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Performance: The Output/Input Ratio

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The Palgrave Handbook of Economic Performance Analysis

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Abstract

This chapter defines the concepts of this Handbook—performance, productivity, efficiency, and profitability—and discusses the interrelations. The most prominent performance measure, total factor productivity growth, is grounded in activity analysis and related to Debreu’s coefficient of resource utilization. The performance literature considers Debreu’s coefficient a component of the Farrell efficiency measure, but it is the other way round: The sway of Debreu’s coefficient is far greater. An important variant, the Debreu-Diewert coefficient of resource utilization, involves a perfect performance aggregation result and admits practical decompositions. Alternative functional forms of performance measures, such as the Malmquist, Törnqvist, and Fisher indices, emerge when instantaneous rates of input and output change are approximated in discrete time in different ways. A recent result by Balk shows that a modification of the Malmquist index stands out, as it is transitive.

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Notes

  1. 1.

    I stick to the performance literature notation of (factor) inputs x, (consumed) outputs y, and intermediate inputs z. In the general equilibrium literature, including Debreu (1951), the notation is (factor) inputs z, (consumed) outputs x, and intermediate inputs y.

  2. 2.

    For example, if the last commodity, l, represents labor, and this is the only nonproduced commodity, then x = Nel, where N is the labor force and el the l-th unit vector.

  3. 3.

    By convention, this vector inequality holds if it holds for all components.

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Acknowledgements

I am grateful to a referee for detailed criticism that prompted numerous improvements.

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  1. Utrecht School of Economics, Utrecht University, Utrecht, The Netherlands

    Thijs ten Raa

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Correspondence to Thijs ten Raa .

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  1. Utrecht School of Economics, Utrecht University, Utrecht, The Netherlands

    Thijs ten Raa

  2. Stern School of Business, New York University, New York, NY, USA

    William H. Greene

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ten Raa, T. (2019). Performance: The Output/Input Ratio. In: ten Raa, T., Greene, W. (eds) The Palgrave Handbook of Economic Performance Analysis. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-030-23727-1_3

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  • DOI: https://doi.org/10.1007/978-3-030-23727-1_3

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