I am reading the book Benchmarking with DEA, SFA, and R by Bogetoft and Otto. In Section 4.8 they discuss the concept of scale efficiency, and I am having trouble interpreting this concept.
The usual output of Data Envelopment Analysis (DEA) is a collection of efficiency scores. If we consider the input efficiency scores, then these scores represent the fraction of a firm's current costs which should, in principle, be able to be used to produce a firm's current output. Thus when a firm is judged as inefficient, a reasonable reaction might be to reduce costs and focus on making internal practices more efficient.
When investigating scale efficiency, one compares two different DEA outputs: one using the assumption of constant returns to scale, and the other using varying returns to scale. This expresses whether a firm is operating at it's "optimal size." If it is not, then using further comparisons of DEA outputs (using increasing or decreasing returns to scale) it is possible to see whether the firm is "too large" or "too small."
While the concept of scale efficiency makes sense to me intuitively, I don't see how the practical response to a scale efficiency analysis is any different from the response to the usual DEA efficiency analysis. For example, suppose we do a DEA input efficiency analysis and find that a firm is inefficient. Then the practical response is to reduce the budget and focus on making internal practices efficient. Suppose now instead that a firm is found to be scale inefficient. The practical response again seems to be to reduce costs and focus on making internal practices more efficient... but what exactly are the proposed gains? With the original DEA analysis we had some estimate of how much we could reduce costs and keep the same level of production. But with a scale efficiency analysis, how much production should expect to keep up given the reduction in the size? Should we expect a proportional reduction in production as well? If so, what is the advantage of downsizing?
Finally, there is the somewhat more confusing case (whose interpretation may help me to make sense of all this) where a firm is judged to be maximally input efficient (i.e. is assigned a score of 1 by the DEA) but is not scale efficient. What is the practical response to this case?
Cross posted at Cross Validated: https://stats.stackexchange.com/questions/144554/how-to-interpret-scale-efficiency-in-dea