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Regularity Of The Generalized Quadratic Production Model: A Counterexample

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  • William Barnett

    (Department of Economics, The University of Kansas)

  • Meenakshi Pasupathy

    (Department of Economics and Finance, School of Business, Baruch College)

Abstract

Recently there has been a growing tendency to impose curvature, but not monotonicity, on specifications of technology. But regularity requires satisfaction of both curvature and monotonicity conditions. Without both satisfied, the second order conditions for optimizing behavior fail and duality theory fails. When neither curvature nor monotonicity are imposed, estimated flexible specifications of technology are much more likely to violate curvature than monotonicity. Hence it has been argued that there is no need to impose or check for monotonicity, when curvature has been imposed globally. But imposition of curvature may induce violations of monotonicity that otherwise would not have occurred. We explore the regularity properties of our earlier results with a multiproduct financial technology specified to be generalized quadratic. In our earlier work, we used the usual approach and accepted the usual view. We now find that imposition of curvature globally and monotonicity locally does not assure monotonicity within the region of the data. Our purpose is to alert researchers to the kinds of problems that we encountered and which we believe are largely being overlooked in the production modelling literature, as we had been overlooking them.

Suggested Citation

  • William Barnett & Meenakshi Pasupathy, 2012. "Regularity Of The Generalized Quadratic Production Model: A Counterexample," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201235, University of Kansas, Department of Economics, revised Sep 2012.
  • Handle: RePEc:kan:wpaper:201235
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    Cited by:

    1. Barnett, William A. & Serletis, Apostolos, 2008. "Consumer preferences and demand systems," Journal of Econometrics, Elsevier, vol. 147(2), pages 210-224, December.
    2. Oum, Tae H. & Yan, Jia & Yu, Chunyan, 2008. "Ownership forms matter for airport efficiency: A stochastic frontier investigation of worldwide airports," Journal of Urban Economics, Elsevier, vol. 64(2), pages 422-435, September.
    3. Fabienne Femenia & Alexandre Gohin, 2007. "Estimating censored and non homothetic demand systems : the generalized maximum entropy appoach," Post-Print hal-02814735, HAL.
    4. 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.
    5. Barnett, William A. & Serletis, Apostolos, 2008. "The Differential Approach to Demand Analysis and the Rotterdam Model," MPRA Paper 12319, University Library of Munich, Germany.
    6. 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.
    7. Serletis, Apostolos & Timilsina, Govinda & Vasetsky, Olexandr, 2009. "On interfuel substitution : some international evidence," Policy Research Working Paper Series 5026, The World Bank.
    8. Alexandre Gohin & Fabienne Féménia, 2009. "Estimating Price Elasticities of Food Trade Functions: How Relevant is the CES‐based Gravity Approach?," Journal of Agricultural Economics, Wiley Blackwell, vol. 60(2), pages 253-272, June.
    9. Wolff, Hendrik & Heckelei, Thomas & Mittelhammer, Ronald C., 2004. "Imposing Monotonicity And Curvature On Flexible Functional Forms," 2004 Annual meeting, August 1-4, Denver, CO 20256, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    10. Apostolos Serletis & Guohua Feng, 2015. "Imposing Theoretical Regularity on Flexible Functional Forms," Econometric Reviews, Taylor & Francis Journals, vol. 34(1-2), pages 198-227, February.
    11. William Barnett & Ikuyasu Usui, 2006. "The Theoretical Regularity Properties of the Normalized Quadratic Consumer Demand Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200609, University of Kansas, Department of Economics.
    12. Feng, Guohua & Serletis, Apostolos, 2008. "Productivity trends in U.S. manufacturing: Evidence from the NQ and AIM cost functions," Journal of Econometrics, Elsevier, vol. 142(1), pages 281-311, January.
    13. Femenia, Fabienne & Gohin, Alexandre, 2007. "Estimating price elasticities of food trade functions: How relevant is the gravity approach?," Working Papers 7211, TRADEAG - Agricultural Trade Agreements.
    14. Serletis, Apostolos & Shahmoradi, Asghar, 2008. "Semi-nonparametric estimates of interfuel substitution in U.S. energy demand," Energy Economics, Elsevier, vol. 30(5), pages 2123-2133, September.
    15. William Barnett & Barry E. Jones & Milka Kirova & Travis D. Nesmith & Meenakshi Pasupathy1, 2004. "The Nonlinear Skeletons in the Closet," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200403, University of Kansas, Department of Economics, revised May 2004.
    16. Serletis, Apostolos & Shahmoradi, Asghar, 2010. "Consumption effects of government purchases," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 892-905, September.
    17. Guohua Feng & Apostolos Serletis, 2009. "Efficiency and productivity of the US banking industry, 1998-2005: evidence from the Fourier cost function satisfying global regularity conditions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 24(1), pages 105-138.
    18. Serletis, Apostolos & Timilsina, Govinda & Vasetsky, Olexandr, 2011. "International evidence on aggregate short-run and long-run interfuel substitution," Energy Economics, Elsevier, vol. 33(2), pages 209-216, March.
    19. Livanis, Grigorios & Moss, Charles B., 2006. "Quasi-fixity and multiproduct firms," Economics Letters, Elsevier, vol. 93(2), pages 228-234, November.

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    More about this item

    Keywords

    Technology; Regularity; Curvature; Production; Flexibility;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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