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Regularity Of The Generalized Quadratic Production Model: A Counterexample

  • William Barnett

    (Department of Economics, The University of Kansas)

  • Meenakshi Pasupathy

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

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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File URL: http://www2.ku.edu/~kuwpaper/2009Papers/201235.pdf
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Paper provided by University of Kansas, Department of Economics in its series WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS with number 201235.

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Length: 32 pages
Date of creation: Sep 2012
Date of revision: Sep 2012
Handle: RePEc:kan:wpaper:201235
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  1. Barnett, William A & Kirova, Milka & Pasupathy, Meenakshi, 1995. "Estimating Policy-Invariant Deep Parameters in the Financial Sector When Risk and Growth Matter," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 27(4), pages 1402-29, November.
  2. 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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  4. Moschini, GianCarlo, 1999. "Imposing Local Curvature Conditions in Flexible Demand System," Staff General Research Papers 1745, Iowa State University, Department of Economics.
  5. William Barnett & Apostolos Serletis & W. Erwin Diewert, 2005. "The Theory of Monetary Aggregation (book front matter)," Macroeconomics 0511008, EconWPA.
  6. Barnett, William A., 2002. "Tastes and technology: curvature is not sufficient for regularity," Journal of Econometrics, Elsevier, vol. 108(1), pages 199-202, May.
  7. Barnett, William A. & Geweke, John & Wolfe, Michael, 1991. "Seminonparametric Bayesian estimation of the asymptotically ideal production model," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 5-50.
  8. Barnett, William A., 1983. "Definitions of 'second order approximation' and of 'flexible functional form'," Economics Letters, Elsevier, vol. 12(1), pages 31-35.
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  10. Gallant, A. Ronald & Golub, Gene H., 1984. "Imposing curvature restrictions on flexible functional forms," Journal of Econometrics, Elsevier, vol. 26(3), pages 295-321, December.
  11. 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 331-38, July.
  12. Koop, Gary & Osiewalski, Jacek & Steel, Mark F J, 1994. "Bayesian Efficiency Analysis with a Flexible Form: The AIM Cost Function," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 339-46, July.
  13. Ramajo Hernandez, Julian, 1994. "Curvature Restrictions on Flexible Functional Forms: An Application of the Minflex Laurent Almost Ideal Demand System to the Pattern of Spanish Demand, 1954-1987," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 431-36, October.
  14. Hancock, Diana, 1985. "The Financial Firm: Production with Monetary and Nonmonetary Goods," Journal of Political Economy, University of Chicago Press, vol. 93(5), pages 859-80, October.
  15. David L. Ryan & Terence J. Wales, 1999. "Flexible And Semiflexible Consumer Demands With Quadratic Engel Curves," The Review of Economics and Statistics, MIT Press, vol. 81(2), pages 277-287, May.
  16. Basmann, R L & Molina, D J & Slottje, D J, 1983. "Budget Constraint Prices as Preference Changing Parameters of Generalized Fechner-Thurstone Direct Utility Functions," American Economic Review, American Economic Association, vol. 73(3), pages 411-13, June.
  17. Cooper, Russel J & McLaren, Keith R & Parameswaran, Priya, 1994. "A System of Demand Equations Satisfying Effectively Global Curvature Conditions," The Economic Record, The Economic Society of Australia, vol. 70(208), pages 26-35, March.
  18. William Barnett, 2005. "Monetary Aggregation," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200510, University of Kansas, Department of Economics, revised Mar 2005.
  19. Barnett, William A., 1980. "Economic monetary aggregates an application of index number and aggregation theory," Journal of Econometrics, Elsevier, vol. 14(1), pages 11-48, September.
  20. Barnett, William A & Fisher, Douglas & Serletis, Apostolos, 1992. "Consumer Theory and the Demand for Money," Journal of Economic Literature, American Economic Association, vol. 30(4), pages 2086-2119, December.
  21. Terrell, Dek, 1996. "Incorporating Monotonicity and Concavity Conditions in Flexible Functional Forms," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(2), pages 179-94, March-Apr.
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