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A Primal-Dual Approach To Nonparametric Productivity Analysis: The Case Of U.S. Agriculture

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  • Jean-Paul CHAVAS

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  • Thomas L. COX

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Abstract

Nonparametric methods for measuring productivity indexes based on bounds for the underlying production technology are presented. Following Banker and Maindiratta, the lower bound is obtained from a primal approach while the upper bound corresponds to a dual approach to nonparametric production analysis. These nonparametric bounds are then used to estimate input-based and output- based distance functions. These radial measures provide the basis for measuring productivity indexes. Application to times series data on U.S. agriculture indicates a large gap between the primal lower bound and the dual upper bound. This generates striking differences between the primal and dual nonparametric productivity indexes.

Suggested Citation

  • Jean-Paul CHAVAS & Thomas L. COX, 1994. "A Primal-Dual Approach To Nonparametric Productivity Analysis: The Case Of U.S. Agriculture," Staff Papers 372, University of Wisconsin Madison, AAE.
    • Handle: RePEc:wop:wiaesp:372
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    1. Afriat, Sidney N, 1972. "Efficiency Estimation of Production Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 13(3), pages 568-598, October.
    2. Fare, Rolf & Shawna Grosskopf & Mary Norris & Zhongyang Zhang, 1994. "Productivity Growth, Technical Progress, and Efficiency Change in Industrialized Countries," American Economic Review, American Economic Association, vol. 84(1), pages 66-83, March.
    3. Hanoch, Giora & Rothschild, Michael, 1972. "Testing the Assumptions of Production Theory: A Nonparametric Approach," Journal of Political Economy, University of Chicago Press, vol. 80(2), pages 256-275, March-Apr.
    4. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "The Economic Theory of Index Numbers and the Measurement of Input, Output, and Productivity," Econometrica, Econometric Society, vol. 50(6), pages 1393-1414, November.
    5. Cox, Thomas L & Chavas, Jean-Paul, 1990. "A Nonparametric Analysis of Productivity: The Case of U.S. Agriculture," European Review of Agricultural Economics, Foundation for the European Review of Agricultural Economics, vol. 17(4), pages 449-464.
    6. Chavas, Jean-Paul & Cox, Thomas L, 1990. "A Non-parametric Analysis of Productivity: The Case of U.S. and Japanese Manufacturing," American Economic Review, American Economic Association, vol. 80(3), pages 450-464, June.
    7. Caves, Douglas W & Christensen, Laurits R & Diewert, W Erwin, 1982. "Multilateral Comparisons of Output, Input, and Productivity Using Superlative Index Numbers," Economic Journal, Royal Economic Society, vol. 92(365), pages 73-86, March.
    8. Banker, Rajiv D & Maindiratta, Ajay, 1988. "Nonparametric Analysis of Technical and Allocative Efficiencies in Production," Econometrica, Econometric Society, vol. 56(6), pages 1315-1332, November.
    9. Diewert, W. E., 1976. "Exact and superlative index numbers," Journal of Econometrics, Elsevier, vol. 4(2), pages 115-145, May.
    10. Varian, Hal R, 1984. "The Nonparametric Approach to Production Analysis," Econometrica, Econometric Society, vol. 52(3), pages 579-597, May.
    11. C. Richard Shumway, 1983. "Supply, Demand, and Technology in a Multiproduct Industry: Texas Field Crops," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 65(4), pages 748-760.
    12. Diewert, W E, 1980. "Capital and the Theory of Productivity Measurement," American Economic Review, American Economic Association, vol. 70(2), pages 260-267, May.
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    Cited by:

    1. Jean-Christophe Bureau & Rolf Färe & Shawna Grosskopf, 1995. "A Comparison Of Three Nonparametric Measures Of Productivity Growth In European And United States Agriculture," Journal of Agricultural Economics, Wiley Blackwell, vol. 46(3), pages 309-326.
    2. Mullen, John D. & Cox, Thomas L., 1995. "The Returns From Research In Australian Broadacre Agriculture," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 39(02), August.
    3. N. Islam, 2000. "An Analysis of Productivity Growth in Western Australian Agriculture," Economics Discussion / Working Papers 00-15, The University of Western Australia, Department of Economics.
    4. Giannis Karagiannis & George Mergos, 2000. "Total Factor Productivity Growth and Technical Change in a Profit Function Framework," Journal of Productivity Analysis, Springer, vol. 14(1), pages 31-51, July.
    5. David Lambert, 1998. "Productivity Measurement from a Reference Technology: A Distance Function Approach," Journal of Productivity Analysis, Springer, vol. 10(3), pages 289-304, November.
    6. Munisamy Gopinath & Terry Roe, 1997. "Sources of Sectoral Growth in an Economy Wide Context: The Case of U.S. Agriculture," Journal of Productivity Analysis, Springer, vol. 8(3), pages 293-310, August.
    7. Asmild, Mette & Paradi, Joseph C. & Reese, David N. & Tam, Fai, 2007. "Measuring overall efficiency and effectiveness using DEA," European Journal of Operational Research, Elsevier, vol. 178(1), pages 305-321, April.
    8. THOMAS COX & John Mullen & Wensheng Hu, 1996. "Nonparametric Measures of the Impacts of Public Research Expenditures on Australian Broadacre Agriculture: Preliminary Results," Wisconsin-Madison Agricultural and Applied Economics Staff Papers 399, Wisconsin-Madison Agricultural and Applied Economics Department.
    9. Mullen, John D. & Cox, Thomas L., 1996. "Measuring Productivity Growth In Australian Broadacre Agriculture," Australian Journal of Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 40(03), December.
    10. Thomas COX & John MULLEN & Wensheng HU, 1996. "Nonparametric Measures Of The Impacts Of Public Research Expenditures On Australian Broadacre Agriculture: Preliminary Results," Staff Papers 399, University of Wisconsin Madison, AAE.
    11. Chalfant, James A. & Eshel, Dafna M. Disegni, 2001. "A Nonparametric Test Of Advertising'S Effectiveness," 2001 Annual meeting, August 5-8, Chicago, IL 20529, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).

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