Signature
SE = TE_CRS / TE_VRS
| Inputs | Definition | Unit |
|---|---|---|
TE_CRS | Score against a frontier that allows no economies or diseconomies of scale | score from 0 to 1 |
TE_VRS | Pure technical efficiency score against a frontier that allows returns to scale to vary, greater than zero | score from 0 to 1 |
SE | Share of technical efficiency under constant returns not explained by pure technical inefficiency | score from 0 to 1 |
|---|
Function
Frontier efficiency measurement function
Maps a decision-making unit's observed inputs, outputs and costs, and a production or cost frontier estimated for comparable units, to efficiency scores between 0 and 1. A score of 1 places the unit on the estimated frontier. The frontier itself is usually estimated by data envelopment analysis, a linear programming method, or by stochastic frontier analysis, a parametric method that separates inefficiency from random noise.
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Implementations
Excel
Scale efficiency from two DEA scores
With the constant returns score in ScoreCRS and the variable returns score in ScoreVRS, Excel returns scale efficiency.
=ScoreCRS/ScoreVRS
Assumptions
Same units, variables and orientation for both frontiers
Both scores come from the same sample, inputs, outputs and orientation, differing only in the returns to scale assumption, so TE_CRS is no greater than TE_VRS.
Direction of scale inefficiency found separately
A scale efficiency below 1 does not show whether the unit is too small or too large. A further model under non-increasing returns to scale identifies which applies.
Worked examples
Small community hospital
A community hospital scores 0.72 against a constant returns frontier and 0.80 against a variable returns frontier. Scale efficiency is 0.9, so most of its measured inefficiency is pure technical inefficiency. The figures are illustrative.
TE_CRS = 0.72; TE_VRS = 0.80; SE = 0.9
Common errors
Recommending mergers from scale efficiency alone
A low scale efficiency score measures production cost only. Centralising services might reduce measured cost while increasing travel, weakening access or reducing resilience, which the score does not capture.
Sources
Textbook on scale efficiency in DEA
Coelli TJ, Rao DSP, O'Donnell CJ, Battese GE. An Introduction to Efficiency and Productivity Analysis. 2nd ed. New York: Springer; 2005. Decomposition of constant returns technical efficiency into pure technical efficiency and scale efficiency, with a non-increasing returns model to identify the nature of scale inefficiency.
Canonical Identity
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