qualifikationsstruktur der Arbeitskräfte (Diffusion of information and communication technology and the qualification structure of th," Mitteilungen aus der Arbeitsmarkt- und Berufsforschung, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany], vol. 35(3), pages 397-410.
    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. 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 - Leibniz Centre for European Economic Research.
    5. Wiebusch, A. & Henning, C., 2004. "Analyse von Transaktionskosten auf dem ländlichen Kreditmarkt in Polen," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 39.
    6. 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.
    7. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Koebel, Bertrand M. & Falk, Martin, 1999. "Curvature conditions and substitution pattern among capital, energy, materials and heterogeneous labour," ZEW Discussion Papers 99-06, ZEW - Leibniz Centre for European Economic Research.
    2. Guy Chapda Nana & Bruno Larue, 2014. "Imposing curvature conditions on flexible functional forms for GNP functions," Empirical Economics, Springer, vol. 47(4), pages 1411-1440, December.
    3. Chapda Nana, Guy & Larue, Bruno, 2012. "Imposing Curvature Conditions on Flexible Functional Forms to GNP Functions," Working Papers 123308, University of Laval, Center for Research on the Economics of the Environment, Agri-food, Transports and Energy (CREATE).
    4. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    5. Atanas Christev & Allen Featherstone, 2009. "A note on Allen-Uzawa partial elasticities of substitution: the case of the translog cost function," Applied Economics Letters, Taylor & Francis Journals, vol. 16(11), pages 1165-1169.
    6. Cranfield, J. A. L. & Pellow, Scott, 2004. "The role of global vs. local negativity in functional form selection: an application to Canadian consumer demands," Economic Modelling, Elsevier, vol. 21(2), pages 345-360, March.
    7. Sauer, J.F., 2005. "“Efficiency Flooding”: Black-Box Frontiers and Policy Implications," International Journal of Applied Econometrics and Quantitative Studies, Euro-American Association of Economic Development, vol. 2(1), pages 17-52.
    8. Johannes Sauer & Klaus Frohberg & Henrich Hockmann, 2006. "Stochastic efficiency measurement: The curse of theoretical consistency," Journal of Applied Economics, Universidad del CEMA, vol. 9, pages 139-166, May.
    9. Sauer, J., 2007. "Monotonicity and Curvature – A Bootstrapping Approach," Proceedings “Schriften der Gesellschaft für Wirtschafts- und Sozialwissenschaften des Landbaues e.V.”, German Association of Agricultural Economists (GEWISOLA), vol. 42, March.
    10. Dawei Zhang & Zhuo (June) Cheng & Hasan A. Qurban H. Mohammad & Barrie R. Nault, 2015. "Research Commentary—Information Technology Substitution Revisited," Information Systems Research, INFORMS, vol. 26(3), pages 480-495, September.
    11. Peters, Cornelius, 2015. "Do age complementarities affect labour productivity? Evidence from German firm level data," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112941, Verein für Socialpolitik / German Economic Association.
    12. Bjarne Jensen & Paul Boer & Jan Daal & Peter Jensen, 2011. "Global restrictions on the parameters of the CDES indirect utility function," Journal of Economics, Springer, vol. 102(3), pages 217-235, April.
    13. William A. Barnett & Ikuyasu Usui, 2007. "The Theoretical Regularity Properties of the Normalized Quadratic Consumer Demand Model," International Symposia in Economic Theory and Econometrics, in: Functional Structure Inference, pages 107-127, Emerald Group Publishing Limited.
    14. Jakir Hussain & Jean-Thomas Bernard, 2016. "Flexible Functional Forms and Curvature Conditions: Parametric Productivity Estimation in Canadian and U.S. Manufacturing Industries," Working Papers 1612e, University of Ottawa, Department of Economics.
    15. O'Donnell, Christopher J. & Coelli, Timothy J., 2005. "A Bayesian approach to imposing curvature on distance functions," Journal of Econometrics, Elsevier, vol. 126(2), pages 493-523, June.
    16. Hendrik Wolff & Thomas Heckelei & Ron Mittelhammer, 2010. "Imposing Curvature and Monotonicity on Flexible Functional Forms: An Efficient Regional Approach," Computational Economics, Springer;Society for Computational Economics, vol. 36(4), pages 309-339, December.
    17. Christopher Parmeter & Kai Sun & Daniel Henderson & Subal Kumbhakar, 2014. "Estimation and inference under economic restrictions," Journal of Productivity Analysis, Springer, vol. 41(1), pages 111-129, February.
    18. 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).
    19. Levent Kutlu & Shasha Liu & Robin C. Sickles, 2022. "Cost, Revenue, and Profit Function Estimates," Springer Books, in: Subhash C. Ray & Robert G. Chambers & Subal C. Kumbhakar (ed.), Handbook of Production Economics, chapter 16, pages 641-679, Springer.
    20. Sauer, Johannes, 2006. "Monotonicity And Curvature - A Bootstrapping Approach," 46th Annual Conference, Giessen, Germany, October 4-6, 2006 14948, German Association of Agricultural Economists (GEWISOLA).

    More about this item

    Keywords

    input demands; concavity; inequality restrictions; Box-Cox;
    All these keywords.

    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; Spatio-temporal Models
    • J21 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Labor Force and Employment, Size, and Structure
    • E23 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Production

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:zbw:zewdip:5352. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/zemande.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.