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Regularity of the Generalized Quadratic Production Model: A Counterexample

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  • William Barnett
  • Meenakshi Pasupathy

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.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 22 (2003)
Issue (Month): 2 ()
Pages: 135-154

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Handle: RePEc:taf:emetrv:v:22:y:2003:i:2:p:135-154

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Keywords: Technology; Regularity; Curvature; Production; Flexibility;

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References

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  18. Basmann, R. L. & Diamond, C. A. & Frentrup, J. C. & White, S. N., 1985. "On deviations between neoclassical and GFT-based true cost-of-living indexes derived from the same demand function system," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 45-66.
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Citations

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Cited by:
  1. Livanis, Grigorios & Moss, Charles B., 2006. "Quasi-fixity and multiproduct firms," Economics Letters, Elsevier, vol. 93(2), pages 228-234, November.
  2. William Barnett & Apostolos Serletis, 2009. "The Differential Approach to Demand Analysis and the Rotterdam Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200902, University of Kansas, Department of Economics, revised Jan 2009.
  3. William Barnett & Apostolos Serletis, 2008. "Consumer preferences and demand systems," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200801, University of Kansas, Department of Economics, revised Jan 2008.
  4. Serletis, Apostolos & Shahmoradi, Asghar, 2010. "Consumption effects of government purchases," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 892-905, September.
  5. 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.
  6. Hendrik Wolff & Thomas Heckelei & Ron Mittelhammer, 2010. "Imposing Curvature and Monotonicity on Flexible Functional Forms: An Efficient Regional Approach," Computational Economics, Society for Computational Economics, vol. 36(4), pages 309-339, December.
  7. 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.
  8. 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.
  9. 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.
  10. 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).
  11. 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.
  12. 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.
  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 & Timilsina, Govinda & Vasetsky, Olexandr, 2009. "On interfuel substitution : some international evidence," Policy Research Working Paper Series 5026, The World Bank.
  15. Fabienne Féménia & Alexandre Gohin, 2009. "Estimating censored and non homothetic demand systems: the generalized maximum entropy approach," Working Papers SMART - LERECO 09-12, INRA UMR SMART.
  16. 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.

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