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Estimating demand with distance functions: Parameterization in the primal and dual

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  • Färe, Rolf
  • Grosskopf, Shawna
  • Hayes, Kathy J.
  • Margaritis, Dimitris
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    Abstract

    Our purpose is to investigate the ability of different parametric forms to 'correctly' estimate consumer demands based on distance functions using Monte Carlo methods. Our approach combines economic theory, econometrics and quadratic approximation. We begin by deriving parameterizations for transformed quadratic functions which are linear in parameters and characterized by either homogeneity or which satisfy the translation property. Homogeneity is typical of Shephard distance functions and expenditure functions, whereas translation is characteristic of benefit/shortage or directional distance functions. The functional forms which satisfy these conditions and include both first- and second-order terms are the translog and quadratic forms, respectively. We then derive a primal characterization which is homogeneous and parameterized as translog and a dual model which satisfies the translation property and is specified as quadratic. We assess functional form performance by focusing on empirical violations of the regularity conditions. Our analysis corroborates results from earlier Monte Carlo studies on the production side suggesting that the quadratic form more closely approximates the 'true' technology or in our context consumer preferences than the translog.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 147 (2008)
    Issue (Month): 2 (December)
    Pages: 266-274

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    Handle: RePEc:eee:econom:v:147:y:2008:i:2:p:266-274

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    Web page: http://www.elsevier.com/locate/jeconom

    Related research

    Keywords: Distance functions Demand Approximation Quadratic Translog Monte Carlo;

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    1. Moschini, Giancarlo, 1998. "The semiflexible almost ideal demand system," European Economic Review, Elsevier, vol. 42(2), pages 349-364, February.
    2. Moschini, GianCarlo & Rizzi, Pier Luigi, 2007. "Deriving a Flexible Mixed Demand System: The Normalized Quadratic Model," Staff General Research Papers 12747, Iowa State University, Department of Economics.
    3. Moschini, GianCarlo & Rizzi, Pier Luigi, 2007. "AJAE Appendix: Deriving a Flexible Mixed Demand System: The Normalized Quadratic Model," American Journal of Agricultural Economics Appendices, Agricultural and Applied Economics Association, vol. 89(4), November.
    4. Barnett, William A & Choi, Seungmook, 1989. "A Monte Carlo Study of Tests of Blockwise Weak Separability," Journal of Business & Economic Statistics, American Statistical Association, vol. 7(3), pages 363-77, July.
    5. Barnett, William A. & Usui, Ikuyasu, 2006. "The Theoretical Regularity Properties of the Normalized Quadratic Consumer Demand Model," MPRA Paper 410, University Library of Munich, Germany.
    6. William Barnett & Ousmane Seck, 2006. "Rotterdam vs Almost Ideal Models: Will the Best Demand Specification Please Stand Up?," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 200605, University of Kansas, Department of Economics.
    7. Eales, James S. & Unnevehr, Laurian J., 1994. "The inverse almost ideal demand system," European Economic Review, Elsevier, vol. 38(1), pages 101-115, January.
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    11. Arthur Lewbel & Krishna Pendakur, 2006. "Tricks With Hicks: The EASI Demand System," Boston College Working Papers in Economics 651, Boston College Department of Economics, revised 26 Nov 2008.
    12. Robert G. Chambers & Rolf Färe, 1998. "Translation homotheticity," Economic Theory, Springer, vol. 11(3), pages 629-641.
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    16. Luenberger, David G., 1992. "Benefit functions and duality," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 461-481.
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    18. Chavas, Jean-Paul, 1984. "The theory of mixed demand functions," European Economic Review, Elsevier, vol. 24(3), pages 321-344, April.
    19. Moschini, GianCarlo, 1998. "Semiflexible Almost Ideal Demand System, The," Staff General Research Papers 1193, Iowa State University, Department of Economics.
    20. Berndt, Ernst R & Darrough, Masako N & Diewert, W E, 1977. "Flexible Functional Forms and Expenditure Distributions: An Application to Canadian Consumer Demand Functions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 18(3), pages 651-75, October.
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    Cited by:
    1. Robert G. Chambers & Rolf Färe & Shawna Grosskopf & Michael Vardanyan, 2008. "Generalized Quadratic Revenue Functions," CESifo Working Paper Series 2404, CESifo Group Munich.
    2. Valentin Zelenyuk, 2011. "A Scale Elasticity Measure for Directional Distance Function and its Dual," CEPA Working Papers Series WP062011, School of Economics, University of Queensland, Australia.
    3. Chavas, Jean-Paul, 2013. "On Demand Analysis and Dynamics: A Benefit Function Approach," 2013 Annual Meeting, August 4-6, 2013, Washington, D.C. 149683, Agricultural and Applied Economics Association.
    4. repec:hal:wpaper:halshs-00447417 is not listed on IDEAS
    5. Matsushita, Kyohei & Yamane, Fumihiro, 2012. "Pollution from the electric power sector in Japan and efficient pollution reduction," Energy Economics, Elsevier, vol. 34(4), pages 1124-1130.
    6. Bellenger, Moriah J. & Herlihy, Alan T., 2010. "Performance-based environmental index weights: Are all metrics created equal?," Ecological Economics, Elsevier, vol. 69(5), pages 1043-1050, March.
    7. Valentin Zelenyuk, 2011. "A Note on Equivalences in Measuring Returns to Scale in Multi-output-multi-input Technologies," CEPA Working Papers Series WP052011, School of Economics, University of Queensland, Australia.
    8. Jean-Paul Chavas & Michele Baggio, 2010. "On duality and the benefit function," Journal of Economics, Springer, vol. 99(2), pages 173-184, March.
    9. Rolf Färe & Carlos Martins-Filho & Michael Vardanyan, 2010. "On functional form representation of multi-output production technologies," Journal of Productivity Analysis, Springer, vol. 33(2), pages 81-96, April.
    10. Vasiliki Fourmouzi & Margarita Genius & Peter Midmore & Vangelis Tzouvelekas, 2009. "Measurement of Consumption efficiency in Price-Quantity Space: A Distance Function Approach," Working Papers 0912, University of Crete, Department of Economics.

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