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A Note on the Flexibility of the Barnett and Hahm Functional Form

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  • Diewert, W. Erwin

Abstract

It is very desirable to find flexible functional forms for unit cost (or profit) functions that are globally concave (or convex). It is easy to find flexible functional forms that are locally well behaved but do not satisfy the required regularity conditions globally. This note examines the global flexibility properties of a unit profit function that was originally suggested by Barnett and Hahm (1994). It is found that this functional form is an improvement over other locally flexible functional forms, in that Barnett and Hahm (BH) functional form for a unit profit function can maintain global convexity while at the same time, it can allow for an arbitrary pattern of substitutes and complements for pairs of outputs and inputs. However, an example shows that the BH functional form is not fully flexible.

Suggested Citation

  • Diewert, W. Erwin, 2015. "A Note on the Flexibility of the Barnett and Hahm Functional Form," Economics working papers erwin_diewert-2015-1, Vancouver School of Economics, revised 09 Jan 2015.
  • Handle: RePEc:ubc:bricol:erwin_diewert-2015-1
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    File URL: http://www.economics.ubc.ca/files/2015/01/pdf_paper_erwin-diewert-15-01-Noteontheflexibility.pdf
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    References listed on IDEAS

    as
    1. Barnett, William A & Hahm, Jeong Ho, 1994. "Financial-Firm Production of Monetary Services: A Generalized Symmetric Barnett Variable-Profit-Function Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(1), pages 33-46, January.
    2. Maksim Isakin & Apostolos Serletis, "undated". "User Costs, the Financial Firm, and Monetary and Regulatory Policy," Working Papers 2015-14, Department of Economics, University of Calgary, revised 01 Jan 2015.
    3. Barnett, William A, 1983. "New Indices of Money Supply and the Flexible Laurent Demand System," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(1), pages 7-23, January.
    4. 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.
    5. W. E. Diewert & T. J. Wales, 1993. "Linear and Quadratic Spline Models for Consumer Demand Functions," Canadian Journal of Economics, Canadian Economics Association, vol. 26(1), pages 77-106, February.
    6. Diewert, Walter E & Wales, Terence J, 1987. "Flexible Functional Forms and Global Curvature Conditions," Econometrica, Econometric Society, vol. 55(1), pages 43-68, January.
    7. Diewert, W E, 1971. "An Application of the Shephard Duality Theorem: A Generalized Leontief Production Function," Journal of Political Economy, University of Chicago Press, vol. 79(3), pages 481-507, May-June.
    8. Barnett, William A & Lee, Yul W, 1985. "The Global Properties of the Miniflex Laurent, Generalized Leontief, and Translog Flexible Functional Forms," Econometrica, Econometric Society, vol. 53(6), pages 1421-1437, November.
    9. Barnett, William A., 2002. "Tastes and technology: curvature is not sufficient for regularity," Journal of Econometrics, Elsevier, vol. 108(1), pages 199-202, May.
    10. Diewert, W. E., 1973. "Functional forms for profit and transformation functions," Journal of Economic Theory, Elsevier, vol. 6(3), pages 284-316, June.
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    More about this item

    Keywords

    Flexible functional forms; unit profit functions; duality; Barnett and Hahm functional form; substitutes and complements in production; Barnett regula;

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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