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Aggregation Issues in the Estimation of Linear Programming Productivity Measures

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  • Shaik, Saleem
  • Mishra, Ashok K.
  • Atwood, Joseph A.

Abstract

This paper demonstrates the sensitivity of the linear programming approach in the estimation of productivity measures in the primal framework using Malmquist productivity index and Malmquist total factor productivity index models. Specifically, the sensitivity of productivity measure to the number of constraints (level of dis-aggregation) and imposition of returns to scale constraints of linear programing is evaluated. Further, the shadow or dual values are recovered from the linear program and compared to the market prices used in the ideal Fisher index approach to illustrate sensitivity. Empirical application to U.S. state-level time series data from 1960-2004 reveal productivity change decreases with increases in the number of constraints. Further, the input and output shadow or dual values are skewed, leading to the difference in the productivity measures due to aggregation.

Suggested Citation

  • Shaik, Saleem & Mishra, Ashok K. & Atwood, Joseph A., 2011. "Aggregation Issues in the Estimation of Linear Programming Productivity Measures," Agribusiness & Applied Economics Report 101783, North Dakota State University, Department of Agribusiness and Applied Economics.
  • Handle: RePEc:ags:nddaae:101783
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    References listed on IDEAS

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    1. Fare, Rolf & Zelenyuk, Valentin, 2003. "On aggregate Farrell efficiencies," European Journal of Operational Research, Elsevier, vol. 146(3), pages 615-620, May.
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    More about this item

    Keywords

    Aggregation; Share-weights; single and multiple output and input; Malmquist productivity index; Malmquist total factor productivity index; Agribusiness; Production Economics;

    JEL classification:

    • O3 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • Q1 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture

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