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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

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.

Suggested Citation

  • Färe, Rolf & Grosskopf, Shawna & Hayes, Kathy J. & Margaritis, Dimitris, 2008. "Estimating demand with distance functions: Parameterization in the primal and dual," Journal of Econometrics, Elsevier, vol. 147(2), pages 266-274, December.
  • Handle: RePEc:eee:econom:v:147:y:2008:i:2:p:266-274
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. Rouhani, Omid M. & Niemeier, Debbie & Knittel, Christopher R. & Madani, Kaveh, 2013. "Integrated modeling framework for leasing urban roads: A case study of Fresno, California," Transportation Research Part B: Methodological, Elsevier, vol. 48(C), pages 17-30.
    4. Chambers, Robert & Färe, Rolf & Grosskopf, Shawna & Vardanyan, Michael, 2013. "Generalized quadratic revenue functions," Journal of Econometrics, Elsevier, vol. 173(1), pages 11-21.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Jean-Paul Chavas & Michele Baggio, 2010. "On duality and the benefit function," Journal of Economics, Springer, vol. 99(2), pages 173-184, March.
    10. 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.
    11. Feng, Guohua & Serletis, Apostolos, 2014. "Undesirable outputs and a primal Divisia productivity index based on the directional output distance function," Journal of Econometrics, Elsevier, vol. 183(1), pages 135-146.
    12. repec:hal:wpaper:halshs-00447417 is not listed on IDEAS

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