Abstract
We discuss and propose new results regarding combined production efficiencies of an aggregate group, such as industry or region. Based on the production economic notion of aggregate technology, we present an algebraic representation of the aggregation output set, and use this to derive a new decomposition of the aggregation unit’s technical efficiency, e.g. a group’s technical efficiency. Our novel decomposition can identify more clearly the inefficiency due to the underlying units and the inefficiency due to the aggregation. For the special single output case, the proposed aggregation measure is consistent with the extant literature, and identical to Farrell’s measure of structural efficiency of a group. However, for the general multiple outputs case we show that there is a gap between the proposed measure and the extant literature. We illustrate the formal results with a numerical example based on a dataset from literature.
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Notes
\({{\mathbb{R}}}^{d}\) denotes the d-dimensional Euclidean space, and \({{\mathbb{R}}}_{+}^{d}\) its nonnegative orthant. Sets are denoted by uppercase calligraphic letters and vectors by lowercase boldface letters. An exception is the price-vector denoted by uppercase boldface P. All vectors are implicitly column vectors. For vectors \({{{\bf{a}}}},{{{\bf{b}}}}\in {{\mathbb{R}}}^{d}\), the inequality a≥b (a > b) means that ai≥bi (ai > bi), for all i = 1, …, d.
The notation with sub-script FZ indicates the respective measures are as defined by Färe and Zelenyuk (2003).
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Begen, M.A., Ødegaard, F. & Sadeghi, J. On aggregation of technical and revenue efficiency measures. J Prod Anal (2023). https://doi.org/10.1007/s11123-023-00710-2
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DOI: https://doi.org/10.1007/s11123-023-00710-2