IDEAS home Printed from https://ideas.repec.org/p/wpa/wuwpem/0112001.html
   My bibliography  Save this paper

Regularity Of The Generalized Quadratic Production Model: A Counterexample

Author

Listed:
  • William A. Barnett

    (Washington University in St. Louis)

  • Meenakshi Pasupathy

    (Baruch College-CUNY)

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 A. Barnett & Meenakshi Pasupathy, 2001. "Regularity Of The Generalized Quadratic Production Model: A Counterexample," Econometrics 0112001, EconWPA.
  • Handle: RePEc:wpa:wuwpem:0112001 Note: Type of Document - Word; prepared on IBM PC; to print on HP;
    as

    Download full text from publisher

    File URL: http://econwpa.repec.org/eps/em/papers/0112/0112001.pdf
    Download Restriction: no

    File URL: http://econwpa.repec.org/eps/em/papers/0112/0112001.ps.gz
    Download Restriction: no

    File URL: http://econwpa.repec.org/eps/em/papers/0112/0112001.doc.gz
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Barnett, William A., 1983. "Definitions of 'second order approximation' and of 'flexible functional form'," Economics Letters, Elsevier, vol. 12(1), pages 31-35.
    2. William A. Barnett & Douglas Fisher & Apostolos Serletis, 2006. "Consumer Theory and the Demand for Money," World Scientific Book Chapters,in: Money And The Economy, chapter 1, pages 3-43 World Scientific Publishing Co. Pte. Ltd..
    3. 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 431-436, October.
    4. William Barnett & Apostolos Serletis & W. Erwin Diewert, 2005. "The Theory of Monetary Aggregation (book front matter)," Macroeconomics 0511008, EconWPA.
    5. 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.
    6. Barnett, William A. & Lee, Yul W. & Wolfe, Michael, 1987. "The global properties of the two minflex Laurent flexible functional forms," Journal of Econometrics, Elsevier, vol. 36(3), pages 281-298, November.
    7. 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 339-346, July.
    8. 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.
    9. 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.
    10. 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.
    11. William Barnett, 2005. "Monetary Aggregation," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200510, University of Kansas, Department of Economics, revised Mar 2005.
    12. Gallant, A. Ronald & Golub, Gene H., 1984. "Imposing curvature restrictions on flexible functional forms," Journal of Econometrics, Elsevier, pages 295-321.
    13. 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.
    14. 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.
    15. Diewert, W. E. & Wales, T. J., 1995. "Flexible functional forms and tests of homogeneous separability," Journal of Econometrics, Elsevier, vol. 67(2), pages 259-302, June.
    16. Terrell, Dek, 1996. "Incorporating Monotonicity and Concavity Conditions in Flexible Functional Forms," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(2), pages 179-194, March-Apr.
    17. Barnett,William A. & Cornet,Bernard & D'Aspremont,Claude & Gabszewicz,Jean & Mas-Colell,Andreu (ed.), 1991. "Equilibrium Theory and Applications," Cambridge Books, Cambridge University Press, number 9780521392198, March.
    18. 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 411-413, June.
    19. Barnett, William A., 2002. "Tastes and technology: curvature is not sufficient for regularity," Journal of Econometrics, Elsevier, vol. 108(1), pages 199-202, May.
    20. 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 1402-1429, November.
    21. Hancock, Diana, 1985. "The Financial Firm: Production with Monetary and Nonmonetary Goods," Journal of Political Economy, University of Chicago Press, vol. 93(5), pages 859-880, October.
    22. 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.
    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. 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. 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.
    4. Barnett, William A. & Serletis, Apostolos, 2008. "The Differential Approach to Demand Analysis and the Rotterdam Model," MPRA Paper 12319, University Library of Munich, Germany.
    5. Serletis, Apostolos & Timilsina, Govinda & Vasetsky, Olexandr, 2009. "On interfuel substitution : some international evidence," Policy Research Working Paper Series 5026, The World Bank.
    6. 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.
    7. 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).
    8. 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-LERECO.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. Serletis, Apostolos & Shahmoradi, Asghar, 2010. "Consumption effects of government purchases," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 892-905, September.
    15. 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.
    16. 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.
    17. Livanis, Grigorios & Moss, Charles B., 2006. "Quasi-fixity and multiproduct firms," Economics Letters, Elsevier, vol. 93(2), pages 228-234, November.

    More about this item

    Keywords

    Technology; Regularity; Curvature; Production; Flexibility;

    JEL classification:

    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • E41 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Demand for Money
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C43 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Index Numbers and Aggregation
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:wpa:wuwpem:0112001. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (EconWPA). General contact details of provider: http://econwpa.repec.org .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.